Structural design of a sandwich wall
as the quay wall for the future
And an investigation to apply parametric design to quay wall structures
Final report
Priscilla Bonte
M.Sc. Thesis
Delft, January 2007
Sandwich wall as the quay wall for the future
2
Sandwich wall as the quay wall for the future
Practical information
Author
Priscilla Bonte
Dirklangenstraat 16A
2611 HW Delft
Email: [email protected]
Phone: 06 24279587
Graduation committee
Prof. drs. ir. J.K. Vrijling
Email: [email protected]
Phone: 015 2785278
ir. W.F. Molenaar
Email: [email protected]
Phone: 015 2789447
ir. L.A.M. Groenewegen
Email: [email protected]
Phone: 0182 590470
ir. W.J.M. Peperkamp
Email: [email protected]
Phone: 015 2784576
3
Sandwich wall as the quay wall for the future
4
Sandwich wall as the quay wall for the future
Preface
This report is the final piece of the Master of Science thesis titled “Sandwich wall as the quay wall for the
future”. This thesis is part of the structural hydraulic engineering curriculum at the faculty of Civil
Engineering and Geosciences of Delft University of Technology. This study has been performed in the office
and under the supervision of Delta Marine Consultants.
This thesis work has been assessed and supported by the graduation committee, which consist of the
following members:
•
•
•
•
prof. drs. ir. J.K. Vrijling
ir. W.F. Molenaar
ir. W.J.M Peperkamp
ir. L.A.M. Groenewegen
Delft University of Technology
Delft University of Technology
Delft University of Technology
Delta Marine Consultants
By this means I would like to thank all the graduation committee and all colleagues of Delta Marine
Consultants who gave their support during my thesis work.
Gouda, December 2006-12-21
Priscilla Bonte
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Sandwich wall as the quay wall for the future
Abstracts
Large public works are generally assigned by means of public tenders. Several contractors submit a tender,
while only one contractor is awarded the project. The other contractors produced a design without getting
a direct reward for their efforts. Especially in case the tender has not been granted to a contractor it would
be favourable for that contractor to be able to save time and costs in the tender phase. A new design
method may reduce the design costs in the tender phase.
In this report an attempt is made to develop a new design method for quay walls. Previous quay walls
designs are being analysed and an attempt is made to find relations between external conditions and
design parameter of the structure. When such relations exist they can be used as design graphs. The new
design method will be called reference based design. In this thesis this new method has been applied to
block walls and to sheet pile walls.
The block wall designs have been examined for the following relations.
• Retaining height vs. number of blocks in a cross section;
• Retaining height vs. concrete volume per meter wall;
• Dimensions of the separate blocks vs. elevation of the blocks;
It proves to be possible to find a relation for the number of blocks and for the concrete volume per meter
wall based on only the retaining height. To increase the reliability of the assumed relation and to be able to
extrapolate the results theoretical relations have been derived. These will be included in the design graphs.
The sheet pile wall designs have been investigated for the following relations.
• Retaining height vs. embedded length;
• Retaining height vs. steel volume per meter wall;
The data of these two investigated relations shows a considerable degree of scatter. Therefore theoretical
relations have been derived which can be used when the data set does not lead to unambiguous results.
The theoretical relation for the embedded length is based on both the Blum method and on minimum
stability requirements. With these theoretical relations it proves to be possible to estimate the embedded
length and the steel volume per meter wall.
The second part of this thesis focuses on the development of a new type of quay wall, which will be
designed for the expected future situation. In the last couple of decades significant changes have been
taking place regarding container transport by ships. These changes have an effect on the quay walls at
which these ships can be moored. First of all container ship sizes are increasing continuously. Furthermore
harbour operations are being optimised and modernised constantly; this leads to heavier loads on quay
walls. When both these trends will maintain quay walls for mooring these large container ships will have to
become very large and very strong in the future.
A new quay wall concept may be more economical in case of these very large and strong quay walls which
are expected to be needed in the future. Several new types of quay walls have been considered and a
sandwich quay wall is selected as the most promising concept for the future. This sandwich wall will be
designed for the largest ship ever expected and the future loads on the quay wall have been estimated.
Based on the design ship and the estimated loads a case study has been defined, which will be the basis of
the design of the sandwich wall. The wall will be designed for the Maasvlakte 2 at the Port of Rotterdam
and the retaining height of the wall will be 32m.
The sandwich wall consists of two rows of steel piles and a jet grout mass between these two pile rows.
The steel piles are equipped with steel rings to be able to transfer a certain shear force from the piles into
the grout. These steel rings facilitate a shear connection, which causes the wall to behave as a composite
structure. This composite action has a favourable effect on both the strength and the stiffness of the wall.
On top of the sandwich wall a relieving floor structure will be constructed; this is very common for large
wall structures. An impression of the sandwich quay wall can be seen in the figure below.
6
Sandwich wall as the quay wall for the future
First a preliminary design has been made to gain some insight in the behaviour of the structure and to
create a starting point for the optimisation of the sandwich wall. The preliminary design is based on
assumptions and simple calculations. The main dimension of the wall structure which need to be
determined are indicated in the figure below and the values of these parameter in the preliminary design
phase are included in the table hereunder.
ctc
C
D
h
Diameter and wall thickness of the piles
After deriving a preliminary design the wall structure can be optimised; this optimisation will be based on
costs. The parameters of the sandwich wall resulting from the optimisation are included in the following
table.
D
t
h
ctc
L
hg
760
14
2.0
1.6
34
34
mm
mm
m
m
m
m
Pile diameter
Wall thickness piles
Centre-to-centre distance between the two pile rows
Centre-to-centre distance of the piles
Height of the steel piles
Height of the grout mass
The optimised design of the sandwich wall has been compared to a reference design to investigate the
economic competitiveness of the sandwich wall. A combi wall has been selected for the reference design,
as this type of quay wall is generally the cheapest solution for wall structures in sandy soil with a large
retaining height. The combi wall has been designed for the same load case as the sandwich wall.
The costs of both the combi wall and the sandwich wall have been estimated. Although the sandwich wall
requires a much smaller amount of steel than the combi wall the sandwich wall proves to be more
7
Sandwich wall as the quay wall for the future
expensive. The largest contribution in the costs of the sandwich wall results from the welding of the steel
rings around the piles. These welding costs form approximately 48% of the cost of the sandwich wall.
It may be possible that in the future, due to certain changes, the sandwich wall becomes more attractive.
As the amount of steel in the sandwich wall is relatively small an increase in the price of steel makes the
sandwich wall economically more attractive. Furthermore, when experience is gained regarding jet grouting
this probably allows for a sandwich wall design with less overcapacity in the shear rings. When the number
of shear rings can be reduced the welding costs can be reduced, hence the sandwich wall will become more
competitive.
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Sandwich wall as the quay wall for the future
Table of contents
CHAPTER 1
INTRODUCTION AND PROBLEM DESCRIPTION
16
1.1
Introduction
16
1.2
Outline report
16
1.3
Problem analysis
16
1.4
Objectives
17
CHAPTER 2
NEW QUAY WALL DESIGN METHOD
18
2.1 Reference based design
2.1.1
Methodology
2.1.2
Constructing the database
18
18
18
2.2 Reference based design applied to block walls
2.2.1
Number of blocks in a cross section vs. retaining height
2.2.2
Concrete volume per meter wall vs. retaining height
2.2.3
Average block dimensions
2.2.4
Dimensions of the separate blocks
19
19
20
22
22
2.3 Reference based design applied to sheet pile walls
2.3.1
Embedded length vs. the retaining height
2.3.2
Steel volume per meter wall vs. retaining height
25
25
26
2.4 Conclusions reference based design
2.4.1
Conclusions reference based design applied to block walls
2.4.2
Conclusions reference based design applied to sheet pile walls
28
28
29
CHAPTER 3
31
THE FUTURE OF QUAY WALLS
3.1
Developments regarding quay wall design
31
3.2
Sandwich wall
32
3.3
Frozen quay wall
33
3.4
Floating quay
34
3.5
Container land
34
3.6
Tunnel-type quay wall
35
3.7
Secant pile wall
36
3.8
Selection of the quay wall for the future
36
CHAPTER 4
CASE STUDY
39
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Sandwich wall as the quay wall for the future
4.1
Description project site
39
4.2 Investigation design situation
4.2.1
Ship developments
4.2.2
Tidal water levels
4.2.3
Retaining height
4.2.4
Load developments
4.2.4.1
Vertical loads on the wall
4.2.4.2
Horizontal loads on the wall
39
40
40
40
41
42
42
4.3 Outline design situation
4.3.1
Design philosophy
4.3.2
Calculation method
4.3.3
Design load cases for the design of the sandwich wall
44
45
46
47
CHAPTER 5
52
PRELIMINARY DESIGN SANDWICH WALL
5.1
General
52
5.2
Relieving floor structure
52
5.3
Structural system of the wall structure
54
5.4
Pile layout
54
5.5 Estimation of the wall height
5.5.1
Minimum embedded length with respect to moment equilibrium
5.5.2
Embedded length calculated with Blum method
55
55
56
5.6 Dimensions horizontal cross section of the wall
5.6.1
Estimating the distance h between the two pile rows
5.6.2
Estimating the gap width C between the piles in one row
5.6.3
Estimates for the distance ctc and for the pile dimensions D and t
58
58
59
60
CHAPTER 6
63
6.1
OPTIMISATION OF THE PRELIMINARY DESIGN
Installation method of the steel piles
63
6.2 Grout properties
6.2.1
Derivation of strength parameters of the in-situ grout columns
6.2.2
Influence grout properties on the preliminary design
63
63
65
6.3 Relieving floor structure
6.3.1
Cross sectional layout
6.3.2
Longitudinal layout
6.3.3
Normal force resulting from superstructure
65
65
66
67
6.4
Base design for optimisation
68
6.5
Optimisation wall height
70
6.6 Optimisation dimensions cross section
6.6.1
Optimising the distance h between the two pile rows
72
72
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Sandwich wall as the quay wall for the future
6.6.2
Optimising the distance ctc between the piles in one row
72
6.7 The shear connection
6.7.1
Crushing of the grout
6.7.2
Development of shear stresses inside the grout mass
73
73
75
6.8 Verification of the anchorage
6.8.1
Design of the wall-relieving floor connection
6.8.2
Verification of anchor force
77
77
78
6.9 Reflection of the safety level of the sandwich wall
6.9.1
Safety of the shear connection
6.9.2
Effect of failure of the shear connection
80
80
81
CHAPTER 7
83
ECONOMIC EVALUATION SANDWICH WALL DESIGN
7.1
Basic assumptions for reference design
83
7.2
Design combi wall
83
7.3
Comparison sandwich wall and combi wall
85
7.4
Future prospects sandwich wall
86
7.5
Comparison combi wall with reference based designs
87
CHAPTER 8
CONCLUSIONS AND RECOMMENDATIONS
89
8.1
Conclusions
89
8.2
Recommendations
90
Appendixes
APPENDIX A:
APPENDIX B-1:
APPENDIX B-2:
APPENDIX C:
APPENDIX D:
APPENDIX E:
APPENDIX F:
APPENDIX G:
APPENDIX H:
APPENDIX I:
APPENDIX J:
APPENDIX K:
APPENDIX L-1:
APPENDIX L-2:
LITERATURE STUDY
DATA SETS REFERENCE BASED DESIGN
THEORETICAL BACKGROUND REFERENCE BASED DESIGN
STABILITY CHECK TUNNEL-TYPE QUAY WALL
CONE PENETRATION TEST MAASVLAKTE 1
BLUM CALCULATION
CULLMAN METHOD
PUNCH OF THE GROUT MASS
MSHEET REPORT PRELIMINARY SANDWICH WALL DESIGN
FULL SCALE GROUT TESTS AMSTERDAM
ESA-PRIMA WIN REPORT RELIEVING FLOOR STRUCTURE
MSHEET CALCULATION MINIMUM WALL HEIGHT
OPTIMISATION WALL HEIGHT
OPTIMISATION CROSS SECTION
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Sandwich wall as the quay wall for the future
APPENDIX M-1:
APPENDIX M-2:
APPENDIX N:
APPENDIX O:
APPENDIX P-1:
APPENDIX P-2:
APPENDIX Q:
SHEAR STRESSES GENERAL
SHEAR STRESSES IN SANDWICH WALL
REINFORCEMENT TOE OF RELIEVING FLOOR STRUCTURE
MSHEET REPORT OPTIMISED SANDWICH WALL DESIGN
DESIGN COMBI WALL
MSHEET REPORT COMBI WALL DESIGN
WELD CALCULATION OF THE SHEAR RINGS
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Sandwich wall as the quay wall for the future
List of tables
Table
Table
Table
Table
Table
Table
Table
Table
Table
Table
Table
Table
Table
Table
Table
Table
Table
Table
Table
Table
Table
Table
Table
3-1:
4-1:
4-2:
4-3:
4-4:
4-5:
4-6:
4-7:
4-8:
5-1:
5-2:
Assessment of new quay wall types as the quay wall for the future
Dimension PanaMax, SuezMax and MalaccaMax
Contributions to retaining height
Distributed loads based on the number of layers of containers
Bollard forces based on water displacement
Assumed values and derived loads used in the quay wall calculations
Partial safety factors for soil parameters
Partial load factors for results of sheet pile calculations
Summary of the fully loaded and the least loaded design load case
Assumed width and depth of the relieving floor, based on the Euromax quay wall
Results of the calculation of the minimum wall height based on overall stability applied to the
fully loaded load case
5-3: Dimensions and deformation of the preliminary design, resulting from the iteration process
6-1: Lower and upper limit of the average unconfined compressive strength taken from literature
6-2: Derived strength parameters of the in-situ grout columns based on two different methods
6-3: Summary of strength properties of the in-situ grout
6-4: Results of crushing calculations for various values of the distance ctc
6-5: Summary of optimised design parameters
6-6: Summary of the full scale test results of interest, regarding the compressive grout strength
7-1: Main parameters of the combi wall design, used for comparison with the sandwich wall
7-2: Listing of several properties of the sandwich wall design and of the combi wall design
7-3: Cost estimates for the sandwich wall
7-4: Cost estimates for the combi wall
7-5: Estimates of the material costs of a reference based sheet pile wall design
37
40
41
43
44
44
45
45
47
53
56
62
64
64
73
75
77
80
84
85
86
86
88
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Sandwich wall as the quay wall for the future
List of figures
Figure 2-1: Number of blocks vs. retaining height and line of constant average block height <H>
19
Figure 2-2: Relation concrete volume per meter wall vs. retaining height for block walls
20
Figure 2-3: Load cases used for the comparison of the data points in figure 2-2 with theoretical relations
between the concrete volume and the retaining height of block walls
21
Figure 2-4: Concrete volume vs. retaining height compared to moment equilibrium requirements (left) and
horizontal equilibrium requirements (right)
21
Figure 2-5: 3-D illustration of a block of the Richards Bay block wall in South Africa
22
Figure 2-6: Two examples of the application of the adjusted scale used for the distribution of the block
dimensions over the height of the wall
23
Figure 2-7: Distribution of the ratio B/H of the separate blocks over the wall height for all quay walls in the
data set (left) and for walls consisting of 7 blocks (right)
23
Figure 2-8: Block width distribution over the wall height for all quay walls in the data set (left) and for walls
consisting of 7 blocks (right)
24
Figure 2-9: Block height distribution over the wall height for all quay walls in the data set
24
Figure 2-10: Embedded length vs. retaining height
25
Figure 2-11: Limit cases used for the comparison of the data points in figure 2-10 with theoretical relations
between the retaining height and the embedded length
26
Figure 2-12: Data points of embedded length vs. retaining height for sheet pile walls compared to the Blum
method applied to the defined upper and lower limit case
26
Figure 2-13: Steel volume per meter wall vs. retaining height
27
Figure 2-14: Data points compared to the steel volume per meter wall taken from profile tables
28
Figure 2-15: Estimation of application intervals of several sheet pile profiles, describing the general relation
of the steel volume per meter wall
28
Figure 2-16: Design graph for estimating the number of blocks in a cross section of a block wall
29
Figure 2-17: Design graph for determining the concrete volume per meter wall of block walls
29
Figure 2-18: Possible design graphs for the retaining height (left) and for the steel volume per meter wall
(right)
30
Figure 3-1: Developments of load and strength in time
31
Figure 3-2: Illustration of a sandwich wall [3.4]
32
Figure 3-3: Creating a grout column
33
Figure 3-4: Illustration of the container land quay wall concept
34
Figure 3-5: Construction phase and end phase of tunnel type quay wall
35
Figure 3-6: Illustration secant pile wall
36
Figure 4-1: Plan view of planned location for Maasvlakte 2
39
Figure 4-2: Illustration of the separate contributions adding up to the retaining height
41
Figure 4-3: Illustration maximum head difference over the wall and the design groundwater level [4.2] 42
Figure 4-4: Illustration Blum method: schematisation of a quay wall as a beam
46
Figure 4-5: Illustration spring model for the description of the soil properties
47
Figure 4-6: Illustration of fully loaded design load case
48
Figure 4-7: Illustration of least loaded design load case
48
Figure 4-8: 3-D schematisation of fully loaded design load case, not on scale
49
Figure 5-1: Illustration of terms and materials of the relieving floor structure
52
Figure 5-2: Illustration of an axial load on the wall enhancing the maximum bending moment and an
eccentric load on the wall reducing the maximum bending moment
53
Figure 5-3: Moment of inertia of a beam without and with shear connection
54
Figure 5-4: Two alternatives for pile layout: opposite and diagonally across
55
Figure 5-5: Schematisation of a wall structure as a beam to calculate the minimum required wall height
based on moment equilibrium around anchorage
56
Figure 5-6: Schematisation of loads on the wall structure used for Blum calculation
57
Figure 5-7: Separate load contributions on the wall used for the Blum calculation
57
Figure 5-8: Horizontal cross section of the wall including the parameters to be determined
58
Figure 5-9: Contributions of the soil load acting on the grout and on the piles
59
Figure 5-10: Illustration of lower bound with respect to the distance ctc between the piles
59
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Sandwich wall as the quay wall for the future
Figure
Figure
Figure
Figure
Figure
Figure
Figure
Figure
Figure
Figure
Figure
Figure
Figure
Figure
Figure
Figure
Figure
Figure
Figure
Figure
Figure
Figure
5-11: Design graph used to estimate the ratio R/t for tubular piles subject to bending
61
5-12: Iteration process to find Mmax and corresponding pile diameter D
61
6-1: Relieving floor structure for sandwich quay wall, copied from the Euromax quay wall
66
6-2: Top view of the relieving floor structure, including layout of tensile piles and compressive piles
67
6-3: ESA-Prima Win model of the relieving floor structure and pile system, the wall structure is left
out
68
6-4: Overview of the preliminary design of the sandwich wall, including the preliminary dimensions69
6-5: Three dimensional impression of the configuration of the sandwich wall plus relieving floor
structure
69
6-6: Difference between reaction at the toe in case of overturning and bending of the sandwich wall,
which might occur in case of a reduced grout depth
71
6-7: Development of material costs and wall deformations w_max with varying wall height
71
6-8: Development of material costs with varying distance h
72
6-9: Development of steel and grout costs with varying distance ctc
72
6-10: Illustration of the two opposing effects of increasing the distance ctc
73
6-11: Horizontal and vertical cross section of pile and grout to illustrate crushing of the grout under
a flange
74
6-12: Development of shear stresses and normal stresses in the cross section of the wall
76
6-13: Illustration of the concrete capping beam for the connection between the sandwich wall and
the relieving floor structure
78
6-14: Schematisation of anchor force transferred from capping beam to relieving floor structure and
indication of the tensile and compressive stresses according to the truss analogy
79
6-15: Possible configuration of the reinforcement of the toe of the relieving floor structure
79
6-16: Modified structural system of the sandwich wall in case of failure of the shear connection
81
7-1: Graph containing unity check and steel volume per meter wall for various wall heights
84
7-2: Schematic illustration of the cross section of the combi wall used for comparison with the
sandwich wall
84
7-3: Schematisation of marine installation of the combi wall and land based installation of the
sandwich wall
85
7-4: Design graphs used to derive a cost estimate for a sheet pile wall design
87
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Sandwich wall as the quay wall for the future
Chapter 1
Introduction and problem description
1.1 Introduction
This thesis contains the results of a study with quay walls as the main subject. This report focuses on the
future. Two aspects regarding quay walls are dealt with: the process of designing a quay wall in general
and the structural design of a new quay wall, including an economic evaluation.
In the last couple of decades an increase in scale has been observed with respect to container transport
over water. This increase in scale leads to changing requirements regarding quay walls. Furthermore
changes are taking place in the field of public tendering. Contracts no longer concern only design or only
construction; more and more contracts include both the design and the construction and sometimes even
the maintenance of the structure.
These two developments form the basis of this thesis. With respect to the changes in tender forms an
attempt is made to develop a new design method for quay walls. This new method is meant to save time in
the preliminary design of quay wall structures. Based on the increase in scale of container ship transport a
new quay wall concept will be designed, which is meant to be an economically attractive solution for the
long term future.
1.2 Outline report
The structure of the report is as follows. In chapter 2 the new design method applied to quay walls will be
described. This new method has been applied to two types of quay walls: block walls and sheet pile walls.
Chapter 3 contains the elaboration of a number of new quay wall concepts, which may be applicable as the
quay wall for the future. The advantages and disadvantages of these new quay wall concepts have been
outlined and a selection has been made of which type of quay wall will be designed as the quay wall for the
future. The sandwich wall proves to be the most promising concept.
In chapter 4 the case study is formulated, which will be the basis of the design of the new quay wall
concept. The expected developments of ship sizes and of the loads on quay walls have been investigated
and these developments lead to the definition of the case study. This case study is meant to be a reflection
of the possible upper limit with respect to loads on quay walls and sizes of quay walls.
Chapter 5 describes the preliminary design of the selected new quay wall concept; the sandwich wall. The
preliminary design is meant to gain some insight into the behaviour of the sandwich wall and to form a
starting point from which the optimisation can be started.
The aforementioned optimisation is included in chapter 6. The influence of the various design parameters
have been studied and based on costs the structure has been optimised. This optimisation leads to the
conceptual design of the sandwich wall.
Chapter 7 contains an economic evaluation of the designed sandwich wall. The structure is compared to a
reference design, which has been designed for the exact same situation. A combi wall has been selected as
the reference design as this type of wall generally is the cheapest solution for large quay walls in sandy soil.
1.3 Problem analysis
The first part of this report contains an attempt to develop a new design method for quay walls. Nowadays
contractors are often involved in projects already in the design phases, which for example is the case in
design-and-construct contracts (D&C) and turnkey contracts (TC). This means the contractor produces a
design based on the specification drawn up by the client and also builds the work. The difference between
D&C and TC is the following. In TC the client only provides functional requirements and the contractor
guarantees long term functionality of the project while in D&C the client provides both functional and
16
Sandwich wall as the quay wall for the future
technical requirements and the contractor only guarantees the technical quality of the project. These types
of contracts force contractors to spend time and money on producing designs for projects which have not
been rewarded to them. If time can be saved in the design phases this is an attractive development for
contractors. Therefore an attempt is made to develop a new design method.
The new design method will be based on the experience gained in previous quay wall designs. A database
has to be created in which the design parameters of quay wall designs are stored. The data in the database
is investigated for relations between the external conditions and the design parameters. An attempt is
made to use the found relations as a design tool. This design method is meant to quickly produce a
preliminary design, so in the future time and money can be saved during the design phase.
The second part of this report contains the design of a new type of quay wall. The reason for developing
this new type of quay walls is the continuous increase of ship sizes and loads on quay walls. In this report
only berths for container ships are considered. Container transport in the port of Rotterdam has been
increasing in the last couple of years and this development is expected to continue in the future [1.1].
Larger ships are able to transport more containers at once at a lower rate; this creates the demand for
larger ships.
External loads on quay walls are increasing as well; external loads are for instance crane loads, traffic
loads, bollard forces, etc. Container transport is a sector which has been growing for the last couple of
years and according to [1.2] it will continue to grow in the future. This means more containers will have to
be handled per time unit. This development will probably cause crane loads to increase; containers can be
offloaded faster when a crane can lift several containers at once. The same development is expected for
vehicles used for transporting containers, therefore the traffic load is also likely to increase. Bollard forces
are dependent on the water displacement of the moored ship; larger ships have a larger water
displacement and therefore lead to larger bollard forces.
Larger ships require quay walls with a large retaining height and an increase of the loads demands stronger
quay walls. If these two trends continue in the future quay walls will need to become very large and very
strong. In situation it may be possible that a new type of quay wall is more economical.
1.4 Objectives
The objective of this report consists of two parts. The first aim is to investigate the possibility of developing
a new and fast design method for quay walls. This method will be based on experience gained in earlier
quay wall designs and using this experience in the design of future quay walls. The second objective is to
design the “quay wall for the future”. This new type of quay wall must be an economical solution in a
situation with a very large retaining height and large external loads on the quay wall. It is situated at
Maasvlakte 2.
References
[1.1]
[1.2]
[1.3]
the
[1.4]
http://www.portofrotterdam.com/nl/feiten_cijfers/index.jsp
http://www.havenplan2020.nl/
Final report “Kademuur van de toekomst”,by projectteam Kademuur van de Toekomst by order of
Rotterdam Port Authority [pdf]
“Contracten Menukaart”, by BM Advies [pdf]
17
Sandwich wall as the quay wall for the future
Chapter 2
New quay wall design method
The possibility of developing a new design method will be investigated in this chapter. This method has to
be a fast way to produce a preliminary design. As described in paragraph 1.3 contractors often produce a
design for a project without getting a direct financial reward. This makes it attractive for contractors to
search for a faster design method. An attempt will be made to base this new design method on experience
gained in previous designs. In this thesis the method is applied to quay wall structures.
A large difference exists in how an inexperienced engineer produces a design and how an experienced
designer does it. The difference is, amongst others, in the time it takes them. An experienced designer can
use his experience to produce a good design in a short time. When the designer leaves the company he
takes his experience with him. For the company it would be very useful to be able to preserve this
experience to use it for future quay wall designs.
The new design method discussed in this report is based on using old quay wall designs as a tool for
designing new quay walls. This method will be called reference based design. The basis for this method is a
database containing the most important parameters of previous quay wall designs. Relations between the
external conditions and the design parameters have to be investigated. These relations may prove to be
useful as a design tool to produce a preliminary design in a very short span of time.
2.1 Reference based design
2.1.1
Methodology
First a database containing information about previous quay wall designs has to be present. This database
is constructed using mainly design drawings. If the specifications of a quay wall design are present it is very
useful to include them in the database; however, this is not always the case. The most important
parameters of the quay wall designs are stored in the database and the data has to be examined for
relations which can be used in future designs.
The first step is using the database to select a type of quay wall. Quay walls can be divided into four main
categories and within these main categories several types of quay walls exist. A description of the different
types of quay walls can be found in appendix A. The selection of the type of quay wall can be based on the
properties of the subsoil, the tidal range, the local availability of materials or simply based on similar
situations. Generally not one type of quay wall is applicable for a specific situation. One type, potentially
the best, has to be selected by the designer. The database should provide the all the considered
alternatives and lead to a selection of the most favourable or economic type of quay wall.
The second step is to use the database to estimate the dimensions and material quantities of the quay wall
to come to a preliminary design. For each type of quay wall relations have been identified between the
external conditions and the design parameters. These relations can be used as a tool in the design of a
quay wall.
2.1.2
Constructing the database
To be able to construct a useful and reliable database many quay wall designs have to be collected. The
number of available quay wall designs during this thesis was limited. The available information only consists
of the design drawings; the accompanying specifications for the quay walls were not available. Sufficient
designs of each type of quay wall need to be available to obtain a reliable data set. If the data set is too
small the reliability of the relations, which are based on this data, is questionable.
For every type of quay wall a table containing the most important parameters is drawn up. After collecting
the available quay wall designs at DMC the result is:
• 8 Block wall designs;
• 6 Sheet pile wall designs;
• 1 Cellular wall design;
18
Sandwich wall as the quay wall for the future
•
•
2 L-wall designs;
1 Caisson wall design;
The total number of available designs is too small to be able to use the database for the selection of the
type of quay wall. Furthermore the absence of the project specifications, which may be useful for the
selection of the type of quay wall, adds up to the lack of information. At this point the selection of the type
of quay wall can not be included in the investigation of the new design method.
The designs available at DMC have been investigated for relations between the external conditions and the
design parameters. It is clear that not enough cellular wall, L-wall and caisson wall designs are available
apply the new design method to. For block walls and sheet pile walls the data set is somewhat larger,
which makes it possible to search for relations. However, the reliability of these relations is limited because
the data set is not large enough to produce reliable results. The data sets for the block walls and the sheet
pile walls are included in appendix B-1. These two types of quay walls will be subjected to the reference
based design method.
2.2 Reference based design applied to block walls
The data set for block walls consists of the design drawings of 8 quay walls and is based on the parameters
of the typical cross sections of these walls. The parameters which can be read from the design drawings
are included in the database and the data set is investigated for relations which can be used as a design
tool. The only external parameter which was included in all the design drawings was the retaining height.
Therefore an attempt is made to find relations between the design parameters and the retaining height.
Number of blocks in a cross section vs. retaining height
2.2.1
Number of blocks [-]
The first design parameter which will be investigated is the number of blocks in a cross section of the wall.
The total number of blocks depends on the length of the quay wall. The coping block, which is often castin-place, is also considered to be one of the blocks and is therefore included in the number of blocks. The
relation is shown in figure 2-1.
15
14
13
12
11
10
9
8
7
6
5
4
3
2
1
0
<H>=2 m
<H>=1,5 m
<H>=3 m
<H>=4 m
0
5
10
15
20
25
30
35
Re taining he ight [m ]
Figure 2-1: Number of blocks vs. retaining height and line of constant average block height <H>
The points in figure 2-1 show an increase of the number of blocks for larger retaining heights. The relation
between the retaining height and the number of blocks seems to be linear, but includes a certain degree of
scatter. In the above figure lines of equal average block height are included; in the available data set the
average block height varies between 1.5m and 3.5m. The average of the data set is described by a block
height of approximately 2m.
In case of a linear relation the average block height is independent of the retaining height. So the range of
1.5m to 3.5m is applicable for each retaining height. This can be explained in the following way. A
contractor would want to make the blocks as large as possible; larger blocks means less blocks in total.
When less blocks have to be poured this also leads to less transportation and installation operations.
19
Sandwich wall as the quay wall for the future
However, if the height of the blocks is too large problems can occur with pouring of the (mass) concrete,
and transportation and installation can become too expensive due to larger trucks and cranes. These
considerations lead to a block size independent of the retaining height.
Although the data set shows a considerable degree of scatter it is possible to use figure 2-1. The line
corresponding with the blocks of 2m describes the data set relatively well. The number of blocks obviously
needs to be an integer, so based on the 2m-line the number of blocks for a certain retaining height can be
selected.
Furthermore the number of blocks is relatively unimportant; it does not influence the stability or the
strength of the wall directly. The number of blocks can not be considered separately, it is linked to the
average block dimensions. By dividing the total concrete volume per meter wall over the number of blocks
the average dimensions of the blocks can be estimated. Hence the concrete volume per meter wall is of
much greater importance. The relation between the concrete volume per meter wall and the retaining
height will be investigated in the next paragraph.
Concrete volume per meter wall vs. retaining height
2.2.2
Subsequently the relation between the retaining height and the concrete volume per meter wall will be
investigated. This relation can be used for determining the average dimensions of the blocks, but also to
make an estimate of the costs of the wall. The relation between the concrete volume and the retaining
height is shown in the figure below.
160
Concrete volume per m wall
[m3/m]
140
120
100
80
60
40
20
0
0
5
10
15
Re taining he ight [m ]
20
25
Figure 2-2: Relation concrete volume per meter wall vs. retaining height for block walls
A block wall is a gravity structure; the weight and therefore the volume of the wall secures the stability of
the structure. Both moment equilibrium and the equilibrium in horizontal direction have to be achieved. The
data points in figure 2-2 show an increase of the concrete volume per meter wall for larger retaining
heights. The data in figure 2-2 will be compared to the theoretical relation between the concrete volume
and the retaining height.
For the theoretical relation between the concrete volume and the retaining height two limit cases and one
representative load case have been identified. These three load cases are illustrated in figure 2-3. The
lower limit case leads to the smallest loads on the structure and therefore requires the smallest concrete
volume. The upper limit case leads to the largest loads on the structure hence to the largest required
concrete volume. Furthermore a load case has been drawn up which should represent the data set. The
representative load case is an arbitrarily chosen configuration, which is a possible design load case for any
block wall. Appendix B-2 contains the complete elaboration of these three load cases on which the
theoretical relations are based.
20
Sandwich wall as the quay wall for the future
Lower limit case
Representative case
Upper limit case
p
B
p
h0
Vc, %c
hmax
Vc, %c
p
Vc, %c
H
K0, %soiil
K0, %soiil
K0, %soiil
Figure 2-3: Load cases used for the comparison of the data points in figure 2-2 with theoretical relations
between the concrete volume and the retaining height of block walls
Based on stability requirements two relations can be found between concrete volume and the retaining
height. The first relation follows from moment equilibrium and the second expression can be derived from
equilibrium of horizontal forces. The derivation of the expressions for these two relations is included in
Appendix B-2 and the resulting relations are included in figure 2-4.
800
600
Upper limit
m o m ent equilibrium
Upper lim it
ho rizo ntal
equilibrium
500
600
500
M o ment equilibrium :
representative case
400
300
200
Lo wer limit
m o m ent equilibrium
100
Concrete volume per m w all
[m3/m]
Concrete volume per m w all
[m3/m]
700
400
300
Ho rizo ntal equilibrium :
representative case
200
100
Lo wer lim it
ho rizo ntal
equilibrium
0
0
0
5
10
15
20
Re taining he ight [m ]
25
0
5
10
15
20
Re taining he ight [m ]
25
Figure 2-4: Concrete volume vs. retaining height compared to moment equilibrium requirements (left) and
horizontal equilibrium requirements (right)
The red lines in the two graphs in figure 2-4 show the upper and lower limit of the necessary concrete
volume for a certain retaining height. Obviously all data points are situated between the red lines. The
black lines should correspond more or less with the data points. The six blue data points are described best
by the black line of the moment equilibrium requirements. Apparently moment equilibrium requirements are
governing for these quay walls. The purple data point is described better by the black line of the horizontal
equilibrium requirements, so horizontal equilibrium requirements seem to be governing for this quay wall.
The purple data point represents the Richards Bay block wall in South Africa. When the design of this quay
wall is examined more closely and compared to the designs of the other block walls one aspect stands out.
The blocks of the South Africa quay wall are not solid blocks, but are I-shaped blocks as can be seen in
figure 2-5. This adjusted shape of the blocks reduces the weight and therefore the concrete volume per
meter wall. This has the effect that equilibrium in horizontal direction becomes governing. For the other
block walls in the data set, which consist of solid blocks, moment equilibrium is governing.
21
Sandwich wall as the quay wall for the future
Figure 2-5: 3-D illustration of a block of the Richards Bay block wall in South Africa
Based on the theoretical relations included in figure 2-4 the conclusion can be drawn that it is not possible
to describe the data set with one unambiguous relation. The relation is dependent on the governing
stability requirement: moment equilibrium or equilibrium of horizontal forces. For a block wall consisting of
solid blocks moment equilibrium requirements are mostly governing.
Based on the available data and the derived theoretical relation the following can be said about the design
tools. The data points are situated on a nice curved line, which is fairly well described by the moment
equilibrium line of the representative load case. So for new designs with a retaining height within the range
of the available data set the data points can be used. For larger retaining heights it is advisable to use the
moment equilibrium line of the representative load case as a design tool.
The deviating data point corresponding with the I-shaped block wall in South Africa will not be included in
the design graph as these graphs are meant to produce a rough preliminary design. The I-shape is most
likely the result of an optimisation with respect to material use. The optimisation will be performed in a
later design stage and is not included in the preliminary design; hence the deviating data point is neglected.
2.2.3
Average block dimensions
With the relations derived in the previous two paragraphs the average block dimensions can be determined.
The average block height <H> has been determined by selecting the number of blocks in paragraph 2.2.1.
By dividing the retaining height by the number of blocks the average block height can be found. The
average block height has also been included in the design graph in figure 2-1. The average block width
remains to be determined.
It is unnecessary to plot the data of the data set to find a relation between the block width and the
retaining height to base the average block width on. The average block width can be found by dividing the
concrete volume per meter wall, found in the previous paragraph by the number of blocks and by the
retaining height of the block wall. The formula for determining the average block width is shown in formula
(2.1).
B =
Vtotal
H wall
(2.1)
In which:
Average block width;
Total concrete volume per meter wall (derived in paragraph 2.2.2);
Retaining height of the wall;
<B>:
Vtotal:
Hwall:
2.2.4
Dimensions of the separate blocks
An attempt is made to find a trend in the distribution of both the block width and the block height over the
height of the quay wall. The quay walls in the data set consist of different numbers of blocks. To be able to
compare the data an adjusted scale is introduced to describe the elevation of a block. The top block gets
the value 1 and the bottom block the value 0. The values for the blocks in between are linearly
22
Sandwich wall as the quay wall for the future
interpolated, this corresponds with formula (2.2). Figure 2-6 shows two examples of the application of the
adjusted scale.
1
* (i 1)
(# 1)
ai =
(2.2)
In which:
ai:
Value of the ith block from the bottom;
#:
Number of blocks in a cross section of the wall;
i:
Number of the block, the bottom block being 0, the top block is 1;
1
,
1
+
½
0
0
Figure 2-6: Two examples of the application of the adjusted scale used for the distribution of the block
dimensions over the height of the wall
There are two possibilities for investigating the dimensions of the separate blocks: investigating the
distribution of the ratio Bblock/Hblock over the height or investigating Bblock and Hblock separately. The resulting
graphs are shown in the figures below.
1
Adjusted scale wall height [-]
Adjusted scale wall height [-]
1
0,8
0,6
0,4
0,2
0,8
0,6
0,4
0,2
0
0
0
1
2
3
4
5
Ratio block w idth ove r block he ight [-]
6
7
0
1
2
3
Ratio block w idth ove r block he ight [-]
4
5
Figure 2-7: Distribution of the ratio B/H of the separate blocks over the wall height for all quay walls in the
data set (left) and for walls consisting of 7 blocks (right)
The lines in the figure above show very little correlation. Therefore it does not seem possible to determine
the dimensions of the separate blocks based on the ratio block width over block height. However, some
lines in figure 2-7 are similar. The number of blocks in a cross section of the wall may have an influence on
the block dimensions. In the figure below the data of three quay walls consisting of an equal number of
blocks is singled out. The quay walls in Thailand, Kuwait and the United Arab Emirates all consist of 7
blocks.
23
Sandwich wall as the quay wall for the future
The shapes of the three lines in the right-hand figure in figure 2-7 are similar, but they are not equal.
Because the relation is only based on three quay walls and still some scatter exists in the results the
relation is not reliable. The block width and the block height have to be considered separately to be able to
determine the dimensions of the separate blocks.
1
Adjusted scale wall height [-]
Adjusted scale wall height [-]
1
0,8
0,6
0,4
0,2
0,8
0,6
0,4
0,2
0
0
0%
20%
40%
60%
80%
100%
120%
140%
0%
160%
20%
40%
60%
80%
100%
120%
140%
160%
Block w idth as a pe rce ntage of the ave rage block w idth
Block w idth as a pe rce ntage of the ave rage block w idth
Figure 2-8: Block width distribution over the wall height for all quay walls in the data set (left) and for walls
consisting of 7 blocks (right)
The distribution of the block width over the height of the wall also shows a large degree of scatter. On
average the lines in the right-hand figure in figure 2-8 show that the top blocks have a smaller width than
the average block and the width of the bottom blocks is larger than the average width. Also for the
distribution of the block width over the height of the wall the quay walls with an equal number of blocks are
singled out. This is shown in the left-hand picture in figure 2-8. These three singled out line are very
similar. The number of blocks probably influences the distribution of the block width over the height. In
spite of the similarity in the right-hand picture in figure 2-8 still some uncertainty remains in this statement.
This uncertainty results from the small data set on which this statement is founded; three quay walls
cannot form a reliable data set. More data is necessary to improve the reliability of the found relation.
Nonetheless, it is also very well possible that additional data contradicts this statement and the found
relation.
The distribution of the block height over the height of the wall is considered in the same way as the
distribution of the block width over the height. The result is shown in figure 2-9, left-hand picture. The
scatter in these lines is somewhat smaller than in figure 2-8. Again the data of walls consisting of 7 blocks
has been singled out and plotted in the right-had picture of figure 2-9.
1
Adjusted scale wall height [-]
Adjusted scale wall height [-]
1
0,8
0,6
0,4
0,2
0
0%
20%
40%
60%
80%
100%
120%
140%
160%
180%
Block he ight as a pe rce ntage of the average block he ight
200%
0,8
0,6
0,4
0,2
0
0%
20%
40%
60%
80%
100% 120% 140% 160% 180% 200%
Block he ight as a pe rce ntage of the average block he ight
Figure 2-9: Block height distribution over the wall height for all quay walls in the data set
On average the height of the blocks is close to the average block height. The largest deviation between the
lines in figure 2-9 occurs around the top block. This can be explained by the fact the top block is mostly a
cast-in-place coping beam. The height of the coping beam is dependent on the harbour water level.
24
Sandwich wall as the quay wall for the future
Like in figure 2-8 and figure 2-7 the singled out lines indicate that the distribution of the block height is
dependent on the number of blocks. The reliability of this statement however is still limited due to the small
data set. More data is needed to increase the reliability of the data set.
2.3 Reference based design applied to sheet pile walls
A sheet pile wall is a wall structure as described in appendix A; besides the retaining height the wall also
has an embedded length which contributes the stability of the wall. A sheet pile wall is often anchored near
the top of the wall, which also contributes to the stability. Sheet pile walls can be constructed in
combination with a relieving floor structure; this is often economical for large retaining heights. The sheet
pile wall designs in the data set are all anchored sheet pile wall structures, constructed without a relieving
floor.
Embedded length vs. the retaining height
2.3.1
Compared to a block wall a sheet pile wall has fewer parameters which have to be determined to design a
typical cross section. The first parameter to be investigated is the embedded length of the wall. The relation
between the embedded length and the retaining height is shown in figure 2-10.
Upper limit
moment
equilibrium
30
Embedded length [m]
25
20
15
Low er limit
mo ment
equilibrium
10
5
0
0
5
10
15
20
25
30
Re taining he ight [m ]
Figure 2-10: Embedded length vs. retaining height
An upper and a lower limit case have been defined between which all the data points theoretically will be
situated. For both these two limit cases moment equilibrium around the upper support needs to be
achieved. An illustration of the limit cases can be seen in figure 2-11. In the lower limit case the net
horizontal water pressures on the wall are zero; the vertical water pressures are assumed to be small
enough to be neglected.
In the upper limit case the head difference over the wall causes an additional load due to water pressures.
Furthermore the soil pressures are increased due to the surface load p, which is given a value of 40kN/m3.
Both limit cases are based on an anchored sheet pile wall because all the walls in the data set are
anchored. The anchorage of these limit cases is applied at the top of the wall; generally the anchorage will
be applied lower. However, for schematisation purposes the anchorage is applied at the top. The results of
the moment equilibrium calculation for both the upper and the lower limit case have been included in figure
2-10. Evidently all data points are situated between these two limits.
25
Sandwich wall as the quay wall for the future
Lower limit case
h
p
Ka,
%soil
Ka,
%soil
d
Upper limit case
Kp,
%soil
Kp,
%soil
Figure 2-11: Limit cases used for the comparison of the data points in figure 2-10 with theoretical relations
between the retaining height and the embedded length
The data set has also been compared to the results of the Blum calculation. Again the upper limit and the
lower limit are considered. It is generally known that the Blum method leads to relatively large embedded
lengths, therefore the lower limit calculated with the Blum method is not actually a lower limit with respect
to the embedded length. The Blum method is not based on stability requirements. The method accounts for
reduction of the maximum bending moment in the wall due to a fixed end moment at the toe. This allows
for a more slender design of the wall. This statement corresponds with the results in the figure below.
Some of the points of the data set are situated below the Blum lower limit line, hence it is not really a lower
limit.
Upper limit Blum
30
Embedded length [m]
25
Low er limit
Blum
20
15
10
5
0
0
5
10
15
20
25
30
Retaining he ight [m ]
Figure 2-12: Data points of embedded length vs. retaining height for sheet pile walls compared to the Blum
method applied to the defined upper and lower limit case
The data set is too small and too scattered to use as a reliable design tool. With the currently available data
it is advisable to use the upper limit with respect to moment equilibrium or the Blum upper limit for the
design of a new quay wall structure. Both these methods lead to an overestimation of the embedded length
when compared to the data points; all data points are situated below both lines. However, this
overestimation may not be a problem in the preliminary design phase as it can be optimised in a later
design stage.
2.3.2
Steel volume per meter wall vs. retaining height
The relation between the steel volume per meter wall and the retaining height can be used as an indication
of the costs of the wall. This relation derived from the data set is shown in figure 2-13.
26
Sandwich wall as the quay wall for the future
2,500
Steel volume [m3/m]
2,000
1,500
1,000
0,500
0,000
0
5
10
15
20
25
30
Re taining he ight [m ]
Figure 2-13: Steel volume per meter wall vs. retaining height
The data points in figure 2-13 show an increase in steel volume per meter wall with increasing retaining
height. It is difficult to find a theoretical basis for this linear relation due to the following reason. As the
retaining height becomes larger the bending moment in the wall will increase. For a sheet pile wall to be
able to resist this larger bending moment the moment of inertia must be increased. The moment of inertia
generally consists of two contributions: the Eigen part and the Steiner part (2.3). The Eigen moment of
inertia is related to the cross sectional area as can be seen in (2.4), in which z is the distance to the neutral
axis. The Steiner moment of inertia in formula (2.5) accounts for the distribution of the material in the cross
section. Therefore it is not possible to derive a theoretical relation between the steel area and the retaining
height.
I zz = I eigen + I steiner
(2.3)
I eigen = z 2 dA
(2.4)
I steiner = Az 2
(2.5)
However, many tables are available containing information about sheet pile profiles. These tables have
been used to plot the lines in figure 2-14. For several profiles the steel volume per meter wall is calculated
for various values of the retaining height. The weight per square meter of the profiles is shown in the
legend.
When the results derived from the profile tables are compared to the data points the following can be
concluded. As can be seen in the figure below the data set can not be described by one single profile.
Logically the data points with larger retaining heights are better described by the heavier profiles, with
higher weight per square meter and a larger moment of inertia. Hence the data set can be described by
applying a certain profile for a certain range of retaining heights. This approach has been applied in figure
2-15.
27
Sandwich wall as the quay wall for the future
2,500
Data
Steel volume per meter wall [m3/m]
83kg/m2
175kg/m2
2,000
206kg/m2
235kg/m2
267kg/m2
1,500
299kg/m2
1,000
0,500
0,000
0
10
20
30
Retaining height [m]
Figure 2-14: Data points compared to the steel volume per meter wall taken from profile tables
Steel volume per meter wall [m3/m]
2,500
Data
83kg/m2
175kg/m2
2,000
206kg/m2
235kg/m2
1,500
267kg/m2
299kg/m2
1,000
0,500
0,000
0
5
10
15
20
25
30
35
Retaining height [m]
Figure 2-15: Estimation of application intervals of several sheet pile profiles, describing the general relation
of the steel volume per meter wall
From the above figure can be derived that the steel volume per meter wall is not only dependent on the
retaining height, but also on the used sheet pile profile. However, these results can be used as a design
tool for sheet pile walls.
2.4 Conclusions reference based design
For both block walls and sheet pile walls the conclusion is that the data set consisting of old designs needs
to be large enough to get reliable results. The available data sets are too small to obtain reliable
information. However, supported by some theoretical relations design graphs can be constructed.
2.4.1
Conclusions reference based design applied to block walls
Notwithstanding the aforementioned uncertainty the results for reference based design applied to block
walls are promising. Based on only the retaining height it is possible to determine the number of blocks, the
total concrete volume and the average block dimensions.
28
Sandwich wall as the quay wall for the future
The number of blocks in a cross section of the wall can be determined by using the data set in combination
with the line corresponding with an average block height of 2m. The design graph to be used is shown in
figure 2-16.
Number of blocks [-]
15
14
13
12
11
10
9
8
7
6
5
4
3
2
1
0
<H>=2 m
0
5
10
15
20
25
30
Re taining he ight [m ]
Figure 2-16: Design graph for estimating the number of blocks in a cross section of a block wall
In case the retaining height is within the range of the data set the concrete volume per meter wall can be
derived from the data points. For retaining heights outside the range of the available data set the line
corresponding with moment equilibrium for the representative load case can be used. The diverging data
point corresponding with the quay wall in South Africa, with the I-shaped blocks, has been removed from
the graph. The resulting design graph is shown in the figure below.
Moment
equilibrium:
representative
case
400
Concrete volume per m wall
[m3/m]
350
300
250
200
150
100
50
0
0
5
10
15
20
25
Retaining height [m]
Figure 2-17: Design graph for determining the concrete volume per meter wall of block walls
Based on the design graphs in figure 2-16 and figure 2-17 the average block dimensions can be determined
as described in paragraph 2.2.3. From the investigation in paragraph 2.2.4 can be concluded that it is not
possible to derive the dimensions of each separate block. This is not surprising as this is part of the
optimisation phase. In conclusion the average dimensions and material quantities can be estimated with the
reference based design method.
2.4.2
Conclusions reference based design applied to sheet pile walls
First of all the found relations for the sheet pile walls are only applicable for anchored sheet pile walls
without a relieving floor structure.
29
Sandwich wall as the quay wall for the future
The data set describing the relation between the retaining height and the embedded length shows a large
degree of scatter. Therefore it is not possible to use the current data set as a design tool. Upper limit line
with respect to moment equilibrium and the Blum upper limit line can both be used to determine the
embedded length. There is however a large difference in the results of these two methods.
The Blum method leads to a larger embedded length, which leads to a reduction of the maximum bending
moment and allows for a more slender design of the wall. The upper limit with respect to moment
equilibrium leads to a lower embedded length, but probably requires a heavier cross section of the wall. It
is clear that the relation between the steel volume per meter wall and the retaining height is linked to the
choice of which method is used for the embedded length. Both the design graphs for the embedded length
and for the steel volume per meter wall are shown below.
Upper limit Blum
Upper limit
moment
equilibrium
25
Embedded length [m]
2,500
Steel volume per m eter wall [m3/m]
30
20
15
10
5
Data
83kg/m2
175kg/m2
2,000
206kg/m2
235kg/m2
1,500
267kg/m2
299kg/m2
1,000
0,500
0,000
0
0
0
5
10
15
20
25
30
5
10
15
20
25
30
35
Retaining height [m]
Retaining height [m]
Figure 2-18: Possible design graphs for the retaining height (left) and for the steel volume per meter wall
(right)
The upper limit moment equilibrium line already leads to a larger embedded length than the data points
indicate. Combining this line with the design graph for the steel volume per meter wall seems a reasonable
method to come to a preliminary design. In paragraph 7.5 the results of this method have been compared
to a combi wall designed with the regular method. These results show that a relatively good estimation of
the material quantities can be made with the reference based design method.
References
[2.1]
Archives Delta Marine Consultants, Gouda
30
Sandwich wall as the quay wall for the future
Chapter 3
The future of quay walls
3.1 Developments regarding quay wall design
During the last couple of decades ship dimensions have increased significantly and the expectation is that
ship sizes will keep increasing in the future [3.1]. For quay wall design the draught of a ship is the most
important dimension; it determines the retaining height to a large extent. The retained soil causes a
horizontal load on the wall; this load increases with larger retaining heights. Besides the load resulting from
the retained soil the external loads on the quay wall are also increasing [3.8]. This means that in the future
quay walls do not only have to be larger, but also stronger.
The expected increase of the required size and strength of quay walls develops more or less continuously in
time. Due to this development many quay walls loose their functionality before their economic lifetime has
ended: the technical lifetime of the structure is shorter than the economic lifetime. For future quay walls it
may be economical to account for these increasing requirements in the design. This can be done in two
ways: one can attempt to follow the changing requirements or one can anticipate. This idea is illustrated in
figure 3-1.
Strength and size
Development of strength and size
Required
Follow trend 1
Conventional
Anticipate
Follow trend 2
Time
Figure 3-1: Developments of load and strength in time
The figure above shows that conventional quay wall design does anticipate on future developments to a
certain extent. However, this anticipation does not necessarily prevent quay walls from losing their
functionality before the end of their technical lifetime. When the choice is made to follow the requirements
the quay wall always or almost always meets the requirements, depending on the moment of upgrading.
However, the quay wall will generally be out of service during upgrading of the wall. There are more
moments of upgrading as the trend is followed more closely. This is shown in the difference between the
lines of “follow trend 1” and “follow trend 2” in figure 3-1. When the future situation is anticipated upon the
quay wall is much larger and stronger than necessary during most its lifetime. This seems very expensive,
but on the other hand no downtime is experienced due to upgrading and the quay wall will meet the
requirements during its entire lifetime. The economic study to determine which approach is cheaper is
beyond the scope of this thesis. The choice is made to anticipate on the future developments and to
develop a new quay wall concept for this situation. The quay wall for this extreme case will be called “The
quay wall for the future”.
The increase of the requirements in time is not likely to continue indefinitely. The upper limit is determined
by the largest expected ship ever and the largest expected loads ever. This extreme situation which is still
likely to occur in the future will be investigated in paragraph 4.2.
31
Sandwich wall as the quay wall for the future
In the following paragraphs a several new quay wall concepts will be discussed. These concepts are the
result of some research and suggestions from people at TU Delft and Delta Marine Consultants. Afterwards
a selection will be made of which new type of quay wall will be designed as the quay wall for the future.
3.2 Sandwich wall
In Amsterdam a new metro line is being constructed: the North-South line. A submersible tunnel will be
built under the Central Station for the passage of the metro line under the station. A building pit is
constructed under the station which the tunnel elements will be floated into and sunk at the right position.
The building pit is realised with two “Sandwich walls”; walls consisting of two rows of Tubex piles and a
grout mass between the two rows of piles [3.4]. The sandwich wall is illustrated in figure 3-2; the figure is
not on scale and the included dimensions are indicative.
2,5 m
D
0,4 m
1,0 m
Figure 3-2: Illustration of a sandwich wall [3.4]
Around the tubular piles steel rings are welded to secure the interaction between the steel and the grout
mass; this makes the steel piles and the grout act as a composite structure. This sandwich wall makes a
very strong and stiff retaining wall; therefore it might also be applicable as a quay wall. The sandwich wall
in Amsterdam has to be installed under the monumental Central Station; this leads to restrictions regarding
vibrations. This is the reason for using expensive Tubex piles; in case of a quay wall structure it is not likely
to have such restrictions, so cheaper piles can probably be used. The installation method of the piles is a
point of attention, the steel rings around the piles may cause problems in case of pile driving.
The grout mass between the two rows of steel piles is installed with a technique called jet grouting. This
technique is described in appendix A. Grout columns are created as shown in figure 3-3. By making
overlapping grout columns a continuous grout mass is created.
32
Sandwich wall as the quay wall for the future
Figure 3-3: Creating a grout column
Jet grouting requires an extensive soil investigation and an accurate quality control program. The
composition of the subsoil needs to be investigated carefully for the engineer to be able to design the grout
columns. The grout mixture is determined by the properties of the different soil layers in the subsoil and
the required strength of the grout columns. A layer of dense soil requires a larger injection pressure than a
less dense layer to obtain a certain column width. A good quality control program is necessary because it is
difficult to check the installation process during the creation of the grout columns; it is only possible to
measure the results after the columns have been installed. The position of each installed column has to be
measured at several different depths; this as-built information can be used to determine the position and
installation parameters of the next grout column, if this proves to be necessary to obtain a solid grout
mass.
The grout mass has two functions: it has to transfer a shear force for the wall to behave as a composite
structure and furthermore it has to secure the sand tightness of the wall. Both these function require an
extensive quality control program. The grout mass does not need to be water tight; in fact it is favourable
when it is not water tight, this reduces the head difference and therefore the water pressure on the wall.
However, it is difficult to guarantee the sand tightness in case the wall is not water tight. Therefore the wall
probably also needs to be water tight.
A sandwich wall can be combined with a relieving floor structure; in practice almost all wall structures with
a large retaining height are constructed in combination with a relieving floor structure and anchorage.
Apparently this is the most economical solution. A relieving floor reduces some of the loads on the quay
wall; as a result the embedded length of the wall can be smaller and a more slender design can be made.
The advantage of a sandwich wall is that the steel in the structure is used very efficiently. Due to the
composite action the steel piles are loaded mainly by normal forces rather than by bending. Relatively little
steel is needed to take up a certain bending moment, this is favourable with respect to the current high
steel prices.
3.3 Frozen quay wall
A very innovative concept is creating a vertical quay wall by freezing the ground water in the subsoil. In the
ground a pipeline system is installed through which the cooling liquid flows to freeze the ground water.
Around these cooling pipes columns of frozen soil are created. As the temperature of the soil decreases the
diameter of these ice columns increases until a solid frozen soil mass is created. Once the total soil mass is
frozen less energy is needed to maintain the low soil temperature. It is very important for the cooling
system to have a back-up electricity generator, which secures the safety of the quay wall in case of a
power failure.
The frozen body is protected by an insulation shield at the interface of water and soil. On top of the frozen
soil mass a concrete slab is poured to protect it from sun radiation and other factors which may harm the
33
Sandwich wall as the quay wall for the future
frozen soil. Freezing the ground changes the properties of the soil. The bearing capacity of the soil
increases, the porosity decreases and a large cohesion is added to the soil. These properties make frozen
soil applicable as a retaining structure. The structure functions as a gravity structure; overall stability is
secured by the weight of the frozen soil mass. Ice and soil are both able to take up compressive forces, but
they are hardly able to resist tensile forces. It may be necessary to adjust the shape of the frozen soil body
such that only compressive stresses are present in the structure, for example shaped like an arch.
This type of quay wall seems a very expensive solution, but one has to bear in mind that besides the
cooling installation and the protection shields very little construction materials are used. However, in the
long run the costs of this solution may be very high because there of the continuous energy costs for the
cooling installation.
3.4 Floating quay
The main problem with large retaining heights is the horizontal load resulting from the retained soil. In case
of a floating structure the load due to retained soil is absent, which makes it a very attractive solution.
There can be a sloping bed under the floating structure, or the structure can be connected to an existing
retaining wall. If a slope is applied under the floating structure it has to be protected from erosion due to
waves and currents. For large retaining heights the slope can be very long. For instance, for a slope 1:3
and a retaining height of 25m the length of the slope is 75m.
A floating quay consists of a hollow concrete or steel structure, which is able to move in vertical direction,
along with the water level. The structure must be anchored to the harbour bottom to secure the positions
of the quay. This can be realised with for example suction anchorage or spud legs. A connection between
floating structure and main land has to be realised which allows vehicles to access the quay.
3.5 Container land
In case of temporary need of extra space in a harbour the Container land solution can be an attractive and
cheap option. This quay wall consists of packages of a number of stacked and vertically connected
containers. On top of the upper container and underneath the lowest container a concrete slab is placed.
This slab leads the loads to the corners of the containers, which are the strongest elements of a container.
These packages are simply placed on the harbour bottom, in front of the original quay wall. In this way
extra harbour space can be created in a short time. An illustration of this concept can be seen in figure 3-4
Figure 3-4: Illustration of the container land quay wall concept
This new concept has a very temporary character. The strength of this concept is in the construction time
and the costs. Because containers can be used which are no longer applicable for transportation purposes
the costs are low. If a container land quay wall is constructed for a longer period measures have to be
taken to prevent corrosion of the steel, to prevent (uneven) settlement of the packages and protection of
34
Sandwich wall as the quay wall for the future
the harbour bottom against scour is necessary. These measures are at the expense of the short
construction time and low costs.
3.6 Tunnel-type quay wall
For a very long quay wall it may be possible to construct a quay wall by drilling a tunnel. A start shaft and
an end shaft have to be constructed; between these shafts the tunnel is drilled. This tunnel needs to be
filled with sand or water to make the structure stronger and to prevent if from floating. The tunnel lining
and the fill material inside the tunnel have to be able to withstand all earth and water pressures. On top of
the structure a concrete beam or L-wall has to be constructed to fill the height from the top from the tunnel
up to ground level. In front of the quay wall fender piles have to be placed to protect the structure from
ship impacts.
The tunnel is drilled underground, at a certain distance below the surface. After completion of the tunnel
the soil in front and on top of the tunnel can be excavated to create the harbour and to construct the
concrete structure on top of the tunnel.
Ship
Figure 3-5: Construction phase and end phase of tunnel type quay wall
This type of structure can be used for storage purposes; in that case the stored mass inside the tunnel
contributes to the strength and the stability of the structure. Therefore a ballast system needs to be
present to secure the strength and stability when the stored material is taken out of the structure.
The loads on a tunnel type quay wall are very different from the loads on a regular drilled tunnel. A regular
drilled tunnel is radially loaded by earth and water pressures. These loads lead to mainly compressive
stresses in the concrete lining. This is the reason why the tunnel lining can be relatively thin in case of a
regular drilled tunnel. The loads on a tunnel-type quay wall do not correspond well to the shape of the
structure. A circular cross section is favourable when it is loaded by a uniform compressive force. The quay
wall version is loaded asymmetrically, which leads to torsion and tensile stresses in the concrete lining. The
fill inside de tunnel needs to support the lining, otherwise the lining needs to be very heavy.
Besides the forces in the lining the overall stability of the structure is a point of attention. Appendix C
contains a rough stability calculation of a tunnel-type quay wall. This stability calculation proves that a
stable tunnel-type quay wall is possible in case the diameter of the lining is 48m, with 21m “embedded
length”. A bored tunnel with such a large diameter has never been constructed before. The largest
diameter realised at the time of writing is 15m, at the Groenehart tunnel.
Although no actual figures are available the costs are expected to be relatively high due to the construction
of the start and the end shaft and the drilling machine itself. Furthermore it is probably not possible to
construct a tunnel with the large dimension required for the overall stability.
35
Sandwich wall as the quay wall for the future
3.7 Secant pile wall
Delta Marine Consultants proposed a secant pile wall as a new quay wall structure. A design was made for
the Euromax terminal at Maasvlakte 1 in the Port of Rotterdam, but this was not the most economic design
for that specific situation. However, it may be an economic solution for a different situation.
A secant pile wall consists of prestressed concrete cylinders, placed in one row and located at a certain
distance from each other. They are penetrated into the harbour bottom and are filled with soil. Grout
columns are positioned between the concrete cylinders to fill the gaps between the cylinders and to secure
the sand tightness of the wall. The diameter of the concrete cylinders is in the order of 2 or 3 meters and
the distance between the cylinders, which has to be filled up by the grout columns, is approximately half a
meter. The dimensions of the grout columns are difficult to estimate; most important for the grout columns
is to close the gap between the concrete cylinders. An illustration of this concept is shown in figure 3-6, the
dimensions are indicative.
0.5m
3m
Figure 3-6: Illustration secant pile wall
The concrete cylinders are pushed or driven into the subsoil, while excavating the soil inside them.
Regarding installation and transportation considerations it may be necessary to divide the cylinders into
smaller parts and to prestress the segments after installation. On top of this wall structure a relieving floor
structure can be placed to reduce the soil loads on the wall. As explained in the previous paragraph it is not
likely for wall structures with large retaining heights to be economically attractive without a relieving floor
structure or anchorage.
A secant pile wall is a very strong and durable structure. No steel is directly exposed to the harbour water,
assumed that sufficient concrete cover on the reinforcement has been realised; this contributes to the
durability of the structure. The installation of the concrete piles is a point of attention; they will probably
have to be installed in segments and the segments have to be connected to each other. In that case the
prestressing has to be applied in a wet environment by means of post-tensioning. This is expected to be
very expensive and at the same time has a negative effect on the durability of the prestressing steel.
3.8 Selection of the quay wall for the future
During the description of the new quay wall concepts in the previous paragraphs some of the advantages
and disadvantages have been mentioned. The table below summarises the advantages and disadvantages
36
Sandwich wall as the quay wall for the future
of the several quay wall concepts. Each criterion is valued with plusses and minuses, ranging from ++ to --.
When a concept does not perform particularly well or particularly bad on a certain criterion a score of 0 will
be given.
Table 3-1: Assessment of new quay wall types as the quay wall for the future
Criterion
Durability
Innovation
Applicability long term
Costs
Applicability large
retaining height
Material efficiency/
material use
Summation
Sandwich
wall
0
++
+
0
Frozen
quay wall
++
0
--
Floating
quay
0
+
+
0
Container
land quay
-0
-+
Tunnel
type quay
+
++
+
--
Secant pile
wall
+
++
+
0
+
0
++
-
0
+
++
++
0
+
-
0
+6
+1
+4
-3
+1
+5
The criteria included in the table below will be explained. Durability indicates the degree of decay of the
structure. A concrete structure in water is generally more durable than a steel structure in water, due to
oxidation of the steel. This is reflected by the good score of the secant pile wall, which is the only concrete
structure considered.
With respect to innovation the following can be said. All the considered concepts are new, therefore most
of them get a good score on innovation. Only the container land quay gets a zero score because the
concept has already been completely developed.
On the criterion of applicability on the long term the frozen quay wall gets a zero score; this is mainly based
on the development of the costs in time. The construction costs are relatively low, but the continuous
cooling costs lead to high costs on the long term. The container land quay wall scores very low on this
criterion as it is primarily used as a temporary harbour expansion.
The cost criterion is not based on actual figures; it is only based on the indication of the costs described in
the previous paragraphs. The container land quay wall gets a good score on costs as it is composed of old
sea container, which can no longer be used for transportation purposes. The bad score of the frozen quay
wall again is the result of the development of the costs in time.
From the results in table 3-1 can be concluded that a floating quay probably is the best solution for quay
walls with large retaining heights. The applicability of the container land solution is limited to the retaining
height of existing quay walls. The container packages are placed in front of an existing quay wall, so the
retaining height is in the order of the retaining height of the existing quay wall.
The material efficiency is meant to give an indication of quantities of necessary construction materials. The
sandwich wall is very efficient in steel use and the frozen quay wall hardly needs any construction
materials. Therefore these two concepts score especially good on this criterion. The large dimensions of the
tunnel type quay wall required for overall stability together with the fill material lead to the bad score for
the tunnel type quay wall.
The summation in table 3-1 shows that the sandwich wall has the best score as the quay wall for the
future. The design of a sandwich wall as the quay wall for the future will be described in the following
chapters.
References
[3.1]
[3.2]
Handboek kademuren, CUR 211, by Gemeentewerken Rotterdam and Port of Rotterdam;
Report “De vrieskade, kademuur van de toekomst” ct5313, by van Oosten and van der Plicht;
37
Sandwich wall as the quay wall for the future
[3.3]
[3.4]
[3.5]
[3.6]
[3.7]
[3.8]
the
Living with the ports, multiple use of space, Nationale Havenraad [pdf]
“Sandwichwand onder Amsterdam Centraal Station”, by Royal Haskoning [pdf]
www.actuelewaterdata.nl
Port engineering, by Gregory P. Tsinker;
Lecture notes ct5313, Structures in hydraulic engineering;
Final report “Kademuur van de toekomst”,by projectteam Kademuur van de Toekomst by order of
Rotterdam Port Authority [pdf]
38
Sandwich wall as the quay wall for the future
Chapter 4
Case study
4.1 Description project site
For the elaboration of a sandwich wall as the quay wall for the future a project site is selected: Maasvlakte
2 at the port of Rotterdam. This is done because the conditions at the project site determine the
applicability and the feasibility of the quay wall to a large extent. A quay wall which is economically
attractive in Rotterdam may be impossible to construct at a different location.
Rotterdam is one of the world’s largest container ports, handling over 90 million tons of containers in 2005
[1.1]. This is the main reason for taking the port of Rotterdam as a reference situation. Another reason to
choose for Rotterdam is the intention of the Rotterdam Port Authority to remain one of the leading
container ports in the future [1.2]; the realisation of Maasvlakte 2 can be seen as a confirmation of this
statement.
Maasvlakte 2 is an expansion of the port of Rotterdam located next to Maasvlakte 1; figure 4-1 shows the
location of the planned Maasvlakte 2. The project is in tender phase at the time of writing and the
reclamation works are likely to start in 2008.
Figure 4-1: Plan view of planned location for Maasvlakte 2
The future ground level of the Maasvlakte 2 will be NAP +5.0m, this will be used in the design of the
sandwich wall. The whole area of approximately 2000 hectares consists of newly reclaimed land; therefore
the assumption is made that the soil from the surface down to the harbour bottom (approx. NAP -22m) is
homogeneous and consists of medium coarse sand. For the soil below the harbour bottom the CPT from
Maasvlakte 1, added in appendix D is assumed to be representative. Between NAP -22m and NAP -26m a
layer of silty sand is situated, otherwise the soil consists of medium fine sand.
4.2 Investigation design situation
The aim is to construct a quay wall for the most extreme situation which is still likely to occur in the future.
This expected future situation is called the design situation; from the design situation design load cases can
be derived. The design situation is determined by making an indication of the expected:
4.2.1
4.2.3
4.2.4
Ship developments;
Retaining height;
Load developments;
39
Sandwich wall as the quay wall for the future
4.2.1
Ship developments
It is likely to expect that ship sizes will keep increasing in the future, because this has been the case for
many decades. It is not necessary to design for the largest ship ever. The largest ships at the moment of
writing are super tankers and it is not likely that this will change in the future. However, tankers do not
need quay walls for the purpose of loading and unloading. They can be moored to a jetty or an offshore
mooring buoy equipped with pipes to unload their cargo, which often consists of liquid bulk. Quay walls are
equipped with cranes to load and unload ships. The largest ships which use quay wall facilities are
container ships.
Container ships are characterised by the dimensions of the channel through which they can just fit. The
largest ship which can just fit through the locks of the Panama Canal is characterised as PanaMax. At this
moment plans are made to widen and deepen the Panama Canal and to construct a new set of locks. This
is necessary to be able to compete with the Suez Canal, because more and more container transport occurs
per post-PanaMax ship [4.13]. The dimensions of the new PanaMax ship are included in table 4-1. The
largest ship which can just fit through the Suez Canal is characterised as SuezMax. In the future the Suez
Canal will probably be deepened to allow for oil tankers to fit through the canal, the new maximum draught
will be 22m. However, this is just a speculation; no actual plans have been made yet. MalaccaMax indicates
the largest ship which can just fit through the Strait of Malacca. The expectation is that transportation costs
for these large types of ships will be approximately 30% lower than for a typical 5000 to 6000 TEU
container ship today [4.14]. The dimensions of these three types of ships are shown in the table below.
Table 4-1: Dimension PanaMax, SuezMax and MalaccaMax
Length
Width
Draught
Tonnage
m
m
m
TEU
New PanaMax ship1
366
49
15
12000
Current SuezMax ship2
500
50
16.4
12000
MalaccaMax ship
470
60
21
18000
A MalaccaMax ship has the largest draught of all container ships and is considered to be a maximum.
Transportation costs of these large ships are considerably lower than of medium sized ships. Therefore the
MalaccaMax ship with dimensions as included in table 4-1 is taken as the design ship for the quay wall for
the future. In the future the Suez Canal will probably also be able to handle these large ships.
4.2.2
Tidal water levels
The tide plays an important role in the design of a quay wall. Obviously during low tide the water depth is
smaller than during high tide. The water depth needs to be large enough for ships to sail in. Therefore the
different tide related water levels have been listed below.
Low low water spring
Average low water
Mean sea level
Average high water
High high water spring
4.2.3
NAP
NAP
NAP
NAP
NAP
-1.48m
-0.69m
+0.06m
+1.26m
+1.85m
Retaining height
As the design ship is defined the necessary retaining height of the quay wall can be determined. The
separate contributions to the retaining height are included in table 4-2. Figure 4-2 shows an illustration of
the different components which together form the retaining height.
1
Dimensions of the design ship used in the design of the new locks in the Panama Canal. All channels are
deepened to allow for this type of ship to pass safely.
2
The current maximum ship size for the Suez Canal is included in the table because expansion plans for the
Suez Canal are not as concrete as for the Panama Canal
40
Sandwich wall as the quay wall for the future
Table 4-2: Contributions to retaining height
Draught design ship (MalaccaMax)
Keel clearance (15 % of draught)
Measuring inaccuracies
Fluctuations due to maintenance
Dredging tolerances
21
2.7
0.5
0.5
0.8
m
m
m
m
m
Ground level Maasvlakte 2, NAP
Low Low Water Spring Rotterdam, NAP
Retaining height
+5.0
-1.48
32
m
m
m
Top of the quay wall
LLWS
Design ship
Draught design ship
Retaining height
Keel clearance
Measuring inaccuracies
and maintenance
Dredging tolerance
Figure 4-2: Illustration of the separate contributions adding up to the retaining height
Because the ground level of the future Maasvlakte 2 is used in determining the necessary retaining height
sea level rise does not play a role. Sea level rise is most likely accounted for in the design of the Maasvlakte
2. The retaining height is based on LLWS, this means the design ship is able to berth at all times.
Furthermore it is possible for even larger ships to berth during higher water levels, if these should come
into being.
4.2.4
Load developments
To be able to predict if the loads on quay walls will become larger on the long run, the origin of the loads
will be investigated. The loads can be divided into horizontal loads and vertical loads. All the loads on the
wall will be considered in the cross section of the wall and distributed loads are expressed per meter wall.
The resulting bending moments and transverse forces will also be calculated per meter wall.
41
Sandwich wall as the quay wall for the future
4.2.4.1
Vertical loads on the wall
The most important vertical load on a quay wall is the weight of the crane. Often one of the crane rails is
founded on the quay wall, so the quay wall has to be able to bear these forces and transfer them to the
subsoil. Due to technical developments lifting capacities are increasing hence the loads from the crane on
the quay wall become larger.
It is likely that in the future cranes will be able to lift several containers at once; this development leads to
larger crane loads on the quay wall. At the moment of writing cranes exist which can lift two 20-feet
containers in line. The next step will probably be cranes lifting two 40-feet containers in line and thereafter
maybe cranes lifting 4 20-feet containers. The latter case increases the crane load up to 1300kN per wheel
[4.4]. The crane which in the future will be used at the Euromax terminal, which is currently being
constructed at the Maasvlakte 1 is one of the largest cranes at this moment. This crane has 8 wheels at a
distance of 1.05 m from each other. This same crane will be used in this report together with the expected
future wheel load of 1300kN. This crane load can be represented by a distributed load of 1238kN/m over a
width of 8.4m.
The distance between the two rails is 35m; the crane rail at the land side is founded on a separate pile
system and does not lead to additional forces on the quay wall.
4.2.4.2
Horizontal loads on the wall
Quay walls are loaded by several types of horizontal loads. First a distributed horizontal load acts over the
height of the quay wall; this load is caused by the retained soil. The soil does not maintain a vertical slope
by itself; it has to be kept vertical and this leads to horizontal soil pressures on the wall.
Generally the pores of the soil are filled with ground water, which also creates a horizontal load on the wall.
On the opposite side of the wall the pore water pressure is opposed water pressure resulting from the
harbour water. To determine the resulting water pressure on the wall the maximum head difference over
the wall needs to be determined.
The design head difference is described in [4.2]; figure 4-3 illustrates the maximum head difference CHw
over the quay wall. This figure is applicable for wall structures without drainage.
Design ground water level
Figure 4-3: Illustration maximum head difference over the wall and the design groundwater level [4.2]
For the Maasvlakte 2 LLWS is equal to NAP–1.5m and the average of HW and LW is NAP+0.3m. With the
aid of formula (4.1) this leads to a design head difference of 2.1m. The design ground water level lies at
NAP+0.6m.
42
Sandwich wall as the quay wall for the future
Hw =
HW + LW
2
LLWS + 0,3
(4.1)
Waves cause an additional elevation of the water level. Inside the harbour the significant wave height will
generally be very small because the harbour is sheltered by a breakwater. Only waves larger than 0.5m
have to be taken into account [4.2]. The assumption is made that the harbour is sheltered adequately and
the waves are smaller than 0.5m. Therefore the head difference does not need to be increased to account
for waves.
Surface loads on the area behind the quay wall increase the horizontal soil stress and therefore cause an
additional load on the wall. The EAU 1996 prescribes a distributed load inside the cargo handling area,
which is situated directly behind the quay wall, of 60kN/m2 over a width of 2m, or 40kN/m2 over a width of
3.5m to account for heavy vehicles or construction gear. This load may become larger in the future, for
instance when container handling vehicles are also able to carry several containers. The maximum value of
60kN/m2 is increased with an arbitrary percentage of 25% to allow for larger loads in the future. This leads
to a surface load of 75kN/m2 inside the cargo handling area, over a width of 2m.
Outside the cargo handling area containers and other goods can be stored. This vertical load has the same
effect as the load inside the cargo handling area. The surface load outside the cargo handling area is also
estimated at 75kN/m2 for the future. Loads due to stored containers are included in table 4-3. When this
data is extrapolated 75kN/m2 coincides with approximately 7 to 8 layers of stored containers. A stack of 8
containers has a height of approximately 19.2m; this is high, however it is possible. Choosing this load
equal to the load inside the cargo handling area is also convenient for calculation purposes.
Table 4-3: Distributed loads based on the number of layers of containers
1
2
3
4
5
layer
layer
layer
layer
layer
of
of
of
of
of
containers
containers
containers
containers
containers
15
25
30
40
50
kN/m2
kN/m2
kN/m2
kN/m2
kN/m2
The second cause of horizontal loads on a quay wall is induced by ships which are moored at the quay; the
bollard forces. Due to wind, currents and waves the ship moves as it is moored to the quay. These ship
motions lead to tensile forces in the mooring lines, which are connected to the quay wall. The forces are
represented by horizontally directed concentrated loads acting on the top of the wall. They are dependent
on the water displacement of the design ship. The water displacement can be calculated with the following
formula.
G = L * B * D * CB *
w
(4.2)
In which:
G:
Water displacement [t];
L:
Length of the design ship [m];
B:
Width of the design ship [m];
D:
Draught of the design ship [m];
CB:
Block coefficient of the design ship [-];
Tw:
Density of the water [t/m3];
The block coefficient for sea going ships is 0.5 to 0.8; a value of 0.8 is estimated for the design ship. The
density of water is set to 1.02Mton/m3, which means salt water is accounted for. The design ship is a
MalaccaMax ship with dimensions: L = 470m, B = 60m and D = 21m. Substituting these values into
formula (4.2) results in a water displacement of approximately 540000 tons. The corresponding bollard
force can be read from table 4-4 and has a representative value of 2000kN.
43
Sandwich wall as the quay wall for the future
Table 4-4: Bollard forces based on water displacement
Water displacement in tons
Up to 2000
Up to 10000
Up to 20000
Up to 50000
Up to 100000
Up to 200000
> 200000
Bollard forces [kN](representative values)
100
300
600
800
1000
1500
2000
The final horizontal load on the quay wall is the result of movements of the crane, caused mainly by
swaying of the lifted containers. The horizontal crane loads have a value of approximately 10 to 15% of the
vertical crane load. A representative value of 156kN/wheel is used for quay wall calculations in this report,
which is equal to 12% of the vertical crane load. This force acts at the top of the wall and can be
represented by a distributed load of 149kN/m over a width of 8.4m.
Horizontal loads directed towards the retained soil, like ship impact and forces resulting from the berthing
process, are neglected. The largest impact forces are taken up by fenders and mooring dolphins and the
remaining part is relatively small; the assumption is made that the soil behind the wall is able to take up
these forces. Therefore these loads are not included in the design of the sandwich wall.
4.3 Outline design situation
The loads derived in the previous paragraphs will be combined to draw up the design load cases, which will
be used for designing the sandwich wall, combined with a relieving floor structure. The table below
summarises the derived loads and other assumed parameters, which will be used in the quay wall
calculations.
Table 4-5: Assumed values and derived loads used in the quay wall calculations
Parameter
soil,sat
soil,dry
water
Retaining height
Top quay wall
Maximum head difference
!
" ($2/3* )
Ka
Kp
qsurface
Fbollard
Fcrane, vert
Fcrane,hor
Value
20
16
10
30
32
+5.0
2.1
0
0
20
0.297
6.105
75
2000
1238
149
Unit
kN/m3
kN/m3
kN/m3
V
m
m
m
V
V
V
kN/m2
kN
kN/m
kN/m
Description
Volumetric weight of saturated soil
Volumetric weight of dry soil
Volumetric weight of water
Friction angle of the soil
With respect to NAP
Difference groundwater level and harbour water level
Angle of the wall (with vertical)
Angle of the area behind the wall (with horizontal)
Friction angle between wall and soil
Active earth pressure coefficient
Passive earth pressure coefficient
Distributed surface load (representative value)
Bollard force (representative value)
Distributed vertical crane load (representative value)
Distributed horizontal crane load (representative value)
The above table includes values for the active and passive earth coefficient; this contradicts with the earlier
statement of the sandwich wall being a very stiff wall. In case of a stiff wall, hence small deformations, it is
more likely that neutral earth pressure is applicable. However, MSheet calculations, which will be performed
in the following chapters, show that the horizontal deformations of the wall are large enough for active and
passive earth pressure to develop.
44
Sandwich wall as the quay wall for the future
4.3.1
Design philosophy
The design method described in CUR 211 will be used for the design of the sandwich wall as the quay wall
for the future [4.1]. This method is very well applicable for wall structures in combination with a relieving
floor structure and under conditions similar to the conditions in Rotterdam. The used design method applies
a safety factor of 1.3 on the normal forces, transverse forces and the bending moments. All other load and
material factors are equal to 1. The advantage of this approach is that the distribution of the forces in the
structure corresponds with the physical behaviour of the structure.
Recently the method of designing quay walls has changed from deterministic to probabilistic. The
probabilistic approach is based on producing a design with a total probability of failure which must be
smaller than a certain maximum allowable value. All variables are considered to be stochastic. The
maximum probability of failure is determined by the risk, which is defined as probability * consequences.
More severe consequences should have a smaller probability of failure. Each failure mechanism is subjected
to a probabilistic analysis to check whether all safety criteria are met.
In the Dutch standards three limit states are defined: two ultimate limit states (ULS), 1A and 1B and one
serviceability limit state (SLS) 2. ULS 1A concerns the strength and the stability of the structure and
happens when a failure mechanism occurs due to:
• Failure of a sheet pile;
• Loss of overall stability;
• Insufficient bearing capacity of the foundation;
• Insufficient passive soil resistance;
• Failure of the piling system or anchorage;
• Internal erosion of the soil;
ULS 1B occurs when deformations of the quay wall lead to severe structural damage to parts of the
structure or to nearby structures or installations. SLS 2 concerns deformations under serviceability loads
and occurs when:
• Deformations affect the appearance or the efficient use of the structure or of the nearby structures
or installations;
• Deformations exceed values which are acceptable for serviceability or which do not meet specific
deformation requirements;
A semi-probabilistic design approach is used, which agrees with the Dutch standards regarding quay wall
structures. The method in CUR 211 is based on safety class 2; failure of a large quay wall structure
generally results in large economical damage, but limited personal risk [4.1]. The safety factors are the
result of a probabilistic analysis and are included in table 4-6. The values of the partial safety factors in
table 4-6 are applicable for all limit states. The values in table 4-7 are applicable for ULS 1A and 1B, the
partial safety factors for SLS 2 all have a value of 1.00.
Table 4-6: Partial safety factors for soil parameters
Parameter
c
"
K
E
3
Partial safety factor,
1.00
1.00
1.00
1.00
1.00
1.00
1.00
m
Description
Volumetric weight of soil
Angle of internal friction
Cohesion
Friction angle between soil and wall
Soil coefficient
Young’s modulus of soil
Poison’s ratio
Table 4-7: Partial load factors for results of sheet pile calculations
Parameter
Moments, normal forces, transverse forces
Partial safety factor,
1.3
s
45
Sandwich wall as the quay wall for the future
Anchor force resulting from sheet pile calculation
Epas max / Epas mob.
1.2
1.3
In the above table Epas max/Epas mob. indicates the percentage of mobilised earth pressure. CUR 211 also
prescribes partial safety factors for the harbour bottom level, the harbour water level and the groundwater
level. These values have been derived for the expected future situation and already include a certain
degree of safety. Therefore these safety factors are neglected.
In the above described design philosophy there are no requirements with respect to the wall deformations.
However, it is clear that when the horizontal deformations become too large problems might occur
regarding the sand and water tightness of the wall. Possibly also problems with moored ships colliding with
the protruding wall might occur. Therefore the choice is made to restrict the horizontal deformations. With
respect to quay walls situated near railway tracks Prorail3 requires a restriction of the horizontal
deformations; the horizontal wall deformations must be smaller than 1/100th of the retaining height [4.2].
Calculation method
4.3.2
Two different calculation methods are used during the design of the sandwich wall: the Blum method,
which is based on a rigid-plastic soil model and a calculation method based on a bilinear spring soil model.
The Blum method is suitable for a hand calculation of the minimum required embedded length. It is based
on the assumption that at the moment of failure the deformations in the soil are large enough to allow for
maximum shear stress to develop. This assumption leads to the application of the minimum active and the
maximum passive earth pressure coefficient for the calculation of the horizontal earth pressures. Appendix
A contains an explanation of the calculations of horizontal soil stresses and earth pressure coefficients. The
soil pressures are known because the earth pressure coefficients are known; this makes it possible to
perform the sheet pile calculation as a beam calculation. The schematisation of a wall structure as a beam,
which is used for the Blum calculation is shown in figure 4-4.
l1
l2
Figure 4-4: Illustration Blum method: schematisation of a quay wall as a beam
The above described Blum method is a simplification of the bilinear spring model for the representation of
the soil properties. In case the soil deformations are not large enough for minimum active and maximum
passive earth pressure to occur the spring model is applicable. This model includes the dependence of the
earth pressure on the soil deformations. The range between the minimum and the maximum earth pressure
is described by a linear relation as can be seen in figure 4-5. The inclination of this linear relation
represents the subgrade reaction modulus of the soil.
3
Dutch railway authority
46
Sandwich wall as the quay wall for the future
K
Kp
k
K0
Ka
;
Figure 4-5: Illustration spring model for the description of the soil properties
The Blum method based on Ka and Kp is very suitable for hand calculations of the quay wall, however it is a
rough estimation of the actual behaviour of soil. The more detailed spring model is not suitable for hand
calculation; it is the basis for many computer models. An example of such a model is MSheet. MSheet
contains three calculation models: a model based on K0, Ka and Kp, which is a rigid-plastic model, a model
based on the Culmann method, which is a spring model and the third model is a combination of the
previous two models. For more detailed elaboration of the quay wall structures the method Culmann in
MSheet will be used. The Culmann method is described in Appendix F.
4.3.3
Design load cases for the design of the sandwich wall
Two load cases have been identified which will be used for the design of the sandwich wall: the fully loaded
case and the least loaded case. Intermediate load cases have been studied, but will not be governing in the
design. In the fully loaded case all design loads, derived in the previous chapter are present and the head
difference over the wall is equal to the design head difference. In the least loaded case all of the external
loads are absent, except for the weight of the relieving floor structure and the soil above the relieving floor.
The head difference over the wall is modified and works in opposite direction. The harbour water level is
equal to HHWS (high high water spring) and the ground water level is maintained at the design
groundwater level. These load cases are summarised in table 4-8 and illustrated in figure 4-6 and figure
4-7.
Table 4-8: Summary of the fully loaded and the least loaded design load case
Vertical crane load
Horizontal crane load
Bollard force
Surface load
Head difference
Harbour water level
Groundwater level
Fully loaded case
Present
Present
Present
Present
+2.1m
NAP-1.48m (LLWS)
NAP+0.6m
Least loaded case
Absent
Absent
Absent
Absent
-1.25m
NAP+1.85m (HHWS)
NAP+0.6m
47
Sandwich wall as the quay wall for the future
Fcrane,vert
Fcrane,hor
Fbollard
psurface
NAP+5.0m
NAP+0.6m
NAP-1.5m
NAP-2.0m
NAP-27.0m
Figure 4-6: Illustration of fully loaded design load case
NAP+5.0m
NAP+1.85m
NAP+0.6m
NAP-2.0m
NAP-27.0m
Figure 4-7: Illustration of least loaded design load case
48
Sandwich wall as the quay wall for the future
The governing load case for the design of the sandwich wall will most likely be the fully loaded situation.
However, the design has to be verified with the least loaded case as well. The retained soil mass causes a
bending moment in the wall. The partial foundation of the relieving floor structure on the sandwich wall
causes a normal force on the wall which enhances the bending moment due to second-order effects. The
normal force on the wall differs in the two load cases. The values of the normal force are dependent on the
design of the relieving floor structure and will be determined in paragraph 6.3.3. Below an additional
illustration of the loads in the fully loaded load case can be observed.
qcrane,vert
qcrane,hor
8.4m
qsurface
Fbollard
Figure 4-8: 3-D schematisation of fully loaded design load case, not on scale
An additional remark needs to be made with respect to the construction phases of the sandwich wall. Often
the construction phases lead to additional load cases. For example, when the soil in front of the wall
structure is partly excavated before applying the anchorage. The wall can then temporarily be considered
as a cantilevered beam; after applying the anchorage the wall can be schematised as a simply supported
beam. However, the construction phases will not lead to additional load cases for the sandwich wall. The
construction phases are schematised in Figure 4-9.
49
Sandwich wall as the quay wall for the future
Phase 1:
Small excavation
Phase 2:
Construction wall
structure
Phase 3:
Construction
relieving floor
structure plus
anchorage and
foundation piles
Phase 4:
Back filling at land
side and
excavation at
water side
Figure 4-9: Construction phases sandwich wall
In construction phase 3 the relieving floor structure will be constructed. The relieving floor structure is
connected to the wall structure is such a way that it provides the anchorage. Due to this configuration the
wall is anchored before excavation works at the front of the wall start. Therefore the construction phases
do not lead to additional load cases.
References
[4.1]
[4.2]
[4.3]
Handboek kademuren, CUR 211, by Gemeentewerken Rotterdam and Port of Rotterdam;
CUR 166, ctco5331, Damwand constructies, Grondconstructies en grondkerende constructies
“Sandwichwand onder Amsterdam Centraal Station”, by Royal Haskoning [pdf]
50
Sandwich wall as the quay wall for the future
[4.4]
Final report “Kademuur van de toekomst”,by projectteam Kademuur van de Toekomst by order of
the Rotterdam Port Authority [pdf]
[4.5]
Practical guide to grouting of underground structures, by Raymond W. Henn;
[4.6]
Earth pressure and earth retaining structures, by C.R.I. Clayton, J. Milititski and R.I. Woods
[4.7]
www.wikipedia.org
[4.8]
www.dot.ca.gov/hq/esc/construction/ Manuals/TrenchingandShoring/ch4_earth.pdf
[4.9]
EAU 2006, Recommendations of the committee for waterfront structures, harbours and waterways.
[4.10] NEN6720, Voorschriften beton, TGB1990
[4.11] Grouting in geotechnical engineering, ASCE/AIME
[4.12] www.maasvlakte2.com
[4.13] “Proposal for the expansion of the Panama Canal, third set of locks project”, by ACP [pdf]
[4.14] http://www.solentwaters.co.uk
[4.15] Grond mechanica, met beginselen van de funderingstechniek, by van der Veen, Horvath and van
Kooperen
[4.16] Krupp Hoesch Stahl, Spundwand handbuch, Berechnung
[4.17] www.hetgetij.nl
51
Sandwich wall as the quay wall for the future
Chapter 5
Preliminary design sandwich wall
5.1 General
A sandwich wall is a soil retaining wall consisting of two rows of steel tubular piles and grout columns in
between the piles. The steel piles together with the grout mass take up the forces and bending moments in
the wall. A shear connection between the piles and the grout mass needs to be realised for the wall to
behave as a composite element. The sand and water tightness of the wall are secured by the grout mass.
As mentioned in paragraph 4.1 the Maasvlakte 2 is taken as a reference situation; this is newly reclaimed
land and therefore a homogeneous soil mass is assumed, consisting of sand. The homogeneity of the soil is
very important for the installation of the grout columns. The structure will be designed based on the case
study described in the previous chapter.
The sandwich wall will be combined with a relieving floor structure. The figure below illustrates the terms
which will be used to describe the separate elements of the quay wall.
Concrete
Soil
Relieving floor
structure
Grout
Wall structure
Steel
Soil
Soil
Figure 5-1: Illustration of terms and materials of the relieving floor structure
For the preliminary design of the sandwich wall a rough calculation of the overall dimensions of the wall
structure will be made. The dimensions of the relieving floor will be estimated and a first estimation of the
height of the wall structure is made. Furthermore the necessary dimensions of the steel piles of the
sandwich wall can be calculated.
5.2 Relieving floor structure
First of all the dimensions of the relieving floor structure are estimated to determine the load reduction on
the wall structure. It is not necessary in this stage to design the relieving floor structure in detail; the
parameters which account for the load reduction on the wall are only the depth and the width of the
relieving floor.
52
Sandwich wall as the quay wall for the future
As a first approximation the depth and the width of the relieving floor of the Euromax quay wall are copied,
as this quay wall will be the largest quay wall in the Netherlands when it is completed. Although the
sandwich quay wall will be larger than the Euromax quay wall the dimensions of the Euromax relieving floor
structure are reasonable to start with. The chosen values for the relieving floor are included in the table
below.
Table 5-1: Assumed width and depth of the relieving floor, based on the Euromax quay wall
Depth below field level
Width
7
20
m
m
Generally the relieving floor structure will be founded partly on the wall structure and partly on foundation
piles. This means that a vertical force and possibly also a horizontal force is acting on the wall structure
originating from the relieving floor structure. However, in this preliminary design stage these forces are
neglected as these forces are dependent on the configuration of the relieving floor structure, which has not
been determined yet.
Neglecting the forces on the wall originating from the superstructure has two possible effects. A distinction
will be made between an axial load on the wall structure and an eccentric load on the wall. The two
alternatives are schematised in figure 5-2.
Axial load on the wall
Bending moment
line
Soil and water
pressure
Enhanced bending moment
Eccentric load on the wall
Bending moment
line
Soil and water
pressure
Reduced bending moment
Figure 5-2: Illustration of an axial load on the wall enhancing the maximum bending moment and an
eccentric load on the wall reducing the maximum bending moment
An axial load on the wall enhances the bending moments in the wall due to second order effects and will
lead to larger dimensions. An eccentric load as illustrated in figure 5-2 causes a bending moment which
opposes the bending moment caused by the retained soil and water. This opposing bending moment
reduces the bending moments in the wall.
The preliminary design phase serves two purposes. The first one is to create a base design which can be
modified in the optimisation phase. The second purpose is to gain some insight in the structural behaviour
of the wall and to identify the difficulties in the design. Hence for simplicity considerations the forces
resulting from the relieving floor structure will be neglected in the preliminary design phase.
53
Sandwich wall as the quay wall for the future
Some additional assumptions with respect to the connection between the wall and the relieving floor
structure are made at this point. The connection will be hinged to prevent additional bending moments in
both the wall and the relieving floor structure. Furthermore the connection will be constructed such that
anchorage of the wall structure is obtained. The exact configuration of this connection will be determined in
a later design stage.
5.3 Structural system of the wall structure
The wall structure consists of two rows of steel piles interlocking a grout mass. The structural system of the
wall depends on the interface of the steel piles and the grout mass. The structural design of the sandwich
wall is based on the assumption that the interface is able to transfer a certain shear force, so the wall
behaves as a composite element. In case this shear force can not be transferred the wall consists of two
separately bending piles.
Composite action of the steel and the grout leads to a very efficient use of the steel, which is located at the
outer ends of the cross section. Composite action is facilitated by a shear connection between the grout
and the steel piles. For this purpose the piles are equipped with steel rings. The difference between full
shear connection and no shear connection is illustrated in the figure 5-3.
E, Izz, A
Izz,tot = 2Izz
h
E, Izz, A
E, Izz, A
Izz,tot = 2Izz + 2A(0.5h)2
h
E, Izz, A
Figure 5-3: Moment of inertia of a beam without and with shear connection
From the above picture it becomes clear that full shear connection leads to a significantly larger moment of
inertia than the configuration without shear connection. However, some remarks have to be made with
respect to this shear connection. For the shear connection to be realised the grout needs to enclose the
piles very accurately. However, it is difficult to check the connection between the steel and the grout during
installation. Only after completion of the installation of the jet grout columns tests can be performed to
check the connection.
5.4 Pile layout
The steel piles can be positioned in two ways: opposite each other or diagonally across each other, see
figure 5-4.
54
Sandwich wall as the quay wall for the future
Opposite
Diagonally across
Figure 5-4: Two alternatives for pile layout: opposite and diagonally across
The layout does not influence the strength of the total wall structure; the required steel volume is equal in
both cases. However, when the singled out pieces on the right-hand side of figure 5-4 are considered an
important difference can be identified in the two alternatives. When the piles are placed opposite from each
other the shear forces in the wall are only transferred in cross direction. This makes it possible to describe
the forces in the wall as a 1-D system. In case the piles are places diagonally across the forces are also
spread in long direction, which makes it a 2-D configuration. To keep the wall calculations rather simple the
choice is made to place the piles opposite from each other.
5.5 Estimation of the wall height
To gain some insight in the behaviour of wall structures the minimum required embedded length can be
calculated by hand. The minimum required wall height can be calculated by obtaining moment equilibrium
around the anchorage. This calculated length forms the lower limit with respect to the stability of the
structure. The passive soil resistance is just large enough to resist the active earth pressures.
However, in practice wall structures will mostly have a larger embedded length than the minimum required
length. This has a number of reasons. First of all additional length leads to a higher level of safety to
account for unexpected scour effects or other unforeseen aspects which might endanger the stability of the
structure. Furthermore the additional embedded length causes a redistribution of the bending moments and
reduces the maximum bending moment in the wall. This moment reduction may allow for a more slender
design which leads to a reduction of the total steel volume. The Blum method will be used to determine the
larger wall height which accounts for bending moment redistribution.
5.5.1
Minimum embedded length with respect to moment equilibrium
The minimum wall length can easily be determined by schematising the wall structure as a bending beam.
The relieving floor provides anchorage at the top of the quay wall. This is schematised as a hinged support.
The top is held in position by this support; rotation of the structure around this support is counteracted by
the soil and water pressures on the wall. The passive soil resistance can be schematised also as a hinged
support, at a depth of two-third of the embedded length. This schematisation is shown in figure 5-5.
55
Sandwich wall as the quay wall for the future
Anchor force
l1
l2
2 l
3
1 l
3
2
2
Figure 5-5: Schematisation of a wall structure as a beam to calculate the minimum required wall height
based on moment equilibrium around anchorage
The fully loaded design load case described in 4.3.3 is used in this calculation. The least loaded case has
also been considered, but proves to be not governing. For the fully loaded case the necessary embedded
length is calculated based on the stability condition that requiring sum of all moments around point A to be
zero. The results are included in table 5-2.
Table 5-2: Results of the calculation of the minimum wall height based on overall stability applied to the
fully loaded load case
l1
l2
L
H
5.5.2
Wall height above harbour bottom
Embedded length
Total height of the wall structure (l1 + l2)
Total height of the quay wall, incl. relieving floor structure
25
11.4
36.4
43.4
m
m
m
m
Embedded length calculated with Blum method
Generally the wall will be constructed larger than the minimum wall height. The additional embedded length
will function as a fixed end moment and therefore reduces the maximum bending moment in the wall. The
additional embedded length may lead to a reduction of the cross section, such that the material costs will
be reduced. However, it may also be the case that the material reduction due to reduced bending moment
is insufficient to counteract the additional material due to the additional embedded length. In the latter
case the minimum embedded length will probably be the most economical solution. The Blum calculation in
this paragraph is based on the method described by Verruijt [5.12].
A fixed end is assumed at the lower side of the wall, with a bending moment equal to zero and a transverse
force unequal to zero. The fixation is rigid enough such that there is no displacement, rotation or curvature
at the toe. A schematisation of the loads on the wall used for the Blum calculation is shown in figure 5-6.
The effect of the applied relieving floor can be seen in the development of the soil stresses. The working of
a relieving floor has been described in appendix A. The separate load contributions used in the Blum
calculation are included in figure 5-7.
56
Sandwich wall as the quay wall for the future
h
l1
h;
l2
Figure 5-6: Schematisation of loads on the wall structure used for Blum calculation
6.
1. Passive soil
2. Water pressure
3. Active soil
4. Relieving floor 1
5. Relieving floor 2
6. Anchorage
h
l1
h;
l2
1.
2.
3.
4.
5.
Figure 5-7: Separate load contributions on the wall used for the Blum calculation
The wall is schematised as a cantilevered beam loaded by six external loads as can be seen in the above
schematisation. The influence of the relieving floor has been modelled with two load components: “relieving
floor 1” and “relieving floor 2”. According to the Blum method the following requirements have to be met
[5.12].
•
•
Displacement at the top of the wall must be zero;
Bending moment at the toe of the wall must be zero;
For the six separate loads the horizontal deformation at the top of the wall can be calculated as a function
of the embedded length l2. A more detailed elaboration of the Blum calculation can be seen in appendix E.
The result of the Blum calculation is an embedded length of 27.28m.
57
Sandwich wall as the quay wall for the future
The Blum method generally leads to large wall heights, as is the case for the calculation in appendix E.
However, the wall height will be optimised in the next chapter. At this point a preliminary value needs to be
determined which functions as the starting point for the optimisation. The calculated value of 52m will be
the preliminary value for the wall height of the sandwich wall.
5.6 Dimensions horizontal cross section of the wall
The next step is to zoom in on the wall structure and to consider the dimensions in a horizontal cross
section. Figure 5-8 shows part of the horizontal cross section and the parameters which need to be
determined are indicated.
ctc
C
D
h
Diameter and wall thickness of the piles
Figure 5-8: Horizontal cross section of the wall including the parameters to be determined
In the above figure h is the centre-to-centre distance of the two pile rows, the total width of the wall is
equal to h plus the pile diameter. The gap width between the piles is called C, this width will be used to
determine the distance ctc between the piles in one row. The values for the different parameters will be
derived based on qualitative considerations, except for the pile diameter. The required pile diameter will be
calculated based on the fully loaded design load case.
5.6.1
Estimating the distance h between the two pile rows
In this paragraph a preliminary value for the distance h between the two pile rows will be derived
qualitatively. The parameter h has a large influence on the moment of inertia of the wall structure, as can
be seen in figure 5-3. Therefore a large value of h leads to a strong and stiff wall. In general increasing h
requires a smaller pile diameter to obtain a certain bending moment resistance and the horizontal wall
deformations will be reduced.
However, an increase of h requires a larger grout volume; this probably leads to an increase of material
costs. An increase of h leads to a larger grout volume and increases the moment of inertia. Due to this
larger moment of inertia a smaller pile diameter is needed, which leads to a reduction of the steel volume.
The total material costs are expected to grow when h increases. Based on these considerations the choice
is made to keep the grout mass as small as possible.
A lower limit for the distance h has to be determined if h is to be made as small as possible. The main
function of the grout columns is to secure the sand tightness of the wall. So the lower bound for h will be
determined by the sand tightness of the grout mass. It is clear that a large degree of overlap between the
grout columns increases the sand tightness. The average diameter applied in Amsterdam is 1.0m, this value
will also be used for the average diameter of the grout columns in this report [5.2]. The assumption is
made that a thickness of two grout columns provides enough safety with respect to the sand tightness of
58
Sandwich wall as the quay wall for the future
the wall. Consequently the minimum value for h is 2.0m. The assumption is made to keep the grout mass
as small as possible; hence the preliminary value for h is equal to 2.0m.
5.6.2
Estimating the gap width H between the piles in one row
First a qualitative review of the influence of increasing C on the structural behaviour of the wall is made. A
larger value for C leads to a larger value for ctc. This means that each set of pile is loaded heavier, so a
larger pile diameter is required to obtain a certain bending moment resistance. Furthermore a larger load
has to be transferred from the grout to the piles as can be seen in figure 5-9.
pile
grout
pile
load
Figure 5-9: Contributions of the soil load acting on the grout and on the piles
To derive a value for the distance C two limit cases have been drawn up. As a lower bound configuration
the piles are placed directly next to each other, with no space between them.
ctc = D
D
h = 2m
Figure 5-10: Illustration of lower bound with respect to the distance ctc between the piles
In this lower bound situation it is clear that the grout mass no longer provides the sand tightness of the
wall. In that case the wall can be characterised more or less like a cofferdam. Therefore the assumption is
made that C must be larger than zero.
The upper bound situation is determined by the strength of the grout mass. When the steel piles are placed
too far from each other the grout can be punched through the gaps between the piles. This failure mode is
based on the shear strength of the grout. The shear strength of grout is copied from a sample described in
literature, which is equal to 0.178MPa [5.11]. The punch calculation is included in appendix G.
59
Sandwich wall as the quay wall for the future
The upper limit of the distance C resulting from the punch calculation is 3.15m. This leads to the following
range of possible values for C.
Technical range for C:
0<
3.15 m
Based on this range it is not possible to determine a preliminary value for C. Additional restrictions are
necessary to choose a certain value for C within the above range. The following assumptions are made.
•
•
It should be possible to close the gap between two piles with one grout column and have 0.1m
overlap at each side (C Y 0.8m);
The gap width should be large enough to create a grout columns between the piles (C Z 0.3m);
Based on theses assumptions a value of 0.6m is chosen as preliminary value for the gap width C. This value
will be studied in more detail and possibly optimised in the next chapter.
5.6.3
Estimates for the distance ctc and for the pile dimensions D and t
The centre-to-centre distance ctc and the pile diameter D can not be considered separately, because they
influence each other. This can be concluded from equations (5.2) and (5.3). The bending moment in one
pile can be calculated with the following formula.
M pile =
M distr * ctc
2
(5.1)
The retained soil and water generate a bending moment in the wall, which is taken up by both the steel
piles and the grout mass. As the distance ctc is increased each pile has to resist a larger moment Mpile. For
a pile to resist this larger bending moment the moment of inertia must be increased. The moment of inertia
becomes larger by increasing the pile diameter D or the pile thickness t. Increasing D is much more
effective than increasing t, because Ipile is related to D3.
From the above considerations can be concluded that ctc and D are indeed coupled. The formula below
shows that, by estimating of the pile diameter D, the distance ctc can be determined.
ctc =
+D
0.6m + D
(5.2)
Before estimating values for the diameter and the wall thickness the ratio R/t is considered, in which R is
the pile radius. This ratio can be found based on the graph in figure 5-11. This graph is applicable for
tubular piles loaded by bending. Although the steel piles in the sandwich wall are mainly loaded by normal
forces and to a lesser degree by bending the graph can serve as a tool for estimating the wall thickness.
Figure 5-11 gives a relation between the yield stress of the steel and the ratio R/t, which means that a steel
type has to be selected first. The same source prescribes that from the economical point of view it is always
convenient for a certain bending moment to select piles with a large diameter maintaining the wall
thickness as low as possible by using high strength steels.
Based on the above statement steel with a yield strength fy of 355MPa and a tensile strength ft of 510MPa
is selected. The elastic bending moment of the piles needs to be reached before local buckling of the pile
occurs, this means that area B in figure 5-11 is applicable. A yield stress of 355MPa, or 35.5kg/mm2 leads
to the following design ratio [5.10].
R
= 40
t
D
= 80
t
(5.3)
60
Sandwich wall as the quay wall for the future
Figure 5-11: Design graph used to estimate the ratio R/t for tubular piles subject to bending
The necessary pile diameter can be determined iteratively with the aid of the computer program MSheet.
The iteration process is schematised in figure 5-12. This calculation has been performed based on the fully
loaded load case, which is expected to be governing. The dimensions will be verified in the least loaded
loads case.
Estimate D
Derive t and ctc and
calculate EI
t = D / 80
ctc = 0.6 m + D
Enter EI in MSheet and
calculate Mmax
Determine required D to
take up Mmax
Figure 5-12: Iteration process to find Mmax and corresponding pile diameter D
61
Sandwich wall as the quay wall for the future
In the flow chart on the previous page can be seen that the bending stiffness of the wall needs to be
entered in MSheet. The bending stiffness consists of two contributions: partly of the steel piles and partly
of the grout mass. Therefore an assumption regarding the Young’s modulus of the grout needs to be made.
The Young’s modulus of grout at this point is estimated at 15000 MPa. This value is based on the Young’s
modulus of a B5 strength concrete and approximately reduced with a factor 0.5. This estimated value will
be checked in a later design stage.
The input in MSheet and the resulting bending moments, transverse forces and displacements are included
in appendix H. The results from this iterative process are shown in table 5-3; these values include a safety
factor of 1.3.
Table 5-3: Dimensions and deformation of the preliminary design, resulting from the iteration process
D
t
h
ctc
l2
wmax
628
8
2.0
1.1
27
76
mm
mm
m
m
m
mm
Pile diameter
Wall thickness piles
Centre-to-centre distance between the two pile rows
Centre-to-centre distance of the piles
Embedded length
Maximum horizontal deformation
The dimensions determined based on the fully loaded case have been verified with the least loaded case.
This means that the surface load has been removed and the head difference over the wall has been
modified. The load on the wall originating from the relieving floor structure have not been included in the
design yet, so absence of the crane load does not affect the loads. The MSheet calculation of the least
loaded case shows that the maximum bending moment, the maximum transverse force and the maximum
horizontal deformation are smaller than for the fully loaded case. Therefore the design also complies with
the least loaded case.
Although a full shear connection has been assumed in the preliminary design the actual configuration of the
shear connection has not been designed yet. In the next chapter the shear connection will be designed in
more detail.
References
[5.1]
Handbook Kademuren, CUR 211
[5.2]
Sandwichwand onder Amsterdam Centraal Station, by Royal Haskoning [pdf]
[5.3]
NEN6720, Voorschriften beton, TGB1990
[5.4]
Betoniek March 2002, cement in de grond [pdf]
[5.5]
Overspannend staal, construeren A and construeren B
[5.6]
Grondmechanica, met beginselen van de funderingstechniek, by van der Veen, Horvat and van
Kooperen
[5.7]
Handboek constructieve waterbouw, ct3330, by van Baars, Kuijper, and others
[5.8]
Moderne funderingstechnieken, by prof, A.F. van Weele
[5.9]
EAU 2006, Recommendations of the committee for waterfront structures, harbours and waterways
[5.10] Mannesmann-Stahlform
[5.11] Grouting in the ground, Institution of Civil Engineers, edited by A.L. Bell;
[5.12] Grondmechanica, by A. Verruijt
62
Sandwich wall as the quay wall for the future
Chapter 6
Optimisation of the preliminary design
In the previous chapter a preliminary design of the sandwich quay wall was made. The next step is to
further elaborate and optimise the preliminary design. The installation method may have a large influence
on the design. Therefore the method for installing both the steel piles and the grout columns will be
described in more detail. The characteristics of the grout columns will be specified to come to a more
detailed design. Furthermore the relieving floor structure and its pile foundation will be elaborated upon,
the wall height and the dimensions of the cross section will be optimised based on costs.
6.1 Installation method of the steel piles
The steel piles can be installed by a number of methods, for example pile driving, augering, boring,
vibrating, etc. The installation method may influence the design, for instance pile driving requires a larger
the wall thickness of the piles than for instance augering. Therefore it is necessary to determine the
installation method first before optimising the design.
As mentioned before the wall thickness of the steel piles has to have a certain value to be able to withstand
the high pile driving induced stresses. The minimum required wall thickness t to be able to withstand all pile
driving induced loads is prescribed by the following design formula [6.3].
t = 6.35 +
D
100
(6.1)
In which D is the pile diameter. This formula accounts for sustained hard driving up to 820 blows per meter
with the largest size hammer to be used.
In case of the sandwich wall the steel piles are equipped with rings. Pile driving leads to accelerations of
approximately 100*g which may cause protruding elements to be pushed off. However, if the thickness of
the rings around the piles is limited it is possible to drive the piles without damaging the rings. It might be
necessary to apply a full weld to resist the accelerations. Calculations regarding the loads on the steel
caused by pile driving are too extended to perform as part as this thesis. Therefore the assumption is made
that when the ring thickness is smaller than 30mm it is possible to drive the piles without damaging the
rings.
The costs of augering, boring or vibrating will generally be higher than the costs of pile driving, therefore
pile driving is preferred. At this point the choice is made to drive the steel piles into the subsoil. However, if
in a later design stage pile driving proves to be not possible or not favourable the installation method can
be changed.
The installation method of the grout columns has been described in appendix A and will not be further
elaborated upon. However, the properties of the in-situ grout columns will be discussed in the next
paragraph.
6.2 Grout properties
6.2.1
Derivation of strength parameters of the in-situ grout columns
To be able to optimise the preliminary design some further information is obtained with respect to the
strength properties of the grout columns. The compressive, tensile and shear strength and the Young’s
modulus are derived from the results of a number of full scale tests [6.5]. These full scale tests have been
performed in Amsterdam; the subsoil at the test location consists of several layers, varying from peat and
clay to very dense sand. The tests and some of the test results are described in appendix I.
From the full scale tests relations are found to derive the strength properties of the in-situ grout columns in
the Amsterdam sand layers.
63
Sandwich wall as the quay wall for the future
Compressive strength of grout in sand can be derived from the water-cement ratio of the grout mixture.
This relation is applicable for 0.6 < wcr < 1.4.
f c = 7 + 8.10( wcr ) 2
(6.2)
Tensile strength of grout in sand can be derived from the compressive strength.
f ct , sp = 0.3 ( f c )
3/ 5
(6.3)
Young’s modulus of grout in sand is also related to the compressive strength. This equation gives the
Young’s modulus at 30-70% of the failure compressive strength.
Ecm = 800 ( f c )
1/ 2
(6.4)
The shear strength of the grout has been determined by performing triaxial test and using Mohr’s circle in
combination with the results of the UCS (Unconfined Compressive Strength) tests [6.5]. Appendix I contains
some results of the measured friction angle and shear strength, but no generalised relation is derived. The
table in appendix I indicates a mean value of the shear strength of grout in sand of 10.9MPa, with a
standard deviation of 3.6MPa.
From published information on projects where the strength of the jet grouted columns was recorded it is
possible to derive an indication for the average grout strength in several soil types [6.5]. These values are
included in table 6-1.
Table 6-1: Lower and upper limit of the average unconfined compressive strength taken from literature
Average UCS [MPa]
Soil type
Lower limit
1
3
5
10
10
Peat
Clay
Silt
Sand
Gravel
Upper limit
6
7
15
40
40
Based on the above two methods are proposed to derive the strength properties of the grout columns. The
first method is to use equations (6.2) and (6.3). In order to perform this calculation the water/cement ratio
needs to be estimated; in this case a wcr of 1.0 is assumed, which was also the wcr of the grout columns in
the full scale test.
Another method is to derive the strength parameters of the grout from the lower limit of the average
unconfined compressive strength (UCS) in sand, see table 6-1. Based on the Dutch concrete code NEN6720
the tensile and shear strength and the Young’s modulus can be derived from the unconfined compressive
strength. The results of these two methods are included in table 6-2.
Table 6-2: Derived strength parameters of the in-situ grout columns based on two different methods
Lower limit UCS
Derived from eq. (6.2) and (6.3)
Compressive strength
10.0
MPa
15.1
MPa
Tensile strength
Shear strength
0.94
0.38
MPa
MPa
1.53
-
MPa
MPa
Young's modulus
26418
MPa
3109
MPa
Based on the results in table 6-2 the compressive and tensile strength are taken from the lower limit UCS
method, which seems to give more conservative values than eq. (6.2) and (6.3). When these values are
64
Sandwich wall as the quay wall for the future
compared to the results of the full scale tests this seems a relatively safe approach. The young’s modulus
however, is significantly lower in the second method. Presumably the Young’s modulus of grout is better
described by eq. (6.3), than by the Dutch concrete code. Therefore the Young’s modulus is taken from the
second method.
With respect to the shear strength of the grout the test result is appendix I are compared to the shear
strength derived with the concrete code. The results of the in-situ test (average 10.9MPa) show a
significantly larger value for the shear strength than the value derived with the code (0.38MPa: average
lower limit). The assumption is made that the method based on the concrete code leads to too conservative
values. The shear strength of grout which will be used in the design of the sandwich wall is therefore based
on the in-situ test results and is taken as the average minus two times the standard deviation. In case of a
standard normal distribution of the shear strength the probability of a smaller shear strength is 2.5%, which
seems safe enough. This approach leads to a shear strength of 3.7MPa.
6.2.2
Influence grout properties on the preliminary design
In the preliminary design a Young’s modulus of grout of 15000MPa has been used. However The newly
derived value for the Young’s modulus is much lower than the value used earlier. This lower Young’s
modulus of the grout has a large effect on the bending stiffness of the wall. To investigate the influence of
this change an MSheet calculation is performed with al dimensions equal to the preliminary design and only
the Young’s modulus update to the newly derived value.
The MSheet calculation results show that the horizontal deformations increase. Because the horizontal soil
load is dependent on the deformations the maximum bending moment in the wall is reduced. Therefore a
smaller pile diameter can be applied. Hence the lower Young’s modulus of grout also has a positive effect
on the structural design. Regarding the wall deformations the restriction prescribed by Prorail as explained
in 0 has to be fulfilled: the maximum horizontal deformation must smaller than 320mm. This has to be born
in mind throughout the design process. The new Young’s modulus of grout combined with the dimension of
the preliminary design leads to a maximum horizontal deformation of 186mm, which is smaller than the
aforementioned restriction.
Further on in this chapter the wall structure will be optimised based on costs. The dimensions of the wall
structure will be varied and their influence on the costs will be studied. Beside the optimisation of the
dimensions in the cross section the wall height and the depth of the grout mass will be specified. Before
starting the optimisation the relieving floor structure will be described in more detail.
6.3 Relieving floor structure
Up to this point only the overall dimensions of the relieving floor structure have been specified. These
dimensions were copied from the relieving floor structure of the Euromax quay wall. As the relieving floor
structure is partly founded on the wall structure it causes an additional loading on the wall.
The magnitude of this load will be determined for both the fully loaded and the least loaded load case.
However, first the design of the relieving floor will structure will be determined in more detail.
6.3.1
Cross sectional layout
The cross sectional layout of the relieving floor structure, including the pile system is copied from the
Euromax quay wall. A schematic illustration is included in figure 6-1.
65
Sandwich wall as the quay wall for the future
3m
17m
7m
1m
1
1
1
3
Tensile piles
Compressive piles
Figure 6-1: Relieving floor structure for sandwich quay wall, copied from the Euromax quay wall
In the above figure can be seen that the superstructure provides the anchorage of the wall structure by
means of a toe. This configuration of the connection of relieving floor and wall structure has the effect that
only a normal force is added to the wall structure. The horizontal force has already been included in the
preliminary design because of the assumption of anchorage of the wall structure.
The pile system, which the relieving floor structure is partly founded on is composed of tensile piles and
compressive pile, as can be seen in figure 6-1. The types of pile will also be copied form the Euromax
relieving floor. The tensile piles consist of HEB600 profiles, with a length of approximately 50m and
grouting at the toe of the piles. The compressive piles consist of vibro-piles with a diameter of 670mm and
a length of approximately 30m. The slope of the tensile piles, 1:1, is steeper than the slope of the
compressive piles, 1:3. This difference originates from their function; when the pile forces are resolved the
tensile piles have a larger horizontal component and the compressive piles have a larger vertical
component. So the tensile piles mainly take up the horizontal forces, like the anchor force and the bollard
force and the compressive piles mainly take up the vertical loads, like the surface load ant the weight of the
soil resting on the relieving floor.
The loads corresponding with both the fully loaded and the least loaded load case, as described in
paragraph 4.3.3, are applied to the structure. For both load cases the additional load on the wall structure,
originating from the relieving floor structure will be calculated. Before performing these calculations the
longitudinal layout needs to be determined.
6.3.2
Longitudinal layout
Before the normal force acting on the sandwich wall, originating from the relieving floor structure can be
calculated the longitudinal lay out has to be determined. The relieving floor structure is not one solid
structure with the length of the total quay wall, but it consists of several sections. The width of the sections
is copied from the Euromax relieving floor and is 22.5m.
Per section four tensile piles with a centre-to-centre distance of 5.6m are applied. The centre-to-centre
distance of the compressive piles is 2.8m, which corresponds with 8 x 2 piles. The length of the tensile piles
is 52m and the length of the compressive piles is 31m. Figure 6-2 illustrates the layout of the pile
foundation of the relieving floor.
66
Sandwich wall as the quay wall for the future
3m
17m
22.5m
2.8m
5.6m
Shear keys
Figure 6-2: Top view of the relieving floor structure, including layout of tensile piles and compressive piles
The separate segments are connected in transverse direction by means of shear keys as indicated in the
above figure. The function of these shear keys is to prevent differences in settlement between the
segments. One of the crane rails is located on the relieving floor structure and very little displacements in
the crane rails are allowed.
6.3.3
Normal force resulting from superstructure
The relieving floor structure is founded partly on the sandwich wall; this causes a normal force in the wall
structure. After determining the cross and longitudinal layout of the relieving floor structure it is possible to
calculate the magnitude of this normal force. This calculation is performed in the computer package ESAPrima Win, which is a finite element modelling program. The support of the relieving floor structure on the
sandwich wall is modelled as a hinged support, only supporting the structure in vertical direction. The
support does not prevent rotation in any direction and also does not prevent horizontal movement in
longitudinal and cross direction of the quay wall. The resulting model is shown in the figure below; the
applied supports are not included in the model.
67
Sandwich wall as the quay wall for the future
Figure 6-3: ESA-Prima Win model of the relieving floor structure and pile system, the wall structure is left
out
The resulting vertical support reaction is a distributed load, of which the value varies along the length of
the wall. In the design of the sandwich wall the average of this support reaction will be used, which is equal
to approximately 1860kN/m for the fully loaded case and 490kN/m for the least loaded design load case.
These values include a safety factor of 1.3. The ESA-Prima Win data of the fully loaded case is included in
Appendix J.
The support reaction calculated in ESA-Prima Win is translated into a normal force on the wall structure and
will be included in the MSheet wall calculations. The value calculated in ESA-Prima Win has been verified
with hand calculations, which are of the same order of magnitude.
6.4 Base design for optimisation
At this point all necessary boundary conditions have been specified. A base design including all the loads
and boundary conditions will be outlined before starting the optimisation of the sandwich wall.
In the previous paragraphs the following boundary conditions have been derived.
• The steel piles will be installed by pile driving; therefore the wall thickness will be determined
D
with: t = 6.35 +
;
100
• The compressive strength of grout is 10MPa;
• The shear strength of grout is 3.7MPa;
• The normal force on the wall originating from the relieving floor structure is equal to 1860kN/m;
The design load case has been derived in chapter 4 and will not be repeated here. The dimensions of the
sandwich wall as derived in the preliminary design phase are included in figure 6-4.
68
Sandwich wall as the quay wall for the future
Figure 6-4: Overview of the preliminary design of the sandwich wall, including the preliminary dimensions
The configuration of the relieving floor structure and the pile foundation have been derived in the previous
paragraph. An artist impression of the sandwich wall plus superstructure can be seen in figure 6-5.
Figure 6-5: Three dimensional impression of the configuration of the sandwich wall plus relieving floor
structure
69
Sandwich wall as the quay wall for the future
6.5 Optimisation wall height
Now all data is available to start the optimisation of the wall structure. In the preliminary design the
embedded length of the wall was derived from a rule of thumb, which leads to an embedded length of
25m. This is the embedded length for both the grout mass and the steel piles. The used rule of thumb is
generally applicable for anchored wall structures, which means that the load reduction caused by the
superstructure is not accounted for. Therefore it is likely that a reduction of the embedded length leads to a
more economical design.
The minimum required embedded length of the wall has been calculated in 5.5.1, according to the Blum
method. This method is based on the assumption that the deformations in the wall are large enough for
minimum active and maximum passive earth pressure to be mobilised. A more accurate method for
determining the horizontal soil pressures is based on a spring model. The minimum required embedded
length has also been calculated in MSheet, which is based on a bilinear spring model. The results of this
calculation are included in appendix K.
The depth of both the piles L and the depth of the grout mass hg are varied to optimise both parameters.
For a certain value of hg the pile height L is varied and the corresponding bending moment and deformation
are calculated in MSheet. The required pile diameter is derived from the maximum bending moment and
the material costs are calculated. This is repeated for various values of hg. The results of this investigation
are included in appendix L-1. The following values have been used to estimate the material costs.
Jet grouting
Steel piles
Pile driving
400
2000
1500
€/m3 (all in)
€/ton (incl. fabrication)
€/pile
The pile driving rate is based on installing approximately 3 to 4 piles per day. The aforementioned
investigation shows that grout and steel have a comparable contribution in the material costs. Therefore
the wall height is optimised when the steel and grout volume are minimised. The results in appendix L-1
show that in all studied wall configurations the material cost are minimised when the wall height is as small
as possible. Based on this statement the configuration with a grout height of 27m and steel piles with a
height of 34m is the most economical configuration.
However, when the structural function of the grout is considered this configuration causes some problems.
The grout needs to facilitate composite action of the wall by transferring a shear force equal to the
transverse force in the wall. A couple of meters below the harbour bottom the shear force in the wall has a
local maximum, which is only marginally smaller than the absolute maximum. When no grout is applied at
this depth this effects the bending stiffness of the wall.
When the development of transverse forces over the wall height is considered the maximum is located at a
certain depth below the harbour bottom. Besides the grout mass the soil itself also has a certain shear
strength, dependent on the effective soil stresses. However, this shear strength of the soil is unreliable.
When settlement occurs under the grout mass and the grout itself does not settle the effective stresses at
this point are zero, so the shear strength is zero. Therefore grout will be applied down to the toe of the
steel piles.
The anchorage of the wall has been modelled as a rigid support. However, in practice it may be possible
that deformations occur at this support. These deformations may have an effect on the behaviour of the
wall structure. An additional reason has been identified to apply grout down to the toe of the steel piles.
When these deformations at the anchorage occur overturning might become dominant over bending of the
wall in case of a reduced grout depth. The wall calculations have been performed in MSheet, which models
the wall as a line element. The sandwich wall has a certain width and this overturning effect is not included
in the MSheet calculations. In case of overturning the piles at the landward side are pulled out of the soil
and the piles at the water side are pushed into the subsoil. The difference between bending and
overturning is illustrated in figure 6-6.
70
Sandwich wall as the quay wall for the future
Overturning
Bending
Figure 6-6: Difference between reaction at the toe in case of overturning and bending of the sandwich wall,
which might occur in case of a reduced grout depth
If the grout was to be installed down to a smaller depth this overturning effect would need to be studied
carefully. Due to the choice of applying the grout mass down to the toe of the steel piles it is not necessary
to perform this investigation.
In case the height of the grout mass is equal to the height of the steel piles the graph in figure 6-7 is used
for the economic optimisation.
80000
250
Hor. displacements [mm]
60000
50000
150
40000
100
30000
20000
50
Material costs [Euro/m]
70000
200
10000
0
0
32
37
42
47
52
Wall he ight [m ]
w _max
Grout costs
Steel costs
Total costs
Figure 6-7: Development of material costs and wall deformations w_max with varying wall height
In the above graph can be seen that the steel costs have a minimum at a wall height of approximately
42m, however, the grout costs increase significantly with the wall height. As a result the material costs are
minimal for the minimum wall height of 34m. Therefore this configuration is selected as the optimal wall
height.
The costs of the steel rings have not been included in the above analysis. The influence of the steel rings is
as follows. Longer piles require more rings, in case the distance between the rings remains equal.
Therefore the costs of the rings will be higher for longer piles, thus the lowest costs of the rings correspond
with the smallest pile length. Because the result of the above costs analysis leads to the smallest possible
wall height it is not necessary to include the costs of the rings.
71
Sandwich wall as the quay wall for the future
6.6 Optimisation dimensions cross section
The distances h and ctc can be varied to study their influence on the material costs. Based on the results of
this investigation the dimensions in the cross section will be optimised.
Optimising the distance h between the two pile rows
6.6.1
Up to this point the distance h between the two piles rows was 2.0m, which was the minimum required
width with respect to soil tightness of the wall. In appendix L-2 the distance h has been varied between 2m
and 3m. The required pile diameter is determined and the material costs and deformations are calculated.
Increasing h leads to a larger moment of inertia of the wall. The effect is a reduction of deformations and
less steel is necessary to resist the loads.
70000
Material costs [Euro/m wall]
60000
50000
40000
30000
20000
10000
0
1,8
2
2,2
2,4
2,6
2,8
3
3,2
h [m ]
Cos ts s teel
cos ts grout
Total cos ts
Figure 6-8: Development of material costs with varying distance h
In the above graph the most important results from the investigation described in appendix L-2 are shown.
As can be observed, the steel costs decrease and the grout costs increase as h becomes larger.
Nevertheless the increase of the grout costs is dominant so the total material costs increase with h. Based
on this consideration the distance h is maintained at its minimum value of 2.0m.
6.6.2
Optimising the distance ctc between the piles in one row
With the derived values for the wall height L and the wall thickness h the influence of varying the distance
ctc between the piles in one row can be studied. For several values of ctc the deformations and the
material costs are calculated. The results are included in appendix L-2.
Material costs [Euro/m wall]
60000
50000
40000
30000
20000
10000
0
0
0,5
1
1,5
2
2,5
3
ctc [m ]
Cos ts s teel
cos ts grout
Total cos ts
Figure 6-9: Development of steel and grout costs with varying distance ctc
72
Sandwich wall as the quay wall for the future
The results of the investigation regarding the distance ctc show that both the steel costs and the grout
costs per meter wall decrease as the distance ctc increases. This can be explained in the following way.
Increasing the distance ctc has two opposing effects. On one hand more grout is needed due to the
increase of ctc. This is shown in the left-hand picture in figure 6-10. On the other hand each pile is loaded
heavier and therefore a larger pile diameter is needed. The larger pile diameter leads to a reduction of the
grout volume as can be seen in the right-hand picture in figure 6-10. The effect of the grout reduction due
to the larger pile diameter is dominant so the grout volume per meter wall decreases with ctc.
Increase of grout volume due to
larger width
Decrease of grout volume due to
larger pile diameter
Increase
Decrease
Figure 6-10: Illustration of the two opposing effects of increasing the distance ctc
Besides the material costs increasing ctc also has an influence on the shear stresses in the cross section.
This influence needs to be studied before the optimal value of ctc can be determined.
6.7 The shear connection
The grout mass needs to be able to transfer shear force equal to the maximum transverses force in the wall
to facilitate composite action of the wall. Both the steel-grout interface and the grout mass itself should be
able to resist the shear forces resulting from the loads. In general two failure modes with respect to the
shear connection have been identified: crushing of the grout under the flange and internal shear failure of
the grout. These two failure modes will be described in the following paragraphs. The strength properties of
the grout, which were determined in paragraph 6.2 are summarised in table 6-3.
Table 6-3: Summary of strength properties of the in-situ grout
Compressive strength
Tensile strength
Shear strength
Young’s modulus
6.7.1
10
0.94
3.7
3109
MPa
MPa
MPa
MPa
Crushing of the grout
In the design of the shear connection the assumption is made that crushing of the grout needs to be
prevented. The shear connection leads to a shear force which needs to be transferred by the steel-grout
interface. This shear force is taken up by compression in the grout under the flanges. The figure below
shows a cross section of a pile and part of the grout mass. In this figure the dark grey areas indicate the
compression zones in the grout. The red dashed area shows the theoretical crushing area; this is half the
flange area.
73
Sandwich wall as the quay wall for the future
Vertical cross section pile and grout
Horizontal cross section pile and grout
30mm
30mm
30mm
200mm
Figure 6-11: Horizontal and vertical cross section of pile and grout to illustrate crushing of the grout under
a flange
For various values of ctc the transverse forces in the wall have been calculated in MSheet. In all
configurations the absolute maximum can be seen at a couple of meters below the harbour bottom. A
second local maximum occurs at the top of the wall and is caused by the anchorage. The shear connection
will be designed for the local maximum which is somewhat smaller than the absolute maximum. The result
of this approach is a reduced safety factor with respect to crushing of the grout at the absolute maximum
shear force. This reduced safety factor is compensated by a conservative design of the shear rings.
For several values of ctc the design shear force has been determined. With these values the resulting
compressive stresses in the grout can be calculated with formula (6.5).
crushing
=
Vd
Af n
(6.5)
In which:
]crushing: Compressive stress in the grout under a flange;
Af:
Compression area of the grout;
n:
Number of flanges over which the representative shear force Vd is distributed;
The representative shear force is assumed to be present over 1m of the wall, therefore n is the number of
rings per meter. In formula (6.5) can be seen that the thickness of the flange and the number of flanges
per meter need to be determined before the compressive stress in the grout can be calculated. The flange
thickness is 30mm. Practical experience from the field indicates that this width of the rings is small enough
to prevent problems during pile driving. The centre-to-centre distance of the rings hf is estimated at
200mm. With these selected values the following results are found.
74
Sandwich wall as the quay wall for the future
Table 6-4: Results of crushing calculations for various values of the distance ctc
ctc [m]
Vrep [kN]
Icrushing [MPa]
0.8
0.9
700
788
5.7
6.0
Safety factor
1.76
1.67
1.0
1.1
875
963
6.3
6.6
1.59
1.52
1.2
1.3
1051
1138
6.8
7.1
1.46
1.41
1.4
1.5
1226
1313
7.3
7.6
1.37
1.32
1.6
1.7
1401
1489
7.8
8.0
1.29
1.25
1.8
1.9
1576
1664
8.2
8.4
1.22
1.19
2.0
2.1
1751
1839
8.6
8.8
1.17
1.14
2.2
2.3
1927
2014
8.9
9.1
1.12
1.10
2.4
2.5
2102
2189
9.3
9.5
1.08
1.06
The value Vrep in table 6-4 is taken from the MSheet calculation and does not include a safety factor. By
comparing the calculated compressive stress with the compressive strength of the grout the safety factor
has been calculated.
Increasing the distance ctc has two opposing effects: in paragraph 6.6.2 can be seen that increasing ctc
leads to a reduction of the material costs, however the results in table 6-4 show that the compressive grout
stresses grow with ctc and the safety level with respect to crushing is reduced. The selection of the
distance ctc will be based on the design philosophy described in paragraph 0, which is according to [6.1].
This method is based on an overall safety factor of 1.3, so with respect to crushing of the grout also a
safety factor of 1.3 is desired. The above table shows that this is the case when ctc is equal to 1.6.
The results in table 6-4 are based on the local maximum of the shear force, which is situated a couple of
meters below the harbour bottom. When the same calculations are performed with the absolute maximum
of the shear force a smaller safety factor is the result. In case ctc is 1.6m the safety factor based on the
absolute maximum is 1.12. This means that in theory also the maximum shear force can be transferred by
the shear connection, however, with a lower degree of safety.
The distance ctc is adjusted from 1.1m in the preliminary design to 1.6m as the optimal configuration.
However, the shear stresses inside the grout mass still need to be checked. If the internal shear stresses
prove to be too large the distance ctc will be modified.
6.7.2
Development of shear stresses inside the grout mass
Besides the transfer of the shear force form the steel piles into the grout mass the grout mass itself should
also be able to withstand the internal shear stresses. Appendix M-1 describes the development of shear
stresses in the cross section. Two critical failure modes exist for which the shear stresses need to be
checked. The first failure mode implies shear of only the steel piles and in the second failure mode shear
failure occurs inside the grout mass.
In the first failure mode a shear plane develops around a pile; a pile is vertically pulled out of the grout
mass. The linear elastic approach is not applicable for inhomogeneous cross sections; the theory described
in appendix M-1 will be applied.
75
Sandwich wall as the quay wall for the future
The maximum gradient in the bending moment situated at the local maximum of the shear force is taken
from the MSheet calculation. This results in the values M1 and M2, at a distance Ch of 1m apart. When only
the pile is loaded the normal force in the piles is calculated with the following formula.
Fi =
Mi
h
(6.6)
In this way for both moments M1 and M2 the corresponding pile forces F1 and F2 are calculated and the
difference of these two forces is CF. With this value the shear stress at the shear plane around the pile can
be calculated, according to the following formula.
pile
=
F
B h
(6.7)
The width B is indicated in figure 6-12 and is taken as half the outer perimeter of the flanges. The selected
configuration of ctc = 1.6m leads to a ?pile of 0.86MPa. The resulting safety factor can be calculated by
comparing this value to the shear strength of the grout and is approximately 4.3. So a high degree of
safety with respect to shear failure of a pile is included in the design.
The second failure mode which has been identified concern shear failure inside the grout mass. The
development of the shear stresses in the cross section is schematised in the figure below. The maximum
shear stress ?b is situated at a certain distance below the centre line (at the compression side).
ctc
Shear stresses
Normal stresses
F_t
tension
Lb
h
Lb
F_g
s
La
F_s
compression
Figure 6-12: Development of shear stresses and normal stresses in the cross section of the wall
As can be seen in the above figure, only the normal stresses caused by the bending moment are
considered. The normal force on the wall originating from the superstructure is not included. Shear stresses
are caused by a gradient in the bending moment, therefore the normal force can be neglected.
Again the bending moments M1 and M2 are used. By means of iteration first the normal stresses and the
height s of the grout compression zone need to be calculated. The tensile strength of grout is neglected as
it is very small compared to the other strength parameters. When the normal stresses are known the shear
stress ?b can be calculated. For the selected configuration the maximum shear stress in the grout mass is
76
Sandwich wall as the quay wall for the future
equal to 0.69 MPa, the safety factor on this failure mode is 5.3. Also with respect to internal shear failure of
the grout mass a high degree of safety is included in the design. Appendix M-2 contains some more
detailed information on these calculations.
The shear stresses inside the grout mass prove to be not governing in the design; the crushing failure
mode is governing. Therefore it is not necessary to calculate the internal shear stresses for each possible
value of the distance ctc as was done for the crushing failure mode. Verifying the shear stresses for the
optimal configuration based on the crushing failure mode is sufficient.
The selected value of 1.6m for the distance ctc does not lead to problems regarding the internal shear
stresses. All design parameters of the sandwich wall have been optimised and the results of the
optimisation are summarised in table 6-5. The MSheet report corresponding with the optimised sandwich
wall design is included in appendix O.
Table 6-5: Summary of optimised design parameters
D
t
h
ctc
L
hg
760
14
2.0
1.6
34
34
mm
mm
m
m
m
m
Pile diameter
Wall thickness piles
Centre-to-centre distance between the two pile rows
Centre-to-centre distance of the piles
Height of the steel piles
Height of the grout mass
6.8 Verification of the anchorage
The sandwich wall is anchored at the top. This anchorage is realised by means of the relieving floor
structure as has been described in paragraph 6.3. A calculation needs to be made to verify whether the
connection between the wall structure and the relieving floor is able to transfer the design anchor force.
However, before performing this calculation the connection will be designed in more detail.
6.8.1
Design of the wall-relieving floor connection
It is not practical to connect the sandwich wall to the relieving floor structure without certain measures.
This is caused mainly by the shape of the sandwich wall; the front edge of the wall is not straight. To be
able to make a good connection an in-situ capping beam will be constructed on top of the wall structure.
The capping beam and the connection between the sandwich wall and the relieving floor are shown in
figure 6-13. First the top layer of the grout columns needs to be broken away, such that the upper part of
the steel piles is uncovered. Then a cast in place concrete beam is constructed on top of the wall structure.
77
Sandwich wall as the quay wall for the future
3000
500
1000
500
2000
Figure 6-13: Illustration of the concrete capping beam for the connection between the sandwich wall and
the relieving floor structure
The capping beam in the connection between the wall structure and the relieving floor has an additional
advantage. It contributes in the shear connection at the top of the wall structure. In paragraph 6.7 the
shear connection has been elaborated upon. The design of the shear connection is based on the local
maximum of the transverse forces, just below the harbour bottom. The absolute maximum transverse force
is caused by the anchorage of the wall and is situated at the top. Due to this assumption in the design a
lower safety factor is present at the top of the wall regarding crushing of the grout. The concrete capping
beam contributes to the shear connection, additional to the contribution of the steel rings. Therefore the
safety of the shear connection is increased.
6.8.2
Verification of anchor force
The anchor force of the wall is transferred from the wall, via the concrete capping beam to the relieving
floor structure by means of the toe, as can be seen in figure 6-13. The force is then transferred to the
subsoil by the tensile piles as described in paragraph 6.3. In this paragraph a rough calculation of the
required reinforcement is made to determine if the toe is able to take up the anchor force. If too much
reinforcement is required this indicates the anchor force being too large for the toe to resist and has to be
taken up in a different way.
The anchor force in the fully loaded design case is governing and will be used in this calculation. The
capping beam is assumed to spread the loads in longitudinal direction, such that a uniform load on the toe
of the relieving floor structure is the result. The largest stresses in the reliving floor structure are present
when the wall is slightly rotated at the top so the anchor force is applied at the lower side of the toe. This is
illustrated in figure 6-14. This figure also indicates the critical stresses in the relieving floor structure.
78
Sandwich wall as the quay wall for the future
Relieving floor structure
Compression
Tension
500
Fa
500
1000
Concrete capping beam
3000
Figure 6-14: Schematisation of anchor force transferred from capping beam to relieving floor structure and
indication of the tensile and compressive stresses according to the truss analogy
When the toe is analysed based on truss analogy the red lines indicate the location of the tensile stresses
and the blue lines indicate compression. Stirrups will be applied; these are however not included in the
truss analogy. The reinforcement percentages have been calculated in appendix N, based on these
percentages can be concluded that an acceptable amount of reinforcement is required to take up the
anchor force. The configuration of the reinforcement of the toe used in the calculations is illustrated in
Figure 6-15.
6 25mm per meter
6 25mm per meter
5 10mm per meter
500mm
5 10mm per meter
5 10mm per meter
500mm
Figure 6-15: Possible configuration of the reinforcement of the toe of the relieving floor structure
79
Sandwich wall as the quay wall for the future
6.9 Reflection of the safety level of the sandwich wall
The shear connection of the sandwich wall is very important for the structural behaviour and the overall
stability of the wall. This shear connection is facilitated by the grout columns and the rings around the steel
piles. Because of an uncertainty in both the location and the strength parameters of the grout it is
important to investigate the overall safety with respect to the grout columns.
In case the shear connection fails the structural system of the wall is changed. The wall then consists of
two separately bending beams. This has a great effect on both the strength and the stiffness of the wall. To
get some more insight in the overall safety level of the wall the safety in the shear connection is studied in
more detail. Furthermore it is important to investigate what happens in case the shear connection fails.
6.9.1
Safety of the shear connection
The safety level of the designed shear connection consists of two parts; first of all the safety included in the
grout parameters and second the design of the connection. The grout parameters which have been used in
the design are the compressive strength, the shear strength and the Young’s modulus. In paragraph 6.2.1
an assumption has been made regarding the tensile strength of the grout. However, this strength is very
low and has therefore been neglected in the design of the sandwich wall.
The shear strength of grout is determined by taking the mean grout strength and subtracting twice the
standard deviation. In case of a standard normal distribution of the shear strength the probability of a
smaller shear strength is only 2.5%. This approach leads to a relatively safe estimate for the shear strength
of grout.
The compressive grout strength is taken as the lower limit of the average unconfined compressive strength,
based on projects where the strength of the jet grout columns has been recorded. It is difficult to
determine how safe this value actually is. To gain some more insight the selected value is compared to the
results of the full scale tests described in appendix I. Only the grout strength in the sand layers is
considered. The table below shows the results of the full scale tests which are of interest for the
comparison of the compressive strength. Only single jet systems are considered.
Table 6-6: Summary of the full scale test results of interest, regarding the compressive grout strength
wcr
Layer
First sand layer
Upper second sand layer
Lower second sand layer
0.8
mean
7.9
33.1
-
1.0
sd
3.6
16.4
-
mean
19.6
14.6
22.3
1.2
sd
12.6
3.9
12.9
mean
4.4
23.0
-
sd
3.0
13.2
When the results in the above table are compared to the selected value of 10MPa it can be observed that
two lower values have been measured, but mostly higher values. The standard deviation of the
compressive strength is rather large. Therefore the selected value is not very safe.
To include some additional safety in the design of the sandwich wall the steel ring which facilitate the shear
connection are applied over the total height of the wall. This has the advantage that local failure of the
shear connection can be compensated by the adjoining rings. Generally it would be possible for the
distribution of the shear rings to follow the development of the transverse forces in the wall. However, with
respect to the safety level of the sandwich wall ring will be applied over the total height.
Furthermore the design of the shear connection is based on the assumption that no crushing of the grout
under the rings is allowed. In practice this may not be a problem; crushing of the grout allows for some
deformation but the material is still able to take up some compressive forces. In case crushing of the grout
under the rings is allowed the connection can be called a partial shear connection.
80
Sandwich wall as the quay wall for the future
These three design principles lead to a relatively safe design. However it is also very important to know
what happens in case of total failure of the shear connection. This will be described in the following
paragraph.
Effect of failure of the shear connection
6.9.2
To gain some insight in the safety level of the design of the sandwich wall the risk of failure of the shear
connection will be investigated. In case of failure the structural system of the wall is changed from a
composite element into two separate bending piles. This has a large effect on the bending stiffness of the
wall. The bending stiffness EI is changed from 5.2*106 kNm2/m in case of full shear connection to 5.3*105
kNm2/m for the changed system. A calculation with the lower bending stiffness has been performed in
MSheet.
Before discussing the results of the MSheet calculation a qualitative consideration of failure of the shear
connection will be made. It is not likely that the shear connection will fail at once. Probably local failure of
the grout leads to an increase in deformations, the failure in the grout will gradually expand until there is
no shear connection left. In that case the deformations probably have become very large and the MSheet
calculation needs to reveal if the maximum bending moment is too large for the piles to resist.
The Msheet calculation shows that the maximum bending moment in case of failure of the shear connection
is larger than the maximum bending moment in the fully loaded design load case. However, the
deformations have increased considerably. The anchor force decreases slightly and the maximum horizontal
deformation of the wall in case of shear failure is 2.2m. The anchor force becomes slightly smaller in case
of shear failure.
The separate bending piles in case of shear failure are loaded mainly by bending. The structural system of
the wall change into two separate bending piles; the grout mass has not structural function and can be
modelled as spacers. An schematisation of the modified structural system can bee seen in the figure below.
Soil load
Grout modelled
as spacers
Steel pile
Steel pile
Figure 6-16: Modified structural system of the sandwich wall in case of failure of the shear connection
The ultimate stresses in the steel piles of the new system are calculated with the following formula. The
normal force in the wall originating from the relieving floor structure has been neglected at this point.
max
=
M max, d z
2 I zz , pile
(6.8)
81
Sandwich wall as the quay wall for the future
In which:
Md :
Design value of the maximum bending moment in the wall;
z:
Distance between the point of ultimate stress and the neutral axis;
Izz,pile: Moment of inertia of a pile;
The maximum bending moment has been calculated in MSheet and the distance z in the modified structural
system is equal to half the pile diameter. The fully loaded design case leads to ultimate stresses which are
much larger than the allowable stress of 355MPa. When the stresses due to the normal force in the wall are
added the ultimate stress becomes even larger. Hence the wall is not able to resist the loads of the fully
loaded load case in case of shear failure.
As described earlier shear failure is preceded by an increase in horizontal deformations; these deformations
may function as a warning. This warning can be used to reduce some of the loads on the sandwich wall in
case of shear failure. A simple calculation has been performed to determine the maximum allowable
bending moment in the wall, which does not lead to larger stresses than the allowable shear stress. This
maximum allowable bending moment has a value of approximately 1375kNm/m. When all the loads on the
wall are removed it is still not possible to achieve a bending moment which is small enough. Even only the
retained soil mass leads to a bending moment which is in the order of 8000kNm/m. Therefore failure of the
shear connection will probably lead to collapse of the wall.
References
[6.1] Handboek kademuren, CUR 211, by Gemeentewerken Rotterdam and Port of Rotterdam;
[6.2] CUR 166, Damwand constructies 4e druk;
[6.3] API, Recommended practice for planning design and constructed fixed offshore platforms –
working stress design, dec. 2000
[6.4] Grouting in the ground, Institution of Civil Engineers, edited by A.L. Bell;
[6.5] Grouting for pile foundation improvement, Ph D thesis of A.E.C. van der Stoel;
[6.6] Lecture notes Reinforced concrete ct3050, by prof. dr. ir. J.C. Walraven
[6.7] NEN6720, Voorschriften beton, TGB1990
[6.8] Archives Delta Marine Consultants
82
Sandwich wall as the quay wall for the future
Chapter 7
Economic evaluation sandwich wall design
7.1 Basic assumptions for reference design
To get an idea of the economic feasibility of the designed sandwich wall a comparison is made with a
conventional type quay wall, designed for the same situation. A combi wall has been selected for the
reference design because it often is the most economic solution for quay walls in sandy soil, with a large
retaining height. The combi wall is combined with a relieving floor structure. The superstructure of the
combi wall is exactly the same as the superstructure of the sandwich wall. Therefore the loads on the wall
structure originating from the superstructure are also equal.
The design of the combi wall will be based on the case study described in chapter 4. An attempt is made to
make a fair comparison between the sandwich wall and the combi wall. Therefore all loads, water levels,
soil surfaces and soil properties are equal for both the sandwich wall and the combi wall. The fully loaded
design load case used for the design of the sandwich wall will also be used for the design of the combi wall.
The steel used in the combi wall design has a yield strength of 355MPa, as is the case for the steel piles in
the sandwich wall design. Often combi walls will be designed with a yield strength of the steel of 435MPa.
However, to get a fair comparison the steel strength of the combi wall is selected to be equal to the steel
strength of the sandwich wall.
Due to the large retaining height quite a large pile diameter is expected to be needed for the combi wall.
Therefore the choice is made to apply only one sheet pile between the tubular piles. Generally two or three
intermediate sheet piles will be applied to cope with inaccuracies of the pile positions and orientations.
However more intermediate sheet piles cause the tubular piles to be loaded even heavier. This leads to an
even larger required pile diameter.
Although a small inclination of the wall may have a positive effect on the design of the quay wall the
reference design will be positioned vertically. This choice is made because the sandwich wall is also
positioned vertically. Based on these assumptions a fair comparison can be made between the sandwich
wall and the combi wall, which functions as a reference design.
7.2 Design combi wall
Several combi wall profiles have been listed and for various pile heights the maximum bending moment has
been calculated in MSheet. Based on this bending moment the smallest possible profile has been
determined. In this way the required steel volume for a certain pile height can be calculated. These
operations lead to the following graph.
83
2,70
1,10
2,60
1,05
2,50
1,00
2,40
0,95
2,30
0,90
2,20
0,85
2,10
Unity check [-]
Steel volume per meter wall [m3/m]
Sandwich wall as the quay wall for the future
0,80
34
35
36
37
38
39
40
41
42
43
44
45
Wall height [m]
Steel volume
Unity check
Figure 7-1: Graph containing unity check and steel volume per meter wall for various wall heights
The above graph shows that all unity checks are smaller than 1, so all profiles are able to resist the loads.
However, because the profiles are increased in steps the unity check varies somewhat. In the above graph
can be seen that the smallest wall height leads to the smallest steel volume per meter wall. The minimum
wall height with respect to overall stability has been calculated in MSheet and is 33.4m. Based on this
information the wall height of the combi wall is set at 34m. This is equal to the wall height of the sandwich
wall, so no differences in wall height exist which may influence the comparison. The design parameters of
the combi wall are included in the table below and a schematic illustration can be seen in table 7-1.
Table 7-1: Main parameters of the combi wall design, used for comparison with the sandwich wall
Diameter tubular pile
Wall thickness
Wall height
Bending stiffness EIcombi
2420
31
34
9.37*106
mm
mm
m
kNm2/m
31
2420
1250
2420
Figure 7-2: Schematic illustration of the cross section of the combi wall used for comparison with the
sandwich wall
The calculations performed for the combi wall design are described in more detail in appendix P-1. The
MSheet report corresponding with the selected combi wall configuration is included in appendix P-2. As
mentioned in the previous paragraph the combi wall will be combined with a relieving floor structure. A
cast-in-place concrete capping beam will be constructed on top of the combi wall to facilitate a proper
connection. The superstructure is exactly the same as for the sandwich wall, therefore only the designs of
the wall structures need to be compared.
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Sandwich wall as the quay wall for the future
Since the design of the combi wall is finished it can be compared to the sandwich wall design. Based on this
comparison an evaluation of the economic feasibility of the sandwich wall will be made.
7.3 Comparison sandwich wall and combi wall
Several properties of both the sandwich wall and the combi wall have been listed in the table below. These
properties will be used to describe the differences between the two wall types and to make an estimate of
the economic feasibility of the sandwich wall.
Table 7-2: Listing of several properties of the sandwich wall design and of the combi wall design
Property
Unit
Sandwich wall
Combi wall
Pile diameter
Wall thickness piles
mm
mm
760
14
2420
31
m
kNm2/m
2.76
5.38*106
2.42
9.37*106
m3/m
mm
1.32
214
2.29
131
Total width of the wall
Bending stiffness
Steel volume per meter wall
Maximum horizontal deformation
First of all there is a large difference in the required pile diameter. The pile diameter of the combi wall is
too large to be able to install with land based equipment. Although an equal installation method would be
fairest with respect to the comparison the choice is made to apply marine installation for both the piles and
the sheet piles of the combi wall. The land based installation method of the sandwich wall, described in
paragraph 6.1, remains unchanged. Also the relieving floor structure of both the combi wall and the
sandwich wall are constructed from land. A schematisation of the marine installation of the combi wall can
be seen in the figure below
Figure 7-3: Schematisation of marine installation of the combi wall and land based installation of the
sandwich wall
Installation of the piles from land will generally be cheaper than a marine installation. Furthermore piles
with a larger diameter are also more expensive to produce and to transport than piles with a smaller
diameter.
85
Sandwich wall as the quay wall for the future
In Table 7-2 can be seen that the deformations of the combi wall are much smaller than the deformations
of the sandwich wall. This difference is caused by the difference in bending stiffness of the wall.
For both the sandwich wall and the combi wall design an estimate of the costs of the wall structure has
been made. The relieving floor structure is the same for both alternatives, so it has been neglected in the
costs comparison. The tables below contain the costs estimates for both the sandwich wall and the combi
wall design.
Table 7-3: Cost estimates for the sandwich wall
Sandwich wall
Steel piles
Welding
Pile driving
Grout
Capping beam
Total
unit price
1,10
143
1500
400
150
euro/kg
euro/ring
euro/pile
euro/m3
euro/m3
Land based installation
quantity
1,32
m3/m
212,5
rings/m
1,25
piles/m
58,98
m3/m
3
m3/m
costs
7121
30442
2250
23594
450
63856
euro/m
euro/m
euro/m
euro/m
euro/m
euro/m
Table 7-4: Cost estimates for the combi wall
Combi wall
Tubular piles
Pile driving
Sheet piles
Sheet pile driving
Capping beam
Total
unit price
2,20
2500
1,10
1000
150
euro/kg
euro/pile
euro/kg
euro/sheet
euro/m3
Marine installation
quantity
2.12
m3/m
0.27
piles/m
0.17
m3/m
0.27
sheets/m
3.0
m3/m
costs
36691
681
1440
272
450
39535
euro/m
euro/m
euro/m
euro/m
euro/m
euro/m
When the total costs per meter wall are considered the costs of the sandwich wall are approximately 1.6
times higher than the costs of the combi wall. The largest contribution in the costs of the sandwich wall
results from welding the steel rings around the piles. The thickness of the weld has been calculated in
appendix Q. In the sandwich wall design derived in this thesis the rings are applied over the total height of
the wall, with a constant centre-to-centre distance of 200mm. This leads to 170 rings per pile.
Furthermore the grout costs are a large part of the costs of the sandwich wall. This is mainly caused by the
large grout volume, which is needed to secure the sand tightness of the wall.
The shear force which needs to be transferred by the steel rings is however not constant over the height of
the wall. When the distribution of the rings over the pile follows the distribution of the shear force less rings
can be applied.
The continuous distribution of the rings is based on safety considerations, as has been described in
paragraph 6.9.1. Theoretically the distribution of the rings can follow the distribution of the shear force.
However, the overcapacity of the current design of the sandwich wall is necessary to obtain a high enough
safety level. The additional safety included in the distribution of the rings compensates the uncertainty in
both the location and the strength parameters of the grout.
7.4 Future prospects sandwich wall
Based on the current sandwich wall design a sandwich wall does not seem an economic solution for the
large quay walls expected in the future. However, certain changes may make the sandwich wall more
competitive.
86
Sandwich wall as the quay wall for the future
The main difference and the largest advantage of the sandwich wall is the difference in required steel
volume. In the last couple of years steel prices have risen considerably due to the high steel demand in
countries like China and India. When steel prices keep rising this makes the sandwich wall more attractive.
When the steel price becomes 1.8 times the steel price used in the design the sandwich wall and the combi
wall are economically equally attractive.
Furthermore potential for increasing the economical competitiveness exists in reducing the welding costs.
The current design is based on a continuous distribution of the shear rings over the total height of the wall.
This is done to compensate the insecurity in the grout columns and in this way to achieve a safe design.
When more experience is gained in jet grout projects is may be possible to let the distribution of the rings
follow the distribution of the shear forces in a safe way. When fewer rings can be applied the welding costs
can be reduced.
The grout costs are high due to the large required grout volume of the sandwich wall. In the current design
the grout columns have been applied down to the toe of the steel piles. This again is based on safety
considerations. It may also be possible to install the grout columns down to a smaller depth than the steel
piles. However, some investigation is needed to be able to predict the effect of this reduction of the grout
depth.
In conclusion the sandwich wall designed in this thesis is not economically attractive based on the costs
currently used costs estimates. It is however possible that the sandwich wall becomes more attractive in
the future. A rising steel price and more experience with jet grout projects contribute to the economic
attractiveness of the sandwich wall.
7.5 Comparison combi wall with reference based designs
Based on the case study described in chapter 4 a sheet pile wall design and a block wall design can be
made. The material costs of the reference based sheet pile wall design will be compared to the material
costs of the combi wall design, which has been used for the economic evaluation of the sandwich wall. With
this comparison it is possible to investigate if the reference based design method leads to reasonable
estimates.
The embedded length and the steel volume per meter wall of a sheet pile wall can both be derived from the
retaining height. The design graphs for sheet pile walls are shown below.
Data
2,500
30
83kg/m2
175kg/m2
206kg/m2
Steel volum e per m eter wall [m3/m]
Embedded length [m]
25
20
15
10
5
0
0
5
10
15
20
Retaining he ight [m ]
25
30
2,000
235kg/m2
299kg/m2
267kg/m2
1,500
1,000
0,500
0,000
0
5
10
15
20
25
30
35
Reta ining height [m ]
Figure 7-4: Design graphs used to derive a cost estimate for a sheet pile wall design
Based on these graphs the steel costs of a sheet pile wall can be estimated. These design graphs are
applicable for anchored sheet pile walls, however, the costs of the anchorage are not included. The cost
estimates for the reference based sheet pile wall design are included in table 7-5.
87
Sandwich wall as the quay wall for the future
Table 7-5: Estimates of the material costs of a reference based sheet pile wall design
Retaining height
Embedded length
Steel volume per meter wall
Steel costs
Total steel costs
32
35
2.7
2
42390
m
m
m3/m
€/kg
€/m
The costs of the combi wall designed as a reference design for the comparison with the sandwich wall have
been compared to the cost estimate of the sheet pile wall derived with the reference based design method.
Only the direct steel costs are considered. The steel costs of the combi wall design are equal to €38131 per
meter wall. The difference with the costs derived with the reference based design method is small. This
shows that the reference based design method provides a relatively good first estimate of the required
amount of steel and of the direct steel costs.
References
[7.1]
[7.2]
[7.3]
Archives Delta Marine Consultants
Overspannend staal, construeren A
Bender International
88
Sandwich wall as the quay wall for the future
Chapter 8
Conclusions and recommendations
In this chapter the conclusions with respect to the reference absed design method and the sandwich wall
designed for the case study described in chapter 4 will be drawn. Furthermore some recommendations will
be made; mostly regarding additional investigations to increase the reliability and applicability of the
reference base design method and to improve the safety level of the sandwich wall.
8.1 Conclusions
In the first part of this thesis the reference based design method for quay walls has been proposed; this
method has been applied to block walls and sandwich walls. Design graphs have been derived containing
both the data set and a theoretical relation to supplement the data set. For both block walls and sheet pile
walls it proves to be possible to estimate the main design parameters and to estimate the required material
quantities, based on only the retaining height. The design graph for sheet pile walls has been verified with
the combi wall design, described in paragraph 7.2. This verification proves that the steel volume per meter
wall estimated with the reference based design method is in the same order as the steel volume derived
with the regular design method. Hence the design graph for the steel volume per meter wall of a sheet pile
wall leads to good results.
The following conclusions can be drawn with respect to the reference based design method applied to block
walls and sheet piles walls.
•
•
•
•
•
The reference based design method can be used to estimate the number of blocks in a cross
section of a block wall, based on only the retaining height;
The concrete volume per meter wall of a block wall can be estimated with the reference based
design method, based on only the retaining height;
The average height and width of the blocks in a block wall can be derived from the design graphs
for the number of blocks and the concrete volume per meter wall;
For sheet piles walls the embedded length can be estimated with the reference based design
method;
The reference based design method leads to a relatively good estimate of the required steel
volume per meter wall of sheet pile walls;
The second part of this thesis concerns a new type of quay wall: the sandwich wall. This sandwich wall has
been designed for the largest retaining height and the heaviest loads expected for the future. The most
important conclusion which can be drawn from this second part is that, in theory, it seems possible to
construct a sandwich wall as a quay wall. However the costs of such a quay wall are relatively high. The
designed sandwich wall proves to be more expensive than a combi wall designed for the same situation.
So, based on the currently applicable cost estimates the sandwich wall does not form an economical
solution for the future.
However, in the future changes may occur, such as an increase of the steel price and the increase of
knowledge about the safety level and accuracy of jet grouting. When the steel price rises the sandwich wall
become more attractive as it contains a relatively small amount of steel. Better knowledge and experience
with jet grouting allows for a less conservative design. The sandwich wall design derived in this thesis
contains a high degree of overcapacity, which compensates the uncertainty in the location and the strength
of the grout columns. The strength and the location of the grout columns are of major importance for the
shear connection between the steel piles and the grout mass.
In summary, the following conclusions can be drawn regarding the sandwich wall as the quay wall for the
future.
• Based on the currently applicable cost estimates the sandwich wall designed in this thesis is more
expensive than the combi wall designed as a reference;
• A rising steel price makes the sandwich wall economically more attractive, due to the low steel use
of the sandwich wall;
89
Sandwich wall as the quay wall for the future
•
More experience in jet grouting projects may lead to the possibility of creating a sandwich wall
design with less overcapacity in a safe way;
8.2 Recommendations
With respect to the reference based design method the main recommendation is to collect more designs to
expand the data set. This will increase the reliability of the currently derived design graphs and broaden the
applicability of the method.
•
•
•
More designs of different types of quay walls need to be collected to be able to use the reference
based design method to select the type of quay wall for a project;
More designs of different types of quay wall need to be collected to be able to develop design
graphs for the remaining quay wall types;
More block wall designs and sheet pile wall designs need to be collected to support the current
design graphs;
With respect to the sandwich wall a number of investigations can be performed which allow for a less
conservative design, mainly regarding the shear rings.
•
•
•
In situ test need to be performed to increase the knowledge and reliability with respect to the
strength parameters of grout in sandy soil;
Scale tests or computer model (FEM) studies needs to be performed to investigate the shear
connection between steel piles and a grout mass, the best method would be a full scale test;
The effect of corrosion on the steel piles and specifically the shear connection needs to be studied;
Furthermore studies need to be performed to optimise the costs of the sandwich wall.
•
•
•
•
Investigate the sand tightness and the water tightness of a jet grout mass, this may allow for a
smaller width of the grout mass, hence reducing the grout costs;
The influence of grout columns installed down to a smaller depth than the steel piles needs to be
studied; this may reduce the grout costs;
Modify the dimensions of the relieving floor structure to investigate if a larger relieving floor
structure leads to a more economical design of the sandwich wall;
An economic evaluation needs to be performed to investigate if installing the pile by augering
makes the sandwich wall economically more attractive. Augering of the piles is generally more
expensive than pile driving. However, augering allows for a larger thickness of the steel rings. In
this way fewer rings can be applied and the welding costs can be reduced. Furthermore a smaller
wall thickness of the piles can be applied, which decreases the steel costs.
90
Sandwich wall as the quay wall for the future
91
Appendixes
Appendixes
Appendix A: Literature study
Introduction to quay walls
A quay wall is a water and soil retaining structure used for the berthing of ships. In general a quay wall is
equipped with bollards for mooring ships and with fenders to protect both the ship and the quay from
impacts. Quay walls are applied at locations of exchange between land and water. This can concern both
people and goods. In the paragraph below the evolution of quay walls in the last centuries is elaborated.
The origin of quay walls
People have been using water for transport purposes since ancient times. On the frontier between land and
water quay wall are built to facilitate the exchange between land and the ships on water. The first quay
walls were made of natural stones. The Romans already invented some sort of concrete that was used
amongst others for the construction of quay walls. This material offered more possibilities in the field of
Construction than only the use of natural stones.
In the days of the Vikings the first ships with keels came into being, this increased the necessary depths of
harbours significantly. Until that time quay walls were constructed mainly from masonry and timber planks.
For the transhipment of goods cranes were developed, first out of timber, later also out of steel. As a result
of these cranes quay wall with larger bearing capacities were built. The development of steam ships in the
nineteenth century lead to an increase of the tonnage and the draught of ships. The larger draught of ships
increased the necessary retaining height of quay walls.
Increasing ship dimensions in the last couple of decades
The dimensions of ships determine the design of harbours and quay walls to a large extent. Especially the
last couple of decennia ship dimensions increased significantly.
Tankers and liquid bulk carriers
After the second word war the consumption of oil grew rapidly, this caused the transport of oil per tanker
to increase. Beside this ship dimensions increased simultaneously. In the 1960’s the larges oil tankers were
less than 100000 tons dwt. In the year 2000 the largest ship was more than 300 million tons dwt. The
largest tanker in 2006 is the Knock Nevis, which is an Ultra Large Crude Carrier (ULCC) with a draught of
24.6 m [0.8].
Container ships
Transport of goods in containers in the 1950’s mainly took place in America. In the second half of the
1960’s it was introduced in Europe. At that time the first generation container ship had a draught of 9 m.
The evolution of container ships since the introduction in Europe is illustrated in the table below [0.2].
1st generation
2nd generation
3rd generation
4th generation
Post PanaMax
6th generation
7th generation
Time
period
DWT
(average)
Number of
TEUs
Maximum
length[m]
Maximum
width [m]
End 1960s
1970s
Early 1980s
Mid 1980s
After 1990
End 1990s
After 2003
14000
30000
45000
57000
67000
104000
123000
300–1100
800–1700
1700-3000
4000–4500
4300-8000
8000
12500-18000
200
240
300
310
340
347
400
27
30
32
32.3
39.4-45
42.8
63.8
Maximum
draught
[m]
9.0
10.5
11.5
12.5
13.5
145
14.7-21
Appendixes
Dry bulk carriers
Dimensions of carriers for materials like ore and coal have increased significantly in the last couple of
decades. The very deep ore carriers have been normative for the harbour entrance of the Rotterdam
harbour. The Berge Stahl, which is the largest VLOC (very large ore carrier) in 2006, has a draught of 23 m
[0.9].
Ro-ro ships
Roll on-roll off ships (ro-ro ships) transport goods which can be rolled on and off the ships. Examples are
trucks and cars. These ships are not especially large, but they do influence the quay wall design. The quay
wall has to be equipped with slopes or ramps so that trucks and cars can access the vessel.
Functions of quay walls
The main functions of a quay wall are:
• Retaining soil and water;
• Transfer loads from cranes and goods to the subsoil;
• Provide a safe mooring place for ships;
At the land side of the quay wall there is a large retained soil body, generally with ground water in the
pores. This soil mass has to be forced into an unnatural position: vertically. Without measures the soil body
is shaped as a slope in stead of a vertical wall. The angle of this slope is called the angle of internal friction.
For non-cohesive soils this angle varies between 30º and 40º. The difference between the forced position
and the angle of internal friction causes a horizontal loading on the retaining wall. In the case of a water
level difference over the wall this leads to an additional horizontal force.
Quay walls are often applied in ports of transshipment. The goods are often loaded and unloaded using
large cranes that can be moved along the quay on rails. The terrain behind the quay wall is often used to
store the unloaded goods. The crane and the stored goods create an additional loading on the soil, both in
horizontal and vertical direction. The quay wall has to be able to bear these loads and transfer them to the
subsoil.
For mooring of the ships the quay wall has to be equipped with bollards for securing the positions of the
ship and with fenders for the protection of both the ship and the quay wall. In the description of this
function the word safe is included. This means that structures have to be present to shelter the quay from
waves and currents. These are often structures like breakwaters. Also the orientation of the quay wall with
respect to the dominant wave and wind direction plays a role.
Types of quay walls
Main shapes of quay walls
The variety of possible quay walls shapes is very large. A first, rough distinction can be made by dividing
them into four main groups:
• Gravity structures;
• Ground penetrating structures;
• Relieving floor structures;
• Platform over a slope;
Gravity structures
Gravity structures are characterised by the way stability of the structure is achieved. The dead weight of
the structure is very large for this type of structures. This large weight often causes high pressures under
the structure so the soil on which the structure is founded needs to have a high bearing capacity. This is
the main reason why gravity structures are applied rarely in the Netherlands; our clay and peat have very
limited bearing capacity. Gravity structures are applied more frequently in countries with rock in the
bottom.
Appendixes
Stability gravity structures
A stable structure means equilibrium of horizontal and vertical forces and equilibrium of moments. The
forces acting on a gravity structure are shown in the picture below, loads from cranes and stored good are
neglected in this case.
Soil and pore water
Weight
Harbour water
S
Fw
Upward water pressure
Equilibrium of vertical forces is achieved when the weight of the structure is larger than the upward
directed water pressure under the structure; this is often the case for gravity structures.
Equilibrium in horizontal direction is created by the friction force Fw; the loads resulting from the soil and
pore water and from the harbour water are fixed and are unequal. The friction force is equal to this
difference with a maximum as shown in the formula below.
Fw = W * f = W * tan
and
In this formula _ is the friction angle between the structure and the soil and ` is the angle of internal
friction of the soil. W is the weight of the structure and f is a friction factor.
For moment equilibrium the moment around point S is considered. The soil and pore water and the upward
water pressure cause a driving moment and the harbour water and the weight a resisting moment. The
weight must be large enough to prevent rotation around S.
Block walls
A Block wall consists of stacked concrete blocks; they can be either reinforced or non-reinforced. The blocks
are not connected to each other; they are pressed together by their dead weight. The illustration in the
picture below shows blocks equipped with shear connectors which contribute to the shear resistance.
Besides the stability of the quay wall as a whole the stability of the separate blocks also has to be secured.
A block wall is very easy to build because the prefabricated concrete blocks only need to be stacked. Often
an in-situ cast capping beam is constructed on top of the upper block.
Appendixes
L-wall
An L-wall is a concrete structure that consists of a horizontal and a vertical slab, which are connected to
each other in the shape of an L. This structure can both be prefabricated or constructed in-situ. On the
horizontal slab a large soil mass rests. This soil mass has two opposed effects: the soil mass works as a
horizontal load on the vertical slab, but also contributes to the stability of the structure, because it presses
down on the horizontal slab. The dead weight of the concrete structure is not especially large, but the
contributing soil weight gives this type of structure the behaviour of a gravity structure. This type of
structure can be applied when the soil is not strong enough for a block wall. An advantage is that due to
the contribution soil material can be saved. An example of an L-wall is shown in the following picture.
Caisson wall
A caisson is a large, hollow, concrete box structure consisting of cells. There are two installation methods
for caisson walls: the dry method and the wet method. In the dry method the caissons are constructed on
land, near or at the quay wall location. The caisson is constructed with a hole in the bottom slab and has
cutting edges below the bottom. The soil below the caisson is excavated through the hole in the bottom;
inside the caisson there is an over pressure which prevents water from flowing into the caisson. When
enough soil is excavated the pressure under the cutting edge becomes so large that the soil under it
collapses and the caisson sinks into the soil. This continues until the final depth is reached and the caisson
is filled with soil. Due to the overpressure in the caisson during installation this is called a pneumatic
caisson.
In the wet method the caissons consist of a solid bottom slab wand walls, but no roof. The caissons are
prefabricated in a building dock and are transported to the quay location over water by letting them float.
Appendixes
This requires a water connection between the building dock and the quay wall location. Often building
docks are situated beside a river. At the future quay location the caissons are sunk to the bottom and the
hollow space inside them is filled with soil. The space behind the caissons is filled up with soil. In this way a
heavy quay wall structure is constructed. An example is shown below.
Prefabricated caissons are a good solution if there is limited construction space at the location of the future
quay. This method is economical with respect to the use of materials, but very labour-intensive.
Cellular wall
A cellular wall consists of sheet piles connected together in the shape of large circles with a diameter of
approximately 20 to 30 m. Also for this type of quay wall there are two construction methods: a land based
method and a marine method. In the land based method the sheet piles are driven into the soil in the
shape of large circles, which are called cells. The cells are placed at a certain distance from each other and
the connection between the cells is realised with sheet piles, an illustration is shown in the following figure.
When the wall is completed the soil in front of the wall is excavated. In the marine method the cells are
prefabricated on land and placed on the harbour bottom as shown below. When the cells are at the right
position they are filled with soil and the area behind them is backfilled.
Appendixes
In both situations the penetration depth of the cells into the harbour bottom is negligible, the stability of
the structure results completely from the weight of the cells containing the soil. These types of structures
require little material and the land based method requires limited soil works. However, there is a large risk
with respect to ship collision. If one or more of the sheet piles fails the soil can flow out of the cell into the
harbour. This can endanger the stability of the whole structure. A thorough protection against ship collision
needs to be realised, for example by fenders and mooring dolphins. Another point of attention is corrosion
of the steel; a coating or cathodic protection can be applied to protect the steel.
Coffer dam wall
Two parallel rows of sheet piles are placed at a certain distance from each other. The two rows of sheet
piles are connected to each other by a tensile element and the area in between is filled with sand. An
example is shown in the picture below. The soil is interlocked between the sheet pile walls and contributes
to the mass of the structure, which becomes very large. The sheet piles have a penetration length into the
harbour bottom of 0,5 to 1 times the retaining height. This type of structure is a combination of a gravity
structure and a soil penetrating structure. The stability of the wall results from both the shear resistance
caused by the large weight and the penetration length into the subsoil.
This type of quay wall can be used as a regular quay wall with water on one side and land on the other, but
it can also be used as a jetty allowing ships to be moored at both sides. A cofferdam requires little material,
but it is very sensitive to ship collision. Like for a cellular wall the failure of one or more of the sheet piles
can endanger the stability of the total structure. For a cofferdam the damage can be even lager because no
partitioning is applied along the wall.
Appendixes
Wall structures
The most simple type of quay wall is a wall consisting of sheets driven into the subsoil. If the sheets
penetrate deep enough into the soil they can retain a soil mass. The penetration of the sheet into the
subsoil generates a fixed-end moment that secures the stability of the wall. This type of quay wall can
consist of timber planks in the case of small retaining heights, of presetressed concrete sheet pile for
medium retaining heights an of steel sheet piles for larger retaining heights.
A diaphragm wall is comparable to a concrete sheet pile wall; however, the construction method is
completely different. A guidance frame is placed at ground level for the positioning of the wall. Then a
trench is dug for the first element using the frame as a guide. The excavation is filled with bentonite to
support the walls. When the excavation is complete the reinforcement is hung from the guidance frame and
the concrete is poured from the bottom up, pushing out the bentonite. After the first element is constructed
and trench for the second element is dug, and so on.
Wall structure without anchorage
A quay wall can be constructed as a wall without anchorage. The stability of the wall has to be secured by
the moment generated by the penetration of the wall into the subsoil. The penetration length into the soil
has to be twice the retaining height of the wall [0.2]. This means that a large part of the structure is
situated below the harbour bottom. It is important to check the deformations of the wall when this type of
structure is used, they might become very large.
Anchored wall structures
Besides the penetration into the subsoil anchorage can be applied to secure the stability of the structure. It
reduces the embedded length of the wall to once the retaining height instead of twice for an unanchored
wall and it reduces the maximum moment in the wall. The anchorage consists of a horizontal or inclined
tensile element attached to the upper side of the wall. At the end of the tensile element the anchorage
element is attached. The figure below shows some examples of anchorage systems. The anchorage
element has to be located deep enough below ground level to prevent yielding of the soil in front of the
element. The application of anchorage is not only used to secure the stability, but also to reduce
deformations.
Relieving floor structures
A relieving floor is a small L-wall that is placed on top of a wall structure; this can be a sheet pile wall, a
combi-wall, a diaphragm wall or any other type of wall structure. The relieving floor reduces the horizontal
load on the wall structure. This effect makes it possible to use a lighter wall profile and to reduce the
embedded length of the wall structure. At the sea side the relieving floor is founded on the wall structure,
at the land side the foundation is constructed of tension and compression piles.
The working of a relieving floor is shown below. The load diagram right of the relieving floor illustrates the
effective soil pressures without a relieving floor. The diagram under the relieving floor shows that over the
height h` there is no influence of the loads above the relieving floor. This influence starts where the line
with angle ` crosses the wall. From this point the influence increases until the height ha under the relieving
Appendixes
floor, where the influence is fully present again. From that point the loads are equal to the situation without
relieving floor (right-hand diagram).
P'k0
hN
N
hO
O
P'k0
It is possible to prefabricate a relieving floor; this may be beneficial if it is possible to install the prefab
relieving floor at low tide. However, for large retaining heights the dimensions of the relieving floor need to
be very large to get sufficient relief; prefabrication is no longer attractive for these large structures,
especially transportation and installation will be very difficult. As an example: the relieving floor of the
Euromax terminal has a height of 7 m and a width of 20 m.
Platform Structure over a slope
Platform over a slope
A simple way of creating a mooring facility at deeper water is to build a jetty like structure over the existing
slope. The difference in height between the harbour bottom and ground level is in this case overcome by a
slope instead of a vertical wall. A disadvantage of this type of structures is that during berthing the water
moved by the ship can flow away freely under the jetty like structure. This enlarges the berthing force on
the structure, however the flow forces on the harbour bottom are reduced significantly. Obviously the slope
has to be protected against erosion due to currents and waves, for example with a layer of asphalt or rip
rap. This type of structures can be applied when the bearing capacity of the subsoil is limited and when
there is already a protected slope.
Platform over slope and vertical wall
If there is limited space in the harbour the length of the structure that extends into the harbour can be
reduced by creating a vertical wall at the top end of the slope. This structure is combination of a vertical
wall and a platform over a slope. The picture below shows examples a platform structure over a slope, with
and without a vertical wall.
Appendixes
Geotechnics
Soil stresses
On a unit particle of soil normal stresses and shear stresses work in three directions as shown in the figure
below. Even in the most simple case, which is a half-infinite, unloaded soil mass it is difficult to describe all
the stresses in the soil due to its dead weight.
The unit particle must have equilibrium in all directions and moment equilibrium requires that the shear
stresses are symmetrical. This leads to the following set of equations.
xx
x
xy
x
xz
x
yx
+
y
yy
+
y
yz
+
y
yz
=
zy
zx
=
xz
xy
=
yx
+
+
+
zx
z
zy
z
zz
z
=0
=0
=0
Appendixes
The vertical normal stress is assumed to increase linearly with depth, proportional to the volumetric weight
of the soil. This leads to
xx
=
yy
= f (z )
yz
=
zy
=0
zx
=
xz
=0
xy
=
yx
=0
zz
= z , based on this assumption the following must be true.
We have to find the function f(z) which describes the horizontal normal stresses in the soil. We choose to
write this function as a function of the vertical normal stress which leads to:
xx
=
=K
yy
zz
=K z
In this notation K is called the earth pressure coefficient; it represents the ratio between the horizontal and
the vertical normal stresses in the soil.
K=
yy
=
xx
zz
zz
The failure criterion of Mohr-Coulomb is a good approximation for soil. Because the stresses in x and y
direction are equal the system can be reduced to a 2D system. With the help of Mohr’s circle an expression
for K can be derived.
The Illustration on the right-hand side shows the meaning of the two principal stresses ]1 and ]3, c is the
cohesion in the soil and b represents the angle of internal friction. The normal stresses are on the
horizontal axes and the shear stresses on the vertical axes. The centre and the radius of the circle are
described by the following formulae.
m= 1
r=1
2
2
(
1
3
+
3
1
)=
=
The centre of the circle represents the average normal stress in the soil and the radius corresponds with
the maximum shear stress in the soil.
Appendixes
Now Mohr’s circle is applied to the unit particle of soil. Assume that ]zz is known and is the major principle
stress ]3, therefore ]1 is the minor principle stress representing the horizontal normal stress. Based on
Mohr’s circle can be written:
1
sin =
1
2
(
1
2(
+
1
3
3
)
) + c cot
After some elaboration this leads to:
3
=
1 sin
1 + sin
cos
2c
1 + sin
1
In case of a cohesionless soil this expression reduces to:
3
=
1 sin
1 + sin
1
=K
1
This agrees with the earlier derived expression for the earth coefficient. If ]zz is taken as the minor principle
stress ]1 we can rewrite the previous equation as:
1
=
1 + sin
1 sin
3
=
1
K
1
Now we have to interpret the physical meaning of these two equations; this means that we have to
determine when minimum horizontal normal stress occurs and when maximum horizontal normal stress.
This interpretation will be made based on the situation of a soil mass behind a retaining wall.
It can be expected that the smallest horizontal normal stress occurs in the case of a yielding retaining wall;
the soil pushes towards the wall and the wall gives way. This minimum soil stress is called active soil stress.
The earth pressure coefficient K is replaced by Ka which leads to:
3
=
1 sin
1 + sin
1
= Ka
1
Ka =
1 sin
1 + sin
The maximum value for the horizontal normal stress occurs in the situation when the retaining wall is
pushed towards the soil and the soil gives way. In that situation the stresses in the soil are called passive.
When 1/K is replaced by the passive earth coefficient Kp this leads to:
1
=
1 + sin
1 sin
3
= Kp
1
Kp =
1 + sin
1 sin
Both the situation with maximum and the situation with minimum horizontal soil stress are based on
deformations of the soil. The situation with zero deformation in the soil is also considered; this is only
possible in the case of a very stiff retaining wall. In that case the soil pressures are called neutral and the
neutral earth coefficient K0 is applicable. The expression for K0 can not be derived theoretically; there is
simply not theoretical background. We can use the correlation of Jáky to estimate the value of K0.. The
picture below shows how the value of the earth pressure coefficient is dependent on the deformations of
the soil.
Appendixes
K0
1 sin
In this elaboration of Ka and Kp the surface of the soil is assumed horizontal and the wall is positioned
vertically. For a sloping area behind the quay wall and an inclined wall Coulomb derived the following
formulas for the active and passive earth pressure coefficients.
cos 2 ( + )
Ka =
cos
2
sin( + ) sin(
)
1+
cos(
) cos( + )
cos 2 (
Kp =
cos
2
1
sin(
cos(
2
)
) sin( + )
) cos( + )
2
In which:
d:
Angle of the wall with vertical;
e:
Angle of the area behind the quay wall with horizontal;
Generally there is groundwater in the pores of the soil; the above elaboration considers a situation without
pore water. For the calculation of the horizontal stresses it is important to separate the water pressures and
the soil pressures. The soil pressures in the above elaboration represent the contribution of the grains to
the total soil stress: the effective stress. The earth pressure coefficient must be applied only to the effective
soil stresses; water pressure is omni-directional, which means that the horizontal pressure is equal to the
Appendixes
vertical pressure. The total stress is obtained by adding the water pressures and the effective soil stresses.
In the most general form this can be written as:
= '+ pw
In which pw is the pore water pressure and ]’ is the effective soil stress.
Failure of soil
In soil mechanics generally two limit states are defined:
• Shear failure of the soil (Ultimate Limit State, ULS);
• Excessive deformations of the soil (Serviceability Limit State, SLS);
The ULS is based on exceedance of the maximum shear stress ff. This maximum shear stress can be
derived from Mohr’s circle and can be written as:
f
= c + ' tan
For shear failure to occur the grains have to slide over each other as shown below; this picture clearly
illustrates that this leads to an increase of the pore volume of the soil. This phenomenon is called dilatancy.
Shear failure occurs either on a straight sliding plane or on a curved sliding plane. There are several models
for the description of the behaviour of soil that work with a straight sliding plane. Most of these methods
prescribe a fixed angle a for the sliding plane. Some examples of methods using straight sliding planes:
=
•
Mohr-Coulomb (
•
Krey (
•
•
Culman (Varying a to find the governing situation);
Calculation quay wall plus relieving floor (a dependent on ` and _);
=
2
4
2
);
);
In the above expressions ` is the angle of internal friction of the soil and _ is the friction angle between a
wall structure and the retained soil.
Large deformations in a soil mass do not necessarily mean failure of the soil. It can however lead to failure
of other structures in or near the deformed soil. As an example we can consider settlement of soil or more
specifically uneven settlement of soil. Structures founded on soil with uneven settlements can be severely
damaged because shear stresses and tensile stresses can develop in the structure.
Grouting
In two of the new concepts described in this thesis grout columns are part of the construction. The grout
columns are created by jet grouting. The process of jet grouting will be described in this chapter. The aim
is to reduce the permeability of the soil in such away that no sand can be transported through the grout
columns and to strengthen the soil to be able to function as a foundation for one of the crane rails.
Appendixes
Jet grouting
Jet grouting is a process that consists of disaggregation of the soil and its mixing with (and partial
replacement by) a cementing agent. The disaggregation is achieved by a high-energy jet of a fluid, which
can be the cementing agent itself. Jet grouting increases the strength and the stiffness and reduces the
permeability of the soil.
The following definitions are given before explaining the process of jet grouting.
• The rig is a rotary rig able to automatically regulate the rotation and translation of the jet grouting
string and monitor;
• The string is used to convey the grouting materials down-hole to the required depth;
• The monitor is a device attached to the end of the jet grouting string, comprising a drill bit and
nozzles;
• A nozzle is a device especially manufactured and fitted into the monitor, which is designed to
transform a high pressure fluid flow in the string in a high speed jet, directed at the soil;
The jet grouting string and monitor are drilled to the required depth by the rig, after which they are pulled
and rotated whilst jetting the grouting material under high pressure from the monitor. The soil is eroded,
partly mixed with the cement grout and partly pushed to the surface along the string. The effluent that
comes to the surface during jet grouting is called spoil. This process is illustrated in the picture below.
The diameter of the grout column is amongst others dependent on the diameter of the nozzles. The
diameter of the nozzles determined the length of the zone before the jet becomes unfocussed and
discontinuous Ra, which is 300 times the nozzle diameter. The diameter of the grout columns is
approximately 2 times Ra and therefore 600 times the nozzle diameter.
Several
•
•
•
•
different jet grouting systems can be distinguished:
Single fluid system;
Double fluid (air) system;
Double fluid (water) system;
Triple fluid system;
In the single fluid system the disaggregation of the soil is obtained by the cementing agent itself. In the
double and triple fluid system the disaggregation is obtained by another fluid, being air or water. The single
fluid system leads to the highest grout strengths, therefore the double and triple fluid systems are
disregarded.
Jet grouting elements and structures
A jet grouted element is a volume of soil treated through a single drilled hole. The most common types of
jet grout elements are:
• Jet grout column, which is a cylindrical jet grouted element;
• Jet grout panel, which is a plane jet grouted element;
Appendixes
A number of jet grouted elements can form a jet grouting structure, the most common structures are:
• Diaphragm: a wall obtained by making interlocked elements;
• Slab: a horizontal structure formed by interlocked elements;
• Canopy: an arch formed by interlocked horizontal of sub-horizontal elements;
• Block: a three dimensional element formed by interlocked elements;
The elements forming the structure can either be created in a fresh in fresh sequence or in a primary-
secondary sequence, see picture below.
Fresh in fresh sequence
Primary-secondary sequence
Types of grout
The large variety of grout mixtures can be divided into three classes:
• Bentonite-cement grout;
• Clay-cement grout;
• Chemical grouts;
The ratio between the components of the mixture can vary, this leads to very different mixtures within a
certain class. For instance the water-cement ratio, a mix with a wcr of 0.4 behaves different than a mix
with a wcr of 1.0.
For permeation grouting clay-cement grout and chemical grout are most suitable. An important aspect of
the grout mixture for the purpose of permeation grouting is that the particles in the mixture have to be
very small. If the particles are too large clogging of grout particles in the soil can occur. When this happens
a grout cake is created around the injection needle, the grout can not penetrate any further into the soil.
The largest particles are in the cement, so the cement has to be chosen with care. Clay-grout and chemical
grout have smaller particles than cement grout, therefore they are more suitable for permeation grouting.
Cement is a very expensive material. By using sand as a filler the amount of cement can be reduced and
the grout becomes cheaper. Another advantage of using sand in grout is that it reduces the shrinkage of
the hardened grout. The grout undergoes a volume reduction during hardening. The amount of volume
change is dependent on the water-cement ratio. The decrease in volume will be larger for a higher watercement ratio.
Other materials can be added to the grout to influence the behaviour, they are called admixtures.
Dispersants can be used to reduce the tendency of the cement particles to flocculate. This enhances the
ability of the grout to penetrate small openings. Accelerators can be added to the grout to shorten the
hardening time of the cement. Gas-producing agents are applied to reduce volume reductions or shrinkage.
Groutability
The groutability of a soil means the degree in which that soil is suitable for permeation grouting. The
groutability ratio (GR) is a useful parameter to check the applicability of Portland cement grout in sand. It is
given by: GR = D15 / D95 in which
Appendixes
D15:
D95:
the particle diameter of the soil to be grouted, 15 % of which is finer by weight;
the particle diameter of the soil to be grouted, 95 % of which is finer by weight;
The groutability of the soil can be judged in the following way:
GR > 24:
usual;
24 < GR < 19:
difficult;
19 < GR < 11:
not likely;
GR < 11:
not possible;
The groutability of soil using chemical grouts is indicated by the permeability constant k [cm/s]. The
groutability is determined in the following way:
k < 10-6:
ungroutable;
10-6 < k < 10-5:
difficult to impossible;
-5
-3
10 < k < 10 :
difficult;
10-3 < k < 10-1:
groutable with all commonly used chemical grouts;
k > 10-1:
use suspended solid grouts or chemical grouts with fillers;
Quality control
Quality control is very important for underground grouting. A good quality control program is necessary to
ensure the technical requirements of the grouting. The quality control program starts with the design of the
grouting. The design must be adequate to meet the requirements and at the same time be flexible for
construction purposes.
Certificates and test reports of de grout mixture have to be added to the quality control document.
Certificates are written statements by material suppliers that their products meet a specific standard. Test
reports contain results of tests performed on the grout mixture. They are used to check if the grout mixture
meets the requirements.
The grouting engineer produces inspection records to record all work activity. The inspection records
contain drilling reports of coring samples and grouting reports with the properties of the mixtures. Tests are
performed both in the field and in a laboratory. The test results have to be added to the quality control
document.
In two of the new concepts of chapter 3 grout columns are part of the construction. The grout columns are
created by jet grouting. The process of jet grouting will be described in this chapter. The aim is to reduce
the permeability of the soil in such away that no sand can be transported through the grout columns and to
strengthen the soil to be able to function as a foundation for one of the crane rails.
Reference based design
The new design method proposed in this thesis was initially named fuzzy logic design. With the amount of
data that was available regarding quay wall it was not possible to base the new design method on fuzzy
logic relations and the name was changed to reference based design. However, for possible future
continuation of the fuzzy logic design method the information obtained about fuzzy logic is included in this
appendix.
Background information fuzzy logic
Fuzzy logic is an implementation of fuzzy set theory, which is an extension of classical set theory. Set
theory is used to describe the properties of a set of which an element is or is not a member. According to
classical set theory membership of an element to a set can be assessed in binary terms; it can either be a
member: 1 or not a member: 0.
Fuzzy set theory allows gradual assessment of membership of an element with relation to a set. This is
described by a membership function µ → [0,1]. An example of a membership function is illustrated below.
Appendixes
Example member function
1,5
Mu(x)
1
0,5
0
x
Fuzzy logic was introduced in 1965 by Prof. Lotfi A. Zadeh at the University of California in Berkeley, USA. It
is used to overcome uncertainties in natural language and to be able to use these uncertainties in a formal
way. Words like “small” or “cold” cannot be defined as quantities, while size and temperature are. The
concept of cold can not be defined within explicit boundaries.
As an example of a fuzzy logic system we consider central heating. In order for the system to work properly
“cold”, “warm” and “hot” have to be defined. This can be done like is shown in the figure below.
Example central heating
1,5
member value
1
cold
warm
hot
0,5
0
Temperature
Fuzzy logic is often used in measuring and control engineering applications. The list below shows some
examples of where fuzzy logic is used:
• Automobile systems like ABS and Cruise Control;
• Air conditioning and central heating;
• Rice cookers;
• Dishwashers and washing machines;
• Elevators;
Appendixes
From this list it is clear that fuzzy logic systems are often used to control processes which are subject to
human taste and opinion or which depend on the situation.
Fuzzy logic as a design methodology
Fuzzy logic can be used as a simple and fast design method. With a fuzzy logic design methodology some
time consuming steps are eliminated. In the case of designing a quay wall these steps are generating
alternatives and assessing them to find the most economical solution. In the scheme below the
conventional quay wall design method and the fuzzy logic design method are compared.
Conventional design method
Fuzzy logic design method
Requirements and specifications
Requirements and specifications
Generate alternative solutions
Evaluate and assess the alternatives
Apply fuzzy logic relations to come to a
preliminary design
Choose the best alternative
Elaborate into final design
Elaborate into final design
The number of steps in the design procedure is reduced from 5 to 3. Especially generating the alternatives
and the assessment are very time consuming operations. These are replaced by applying the fuzzy logic
relations, which is a very fast method to determine the main dimensions of the quay wall.
Fuzzy logic relations
The fuzzy logic relations which are used in the alternative design method will be explained in more detail.
The fuzzy logic relations for the design of quay walls consist of two parts. The first part is used to select the
type of quay wall and the second part leads to the main dimensions of the structure. It is necessary to
select the type of quay wall first because the fuzzy logic relations are different for each type of quay walls.
The fuzzy logic relations consist of empirical relations which have been derived from quay wall designs from
the past.
Link design method to fuzzy set theory
The above description of fuzzy logic theory can be linked to quay wall design in the following way. It is
clear that a certain retaining height does not lead to one quay wall solution; many different types of
Appendixes
structures can create a good design. It is likely that for a certain retaining height one type of structure is
more suitable than another. This can be expressed as the applicability of a structure, ranging from 0 to 1:
an applicability of 0 means that the type of structure can not be used, while 1 means that the structure is
the only possible solution. Possible relations between the retaining height and the applicability of a
structure are illustrated in the graph below.
Example fuzzy logic in quay wall design
1,2
Member value (applicability)
1
0,8
a
b
c
0,6
d
summation
0,4
0,2
0
0
5
10
15
20
25
30
35
Retaining height
In this hypothetical graph four different types of quay walls are used: type a to d. The member value is
expressed as the applicability of a type of structure. The total member value has a maximum of 1, so the
applicability or member value of a type of structure has to be seen relative to the member values of the
other types of structures. If two types of structures both have and applicability of 0,5 this does not mean
they are both 50 % applicable; it means that they are equally applicable. From this graph we can tell that
type c is more applicable for smaller retaining heights, type a is applicable for very large retaining heights,
type d for the intermediate retaining heights and type b is equally applicable for all retaining heights.
The retaining height is not the only parameter that influences the degree in which a type of structure is
applicable. This example only illustrates the use of fuzzy logic in quay wall design. If the same graph is
drawn up for the bearing capacity of the subsoil or the cpt-value of the subsoil this can lead to
contradicting conclusions. By combining the available relations the most suitable type of structure can be
selected. The next step is to use design graphs to estimate the dimensions of the quay wall and the
quantities of used materials.
For every type of quay wall structure relations have to be found between the external conditions and the
design parameters. These relations can be used to come to a preliminary design in a very short time. The
investigation for these relations is based on design drawings only; this means that limited data is available.
In this way experience from the past is used in the design of new quay walls.
References
[0.1]
Grouting in the ground, by A.L. Bell;
[0.2]
Handboek kademuren, CUR Gemeentewerken Rotterdam and Port of Rotterdam;
[0.3]
Port engineering, by Gregory P. Tsinker;
[0.4]
Lecture notes ct5313, Structures in hydraulic engineering;
[0.5]
internet site: http://www.royalhaskoning.com/NR/rdonlyres/5B4644B1-E949-4201-A3C32F9C021BBDB0/10638/SandwichwandAdamCS.PDF
[0.6]
Living with the ports, multiple use of space, Nationale Havenraad [pdf]
Appendixes
[0.7]
Final report “Kademuur van de toekomst”,by projectteam Kademuur van de Toekomst by
order of the Rotterdam Port Authority [pdf]
[0.8]
http://www.dxman.com/undir/big-ship/jahre%20viking.htm
[0.9]
www.wikipedia.org
Appendixes
Appendix B-1: Data sets reference based design
Block wall designs
# of
blocks
6
6
6
4
11
7
8
3
Location
Phuket, Thailand
Shuaiba. Kuwait
Abu Dhabi, UAE
Ras Abu Khamis, Saudi Arabia
Richards bay, South Afrika
Yemen LNG terminal
Ghana
Guangzhou, China
Block width
Phuket, Thailand
Shuaiba. Kuwait
Abu Dhabi, UAE
Ras Abu Khamis, Saudi Arabia
Richards bay, South Afrika
Yemen LNG terminal
Ghana
Guangzhou, China
1st
Block width
Phuket, Thailand
Shuaiba. Kuwait
Abu Dhabi, UAE
Ras Abu Khamis, Saudi Arabia
Richards bay, South Afrika
Yemen LNG terminal
Ghana
Guangzhou, China
1st
8
10,5
7,5
5,1
10,65
6,5
6,35
7,1
2
2,4
2
1,9
1,7
1,5
1,3
2,8
Concrete
Average block Retaining Width lowest
Tidal
Thickness of
volume[m3/m] volume [m3/m] height [m]
block[m]
range [m] rock bed [m]
85,3175
14,22
15,5
7,5
3
1,5
135,3255
22,55
19,5
10,5
4,00
1,5
90,175
15,03
16,7
6,25
2,3
1
33,83
8,46
9,5
4,4
2,50
1,25
453,6432
41,24
25,2
10,35
2,50
0,5
70,515
10,07
14
6,5
3,50
1,4
68,61
8,58
13,9
6,35
1,30
0,5-3
50,98
16,99
12,2
7,1
4,50
5,85
(B/H)average
3,3
3,4
2,8
2,4
4,5
3,8
4,7
2,3
2nd 3rd
4th
5th
6th
7th
8th
9th
10th 11th Average
8,75 7,75 6,75 5,25
5
6,9
10,5 10,5
8
7
7
8,9
8,25 7,25 6,25 5,25
4,5
6,5
4,4
5,2 3,75
4,6
10,5 10,65
10
9,5
8,5
8
8
8
7
7,9
9,0
6,25 7,35 6,25
6,1
5,7 5,25
6,2
6,15 6,15 6,15 6,15 6,15 6,15 7,45
6,3
4,9
7,4
6,5
2nd
3rd
4th
5th
6th
7th
8th
9th
10th 11th Average
1,85
2
2,3
2,5 2,05
2,1
2,4
2,4 2,88 2,88 2,88
2,6
2 2,25
2,5 2,75
2,5
2,3
1,8
1,9
2
1,9
1,7
1,7
1,8
1,9
2,1
2,2
2,2
2,1 2,45 2,15
2,0
1,5
1,5
1,5
1,8
1,8
1,9
1,6
1,4
1,4
1,4
1,4
1,4
1,4
1,2
1,4
3
2,7
2,8
Sheet pile wall designs
Location
Rotterdam1
Vlissingen1
Vlissingen2
Trinidad&Tobago
Rotterdam Beerkanaal
Westerscheldeterminal
Retaining Length sheet Penetration
height [m]
piles [m]
depth [m]
12
17,75
7
19
26
14
10,06
21,06
11
15,65
23
9,35
16,65
33,15
17,85
27,75
42
16,5
relative to
total length
0,39
0,54
0,52
0,41
0,54
0,39
Profiles
Type of wall
Larssen 430/12
PSp1012+PZi610/PZi510
Larssen 430/12
ø1220x20+AZ36
ø1420x17,5+Pu25(tripple)
ø1220x70+AZ26
Sheet piles
Sheet piles
Sheet piles
Combi wall
Combi wall
Combi wall
Steel volume
[m3/m]
0,520
0,248
0,617
0,805
0,770
0,923
Appendixes
Appendix B-2: Theoretical relations reference based design
Theoretical relations for block walls
Relation retaining height – concrete volume
Three load cases have been drawn up for the theoretically derived relation between the concrete volume
per meter wall and the retaining height. The load cases and the corresponding loads are shown in the
picture below. These three configurations have to meet stability requirements: the sum of all moments
around point S must be zero and the sum of all horizontal forcers must be zero.
Lower limit case
Representative case
Upper limit case
p
B
p
h0
Vc, %c
hmax
Vc, %c
p
Vc, %c
H
K0, %soiil
K0, %soiil
K0, %soiil
In the lower limit case only soil pressures and no water pressures act on the structure. Therefore the
structure is loaded by a horizontal force Hlow, which is the resultant of the soil pressures and which acts at a
distance alow from the bottom of the structure. This horizontal force must be compensated by the weight
induces friction force at the bottom of the structure to obtain equilibrium of horizontal forces. Furthermore
moment equilibrium around point S needs to be fulfilled. The picture below shows the forces acting on the
structure.
p
B
H
G
Hlow
alow
s
Wlow
Equilibrium of horizontal forces
H low < Wlow
H low = K 0
Wlow = BH
(
pH + 1
c
f
2
soil H
2
)
Moment equilibrium
M S =0
H low alow = 1 BG
2
H low alow = 1 H c B 2
2
Appendixes
A representative case has been estimated as an approximation for the data points. This load case leads to a
horizontal load due to only soil pressures. Because the water level is equal at both sides of the structures
the net horizontal water pressure is zero. The water around the structure does however result in an
uplifting force under the structure. Again the horizontal load needs to be balanced by the weight induced
friction force. The uplifting force caused by the water around the structure reduces the normal force on the
soil, hence reduces the friction force. The loads on the structure corresponding with the representative case
are schematised below.
p
B
h0
H
G
Hrep
arep
s
Wrep
Vrep
Equilibrium of horizontal forces
H rep < Wrep
H rep = K0 p H + 1 K 0
2
(
)
s , dry h0
(
Wrep = G Vrep f = BH
Vrep = B
water
(H
2
B
c
Moment equilibrium
M S =0
+ K0
water
(H
h0 ) )
h0 ) + 1 K 0 (
2
s , dry h0
(H
h0 )
s
water
)( H
h0 )
2
(
H rep arep = 1 B G Vrep
2
)
Furthermore an upper limit case has been derived, below which all data points must be situated. In the
most extreme case the head over the wall is equal to the retaining height. However, this will never occur in
case of a block wall as the joints between the blocks are too large for this large head to develop. A head
Chmas of 6m has been estimated as the maximum head over a block wall. The loads on a block wall in the
upper limit case are illustrated below.
p
B
hmax
H
G
Hup,2
aup,2
Hup,1
aup,1
s
Wup
Vup
Equilibrium of horizontal forces
Moment equilibrium
Appendixes
H up ,1 H up ,2 < Wup
(
2
2
(H
H up ,1 = K 0 pH + 1
H up ,2 = 1
(
water
)
sH
2
M S =0
)
hmax )
(
H up ,1 aup ,1 H up ,2 aup,2 = 1 B G Vrep
2
)
2
Wup = G Vup f
Vup = B
water
(H
hmax ) + 1 B
2
water
hmax
With the equations above the necessary concrete volume can be calculated for various retaining heights. To
be able to do this values have to be assigned several parameters. The selected values are included in the
table below.
40
6.5
20
17
10
0.5
4
6.5
p
B
s
s,dry
water
f
h0
Chmas
kN/m2
m
kN/m3
kN/m3
kN/m3
m
m
Surface load
Width of a block wall
Volumetric weight of saturated soil
Volumetric weight of dry soil
Volumetric weight of water
Friction factor for a concrete-soil interface
Distance water level below field in representative case
Maximum head over a block wall
The horizontal soil pressures have been calculated with the neutral earth coefficient K0. When the
deformations of the wall are large enough one can apply the active earth coefficient Ka which leads to
smaller earth pressures on the wall. However, a block wall is a very rigid structure and the deformations
will probably be very small. Therefore the choice is made to work with K0.
Theoretical relations for sheet pile walls
Relation retaining height – embedded length
The theoretical relation between the embedded length d and the retaining height h of a sheet pile wall can
be derived from moment equilibrium around the top of the wall. An upper and a lower limit state are
defined between which all data must lie. The configurations of the limit states are shown in the picture
below. The left picture represents the lower limit state and the right picture the upper limit state.
Lower limit case
h
d
p
Ka,
%soil
Ka,
%soil
Kp,
%soil
Upper limit case
Kp,
%soil
Appendixes
The lower limit state leads to the smallest loads on the wall and the upper limit state leads to the larges
loads. The area behind the quay wall is loaded by a terrain load of 40 kN/m3 in the upper limit state. The
loads on the sheet pile wall for both limit states are schematised in the picture below.
A
A
h
Fa,low
d
Fp,low
Fa ,low = 1 K a ( soil
2
F p ,low = 1 K p ( soil
2
Fa ,up = 1 K a ( soil
2
F p ,up = 1 K p ( soil
2
Fload = K a p (h + d )
Fa,up
Fp,up
water
)(h + d )2
water
)d 2
water
water
)(h + d )2 + 1 2
)d 2 + 1 2
water
water
(h + d )2
d2
Moment equilibrium around point A leads to the minimum required embedded length d.
lower limit state
upper limit state
Fa.low 2
2 Fa ,up (h + d ) + 1 Fload (h + d ) = F p ,up h + 2 d
3
2
3
3
(h + d ) = Fp.low (h + 2 3 d )
(
)
By means of iteration the embedded length d can be found for a certain retaining height.
Furthermore the data set has been compared to the embedded length calculated with the Blum method.
Again the upper limit and the lower limit case are considered. The Blum method schematises the wall as a
cantilevered beam loaded by the soil and water loads and by the anchor force. The schematisation of both
the upper and the lower limit case can be seen in the picture below.
Appendixes
Lower limit case
Upper limit case
T
T
qa
qa
qp
qp
h
d
The embedded length d is adjusted such that the horizontal displacement at the top of the wall is zero and
that the bending moment at the toe is zero. The following formulas have been used for the lower limit
case.
Active soil:
ua ,low =
Passive soil:
u p ,low =
Anchor force:
ut ,low =
Ka (
soil
water
)( h + d )
5
30 EI
Kp (
soil
water
)d
5
30 EI
Tlow ( h + d )
+
Kp (
soil
water
)d
4
h
24 EI
3
3 EI
In the above formulas the anchor force T is still unknown. This force results from the requirement that the
bending moment at the toe of the wall is equal to zero.
Tlow ( h + d ) =
1
Ka (
6
soil
water
)( h + d )
1
Kp (
6
3
soil
water
)d
3
By combining these four expressions the embedded length can be found which leads to zero deformations
at the top of the wall. The same operations have been performed for the upper limit case. Additional to the
lower limit case are the water pressures and the surface load. The following formulas have been used for
the upper limit case.
Active soil:
ua ,up =
Passive soil:
u p ,up =
Surface load:
us ,up =
Anchor force:
ut ,up =
(K (
a
soil
water
)+
)( h + d )
5
water
30 EI
(K (
p
soil
water
)+
30 EI
K a ps d
8 EI
)d + (K (
5
water
p
soil
water
)+
)d h
4
water
24 EI
4
Tup ( h + d )
3
3 EI
Again the anchor force T is obtained by the requirement that the bending moment at the toe is zero.
Appendixes
Tup ( h + d ) =
1
( Ka (
6
soil
water
)+
)(h + d )
3
water
+
2
1
1
K a ps ( h + d )
Kp (
2
6
(
soil
water
)+
water
)d
3
The results for both the lower limit case and the upper limit case for the embedded length have been
plotted in the figure below.
Upper limit Blum
30
Embedded length [m]
25
Low er limit
Blum
20
15
10
5
0
0
5
10
15
20
25
30
Re taining he ight [m ]
Relation retaining height – steel volume per meter wall
To find the theoretical relation between the retaining height and the steel volume per meter wall the sheet
pile wall is schematised as a simply supported beam, loaded by a linearly increasing distributed load. The
passive soil load generates the right-hand support. This schematisation is illustrated in the picture below.
q(h)
H
The span H in the above schematisation is equal to the retaining height plus two-third of the embedded
length
A certain retaining height leads to a bending moment M(h) in the wall with a maximum of Mmax. Both M(h)
and Mmax will be derived.
M ( h ) = V ( h ) dh =
(
q ( h) = K a (
)h
V (h) =
soil
water
q (h)dh =
)
q ( h ) dh dh
Ka (
soil
! 1
M (h) = V (h)dh = # K a (
% 2
water
soil
) h dh =
water
1
Ka (
2
soil
) h 2 + C1 "$ dh =
&
water
1
Ka (
6
) h 2 + C1
soil
water
) h3 + C1h + C2
Appendixes
The constants C1 and C2 follow from the boundary conditions at h=0 and h=H.
M (0) = 0 ' C 2 = 0
M (H ) = 0 '
C1 =
1
Ka (
6
1
Ka (
6
soil
soil
water
water
) H 3 + C1H = 0
)H2
The bending moment and the transverse force in the wall are described by the following equations.
1
K a ( soil
6
1
V ( h) =
K a ( soil
2
M ( h) =
1
K a ( soil
6
1
2
K a ( soil
water ) h +
6
water
) h3 +
water
water
) H 2h
)H2
The maximum bending moment in the wall is located at the height where the transverse force V(h) is zero.
1
Ka (
2
h=
soil
1
H
2
water
) h2 +
1
Ka (
6
soil
water
)H2 = 0
0.7 H
The maximum bending moment is equal to:
M max
1
=
Ka (
6
M max =
1
Ka (
12
2
soil
soil
! 1
" 1
H $ + Ka (
water ) #
% 2 & 6
1
2
K a ( soil
water ) H +
6 2
soil
water
water
! 1
"
H$
% 2 &
)H2 #
)H3
The above formula describes the relation between the maximum bending moment in the wall and the
fictitious span H, which is related to the retaining height. The sheet pile wall needs to have a certain
moment of inertia to be able to withstand the maximum bending moment. The moment of inertia is related
to the steel area and by multiplying the area with the total height of the sheet piles the steel
The total steel volume in a sheet pile wall is described by the following formula.
Vwall = BH tot t%
In which:
B:
Width of the quay wall;
Htot:
Total height of the sheet piles;
t% :
Fictitious wall thickness;
When the steel volume per meter wall is considered B becomes 1 m. The total wall height Htot, which
consists of the retaining height minus the height of the coping beam and plus the embedded length.
H tot = h hcoping + d
Htot is related to the retaining height
()
3
I zz = r 2 dA = 1 Bt% = 1 t%
12
12
3
Appendixes
Appendix C: Stability tunnel-type quay wall
A rough calculation is made to get a first impression of the feasibility of a tunnel-type quay wall. A
schematisation of the cross section and the loads on the structure is shown in the picture below.
D
M
positive
Fcoping
h%
Flining
d
Fh2
Din
Fh3
Ffill
din
Fh1
Fh4
Fv1
Fv2
Horizontal forces on the structure:
2(
Fh 2 = K a p * h
Fh1 = K a 1
Fh 3 = 1
2
water
Fh 4 = 1 K p (
2
soil
water
) h2 + 1 2
water
h2
d2
soil
water
) din2
Vertical forces on the structure:
Fv1 = d
water
D
h d ) water D
2(
= concrete Dh%
Fv 2 = 1
Fcoping
Flining =
Ffill =
For the
Ka:
Kp:
isoil:
4
4
(D
Din2
2
Din2
)
concrete
fill
stability calculations the following values are estimated.
Active earth coefficient
Passive earth coefficient
Volumetric weight of saturated soil
=0.3
=3
=20 kN/m3
h
Appendixes
iwater:
h:
p:
d:
din:
D:
Volumetric weight of water
Total height of the structure
Terrain load on the area behind the structure
Height of the structure down from the water level
Embedded depth of the structure
Outer diameter of the lining and width of the coping
h% :
Fictitious height of the coping
=10 kN/m3
= 34 m
= 75 kN/m2
= 31 m
=2m
= 30 m
=
=
=
=
din:
Inner diameter of the lining
iconcrete: Volumetric weight of concrete
ifill:
Volumetric weight of the fill material
4m
variable
24 kN/m3
20 kN/m3
The estimation of the soil pressures is based on the Blum method, which assumes minimum active and
maximum passive earth pressure at the moment of failure. This indicates that the soil deformation become
very large. This assumption leads to optimistic results, because the passive earth pressure is maximised. If
the results of this calculation show that the structure is unstable it will most likely also be the case in
reality.
The stability needs to be verified in two directions:
• Equilibrium of horizontal forces;
• Moment equilibrium;
If the first stability check leads to an unstable situation it is unnecessary to perform the second stability
calculation.
Horizontal equilibrium
In a stable situation the resulting horizontal force is directed towards the soil side. Generally for gravity
structures there is friction force at the interface between the bottom of the structure and the subsoil which
also contributes to the horizontal forces. However, in case of a circular cross section the structure will
probably roll instead of slide. Therefore it is not possible for a friction force to develop. This has the effect
that the vertical forces have no influence on the horizontal stability.
So only the horizontal forces Fh1, Fh2, Fh3 and Fh4 are of interest in the horizontal stability calculation. The
depth din which accounts for the passive earth pressure can be varied to investigate if a stable situation
exists. The results of this investigation are shown in the graph below. A negative value of the resulting
horizontal force indicates that the resultant is directed towards the water side, which corresponds with an
unstable situation.
500
Resulting hor. force [kN/m]
0
-500
0
5
10
15
-1000
-1500
-2000
-2500
-3000
-3500
-4000
d_in [m ]
20
25
Appendixes
From the above graph can be concluded that a stable situation exists when din is larger than 21m. The
required diameter of the tunnel lining then becomes 48. Although the stable situation requires very large
dimensions it is possible to obtain a stable situation.
Moment equilibrium
For completeness the moment equilibrium of the tunnel-type quay wall is also investigated. Again the
distance din is varied and the resulting moment is calculated. The results of these calculations are included
in the graph below. The positive moment direction is indicated in the schematisation of the structure and
the loads. A positive resulting moment leads to a stable situation.
15000
Resulting moment [kNm/m]
10000
5000
0
-5000 0
0,5
1
1,5
2
2,5
-10000
-15000
-20000
-25000
-30000
d_in [m ]
In the above graph can be seen moment equilibrium is achieved when din is larger than approximately
1.4m. However in that case there is no equilibrium of horizontal forces.
Appendixes
Appendix D: Cone Penetration Test Maasvlakte 1
Appendixes
Appendix E: Blum calculation
The Blum calculation is used for calculating a wall height which is larger than the minimum wall height. This
leads to redistribution of the bending moments and reduces the maximum bending moment in the wall. The
wall structure is schematised as a cantilevered beam subjected to six external loads as schematised below.
6.
1. Relieving floor 1
2. Passive soil
3. Water pressure
4. Active soil
5. Relieving floor 2
6. Anchorage
h
l1
h;
l2
1.
2.
3.
4.
5.
The Blum method assumes a fixed end at the toe of the wall, at which the deformation w, the angle w’ and
the angular deformation, and therefore the bending moment, are zero. The following requirements have to
be met:
wtop = 0
The displacement at the top must be zero;
M toe = 0
The bending moment at the toe must be zero;
The deformation of the top has been calculated for each separate load component, as a function of the
embedded length l2. The embedded length must be found for which the summation of these deformations
is zero.
The deformations at the top due to the six separate loads can be calculated with the following formulas.
q ( l2 )
5
Loads 1, 2, 5:
w=
Load 3:
w=
Load 4:
w=
Load 6:
w=
30 EI
+
q ( l1 + l2 )
ql1 ( l2 )
4
24 EI
4
8 EI
q ( l1 + l2 )
5
30 EI
T ( l1 + l2 )
3
3 EI
The formula for the deformation duet o load 6 contains the anchor force T. By obtaining a bending moment
equal to zero at the toe T can be determined.
T ( l1 + l2 ) = H1 a1 + H 2 a2 + H 3 a3 + H 4 a4 + H 5 a5 + H 6 a6
Appendixes
In the above formula H is the resulting horizontal force of the separate loads and a is the distance of the
load to the toe. The results of the calculation are included in the table below. A value of 1 has been used
for the bending stiffness EI, because it has no influence on the final result.
Passive soil
Water pressure
Active soil
Relieving floor 2
Relieving floor 1
Anchorage
h
25
h
25
h
25
h_phi
0
h_teta
0
h
25
d
27,28
d
27,28
d
27,28
d_phi
52,28
d_teta
52,28
d
27,28
q_p
30
q_w
21
q_a
3
q_r2
3
q_r1
3
T
642
a2
9
a3
26
a4
7
a5
14
a1
9
a6
52,28
u2
32*106
u3
19*106
u4
43*106
u5
3*106
u1
3*106
u6
30*106
In case the embedded length is 27.28m the deformations at the top of the wall are zero and the fixed end
moment at the toe of the wall is also equal to zero.
Appendixes
Appendix F: Cullman method
For non-horizontal surfaces the values for the earth pressure coefficients can be found using the Culmann
method. The assumption of a straight sliding plane under an angle a is made. In case of a retaining wall
the situation can be schematised as shown below.
B
Load polygon
W
T
N
B
;
T
N
h
W
Q
Q
;
For every layer of soil in the sliding plane an equilibrium calculation is made resulting in the load Q on the
wall and the angle _ of this load. In the above schematisation a uniform soil mass is assumed. On the
sliding plane there is a resistance against sliding of the soil mass, which consist of the force T parallel to the
sliding plan and the force N perpendicular to the sliding plane.
The depth of the intersection of the sliding plane with the wall is called h. For every value of h the angle a
is varied and for each a the load Q on the wall and corresponding angle are calculated. The angle a that
leads to the largest value for Q represents the governing sliding plane. The result is an iterative process
which is not suitable for hand calculation. All governing sliding planes together lead to the total load on the
wall and the development of soil pressures over the height of the wall.
The Culmann method is based on a spring model for the description of the soil. For a certain value of a at a
certain height h the load Q is calculated based on the deformations in the soil. The computer program
MSheet of the MSeries package developed by GeoDelft is one of the many computer programs which is
based on the Culmann method.
Appendixes
Appendix G: Punch of the grout mass
The grout mass is compared to a very low strength concrete, approximately B5.The shear strength of
concrete is determined with the following formula.
! 0.7(1.05 + 0.05 f ck' ) "
f1 = 0.4 fb = 0.4 #
$
m
%
&
When the strength of the grout is compared to a B5 concrete the maximum shear strength of the grout is
0.26MPa. The formula above already includes a material factor, which is equal to 1.4. An additional safety
factor is applied to account for the uncertainty in the geometry of the grout columns. The shear strength of
a B5 concrete is divided by this additional safety factor, which has a value of 1.5. This leads to a maximum
allowable shear stress in the grout of 0.17 MPa. The described failure mode is illustrated below.
L
L
qdistr
Besides the allowable shear stress in the grout an estimation of the actual shear stress has to be made. The
actual shear stress can be calculated as follows.
=
1 qdistr
2 h
An estimation of the load qdistr is based on the Blum method. Only minimum active and maximum passive
earth pressures are applied, leading to the schematisation in shown below. The dimensions in this figure
are the result of the calculation to determine the minimum wall height with respect to overall stability,
performed earlier in this report. The values from the fully loaded design case are used for the punch
calculation as these lead to the largest horizontal load on the wall.
Appendixes
25 m
11.4 m
pp
pa = K a (
pp = K p (
pa
) L = 220 kN / m
) d = 340 kN / m
2
soil , sat
water
soil , sat
water
2
The load qdistr equals the difference between pa and pp, which is 220kN/m2. Substituting this load and the
maximum allowable shear stress into equation to calculate the shear stress, the result is a maximum value
for C of 3.15m.
The schematisation used for the punch calculation does not include the enhanced soil pressures due to the
surface loads. This approach leads to more conservative results as it increases the difference between pa
and pp.
Appendixes
Appendix H: MSheet report preliminary sandwich wall design
Appendixes
Appendixes
Appendix I: Full scale grout tests Amsterdam
The tests are performed in Amsterdam. The subsoil consists of various layers as can be seen in the table
below.
Layer no.
0
1
2
3
4
5
6
7
8
Layer name
Greenfield
Made ground
Peat
Upper clay layer
Lower clay layer
1st sand layer
Intermediate layer (Alleröd)
Upper 2nd sand layer
Lower 2nd sand layer
Eemclay layer
Composition
Made ground and rubble
Clayey peat
Clay with a low sand content
Silty clay
Dense sand
Silty sand with clay lenses
Very dense sand
Dense sand
Stiff to very stiff clay
Bottom (m; NAP)
+0.5
-0.5
-5.5
-8.0
-12.5
-15.0
-18.0
-21.0
-30.0
-45.0
For the sandwich wall the results of the grout in the layers 4, 6 and 7; the sand layers are of main interest.
However, the results from the other layers are used to gain some insight in the behaviour of grout in
different materials.
The aim of the tests is to investigate the effects of grouting on pile foundations. At the test location 3
wooden piles and three concrete piles are installed in the subsoil as can be seen in the picture below. The
test grout columns are also indicated in this picture. The grout columns A, B, C, and D are constructed
without a connection with the test piles (right-hand picture) and the other columns have an overlap with
the test piles (left-hand picture).
All grout columns have a design diameter of 1m and are constructed with a single jet system, except for
column C, which has a design diameter of 2m and is constructed with a double jet system.
Collumn
A, B
C, D
E, F
X1
X2
W1, W2, W3
Grouting depth, NAP [m]
From
To
-35
-2
-35
-2
-22
-10
-22
-2
-22
-2
-13.5
-11.5
wcr
1.0
1.0
1.0
0.8
1.2
1.0
Appendixes
Results of the test to measure the strength properties.
Unconfined compressive strength
Only the results of columns A and B are considered, because these columns do not overlap the steel and
timber piles and they are constructed with a single jet system.
Layer no.
1
2
3
4
5
6
7
8
Layer name
Peat
Upper clay layer
Lower clay layer
1st sand layer
Intermediate layer
Upper 2nd sand layer
Lower 2nd sand layer
Eemclay layer
Mean UCS [MPa]
2.4
3.4
11.8
19.6
12.9
14.6
22.3
14.7
Standard deviation [Mpa]
0.1
1.0
8.9
12.6
8.3
3.9
12.9
7.4
Mean Tensile strength
[MPa]
Standard deviation [Mpa]
0.6
0.7
2.0
1.5
2.1
1.8
0.7
0.2
0.7
0.4
0.1
0.8
1.2
0.2
Mean E-modulus [MPa]
633
1197
2623
3449
2551
2812
3528
3687
Standard deviation [Mpa]
184
914
1166
1249
1007
381
1369
673
Tensile strength
Layer no.
Layer name
1
2
3
4
5
6
7
8
Peat
Upper clay layer
Lower clay layer
1st sand layer
Intermediate layer
Upper 2nd sand layer
Lower 2nd sand layer
Eemclay layer
Young’s modulus
Layer no.
1
2
3
4
5
6
7
8
Layer name
Peat
Upper clay layer
Lower clay layer
1st sand layer
Intermediate layer
Upper 2nd sand layer
Lower 2nd sand layer
Eemclay layer
Shear strength and friction angle
Layer no.
Layer name
2
3
5
6
8
Upper clay layer
Lower clay layer
Intermediate layer
Upper 2nd sand layer
Eemclay layer
Mean
Friction angle
Shear strength
38.7
0.9
39.5
1.7
42.1
2.5
34.0
2.8
26.5
3.6
Standard deviation
Friction angle
Shear strength
16.3
0.7
10.7
2.0
19.6
1.8
21.0
1.8
Appendixes
Appendix J: ESA-prima Win report relieving floor structure
Inhoudsopgave
Basisgegevens , gebruikte materialen
Materialenlijst
Knopen
Staven
Randen
2D macro's
Doorsnede-eig. , standaard , gebruikte profielen
Basisgegevens , gebruikte materialen
Materialenlijst
Knopen
Staven
Randen
2D macro's
Doorsnede-eig. , standaard , gebruikte profielen
Basisgegevens
Structuurtype : Algemeen XYZ
Aantal
Aantal
Aantal
Aantal
Aantal
Aantal
Aantal
Aantal
knopen:
staven:
1D macro's:
randlijnen:
2D macro's:
profielen:
belastingsgev.:
materialen:
Materiaal
Naam
S 355
46
20
20
7
2
4
2
3
Appendixes
Naam
Treksterkte
Vloeigrens
E-modulus
Poisson coëff.
Specifiek gewicht
Uitzettingscoëff.
510.000 MPa
355.000 MPa
210000.00 MPa
0.30
7850.000 kg/m^3
0.012 mm/m.K
E-modulus
Poisson coëff.
Specifiek gewicht
Uitzettingscoëff.
33500.00 MPa
0.20
2500.000 kg/m^3
0.01 mm/m.K
E-modulus
Poisson coëff.
Specifiek gewicht
Uitzettingscoëff.
36000.00 MPa
0.20
2500.000 kg/m^3
0.01 mm/m.K
C35/45
B 55
Materialenlijst
Groep staven: 1/20
nr.
Naam
Kwaliteit
3
4
HEA650
REC (600,600)
S 355
C35/45
Eenh. gewicht
kg/m
189.97
900.00
Lengte
m
260.22
505.96
Massa
kg
49433.10
455368.02
Materialenlijst - Macro2D
Groep staven: 1/2
nr.
Naam
Kwaliteit
9
C35/45 C35/45
Specifieke massa
kgm^3
2500.00
Totaal gewicht van constructie: 2642301.12 kg
Verfoppervlakte: 1852.62 m^2
Knopen
knoop
1
2
3
4
5
6
7
8
9
10
11
12
X
m
-11.250
11.250
11.250
-11.250
-11.250
11.250
-2.800
-2.800
-8.400
-8.400
2.800
2.800
Y
m
0.000
0.000
18.500
18.500
0.000
0.000
0.000
46.000
0.000
46.000
0.000
46.000
Z
m
0.000
0.000
0.000
0.000
6.500
6.500
0.000
-46.000
0.000
-46.000
0.000
-46.000
Volume Massa
m^3
kg
855.00 2137500.00
Appendixes
knoop
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
X
m
1.400
1.400
1.400
1.400
-1.400
-1.400
-1.400
-1.400
-4.200
-4.200
-4.200
-4.200
4.200
4.200
4.200
4.200
8.400
8.400
-7.000
-7.000
-7.000
-7.000
-9.800
-9.800
-9.800
-9.800
7.000
7.000
7.000
7.000
9.800
9.800
9.800
9.800
Y
m
15.500
5.500
17.500
7.500
15.500
5.500
17.500
7.500
15.500
5.500
17.500
7.500
15.500
5.500
17.500
7.500
0.000
46.000
15.500
5.500
17.500
7.500
15.500
5.500
17.500
7.500
15.500
5.500
17.500
7.500
15.500
5.500
17.500
7.500
Z
m
0.000
-30.000
0.000
-30.000
0.000
-30.000
0.000
-30.000
0.000
-30.000
0.000
-30.000
0.000
-30.000
0.000
-30.000
0.000
-46.000
0.000
-30.000
0.000
-30.000
0.000
-30.000
0.000
-30.000
0.000
-30.000
0.000
-30.000
0.000
-30.000
0.000
-30.000
Staven
macro
staaf
knoop 1
knoop 2
1
2
3
4
5
6
7
8
9
10
11
1
2
3
4
5
6
7
8
9
10
11
7
9
11
13
15
17
19
21
23
25
27
8
10
12
14
16
18
20
22
24
26
28
Lengte
m
65.054
65.054
65.054
31.623
31.623
31.623
31.623
31.623
31.623
31.623
31.623
Rx
deg
0.00
0.00
0.00
0.00
0.00
0.00
0.00
0.00
0.00
0.00
0.00
Profiel
Kwaliteit
3
3
3
4
4
4
4
4
4
4
4
S 355
S 355
S 355
C35/45
C35/45
C35/45
C35/45
C35/45
C35/45
C35/45
C35/45
-
HEA650
HEA650
HEA650
REC (600,600)
REC (600,600)
REC (600,600)
REC (600,600)
REC (600,600)
REC (600,600)
REC (600,600)
REC (600,600)
Appendixes
macro
staaf
knoop 1
knoop 2
12
13
14
15
16
17
18
19
20
12
13
14
15
16
17
18
19
20
29
31
33
35
37
39
41
43
45
30
32
34
36
38
40
42
44
46
Lengte
m
65.054
31.623
31.623
31.623
31.623
31.623
31.623
31.623
31.623
Rx
deg
0.00
0.00
0.00
0.00
0.00
0.00
0.00
0.00
0.00
Profiel
Kwaliteit
3
4
4
4
4
4
4
4
4
S 355
C35/45
C35/45
C35/45
C35/45
C35/45
C35/45
C35/45
C35/45
-
HEA650
REC (600,600)
REC (600,600)
REC (600,600)
REC (600,600)
REC (600,600)
REC (600,600)
REC (600,600)
REC (600,600)
Randen
randlijn
1
2
3
4
5
6
7
type
Lijn
Lijn
Lijn
Lijn
Lijn
Lijn
Lijn
knoop
1,2
2,3
3,4
4,1
1,5
5,6
6,2
2D macro's
num type
1
C35/45
Rand:
Knopen :
2
C35/45
Rand:
Dikte 1.00 m
1,2,3,4
7,13,15,17,19,21,23,25,27,9,11,45,31,33,35,37,39,41,43
Dikte 3.00 m
5,6,7,1
Profielen
+z
+y
HEA650
Appendixes
Doorsnedeno. 3 HEA650
Materiaal : 3 - S 355
A
:
2.420000e+004 mm^2
Ay/A :
0.555
Iy
:
1.750000e+009 mm^4
Iyz :
0.000000e+000 mm^4
Iw
:
1.113965e+013 mm^6
Wely :
5.470000e+006 mm^3
Wply :
6.140000e+006 mm^3
cy
:
150.00 mm
iy
:
268.91 mm
dy
:
-0.00 mm
Omtrek :
Breedte
Lijfdikte
0.336
1.170000e+008 mm^4
4.480000e+006 mm^4
Welz :
Wplz :
cz
:
iz
:
dz
:
2453.00 mm
7.820000e+005 mm^3
1.206000e+006 mm^3
320.00 mm
69.53 mm
0.00 mm
300.00 mm
13.50 mm
H 600
Controletype: I-profiel
Hoogte
640.00 mm
Flensdikte
26.00 mm
Straal
27.00 mm
Az/A :
Iz
:
It
:
+z
+y
B 600
REC (600,600)
Doorsnedeno. 4 REC (600,600)
Materiaal : 9 - C35/45
A
:
Ay/A :
Iy
:
Iyz :
Iw
:
Wely :
Wply :
cy
:
iy
:
dy
:
Omtrek :
3.600000e+005
0.833
1.080000e+010
0.000000e+000
0.000000e+000
3.600000e+007
5.400001e+007
300.00 mm
173.21 mm
0.00 mm
mm^2
mm^4
mm^4
mm^6
mm^3
mm^3
Az/A :
Iz
:
It
:
0.833
1.080000e+010 mm^4
1.822176e+010 mm^4
Welz :
Wplz :
cz
:
iz
:
dz
:
2400.00 mm
3.600000e+007 mm^3
5.400001e+007 mm^3
300.00 mm
173.21 mm
0.00 mm
Appendixes
Controletype: A-typische doorsnede
Basisgegevens
Structuurtype : Algemeen XYZ
Aantal
Aantal
Aantal
Aantal
Aantal
Aantal
Aantal
Aantal
knopen:
staven:
1D macro's:
randlijnen:
2D macro's:
profielen:
belastingsgev.:
materialen:
46
20
20
7
2
4
2
3
Materiaal
Naam
S 355
Treksterkte
Vloeigrens
E-modulus
Poisson coëff.
Specifiek gewicht
Uitzettingscoëff.
510.000 MPa
355.000 MPa
210000.00 MPa
0.30
7850.000 kg/m^3
0.012 mm/m.K
E-modulus
Poisson coëff.
Specifiek gewicht
Uitzettingscoëff.
33500.00 MPa
0.20
2500.000 kg/m^3
0.01 mm/m.K
E-modulus
Poisson coëff.
Specifiek gewicht
Uitzettingscoëff.
36000.00 MPa
0.20
2500.000 kg/m^3
0.01 mm/m.K
C35/45
B 55
Materialenlijst
Groep staven: 1/20
nr.
Naam
Kwaliteit
3
4
HEA650
REC (600,600)
S 355
C35/45
Eenh. gewicht
kg/m
189.97
900.00
Lengte
m
260.22
505.96
Materialenlijst - Macro2D
Groep staven: 1/2
nr.
Naam
Kwaliteit
Specifieke massa
kgm^3
Volume Massa
m^3
kg
Massa
kg
49433.10
455368.02
Appendixes
nr.
Naam
Kwaliteit
9
C35/45 C35/45
Specifieke massa
kgm^3
2500.00
Totaal gewicht van constructie: 2642301.12 kg
Verfoppervlakte: 1852.62 m^2
Knopen
knoop
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
X
m
-11.250
11.250
11.250
-11.250
-11.250
11.250
-2.800
-2.800
-8.400
-8.400
2.800
2.800
1.400
1.400
1.400
1.400
-1.400
-1.400
-1.400
-1.400
-4.200
-4.200
-4.200
-4.200
4.200
4.200
4.200
4.200
8.400
8.400
-7.000
-7.000
-7.000
-7.000
-9.800
-9.800
-9.800
-9.800
7.000
7.000
7.000
Y
m
0.000
0.000
18.500
18.500
0.000
0.000
0.000
46.000
0.000
46.000
0.000
46.000
15.500
5.500
17.500
7.500
15.500
5.500
17.500
7.500
15.500
5.500
17.500
7.500
15.500
5.500
17.500
7.500
0.000
46.000
15.500
5.500
17.500
7.500
15.500
5.500
17.500
7.500
15.500
5.500
17.500
Z
m
0.000
0.000
0.000
0.000
6.500
6.500
0.000
-46.000
0.000
-46.000
0.000
-46.000
0.000
-30.000
0.000
-30.000
0.000
-30.000
0.000
-30.000
0.000
-30.000
0.000
-30.000
0.000
-30.000
0.000
-30.000
0.000
-46.000
0.000
-30.000
0.000
-30.000
0.000
-30.000
0.000
-30.000
0.000
-30.000
0.000
Volume Massa
m^3
kg
855.00 2137500.00
Appendixes
knoop
42
43
44
45
46
X
m
7.000
9.800
9.800
9.800
9.800
Y
m
7.500
15.500
5.500
17.500
7.500
Z
m
-30.000
0.000
-30.000
0.000
-30.000
Staven
macro
staaf
knoop 1
knoop 2
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
7
9
11
13
15
17
19
21
23
25
27
29
31
33
35
37
39
41
43
45
8
10
12
14
16
18
20
22
24
26
28
30
32
34
36
38
40
42
44
46
Lengte
m
65.054
65.054
65.054
31.623
31.623
31.623
31.623
31.623
31.623
31.623
31.623
65.054
31.623
31.623
31.623
31.623
31.623
31.623
31.623
31.623
Rx
deg
0.00
0.00
0.00
0.00
0.00
0.00
0.00
0.00
0.00
0.00
0.00
0.00
0.00
0.00
0.00
0.00
0.00
0.00
0.00
0.00
Profiel
Kwaliteit
3
3
3
4
4
4
4
4
4
4
4
3
4
4
4
4
4
4
4
4
S 355
S 355
S 355
C35/45
C35/45
C35/45
C35/45
C35/45
C35/45
C35/45
C35/45
S 355
C35/45
C35/45
C35/45
C35/45
C35/45
C35/45
C35/45
C35/45
-
HEA650
HEA650
HEA650
REC (600,600)
REC (600,600)
REC (600,600)
REC (600,600)
REC (600,600)
REC (600,600)
REC (600,600)
REC (600,600)
HEA650
REC (600,600)
REC (600,600)
REC (600,600)
REC (600,600)
REC (600,600)
REC (600,600)
REC (600,600)
REC (600,600)
Randen
randlijn
1
2
3
4
5
6
7
type
Lijn
Lijn
Lijn
Lijn
Lijn
Lijn
Lijn
knoop
1,2
2,3
3,4
4,1
1,5
5,6
6,2
2D macro's
num type
1
C35/45
Rand:
Knopen :
Dikte 1.00 m
1,2,3,4
7,13,15,17,19,21,23,25,27,9,11,45,31,33,35,37,39,41,43
Appendixes
Profielen
+z
+y
HEA650
Doorsnedeno. 3 HEA650
Materiaal : 3 - S 355
A
:
2.420000e+004 mm^2
Ay/A :
0.555
Iy
:
1.750000e+009 mm^4
Iyz :
0.000000e+000 mm^4
Iw
:
1.113965e+013 mm^6
Wely :
5.470000e+006 mm^3
Wply :
6.140000e+006 mm^3
cy
:
150.00 mm
iy
:
268.91 mm
dy
:
-0.00 mm
Omtrek :
Az/A :
Iz
:
It
:
0.336
1.170000e+008 mm^4
4.480000e+006 mm^4
Welz :
Wplz :
cz
:
iz
:
dz
:
2453.00 mm
7.820000e+005 mm^3
1.206000e+006 mm^3
320.00 mm
69.53 mm
0.00 mm
Controletype: I-profiel
640.00 mm
26.00 mm
27.00 mm
Breedte
Lijfdikte
300.00 mm
13.50 mm
H 600
Hoogte
Flensdikte
Straal
+z
+y
B 600
Appendixes
REC (600,600)
Doorsnedeno. 4 REC (600,600)
Materiaal : 9 - C35/45
A
:
Ay/A :
Iy
:
Iyz :
Iw
:
Wely :
Wply :
cy
:
iy
:
dy
:
Omtrek :
3.600000e+005
0.833
1.080000e+010
0.000000e+000
0.000000e+000
3.600000e+007
5.400001e+007
300.00 mm
173.21 mm
0.00 mm
mm^2
mm^4
mm^4
mm^6
mm^3
mm^3
Controletype: A-typische doorsnede
Az/A :
Iz
:
It
:
0.833
1.080000e+010 mm^4
1.822176e+010 mm^4
Welz :
Wplz :
cz
:
iz
:
dz
:
2400.00 mm
3.600000e+007 mm^3
5.400001e+007 mm^3
300.00 mm
173.21 mm
0.00 mm
Appendixes
Appendix K:
MSheet calculation minimum wall height
h_g = 27m
Sheet Piling
Length
[m]
Mobilized
Resistance
[%]
Maximum
Negative
[kNm]
45.00
37.3
44.50
38.2
44.00
39.3
43.50
40.4
43.00
41.6
42.50
42.9
42.00
44.3
41.50
45.8
41.00
47.5
40.50
49.3
40.00
51.2
39.50
53.5
39.00
55.9
38.50
58.9
38.00
62.5
37.50
66.3
37.00
70.2
36.50
74.0
36.00
77.5
35.50
80.6
35.00
83.5
34.50
86.8
34.00
90.7
33.50
98.2
33.00 Sheet piling unstable
-9730.6
-9730.6
-9730.5
-9730.7
-9730.8
-9731.0
-9730.6
-9730.9
-9731.2
-9731.1
-9731.6
-9734.0
-9739.1
-9751.5
-9777.3
-9822.8
-9891.1
-9983.9
-10093.9
-10204.1
-10301.3
-10369.5
-10409.7
-10401.2
Sheet Piling
Length
[m]
Mobilized
Resistance
[%]
Maximum
Negative
[kNm]
45.00
44.50
44.00
43.50
43.00
42.50
42.00
41.50
41.00
40.50
40.00
39.50
39.00
38.50
36.9
37.8
38.9
40.0
41.2
42.4
43.8
45.3
46.9
48.6
50.6
52.7
55.1
57.8
-9915.8
-9915.9
-9915.6
-9916.0
-9916.2
-9915.9
-9916.3
-9916.4
-9916.0
-9916.4
-9916.6
-9918.0
-9921.8
-9929.6
Moment
Positive
[kNm]
1356.9
1354.6
1356.9
1356.9
1354.3
1355.6
1356.4
1354.6
1354.2
1354.5
1352.0
1345.1
1330.1
1297.1
1235.1
1134.0
990.5
802.1
586.8
374.4
188.9
65.6
3.4
0.2
Maximum
Displacement
[mm]
-196.1
-196.2
-196.1
-196.2
-196.2
-196.2
-196.1
-196.2
-196.2
-196.3
-196.5
-197.4
-198.9
-202.4
-208.9
-219.5
-233.7
-250.7
-267.6
-280.6
-287.2
-287.0
-281.3
-294.8
h_g = 28m
Moment
Positive
[kNm]
1047.4
1048.6
1047.8
1046.3
1047.6
1047.5
1046.2
1046.3
1047.3
1046.5
1043.2
1038.1
1024.5
998.4
Maximum
Displacement
[mm]
-146.3
-146.3
-146.3
-146.3
-146.3
-146.3
-146.3
-146.3
-146.3
-146.4
-146.5
-146.9
-147.8
-149.4
Appendixes
60.9
38.00
37.50
64.5
37.00
68.1
36.50
71.8
36.00
75.3
35.50
78.6
35.00
81.9
34.50
85.7
34.00
90.3
33.50
98.2
33.00 Sheet piling unstable
-9946.4
-9977.6
-10027.5
-10096.8
-10179.4
-10266.4
-10343.4
-10400.0
-10428.3
-10402.3
948.6
869.9
756.4
610.1
442.6
272.4
130.3
31.7
1.5
0.1
-152.3
-157.2
-164.0
-172.2
-180.5
-187.3
-190.7
-190.1
-187.5
-204.7
Sheet Piling
Length
[m]
Maximum Moment
Negative
Positive
[kNm]
[kNm]
Maximum
Displacement
[mm]
45.00
36.6
44.50
37.5
44.00
38.5
43.50
39.6
43.00
40.8
42.50
42.0
42.00
43.4
41.50
44.8
41.00
46.4
40.50
48.1
40.00
50.0
39.50
52.1
39.00
54.4
38.50
57.0
38.00
59.9
37.50
63.1
37.00
66.4
36.50
69.9
36.00
73.4
35.50
76.9
35.00
80.5
34.50
84.6
34.00
90.8
33.50
98.2
33.00 Sheet piling unstable
-10088.5
-10088.2
-10088.5
-10088.7
-10088.4
-10088.8
-10088.9
-10088.6
-10088.9
-10088.9
-10089.1
-10090.2
-10092.1
-10098.3
-10109.9
-10131.9
-10167.9
-10218.2
-10280.0
-10344.9
-10403.1
-10444.7
-10445.2
-10403.4
-119.7
-119.6
-119.7
-119.7
-119.7
-119.7
-119.7
-119.7
-119.7
-119.7
-119.8
-120.1
-120.5
-121.5
-123.0
-125.4
-128.8
-132.6
-136.5
-139.4
-140.7
-140.1
-140.7
-157.2
Sheet Piling
Length
[m]
Mobilized
Resistance
[%]
Maximum Moment
Negative
Positive
[kNm]
[kNm]
Maximum
Displacement
[mm]
45.00
44.50
44.00
43.50
36.3
37.2
38.2
39.3
-10246.6
-10246.7
-10246.8
-10246.7
-106.5
-106.5
-106.5
-106.5
h_g = 29m
Mobilized
Resistance
[%]
798.4
798.4
797.2
797.5
798.0
797.6
796.6
797.7
798.0
795.0
793.2
787.4
772.8
749.3
707.0
639.3
545.4
429.0
298.7
168.6
65.5
4.8
0.1
0.1
h_g = 30m
616.3
616.3
615.5
615.7
Appendixes
40.5
43.00
42.50
41.7
42.00
43.0
41.50
44.4
41.00
46.0
40.50
47.7
40.00
49.6
39.50
51.6
39.00
53.9
38.50
56.4
38.00
59.1
37.50
62.1
37.00
65.2
36.50
68.6
36.00
71.9
35.50
75.5
35.00
79.3
34.50
84.4
34.00
90.8
33.50
98.2
33.00 Sheet piling unstable
-10246.9
-10247.0
-10247.1
-10247.1
-10247.0
-10247.1
-10247.0
-10247.4
-10249.2
-10253.3
-10262.1
-10278.6
-10305.4
-10343.4
-10390.0
-10439.0
-10481.0
-10498.6
-10466.8
-10404.8
615.7
615.3
614.8
615.3
615.0
613.4
610.5
603.1
587.7
561.6
518.8
460.0
378.8
280.9
177.2
83.1
16.5
0.4
0.1
0.1
-106.5
-106.5
-106.5
-106.5
-106.5
-106.5
-106.6
-106.8
-107.1
-107.7
-108.6
-109.9
-111.6
-113.5
-115.2
-116.4
-116.5
-116.3
-118.5
-135.0
Sheet Piling
Length
[m]
Maximum Moment
Negative
Positive
[kNm]
[kNm]
Maximum
Displacement
[mm]
-10388.9
-10389.0
-10389.0
-10389.1
-10389.3
-10389.2
-10389.3
-10389.3
-10389.1
-10389.0
-10388.6
-10388.6
-10389.5
-10393.0
-10400.7
-10415.1
-10437.9
-10470.0
-10508.4
-10547.2
-10572.5
-10552.0
-10492.2
-10406.0
-100.9
-100.9
-100.9
-100.9
-100.9
-100.9
-100.9
-100.9
-100.9
-101.0
-101.0
-101.2
-101.4
-101.9
-102.5
-103.3
-104.3
-105.3
-106.0
-106.3
-106.1
-106.7
-110.0
-126.2
h_g = 31m
Mobilized
Resistance
[%]
45.00
36.1
44.50
37.0
44.00
38.0
43.50
39.1
43.00
40.2
42.50
41.4
42.00
42.7
41.50
44.2
41.00
45.7
40.50
47.4
40.00
49.2
39.50
51.3
39.00
53.5
38.50
55.9
38.00
58.6
37.50
61.4
37.00
64.4
36.50
67.6
36.00
71.0
35.50
74.6
35.00
78.7
34.50
84.4
34.00
90.8
33.50
98.2
33.00 Sheet piling unstable
494.2
494.2
493.9
493.4
493.8
493.5
492.6
493.3
492.7
490.6
486.7
477.3
459.5
432.7
389.7
330.8
256.1
171.0
89.8
25.1
0.9
0.1
0.1
0.1
Appendixes
h_g = 32m
Sheet Piling
Length
[m]
Mobilized
Resistance
[%]
Maximum
Negative
[kNm]
Moment
Positive
[kNm]
415.7
414.7
415.2
415.1
414.5
414.6
414.6
414.3
413.1
411.6
406.4
395.2
377.9
347.0
303.6
244.5
174.1
98.8
35.5
2.0
0.2
0.1
0.1
0.1
Maximum
Displacement
[mm]
45.00
36.0
44.50
36.9
44.00
37.9
43.50
38.9
43.00
40.1
42.50
41.3
42.00
42.6
41.50
44.0
41.00
45.5
40.50
47.2
40.00
49.0
39.50
51.0
39.00
53.2
38.50
55.6
38.00
58.2
37.50
60.9
37.00
63.9
36.50
66.9
36.00
70.2
35.50
74.0
35.00
78.7
34.50
84.3
34.00
90.7
33.50
98.2
33.00 Sheet piling unstable
-10490.9
-10491.0
-10491.0
-10491.1
-10491.2
-10491.2
-10491.3
-10491.2
-10491.0
-10490.6
-10490.0
-10490.2
-10491.3
-10495.5
-10504.2
-10520.0
-10544.5
-10577.5
-10613.7
-10643.2
-10641.8
-10586.8
-10508.9
-10406.7
-98.9
-98.9
-98.9
-98.9
-98.9
-98.9
-98.9
-99.0
-99.0
-99.0
-99.1
-99.2
-99.4
-99.8
-100.2
-100.8
-101.4
-101.9
-102.2
-102.2
-102.2
-103.6
-107.5
-124.0
Sheet Piling
Length
[m]
Mobilized
Resistance
[%]
Maximum MomentMaximum
Negative
PositiveDisplacement
[kNm]
[kNm]
[mm]
45.00
44.50
44.00
43.50
43.00
42.50
42.00
41.50
41.00
40.50
40.00
39.50
39.00
38.50
38.00
35.9
36.8
37.8
38.9
40.0
41.2
42.5
43.9
45.4
47.1
48.9
50.9
53.1
55.5
58.0
-10532.4
-10532.5
-10532.6
-10532.8
-10532.9
-10532.9
-10533.0
-10532.8
-10532.5
-10531.9
-10531.3
-10531.3
-10533.2
-10539.2
-10551.6
h_g = 33m
382.6
382.7
381.4
382.4
382.0
381.1
382.1
381.3
380.4
378.2
372.8
361.2
342.4
310.2
263.4
-98.6
-98.6
-98.6
-98.6
-98.6
-98.6
-98.6
-98.6
-98.6
-98.6
-98.7
-98.8
-99.0
-99.3
-99.7
Appendixes
60.7
37.50
37.00
63.5
36.50
66.6
36.00
69.9
35.50
73.8
35.00
78.7
34.50
84.3
34.00
90.7
33.50
98.2
33.00 Sheet piling unstable
-10572.9
-10604.6
-10643.0
-10679.5
-10696.1
-10671.8
-10598.3
-10513.1
-10407.0
Sheet Piling
Length
[m]
Maximum
Negative
[kNm]
201.7
129.8
60.3
12.1
0.2
0.1
0.1
0.1
0.1
-100.1
-100.5
-100.8
-100.9
-100.8
-101.1
-102.8
-107.1
-123.8
h_g = 34m
Mobilized
Resistance
[%]
45.00
36.0
44.50
36.9
44.00
37.9
43.50
38.9
43.00
40.1
42.50
41.3
42.00
42.6
41.50
44.0
41.00
45.5
40.50
47.2
40.00
49.0
39.50
51.0
39.00
53.2
38.50
55.6
38.00
58.1
37.50
60.7
37.00
63.5
36.50
66.4
36.00
69.7
35.50
73.8
35.00
78.7
34.50
84.3
34.00
90.7
33.50
98.2
33.00 Sheet piling unstable
-10497.3
-10497.4
-10497.6
-10497.8
-10498.0
-10498.1
-10498.2
-10498.1
-10497.7
-10497.2
-10497.2
-10498.6
-10503.7
-10515.5
-10537.3
-10571.6
-10617.3
-10666.4
-10705.2
-10713.5
-10676.8
-10600.0
-10513.3
-10406.9
Sheet Piling
Length
[m]
Mobilized
Resistance
[%]
Maximum
Negative
[kNm]
45.00
44.50
44.00
43.50
43.00
36.2
37.1
38.1
39.2
40.3
-10382.0
-10382.3
-10382.6
-10382.9
-10383.3
Moment
Positive
[kNm]
420.3
420.5
420.4
419.5
419.8
419.5
419.2
419.4
418.5
415.9
410.8
398.2
374.5
336.2
278.9
203.9
120.7
47.3
5.1
0.3
0.1
0.1
0.1
0.1
Maximum
Displacement
[mm]
-98.6
-98.6
-98.6
-98.6
-98.6
-98.6
-98.6
-98.6
-98.6
-98.7
-98.7
-98.9
-99.1
-99.4
-99.7
-100.1
-100.4
-100.6
-100.5
-100.5
-101.0
-102.8
-107.1
-123.8
h_g = 35m
Moment
Positive
[kNm]
582.4
581.7
581.0
581.0
580.2
Maximum
Displacement
[mm]
-98.4
-98.4
-98.4
-98.4
-98.4
Appendixes
41.6
42.50
42.00
42.9
41.50
44.3
41.00
45.9
40.50
47.5
40.00
49.4
39.50
51.4
39.00
53.7
38.50
56.0
38.00
58.5
37.50
61.0
37.00
63.6
36.50
66.4
36.00
69.7
35.50
73.8
35.00
78.7
34.50
84.3
34.00
90.7
33.50
98.2
33.00 Sheet piling unstable
-10383.6
-10383.7
-10383.7
-10383.5
-10383.4
-10384.8
-10389.9
-10403.0
-10429.1
-10472.5
-10532.2
-10600.6
-10664.9
-10708.4
-10715.0
-10676.5
-10599.9
-10513.3
-10406.9
Sheet Piling
Length
[m]
Maximum
Negative
[kNm]
579.6
579.8
579.2
578.1
575.5
566.6
547.3
510.3
447.5
357.1
247.6
136.3
48.7
4.3
0.1
0.1
0.1
0.1
0.1
-98.4
-98.4
-98.5
-98.5
-98.5
-98.6
-98.8
-99.0
-99.4
-99.8
-100.2
-100.5
-100.6
-100.5
-100.5
-101.0
-102.8
-107.1
-123.8
h_g = 36m
Mobilized
Resistance
[%]
45.00
36.6
44.50
37.6
44.00
38.6
43.50
39.7
43.00
40.8
42.50
42.1
42.00
43.4
41.50
44.9
41.00
46.5
40.50
48.2
40.00
50.1
39.50
52.2
39.00
54.4
38.50
56.7
38.00
58.9
37.50
61.3
37.00
63.7
36.50
66.4
36.00
69.7
35.50
73.8
35.00
78.7
34.50
84.3
34.00
90.7
33.50
98.2
33.00 Sheet piling unstable
-10193.3
-10193.7
-10194.2
-10194.9
-10195.5
-10196.0
-10196.3
-10196.2
-10196.6
-10198.7
-10206.2
-10225.1
-10262.6
-10323.6
-10406.9
-10499.1
-10589.8
-10663.3
-10708.8
-10714.8
-10676.5
-10599.9
-10513.3
-10406.9
Moment
Positive
[kNm]
897.8
897.0
896.2
895.2
894.3
893.7
893.2
892.8
890.4
882.2
860.9
814.8
732.8
610.1
453.1
293.0
150.1
49.8
4.0
0.2
0.1
0.1
0.1
0.1
Maximum
Displacement
[mm]
-97.6
-97.6
-97.6
-97.6
-97.6
-97.6
-97.6
-97.6
-97.6
-97.7
-97.9
-98.2
-98.6
-99.2
-99.8
-100.2
-100.5
-100.6
-100.5
-100.5
-101.0
-102.8
-107.1
-123.8
Appendixes
Appendix L-1: Optimisation wall height
h_g = 27 m
27
L
50
49
48
47
46
45
44
43
42
41
40
39
38
37
36
35
34
Diameter
562
562
562
562
562
562
562
562
562
562
562
564
567
575
585
592
594
ctc = 1,1 m
1,1
A_steel
20684
20684
20684
20684
20684
20684
20684
20684
20684
20684
20684
20793
20957
21398
21954
22347
22460
h=2m
2
w_max
255
255
255
255
255
255
255
255
255
256
257
260
273
291
305
305
296
Costs_g
19164
19164
19164
19164
19164
19164
19164
19164
19164
19164
19164
19147
19121
19050
18961
18898
18879
Costs_s
1946
1907
1868
1829
1790
1752
1713
1674
1635
1596
1557
1526
1499
1490
1487
1472
1437
total costs
21111
21072
21033
20994
20955
20916
20877
20838
20799
20760
20721
20673
20620
20540
20448
20369
20316
h_g = 29 m
29
L
50
49
48
47
46
45
44
43
42
41
40
39
38
37
36
35
34
Diameter
570
570
570
570
570
570
570
570
570
570
570
571
573
579
586
591
592
ctc = 1,1 m
1,1
A_steel
21122
21122
21122
21122
21122
21122
21122
21122
21122
21122
21122
21177
21287
21619
22010
22291
22347
h=2m
V_grout
2
w_max
217
217
217
217
217
217
217
217
217
217
217
219
225
232
238
238
236
2
64
Costs_s
total costs
1987
22496
1948
22457
1908
22417
1868
22377
1828
22337
1789
22298
1749
22258
1709
22218
1669
22178
1630
22139
1590
22099
1554
22054
1522
22003
1505
21929
1491
21847
1468
21775
1430
21727
Costs_g
20509
20509
20509
20509
20509
20509
20509
20509
20509
20509
20509
20500
20481
20423
20356
20307
20297
h_g = 29m
h_g = 27m
300
290
350
15000
330
10000
310
290
5000
270
250
37
42
47
270
250
h_g = 31 m
31
L
50
49
48
47
46
45
44
43
42
41
40
39
38
37
36
35
34
Grout costs
Diameter
574
574
574
574
574
574
574
574
574
574
574
575
577
582
588
592
592
Steel costs
ctc = 1,1 m
1,1
A_steel
21342
21342
21342
21342
21342
21342
21342
21342
21342
21342
21342
21398
21508
21786
22122
22347
22347
10000
240
230
5000
220
200
52
0
32
Pile length [m]
w_max
15000
260
210
0
32
20000
280
Material costs [Euro/m]
370
Hor. displacements [mm]
20000
Material costs [Euro/m]
Hor. displacements [mm]
390
34
36
38
40
42
44
46
48
50
52
Pile length [m]
w_max
Tatal costs
h=2m
V_grout
68
2
w_max
209
209
209
209
209
209
209
209
209
209
209
211
214
218
220
219
219
Costs_g
21883
21883
21883
21883
21883
21883
21883
21883
21883
21883
21883
21873
21852
21801
21739
21697
21697
Costs_s
2008
1968
1928
1888
1847
1807
1767
1727
1687
1647
1606
1570
1538
1517
1499
1472
1430
total costs
23891
23851
23811
23771
23730
23690
23650
23610
23570
23530
23489
23443
23390
23318
23238
23169
23127
h_g = 32 m
32
L
50
49
48
47
46
45
44
43
42
41
40
39
38
37
36
35
34
Diameter
573
573
573
573
573
573
573
573
573
574
574
575
577
582
588
593
592
Grout costs
Steel costs
ctc = 1,1 m
1,1
A_steel
21287
21287
21287
21287
21287
21287
21287
21287
21287
21342
21342
21398
21508
21786
22122
22403
22347
h_g = 31m
Tatal costs
h=2m
V_grout
70
Costs_s
total costs
2003
24602
1963
24562
1923
24522
1883
24482
1843
24442
1803
24402
1763
24362
1723
24322
1682
24282
1647
24235
1606
24195
1570
24149
1538
24095
1517
24021
1499
23939
1476
23862
1430
23827
2
w_max
209
209
209
209
209
209
209
209
209
209
209
211
214
217
218
216
218
Costs_g
22599
22599
22599
22599
22599
22599
22599
22599
22599
22589
22589
22578
22557
22504
22440
22386
22397
h_g = 32m
250
25000
245
250
30000
245
230
15000
225
220
10000
215
210
5000
205
200
0
32
34
36
38
40
42
44
46
Pile length [m]
w_max
Grout costs
Steel costs
Tatal costs
48
50
52
25000
240
Material costs [Euro/m]
Material costs [Euro/m]
Hor. displacements [mm]
20000
235
Hor. displacements [mm]
240
235
20000
230
225
15000
220
10000
215
210
5000
205
200
0
32
34
36
w_max
38
40
42
44
Pile length [m]
Grout costs
Steel costs
46
Tatal costs
48
50
52
Appendixes
h_g = 33 m
33
L
50
49
48
47
46
45
44
43
42
41
40
39
38
37
36
35
34
Diameter
571
571
571
571
571
571
571
571
571
571
572
572
576
582
589
593
592
ctc = 1,1 m
1,1
A_steel
21177
21177
21177
21177
21177
21177
21177
21177
21177
21177
21232
21232
21453
21786
22178
22403
22347
h=2m
V_grout
2
w_max
210
210
210
210
210
210
210
210
210
210
210
212
215
217
217
216
218
73
Costs_s
total costs
1993
25320
1953
25280
1913
25240
1873
25200
1833
25160
1793
25120
1753
25081
1714
25041
1674
25001
1634
24961
1598
24915
1558
24875
1534
24807
1517
24725
1502
24633
1476
24561
1430
24527
Costs_g
23327
23327
23327
23327
23327
23327
23327
23327
23327
23327
23316
23316
23273
23208
23130
23086
23097
h_g = 35 m
35
L
50
49
48
47
46
45
44
43
42
41
40
39
38
37
36
35
34
Diameter
558
558
558
558
558
558
558
558
558
558
559
562
570
580
588
593
ctc = 1,1 m
1,1
A_steel
20466
20466
20466
20466
20466
20466
20466
20466
20466
20466
20521
20684
21122
21675
22122
22403
h_g = 33m
h=2m
V_grout
2
w_max
210
210
210
210
210
210
210
210
210
210
211
214
217
219
218
215
Costs_g
24888
24888
24888
24888
24888
24888
24888
24888
24888
24888
24876
24843
24752
24637
24544
24485
77
Costs_s
total costs
1926
26813
1887
26775
1849
26736
1810
26698
1772
26659
1733
26621
1695
26582
1656
26544
1618
26505
1579
26467
1545
26421
1518
26361
1510
26263
1509
26147
1499
26043
1476
25960
h_g = 35m
230
30000
225
25000
225
25000
20000
15000
210
10000
205
5000
200
0
32
34
36
38
40
42
44
46
48
50
Material costs [Euro/m]
Material costs [Euro/m]
220
215
Hor. displacements [mm]
30000
Hor. displacements [mm]
230
220
20000
215
15000
210
10000
205
5000
200
52
0
0
10
20
30
Pile length [m]
w_max
h_g = 37 m
37
L
50
49
48
47
46
45
44
43
42
41
40
39
38
37
36
35
34
Diameter
538
538
538
538
538
538
538
538
538
539
544
555
568
580
Grout costs
Steel costs
ctc = 1,1 m
1,1
A_steel
19394
19394
19394
19394
19394
19394
19394
19394
19394
19447
19713
20304
21012
21675
40
50
60
Pile length [m]
Tatal costs
h=2m
V_grout
2
w_max
205
205
205
205
205
205
205
205
205
205
209
213
217
219
Grout costs
Diameter
498
498
498
498
499
500
503
508
515
526
539
554
568
580
588
593
592
ctc = 1,1 m
1,1
A_steel
17323
17323
17323
17323
17373
17424
17576
17831
18191
18762
19447
20250
21012
21675
22122
22403
22347
Grout to toe
81
Costs_s
total costs
1825
28366
1788
28330
1752
28293
1715
28257
1679
28220
1642
28184
1606
28147
1569
28111
1533
28074
1500
28030
1484
27957
1490
27835
1503
27693
1509
27554
Costs_g
26541
26541
26541
26541
26541
26541
26541
26541
26541
26530
26473
26345
26191
26045
w_max
L
50
49
48
47
46
45
44
43
42
41
40
39
38
37
36
35
34
h_g = 37m
Steel costs
Total costs
h=2m
2
w_max
179
179
179
179
180
181
183
187
193
200
207
213
217
218
218
218
218
2
Costs_g
36459
35729
35000
34271
33529
32787
32021
31231
30419
29560
28681
27781
26899
26045
25245
24485
23797
Costs_s
1630
1597
1565
1532
1504
1475
1455
1443
1438
1448
1464
1486
1503
1509
1499
1476
1430
total costs
38088
37327
36565
35803
35033
34263
33476
32674
31856
31008
30145
29268
28401
27554
26744
25960
25227
L = h_g
220
30000
20000
214
212
15000
210
10000
208
5000
206
204
0
32
34
36
38
40
42
44
46
48
50
Hor. displacements [mm]
216
Material costs [Euro/m]
Hor. displacements [mm]
25000
35000
200
30000
25000
150
20000
100
15000
10000
50
5000
0
0
32
37
42
47
Wall height [m]
52
Pile length [m]
w_max
Grout costs
Steel costs
Total costs
w_max
Grout costs
Steel costs
Total costs
52
Material costs [Euro/m]
40000
250
218
Appendixes
Appendix L-2: Optimisation cross section
h
2
2,1
2,2
2,3
2,4
2,5
2,6
2,7
2,8
2,9
3
D
489
469
450
433
417
403
390
378
367
356
347
A_p [mm2]
22337
21394
20499
19698
18944
18284
17671
17106
16588
16069
15645
V_s [ton]
1,38
1,32
1,27
1,22
1,17
1,13
1,09
1,06
1,03
0,99
0,97
V_g [m3]
313293
328973
344653
360333
376011
391690
407368
423045
438722
454399
470076
Costs
grout [E/m]
359075
377047
395018
412989
430959
448928
466897
484865
502833
520802
538769
Costs
steel [E/m]
1572
1506
1443
1386
1333
1287
1244
1204
1167
1131
1101
Material
Cost [E/m]
360647
378552
396461
414375
432292
450215
468141
486069
504001
521932
539870
500000
200
400000
150
300000
100
200000
50
100000
0
Material costs [Euro/m]
600000
250
Hor. displacements [mm]
w_max
[mm]
222
205
190
177
164
153
143
134
125
118
111
0
1,8
2
2,2
2,4
2,6
2,8
3
3,2
ctc [m]
w_max
h
2
D
367
404
441
478
515
552
589
626
662
699
ctc
0,8
0,9
1
1,1
1,2
1,3
1,4
1,5
1,6
1,7
m
A_p [mm2]
16588
18331
20075
21818
23562
25306
27049
28793
30489
32233
Costs steel
V_s [ton/m]
1,41
1,39
1,37
1,35
1,34
1,32
1,31
1,31
1,30
1,29
costs grout
V_g [m3/m]
63,50
63,16
62,81
62,45
62,10
61,74
61,38
61,02
60,69
60,33
Total costs
costs
grout
25402
25263
25123
24981
24839
24696
24553
24409
24274
24130
costs
steel
1459
1433
1413
1396
1382
1370
1360
1351
1341
1334
Material
Cost [E/m]
26861
26696
26536
26377
26221
26066
25913
25760
25615
25464
30000
230
25000
228
20000
226
224
15000
222
10000
220
5000
218
216
0
0,7
0,9
1,1
1,3
1,5
ctc [m]
w_max
Costs steel
costs grout
Total costs
1,7
Material costs [Euro/m]
Hor. displacements [mm]
232
w_max
[mm]
231
218
219
220
220
221
221
221
222
222
Appendixes
Appendix M-1: Shear stresses
A slice of a loaded beam with a width Cx is considered. The bending moment in the beam varies with x
such that the bending moment M1 at the left side of the slice is unequal to the bending moment M2 at the
right side of the slice. Due to the inequality of the bending moments the development of the normal
stresses differs at both sides of the slice. This is illustrated in the picture below.
load
beam
Cx
Moment line
M1 M2
A
z1
F1
A
CF
F2
Cx
By integrating the normal stresses over the height z1 and multiplying with the width the forces F1 and F2
are calculated. At the lower side of section A-A in the above picture a force CF acts, which is equal to the
difference of the forces F1 and F2. The force CF needs to be counteracted to obtain equilibrium of section
A-A. The result is a shear force equal to CF on section A-A; the shear stress is described by the following
formula.
=
F
x
The above derived relation is based on a homogeneous cross section of the beam. The next step is to
consider a beam consisting of two different materials with Young’s moduli E1 and E2.
Appendixes
Strain
Normal stresses
Normal stresses
Strain
E1
E2
A
z2
F1
A
CF
E1
F2
Cx
The development of the strain is continuous at both sides of the singled out slide. However The normal
stress according to Hooke’s law is:
( z) = E ( z)(
In which:
](z):
Normal stress;
E(z):
Young’s modulus of the material at the height z;
n:
Strain;
Due to the discontinuity of the Young’s modulus over the height of the beam the normal stresses are
discontinuous over the height of the beam. By integrating the stresses over the height z2 and multiplying
by the width the forces F1 and F2 are calculated and the difference of these forces is CF. At the lower side
of section A-A the force CF acts which needs to be opposed to obtain equilibrium of the considered section.
Again the result is a shear force at section A-A equal to CF and the shear stress is obtained by dividing over
Cx and the shear width.
Appendixes
Appendix M-2: Shear stresses optimised design
For the optimised design, of which the parameters are included in the table below, the governing shear
stresses have been calculated.
D
t
h
ctc
L = hg
tf
hf
735
14
2.0
1.6
34
30
200
mm
mm
m
m
m
mm
mm
Pile diameter
Wall thickness pile
Centre-to-centre distance between pile rows
Centre –to-centre distance between the piles in a row
Height of the piles and the grout mass
Thickness flanges
Centre-to-centre distance of the flanges
Shear failure around a pile
In the picture below the failure mechanism is illustrated. The pile and the grout between the rings are
vertically pulled out of the grout mass. The shear plane has a width B as indicated below, which is equal to
half the outer perimeter of the flange.
tension
B
grout
compression
M1
h
F1
8544
2.0
kNm
m
4272
kN
M2
h
F2
6461
2.0
kNm
m
3230
kN
F = F1 F 2 = 1042 kN
F
= 0.87 MPa
pile =
B h
Appendixes
The distance Ch between M1 and M2 is 1000mm and the width B of the shear plane is 1198mm. The
resulting safety factor is calculated with the following formula.
s
=
f1
pile
In the above formula f1 is the shear strength of grout, which is equal to 3.7 MPa. The result is a safety
factor of 4.3.
Shear failure in grout mass
The maximum shear stress is located at a certain distance from the centre line of the cross section. The
distribution of the forces in grout and in the steel piles needs to be iterated.
Shear stresses
ctc
Normal stresses
F_t
Tension
b
h
b
F_g
B
a
s
F_s
Compression
A bending moment leads to tension in one pile and compression in the other pile and in the grout. The
magnitude of these three components is calculated iteratively in excel. The height of the grout compression
zone is also iterated in excel and is independent of the bending moment. This iteration is performed for
both M1 and M2 and the results are included in the table below.
Force distribution for M1
F_t1
4558 kN
sigma_s
116 Mpa
sigma_g
1,72 Mpa
F_g1
956 kN
F_s1
3603 kN
F_c1
4558 kN
Force distribution for M2
F_t2
3447 kN
sigma_s
88 Mpa
sigma_g
1,30 Mpa
F_g2
723 kN
F_s2
2724 kN
F_c2
3447 kN
s
s
equilibrium
Moment
0,70 m
0 must be zero
8544 kNm
equilibrium
Moment
0,70 m
0 must be zero
6461 kNm
The difference between F_t1 and F_t2 leads to the shear force CF_t and the maximum shear force in the
grout mass is calculating as follows.
Appendixes
b
=
F _t
ctc h
The result of this calculation with ctc equal to 1.6m and Ch being 1000mm is a maximum shear stress of
0.69 MPa and a safety factor of 5.3.
Appendix N: Reinforcement of the toe
The anchor force of the wall structure acts at the toe of the relieving floor structure. A schematic
representation of this detail can be seen below. In this picture the compressive and tensile stresses are
included based on the truss analogy. This truss analogy forms the basis for the required reinforcement of
the toe.
3.
Compression
due to bending
1.
Tension due to
bending
2.
Tension due to
transverse force
htoe
4.
Compression diagonal
Fa
btoe
The dimensions of the toe need to be estimated. The height htoe and the width btoe are both estimated at
500mm. A calculation will be made to see if the required reinforcement fits in the toe. The calculations have
been performed with a safety factor of 1.3 included in the anchor force Fa. The resulting value for the
anchor force is 1136kN/m.
Tensions due to bending
The anchor force Fa leads to a bending moment at the top of the toe. The result of this bending moment is
tension on the inner side and compression in the outer side, as can be seen in the above picture.
Reinforcement needs to be applied to take up the tensile stresses at the inner side of the toe. The required
reinforcement is calculated with the following formulas.
Appendixes
M = Fa htoe
z 0.9htoe
M
Fs1 =
z
Fs1
As1 =
fs
In the above formula fy is the yield strength of the reinforcement, which is 435MPa. The results are
included in the table below and show that 6 bars of 25mm diameter are needed to take up the tensile
stresses due to bending. Additionally the height of the compression zone due to bending xu has been
calculated.
M
z
Fc
x_u
568
450
1262
80
kNm/m
mm
kN/m
mm
Fs2
As2
1262
2901
kN/m
mm2/m
A(25mm)
491
6
mm2
# of bars per meter
The calculated reinforcement of 6b25 per meter easily fits in the toe, with a centre-to-centre distance
which is large enough to prevent problems with aggregate in the concrete. This is illustrated in the
following picture.
Bottom view of the toe and relieving floor
167mm
1000mm
Additionally the reinforcement percentage of the toe of this particular part of the reinforcement has been
calculated.
A
)0 = s
Ac
The concrete area Ac can be derived from the above picture and is equal to 1m*0.5m. The steel area As can
be read from the table above. The reinforcement percentage of this specific part of the reinforcement is
0.59%
Appendixes
Tension due to transverse force
As can be seen in the illustration on the previous page the transverse force in the toe caused by the anchor
force causes tension in horizontal direction. The required reinforcement to take up this tension is calculated
with the following formulas and the results are included in the table below.
Fs 2 = Fa
As 2 =
Fa
fy
Fs2
As2
1136
2611
kN/m
mm2/m
A(25mm)
491
6
mm2
# of bars per meter
The same amount of reinforcement as in the previous section is needed to take up the tension due to the
transverse force, which is 6b25 per meter. Also for this part of the reinforcement the reinforcement
percentage has been calculated. Although the rebars are situated above the toe, the reinforcement
percentage has been calculated as if it were in the toe and is equal to 0.59%.
Compression diagonal
Perpendicular to the compression diagonal tensile stresses are present. These tensile stresses have not
been included in the picture on the pervious page, as it is not according to the truss analogy. The origin of
these tensile stresses is shown in the following schematisation.
C
T
T
C
Both the force in the compression diagonal and the tensile force are equal to the transverse force times
½p2. Although this tensile force is not described by the truss analogy it is necessary to apply
reinforcement to take up these tensile stresses. Two possible solutions have been identified for this
reinforcement: stirrups and tensile bars. These two possibilities are shown below.
Appendixes
Stirrup solution
Tensile bar solution
The calculation has been performed with the tensile bar solution (right-hand picture). The contribution of
the concrete which can generally be subtracted from the shear force has been neglected. The stirrups will
be designed to resist the total force Fa.
Fa
z
Ass/t
t
Ass
# of layers in the toe
# of bars per meter per layer
1136
450
45
9.40
150
1410
4
6
kN/m
mm
º
mm2/mm/m
mm
mm2/m
-
Also this reinforcement fits easily into the structure. The distance t is selected as 150mm. In this way 4
bars fit in the toe in vertical direction. 5 Bars per meter in horizontal direction results in a centre-to-centre
distance of 200mm. The reinforcement percentage of the toe for the tensile bars is equal to 0.56%.
Appendixes
Appendix O: MSheet report optimised sandwich wall design
Appendixes
Appendixes
Appendix P-1: Design combi wall
The pre-defined combi wall profiles consist of tubular piles with two intermediate sheet piles. The sheet
piles are Larssen sheet piles with a width of 600mm. The locks have a width of 50mm.
D [mm]
2470
2420
2370
2320
2270
2220
2170
2120
2070
2020
t [mm]
31
31
30
30
29
29
28
28
27
27
I [mm4]
1.77E+11
1.64E+11
1.51E+11
1.39E+11
1.28E+11
1.18E+11
1.08E+11
9.91E+10
9.06E+10
8.26E+10
W [mm3/m]
3.85E+07
3.69E+07
3.53E+07
3.37E+07
3.21E+07
3.06E+07
2.92E+07
2.78E+07
2.64E+07
2.50E+07
B [mm]
3720
3670
3620
3570
3520
3470
3420
3370
3320
3270
EI [kNm2/m] Ap [mm2]
9.99E+06
237911
9.37E+06
229329
8.77E+06
220903
8.21E+06
212632
7.66E+06
204516
7.14E+06
196557
6.65E+06
188752
6.18E+06
181103
5.73E+06
173610
5.31E+06
166272
The wall thickness of the profiles included on the above table is large enough to allow for pile driving. The
wall thickness has been determined with the following relation.
t = 6.35 +
D
100
The pile height has been varied and the associated maximum bending moment has been calculated in
MSheet. Based on the design value (safety factor of 1.3) of the maximum bending moment the smallest
profile which is able to resist this bending moment is selected. The unity check has been performed for the
selected profile and the steel volume per meter wall has been calculated. The results for various values of
the wall height L are included in the table below.
L [m]
34
35
36
37
38
39
40
41
42
43
44
45
M [kNm]
35192
35622
35497
34336
33489
31840
30099
28409
26909
26223
25207
24941
Md
45749.6
46308.6
46146.1
44636.8
43535.7
41392
39128.7
36931.7
34981.7
34089.9
32769.1
32423.3
D
2420
2420
2420
2370
2370
2320
2270
2220
2170
2170
2120
2120
sigma_max
338
342
341
350
341
344
346
347
351
342
350
347
UC
0.95
0.96
0.96
0.99
0.96
0.97
0.97
0.98
0.99
0.96
0.99
0.98
Vp [m3]
7.80
8.03
8.26
8.17
8.08
8.29
8.18
8.06
7.93
8.12
7.97
8.15
The results in the above table have been plotted to be able to select a wall height.
V sheet
0.612
0.63
0.648
0.666
0.684
0.702
0.72
0.738
0.756
0.774
0.792
0.81
Vsteel/m
2.29
2.36
2.43
2.44
2.42
2.52
2.53
2.54
2.54
2.60
2.60
2.66
2,70
1,10
2,60
1,05
2,50
1,00
2,40
0,95
2,30
0,90
2,20
0,85
2,10
Unity check [-]
Steel volume per meter wall [m3/m]
Appendixes
0,80
34
35
36
37
38
39
40
41
42
43
44
45
Wall height [m]
Steel volume
Unity check
The minimum wall height has also been calculated in MSheet; the results are shown below.
Sheet piling length [m] Mobilised resistance [%]
36.0
35.9
35.8
35.7
35.6
35.5
35.4
35.3
35.2
35.1
35.0
34.9
34.8
34.7
34.6
34.5
34.4
34.3
34.2
34.1
34.0
33.9
33.8
33.7
33.6
33.5
33.4
70.8
71.4
72.1
72.8
73.5
74.2
75.0
75.9
76.7
77.7
78.8
79.8
80.9
82.0
83.2
84.4
85.6
86.8
88.1
89.4
90.8
92.2
93.5
95.2
96.7
98.3
99.9
Maximum bending moment [kNm]
Negative
-28597.2
-28635.8
-28669.6
-28699.0
-28724.8
-28748.1
-28769.6
-28782.6
-28790.8
-28793.8
-28791.0
-28784.6
-28771.8
-28750.7
-28720.9
-28690.1
-28656.6
-28624.2
-28588.6
-28552.8
-28513.3
-28471.7
-28422.1
-28366.4
-28317.9
-28278.7
-28254.7
Positive
196.2
145.9
103.6
69.2
40.3
19.2
4.5
2.4
2.4
1.4
1.4
1.3
0.7
0.7
0.4
0.4
0.4
0.4
0.4
0.4
0.4
0.4
0.4
0.4
0.4
0.4
0.4
Maximum
displacement [mm]
-144.7
-144.7
-144.6
-144.6
-144.5
-144.5
-144.4
-144.4
-144.3
-144.3
-144.3
-144.4
-144.4
-144.6
-144.9
-145.3
-145.7
-146.2
-146.9
-147.7
-148.7
-150.1
-152.0
-155.5
-159.3
-164.8
-177.0
Appendixes
Appendix P-2: MSheet report combi wall design
Appendixes
Appendixes
Appendix Q: Weld calculation of the shear rings
To get an idea of the necessary thickness of the welds of the rings around the steel piles a rough
calculation has been made. The calculation is based on an acceleration during pile driving of 100g. By
multiplying with the weight of a ring the force on the ring due to pile driving can be calculated. This force
will be used in the calculation of the weld. The picture below shows a schematic illustration of the rebar
welded to the steel pile. The weld is schematised as a butt weld with gap.
FILLET WELD
a
BUTT WELD WITH GAP
1) Butt joint
60<M<120
anom
t
t
F3
a=anom-2
2) T-connetcion (with large gap)
anom
F1
F2
L
SO3 of t/5
Fd
t
a=anom-2
Betreft:
lower support strip to marker support plate
F1 =
0 kN
Load perpendicular to welding direction
F2 =
0 kN
Load parallel to welding direction
F3 =
13,5 kN
Load in cross direction
Leff =
n=
t=
a=
S
ft;d =
=
m =
Effective length of the weld
Number of welds
Thickness t
Thickness of the weld at a_nom
Steel type base material
Tensile strength
Welding factor
Model factor
2390
1
30
6
355
510
0,9
1,25
mm
0
mm
mm
N/mm
2
EXAMINATION ACCORDING TO art. 13.4 van NEN 6770 (based on average stresses)
Qw;s;d / f w;u;d < 1
Qw;s;d = Fd / Aeff =
2
2
13,5 / 14.340 x 1000 =
2 1/2
Fd = (F1 +F2 +F3 )
=
Aeff =a.Leff .n
fw;u;d = ft;d / [
Unity check :
x
Qw;s;d / f w;u;d =
1/2
m x(3) ]
=
=
=
13,5 kN
=
14340 mm2
510 / ( 0,90x1,25 x 3^(0,5) ) =
0,9 / 261,7 =
0,9 N/mm2
=
261,7 N/mm2
0,0036 < 1
Appendixes
The minimum weld thickness at anom due to the thickness of the rebar is 6mm. The unity check shows that
such a weld can easily take up the forces due to pile driving. Therefore a weld of 6mm is applied. The
assumption is made that such a weld can be applied in one layer.