Seismisk analyse / dimensjonering
av beholdere/tank
Anton Gjørven
Thanh Ngan Nguyen
Background
 The purpose with this presentation is
 to demonstrate different calculation methods and design principles for
seismic response of "full containment" (stand-alone steel inner tank,
separated from outer concrete cylinder) LNG (liquefied natural gas) tanks
 to show how an earthquake can impact the design of the steel inner tank.
The basic principles of anchoring/no anchoring of the steel inner tank is a
significant factor of the costs of an LNG tank.
NEED2012
Background
 Relevant projects
 Risavika: H = 20 m (Ht = 21 m), R = 22.5 m, H/R = 0.89
 Lysekil: H = 37.5 m (Ht = 38.2 m), R = 16 m, H/R = 2.34
 Lysekil: High H/R-ratio is a challenge when considering safe shutdown
earthquake (SSE - return period 4975 years. Operating basis earthquake
(OBE) - return period 475 years)
NEED2012
Background
 Response calculations and design are normally based on hand
calculations using standards
 Analyses, both explicit and implicit, have been executed to compare
and validate the hand calculations
 Parameters of interest:
 Base shear and overturning moment (foundation, stresses in bottom
insulation layers)
 Compressive stress in tank wall ("elephant foot" buckling, EC8-4 A.10)
 Uplift and anchorage of tank
Typical "elephant foot buckling"
NEED2012
Foto: Prof. J.M. Rotter, The University of Edinburgh
Basic design assumptions
 General: Eurocode 2 (Concrete) and Eurocode 3 (Steel)
 Tanks: Eurocode 1, Part 4 (Action on tanks) and Eurocode 3, Part 4-2
(Design of steel tanks)
 Eurocode 8 (Earthquake), Part 1 (General)
 Chapter 3: Ground conditions and seismic excitation
NEED2012
Ref.: NS-EN 1998-1:2004/NA:2008 Figure NA.3(903)
Ref.: NS-EN 1998-1:2004/NA:200
Figure NA.3(901)
 Eurocode 8, Part 4 (Silos, tanks and pipelines)
 Chapter 2: General
 Chapter 4: Specific rules for tanks
 Annex A: Seismic analysis procedures for tanks
Basic design assumptions
 EN 1473 (Installation and equipment for LNG)
 Structural parts vital for the plant safety shall remain operational after both
operating basis earthquake (OBE) and safe shutdown earthquake (SSE)
 EN 14620 (Design and manifacture of steel tanks for storage of LNG)
 Part 1 (General)
•
•
•
•
7.1.4 Earthquake design: "For … full containment tanks, the primary liquid container shall be
designed to contain the liquid during an OBE and SSE action."
7.3.2.2.13: OBE earthquake
7.3.3.3: SSE earthquake
Annex C: Seismic analysis
 Part 2 (Metallic components)
•
•
NEED2012
5.1.2.2: Requirements to allowable tensile stress in tank anchorage for OBE and SSE (NB:
Allowable stress theory, not limit state theory)
5.8.1: Other requirements to tank anchorage
 Part 3 (Concrete components)
 Part 4 (Insulation components)
•
•
6.3.2.2.1: Overall safety factor for brittle materials (insulation) for OBE and SSE (NB: Allowable
stress theory)
Annex C: Tank bottom insulation - Limit state theory
 Part 5 (Testing, drying, purging and cool-down)
Design of LNG tanks
Foto: Norconsult. Steel roof
under construction.
NEED2012
Foto: Norconsult. An LNG tank is a complex structure. Here is the outer concrete
wall from one of our projects - picture is taken from below and upwards.
Design of LNG tanks
 The steel inner tank is the part where the seismic conditions can have a
significant influence to basic design, for example the anchoring of the
inner tank.
 The "slenderness" of the tank or the ratio H/R combined with the
ground condition govern the anchoring system to be used.
NEED2012
Explicit analysis - Abaqus
NEED2012
 In an explicit analysis, the earthquake excitation is defined with a time
history
 The model consists of the container – a cylinder (open top) made by
steel filled with LNG
 Two cases are studied –without and with anchors (“smeared”
representation)
 For each case, one earthquake definition based on Norwegian
Standards has been used
 The FE model does not consider the outer concrete cylinder since the
obtained results (max. displacement during earthquake) indicate that
the interaction forces will be negligible
 Model definition:
 Steel tank: Shell elements
 LNG: Continuum elements. Material defined by wave speed and dynamic
viscosity (Equation of state (EOS) material model - only available in
Abaqus/Explicit)
Explicit analysis - Abaqus
 FE model, interactions:
 Steel tank and LNG
 Steel tank and bottom layers
(Foamglas, sand)
 Bottom layers and ”rock”
(analytical rigid surface)
NEED2012
Explicit analysis - Abaqus
 Gravity load (LNG) is initially in equilibrium with a hydrostatic pressure
 The initial stress state is obtained with a dynamic (explicit) approach
using time integration
 This is done by increasing the gravity load with a smooth amplitude
curve in 10 seconds, thereafter continued 10 seconds further without
any load change in order to decrease oscillations of the unbalanced
solution
 Stress state in LNG and tank wall is checked
NEED2012
Explicit analysis - Abaqus
 The earthquake excitation is applied at the reference node for the
“rock” as prescribed acceleration in the 1- and 3-directions
 The base acceleration has been multiplied by factors 1 respectively 0.3
for these directions and the earthquake is analyzed during 10 seconds
NEED2012
Explicit analysis - Abaqus
 Without anchors
NEED2012
Explicit analysis - Abaqus
 With anchors
NEED2012
Explicit analysis - Abaqus
 Vertical section force lower part of wall (positive indicates risk of uplift)
without anchors
NEED2012
with anchors (higher
stress on
compression side,
reduced risk of uplift
on tension side)
Explicit analysis - Abaqus
 Envelope of minimum contact pressure (negative indicates risk of
uplift)
Without anchors
NEED2012
With anchors
Explicit analysis - Abaqus
 Envelope of maximum contact pressure
Without anchors
NEED2012
With anchors (higher
pressure!)
Explicit analysis - Abaqus
 History plot of uplift at the corner of the tank
 Vertical section force in anchors
NEED2012
EC8-4 A.9: Effect of uplift on stress in the wall (unachored)
 EN 1998-4:2006 (E) Figure A.11:
NEED2012
 EN 1998-4:2006 (E) A.9.2:
Explicit analysis - Abaqus
 Rigid (dashed line) vs. elastic (solid line) bed, history plot of vertical
section force
Without anchors
(small differences)
NEED2012
With anchors (elastic
bed gives generally
higher compression
forces than rigid bed)
Explicit analysis - Abaqus
SUMMARY AND CONCLUSIONS
NEED2012
 Material model for LNG
 EOS material is used
 Elastic material is also possible - gives more balanced initial state
 Elastic material shows less damping during seismic excitation
 Results when using anchors are very similar to the case without
anchors
 Max. vertical displacement for the case without anchors is slightly
higher than with anchors
 However, the uplift seems to have a rather small impact on the vertical
stresses in the tank wall
 The case with anchors has actually increased section force compared to
the case without anchors
 An explicit analysis is probably a very good approach to study the
dynamic behaviour for an LNG tank excited by seismic action
Simplified calcuation of overturing moment
⋅ 0.8 ⋅
1.0 ⋅ 0.8 ⋅ 0.5
⋅ 1.0 ⋅
OBE (475 years):
⋅
NEED2012
⋅
⋅
1.5 ⋅ 30000
⋅ 490
⋅ 0.667
SSE (4 975 years):
1.0,
3.0 →
276
⋅
3.0
1.5
552
⋅ 18.75
276
⋅ ⋅
2.5
1.5
2.5
0.667
Hand calculations - Malhotra
 EC8-4 A.3.2.2
 Simplified method for fixed base tanks
 The response is splitted into impulsive and convective part, impulsive is
dominating for high tanks
 EN 1998-4:2006 (E) Table A.2:
NEED2012
Hand calculations - Malhotra
 Acceleration from elastic response spectrum, EC8-1
 Return period other than TNCR = 475 years is taken into account with the
importance factor γI (evaluated from EC8-1 2.1(4) Note)
 Impulsive damping ξ = 2 %, convective damping ξ = 0.5 %
 Impulsive and convective period → EC8-4 Eq. (A.35) and (A.36)
NEED2012
 Base shear and moment → EC8-4 Eq. (A.37) and (A.38)
Hand calculations - Malhotra
 Compressive stress
 Tension force
 Number of anchors
⋅
2
⋅
 Uplift?
 Unachored → EC8-4 A.9: Effect of uplift on stress in the wall
OBE
SSE
NEED2012
Ref.: EN 1998-4:2006 (E) Figure A.11
Response spectra for hand calculations
"
NEED2012
Simplified calculations:
1.5
5%
Max. value of spectrum
Malhotra/EC8-4:
1.0" (elastic response spectrum)
2%
Period
0.4 ?
Partial factors for LNG tank design
OBE (475 yrs)
Limit state
Load
factor
Material
factor
q
Ordinary ULS
Yes
Yes
No (1.0)
No (1.0)
No (1.0)
Yes?
SSE (4975 yrs) Accidental ULS
NEED2012
Implicit analysis - Abaqus
 EC8-4 A.2
Ref.: EN 1998-4:2006 (E) Figure A.1
NEED2012
 Why not implicit analysis with response spectrum step?
 Material model for the fluid?
 Interaction between the fluid and the flexible steel wall?
 Hydrodynamic pressure: Motion of the fluid due to seismic excitation is
preserved as "snapshot" of max. pressure ("pushover" analysis)
Implicit analysis - Abaqus
 The rigid impulsive
(hydrodynamic) pressure is
applied on the tank wall for the
acceleration from the elastic
response spectrum
 The LNG fluid is also applied as a
hydrostatic pressure
 A contact algorithm is applied
between the tank bottom and an
analytical rigid surface, allowing
for separation
 Base shear and moment
 corresponds well with Malhotra's
simplified method
NEED2012
Implicit analysis - Abaqus
 Stresses in tank wall and anchors, in addition to uplift may be studied
NEED2012
 Results obtained from implicit analysis are in good agreement with
hand calculations
 SSE: Uplift and stress in wall OK with anchors, not OK without. Unanchored
case: Highly increased stresses due to extensive deformations
 OBE: OK with and without anchors. Unanchored case: Increased
compressive stress is moderate
 An implicit analysis is more conservative than an explicit analysis. It is
in good agreement with hand calculations and may not give any new
information of the behaviour that can be found by simplified methods.
Summary
 Several types of calculations/analyses - benefits and limitations
 Simplified hand calculations
 Simplified procedure - Malhotra
 Implicit analysis
 Explicit analysis
 Which results are trustworthy?
 Unachored tanks: Increased compressive stress when uplifted
(Eurocode, implicit model (moderate!))
 Anchored tanks: Increased compressive stress due to tension in
anchors (explicit model)
NEED2012
Summary (continued)
Overturning moment
[MNm]
Hand calculations
(Malhotra)
Base shear [MN∙10]
Abaqus implicit
Tension in anchoring
[kN]
NEED2012
Abaqus explicit
Compression in tank
wall (with anchors)
[MPa ∙10]
0
500
1000
Conclusions
 Calculation method may govern the decisions regarding the necessity
of anchoring the tank
 Advanced FE methods (explicit analyses) tend to give reduced values of
the governing parameters (hand calculations are more conservative)
 The complexity of explicit analyses is very high and need a lot of
engineering time
NEED2012