Course
Year
Version
: S0484/Foundation Engineering
: 2007
: 1/0
Session 15 – 16
SHEET PILE STRUCTURES
SHEET PILE STRUCTURES
Topic:
• Anchored Sheet Pile
• Braced Cut
CALCULATION STEPS
ANCHORED SHEET PILE – FREE – SAND
CALCULATION STEPS
ANCHORED SHEET PILE – FREE – SAND
1. Determine the value of Ka and Kp

2
K a  tan  45  
2



K p  tan 2  45  
2

2. Calculate p1and p2 with L1 and L2 are known
p1   .L1.K a
p2   .L1   '.L2 K a
3. Calculate L3
z  L  L3 
p2
 ' K p  K a 
4. Calculate P as a resultant of area ACDE
5. Determine the center of pressure for the area ACDE ( z )
CALCULATION STEPS
ANCHORED SHEET PILE – FREE – SAND
6. Calculate L4



3P L1  L2  L3   z  l1
L  1,5L l2  L2  L3  
0
 ' K p  K a 
3
4
2
4
Determination of penetration depth of sheet pile (D)
Dtheoretical = L3 + L4
Dactual = (1.3 – 1.4) Dtheoretical
Determination of anchor force
F = P – ½ [’(Kp – Ka)]L42
CALCULATION STEPS
ANCHORED SHEET PILE – FREE – CLAY
CALCULATION STEPS
ANCHORED SHEET PILE – FREE – CLAY
1. Determine the value of Ka and Kp

2
K a  tan  45  
2



K p  tan 2  45  
2

In case of saturated soft clay with internal friction angle () = 0, we got
Ka = Kp = 1
2. Calculate p1and p2 with L1 and L2 are known
p1   .L1.K a
p2   .L1   '.L2 K a
3. Calculate the resultant of the area ACDE (P1) and z1 (the center of
pressure for the area ACDE)
CALCULATION STEPS
ANCHORED SHEET PILE – FREE – CLAY
4. Calculate p6
p6  4c  L1   ' L2 
Determination of penetration depth of sheet pile (D)
p6.D2 + 2.p6.D.(L1+L2-l1) – 2.P1.(L1+L2-l1-z1) = 0
Determination of anchor force
F = P1 – p6 . D
CALCULATION STEPS
ANCHORED SHEET PILE – FIXED – SAND
J
CALCULATION STEPS
ANCHORED SHEET PILE – FIXED – SAND
1. Determine the value of Ka and Kp

2
K a  tan  45  
2



K p  tan 2  45  
2

2. Calculate p1and p2 with L1 and L2 are known
p1   .L1.K a
p2   .L1   '.L2 K a
3. Calculate L3
z  L  L3 
p2
 ' K p  K a 
CALCULATION STEPS
ANCHORED SHEET PILE – FIXED – SAND
4. determine L5 from
the following curve (L1
and L2 are known)
CALCULATION STEPS
ANCHORED SHEET PILE – FIXED – SAND
5. Calculate the span of the equivalent beam as l2 + L2 + L5 = L’
6. Calculate the total load of the span, W. This is the area of the
pressure diagram between O’ and I
7. Calculate the maximum moment, Mmax, as WL’/8
CALCULATION STEPS
ANCHORED SHEET PILE – FIXED – SAND
8. Calculate P’ by taking the moment about O’, or
1
P' 
L'
(moment of area ACDJI about O’)
9. Calculate D as
D  L5  1.2
6 P'
K p  K a  '
10. Calculate the anchor force per unit length, F, by taking the moment
about I, or
1
F
L'
(moment of area ACDJI about I)
BRACED CUT
Type of Braced cut
BRACED CUT
Type of Braced cut
PRESSURE ENVELOPE
Cuts in Sand
pa = 0.65HKa
Where:
 = unit weight
H = height of the cut
Ka = Rankine active pressure coefficient
= tan2(45-/2)
PRESSURE ENVELOPE
• Cuts in Stiff Clay
pa = 0.2H to 0.4H
Which is applicable to the condition
H
4
c
PRESSURE ENVELOPE
• Cuts in Stiff Clay
The pressure pa is the larger of
  4c 

pa  H 1  
  H 
or
pa  0.3H
Where:
 = unit weight of clay
c = undrained cohesion (=0)
Which is applicable to the condition
H
c
4
PRESSURE ENVELOPE
Limitations:
1. The pressure envelopes are sometimes referred to as
apparent pressure envelopes. The actual pressure
distribution is a function of the construction sequence
and the relative flexibility of the wall.
2. They apply to excavations having depths greater than
about 20 ft (6m)
3. They are based on the assumption that the water table
is below the bottom of the cut
4. Sand is assumed to be drained with zero pore water
pressure
5. Clay is assumed to be undrained and pore water
pressure is not considered
PRESSURE ENVELOPE
• Cuts in Layered Soil

1
 s .K s .H s2 . tan s  H  H s .n'.qu
2H
1
 av   s .H s  H  H s  c 
H
Where:
cav 

H = total height of the cut
s = unit weight of sand
Hs = thickness of sand layer
Ks = a lateral earth pressure coefficient for the
sand layer (1)
s = friction angle of sand
qu = unconfined compression strength of clay
n’ = a coefficient of progressive failure (ranging
from 0.5 to 1.0; average value 0.75)
c = saturated unit weight of clay layer
PRESSURE ENVELOPE
• Cuts in Layered Soil
1
c1.H1  c2 .H 2  ...  cn .H n 
H
1
  1.H1   2 .H 2   3 .H 3  ...   n .H n 
H
cav 
 av
Where:
c1, c2,…,cn = undrained cohesion in layers 1,2,..,n
H1, H2,…,Hn = thickness of layers 1, 2, …, n
1, 2, … n = unit weight of layers 1, 2, … , n
DESIGN OF VARIOUS COMPONENTS OF
A BRACED CUT
Struts
- Should have a minimum vertical spacing of about 9 ft
(2.75 m) or more.
- Actually horizontal columns subject to bending
- The load carrying capacity of columns depends on the
slenderness ratio.
- The slenderness ratio can be reduced by providing
vertical and horizontal supports at intermediate points
- For wide cuts, splicing the struts may be necessary.
- For braced cuts in clayey soils, the depth of the first strut
below the ground surface should be less than the depth
of tensile crack, zc
DESIGN OF VARIOUS COMPONENTS OF
A BRACED CUT
Struts
General Procedures:
1. Draw the pressure envelope for the braced cut
DESIGN OF VARIOUS COMPONENTS OF
A BRACED CUT
Struts
General Procedures:
2. Determine the reactions for the two simple cantilever
beams (top and bottom) and all the simple beams
between. In the following figure, these reactions are A,
B1, B2, C1, C2 and D
DESIGN OF VARIOUS COMPONENTS OF
A BRACED CUT
Struts
General Procedures:
3.
The strut loads may be calculated as follows:
PA = (A)(s)
PB = (B1+B2)(s)
PC = (C1+C2)(s)
PD = (D)(s)
where:
PA, PB, PC, PD = loads to be taken by the individual struts at level
A, B, C
and D, respectively
A, B1, B2, C1, C2, D = reactions calculated in step 2
s = horizontal spacing of the struts
4.
Knowing the strut loads at each level and intermediate bracing
conditions allows selection of the proper sections from the steel
construction manual.
DESIGN OF VARIOUS COMPONENTS OF
A BRACED CUT
Sheet Piles
General Procedures:
1.
Determine the maximum bending
moment
2.
Determine the maximum value of the
maximum bending moments (Mmax)
obtained in step 1.
3.
Obtain the required section modulus of
the sheet piles
S
M max
 all
where  all  allowable flexural stress of the sheet pile material
4.
Choose the sheet pile having a section
modulus greater than or equal to the
required section modulus
DESIGN OF VARIOUS COMPONENTS OF
A BRACED CUT
Wales
At level A, M max
At level B, M max
At level A, M max
At level A, M max

As 2 

8

B1  B2  s 2

8

C1  C2  s 2

8

D s2

8
 
 
 
then
S
M max
 all
Where A, B1, B2, C1, C2, and D are the reactions under the struts per unit length
of the wall
EXAMPLE
Refer to he braced cut shown in the following figure:
a.
Draw the earth pressure envelope and determine the strut loads.
(Note: the struts are spaced horizontally at 12 ft center to center)
b.
Determine the sheet pile section
c.
Determine the required section modulus of the wales at level A (all
= 24 kip/in2)
EXAMPLE
EXAMPLE
EXAMPLE
EXAMPLE