Client: (Client Name Here)Project: (Project Name Here)Description: (Description of what is being calculated)

Sheet: _____ of _____

Date: mm/dd/yyJob No: ########

By: (Author) Chkd By: _____

Cantilever Sheet Pile Wall in Cohesionless Soil

ReferenceThese calculations are in accordance with IBC 2006 and ASCE 7-05. They are based on theprocedures outlined in ACI 350.3-06, with modifications as required per ASCE 7-05.

The resulting forces are Strength Level Forces.

Task : 1) Design length of a cantilever sheet 2) Select sheet pile section

C 0Cs - Cohesion of Soil

(For Cohesionless soil, C is zero)

Note : The calculations are done for 1ft strip width.

CalculationsPage 1 of 7

PF - 6.6.#

Client: (Client Name Here)Project: (Project Name Here)Description: (Description of what is being calculated)

Sheet: _____ of _____

Date: mm/dd/yyJob No: ########

By: (Author) Chkd By: _____

Design Parameters Reference

h = Height of Pile above dredge line h 12 ft

D = Height of Pile below dredge line

L1 = Height of Pile above water table

L2 = Height of Pile above dredge line upto water-table

L3 = Height of Pile above dredge line

L4 = Height of Pile below dredge line D - L3

= Unit weight of homogeneous Soil γ 115pcf

sat = Specific unit weight of Soil γsat 52.6pcf

ϕ = Angle of internal soil friction ϕ 30°

Ka = Active earth pressure Coefficient Ka tan 45°( )ϕ

2

2

0.333

Kp = Passive earth pressureCoefficient Kp = 1/ Ka Kp tan 45°( )ϕ

2

2

3

K'p = Coefficient K'p = Kp/SF SF = 1.5 - 2.0K'p

Kp

1.52

Surcharge:

q = Soil surcharge q 0psf

The active earth pressure at bottom of excavation is;

Pa = γ.h.Ka + q.Ka Pa γ h Ka q Ka

Pa 460 psf

The lateral force Ha1 is calculated asHa1 γ Ka

h2

2 q Ka h

Ha1 = γ.h.Ka.h/2 + q.Kah

Ha1 2.76 103

plf

Below the bottom of excavation, the sheet pile is subjected to active pressure on the earthside and passive pressure on the excavation side. Since the passive pressure is larger thanactive pressure, the lateral pressure on the earth side decreases.

CalculationsPage 2 of 7

PF - 6.6.#

Client: (Client Name Here)Project: (Project Name Here)Description: (Description of what is being calculated)

Sheet: _____ of _____

Date: mm/dd/yyJob No: ########

By: (Author) Chkd By: _____

At depth "a" below the dredge line, the earth pressure is zero. The depth "a" is calculated as

Referencea

Pa

γ Kp Ka

a 1.5 ft

When the sheet pile rotates away from the earth side, there are active on the earth side and passive pressure on the other side i.e, excavation side

The corresponding lateral force Ha2 Paa

2

Ha2 345 plf

Assume Trial Depth Y (choose arbitrary value for "Y") Y 10.55ft

The pressure at the bottom of sheet pile on the excavation side P1

P1 γ Kp Ka Y 3.235 103

psf P1 3.235 103

psf

The pressure at the bottom of sheet pile on the earth side P2

P2 γ Kp h a Y( ) q Kp γ Ka a Y( ) 7.835 103

psf

P2 7.835 103

psfDerive the depth Z from ΣFx = 0

Summarize lateral forces, ΣFx = Ha1 Ha2 Hp1 Hp2 = 0

Hence solving the equation for Z ZP1 Y 2 Ha1 Ha2

P1 P2 Z 2.522 ft

Derive the depth of embedment D = Y + a

Verify the assumed depth Y and Z calculated above from ΣMO = 0

Both P1 and P2 are function of Y, hence to determine Y, take moment about bottom of sheet pile "O"

and equate the resultant "R" to zero or closed to zero

The depth Y can be determined from a trial and error process.

Close to "zero",Hence OKR Ha1

h

3a Y

Ha22 a

3Y

P1 Y

2

6 P1 P2 Z

2

6 3.908 lbf

Check_R "OK" R 0=if

"Revise Y" otherwise

CalculationsPage 3 of 7

PF - 6.6.#

Client: (Client Name Here)Project: (Project Name Here)Description: (Description of what is being calculated)

Sheet: _____ of _____

Date: mm/dd/yyJob No: ########

By: (Author) Chkd By: _____

ReferenceThe embedment depth "D" D Y a 12.05 ft D 12.05 ft

The design depth of sheet pile (Lp)

Fs is factor of safety from 1.2 to 1.4 Fs 1.2 Lp h Fs D

Lp 26.46 ft

Selection of Sheet Pile Section : (Based on maximum moment and shear)

Find maximum shear force

The maximum shear force is usually located at D where lateral earth pressure change from active to passive.

Vmax Ha1 Ha2 Vmax 3.105 103

plf

Find maximum moment which occurs at the point of zero shear:

The maximum moment locates at where shear stress equals to zero between C and D shown in figure above

Assume the maximum moment located at a distance "y" below point C, then

Ha1 Ha2 γ Kp Ka y

2

2 y

2 Ha1 Ha2

γ Kp Ka y 4.5 ft

ΣMmax Ha1h

3a y

Ha22 a

3y

γ Kp Ka y

3

6 ΣMmax 24.84

kip ft

ft

Determine minimum section modulus:

Allowable Bending stress σallow 32ksi

Required Section Modulus SΣMmax

σallow

S 9.32in

3

ft

Ssp 5.5in

3

ft

Select sheet pile section modulus per foot of wall

check "OK" Ssp Sif

"FAILS" otherwise

check "FAILS"

CalculationsPage 4 of 7

PF - 6.6.#