Mathcad - New Sheet Pile Design - MATHCAD TEMPLATE

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

Sheet: _____ of _____  Date: mm/dd/yy Job No: ######## By: (Author) Chkd By: _____ 

Cantilever Sheet Pile Wall in Cohesionless Soil These calculations are in accordance with IBC 2006 and ASCE 7-05. 7-05. They are based based on the procedures procedu res outlined in ACI A CI 350.3-06, with modific ations as requ required ired per ASCE 7-05 7-05..

Reference

The resulting forces are Strength Level Forces.

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

Cs - Cohesion of Soil

C  0

(For Cohesionless soil, C is zero) Note : The calculations are done for 1ft strip width.

Calculations Page 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/yy Job No: ######## By: (Author) Chkd By: _____ 

Design Parameters

Reference

h  12  ft

h = Height of Pile above dredge line 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

ϕ   K a  tan ( 45°)   0.333 2   

Kp = Passive earth pressureCoefficient

ϕ   K  3  p  tan ( 45°)  2   

2

2

K'p = Coefficient

K' p = K   p/SF

K   p = 1/ K a

SF = 1.5 - 2.0 K' p 

K   p 1.5



2

Surcharge: q = Soil surcharge

q  0psf  

The active earth pressure at bottom of excavation is; Pa = γ.h.Ka + q.Ka

Pa  γ  h  K a  q  K a Pa  460 psf 

The lateral force Ha1 is calculated as Ha1 = γ.h.Ka. h/2 + q.Ka h

Ha1  γ  K a 

h

2

2

 q  K a  h

3

Ha1  2.76  10 plf 

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

Calculations Page 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/yy Job No: ######## By: (Author) Chkd By: _____ 

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

Pa

a 

a



γ   K   p

Reference



K 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 Ha2  Pa 

The corresponding lateral force

a 2

Ha2  345 plf 

 Ass ume Trial Depth Y

Y  10.55ft

(choose arbitrary value for "Y")

The pressure at the bottom of sheet pile on the excavation side P1 P1  γ   K   p



K a  Y  3.235



3

10 psf 

P1



3.235

3



10 psf 



10 psf 

The pressure at the bottom of sheet pile on the earth side P2 P2  γ  K   p  ( h

a

Y)

 q  K  p  γ  K a  ( a 

Y)



7.835



3

10 psf  P2



7.835

3

Derive the depth Z from ΣFx = 0 Summarize lateral forces,

ΣFx

= Ha1  Ha2  H p1

Z 

Hence solving the equation for Z



H p2 = 0

P1  Y  2  Ha1  Ha2 P1



Z

P2



2.522 ft

Derive the depth of embedment D = Y + a Verify the as sumed 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 t rial and error process.

 h

 2  a

R  Ha1   a  Y   Ha2  3      

3

 Y    

2

P1  Y 6

2



P1  P2 

Z

Check_R 

6



3.908 lbf 

Close to "zero", Hence OK

"OK" if  R = 0 "Revise Y" otherwise

Calculations Page 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/yy Job No: ######## By: (Author) Chkd By: _____ 

D  Y  a

The embedment depth "D"



12.05 ft

Reference

D  12.05 ft

The design depth of sheet pile (Lp) Fs  1.2

Fs is factor of safety from 1.2 to 1.4

L p  h L p





Fs  D

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. 3 Vmax  Ha1  Ha2 Vmax  3.105  10 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  Ass ume the maximum moment locat ed at a dist ance "y" below point C, then

 Ha1  Ha2 

γ   K   p



K a  y

2

2



y 

2   Ha1  Ha2

γ   K   p



K a

3 γ   K  h 2a  p  K a  y         ΣM max  Ha1   a  y  Ha2  y  6  3     3  

y



4.5 ft

ΣM max



24.84

kip  ft ft

Determine minimum section modulus: σallow  32ksi

 Allowable Bending stress Required Section Modulus

S 

ΣM max σallow

3

9.32 

in

Ssp  5.5

in

S



ft 3

Select sheet pile section modulus per foot of wall

check 

"OK" if  Ssp

S

check



ft

"FAILS"

"FAILS" otherwise

Calculations Page 4 of 7

PF - 6.6.#