Governing equation:

Governing equation:Equilibrium of force in horizontal direction

Equilibrium of force in vertical direction

Equilibrium of moment about some point

Cantilever sheet pile wall

Equation for calculation in the cantilever sheet pile wallActive earth pressure coefficient can be found from this equation when soil surface in horizontal direction and wall in vertical direction (= 0)

Passive earth pressure coefficient can be found from the passive earth pressure reduction factor time the constant. These information depend on the friction angle of wall and ratio of angle of soil surface from horizontal plane with soil friction angle (=0), angle of wall from horizontal plane (=90), and ratio of friction angle of soil and wall with friction angle of soil (=1/2). The information is in the table.

kreduction factorkp

101.640.9291.52

152.190.8811.93

203.010.8242.48

254.290.7593.26

306.420.6864.40

3510.20.6036.15

4017.50.5128.96

4533.50.41413.87

5074.30.31323.26

INCLUDEPICTURE "http://www.ce.cmu.edu/~sj2/12-740/project/specific/equati3.gif" \* MERGEFORMATINET X axis is the value of friction angle of soil. Y axis is the value of passive earth pressure coefficient. Left graph is from the information in the table. Right graph is from the same information but use trend line order 5.

After plot this information in Excel and use the trend line of power order 5 the find the equation for this series of information. I get this equation for kpkp = 7.702*10-7 5 - 9.1*10-5 4 + 0.004355 3 - 0.0965 2 + 1.0772 3.1148Active and Passive earth pressure can be found from the production of the soil specific weight and the active or passive earth pressure coefficient

Hydrostatic earth pressure can be found from the active earth pressure time the height of soil.

The point that active earth pressure is equal to the passive earth pressure

The resultant of the forces action about the point that active pressure is equal to the passive pressure. The result of summation of force from distance d + m or point A.

The location for the force Ph is found from taking moment about the point A by using the triangle area rule.

Use the equilibrium of moment about point A to find the depth of penetration (x).

Equation for solving depth of penetration (x) in the iteration method

Find the zero-shear point by using the equilibrium of force in horizontal direction. We will get the depth b.

The maximum moment occurs at the zero-shear point. Take moment at the zero-shear point.

Minimum section modulus can be found by dividing the maximum moment by the allowable stress of the wall material.

Anchored sheet pile wall

For anchored sheet pile wall, all step is the same as one for the cantilever sheet pile wall except the step and equation for the depth of penetration (x) because the anchored sheet pile is design base on the free earth supported while the cantilever sheet pile design base on the fix earth supported. For the anchored sheet pile wall, moreover, the equation for finding the depth of penetration is from the equilibrium about the anchored rod instead of point A.

Find the tension in the anchored rod by using the equilibrium of the horizontal force.

Find the zero-shear point and the maximum moment about the zero-shear point

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