# Cantilever Sheet Pile Walls Penetrating Sandy Soils

Courses > Foundation Analysis and Design > Sheet-pile Walls: Cantilevered and Anchored > Cantilever Sheet Pile Walls Penetrating Sandy Soils

### Introduction

Connected or semi-connected sheet piles are often used to build continuous walls for waterfront structures that range from small waterfront pleasure boat launching facilities to large dock facilities. In contrast to the construction of other types of retaining wall, the building of sheet-pile walls does not usually require dewatering of the site. Sheet piles are also used for some temporary structures, such as braced cuts. Several types of sheet pile are commonly used in construction: (a) wooden sheet piles, (b) precast concrete sheet piles, and (c) steel sheet piles. Aluminum sheet piles are also marketed.

Sheet-pile walls may be divided into two basic categories: (a) cantilever and (b) anchored.

### Concepts and Formulas

Variation of net pressure diagram and variation of moment versus depth of a cantilevered sheet pile wall is shown below:

The objective in analysis of sheet pile walls is to get to a depth of embedment (D) sufficient for the wall stability. For this purpose, one needs to know the lateral earth pressure theory first.

Step-by-step procedure for obtaining pressure diagram is given below:

1. Calculate Ka and Kp (active and passive earth pressure), based on Rankine's method or Coulomb's method;

2. Calculate horizontal stress at point "C" and "D" respectively as:

$\sigma'_1=\gamma L_1 K_a$

$\sigma'_2=(\gamma L_1 +\gamma_b L_2) K_a$

3. Calculate L3

$L_3 = \frac{\sigma'_2}{\gamma_b (K_p-K_a)}$

4. Calculate P equal to the area of ACDE.

5. Calculate the distance of P from point "E" (called z-bar on figure), by taking the moment about point "E" (P has to induce equal moment to the pressure of ACDE area).

6. Calculate

$\sigma'_5=(\gamma L_1 + \gamma_b L_2)K_p + \gamma_b L_3 (K_p-K_a)$

7. Calculate

$A_1 = \frac{\sigma'_5}{\gamma_b (K_b-K_a)}$

$A_2 = \frac{8P}{\gamma_b (K_b-K_a)}$

$A_3 = \frac{6P[2\bar{z} \gamma_b (K_p-K_a) +\sigma'_5]}{\gamma_p^2 (K_b-K_a)^2}$

$A_4= \frac{P(6\bar{z}\sigma'_5+4P)}{\gamma_b^2 (K_p-K_a)^2}$

8. Solve the following equation to get L4

$L_4^4+A_1L_4^3-A_2L_4^2-A_3L_4-A_4=0$

9. Calculate

$\sigma'_4=\sigma'_5+\gamma_b L_4(K_p-K_a)$

10. Calculate

$\sigma'_3=L_4(K_p-K_a)\gamma_b$

11. Obtain L5

$L_5=\frac{\sigma'_3 L_4-2P}{\sigma'_3+\sigma'_4}$

12. Draw the pressure diagram like the one given above, for which the depth of embedment is

D = L3 + L4

Refer to Factors of Safety for Cantilevered Sheet Pile Walls to learn how to apply factors of safety

There is an EXCEL spreadsheet developed to the abovementioned procedure almost automatically, you can download it from the Files section below this article

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