The exact method involves the solution of fourth order equation, which is quite laborious. For practical problems simplified method of structure of cantilever sheet pile walls is generally used. In the simplified method the passive pressure is replaced by concentrated load acting at the bottom of the pile. The simplified method arrangement is shown in Fig,1 above. Taking moments of all the forces about the base of the pile we get,
KPD3 – Ka (H + D)3 = 0 ———- (2)
The solution of the above Eq.(9) gives the value of D, which is at least a guide for the depth of penetration. The depth calculated should be increased by at least 20 % to provide a factor of safety and to allow extra length to develop the passive resistance R. The data on depth of penetration is applicable to cohensionless soils with no hydrostatic pressure as suggested by Henry is given in Table 1 below.
Table 1 Approximate depths of embedment as given by Henry
Angle of internal friction, degrees ( É¸ )
Depth of Penetration (D)