## Example

A vertical 4 m high wall is founded on a relatively impervious soil and is supporting soil with the properties: <j>' = 40°, c' = 0,S — 20°, 7sat = 20kN/m3.

The surface of the retained soil is horizontal and is level with the top of the wall. If the wall is subjected to heavy and prolonged rain such that the retained soil becomes saturated and its surface flooded, determine the maximum horizontal thrust that will be exerted on to the wall:

(i) if there is no drainage system;

(ii) if there is the drainage system of Fig. 6.22d;

(iii) if there is the drainage system of Fig. 6.22e.

Solution

(i) No drainage

As we have been given a value for the angle of wall friction it is more realistic to use the Culmann line construction. The total pressure on the back of the wall will be the summation of the pressure from the submerged soil and the pressure from the water.

Four trial wedges have been chosen and are shown in Fig. 6.25a and the corresponding force diagram in Fig. 6.25b.

Maximum Pa due to submerged soil= 16kN Horizontal component of Pa= 16.0 x cos 20° = 15kN

Horizontal thrust from water pressure — 9.81 x — = 78.5 kN Total horizontal thrust — 93.5 kN/m run of wall

(ii) With vertical drain on back of wall

The flow net for steady seepage from the flooded surface of the soil into the drain is shown in Fig. 6.25c. From this diagram it is possible to determine the distribution of the excess hydrostatic head, hw, along the length of the failure surface of each of the four trial wedges. These distributions are shown in Fig. 6.25d and the area of each diagram times the unit weight of water gives the upward force, Pw, acting at right-angles to each failure plane. The tabulated calculations are:

 Wedge Saturated weight (kN) Pw (kN)
0 0