## Ccz

Fig. 6.15 The effect of cohesion on active pressure.

At depth, h, both soils are subjected to the same major principal stress a\ = 7h. The minor principal stress for the cohesionless soil is <73 but for the cohesive soil it is only <73c, the difference being due to the cohesive strength, c, that is represented by the lengths AB or EF.

Consider triangle HGF:

Difference between <73 and a^, HF

Hence the active pressure, pa, at depth h in a soil exhibiting both frictional and cohesive strength and having a horizontal upper surface is given by the expression:

This expression was formulated by Bell (1915) and is often referred to as Bell's solution.

The active pressure diagram for such a soil is shown in Fig. 6.16. The negative values of pa extending down from the top of the wall to a depth of hc indicate that this zone of soil is in a state of suction. However soils cannot

really withstand tensile stress and cracks may form within the soil. It is therefore unwise to assume that any negative active pressures exist within the depth hc. For design purposes the active pressure value over the depth hc should be taken as equal to zero.

### 6.5.2 Depth of the tension zone

In Fig. 6.16 the depth of the tension zone was given the symbol hc. It is possible for cracks to develop over this depth and a value for hc is often required.

If pa in the expression

Pa = Ka7hc - 2c tan is put equal to zero we can obtain an expression for hc: 2C |45"-i he = —— tan

0 0