## Soil Mechanics Exercises

A proposed cutting is to have the dimensions shown in Fig. 5.32. The soil has the following properties: </> = 15°, c = 13.5 kN/m2, 7 = 19.3 kN/m3.

Determine the factor of safety against slipping for the slip circle shown (i) ignoring tension cracks and (ii) allowing for a tension crack.

Investigate the stability of the embankment shown in Fig. 5.33. The embankment consists of two soils, both with bulk densities of 19.3 kN/m3;

the upper soil has c = 7.2kN/m2 and 0=30°, whilst the lower soil has c = 32.5 kN/m2 and 0 = 0°. Analyse the slip circle shown (ignore tension cracks).

Answer F = 1.2 EXERCISE 5.3

The surface of a granular soil mass is inclined at 25° to the horizontal. The soil is saturated throughout with a water content of 15.8 per cent, particle specific gravity of 2.65 and an angle of internal friction of 38°.

At a depth of 1.83 m water is seeping through the soil parallel to the surface.

Determine the factor of safety against slipping on a plane parallel to the surface of the soil at a vertical depth of 3.05 m below the surface.

What would be the factor of safety for the same plane if the level of the seeping water lifted up to the surface of the soil?

Answer 0.91 EXERCISE 5.4

Using Taylor's curves, determine the factor of safety for the following slopes (assume D = 1.0):

H = 30.5 m, (3 = 40°, c = 10.8 kN/m2, <p = 35°, 7 = 14.4 kN/m3

Answer Approximately 1.25

H = 15.25 m, j3 = 20°, c = 24.0 kN/m2, <f> = 0°, 7 = 19.3 kN/m3

Answer 0.8

H = 22.8m, ¡3 = 30°, c = 9.6kN/m2, </> = 25°, 7 = 16.1 kN/m3 Answer 1.2

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