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Retaining wall problem example 3

A retaining wall has a vertical back and is 7.32 m high. The soil is sandy loam of unit weight 17.3 kN/m3. It has a cohesion of 12 kN/m2 and 0 = 20°. Neglecting wall friction, determine the active thrust on the wall. The upper surface of the fill is horizontal.
(Refer to Fig. 11.14) When the material exhibits cohesion, the pressure on the wall at a depth z is given by (Eq. 11.30)
sol 1
When the depth is small the expression for z is negative because of the effect of cohesion up to a
theoretical depth z0. The soil is in tension and the soil draws away from the wall.
sol 2
Theoretically the area of the upper triangle in Fig. 11.14(b) to the left of the pressure axis represents a tensile force which should be subtracted from the compressive force on the lower part of the wall below the depth ZQ. Since tension cannot be applied physically between the soil and the wall, this tensile force is neglected. It is therefore commonly assumed that the active earth pressure is represented by the shaded area in Fig. 1 1 . 14(c). The total pressure on the wall is equal to the area of the triangle in Fig. 1 1.14(c).
sol 3