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Question
A retaining wall 6m high supports a backfill with a surcharge angle of 10. The back of the wall is inclined to the vertical at a positive batter angle of 6°. If the angle of wall friction is 8°, the resultant active earth pressure will act at distance 2 m above base and inclined to the vertical at an angle of :
A.
83°
B.
80°
C.
84°
D.
76°
Answer ( Option D)

76°

Solution

The force acting on the wedge of soil are as follows:
1. Weight of soils wedge 'w' acting vertically downward.
2. Resultant thrust 'Pa' between the soil and wall acting at downward angle 'd' with the normal to the inclined face of wall.
3. Resultant soil reaction 'R' acting at downward acting of 'f' with the normal to slip plane.
Where,
β = Surcharge angle
θ = Angle made by inclined face of wall with vertical.
δ = Angle of friction between wall and soil
Φ = Friction angle of soil
λ = Angle made by slip plane with horizontal
Hence, the resultant active earth pressure 'Pa' inclined to the vertical 'w' at an angle of,
= 90 - θ - δ
= 90 - 6 - 8 = 76°

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