Section 4: Soil and Water Conservation Engineering
Soil Mechanics
Subtopic: Active and passive earth pressures
Question Statement:
A 3 m high retaining wall supports sandy soil of unit weight 18.5 kN m⁻³. The angle of shearing resistance (ϕ) is 30° and the surface of soil is horizontal. The magnitude of the active thrust (in kN m⁻¹) and its acting point from the top (in m) are
Options:
(A) 27.75 and 1
(B) 249.75 and 1
(C) 27.75 and 2
(D) 249.75 and 2
Official Answer Key:
C
Step-by-Step Solution & Explanation
Rankine's active earth-pressure coefficient: Ka = (1−sinϕ)/(1+sinϕ) = (1−sin30)/(1+sin30) = (1−0.5)/(1+0.5) = 0.5/1.5 = 0.3333. Total active thrust per unit length: Pa = ½×Ka×γ×H² = ½×0.3333×18.5×3² = 27.75 kN/m. For a triangular pressure distribution, the resultant acts at H/3 from the base, i.e. at 2H/3 = 2 m from the top → matching option (C). Option (D) has an order-of-magnitude arithmetic slip (missing the ½ factor twice); (A) has the wrong acting point (H/3 from top instead of from base).
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