Q1: The stem of a cantilever retaining wall which retains earth level with top is 6 m. If the angle of repose and weight of the soil per cubic metre are 30° and 2000 kg respectively, the effective width of the stem at the bottom, is

ANS:C - 53.5

To determine the effective width of the stem at the bottom of the cantilever retaining wall, we need to consider the equilibrium of forces acting on the wall, including the horizontal force exerted by the soil and the weight of the wall itself. First, let's calculate the horizontal force exerted by the soil on the wall using Rankine's theory: H=1/2​×γ×H^2×tan^2(δ) Where:

• H is the height of the wall (6 m),
• γ is the unit weight of the soil (2000 kg/m³),
• δ is the angle of repose of the soil (30°).

Substituting the given values: H=1/2​×2000×(6)^2×tan^2(30°) H=6000N/m Next, to find the effective width of the stem at the bottom (B), we set the moment produced by the soil pressure equal to the resisting moment to maintain equilibrium: Overturning moment=Resisting momentOverturning moment=Resisting moment (H×6)=(H×B×B/2​) 6H=1/2​HB^2 12=B^2 B=1root2​ B=3.46m