## Numerical on design of a Retaining wall

**Q. **Determine suitable dimensions of a cantilever retaining wall, which is required to support a bank of earth 4.0 m high above the ground level on the toe side of the wall. Consider the backfill surface to be inclined at an angle of 15^{o} with the horizontal. Assume good soil for foundation at a depth of 1.25 m below the ground level with a safe bearing capacity of 160 kN/m^{2}. Further assume the backfill to comprise granular soil with a unit weight of 16 kN/m^{3} and an angle of shearing resistance of 30^{o}. Assume the coefficient of friction between soil and concrete to be 0.5.

**SOLUTION**

**2. Preliminary proportions**

• Thickness of footing base slab ≈ 0.08h = 0.08 × 5.25 = 0.42 m

Assume a thickness of 420 mm.

• Assume a stem thickness of 450 mm at the base of the stem, tapering to a value of 150 mm at the top of the wall.

• For an economical proportioning of the length L of the base slab, it will be assumed that the vertical reaction R at the footing base is in line with the front face of the stem. For such a condition, (assuming the height above top of wall to be about 0.4 m), the length of the heel slab (inclusive of stem thickness)

• Assuming a triangular base pressure distribution,

**L = 1.5X = 3.0 m
**

**3. Stability against overturning**

**= 5250 2000 tan 15 ^{o} = 5786 mm**