Question

A 5m high vertical wall has a saturated clay backfill. The saturated unit weight and cohesion of clay are $18kN/m^3$ and 20 kPa, respectively. The angle of internal friction of clay is zero. In order to prevent development of tension zone, the height of the wall is required to be increased. Dry sand is used as backfill above the clay for the increased portion of the wall. The unit weight and angle of internal friction of sand are $16kN/m^3$ and ${30}^{\circ }$, respectively. Assume that the back of the wall is smooth and top of the backfill is horizontal. To prevent the development of tension zone, the minimum height (in m, round off to one decimal place) by which the wall has to be raised, is .

• A. 2.5

Answer 1

The correct option is A 2.5
Let the minimum height of backfill = H







To prevent the development of tension zone the pressure at the junction of clay and sand in the clay will be zero

$K_a\left(forclay\right)=\frac{1-sin{0}^{\circ }}{1+sin{0}^{\circ }}=1$

$So:-2C=K_{a\left(clay\right)}\times {\gamma }_{sand}\times H$

$H=\frac{2C}{{\gamma }_{sand}}=\frac{2\times 20}{16}=2.5m$