Question

A 3 m high retaining wall is supporting a saturated sand (saturated due to capillary action) of bulk density $18kN/m^3$ and angle of shearing resistance ${30}^{\circ }$. The change in magnitude of active earth pressure at the base due to rise in ground water table from the base of the footing to the ground surface shall $[{\gamma }_w=10kN/m^3]$

• A. Increase by $20kN/m^2$
• B. Decrease by $20kN/m^2$
• C. Increase by $30kN/m^2$
• D. Decreases by $30kN/m^2$

Answer 1

The correct option is A Increase by $20kN/m^2$

Angle of shearing resistance

$\varphi ={30}^{\circ }$

Active earth pressure coefficient;

$K_a=\frac{1-sin\varphi }{1+sin\varphi }$

$=\frac{1-sin{30}^{\circ }}{1+sin{30}^{\circ }}=\frac{1}{3}$

Active earth pressure at the base,

$P_a=K_a{\sigma }_z$

$=K_a\gamma z$

$=\frac{1}{3}\times 18\times 3$

$=18kN/m^2$

Active earth pressure at the base when water table is at the ground surface

$P{a}_2=K_a{\gamma }_{sub}z+1\times {\gamma }_w\times z$

$=\frac{1}{3}(18-10)\times 3+10\times 3$

$=38kN/m^2$

Change in earth pressure

= 38 - 18

$=20kN/m^2\left(increase\right)$