Question

In a cohesionless soil deposit having a unit weight of $1.5t/m^3$ and an angle of internal friction of ${30}^{\circ },$ the active and passive lateral earth pressure intensities $\left(int/m^2\right)$ at a depth of 10 m will, respectively, be

• A. 15 and 5
• B. 5 and 15
• C. 10 and 20
• D. 20 and 10

Answer 1

The correct option is B 5 and 15

$\begin{array}{cc}& \text{Maximum active pressure,}\\ p_A& =K_A{\sigma }_z\\ \text{where}{K}_A& =\frac{1-\sin \varphi }{1+\sin \varphi }\\ & \text{Maximum passive pressure,}\\ p_P& =K_P{\sigma }_z\\ \text{where}{k}_P& =\frac{1+\sin \varphi }{1-\sin \varphi }\\ \text{For}\varphi & ={30}^{\circ },K_A=\frac{1}{3}\\ \text{and}{K}_P& =3\\ {\sigma }_z& =1.5\times 10=15t/m^2\\ \therefore p_A& =\frac{1}{3}\times 15=5t/m^2\\ p_P& =3\times 15=45t/m^2\end{array}$
$\text{In the case of passive pressure full strain}\text{mobilization may not taken place and so actual}\text{passive pressure will be less than maximum value.}$