Question

A wall with smooth vertical back and 10 meters height retains cohesionless material with a horizontal surface. The cohesionless material weights $4.91kN/m^3$ and has an angle of internal friction of ${30}^{\circ }.$ The total active earth pressure is

• A. 81. 585 kN/m length of wall
• B. 91. 585 kN/m length of wall
• C. 40.743 kN/m${}^2$
• D. 8.158 kN/m${}^2$

Answer 1

The correct option is A 81. 585 kN/m length of wall

$P_a=\frac{1}{2}{K}_a\gamma h^2{K}_a=\frac{1-\sin \varphi }{1+\sin \varphi }=\frac{1-\sin {30}^{\circ }}{1+\sin {30}^{\circ }}=\frac{1}{3}\therefore P_a=\frac{1}{2}\times \frac{1}{3}\times 4.91\times {10}^2=81.83kN/m\text{Length of wall}$