Question

A soil profile above the rock surface for a ${30}^{\circ }$ infinite slope is shown in the figure where $S_u$ is the undrained shear strength and ${\gamma }_t$ is unit weight. The slip will occur at a depth of (assume $\varphi =0$)

• A. $3m$
• B. $4m$
• C. $6m$
• D. $8m$

Answer 1

The correct option is B $4m$

At soil A

$\tau ={\gamma }_{t}z\cos \beta \sin \beta$

At 5 m depth

$\tau =17\times 5\times \cos {30}^{\circ }\times \sin {30}^{\circ }$

$=36.80kN/m^2$

$S_u=30kN/m^2$

$S_u<\tau \text{so slip occurs in 1st layer}$

Let failure be at x m in soil A



${\tau }_x=S_u$

$17\times x\times \cos {30}^{\circ }\times \sin {30}^{\circ }=30$

$x=4.07m\simeq 4.0m$