Question

Using ${\varphi }_u=0$ analysis and assuming plane failure as shown, the minimum factor of safety against shear failure of a vertical cut of height 4 m in a pure clay having $C_u=120kN/m^{2}and{\gamma }_{sat}=20kN/m^3$ is

• A. 1
• B. 6
• C. 10
• D. 20

Answer 1

The correct option is B 6

${\varphi }_u=0$

$C_u=120kN/m^2$

${\gamma }_{sat}=20kN/m^3$

Height of vertical cut,

H = 4m

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

Maximum unsupported height of excavation

$H_{max}=\frac{4C}{\gamma \sqrt{K_a}}$

$=\frac{4\times 120}{20}=24m$

$FOS=\frac{H_{max}}{H}=\frac{24}{4}=6$