Question

For the construction of a highway a cut is to be made as shown in the figure.
The soil exhibits c' = 20kPa, ${\varphi }^{\prime }={18}^{\circ }$, and the undrained shear strength = 80 kPa. The unit weight of water is 9.81 $kN/m^3$. The unit weights of the soil above and below the ground water table are 18 and $20kN/m^3$, respectively. If the shear stress at a point A is 50 kPa, the factors of safety against the shear failure at this point, considering the undrained and drained conditions respectively, would be

• A. 1.6 and 0.9
• B. 0.9 and 1.6
• C. 0.6 and 1.2
• D. 1.2 and 0.6

Answer 1

The correct option is A 1.6 and 0.9

Case-I : Undrained condition

$F.O.S=\frac{resistingshearstrength}{Actingshearstress}$

$=\frac{80}{50}=1.6$

Case-II: Drained condition

$F.o.S=\frac{\overline{\sigma }tan{\varphi }^{\prime }+c^{\prime }}{Actingshearstress}$

$=\frac{[2\times 18+4(20-9.81\left)\right]\times tan{18}^{\circ }+20}{50}$

= 0.9