Question

A canel having side slopes 1 : 1 is proposed to be constructed in a cohesive soil to a depth of 10m below the ground surface. The soil properties are ${\varphi }_u={15}^{\circ },c_u=12kPa,e=1.0,G=\mathrm{2.65.}$

If taylors stability number $S_n$ is 0.08 and if the canel flows full, the factor of safety with respect to cohesion against failure of the canel bank slopes will be

• A. 3.7
• B. 1.85
• C. 1.0
• D. None of these

Answer 1

The correct option is B 1.85

${\varphi }_f={15}^{\circ }$

$C_u=12kPa$

e = 1.0

G = 2.65

$S_n=0.08$

When canel flows full, soil of canel bank will be in submerged condition

${\gamma }_{sub}=\left(\frac{G-1}{1+e}\right){\gamma }_w$

$=\left(\frac{2.65-1}{1+1}\right){\gamma }_w$

$=9.81\times \frac{1.65}{2}=8.093KN/m^3$

Taylors sability number,

$S=\frac{C_m}{{\gamma }_{sub}.H}$

$=\frac{C_u}{{\gamma }_{sub}.H.FOS}$

$FOS=\frac{C_u}{{\gamma }_{sub}.H.S_n}$

$=\frac{12}{8.093\times 10\times 0.08}$

= 1.85

where,

$C_m=mobilisedcohesion$

$FOS=\frac{C_u}{C_m}$