Question

The depth of tension crack in a soft clay $({\varphi }_u=0)$ is

• A. $\frac{4C_u}{\gamma }$
• B. $\frac{2C_u}{\gamma }$
• C. $\frac{C_u}{\gamma }$
  
• D. $\frac{C_u}{2\gamma }$

Answer 1

The correct option is B $\frac{2C_u}{\gamma }$

We know that

$P_a=K_a\gamma z-2c\sqrt{K_a}$

$at,z=0P_a=-2c\sqrt{K_a}$

and, $P_a=0at$

$z=z_0=\frac{2c}{\gamma \sqrt{K_a}}...\left(i\right)$


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

Given, $\varphi =0$

$K_a=\frac{1-sin{0}^{\circ }}{1+sin{0}^{\circ }}=1$

From (i)

Depth of tension crack

$z_0=\frac{2c}{\gamma \sqrt{1}}=\frac{2c}{\gamma }$

Note : Another most important observation can be made from the above pressure distribution diagram that net total active earth pressure is zero upto a depth $2z_0$. which implies that we can make an unbraced cut in clayey soil upto a depth of $2z_0$

Hence critical depth of vertical cut in a cohesive soil is given by

$H_c=2z_0=\frac{4c}{\gamma \sqrt{K_a}}$