Question

In cohesive soils the depth of tension crack $\left(Z_{cr}\right)$ is likely to be

• A. $Z_{cr}\ge \frac{2C}{\gamma }tan({45}^{\circ }-\frac{\varphi }{2})$
• B. $Z_{cr}\ge \frac{2C}{\gamma }tan({45}^{\circ }+\frac{\varphi }{2})$
• C. $Z_{cr}\ge \frac{4C}{\gamma }tan({45}^{\circ }-\frac{\varphi }{2})$
• D. $Z_{cr}\ge \frac{4C}{\gamma }tan({45}^{\circ }+\frac{\varphi }{2})$

Answer 1

The correct option is B $Z_{cr}\ge \frac{2C}{\gamma }tan({45}^{\circ }+\frac{\varphi }{2})$

Depth of tension crack

$Z_0=\frac{2c}{\gamma \sqrt{K_a}}$

Where,

$K_a=\frac{1-sin\varphi }{1+sin\varphi }=ta{n}^2(45-\frac{\varphi }{2})$

$=\frac{1}{ta{n}^2(45+\frac{\varphi }{2})}$

$Z_0=\frac{2c}{\gamma \sqrt{\frac{1}{ta{n}^2(45+\frac{\varphi }{2})}}}$

$Z_0=\frac{2c}{\gamma }tan(45+\frac{\varphi }{2})$