Question

A soil fails under an axial vertical stress of $100kN/m^2$ in unconfined compression test. The failure plane makes an angle of $50°$ with the horizontal. The shear parameters ${}^{\prime }{c}^{\prime }$ and ${}^{\prime }{\Phi }^{\prime }$ respectively will be

• A. $41.9kN/m^2,0^o$
• B. $50.0kN/m^2,0^o$
• C. $41.9kN/m^2,0^o$
• D. $50.0kN/m^2,0^o$

Answer 1

The correct option is C $41.9kN/m^2,0^o$

The angle of failure from horizontal
$\alpha ={45}^o+\frac{\Phi }{2}$
$\Rightarrow \Phi =({50}^o-{45}^o)\times 2$
$\Rightarrow \Phi ={10}^o$
$\text{In this case,}{\sigma }_1=100kN/m^2$ and ${\sigma }_3=0$
$\text{But}{\sigma }_1=2ctan(45+\frac{\Phi }{2})$
$\Rightarrow c=\frac{100}{2tan{50}^o}=41.9kN/m^2$