Question

A dry sand specimen is put through a triaxial test. The cell pressure is $50kPa$ and the deviator stress at failure is $100kPa$, the angle of internal friction for the sand specimen is

• A. ${15}^o$
• B. ${30}^o$
• C. ${37}^o$
• D. ${45}^o$

Answer 1

The correct option is B ${30}^o$

$\text{For sand cohesion,}c=0$
${\sigma }_1={\sigma }_3{N}_{\Phi }$
$N_{\Phi }=ta{n}^2(45+\frac{\Phi }{2})$
${\sigma }_1=100+50=150kPa$
${\sigma }_3=50kPa$
$\text{Now,}150=50N_{\Phi }$
$\Rightarrow N_{\Phi }=3$
$\Rightarrow tan(45+\frac{\Phi }{2})=\sqrt{3}$
$\Rightarrow 45+\frac{\Phi }{2}={60}^o$
$\Rightarrow \Phi ={30}^o$