Section 4: Soil and Water Conservation Engineering
Soil Shear Strength & Mohr-Coulomb Theory
Subtopic: Triaxial compression of cohesionless sand
Question Statement:
A cohesionless sand specimen ($c = 0$, $\phi = 30^\circ$) is tested in a consolidated-drained triaxial test under a confining cell pressure of $\sigma_3 = 100\text{ kPa}$. The deviator stress $(\sigma_1 - \sigma_3)$ at failure is ________ $\text{kPa}$ (round off to one decimal place).
Answer Key:
200.0
Step-by-Step Solution & Explanation
For a cohesionless soil ($c = 0$), the principal stresses at failure are related by:
$\sigma_1 = \sigma_3 \tan^2\left(45^\circ + \frac{\phi}{2}\right)$
For $\phi = 30^\circ$, $45^\circ + \phi/2 = 60^\circ$, and $\tan^2(60^\circ) = (\sqrt3)^2 = 3$.
$\sigma_1 = 3 \sigma_3 = 3 \times 100 = 300.0\text{ kPa}$
The deviator stress at failure is:
$\sigma_d = \sigma_1 - \sigma_3 = 300.0 - 100 = 200.0\text{ kPa}$