Section 4: Soil and Water Conservation Engineering
Soil Shear Strength & Mohr-Coulomb Theory
Subtopic: Shear strength on failure plane
Question Statement:
A cohesive-frictional soil sample has an effective cohesion of $c' = 30.0\text{ kPa}$ and effective internal friction angle $\phi' = 30^\circ$. As illustrated in the Mohr-Coulomb failure envelope, the shear strength on a plane subjected to an effective normal stress $\sigma_n' = 100.0\text{ kPa}$ is ________ $\text{kPa}$ (round off to two decimal places).
Answer Key:
87.74
Step-by-Step Solution & Explanation
From the Mohr-Coulomb failure criterion:
$\tau_f = c' + \sigma_n' \tan \phi'$
Given $c' = 30.0\text{ kPa}$, $\phi' = 30^\circ$ ($\tan 30^\circ = \frac{1}{\sqrt3} \approx 0.57735$), and $\sigma_n' = 100.0\text{ kPa}$:
$\tau_f = 30.0 + 100.0 \times 0.57735 = 30.0 + 57.73 = 87.74\text{ kPa}$