Question

In the given figure, Point O indicates the stress point of a soil element at initial non-hydrostatic stress condition. For the stress path (OP), which of the following loading conditions is correct? \includegraphics[width=0.5\linewidth]{image11.png}

• A. \( \sigma_v \) is increasing and \( \sigma_h \) is constant.
• B. \( \sigma_v \) is constant and \( \sigma_h \) is increasing.
• C. \( \sigma_v \) is increasing and \( \sigma_h \) is decreasing.
• D. \( \sigma_v \) is decreasing and \( \sigma_h \) is increasing.

Hint:

In stress path analysis, the deviatoric stress \( q \) corresponds to the difference between vertical and horizontal stresses. The stress path gives insight into how the stress components change as the loading conditions evolve.

Answer 1

The Correct Option is A

We are given a stress path from Point O to Point P, where: - \( q = \frac{\sigma_v - \sigma_h}{2} \) is the deviatoric stress. - \( p = \frac{\sigma_v + \sigma_h}{2} \) is the mean stress. From the figure, we can see that as we move along the stress path (OP), the point P represents a stress state where both the vertical stress (\(\sigma_v\)) and the horizontal stress (\(\sigma_h\)) are changing. The path is such that the stress difference between \(\sigma_v\) and \(\sigma_h\) is decreasing while the mean stress is increasing, which implies: - \(\sigma_v\) is increasing. - \(\sigma_h\) remains constant, as both stresses are moving along a diagonal path where the difference between them changes but the individual stresses are increasing. Thus, the correct answer is option A: \[ \boxed{\text{A:} \ \sigma_v \text{ is increasing and } \sigma_h \text{ is constant.}} \]