Question

The Mohr circle of stress of a dry porous rock is shown in the figure. If the rock is fully saturated with a pore pressure \( p \), then the Mohr circle takes the form of 

• A. A
• B. B
• C. C
• D. D

Hint:

When a material is saturated with pore pressure, the effective stresses are the original stresses minus the pore pressure.

Answer 1

The Correct Option is A

The Mohr circle represents the state of stress at a point in a material. For a dry porous rock, the Mohr circle is constructed based on the principal stresses \( \sigma_1 \) and \( \sigma_3 \). When the rock becomes fully saturated with pore pressure \( p \), the effective stresses change. - Effective stress refers to the stress that actually contributes to the deformation of the rock, which is the total stress minus the pore pressure. - The effective normal stresses are \( \sigma_1 - p \) and \( \sigma_3 - p \), where \( p \) is the pore pressure. - As a result, the Mohr circle is shifted such that both the horizontal (normal) stresses \( \sigma_1 \) and \( \sigma_3 \) are reduced by the amount of the pore pressure \( p \).
Hence, the correct representation of the Mohr circle with a pore pressure \( p \) is option (A) \( \sigma_3 - p, \sigma_1 - p \).