Question

For a saturated soil mass, how is shear strength calculated using effective stress parameters?

• A. $\tau = c + \sigma \tan \phi$
• B. $\tau = c' + \sigma' \tan \phi'$
• C. $\tau = \sigma \tan \phi$
• D. $\tau = c' + \sigma \tan \phi'$

Hint:

Remember: Saturated soil → Always use effective stress ($\sigma'$).

Answer 1

The Correct Option is B

Step 1: Understanding the Concept:
In saturated soils, the total normal stress (\(\sigma\)) is the sum of the effective stress (\(\sigma'\)) carried by the soil skeleton and the pore water pressure (\(u\)).
Step 2: Key Formula or Approach:
According to Terzaghi's principle, soil behavior is governed by effective stress. The Mohr-Coulomb equation for shear strength (\(\tau\)) using effective stress parameters is:
\[ \tau = c' + \sigma' \tan \phi' \] Where:
- \(c'\) = Effective cohesion.
- \(\sigma'\) = Effective normal stress (\(\sigma - u\)).
- \(\phi'\) = Effective angle of internal friction.
Step 3: Detailed Explanation:
- Option (A) represents total stress analysis.
- Option (D) is incorrect because it mixes effective parameters with total stress.
- For long-term stability in saturated soils, effective stress analysis (B) is required.
Step 4: Final Answer:
The correct expression is \(\tau = c' + \sigma' \tan \phi'\).