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

Concept: Shear strength of soil is given by the Mohr-Coulomb failure criterion using effective stress parameters for saturated soils.
Step 1: Effective stress concept.
In saturated soil, pore water pressure reduces the effective stress: \[ \sigma' = \sigma - u \]
Step 2: Shear strength equation.
\[ \tau = c' + \sigma' \tan \phi' \]
Step 3: Meaning of terms.

• $c'$ = effective cohesion
• $\sigma'$ = effective normal stress
• $\phi'$ = angle of internal friction

Step 4: Evaluating the options.

• $\tau = c + \sigma \tan \phi$ $\rightarrow$ Total stress form (incorrect)
• $\tau = c' + \sigma' \tan \phi'$ $\rightarrow$ Correct
• $\tau = \sigma \tan \phi$ $\rightarrow$ Missing cohesion (incorrect)
• $\tau = c' + \sigma \tan \phi'$ $\rightarrow$ Uses total stress incorrectly (incorrect)

Step 5: Conclusion.
Thus, shear strength is given by $\tau = c' + \sigma' \tan \phi'$.