Question

In an undrained triaxial test on a saturated clay, the Poisson's ratio is

• A. $\frac{{\sigma }_3}{{\sigma }_1+{\sigma }_3}$
• B. $\frac{{\sigma }_3}{{\sigma }_1-{\sigma }_3}$
• C. $\frac{{\sigma }_1-{\sigma }_3}{{\sigma }_3}$
• D. $\frac{{\sigma }_1+{\sigma }_3}{{\sigma }_3}$

Answer 1

The correct option is A $\frac{{\sigma }_3}{{\sigma }_1+{\sigma }_3}$

In undrained triaxial test on a saturated clay volumetric strain is zero.

However to solve the problem we take lateral strain equal to zero (although it is not there)

${\epsilon }_3=0=\frac{{\sigma }_3}{E}-\frac{\mu {\sigma }_1}{E}-\frac{\mu {\sigma }_2}{E}$

and

${\sigma }_3={\sigma }_2$

$\Rightarrow \mu ({\sigma }_3+{\sigma }_1)={\sigma }_3$

$\mu =\left(\frac{{\sigma }_3}{{\sigma }_3+{\sigma }_1}\right)$