Question

The total horizontal and Vertical stresses at a point X in a saturated sandy medium are 170 kPa and 300 kPa, respectively. The static pore- water pressure is 30 kPa. At failure, the excess pore-water pressure is measured to be 94.50 kPa and the shear stresses on the vertical and horizontal planes passing through the point X and zero. Effective cohesion is 0 kPa and effective angle of internal friction is ${36}^{\circ }$. The shear strength (kPa, up to two decimal places) at point X is

• A. 52.52

Answer 1

The correct option is A 52.52
Major effective principle stress $\left({\overline{\sigma }}_1\right)$

= 300 - 30 - 94.5 MPa

= 175.5 MPa

Minor effective principal stress

= 170 - 30 - 94.5 Mpa

$\left({\overline{\sigma }}_3\right)$ = 45.5 MPa

Shear strength = C + $\overline{\sigma }tan\varphi$

C = 0, $\varphi ={36}^{\circ }$ (given)

$\overline{\sigma }$ = effective stress at the plane of failure normal.


$\angle OBA=90-{36}^{\circ }={54}^{\circ }$

$BD=65cos{54}^{\circ }=38.21KPa$

$\overline{\sigma }=(45.5+65-38.21)=72.3KPa$

$\therefore$ $\text{Shear strength}=72.3tan{36}^{\circ }$

= 52.52 KPa