The total horizontal and vertical stresses at a point X in a saturated sandy medium are 170 kPa and 300 kPa

Q. 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 are zero. Effective cohesion is 0 kPa and effective angle of internal friction is 36°. The shear strength (in kPa, up to two decimal places) at point X is       

Ans: 51.50 – 53.50

Sol:

Effective angle of internal friction = ϕ

Critical shear plane = α

Vertical stresses = σ1

Horizontal stress = σ2

Normal Stress = σn

Excess pore-water pressure = u