SSC JE Civil Engineering 30-Oct-2020 Shift 2 Paper

Concept:
Coulomb's equation,
τ = C + σ tan ϕ
Where,
τ = Shear strength of soil
C = Apparent cohesion
σ = Normal stress on the plane of rupture
ϕ = Angle of internal friction
Calculation:
Given,
${\mathrm{\sigma }}_1$ = 150 kN/ ${\mathrm{m}}^2$ , ${\mathrm{\sigma }}_2$ = 250 kN/${\mathrm{m}}^2$
${\mathrm{\tau }}_1$ = 110 kN/${\mathrm{m}}^2$ , ${\mathit{\tau }}_2$ = 120 kN/${\mathrm{m}}^2$
We know,
τ = C + σ tan ϕ
When, ${\mathrm{\sigma }}_1$ = 150 kN/${\mathrm{m}}^2$ and ${\mathit{\tau }}_1$ = 110 kN/${\mathrm{m}}^2$
110 = C + 150 tan ϕ........(1)
When, ${\mathrm{\sigma }}_1$ = 250 kN/${\mathrm{m}}^2$ and ${\mathrm{\tau }}_1$ = 120 kN/${\mathrm{m}}^2$
120 = C + 250 tan ϕ........(2)
Equation (2) - (1)
10 = 100 tan ϕ
tan ϕ = 0.1
Put tan ϕ in equation (1),
110 = C + 150 × 0.1
C = 95 kN/${\mathrm{m}}^2$.