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

Concept:
Shear strength of soil:
Shear strength of the soil is the capacity of soil to resist shearing stresses. It can be defined as the maximum value of shear stress that can be mobilized within a soil mass. If this value exceeded by the shear stress on any plane or a surfaceata point, failure will occur in soil because of the movement of a portion of the soil mass along that particular plane. The soil is then said to fail in shear. Therefore, shear strength generally represented the strength of the soil.
Shear strength of soil is given as:
$\mathrm{\tau }=\mathrm{C}+\overline{\mathrm{\sigma }}\tan \mathrm{ɸ}$
$\mathrm{\tau }=\mathrm{Shear}\mathrm{strength}\mathrm{of}\mathrm{the}\mathrm{soil}$
$\mathit{C}=\mathrm{Cohesion}\mathrm{of}\mathrm{the}\mathrm{soil}$
$\mathrm{ɸ}=\mathrm{Angle}\mathrm{of}\mathrm{internal}\mathrm{friction}\mathrm{of}\mathrm{the}\mathrm{soil}$
$\overline{\mathrm{\sigma }}=\mathrm{Effective}\mathrm{stress}\mathrm{acting}\mathrm{on}\mathrm{the}\mathrm{soil}\mathrm{at}\mathrm{a}\mathrm{point}$
Calculation:
$\overline{\mathrm{\sigma }}=\mathrm{\sigma }-\mathrm{u}$
$\overline{\mathrm{\sigma }}=295-120$
$\overline{\mathrm{\sigma }}=175\mathrm{kN}∕{\mathrm{m}}^2$
$\mathit{c}=120\mathrm{kN}∕{\mathrm{m}}^2$
$\mathrm{ɸ}=30°$
$\mathrm{\tau }=12+175\tan 30°$
$\mathrm{\tau }=113.15\mathrm{kN}∕{\mathrm{m}}^2$