# A soil has an angle of shearing of 30° and cohesion of 35 kN/m2. If the specimen of this soil is subjected to a tri-axial compression test, then the v

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A soil has an angle of shearing of 30° and cohesion of 35 kN/m2. If the specimen of this soil is subjected to a tri-axial compression test, then the value of lateral pressure in the cell for failure to occur at total stress of 300 kN/m2 will be
1. 243.21 kN/m2
2. 44.41 kN/m2
3. 103.21 kN/m2
4. 59.59 kN/m2

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Correct Answer - Option 4 : 59.59 kN/m2

Concept:

Relationship between C and principal stresses at failure:

Mohr coulomb failure criteria can be expressed in terms of the relationship between the principal stresses σ1 and σ3

${σ _1} = {σ _3}{\tan ^2}\left( {{{45}^o} + \frac{ϕ }{2}} \right) + 2C\tan \left( {{{45}^o} + \frac{ϕ }{2}} \right)$

Where, σ1 = Total principal stress, σ3 = Lateral princiapl stress

C = Cohesion, ϕ = angle of shearing or friction angle

Calculation:

Given,

C = 35 kN/m2, σ1 = 300 kN/m2, ϕ = 30°

∵ We know that, ${σ _1} = {σ _3}{\tan ^2}\left( {{{45}^o} + \frac{ϕ }{2}} \right) + 2C\tan \left( {{{45}^o} + \frac{ϕ }{2}} \right)$

⇒ $300 = {σ _3}{\tan ^2}\left( {{{45}^o} + \frac{{{{30}^o}}}{2}} \right) + 2 \times 35 \times \tan \left( {{{45}^o} + \frac{{{{30}^o}}}{2}} \right)$

σ3 = 59.585 kN/m2