Computation of Consolidation Settlement

Problem 1. Compute consolidation settlement of a 2.5m thick clay layer due to an increase of 30 kN/m² pressure at the mid height of the layer. If vertical stress at the mid height

of layer is 40 kN/m². Given, initial void ratio e₀ =0.7 and compression index C_c = 0.25.

Exam Name: Sylhet Gas Field 2017

 Solution:
We know,
Consolidation settlement,
                  S_c =   {C_c H_c / (1 + e₀)} * log ₁₀   {(σ_o' + ㅿσ_o') / σ_o'}
      Here,  C_c  = 0.25
                  H_c= 2.5 m
                  e₀ = 0.7
                  σ_o'= 40 kN/m²
              ㅿσ_o'= 30 kN/m²         

             ∴  S_c = {(0.25 * 2.4)/ (1 + 0.7)}* log ₁₀   {(40+ 30) /40}
                      = 0.089 m
Answer: 89 mm 

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Problem 2. Calculate the consolidation settlement of 3m deep clay layer due to increase of 40 kN/m² pressure at mid height of clay layer. Given the effective vertical stress at mid height of layer 40 kN/m²,  e₀ =0.7 and C_c = 0.28.?
Exam Name: Easteni Refinery Ltd. 2017

Solution: 

We know,
Consolidation settlement,
                  S_c =   {C_c H_c / (1 + e₀)} * log ₁₀   {(σ_o' + ㅿσ_o') / σ_o'}
      Here,  C_c  = 0.28
                  H_c= 3 m
                  e₀ = 0.8
                  σ_o'= 50 kN/m²
              ㅿσ_o'= 40 kN/m²         

             ∴  S_c = {(0.28 * 3)/ (1 + 0.8)}* log ₁₀   {(50+ 40) /50}
                      = 0.119 m

 Answer: 119 mm 

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Problem 3. The thickness of clay layer is 2.5 m, the value of void is 0.7 and compression index is 0.28. The existing pressure at the mid of the layer is 40 kN/m² and 30 kN/m² is applied to the mid height of the layer. Find the consolidation settlements of the layer.?
Exam Name: Gas Transmission Company Ltd. 2016, PGCB 2015


Solution: 
We know,
Consolidation settlement,
                  S_c =   {C_c H_c / (1 + e₀)} * log ₁₀   {(σ_o' + ㅿσ_o') / σ_o'}
      Here,  C_c  = 0.28
                  H_c= 2.5 m
                  e₀ = 0.7
                  σ_o'= 40 kN/m²
              ㅿσ_o'= 30 kN/m²         

             ∴  S_c = {(0.28 * 2.5)/ (1 + 0.7)}* log ₁₀   {(40+ 30) /40}
                      = 0.1 m

 Answer: 100 mm 

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