Consolidation settlement worksheet with answers

Free printable Consolidation settlement worksheet: 6 problems from easy to exam level, with an answer key. Print it or save it as a PDF.

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1.Easy
Δσ = 100 kPasandclayCc​ = 0.4e0​ = 0.8σ′0​ = 105 kPa10 mwater table

A 10 m thick layer of normally consolidated clay (Cc = 0.4, e₀ = 0.8) has an effective vertical stress of 105 kPa at its mid-depth. A wide fill raises the vertical stress in the clay by 100 kPa. Treat the layer as one sublayer with the stresses at its mid-depth. Find the primary consolidation settlement S in mm.

H = 10 mCc = 0.4e0 = 0.8σ′0 = 105 kPaΔσ = 100 kPa
S = mm
2.Easy
Δσ = 145 kPasandclayCc​ = 0.6e0​ = 1.25σ′0​ = 55 kPa7.5 mwater table

A 7.5 m thick layer of normally consolidated clay (Cc = 0.6, e₀ = 1.25) has an effective vertical stress of 55 kPa at its mid-depth. A wide fill raises the vertical stress in the clay by 145 kPa. Treat the layer as one sublayer with the stresses at its mid-depth. Find the primary consolidation settlement S in mm.

H = 7.5 mCc = 0.6e0 = 1.25σ′0 = 55 kPaΔσ = 145 kPa
S = mm
3.Medium
Δσ = 220 kPasandclayCc​ = 0.5, Cr​ = 0.03e0​ = 1.15σ′0​ = 90 kPaσ′p​ = 190 kPa2.5 mwater table

A 2.5 m thick overconsolidated clay layer has Cc = 0.5, Cr = 0.03 and e₀ = 1.15. At its mid-depth the effective vertical stress is 90 kPa and the preconsolidation pressure is 190 kPa. A new building adds 220 kPa of vertical stress at mid-depth. Find the primary consolidation settlement S in mm.

H = 2.5 mCc = 0.5Cr = 0.03e0 = 1.15σ′0 = 90 kPaσ′p = 190 kPaΔσ = 220 kPa
S = mm
4.Medium
Δσ = 30 kPasandclayCc​ = 0.35, Cr​ = 0.02e0​ = 1σ′0​ = 120 kPaσ′p​ = 170 kPa4 mwater table

A 4 m thick overconsolidated clay layer has Cc = 0.35, Cr = 0.02 and e₀ = 1. At its mid-depth the effective vertical stress is 120 kPa and the preconsolidation pressure is 170 kPa. A new building adds 30 kPa of vertical stress at mid-depth. Find the primary consolidation settlement S in mm.

H = 4 mCc = 0.35Cr = 0.02e0 = 1σ′0 = 120 kPaσ′p = 170 kPaΔσ = 30 kPa
S = mm
5.Hard
sandclayH = 9.5 mcv​ = 1 m²/year9.5 msandwater table

A clay layer 9.5 m thick has a coefficient of consolidation cv = 1 m²/year. It lies between two sand layers, so water drains out at the top and the bottom. For 50% average consolidation the time factor is Tv = 0.197. How many years t does the layer take to reach 50% consolidation?

H = 9.5 mcv = 1 m²/yearU = 50%Tv = 0.197double drainage
t = years
6.Hard
sandclayH = 8.5 mcv​ = 2 m²/year8.5 msandwater table

A clay layer 8.5 m thick has a coefficient of consolidation cv = 2 m²/year. It lies between two sand layers, so water drains out at the top and the bottom. For 50% average consolidation the time factor is Tv = 0.197. How many years t does the layer take to reach 50% consolidation?

H = 8.5 mcv = 2 m²/yearU = 50%Tv = 0.197double drainage
t = years

Answer key

  1. 1. S = 645.7 mm
  2. 2. S = 1121 mm
  3. 3. S = 134.9 mm
  4. 4. S = 3.876 mm
  5. 5. t = 4.445 years
  6. 6. t = 1.779 years

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