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 = 50 kPasandclayCc​ = 0.45e0​ = 1σ′0​ = 85 kPa2.5 mwater table

A 2.5 m thick layer of normally consolidated clay (Cc = 0.45, e₀ = 1) has an effective vertical stress of 85 kPa at its mid-depth. A wide fill raises the vertical stress in the clay by 50 kPa. Treat the layer as one sublayer with the stresses at its mid-depth. Find the primary consolidation settlement S in mm.

H = 2.5 mCc = 0.45e0 = 1σ′0 = 85 kPaΔσ = 50 kPa
S = mm
2.Easy
Δσ = 45 kPasandclayCc​ = 0.15e0​ = 1.35σ′0​ = 100 kPa3.5 mwater table

A 3.5 m thick layer of normally consolidated clay (Cc = 0.15, e₀ = 1.35) has an effective vertical stress of 100 kPa at its mid-depth. A wide fill raises the vertical stress in the clay by 45 kPa. Treat the layer as one sublayer with the stresses at its mid-depth. Find the primary consolidation settlement S in mm.

H = 3.5 mCc = 0.15e0 = 1.35σ′0 = 100 kPaΔσ = 45 kPa
S = mm
3.Medium
Δσ = 20 kPasandclayCc​ = 0.45, Cr​ = 0.04e0​ = 1.15σ′0​ = 105 kPaσ′p​ = 195 kPa7.5 mwater table

A 7.5 m thick overconsolidated clay layer has Cc = 0.45, Cr = 0.04 and e₀ = 1.15. At its mid-depth the effective vertical stress is 105 kPa and the preconsolidation pressure is 195 kPa. A new building adds 20 kPa of vertical stress at mid-depth. Find the primary consolidation settlement S in mm.

H = 7.5 mCc = 0.45Cr = 0.04e0 = 1.15σ′0 = 105 kPaσ′p = 195 kPaΔσ = 20 kPa
S = mm
4.Medium
Δσ = 200 kPasandclayCc​ = 0.5, Cr​ = 0.04e0​ = 0.75σ′0​ = 120 kPaOCR = 1.52 mwater table

A 2 m thick overconsolidated clay layer has Cc = 0.5, Cr = 0.04 and e₀ = 0.75. At its mid-depth the effective vertical stress is 120 kPa and the overconsolidation ratio is OCR = 1.5. A new building adds 200 kPa of vertical stress at mid-depth. Find the primary consolidation settlement S in mm.

H = 2 mCc = 0.5Cr = 0.04e0 = 0.75σ′0 = 120 kPaOCR = 1.5Δσ = 200 kPa
S = mm
5.Hard
sandclayH = 4.5 mcv​ = 2.5 m²/year4.5 msandwater table

A clay layer 4.5 m thick has a coefficient of consolidation cv = 2.5 m²/year. It lies between two sand layers, so water drains out at the top and the bottom. For 80% average consolidation the time factor is Tv = 0.567. How many years t does the layer take to reach 80% consolidation?

H = 4.5 mcv = 2.5 m²/yearU = 80%Tv = 0.567double drainage
t = years
6.Hard
sandclayH = 5 mcv​ = 2 m²/year5 mimpervious rockwater table

A clay layer 5 m thick has a coefficient of consolidation cv = 2 m²/year. It lies on impervious rock, with sand above it, so water drains out only at the top. For 70% average consolidation the time factor is Tv = 0.403. How many years t does the layer take to reach 70% consolidation?

H = 5 mcv = 2 m²/yearU = 70%Tv = 0.403single drainage
t = years

Answer key

  1. 1. S = 113 mm
  2. 2. S = 36.05 mm
  3. 3. S = 10.57 mm
  4. 4. S = 150.8 mm
  5. 5. t = 1.148 years
  6. 6. t = 5.038 years

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