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 = 20 kPasandclayCc​ = 0.4e0​ = 1.1σ′0​ = 65 kPa4.5 mwater table

A 4.5 m thick layer of normally consolidated clay (Cc = 0.4, e₀ = 1.1) has an effective vertical stress of 65 kPa at its mid-depth. A wide fill raises the vertical stress in the clay by 20 kPa. Treat the layer as one sublayer with the stresses at its mid-depth. Find the primary consolidation settlement S in mm.

H = 4.5 mCc = 0.4e0 = 1.1σ′0 = 65 kPaΔσ = 20 kPa
S = mm
2.Easy
Δσ = 95 kPasandclayCc​ = 0.2e0​ = 0.7σ′0​ = 135 kPa8.5 mwater table

An 8.5 m thick layer of normally consolidated clay (Cc = 0.2, e₀ = 0.7) has an effective vertical stress of 135 kPa at its mid-depth. A wide fill raises the vertical stress in the clay by 95 kPa. Treat the layer as one sublayer with the stresses at its mid-depth. Find the primary consolidation settlement S in mm.

H = 8.5 mCc = 0.2e0 = 0.7σ′0 = 135 kPaΔσ = 95 kPa
S = mm
3.Medium
Δσ = 130 kPasandclayCc​ = 0.25, Cr​ = 0.02e0​ = 0.7σ′0​ = 105 kPaOCR = 2.53 mwater table

A 3 m thick overconsolidated clay layer has Cc = 0.25, Cr = 0.02 and e₀ = 0.7. At its mid-depth the effective vertical stress is 105 kPa and the overconsolidation ratio is OCR = 2.5. A new building adds 130 kPa of vertical stress at mid-depth. Find the primary consolidation settlement S in mm.

H = 3 mCc = 0.25Cr = 0.02e0 = 0.7σ′0 = 105 kPaOCR = 2.5Δσ = 130 kPa
S = mm
4.Medium
Δσ = 25 kPasandclayCc​ = 0.45, Cr​ = 0.04e0​ = 1.1σ′0​ = 40 kPaσ′p​ = 70 kPa5.5 mwater table

A 5.5 m thick overconsolidated clay layer has Cc = 0.45, Cr = 0.04 and e₀ = 1.1. At its mid-depth the effective vertical stress is 40 kPa and the preconsolidation pressure is 70 kPa. A new building adds 25 kPa of vertical stress at mid-depth. Find the primary consolidation settlement S in mm.

H = 5.5 mCc = 0.45Cr = 0.04e0 = 1.1σ′0 = 40 kPaσ′p = 70 kPaΔσ = 25 kPa
S = mm
5.Hard
sandclayH = 7.5 mcv​ = 2 m²/year7.5 msandwater table

A clay layer 7.5 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 60% average consolidation the time factor is Tv = 0.287. How many years t does the layer take to reach 60% consolidation?

H = 7.5 mcv = 2 m²/yearU = 60%Tv = 0.287double drainage
t = years
6.Hard
sandclayH = 7.5 mcv​ = 3 m²/year7.5 mimpervious rockwater table

A clay layer 7.5 m thick has a coefficient of consolidation cv = 3 m²/year. It lies on impervious rock, with sand above it, so water drains out only at the top. For 90% average consolidation the time factor is Tv = 0.848. How many years t does the layer take to reach 90% consolidation?

H = 7.5 mcv = 3 m²/yearU = 90%Tv = 0.848single drainage
t = years

Answer key

  1. 1. S = 99.86 mm
  2. 2. S = 231.4 mm
  3. 3. S = 12.35 mm
  4. 4. S = 22.09 mm
  5. 5. t = 2.018 years
  6. 6. t = 15.9 years

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