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 = 75 kPasandclayCc​ = 0.25e0​ = 1.1σ′0​ = 90 kPa5.5 mwater table

A 5.5 m thick layer of normally consolidated clay (Cc = 0.25, e₀ = 1.1) has an effective vertical stress of 90 kPa at its mid-depth. A wide fill raises the vertical stress in the clay by 75 kPa. Treat the layer as one sublayer with the stresses at its mid-depth. Find the primary consolidation settlement S in mm.

H = 5.5 mCc = 0.25e0 = 1.1σ′0 = 90 kPaΔσ = 75 kPa
S = mm
2.Easy
Δσ = 55 kPasandclayCc​ = 0.35e0​ = 1.3σ′0​ = 105 kPa2 mwater table

A 2 m thick layer of normally consolidated clay (Cc = 0.35, e₀ = 1.3) has an effective vertical stress of 105 kPa at its mid-depth. A wide fill raises the vertical stress in the clay by 55 kPa. Treat the layer as one sublayer with the stresses at its mid-depth. Find the primary consolidation settlement S in mm.

H = 2 mCc = 0.35e0 = 1.3σ′0 = 105 kPaΔσ = 55 kPa
S = mm
3.Medium
Δσ = 30 kPasandclayCc​ = 0.5, Cr​ = 0.04e0​ = 0.7σ′0​ = 110 kPaσ′p​ = 180 kPa7.5 mwater table

A 7.5 m thick overconsolidated clay layer has Cc = 0.5, Cr = 0.04 and e₀ = 0.7. At its mid-depth the effective vertical stress is 110 kPa and the preconsolidation pressure is 180 kPa. A new building adds 30 kPa of vertical stress at mid-depth. Find the primary consolidation settlement S in mm.

H = 7.5 mCc = 0.5Cr = 0.04e0 = 0.7σ′0 = 110 kPaσ′p = 180 kPaΔσ = 30 kPa
S = mm
4.Medium
Δσ = 120 kPasandclayCc​ = 0.25, Cr​ = 0.02e0​ = 0.85σ′0​ = 100 kPaOCR = 1.53.5 mwater table

A 3.5 m thick overconsolidated clay layer has Cc = 0.25, Cr = 0.02 and e₀ = 0.85. At its mid-depth the effective vertical stress is 100 kPa and the overconsolidation ratio is OCR = 1.5. A new building adds 120 kPa of vertical stress at mid-depth. Find the primary consolidation settlement S in mm.

H = 3.5 mCc = 0.25Cr = 0.02e0 = 0.85σ′0 = 100 kPaOCR = 1.5Δσ = 120 kPa
S = mm
5.Hard
sandclayH = 9.5 mcv​ = 0.5 m²/year9.5 mimpervious rockwater table

A clay layer 9.5 m thick has a coefficient of consolidation cv = 0.5 m²/year. It lies on impervious rock, with sand above it, so water drains out only at the top. For 80% average consolidation the time factor is Tv = 0.567. How many years t does the layer take to reach 80% consolidation?

H = 9.5 mcv = 0.5 m²/yearU = 80%Tv = 0.567single drainage
t = years
6.Hard
sandclayH = 4.5 mcv​ = 1.5 m²/year4.5 msandwater table

A clay layer 4.5 m thick has a coefficient of consolidation cv = 1.5 m²/year. It lies between two sand layers, so water drains out at the top and the bottom. For 70% average consolidation the time factor is Tv = 0.403. How many years t does the layer take to reach 70% consolidation?

H = 4.5 mcv = 1.5 m²/yearU = 70%Tv = 0.403double drainage
t = years

Answer key

  1. 1. S = 172.4 mm
  2. 2. S = 55.67 mm
  3. 3. S = 18.48 mm
  4. 4. S = 85.33 mm
  5. 5. t = 102.3 years
  6. 6. t = 1.36 years

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