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 = 90 kPasandclayCc​ = 0.5e0​ = 0.85σ′0​ = 85 kPa10 mwater table

A 10 m thick layer of normally consolidated clay (Cc = 0.5, e₀ = 0.85) has an effective vertical stress of 85 kPa at its mid-depth. A wide fill raises the vertical stress in the clay by 90 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 = 0.5e0 = 0.85σ′0 = 85 kPaΔσ = 90 kPa
S = mm
2.Easy
Δσ = 60 kPasandclayCc​ = 0.3e0​ = 1.05σ′0​ = 80 kPa2 mwater table

A 2 m thick layer of normally consolidated clay (Cc = 0.3, e₀ = 1.05) has an effective vertical stress of 80 kPa at its mid-depth. A wide fill raises the vertical stress in the clay by 60 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 = 0.3e0 = 1.05σ′0 = 80 kPaΔσ = 60 kPa
S = mm
3.Medium
Δσ = 100 kPasandclayCc​ = 0.2, Cr​ = 0.05e0​ = 1.15σ′0​ = 105 kPaσ′p​ = 225 kPa5 mwater table

A 5 m thick overconsolidated clay layer has Cc = 0.2, Cr = 0.05 and e₀ = 1.15. At its mid-depth the effective vertical stress is 105 kPa and the preconsolidation pressure is 225 kPa. A new building adds 100 kPa of vertical stress at mid-depth. Find the primary consolidation settlement S in mm.

H = 5 mCc = 0.2Cr = 0.05e0 = 1.15σ′0 = 105 kPaσ′p = 225 kPaΔσ = 100 kPa
S = mm
4.Medium
Δσ = 120 kPasandclayCc​ = 0.4, Cr​ = 0.02e0​ = 0.65σ′0​ = 110 kPaσ′p​ = 210 kPa8 mwater table

An 8 m thick overconsolidated clay layer has Cc = 0.4, Cr = 0.02 and e₀ = 0.65. At its mid-depth the effective vertical stress is 110 kPa and the preconsolidation pressure is 210 kPa. A new building adds 120 kPa of vertical stress at mid-depth. Find the primary consolidation settlement S in mm.

H = 8 mCc = 0.4Cr = 0.02e0 = 0.65σ′0 = 110 kPaσ′p = 210 kPaΔσ = 120 kPa
S = mm
5.Hard
sandclayH = 4 mcv​ = 5 m²/year4 mimpervious rockwater table

A clay layer 4 m thick has a coefficient of consolidation cv = 5 m²/year. It lies on impervious rock, with sand above it, so water drains out only at the top. For 50% average consolidation the time factor is Tv = 0.197. How many years t does the layer take to reach 50% consolidation?

H = 4 mcv = 5 m²/yearU = 50%Tv = 0.197single drainage
t = years
6.Hard
sandclayH = 3.5 mcv​ = 3 m²/year3.5 mimpervious rockwater table

A clay layer 3.5 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 80% average consolidation the time factor is Tv = 0.567. How many years t does the layer take to reach 80% consolidation?

H = 3.5 mcv = 3 m²/yearU = 80%Tv = 0.567single drainage
t = years

Answer key

  1. 1. S = 847.6 mm
  2. 2. S = 71.13 mm
  3. 3. S = 33.79 mm
  4. 4. S = 103.9 mm
  5. 5. t = 0.6304 years
  6. 6. t = 2.315 years

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