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 = 95 kPasandclayCc​ = 0.3e0​ = 1.25σ′0​ = 120 kPa3 mwater table

A 3 m thick layer of normally consolidated clay (Cc = 0.3, e₀ = 1.25) has an effective vertical stress of 120 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 = 3 mCc = 0.3e0 = 1.25σ′0 = 120 kPaΔσ = 95 kPa
S = mm
2.Easy
Δσ = 125 kPasandclayCc​ = 0.45e0​ = 1.15σ′0​ = 45 kPa2.5 mwater table

A 2.5 m thick layer of normally consolidated clay (Cc = 0.45, e₀ = 1.15) has an effective vertical stress of 45 kPa at its mid-depth. A wide fill raises the vertical stress in the clay by 125 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 = 1.15σ′0 = 45 kPaΔσ = 125 kPa
S = mm
3.Medium
Δσ = 50 kPasandclayCc​ = 0.35, Cr​ = 0.03e0​ = 0.7σ′0​ = 45 kPaσ′p​ = 75 kPa4.5 mwater table

A 4.5 m thick overconsolidated clay layer has Cc = 0.35, Cr = 0.03 and e₀ = 0.7. At its mid-depth the effective vertical stress is 45 kPa and the preconsolidation pressure is 75 kPa. A new building adds 50 kPa of vertical stress at mid-depth. Find the primary consolidation settlement S in mm.

H = 4.5 mCc = 0.35Cr = 0.03e0 = 0.7σ′0 = 45 kPaσ′p = 75 kPaΔσ = 50 kPa
S = mm
4.Medium
Δσ = 30 kPasandclayCc​ = 0.2, Cr​ = 0.03e0​ = 1σ′0​ = 55 kPaσ′p​ = 95 kPa5.5 mwater table

A 5.5 m thick overconsolidated clay layer has Cc = 0.2, Cr = 0.03 and e₀ = 1. At its mid-depth the effective vertical stress is 55 kPa and the preconsolidation pressure is 95 kPa. A new building adds 30 kPa of vertical stress at mid-depth. Find the primary consolidation settlement S in mm.

H = 5.5 mCc = 0.2Cr = 0.03e0 = 1σ′0 = 55 kPaσ′p = 95 kPaΔσ = 30 kPa
S = mm
5.Hard
sandclayH = 9.5 mcv​ = 2 m²/year9.5 msandwater table

A clay layer 9.5 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 70% average consolidation the time factor is Tv = 0.403. How many years t does the layer take to reach 70% consolidation?

H = 9.5 mcv = 2 m²/yearU = 70%Tv = 0.403double drainage
t = years
6.Hard
sandclayH = 5.5 mcv​ = 5 m²/year5.5 mimpervious rockwater table

A clay layer 5.5 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 80% average consolidation the time factor is Tv = 0.567. How many years t does the layer take to reach 80% consolidation?

H = 5.5 mcv = 5 m²/yearU = 80%Tv = 0.567single drainage
t = years

Answer key

  1. 1. S = 101.3 mm
  2. 2. S = 302 mm
  3. 3. S = 112.7 mm
  4. 4. S = 15.6 mm
  5. 5. t = 4.546 years
  6. 6. t = 3.43 years

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