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 = 85 kPasandclayCc​ = 0.6e0​ = 0.8σ′0​ = 40 kPa7 mwater table

A 7 m thick layer of normally consolidated clay (Cc = 0.6, e₀ = 0.8) has an effective vertical stress of 40 kPa at its mid-depth. A wide fill raises the vertical stress in the clay by 85 kPa. Treat the layer as one sublayer with the stresses at its mid-depth. Find the primary consolidation settlement S in mm.

H = 7 mCc = 0.6e0 = 0.8σ′0 = 40 kPaΔσ = 85 kPa
S = mm
2.Easy
Δσ = 115 kPasandclayCc​ = 0.45e0​ = 1σ′0​ = 100 kPa6 mwater table

A 6 m thick layer of normally consolidated clay (Cc = 0.45, e₀ = 1) has an effective vertical stress of 100 kPa at its mid-depth. A wide fill raises the vertical stress in the clay by 115 kPa. Treat the layer as one sublayer with the stresses at its mid-depth. Find the primary consolidation settlement S in mm.

H = 6 mCc = 0.45e0 = 1σ′0 = 100 kPaΔσ = 115 kPa
S = mm
3.Medium
Δσ = 20 kPasandclayCc​ = 0.45, Cr​ = 0.06e0​ = 0.65σ′0​ = 65 kPaσ′p​ = 135 kPa4 mwater table

A 4 m thick overconsolidated clay layer has Cc = 0.45, Cr = 0.06 and e₀ = 0.65. At its mid-depth the effective vertical stress is 65 kPa and the preconsolidation pressure is 135 kPa. A new building adds 20 kPa of vertical stress at mid-depth. Find the primary consolidation settlement S in mm.

H = 4 mCc = 0.45Cr = 0.06e0 = 0.65σ′0 = 65 kPaσ′p = 135 kPaΔσ = 20 kPa
S = mm
4.Medium
Δσ = 170 kPasandclayCc​ = 0.25, Cr​ = 0.02e0​ = 0.6σ′0​ = 120 kPaσ′p​ = 170 kPa8 mwater table

An 8 m thick overconsolidated clay layer has Cc = 0.25, Cr = 0.02 and e₀ = 0.6. At its mid-depth the effective vertical stress is 120 kPa and the preconsolidation pressure is 170 kPa. A new building adds 170 kPa of vertical stress at mid-depth. Find the primary consolidation settlement S in mm.

H = 8 mCc = 0.25Cr = 0.02e0 = 0.6σ′0 = 120 kPaσ′p = 170 kPaΔσ = 170 kPa
S = mm
5.Hard
sandclayH = 2 mcv​ = 1.5 m²/year2 mimpervious rockwater table

A clay layer 2 m thick has a coefficient of consolidation cv = 1.5 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 = 2 mcv = 1.5 m²/yearU = 80%Tv = 0.567single drainage
t = years
6.Hard
sandclayH = 7.5 mcv​ = 3 m²/year7.5 msandwater table

A clay layer 7.5 m thick has a coefficient of consolidation cv = 3 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 = 7.5 mcv = 3 m²/yearU = 70%Tv = 0.403double drainage
t = years

Answer key

  1. 1. S = 1155 mm
  2. 2. S = 448.8 mm
  3. 3. S = 16.95 mm
  4. 4. S = 305.1 mm
  5. 5. t = 1.512 years
  6. 6. t = 1.889 years

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