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​ = 0.6e0​ = 0.95σ′0​ = 120 kPa4 mwater table

A 4 m thick layer of normally consolidated clay (Cc = 0.6, e₀ = 0.95) 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 = 4 mCc = 0.6e0 = 0.95σ′0 = 120 kPaΔσ = 95 kPa
S = mm
2.Easy
Δσ = 110 kPasandclayCc​ = 0.3e0​ = 1.3σ′0​ = 95 kPa4 mwater table

A 4 m thick layer of normally consolidated clay (Cc = 0.3, e₀ = 1.3) has an effective vertical stress of 95 kPa at its mid-depth. A wide fill raises the vertical stress in the clay by 110 kPa. Treat the layer as one sublayer with the stresses at its mid-depth. Find the primary consolidation settlement S in mm.

H = 4 mCc = 0.3e0 = 1.3σ′0 = 95 kPaΔσ = 110 kPa
S = mm
3.Medium
Δσ = 140 kPasandclayCc​ = 0.4, Cr​ = 0.06e0​ = 1.05σ′0​ = 110 kPaOCR = 2.56 mwater table

A 6 m thick overconsolidated clay layer has Cc = 0.4, Cr = 0.06 and e₀ = 1.05. At its mid-depth the effective vertical stress is 110 kPa and the overconsolidation ratio is OCR = 2.5. A new building adds 140 kPa of vertical stress at mid-depth. Find the primary consolidation settlement S in mm.

H = 6 mCc = 0.4Cr = 0.06e0 = 1.05σ′0 = 110 kPaOCR = 2.5Δσ = 140 kPa
S = mm
4.Medium
Δσ = 40 kPasandclayCc​ = 0.3, Cr​ = 0.06e0​ = 1.1σ′0​ = 115 kPaσ′p​ = 225 kPa5.5 mwater table

A 5.5 m thick overconsolidated clay layer has Cc = 0.3, Cr = 0.06 and e₀ = 1.1. At its mid-depth the effective vertical stress is 115 kPa and the preconsolidation pressure is 225 kPa. A new building adds 40 kPa of vertical stress at mid-depth. Find the primary consolidation settlement S in mm.

H = 5.5 mCc = 0.3Cr = 0.06e0 = 1.1σ′0 = 115 kPaσ′p = 225 kPaΔσ = 40 kPa
S = mm
5.Hard
sandclayH = 4.5 mcv​ = 5 m²/year4.5 mimpervious rockwater table

A clay layer 4.5 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 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 = 5 m²/yearU = 70%Tv = 0.403single drainage
t = years
6.Hard
sandclayH = 5.5 mcv​ = 3 m²/year5.5 msandwater table

A clay layer 5.5 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 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 = 3 m²/yearU = 80%Tv = 0.567double drainage
t = years

Answer key

  1. 1. S = 311.7 mm
  2. 2. S = 174.3 mm
  3. 3. S = 62.61 mm
  4. 4. S = 20.37 mm
  5. 5. t = 1.632 years
  6. 6. t = 1.429 years

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