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 = 35 kPasandclayCc​ = 0.25e0​ = 0.7σ′0​ = 135 kPa9.5 mwater table

A 9.5 m thick layer of normally consolidated clay (Cc = 0.25, e₀ = 0.7) has an effective vertical stress of 135 kPa at its mid-depth. A wide fill raises the vertical stress in the clay by 35 kPa. Treat the layer as one sublayer with the stresses at its mid-depth. Find the primary consolidation settlement S in mm.

H = 9.5 mCc = 0.25e0 = 0.7σ′0 = 135 kPaΔσ = 35 kPa
S = mm
2.Easy
Δσ = 25 kPasandclayCc​ = 0.35e0​ = 1.25σ′0​ = 115 kPa5 mwater table

A 5 m thick layer of normally consolidated clay (Cc = 0.35, e₀ = 1.25) has an effective vertical stress of 115 kPa at its mid-depth. A wide fill raises the vertical stress in the clay by 25 kPa. Treat the layer as one sublayer with the stresses at its mid-depth. Find the primary consolidation settlement S in mm.

H = 5 mCc = 0.35e0 = 1.25σ′0 = 115 kPaΔσ = 25 kPa
S = mm
3.Medium
Δσ = 160 kPasandclayCc​ = 0.45, Cr​ = 0.03e0​ = 1.1σ′0​ = 55 kPaσ′p​ = 95 kPa3 mwater table

A 3 m thick overconsolidated clay layer has Cc = 0.45, Cr = 0.03 and e₀ = 1.1. At its mid-depth the effective vertical stress is 55 kPa and the preconsolidation pressure is 95 kPa. A new building adds 160 kPa of vertical stress at mid-depth. Find the primary consolidation settlement S in mm.

H = 3 mCc = 0.45Cr = 0.03e0 = 1.1σ′0 = 55 kPaσ′p = 95 kPaΔσ = 160 kPa
S = mm
4.Medium
Δσ = 70 kPasandclayCc​ = 0.4, Cr​ = 0.05e0​ = 1.1σ′0​ = 55 kPaOCR = 1.53 mwater table

A 3 m thick overconsolidated clay layer has Cc = 0.4, Cr = 0.05 and e₀ = 1.1. At its mid-depth the effective vertical stress is 55 kPa and the overconsolidation ratio is OCR = 1.5. A new building adds 70 kPa of vertical stress at mid-depth. Find the primary consolidation settlement S in mm.

H = 3 mCc = 0.4Cr = 0.05e0 = 1.1σ′0 = 55 kPaOCR = 1.5Δσ = 70 kPa
S = mm
5.Hard
sandclayH = 3.5 mcv​ = 3 m²/year3.5 msandwater table

A clay layer 3.5 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 60% average consolidation the time factor is Tv = 0.287. How many years t does the layer take to reach 60% consolidation?

H = 3.5 mcv = 3 m²/yearU = 60%Tv = 0.287double drainage
t = years
6.Hard
sandclayH = 5.5 mcv​ = 0.8 m²/year5.5 mimpervious rockwater table

A clay layer 5.5 m thick has a coefficient of consolidation cv = 0.8 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 = 0.8 m²/yearU = 80%Tv = 0.567single drainage
t = years

Answer key

  1. 1. S = 139.9 mm
  2. 2. S = 66.45 mm
  3. 3. S = 238.2 mm
  4. 4. S = 115.7 mm
  5. 5. t = 0.293 years
  6. 6. t = 21.44 years

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