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 = 115 kPasandclayCc​ = 0.35e0​ = 1.2σ′0​ = 75 kPa4.5 mwater table

A 4.5 m thick layer of normally consolidated clay (Cc = 0.35, e₀ = 1.2) has an effective vertical stress of 75 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 = 4.5 mCc = 0.35e0 = 1.2σ′0 = 75 kPaΔσ = 115 kPa
S = mm
2.Easy
Δσ = 75 kPasandclayCc​ = 0.3e0​ = 0.9σ′0​ = 65 kPa9 mwater table

A 9 m thick layer of normally consolidated clay (Cc = 0.3, e₀ = 0.9) has an effective vertical stress of 65 kPa at its mid-depth. A wide fill raises the vertical stress in the clay by 75 kPa. Treat the layer as one sublayer with the stresses at its mid-depth. Find the primary consolidation settlement S in mm.

H = 9 mCc = 0.3e0 = 0.9σ′0 = 65 kPaΔσ = 75 kPa
S = mm
3.Medium
Δσ = 70 kPasandclayCc​ = 0.35, Cr​ = 0.03e0​ = 0.8σ′0​ = 55 kPaσ′p​ = 135 kPa4 mwater table

A 4 m thick overconsolidated clay layer has Cc = 0.35, Cr = 0.03 and e₀ = 0.8. At its mid-depth the effective vertical stress is 55 kPa and the preconsolidation pressure is 135 kPa. A new building adds 70 kPa of vertical stress at mid-depth. Find the primary consolidation settlement S in mm.

H = 4 mCc = 0.35Cr = 0.03e0 = 0.8σ′0 = 55 kPaσ′p = 135 kPaΔσ = 70 kPa
S = mm
4.Medium
Δσ = 70 kPasandclayCc​ = 0.25, Cr​ = 0.03e0​ = 1.05σ′0​ = 110 kPaOCR = 1.55 mwater table

A 5 m thick overconsolidated clay layer has Cc = 0.25, Cr = 0.03 and e₀ = 1.05. At its mid-depth the effective vertical stress is 110 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 = 5 mCc = 0.25Cr = 0.03e0 = 1.05σ′0 = 110 kPaOCR = 1.5Δσ = 70 kPa
S = mm
5.Hard
sandclayH = 2.5 mcv​ = 1.5 m²/year2.5 mimpervious rockwater table

A clay layer 2.5 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 50% average consolidation the time factor is Tv = 0.197. How many years t does the layer take to reach 50% consolidation?

H = 2.5 mcv = 1.5 m²/yearU = 50%Tv = 0.197single drainage
t = years
6.Hard
sandclayH = 10 mcv​ = 2.5 m²/year10 mimpervious rockwater table

A clay layer 10 m thick has a coefficient of consolidation cv = 2.5 m²/year. It lies on impervious rock, with sand above it, so water drains out only at the top. For 60% average consolidation the time factor is Tv = 0.287. How many years t does the layer take to reach 60% consolidation?

H = 10 mcv = 2.5 m²/yearU = 60%Tv = 0.287single drainage
t = years

Answer key

  1. 1. S = 289 mm
  2. 2. S = 473.5 mm
  3. 3. S = 23.77 mm
  4. 4. S = 35.93 mm
  5. 5. t = 0.8208 years
  6. 6. t = 11.48 years

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