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 = 65 kPasandγ = 18.5 kN/m³5 mclayγsat​ = 18 kN/m³Cc​ = 0.3, e0​ = 0.959 mwater tableX

A 9 m thick normally consolidated clay layer (γsat = 18 kN/m³, Cc = 0.3, e₀ = 0.95) lies below 5 m of sand (γ = 18.5 kN/m³). The water table is at the top of the clay; use γw = 9.81 kN/m³. A wide fill raises the vertical stress throughout the clay by 65 kPa. Treat the layer as one sublayer with the stresses at its mid-depth. Find the primary consolidation settlement S in mm.

sand: Hs = 5 m, γ = 18.5 kN/m³clay: H = 9 m, γsat = 18 kN/m³γw = 9.81 kN/m³Cc = 0.3e0 = 0.95Δσ = 65 kPa
S = mm
2.Easy
Δσ = 140 kPasandclayCc​ = 0.4e0​ = 0.7σ′0​ = 40 kPa3.5 mwater table

A 3.5 m thick layer of normally consolidated clay (Cc = 0.4, e₀ = 0.7) has an effective vertical stress of 40 kPa at its mid-depth. A wide fill raises the vertical stress in the clay by 140 kPa. Treat the layer as one sublayer with the stresses at its mid-depth. Find the primary consolidation settlement S in mm.

H = 3.5 mCc = 0.4e0 = 0.7σ′0 = 40 kPaΔσ = 140 kPa
S = mm
3.Medium
Δσ = 85 kPasandclayCc​ = 0.4, Cr​ = 0.02e0​ = 1σ′0​ = 75 kPaσ′p​ = 175 kPa4 mwater table

A 4 m thick overconsolidated clay layer has Cc = 0.4, Cr = 0.02 and e₀ = 1. At its mid-depth the effective vertical stress is 75 kPa and the preconsolidation pressure is 175 kPa. A new building adds 85 kPa of vertical stress at mid-depth. Find the primary consolidation settlement S in mm.

H = 4 mCc = 0.4Cr = 0.02e0 = 1σ′0 = 75 kPaσ′p = 175 kPaΔσ = 85 kPa
S = mm
4.Medium
Δσ = 50 kPasandclayCc​ = 0.3, Cr​ = 0.04e0​ = 0.8σ′0​ = 105 kPaOCR = 1.56.5 mwater table

A 6.5 m thick overconsolidated clay layer has Cc = 0.3, Cr = 0.04 and e₀ = 0.8. At its mid-depth the effective vertical stress is 105 kPa and the overconsolidation ratio is OCR = 1.5. A new building adds 50 kPa of vertical stress at mid-depth. Find the primary consolidation settlement S in mm.

H = 6.5 mCc = 0.3Cr = 0.04e0 = 0.8σ′0 = 105 kPaOCR = 1.5Δσ = 50 kPa
S = mm
5.Hard
sandclayH = 3 m3 mimpervious rockwater table

In a laboratory oedometer test, a clay specimen 19 mm thick, drained at the top and bottom, reaches 50% consolidation in 4 min. In the field the same clay forms a layer 3 m thick. It lies on impervious rock, with sand above it, so water drains out only at the top. How many days t does the field layer take to reach 50% consolidation?

hlab = 19 mmtlab = 4 minH = 3 mfield: single drainage
t = days
6.Hard
sandclayH = 10 mcv​ = 1 m²/year10 mimpervious rockwater table

A clay layer 10 m thick has a coefficient of consolidation cv = 1 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 = 10 mcv = 1 m²/yearU = 80%Tv = 0.567single drainage
t = years

Answer key

  1. 1. S = 244.8 mm
  2. 2. S = 537.9 mm
  3. 3. S = 13.16 mm
  4. 4. S = 24.43 mm
  5. 5. t = 277 days
  6. 6. t = 56.7 years

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