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 = 50 kPasandγ = 17 kN/m³4.5 mclayγsat​ = 19 kN/m³Cc​ = 0.4, e0​ = 1.36 mwater tableX

A 6 m thick normally consolidated clay layer (γsat = 19 kN/m³, Cc = 0.4, e₀ = 1.3) lies below 4.5 m of sand (γ = 17 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 50 kPa. Treat the layer as one sublayer with the stresses at its mid-depth. Find the primary consolidation settlement S in mm.

sand: Hs = 4.5 m, γ = 17 kN/m³clay: H = 6 m, γsat = 19 kN/m³γw = 9.81 kN/m³Cc = 0.4e0 = 1.3Δσ = 50 kPa
S = mm
2.Easy
Δσ = 65 kPasandγ = 18.5 kN/m³5.5 mclayγsat​ = 17.5 kN/m³Cc​ = 0.5, e0​ = 1.43 mwater tableX

A 3 m thick normally consolidated clay layer (γsat = 17.5 kN/m³, Cc = 0.5, e₀ = 1.4) lies below 5.5 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 = 5.5 m, γ = 18.5 kN/m³clay: H = 3 m, γsat = 17.5 kN/m³γw = 9.81 kN/m³Cc = 0.5e0 = 1.4Δσ = 65 kPa
S = mm
3.Medium
Δσ = 50 kPasandclayCc​ = 0.4, Cr​ = 0.03e0​ = 1.15σ′0​ = 65 kPaσ′p​ = 125 kPa5 mwater table

A 5 m thick overconsolidated clay layer has Cc = 0.4, Cr = 0.03 and e₀ = 1.15. At its mid-depth the effective vertical stress is 65 kPa and the preconsolidation pressure is 125 kPa. A new building adds 50 kPa of vertical stress at mid-depth. Find the primary consolidation settlement S in mm.

H = 5 mCc = 0.4Cr = 0.03e0 = 1.15σ′0 = 65 kPaσ′p = 125 kPaΔσ = 50 kPa
S = mm
4.Medium
Δσ = 180 kPasandclayCc​ = 0.25, Cr​ = 0.06e0​ = 0.7σ′0​ = 80 kPaOCR = 2.52.5 mwater table

A 2.5 m thick overconsolidated clay layer has Cc = 0.25, Cr = 0.06 and e₀ = 0.7. At its mid-depth the effective vertical stress is 80 kPa and the overconsolidation ratio is OCR = 2.5. A new building adds 180 kPa of vertical stress at mid-depth. Find the primary consolidation settlement S in mm.

H = 2.5 mCc = 0.25Cr = 0.06e0 = 0.7σ′0 = 80 kPaOCR = 2.5Δσ = 180 kPa
S = mm
5.Hard
sandclayH = 2 mcv​ = 1.2 m²/year2 mimpervious rockwater table

A clay layer 2 m thick has a coefficient of consolidation cv = 1.2 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 = 1.2 m²/yearU = 80%Tv = 0.567single drainage
t = years
6.Hard
sandclayH = 5 mcv​ = 1.2 m²/year5 mimpervious rockwater table

A clay layer 5 m thick has a coefficient of consolidation cv = 1.2 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 = 5 mcv = 1.2 m²/yearU = 70%Tv = 0.403single drainage
t = years

Answer key

  1. 1. S = 177.8 mm
  2. 2. S = 123.1 mm
  3. 3. S = 17.29 mm
  4. 4. S = 77 mm
  5. 5. t = 1.89 years
  6. 6. t = 8.396 years

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