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 = 100 kPasandγ = 18 kN/m³2.5 mclayγsat​ = 19 kN/m³Cc​ = 0.5, e0​ = 0.89 mwater tableX

A 9 m thick normally consolidated clay layer (γsat = 19 kN/m³, Cc = 0.5, e₀ = 0.8) lies below 2.5 m of sand (γ = 18 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 100 kPa. Treat the layer as one sublayer with the stresses at its mid-depth. Find the primary consolidation settlement S in mm.

sand: Hs = 2.5 m, γ = 18 kN/m³clay: H = 9 m, γsat = 19 kN/m³γw = 9.81 kN/m³Cc = 0.5e0 = 0.8Δσ = 100 kPa
S = mm
2.Easy
Δσ = 45 kPasandγ = 18 kN/m³5 mclayγsat​ = 19 kN/m³Cc​ = 0.25, e0​ = 1.39 mwater tableX

A 9 m thick normally consolidated clay layer (γsat = 19 kN/m³, Cc = 0.25, e₀ = 1.3) lies below 5 m of sand (γ = 18 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 45 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 kN/m³clay: H = 9 m, γsat = 19 kN/m³γw = 9.81 kN/m³Cc = 0.25e0 = 1.3Δσ = 45 kPa
S = mm
3.Medium
Δσ = 90 kPasandclayCc​ = 0.3, Cr​ = 0.05e0​ = 0.85σ′0​ = 90 kPaOCR = 2.55.5 mwater table

A 5.5 m thick overconsolidated clay layer has Cc = 0.3, Cr = 0.05 and e₀ = 0.85. At its mid-depth the effective vertical stress is 90 kPa and the overconsolidation ratio is OCR = 2.5. A new building adds 90 kPa of vertical stress at mid-depth. Find the primary consolidation settlement S in mm.

H = 5.5 mCc = 0.3Cr = 0.05e0 = 0.85σ′0 = 90 kPaOCR = 2.5Δσ = 90 kPa
S = mm
4.Medium
Δσ = 160 kPasandclayCc​ = 0.2, Cr​ = 0.03e0​ = 0.65σ′0​ = 80 kPaOCR = 2.54 mwater table

A 4 m thick overconsolidated clay layer has Cc = 0.2, Cr = 0.03 and e₀ = 0.65. At its mid-depth the effective vertical stress is 80 kPa and the overconsolidation ratio is OCR = 2.5. A new building adds 160 kPa of vertical stress at mid-depth. Find the primary consolidation settlement S in mm.

H = 4 mCc = 0.2Cr = 0.03e0 = 0.65σ′0 = 80 kPaOCR = 2.5Δσ = 160 kPa
S = mm
5.Hard
sandclayH = 5 mcv​ = 3 m²/year5 msandwater table

A clay layer 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 90% average consolidation the time factor is Tv = 0.848. How many years t does the layer take to reach 90% consolidation?

H = 5 mcv = 3 m²/yearU = 90%Tv = 0.848double drainage
t = years
6.Hard
sandclayH = 7.5 mcv​ = 0.8 m²/year7.5 mimpervious rockwater table

A clay layer 7.5 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 50% average consolidation the time factor is Tv = 0.197. How many years t does the layer take to reach 50% consolidation?

H = 7.5 mcv = 0.8 m²/yearU = 50%Tv = 0.197single drainage
t = years

Answer key

  1. 1. S = 835.1 mm
  2. 2. S = 125.2 mm
  3. 3. S = 44.75 mm
  4. 4. S = 67.33 mm
  5. 5. t = 1.767 years
  6. 6. t = 13.85 years

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