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 = 120 kPasandγ = 18 kN/m³5 mclayγsat​ = 19.5 kN/m³Cc​ = 0.2, e0​ = 0.859 mwater tableX

A 9 m thick normally consolidated clay layer (γsat = 19.5 kN/m³, Cc = 0.2, e₀ = 0.85) 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 120 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 = 19.5 kN/m³γw = 9.81 kN/m³Cc = 0.2e0 = 0.85Δσ = 120 kPa
S = mm
2.Easy
Δσ = 20 kPasandγ = 18.5 kN/m³5.5 mclayγsat​ = 19.5 kN/m³Cc​ = 0.3, e0​ = 0.656 mwater tableX

A 6 m thick normally consolidated clay layer (γsat = 19.5 kN/m³, Cc = 0.3, e₀ = 0.65) 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 20 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 = 6 m, γsat = 19.5 kN/m³γw = 9.81 kN/m³Cc = 0.3e0 = 0.65Δσ = 20 kPa
S = mm
3.Medium
Δσ = 110 kPasandclayCc​ = 0.35, Cr​ = 0.06e0​ = 0.6σ′0​ = 110 kPaOCR = 28 mwater table

An 8 m thick overconsolidated clay layer has Cc = 0.35, Cr = 0.06 and e₀ = 0.6. At its mid-depth the effective vertical stress is 110 kPa and the overconsolidation ratio is OCR = 2. A new building adds 110 kPa of vertical stress at mid-depth. Find the primary consolidation settlement S in mm.

H = 8 mCc = 0.35Cr = 0.06e0 = 0.6σ′0 = 110 kPaOCR = 2Δσ = 110 kPa
S = mm
4.Medium
Δσ = 15 kPasandclayCc​ = 0.3, Cr​ = 0.05e0​ = 0.85σ′0​ = 80 kPaσ′p​ = 110 kPa7 mwater table

A 7 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 80 kPa and the preconsolidation pressure is 110 kPa. A new building adds 15 kPa of vertical stress at mid-depth. Find the primary consolidation settlement S in mm.

H = 7 mCc = 0.3Cr = 0.05e0 = 0.85σ′0 = 80 kPaσ′p = 110 kPaΔσ = 15 kPa
S = mm
5.Hard
sandclayH = 7 mcv​ = 5 m²/year7 msandwater table

A clay layer 7 m thick has a coefficient of consolidation cv = 5 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 = 7 mcv = 5 m²/yearU = 90%Tv = 0.848double drainage
t = years
6.Hard
sandclayH = 3 mcv​ = 0.5 m²/year3 mimpervious rockwater table

A clay layer 3 m thick has a coefficient of consolidation cv = 0.5 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 = 3 mcv = 0.5 m²/yearU = 80%Tv = 0.567single drainage
t = years

Answer key

  1. 1. S = 270.8 mm
  2. 2. S = 67.4 mm
  3. 3. S = 90.31 mm
  4. 4. S = 14.12 mm
  5. 5. t = 2.078 years
  6. 6. t = 10.21 years

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