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 = 90 kPasandγ = 19 kN/m³5 mclayγsat​ = 17.5 kN/m³Cc​ = 0.5, e0​ = 1.18 mwater tableX

An 8 m thick normally consolidated clay layer (γsat = 17.5 kN/m³, Cc = 0.5, e₀ = 1.1) lies below 5 m of sand (γ = 19 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 90 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 = 19 kN/m³clay: H = 8 m, γsat = 17.5 kN/m³γw = 9.81 kN/m³Cc = 0.5e0 = 1.1Δσ = 90 kPa
S = mm
2.Easy
Δσ = 65 kPasandγ = 18.5 kN/m³5 mclayγsat​ = 18.5 kN/m³Cc​ = 0.45, e0​ = 1.357 mwater tableX

A 7 m thick normally consolidated clay layer (γsat = 18.5 kN/m³, Cc = 0.45, e₀ = 1.35) 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 = 7 m, γsat = 18.5 kN/m³γw = 9.81 kN/m³Cc = 0.45e0 = 1.35Δσ = 65 kPa
S = mm
3.Medium
Δσ = 55 kPasandclayCc​ = 0.3, Cr​ = 0.05e0​ = 0.9σ′0​ = 110 kPaσ′p​ = 180 kPa5 mwater table

A 5 m thick overconsolidated clay layer has Cc = 0.3, Cr = 0.05 and e₀ = 0.9. At its mid-depth the effective vertical stress is 110 kPa and the preconsolidation pressure is 180 kPa. A new building adds 55 kPa of vertical stress at mid-depth. Find the primary consolidation settlement S in mm.

H = 5 mCc = 0.3Cr = 0.05e0 = 0.9σ′0 = 110 kPaσ′p = 180 kPaΔσ = 55 kPa
S = mm
4.Medium
Δσ = 220 kPasandclayCc​ = 0.35, Cr​ = 0.04e0​ = 1.2σ′0​ = 55 kPaσ′p​ = 135 kPa3.5 mwater table

A 3.5 m thick overconsolidated clay layer has Cc = 0.35, Cr = 0.04 and e₀ = 1.2. At its mid-depth the effective vertical stress is 55 kPa and the preconsolidation pressure is 135 kPa. A new building adds 220 kPa of vertical stress at mid-depth. Find the primary consolidation settlement S in mm.

H = 3.5 mCc = 0.35Cr = 0.04e0 = 1.2σ′0 = 55 kPaσ′p = 135 kPaΔσ = 220 kPa
S = mm
5.Hard
sandclayH = 8.5 mcv​ = 5 m²/year8.5 mimpervious rockwater table

A clay layer 8.5 m thick has a coefficient of consolidation cv = 5 m²/year. It lies on impervious rock, with sand above it, so water drains out only at the top. For 90% average consolidation the time factor is Tv = 0.848. How many years t does the layer take to reach 90% consolidation?

H = 8.5 mcv = 5 m²/yearU = 90%Tv = 0.848single drainage
t = years
6.Hard
sandclayH = 7.5 mcv​ = 3 m²/year7.5 msandwater table

A clay layer 7.5 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 80% average consolidation the time factor is Tv = 0.567. How many years t does the layer take to reach 80% consolidation?

H = 7.5 mcv = 3 m²/yearU = 80%Tv = 0.567double drainage
t = years

Answer key

  1. 1. S = 446.5 mm
  2. 2. S = 247.1 mm
  3. 3. S = 23.17 mm
  4. 4. S = 196.9 mm
  5. 5. t = 12.25 years
  6. 6. t = 2.658 years

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