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 = 130 kPasandγ = 19 kN/m³6 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 6 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 130 kPa. Treat the layer as one sublayer with the stresses at its mid-depth. Find the primary consolidation settlement S in mm.

sand: Hs = 6 m, γ = 19 kN/m³clay: H = 9 m, γsat = 19 kN/m³γw = 9.81 kN/m³Cc = 0.5e0 = 0.8Δσ = 130 kPa
S = mm
2.Easy
Δσ = 150 kPasandγ = 18 kN/m³5 mclayγsat​ = 18.5 kN/m³Cc​ = 0.2, e0​ = 0.953 mwater tableX

A 3 m thick normally consolidated clay layer (γsat = 18.5 kN/m³, Cc = 0.2, e₀ = 0.95) 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 150 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 = 3 m, γsat = 18.5 kN/m³γw = 9.81 kN/m³Cc = 0.2e0 = 0.95Δσ = 150 kPa
S = mm
3.Medium
Δσ = 15 kPasandclayCc​ = 0.4, Cr​ = 0.06e0​ = 0.9σ′0​ = 75 kPaσ′p​ = 155 kPa4.5 mwater table

A 4.5 m thick overconsolidated clay layer has Cc = 0.4, Cr = 0.06 and e₀ = 0.9. At its mid-depth the effective vertical stress is 75 kPa and the preconsolidation pressure is 155 kPa. A new building adds 15 kPa of vertical stress at mid-depth. Find the primary consolidation settlement S in mm.

H = 4.5 mCc = 0.4Cr = 0.06e0 = 0.9σ′0 = 75 kPaσ′p = 155 kPaΔσ = 15 kPa
S = mm
4.Medium
Δσ = 100 kPasandclayCc​ = 0.3, Cr​ = 0.02e0​ = 0.85σ′0​ = 40 kPaσ′p​ = 70 kPa5.5 mwater table

A 5.5 m thick overconsolidated clay layer has Cc = 0.3, Cr = 0.02 and e₀ = 0.85. At its mid-depth the effective vertical stress is 40 kPa and the preconsolidation pressure is 70 kPa. A new building adds 100 kPa of vertical stress at mid-depth. Find the primary consolidation settlement S in mm.

H = 5.5 mCc = 0.3Cr = 0.02e0 = 0.85σ′0 = 40 kPaσ′p = 70 kPaΔσ = 100 kPa
S = mm
5.Hard
sandclayH = 6.5 mcv​ = 3 m²/year6.5 mimpervious rockwater table

A clay layer 6.5 m thick has a coefficient of consolidation cv = 3 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 = 6.5 mcv = 3 m²/yearU = 70%Tv = 0.403single drainage
t = years
6.Hard
sandclayH = 7.5 mcv​ = 1 m²/year7.5 msandwater table

A clay layer 7.5 m thick has a coefficient of consolidation cv = 1 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 = 7.5 mcv = 1 m²/yearU = 90%Tv = 0.848double drainage
t = years

Answer key

  1. 1. S = 660.2 mm
  2. 2. S = 120.1 mm
  3. 3. S = 11.25 mm
  4. 4. S = 282.9 mm
  5. 5. t = 5.676 years
  6. 6. t = 11.92 years

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