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 = 25 kPasandclayCc​ = 0.25e0​ = 0.7σ′0​ = 60 kPa10 mwater table

A 10 m thick layer of normally consolidated clay (Cc = 0.25, e₀ = 0.7) has an effective vertical stress of 60 kPa at its mid-depth. A wide fill raises the vertical stress in the clay by 25 kPa. Treat the layer as one sublayer with the stresses at its mid-depth. Find the primary consolidation settlement S in mm.

H = 10 mCc = 0.25e0 = 0.7σ′0 = 60 kPaΔσ = 25 kPa
S = mm
2.Easy
Δσ = 65 kPasandγ = 17.5 kN/m³5 mclayγsat​ = 18.5 kN/m³Cc​ = 0.2, e0​ = 0.85 mwater tableX

A 5 m thick normally consolidated clay layer (γsat = 18.5 kN/m³, Cc = 0.2, e₀ = 0.8) lies below 5 m of sand (γ = 17.5 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 = 17.5 kN/m³clay: H = 5 m, γsat = 18.5 kN/m³γw = 9.81 kN/m³Cc = 0.2e0 = 0.8Δσ = 65 kPa
S = mm
3.Medium
Δσ = 10 kPasandclayCc​ = 0.3, Cr​ = 0.04e0​ = 0.85σ′0​ = 110 kPaσ′p​ = 190 kPa3.5 mwater table

A 3.5 m thick overconsolidated clay layer has Cc = 0.3, Cr = 0.04 and e₀ = 0.85. At its mid-depth the effective vertical stress is 110 kPa and the preconsolidation pressure is 190 kPa. A new building adds 10 kPa of vertical stress at mid-depth. Find the primary consolidation settlement S in mm.

H = 3.5 mCc = 0.3Cr = 0.04e0 = 0.85σ′0 = 110 kPaσ′p = 190 kPaΔσ = 10 kPa
S = mm
4.Medium
Δσ = 50 kPasandclayCc​ = 0.35, Cr​ = 0.05e0​ = 0.65σ′0​ = 45 kPaσ′p​ = 145 kPa3 mwater table

A 3 m thick overconsolidated clay layer has Cc = 0.35, Cr = 0.05 and e₀ = 0.65. At its mid-depth the effective vertical stress is 45 kPa and the preconsolidation pressure is 145 kPa. A new building adds 50 kPa of vertical stress at mid-depth. Find the primary consolidation settlement S in mm.

H = 3 mCc = 0.35Cr = 0.05e0 = 0.65σ′0 = 45 kPaσ′p = 145 kPaΔσ = 50 kPa
S = mm
5.Hard
sandclayH = 7 mcv​ = 1.2 m²/year7 msandwater table

A clay layer 7 m thick has a coefficient of consolidation cv = 1.2 m²/year. It lies between two sand layers, so water drains out at the top and the bottom. 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 mcv = 1.2 m²/yearU = 50%Tv = 0.197double drainage
t = years
6.Hard
sandclayH = 6.5 mcv​ = 1.2 m²/year6.5 msandwater table

A clay layer 6.5 m thick has a coefficient of consolidation cv = 1.2 m²/year. It lies between two sand layers, so water drains out at the top and the bottom. For 60% average consolidation the time factor is Tv = 0.287. How many years t does the layer take to reach 60% consolidation?

H = 6.5 mcv = 1.2 m²/yearU = 60%Tv = 0.287double drainage
t = years

Answer key

  1. 1. S = 222.5 mm
  2. 2. S = 112.7 mm
  3. 3. S = 2.86 mm
  4. 4. S = 29.5 mm
  5. 5. t = 2.011 years
  6. 6. t = 2.526 years

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