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 = 105 kPasandγ = 17 kN/m³5.5 mclayγsat​ = 18 kN/m³Cc​ = 0.45, e0​ = 0.64 mwater tableX

A 4 m thick normally consolidated clay layer (γsat = 18 kN/m³, Cc = 0.45, e₀ = 0.6) lies below 5.5 m of sand (γ = 17 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 105 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 = 17 kN/m³clay: H = 4 m, γsat = 18 kN/m³γw = 9.81 kN/m³Cc = 0.45e0 = 0.6Δσ = 105 kPa
S = mm
2.Easy
Δσ = 80 kPasandclayCc​ = 0.5e0​ = 0.85σ′0​ = 95 kPa5 mwater table

A 5 m thick layer of normally consolidated clay (Cc = 0.5, e₀ = 0.85) has an effective vertical stress of 95 kPa at its mid-depth. A wide fill raises the vertical stress in the clay by 80 kPa. Treat the layer as one sublayer with the stresses at its mid-depth. Find the primary consolidation settlement S in mm.

H = 5 mCc = 0.5e0 = 0.85σ′0 = 95 kPaΔσ = 80 kPa
S = mm
3.Medium
Δσ = 65 kPasandclayCc​ = 0.45, Cr​ = 0.02e0​ = 1.2σ′0​ = 70 kPaσ′p​ = 180 kPa3.5 mwater table

A 3.5 m thick overconsolidated clay layer has Cc = 0.45, Cr = 0.02 and e₀ = 1.2. At its mid-depth the effective vertical stress is 70 kPa and the preconsolidation pressure is 180 kPa. A new building adds 65 kPa of vertical stress at mid-depth. Find the primary consolidation settlement S in mm.

H = 3.5 mCc = 0.45Cr = 0.02e0 = 1.2σ′0 = 70 kPaσ′p = 180 kPaΔσ = 65 kPa
S = mm
4.Medium
Δσ = 170 kPasandclayCc​ = 0.25, Cr​ = 0.05e0​ = 0.75σ′0​ = 65 kPaσ′p​ = 155 kPa5 mwater table

A 5 m thick overconsolidated clay layer has Cc = 0.25, Cr = 0.05 and e₀ = 0.75. At its mid-depth the effective vertical stress is 65 kPa and the preconsolidation pressure is 155 kPa. A new building adds 170 kPa of vertical stress at mid-depth. Find the primary consolidation settlement S in mm.

H = 5 mCc = 0.25Cr = 0.05e0 = 0.75σ′0 = 65 kPaσ′p = 155 kPaΔσ = 170 kPa
S = mm
5.Hard
sandclayH = 2 mcv​ = 0.5 m²/year2 msandwater table

A clay layer 2 m thick has a coefficient of consolidation cv = 0.5 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 = 2 mcv = 0.5 m²/yearU = 90%Tv = 0.848double drainage
t = years
6.Hard
sandclayH = 3.5 mcv​ = 2 m²/year3.5 msandwater table

A clay layer 3.5 m thick has a coefficient of consolidation cv = 2 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 = 3.5 mcv = 2 m²/yearU = 80%Tv = 0.567double drainage
t = years

Answer key

  1. 1. S = 327.7 mm
  2. 2. S = 358.5 mm
  3. 3. S = 9.076 mm
  4. 4. S = 183 mm
  5. 5. t = 1.696 years
  6. 6. t = 0.8682 years

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