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 = 85 kPasandγ = 17 kN/m³4 mclayγsat​ = 18.5 kN/m³Cc​ = 0.4, e0​ = 1.2510 mwater tableX

A 10 m thick normally consolidated clay layer (γsat = 18.5 kN/m³, Cc = 0.4, e₀ = 1.25) lies below 4 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 85 kPa. Treat the layer as one sublayer with the stresses at its mid-depth. Find the primary consolidation settlement S in mm.

sand: Hs = 4 m, γ = 17 kN/m³clay: H = 10 m, γsat = 18.5 kN/m³γw = 9.81 kN/m³Cc = 0.4e0 = 1.25Δσ = 85 kPa
S = mm
2.Easy
Δσ = 20 kPasandclayCc​ = 0.25e0​ = 1.05σ′0​ = 95 kPa9 mwater table

A 9 m thick layer of normally consolidated clay (Cc = 0.25, e₀ = 1.05) has an effective vertical stress of 95 kPa at its mid-depth. A wide fill raises the vertical stress in 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.

H = 9 mCc = 0.25e0 = 1.05σ′0 = 95 kPaΔσ = 20 kPa
S = mm
3.Medium
Δσ = 80 kPasandclayCc​ = 0.4, Cr​ = 0.04e0​ = 1.15σ′0​ = 45 kPaσ′p​ = 135 kPa7 mwater table

A 7 m thick overconsolidated clay layer has Cc = 0.4, Cr = 0.04 and e₀ = 1.15. At its mid-depth the effective vertical stress is 45 kPa and the preconsolidation pressure is 135 kPa. A new building adds 80 kPa of vertical stress at mid-depth. Find the primary consolidation settlement S in mm.

H = 7 mCc = 0.4Cr = 0.04e0 = 1.15σ′0 = 45 kPaσ′p = 135 kPaΔσ = 80 kPa
S = mm
4.Medium
Δσ = 60 kPasandclayCc​ = 0.35, Cr​ = 0.06e0​ = 1.15σ′0​ = 70 kPaOCR = 1.52 mwater table

A 2 m thick overconsolidated clay layer has Cc = 0.35, Cr = 0.06 and e₀ = 1.15. At its mid-depth the effective vertical stress is 70 kPa and the overconsolidation ratio is OCR = 1.5. A new building adds 60 kPa of vertical stress at mid-depth. Find the primary consolidation settlement S in mm.

H = 2 mCc = 0.35Cr = 0.06e0 = 1.15σ′0 = 70 kPaOCR = 1.5Δσ = 60 kPa
S = mm
5.Hard
sandclayH = 5 mcv​ = 0.5 m²/year5 msandwater table

A clay layer 5 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 80% average consolidation the time factor is Tv = 0.567. How many years t does the layer take to reach 80% consolidation?

H = 5 mcv = 0.5 m²/yearU = 80%Tv = 0.567double drainage
t = years
6.Hard
sandclayH = 8 mcv​ = 3 m²/year8 msandwater table

A clay layer 8 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 70% average consolidation the time factor is Tv = 0.403. How many years t does the layer take to reach 70% consolidation?

H = 8 mcv = 3 m²/yearU = 70%Tv = 0.403double drainage
t = years

Answer key

  1. 1. S = 437.6 mm
  2. 2. S = 91.07 mm
  3. 3. S = 57.78 mm
  4. 4. S = 40.03 mm
  5. 5. t = 7.088 years
  6. 6. t = 2.149 years

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