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 = 100 kPasandclayCc​ = 0.25e0​ = 1.4σ′0​ = 90 kPa5.5 mwater table

A 5.5 m thick layer of normally consolidated clay (Cc = 0.25, e₀ = 1.4) has an effective vertical stress of 90 kPa at its mid-depth. A wide fill raises the vertical stress in the clay by 100 kPa. Treat the layer as one sublayer with the stresses at its mid-depth. Find the primary consolidation settlement S in mm.

H = 5.5 mCc = 0.25e0 = 1.4σ′0 = 90 kPaΔσ = 100 kPa
S = mm
2.Easy
Δσ = 90 kPasandγ = 18.5 kN/m³5.5 mclayγsat​ = 19.5 kN/m³Cc​ = 0.3, e0​ = 1.056 mwater tableX

A 6 m thick normally consolidated clay layer (γsat = 19.5 kN/m³, Cc = 0.3, e₀ = 1.05) lies below 5.5 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 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 = 5.5 m, γ = 18.5 kN/m³clay: H = 6 m, γsat = 19.5 kN/m³γw = 9.81 kN/m³Cc = 0.3e0 = 1.05Δσ = 90 kPa
S = mm
3.Medium
Δσ = 120 kPasandclayCc​ = 0.35, Cr​ = 0.04e0​ = 1.1σ′0​ = 85 kPaOCR = 24 mwater table

A 4 m thick overconsolidated clay layer has Cc = 0.35, Cr = 0.04 and e₀ = 1.1. At its mid-depth the effective vertical stress is 85 kPa and the overconsolidation ratio is OCR = 2. A new building adds 120 kPa of vertical stress at mid-depth. Find the primary consolidation settlement S in mm.

H = 4 mCc = 0.35Cr = 0.04e0 = 1.1σ′0 = 85 kPaOCR = 2Δσ = 120 kPa
S = mm
4.Medium
Δσ = 120 kPasandclayCc​ = 0.2, Cr​ = 0.03e0​ = 1.1σ′0​ = 45 kPaOCR = 32 mwater table

A 2 m thick overconsolidated clay layer has Cc = 0.2, Cr = 0.03 and e₀ = 1.1. At its mid-depth the effective vertical stress is 45 kPa and the overconsolidation ratio is OCR = 3. A new building adds 120 kPa of vertical stress at mid-depth. Find the primary consolidation settlement S in mm.

H = 2 mCc = 0.2Cr = 0.03e0 = 1.1σ′0 = 45 kPaOCR = 3Δσ = 120 kPa
S = mm
5.Hard
sandclayH = 8.5 mcv​ = 2 m²/year8.5 msandwater table

A clay layer 8.5 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 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 = 2 m²/yearU = 90%Tv = 0.848double drainage
t = years
6.Hard
sandclayH = 9.5 mcv​ = 1.2 m²/year9.5 msandwater table

A clay layer 9.5 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 70% average consolidation the time factor is Tv = 0.403. How many years t does the layer take to reach 70% consolidation?

H = 9.5 mcv = 1.2 m²/yearU = 70%Tv = 0.403double drainage
t = years

Answer key

  1. 1. S = 185.9 mm
  2. 2. S = 199.6 mm
  3. 3. S = 77.14 mm
  4. 4. S = 30.23 mm
  5. 5. t = 7.659 years
  6. 6. t = 7.577 years

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