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/m³2 mclayγsat​ = 17.5 kN/m³Cc​ = 0.35, e0​ = 1.43 mwater tableX

A 3 m thick normally consolidated clay layer (γsat = 17.5 kN/m³, Cc = 0.35, e₀ = 1.4) lies below 2 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 = 2 m, γ = 17 kN/m³clay: H = 3 m, γsat = 17.5 kN/m³γw = 9.81 kN/m³Cc = 0.35e0 = 1.4Δσ = 105 kPa
S = mm
2.Easy
Δσ = 150 kPasandclayCc​ = 0.2e0​ = 1.15σ′0​ = 90 kPa2 mwater table

A 2 m thick layer of normally consolidated clay (Cc = 0.2, e₀ = 1.15) has an effective vertical stress of 90 kPa at its mid-depth. A wide fill raises the vertical stress in 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.

H = 2 mCc = 0.2e0 = 1.15σ′0 = 90 kPaΔσ = 150 kPa
S = mm
3.Medium
Δσ = 170 kPasandclayCc​ = 0.4, Cr​ = 0.06e0​ = 0.75σ′0​ = 80 kPaOCR = 34 mwater table

A 4 m thick overconsolidated clay layer has Cc = 0.4, Cr = 0.06 and e₀ = 0.75. At its mid-depth the effective vertical stress is 80 kPa and the overconsolidation ratio is OCR = 3. A new building adds 170 kPa of vertical stress at mid-depth. Find the primary consolidation settlement S in mm.

H = 4 mCc = 0.4Cr = 0.06e0 = 0.75σ′0 = 80 kPaOCR = 3Δσ = 170 kPa
S = mm
4.Medium
Δσ = 60 kPasandclayCc​ = 0.2, Cr​ = 0.02e0​ = 0.75σ′0​ = 40 kPaσ′p​ = 90 kPa3 mwater table

A 3 m thick overconsolidated clay layer has Cc = 0.2, Cr = 0.02 and e₀ = 0.75. At its mid-depth the effective vertical stress is 40 kPa and the preconsolidation pressure is 90 kPa. A new building adds 60 kPa of vertical stress at mid-depth. Find the primary consolidation settlement S in mm.

H = 3 mCc = 0.2Cr = 0.02e0 = 0.75σ′0 = 40 kPaσ′p = 90 kPaΔσ = 60 kPa
S = mm
5.Hard
sandclayH = 7.5 mcv​ = 4 m²/year7.5 msandwater table

A clay layer 7.5 m thick has a coefficient of consolidation cv = 4 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 = 7.5 mcv = 4 m²/yearU = 70%Tv = 0.403double drainage
t = years
6.Hard
sandclayH = 7 mcv​ = 3 m²/year7 msandwater table

A clay layer 7 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 = 7 mcv = 3 m²/yearU = 70%Tv = 0.403double drainage
t = years

Answer key

  1. 1. S = 227.2 mm
  2. 2. S = 79.25 mm
  3. 3. S = 81.64 mm
  4. 4. S = 27.76 mm
  5. 5. t = 1.417 years
  6. 6. t = 1.646 years

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