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​ = 0.45e0​ = 1.35σ′0​ = 120 kPa9.5 mwater table

A 9.5 m thick layer of normally consolidated clay (Cc = 0.45, e₀ = 1.35) has an effective vertical stress of 120 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 = 9.5 mCc = 0.45e0 = 1.35σ′0 = 120 kPaΔσ = 100 kPa
S = mm
2.Easy
Δσ = 130 kPasandγ = 17.5 kN/m³5.5 mclayγsat​ = 18.5 kN/m³Cc​ = 0.4, e0​ = 1.053 mwater tableX

A 3 m thick normally consolidated clay layer (γsat = 18.5 kN/m³, Cc = 0.4, e₀ = 1.05) lies below 5.5 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 130 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 = 17.5 kN/m³clay: H = 3 m, γsat = 18.5 kN/m³γw = 9.81 kN/m³Cc = 0.4e0 = 1.05Δσ = 130 kPa
S = mm
3.Medium
Δσ = 120 kPasandclayCc​ = 0.5, Cr​ = 0.03e0​ = 1.15σ′0​ = 40 kPaOCR = 2.54 mwater table

A 4 m thick overconsolidated clay layer has Cc = 0.5, Cr = 0.03 and e₀ = 1.15. At its mid-depth the effective vertical stress is 40 kPa and the overconsolidation ratio is OCR = 2.5. A new building adds 120 kPa of vertical stress at mid-depth. Find the primary consolidation settlement S in mm.

H = 4 mCc = 0.5Cr = 0.03e0 = 1.15σ′0 = 40 kPaOCR = 2.5Δσ = 120 kPa
S = mm
4.Medium
Δσ = 140 kPasandclayCc​ = 0.3, Cr​ = 0.06e0​ = 0.6σ′0​ = 110 kPaσ′p​ = 230 kPa7.5 mwater table

A 7.5 m thick overconsolidated clay layer has Cc = 0.3, Cr = 0.06 and e₀ = 0.6. At its mid-depth the effective vertical stress is 110 kPa and the preconsolidation pressure is 230 kPa. A new building adds 140 kPa of vertical stress at mid-depth. Find the primary consolidation settlement S in mm.

H = 7.5 mCc = 0.3Cr = 0.06e0 = 0.6σ′0 = 110 kPaσ′p = 230 kPaΔσ = 140 kPa
S = mm
5.Hard
sandclayH = 10 mcv​ = 0.8 m²/year10 mimpervious rockwater table

A clay layer 10 m thick has a coefficient of consolidation cv = 0.8 m²/year. It lies on impervious rock, with sand above it, so water drains out only at the top. For 70% average consolidation the time factor is Tv = 0.403. How many years t does the layer take to reach 70% consolidation?

H = 10 mcv = 0.8 m²/yearU = 70%Tv = 0.403single drainage
t = years
6.Hard
sandclayH = 3 mcv​ = 2.5 m²/year3 msandwater table

A clay layer 3 m thick has a coefficient of consolidation cv = 2.5 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 = 3 mcv = 2.5 m²/yearU = 60%Tv = 0.287double drainage
t = years

Answer key

  1. 1. S = 478.9 mm
  2. 2. S = 199.2 mm
  3. 3. S = 212.1 mm
  4. 4. S = 141 mm
  5. 5. t = 50.38 years
  6. 6. t = 0.2583 years

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