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 = 20 kPasandγ = 17 kN/m³5 mclayγsat​ = 18.5 kN/m³Cc​ = 0.15, e0​ = 0.95 mwater tableX

A 5 m thick normally consolidated clay layer (γsat = 18.5 kN/m³, Cc = 0.15, e₀ = 0.9) lies below 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 20 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 m, γ = 17 kN/m³clay: H = 5 m, γsat = 18.5 kN/m³γw = 9.81 kN/m³Cc = 0.15e0 = 0.9Δσ = 20 kPa
S = mm
2.Easy
Δσ = 140 kPasandγ = 18 kN/m³4.5 mclayγsat​ = 18.5 kN/m³Cc​ = 0.3, e0​ = 1.29 mwater tableX

A 9 m thick normally consolidated clay layer (γsat = 18.5 kN/m³, Cc = 0.3, e₀ = 1.2) lies below 4.5 m of sand (γ = 18 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 140 kPa. Treat the layer as one sublayer with the stresses at its mid-depth. Find the primary consolidation settlement S in mm.

sand: Hs = 4.5 m, γ = 18 kN/m³clay: H = 9 m, γsat = 18.5 kN/m³γw = 9.81 kN/m³Cc = 0.3e0 = 1.2Δσ = 140 kPa
S = mm
3.Medium
Δσ = 170 kPasandclayCc​ = 0.5, Cr​ = 0.02e0​ = 0.65σ′0​ = 50 kPaσ′p​ = 120 kPa5 mwater table

A 5 m thick overconsolidated clay layer has Cc = 0.5, Cr = 0.02 and e₀ = 0.65. At its mid-depth the effective vertical stress is 50 kPa and the preconsolidation pressure is 120 kPa. A new building adds 170 kPa of vertical stress at mid-depth. Find the primary consolidation settlement S in mm.

H = 5 mCc = 0.5Cr = 0.02e0 = 0.65σ′0 = 50 kPaσ′p = 120 kPaΔσ = 170 kPa
S = mm
4.Medium
Δσ = 20 kPasandclayCc​ = 0.3, Cr​ = 0.05e0​ = 1.1σ′0​ = 100 kPaOCR = 1.53 mwater table

A 3 m thick overconsolidated clay layer has Cc = 0.3, Cr = 0.05 and e₀ = 1.1. At its mid-depth the effective vertical stress is 100 kPa and the overconsolidation ratio is OCR = 1.5. A new building adds 20 kPa of vertical stress at mid-depth. Find the primary consolidation settlement S in mm.

H = 3 mCc = 0.3Cr = 0.05e0 = 1.1σ′0 = 100 kPaOCR = 1.5Δσ = 20 kPa
S = mm
5.Hard
sandclayH = 7 mcv​ = 1.5 m²/year7 mimpervious rockwater table

A clay layer 7 m thick has a coefficient of consolidation cv = 1.5 m²/year. It lies on impervious rock, with sand above it, so water drains out only at the top. For 60% average consolidation the time factor is Tv = 0.287. How many years t does the layer take to reach 60% consolidation?

H = 7 mcv = 1.5 m²/yearU = 60%Tv = 0.287single drainage
t = years
6.Hard
sandclayH = 2 mcv​ = 2.5 m²/year2 msandwater table

A clay layer 2 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 50% average consolidation the time factor is Tv = 0.197. How many years t does the layer take to reach 50% consolidation?

H = 2 mcv = 2.5 m²/yearU = 50%Tv = 0.197double drainage
t = years

Answer key

  1. 1. S = 29.45 mm
  2. 2. S = 411.9 mm
  3. 3. S = 421.9 mm
  4. 4. S = 5.656 mm
  5. 5. t = 9.375 years
  6. 6. t = 0.0788 years

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