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 = 150 kPasandγ = 17.5 kN/m³6 mclayγsat​ = 19 kN/m³Cc​ = 0.6, e0​ = 0.658 mwater tableX

An 8 m thick normally consolidated clay layer (γsat = 19 kN/m³, Cc = 0.6, e₀ = 0.65) lies below 6 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 150 kPa. Treat the layer as one sublayer with the stresses at its mid-depth. Find the primary consolidation settlement S in mm.

sand: Hs = 6 m, γ = 17.5 kN/m³clay: H = 8 m, γsat = 19 kN/m³γw = 9.81 kN/m³Cc = 0.6e0 = 0.65Δσ = 150 kPa
S = mm
2.Easy
Δσ = 65 kPasandγ = 17.5 kN/m³2.5 mclayγsat​ = 19.5 kN/m³Cc​ = 0.15, e0​ = 1.44 mwater tableX

A 4 m thick normally consolidated clay layer (γsat = 19.5 kN/m³, Cc = 0.15, e₀ = 1.4) lies below 2.5 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 65 kPa. Treat the layer as one sublayer with the stresses at its mid-depth. Find the primary consolidation settlement S in mm.

sand: Hs = 2.5 m, γ = 17.5 kN/m³clay: H = 4 m, γsat = 19.5 kN/m³γw = 9.81 kN/m³Cc = 0.15e0 = 1.4Δσ = 65 kPa
S = mm
3.Medium
Δσ = 10 kPasandclayCc​ = 0.2, Cr​ = 0.04e0​ = 1σ′0​ = 115 kPaσ′p​ = 195 kPa3 mwater table

A 3 m thick overconsolidated clay layer has Cc = 0.2, Cr = 0.04 and e₀ = 1. At its mid-depth the effective vertical stress is 115 kPa and the preconsolidation pressure is 195 kPa. A new building adds 10 kPa of vertical stress at mid-depth. Find the primary consolidation settlement S in mm.

H = 3 mCc = 0.2Cr = 0.04e0 = 1σ′0 = 115 kPaσ′p = 195 kPaΔσ = 10 kPa
S = mm
4.Medium
Δσ = 90 kPasandclayCc​ = 0.5, Cr​ = 0.03e0​ = 1.1σ′0​ = 95 kPaOCR = 1.56 mwater table

A 6 m thick overconsolidated clay layer has Cc = 0.5, Cr = 0.03 and e₀ = 1.1. At its mid-depth the effective vertical stress is 95 kPa and the overconsolidation ratio is OCR = 1.5. A new building adds 90 kPa of vertical stress at mid-depth. Find the primary consolidation settlement S in mm.

H = 6 mCc = 0.5Cr = 0.03e0 = 1.1σ′0 = 95 kPaOCR = 1.5Δσ = 90 kPa
S = mm
5.Hard
sandclayH = 3.5 m3.5 msandwater table

In a laboratory oedometer test, a clay specimen 25 mm thick, drained at the top and bottom, reaches 50% consolidation in 12 min. In the field the same clay forms a layer 3.5 m thick. It lies between two sand layers, so water drains out at the top and the bottom. How many days t does the field layer take to reach 50% consolidation?

hlab = 25 mmtlab = 12 minH = 3.5 mfield: double drainage
t = days
6.Hard
sandclayH = 4.5 mcv​ = 3 m²/year4.5 mimpervious rockwater table

A clay layer 4.5 m thick has a coefficient of consolidation cv = 3 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 = 4.5 mcv = 3 m²/yearU = 60%Tv = 0.287single drainage
t = years

Answer key

  1. 1. S = 911.9 mm
  2. 2. S = 76.85 mm
  3. 3. S = 2.173 mm
  4. 4. S = 177 mm
  5. 5. t = 163.3 days
  6. 6. t = 1.937 years

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