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 = 130 kPasandγ = 19 kN/m³5 mclayγsat​ = 19.5 kN/m³Cc​ = 0.2, e0​ = 0.67 mwater tableX

A 7 m thick normally consolidated clay layer (γsat = 19.5 kN/m³, Cc = 0.2, e₀ = 0.6) lies below 5 m of sand (γ = 19 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 m, γ = 19 kN/m³clay: H = 7 m, γsat = 19.5 kN/m³γw = 9.81 kN/m³Cc = 0.2e0 = 0.6Δσ = 130 kPa
S = mm
2.Easy
Δσ = 20 kPasandclayCc​ = 0.3e0​ = 0.75σ′0​ = 75 kPa2 mwater table

A 2 m thick layer of normally consolidated clay (Cc = 0.3, e₀ = 0.75) has an effective vertical stress of 75 kPa at its mid-depth. A wide fill raises the vertical stress in 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.

H = 2 mCc = 0.3e0 = 0.75σ′0 = 75 kPaΔσ = 20 kPa
S = mm
3.Medium
Δσ = 25 kPasandclayCc​ = 0.3, Cr​ = 0.04e0​ = 0.95σ′0​ = 45 kPaσ′p​ = 75 kPa6 mwater table

A 6 m thick overconsolidated clay layer has Cc = 0.3, Cr = 0.04 and e₀ = 0.95. At its mid-depth the effective vertical stress is 45 kPa and the preconsolidation pressure is 75 kPa. A new building adds 25 kPa of vertical stress at mid-depth. Find the primary consolidation settlement S in mm.

H = 6 mCc = 0.3Cr = 0.04e0 = 0.95σ′0 = 45 kPaσ′p = 75 kPaΔσ = 25 kPa
S = mm
4.Medium
Δσ = 20 kPasandclayCc​ = 0.5, Cr​ = 0.02e0​ = 0.7σ′0​ = 110 kPaσ′p​ = 150 kPa6.5 mwater table

A 6.5 m thick overconsolidated clay layer has Cc = 0.5, Cr = 0.02 and e₀ = 0.7. At its mid-depth the effective vertical stress is 110 kPa and the preconsolidation pressure is 150 kPa. A new building adds 20 kPa of vertical stress at mid-depth. Find the primary consolidation settlement S in mm.

H = 6.5 mCc = 0.5Cr = 0.02e0 = 0.7σ′0 = 110 kPaσ′p = 150 kPaΔσ = 20 kPa
S = mm
5.Hard
sandclayH = 8 mcv​ = 0.5 m²/year8 mimpervious rockwater table

A clay layer 8 m thick has a coefficient of consolidation cv = 0.5 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 = 8 mcv = 0.5 m²/yearU = 60%Tv = 0.287single drainage
t = years
6.Hard
sandclayH = 8 mcv​ = 1 m²/year8 mimpervious rockwater table

A clay layer 8 m thick has a coefficient of consolidation cv = 1 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 = 8 mcv = 1 m²/yearU = 70%Tv = 0.403single drainage
t = years

Answer key

  1. 1. S = 265 mm
  2. 2. S = 35.2 mm
  3. 3. S = 23.62 mm
  4. 4. S = 5.548 mm
  5. 5. t = 36.74 years
  6. 6. t = 25.79 years

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