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 = 25 kPasandγ = 19 kN/m³5 mclayγsat​ = 19 kN/m³Cc​ = 0.35, e0​ = 1.056 mwater tableX

A 6 m thick normally consolidated clay layer (γsat = 19 kN/m³, Cc = 0.35, e₀ = 1.05) 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 25 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 = 6 m, γsat = 19 kN/m³γw = 9.81 kN/m³Cc = 0.35e0 = 1.05Δσ = 25 kPa
S = mm
2.Easy
Δσ = 65 kPasandclayCc​ = 0.25e0​ = 0.75σ′0​ = 130 kPa4 mwater table

A 4 m thick layer of normally consolidated clay (Cc = 0.25, e₀ = 0.75) has an effective vertical stress of 130 kPa at its mid-depth. A wide fill raises the vertical stress in 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.

H = 4 mCc = 0.25e0 = 0.75σ′0 = 130 kPaΔσ = 65 kPa
S = mm
3.Medium
Δσ = 40 kPasandclayCc​ = 0.45, Cr​ = 0.02e0​ = 1.1σ′0​ = 100 kPaσ′p​ = 180 kPa7.5 mwater table

A 7.5 m thick overconsolidated clay layer has Cc = 0.45, Cr = 0.02 and e₀ = 1.1. At its mid-depth the effective vertical stress is 100 kPa and the preconsolidation pressure is 180 kPa. A new building adds 40 kPa of vertical stress at mid-depth. Find the primary consolidation settlement S in mm.

H = 7.5 mCc = 0.45Cr = 0.02e0 = 1.1σ′0 = 100 kPaσ′p = 180 kPaΔσ = 40 kPa
S = mm
4.Medium
Δσ = 130 kPasandclayCc​ = 0.25, Cr​ = 0.03e0​ = 0.95σ′0​ = 60 kPaσ′p​ = 110 kPa5 mwater table

A 5 m thick overconsolidated clay layer has Cc = 0.25, Cr = 0.03 and e₀ = 0.95. At its mid-depth the effective vertical stress is 60 kPa and the preconsolidation pressure is 110 kPa. A new building adds 130 kPa of vertical stress at mid-depth. Find the primary consolidation settlement S in mm.

H = 5 mCc = 0.25Cr = 0.03e0 = 0.95σ′0 = 60 kPaσ′p = 110 kPaΔσ = 130 kPa
S = mm
5.Hard
sandclayH = 9.5 mcv​ = 1 m²/year9.5 mimpervious rockwater table

A clay layer 9.5 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 80% average consolidation the time factor is Tv = 0.567. How many years t does the layer take to reach 80% consolidation?

H = 9.5 mcv = 1 m²/yearU = 80%Tv = 0.567single drainage
t = years
6.Hard
sandclayH = 3 mcv​ = 1.2 m²/year3 mimpervious rockwater table

A clay layer 3 m thick has a coefficient of consolidation cv = 1.2 m²/year. It lies on impervious rock, with sand above it, so water drains out only at the top. For 90% average consolidation the time factor is Tv = 0.848. How many years t does the layer take to reach 90% consolidation?

H = 3 mcv = 1.2 m²/yearU = 90%Tv = 0.848single drainage
t = years

Answer key

  1. 1. S = 82.58 mm
  2. 2. S = 100.6 mm
  3. 3. S = 10.44 mm
  4. 4. S = 172.4 mm
  5. 5. t = 51.17 years
  6. 6. t = 6.36 years

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