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 = 105 kPasandγ = 19 kN/m³3 mclayγsat​ = 19.5 kN/m³Cc​ = 0.2, e0​ = 0.810 mwater tableX

A 10 m thick normally consolidated clay layer (γsat = 19.5 kN/m³, Cc = 0.2, e₀ = 0.8) lies below 3 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 105 kPa. Treat the layer as one sublayer with the stresses at its mid-depth. Find the primary consolidation settlement S in mm.

sand: Hs = 3 m, γ = 19 kN/m³clay: H = 10 m, γsat = 19.5 kN/m³γw = 9.81 kN/m³Cc = 0.2e0 = 0.8Δσ = 105 kPa
S = mm
2.Easy
Δσ = 30 kPasandclayCc​ = 0.5e0​ = 0.65σ′0​ = 65 kPa10 mwater table

A 10 m thick layer of normally consolidated clay (Cc = 0.5, e₀ = 0.65) has an effective vertical stress of 65 kPa at its mid-depth. A wide fill raises the vertical stress in the clay by 30 kPa. Treat the layer as one sublayer with the stresses at its mid-depth. Find the primary consolidation settlement S in mm.

H = 10 mCc = 0.5e0 = 0.65σ′0 = 65 kPaΔσ = 30 kPa
S = mm
3.Medium
Δσ = 100 kPasandclayCc​ = 0.35, Cr​ = 0.03e0​ = 1σ′0​ = 50 kPaσ′p​ = 90 kPa6.5 mwater table

A 6.5 m thick overconsolidated clay layer has Cc = 0.35, Cr = 0.03 and e₀ = 1. At its mid-depth the effective vertical stress is 50 kPa and the preconsolidation pressure is 90 kPa. A new building adds 100 kPa of vertical stress at mid-depth. Find the primary consolidation settlement S in mm.

H = 6.5 mCc = 0.35Cr = 0.03e0 = 1σ′0 = 50 kPaσ′p = 90 kPaΔσ = 100 kPa
S = mm
4.Medium
Δσ = 45 kPasandclayCc​ = 0.5, Cr​ = 0.05e0​ = 0.65σ′0​ = 75 kPaσ′p​ = 185 kPa5.5 mwater table

A 5.5 m thick overconsolidated clay layer has Cc = 0.5, Cr = 0.05 and e₀ = 0.65. At its mid-depth the effective vertical stress is 75 kPa and the preconsolidation pressure is 185 kPa. A new building adds 45 kPa of vertical stress at mid-depth. Find the primary consolidation settlement S in mm.

H = 5.5 mCc = 0.5Cr = 0.05e0 = 0.65σ′0 = 75 kPaσ′p = 185 kPaΔσ = 45 kPa
S = mm
5.Hard
sandclayH = 10 m10 mimpervious rockwater table

In a laboratory oedometer test, a clay specimen 20 mm thick, drained at the top and bottom, reaches 50% consolidation in 10 min. In the field the same clay forms a layer 10 m thick. It lies on impervious rock, with sand above it, so water drains out only at the top. How many days t does the field layer take to reach 50% consolidation?

hlab = 20 mmtlab = 10 minH = 10 mfield: single drainage
t = days
6.Hard
sandclayH = 9 mcv​ = 5 m²/year9 msandwater table

A clay layer 9 m thick has a coefficient of consolidation cv = 5 m²/year. It lies between two sand layers, so water drains out at the top and the bottom. For 70% average consolidation the time factor is Tv = 0.403. How many years t does the layer take to reach 70% consolidation?

H = 9 mcv = 5 m²/yearU = 70%Tv = 0.403double drainage
t = years

Answer key

  1. 1. S = 333.4 mm
  2. 2. S = 499.4 mm
  3. 3. S = 277.2 mm
  4. 4. S = 34.02 mm
  5. 5. t = 6944 days
  6. 6. t = 1.632 years

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