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 = 120 kPasandclayCc​ = 0.4e0​ = 0.7σ′0​ = 110 kPa8.5 mwater table

An 8.5 m thick layer of normally consolidated clay (Cc = 0.4, e₀ = 0.7) has an effective vertical stress of 110 kPa at its mid-depth. A wide fill raises the vertical stress in the clay by 120 kPa. Treat the layer as one sublayer with the stresses at its mid-depth. Find the primary consolidation settlement S in mm.

H = 8.5 mCc = 0.4e0 = 0.7σ′0 = 110 kPaΔσ = 120 kPa
S = mm
2.Easy
Δσ = 35 kPasandγ = 18.5 kN/m³5 mclayγsat​ = 19 kN/m³Cc​ = 0.45, e0​ = 0.87 mwater tableX

A 7 m thick normally consolidated clay layer (γsat = 19 kN/m³, Cc = 0.45, e₀ = 0.8) lies below 5 m of sand (γ = 18.5 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 35 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 = 18.5 kN/m³clay: H = 7 m, γsat = 19 kN/m³γw = 9.81 kN/m³Cc = 0.45e0 = 0.8Δσ = 35 kPa
S = mm
3.Medium
Δσ = 110 kPasandclayCc​ = 0.25, Cr​ = 0.03e0​ = 1.2σ′0​ = 85 kPaOCR = 2.54.5 mwater table

A 4.5 m thick overconsolidated clay layer has Cc = 0.25, Cr = 0.03 and e₀ = 1.2. At its mid-depth the effective vertical stress is 85 kPa and the overconsolidation ratio is OCR = 2.5. A new building adds 110 kPa of vertical stress at mid-depth. Find the primary consolidation settlement S in mm.

H = 4.5 mCc = 0.25Cr = 0.03e0 = 1.2σ′0 = 85 kPaOCR = 2.5Δσ = 110 kPa
S = mm
4.Medium
Δσ = 210 kPasandclayCc​ = 0.2, Cr​ = 0.03e0​ = 1σ′0​ = 105 kPaσ′p​ = 165 kPa7.5 mwater table

A 7.5 m thick overconsolidated clay layer has Cc = 0.2, Cr = 0.03 and e₀ = 1. At its mid-depth the effective vertical stress is 105 kPa and the preconsolidation pressure is 165 kPa. A new building adds 210 kPa of vertical stress at mid-depth. Find the primary consolidation settlement S in mm.

H = 7.5 mCc = 0.2Cr = 0.03e0 = 1σ′0 = 105 kPaσ′p = 165 kPaΔσ = 210 kPa
S = mm
5.Hard
sandclayH = 4 mcv​ = 3 m²/year4 mimpervious rockwater table

A clay layer 4 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 50% average consolidation the time factor is Tv = 0.197. How many years t does the layer take to reach 50% consolidation?

H = 4 mcv = 3 m²/yearU = 50%Tv = 0.197single drainage
t = years
6.Hard
sandclayH = 9 mcv​ = 2.5 m²/year9 msandwater table

A clay layer 9 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 90% average consolidation the time factor is Tv = 0.848. How many years t does the layer take to reach 90% consolidation?

H = 9 mcv = 2.5 m²/yearU = 90%Tv = 0.848double drainage
t = years

Answer key

  1. 1. S = 640.7 mm
  2. 2. S = 188.1 mm
  3. 3. S = 22.13 mm
  4. 4. S = 232.7 mm
  5. 5. t = 1.051 years
  6. 6. t = 6.869 years

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