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 = 55 kPasandclayCc​ = 0.6e0​ = 1.15σ′0​ = 110 kPa5.5 mwater table

A 5.5 m thick layer of normally consolidated clay (Cc = 0.6, e₀ = 1.15) has an effective vertical stress of 110 kPa at its mid-depth. A wide fill raises the vertical stress in the clay by 55 kPa. Treat the layer as one sublayer with the stresses at its mid-depth. Find the primary consolidation settlement S in mm.

H = 5.5 mCc = 0.6e0 = 1.15σ′0 = 110 kPaΔσ = 55 kPa
S = mm
2.Easy
Δσ = 50 kPasandclayCc​ = 0.2e0​ = 1σ′0​ = 70 kPa7.5 mwater table

A 7.5 m thick layer of normally consolidated clay (Cc = 0.2, e₀ = 1) has an effective vertical stress of 70 kPa at its mid-depth. A wide fill raises the vertical stress in the clay by 50 kPa. Treat the layer as one sublayer with the stresses at its mid-depth. Find the primary consolidation settlement S in mm.

H = 7.5 mCc = 0.2e0 = 1σ′0 = 70 kPaΔσ = 50 kPa
S = mm
3.Medium
Δσ = 150 kPasandclayCc​ = 0.25, Cr​ = 0.05e0​ = 0.75σ′0​ = 90 kPaOCR = 2.52.5 mwater table

A 2.5 m thick overconsolidated clay layer has Cc = 0.25, Cr = 0.05 and e₀ = 0.75. At its mid-depth the effective vertical stress is 90 kPa and the overconsolidation ratio is OCR = 2.5. A new building adds 150 kPa of vertical stress at mid-depth. Find the primary consolidation settlement S in mm.

H = 2.5 mCc = 0.25Cr = 0.05e0 = 0.75σ′0 = 90 kPaOCR = 2.5Δσ = 150 kPa
S = mm
4.Medium
Δσ = 110 kPasandclayCc​ = 0.5, Cr​ = 0.02e0​ = 0.6σ′0​ = 45 kPaσ′p​ = 105 kPa5.5 mwater table

A 5.5 m thick overconsolidated clay layer has Cc = 0.5, Cr = 0.02 and e₀ = 0.6. At its mid-depth the effective vertical stress is 45 kPa and the preconsolidation pressure is 105 kPa. A new building adds 110 kPa of vertical stress at mid-depth. Find the primary consolidation settlement S in mm.

H = 5.5 mCc = 0.5Cr = 0.02e0 = 0.6σ′0 = 45 kPaσ′p = 105 kPaΔσ = 110 kPa
S = mm
5.Hard
sandclayH = 4.5 mcv​ = 5 m²/year4.5 mimpervious rockwater table

A clay layer 4.5 m thick has a coefficient of consolidation cv = 5 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 = 4.5 mcv = 5 m²/yearU = 90%Tv = 0.848single drainage
t = years
6.Hard
sandclayH = 9 m9 mimpervious rockwater table

In a laboratory oedometer test, a clay specimen 20 mm thick, drained at the top and bottom, reaches 50% consolidation in 5 min. In the field the same clay forms a layer 9 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 = 5 minH = 9 mfield: single drainage
t = days

Answer key

  1. 1. S = 270.3 mm
  2. 2. S = 175.6 mm
  3. 3. S = 38.43 mm
  4. 4. S = 316 mm
  5. 5. t = 3.434 years
  6. 6. t = 2813 days

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