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 = 110 kPasandclayCc​ = 0.5e0​ = 1.2σ′0​ = 70 kPa9 mwater table

A 9 m thick layer of normally consolidated clay (Cc = 0.5, e₀ = 1.2) has an effective vertical stress of 70 kPa at its mid-depth. A wide fill raises the vertical stress in the clay by 110 kPa. Treat the layer as one sublayer with the stresses at its mid-depth. Find the primary consolidation settlement S in mm.

H = 9 mCc = 0.5e0 = 1.2σ′0 = 70 kPaΔσ = 110 kPa
S = mm
2.Easy
Δσ = 150 kPasandclayCc​ = 0.15e0​ = 0.95σ′0​ = 105 kPa2 mwater table

A 2 m thick layer of normally consolidated clay (Cc = 0.15, e₀ = 0.95) has an effective vertical stress of 105 kPa at its mid-depth. A wide fill raises the vertical stress in the clay by 150 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 = 0.15e0 = 0.95σ′0 = 105 kPaΔσ = 150 kPa
S = mm
3.Medium
Δσ = 80 kPasandclayCc​ = 0.2, Cr​ = 0.03e0​ = 0.75σ′0​ = 65 kPaOCR = 36 mwater table

A 6 m thick overconsolidated clay layer has Cc = 0.2, Cr = 0.03 and e₀ = 0.75. At its mid-depth the effective vertical stress is 65 kPa and the overconsolidation ratio is OCR = 3. A new building adds 80 kPa of vertical stress at mid-depth. Find the primary consolidation settlement S in mm.

H = 6 mCc = 0.2Cr = 0.03e0 = 0.75σ′0 = 65 kPaOCR = 3Δσ = 80 kPa
S = mm
4.Medium
Δσ = 55 kPasandclayCc​ = 0.4, Cr​ = 0.05e0​ = 0.95σ′0​ = 60 kPaσ′p​ = 170 kPa4 mwater table

A 4 m thick overconsolidated clay layer has Cc = 0.4, Cr = 0.05 and e₀ = 0.95. At its mid-depth the effective vertical stress is 60 kPa and the preconsolidation pressure is 170 kPa. A new building adds 55 kPa of vertical stress at mid-depth. Find the primary consolidation settlement S in mm.

H = 4 mCc = 0.4Cr = 0.05e0 = 0.95σ′0 = 60 kPaσ′p = 170 kPaΔσ = 55 kPa
S = mm
5.Hard
sandclayH = 3 m3 msandwater table

In a laboratory oedometer test, a clay specimen 20 mm thick, drained at the top and bottom, reaches 50% consolidation in 4 min. In the field the same clay forms a layer 3 m thick. It lies between two sand layers, so water drains out at the top and the bottom. How many days t does the field layer take to reach 50% consolidation?

hlab = 20 mmtlab = 4 minH = 3 mfield: double drainage
t = days
6.Hard
sandclayH = 7.5 mcv​ = 5 m²/year7.5 mimpervious rockwater table

A clay layer 7.5 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 50% average consolidation the time factor is Tv = 0.197. How many years t does the layer take to reach 50% consolidation?

H = 7.5 mcv = 5 m²/yearU = 50%Tv = 0.197single drainage
t = years

Answer key

  1. 1. S = 839 mm
  2. 2. S = 59.28 mm
  3. 3. S = 35.84 mm
  4. 4. S = 28.98 mm
  5. 5. t = 62.5 days
  6. 6. t = 2.216 years

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