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 = 30 kPasandclayCc​ = 0.2e0​ = 0.95σ′0​ = 110 kPa7 mwater table

A 7 m thick layer of normally consolidated clay (Cc = 0.2, e₀ = 0.95) has an effective vertical stress of 110 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 = 7 mCc = 0.2e0 = 0.95σ′0 = 110 kPaΔσ = 30 kPa
S = mm
2.Easy
Δσ = 135 kPasandclayCc​ = 0.45e0​ = 1.25σ′0​ = 95 kPa3.5 mwater table

A 3.5 m thick layer of normally consolidated clay (Cc = 0.45, e₀ = 1.25) has an effective vertical stress of 95 kPa at its mid-depth. A wide fill raises the vertical stress in the clay by 135 kPa. Treat the layer as one sublayer with the stresses at its mid-depth. Find the primary consolidation settlement S in mm.

H = 3.5 mCc = 0.45e0 = 1.25σ′0 = 95 kPaΔσ = 135 kPa
S = mm
3.Medium
Δσ = 210 kPasandclayCc​ = 0.25, Cr​ = 0.03e0​ = 0.75σ′0​ = 105 kPaσ′p​ = 175 kPa3.5 mwater table

A 3.5 m thick overconsolidated clay layer has Cc = 0.25, Cr = 0.03 and e₀ = 0.75. At its mid-depth the effective vertical stress is 105 kPa and the preconsolidation pressure is 175 kPa. A new building adds 210 kPa of vertical stress at mid-depth. Find the primary consolidation settlement S in mm.

H = 3.5 mCc = 0.25Cr = 0.03e0 = 0.75σ′0 = 105 kPaσ′p = 175 kPaΔσ = 210 kPa
S = mm
4.Medium
Δσ = 140 kPasandclayCc​ = 0.45, Cr​ = 0.02e0​ = 1.2σ′0​ = 115 kPaOCR = 26 mwater table

A 6 m thick overconsolidated clay layer has Cc = 0.45, Cr = 0.02 and e₀ = 1.2. At its mid-depth the effective vertical stress is 115 kPa and the overconsolidation ratio is OCR = 2. A new building adds 140 kPa of vertical stress at mid-depth. Find the primary consolidation settlement S in mm.

H = 6 mCc = 0.45Cr = 0.02e0 = 1.2σ′0 = 115 kPaOCR = 2Δσ = 140 kPa
S = mm
5.Hard
sandclayH = 9.5 mcv​ = 2 m²/year9.5 msandwater table

A clay layer 9.5 m thick has a coefficient of consolidation cv = 2 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 = 9.5 mcv = 2 m²/yearU = 70%Tv = 0.403double drainage
t = years
6.Hard
sandclayH = 3.5 m3.5 mimpervious rockwater 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 3.5 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 = 4 minH = 3.5 mfield: single drainage
t = days

Answer key

  1. 1. S = 75.19 mm
  2. 2. S = 268.8 mm
  3. 3. S = 140.9 mm
  4. 4. S = 71.42 mm
  5. 5. t = 4.546 years
  6. 6. t = 340.3 days

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