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 = 50 kPasandclayCc​ = 0.5e0​ = 0.9σ′0​ = 80 kPa6 mwater table

A 6 m thick layer of normally consolidated clay (Cc = 0.5, e₀ = 0.9) has an effective vertical stress of 80 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 = 6 mCc = 0.5e0 = 0.9σ′0 = 80 kPaΔσ = 50 kPa
S = mm
2.Easy
Δσ = 125 kPasandclayCc​ = 0.15e0​ = 0.9σ′0​ = 120 kPa2.5 mwater table

A 2.5 m thick layer of normally consolidated clay (Cc = 0.15, e₀ = 0.9) has an effective vertical stress of 120 kPa at its mid-depth. A wide fill raises the vertical stress in the clay by 125 kPa. Treat the layer as one sublayer with the stresses at its mid-depth. Find the primary consolidation settlement S in mm.

H = 2.5 mCc = 0.15e0 = 0.9σ′0 = 120 kPaΔσ = 125 kPa
S = mm
3.Medium
Δσ = 150 kPasandclayCc​ = 0.45, Cr​ = 0.02e0​ = 1.1σ′0​ = 110 kPaOCR = 2.52 mwater table

A 2 m thick overconsolidated clay layer has Cc = 0.45, Cr = 0.02 and e₀ = 1.1. At its mid-depth the effective vertical stress is 110 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 mCc = 0.45Cr = 0.02e0 = 1.1σ′0 = 110 kPaOCR = 2.5Δσ = 150 kPa
S = mm
4.Medium
Δσ = 130 kPasandclayCc​ = 0.4, Cr​ = 0.06e0​ = 1.1σ′0​ = 40 kPaσ′p​ = 70 kPa6.5 mwater table

A 6.5 m thick overconsolidated clay layer has Cc = 0.4, Cr = 0.06 and e₀ = 1.1. At its mid-depth the effective vertical stress is 40 kPa and the preconsolidation pressure is 70 kPa. A new building adds 130 kPa of vertical stress at mid-depth. Find the primary consolidation settlement S in mm.

H = 6.5 mCc = 0.4Cr = 0.06e0 = 1.1σ′0 = 40 kPaσ′p = 70 kPaΔσ = 130 kPa
S = mm
5.Hard
sandclayH = 9 mcv​ = 3 m²/year9 mimpervious rockwater table

A clay layer 9 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 80% average consolidation the time factor is Tv = 0.567. How many years t does the layer take to reach 80% consolidation?

H = 9 mcv = 3 m²/yearU = 80%Tv = 0.567single drainage
t = years
6.Hard
sandclayH = 5 m5 msandwater 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 5 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 = 5 minH = 5 mfield: double drainage
t = days

Answer key

  1. 1. S = 332.9 mm
  2. 2. S = 61.18 mm
  3. 3. S = 7.116 mm
  4. 4. S = 522.2 mm
  5. 5. t = 15.31 years
  6. 6. t = 217 days

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