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 = 135 kPasandclayCc​ = 0.25e0​ = 0.75σ′0​ = 60 kPa7.5 mwater table

A 7.5 m thick layer of normally consolidated clay (Cc = 0.25, e₀ = 0.75) has an effective vertical stress of 60 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 = 7.5 mCc = 0.25e0 = 0.75σ′0 = 60 kPaΔσ = 135 kPa
S = mm
2.Easy
Δσ = 120 kPasandclayCc​ = 0.3e0​ = 1σ′0​ = 120 kPa8.5 mwater table

An 8.5 m thick layer of normally consolidated clay (Cc = 0.3, e₀ = 1) has an effective vertical stress of 120 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 = 0.3e0 = 1σ′0 = 120 kPaΔσ = 120 kPa
S = mm
3.Medium
Δσ = 15 kPasandclayCc​ = 0.3, Cr​ = 0.02e0​ = 0.6σ′0​ = 70 kPaσ′p​ = 110 kPa6 mwater table

A 6 m thick overconsolidated clay layer has Cc = 0.3, Cr = 0.02 and e₀ = 0.6. At its mid-depth the effective vertical stress is 70 kPa and the preconsolidation pressure is 110 kPa. A new building adds 15 kPa of vertical stress at mid-depth. Find the primary consolidation settlement S in mm.

H = 6 mCc = 0.3Cr = 0.02e0 = 0.6σ′0 = 70 kPaσ′p = 110 kPaΔσ = 15 kPa
S = mm
4.Medium
Δσ = 20 kPasandclayCc​ = 0.25, Cr​ = 0.04e0​ = 0.95σ′0​ = 110 kPaOCR = 2.58 mwater table

An 8 m thick overconsolidated clay layer has Cc = 0.25, Cr = 0.04 and e₀ = 0.95. At its mid-depth the effective vertical stress is 110 kPa and the overconsolidation ratio is OCR = 2.5. A new building adds 20 kPa of vertical stress at mid-depth. Find the primary consolidation settlement S in mm.

H = 8 mCc = 0.25Cr = 0.04e0 = 0.95σ′0 = 110 kPaOCR = 2.5Δσ = 20 kPa
S = mm
5.Hard
sandclayH = 8 mcv​ = 1 m²/year8 msandwater table

A clay layer 8 m thick has a coefficient of consolidation cv = 1 m²/year. It lies between two sand layers, so water drains out at the top and the bottom. For 80% average consolidation the time factor is Tv = 0.567. How many years t does the layer take to reach 80% consolidation?

H = 8 mcv = 1 m²/yearU = 80%Tv = 0.567double drainage
t = years
6.Hard
sandclayH = 2 mcv​ = 1 m²/year2 msandwater table

A clay layer 2 m thick has a coefficient of consolidation cv = 1 m²/year. It lies between two sand layers, so water drains out at the top and the bottom. For 60% average consolidation the time factor is Tv = 0.287. How many years t does the layer take to reach 60% consolidation?

H = 2 mcv = 1 m²/yearU = 60%Tv = 0.287double drainage
t = years

Answer key

  1. 1. S = 548.4 mm
  2. 2. S = 383.8 mm
  3. 3. S = 6.324 mm
  4. 4. S = 11.91 mm
  5. 5. t = 9.072 years
  6. 6. t = 0.287 years

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