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 = 125 kPasandclayCc​ = 0.5e0​ = 1σ′0​ = 130 kPa9.5 mwater table

A 9.5 m thick layer of normally consolidated clay (Cc = 0.5, e₀ = 1) has an effective vertical stress of 130 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 = 9.5 mCc = 0.5e0 = 1σ′0 = 130 kPaΔσ = 125 kPa
S = mm
2.Easy
Δσ = 135 kPasandclayCc​ = 0.3e0​ = 0.6σ′0​ = 135 kPa2.5 mwater table

A 2.5 m thick layer of normally consolidated clay (Cc = 0.3, e₀ = 0.6) has an effective vertical stress of 135 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 = 2.5 mCc = 0.3e0 = 0.6σ′0 = 135 kPaΔσ = 135 kPa
S = mm
3.Medium
Δσ = 270 kPasandclayCc​ = 0.25, Cr​ = 0.06e0​ = 0.8σ′0​ = 55 kPaσ′p​ = 175 kPa7 mwater table

A 7 m thick overconsolidated clay layer has Cc = 0.25, Cr = 0.06 and e₀ = 0.8. At its mid-depth the effective vertical stress is 55 kPa and the preconsolidation pressure is 175 kPa. A new building adds 270 kPa of vertical stress at mid-depth. Find the primary consolidation settlement S in mm.

H = 7 mCc = 0.25Cr = 0.06e0 = 0.8σ′0 = 55 kPaσ′p = 175 kPaΔσ = 270 kPa
S = mm
4.Medium
Δσ = 20 kPasandclayCc​ = 0.35, Cr​ = 0.06e0​ = 0.8σ′0​ = 75 kPaOCR = 1.53 mwater table

A 3 m thick overconsolidated clay layer has Cc = 0.35, Cr = 0.06 and e₀ = 0.8. At its mid-depth the effective vertical stress is 75 kPa and the overconsolidation ratio is OCR = 1.5. A new building adds 20 kPa of vertical stress at mid-depth. Find the primary consolidation settlement S in mm.

H = 3 mCc = 0.35Cr = 0.06e0 = 0.8σ′0 = 75 kPaOCR = 1.5Δσ = 20 kPa
S = mm
5.Hard
sandclayH = 8 mcv​ = 3 m²/year8 msandwater table

A clay layer 8 m thick has a coefficient of consolidation cv = 3 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 = 8 mcv = 3 m²/yearU = 70%Tv = 0.403double drainage
t = years
6.Hard
sandclayH = 5.5 mcv​ = 5 m²/year5.5 msandwater table

A clay layer 5.5 m thick has a coefficient of consolidation cv = 5 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 = 5.5 mcv = 5 m²/yearU = 70%Tv = 0.403double drainage
t = years

Answer key

  1. 1. S = 694.9 mm
  2. 2. S = 141.1 mm
  3. 3. S = 378.7 mm
  4. 4. S = 10.27 mm
  5. 5. t = 2.149 years
  6. 6. t = 0.6095 years

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