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​ = 0.25e0​ = 1.3σ′0​ = 55 kPa2.5 mwater table

A 2.5 m thick layer of normally consolidated clay (Cc = 0.25, e₀ = 1.3) has an effective vertical stress of 55 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 = 0.25e0 = 1.3σ′0 = 55 kPaΔσ = 125 kPa
S = mm
2.Easy
Δσ = 145 kPasandclayCc​ = 0.3e0​ = 1.35σ′0​ = 50 kPa5 mwater table

A 5 m thick layer of normally consolidated clay (Cc = 0.3, e₀ = 1.35) has an effective vertical stress of 50 kPa at its mid-depth. A wide fill raises the vertical stress in the clay by 145 kPa. Treat the layer as one sublayer with the stresses at its mid-depth. Find the primary consolidation settlement S in mm.

H = 5 mCc = 0.3e0 = 1.35σ′0 = 50 kPaΔσ = 145 kPa
S = mm
3.Medium
Δσ = 120 kPasandclayCc​ = 0.25, Cr​ = 0.04e0​ = 1.05σ′0​ = 65 kPaOCR = 2.52.5 mwater table

A 2.5 m thick overconsolidated clay layer has Cc = 0.25, Cr = 0.04 and e₀ = 1.05. At its mid-depth the effective vertical stress is 65 kPa and the overconsolidation ratio is OCR = 2.5. A new building adds 120 kPa of vertical stress at mid-depth. Find the primary consolidation settlement S in mm.

H = 2.5 mCc = 0.25Cr = 0.04e0 = 1.05σ′0 = 65 kPaOCR = 2.5Δσ = 120 kPa
S = mm
4.Medium
Δσ = 110 kPasandclayCc​ = 0.5, Cr​ = 0.06e0​ = 0.75σ′0​ = 80 kPaσ′p​ = 130 kPa7 mwater table

A 7 m thick overconsolidated clay layer has Cc = 0.5, Cr = 0.06 and e₀ = 0.75. At its mid-depth the effective vertical stress is 80 kPa and the preconsolidation pressure is 130 kPa. A new building adds 110 kPa of vertical stress at mid-depth. Find the primary consolidation settlement S in mm.

H = 7 mCc = 0.5Cr = 0.06e0 = 0.75σ′0 = 80 kPaσ′p = 130 kPaΔσ = 110 kPa
S = mm
5.Hard
sandclayH = 5 mcv​ = 3 m²/year5 mimpervious rockwater table

A clay layer 5 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 60% average consolidation the time factor is Tv = 0.287. How many years t does the layer take to reach 60% consolidation?

H = 5 mcv = 3 m²/yearU = 60%Tv = 0.287single drainage
t = years
6.Hard
sandclayH = 2.5 mcv​ = 1.5 m²/year2.5 mimpervious rockwater table

A clay layer 2.5 m thick has a coefficient of consolidation cv = 1.5 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 = 2.5 mcv = 1.5 m²/yearU = 50%Tv = 0.197single drainage
t = years

Answer key

  1. 1. S = 139.9 mm
  2. 2. S = 377.3 mm
  3. 3. S = 36.58 mm
  4. 4. S = 380.2 mm
  5. 5. t = 2.392 years
  6. 6. t = 0.8208 years

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