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 = 55 kPasandclayCc​ = 0.45e0​ = 1.35σ′0​ = 85 kPa5.5 mwater table

A 5.5 m thick layer of normally consolidated clay (Cc = 0.45, e₀ = 1.35) has an effective vertical stress of 85 kPa at its mid-depth. A wide fill raises the vertical stress in the clay by 55 kPa. Treat the layer as one sublayer with the stresses at its mid-depth. Find the primary consolidation settlement S in mm.

H = 5.5 mCc = 0.45e0 = 1.35σ′0 = 85 kPaΔσ = 55 kPa
S = mm
2.Easy
Δσ = 90 kPasandclayCc​ = 0.3e0​ = 0.6σ′0​ = 150 kPa3.5 mwater table

A 3.5 m thick layer of normally consolidated clay (Cc = 0.3, e₀ = 0.6) has an effective vertical stress of 150 kPa at its mid-depth. A wide fill raises the vertical stress in the clay by 90 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 = 0.3e0 = 0.6σ′0 = 150 kPaΔσ = 90 kPa
S = mm
3.Medium
Δσ = 190 kPasandclayCc​ = 0.2, Cr​ = 0.04e0​ = 0.7σ′0​ = 60 kPaσ′p​ = 110 kPa6 mwater table

A 6 m thick overconsolidated clay layer has Cc = 0.2, Cr = 0.04 and e₀ = 0.7. At its mid-depth the effective vertical stress is 60 kPa and the preconsolidation pressure is 110 kPa. A new building adds 190 kPa of vertical stress at mid-depth. Find the primary consolidation settlement S in mm.

H = 6 mCc = 0.2Cr = 0.04e0 = 0.7σ′0 = 60 kPaσ′p = 110 kPaΔσ = 190 kPa
S = mm
4.Medium
Δσ = 10 kPasandclayCc​ = 0.35, Cr​ = 0.06e0​ = 0.8σ′0​ = 65 kPaσ′p​ = 145 kPa3 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 65 kPa and the preconsolidation pressure is 145 kPa. A new building adds 10 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 = 65 kPaσ′p = 145 kPaΔσ = 10 kPa
S = mm
5.Hard
sandclayH = 8 mcv​ = 1.2 m²/year8 mimpervious rockwater table

A clay layer 8 m thick has a coefficient of consolidation cv = 1.2 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 = 8 mcv = 1.2 m²/yearU = 80%Tv = 0.567single drainage
t = years
6.Hard
sandclayH = 9 mcv​ = 2.5 m²/year9 mimpervious rockwater table

A clay layer 9 m thick has a coefficient of consolidation cv = 2.5 m²/year. It lies on impervious rock, with sand above it, so water drains out only at the top. For 90% average consolidation the time factor is Tv = 0.848. How many years t does the layer take to reach 90% consolidation?

H = 9 mcv = 2.5 m²/yearU = 90%Tv = 0.848single drainage
t = years

Answer key

  1. 1. S = 228.2 mm
  2. 2. S = 134 mm
  3. 3. S = 288.8 mm
  4. 4. S = 6.215 mm
  5. 5. t = 30.24 years
  6. 6. t = 27.48 years

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