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​ = 0.15e0​ = 1σ′0​ = 115 kPa3 mwater table

A 3 m thick layer of normally consolidated clay (Cc = 0.15, e₀ = 1) has an effective vertical stress of 115 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 = 3 mCc = 0.15e0 = 1σ′0 = 115 kPaΔσ = 135 kPa
S = mm
2.Easy
Δσ = 145 kPasandclayCc​ = 0.15e0​ = 0.95σ′0​ = 70 kPa5.5 mwater table

A 5.5 m thick layer of normally consolidated clay (Cc = 0.15, e₀ = 0.95) has an effective vertical stress of 70 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 = 5.5 mCc = 0.15e0 = 0.95σ′0 = 70 kPaΔσ = 145 kPa
S = mm
3.Medium
Δσ = 40 kPasandclayCc​ = 0.4, Cr​ = 0.06e0​ = 0.8σ′0​ = 100 kPaσ′p​ = 180 kPa6.5 mwater table

A 6.5 m thick overconsolidated clay layer has Cc = 0.4, Cr = 0.06 and e₀ = 0.8. At its mid-depth the effective vertical stress is 100 kPa and the preconsolidation pressure is 180 kPa. A new building adds 40 kPa of vertical stress at mid-depth. Find the primary consolidation settlement S in mm.

H = 6.5 mCc = 0.4Cr = 0.06e0 = 0.8σ′0 = 100 kPaσ′p = 180 kPaΔσ = 40 kPa
S = mm
4.Medium
Δσ = 180 kPasandclayCc​ = 0.4, Cr​ = 0.02e0​ = 1.15σ′0​ = 50 kPaσ′p​ = 90 kPa7 mwater table

A 7 m thick overconsolidated clay layer has Cc = 0.4, Cr = 0.02 and e₀ = 1.15. At its mid-depth the effective vertical stress is 50 kPa and the preconsolidation pressure is 90 kPa. A new building adds 180 kPa of vertical stress at mid-depth. Find the primary consolidation settlement S in mm.

H = 7 mCc = 0.4Cr = 0.02e0 = 1.15σ′0 = 50 kPaσ′p = 90 kPaΔσ = 180 kPa
S = mm
5.Hard
sandclayH = 2.5 mcv​ = 5 m²/year2.5 mimpervious rockwater table

A clay layer 2.5 m thick has a coefficient of consolidation cv = 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 = 2.5 mcv = 5 m²/yearU = 90%Tv = 0.848single drainage
t = years
6.Hard
sandclayH = 8 mcv​ = 1 m²/year8 mimpervious rockwater table

A clay layer 8 m thick has a coefficient of consolidation cv = 1 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 = 8 mcv = 1 m²/yearU = 90%Tv = 0.848single drainage
t = years

Answer key

  1. 1. S = 75.88 mm
  2. 2. S = 206.2 mm
  3. 3. S = 31.66 mm
  4. 4. S = 547.3 mm
  5. 5. t = 1.06 years
  6. 6. t = 54.27 years

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