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 = 25 kPasandclayCc​ = 0.45e0​ = 1σ′0​ = 65 kPa9 mwater table

A 9 m thick layer of normally consolidated clay (Cc = 0.45, e₀ = 1) has an effective vertical stress of 65 kPa at its mid-depth. A wide fill raises the vertical stress in the clay by 25 kPa. Treat the layer as one sublayer with the stresses at its mid-depth. Find the primary consolidation settlement S in mm.

H = 9 mCc = 0.45e0 = 1σ′0 = 65 kPaΔσ = 25 kPa
S = mm
2.Easy
Δσ = 110 kPasandclayCc​ = 0.4e0​ = 0.8σ′0​ = 55 kPa4.5 mwater table

A 4.5 m thick layer of normally consolidated clay (Cc = 0.4, e₀ = 0.8) has an effective vertical stress of 55 kPa at its mid-depth. A wide fill raises the vertical stress in the clay by 110 kPa. Treat the layer as one sublayer with the stresses at its mid-depth. Find the primary consolidation settlement S in mm.

H = 4.5 mCc = 0.4e0 = 0.8σ′0 = 55 kPaΔσ = 110 kPa
S = mm
3.Medium
Δσ = 35 kPasandclayCc​ = 0.2, Cr​ = 0.02e0​ = 0.7σ′0​ = 60 kPaσ′p​ = 140 kPa7 mwater table

A 7 m thick overconsolidated clay layer has Cc = 0.2, Cr = 0.02 and e₀ = 0.7. At its mid-depth the effective vertical stress is 60 kPa and the preconsolidation pressure is 140 kPa. A new building adds 35 kPa of vertical stress at mid-depth. Find the primary consolidation settlement S in mm.

H = 7 mCc = 0.2Cr = 0.02e0 = 0.7σ′0 = 60 kPaσ′p = 140 kPaΔσ = 35 kPa
S = mm
4.Medium
Δσ = 35 kPasandclayCc​ = 0.45, Cr​ = 0.03e0​ = 0.95σ′0​ = 115 kPaσ′p​ = 225 kPa6.5 mwater table

A 6.5 m thick overconsolidated clay layer has Cc = 0.45, Cr = 0.03 and e₀ = 0.95. At its mid-depth the effective vertical stress is 115 kPa and the preconsolidation pressure is 225 kPa. A new building adds 35 kPa of vertical stress at mid-depth. Find the primary consolidation settlement S in mm.

H = 6.5 mCc = 0.45Cr = 0.03e0 = 0.95σ′0 = 115 kPaσ′p = 225 kPaΔσ = 35 kPa
S = mm
5.Hard
sandclayH = 3 mcv​ = 0.5 m²/year3 mimpervious rockwater table

A clay layer 3 m thick has a coefficient of consolidation cv = 0.5 m²/year. It lies on impervious rock, with sand above it, so water drains out only at the top. For 70% average consolidation the time factor is Tv = 0.403. How many years t does the layer take to reach 70% consolidation?

H = 3 mcv = 0.5 m²/yearU = 70%Tv = 0.403single drainage
t = years
6.Hard
sandclayH = 8 mcv​ = 4 m²/year8 mimpervious rockwater table

A clay layer 8 m thick has a coefficient of consolidation cv = 4 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 = 8 mcv = 4 m²/yearU = 50%Tv = 0.197single drainage
t = years

Answer key

  1. 1. S = 286.2 mm
  2. 2. S = 477.1 mm
  3. 3. S = 16.44 mm
  4. 4. S = 11.54 mm
  5. 5. t = 7.254 years
  6. 6. t = 3.152 years

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