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 = 35 kPasandclayCc​ = 0.35e0​ = 0.95σ′0​ = 65 kPa8 mwater table

An 8 m thick layer of normally consolidated clay (Cc = 0.35, e₀ = 0.95) has an effective vertical stress of 65 kPa at its mid-depth. A wide fill raises the vertical stress in the clay by 35 kPa. Treat the layer as one sublayer with the stresses at its mid-depth. Find the primary consolidation settlement S in mm.

H = 8 mCc = 0.35e0 = 0.95σ′0 = 65 kPaΔσ = 35 kPa
S = mm
2.Easy
Δσ = 25 kPasandclayCc​ = 0.4e0​ = 1.2σ′0​ = 145 kPa4.5 mwater table

A 4.5 m thick layer of normally consolidated clay (Cc = 0.4, e₀ = 1.2) has an effective vertical stress of 145 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 = 4.5 mCc = 0.4e0 = 1.2σ′0 = 145 kPaΔσ = 25 kPa
S = mm
3.Medium
Δσ = 210 kPasandclayCc​ = 0.4, Cr​ = 0.06e0​ = 1.15σ′0​ = 50 kPaσ′p​ = 130 kPa5.5 mwater table

A 5.5 m thick overconsolidated clay layer has Cc = 0.4, Cr = 0.06 and e₀ = 1.15. At its mid-depth the effective vertical stress is 50 kPa and the preconsolidation pressure is 130 kPa. A new building adds 210 kPa of vertical stress at mid-depth. Find the primary consolidation settlement S in mm.

H = 5.5 mCc = 0.4Cr = 0.06e0 = 1.15σ′0 = 50 kPaσ′p = 130 kPaΔσ = 210 kPa
S = mm
4.Medium
Δσ = 210 kPasandclayCc​ = 0.35, Cr​ = 0.02e0​ = 0.95σ′0​ = 90 kPaσ′p​ = 190 kPa3 mwater table

A 3 m thick overconsolidated clay layer has Cc = 0.35, Cr = 0.02 and e₀ = 0.95. At its mid-depth the effective vertical stress is 90 kPa and the preconsolidation pressure is 190 kPa. A new building adds 210 kPa of vertical stress at mid-depth. Find the primary consolidation settlement S in mm.

H = 3 mCc = 0.35Cr = 0.02e0 = 0.95σ′0 = 90 kPaσ′p = 190 kPaΔσ = 210 kPa
S = mm
5.Hard
sandclayH = 7.5 mcv​ = 2.5 m²/year7.5 mimpervious rockwater table

A clay layer 7.5 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 50% average consolidation the time factor is Tv = 0.197. How many years t does the layer take to reach 50% consolidation?

H = 7.5 mcv = 2.5 m²/yearU = 50%Tv = 0.197single drainage
t = years
6.Hard
sandclayH = 2 mcv​ = 1.2 m²/year2 mimpervious rockwater table

A clay layer 2 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 90% average consolidation the time factor is Tv = 0.848. How many years t does the layer take to reach 90% consolidation?

H = 2 mcv = 1.2 m²/yearU = 90%Tv = 0.848single drainage
t = years

Answer key

  1. 1. S = 268.6 mm
  2. 2. S = 56.52 mm
  3. 3. S = 371.7 mm
  4. 4. S = 116.8 mm
  5. 5. t = 4.433 years
  6. 6. t = 2.827 years

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