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 = 140 kPasandclayCc​ = 0.5e0​ = 1.1σ′0​ = 135 kPa2 mwater table

A 2 m thick layer of normally consolidated clay (Cc = 0.5, e₀ = 1.1) has an effective vertical stress of 135 kPa at its mid-depth. A wide fill raises the vertical stress in the clay by 140 kPa. Treat the layer as one sublayer with the stresses at its mid-depth. Find the primary consolidation settlement S in mm.

H = 2 mCc = 0.5e0 = 1.1σ′0 = 135 kPaΔσ = 140 kPa
S = mm
2.Easy
Δσ = 80 kPasandclayCc​ = 0.4e0​ = 1.35σ′0​ = 70 kPa7.5 mwater table

A 7.5 m thick layer of normally consolidated clay (Cc = 0.4, e₀ = 1.35) has an effective vertical stress of 70 kPa at its mid-depth. A wide fill raises the vertical stress in the clay by 80 kPa. Treat the layer as one sublayer with the stresses at its mid-depth. Find the primary consolidation settlement S in mm.

H = 7.5 mCc = 0.4e0 = 1.35σ′0 = 70 kPaΔσ = 80 kPa
S = mm
3.Medium
Δσ = 20 kPasandclayCc​ = 0.4, Cr​ = 0.04e0​ = 0.7σ′0​ = 85 kPaσ′p​ = 125 kPa2 mwater table

A 2 m thick overconsolidated clay layer has Cc = 0.4, Cr = 0.04 and e₀ = 0.7. At its mid-depth the effective vertical stress is 85 kPa and the preconsolidation pressure is 125 kPa. A new building adds 20 kPa of vertical stress at mid-depth. Find the primary consolidation settlement S in mm.

H = 2 mCc = 0.4Cr = 0.04e0 = 0.7σ′0 = 85 kPaσ′p = 125 kPaΔσ = 20 kPa
S = mm
4.Medium
Δσ = 80 kPasandclayCc​ = 0.35, Cr​ = 0.03e0​ = 0.8σ′0​ = 85 kPaOCR = 1.52.5 mwater table

A 2.5 m thick overconsolidated clay layer has Cc = 0.35, Cr = 0.03 and e₀ = 0.8. At its mid-depth the effective vertical stress is 85 kPa and the overconsolidation ratio is OCR = 1.5. A new building adds 80 kPa of vertical stress at mid-depth. Find the primary consolidation settlement S in mm.

H = 2.5 mCc = 0.35Cr = 0.03e0 = 0.8σ′0 = 85 kPaOCR = 1.5Δσ = 80 kPa
S = mm
5.Hard
sandclayH = 6.5 mcv​ = 1 m²/year6.5 msandwater table

A clay layer 6.5 m thick has a coefficient of consolidation cv = 1 m²/year. It lies between two sand layers, so water drains out at the top and the bottom. For 50% average consolidation the time factor is Tv = 0.197. How many years t does the layer take to reach 50% consolidation?

H = 6.5 mcv = 1 m²/yearU = 50%Tv = 0.197double drainage
t = years
6.Hard
sandclayH = 9 m9 mimpervious rockwater table

In a laboratory oedometer test, a clay specimen 20 mm thick, drained at the top and bottom, reaches 50% consolidation in 5 min. In the field the same clay forms a layer 9 m thick. It lies on impervious rock, with sand above it, so water drains out only at the top. How many days t does the field layer take to reach 50% consolidation?

hlab = 20 mmtlab = 5 minH = 9 mfield: single drainage
t = days

Answer key

  1. 1. S = 147.1 mm
  2. 2. S = 422.5 mm
  3. 3. S = 4.319 mm
  4. 4. S = 61.77 mm
  5. 5. t = 2.081 years
  6. 6. t = 2813 days

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