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 = 145 kPasandclayCc​ = 0.35e0​ = 1.3σ′0​ = 135 kPa3 mwater table

A 3 m thick layer of normally consolidated clay (Cc = 0.35, e₀ = 1.3) has an effective vertical stress of 135 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 = 3 mCc = 0.35e0 = 1.3σ′0 = 135 kPaΔσ = 145 kPa
S = mm
2.Easy
Δσ = 50 kPasandclayCc​ = 0.35e0​ = 1.3σ′0​ = 55 kPa4.5 mwater table

A 4.5 m thick layer of normally consolidated clay (Cc = 0.35, e₀ = 1.3) has an effective vertical stress of 55 kPa at its mid-depth. A wide fill raises the vertical stress in the clay by 50 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 = 0.35e0 = 1.3σ′0 = 55 kPaΔσ = 50 kPa
S = mm
3.Medium
Δσ = 220 kPasandclayCc​ = 0.25, Cr​ = 0.06e0​ = 0.7σ′0​ = 100 kPaσ′p​ = 200 kPa3.5 mwater table

A 3.5 m thick overconsolidated clay layer has Cc = 0.25, Cr = 0.06 and e₀ = 0.7. At its mid-depth the effective vertical stress is 100 kPa and the preconsolidation pressure is 200 kPa. A new building adds 220 kPa of vertical stress at mid-depth. Find the primary consolidation settlement S in mm.

H = 3.5 mCc = 0.25Cr = 0.06e0 = 0.7σ′0 = 100 kPaσ′p = 200 kPaΔσ = 220 kPa
S = mm
4.Medium
Δσ = 40 kPasandclayCc​ = 0.5, Cr​ = 0.02e0​ = 0.6σ′0​ = 80 kPaOCR = 2.52 mwater table

A 2 m thick overconsolidated clay layer has Cc = 0.5, Cr = 0.02 and e₀ = 0.6. At its mid-depth the effective vertical stress is 80 kPa and the overconsolidation ratio is OCR = 2.5. A new building adds 40 kPa of vertical stress at mid-depth. Find the primary consolidation settlement S in mm.

H = 2 mCc = 0.5Cr = 0.02e0 = 0.6σ′0 = 80 kPaOCR = 2.5Δσ = 40 kPa
S = mm
5.Hard
sandclayH = 7.5 mcv​ = 1.2 m²/year7.5 mimpervious rockwater table

A clay layer 7.5 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 = 7.5 mcv = 1.2 m²/yearU = 90%Tv = 0.848single drainage
t = years
6.Hard
sandclayH = 3 m3 mimpervious rockwater table

In a laboratory oedometer test, a clay specimen 20 mm thick, drained at the top and bottom, reaches 50% consolidation in 4 min. In the field the same clay forms a layer 3 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 = 4 minH = 3 mfield: single drainage
t = days

Answer key

  1. 1. S = 144.6 mm
  2. 2. S = 192.3 mm
  3. 3. S = 142.2 mm
  4. 4. S = 4.402 mm
  5. 5. t = 39.75 years
  6. 6. t = 250 days

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