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 = 45 kPasandclayCc​ = 0.4e0​ = 1.4σ′0​ = 80 kPa2.5 mwater table

A 2.5 m thick layer of normally consolidated clay (Cc = 0.4, e₀ = 1.4) has an effective vertical stress of 80 kPa at its mid-depth. A wide fill raises the vertical stress in the clay by 45 kPa. Treat the layer as one sublayer with the stresses at its mid-depth. Find the primary consolidation settlement S in mm.

H = 2.5 mCc = 0.4e0 = 1.4σ′0 = 80 kPaΔσ = 45 kPa
S = mm
2.Easy
Δσ = 150 kPasandclayCc​ = 0.25e0​ = 1.35σ′0​ = 120 kPa4 mwater table

A 4 m thick layer of normally consolidated clay (Cc = 0.25, e₀ = 1.35) has an effective vertical stress of 120 kPa at its mid-depth. A wide fill raises the vertical stress in the clay by 150 kPa. Treat the layer as one sublayer with the stresses at its mid-depth. Find the primary consolidation settlement S in mm.

H = 4 mCc = 0.25e0 = 1.35σ′0 = 120 kPaΔσ = 150 kPa
S = mm
3.Medium
Δσ = 45 kPasandclayCc​ = 0.3, Cr​ = 0.04e0​ = 0.7σ′0​ = 110 kPaσ′p​ = 200 kPa8 mwater table

An 8 m thick overconsolidated clay layer has Cc = 0.3, Cr = 0.04 and e₀ = 0.7. At its mid-depth the effective vertical stress is 110 kPa and the preconsolidation pressure is 200 kPa. A new building adds 45 kPa of vertical stress at mid-depth. Find the primary consolidation settlement S in mm.

H = 8 mCc = 0.3Cr = 0.04e0 = 0.7σ′0 = 110 kPaσ′p = 200 kPaΔσ = 45 kPa
S = mm
4.Medium
Δσ = 100 kPasandclayCc​ = 0.2, Cr​ = 0.05e0​ = 0.95σ′0​ = 85 kPaOCR = 1.58 mwater table

An 8 m thick overconsolidated clay layer has Cc = 0.2, Cr = 0.05 and e₀ = 0.95. At its mid-depth the effective vertical stress is 85 kPa and the overconsolidation ratio is OCR = 1.5. A new building adds 100 kPa of vertical stress at mid-depth. Find the primary consolidation settlement S in mm.

H = 8 mCc = 0.2Cr = 0.05e0 = 0.95σ′0 = 85 kPaOCR = 1.5Δσ = 100 kPa
S = mm
5.Hard
sandclayH = 9 mcv​ = 2.5 m²/year9 mimpervious rockwater table

A clay layer 9 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 = 9 mcv = 2.5 m²/yearU = 50%Tv = 0.197single drainage
t = years
6.Hard
sandclayH = 7.5 m7.5 msandwater 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 7.5 m thick. It lies between two sand layers, so water drains out at the top and the bottom. How many days t does the field layer take to reach 50% consolidation?

hlab = 20 mmtlab = 5 minH = 7.5 mfield: double drainage
t = days

Answer key

  1. 1. S = 80.76 mm
  2. 2. S = 149.9 mm
  3. 3. S = 28.04 mm
  4. 4. S = 168.8 mm
  5. 5. t = 6.383 years
  6. 6. t = 488.3 days

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