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​ = 0.25e0​ = 1.35σ′0​ = 125 kPa4.5 mwater table

A 4.5 m thick layer of normally consolidated clay (Cc = 0.25, e₀ = 1.35) has an effective vertical stress of 125 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 = 4.5 mCc = 0.25e0 = 1.35σ′0 = 125 kPaΔσ = 35 kPa
S = mm
2.Easy
Δσ = 90 kPasandclayCc​ = 0.5e0​ = 1σ′0​ = 80 kPa9.5 mwater table

A 9.5 m thick layer of normally consolidated clay (Cc = 0.5, e₀ = 1) has an effective vertical stress of 80 kPa at its mid-depth. A wide fill raises the vertical stress in the clay by 90 kPa. Treat the layer as one sublayer with the stresses at its mid-depth. Find the primary consolidation settlement S in mm.

H = 9.5 mCc = 0.5e0 = 1σ′0 = 80 kPaΔσ = 90 kPa
S = mm
3.Medium
Δσ = 140 kPasandclayCc​ = 0.45, Cr​ = 0.03e0​ = 0.95σ′0​ = 65 kPaσ′p​ = 165 kPa2 mwater table

A 2 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 65 kPa and the preconsolidation pressure is 165 kPa. A new building adds 140 kPa of vertical stress at mid-depth. Find the primary consolidation settlement S in mm.

H = 2 mCc = 0.45Cr = 0.03e0 = 0.95σ′0 = 65 kPaσ′p = 165 kPaΔσ = 140 kPa
S = mm
4.Medium
Δσ = 80 kPasandclayCc​ = 0.45, Cr​ = 0.06e0​ = 1.15σ′0​ = 110 kPaOCR = 1.56.5 mwater table

A 6.5 m thick overconsolidated clay layer has Cc = 0.45, Cr = 0.06 and e₀ = 1.15. At its mid-depth the effective vertical stress is 110 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 = 6.5 mCc = 0.45Cr = 0.06e0 = 1.15σ′0 = 110 kPaOCR = 1.5Δσ = 80 kPa
S = mm
5.Hard
sandclayH = 5 m5 msandwater table

In a laboratory oedometer test, a clay specimen 25 mm thick, drained at the top and bottom, reaches 50% consolidation in 12 min. In the field the same clay forms a layer 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 = 25 mmtlab = 12 minH = 5 mfield: double drainage
t = days
6.Hard
sandclayH = 8 mcv​ = 1.2 m²/year8 mimpervious rockwater table

A clay layer 8 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 60% average consolidation the time factor is Tv = 0.287. How many years t does the layer take to reach 60% consolidation?

H = 8 mcv = 1.2 m²/yearU = 60%Tv = 0.287single drainage
t = years

Answer key

  1. 1. S = 51.32 mm
  2. 2. S = 777.5 mm
  3. 3. S = 55.96 mm
  4. 4. S = 115.3 mm
  5. 5. t = 333.3 days
  6. 6. t = 15.31 years

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