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 = 120 kPasandclayCc​ = 0.45e0​ = 0.95σ′0​ = 40 kPa8.5 mwater table

An 8.5 m thick layer of normally consolidated clay (Cc = 0.45, e₀ = 0.95) has an effective vertical stress of 40 kPa at its mid-depth. A wide fill raises the vertical stress in the clay by 120 kPa. Treat the layer as one sublayer with the stresses at its mid-depth. Find the primary consolidation settlement S in mm.

H = 8.5 mCc = 0.45e0 = 0.95σ′0 = 40 kPaΔσ = 120 kPa
S = mm
2.Easy
Δσ = 75 kPasandclayCc​ = 0.35e0​ = 1.1σ′0​ = 85 kPa8.5 mwater table

An 8.5 m thick layer of normally consolidated clay (Cc = 0.35, e₀ = 1.1) has an effective vertical stress of 85 kPa at its mid-depth. A wide fill raises the vertical stress in the clay by 75 kPa. Treat the layer as one sublayer with the stresses at its mid-depth. Find the primary consolidation settlement S in mm.

H = 8.5 mCc = 0.35e0 = 1.1σ′0 = 85 kPaΔσ = 75 kPa
S = mm
3.Medium
Δσ = 70 kPasandclayCc​ = 0.4, Cr​ = 0.04e0​ = 0.95σ′0​ = 75 kPaσ′p​ = 135 kPa7 mwater table

A 7 m thick overconsolidated clay layer has Cc = 0.4, Cr = 0.04 and e₀ = 0.95. At its mid-depth the effective vertical stress is 75 kPa and the preconsolidation pressure is 135 kPa. A new building adds 70 kPa of vertical stress at mid-depth. Find the primary consolidation settlement S in mm.

H = 7 mCc = 0.4Cr = 0.04e0 = 0.95σ′0 = 75 kPaσ′p = 135 kPaΔσ = 70 kPa
S = mm
4.Medium
Δσ = 20 kPasandclayCc​ = 0.2, Cr​ = 0.06e0​ = 0.9σ′0​ = 45 kPaOCR = 1.54 mwater table

A 4 m thick overconsolidated clay layer has Cc = 0.2, Cr = 0.06 and e₀ = 0.9. At its mid-depth the effective vertical stress is 45 kPa and the overconsolidation ratio is OCR = 1.5. A new building adds 20 kPa of vertical stress at mid-depth. Find the primary consolidation settlement S in mm.

H = 4 mCc = 0.2Cr = 0.06e0 = 0.9σ′0 = 45 kPaOCR = 1.5Δσ = 20 kPa
S = mm
5.Hard
sandclayH = 8.5 mcv​ = 1 m²/year8.5 mimpervious rockwater table

A clay layer 8.5 m thick has a coefficient of consolidation cv = 1 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 = 8.5 mcv = 1 m²/yearU = 50%Tv = 0.197single drainage
t = years
6.Hard
sandclayH = 5.5 m5.5 msandwater table

In a laboratory oedometer test, a clay specimen 19 mm thick, drained at the top and bottom, reaches 50% consolidation in 5 min. In the field the same clay forms a layer 5.5 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 = 19 mmtlab = 5 minH = 5.5 mfield: double drainage
t = days

Answer key

  1. 1. S = 1181 mm
  2. 2. S = 389.2 mm
  3. 3. S = 81.22 mm
  4. 4. S = 20.17 mm
  5. 5. t = 14.23 years
  6. 6. t = 291 days

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