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​ = 0.25e0​ = 1.4σ′0​ = 145 kPa10 mwater table

A 10 m thick layer of normally consolidated clay (Cc = 0.25, e₀ = 1.4) has an effective vertical stress of 145 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 = 10 mCc = 0.25e0 = 1.4σ′0 = 145 kPaΔσ = 45 kPa
S = mm
2.Easy
Δσ = 30 kPasandclayCc​ = 0.5e0​ = 0.6σ′0​ = 115 kPa4.5 mwater table

A 4.5 m thick layer of normally consolidated clay (Cc = 0.5, e₀ = 0.6) has an effective vertical stress of 115 kPa at its mid-depth. A wide fill raises the vertical stress in the clay by 30 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 = 0.5e0 = 0.6σ′0 = 115 kPaΔσ = 30 kPa
S = mm
3.Medium
Δσ = 140 kPasandclayCc​ = 0.25, Cr​ = 0.06e0​ = 1.05σ′0​ = 90 kPaOCR = 25 mwater table

A 5 m thick overconsolidated clay layer has Cc = 0.25, Cr = 0.06 and e₀ = 1.05. At its mid-depth the effective vertical stress is 90 kPa and the overconsolidation ratio is OCR = 2. A new building adds 140 kPa of vertical stress at mid-depth. Find the primary consolidation settlement S in mm.

H = 5 mCc = 0.25Cr = 0.06e0 = 1.05σ′0 = 90 kPaOCR = 2Δσ = 140 kPa
S = mm
4.Medium
Δσ = 120 kPasandclayCc​ = 0.35, Cr​ = 0.06e0​ = 0.95σ′0​ = 50 kPaσ′p​ = 80 kPa6 mwater table

A 6 m thick overconsolidated clay layer has Cc = 0.35, Cr = 0.06 and e₀ = 0.95. At its mid-depth the effective vertical stress is 50 kPa and the preconsolidation pressure is 80 kPa. A new building adds 120 kPa of vertical stress at mid-depth. Find the primary consolidation settlement S in mm.

H = 6 mCc = 0.35Cr = 0.06e0 = 0.95σ′0 = 50 kPaσ′p = 80 kPaΔσ = 120 kPa
S = mm
5.Hard
sandclayH = 4 mcv​ = 1.5 m²/year4 msandwater table

A clay layer 4 m thick has a coefficient of consolidation cv = 1.5 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 = 4 mcv = 1.5 m²/yearU = 50%Tv = 0.197double drainage
t = years
6.Hard
sandclayH = 9 mcv​ = 3 m²/year9 msandwater table

A clay layer 9 m thick has a coefficient of consolidation cv = 3 m²/year. It lies between two sand layers, so water drains out at the top and the bottom. For 80% average consolidation the time factor is Tv = 0.567. How many years t does the layer take to reach 80% consolidation?

H = 9 mcv = 3 m²/yearU = 80%Tv = 0.567double drainage
t = years

Answer key

  1. 1. S = 122.3 mm
  2. 2. S = 141.6 mm
  3. 3. S = 109 mm
  4. 4. S = 390.2 mm
  5. 5. t = 0.5253 years
  6. 6. t = 3.827 years

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