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 = 70 kPasandγ = 17 kN/m³3 mclayγsat​ = 17.5 kN/m³Cc​ = 0.25, e0​ = 0.63 mwater tableX

A 3 m thick normally consolidated clay layer (γsat = 17.5 kN/m³, Cc = 0.25, e₀ = 0.6) lies below 3 m of sand (γ = 17 kN/m³). The water table is at the top of the clay; use γw = 9.81 kN/m³. A wide fill raises the vertical stress throughout the clay by 70 kPa. Treat the layer as one sublayer with the stresses at its mid-depth. Find the primary consolidation settlement S in mm.

sand: Hs = 3 m, γ = 17 kN/m³clay: H = 3 m, γsat = 17.5 kN/m³γw = 9.81 kN/m³Cc = 0.25e0 = 0.6Δσ = 70 kPa
S = mm
2.Easy
Δσ = 110 kPasandclayCc​ = 0.35e0​ = 0.75σ′0​ = 65 kPa6.5 mwater table

A 6.5 m thick layer of normally consolidated clay (Cc = 0.35, e₀ = 0.75) has an effective vertical stress of 65 kPa at its mid-depth. A wide fill raises the vertical stress in the clay by 110 kPa. Treat the layer as one sublayer with the stresses at its mid-depth. Find the primary consolidation settlement S in mm.

H = 6.5 mCc = 0.35e0 = 0.75σ′0 = 65 kPaΔσ = 110 kPa
S = mm
3.Medium
Δσ = 130 kPasandclayCc​ = 0.5, Cr​ = 0.05e0​ = 0.95σ′0​ = 85 kPaOCR = 33 mwater table

A 3 m thick overconsolidated clay layer has Cc = 0.5, Cr = 0.05 and e₀ = 0.95. At its mid-depth the effective vertical stress is 85 kPa and the overconsolidation ratio is OCR = 3. A new building adds 130 kPa of vertical stress at mid-depth. Find the primary consolidation settlement S in mm.

H = 3 mCc = 0.5Cr = 0.05e0 = 0.95σ′0 = 85 kPaOCR = 3Δσ = 130 kPa
S = mm
4.Medium
Δσ = 70 kPasandclayCc​ = 0.3, Cr​ = 0.06e0​ = 0.75σ′0​ = 85 kPaOCR = 1.52 mwater table

A 2 m thick overconsolidated clay layer has Cc = 0.3, Cr = 0.06 and e₀ = 0.75. At its mid-depth the effective vertical stress is 85 kPa and the overconsolidation ratio is OCR = 1.5. A new building adds 70 kPa of vertical stress at mid-depth. Find the primary consolidation settlement S in mm.

H = 2 mCc = 0.3Cr = 0.06e0 = 0.75σ′0 = 85 kPaOCR = 1.5Δσ = 70 kPa
S = mm
5.Hard
sandclayH = 2 mcv​ = 2 m²/year2 msandwater table

A clay layer 2 m thick has a coefficient of consolidation cv = 2 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 = 2 mcv = 2 m²/yearU = 50%Tv = 0.197double drainage
t = years
6.Hard
sandclayH = 5.5 mcv​ = 5 m²/year5.5 msandwater table

A clay layer 5.5 m thick has a coefficient of consolidation cv = 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 = 5.5 mcv = 5 m²/yearU = 50%Tv = 0.197double drainage
t = years

Answer key

  1. 1. S = 152.9 mm
  2. 2. S = 559.2 mm
  3. 3. S = 31 mm
  4. 4. S = 41.16 mm
  5. 5. t = 0.0985 years
  6. 6. t = 0.298 years

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