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 = 80 kPasandγ = 19 kN/m³3 mclayγsat​ = 18 kN/m³Cc​ = 0.25, e0​ = 1.24 mwater tableX

A 4 m thick normally consolidated clay layer (γsat = 18 kN/m³, Cc = 0.25, e₀ = 1.2) lies below 3 m of sand (γ = 19 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 80 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 = 19 kN/m³clay: H = 4 m, γsat = 18 kN/m³γw = 9.81 kN/m³Cc = 0.25e0 = 1.2Δσ = 80 kPa
S = mm
2.Easy
Δσ = 45 kPasandγ = 18 kN/m³5.5 mclayγsat​ = 17.5 kN/m³Cc​ = 0.4, e0​ = 0.94 mwater tableX

A 4 m thick normally consolidated clay layer (γsat = 17.5 kN/m³, Cc = 0.4, e₀ = 0.9) lies below 5.5 m of sand (γ = 18 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 45 kPa. Treat the layer as one sublayer with the stresses at its mid-depth. Find the primary consolidation settlement S in mm.

sand: Hs = 5.5 m, γ = 18 kN/m³clay: H = 4 m, γsat = 17.5 kN/m³γw = 9.81 kN/m³Cc = 0.4e0 = 0.9Δσ = 45 kPa
S = mm
3.Medium
Δσ = 95 kPasandclayCc​ = 0.2, Cr​ = 0.06e0​ = 0.6σ′0​ = 110 kPaσ′p​ = 210 kPa6 mwater table

A 6 m thick overconsolidated clay layer has Cc = 0.2, Cr = 0.06 and e₀ = 0.6. At its mid-depth the effective vertical stress is 110 kPa and the preconsolidation pressure is 210 kPa. A new building adds 95 kPa of vertical stress at mid-depth. Find the primary consolidation settlement S in mm.

H = 6 mCc = 0.2Cr = 0.06e0 = 0.6σ′0 = 110 kPaσ′p = 210 kPaΔσ = 95 kPa
S = mm
4.Medium
Δσ = 70 kPasandclayCc​ = 0.2, Cr​ = 0.05e0​ = 1.15σ′0​ = 120 kPaOCR = 27.5 mwater table

A 7.5 m thick overconsolidated clay layer has Cc = 0.2, Cr = 0.05 and e₀ = 1.15. At its mid-depth the effective vertical stress is 120 kPa and the overconsolidation ratio is OCR = 2. A new building adds 70 kPa of vertical stress at mid-depth. Find the primary consolidation settlement S in mm.

H = 7.5 mCc = 0.2Cr = 0.05e0 = 1.15σ′0 = 120 kPaOCR = 2Δσ = 70 kPa
S = mm
5.Hard
sandclayH = 9.5 mcv​ = 1.5 m²/year9.5 msandwater table

A clay layer 9.5 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 90% average consolidation the time factor is Tv = 0.848. How many years t does the layer take to reach 90% consolidation?

H = 9.5 mcv = 1.5 m²/yearU = 90%Tv = 0.848double drainage
t = years
6.Hard
sandclayH = 3.5 mcv​ = 5 m²/year3.5 msandwater table

A clay layer 3.5 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 80% average consolidation the time factor is Tv = 0.567. How many years t does the layer take to reach 80% consolidation?

H = 3.5 mcv = 5 m²/yearU = 80%Tv = 0.567double drainage
t = years

Answer key

  1. 1. S = 145.5 mm
  2. 2. S = 121.3 mm
  3. 3. S = 60.83 mm
  4. 4. S = 34.81 mm
  5. 5. t = 12.76 years
  6. 6. t = 0.3473 years

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