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 = 140 kPasandγ = 17 kN/m³5 mclayγsat​ = 18 kN/m³Cc​ = 0.25, e0​ = 1.26 mwater tableX

A 6 m thick normally consolidated clay layer (γsat = 18 kN/m³, Cc = 0.25, e₀ = 1.2) lies below 5 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 140 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 m, γ = 17 kN/m³clay: H = 6 m, γsat = 18 kN/m³γw = 9.81 kN/m³Cc = 0.25e0 = 1.2Δσ = 140 kPa
S = mm
2.Easy
Δσ = 110 kPasandclayCc​ = 0.6e0​ = 1.35σ′0​ = 95 kPa3 mwater table

A 3 m thick layer of normally consolidated clay (Cc = 0.6, e₀ = 1.35) has an effective vertical stress of 95 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 = 3 mCc = 0.6e0 = 1.35σ′0 = 95 kPaΔσ = 110 kPa
S = mm
3.Medium
Δσ = 35 kPasandclayCc​ = 0.4, Cr​ = 0.02e0​ = 0.6σ′0​ = 85 kPaσ′p​ = 125 kPa2.5 mwater table

A 2.5 m thick overconsolidated clay layer has Cc = 0.4, Cr = 0.02 and e₀ = 0.6. At its mid-depth the effective vertical stress is 85 kPa and the preconsolidation pressure is 125 kPa. A new building adds 35 kPa of vertical stress at mid-depth. Find the primary consolidation settlement S in mm.

H = 2.5 mCc = 0.4Cr = 0.02e0 = 0.6σ′0 = 85 kPaσ′p = 125 kPaΔσ = 35 kPa
S = mm
4.Medium
Δσ = 130 kPasandclayCc​ = 0.5, Cr​ = 0.05e0​ = 1σ′0​ = 65 kPaσ′p​ = 165 kPa6 mwater table

A 6 m thick overconsolidated clay layer has Cc = 0.5, Cr = 0.05 and e₀ = 1. At its mid-depth the effective vertical stress is 65 kPa and the preconsolidation pressure is 165 kPa. A new building adds 130 kPa of vertical stress at mid-depth. Find the primary consolidation settlement S in mm.

H = 6 mCc = 0.5Cr = 0.05e0 = 1σ′0 = 65 kPaσ′p = 165 kPaΔσ = 130 kPa
S = mm
5.Hard
sandclayH = 9 mcv​ = 1.5 m²/year9 msandwater table

A clay layer 9 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 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 = 1.5 m²/yearU = 80%Tv = 0.567double drainage
t = years
6.Hard
sandclayH = 2.5 mcv​ = 5 m²/year2.5 msandwater table

A clay layer 2.5 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 = 2.5 mcv = 5 m²/yearU = 80%Tv = 0.567double drainage
t = years

Answer key

  1. 1. S = 243.8 mm
  2. 2. S = 255.9 mm
  3. 3. S = 4.68 mm
  4. 4. S = 169.5 mm
  5. 5. t = 7.654 years
  6. 6. t = 0.1772 years

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