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 = 55 kPasandclayCc​ = 0.4e0​ = 1.1σ′0​ = 95 kPa7.5 mwater table

A 7.5 m thick layer of normally consolidated clay (Cc = 0.4, e₀ = 1.1) has an effective vertical stress of 95 kPa at its mid-depth. A wide fill raises the vertical stress in the clay by 55 kPa. Treat the layer as one sublayer with the stresses at its mid-depth. Find the primary consolidation settlement S in mm.

H = 7.5 mCc = 0.4e0 = 1.1σ′0 = 95 kPaΔσ = 55 kPa
S = mm
2.Easy
Δσ = 105 kPasandγ = 17 kN/m³4.5 mclayγsat​ = 19 kN/m³Cc​ = 0.4, e0​ = 0.85 mwater tableX

A 5 m thick normally consolidated clay layer (γsat = 19 kN/m³, Cc = 0.4, e₀ = 0.8) lies below 4.5 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 105 kPa. Treat the layer as one sublayer with the stresses at its mid-depth. Find the primary consolidation settlement S in mm.

sand: Hs = 4.5 m, γ = 17 kN/m³clay: H = 5 m, γsat = 19 kN/m³γw = 9.81 kN/m³Cc = 0.4e0 = 0.8Δσ = 105 kPa
S = mm
3.Medium
Δσ = 45 kPasandclayCc​ = 0.2, Cr​ = 0.06e0​ = 0.9σ′0​ = 100 kPaσ′p​ = 170 kPa3 mwater table

A 3 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 100 kPa and the preconsolidation pressure is 170 kPa. A new building adds 45 kPa of vertical stress at mid-depth. Find the primary consolidation settlement S in mm.

H = 3 mCc = 0.2Cr = 0.06e0 = 0.9σ′0 = 100 kPaσ′p = 170 kPaΔσ = 45 kPa
S = mm
4.Medium
Δσ = 80 kPasandclayCc​ = 0.5, Cr​ = 0.05e0​ = 0.6σ′0​ = 85 kPaσ′p​ = 195 kPa7.5 mwater table

A 7.5 m thick overconsolidated clay layer has Cc = 0.5, Cr = 0.05 and e₀ = 0.6. At its mid-depth the effective vertical stress is 85 kPa and the preconsolidation pressure is 195 kPa. A new building adds 80 kPa of vertical stress at mid-depth. Find the primary consolidation settlement S in mm.

H = 7.5 mCc = 0.5Cr = 0.05e0 = 0.6σ′0 = 85 kPaσ′p = 195 kPaΔσ = 80 kPa
S = mm
5.Hard
sandclayH = 6 mcv​ = 1.2 m²/year6 msandwater table

A clay layer 6 m thick has a coefficient of consolidation cv = 1.2 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 = 6 mcv = 1.2 m²/yearU = 50%Tv = 0.197double drainage
t = years
6.Hard
sandclayH = 4.5 mcv​ = 1 m²/year4.5 msandwater table

A clay layer 4.5 m thick has a coefficient of consolidation cv = 1 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 = 4.5 mcv = 1 m²/yearU = 50%Tv = 0.197double drainage
t = years

Answer key

  1. 1. S = 283.4 mm
  2. 2. S = 347.7 mm
  3. 3. S = 15.29 mm
  4. 4. S = 67.52 mm
  5. 5. t = 1.478 years
  6. 6. t = 0.9973 years

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