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 = 25 kPasandclayCc​ = 0.15e0​ = 1.3σ′0​ = 55 kPa5.5 mwater table

A 5.5 m thick layer of normally consolidated clay (Cc = 0.15, e₀ = 1.3) has an effective vertical stress of 55 kPa at its mid-depth. A wide fill raises the vertical stress in the clay by 25 kPa. Treat the layer as one sublayer with the stresses at its mid-depth. Find the primary consolidation settlement S in mm.

H = 5.5 mCc = 0.15e0 = 1.3σ′0 = 55 kPaΔσ = 25 kPa
S = mm
2.Easy
Δσ = 65 kPasandγ = 18.5 kN/m³3.5 mclayγsat​ = 19.5 kN/m³Cc​ = 0.15, e0​ = 0.755 mwater tableX

A 5 m thick normally consolidated clay layer (γsat = 19.5 kN/m³, Cc = 0.15, e₀ = 0.75) lies below 3.5 m of sand (γ = 18.5 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 65 kPa. Treat the layer as one sublayer with the stresses at its mid-depth. Find the primary consolidation settlement S in mm.

sand: Hs = 3.5 m, γ = 18.5 kN/m³clay: H = 5 m, γsat = 19.5 kN/m³γw = 9.81 kN/m³Cc = 0.15e0 = 0.75Δσ = 65 kPa
S = mm
3.Medium
Δσ = 140 kPasandclayCc​ = 0.5, Cr​ = 0.04e0​ = 0.6σ′0​ = 75 kPaσ′p​ = 105 kPa7 mwater table

A 7 m thick overconsolidated clay layer has Cc = 0.5, Cr = 0.04 and e₀ = 0.6. At its mid-depth the effective vertical stress is 75 kPa and the preconsolidation pressure is 105 kPa. A new building adds 140 kPa of vertical stress at mid-depth. Find the primary consolidation settlement S in mm.

H = 7 mCc = 0.5Cr = 0.04e0 = 0.6σ′0 = 75 kPaσ′p = 105 kPaΔσ = 140 kPa
S = mm
4.Medium
Δσ = 170 kPasandclayCc​ = 0.35, Cr​ = 0.02e0​ = 0.7σ′0​ = 110 kPaOCR = 22 mwater table

A 2 m thick overconsolidated clay layer has Cc = 0.35, Cr = 0.02 and e₀ = 0.7. At its mid-depth the effective vertical stress is 110 kPa and the overconsolidation ratio is OCR = 2. A new building adds 170 kPa of vertical stress at mid-depth. Find the primary consolidation settlement S in mm.

H = 2 mCc = 0.35Cr = 0.02e0 = 0.7σ′0 = 110 kPaOCR = 2Δσ = 170 kPa
S = mm
5.Hard
sandclayH = 8.5 mcv​ = 1 m²/year8.5 msandwater table

A clay layer 8.5 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 90% average consolidation the time factor is Tv = 0.848. How many years t does the layer take to reach 90% consolidation?

H = 8.5 mcv = 1 m²/yearU = 90%Tv = 0.848double drainage
t = years
6.Hard
sandclayH = 9.5 m9.5 msandwater table

In a laboratory oedometer test, a clay specimen 19 mm thick, drained at the top and bottom, reaches 50% consolidation in 4 min. In the field the same clay forms a layer 9.5 m thick. It lies between two sand layers, so water drains out at the top and the bottom. How many days t does the field layer take to reach 50% consolidation?

hlab = 19 mmtlab = 4 minH = 9.5 mfield: double drainage
t = days

Answer key

  1. 1. S = 58.37 mm
  2. 2. S = 102.1 mm
  3. 3. S = 706.4 mm
  4. 4. S = 50.21 mm
  5. 5. t = 15.32 years
  6. 6. t = 694.4 days

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