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 = 30 kPasandclayCc​ = 0.3e0​ = 1.2σ′0​ = 105 kPa8.5 mwater table

An 8.5 m thick layer of normally consolidated clay (Cc = 0.3, e₀ = 1.2) has an effective vertical stress of 105 kPa at its mid-depth. A wide fill raises the vertical stress in the clay by 30 kPa. Treat the layer as one sublayer with the stresses at its mid-depth. Find the primary consolidation settlement S in mm.

H = 8.5 mCc = 0.3e0 = 1.2σ′0 = 105 kPaΔσ = 30 kPa
S = mm
2.Easy
Δσ = 120 kPasandγ = 18 kN/m³3 mclayγsat​ = 19 kN/m³Cc​ = 0.5, e0​ = 0.959 mwater tableX

A 9 m thick normally consolidated clay layer (γsat = 19 kN/m³, Cc = 0.5, e₀ = 0.95) lies below 3 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 120 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 = 18 kN/m³clay: H = 9 m, γsat = 19 kN/m³γw = 9.81 kN/m³Cc = 0.5e0 = 0.95Δσ = 120 kPa
S = mm
3.Medium
Δσ = 25 kPasandclayCc​ = 0.35, Cr​ = 0.03e0​ = 1σ′0​ = 115 kPaσ′p​ = 165 kPa3.5 mwater table

A 3.5 m thick overconsolidated clay layer has Cc = 0.35, Cr = 0.03 and e₀ = 1. At its mid-depth the effective vertical stress is 115 kPa and the preconsolidation pressure is 165 kPa. A new building adds 25 kPa of vertical stress at mid-depth. Find the primary consolidation settlement S in mm.

H = 3.5 mCc = 0.35Cr = 0.03e0 = 1σ′0 = 115 kPaσ′p = 165 kPaΔσ = 25 kPa
S = mm
4.Medium
Δσ = 160 kPasandclayCc​ = 0.35, Cr​ = 0.02e0​ = 1.15σ′0​ = 115 kPaOCR = 25.5 mwater table

A 5.5 m thick overconsolidated clay layer has Cc = 0.35, Cr = 0.02 and e₀ = 1.15. At its mid-depth the effective vertical stress is 115 kPa and the overconsolidation ratio is OCR = 2. A new building adds 160 kPa of vertical stress at mid-depth. Find the primary consolidation settlement S in mm.

H = 5.5 mCc = 0.35Cr = 0.02e0 = 1.15σ′0 = 115 kPaOCR = 2Δσ = 160 kPa
S = mm
5.Hard
sandclayH = 4.5 mcv​ = 0.8 m²/year4.5 msandwater table

A clay layer 4.5 m thick has a coefficient of consolidation cv = 0.8 m²/year. It lies between two sand layers, so water drains out at the top and the bottom. For 60% average consolidation the time factor is Tv = 0.287. How many years t does the layer take to reach 60% consolidation?

H = 4.5 mcv = 0.8 m²/yearU = 60%Tv = 0.287double drainage
t = years
6.Hard
sandclayH = 7 m7 msandwater table

In a laboratory oedometer test, a clay specimen 20 mm thick, drained at the top and bottom, reaches 50% consolidation in 15 min. In the field the same clay forms a layer 7 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 = 20 mmtlab = 15 minH = 7 mfield: double drainage
t = days

Answer key

  1. 1. S = 126.5 mm
  2. 2. S = 816.5 mm
  3. 3. S = 4.485 mm
  4. 4. S = 84.88 mm
  5. 5. t = 1.816 years
  6. 6. t = 1276 days

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