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.

New worksheetPractise online with hints

For teachers: free to print, copy and use in class. Every new worksheet has new values and its own answer key. A link to ExamProblems on your course page is appreciated.

Name: ____________________   Date: ____________

1.Easy
Δσ = 40 kPasandclayCc​ = 0.2e0​ = 0.75σ′0​ = 80 kPa8.5 mwater table

An 8.5 m thick layer of normally consolidated clay (Cc = 0.2, e₀ = 0.75) has an effective vertical stress of 80 kPa at its mid-depth. A wide fill raises the vertical stress in the clay by 40 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 = 0.2e0 = 0.75σ′0 = 80 kPaΔσ = 40 kPa
S = mm
2.Easy
Δσ = 45 kPasandγ = 18 kN/m³3.5 mclayγsat​ = 19 kN/m³Cc​ = 0.25, e0​ = 0.857 mwater tableX

A 7 m thick normally consolidated clay layer (γsat = 19 kN/m³, Cc = 0.25, e₀ = 0.85) lies below 3.5 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 = 3.5 m, γ = 18 kN/m³clay: H = 7 m, γsat = 19 kN/m³γw = 9.81 kN/m³Cc = 0.25e0 = 0.85Δσ = 45 kPa
S = mm
3.Medium
Δσ = 130 kPasandclayCc​ = 0.2, Cr​ = 0.03e0​ = 0.75σ′0​ = 120 kPaOCR = 33.5 mwater table

A 3.5 m thick overconsolidated clay layer has Cc = 0.2, Cr = 0.03 and e₀ = 0.75. At its mid-depth the effective vertical stress is 120 kPa and the overconsolidation ratio is OCR = 3. A new building adds 130 kPa of vertical stress at mid-depth. Find the primary consolidation settlement S in mm.

H = 3.5 mCc = 0.2Cr = 0.03e0 = 0.75σ′0 = 120 kPaOCR = 3Δσ = 130 kPa
S = mm
4.Medium
Δσ = 90 kPasandclayCc​ = 0.3, Cr​ = 0.03e0​ = 1.1σ′0​ = 95 kPaσ′p​ = 135 kPa3 mwater table

A 3 m thick overconsolidated clay layer has Cc = 0.3, Cr = 0.03 and e₀ = 1.1. At its mid-depth the effective vertical stress is 95 kPa and the preconsolidation pressure is 135 kPa. A new building adds 90 kPa of vertical stress at mid-depth. Find the primary consolidation settlement S in mm.

H = 3 mCc = 0.3Cr = 0.03e0 = 1.1σ′0 = 95 kPaσ′p = 135 kPaΔσ = 90 kPa
S = mm
5.Hard
sandclayH = 3 mcv​ = 1.5 m²/year3 mimpervious rockwater table

A clay layer 3 m thick has a coefficient of consolidation cv = 1.5 m²/year. It lies on impervious rock, with sand above it, so water drains out only at the top. For 70% average consolidation the time factor is Tv = 0.403. How many years t does the layer take to reach 70% consolidation?

H = 3 mcv = 1.5 m²/yearU = 70%Tv = 0.403single drainage
t = years
6.Hard
sandclayH = 9 mcv​ = 2.5 m²/year9 msandwater table

A clay layer 9 m thick has a coefficient of consolidation cv = 2.5 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 = 9 mcv = 2.5 m²/yearU = 60%Tv = 0.287double drainage
t = years

Answer key

  1. 1. S = 171.1 mm
  2. 2. S = 159.1 mm
  3. 3. S = 19.13 mm
  4. 4. S = 65.19 mm
  5. 5. t = 2.418 years
  6. 6. t = 2.325 years

Full step-by-step solutions: practise this topic on examproblems.com.