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 = 130 kPasandclayCc​ = 0.5e0​ = 1σ′0​ = 45 kPa4.5 mwater table

A 4.5 m thick layer of normally consolidated clay (Cc = 0.5, e₀ = 1) has an effective vertical stress of 45 kPa at its mid-depth. A wide fill raises the vertical stress in the clay by 130 kPa. Treat the layer as one sublayer with the stresses at its mid-depth. Find the primary consolidation settlement S in mm.

H = 4.5 mCc = 0.5e0 = 1σ′0 = 45 kPaΔσ = 130 kPa
S = mm
2.Easy
Δσ = 150 kPasandγ = 19 kN/m³3.5 mclayγsat​ = 19 kN/m³Cc​ = 0.5, e0​ = 0.73 mwater tableX

A 3 m thick normally consolidated clay layer (γsat = 19 kN/m³, Cc = 0.5, e₀ = 0.7) lies below 3.5 m of sand (γ = 19 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 150 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 = 19 kN/m³clay: H = 3 m, γsat = 19 kN/m³γw = 9.81 kN/m³Cc = 0.5e0 = 0.7Δσ = 150 kPa
S = mm
3.Medium
Δσ = 200 kPasandclayCc​ = 0.4, Cr​ = 0.06e0​ = 0.85σ′0​ = 65 kPaOCR = 2.56 mwater table

A 6 m thick overconsolidated clay layer has Cc = 0.4, Cr = 0.06 and e₀ = 0.85. At its mid-depth the effective vertical stress is 65 kPa and the overconsolidation ratio is OCR = 2.5. A new building adds 200 kPa of vertical stress at mid-depth. Find the primary consolidation settlement S in mm.

H = 6 mCc = 0.4Cr = 0.06e0 = 0.85σ′0 = 65 kPaOCR = 2.5Δσ = 200 kPa
S = mm
4.Medium
Δσ = 70 kPasandclayCc​ = 0.35, Cr​ = 0.06e0​ = 0.85σ′0​ = 90 kPaσ′p​ = 170 kPa2 mwater table

A 2 m thick overconsolidated clay layer has Cc = 0.35, Cr = 0.06 and e₀ = 0.85. At its mid-depth the effective vertical stress is 90 kPa and the preconsolidation pressure is 170 kPa. A new building adds 70 kPa of vertical stress at mid-depth. Find the primary consolidation settlement S in mm.

H = 2 mCc = 0.35Cr = 0.06e0 = 0.85σ′0 = 90 kPaσ′p = 170 kPaΔσ = 70 kPa
S = mm
5.Hard
sandclayH = 3 mcv​ = 5 m²/year3 msandwater table

A clay layer 3 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 50% average consolidation the time factor is Tv = 0.197. How many years t does the layer take to reach 50% consolidation?

H = 3 mcv = 5 m²/yearU = 50%Tv = 0.197double drainage
t = years
6.Hard
sandclayH = 7.5 mcv​ = 0.5 m²/year7.5 msandwater table

A clay layer 7.5 m thick has a coefficient of consolidation cv = 0.5 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 = 7.5 mcv = 0.5 m²/yearU = 50%Tv = 0.197double drainage
t = years

Answer key

  1. 1. S = 663.6 mm
  2. 2. S = 403.8 mm
  3. 3. S = 353 mm
  4. 4. S = 16.21 mm
  5. 5. t = 0.08865 years
  6. 6. t = 5.541 years

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