Geotechnical Engineering: practice problems and exam questions

Soil mechanics for civil engineers: soil properties, stresses in the ground, pore water pressure and effective stress.

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Cram pack (PDF)Formula sheets, method steps and practice problems with full solutions, ready to print.

Topics in this course

  1. Effective stress in soilwater table at surface · water table in the layer · two layerscalculations
  2. Consolidation settlementnormally consolidated clay · overconsolidated clay · time for consolidationcalculations
  3. Hydrostatic forcevertical wall · submerged gate · centre of pressurecalculations

Exam tips for Geotechnical Engineering

  • Effective stress = total stress − pore water pressure.
  • Below the water table, use the saturated unit weight for total stress.
  • Draw the soil profile with every layer and the water table before you calculate.

Worked examples

Effective stress in soilEasy
sandγsat​ = 20 kN/m³11 mwater tableXz = 8 m

For the soil profile shown, find the total vertical stress σ at point X.

z = 8 mzw = 0 mγw = 9.81 kN/m³sand: γsat = 20 kN/m³

Find σ (kPa)

Show hints
  1. Effective stress = total stress − pore water pressure.
  2. Use the dry unit weight above the water table and the saturated unit weight below it.
  3. σ = 160 kPa.
Show the answer and the step-by-step solution

Effective stress (Terzaghi): the soil skeleton carries σ′ = σ − u. The total stress σ is the weight of everything above the point, Σγ·h, using the dry unit weight above the water table and the saturated unit weight below it. Below the water table the pore water pressure is hydrostatic: u = γw·(depth below the water table).

Total stress

Add the weight of each soil band above X. Above the water table use the dry unit weight, below it the saturated one.

σ = γsat·z = 20·8 = 160 kPa

Answer

σ = 160 kPa
Consolidation settlementMedium
Δσ = 230 kPasandclayCc​ = 0.5, Cr​ = 0.02e0​ = 1.2σ′0​ = 50 kPaσ′p​ = 150 kPa2 mwater table

A 2 m thick overconsolidated clay layer has Cc = 0.5, Cr = 0.02 and e₀ = 1.2. At its mid-depth the effective vertical stress is 50 kPa and the preconsolidation pressure is 150 kPa. A new building adds 230 kPa of vertical stress at mid-depth. Find the primary consolidation settlement S in mm.

H = 2 mCc = 0.5Cr = 0.02e0 = 1.2σ′0 = 50 kPaσ′p = 150 kPaΔσ = 230 kPa

Find S (mm)

Show hints
  1. Compare the final stress σ′₀ + Δσ with the preconsolidation pressure.
  2. σ′f = 50 + 230 = 280 kPa > σ′p = 150 kPa.
  3. Split the stress range at σ′p: Cr from σ′₀ to σ′p, then Cc from σ′p to σ′f.
Show the answer and the step-by-step solution

Primary consolidation of a clay layer of thickness H, using the effective stress at the middle of the layer: σ′f = σ′0 + Δσ. Normally consolidated clay: S = Cc·H/(1 + e0)·log₁₀(σ′f/σ′0). Overconsolidated clay recompresses along Cr up to the preconsolidation pressure σ′p and follows Cc only beyond it. Time: t = Tv·Hdr²/cv, where the drainage path Hdr is H/2 when water can leave at the top and bottom, and H when only one side drains.

Compare with the preconsolidation pressure

σ′f = 50 + 230 = 280 kPa > 150 kPa

Settlement

Recompression up to σ′p, virgin compression beyond it.

S = 0.02·2/(1 + 1.2)·log₁₀(150/50) + 0.5·2/(1 + 1.2)·log₁₀(280/150)
S = 8.675 + 123.2 = 131.9 mm

Answer

S = 131.9 mm

How practising works

  • “Practise this course” mixes problems from all its topics, like a real exam.
  • Every problem has new values, so you learn the method instead of an answer.
  • Stuck? Open a small hint first, and the full explanation only when you need it.
  • Mock exams are timed and have no hints, and you get your score and a full review at the end.

Calculators for this course

Consolidation settlement calculatorDensity calculator (mass, volume and density)

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