Effective Stress

σ^{'} = σ - u

Terzaghi’s principle: soil strength and compressibility depend on effective stress σ' (intergranular), not total stress. Pore pressure u = h γ_w under hydrostatic conditions. Below the water table, use buoyant unit weight γ' = γ_sat − γ_w for vertical effective stress increments.

$σ$ (kPa): Total vertical stress
$u$ (kPa): Pore-water pressure
$γ^{'}$ (kN/m³): Buoyant unit weight

Step-by-step solved example

Sand: γ_moist = 18 kN/m³ above WT (2 m), γ_sat = 20 kN/m³. WT at 2 m. σ' at 5 m depth?

σ' = σ − u. Water table draws the pore-pressure line.

1. Total stress
σ = 18×2 + 20×3 = 36 + 60 = 96 kPa.
2. Pore pressure and σ'
u = 9.81×3 ≈ 29.4 kPa. σ' = 96 − 29.4 = 66.6 kPa.
$σ^{'} = 66.6 kPa$

Answer: 66.6 kPa

10 practice questions

0/10 correct

1.At the water table, hydrostatic u is

2.γ' for γ_sat = 20 kN/m³ is about

3.Capillary rise above WT makes u

4.A rapid drawdown can temporarily leave u

5.σ_v at 3 m in dry soil γ = 17 kN/m³ is

6.Void ratio e is

7.Porosity n related to e by

8.Saturated unit weight γ_sat =

9.If u = σ, effective stress is

10.Dry sand 4 m, then WT rises to the surface. σ' at 4 m