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Civil

Effective stress in saturated soil

Stress carried by the soil grains after pore-water pressure is subtracted.

Ref
CIV-06
Rev
v1
Field
Civil
Result
σ′ [kPa]

σ′ effective stress, σ total normal stress, u pore-water pressure, ρ_w = 1000 kg/m³ water density, h the depth below the water table. Compression is positive.

In wet soil, the water carries some of the load. The grains only feel the total stress minus the water pressure, and it is this effective stress that controls the soil’s strength and settlement.

Calculator

Solve for
kPa
kPa
50600
m
0.520
  • Pore-water pressure u49.03 kPa
  • Effective ÷ total stress67.31 %

What drives the result

Each variable is moved across its typical range while the others stay at the values above. The longest bar is the key driver.

Effective stress (kPa) current value 101 kPa
σTotal stressKey driver
0.967551
hDepth below the water table
−46.1145
  • Raising the water table lowers the effective stress and the soil’s shear strength. This is a leading cause of landslides and foundation failures after heavy rain.
  • When pore pressure rises to equal the total stress, the effective stress is zero and the soil behaves like a liquid.
  • The water pressure part is the same hydrostatic ρgh used for any still liquid.
Chart data as tables

Ranked variables

VariableTypical rangeLowest resultHighest resultSwing (kPa)Local stepChange in result
σ Total stress50 to 600 kPa0.9667551550+10%+14.9 %
h Depth below the water table0.5 to 20 m−46.13145.1191.2+10%−4.86 %

Sweep of Depth below the water table

Depth below the water table (m)Effective stress (kPa)
0.5145.1
2.938121.2
5.37597.29
7.81373.39
10.2549.48
12.6925.58
15.131.674
17.56−22.23
20−46.13

Sweep one variable

Effective stress (kPa)Hover, touch, or use the arrow keys on the chart
−50050100150 5101520 Depth below the water table (m) now 101

Variables and how each one contributes

σ′

Effective stress

Result · kPa

What the equation gives you. Everything else feeds it.

σ

Total stress

kPa · typical 50 to 600

Total vertical stress at the depth considered (soil weight plus surface loads). Directly adds to the effective stress.

h

Depth below the water table

m · typical 0.5 to 20

Vertical distance from the water table down to the point. Raises pore pressure by about 9.8 kPa per metre, lowering the effective stress.

Worked example with the values above

  1. Pore pressure: u = ρwgh = 1000 × 9.80665 × 5 = 49,030 Pa = 49.03 kPa.
  2. Subtract from the total stress: 150 − 49.03.
  3. σ′ = 101 kPa.

Assumptions and limits

  • Fully saturated soil with a hydrostatic water table (no seepage).
  • Compression positive.
  • Constant water density.

Common mistakes

  • Forgetting to subtract pore pressure.
  • Measuring depth from the surface instead of from the water table.
  • Using this above the water table in unsaturated soil.

Statistics and uncertainty

The result is a difference between two similar-sized stresses, so errors in each are magnified. If u is 40% of σ, a 5% error in each term gives roughly a 9% error in σ′. Water table position is often the greatest uncertainty.

Where it is used

  • Foundation and retaining-wall design.
  • Slope stability.
  • Trafficability and track design on wet ground.

Maths you need

  • Hydrostatic pressure: u = ρgh
  • Stress: force per unit area

Related formulas

Practise this formula