Geotechnical Resource

Effective Stress in Soil: Layered Calculation

A practical layered-soil calculation for total vertical stress, hydrostatic pore pressure and vertical effective stress.

Table of contents

Effective stress is the portion of total stress carried through the soil skeleton. It is a central concept in settlement, consolidation, shear strength, earth pressure and foundation calculations.

For a saturated soil under conventional soil-mechanics sign conventions:

$$ \sigma' = \sigma-u $$

Where total stress and pore water pressure are known, effective stress can be calculated. The appropriate stress path, drainage condition and pore-pressure model still require engineering judgement.

Vertical total stress

For horizontal layers, the vertical total stress at a nominated depth can be calculated by summing the unit weight of each layer multiplied by the thickness included above that depth:

$$ \sigma_v = \sum_{i=1}^{n}\gamma_i h_i+q $$

Symbol	Meaning	Common unit
$\sigma_v$	Total vertical stress	kPa
$\gamma_i$	Total unit weight of layer $i$	kN/m3
$h_i$	Included thickness of layer $i$	m
$q$	Uniform surface surcharge	kPa

Because 1 kN/m2 equals 1 kPa, multiplying kN/m3 by metres gives kPa.

Only the portion of a layer above the calculation depth is included.

Hydrostatic pore water pressure

Below a nominated water table, hydrostatic pore pressure is:

$$ u = \gamma_w h_w $$

Where:

$\gamma_w$ is the unit weight of water used in the calculation
$h_w$ is the vertical depth below the water table

In the simple model on this page, pore pressure above the water table is set to zero. This does not model capillary suction, perched water, artesian conditions or excess pore pressure.

Vertical effective stress

The vertical effective stress is:

$$ \sigma'_v = \sigma_v-u $$

Changes in effective stress influence soil compression and shearing resistance. A correct arithmetic result does not establish that the simplified pore-pressure assumptions represent the site.

Layered worked example

Assume:

Layer	Depth	Total unit weight
Layer 1	0 to 2 m	18 kN/m3
Layer 2	2 to 5 m	20 kN/m3

Additional information:

calculation depth = 5 m
water-table depth = 1 m
water unit weight = 9.81 kN/m3
surface surcharge = 0 kPa

Step 1: total vertical stress

$$ \sigma_v=(18\times2)+(20\times3) $$ $$ \sigma_v=36+60=96\ \mathrm{kPa} $$

Step 2: pore water pressure

The calculation point is 4 m below the water table:

$$ u=9.81\times4=39.24\ \mathrm{kPa} $$

Step 3: effective stress

$$ \sigma'_v=96-39.24=56.76\ \mathrm{kPa} $$

The vertical effective stress at 5 m is 56.76 kPa under the stated assumptions.

Effect of a uniform surcharge

If a 10 kPa surface surcharge is added and is treated as a uniform vertical stress increment at the point:

$$ \sigma_v=96+10=106\ \mathrm{kPa} $$

With unchanged hydrostatic pore pressure:

$$ \sigma'_v=106-39.24=66.76\ \mathrm{kPa} $$

This simple surcharge treatment is not a substitute for calculating stress distribution beneath a finite loaded area.

Model assumptions

The basic layered calculation assumes:

level ground
vertical one-dimensional stress
horizontal layers
entered total unit weights are appropriate
one hydrostatic water table
zero pore pressure above the water table
no capillary suction
no excess pore pressure
no seepage-induced pressure variation
no finite-load stress distribution unless separately calculated

Each assumption should be visible in a saved project calculation.

Common input errors

Using submerged unit weight in total stress and subtracting water again

This can double-count buoyancy. The calculation basis must remain consistent.

Ignoring partial layers

If the calculation depth falls inside a layer, include only the thickness above that depth.

Treating every wet layer as saturated

Unit weight and pore-pressure assumptions are separate inputs. A layer below a nominated water table may require a saturated unit weight, but the calculator should not change it silently.

Using a vertical distance that is not pressure head

Hydrostatic pore pressure uses pressure head. Non-hydrostatic conditions require a different pore-pressure model.

Forgetting surcharge

A known applicable surface load should be included or expressly omitted.

Validation rules

A layered calculator should:

require continuous, non-overlapping layer depths
block gaps and overlaps
block a calculation depth outside the entered profile
show each layer contribution
show the water depth used
show total stress, pore pressure and effective stress separately
warn if effective stress is negative
retain the water unit weight and surcharge used
state whether pore pressure is hydrostatic or entered directly

When a more advanced analysis is needed

The simple model is not sufficient for:

sloping ground
drawdown or upward seepage
perched or artesian groundwater
capillary suction
construction-generated excess pore pressure
transient consolidation
finite footing or embankment stress distribution
unsaturated-soil analysis
effective stress around excavations or dewatering systems

Review checklist

Ask the reviewing geotechnical engineer to confirm:

Total and effective stress sign conventions are clear.
The water table and hydrostatic assumptions are acceptable.
Unit weights are not altered automatically.
Layer boundaries and partial-layer calculations are handled correctly.
Surcharge treatment is properly limited.
Negative effective stress produces a warning.
The example result of 56.76 kPa is reproduced independently.