Effective Stress Calculator

Calculator overview

Inputs and outputs

This summary comes from the calculator's published input and output contract.

Inputs

Query Depth: About this input

The depth below ground surface, in metres, at which the stresses are reported. It must lie within the layers you have defined. The model carries no soil below the bottom of the profile, so a deeper query is refused rather than answered: add a layer thick enough to reach the depth you want.

Unit m Default 6 Range At least 0
Layer 3 Unit Weight: About this input

The unit weight of the third soil layer, in kilonewtons per cubic metre.

Unit kN/m3 Default 18 Range At least 0
Layer 3 Thickness: About this input

The thickness of the third soil layer down from the surface, in metres. Set it to zero if there is no third layer.

Unit m Default 5 Range At least 0
Water Unit Weight: About this input

The unit weight of water, in kilonewtons per cubic metre, used to compute pore pressure below the water table. It is close to 9.81.

Unit kN/m3 Default 9.81 Range At least 0
Water Table Depth: About this input

The depth to the water table below ground surface, in metres. Soil above it is treated as unsubmerged and below it as generating pore pressure.

Unit m Default 2
Stress Increase Method: About this input

How the footing pressure is spread with depth, such as the 2 to 1 method or the Boussinesq solution. The two give different stress increases at the same depth.

Default 2:1 Allowed 2:1, Boussinesq
Layer 2 Unit Weight: About this input

The unit weight of the second soil layer, in kilonewtons per cubic metre.

Unit kN/m3 Default 20 Range At least 0
Footing Width: About this input

The plan width of the loaded footing, in metres, used to spread its load with depth.

Unit m Default 2 Range At least 0
Footing Load: About this input

The vertical load applied by the footing, in kilonewtons, whose pressure is spread down to the query depth.

Unit kN Default 1000 Range At least 0
Footing Length: About this input

The plan length of the loaded footing, in metres, used to spread its load with depth.

Unit m Default 2 Range At least 0
Layer 2 Thickness: About this input

The thickness of the second soil layer down from the surface, in metres.

Unit m Default 3 Range At least 0
Layer 1 Unit Weight: About this input

The unit weight of the topmost soil layer, in kilonewtons per cubic metre.

Unit kN/m3 Default 17 Range At least 0
Layer 1 Thickness: About this input

The thickness of the topmost soil layer, in metres.

Unit m Default 2 Range At least 0

Outputs

Pore Water Pressure At: About this output

The pore water pressure at the query depth, in kilopascals, from the height of water above that point. It is zero above the water table, and it is read at the same depth as the total vertical stress.

Unit kPa
Stress Increase Under Footing: About this output

The added vertical stress at the query depth from the footing load, in kilopascals, by the chosen spreading method.

Unit kPa
Total Vertical Stress At: About this output

The total vertical stress at the query depth, in kilopascals, from the full weight of soil above including any water. It is read at the same depth as the pore water pressure, so the two can never disagree. When the query depth is below the profile you have defined, the page shows the refusal in place of the results.

Unit kPa
Effective Vertical Stress At: About this output

The vertical effective stress at the query depth, in kilopascals: total stress minus pore water pressure. Effective stress, not total, governs strength and settlement. It cannot be negative in a real profile, which is why the model refuses a depth below the soil you have described rather than reporting a difference between two depths.

Unit kPa
Model Status: About this output

The overall check on your entries, shown above the results. It reads OK when the inputs are usable, NOT VALID with a reason when an entry makes the model meaningless, or CHECK with a reason when a result is valid but worth a second look. Read it before you trust the numbers below.

No unit declared
New Effective Stress: About this output

The effective vertical stress at the query depth after the footing is applied, in kilopascals: the original effective stress plus the footing stress increase.

Unit kPa

What it is

The Effective Stress Calculator works out the vertical stresses in the ground at a chosen depth. It sums the weight of up to three soil layers to give the total vertical stress, subtracts the pore water pressure to give the effective stress, and adds the stress increase from a footing to show what the soil carries once the structure is built.

It works in SI units: metres for depths and footing dimensions, kilonewtons per cubic metre for unit weights, kilonewtons for the footing load, and kilopascals for every stress.

Use it to build a stress profile for settlement, bearing or slope work. Effective stress is the quantity that governs soil strength and compressibility, and getting the water table right matters as much as getting the soil weights right.

Methodology

Purpose and model boundary

This model calculates total vertical stress, pore-water pressure and effective vertical stress at a selected depth through a three-layer soil profile. It can also estimate the stress increase beneath a rectangular footing using either the workbook's 2:1 distribution or Boussinesq closed-form method. It is a profile and load-increment calculator, not a settlement, bearing-capacity or slope-stability design.

All calculations remain in the spreadsheet. The page sends the named inputs to the calculation service and displays its outputs and status.

Inputs and units

Input group	Values used by the model
Soil profile	Thickness and total unit weight for each of three layers, in m and kN/m³.
Groundwater	Water-table depth in m and water unit weight `γw` in kN/m³.
Query	Depth `z` below ground surface, m.
Footing	Load `Q` in kN, width `B` and length `L` in m.
Stress method	`2:1` or Boussinesq.

Governing relationships

Total vertical stress is the sum of γi × thicknessi above the query point, truncated within the layer containing z. Pore pressure is u = γw × max(0, z − zw), where zw is the water-table depth. Effective stress follows Terzaghi's relationship σ'v = σv − u.

For the 2:1 method the footing stress spreads with depth and the increment follows Δσ = Q / [(B+z)(L+z)]. The Boussinesq option applies the workbook's closed-form rectangular influence factor to the uniform footing pressure. The final reported stress is σ'new = σ'v + Δσ.

Calculation sequence

Validate query depth, unit weights, layer dimensions, footing dimensions, load and method.
Accumulate total overburden stress through the defined layers.
Calculate hydrostatic pore pressure below the water table.
Subtract pore pressure to obtain effective vertical stress.
Evaluate the selected footing stress-increase method and add it to the initial effective stress.
Produce the total/effective/pore stress profile and workbook status.

Outputs and interpretation

Total stress includes the weight of soil and water; effective stress is the portion carried by the soil skeleton. The footing stress increase is an idealized load increment and the new effective stress is their sum at the query depth. The chart shows the three profile components so groundwater and layer changes can be interpreted together.

Validation and status logic

Condition	Returned status
Query depth or water unit weight is nonpositive	`NOT VALID: query depth and water unit weight must be positive`
Query depth is below the bottom of the three authored layers	`CHECK: query depth is below the defined layers; stress is not extrapolated`
Inputs are usable and the query lies within the profile	`OK`

Input checking also enforces the published method choices and numeric bounds before the workbook call.

Assumptions and limitations

Each layer has a uniform total unit weight and horizontal boundaries.
Groundwater is hydrostatic at one horizontal water-table elevation.
Below the water table the entered soil unit weight must be a total/saturated value; the model subtracts pore pressure separately.
The 2:1 and Boussinesq methods are approximate elastic stress-distribution methods and can differ materially near the footing.
Footing embedment, nonuniform contact pressure, layered stiffness, anisotropy, consolidation and three-dimensional boundary effects are omitted.
The profile is not extrapolated below the third layer.

Restrictions and non-computing states

This calculator restricts the stress method to its authored list and requires values within declared bounds. When z is below the profile, the returned stress is held at the profile bottom and accompanied by CHECK; it must not be read as an extrapolated subsurface prediction. Numerical residues accompanying NOT VALID are not valid results.

Errors and warnings

A rejected entry means the request did not meet the published input rules. NOT VALID identifies a state in which the stress calculation is not meaningful. CHECK identifies the explicit profile-depth limitation. A calculation-service error is an availability failure, not a geotechnical result.

References

The workbook derives its relations rather than reproducing any table, chart or figure from a specification, standard or agency publication. Total stress is a sum of layer weights, pore pressure is hydrostatic, and the two spread methods are the standard 2:1 approximation and the Boussinesq elastic solution.

Wikipedia. Effective stress, for Terzaghi's principle and its consequences. https://en.wikipedia.org/wiki/Effective_stress
Wikipedia. Boussinesq's problem, for the elastic half-space solution used by the Boussinesq method. https://en.wikipedia.org/wiki/Boussinesq%27s_problem
University of the West of England. Vertical stress in the ground, a teaching reference for the stress profile. https://environment.uwe.ac.uk/geocal/soilmech/stresses/stresses.htm

Soil unit weights and the water table depth must come from site investigation. The values shipped with the workbook are illustrative and carry no authority.

Additional source notes migrated from Methodology

The workbook implements Terzaghi effective stress and the documented 2:1 and Boussinesq rectangular-load relationships. Site investigation data, the governing design method and review by a licensed geotechnical engineer control real applications.

Frequently asked questions

Why does effective stress matter more than total stress?

Because it is the part of the load actually carried by the soil grains pressing against each other, and that is what governs strength and compressibility. Water in the pores carries pressure but offers no shear resistance. Two sites with identical total stress but different water tables behave completely differently, which is why raising a water table can trigger a failure without anything being built.

What is the difference between the 2:1 method and Boussinesq?

The 2:1 method assumes the load spreads at a fixed two-vertical-to-one-horizontal slope, so the loaded area grows linearly with depth. It is a geometric approximation with no theory behind it. Boussinesq is the elastic-theory solution for a load on a homogeneous elastic half-space. Boussinesq is more rigorous and usually gives a smaller increase directly under a footing; the 2:1 method is conservative for settlement work and simpler to check by hand. Neither is right for real soil, which is neither elastic nor homogeneous.

Why is the footing's contribution so much smaller than its bearing pressure?

Because the load spreads as it travels down. In the shipped example a 1,000 kN load on a 2 by 2 metre footing applies 250 kPa at founding level, but by 6 metres depth the 2:1 method has spread it over 8 by 8 metres and it contributes only 15.6 kPa. That attenuation is why deep soft layers matter less than shallow ones, and why entering a bearing pressure directly into a settlement calculation badly overestimates the result.

Does the tool account for the soil I dig out to place the footing?

No. The stress increase is the full footing load spread from founding level, with no credit for the weight of soil removed during excavation. For a footing at any depth that credit is real (the net increase is the bearing pressure minus the overburden that used to be there), so treating the whole load as new is conservative.

Is the pore pressure right if water is flowing?

No. The tool computes hydrostatic pore pressure from the height of water above the query depth, which assumes static groundwater. Where water is seeping vertically (upward under artesian pressure, or downward through a draining layer) the actual pore pressure departs from hydrostatic, and upward seepage in particular reduces effective stress and can approach zero in the extreme. Seepage is not modelled here.

Can I use this under the corner or edge of a footing?

No. Both methods here give the stress increase under the centre of a single rectangular footing. Stress under a corner or an edge is lower, and the standard approach is to superpose corner solutions, which this tool does not do. It also does not model overlap from neighbouring footings, which matters when they are close relative to their width.

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