Geotechnical Calculators: Foundations, Stress & Bearing Capacity

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Engineering reference

Geotechnical & Foundations: theory, method, and sources

This civil & structural engineering workspace publishes 11 governing equations, 6 stated assumptions, 1 documented boundary, and 2 sources so the numbers it returns can be checked rather than taken on trust.

Calculations run locallyCalculation & source methodology

How this tool works

Ten modules cover the soil mechanics chain from phase relations through bearing capacity, settlement, consolidation, lateral earth pressure, slope stability, seepage, and pile capacity.

Each module reports the intermediate quantities engineers check by hand — void ratio, effective stress, bearing factors, Rankine coefficients — rather than only a final number, so the arithmetic can be followed and verified.

Calculators and topics covered

soil mechanics
foundations
earth pressure
settlement
seepage
effective stress
bearing capacity
Rankine
consolidation
slope stability
Darcy law
pile capacity

Core equations

\text{phase relations:}\quad n = \frac{e}{1 + e},\; \gamma _{d} = \frac{G_{s}\; \gamma _{w}}{1 + e}

\text{effective stress:}\quad \sigma ^{\prime} = \sigma - u\; \text{where}\; u = \gamma _{w}\; z_{w}

\text{Terzaghi bearing capacity:}\quad q_{u} = cN_{c} + qN_{q} + \frac{1}{2} \gamma BN_{\gamma }

\text{bearing factors:}\quad N_{q} = e^{\pi \; \tan \; \varphi }\; tan^{2} \left(45 {}^{\circ} \frac{+ \varphi }{2}\right),\; N_{c} = \left(N_{q} - 1\right) cot\; \varphi

\text{elastic settlement:}\quad S = \frac{qB \left(1 - \nu ^{2}\right) I_{f}}{E}

\text{consolidation time:}\quad t = \frac{T_{v}\; H_{dr}^{2}}{C_{v}}

\text{Rankine coefficients:}\quad K_{a} = tan^{2} \left(45 {}^{\circ} \frac{- \varphi }{2}\right),\; K_{p} = tan^{2} \left(45 {}^{\circ} \frac{+ \varphi }{2}\right)

\text{earth pressure:}\quad P_{a} = \frac{1}{2} K_{a}\; \gamma H^{2} + K_{a}\; q_{s}\; H

\text{infinite slope:}\quad FS = \frac{c + \left(\gamma z\; cos^{2} \beta - u\right) \tan \; \varphi }{\gamma z\; \sin \; \beta \; \cos \; \beta }

\text{Darcy seepage:}\quad Q = kiA

\text{pile capacity:}\quad Q_{\mathrm{ult}} = q_{p}\; A_{p} + f_{s}\; A_{s}

Method and assumptions

Assumptions

Soil is treated as homogeneous and isotropic within each layer, with a single friction angle and unit weight.
Bearing capacity uses the Terzaghi general shear form without shape, depth, or inclination factors.
Settlement is elastic and immediate; secondary compression and creep are not modelled.
Consolidation follows one-dimensional Terzaghi theory with a constant coefficient of consolidation.
Earth pressure uses Rankine theory, which assumes a smooth vertical wall, horizontal backfill, and sufficient wall movement to mobilize the active or passive state.
Pile capacity is the sum of unfactored tip and shaft resistances with no group effects or negative skin friction.

Limitations and design boundaries

Educational screening models only. Site investigation, laboratory testing, groundwater characterization, local practice, governing standards, and review by a qualified geotechnical engineer are required for real projects.

Sources and references

Primary sources are preferred for ratings, standards, manufacturer data, and externally defined constants.

Source policy

Das and Sobhan, Principles of Geotechnical Engineering
Coduto et al., Geotechnical Engineering