Effective Stress Calculator

Terzaghi's principle states that the stress controlling soil deformation and strength is not the total stress but the portion carried by the grain skeleton, sigma prime = sigma - u. Water in the voids pushes equally in all directions and cannot transmit shear, so it contributes nothing to interparticle friction; only the intergranular component does. The calculator builds sigma by summing unit weight times thickness down the profile, using the moist unit weight above the water table and the saturated unit weight below it, then subtracts a hydrostatic pore pressure u = 9.81 * (z - zw) plus any excess pore pressure you specify. Common inputs are 16 to 19 kN per cubic meter for moist sand or silt and 19 to 21 kN per cubic meter saturated, so a profile with the water table at the surface gains only about 10 kPa of effective stress per meter of depth against roughly 20 kPa of total stress. The excess pore pressure field matters because it is the transient part. Loading a saturated clay initially transfers essentially the whole stress increment to the water, since water is far less compressible than the soil skeleton; that excess then bleeds off over months or years as consolidation proceeds and sigma prime climbs to its final value. Working the principle in reverse explains several failure modes: raising the water table or generating excess pressure by earthquake shaking drives sigma prime down and strength with it, and when upward seepage produces a gradient near the critical value of about 1.0 the effective stress reaches zero and sand boils or heaves. The main limitations of this simple profile are that it assumes hydrostatic equilibrium below a single water table, ignores capillary suction above it, and does not represent artesian layers, downward seepage, or surcharge from foundations.

Karl Terzaghi arrived at the concept while studying the permeability and compression of clay at Robert College in Constantinople between 1918 and 1923. His 1923 paper on the calculation of the permeability coefficient of clay from the course of hydrodynamic stress phenomena, presented to the Vienna Academy of Sciences, introduced the consolidation theory in which load is shared between pore water and the grain skeleton. Erdbaumechanik auf bodenphysikalischer Grundlage followed in 1925 and made the framework a discipline. Terzaghi stated the principle in its familiar compact form at the First International Conference on Soil Mechanics and Foundation Engineering held at Harvard in 1936, where he emphasized that all measurable effects of a change of stress are exclusively due to changes in effective stress. The idea was contested at the time. Paul Fillunger, Terzaghi's colleague at the Technische Hochschule in Vienna, attacked the consolidation theory in the mid-1930s in a dispute that grew bitter and ended in Fillunger's death in 1937 after an academic commission ruled against him; his own porous-media work was later recognized as an early contribution to mixture theory. Subsequent research refined the boundaries of the principle rather than overturning it. Arthur Skempton in 1960 showed that the simple subtraction sigma minus u is an excellent approximation for soils but requires a compressibility correction for rock and concrete, where grain contact areas and mineral compressibility are not negligible. Alan Bishop in 1959 extended the expression to unsaturated soils using a saturation-dependent parameter, and Maurice Biot had already generalized consolidation to three dimensions in 1941.