Overburden Pressure Calculator

Overburden pressure, also called geostatic or lithostatic vertical stress, is the weight per unit area of everything lying above a point in the ground. Under level terrain with no structures it is the running sum of unit weight times thickness for each layer, so the vertical stress gradient is simply the unit weight of the material. Practical gradients are easy to remember: soils at 18 to 21 kN per cubic meter add about 18 to 21 kPa per meter of depth, sedimentary rock near a bulk density of 2.3 g per cubic centimeter gives roughly 22.6 kPa per meter, which petroleum engineers quote as about 1 psi per foot, and hydrostatic pore pressure builds at 9.81 kPa per meter, close to 0.433 psi per foot. Subtracting the pore pressure leaves the effective vertical stress, so below the water table the effective gradient falls to roughly 8 to 11 kPa per meter, which is why deep saturated deposits are far less stiff than their depth alone would suggest. The horizontal companion is the at-rest coefficient K0, the ratio of horizontal to vertical effective stress in ground that has not deformed laterally. Jaky's 1944 expression K0 = 1 - sin(phi) is the standard estimate for normally consolidated soil and yields about 0.5 at a friction angle of 30 degrees and 0.36 at 40 degrees, with normally consolidated clays generally 0.5 to 0.7. Overconsolidated soils retain locked-in horizontal stress and can exceed K0 of 1, occasionally approaching 2 or 3 in heavily overconsolidated clays such as the London Clay, which matters for retaining walls, basement walls, and tunnel linings. Effective overburden also serves as the normalizing stress for in-situ tests, where SPT and CPT results are corrected to a reference of one atmosphere, about 100 kPa, and as the baseline against which the preconsolidation pressure is compared to establish the overconsolidation ratio. The calculation assumes level ground, laterally confined conditions, hydrostatic groundwater, and no surface surcharge; artesian pressures, vertical seepage, capillary tension above the water table, sloping ground, and foundation loads all require separate treatment.

The idea that buried material carries the weight of the column above it was in use in mining and geology well before soil mechanics existed, and William Rankine's 1857 paper On the Stability of Loose Earth gave the first rigorous treatment of the associated lateral pressures, deriving active and passive limiting states for a granular mass. Rankine's theory, along with Coulomb's earlier wedge analysis of 1773, addressed the extreme states reached when a wall moves, but not the intermediate at-rest condition that describes undisturbed ground. That gap was filled by the Hungarian engineer Jozsef Jaky, who published the relation between the at-rest coefficient and the friction angle in 1944 in the Journal of the Society of Hungarian Architects and Engineers, deriving it from consideration of a granular material at rest in a sand pile. Karl Terzaghi's effective stress principle of the 1920s and 1930s had already split the geostatic stress into intergranular and pore water components, and Terzaghi and Ralph Peck's Soil Mechanics in Engineering Practice of 1948 turned the layered summation into routine design procedure. Petroleum geology developed the same arithmetic independently for borehole pressure prediction, and M. King Hubbert and William Rubey used the ratio of pore pressure to overburden in their influential 1959 Geological Society of America papers arguing that abnormally high fluid pressures allow large overthrust sheets to slide on very low apparent friction. Later refinements include the correlation of K0 with stress history by Paul Mayne and Fred Kulhawy in 1982, which multiplies the Jaky value by the overconsolidation ratio raised to the sine of the friction angle.