Tectonic Stress Calculator

Stress in the upper crust is described by three orthogonal principal components, and this tool resolves the two that dominate at shallow depth: the vertical or lithostatic stress produced by the weight of overburden, and the horizontal stress the rock develops in response. Vertical stress follows Sv = rho*g*z directly, so a granite column of 2700 kg/m3 accumulates about 26.5 MPa for every kilometre of depth and reaches roughly 265 MPa at 10 km. Horizontal stress is not free to match it. If the rock is laterally confined and deforms elastically, uniaxial-strain theory gives the ratio K0 = nu/(1 - nu), so a Poisson ratio of 0.25 puts Sh at only one third of Sv. Plate-boundary strain is superimposed as E times epsilon, meaning a strain of 1e-4 in rock with a Young modulus of 50 GPa adds about 5 MPa. What actually drives failure is effective stress, the total stress minus pore fluid pressure. A hydrostatic column adds roughly 9.81 MPa per kilometre, so at 10 km the effective vertical stress is near 167 MPa rather than 265 MPa. Comparing that to a Mohr-Coulomb strength envelope with cohesion around 10 MPa and a friction angle of 30 degrees (coefficient 0.577) shows how close a fault sits to slip. The main limitation is the elastic K0 assumption: measured horizontal stresses from hydraulic fracturing tests and borehole breakouts frequently exceed the elastic prediction in the upper 1 to 2 km, and overpressured shale sequences can carry pore pressures approaching lithostatic values.

The idea that rock at depth carries a stress equal in all directions was argued by the Swiss geologist Albert Heim in the late 1870s, and it remained the working assumption until laboratory and mine measurements showed horizontal stress usually differs from vertical. The decisive step for effective stress came from Karl Terzaghi, who in the 1920s demonstrated for soils that deformation and strength depend on total stress minus pore water pressure, a principle later extended to rock. Ernest Masson Anderson published his classification of faulting in 1905 and expanded it in the 1951 book The Dynamics of Faulting, tying normal, thrust, and strike-slip regimes to which principal stress is vertical. Application to deep crustal problems accelerated after M. King Hubbert and William Rubey argued in 1959 that high pore pressure could explain how large overthrust sheets move on low-angle faults. Hubbert and Willis had already described in 1957 how hydraulic fracturing pressures reveal in-situ stress, which became the standard field measurement alongside borehole breakout analysis. James Byerlee summarised laboratory friction data in 1978, giving friction coefficients of roughly 0.6 to 0.85 for most rocks. From 1986 the World Stress Map project began compiling these observations globally, and the resulting database underpins modern reservoir geomechanics and induced-seismicity assessment.