Tectonic Stress Calculator
Our geology & geophysics calculator computes tectonic stress accurately. Enter measurements for results with formulas and error analysis.
Reviewed by Daniel Agrici, Founder & Lead Developer
Formula
Sv = rho*g*z | Sh = (nu/(1-nu))*Sv + E*epsilon
Vertical stress Sv equals rock density times gravity times depth. Horizontal stress Sh combines the lithostatic ratio K0 = nu/(1-nu) times Sv with any tectonic strain contribution. Effective stress equals total stress minus pore fluid pressure.
Worked Examples
Example 1: Stress at 10 km Depth
Problem:Calculate the vertical and horizontal stresses at 10 km depth in granite (density 2700 kg/m^3, Poisson ratio 0.25).
Solution:Sv = 2700 * 9.81 * 10000 = 264.87 MPa\nPp = 1000 * 9.81 * 10000 = 98.1 MPa\nK0 = 0.25/0.75 = 0.333\nSh = 0.333 * 264.87 = 88.29 MPa\nDifferential stress = 264.87 - 88.29 = 176.58 MPa
Result:Sv = 264.87 MPa, Sh = 88.29 MPa
Example 2: With Tectonic Strain
Problem:Add a tectonic strain of 1e-4 (E = 50 GPa) to the above scenario.
Solution:Tectonic stress = 50e9 * 1e-4 = 5 MPa\nSh_total = 88.29 + 5 = 93.29 MPa\nDifferential stress = 264.87 - 93.29 = 171.58 MPa
Result:Sh increases from 88.29 to 93.29 MPa
Frequently Asked Questions
What is tectonic stress?
Tectonic stress is the stress within the Earth's crust caused by the forces driving plate tectonics, including ridge push, slab pull, and mantle convection. It adds to the gravitational lithostatic stress that increases with depth. Tectonic stress determines whether faults are in compression (thrust faulting), extension (normal faulting), or shear (strike-slip faulting). The total stress state at any point in the crust is the sum of gravitational and tectonic contributions, and it controls where and how earthquakes occur.
How does lithostatic stress vary with depth?
Lithostatic (or overburden) stress increases linearly with depth according to Sv = rho * g * z, where rho is rock density, g is gravitational acceleration, and z is depth. For typical crustal rocks with density 2700 kg/m^3, the vertical stress gradient is approximately 26.5 MPa per kilometer of depth. At 10 km depth, the vertical stress is roughly 265 MPa. This simple relationship assumes constant density, though in reality density increases with depth due to compaction and phase changes.
What is the difference between total and effective stress?
Total stress is the force per unit area from the combined weight of rock and fluid above a point. Effective stress is the total stress minus the pore fluid pressure: sigma_eff = sigma_total - Pp. Effective stress is what actually acts on rock grains and controls rock failure, deformation, and fault slip. When pore pressure increases (for example from fluid injection), effective stress decreases, making faults more likely to slip. This principle, first formulated by Terzaghi, is fundamental to understanding earthquake triggering and induced seismicity.
References
Reviewed by Daniel Agrici, Founder & Lead Developer · Editorial policy