# Byerlee's law

Byerlee's law is an experimentally derived law in physics that gives the stress circumstances in the Earth's crust at which fracturing along a geological fault takes place. The relation was determined by American geophysicist James Byerlee, by using experimental data to solve the Mohr–Coulomb failure criterion.[1]

Mohr-Coulombs criterion is a linear function of shear stress over normal stress, at the point of brittle failure inside a material:

$\tau = S _0 + \mu (\sigma _n - P _f)$

In which $\tau$ is the shear stress and $\sigma _n$ the normal stress. $S _0$ is the cohesion or internal strength of the material. The value $P _f$ is the pore fluid pressure inside a rock, which is constant on a small scale and weakens the rock. Byerlee found that in the upper crust, the criterion can be simplified to:

$\tau = 0.85 \sigma _n$

for normal stresses up to 200 MPa; and

$\tau = 50 + 0.6\sigma _n$

for normal stresses higher than 200 MPa. In both formulas the shear stress is given in MPa.

However, the crust is far from a homogeneous material and consists of many rock types. Material constants can therefore vary locally. Even though Byerlee's law is a simplification, it is a good enough approximation for almost all situations. Byerlee's law gets less accurate when pressures and temperatures get higher than normal in the upper crust (e.g. temperatures over 400°C)