Byerlee's law

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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 criterion of Mohr-Coulomb.^[1]

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

$τ = S 0 + μ(σ n - P f)$

In which $τ$ is the shear stress and $σ n$ 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:

$τ = 0,85σ n$

for normal stresses up to 200 M Pa; and

$τ = 50 + 0,6σ n$

for normal stresses higher than 200 M Pa.

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 acurate when pressures and temperatures get higher than normal in the upper crust (e.g. temperatures over 400°C)