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 criterion of Mohr-Coulomb. [Byerlee, J.D.; 1978: "Friction of rocks", Pure Applied Geophysics 116, p. 615-626.]

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

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

In which $au$ 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:

$au\; =\; 0,85\; sigma\; \_n$

for normal stresses up to 200 MPa; and

$au\; =\; 50\; +\; 0,6sigma\; \_n$

for normal stresses higher than 200 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)

ee also

*Mohr-Coulomb criterion
*Mohr circle
*brittle deformation

References