Byerlee's law
Encyclopedia
Byerlee's law is an experiment
ally 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.
Mohr-Coulombs criterion is a linear function
of shear stress
over normal stress, at the point of brittle failure inside a material:
In which
is the shear stress and 
the normal stress. 
is the cohesion
or internal strength of the material. The value
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:
for normal stresses up to 200 MPa
; and
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)
Experiment
An experiment is a methodical procedure carried out with the goal of verifying, falsifying, or establishing the validity of a hypothesis. Experiments vary greatly in their goal and scale, but always rely on repeatable procedure and logical analysis of the results...
ally derived law in physics that gives the stress
Stress (physics)
In continuum mechanics, stress is a measure of the internal forces acting within a deformable body. Quantitatively, it is a measure of the average force per unit area of a surface within the body on which internal forces act. These internal forces are a reaction to external forces applied on the body...
circumstances in the Earth's crust
Crust (geology)
In geology, the crust is the outermost solid shell of a rocky planet or natural satellite, which is chemically distinct from the underlying mantle...
at which fracturing
Fracture
A fracture is the separation of an object or material into two, or more, pieces under the action of stress.The word fracture is often applied to bones of living creatures , or to crystals or crystalline materials, such as gemstones or metal...
along a geological fault takes place. The relation was determined by American
United States
The United States of America is a federal constitutional republic comprising fifty states and a federal district...
geophysicist
Geophysics
Geophysics is the physics of the Earth and its environment in space; also the study of the Earth using quantitative physical methods. The term geophysics sometimes refers only to the geological applications: Earth's shape; its gravitational and magnetic fields; its internal structure and...
James Byerlee, by using experimental data to solve the Mohr-Coulomb failure criterion.
Mohr-Coulombs criterion is a linear function
Linear function
In mathematics, the term linear function can refer to either of two different but related concepts:* a first-degree polynomial function of one variable;* a map between two vector spaces that preserves vector addition and scalar multiplication....
of shear stress
Shear stress
A shear stress, denoted \tau\, , is defined as the component of stress coplanar with a material cross section. Shear stress arises from the force vector component parallel to the cross section...
over normal stress, at the point of brittle failure inside a material:
In which
is the shear stress and the normal stress. is the cohesionCohesion
Cohesion may refer to:* Cohesion , the intermolecular attraction between like-molecules* Cohesion , a measure of how well the lines of source code within a module work together...
or internal strength of the material. The value
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:for normal stresses up to 200 MPa
Pascal (unit)
The pascal is the SI derived unit of pressure, internal pressure, stress, Young's modulus and tensile strength, named after the French mathematician, physicist, inventor, writer, and philosopher Blaise Pascal. It is a measure of force per unit area, defined as one newton per square metre...
; and
for normal stresses higher than 200 MPa
Pascal (unit)
The pascal is the SI derived unit of pressure, internal pressure, stress, Young's modulus and tensile strength, named after the French mathematician, physicist, inventor, writer, and philosopher Blaise Pascal. It is a measure of force per unit area, defined as one newton per square metre...
. In both formulas the shear stress is given in MPa.
However, the crust is far from a homogeneous
Homogeneous (chemistry)
A substance that is uniform in composition is a definition of homogeneous. This is in contrast to a substance that is heterogeneous.The definition of homogeneous strongly depends on the context used. In Chemistry, a homogeneous suspension of material means that when dividing the volume in half, the...
material and consists of many rock
Rock (geology)
In geology, rock or stone is a naturally occurring solid aggregate of minerals and/or mineraloids.The Earth's outer solid layer, the lithosphere, is made of rock. In general rocks are of three types, namely, igneous, sedimentary, and metamorphic...
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)
See also
- Mohr-Coulomb failure criterion
- Mohr's circle
- Brittle deformation
- Archie's law
- Birch's law