Math 2.0

Geophysics Geodynamics and heat flow Fact

Byerlee's law

Builds on FrictionCauchy stress tensorMohr–Coulomb theory

Statement

Let a pre-existing fault surface in rock carry an effective normal stress σn\sigma_n (normal stress minus pore-fluid pressure) and a shear stress τ\tau. For most rock types, the shear stress needed to make the two sides slide is, to good approximation, τ=0.85 σnfor σn<200 MPa,\tau = 0.85 \, \sigma_n \quad \text{for } \sigma_n < 200 \text{ MPa}, τ=50 MPa+0.6 σnfor 200 MPa≤σn≤1700 MPa.\tau = 50 \text{ MPa} + 0.6 \, \sigma_n \quad \text{for } 200 \text{ MPa} \leq \sigma_n \leq 1700 \text{ MPa}.

Remarks

This is an empirical law, found by Byerlee in 1978 from a compilation of laboratory friction experiments on many rock types. It has the form of a Coulomb friction law, with friction coefficients 0.850.85 and 0.60.6; see Mohr–Coulomb theory. Its most striking feature is that it hardly depends on the rock type. Some minerals, notably several clays, are weaker and do not follow it. Example: at σn=100\sigma_n = 100 MPa, sliding needs τ=85\tau = 85 MPa; at σn=500\sigma_n = 500 MPa it needs τ=350\tau = 350 MPa. The stresses are components of the Cauchy stress tensor on the fault plane, with compression taken positive.

Going deeper

For a student

Since the normal stress grows with depth through the weight of the rock, the law gives a frictional strength of the brittle crust that increases linearly with depth. Combined with a creep law for deeper, hotter rock, this gives the strength envelope of the lithosphere. Used in Anderson's theory of faulting with the friction angle ϕ=arctan⁡0.6≈31∘\phi = \arctan 0.6 \approx 31^\circ, it gives normal faults dipping near 60∘60^\circ and thrust faults dipping near 30∘30^\circ. Pore-fluid pressure lowers the effective normal stress and so weakens faults.

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Cauchy stress tensor, concept, no evidence levelCauchy stress tensorconceptEuclidean space, object, no evidence levelEuclidean spaceobjectMohr–Coulomb theory, concept, no evidence levelMohr–Coulomb theoryconceptOrdinary differential equation, concept, no evidence levelOrdinary differential…conceptClassical mechanics, concept, no evidence levelClassical mechanicsconceptFriction, concept, no evidence levelFrictionconceptByerlee's law, statement, no evidence levelByerlee's lawstatement
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  1. Cauchy stress tensor concept
  2. Euclidean space object
  3. Mohr–Coulomb theory concept
  4. Ordinary differential equation concept
  5. Classical mechanics concept
  6. Friction concept
  7. Byerlee's law statement

Where this leads

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Further reading

  1. Web https://en.wikipedia.org/wiki/Byerlee%27s_law
About this page
TagAGM7AKCGPG
URIm2://AGM7AKCGPG
Kindstatement, fact
WritingW0 stub
MSC86A60, 74A55
StatusThis copy of the site has no build data. Run m2 status AGM7AKCGPG.
AboutFriction
UsesFriction, Cauchy stress tensor, Mohr–Coulomb theory
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Changed3 November 2026

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