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Anderson's Faulting Theory

According to the authors1 2 conjugate fractures form at about 30o from the principal stress σ1 for a particular stress state under certain values of confining pressure and where Coulomb's criterion is applicable. "Faults are shear fractures where there is a prominent displacement of blocks along the fault surface"1. The principal stress surfaces that contain 2 of the principal stresses are directions in which there are no shear stresses, when considering the nature of the stress tensor. In his paper of 1905 Anderson concluded that when taking these facts into consideration the surface of the Earth, when thought of as the boundary layer separating the atmosphere from the lithosphere, is a free surface where no shear stresses are developed, i.e. it is not possible to slide relative to the surface. According to this approach atmospheric stresses are not strong enough to form fractures, topographic relief is negligible, and the surface of the Earth is considered to be perfectly spherical. The principal stress axes need to be either horizontal or vertical and 2 of them have to be parallel to the surface of the Earth, if the surface is a principal stress surface.

Anderson supposed that at any point below the surface of the Earth the common condition should be a hydrostatic state of stress, in any direction the horizontal stresses will have the same magnitude as the vertical stress as a result of gravitational force or lithospheric loading. Faults will form if the magnitude of the stresses is large enough, when the horizontal stresses differ from the vertical load and the development of a regional triaxial stress system. The horizontal stresses need to be altered in 3 possible ways in order to have a triaxial stress state, and considering the vertical load initially remains constant. First, the magnitude is decreased by different amounts according to the orientation such as the larger compressive stress σ1 will be the vertical load and σ2 ± σ3 horizontal stresses.

Second, increasing the horizontal stress levels by different amounts in such a way that the vertical load will be the smaller stress σ3 and σ1 ±  σ2 horizontal stresses.

Third, increasing the magnitude of the stress in one direction and decreasing it in the other, with the result that the vertical load will be σ2, which is smaller than the magnitude of 1 of the horizontal stresses, σ1, and larger than the other, σ3. Coulomb's fracture criterion, τc = τ0 + μ σn, with the coefficient of internal friction (μ) and the cohesive strength (τ0), both of which depend on the nature of the rock that is involved. According to the authors1 many lab experiments have validated the criterion in which the relation between the shear fractures, extension fractures and the orientation of the principal axes have been well established. Anderson concluded that when Coulomb's criterion is combined with the nature of the surface of the Earth as a principal stress surface, only 3 types of faults can occur at the surface of the Earth. These are normal faults, when σ1 is vertical; thrust faults when σ3 is vertical, and strike-slip faults when σ2 is vertical. Normal faults will dip about 60o, and show movements that are purely dip-slip, thrust faults will dip 30o and will also give way to dip-slip displacements, and strike-slip faults will have surfaces that dip 90o and blocks will move horizontally. The authors1 note the relation in all the models between the 2 conjugate faults formed and the principal stress axes. According to Anderson's theory a pair of conjugate faults cross each other with a 60o angle, which is not dependent on the type of fault that is formed. The acute angle between the faults will always be bisected by the main principal stress, σ1, following Coulomb's criterion predicting that fractures produced at 30o from  σ1,  σ2 is positioned where the 2 fault planes intersect, and  σ3 is located at the bisector of the obtuse angle that is formed between the faults.

Sources & Further reading

  1. Leeder, Mike, Perez-Arlucea, Marta, 2006, Physical Processes in Earth and Environmental Sciences, Blackwell Publishing Ltd.
Author: M. H. Monroe
Last updated 11/05/2013

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