The relationship between conjugate shear fractures and the principal stresses in a homogeneous, isotropic, deformed body is shown in the stereoplot given below (\( \sigma_1, \sigma_2, \sigma_3 \) are compressive stresses). Which one of the given fault regimes is indicated according to Anderson’s theory of faulting for the formation of conjugate shear fractures under plane strain?
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In Anderson’s theory, reverse faulting occurs when the compressive stresses are applied along two principal axes with a third axis subjected to tension, resulting in conjugate shear fractures.
In Anderson's theory of faulting, conjugate shear fractures occur when a body is subjected to different principal stresses. According to the theory, the stress regime that leads to conjugate shear fractures involves the application of compressive stresses in two principal directions (\( \sigma_1 \) and \( \sigma_2 \)) and a third direction of tensile stress (\( \sigma_3 \)).
The typical faulting regimes described by Anderson’s theory are:
- Normal faulting occurs when \( \sigma_3 \) is vertical, and the horizontal principal stresses are tensile.
- Reverse faulting occurs when \( \sigma_3 \) is horizontal, and the principal stresses are compressive in nature.
- Strike-slip faulting is observed when the shear stresses are dominant, resulting in horizontal displacement along the fault.
For the conjugate fractures shown in the diagram, the stress pattern corresponds to reverse faulting, as the stress axes align with the characteristics of reverse faults under compressive stress.
Thus, the correct answer is (C) Reverse.
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