โ Scribed by Richard A. Schultz
No coin nor oath required. For personal study only.
Curved slip surfaces are common structures in geologic and geotechnical situations. Important examples include geologic faults and the basal slip surfaces of landslides. The author analyses these structures by using two-dimensional boundary element and fracture mechanics methods to study the influence of curvature on displacements and related deformation of surrounding rock. Although analytical solutions for stresses and displacements associated with a curved crack exist in the literature, solutions for a curved slip surface with friction are not available. Curved slip surfaces are idealized as curviplanar cuts in a linearly elastic plate and a Coulomb frictional slip criterion, tensile failure (cracklike opening) provision, and constraint on slip surface wall interpenetration are included in the model. Remote principal stresses produce sliding displacements along favorably oriented slip surface segments, and stresses in the surrounding plate are calculated from these displacements. Mechanical modeling of ideal circular-arc slip surfaces shows that Mode-II displacements can in general vary in distribution and sense along curved slip surfaces as a function of curvature and remote stress orientation. Because regions of decreased and increased mean normal stress depend on the occurrence and positions of slipping segments, the locations of extensional and contractional deformation strucures need not be located only near the terminations of curved slip surfaces. This result contrasts with predictions and observations of rock fracture near terminations of straight slip surfaces. In the latter case, the ends of slipping segments usually coincide with the slip surface terminations.
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