Stresses in an overthrust sheet and propagation of thrusting: An Airy stress function solution

摘要

An Airy stress function solution is derived for the stress field in an elastic wedge‐shaped overthrust sheet subject to horizontal forces at the rear and at the front. From this stress solution the state of stress on the basal thrust (lower boundary of the sheet) is obtained. Both normal and shear stresses on the basal thrust are affected by the rear pushing and front buttressing forces and by the slopes of the upper and lower boundaries of the wedge‐shaped block. For (1) nonlinear components of external horizontal forces exerted on the vertical edges of the block and/or (2) nonzero slopes of the upper and lower boundaries the normal and shear stresses vary systematically with position along the basal thrust. The ratio of shear and normal stresses along this plane (the “frictional function” of the thrust) can be compared with the friction coefficient to determine where slippage is likely to occur. Since the frictional function is a function of position, the strength is exceeded only on part of the thrust (near the rear for most values of the parameters). The assumption of simultaneous displacement of the whole thrust sheet on the basal plane is therefore not realistic. Even simple static models such as the present one indicate that the motion on thrust faults must be envisaged in terms of progressive, consecutive “dislocation‐typ