Critical wedges in three dimensions: Analytical expressions from Mohr‐Coulomb constrained perturbation analysis

Abstract

We present simple analytical expressions for evaluating three‐dimensional stress fields in critical wedges (Coulomb failure throughout) that are deforming within an oblique convergent zone. We assume that the load and geometry variations in the lateral direction, and the topographic slope, are relatively small. The stress state of a two dimensional critical wedge is perturbed by admitting a small lateral shear, which is accommodated (to maintain criticality) by a reduction in the dominant normal compressive stress. Cohesionless cases are further simplified with Taylor series expansions in the topographic slope. The analytical expressions distinguish the behavior of strong base wedges associated with steep slopes from weak base wedges with more modest slopes, and are reliable for lateral shear values as large as half the lithostatic load. In the weak base case where the vertical shear is small, the orientations of the principal stresses are very sensitive to the perturbation. As the lateral shear increases through relatively small values, the roles of the lateral and vertical coordinate axes are interchanged, with a resultant transition from predominantly thrust failure to strike slip failure. Transition to strike slip in the strong base case is more gradual. The particular value of horizontal shear for which transition occurs also depends on the difference of the minor normal stresses. We produce an analytical expression predicting displacement patterns compatible with those observed in natural and analog orogens. Displacement partitioning is predicted for weak base wedges due to minor changes in lateral boundary conditions associated with variable orogen geometry.