Limit Analysis for post-failure analysis: application to structural geology

Yves M. Leroy

The objective of this talk is to present a simple approach to predict the internal de- formation of frictional wedges resting on weak decollements. The fundamental mode of deformation is by thrusting, corresponding to the onset of two faults (shear bands), the ramp and the hinge, rooting at the same point on the decollement and to the partial activation of the decollement. The position of this point as well as the dips of the two faults are found by application of the kinematics approach of limit analysis. Nature make use of this failure mode to produce a fold which is constructed by simple geo- metrical rules in the spirit of Suppe’s seminal work. The post-failure analysis consists in estimating the bounds for the development of this fold and for the onset of a new thrust and to compare the two bounds to decide on the dominant failure mode. Erosion of the topography and damage accumulation on the activated ramps are accounted for. It is shown how a subcritical wedge (topographic slope less than Rankine’s stability slope) increases its slope by a succession of thrusting events. Under quasi-steady state conditions, these thrusts are periodic in time and space with a time period linearly dependent on the thrust-root depth. These periodic distributions do not occur if ramp damage is accounted for but is observed if erosion and damage are combined. It is also shown how these thrusting events could lead to hinterland vergence of major thrusts, diffuse or localized deformation and exhumation processes.

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