Deformation around a Fault that cuts a Block of Viscous Material
 
    Here we show the calculated deformation field around a fault that cuts the right hand boundary of the block as far as the centre of the block.  The deformation field includes a singularity in the stress components at the fault tip.  For that reason, we concentrate mesh points around the fault-tip as shown in the upper left diagram, but the accuracy with which the deformation field is computed can be checked against an analytic solution for the crack tip.  The fault permits a displacement discontinuity parallel to its direction, but requires continuity in the perpendicular directions, as for a buried geological fault which separates distinct sliding blocks of rock.  If the rock is hot enough (deep in the crust) it creeps like a viscous fluid.


    The two diagrams in the middle row show the variation of the two components of displacement rate: Ux and Uy.  In Ux, we see the transition between a distributed shear flow on the left to the discontinuous displacement on the right.  To balance the horizontal flow, there is also a minor component of vertical flow as shown with Uy.  With elapsed time finite deformation of the block is shown on the lower right diagram.  The variation of displacement and deformation along the fault is diagnostic of the stress vs strain-rate exponent of the viscous material.

Relevant Publications

Barr, T.D., and G.A. Houseman, Distribution of deformation around a fault in a non-linear ductile medium, Geophys. Res. Lett., 19, 1145-1148, 1992.
Barr, T.D., and G.A. Houseman, Deformation fields around a fault embedded in a non-linear ductile medium, Geophys. J. Int., 125, 473-490, 1996.