  We consider the deformation of a geological structure with non-intersecting
faults that can be represented by a layered system of viscoelastic bodies
satisfying rate- and state-depending friction conditions along the common
interfaces. We derive a mathematical model that contains classical Dieterich-
and Ruina-type friction as special cases and accounts for possibly large
tangential displacements. Semi-discretization in time by a Newmark scheme leads
to a coupled system of non-smooth, convex minimization problems for rate and
state to be solved in each time step. Additional spatial discretization by a
mortar method and piecewise constant finite elements allows for the decoupling
of rate and state by a fixed point iteration and efficient algebraic solution
of the rate problem by truncated non-smooth Newton methods. Numerical
experiments with a spring slider and a layered multiscale system illustrate the
behavior of our model as well as the efficiency and reliability of the
numerical solver.
