  Numerous geological observations evidence that inelastic deformation occurs
during sills and laccoliths emplacement. However, most models of sill and
laccolith emplacement neglect inelastic processes by assuming purely elastic
deformation of the host rock. This assumption has never been tested, so that
the role of inelastic deformation on the growth dynamics of magma intrusions
remains poorly understood. In this paper, we introduce the first analytical
model of shallow sill and laccolith emplacement that accounts for
elasto-plastic deformation of the host rock. It considers the intrusion's
overburden as a thin elastic bending plate attached to an
elastic-perfectly-plastic foundation. We find that, for geologically realistic
values of the model parameters, the horizontal extent of the plastic zone lp is
much smaller than the radius of the intrusion a. By modeling the quasi-static
growth of a sill, we find that the ratio lp/a decreases during propagation, as
1/ $\sqrt$ a 4 $\Delta$P , with $\Delta$P the magma overpressure. The model
also shows that the extent of the plastic zone decreases with the intrusion's
depth, while it increases if the host rock is weaker. Comparison between our
elasto-plastic model and existing purely elastic models shows that plasticity
can have a significant effect on intrusion propagation dynamics, with e.g. up
to a doubling of the overpressure necessary for the sill to grow. Our results
suggest that plasticity effects might be small for large sills, but conversely
that they might be substantial for early sill propagation. 2
