Inelastic deformation during sill and laccolith emplacement: Insights from an analytic elastoplastic model

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 elastoplastic 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/a4ΔP, with ΔP 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 elastoplastic 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. Key Points We present an analytical model of igneous sill and laccolith emplacement accounting for inelastic deformation at intrusion tips The size of the inelastic zone scales with the inverse of (1) the intrusion radius and (2) the square root of the magma overpressure Our model shows that the effect of the inelastic zone can be substantial for small intrusions, whereas it decreases with large intrusions