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

TL;DR

This paper presents the first analytical model of sill and laccolith emplacement that incorporates elasto-plastic deformation of host rocks, revealing significant effects of plasticity on intrusion growth and overpressure requirements.

Contribution

Introduces a novel analytical elasto-plastic model for shallow sill and laccolith emplacement, accounting for host rock plasticity and its impact on intrusion dynamics.

Findings

Plastic zone size is smaller than intrusion radius and decreases during growth.

Plasticity increases the overpressure needed for intrusion propagation.

Plastic effects are more significant during early intrusion stages.

Abstract

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