Blister dynamics beneath thick elastic layers

Many geophysical systems involve a coupling between fluid flow and solid deformation, such as drainage of supraglacial lakes, geological carbon sequestration, and the inflation of magmatic bodies. Measurements of surface deformation offer one of the few ways to interrogate these systems.

The behaviour of fluid injected beneath an elastic layer has often been studied as an analogue for such systems. Typically, the elastic layer is assumed to either be thin, behaving as a bending beam, or thick, behaving as a semi-infinite elastic solid. We develop a model of a uniform elastic layer whose thickness spans the thin and thick elastic limits, and consider the injection of viscous fluid beneath an elastic layer separated from a rigid boundary by a thin film.

The behaviour of the system is controlled by three length scales: the thickness of the elastic layer, the depth of the pre-existing film, and an elasto-gravity length scale. We describe the different regimes of behaviour that occur when the fluid pressure within the blister is dominated either by bending stresses or gravity, and the corresponding scaling exponents for the blister height and radius.