Numerical modelling of stress fields and fracture around magma chambers

We investigate the formation of cracks around magma chambers and their relation to caldera collapse. We discuss basic background physics and the causes of caldera collapse events, then examine the suitability of the smoothed particle hydrodynamics (SPH) method for these applications by studying simple two-dimensional systems. The SPH method and equations for solid body materials are discussed, and tested for the stress concentration around a circular hole. The effect of altering the depth of an underground magma chamber is investigated, the results are compared to similar calculations using boundary element techniques. A fracture model is introduced and tested for the brittle fracture of plates in tension. We apply our fracture model to investigate the fractures that develop around magma chambers. We find that our results are in general agreement with experiments. In particular, we find that in the absence of tension a sudden rise in the chamber pressure can initiate fractures, which propagate towards but do not reach the surface. At the same time, fractures can propagate down from the surface towards the chamber. Under tension and pressure increase fractures can develop and reach the surface in a form that could lead to piston collapse. We find that the fractures depend in a complex way on the geometry of the chamber together with the history of country rock tension and sudden jumps in the chamber pressure.