Elasto‐plastic and hydromechanical models of failure around an infinitely long magma chamber

Surface displacements solutions of elastic deformation around an inflating magma chamber generally assume that the associated internal overpressure is limited by the bedrock tensile strength. When considering stress equilibrium in the bedrock adjacent to a spherical or infinitely long cylinder, the gravity body force actually resists tensile failure, thus leading to a much larger pressure threshold. And when considering a Coulomb failure criterion, analytical and numerical models predict that shear failure develops instead of tensile failure. Here, three numerical codes are used to compare elasto‐plastic solutions of surface displacements and patterns of failure in plane‐strain. Shear failure propagates independently from the surface downward, then from the chamber walls upwards, and finally the two plasticized domains connect. Another test with internal underpressure (simulating source deflation) fits standard solutions from tunneling engineering. The effect of pore fluid pressures is also explored. In case of lithostatic fluid pore pressure in the bedrock, the gravity effect cancels out, and tensile failure is enabled for an overpressure close to the tensile strength. Coupled hydromechanical models in undrained conditions indicate that the initial bedrock porosity modifies the evolution of fluid pressure, volumetric strain and effective normal stress, and consequently also the pressure threshold for the onset of failure. We show that a bedrock of low porosity is more prone to fail than a bedrock of high porosity. In summary, our elasto‐plastic and hydromechanical models illustrate the contexts for either tensile or shear failure around magmatic bodies, at the same time complementing and delimiting predictions deduced from elasticity.