Pressure conditions for shear and tensile failure around a circular magma chamber, insight from elasto-plastic modeling

International audienceOverpressure within a circular magmatic chamber embedded in an elastic half space is a widely used model in volcanology. However, this overpressure is generally assumed to be bounded by the bedrock tensile strength, because gravity is neglected. Critical overpressure for wall failure is thus greater. Here, I show analytically and numerically that wall failure occurs in shear rather than in tension, because the Mohr-Coulomb yield stress is less than the tensile yield stress. Numerical modeling of progressively increasing overpressure shows that bedrock failure develops in three stages: (1) tensile failure at the ground surface, (2) shear failure at the chamber wall, and, (3) fault connection from the chamber wall to the ground surface. Predictions of surface deformation and stress with the theory of elasticity break down at stage 3. For wall tensile failure to occur at small overpressure, a state of lithostatic pore fluid pressure is required in the bedrock, which cancels the effect of gravity. Modeled eccentric shear band geometries are consistent with theoretical solutions from engineering plasticity, and compare with shear structures bordering exhumed intrusions. This study shows that the measured ground surface deformation may be misinterpreted when neither plasticity nor fluid pore pressure is accounted for