Pressure conditions for shear and tensile failure around a circular magma chamber; insight from elasto-plastic modelling
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Overpressure 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 since gravity is neglected. Critical overpressure for wall failure is thus greater. It is shown 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 modelling 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. Modelled eccentric shear band geometries are consistent with theoretical solutions from engineering plasticity and compare well with shear structures bordering exhumed intrusions. This study shows that the measured ground surface deformation may be misinterpreted when neither plasticity nor pore-fluid pressure is accounted for.