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

Muriel Gerbault

doi:10.1144/sp367.8

Abstract

Abstract 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. Supplementary material: The numerical benchmark data are available at: http://www.geolsoc.org.uk/SUP18517 .

Highlights

Overpressure within a circular magmatic chamber embedded in an elastic half space is a widely used model in volcanology
In order to explain field observations of tensile failure, which were predicted to occur for less than or an average of 10 MPa of internal overpressure, the main point of this paper is to show that if this is the case, it is necessary to consider a state of near-lithostatic fluid overpressure in the bedrock
In studying the stress conditions for failure around a spherical magma chamber subjected to an internal overpressure, assuming an elasto-plastic bedrock and a simple approximation of fluid pore pressure, I have demonstrated the following points: (a) Failure occurs in shear mode along the chamber walls, and for an internal overpressure about half an order of magnitude greater than the usually inferred limit given by rocks tensile strength

Summary

Introduction

Overpressure within a circular magmatic chamber embedded in an elastic half space is a widely used model in volcanology. If one can justify the development of up to lithostatic pore fluid pressures in the neighbourhood of a magmatic chamber, shear and tensile failure are predicted to occur under relatively small internal overpressures of the order of the tensile strength of rocks (10 MPa).

Results

Conclusion