Mechanical stability of shallow magma chambers

Abstract

The mechanical stability of the wall of a magma chamber depends on the value of the stresses likely to be developed in the immediate vicinity of this boundary in relation to the conditions for failure to occur. Various structural and physical factors contributing to these stresses are systematically analyzed. Models of volcanic systems having an axial symmetry around a vertical axis with an isolated reservoir, filled with magma under pressure, in a homogeneous elastic medium are investigated. Spheroidal magma chambers of different aspect ratios (0.7–2) and approximately the same volume (13.5–14 km3), with tops at 3.5–4.5 km depth, are considered. Stress distributions including the effect of gravity, free surface of the Earth, and remote stresses increasing with depth are calculated by using a numerical finite element method. The development of tensile tangential stresses greater than 10 MPa in the elements adjacent to the wall of the chamber is assumed to be a sufficient condition for its instability. The standard state of stress assumed for the crust (i.e., the boundary conditions imposed at large horizontal distance from the chamber) is varied in a continuous range having as lower limit a state of uniaxial strain in the vertical direction and as upper limit a state of hydrostatic stress. Calculations are first performed by making the assumption that the magma pressure P acting at the top of a chamber equals the lithostatic pressure of the overlying rocks. Alternatively, the upper limit of the values of P (critical pressure Pc) for which the initial shape of a chamber may be stable, according to the assumed necessary conditions for stability, is determined. For boundary conditions corresponding to uniaxial strain and Poisson's ratio v = 0.25, Pc turns out to be approximately half of the lithostatic pressure of the overlying rocks. A simple criterion is proposed to estimate if a chamber may evolve toward a new stable shape when P > Pc. This is highly improbable if P equals the lithostatic pressure of the overburden. Larger values of Poisson's ratio (0.30–0.35) favor stability, yielding critical pressures exceeding the lithostatic pressure. Stability is extremely sensitive to the standard state of stress assumed for the crust. Boundary conditions progressively approaching a hydrostatic state of remote stresses yield increasingly higher critical pressures. It turns out that the density contrast between magma and host rocks is not crucial for stability (for Δρ/ρ < 11%). For the rather large spheroidal chambers investigated, the shape is not a critical factor either. The effect of topographical details (e.g., a volcanic edifice, 1.5 km high and 6 km in radius) is practically irrelevant.