A numerical model for the mechanical behavior of intraplate volcanoes

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Abstract
A new approach toward understanding the mechanical behavior of intraplate volcanoes is offered by first postulating a geological model of the internal structure and then developing an axisymmetric numerical simulation using the finite element method. This enables one to consider the types of fracturing at various depths in terms of state of stress under specific conditions of loading. The geological model is based on comparative field studies of three volcanically active oceanic islands (Marion, Tristan da Cunha, and Reunion) and a dormant one (Gough). The model contains a shallow (3 km deep) magma chamber with distinguishable floor, wall, and roof sections. A magma column rises from the chamber toward a central cone at the surface. Depending on the structural level at which they originate, different dyke and fracture patterns are generated. For the numerical simulation the medium is assumed to be linear elastic, continuous, and isotropic. Different loading combinations are applied, including hydrostatic pressure plus magmatic pressure in the chamber and external pressure that represents regional tectonic effects. It appears that the structural levels of the geological model can be adequately explained by variations in the distribution, intensity, and trajectories of principal stresses σ1, σ2, and σ3. It is concluded that the shape of the magma source is a major factor in the stress pattern. The effect of the driving pressure (Pmag‐ Pext) on the orientation of the principal stresses σ1and σ2is also considered. The sloped surface of the volcanic edifice is found to cause local rotation of the stress field. Finally, the evolution of the stress field with loading path is related to successive structural levels in a dynamic eruptive model.