A new approach toward understanding the simulation using the finite element method. It will be mechanical behavior of intraplate volcanoes is offered by shown (see section below on the physical and elastic first postulating a geological model of the internal structure properties of the model) that the assumption of a linear and then developing an axisymmetric numerical simulation elastic and continuous medium is quite justified in this case. using the finite element method.This enables one to We are mainly interested in the distribution and intensity of consider the types of fracturing at various depths in terms stresses, since they give the most probable sites where of state of stress under specific conditions of loading. The fractures are going to open, keeping in mind that the geological model is based on comparative field studies of medium is continuous. The subject matter of this paper three volcanically active oceanic islands (Marion, Tristan da therefore belongs to the first category of problems discussed Cunha, and R•union) and a dormant one (Gough). The in the historical review below. model contains a shallow (3 km deep) magma chamber with Finally, in the discussion, the geological and numerical distinguishable floor, wall, and roof sections. A magma models are compared. column rises from the chamber toward a central cone at the surface. Depending on the structural level at which they Historical Development of Mechanical originate, different dyke and fracture patterns are generated.
Modeling in VolcanologyFor the numerical simulation the medium is assumed to be linear elastic, continuous, and isotropic. Different loading Previous work on the mechanical behavior of volcanoes combinations are applied, including hydrostatic pressure plus uses both analytical and numerical methods, and can be magmatic pressure in the chamber and external pressure that subdivided into three categories. The first category of represents regional tectonic effects.It appears that the problems is the distribution of stresses inside a volcanic structural levels of the geological model can be adequately edifice. Mechanical models of the internal structure of explained by variations in the distribution, intensity, and volcanoes started with Anderson's [1935] studies on the trajectories of principal stresses o 1, 0 2, and .0 3. It is origin of the cone sheets and ring dykes of Ardnamurchan concluded that the shape of the magma source •s a major in Scotland. By an analytical approach, he derived the factor in the stress pattern. The effect of the driving equations of displacement components due to a radial point pressure (P -P x ) on the orientation of the principal dilatation and a vertical point-push acting in a weightless, stresses o 1 anco 2 is ats semi-infinite, elastic, isotropic half-space. He concluded o considered. The sloped surface of ma e the volcanic edifice is found to cause local rotation of the that cone sheets occupy tensile fractures while ring dykes stress field. Finally, the evolution of the stress field with occupy...