Abstract
The thermal-mechanical response of rock at shallow to medium depth beneath the earth's surface has been modeled as a magma body ascends toward it. The overall stress field is calculated by considering the country rock as a viscous fluid, a thermal-elastic material, or as an elasto-plastic material that fractures when its strength is overcome.
The stress field within and around a spherical magma body surrounded by a homogeneous, Newtonian fluid has been evaluated and can be used at deeper levels in the earth's crust where the viscosity of the country rock is relatively low. With decreasing depth wall rock material becomes more viscous which results in diminishing stress magnitudes. In a highly viscous material shear stress and tangential stress have negligible magnitudes. They become more important by considering a spherical magma chamber rising within a bigger spherical container.
In the thermal-elastic model the current pressure inside the magma body and the stress field within the host rock are determined. A pressure increase of the magma chamber is induced by crystallization of anhydrous minerals associated with exsolution of an aqueous phase. This results in magma chamber expansion and pressure increase since the elastic deformability is limited.
Thermal stress due to heating of country rock material is the most important stress component and is sufficient to fracture brittle country rock. The temperature distribution within the wall rock has a fundamental influence on the fracturing process and its associated stress field. Four regions in the elasto-plastic host rock can be distinguished. From the magma outward, they are: (1) a cataclastic region with shear fractures more or less parallel to the chamber's margin, (2) a thermal-elastic zone with preexisting fractures, (3) a fractured region containing shear fractures with high angles to the interface between magma and host rock, and (4) an almost intact elastic outer region. The fluid pressure of a porous host rock enhances the fracturing process, but the fluid pressure of the magma hinders the development of the cataclastic region. Ascent of a magma body surrounded by a fractured material can occur by stoping, in which disengaged wall rock fragments sink in less dense magma.

Arz, C., 1992. Thermal-mechanical response to an intruding magma chamber.  Unpublished MSc. thesis, State University of New York at Albany. 129 pp., +xiv
University at Albany Science Library call number:  SCIENCE Oversize (*) QE 40 Z899 1992 A79

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