Subsurface Propagation of Thermo-mechanical Fracture Shock Waves in Hydrothermal Regimes

In this paper a one-dimensional analytical model for the mechanism of rock fracturing in hydrothermal regimes is described. The model is based upon the modern thermo-poro-elasticity theory and its two non-linear heat-like equations. On the boundary aquifer-caprock a buried thermomechanical source is supposed to be built up in terms of subsurface fluid-rock coupling dynamics. With this considerations i t is assumed that fluid pore pressure approaches the breakdown pressure of the caprock such that this starts failing. In order to study rock fracturing the variability of fluid-rock thermal diffusivity and fluid diffusivity at the onset of rock failure is taken into account in the two nonlinear heat-like equations. A series of fluid-rock temperature and fluid pore pressure shock wave fronts is obtained as a solution of Burgers' equation. These fronts, moving through the caprock as propagating fractured boundaries, are referred to as thermo-mechanical fracture shock waves. It is found that the speed of thermomechanical fracture shock waves propagation and their amplitude are governed by a coefficient r, whose value depends on the role played by fluidrock thermal diffusivity and fluid diffusivity variations. As a result, the final effect of thermomechanical fracture shock waves is the migration of the top of the aquifer towards a shallower depth with associated increases in the superficial thermomechanical outputs. Moreover, if thermomechanical fracture shock waves are maintained from below by the arrival of other waves, the fractured boundary can further migrate upwards and eventually trigger a catastrophic event such as a phreatic eruption. INTRODUCTION Thermo-mechanical instabilities such as ground surface displacements in hydrothermal domains have been interpreted in terms of a buried thermomechanical source. Generation has been currently considered by either a shallow magma body characterised by episodic mafic and silicic magma mixing, as i t is supposed to have happened for example in Yellowstone, Long Valley and Campi Flegrei silicic calderas, or due to the growth of a 161 batholith (Dvorak and Dzurisin, 1997 and bibliography therein). Recently, an alternative interpretation to this current hypothesis has been proposed, for which thermo-mechanical instabilities may even be triggered by a buried thermo-mechanical source related to subsurface water-rock coupling dynamics (Bonafede, 1991 and 1997; Merlani et al., 1996 and 1997; Natale and Salusti, 1996). As a consequence of such a new tendency and in order to interpret the last ground surface uplift at Campi Flegrei (198284, Italy), Bonafede (1991) initiated the application of modern thermo-poro-elasticity theory to waterrock coupling dynamics at the thermo-mechanical buried source. This was considered to be generated at the bottom of an aquifer and formally interpreted in terms of two non-linear heat-like equations as already stated by Rice and Cleary (1976) and McTigue (1986). From this, he perturbatively modelled the observed ground surface uplift in terms of migration through the Phlegraean aquifer of hot and pressurised supercritical water able to thermo-elastically deform the overburden rock. In the light of Bonafede's study, Natale and Salusti (1996) analytically found that water-rock coupling dynamics at the buried source could generate thermo-mechanical shock waves, migrating throughout either deformable pervious or deformable semi-pervious horizons. Here we examine the case in which modern thermoporo-elasticity theory can even hold to describe rock fracturing through low permeability horizons. Such horizons are thought of as overlying hydrothermal aquifers and acting as caprocks. With these considerations rock fracturing is supposed to start at the aquifer-caprock boundary. By analytically developing the two non-linear one-dimensional heat-like equations upon which modern thermoporo-elasticity theory is based, namely the stressdiffusion equation and the fluid-rock energy equation, it is assumed that at the onset of rock failure fluid-rock thermal diffusivity and fluid diffusivity changes in the heat-like equations. The stress-diffusion equation is here adopted as stated by McTigue (1986). The fluid-rock energy equation is formulated as recently proposed by Natale (1998). The model is based upon data from the last ground surface uplift at Campi Flegrei in Italy (1982-84). However, i t is applicable to any hydrothermal domains as long as conditions for rock failure exist at depth. Finally, Westerly granite is taken into account as the rock type representing the caprock. THE SYSTEM AND THE HEAT-LIKE EOUATIONS Let us consider a hombgeneous. isotropic and laterally boundless water-saturated porous horizon acting as cap rock on an underlying aquifer in the underground of a hydrothermal domain (fig. 1). Such a horizon has a thickness z = b , with the upper bomdary (gromd surface or a certain level at depth)