Closed-form solutions of stresses and displacements around a circular opening in a thermal elasto-plastic medium subjected to a hydrostatic initial stress are given. The solutions have been derived using the equation of equilibrium, compatibility condition, along with the stress-elastic thermal strain relationship, yield criteria, plastic potential and a flow rule. The effects of temperature, support pressure, and strength parameters on the distribution of stresses, displacements and strains are illustrated in the parametric studies. Conclusions of direct engineering significance are outlined.
Study of the thermo-mechanical behaviour of rock materials under elevated temperature is a relatively new challenge to engineering rock mechanics. Recent design and development of energy and resource related underground structures such as nuclear power plants, high-level radioactive waste repositories, oil extraction and storage facilities require adequate understanding of thermo-mechanical properties and behaviour of rocks at relatively low pressure but high temperature environments. Within the last decade, studies have been carried out on thermally-induced microcracks in rock (e.g. Lo and Wai, 1982), and the effects of temperature on the thermo-mechanical properties of rocks have been studied extensively (e.g. Durham and Abey, 1981, nage and Heard, 1981, Mongelli et al, 1982, Drury et al, 1984). Several studies have been made to compare theoretical models with laboratory and field experimental results (e.g. Johnson and Gangi, 1980, Witherspoon 1981, Chan et al., 1980, Van Sambeek et al, 1980, Gregory and Kim, 1981). It has been recognized that in general the temperature prediction by thermo-mechanical models is satisfactory. However, the models used in the theoretical analyses overestimates stresses and displacements from 20 to as much as 100%. The discrepancy has been attributed to:
difficulty in field instrumentation;
existing discontinuities in rock (faults, joints); and
the validity of the theoretical models used. In the thermo-elastic analyses, it has been shown that tangential stress is highly compressive at the tunnel surface and tensile in the vicinity of a heat front in many instances (Lo et al, 1982, Ogawa, 1986).
In this paper solutions of thermal elasto-plastic stresses and displacements are proposed and the results of parametric studies will be presented.
The problem is defined in Figure 1. Consider a circular opening with a radius a being excavated in an infinite thermal elasto-plastic medium which is subjected to isotropic initial stresses Po. The excavation removes the boundary stresses around the circumference of the opening, and the inside of the opening is filled with a liquid or gas so that the opening is subjected to an instantaneous constant increase in temperature V and support pressure Pi. As time increases, the temperature of the medium increases, thus causing thermal stresses and displacements. In the vicinity of the opening, the induced stresses by excavation and by thermal loading may exceed the strength of the material, leading to the development of a plastic zone with a radius b, where b - b(t). It is required to obtain the thermal elasto-plastic stresses and displacements around the opening.
