Calculation of Transient Temperature Field in an Inhomogeneous Rock Mass with a Spherical Cavity Filled with a Heated Liquid

Abstract

The problem under consideration is determination of temperature fields in a rock mass with a spherical cavity that is partly filled with a heated liquid. At that, the tendency to self-heating of the substance stored in the cavity leads to appearance of high-temperature fields, that in turn results in development of significant thermal stresses. Herewith, real physical and mechanical properties of the rock within the rock mass must be taken into consideration. So, the rock mass material is viewed through the lens of its inhomogeneity, which to a considerable extent is determined by temperature fields for any instant of hot fluid storage. Herewith, the temperature process is transient, but taking into consideration slow redistribution of the thermal field during a long period of time, the problem of its calculation can be considered as a quasi-steady-state problem. Temperature field around the cavity is calculated using an explicit difference scheme.

Comparison of the Stress-State Level for the Inhomogeneous Rock Mass with a Spherical Cavity in the Stationary and Non-Stationary Temperature Conditions

“…For the other problem, when some heat is released in the cavity at the time point t = 0 and then propagates in the rock mass, the thermal field is non-stationary. For large time intervals, the temperature propagation in an isotropic medium at action of instantaneous heat sources distributed on a sphere with a radius a, according to [9], is described by the formula:…”

“…Materials and Technologies in Construction and Architecture Fig. 3 shows temperature curves that were obtained in [9] and determined by the first summand in (Eq. 4).…”

Deformation process modeling of the rock mass with spherical cavity created by explosion

“…Fig. 2 shows the temperature curves for some points in time t [7]: It is of considerable interest to study the temperature inhomogeneity effect on the rock mass stress state temperature components values [8,9,10].…”

Calculation of a Radial Inhomogeneous Rock Mass with a Spherical Cavity under the Influence of Thermal Field

“…A nuclear explosion creating an underground cavity almost instantaneously releases in this cavity a large amount of heat and causes a considerable heating of the rock mass in the proximity of the cavity, followed by the heat transmission into the interior of the rock mass and the cooling of the cavity surface. This is a nonstationary process, but excluding from consideration the initial period and taking into account the relatively slow redistribution of the thermal field [1] during the subsequent sufficiently long time, the problem of determining the thermal stresses can be considered as quasi-stationary one [2,3].…”