Issue34

Q. Like et alii, Frattura ed Integrità Strutturale, 34 (2015) 543-553; DOI: 10.3221/IGF-ESIS.34.60 545 The differential expression of the energy balance in FLAC has the form T T v T q q t        (2) where T q is the heat-flux vector in (W/m 2 ), T v q is the volumetric heat-source intensity (W/m 3 ) that is equated to the power density within the material, and t  is the heat stored per unit volume (J/m 3 ). In general, temperature changes may be spurred by changes in both energy storage and volumetric strain, and the thermal constitutive law relating those parameters may be expressed as T v t T M t t t                 (3) where M T and β v are material constants, and T is temperature. FLAC considers a particular case of this law, for which βv = 0 and 1 T v M C   . ρ is the mass density of the medium ( kg/m 3 ), and Cv is the specific heat at constant volume ( J/ kg°C). The hypothesis is that strain changes negligibly affect the temperature. Such an assumption is valid for quasi-static mechanical problems involving solids. Accordingly, we may express v T T C t t        . (4) The substitution of Eq. (4) in Eq. (2) yields the following energy-balance equation: T d v T q P C t        (5) After the material is heated by microwaves, the strain resulting from temperature change can be expressed as , , , i j i j i j T     (6) where , i j  denotes the strain; , i j  is the thermal expansion coefficient (1/°C); and , i j T  is the temperature change. The stress produced by heat can be calculated by Hooke’s law as follows. , , , , (1 2 ) i j i j i j i j E      (7) where , i j  denotes the thermal stress of unit i, j; , i j E is the elastic modulus of unit i,j (Pa); and , i j  is the Poisson’s ratio of unit i, j. Calculation Model This paper takes the rock grains consisting of galena and calcite as the research object. The research object is simplified into a two-dimensional plane strain model, with a rock grain size of 10 mm × 10 mm, and square galena crystal’s side length of 0.6 mm. For mesh generation in FLAC2D, the unit length is 0.05 mm; after generation, the model contains 40,000 units and 40,401 nodes. By writing a random distribution subroutine, in the case of a given mineral content, the galena crystal is randomly distributed within the calcite crystal, without human intervention in the distribution process. After the model is determined, a calcite unit near a galena crystal is defined as a mineral boundary element, as shown in Fig. 2. Mineral boundary occupies only one element, with a width of 0.05 mm.