ON THE PHYSICAL ESSENCE OF b VALUE FOR AE OF ROCK TESTS AND NATURAL EARTHQUAKES IN TERMS OF FRACTURE MECHANICS

The problem of physical essence of b value for AE of rock tests and natural earthquakes-has been a controversial topic during the past two decades. In the present paper the order and* energy of each microfracturing of the microcrack system existing in a rock specimen is discussed from the viewpoint of fracture mechanics, then the whole series of AE and subsequently the value of b can also be determinated. The order of microfracturing depends on the parameters Kei/Kcf where Kei is the effective stress intensity factor of the i-th microcrack and Kci is-the fracture toughness in the site of the i-th crack. The energy of each AE can be expressed as ilofli G1ds where G1 is energy release rate of nicrofracturing, lof and li are the original and final crack lengths respectively and i is the emanating efficiency for the i-th crack. If we assume that the distribution density function of microcrack length l is p(l)=Bl-r where B and are constants, then the expression b = 3/2 can be deduced. Hence we have come to the conclusion that the value of b mirrors essentially the crack-system-configuration of the material which means the distribution of the sizes, shapes and orientations of micro-cracks over the space as well as the distribution of the other concerning physical parameters such as fracture toughness, friction coeficient etc. Our conclusion is somewhat similar in character to Mo-gi's. He concluded that the heterogeneity of the material plays the most important role in determining the value of b. The term heterogeneity of the material of course covers the idea of crack-system-configuration, but we think that our view has a little bit deeper insight to the problem than that of Mogi's.