On the physical essence of theb value for AE of rock tests and natural earthquakes in terms of fracture mechanics

The problem of physical essence of theb value forAE 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 ofAE and subsequently the value ofb are determined. The order of microfracturing depends on the parametersKei/Kci whereKei is the effective stress intensity factor of thei-th microcrack andKci is the fracture toughness in the site of thei-th crack. The energy of eachAE can be expressed asηi ∫ loili Gids whereG is the energy release rate of microcarck,loi andli are the original and final crack lengths respectively andηi is the emanating efficiency for thei-th crack. If we assume that the distribution density function of microcrack lengthl isp(l)=Bl?v whereB andγ are constants, then the expressionb=3γ/2 can be deduced. Hence, we have come to the conclusion that the value ofb mirrors essentially the “crack-system-configuration” of the material, which means the distribution of the sizes, shapes and orientations of microcracks over space as well as the distribution of the other relevant physical parameters such as fracture toughness, friction coefficient, etc. Our conclusion is somewhat similar in character to Mogi’s. He concluded thet the heterogeneity of the material plays the most important role in determining the value ofb. The term heterogeneity 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.