从断裂力学观点探讨 b 值的物理实质
ON THE PHYSICAL ESSENCE OF b VALUE FOR AE OF ROCK TESTS AND NATURAL EARTHQUAKES IN TERMS OF FRACTURE MECHANICS
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摘要: 岩石试验声发射及天然地震的 b 值到底反映了什么样的物理实质,是一个长期以来引起争论的问题.本文运用断裂力学的观点和方法,研究岩石试验试件内微裂纹系中各裂纹的扩展顺序及声发射能量,由此确定整个声发射序列,并进而确定 b 值.如果假设裂纹长度的分布密度函数为 p()=B-.经过力学分析和数学推导,可得到关系式 b=3/2.由此看出:b 值的物理实质是,它反映了介质的断裂构造状态————包括介质中裂纹系的空间分布及其它影响材料中裂纹扩展的物理量(如断裂韧度、摩擦系数等)的空间分布.这一结论与大多数实验及观测结果相符.我们的研究结果与茂木清夫观点有共同之处.茂木清夫认为:介质的不均匀性是决定 b 值的重要因素.介质的不均匀性一词固然也包括了介质的断裂构造状态在内,但是本文之观点比茂木更进一步说明了问题的实质.Abstract: 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.