岩石颗粒边界缺陷分布的概率模型

本文应用概率理论，研究了颗粒结构材料初始边界缺陷的分布问题，提出了一个概率模型，认为材料中的初始边界缺陷不会全部都是孤立地分布，总会有二个、三个或更多个基本边界缺陷相连在一起组成缺陷族的情况，缺陷簇的个数的数学期望值相对于其尺度符合指数衰减强度，衰减指数与缺陷发生的概率及边界网络的相似维数有关。推导得出了颗粒结构材料的拉伸强度与试样尺度、颗粒尺度及缺陷发生概率之间的关系，从理论上论证了材料强度的尺

The Probability Model for Distribution of Grain Boundary Defects in Rock

In this paper,the distribution of original grain boundary defects in granular structure materials is studied and a probability model is presented,based on the theory of probability.It is sugested that not ah orional grain boundary defects in materials are segregately distributed,and defect bunches in which two or more element boundary defects are connected may exist.The expectation for the number of defect bunches seems to obey the exponentially attenuating law with respect to their size. The index of attenuation is relative to the probability of defect occurrence and the fractal of grain boundary nets.The relation of tension strength of grain structure material with the sample scale,grain size and defect occurrence probability is obtained and the scale effects of material strength is theoretically proved.