Similarity rule of crack geometry in statistically homogeneous rock masses

Abstract An nth rank tensor called the generalized fabric tensor is introduced to express crack geometry due to discontinuities like joints and faults in rock masses. Statistically homogeneous rock masses can be regarded as geometrically similar bodies if they are characterized by a common fabric tensor. In order to say that they are also similar in mechanical properties, the crack geometry must be similar in the sense of the generalized fabric tensor. The generalized fabric tensor can be expressed by (1) the number of cracks crossed by a unit length of a scanning line, (2) the number of cracks associated with a unit area of a scanning plane, and (3) the density function E (n) to describe the orientation of crack normal unit vectors n. Since these are all determined by conventional field surveys, one can say that the similarity rule for crack geometry is ready to be used in practical rock mechanics.

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