From a physical perspective, a joint experiences fracturing processes that affect the rock at both microscopic and macroscopic levels. The result is a behaviour that follows a fractal structure.

In the first place, for saw-tooth roughness profiles, the use of the triadic Koch curve appears to be adequate and by means of known correlations the JRC parameter is obtained from the angle measured on the basis of the height and length of the roughnesses. Therefore, JRC remains related to the geometric pattern that defines roughness by fractal analysis.

In the second place, to characterise the geometry of irregularities with softened profiles, consequently, is proposed a characterisation of the fractal dimension of the joints with a circumference arc generator that is dependent on an average contact angle with regard to the mid-plane. The correlation between the JRC and the fractal dimension of the model is established with a defined statistical ratio.

1. Introduction

The shear strength force depends on both the strength of the particles that constitute the rock and the strength of the rock matrix at a higher hierarchical level. The manner in which these mechanical characteristics are connected to joint strength depends on the morphology and, in particular, the roughness of the joint. Thus, various successive degrees of roughness can present themselves on the surface of a rock and could be modelled with a fractal surface if they are statistically self-similar.

It is thus necessary to consider a higher geometrical model than the corresponding to the rock matrix; this model can be created supposing a simple geometry for the joint profile. In this sense, saw-tooth profiles have been commonly used in theoretical and experimental studies. The joint profile can be modelled using more realistic models than the saw-tooth. In any case, for joint movement, the need to retain the geometric roughness implies a greater degree of energy consumption than would be necessary if there were only irregularities of a lower hierarchical rank, such as those described herein. Thus, in this paper is proposed a characterisation of the fractal dimension of the joints with a circumference arc generator.

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