Abstract
Surface reliefs of rock joints are analyzed in geotechnics when shear strength of rocky slopes is estimated. The rock joint profiles actually are self-affine fractal curves and computations of their fractal dimensions require special methods. Many papers devoted to the fractal properties of these profiles were published in the past but only a few of those papers employed a convenient computational method that would have guaranteed a sound value of that dimension. As a consequence, anomalously low dimensions were presented. This contribution deals with two computational modifications that lead to sound fractal dimensions of the self-affine rock joint profiles. These are the modified box-counting method and the modified yard-stick method sometimes called the compass method. Both these methods are frequently applied to self-similar fractal curves but the self-affine profile curves due to their self-affine nature require modified computational procedures implemented in computer programs.
Highlights
Many authors in the past tried to determine joint rock coefficients JRC introduced by Barton and Choubey [1, 2] by means of the fractal dimensions D of joint rock profiles
In the present paper we briefly describe how to modify the conventional box-counting and yard-stick methods to obtain sound values of fractal dimensions for self-affine profiles and, in addition, we present several results performed by these modified methods
Multiplying y-coordinates by a series of large numbers (1x, 50x, 100x, 1000x), we received a set of growing dimensions (1.014, 1,294, 1.299, 1.301). These results show that the unmodified computation (1x) results in anomalously low dimension (1.014) whereas the limiting stable computation (1000x) leads to rather higher dimension (1.301)
Summary
Many authors in the past tried to determine joint rock coefficients JRC introduced by Barton and Choubey [1, 2] by means of the fractal dimensions D of joint rock profiles. The papers referred to in the mentioned overview [3] presented fractal dimensions of rock joint profiles derived from either the standard Barton's profiles [1, 2] or the profiles of natural specimens. The reason why such a low value of D was estimated consisted in the fact that the computations did not employ a convenient method that would have been adapted to self-affine profiles.
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