BOX FRACTAL DIMENSION AS A MEASURE OF STATISTICAL HOMOGENEITY OF JOINTED ROCK MASSES

A written computer programme to estimate the box fractal dimension (D- B) is verified by estimating D-B of the triadic Koch curve for which t he theoretical D is known. The influence of a number of input paramete rs of the box-counting method on the accuracy of estimated D-B is eval uated using the same Koch curve. The employed size range of the applie d box networks was found to be the parameter which has the strongest i nfluence on the accuracy of estimated D-B. This indicated the importan ce of finding the range of self-similarity or self-affinity for the ob ject considered to select the proper range for the box sizes and, in t urn, to obtain accurate estimates of D-B. By calculating D-B for diffe rent block sizes sampled from three generated two-dimensional joint pa tterns, it is shown that D-B can capture the combined effect of joint- size distribution and joint density on the statistical homogeneity of rock masses. The spatial variation of D-B along a 350 m stretch of a t unnel in the shiplock area of the Three Gorges dam site is computed us ing the joint data mapped on the walls and the roof of the tunnel. Thi s spatial variation of D-B is used, along with the visual geological e valuation of the joint trace maps of the tunnel, in making decisions a bout statistical homogeneity of the rock mass around the tunnel. The r esults obtained on statistically homogeneous regions were found to be quite similar to the results obtained from a previous statistical homo geneity investigation which incorporated the effect of number of joint sets and their orientation distributions, but not the spatial variati on of D-B. It is recommended that the spatial variation of D-B is used , along with the results of other methods such as contingency table an alysis and equal area plots, which incorporate the effect of joint ori entation distribution, in addition to the geology of the site, in dete rmining the statistically homogeneous regions of jointed rock masses. (C) 1997 Elsevier Science B.V.