Spatial Distribution Analysis of Attributes of Rock Joints Using Geomathematical Methods

Abstract

Rock mass joints are the discontinuities of intact rock in a geometrical sense, but they contain diverse attributes such as orientation, generation time, dimension, opening width, interstitial minerals, mineralogical alteration, and seepage. The value or degree of these attributes vary with joints, and therefore rock mass joints are regarded to be a multiple set. Geomathematical methods including geostatistics and fuzzy sets theory were applied to deal with such diversity of joints and to reveal the spatial distribution of joint's attributes. Two thousands of joints in the granodiorite, which were observed by the ten horizontal boring cores drilled in the two directions perpendicularly intersecting each other, were chosen for the analysis.
The semivariogram was calculated for the two attribute values based on the several joints which are supposed to be the same fracture. It was made clear that the width of interstitial minerals has the spatial correlation within the range of 20 meters. Two dimensional distribution of the width of interstitial minerals in the study area were estimated by the interpolation method termed kriging. As a result, the continuous joints with relative large width of interstitial minerals were specified and found to be oriented in the northeast and eastnortheast directions.
For the joint analysis by combining several attributes, the degree of mineralogical alteration, the width of alteration halo, and the width of interstitial minerals were selected as the attributes bearing an relation to permeability. The membership functions were defined for the three attributes respectively, and the fuzzy C-means method was applied to classify the observed joints into three groups. One group among them was revealed to have large membership values of the three attributes. Connection of the joints, which belong to this group, along their strikes made it possible to detect water channels in the study area. The seepage flow model was also constructed by a finite element method of two dimensional artesian state and the assumed transmissivity of each group's joints.