Estimation of rock joint diameter distribution using numerically generated joint center volume

Abstract

A new method for estimating rock joint diameter distribution is proposed using joint trace length distribution surveyed in an arbitrary area regardless of the shape of the rock exposure. In order to set an arbitrary area as a survey target, the concept of a sampling surface is newly defined by expanding the conventional sampling window which has been limited to two-dimensional planes. A survey area set on a rock exposure of any shape, from a planar surface to an irregular three-dimensional surface, can be defined as an arbitrarily shaped sampling surface. The new method estimates the rock joint diameter distribution based on the maximum likelihood method using joint center volume generated for an arbitrarily shaped sampling surface. Since the calculation of joint center volume has been limited to conventional sampling windows, a new technique based on Monte Carlo simulation is proposed for which joint center volume can be numerically generated for not only planar-shaped sampling surfaces but also non-planar-shaped sampling surfaces. The proposed numerical generation technique of joint center volume is verified through comparison with the analytically calculated joint center volume in planar-shaped sampling surfaces. In addition, the reliability of the proposed method for estimating rock joint diameter distribution using arbitrarily shaped sampling surfaces is validated under various conditions in which the shape and size of the sampling surface, the orientation of the joint set, and the maximum joint diameter are different. The validation results indicate that rock joint diameter distribution can be estimated within an error rate of less than 10% for most conditions.