ABSTRACT

A new technique to estimate the diameter distribution from the contained trace length distribution was Suggested. In this technique, the diameter distribution is directly obtained from the sample histogram of the contained trace lengths without using any information of the trace length distribution of an infinite window. Compared with the previous method of Song & Lee (200 I), it showed a more accurate result for small sizes of joint samples.

INTRODUCTION

The joint dimension is one of the most difficult properties to measure accurately (Priest, 1993; Villaescusa & Brown, 1992). When the joints are assumed to follow the Poisson disc model (Baecher, 1977), that is, The shape of a joint is of a disc and its center is located randomly in a 3D space, joint diameter can be obtained by two kinds of approaches: one is to use a try and error method (Priest, 1993) and the other is to infer the diameter distribution from a sampled trace length distribution (Song & Lee, 2001). In the first approach, the type and parameters of the diameter distribution are repeatedly re-assumed until the error between the sampled distribution and theoretical distribution of trace lengths becomes lower than a predefined threshold value. That is why this approach is called a distribution-dependent method. In the second approach, the distribution-independent or distribution free, method, the trace length distribution defined in an Infinite sampling window is inferred from the sampled trace length distribution and then, the diameter distribution is obtained from the inferred trace length distribution (Baecher & Lanney, 1978; Dienes, 1979; Kulatilake & Wu, 1986; Warburton, 1980). Both approaches use a pivotal equation in which the inferred trace length distribution is expressed as an integration function of the diameter distribution. The trace length distribution of an infinite sampling window can be estimated from the trace or semi-trace length distribution of a scanline sampling or window sampling nest & Hudson, 1981; Song & Lee, 2001).

Song & Lee (2001) suggested an estimation technique of the trace length distribution of an infinite window using a contained trace length distribution. The contained trace is a trace whose both end points are located in the sampling window (Pahl, 1981; Priest, 1993). They also estimated the diameter distribution from the trace length distribution by numerically converting the equation of diameter and cumulative trace length distribution suggested by Warburton (1980). Song & Lee showed that the trace length distribution of an infinite window could be estimated more efficiently or accurately by using the contained trace lengths rather than dissecting trace lengths of a window sampling or complete trace lengths of a scanline.

In this study, a new approach was developed to estimate the diameter distribution from the contained trace length distribution. With the new approach, the trace length distribution of an infinite window is no more required for estimating the diameter distribution: the diameter distribution is directly obtained from the sample histogram of the contained trace lengths by the least square method.

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