估计迹长概率分布函数的新方法及其应用

A NEW METHOD FOR ESTIMATING PROBABILITY DISTRIBUTION FUNCTION OF TRACE LENGTH AND ITS APPLICATION

本文提出一种估计迹长概率分布函数的新方法。该方法的优点是不需要有节理在测窗上出露长度的数据。

Probability characteristics of trace length are difficult to determine because of limited exposures. Methods presented by Kulatilake and Pahl can not estimate probability distribution function of trace length. So a new method is presented to estimate the mean as well as distribution function of trace length. This method does not need any data of trace length falling on the sampling window, which successfully lessens field work. The discontinuities falling on a sampling window are divided into four types, i.e. the penetrating type, intersecting types with one end above or below the window, and containing type. Dividing intersecting types into two categories can lessen the error induceed during survey. In terms of geometric probability, a new model is built. For one sampling window of certain orientation and size, the author derives a series of equations defining the relations between probabilities of each type and probability distribution function of trace length. In field work, it is easy to record the number of each discontinuity type on a window. So the frequencies of each type on the window can be calculated. For a certain mean and distribution function of trace length, the probability that one discontinuity belongs to each type can be calculated at the full integral areas of orientation and trace length. Then differences between probabilities and actual frequencies can be found. Four types of distribution function has been reported. So a trial and error method is applied to find the mean and distribution function with the lowest difference, which is assumed to be the actual ones. For engineering application, one program for estimating the mean and distribution function of trace length has been designed and was used in the analysis of discontinuity data in the Shiplock area of Three Gorges Project.