Identification of the Representative Volume Element at the Maji Dam Site Based on a Multisample Nonparametric Test

Abstract

A representative volume element (RVE) denotes the size beyond which the fluctuation in the mechanical and geometrical properties of a rock mass significantly decreases, and determining the RVE is very important for evaluating the design, construction and stability of rock engineering projects. In rock mechanics analysis, it is more effective to use nonparametric test methods to check the statistical similarity of small sample sizes and samples that are not described by a specific family of probability distributions. Two-sample nonparametric tests are statistical tests that consider both spatial and size effects and are commonly utilized in RVE calculations; however, these tests cannot simultaneously consider the statistical similarity between any two sample volumes within a certain size range. Therefore, a new multisample nonparametric statistical method (called the Jonckheere–Terpstra test) is presented in this paper to more accurately determine RVE size. The Jonckheere–Terpstra test is a nonparametric test and can be used to determine whether the distributions of multiple independent samples from multiple populations are significantly different. In this work, the fracture geometries at the Maji dam site are simulated using a 3D fracture network model. A total of 100 variable-scale cubes are randomly distributed in the 3D fracture network model, and the statistical distributions of the P32 values for each sample size are estimated by the KS goodness-of-fit test. The results reveal that the probability distribution form of each sample dataset is not identical and that it is difficult to determine the distribution form of the population. The Jonckheere–Terpstra test method was demonstrated to be effective at determining the statistical similarity of all sample volumes by calculating the P32 values and the corresponding cube sizes. An RVE with a size of 14 m was selected as the RVE for the entire rock mass at the Maji dam site along the Nu River.