Discrete Element Analysis of discontinuous rock using the concepts of Chaos and Fractals

近年来，一种被称为混沌工程的新的跨学科方法正在逐步形成，它将数学中发展起来的混沌理论应用于工程问题。在这项研究中，将尝试判断混沌理论在描述岩石表面粗糙度方面的适用性。分析方法包括自相关函数、分维分析、Lyapunor谱分析、时间序列分析和替代方法。这些分析的结果被用来判断岩石表面是否构成混沌的表现。在已经进行的一个模型研究中，表面粗糙度在JRC18~20范围内的岩石观察到了混沌特性。当表面粗糙度小于JRC10时，根本没有发现混沌效应。此外，离散元方法(DEM)也被应用于各种岩土工程问题，如落石、边坡失稳和隧道建设。结果表明，DEM方法非常适合于岩石大变形问题的模拟，未来的研究方向将是寻找混沌方法与DEM方法之间的联系。

In recent years, a new interdisciplinary approach known as chaos engineering, whereby the chaos theory developed in mathematics is applied to engineering problems, is gradually taking shape. In this study, attempt will be made in order to judge the suitability of chaos theory in describing the surface roughness of rocks. The methods of analysis to be performed include auto-correlation function, fractal dimension analysis, Lyapunor spectral analysis, time series analysis and surrogate method. The results from these analyses are used in deciding whether the rock surface constitutes a manifestation of chaos.In one model study already performed, chaos characteristic was observed on a rock with the surface roughness in the range of JRC 18〜20. In case of roughness less than JRC 10, chaos effect was not found at all.In addition, distinct element method (DEM) was also applied to various geo-technical problems such as rock fall, slope failures and tunnel construction. The DEM was found to be highly suitable for simulating problems involving large rock deformations.In future, it is expected that the research will be continued in the direction of finding a link between the chaos approach and DEM approach.