A new iteration clustering method for rock discontinuity sets considering discontinuity trace lengths and orientations
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ORIGINAL PAPER
A new iteration clustering method for rock discontinuity sets considering discontinuity trace lengths and orientations Tiexin Liu 1,2 & Jun Zheng 3
&
Jianhui Deng 2
Received: 16 December 2019 / Accepted: 13 July 2020 # Springer-Verlag GmbH Germany, part of Springer Nature 2020
Abstract Discontinuity clustering is an important and preliminary step in estimating discontinuity properties. To group discontinuities quickly and accurately, in this study, a new iteration clustering method (NICM) based on the data of discontinuity orientations and trace lengths is proposed, with its corresponding algorithm code developed in MATLAB. The method assumes that the trace lengths of the discontinuities obey a specific distribution, through a redistribution of the discontinuities whose membership degree values are unclear to adjust the probability density function of the trace lengths to make them more closely obey the specific distribution. The membership degree value calculation and cluster code determination are two main core modules of NICM. The characteristics of the method were analyzed with three types of numerical models in which the data are synthetic and the clustering results can be clearly grasped. In contrast, the NICM and fuzzy C-means method were applied to group the discontinuities of a rock slope at the Changhe Dam located in Sichuan Province, southwestern China, at the same time. The results clearly demonstrate that (a) a 10% enhancement in the precision can be expected by considering the distribution of the trace lengths; (b) the assumed specific distribution of the trace lengths does not have an obvious effect on the precision improvement; and (c) the problem of hard boundaries can be effectively alleviated by using the method. Keywords Discontinuity sets . Clustering analysis . Trace length . Orientation
Introduction The fractures and joints present in a rock mass are called discontinuities, which divide a large rock mass into many small rock blocks. Discontinuities are much weaker than rock blocks; hence, they govern the deformability, strength, and permeability of rock masses (Peng and Zhang 2007; Zheng et al. 2020). From the perspectives of the morphology and mechanics, many studies have been conducted to estimate the discontinuity properties, which can be mainly divided into the following four categories: the geometric shape * Jun Zheng [email protected] 1
Highway and Bridge Engineering Institute, Dalian Maritime University, Dalian 116026, China
2
State Key Laboratory of Hydraulics and Mountain River Engineering, College of Water Resource & Hydropower, Sichuan University, Chengdu 610065, China
3
Department of Civil Engineering, Zhejiang University, Hangzhou 310058, China
reconstruction based on the trace line information of the discontinuity (Johansson and Stille 2014; Casagrande et al. 2018), network modeling according to the space distributions of the discontinuities present in the studied rock mass (Elmouttie et al. 2010; Boon et al. 2012, 2015; Lei et al. 2017; Azarafza e
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