A Split Three-Characteristics Method for Stress Wave Propagation Through a Rock Mass with Double-Scale Discontinuities
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ORIGINAL PAPER
A Split Three‑Characteristics Method for Stress Wave Propagation Through a Rock Mass with Double‑Scale Discontinuities Lifeng Fan1 · Meng Wang1 · Zhijun Wu2 Received: 6 December 2019 / Accepted: 19 August 2020 © Springer-Verlag GmbH Austria, part of Springer Nature 2020
Abstract A split three-characteristics method was proposed that can be used to analyze the stress wave propagation through a rock mass with double-scale discontinuities (micro-defect (MD) and macro-joint (MJ)). The mechanisms of the effects of MDs and MJs on stress wave propagation were investigated. The characteristic lines were divided into the three basic elements of triangle, diamond and separated diamond elements to calculate the stress, strain and velocity of the stress wave propagation through a rock mass with double-scale discontinuities (MD-MJ). The results show that the effects of MJ on stress wave propagation are related to the macro-joint stiffness, while the effects of MDs on stress wave propagation are related to the viscous coefficient and propagation distance. The comparison of the stress wave propagation through MJs and MD-MJs shows that the traditional MJ model can be regarded as a special case of the present MD-MJ model and the effects of MDs can be neglected when the propagation distance is sufficiently short. However, when the propagation distance is long, the effects of MDs must be considered. The results also show that the present characteristics method can be used to investigate the stress wave propagation through double-scale discontinuities efficiently. Keywords Characteristics method · Micro-defects · Macro-joints · Double-scale discontinuity
1 Introduction Discontinuities ranging from micro-defects to macro-joints widely exist in natural rock masses, which significantly influence the stress wave propagation (Chen et al. 2016; David et al. 2012; Feng et al. 2018; Fakhimi and Fairhurst 1994; Ichikawa et al. 2011; Jaeger et al. 2007; Li et al. 2013, 2019; Niu et al. 2018). The traditional characteristics method has been successfully applied to stress wave propagation through single-scale discontinuities (Zhao and Cai 2001; Zhao et al. 2010; Fan et al. 2012). It is still difficult to analyze the different mechanisms of double-scale discontinuities (macro-joint (MJ) and microdefect (MD)) on stress wave propagation through a rock mass. At present, the study of stress wave propagation through a rock mass with single-scale discontinuities is essentially * Zhijun Wu [email protected] 1
College of Architecture and Civil Engineering, Beijing University of Technology, Beijing 100124, China
State Key Laboratory of Water Resources and Hydropower Engineering Science, School of Civil Engineering, Wuhan University, Wuhan 430072, China
2
based on two different methods. One is the displacement discontinuity method (DDM), and the other is equivalent medium method (EMM). The DDM was widely used to investigate stress wave propagation in a single macro-joint and a group of parallel macro-joints (Cai and Zhao 20
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