Elliptical Hertz-Based General Closure Model for Rock Joints
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TECHNICAL NOTE
Elliptical Hertz‑Based General Closure Model for Rock Joints Zhi Cheng Tang1 · Qing Zhao Zhang2 Received: 22 December 2019 / Accepted: 11 October 2020 © Springer-Verlag GmbH Austria, part of Springer Nature 2020
Keywords Rock joint · Closure displacement · Elliptical Hertz contact theory · Morphology component · Contact state
1 Introduction The hydro-mechanical behavior of rock masses is mainly dominated by the behavior of the contained rock joints (Cook 1992; Grasselli and Egger 2003; Bahaaddini et al. 2014). It is well-recognized that studying the closure behavior of a rock joint at small scale in laboratory is a prerequisite to comprehensively understand the in situ hydro-mechanical behavior of a jointed rock mass (Bandis et al. 1983). The aperture distribution of rock joints in rock masses, which usually behaves as the major pathways of underground water or air, is directly affected by its closure behavior under the action of compressive loading. An understanding of how flow evolves in such aperture is significant to many engineering applications (Hopkins 2000), such as geothermal heat extraction, geologic disposal of high-level nuclear wastes, and oil/gas exploration, and is also relevant in the prediction of natural phenomena including earthquakes (Cook 1992; Hopkins 2000; Nemoto et al. 2009; Zhu et al. 2019; Zou et al. 2019). In addition, wave propagation in rock masses is also closely related to the rock-joint closure, and studying the interaction of stress wave and rock joints is of significance to evaluate the stability of rock engineering structures under dynamic loading, such as tunnels, foundations, and rock slopes (Li et al. 2014a, b, 2017; Chen et al. 2015; Han et al. 2020). The closure displacement of a rock joint under the action of compressive loading is usual non-linear (Kulhawy 1975; Bandis et al. 1983). The relation between closure displacement and normal stress could be empirically described by * Qing Zhao Zhang [email protected] 1
Faculty of Engineering, China University of Geosciences, Wuhan 430074, Hubei, People’s Republic of China
Department of Geotechnical Engineering, Tongji University, Shanghai 200092, People’s Republic of China
2
the initial normal stiffness and the maximum closure displacement. The hyperbolic model, first proposed by Goodman (1976) and further developed by Bandis et al. (1983) and Barton et al. (1985), provides a good fit to experimental data in a wide range of normal stresses for both matching and un-matching rock joints. The empirical model proposed by Bandis et al. (1983) is widely used in practice and academia. There are also several other models available in the literature, such as semi-logarithmic model (Xia et al. 2003), power-law model (Swan 1983; Xia et al. 2003), and exponential model (Malama and Kulatilake 2003). An empirical excess stress model was developed by Li et al. (2020) to capture the rate-dependent compressive behavior of rock joint. Nevertheless, the parameters used in those empirical models should be dete
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