LAUSR

In nature, rock structures such as tunnel walls, rock pillars, excavation roofs, and bridge abutments are often subjected to repetitive/cyclic loads. Cyclic loading could result in accumulated fatigue damage which may prematurely destruct rock structures at a stress level lower than its characterized strength under monotonic conditions (Bagde and Petroš 2005a). Therefore, study on fatigue damage evolution and deformation characteristics of rocks under cyclic loading could facilitate understanding of the failure mechanism of rock, and hence contribute to better evaluate the safety and long-term stability of engineering structures such as underground mines and excavations and nuclear waste repositories (Xu et al. 2012). In the past decades, numerous efforts have been devoted to investigate fatigue damage of rocks under static or quasistatic cyclic loading. After performing a great number of cyclic loading tests on a variety of rock samples, e.g., granite, sandstone, limestone, and salt rock, under confined or unconfined pressure conditions, it is now recognized that the fatigue properties of rock material are dependent on the maximum stress, loading amplitude, and frequency (Bagde and Petros 2005a, b; Cerfontaine and Collin 2018; Tao and Mo 1990; Xiao et al. 2009, 2010). To be more specific, with increasing maximum stress and amplitude, the fatigue life, i.e., the number of cycles before failure, decreases (Fuenkajorn and Phueakphum 2010; Haimson and Kim 1972; Momeni et al. 2015; Singh 1989); the fatigue strength, i.e., the maximum stress a rock material can endure for a given number of loading cycles without failure, and fatigue life slightly increase with increasing strain and stressing rate at the same applied stress level (Lajtai et al. 1991; Momeni et al. 2015; Ray et al. 1999); higher confining pressure results in larger axial strain at failure (Ma et al. 2013; Liu and He 2012). In addition, it was found that there is a threestage, i.e., transient, steady, and accelerated, deformation law of axial strain of rock under cyclic loading with an applied maximum stress level higher than the threshold value (Momeni et al. 2015; Xiao et al. 2010; Zhang et al. 2008). In addition to static or quasi-static cyclic loads, rock structures may also bear low-cycle repetitive dynamic loads such as blasting and earthquakes. For example, during blasting excavation of tunnels, adjacent rock structures and completed tunnel sections are subject to repetitive dynamic loadings from sequential blasting. In enhanced geothermal systems, rock structures such as boreholes are subjected to not only cycles of high pressure during fluid injection process but also repetitive injection-induced seismicity (Giardini 2009; Li et al. 2018a). Moreover, progressive damage accumulation of the underground excavation was also observed under repeated seismic loadings (Ma and Brady 1999). Although the mechanical and fracture properties of rock under dynamic loading have been extensively studied (Li et al. 1999, 2008; Zhang and Zhao 2013; Zhao et al. 1999), dynamic fatigue behaviors of rocks have been rarely * J. B. Zhu [email protected] http://jgxy.tju.edu.cn/teachers.asp?id=180