###### Abstract  
Slate with inherently transverse isotropy is abundant in metamorphic rock, in buildings, and in geotechnical engineering worldwide; the tensile and shear fracture behavior of layered slate is vital to know for engineering applications. In this paper, the Brazilian and semi-circular bend (SCB) tests of layered slate were performed. The fracture characteristics of the slate were investigated by numerical simulations developed by the hybrid finite and cohesive element method (FCEM). Results showed that the measured experimental tensile strength, and mode I fracture toughness of layered slate all showed a typical V-type trend as the bedding angle increased from \(0^{\circ}\) to \(90^{\circ}\), and with divider type. The developed empirical relationship between tensile fracture toughness and tensile strength \(K_{\text{IC}}=0.094\sigma_{t}+0.036\) fitted experimentally and strongly correlated. The mechanical response and fracture patterns predicted by FCEM agreed well with those of the laboratory experiments. Moreover, the shear fracture behavior and mode II fracture toughness of the layered slate were explored by systematic numerical simulations. Research results provide potential insights for further prediction and improvement of the complex fracture behavior of anisotropic rock masses for rock engineering. bedding plane; layered slate; semi-circular bend; cohesive zone model; fracture behavior +
Footnote †: journal: Medical  
For TI slate, [PERSON] et al. [7; 8] conducted a series of experiments to investigate the effects of initial microcrack, bedding angle, and confining pressure, on the physicochemical properties such as fracture angle, compressive strength, and cohesion. [PERSON] [16], and [PERSON] et al. [17] focused on Brazilian and uniaxial compression tests on layered slate and obtained the failure patterns, tensile strength, and compressive strength. The effect of confining and water on mechanical properties was also investigated by [PERSON] et al. [9]. Based on the difference of mechanical properties of layered slate, [PERSON], [PERSON], and [PERSON] et al. [18; 5; 19; 20] studied the fracture patterns by experiment and numerical simulation, concluding that the strength anisotropy has a great influence on the tensile and shear fracture. On the other hand, numerous efforts have been engaged on the mode I (opening tensile) and mixed-mode fracture such as the edge cracked semi-cylinder disk (ECSD) and the semi-circular bend (SCB) method that are widely used in concrete, asphalt concrete, gypsum, and rocks [21; 22; 23; 24; 25; 26; 27; 28; 29; 30; 31; 32; 33; 34], especially for the rocks by the SCB method because of their strengths of simplicity, minimal requirement of machining, and convenience of testing. For example, some research papers assessed the effect of bedding on the tensile fracture behaviors of layered granite [27; 28], and layered sandstone [29; 30; 31; 32; 33; 34]. Moreover, [PERSON] [35], [PERSON] [36], and [PERSON] et al. [37] evaluated the mode I fracture toughness of layered shales using the SCB method. For the fracture test of TI slate, only [PERSON] et al. [38] measured the mode I fracture toughness by the chevron bending method, and [PERSON] et al. [17; 39; 40] carried out experimental research on fracture behavior by the wedge splitting and four/three-point bending method. However, little work has dealt with the SCB test for TI slate up to the present. The reason for this paucity is that the microstructure, mineralogy, and inherent weak planes make slates, from the aspect of specimen preparation of the experiment, very difficult to be tested for such experimental research by the SCB method. Especially, the SCB method needs complex and meticulous preparation for the tiny specimen machining by water lubrication. Recent studies have shown that the cohesive zone model (CZM) can be employed to simulate the fracture behavior of anisotropic materials effectively [41; 42; 43; 44; 45; 46]. [PERSON] et al.