# Tensile Properties and Tensile Failure Criteria of Layered Rocks  
[PERSON] 1,2,3, [PERSON] 2,*, [PERSON] 3 and [PERSON] 1  
1 State Key Laboratory of Mining Response and Disaster Prevention and Control in Deep Coal Mines, Anhui University of Science and Technology, Huainan 232001, China; [EMAIL_ADDRESS] (M.G.); [EMAIL_ADDRESS] (J.Z.) 2 State Key Laboratory of Coastal and Offshore Engineering, Dalian University of Technology, Dalian 116024, China 3 Institute of Unconventional Oil & Gas, Northeast Petroleum University, Daqing 163318, China; [EMAIL_ADDRESS]  
determining the tensile strength of rock materials. The Brazilian disc test is the most commonly adopted method to determine the indirect tensile strength of rock materials [15; 16; 17; 18; 19; 20; 21; 22; 23]. However, during the Brazilian test, a small eccentricity of the axial load may cause large non-uniformities of stress in specimens [24], or stress concentrations may be induced by caps. For transversely isotropic rock masses, failure under the Brazilian test is not necessarily a pure tensile failure; in some cases, it can even be pure shear failure, but it is often a combination of both tensile and shear failure [25; 26; 27]. Although these disadvantages are obviously present in the Brazilian test, it is still widely used in laboratory experimental and numerical studies to investigate the tensile properties of transversely isotropic rocks [28; 29; 30; 31; 32; 33; 34].  
The direct tensile test, which is theoretically the simplest and most effective method for tensile strength determination, is in fact difficult to carry out in the laboratory [35; 36; 37; 38]. Over the past few decades, the anisotropic tensile behavior of layered rocks has been studied by a few researchers through direct tension [39; 40]. Some anisotropic tensile criteria were investigated to predict the tensile strength of layered rocks based on the direct tension test and analytical methods [41; 42; 43]. [PERSON] et al. analyzed the anisotropic tension strength criteria of layered rocks and selected the best one to predict the fracture pressure of the inclined wells in layered formations [44; 45]. [PERSON] et al. investigated the anisotropic direct tensile behavior of laminated and transversely isotropic Midgley Grit sandstone using a particle-based discrete element method [46]. However, the tensile failure modes and failure mechanisms of layered rocks still need to be further studied. Furthermore, the failure criterion of the layered rocks under direct tension should be evaluated based on the failure modes.  
In this work, numerical tests are undertaken to investigate the progressive failure and mechanical behavior of layered rocks under direct and indirect tension using a numerical code RFPA\({}^{\text{2D}}\), which was developed based on the finite element method, statistical theory, and damage mechanics [47]. The influence of layer orientation on tensile behavior is discussed. The main failure modes and failure mechanisms of layered rocks under direct and indirect tension are analyzed. The Single Plane of Weakness failure criterion is then modified based on the failure modes and failure mechanisms of direct tension. The modified SPW (MSPW) failure criterion has been verified by experimental and numerical results. The analytical predictions of the MSPW failure criterion agrees closely with the experimental and numerical results.