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A large amount of slates is distributed along Kangding No. 2 tunnel of Sichuan–Tibet Railway (China). The bedding of the Kangding slate is rich, showing apparent anisotropy of strength. For underground tunnels excavated in the anisotropic rock mass, the rock material is vulnerable to damage in tension because of its low tensile strength. Therefore, the tensile strength and fracture modes are important for the support design of layered surrounding-rock tunnel. In this study, first, a series of direct tensile tests were carried out on slate samples with five kinds of bedding dip angles. Second, the effect of bedding dip angle on the slate's tensile strength, failure modes, and acoustic emission characteristics was analyzed. Third, based on the Nova–Zaninetti criterion and the experiment results, a new phenomenological anisotropic criterion was proposed by introducing anisotropic coefficient, which could describe the nonlinear variation trend of tensile strength with foliation angles. Compared with four typical tensile strength criteria, the accuracy and universality of the new criterion were verified. Finally, the new criterion was implemented into the combined finite-discrete element method (FDEM) to conduct direct tensile simulation of slate with different foliation angles. The results indicated that the direct tensile strength followed an S-shaped increasing trend with the variation of foliation angles. The direct tensile failure modes of slate samples with different foliation angles could be divided into layer activation failure, mixed failure, and rock matrix failure. The acoustic emission process of slate with different bedding inclination under direct tension could be roughly divided into the following three stages: quiet period—stepped saltatory increase—drastic increase. The fitting effect of the new criterion was the highest among Kangding slate and other six typical layered rocks, which showed that the new criterion was suitable for predicting its Brazilian strength and direct tensile strength. At the same time, the numerical simulation results were in good agreement with the experimental results, which further verified the accuracy of the new criterion. Highlights: The acoustic emission characteristic parameters helped to reveal the direct tensile failure characteristics of layered rocks. A new phenomenological anisotropic tensile failure criterion was proposed. The direct tensile test data and the Brazilian splitting test data were used to study the accuracy and universality of the new anisotropic tensile failure criterion. FDEM was used to study the accuracy of the new anisotropic tensile failure criterion. [ABSTRACT FROM AUTHOR]