## 4 Conclusions  
In this study, uniaxial monotonic-loading and cyclic-loading tests were performed on slate specimens at different loading-foliation angles. The anisotropic mechanical properties, damage evolution, AE characteristics and fracture pattern of slate were investigated. This work contributes to a better understanding of the mechanical properties and damage mechanism of transversely isotropic rock, and is instructive for the stability assessment of rock structures in anisotropic formations. The main conclusions are summarized as follows:  
1. The peak strength of specimens varies with the loading-foliation angle under cyclic loading, exhibiting a U-shaped trend similar to that observed under monotonic loading. The strength of the specimens at the same loading-foliation angle is close under both loading paths. The variation in elastic modulus of the specimens under uniaxial cyclic loading confirms the transversely isotropic model. 2. The secant moduli at different positions of the stress-strain curve exhibit unique variation characteristics under cyclic loading. These moduli can reflect the damage evolution process of the specimen with respect to various aspects. \(E_{u}\) and \(E_{20}\) reflect the influence of compaction and the damage effects on the specimen during cyclic loading and unloading. \(E_{s}\) mainly reflects the damage of the specimen caused by the loading-unloading cycles, with \(E_{s}{{}^{-}}\) being more effective in characterizing this feature than \(E_{s}{{}^{+}}\). 3. The input of the total energy density of the specimen is mainly dependent on the loading-foliation angle at the same stress level. The elastic-energy density and the dissipated-energy density are affected by the loading-foliation angle, cyclic stress step and number of cycles. When the degree of damage in the rock is low, increasing the stress level of the cyclic load or increasing the number of cycles can reduce the proportion of dissipated energy. The damage variable is influenced by both the loading-foliation angle and the cyclic stress step. 4. The AE characteristics of the specimen are closely related to the loading condition and the loading-foliation angle, presenting an obvious anisotropy. Under cyclic loading, regardless of cyclic stress step, the AE counts of specimens at \(\beta\) = 0\({}^{\circ}\) are concentrated near the peak region, consistent with the Kaiser effect, whereas those of specimens at the other loading-foliation angles are mainly distributed in the early stage of each cyclic-loading process, exhibiting an obvious Felicity effect. 5. The failure mechanism of slate specimens is jointly determined by the loading-foliation angle, loading condition, and cyclic stress step. The fracture modes are classified into four categories: the tensile fracture along the foliation plane (\(\beta\) = 0\({}^{\circ}\), 90\({}^{\circ}\)), the tensile fracture through the foliation plane (\(\beta\) = 30\({}^{\circ}\), 90\({}^{\circ}\)), the shear fracture along the foliation plane (\(\beta\) = 30\({}^{\circ}\), 45\({}^{\circ}\)) and the shear fracture through the foliation plane (\(\beta\) = 45\({}^{\circ}\), 90\({}^{\circ}\)). The SEM images of corresponding fracture surfaces show different characteristics, with more rock debris formed in the fracture surface of the specimen subjected to cyclic loading than to monotonic loading. K.L. : conceptualization, methodology, writing--original draft, funding acquisition. G.D.: investigation, methodology, data curation, writing--original draft. J.L. : supervision, project administration, funding acquisition. D.H.: investigation, data curation, validation. Y.W. : writing--review and editing, resources. All authors have read and agreed to the published version of the manuscript. This research was funded by (1) the National Natural Science Foundation of China (grant Nos. 52204119, 51979293, 52204118) and (2) the Natural Science Foundation of Hunan Province, China (grant No. 2023J40729). Data Availability Statement:Data is contained within the article.