###### Abstract
However, the theoretical basis and physical significance of the LSR method remain unclear, and the results strongly correlate with crack damage stress [14; 25]. Based on the LSR method, [PERSON] et al. [25] proposed the relative compression strain response method. [PERSON] et al. [26] analyzed the influence of Poisson's ratio on the LSR method and used \(\sigma_{\text{ci}}\) as the end point of the reference line (lateral strain interval response method, LSIR). [PERSON] [27] first adopted volumetric strain to calculate the crack stress thresholds by choosing the start and points of the linear segment of the volumetric strain as the crack closured and crack initiation stress, respectively. [PERSON] [28] considered the axial stress level of the total volumetric strain inversion to be the beginning of crack instability and propagation. [PERSON] and [PERSON] [10] proposed the crack volumetric strain (CVS) method to calculate the crack closure and initiation stress. However, the accuracy of this method is highly dependent on the elastic modulus and Poisson's ratio in the elastic deformation stage. A Poisson's ratio difference of 0.05 resulted in a 40% change in \(\sigma_{\text{ci}}\). In addition, the crack stress thresholds can be calculated through volumetric stiffness-stress curves. The stresses corresponding to the start and end points of the linear segment are crack closure and initiation stresses, respectively [15]. Acoustic emission (AE) is a low-energy seismic event caused by inelastic deformation, such as particle dislocation or crack initiation [29]. Owing to its sensitivity to rock cracking and damage, acoustic emission is an excellent tool for investigating crack evolution in rocks [15]. [PERSON] determined crack stress thresholds using the average ring-down count and cumulative energy [15]. However, this method relies on subjective judgment, making it difficult to guarantee the stability of the results. [PERSON] et al. [14] proposed the cumulative AE hits (CAEHT) method for the quantitative calculation of \(\sigma_{\text{ci}}\), which relies on an S-shaped cumulative hits count curve. However, the cumulative ring count curve for a large number of rocks exhibits a J-shaped pattern, showing a slight inclination in the crack closure and elastic deformation stages and fluctuating sharply in the critical failure stage [25]. In addition, acoustic noise and emission activities are mixed during the test process, making it difficult to distinguish acoustic events caused by crack propagation from noise [19]. Although many researchers have studied crack stress thresholds, the accurate determination of crack stress thresholds remains challenging, and no unified solution is available [30]. In addition, most studies on crack stress thresholds have been focused on dense brittle rocks; however, the deformation and failure patterns of porous rocks are relatively different from dense brittle rocks [31; 32]. Porous rocks exhibit plastic compaction owing to a reduction in the average spacing of rock particles [33], which enables porous rocks to show settlement deformation in engineering [34]. In contrast, the plastic volumetric strain of hard rock is minimal before the peak, and general models such as the Hoek-Brown [35; 36] and Drucker-Prager [37] models do not consider plastic compaction. These differences affect the calculation of crack stress thresholds. In this study, step loading and unloading experiments were carried out on siltstone and granite, and the applicability of several existing methods to siltstone and granite was investigated.