###### Abstract  
Crack stress thresholds in rocks have long been a popular subject in rock mechanics and engineering research. In this study, the applicability of existing methods for determining the crack stress thresholds of granite and weakly cemented porous siltstone is investigated using step loading and unloading tests. In addition, a novel method for decomposing the volumetric strain into solid-phase linear elastic strain, gas-phase nonlinear elastic strain, and plastic volumetric strain is presented. A quantitative calculation method for determining these thresholds is proposed based on the evolution law of the gas-phase volumetric strain and the physical significance of crack stress thresholds. The initiation and termination points of the stationary stage of the gas-phase volumetric strain are determined as \(\sigma_{\text{c}}\) and \(\sigma_{\text{c}\text{d}}\); the point at which the gas-phase strain changes from positive to negative is determined as \(\sigma_{\text{c}\text{d}}\). To validate the proposed method, statistical results of the existing methods after screening are compared with the results of the proposed method. The results show that the proposed method provides reasonable crack stress thresholds for siltstone and granite and is applicable to rocks with similar stress-strain behaviors. The proposed method offers the advantages of independence from other methods, suitability across high and low confining pressures, and the capability for the quantitative calculation and processing of numerous samples. Keywords:triaxial compression; step loading and unloading; stress-strain curve; volumetric strain decomposition; crack stress thresholds +
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occurred if the test was run for a sufficiently long time [10]. Therefore, a reasonable determination of crack stress thresholds is crucial for understanding the process of rock damage [13; 14]. The past four decades have witnessed the development of several methods for the determination of crack stress thresholds of rocks (Figure 1). [PERSON] et al. [15] used the \"sliding window\" approach to calculate axial stiffness and determine crack stress thresholds based on the relationship between axial stiffness and axial stress. [PERSON] [16] proposed a modified axial stiffness method that considers the confining pressure. [PERSON] et al. [17] proposed that 10% of total data was the most appropriate regression interval for determining the \(\sigma_{\text{ci}}\). [PERSON] and [PERSON] [18] proposed a load-unload response ratio method to determine the crack closure and damage stresses. [PERSON] et al. [19] determined crack stress thresholds based on the ratio of the dissipated energy to the total energy. [PERSON] et al. [20] proposed the axial strain response (ASR) method to calculate the crack stress thresholds quantitatively. The ASR method determines the crack closure stress using the maximum axial strain difference between the stress-strain curve and a reference connected point \(O\), \(\sigma_{\text{cd}}\). The compression coefficient response (CCR) method uses the straight line between \(O\) and \(\sigma_{\text{ci}}\) as the reference line [7]. These two methods provide numerical approaches for determining the crack stress thresholds; however, they rely on \(\sigma_{\text{ci}}\) and \(\sigma_{\text{cd}}\), respectively, which are obtained using other methods [21]. Crack stress thresholds can also be determined based on the lateral and volumetric strains. [PERSON] [22] determined \(\sigma_{\text{cc}}\) and \(\sigma_{\text{ci}}\) based on the point at which the lateral strain entered and deviated from the linear stage. [PERSON] [23] determined \(\sigma_{\text{ci}}\) by the instantaneous Poisson's ratio. [PERSON] and [PERSON] [24] proposed the lateral strain response (LSR) method, which determines \(\sigma_{\text{ci}}\) using the maximum lateral strain difference between the stress-strain curve and a reference line connecting the \(O\) and \(\sigma_{\text{cd}}\).