## 4 Discussion  
At present, many scholars focus on the constant stress amplitude load conditions in the study of rock mechanical behaviors under cyclic loading. In addition, the rock samples used in these experiments were mostly hard rocks. However, in field research, the amplitudes of the rock mass stress disturbances in the project were often not constant [31]. This situation does not only exist in mining projects such as the Three Gorges Project. With fluctuations in water storage levels, the rock mass and the dam body on both sides of a river are continuously disturbed by variable stresses. The mechanical response of the argillaceous shale was revealed using indoor fatigue loading tests at different frequencies. The effect of the loading frequency was essentially caused by the differences in the loading rates. It was found that the rock strength, fatigue life, mechanical properties, AE, and damage evolution characteristics all changed regularly at the different loading frequencies.  
Under a constant stress amplitude loading, the deformation and destruction law can be summarized in three forms, as shown in Figure 16a. Among the three forms, the b-class curve rule was more universal, and the axial irreversible deformation of the rock can be divided into an initial stage, an equal speed stage, and an acceleration stage. These stages can be observed in most rock fatigue tests performed on rocks such as marble, red sandstone, and granite [32; 33; 34]. However, the mechanical behavior of rocks under increasing fatigue loading conditions was different from that of fixed amplitude fatigue loading, and the cumulative damage destruction was composed of multiple stages. The sample damage occurred in the last stage, which was defined as the failure stage. Each fatigue stage before the failure stage lasted a long time, and there was no sign of a peak strain acceleration. The deformation pattern in each stage was similar to the \"c\"-type shown in the curve in Figure 16a. However, during the destruction phase, the deformation increased sharply, showing a rapid upward trend, and the sample failed in a short time, which was shown by a small phase similar to the \"a\"-type curve shown in Figure 16a. Therefore, the damage deformation of the rocks under increasing fatigue loading conditions was more complex, and the damage accumulation trend was more similar to that of the \"b\"-type curve shown in Figure 16a. Compared to the fixed amplitude loading condition, the acceleration stage was significantly shorter, as shown in Figure 16b.  
Many similar studies have been conducted; however, all these previous studies had limitations [35; 36]. In this study, using a fine damage variable calculation method, the damage variable was first defined using the axial deformation, and a multi-stage cyclic load comprehensive injury model was then established by our calculations. The model was highly consistent with the test results, and it can be used to predict the fatigue life of the rocks under the increasing-amplitude fatigue loading conditions, which has a considerable engineering significance.  
Figure 16: Typical damage accumulation curves of the rock under cyclic loading: (**a**) family of curves describing the different types of damage evolution; (**b**) three stages of the damage evolution characteristics.