# Indices to Determine the Reliability of Rocks under Fatigue Load Based on Strain Energy Method
## 2 Classification and Calculation Methods of Rock Strain Energy by Tests Results
### Testing Schemes and Experimental Data  
The test schemes adopted cyclic loading and unloading tests under different confining pressures and conducted with the MTS-815 servo-controlled testing machine in the State Key Laboratory of Geo-hazard Prevention and Geo-environment Protection (SKLGP), Chengdu, Sichuan, China. The fresh red sandstone blocks, which were taken from a quarry in Leshan, Sichuan, China were selected for this test. The blocks were cut into several cylindrical samples with 50 mm in diameter and 100 mm in height. The average density of dried red sandstone specimens is about 2.06 g/cm3 and the main mineral constituents are calcite (78.2%) and quartz (0.5%). The X-ray diffraction pattern is shown in Figure 2.  
In this study, cyclic loading and unloading tests under confining pressures of 0 MPA, 5 MPa, 10 MPa, and 20 MPa were designed. By comparing the uniaxial compression deformation stages of rocks classified by some researchers [2; 41; 42] and the deformation stages of cyclic loading and unloading test, stress-strain curves can be divided into 5 stages: (I) crack closure, (II) elastic deformation, (III) crack initiation and stable crack growth,(IV) crack damage and unstable crack growth, and(V) failure and post-peak behavior. In general, the point between stage III and IV is called the crack damage point and be treated as the yield point and the point between stage IV and V is called the peak point.  
During the cyclic loading and unloading test, the rock samples were subjected to axial force with the loading rate of \(1\)kN/s. When the axial force reaches 10 kN, we stopped the loading and start the unloading process. The unloading force was also set at 1 kN/s. In order to avoid the impact of the testing machine on the sample during the reloading process, the sample is loaded when the axial force is 1 kN in the successive unloading process. For subsequent unloading cycles, we increased the unloading force by 10 kN, i.e., during the first cycle the unloading force was set at 10 kN and was 20 kN during the second cycle. In order to obtain more cycles when the rock deformation enters the  
Figure 2: X-ray diffraction pattern of sandstone samples in this study.  
yield stage, we decreased the unloading force of subsequent cycle to 5 kN. We adopted this loading method until the rock deformation reaches the peak point and failure occurred. During post peak stage, we controlled the unloading points manually. This makes the unloading force different for each sample. Despite this approach, the difference of strain energy density evolution in the post-peak and pre-peak stage is still obvious. A representative cyclic loading and unloading stress-strain curve is shown in Figure 3.  
The mechanical properties of red sandstone samples under different confining pressures are shown in Table 1. In Table 1\(\sigma_{3}\) represents confining stress, \(E\) represents the average elastic modulus, the \(\sigma_{\text{cd}}\) and \(\varepsilon_{\text{cd}}\) represents the average crack damage stress and strain respectively, the \(\sigma_{\text{p}}\) and \(\varepsilon_{\text{p}}\) represents the average peak strength and strain respectively.