# Indices to Determine the Reliability of Rocks under Fatigue Load Based on Strain Energy Method
## 5 Conclusions  
According to a series of analysis of test results and literature data, this work studied the evolution of strain energy in the process of rock deformation and its relationship with deformation mechanism classified by new strain energy types. It is observed that the proportion of grain strain energy density and crack strain energy density to total strain energy density can be used as the indices for determine rock stability or failure. The main findings of this study are as follows:  
1. The elastic strain energy density of rock is composed of grain strain energy density and crack strain energy density according to the new division method. Both grain strain energy density and crack strain energy density increase before rock failure, but the growth rate of grain strain energy density decreases after it enters the yield stage.
2. From the point of view of energy distribution, the distribution of grain strain energy density is stable before the yield stage and the proportion of grain strain energy density decreases after entering the yield stage. This indicates that more strain energy density is allocated to the plastic strain energy density, which results in the decrease of grain strain energy density. This phenomenon is consistent with the deformation mechanism of cracks expansion after rock enters the yield stage. However, the distribution of crack strain energy is stable during the pre-peak deformation stage, and it decreases only after the peak stage. We believe that this phenomenon is related to the integrity of the rock because no matter how many cracks grow in the rock, as long as the rock has not failed, the restorable part of the crack is coordinated with the total strain energy density.
3. Through the analysis of the data obtained from other literatures, it is found that the proportion of grain strain energy density to total strain energy density can be used as the index to determine  
Figure 8: The proportion of crack strain energy density to total strain energy density of different rock samples in the pre-peak stage.  
the stability of rock. The proportion of crack strain energy density to total strain energy density can be used as the index to determine rock failure.
4. The proportion of grain strain energy density to total strain energy density is concentrated in the same rock type, which has linear relationship with elastic modulus. The slope of the linear equation between different rocks and elastic modulus will decrease with the increase of uniaxial compression strength of rock under normal conditions.
5. The proportion of crack strain energy density to total strain energy density is stable in the range of 0.04-0.13, which is independent of rock type and elastic modulus.  
It should be noted that these findings are based on limited data, but we believe these data have already opened the door to a new research area. Later, we will enrich these research findings by obtaining more data and popularizing it for engineering applications.  
Conceptualization, H.F. and S.W.; Methodology, H.F.; Validation, H.F., S.W. and X.P.; Formal analysis, H.F. and W.C.; Investigation, S.W. and H.F.; Resources, X.P.; Writing--original draft preparation, H.F.; Writing--review and editing, H.F. and S.W.; Visualization, H.F. and W.C.; Supervision, S.W. and X.P.; Project administration, H.F.; Funding acquisition, S.W.and X.P.  
This research was funded by the Opening Fund of State Key Laboratory of Geohazard Prevention and Geoenvironment Protection (Chengdu University of Technology) No. SKLGP2016K001; National Key R&D Program of China No. 2017 YFC1501002; the National Natural Science Foundation of China No. 41572302.  
We would like to thank [PERSON]'s suggestions and [PERSON]'s help in improving the English of manuscript. We also would like to thank the anonymous reviewers for their helpful comments.  
The authors declare no conflict of interest.