## 3 Experimental Results and Analysis
### Cyclic Loading and Unloading Energy Evolution Law  
Rocks are natural geological materials containing joints and microcracks, which cause non-ideal elastic deformation. As the rock specimen is loaded, a plastic hysteresis occurs in the stress-strain curve, and the envelope area of the curve is equal to the dissipated energy. As the cyclic loading and unloading proceeds, the stress corresponding to the unloading point gradually increases. Correspondingly, the envelope area of the plastic hysteresis loop also increases, and the dissipated energy is used for the development and expansion of cracks, which causes damage to the structure and leads to a decrease in the ability of the rock to store elastic energy. With the increase of stress at the unloading point, the energy absorbed by the rock gradually reaches the limit of the stored elastic energy, and the rock will be damaged. Using the above energy calculation method, the rock energy densities for different stages of the cyclic loading and unloading test were obtained. The energy density obtained from the calculation is plotted in Figure 6. It can be seen from the graph that, under the three loading rates, before the peak stress, the input and elastic energy densities all grow nonlinearly with the increase of stress, and the input energy density grows rapidly, followed by the elastic energy density. The dissipative energy density is high in the first cycle and decreases slightly in the second cycle; then, this trend shows a non-linear pattern, and the growth rate is the slowest among the three energies. The rocks exhibit different deformation characteristics under different stress states, and similarly, their energy evolution law has different characteristics in different deformation stages. In the initial loading stage, corresponding to the rock compacting stage, the accumulated elastic energy in the rock increases slowly, and the dissipation energy caused by the friction of the closure of the original microcracks and misalignment between the rock masses is larger than the \begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Loading Rate** & **Peak Stress** & **Peak** & **Modulus of** & \\
**(KN/S)** & **(MPa)** & **Strain** & **Elasticity (GPa)** & **Type of Damage** \\ \hline
0.2 & 41.17 & 0.0129 & 35.42 & Shear Damage \\
0.5 & 42.27 & 0.00787 & 37.44 & Tension shear damage \\
1 & 44.45 & 0.00566 & 46.19 & Splitting damage \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Table of mechanical parameters of uniaxial compression test. Figure 5: Failure modes of rock with different loading rates. accumulated elastic energy, and the growth of all three types of energy is slow in this stage. In the elastic deformation stage, the rock specimen continuously absorbs energy, and most of the input energy is converted into elastic energy. A small part is used for the formation and expansion of microcracks, and the energy grows approximately linearly. In the plastic stage, more and more input energy is dissipated in the formation, expansion, and nucleation of microcracks inside the rock. The accumulated elastic energy is dissipated in the form of crack surface energy, acoustic emission, and other energy. Near the peak stress stage, the three energy densities show an accelerated growth trend. The elastic energy of the rock specimen reaches its maximum at the end of the plastic stage, which is the peak stress stage. The energy evolution directly reflects the inherent properties of the rock; it can be inferred that the elastic energy is the main driving force for the destruction of the rock specimen. The variation of the elastic energy density indicates that the rock has a certain energy storage limit, which is related to the lithology of the rock and its stress state. The number, size, and distribution of the initial microcracks are the main factors affecting the energy storage limit of the rock. Rocks exhibit different forms of damage at different loading rates. In essence, the different stress states determine how the rock energy is distributed and transformed.