## 3 Experimental Results and Analysis
### Acoustic Emission Characteristics  
Deformation damage of rocks is always accompanied by the release of strain energy, in the form of elastic waves, i.e., acoustic emission phenomenon (AE). The acoustic emission of rocks under load can be divided into two categories: the first category is the acoustic emission caused by violent elastic vibration, due to elastic strain changes; the second category is the acoustic emission caused by microcrack development, friction, and misalignment. Before rock damage, acoustic emission is dominated by the second type of acoustic emission. After rock damage acoustic emission is dominated by the first type, during the  
\begin{table}
\begin{tabular}{c c c} \hline \hline
**Bifurcation Situation** & **Control Parameters \(\mu_{n}\)** & **(\(\mu_{n}\)–\(\mu_{n-1}\))/(\(\mu_{n+1}\)–\(\mu_{n}\))** \\ \hline \(2^{0}\to 2^{1}\) & 3 & / \\ \(2^{1}\to 2^{2}\) & 3.44949 & 4.751466 \\ \(2^{2}\to 2^{3}\) & 3.54409 & 4.656251 \\ \(2^{3}\to 2^{4}\) & 3.56441 & 4.688242 \\ \(2^{4}\to 2^{5}\) & 3.56876 & 4.66874 \\ \(2^{5}\to 2^{6}\) & 3.56969 & 4.6691 \\ \(2^{6}\to 2^{7}\) & 3.56989 & 4.669 \\ \(2^{7}\to 2^{8}\) & 3.56993 & 4.669 \\ \(\ldots\) & \(\ldots\) & \(\ldots\) \\ Periodic \(\rightarrow\) Chaos & 3.569946 & \(\ldots\) \\ \hline \hline \end{tabular}
\end{table}
Table 2: Logistic mapping bifurcation point value.  
energy evolution of rocks, acoustic emission, as a form of dissipative energy, is released in the form of crack expansion before rock destruction. The phenomenon of acoustic emission contains the rich physical and mechanical properties of rocks, especially describing the stress state and dissipative energy characteristics during rock deformation and damage, which provides the possibility for revealing the physical and mechanical processes of rock deformation and damage, as well as forecasting rock damage.  
Figure 15 shows the axial stress, energy, and accumulated energy, with time under 0.2, 0.5, and 1 KN/s cyclic loading and unloading conditions.  
The test results show that there is a relatively active acoustic emission signal at the beginning of loading, after which the acoustic emission signal is somewhat weakened, compared with the beginning of loading. With the continuation of cyclic loading and unloading, the stress at the unloading point increases, and the redeveloped microcracks keep appearing. The acoustic emission signal tends to be active, and the acoustic emission energy increases. This means an increase in dissipated energy, which is consistent with the aforementioned dissipation energy calculation results. When the load approaches the peak stress, acoustic emission is significantly active, and energy appears to increase more significantly, at which time, the microcrack penetrates and the specimen is damaged. In the post-peak fracture stage, the specimen loses the load carrying capacity, and the stored elastic energy is dissipated mainly by the slip friction of the microcrack; the acoustic emission phenomenon disappears at the same time. When the loading stress did not exceed the previous maximum loading stress, there was almost no acoustic emission phenomenon; when the loading stress exceeded the previous maximum loading stress, the acoustic emission phenomenon reappeared and showed a step increase in the cumulative energy curve, indicating that this specimen has Kaiser effect.  
Figure 15: Acoustic emission characteristics of sandstone.