## 4 Discussion
### Dependence of the Kaiser Effect on the Loading Strain Rate  
Figure 10b shows that when the loading strain rate grows from \(10^{-5}\) s\({}^{-1}\) to \(10^{-3}\) s\({}^{-1}\), the \(FR\) increases from 1.06, 0.86, 0.56, 0.46, and 0.37, to 1.35, 1.19, 0.94, 0.81, and 0.70 under \(\sigma_{\rm A}=0.5\sigma_{\rm c}\), \(\sigma_{\rm A}=0.6\sigma_{\rm c}\), \(\sigma_{\rm A}=0.7\sigma_{\rm c}\), \(\sigma_{\rm A}=0.8\sigma_{\rm c}\), and \(\sigma_{\rm A}=0.9\sigma_{\rm c}\) with the increased proportion of 27.36%, 38.37%, 67.86%, 76.09%, and 89.19%, respectively. Taking \(\sigma_{\rm A}=0.5\sigma_{\rm c}\) for example, the \(FR\) increases from 1.06 to 1.21 with the increased proportion of 21.00% as the loading strain rate increases from \(10^{-5}\) s\({}^{-1}\) to \(10^{-4}\) s\({}^{-1}\). When the loading strain rate grows to \(10^{-4}\) s\({}^{-1}\), the \(FR\) increases to 1.35 with an increased proportion of 11.57%. That is to say, the \(FR\) increases as the loading strain rate increases. The Kaiser effect easily appears, and how the loading strain rate influences the Kaiser effect is greatly affected by \(\sigma_{\rm A}\). Moreover, the loading strain rate significantly affects \(FR\) when \(l_{\rm sr}<10^{-4}\) s\({}^{-1}\). The \(FR\) rapidly increases as the loading strain rate increases. When \(l_{\rm sr}\geq 10^{-4}\) s\({}^{-1}\), the loading strain rate has a minor influence on the \(FR\). The impact of loading strain rate on the rock AE features is mainly manifested by the change of AE rate (quantity of AEs generated per second). The higher the AE rate is, the faster the rock specimen is damaged. When the loading strain rate is low (\(l_{\rm sr}<10^{-4}\) s\({}^{-1}\)), internal microcracks are generated and  
Figure 10: Felicity rate variations under various prescribed stresses and loading strain rates, respectively: (a) Felicity rate variations under different prescribed stress levels (relative to \(\sigma_{\rm c}\)); (b) Felicity rate variations under different loading strain rates. expanded for a longer time with a lower AE rate. When the loading strain rate is high (\(l_{\rm sr}\geq 10^{-4}\) s\({}^{-1}\)), additional energy supplies and the internal microcracks of the rock are untimely to be closed, which lowers the resistance needed in the cracking process. This accelerates crack expansion and releases more energies with a higher AE rate. Figure 11 shows that the variation of the cumulative number of AEs versus monitoring time under different loading strain rates is generally similar. The cumulative number of AEs of the rock specimen exhibit nonlinear growth. In the first cyclic loading, new cracks are continuously formed inside the rock and original cracks are expanded and connected. The AEs tend to be active with a gradually increasing number. In the constant loading stage of the 1 st cycle, some closed cracks experience slippage inside the rock, which would continuously generate a certain quantity of AEs. However, the active degree of AEs in this stage is related to \(\sigma_{\rm A}\). When \(\sigma_{\rm A}\) is low (\(\sigma_{\rm A}<0.7\sigma_{\rm c}\)), AEs in this stage are inactive with a small quantity. Consequently, the cumulative quantity of acoustic emissions does not increase. When \(\sigma_{\rm A}\) is high (\(\sigma_{\rm A}\geq 0.7\sigma_{\rm c}\)), the AE is relatively active with a relatively larger quantity. The cumulative quantity of AEs slowly increases. In the unloading stage of the 1 st cycle and the initial loading stage of the 2 nd cycle, few AEs occur. The quantity of AEs basically does not change or slowly increases. In the later loading stage of the 2 nd cycle, the AE becomes active. The cumulative quantity of the AEs rapidly increases. Overall, when the loading strain rate is low (\(l_{\rm sr}<10^{-4}\) s\({}^{-1}\)), the AE rate of the rock is low, and the cumulative quantity of the AEs slowly increases. The slope of the cumulative quantity of the AEs versus monitoring time is small and increases steadily.