## 5 Discussion
### Strain Softening Characteristics of Limestone  
The strain softening property of rock is the decline rate of the curve after the peak stress point slows down with increasing initial damage. To quantitatively analyze the strain softening degree of rock after the peak point of rock with different degrees of initial damage, the strain softening modulus is proposed as:  
\[\eta = \frac{\sigma_{c}-\sigma_{f}}{\varepsilon_{f}-\varepsilon_{c}} \tag{15}\]  
where \(\sigma_{c}\) and \(\varepsilon_{c}\) are the stress and strain at the peak stress points, respectively; \(\sigma_{f}\) and \(\varepsilon_{f}\) are the stress and strain during a complete rupture of the rock, respectively; and \(\eta\) is the strain softening modulus.  
The strain softening modulus of four degrees of initial damage are shown in Table 10.  
Figure 15 shows the strain softening modulus versus the initial damage for limestone. It can be seen from Figure 15 that:  
1. The slopes of the four initial damages are \(-151\), \(-130.2\), \(-105.5\), and \(-85.2\), respectively. The decline rate of the stress peak curve slows down with an increase in the degree of initial damage. The complete rupture point and strain softening degree of rock is different under different initial damages. The strain softening degree and the brittleness of failure strain increases with an increasing of the softening modulus.
2. With the increase in the initial damage the strain softening modulus of rock decreases, and the degree of strain softening increases. The failure ductility of the rock after peak stress is more apparent. Conversely, the smaller the initial damage degree is, the more pronounced the rock's brittle failures are.
3. For the rocks with four initial degrees of damage, the strain softening modulus is much larger than the corresponding initial damage elastic modulus, and the descending section of the stress-strain relationship curve is steeper than the ascending section. Therefore, the results obtained from the analysis of the strain softening properties reflect that the limestone in the experiment is a brittle failure rock. In order to quantify the extent of nonlinearity in the limestone compression behavior, a nonlinear relationship is applied and expressed as: \[\eta = e^{(a+b*D+c*D^{2})}\] (16) where \(\eta\) is the compressive strength; \(D\) is the initial damage; and \(a\), \(b\), and \(c\) are the quotities.  
\begin{table}
\begin{tabular}{c c c c c c} \hline \(\varepsilon\)/\(\mathbf{s^{-1}}\) & \(\mathbf{D}\) & \(\eta\) & \(\varepsilon\)/\(\mathbf{s^{-1}}\) & \(\mathbf{D}\) & \(\eta\) \\ \hline \multirow{4}{*}{\(2\times 10^{-6}\)} & 0.043 & 37.102 & & 0.034 & 36.224 \\  & 0.357 & 31.178 & & 0.357 & 30.884 \\  & 0.625 & 18.853 & & 0.625 & 16.744 \\  & 0.754 & 15.376 & & 0.754 & 14.148 \\  & 0.043 & 28.822 & & 0.043 & 29.825 \\ \multirow{2}{*}{\(2\times 10^{-4}\)} & 0.357 & 24.816 & & 0.357 & 25.922 \\  & 0.625 & 15.551 & & 0.625 & 15.824 \\ \multirow{2}{*}{\(2\times 10^{-6}\)} & 0.754 & 11.400 & & 0.754 & 12.413 \\ \hline \end{tabular}
\end{table}
Table 10: The strain softening modulus of four degrees of initial damage.  
Application of Blasting Parameters Considering Initial Damage in Main Building Construction of Xi Ludu Hydropower Station  
Xi Luodu Hydropower Station is located in Xi Luodu Valley in the lower Jinsha River. The main powerhouse is excavated in layers, and the integrity of surrounding rock is relatively complete-complete. The pre-splitting blasting method was used in the construction of the hydropower station to reduce the influence of blasting excavation on the rock platform. Therefore, it was necessary to carry out an on-site drilling acoustic wave test before construction, determine rock mechanics parameters, and then determine blasting excavation parameters, and carry out blasting test. The field tests are shown in Figure 16.