## 3 Results and Discussion
### Stiffness Degradation  
The secant stiffness \(K\) of the specimens is the ratio of the peak load to the peak displacement in each cycle. It is defined as follows:  
\[K_{\text{i}}=\frac{\left|+F_{\text{i}}\right|+\left|-F_{\text{i}}\right|}{ \left|+\Delta_{\text{i}}\right|+\left|-\Delta_{\text{i}}\right|} \tag{2}\]  
where \(K_{\text{i}}\) is the secant stiffness of the concrete shear wall specimen under cycle i, \(\pm F_{\text{i}}\) is the peak load of the specimen under cycle i, and \(\pm\Delta_{\text{i}}\) is the peak displacement of the specimen under cycle i.  
The secant stiffness degradation curves of the specimens are shown in Figure 13.  
\begin{table}
\begin{tabular}{c c c c c c c} \hline \hline \multirow{2}{*}{**Specimen**} & \multicolumn{6}{c}{**Characteristic Point Displacement (mm)**} & \multirow{2}{*}{**Ductility**} \\ \cline{2-2} \cline{4-6}  & **Crack** & & **Yield** & **Peak** & **Ultimate** & **Coefficient** & **Ratio** \\ \cline{2-6}  & **Displacement** & **Displacement** & **Displacement** & **Displacement** & **Displacement** & **Displacement** \\ \hline RFSW-1 & 2.67 & 6.24 & 12.78 & 24.71 & 3.96 & \(1/52\) \\ CGSW-2 & 2.82 & 6.48 & 12.67 & 24.48 & 3.78 & \(1/53\) \\ CGSW-3 & 2.98 & 6.68 & 12.47 & 23.95 & 3.59 & \(1/54\) \\ \hline \hline \end{tabular}
\end{table}
Table 7: Characteristic point displacement and ductility coefficient of the specimens.  
Figure 13 shows that the secant stiffness degradation curves of the three specimens are similar, and the stiffness degradation of the specimens is obvious. The slope of the secant stiffness degradation curve is larger from cracking to yielding, which indicates that the stiffness degradation of the specimen is faster in this stage. However, the slope of the secant stiffness degradation curve decreases gradually from the specimen yield to the ultimate state, indicating that the stiffness degradation of the specimen becomes slow at this stage.  
In addition, with the increase in the coal gangue replacement rate, the initial secant stiffness of the three specimens decreases gradually because the elastic modulus of coal gangue concrete is lower than that of conventional concrete. The secant stiffness of the three specimens after reaching the limit state is close, indicating that the coal gangue replacement rate is negatively correlated with the degradation rate of specimen stiffness. That is, the stiffness degradation rate of specimen CGSW-3 is more uniform.  
The secant stiffness at the characteristic point of the specimens is shown in Table 8, where \(\beta_{\text{yc}}\), \(\beta_{\text{my}}\), and \(\beta_{\text{um}}\) are stiffness attenuation coefficients. Table 8 shows that the characteristic point secant stiffness of the three specimens decreases with the increasing coal gangue replacement rate. Compared with specimen RFSW-1, the cracking secant stiffness of specimens CGSW-2 and CGSW-3 decreases by 10.6% and 21.0%, respectively, while the ultimate secant stiffness decreases by 10% and 20.6%, respectively. The \(\beta_{\text{yc}}>\beta_{\text{yc}}>\beta_{\text{um}}\) of the three specimens show that the stiffness degradation rate of the three specimens changes from fast to slow.