## 3 Results and Discussion
### Energy Dissipation Capacity  
In this study, the equivalent viscous damping coefficient is used to measure the energy dissipation capacity of the specimen. The larger the equivalent viscous damping coefficient is, the better the energy dissipation capacity of the specimen. It is defined as follows:  
\[\xi=\frac{1}{2\pi}\frac{S_{\text{ABCDA}}}{S_{\text{ADDF}}+S_{\text{ADBE}}} \tag{4}\]  
Figure 14: Strength degradation curves of the specimens.  
where \(S_{\Delta\text{ODF}}\) and \(S_{\Delta\text{OBE}}\) are the areas of triangles surrounded by positive and negative maximum horizontal load values and displacement axes of hysteretic loops, respectively, and \(S_{\Delta\text{BCDA}}\) is the area surrounded by the hysteretic loop. The calculation of the equivalent viscous damping coefficient is shown in Figure 15.  
In Figure 15, Point O represents the origin point, Point B and D represent the maximum horizontal load point of hysteretic loops, Point A and C represents the point at which the hysteresis curve intersects the x-axis, and Point E and F represents the displacement corresponding to the maximum horizontal load point.  
The equivalent viscous damping coefficient of the three specimens is shown in Table 9.  
Table 9 shows that the equivalent viscous damping coefficient of the three specimens increases with increasing loading displacement, indicating that the area of the hysteretic loop of the three specimens gradually increases and the energy dissipation capacity gradually improves at the later stage of loading. In addition, the equivalent viscous damping coefficient of specimen RFSW-1 is larger than those of specimens CGSW-2 and CGSW-3, but the difference is not obvious, indicating that the increase in the coal gauge replacement rate will reduce the energy dissipation capacity of the specimen. This is because the horizontal bearing capacity of gangue concrete shear walls is lower than that of ordinary concrete, and the ductility and plastic deformation ability are poor, so the energy consumption capacity is weak. However, specimens CGSW-2 and CGSW-3 still have a strong energy dissipation capacity.  
Figure 15: Calculation of the equivalent viscous damping coefficient.  
\begin{table}
\begin{tabular}{c c c c c c} \hline \hline
**RFSW-1** & \multicolumn{4}{c}{**CGSW-2**} & \multicolumn{2}{c}{**CGSW-3**} \\ \hline
**Loading Displacement** & \(\xi\) & **Loading Displacement** & \(\xi\) & **Loading Displacement** & \(\xi\) \\ \hline
1.00 & 0.159 & 1.00 & 0.116 & 1.00 & 0.079 \\
1.50 & 0.176 & 1.50 & 0.141 & 1.50 & 0.111 \\
3.00 & 0.182 & & 0.147 & & 0.114 \\
3.00 & 0.  
The ratio of the energy dissipation value of the hysteretic loop of the specimen to its elastic energy is called the energy dissipation coefficient \(E\). It is defined as:  
\[E=\frac{S_{\text{ABCDA}}}{S_{\text{ADOF}}+S_{\text{ADOE}}}=2\pi\xi \tag{5}\]  
The energy dissipation coefficients of the specimens are shown in Figure 16. Figure 16 shows that the energy dissipation coefficient of the specimens increases with increasing horizontal displacement. In the early stage of loading, the energy dissipation coefficient increases rapidly, while in the late stage of loading, it increases slowly. Furthermore, the energy dissipation coefficient of the specimen is negatively correlated with the replacement rate of coal gangue.