## 3 Results and Discussion
### Deformation Capacity  
The ductility coefficient can be used to measure the ductility of structures. In this study, the displacement ductility coefficient is selected to reflect the ductility performance of shear walls. The larger the displacement ductility factor is, the better the ductility and seismic behavior of the specimens. It is defined as follows:  
\[\mu=\frac{\Delta_{u}}{\Delta_{y}} \tag{1}\]  
where \(\Delta_{u}\) is the ultimate displacement of the specimens and \(\Delta_{y}\) is the yield displacement of the specimens.  
The displacement and displacement ductility coefficients corresponding to the characteristic points of the specimens are shown in Table 7.  
Figure 12: Strain curves of the specimens (**a**) RFSW-1 (**b**) CGSW-2 (**c**) CGSW-3 (**d**) Comparison.  
Table 7 shows that with the increase in the coal gauge replacement rate, the yield displacement of the specimens increases gradually. Compared with specimen RFSW-1, specimens CGSW-2 and CGSW-3 increased by 3.8% and 7.1%, respectively. However, the ultimate displacement gradually decreases with the increase in the coal gauge replacement rate. Compared with specimen RFSW-1, specimens CGSW-2 and CGSW-3 decreased by 0.9% and 3.1%, respectively, indicating that the increase in the coal gauge replacement rate will lead to the deterioration of the ductility of the specimens, but the difference is not obvious.  
This is because coal gangue is subjected to tensile circulation under lateral cyclic loading. Since the surface of coal gangue is rougher and the water absorption rate is larger compared to the natural coarse aggregate. Water is sucked in from the cement slurry near the interface before the cement condenses. Thus, the water-ash ratio near the interface is reduced, resulting in higher adhesion strength of cement stone and coal gangue. The tensile strength of the spontaneous combustion gangue concrete depends on the tensile strength of the spontaneous combustion coal gangue aggregate. Moreover, tensile damage is similar to other light aggregate concrete failures, which are prone to damage, running through the coal gangue joint surface of larger particles. Additionally, the tensile strength is lower than that of ordinary concrete, so with the increase of coal gangue replacement rate, the ductility of shear walls becomes worse.  
It can be seen from the displacement ductility coefficient that with increasing coal gangue replacement rate, the displacement ductility coefficient gradually decreases, indicating that the ductility of the specimen is negatively correlated with the coal gangue replacement rate. However, the displacement ductility coefficients of the three specimens in this study are between 3.59 and 3.96, and the ductility meets the requirements. It can be seen from the drift ratio that the drift ratio decreases with increasing coal gangue replacement rate, indicating that the coal gangue has a negative impact on the deformation capacity of the specimens. However, the drift ratios of the three specimens in this study are all greater than the elastoplastic maximum displacement angle of 1/120 required in GB 50011-2010 [38], which proves that the elastoplastic deformation ability of the specimens is good and meets the seismic design requirements of building structures.