## 4 Analysis of the Bearing Capacity and Crack Width of SCGCs
### Bearing Capacity
#### 4.2.2 Model Optimization  
Considering that the coral aggregate is a lightweight aggregate, according to the \"Code for Design of Lightweight Aggregate Concrete Structures\" (JGJ12-2006) [41], the calculation formula for \(N_{\text{u}}\) of a rectangular column under combined axial and bending loads is as follows:  
\[\left\{ \begin{array}{l}N_{\text{u}}\leq f_{\text{cm}}bx+f_{y}^{\prime}A_{ \text{s}}^{\prime}-f_{y}A_{\text{s}}\\ N_{\text{u}}e\leq f_{\text{cm}}bx(h_{0}-x/2)+f_{y}^{\prime}A_{\text{s}}^{\prime }(h_{0}-a_{\text{s}}^{\prime})\\ e=\eta e_{\text{i}}+h/2-a_{\text{s}}\\ \eta=1+\frac{1}{1400(e_{0}/h_{0})}\left(\frac{l_{0}}{h}\right)^{2}\zeta_{1} \zeta_{2}\\ \zeta_{1}=0.5f_{\text{c}}A/N\\ \zeta_{2}=1.3-0.015l_{0}/h\\ e_{\text{i}}=e_{0}+e_{\text{a}}\\ e_{\text{a}}=0.12(0.3h_{0}-e_{0})\end{array} \right. \tag{8}\]  
where \(f_{y}\) and \(f_{y}^{\prime}\) are the tensile and compressive strengths of the reinforcement, in MPa, respectively; \(A_{\text{s}}\) and \(A_{\text{s}}^{\prime}\) are the cross-sectional areas of the tensile and compressive longitudinal reinforcements, in mm\({}^{2}\), respectively; \(a_{\text{s}}\) and \(a_{\text{s}}^{\prime}\) are the distances from the resultant force points of the tensile and compressive reinforcements to the edge of the cross-section, in mm, respectively; \(e\) is the distance between the point of axial load and the resultant force point of the tensile reinforcement, in mm, respectively; \(e_{\text{i}}\) is the initial eccentricity, in mm; \(e_{0}\) is the eccentricity of the axial load relative to the centroid of the cross-section, in mm; \(e_{\text{a}}\) is the additional eccentricity, in mm;\(f_{\text{cm}}\) is the bending compressive strength of the concrete, in MPa, where \(f_{\text{cm}}\) = 1.05\(f_{\text{cm}}\); \(\eta\) is the moment increase factor due to second-order effects; \(l_{0}\) is the effective length of the member, in mm; and \(\zeta_{1}\) and \(\zeta_{2}\) are fitting parameters, where \(\zeta_{2}\) = 1 when \(1l_{0}/h\) < 20. The ultimate bearing capacity (\(N_{\text{u}}\)) of seven SCGC specimens under eccentric loading was calculated based on the JGJ12-2006. The average ratio of the calculated values (\(N_{\text{u}}\)) to the measured values (\(N_{\text{u}}\)) is 3.07, with a coefficient of variation of 0.58. As shown in Figure 26, the bearing capacity calculated according to the JGJ12-2006 is generally overestimated, leading to poor prediction results. The main reasons are as follows: (i) CAGC is the combination of a geopolymer and coral aggregate, whose mechanical properties differ significantly from those of GPC and lightweight aggregate concrete; (ii) The plastic properties of the SSR result in greater deformation and wider cracks in SSRC structures during normal service, and its high ductility leads to different load redistribution and stress redistribution patterns compared to ORC structures. Additionally, the asymmetry in the stress-strain curve of the SSR under tensile and compressive loads also contributes to the inapplicability of the existing bearing capacity calculation formulas. In order to cope with the problems above, Equation (8) is modified in this paper. On the one hand, the differences in equivalent stress calculations are caused by the distinct mechanical properties between the CAGC and LAC. This paper determines the equivalent rectangular stress block for the compression zone of the SCGC based on ensuring that the area of the equivalent rectangular stress block equals the area of the theoretical stress block, and keeping the position of the resultant force unchanged. In the equivalent stress diagram (Figure 27), \(x\) represents the equivalent length (shaded area in Figure 27).