## 4 Conclusions  
In this paper, a SPAM of the GCIM was established, and its theoretical calculation expression was derived. By establishing a FE model of the GCIM, the feasibility of predicting the TC using the theoretical calculation model was verified through numerical analysis. The main achievements are  
1. Based on series and parallel models, a SPAM of the GCIM was established. The theoretical calculation expression of its TC was derived, and verification analysis was conducted through numerical simulation.
2. A 3D FE model of the GCIM was established, and through numerical simulation, the variation pattern of the TC of insulation materials with the VR of GPPs in the three models was obtained. The results of the numerical simulation indicate that within the specified range of VR variations, the value of \(\frac{\Psi 1}{\Psi 2}\) has the greatest impact on the thermal performance of the insulation material, followed by the impact of \(\frac{\Psi 1}{\Psi 4}\), while the impact of \(\frac{\Psi 1}{\Psi 3}\) is the smallest.
3. Through a comparative analysis of theoretical and numerical simulation results, the impact pattern of the VR of GPPs on the thermal performance of the GCIM was obtained. For both the GPP-cement VR model and the GPP-SF VR model, the TC of the GCIM decreases rapidly in the initial stage and stabilizes later, with a critical point at \(\frac{\Psi 1}{\Psi 2}=\frac{\Psi 1}{\Psi 4}=5\).  
This paper proposes a SPAM that can be used to predict the TC of the GCIM. Via numerical simulations, the TC patterns of the GCIM were investigated. The research findings carry significant theoretical and practical value. However, there are certain limitations in  
Figure 18: The variation pattern of TC in the GPP-SF VR model.  
the basic model assumptions, including the one-dimensional heat transfer model and the material random distribution algorithm. These limitations can lead to errors due to the neglect of the effects of thermal radiation and convective heat transfer, as well as the incompleteness of randomness. Subsequent research can further refine the data and methods by considering the introduction of more influencing factors and more complex models for analysis.  
Conceptualization, T.Z. and R.W.; methodology, R.W. and Z.Z.; software, Q.Y. and F.Z.; validation, R.W., Q.Y. and Z.Z.; formal analysis, Z.Z. and F.Z.; investigation, K.Z., J.X. and Z.Z.; resources, T.Z. and R.W.; data curation, K.Z. and J.X.; writing--original draft preparation, T.Z. and R.W.; writing--review and editing, Z.Z. and T.Z.; visualization, K.Z.; supervision, J.X.; project administration, T.Z.; funding acquisition, R.W. and T.Z. All authors have read and agreed to the published version of the manuscript.  
This research was supported by the Zhejiang Provincial Department of Housing and Urban Rural Development Science and Technology Project -- Weitang Subdistrict Shanhe Garden Phase IV (Awards No. 2023K038) and the Jiangxi Provincial Natural Science Foundation (Awards No. 20224 BAB214072).  
The data of this study are available from the corresponding author upon request.  
Authors [PERSON], [PERSON], [PERSON], [PERSON], [PERSON] and [PERSON] were employed by the company Zhejiang Provincial Erjian Construction Group Ltd. The remaining author declares that the research was conducted in the absence of any commercial or financial relationships that could be construed as a potential conflict of interest.