## 6 Conclusions  
This paper studied crack development (intergranular and intragranular) and the physical and mechanical characteristics of granite specimens at high temperatures. Predictive models based on machine learning algorithms and linear regression were implemented to model the relationships between thermal damage and its influencing factors. Existing data, including mineralogical contents and basic physical and mechanical properties of granite specimens, were collected from the literature and re-interpreted.  
In conclusion, the findings of this study can be summarized as follows:  
1. Crack development analysis revealed that no intra- or intergranular cracks occur below 400 \({}^{\circ}\)C; however, intergranular cracks appear between quartz-quartz, quartz-feldspar, and biotite-feldspar at 400 \({}^{\circ}\)C, and additional intergranular and intragranular cracks involving biotite, quartz, and feldspar emerge at 600 \({}^{\circ}\)C.
2. Based on the observed cracking behavior, three temperature zones have been identified: up to 200 \({}^{\circ}\)C, between 200 \({}^{\circ}\)C and 600 \({}^{\circ}\)C, and above 600 \({}^{\circ}\)C.
3. Physical and mechanical tests indicated a steady decrease in density, P-wave velocity, UCS, tensile strength, and elastic modulus, alongside an increase in porosity as the temperature rose from 25 \({}^{\circ}\)C to 800 \({}^{\circ}\)C.
4. Two distinct zones of property change were noted: minimal changes occurred up to 600 \({}^{\circ}\)C, while significant changes were observed between 600 \({}^{\circ}\)C and 800 \({}^{\circ}\)C, supporting the crack development pattern.
5. Predictive models developed using machine learning and linear regression demonstrated excellent performance in estimating TD based on comprehensive input parameters, including mineralogical, physical, and mechanical variables.
6. These models can serve as practical tools for planning underground operations in granite-rich environments subjected to thermal effects.
7. New equations were proposed to determine the TD of rocks at high temperatures.  
Finally, the novelty of this research lies in the use of soft computing techniques to model and predict thermal damage in granite specimens heated up to 800 \({}^{\circ}\)C, using a globally sourced dataset.  
The following supporting information can be downloaded at [[https://www.mdpi.com/article/10.3390/app15116328/s1](https://www.mdpi.com/article/10.3390/app15116328/s1)]([https://www.mdpi.com/article/10.3390/app15116328/s1](https://www.mdpi.com/article/10.3390/app15116328/s1)), Table S1: Thermal damage raw dataset. References [1; 4; 10; 17; 18; 24; 26; 28; 29; 32; 34; 35; 36; 37; 38; 39; 40; 41; 42; 43; 44; 45; 46; 47; 48; 49; 50; 51; 52; 53; 54; 55; 56; 57; 58] are cited in the supplementary materials.  
Conceptualization, G.S. and A.C.A.; methodology, A.C.A.; software, G.S.; validation, G.S. and A.C.A.; formal analysis, A.C.A. and P.M.G.; investigation, G.S.; data curation, G.S.; writing--original draft preparation, G.S.; writing--review and editing, A.C.A.; supervision, A.C.A. and P.M.G.; project administration, A.C.A. All authors have read and agreed to the published version of the manuscript.  
This research received no external funding.  
Not applicable.  
The original contributions presented in this study are included in the article/Supplementary Materials. Further inquiries can be directed to the corresponding author.  
The authors wish to acknowledge the contributions of the anonymous reviewers.  
The authors declare no conflicts of interest.  
The following abbreviations are used in this manuscript:  
\begin{tabular}{l l} SEM & Scanning electron 57 microscopy \\ CT & X-ray microcomputed tomography \\ PM & Polarizing microscope \\ NMR & Nuclear magnetic resonance imaging \\ AE & Acoustic emission \\ TGA & Thermogravimetric 61 analyses \\ DSC & Differential scanning calorimetry \\ XRD & X-ray diffraction \\ MI & Multiple imputation \\ TD & Thermal damage \\ UCS & Unconfined compressive strength \\ \end{tabular}