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Article

Thermal Damage Characterization and Modeling in Granite Samples Subjected to Heat Treatment by Leveraging Machine Learning and Experimental Data

by
Gabit Sansyzbekov
,
Amoussou Coffi Adoko
* and
Paul Mathews George
School of Mining and Geosciences, Nazarbayev University, Astana 010000, Kazakhstan
*
Author to whom correspondence should be addressed.
Appl. Sci. 2025, 15(11), 6328; https://doi.org/10.3390/app15116328
Submission received: 16 April 2025 / Revised: 14 May 2025 / Accepted: 26 May 2025 / Published: 4 June 2025
(This article belongs to the Special Issue Intelligent Technologies in Geotechnical Engineering and Geological Hazards)
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Abstract

Featured Application

The predictive model developed in this study can be used to assess the thermal damage of granite for general applications such as geothermal energy extraction, deep mining, and nuclear waste disposal. By leveraging machine learning and experimental data, the model enables engineers and researchers to evaluate the effect of high temperature on rock properties in underground excavations.

Abstract

High temperatures significantly affect the physical and mechanical properties of rocks in deep geoengineering projects, such as geothermal development, deep mining, and the geological disposal of nuclear waste. Therefore, it is essential to explore the relationship between the thermal damage (TD) of granite and its influencing factors. This paper characterizes the TD of granite specimens subjected to high temperatures of up to 800 °C and proposes a predictive model for this thermal damage. A database, which includes publicly available experimental data of advanced microscopic observations of granite specimens exposed to high-temperature treatments and their changes in physical and mechanical properties, was compiled and analyzed. The collected data revealed a consistent trend: crack development among quartz, feldspar, and biotite minerals was observed to intensify notably between 400 °C and 600 °C, as indicated by changes in the mechanical properties. Based on these characteristics, the relationships between TD and its influential parameters were determined using regression models and several machine learning algorithms. The derived models indicated good predictability performance with a coefficient of determination (R2) varying between 0.60 and 0.97, with the boosted ensemble tree model being the best. Nevertheless, mineral contents were not found to be good predictors of TD, even if they control the evolution of the crack during the heat treatment. It was concluded that the findings of this study could serve as a valuable tool for assessing the thermal damage of rocks.

1. Introduction

Granite is one of the most common rocks in deep geoengineering applications involving high-temperature treatments such as geothermal energy extraction, deep mining, and nuclear waste geological disposal [1,2,3]. For example, enhanced geothermal systems reach 200 °C, while the temperature in underground chambers for nuclear disposal storage now varies from 100 °C to 300 °C and will increase over the storage period [4]. The high temperature damages the reservoir rocks and weakens their physical and mechanical properties, which is a pressing concern in these engineering projects [5,6,7]. In essence, the weakening in macroscopic physical and mechanical properties results from changes in mineral composition and characteristics at high temperatures [8]. Different minerals expand at different rates at high temperatures, and the same mineral can expand at different rates and in many directions [6,9,10]. Such expansion can cause stress accumulation at the edges of minerals, damaging the structure when heated. Therefore, the heated rock may produce intergranular and intragranular microcracks among and within mineral crystals [3]. In addition to these intergranular microcracks in igneous rock, intragranular cracks in some of the weaker mineral elements, like feldspar and biotite grains, also play a role in crack propagation. High temperatures can also induce thermal reactions in minerals that form rocks, altering their composition and structure, resulting in different types of microcracks. As a result, microcrack formation brought on by heat treatment alters the physico-mechanical behaviors of rocks [11,12,13], which eventually impacts any rock engineering design subjected to high temperatures. Therefore, extensive research is required to fully comprehend the impact of high temperatures on rocks spanning from microscopic mineral composition to macroscopic physical and mechanical properties, including mineral composition, dehydration, crystalline state, and the formation of new phases.
Motivated by this importance, extensive studies have been conducted over the past few decades, taking advantage of the availability of technologies such as scanning electron microscopy (SEM), optical microscopy, X-ray microcomputed tomography (CT), polarizing microscope (PM), nuclear magnetic resonance imaging (NMR), and acoustic emission (AE) to reveal the mechanisms of physico-mechanical property deterioration [9]. Additionally, in most existing studies, researchers often combine SEM, thermogravimetric analysis (TGA), and differential scanning calorimetry (DSC) with X-ray diffraction (XRD) pattern analysis to examine the microstructural properties of rock minerals [5]. For example, Zhang, Sun [14] investigated the heat influence on the microstructure of limestone using XRD, SEM, TGA, and DSC tests. Their results indicated that thermal treatment alters the crystallization in addition to causing mineral disintegration. Shen, Zhang [15] conducted comparable research on sandstone samples and reached similar conclusions. Many other studies corroborated how high temperatures affect the pore structure, mechanical characteristics, and mineralogy of rocks, including the study of acoustic emission and fracture morphology characteristics of thermally damaged granite [7], analysis of physical and mechanical behaviors and microscopic mineral characteristics of thermally damaged granite [16], experimental and numerical simulation study of the evolution of mechanical properties of granite after thermal treatment [6], and experimental investigation on the physical/thermal properties of Nahan granite [2].
Nevertheless, despite the numerous studies on the thermal damage (TD) of rock, the relationship between the TD of granite and its influencing factors has not been comprehensively quantified yet [5,12]. Hence, this paper aims to characterize the TD of granite specimens exposed to high temperatures and then propose a predictive model for TD. The wide temperature range (from 25 °C to 800 °C) is selected to describe the physical and mechanical changes in granite, along with the crack development study to better explain the effect of high temperatures on rock.

2. Granite Thermal Damage Dataset Description

The data used for this study consist of the physical and mechanical properties and the microscopic observations of granite specimens exposed to high-temperature treatments that were compiled from the experimental results of existing studies [2,4,10,17,18,19,20,21,22,23,24,25,26,27,28,29]. The rock samples were cylindrical without pre-existing holes and primarily sourced from various international projects, including those in Australia, India, Germany, the UK, Canada, and China, with the experiments conducted under nearly identical conditions. The dataset includes parameters such as temperature (P1), mineral contents—specifically feldspar (P2), quartz (P3), biotite (P4), and other minerals (P5)–elastic modulus (P6), porosity (P7), density (P8), uniaxial compressive strength (P9), tensile strength (P10), and P-wave velocity (P11), all obtained during these experiments. The compiled dataset is available in Supplementary Materials, while sample data are presented in Table 1. To study the damage evolution during the testing, SEM observations of the samples were also collected to study the damage evolution during the testing.
As can be seen in Table 1, the original dataset has many missing points; hence, they need to be handled. In this study, the multiple imputation (MI) technique was implemented by using the mice package in the R program. This procedure consists of seven steps: (1) loading required packages to enable data processing and multiple imputation, (2) exploration of missing data to inform the imputation strategy, (3) setting the imputation method, (4) running the imputation using chained equations over 50 iterations, (5) checking convergence to confirm that stable imputations are generated, (6) analysis of imputed data, and (7) exporting completed dataset. Instead of simply discarding the missing values, MI creates several different datasets by imputing the missing values multiple times and proposes the average value [30]. There are three key stages in MIs: data imputation, data analysis, and results pooling [31]. The first stage involves the generation of several complete datasets. Then, each of the imputed datasets is analyzed separately using the same statistical model. Finally, these multiple analyses’ results are averaged to produce final estimates. MI has many advantages and is often preferred where missing data are common. The resulting dataset is used for the TD.

3. Crack Evolution

The influence of temperature on crack development in granite specimens was revealed through the collected data. Microcracks in the rock are generally classified as intragranular (contained within a single grain), intergranular (along the grain boundaries), and transgranular (affecting more than one grain) [19]. This study examined the intragranular cracks of feldspar, quartz, and biotite minerals at various temperatures and the intergranular cracks at the boundaries between minerals. Samples of the analyzed microscopic images are provided in Figure 1, where red lines indicate the intergranular cracks.
The gathered data and observations indicate that three clear patterns emerge as the temperature increases [18,23,33,34,35,36,37,38,39,40]. From room temperature to about 200 °C, there are generally no visible intergranular cracks in any of the minerals (quartz, feldspar, and biotite). The minerals exhibit a close arrangement, devoid of initial pores or fissures [41]. However, some instances show intergranular cracks between quartz and feldspar minerals when the temperature reaches 200 °C. The initiation of grain boundaries is first observed at the triple junctions of quartz and feldspar minerals, which are typically considered the weakest grain boundaries due to their longer and weaker intergranular bonds. Intergranular cracks between two quartz minerals at 200 °C were also detected. Therefore, this temperature can be regarded as the threshold for the initiation of intergranular cracks in granite.
Upon increasing the temperature to 400 °C, more intergranular cracks appear between two quartz minerals and between quartz and feldspar minerals. More specifically, the intergranular boundary between biotite and feldspar minerals only weakens at 400 °C. These intergranular cracks are caused by strong bound water loss, dihydroxylation loss of constitution water, and solid mineral expansion between 100 and 500 °C, as suggested by previous studies [34]. In contrast, biotite has shown a supporting effect, since the boundaries of biotite with quartz or feldspar did not result in intergranular cracks at 400 °C.
The increase in the temperature to 600 °C leads to an increase in the widths of intergranular cracks between two quartz minerals, quartz and feldspar minerals, and biotite and feldspar minerals. The width of the crack could reach up to 30 µm [34]. However, the intergranular cracks between quartz and biotite minerals initiate at 600 °C. Finally, when the temperature was increased to 800 °C, the width of intergranular cracks between all minerals also increased. At this temperature, more thermal microcracks, which gradually propagate and coalesce within the granite specimens, are observed. Based on these observations, the intergranular crack evolution of granite is summarized in Table 2.
On the other hand, in most experiments, the intragranular cracks initiate starting from 400 °C in feldspar grains with an average width of less than 30 µm [34]. The same goes for large quartz minerals. Crack initiation occurs due to feldspar’s lower strength compared to quartz and biotite. Upon increasing the temperature to 600 °C, intragranular cracks occur not only in the feldspar and quartz minerals but also in the biotite minerals, leading to a significant increase in the number of microcracks [37]. This is mostly because of the α/β transition of quartz minerals, which results in a large increase in the volume of quartz minerals, leading to the generation of a substantial amount of cracks. Heating quartz minerals causes a reversible structural phase transformation referred to as the α/β transition of quartz. Furthermore, the remarkable increase in intragranular cracks is due to the dehydration of minerals, lattice reorganization, shrinkage, and decomposition of minerals. Finally, when the temperature was increased to 800 °C, the width of intergranular cracks between all minerals significantly increased. Biotite affects the formation of cracks inside quartz and feldspar crystals and plays a major role because it expands more when heated compared to quartz and feldspar. The temperature increase led to the observation of more thermal microcracks, which gradually propagated and coalesced within the granite specimens. Based on these microscopic observations, Table 3 summarizes the characteristics of intragranular crack development in granite samples exposed to high-temperature development.

4. Physical and Mechanical Parameters

4.1. Porosity

Figure 2a shows the changes in porosity with temperature. At room temperature, granite exhibits low porosity, indicating minimal visibility of the original pores and fissures. Overall, as the temperature rises, granite porosity increases. This is attributed to the formation of thermal microcracks. However, a slight decrease in porosity was observed, mostly at the beginning of the heat treatment, suggesting mineral grain expansion. Below 100 °C, the loose bonding of rock minerals allows water trapped in tiny pores and between layers to escape. Simultaneously, heat treatment prompts mineral particles to expand, leading to the closure of primary cracks. Consequently, rock porosity slightly decreases. Within the 100–300 °C range, physically combined water within the rock evaporates, exerting pressure that facilitates the expansion of cracks and pores. Notably, differences in thermal expansion between feldspar and quartz become apparent, leading to uncoordinated thermal expansion and crack initiation. In the 300–600 °C range, nearly all trapped and physically combined water evaporates, while chemically bound water dissociates, disrupting the mineral lattice. As a result, erratic trends in porosity are observed within the 300–600 °C temperature range, as shown in Figure 2a. This temperature range may correspond to a transition zone. Despite the continued thermal expansion of mineral particles and the initiation of new cracks, some cracks and pores may close due to particle expansion, resulting in little to no increase in porosity. Overall, porosity exhibits only slight growth up to 600 °C, implying minor structural changes due to existing and new microcrack development. Beyond 600 °C, porosity escalation becomes more pronounced, with significant increases in thermally induced cracks, reaching 5.6% at 800 °C. Thus, the 600–800 °C range marks a critical threshold for temperature-induced changes.

4.2. Density

As shown in Figure 2b, untreated granite has a starting density of about 2.6 g/cm3 and decreases smoothly up to 600 °C. Density decreases by around 0.1 g/cm3 at 700 °C and 0.2 g/cm3 at 800 °C, with the drop being most noticeable. Hence, there are two clear regions: a very low decrease up to 600 °C and a visible decrease between 600 °C and 800 °C, respectively. However, the water content of granite is minimal. Hence, the mass of granite samples does not vary much during heating. Since the rate of mass decrease is far less than the rate of volume increase, the volume increase due to mineral expansion is the leading factor for the decrease in granite density.

4.3. P-Wave Velocity

Figure 2c shows the effect of high temperature on the P-wave velocity. As the heating temperature rises, the P-wave velocity decreases linearly. Below 600 °C, there are minor changes in P-wave velocity. However, beyond 600 °C, there is a substantial decrease, up to 92% compared to untreated samples, indicating the generation of numerous new thermally induced cracks and significant damage to the granite samples. According to many studies, the relationship between P-wave velocity and temperature (T) can be divided into two segments: a mild decline up to 600 °C and a pronounced decline following treatment temperatures exceeding 600 °C. However, it is difficult to observe these regions in Figure 2c.

4.4. UCS and Tensile Strength

Figure 2d,e shows the effect of high temperature on the UCS and tensile strength, respectively. Both parameters decrease with increasing temperature, consistent with thermally induced degradation in rock strength. UCS indicates low correlation with temperature, while the tensile strength shows a high correlation with temperature. This can be explained by the fact that high temperature tends to transform granite samples from a more brittle material to a more ductile material.

4.5. Elastic Modulus

Finally, Figure 2f shows the effect of high temperature on the elastic modulus of granite samples. The EM decreases slowly from 25 °C to 600 °C, followed by a relatively significant reduction after 600 °C. This implies that the emerging and rapid expansion of microcracks, because of internal thermal stress appearing at higher temperatures, significantly reduces the elastic modulus to some degree. Thus, high temperatures damage rocks.

4.6. Physical and Mechanical Parameters Versus Crack Development

According to Section 4.1, Section 4.2, Section 4.3, Section 4.4 and Section 4.5, two distinct regions were observed: very low changes up to 600 °C and notable changes between 600 °C and 800 °C. Consequently, physical and mechanical parameters exhibited a steady change followed by a rapid alteration. After 600 °C, rock properties have been significantly degraded. These findings do not contradict the observations on crack evolution (Section 3) but rather reinforce the results. They highlight the link between microstructural changes and the degradation of mechanical properties. However, the only difference is that two stages of crack evolution are involved at temperatures up to 600 °C. Since this crack evolution occurs at a microscopic level, defining two stages through physical experiments instead of three stages is acceptable. To summarize, the effect of high temperature on the physical and mechanical parameters of rocks can be understood through studying the crack development.

5. Thermal Damage

In this section, the predictive modeling of granite thermal damage (TD) is discussed.

5.1. Definition of TD and Its Influencing Parameters

The TD is often used to characterize the degree of damage to rock after heating, based on variations in the P-wave velocity with temperature, defined in Equation (1) as [42,43]
TDin = 1 − (VpT/Vp0)2
where VpT stands for the P-wave velocity (Vp) of samples after heating treatment, and Vp0 stands for the Vp of the same specimens at room temperature. There are other definitions of thermal damage, but Equation (1) is chosen since P-wave velocity correlates quite well with the crack evolution, which reflects the amount of damage experienced by the sample.
Among the six parameters studied in Section 4, P-wave velocity and tensile strength show a good correlation to the TDin. Figure 3 shows the negative correlation between the predicted TDin and P-wave velocity (Figure 3a) and tensile strength (Figure 3b). Generally, the intact rock sample has a higher P-wave velocity than the fractured one because cracks, air, or fluid gaps slow down the waves. Hence, the trend is that intuitive thermal damage often degrades material properties, reducing the ability to transmit seismic waves. The coefficient of determination R2 is 0.85 and 0.90 for P-wave velocity and the tensile strength, respectively, which shows a strong inverse relationship between these two parameters. Moreover, tensile strength has a higher negative correlation to the TDin. Hence, tensile strength is a good parameter to define TDin, indicating that strong tensile strength prevents TD in rocks. High-temperature treatment can transform brittle material into a more ductile material. Therefore, it is important to employ all key influencing parameters when evaluating the thermal damage.

5.2. Multivariate Regression Model

The imputed dataset is used to derive an empirical equation (TDemp) that can correlate thermal damage with its influencing factors in a more comprehensive way. The correlation between the parameters P1–P10 and TDemp was determined using SPSS (version 24), and after several trials, the following equation was obtained. The coefficient of determination R2 was 0.66. The equation can be described as follows:
TDemp = 0.09 + 0.0003·P1 + 0.002·(P2 + P3 + P4) + 0.024·P7 − 0.0003·P9 − 0.036·P10
The equation indicates that TDemp is directly proportional to the temperature, mineral content, and porosity of granite specimens, while higher UCS and tensile strength have an opposing effect. By observing the parameters’ coefficients, the mineral contents (quartz, feldspar, and biotite) may have almost the same impact on the overall TD, while porosity has the most influence on TD among all parameters. Finally, UCS and BTS have negative effects on TD. In other words, strong granite specimens tend to have lower TD, which makes more sense.
Figure 4 shows a good correlation between the actual (defined in Equation (1)) and predicted TD. Hence, the proposed equation can estimate the thermal damage accurately, where R2 is 0.59. Since a fair agreement of the coefficient of correlation R=0.77 was reached, in the next section, machine learning algorithms are implemented to enhance the results.

5.3. Machine Learning Techniques

The compiled dataset was utilized to develop predictive models for thermal damage estimation using several supervised machine learning algorithms within the MATLAB (R2024b) environment, specifically via the Regression Learner Toolbox. The machine learning workflow consisted of the following key steps: data preprocessing, model selection, training, cross-validation, and performance evaluation. Initially, the dataset was prepared by ensuring consistency and removing any remaining anomalies or extreme outliers. No additional feature scaling or transformation was applied as the toolbox handles these internally when required. Several regression models were then trained, including Regression Tree (Fine Tree), Regression Tree (Coarse Tree), Artificial Neural Network (ANN), Gaussian Process Regression, Support Vector Machine (SVM), SVM (Medium Gaussian), Ensemble Boosted Trees, and Ensemble Bagged Trees. Since the original dataset had many missing points, only 136 full data points were used for model training. All models were trained using the default parameter settings provided by the toolbox. To ensure robust model evaluation and prevent overfitting, 10-fold cross-validation was employed during training. The performance of each model was assessed based on the coefficient of determination (R2) and the root mean square error (RMSE), which measure the proportion of variance explained and the average prediction error, respectively. The results, summarized in Table 4, indicated that model performance varied from fair to excellent, with R2 values ranging between 0.69 and 0.97, and RMSE values ranging from 0.0633 to 0.1902. Figure 5a–c provides representative plots comparing predicted and actual thermal damage values for selected models, visually illustrating the accuracy and reliability of the predictions.
From Table 4, it can be seen that the Gaussian Process Regression is the best-performing model overall, with the highest R2 and lowest RMSE values. Then, SVM, Ensemble Boosted Trees, and Ensemble Bagged Trees models equally showed the second-best prediction performance. Next, the Regression Tree (Fine Tree) model performed quite well, indicating strong predictive capability with relatively low error. However, among these top-five models, Gaussian Process Regression, SVM, and Ensemble Boosted Trees models predicted values slightly outside of the TD range: negative values or larger values than 1 (note that the TD, as per the definition, is between 0 and 1). Hence, despite their good prediction capabilities, these models cannot be suggested for TD prediction. As a result, the Ensemble Bagged Trees model (Figure 5a) and the Regression Tree (Fine Tree) model (Figure 5b) are considered the best. As an illustration of prediction outside the range, the Gaussian Process Regression model (Figure 5c) is given.

5.4. Sensitivity Analysis (Importance of the Input Parameters)

To identify and rank the most influential input parameters affecting thermal damage (TD), a sensitivity analysis was conducted using the ReliefF algorithm implemented in MATLAB (R2024b). This step forms part of the broader machine learning workflow, specifically focusing on feature importance analysis—a critical phase used to interpret model behavior and prioritize variables for further investigation or simplification. The ReliefF method is a distance-based algorithm suitable for regression problems. It estimates the importance (or weight) of each predictor by repeatedly sampling instances and evaluating how well feature values distinguish between instances with similar or different target values. This approach captures not only individual feature effects but also potential interactions with other variables. In this study, the ReliefF function was applied to the input dataset used in the machine learning models. The resulting feature weights indicated the relative importance of each predictor to TD. Figure 6 illustrates the ranked weights, showing the predictors in the following order of importance: P1, P10, P7, P9, P8, P6, P2, P5, P3, and P4 (see Figure 6). Among these, the three most important parameters were identified as (1) temperature, (2) tensile strength, and (3) porosity. These results suggest that mineralogical properties (such as P2 to P5), although expected to be among the top influencing parameters of thermal damage due to differential expansion and microcrack formation during heating, exhibited negative weights and are influenced by TD. Instead, TD mechanics cause changes in mineralogical properties. Interestingly, UCS showed a near-zero weight, implying a limited direct role in the observed TD variations. This may seem counterintuitive, as UCS often initiates cracking. However, it is possible that heating may initiate and close existing microcracks, thereby masking the effects of UCS alone. This outcome highlights the complex interactions among material properties under thermal stress and suggests that a broader set of mechanical and mineralogical features should be considered to fully understand TD behavior.
Since mineralogical properties contribute in a reverse way in the TD process, the mineral content parameters were removed from Equation (2), and the equation was redefined as
TDemp2 = −0.1115 + 0.0007·P1 + 0.018·P7 + 0.0001·(P9/P10)
Similarly, Figure 7 shows the updated correlation between the actual (defined in Equation (1)) and predicted TD (defined in Equation (3)). The updated equation can still estimate the thermal damage very accurately, with an R2 close to 0.94. Compared to the previous equation, a better coefficient of correlation, R = 0.97, was reached.
Further removing the porosity term from Equation (3) leads to
TDemp3 = −0.0991 + 0.0008·P1 − 0.0001·(P9/P10)
Now, Figure 8 shows the updated correlation between the actual (defined in Equation (1)) and predicted TD (defined in Equation (4)). The updated equation can still estimate the thermal damage very accurately, where R2 is close to 0.93.

5.5. Discussions

Since P-wave velocity and tensile strength showed a good correlation to the TDin, these two parameters could be solely used to evaluate the thermal damage. However, granite has different physical, mechanical, and mineralogical properties. It is known that these factors impact the thermal damage process. Therefore, additional parameters need to be included in the TD model for a more comprehensive assessment. As a result, ten parameters were considered to determine TD empirically. Equation (2) indicates that TDemp is directly proportional to the temperature, mineral content, and porosity of granite specimens, while higher UCS and tensile strength have an opposing effect. Hence, the proposed empirical equation contains not only physico-mechanical parameters but mineral content as well. The correlation between the TDin and TDemp is provided in Figure 4.
Since a fair agreement of R = 0.77 was reached, machine learning algorithms were implemented to enhance the results. As a result, among the eight proposed models, the Ensemble Bagged Trees model (Figure 5a) and the Regression Tree (Fine Tree) model (Figure 5b) were considered the best prediction models and outperformed the Gaussian Process Regression model (Figure 5c). The reasons behind this better performance are (1) they are more robust to noise and (2) they make fewer assumptions about the data distribution. They could do even better if the dataset implemented were larger [44,45].
The order of importance of the ten input parameters to evaluate TD in predictive models was assessed, and the results are presented in Figure 6. The three most important parameters were temperature, tensile strength, and porosity. Hence, predictive models with these data can perform well. However, this process indicated that mineralogical properties and UCS exhibited negative weights, being influenced by TD rather than causing it. Therefore, Equation (2) was updated to Equation (3), and Figure 7 was provided, where the updated correlation between the actual and predicted thermal damage is shown. Moreover, Equation (4) was also proposed, where the porosity term is eliminated. Finally, Figure 8 shows the new correlation between the actual and predicted thermal damage considering temperature, UCS, and tensile strength only.
To sum up, three new equations were proposed to determine TD in granites in this study. The main difference is that the new equations do not contain the P-wave velocity parameter as in Equation (1). Figure 3 shows the good correlation between the predicted thermal damage using Equation (1) and tensile strength. However, tensile strength data in the graph are clustered into 4–5 groups (not continuous); therefore, it alone cannot be used to determine the TD of rocks. Figure 4, Figure 7 and Figure 8 show the correlation between the actual and predicted thermal damage based on Equations (2)–(4), respectively. Based on the order of importance of the TD input parameters shown in Figure 6, Equation (3) is better suited to determine the TD. The novelty of this work is the ability to determine the TD at high temperatures by using temperature, porosity, UCS, and tensile strength data, These findings can be very helpful in geothermal energy extraction, deep mining, and nuclear waste disposal applications where rock is exposed to very high temperatures.
As limitations of this work, the samples in the published literature were heated at different heating rates and then cooled either in an oven or in the open air. The duration of the heating process ranged from half an hour to 24 h. Therefore, variations in the heating rate, heating time, and cooling method could affect the test outcomes. Also, the diversity of the collected data could be an issue. Since the experiments were conducted in different environments, the experimental results could be inconsistent. These shortcomings of the present study can be eliminated either by adding more data, including data related to other rock types, to the dataset or by selecting the data from studies with a similar methodology. As a recommendation, other tests, including heat conductivity, specific heat capacity, thermal diffusivity, and thermal expansion, might yield insightful results and should be the focus of further investigations. Despite these limitations, the current study has elaborated on existing data, leveraging machine learning algorithms to establish a comprehensive thermal damage model.

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 °C; however, intergranular cracks appear between quartz–quartz, quartz–feldspar, and biotite–feldspar at 400 °C, and additional intergranular and intragranular cracks involving biotite, quartz, and feldspar emerge at 600 °C.
(2)
Based on the observed cracking behavior, three temperature zones have been identified: up to 200 °C, between 200 °C and 600 °C, and above 600 °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 °C to 800 °C.
(4)
Two distinct zones of property change were noted: minimal changes occurred up to 600 °C, while significant changes were observed between 600 °C and 800 °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.
(8)
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 °C, using a globally sourced dataset.

Supplementary Materials

The following supporting information can be downloaded at https://www.mdpi.com/article/10.3390/app15116328/s1, Table S1: Thermal damage raw dataset. References [1,4,10,17,18,19,20,21,22,23,24,26,28,29,32,34,35,36,37,38,39,40,46,47,48,49,50,51,52,53,54,55,56,57,58] are cited in the supplementary materials.

Author Contributions

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.

Funding

This research received no external funding.

Institutional Review Board Statement

Not applicable.

Informed Consent Statement

Not applicable.

Data Availability Statement

The original contributions presented in this study are included in the article/Supplementary Materials. Further inquiries can be directed to the corresponding author.

Acknowledgments

The authors wish to acknowledge the contributions of the anonymous reviewers.

Conflicts of Interest

The authors declare no conflicts of interest.

Abbreviations

The following abbreviations are used in this manuscript:
SEMScanning electron 57 microscopy
CTX-ray microcomputed tomography
PMPolarizing microscope
NMRNuclear magnetic resonance imaging
AEAcoustic emission
TGAThermogravimetric 61 analyses
DSCDifferential scanning calorimetry
XRDX-ray diffraction
MIMultiple imputation
TDThermal damage
UCSUnconfined compressive strength

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Figure 1. SEM images of heat-treated granites with intergranular cracks highlighted in red [32].
Figure 1. SEM images of heat-treated granites with intergranular cracks highlighted in red [32].
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Figure 2. The effect of temperature on the physical and mechanical properties: (a) porosity; (b) density; (c) P-wave velocity; (d) UCS; (e) tensile strength; (f) elastic modulus.
Figure 2. The effect of temperature on the physical and mechanical properties: (a) porosity; (b) density; (c) P-wave velocity; (d) UCS; (e) tensile strength; (f) elastic modulus.
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Figure 3. The correlation between the predicted thermal damage (TDin) and (a) P-wave velocity and (b) tensile strength.
Figure 3. The correlation between the predicted thermal damage (TDin) and (a) P-wave velocity and (b) tensile strength.
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Figure 4. The correlation between the actual and predicted thermal damage.
Figure 4. The correlation between the actual and predicted thermal damage.
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Figure 5. The correlation between the actual and predicted TD of the best predictive models: (a) Ensemble Bagged Trees model; (b) Regression Tree (Fine tree) model; (c) Gaussian Process Regression model.
Figure 5. The correlation between the actual and predicted TD of the best predictive models: (a) Ensemble Bagged Trees model; (b) Regression Tree (Fine tree) model; (c) Gaussian Process Regression model.
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Figure 6. The order of importance of the TD input parameters.
Figure 6. The order of importance of the TD input parameters.
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Figure 7. The updated correlation between the actual and predicted thermal damage.
Figure 7. The updated correlation between the actual and predicted thermal damage.
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Figure 8. The updated correlation between the actual and predicted thermal damage considering temperature, UCS, and tensile strength only.
Figure 8. The updated correlation between the actual and predicted thermal damage considering temperature, UCS, and tensile strength only.
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Table 1. A sample of the dataset.
Table 1. A sample of the dataset.
Temp, °CFeldspar Content,
%		Quartz Content,
%		Biotite Content,
%		Other Minerals,
%		Elastic Modulus, GPaPorosity, %Density g/cm3UCS, MPaTensile Strength, MPaP-Wave Velocity, km/s
25504055NA0.22.63NA9.034.71
10075205012.96NA2.64134.17.624.04
20072.2111.8915.9022.25NANA149NA3.57
30059.8511.1221.567.4711.120.682.63102.0459.853.52
40083.519.0407.457.36NANA72.514.853.03
50060.5934.095.32020.51.43NA187NA3.09
60063.5927.724.943.755.69NA2.6154.881.51NA
70029501561.82NANA22.438.69NA
80048.3441.784.295.396.96NA2.4938.07NA0.49
Table 2. The development of intergranular cracks due to temperature.
Table 2. The development of intergranular cracks due to temperature.
Temperature (°C)The Neighboring Minerals
Quartz and QuartzQuartz and BiotiteQuartz and FeldsparBiotite and Feldspar
25No intergranular cracks in the mineral boundaries
200Crack initiationNo crack initiationCrack initiationNo crack initiation
400The intergranular cracks occur between two quartz mineralsNo intergranular cracks in the mineral boundariesThe intergranular cracks occur between quartz and feldspar mineralsThe intergranular cracks occur between biotite and feldspar minerals
600Widening of the intergranular cracks in quartz mineralsThe intergranular cracks occur between quartz and biotite mineralsWidening of the intergranular cracks between quartz and feldspar mineralsWidening of the intergranular cracks between biotite and feldspar minerals
800Intergranular cracks fully developed with large apertures.
Table 3. The development of intragranular cracks due to temperature.
Table 3. The development of intragranular cracks due to temperature.
Temperature
(°C)		Mineral
QuartzFeldsparBiotite
200No intragranular cracks
400Intragranular cracks are initiated in large quartz minerals (crystals > 0.5 mm)Intragranular cracks are initiated in feldspar mineralsAlmost intact
600Widening of the intragranular cracks in quartz mineralsWidening of intragranular cracks in feldspar grainsInitiation of intragranular cracks in large weak biotite minerals (parallel to the grain boundaries and grain boundary cracks)
800Macroscopic intragranular cracks with large apertures
Table 4. The performance of the predictive models.
Table 4. The performance of the predictive models.
ModelR2RMSE
Regression Tree (Fine Tree)0.940.0837
Regression Tree (Coarse Tree)0.690.1902
ANN0.890.1110
Gaussian Process Regression0.970.0633
SVM0.950.0790
SVM (Medium Gaussian)0.910.1445
Ensemble Boosted Trees0.950.0741
Ensemble Bagged Trees0.950.0767
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Sansyzbekov, G.; Adoko, A.C.; George, P.M. Thermal Damage Characterization and Modeling in Granite Samples Subjected to Heat Treatment by Leveraging Machine Learning and Experimental Data. Appl. Sci. 2025, 15, 6328. https://doi.org/10.3390/app15116328

AMA Style

Sansyzbekov G, Adoko AC, George PM. Thermal Damage Characterization and Modeling in Granite Samples Subjected to Heat Treatment by Leveraging Machine Learning and Experimental Data. Applied Sciences. 2025; 15(11):6328. https://doi.org/10.3390/app15116328

Chicago/Turabian Style

Sansyzbekov, Gabit, Amoussou Coffi Adoko, and Paul Mathews George. 2025. "Thermal Damage Characterization and Modeling in Granite Samples Subjected to Heat Treatment by Leveraging Machine Learning and Experimental Data" Applied Sciences 15, no. 11: 6328. https://doi.org/10.3390/app15116328

APA Style

Sansyzbekov, G., Adoko, A. C., & George, P. M. (2025). Thermal Damage Characterization and Modeling in Granite Samples Subjected to Heat Treatment by Leveraging Machine Learning and Experimental Data. Applied Sciences, 15(11), 6328. https://doi.org/10.3390/app15116328

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