Study on the thermal damage evolution law of granite considering mesoscopic fabric characteristics

1 Introduction

The mechanical behavior and damage characteristics of granite as an engineering rock material have been extensively investigated. In China, a pilot enhanced geothermal system (EGS) project was launched in the Matouying area of Hebei Province in 2021 (Qi et al., 2024). With the ongoing development of EGS, underground storage, and specialized mineral extraction, thermal damage and crack propagation in granite have become critical considerations in underground engineering.

The mineralogical composition and grain size of granite vary across different regions owing to distinct petrogenetic histories. These variations give rise to pronounced differences in the internal fabric characteristics of granite. Previous experiments have demonstrated that the strength and failure behavior of granite are significantly influenced by its mesoscopic fabric characteristics (Hu et al., 2019; Yan et al., 2024; Li et al., 2024; Wang et al., 2023). In particular, the thermal expansion and contraction of mineral constituents at the mesoscopic level has been identified as the primary mechanism driving thermally induced changes in rock mechanical properties (Liao et al., 2024). While differences in fabric characteristics can, in turn, influence the macroscopic mechanical response of granite. Therefore, investigating the mechanical evolution of thermally damaged granite from the perspective of mesoscopic fabric characteristics is of considerable practical importance.

The mechanical properties of granite are closely related to its mesoscopic fabric; however, experimental results often exhibit considerable scatter in this regard. To clarify this relationship, numerous studies have investigated the correlation between fabric characteristics and strength of granite (Deng et al., 2016; Li et al., 2020). The results indicate that the strength of granite is governed by both grain size and the proportion of minerals with different strengths. Zhang et al. (2022) constructed three models with distinct structural characteristics and conducted uniaxial compression tests. The results showed that the homogenized model failed to adequately reproduce the failure morphology and energy evolution. Furthermore, the granite strength was found to depend on crystal size and the proportion of high-hardness minerals, whereas the stress characteristics exhibited a negative correlation with the heterogeneity factor. Li et al. (2021) employed CT scanning to capture the brittle behavior and mesoscopic failure modes of granite. They further proposed a calibration procedure linking uniaxial mechanical parameters to with mesoscopic parameters. The results indicated that mineral microcrack formation was strongly correlated with crystal boundaries and mineral strength. Guang et al. (2018) refined the characterization of the mesoscopic structure of granite by integrating crystal size, mineral content, and other parameters through a weighted averaging approach to construct a heterogeneity coefficient. They further validated its effectiveness, thereby establishing a quantitative connection between mesoscopic investigations and macroscopic strength in granite. The aforementioned studies have focused on two critical factors in the mesoscopic fabric of granite—mineral content and crystal grain size—that govern variations in its mechanical properties, thereby providing a meso-mechanical theoretical basis for understanding thermal damage in granite.

Laboratory thermal treatment tests remain the primary approach for investigating the thermal damage mechanisms of granite. Numerous studies have employed this method to examine the physical and mechanical properties of granite after high-temperature exposure. Xi et al. (2020), Qin et al. (2020), Wang J. M. et al. (2023) and Xu et al. (2022) investigated physical properties including surface crack distribution, density, porosity, and P-wave velocity, whereas Wang J. M. et al. (2023), Li et al. (2020), Ersoy et al. (2019), Jin et al. (2018) and Zhao et al. (2020) examined mechanical properties such as uniaxial compressive strength, elastic modulus, Poisson’s ratio, and shear strength. These studies confirm that temperature exerts a significant influence on the mechanical properties of crystalline rocks such as granite. To better reflect engineering conditions, several studies have considered damage induced by thermal shock under high-temperature conditions and further investigated the differences among various cooling methods, such as air cooling, water cooling, liquid nitrogen cooling, and carbon dioxide cooling (Shao et al., 2014; Bu et al., 2024; Wu et al., 2019). The results showed that the mechanical properties of granite deteriorated more significantly with increasing cooling rates. Moreover, under a given stable cooling condition, the strength of granite decreased gradually with increasing temperature and exhibited an accelerated decline beyond a certain temperature threshold. However, considerable scatter exists among the reported values of thermal strengthening, temperature thresholds, and strength degradation for different granite types, indicating that the underlying mechanisms require further investigation.

Building on these findings, several studies (Tang et al., 2022; Kang et al., 2021; Zhu et al., 2021) have employed microscopic imaging techniques to investigate the changes in the mesoscopic structure of granite under thermal loading. Scanning electron microscopy (SEM) and optical microscopy were used to observe thermally induced cracks in granite, and differences in crack quantity, width, and length were analyzed, followed by quantitative characterization of the cracks. Other studies (Guo et al., 2023) have utilized CT scanning to examine the crack evolution in granite under high-temperature conditions and have found that the crack content is positively correlated with temperature. Zhao et al. (2008) developed a custom CT testing system and conducted extensive investigations into the mesoscopic characteristics of thermal cracking in granite. The results demonstrated that the mineral grains and cementing materials in granite affect microcrack initiation and propagation, respectively.

The aforementioned studies collectively indicate that the mesoscopic fabric characteristics of granite influence crack development patterns under thermal loading. However, existing thermal damage models have not adequately accounted for the influence of granite fabric characteristics, limiting their applicability to quantitative engineering analysis. Therefore, investigating the damage characteristics under thermal conditions based on mesoscopic fabric parameters of granite is of considerable engineering significance.

2 Theoretical analysis of thermal damage in granite based on mesoscopic fabric characteristics

Rock damage manifests primarily as microcracks generated when internal fabric constituents reach their load-bearing limits. For granite, different minerals exhibit distinct mechanical and thermal properties. Under the combined action of external loading and temperature, microcracks in granite propagate and interact, thereby altering the macroscopic mechanical properties. Therefore, a mesoscopic fabric-based approach is essential for studying thermal damage of granite.

Crystalline rocks such as granite exhibit heterogeneous characteristics over a certain scale. Accordingly, several studies have proposed a polycrystalline damage model based on damage tensor theory for damage analysis (Isaka et al., 2019), as shown in Figure 1.

This theoretical framework quantifies microcrack formation within crystals over a representative volume, where V denotes the volume of the damaged rock, dA _k represents the cavity area of the kth unit cell, and n _*k* is the unit normal vector of that cell. For a single crack void, the analysis can be conducted by treating it as a tetrahedron O-ABC, as illustrated in Figure 2.

In practice, multiple microcrack tetrahedral cavities form within a given region; therefore, the overall damage can be expressed as Equation 1 (Zhang, 2018):

Ω = 3 S V ∑ k = 1 N ∫ V n k ⊗ n k d A k (1)

As can be seen from the damage tensor formula in Equation 1, the thermal damage tensor is formulated analytically on the basis of crack cavity volume. However, it is impractical to quantify every crack cavity parameter precisely in practice; solutions are therefore generally obtained through equivalent-component or energy-inversion schemes. Damage, in turn, is manifested as microcracks formed by the volume changes of rock constituents under temperature effects, as shown in Figure 3. In this context, volume V and volume change dV serve as key parameters for characterizing damage.

Cracks associated with different minerals in granite differ in both scale and density, owing to differences in the thermal expansion characteristics of individual minerals; consequently, calculating damage using an averaging scheme would introduce errors. It is therefore preferable to construct a damage calculation model that accounts separately for damage in each mineral constituent, based on volume-change characteristics.

In experimental investigations, the temperature-induced volumetric change of rock is generally expressed by Equation 2 (Lin, 1991):where β denotes the volumetric thermal expansion coefficient and T represents the temperature.

β = 1 V ∂ V ∂ T (2)

For a given mineral, the temperature-induced volume change dV can be expressed by Equation 3.where V denotes the original volume of a certain mineral.

d V = β · V · d T (3)

Based on the damage principle and the tensor model, it follows that the volume change of a given mineral is correlated with its damage. A function f can be constructed to characterize this variation, thereby introducing the multi-mineral fabric damage parameter ω of granite, as given in Equation 4.where dV _*i* (i = 1, 2, … , n) is the volume change of mineral component i in the granite, V is the calculated volume of the granite, and f is the functional relationship between the volume-change rate and the damage parameter ω.

ω = ∑ i = 1 n f · d V i V (4)

Substituting Equation 3 into Equation 4 yields Equation 5.

ω = ∑ i = 1 n f · β i · V i · d T V (5)

Based on the effective load-bearing area theory and the equivalent strain theory, the key to damage lies in the density and scale of microcracks, and variations in rock modulus are generally the primary means of evaluating macroscopic damage, as expressed in Equation 6.

D = E − E * E (6)

It is well known that the change in the macroscopic modulus E of a material results from the development of mesoscopic microcracks induced by deformation of internal crystals. Hence, the damage variable can be expressed equivalently as D = aω, where a is the equivalent parameter. Because f has the same functional form for each mineral during the solution process, substituting this into Equation 5 allows f and a to be combined into f ^*, as shown in Equation 7.

D = a · ω = f * ∑ i = 1 n β i · V i · d T V (7)

At this stage, once β _*i* and V _*i* are determined, experiments can be conducted to determine D under different temperature conditions, thereby establishing the relationship between damage and volume variables mediated by f ^*, accounting for polycrystalline characteristics.

3 Thermal damage tests on granite with different fabrics

Accurately characterizing the thermal damage behavior of granite is essential in engineering practice. The foregoing theoretical analysis suggests that the damage constitutive relationship of multimineral granite can be determined from a mesoscopic perspective based on variations in the elastic modulus E obtained from damage tests. To further investigate the relationship between microcrack damage and macroscopic mechanical properties, thermal damage tests were conducted on granite specimens with distinct fabrics from different regions.

3.1 Specimen preparation and calibration

Raw granite blocks were collected from three regions in China: Pingjiang (Hunan Province), Changsha (Hunan Province), and Suizhou (Hubei Province). During coring, the integrity of the rock blocks was preserved to ensure that the grain size variability of the specimens met the experimental requirements. The cores obtained from each source were grouped as a single test group and labeled. Each group comprised 31 specimens: 30 test specimens and one reserved non-test specimen. Figure 4a shows the rock coring machine, and Figures 4b–d show the prepared specimens from the granites of each region, respectively.

Following the ISRM suggested methods, cylindrical specimens with dimensions of Φ50 mm × 100 mm were prepared. The end surfaces were machined to a flatness tolerance of no more than 0.05 mm.

The grain characteristics of the granites were observed and measured using an optical microscope equipped with a CCD camera. Twenty fields of view were randomly selected from each granite source for grain size measurement. Distinct differences in grain size were observed among the three sources. The mean grain areas were 0.7837 mm², 1.6894 mm², and 2.3314 mm², respectively. Accordingly, the granite specimens were classified by grain size as fine-grained, medium-grained, and coarse-grained, as shown in Figure 5.

3.2 Thermal testing and microcrack propagation measurement of granite

The thermal damage tests required clear definition of the heating mode and temperature level. To reflect actual engineering conditions, a slow heating–rapid cooling scheme was adopted. The heating procedure started from room temperature with a temperature increment of 20 °C per step; the specimens were held for 5 min after each increment and for 120 min after reaching the target temperature. A YTH-4–10 resistance muffle furnace was used for heating. The cooling method was room-temperature water cooling: the specimens were removed from the furnace, placed in a cooling cylinder, and cooled by flowing water at 25 °C until their temperature dropped to 25 °C, after which they were transferred to a curing box for drying. To minimize potential confounding factors and isolate the temperature effect, identical heating and cooling procedures were used for all test groups. In engineering practice, the temperature of hot dry rock masses is generally below 500 °C; however, with advances in deep underground engineering, projects involving hot dry rock may encounter rock masses at higher temperatures. Meanwhile, lower temperatures can hardly induce noticeable damage in rock, so the rock mass remains stable in the short term. Accordingly, temperature levels of 200, 300, 400, 500, and 600 °C were selected, with a control group kept at room temperature (25 °C). The temperature test procedure is shown in Figure 6.

The microcracks generated within the granite specimens after thermal testing are the primary manifestation of macroscopic damage. Surface microscopic observation and nuclear magnetic resonance (NMR) detection were employed to measure the density and scale of microcracks in the specimens, thereby enabling further analysis of the crack distribution characteristics.

Surface microcracks in granite specimens under different temperature conditions were recorded and are presented in Figure 7. As shown in Figure 7, the surface crack density in granite increased continuously with increasing temperature. At 400 °C, open cracks became observable under the microscope for the first time. At 600 °C, intersecting cracks extending along both transverse and longitudinal directions developed on the specimen surfaces, indicating significant structural displacement within the specimens.

NMR detects water-bearing cracks by measuring the relaxation signals of hydrogen nuclei under an applied magnetic field. The relaxation time T _*d* reflects the pore size, whereas the signal intensity T _*n* indicates the pore content. After thermal treatment, a miniMR-150 low-field NMR instrument (Figure 8) was employed to measure the distribution of water-bearing cracks in the specimens. The results were presented in the form of T₂ spectra.

The NMR test data for the granites were compiled. The results for all grain sizes showed similar variation trends, with the effect being most pronounced in coarse-grained granite. Based on the correspondence between relaxation time Td and crack scale, pores with a relaxation time of 10 m (i.e., a crack scale of 10 μm) were classified as micropores; those with relaxation times of 10–100 m (i.e., 10–100 μm) were classified as medium pores; and those with relaxation times greater than 100 m were classified as large interconnected pores Figure 9 was then plotted using the NMR data for coarse-grained granite. The internal cracks in granite expanded continuously with increasing temperature. At 200 °C, the signal peak was located in the medium-pore range, indicating that no significant crack propagation had occurred within the specimen at this stage. Between 300 °C and 600 °C, the signal peak shifted toward the large-pore range, suggesting that the internal pores had undergone marked expansion over this temperature interval. At 600 °C, the micropores underwent substantial expansion, while the larger pores exhibited a dramatic increase in volume, indicating that the specimen interior had reached an extensively cracked state. Notably, the phase transition temperature of quartz—the dominant mineral constituent in granite—is 573 °C, which may be a key factor responsible for the accelerated crack expansion under high-temperature conditions.

3.3 Mechanical properties testing of granite under different thermal conditions

The macroscopic mechanical properties of granite are critical to engineering stability and are closely related to the measured mesoscopic parameters. To investigate this relationship, mechanical tests were conducted on granite specimens under different temperature conditions. The testing apparatus is shown in Figure 10 Uniaxial compression tests were performed using a servo-controlled testing machine under force-controlled loading; external sensors were used to monitor strain and other relevant parameters. Each temperature group consisted of five specimens. After excluding outliers, the remaining results were averaged, and the average values are presented in Table 1.

TABLE 1. Test results of granite’s ultimate load under different temperature conditions (MPa).

The test results indicate that the ultimate strength of the specimens decreased progressively with increasing temperature. A further comparison of the failure modes of coarse-grained granite is presented in Figure 11 At 600 °C, the specimen exhibited a certain degree of plastic deformation upon reaching the ultimate load, and its strength was only 57.9% of that at 200 °C.

A comparison of the failure modes under different temperature conditions reveals the following characteristics. Between 200 °C and 300 °C, relatively distinct through-going cracks were observed in the specimens, indicating that the internal structure remained relatively stable, with few microcracks and was capable of storing a certain amount of elastic potential energy. From 400 °C to 500 °C, the specimens exhibited pronounced spalling, indicating extensive microcrack propagation and partial disaggregation of the internal structure. At 600 °C, extensive collapse occurred upon failure, accompanied by a rapid decline in load-bearing capacity. This indicates that the internal structure of the granite could no longer maintain its original stability.

3.4 Analysis of macroscopic and mesoscopic damage mechanisms

The development and propagation of microcracks give rise to rock damage at the macroscopic scale. However, this process is difficult to quantify experimentally. Numerous studies have proposed the damage variable D, calculated from the elastic modulus E, as a parameter that effectively characterizes the internal damage state of rock in engineering applications. Accordingly, the elastic modulus of granite specimens under different thermal conditions was calculated, and the results are presented in Table 2.

TABLE 2. Elastic modulus results of granite under different temperature conditions (GPa).

The theoretical analysis and experimental results collectively indicate that the formation of mesoscopic microcracks constitutes the essence of macroscopic damage. Because the mesoscopic and macroscopic damage calculations yield consistent expressions in the experiments, the macroscopic damage variable D and the mesoscopic thermal damage parameter ω can be determined in a unified manner by substituting the elastic modulus E into Equation 6.

To further solve for f ^*** in Equation 7 and establish the relationship between mesoscopic structural damage and fabric characteristics, the parameters β _*j* and V _*i* must first be determined. Microscopic observations were conducted on the granite specimens, and the mineral composition proportions of each granite type were obtained using a mineral image recognition technique (Dai et al., 2026), as listed in Table 3.

TABLE 3. Mineral proportions of different granites.

Thermal expansion coefficients for feldspar, quartz, and biotite were taken from the literature (Guo et al., 2023; Zhao, 2016; Hu et al., 2023; Yin et al., 2022) as 8 × 10⁻⁶/°C, 11.5 × 10⁻⁶/°C, and 6.5 × 10⁻⁶/°C, respectively. Substituting these into the calculation yielded the f ^*values at temperatures of 200 °C–600 °C, as presented in Table 4.

TABLE 4. Calculated f ^* values under different temperature conditions.

The variation in f ^***indicates that the correspondence between structural characteristics and damage parameters varies continuously with both temperature and crystal size. Accordingly, f ^***can be regarded as a function of temperature and grain size. Based on the observed data trends, a nonlinear fitting approach was adopted to process the results, as illustrated in Figure 12.

As shown in Figure 12 the multi-component thermal parameter f ^*** of granite with the three grain sizes exhibited an increasing trend with increasing temperature, and the growth rate progressively accelerated. This indicates that temperature is the key variable governing damage development. Meanwhile, f ^*** increased with grain size across all temperatures.

ω = 23.98 + 0.00000334 T 2.69 ∑ i = 1 n β i V i · d T C o a r s e − g r a i n e d ω = 13.95 + 0.000126 T 2.17 ∑ i = 1 n β i V i · d T M e d i u m − g r a i n e d ω = 7.38 + 0.000184 T 2.13 ∑ i = 1 n β i V i · d T F i n e − g r a i n e d (8)

Substituting f ^*** into Equation 7 yields the thermal damage calculation formula for granite, expressed as Equation 8, which can be used to determine thermal damage in granite under different conditions.

4 Numerical simulation of thermal damage in granite

Numerical methods have been widely applied in geotechnical engineering in recent years and serve as an important complement to traditional experimental investigations. These methods offer substantial advantages in theoretical analysis and visualization, enabling direct observation of microcrack propagation processes. To validate the theoretical damage law derived from mesoscopic fabric characteristics and to further explore the thermal damage mechanisms and evolution of granite, numerical simulations were conducted using the mesoscopic particle flow discrete element method (DEM).

4.1 Construction of the thermal damage numerical model

In constructing the numerical model, the widely recognized grain-based model (GBM) method was adopted to generate granite crystal models with controlled crystal variations (Xu et al., 2018; Liu et al., 2020; Liu and Cai, 2020). Based on the crystal sizes observed microscopically and the laboratory mechanical test results, the crystal framework was filled with base particles 0.15 mm in diameter, striking a balance between model fidelity and computational efficiency. For the mineral crystals, mean crystal areas were set to 0.78 mm², 1.69 mm², and 2.4 mm², respectively, and the crystal size distribution was adjusted using a heterogeneity coefficient, as shown in Figure 13. Finally, the model parameters were determined through trial-and-error calibration. In the temperature numerical tests, the thermal loading in the experiments was simulated using a temperature–volume model coupled with a thermo-mechanical conversion model. The modeling workflow and mesoscopic parameters are as follows: Table 5.

• Identify the crystal characteristics on the granite surface and determine the mineral composition and distribution patterns accordingly.
• Construct the crystal boundary model and generate the different mineral constituents within the granite, as shown in Figure 13.
• Assign the mesoscopic parameters of the granite crystals and crystal boundaries.
• Verify the macroscopic mechanical properties of the model and calibrate the mesoscopic parameters.
• Import the thermo-mechanical coupling model and assign the corresponding parameters, as listed in.
• Configure the temperature conduction model for the granite specimen.

TABLE 5. PFC mesoscopic parameters.

The principle of particle-scale thermal action is illustrated in Figure 13 where Δr is the change in particle radius due to temperature effects, and ΔF _*n* is the force generated by the particle volume change under the thermal effects. To replicate water cooling, a temperature module was first added to the model so that the particles were assigned a temperature attribute and temperature transfer was implemented based on the contact model. The laboratory tests all adopted external heating and cooling. Correspondingly, in the numerical tests, a layer of particles capable of maintaining a fixed temperature was placed on the outermost surface of the specimen, through which temperature was transferred toward the interior, with the temperature transfer parameters set accordingly. For the water-cooling test, the boundary temperature particles were set to 25 °C, thereby achieving heat transfer and cooling.

4.2 Numerical tests on granite based on fabric characteristics

The crystal fabric characteristics of granite are a key factor governing its damage and were therefore explicitly incorporated into both the model construction and numerical testing procedures. Based on the laboratory test results, three numerical models with coarse, medium, and fine crystal features were constructed, and their mesoscopic parameters were calibrated to reproduce the experimental macroscopic strength values. The uniaxial compressive strength of the numerical specimens is presented in Figure 14.

The thermal numerical test protocol was consistent with the laboratory test scheme, with temperature levels set at 200, 300, 400, 500, and 600 °C. The specimens were slowly heated to the target temperature and held for 20 min, followed by rapid cooling to room temperature (25 °C) via thermal conduction. Crack statistics were collected from the specimens after thermal treatment, and the results are presented in Figure 15.

4.3 Damage calculation and analysis of granite with different fabric characteristics

Numerical methods provide an effective means of monitoring the development of microcracks within granite. At the mesoscopic level, microcracks essentially serve as the fundamental units of damage quantification. Therefore, the microcracks generated by temperature variations can be regarded as a direct measure of the damage incurred by the specimen. Accordingly, the ratio of newly generated cracks to the total number of bonds is defined as the microcrack damage in the numerical test. By comparing this value with the damage calculated from the macroscopic modulus and that predicted by the theoretical formula, the law governing thermal damage evolution can be further clarified. The results are presented in Figure 16.

A comparison of the damage results obtained using different methods reveals consistent variation trends across all approaches. This indicates that the theoretically calculated damage parameters provide a meaningful reference and can be used to reasonably estimate thermal damage in granite. The damage parameter increased progressively with increasing temperature, and its growth accelerated when the temperature exceeded 400 °C. The damage growth rate of coarse-grained granite was slightly higher than that of medium- and fine-grained granite, suggesting that larger crystal sizes promote microcrack expansion under thermal loading.

A comparison among the three damage calculation methods shows that, for medium- and fine-grained granite, the microcrack damage obtained from numerical tests differed from the modulus-based damage and the theoretically predicted damage. This indicates that when the crystal size is relatively small, the formation of microcrack damage additionally affects the stability of the surrounding crystals. From a mesoscopic perspective, smaller crystals may undergo dislocation along the expanding microcracks, thereby reducing the overall stability of the specimen.

5 Conclusion

This study investigated the thermal damage behavior of granite in relation to its mesoscopic fabric characteristics through theoretical analysis, laboratory tests, and numerical simulations. The main conclusions are as follows.

• The microcracks induced by thermal shock differ among the various minerals contained in granite. The microcracks developed continuously with increasing temperature, forming macroscopic cracks at 400°C–600 °C and propagating primarily along crystal boundaries.
• The damage law of granite is influenced by its mesoscopic crystal size. Based on theoretical derivation and the laboratory test data, the thermal damage characteristic function f ^*** of each mineral in granite can be determined, and this function follows a power-law relationship with temperature.
• The GBM approach coupled with the thermo-mechanical model can effectively simulate the mesoscopic characteristics and thermal response of granite. The numerical tests demonstrate that variations in mineral composition give rise to microcracks with distinct characteristics, and the resulting damage law is similar to the macroscopic modulus damage law. When the crystal size of granite is small, the microcracks may induce a greater damage effect.

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Footnotes

Edited by: Wenling Tian, China University of Mining and Technology, China

Reviewed by: Mohua Bu, China University of Mining and Technology, Beijing, China

Maoqi Liu, Hunan University of Science and Technology, China