Open AccessArticle Study on the Energy Evolution Law of Sandstone and Its Implications for Rockburst Prevention Considering Particle Effect Under Thermal Action 1 State Key Laboratory of Geohazard Prevention and Geoenvironment Protection, Chengdu University of Technology, Chengdu 610059, China 2 School of Emergency Management, Xihua University, Chengdu 610039, China 3 Key Laboratory of Landslide Risk Early-Warning and Control, Ministry of Emergency Management, Chengdu University of Technology, Chengdu 610059, China * Author to whom correspondence should be addressed. Appl. Sci. 2026, 16(12), 5813; https://doi.org/10.3390/app16125813 (registering DOI) Submission received: 25 April 2026 / Revised: 28 May 2026 / Accepted: 2 June 2026 / Published: 9 June 2026 Abstract Rockburst is one of the major geological hazards in the construction of deep-buried and high-geotemperature tunnels. Using triaxial compression tests and acoustic emission (AE) techniques, this paper conducts a preliminary exploratory investigation on the deformation and failure characteristics, mechanical parameters, acoustic emission responses and energy evolution laws of typical rockburst-prone rocks under confining pressures of 10–30 MPa and temperatures of 100–250 °C. The results show that within the research scope, sandstone exhibits brittle characteristics including compaction, linear elasticity, crack initiation and propagation, stable crack propagation stage, accelerated crack propagation stage, and stress drop stage. Within a certain range, peak strength and damage strength increase with the rise in confining pressure and temperature. The elastic modulus increases with rising confining pressure. The damage point may be the critical point of energy conversion and acoustic emission activity. After damage, the work done by external forces is mainly converted into dissipated energy. With the intensification of surrounding rock damage, the ratio of elastic strain energy to total energy gradually decreases, while the ratio of dissipated energy to total energy gradually increases. Acoustic emission activity increases significantly at the damage point and reaches its peak at the peak strength. The cumulative acoustic emission ring count and cumulative energy increase slowly before the peak and grow rapidly after the peak. Under thermo-mechanical action, new cracks in sandstone preferentially initiate along grain boundaries, and the inconsistent deformation between grains will promote the formation of transgranular cracks. The connection, convergence and final penetration of cracks lead to sample failure. The elevation of temperature and confining pressure can enhance the bearing capacity of sandstone, indicating that a high-temperature and high-stress environment may be conducive to the occurrence of rockbursts. The research results provide scientific support for an in-depth understanding of the mechanical behavior and instability risk of rockburst in deep-buried and high-geotemperature tunnels, and can provide a theoretical basis for rockburst prevention and control of high-geotemperature tunnels of the CZ Railway. Keywords: sandstone; energy evolution; particle effect; triaxial compression test; rockburst 1. Introduction With the rapid advancement of deep underground space development, the risk of rockburst in deep-buried tunnels under high-geotemperature and high-stress environments has increased significantly [ 1]. As a typical high in situ stress geological hazard, rockburst is accompanied by the release of intense energy, posing a serious threat to tunnel construction safety. According to the definition of rockburst disaster, its essence is a phenomenon in which the surrounding rock releases accumulated elastic strain energy, leading to sudden damage and ejection of the rock mass [ 2]. The surrounding rock of deep-buried tunnels is often in a three-dimensional unequal stress state, and high geotemperature environments are widely present in deep structural zones and high geothermal flux areas. The mechanical behavior of rock masses under such thermal environments is extremely complex. High-geotemperature tunnels are generally divided into dry-heat and wet-heat environments. A large number of engineering cases have revealed that under dry-heat environments, adverse phenomena such as spalling and cracking of sandstone tunnel surrounding rock and initial support are prominent ( Figure 1a,b). Sandstone is a typical sedimentary rock widely distributed on land and seabed, composed of quartz, feldspar and other fine-grained minerals, with grains generally ranging from 0.063 to 2 mm. The connection and structural characteristics between these grains endow sandstone with a certain degree of strength and stability, forming unique brittle fracture and energy evolution characteristics. Its special structure and texture make it prone to disasters such as collapse and rockburst in deep tunnel engineering ( Figure 1c,d) [ 3, 4]. For example, in the YK53+908–YK53+912 section of Gaoloushan Tunnel on WJ Expressway, a blasting-induced impact rockburst occurred in the sandstone stratum ( Figure 1d). After the blasting, clear rock fracture sounds were heard, followed by large-area ejection and collapse at the vault and the haunches on both sides [ 4]. Therefore, understanding the mechanical characteristics, energy evolution law and particle effect of sandstone under dry-heat environments is very important for predicting and preventing rockbursts in deep-buried and high-geotemperature tunnels. Numerous experimental studies have shown that high temperature exerts a significant influence on the mechanical parameters of sandstone, such as elastic modulus, strength, and peak strain. After high-temperature treatment or under real high-temperature conditions, the elastic modulus of sandstone generally tends to increase initially and then decrease with a further rise in temperature, which is related to microscopic mechanisms such as pore closure/propagation and thermal expansion of minerals [ 5]. In high-temperature triaxial tests, the variation relationship between elastic modulus and temperature also depends on the confining condition and temperature range [ 6]. Further in situ high-temperature triaxial compression tests have shown that under high-temperature conditions, the changes in sandstone parameters such as peak strength, elastic modulus, and Poisson’s ratio with temperature and confining pressure have complex nonlinear relationships [ 7]. In real high-temperature environments, the increase in temperature is usually accompanied by thermal damage and physical structure changes, which in turn lead to the transformation of elastic parameters and failure modes [ 8]. Traditional uniaxial tests cannot fully simulate the three-dimensional stress state of real underground surrounding rock, while triaxial tests can more truly reflect the mechanical response of deep rock masses under in situ stress conditions, including indicators such as peak strength, fracture angle, and deformation modulus [ 9]. True triaxial tests have shown that under the coupling effect of high temperature and high in situ stress, both the shear failure and brittle failure modes of sandstone are significantly affected, and the temperature and normal stress jointly determine the critical failure conditions. In addition, triaxial cyclic loading/unloading tests have revealed that under different intermediate principal stress conditions, the energy absorption and dissipation behaviors of sandstone show complex changes, reflecting the energy evolution law of microcrack initiation, propagation, connection and macroscopic failure [ 10]. Although numerous studies have explored the mechanical parameters, elastic modulus and failure modes of rocks under high-temperature and high-stress conditions, most of them focus on the high-temperature range from room temperature to 600–1000 °C. Relatively few investigations have been carried out on small-gradient temperature differences within the engineering temperature range (room temperature to 250 °C), and studies concerning the temperature effect on rockbursts are even more scarce. Therefore, based on triaxial loading tests, this paper firstly studies the mechanical behaviors, AE energy evolution, particle effects and thermal effects of sandstone in dry thermal environments. Then, it was found that an increase in temperature and confining pressure could enhance the bearing capacity of sandstone, indicating that a high-temperature and high-pressure environment might be conducive to the occurrence of rockbursts. 2. Test Introduction 2.1. Test Apparatus The tests were carried out using the IRSM-THM-1500 multi-field coupling testing system ( Figure 2) from the Experimental Center of the School of Emergency Management, Xihua University. The IRSM-THM-1500 testing equipment was developed by the Institute of Rock and Soil Mechanics, Chinese Academy of Sciences, Wuhan, China. This apparatus can perform mechanical tests on rock specimens under thermo-hydro-mechanical (THM) coupling conditions, including uniaxial compression, triaxial compression, creep, and stress relaxation tests. The system has a frame stiffness of 8 MN/mm, a maximum axial load of 150 tons, a maximum confining pressure of 60 MPa, and an operating temperature range from room temperature to 95 °C. The test system is equipped with a muffle furnace and acoustic emission (AE) equipment, enabling real-time monitoring of acoustic emission signals during the tests. 4. Energy Evolution Law Energy dissipation occurs during the initiation, propagation, coalescence and slip of rock cracks in the failure process. Energy dissipation reflects the process of rock damage and degradation, and the essence of rock deformation and failure under loading is a process of energy dissipation. In this experiment, the sandstone specimens were first heated, then naturally cooled, and finally subjected to triaxial compression tests after cooling. Considering the deformation of rocks during triaxial compression, this process is assumed to be a closed system without heat exchange with the external environment. According to the first law of thermodynamics: U = Ud + Ue + U0 (1) where U is the total energy. Ud is dissipation energy. Ue is elastic strain energy. U0 is the work done by the initial confining pressure on the sample at the beginning of the test. The total energy U and the Ue elastic strain energy of rock can be calculated by the following formula: U = ∫ σ 1 d ε 1 + 2 ∫ σ 3 d ε 3 + U 0 (2) U 0 = 3 ( 1 − 2 μ ) 2 E 0 ( σ 3 0 ) 2 (3) U e = 1 2 E u [ σ 1 2 + 2 σ 3 2 − 2 μ ( 2 σ 1 σ 3 + σ 3 2 ) ] (4) where E0 and μ are the initial elastic modulus and initial Poisson’s ratio of rock. Eu and μ are the unloading elastic modulus of rock and Poisson’s ratio at unloading. σ 3 0 is the initial confining pressure value. The statistical analysis of energy at the initial stage, damage stage, peak stage and residual stage of rock was carried out, and the results are shown in Figure 8. As shown in Figure 8, the elastic strain energy is greater than the dissipated energy at the initial and damage stages. However, the dissipated energy is larger than the elastic strain energy at the peak and residual stages. This indicates that before damage, the work done by external forces is mainly converted into elastic strain energy, whereas after damage, it is primarily transformed into dissipated energy. The total energy exhibits an increasing trend throughout the entire process, with a relatively large increment before the damage point and a smaller increment after damage. At the initial stage, all specimens possess a certain amount of dissipated energy, accounting for 0.05–18.80% of the total energy, which is mainly related to the inherent properties of the sandstone specimens. As mentioned previously, the strength of the sandstone specimens in this study is relatively low, with peak strength ranging from 19.7 MPa to 22.46 MPa under confining pressures of 10–30 MPa. Therefore, prior to axial loading, microcracks may have occurred in weaker zones inside the specimens, leading to a certain amount of energy consumption. Similarly, at the residual stage, all specimens retain a considerable amount of elastic strain energy, accounting for 10.93–42.95% of the total energy. Such a relatively high proportion is mainly attributed to the confining pressure. Even after failure, the specimen remains in a compressed state due to confining pressure, with a certain amount of elastic strain energy still stored inside. By comparing the ratio curves of elastic strain energy to total energy, it can be found that with the increase in stress and the progressive deterioration of the specimen, the ratio of elastic strain energy to total energy decreases continuously. In contrast, the ratio of dissipated energy to total energy increases gradually. To further analyze the effects of confining pressure and temperature on the energy evolution law, the energy values at the damage point and peak point were selected for in-depth analysis, and the results are shown in Figure 9. As shown in Figure 9a, the total energy, elastic strain energy and dissipated energy exhibit the same variation trend with increasing confining pressure, characterized by first increasing and then decreasing. At 20 MPa, the total energy, elastic strain energy and dissipated energy all reach their maximum values at both the damage point and the peak point. The maximum total energy at damage is 0.43 MJ/m 3, and that at the peak is 0.56 MJ/m 3. The dispersion of energy data is the largest at 20 MPa and the damage point. At the peak point, the values of dissipated energy and elastic strain energy are close to each other. As shown in Figure 9b, all energy components show similar variation trends with temperature. Energy decreases significantly in the range of 100–150 °C. In the range of 150–180 °C, energy obviously increases, but the increment is smaller than the previous decrement. Energy decreases slightly in the range of 180–250 °C. All energy components reach their minimum values at 150 °C. For example, the total energy at damage is 0.24 MJ/m 3, and that at the peak is 0.37 MJ/m 3. Comparative analysis of energy evolution with confining pressure and temperature shows that the dispersion of elastic strain energy and dissipated energy is relatively small under different temperatures, but larger under different confining pressures. Meanwhile, at the peak point, elastic strain energy and dissipated energy are close in magnitude, while the difference is more significant at the damage point. This indicates that confining pressure and temperature exert different influences on the energy evolution of the specimens at different stages, and the energy response may be more sensitive at the damage stage. 5. Discussion 5.1. Sensitivity Analysis The influence of temperature and confining pressure on the mechanical properties of sandstone is analyzed by means of the sensitivity coefficient. The formula for calculating the sensitivity coefficient is as follows: S = Δ A A ÷ Δ B B (5) where S represents the sensitivity coefficient, ΔA and A denote the variation and original value of the dependent variable, respectively, and ΔB and B denote the variation and original value of the independent variable, respectively. As shown in Figure 10a, significant differences in the mechanical properties of rock are observed when the confining pressure increases from 10 MPa to 20 MPa and 30 MPa. The sensitivity of peak strength to confining pressure increases remarkably with rising confining pressure. When the confining pressure increases from 10 MPa to 20 MPa, the sensitivity coefficient rises significantly from 0.015 to 0.070, representing a 4.7-fold increase. This indicates that within a relatively low confining pressure range, the sandstone strength responds slowly to the increase in confining pressure. However, once the confining pressure exceeds a certain critical value (10 MPa), the sensitivity of rock strength to confining pressure increases sharply, and the strengthening effect of confining pressure becomes prominent. In contrast, the sensitivity of volumetric peak strain to confining pressure is relatively stable. When the confining pressure increases from 10 MPa to 20 MPa and 30 MPa, the sensitivity coefficients are 0.311 and 0.322 respectively, showing only a 3.5% increase. This result suggests that the volumetric deformation of sandstone responds slowly to changes in confining pressure, and the deformation resistance of the rock does not change significantly during the increase in confining pressure but tends to be stable. As shown in Figure 10b, when the temperature increases from 100 °C to 150 °C, 180 °C and 250 °C respectively, various mechanical parameters exhibit different degrees of sensitivity to temperature change. The sensitivity of peak strength to temperature shows a trend of increasing first and then decreasing. When the temperature rises from 100 °C to 180 °C, the sensitivity coefficient increases from 0.246 to 0.390, indicating that the response of sandstone peak strength to temperature change is significantly enhanced within this temperature range. However, when the temperature further rises to 250 °C, the sensitivity coefficient decreases to 0.145, suggesting that beyond a certain temperature threshold, the sensitivity of peak strength to temperature decreases significantly, and the weakening effect of temperature on sandstone strength tends to moderate. The sensitivity of axial peak strain to temperature shows an overall gradual decreasing trend. When the temperature rises to 150 °C and 180 °C, the sensitivity coefficients of axial peak strain are 0.119 and 0.111 respectively, with no obvious change. After further increasing to 250 °C, the sensitivity coefficient drops significantly to 0.033, indicating that the sensitivity of axial deformation to temperature rise is greatly weakened at high temperatures, and the ductile deformation response of sandstone tends to be stable. The sensitivity of volumetric peak strain decreases significantly with increasing temperature. The sensitivity coefficient gradually decreases from 1.310 (100–150 °C) to 0.780 (150–180 °C) and 0.304 (180–250 °C), indicating that with continuous temperature rise, the sensitivity of sandstone volumetric deformation to temperature change is significantly weakened. This reflects that the thermal damage of internal pores and microcracks tends to stabilize gradually at high temperatures, and the volumetric response of the rock structure is gradually reduced. In summary, confining pressure exhibits a significant differential effect on the peak strength and deformability of sandstone, among which the sensitivity of rock strength to confining pressure variation is much higher than that of volumetric deformation. It can be inferred that the strength enhancement effect of sandstone under confining pressure is significantly greater than the improvement of its deformation resistance, and the change in confining pressure has a more prominent influence on sandstone strength. This phenomenon reveals the decisive role of internal crack closure and structural densification of sandstone under confining pressure in determining rock strength. Obvious differences exist in the sensitivity of sandstone peak strength and strain to temperature variation. The sensitivity of peak strength shows a trend of first increasing and then decreasing, whereas the sensitivity of axial and volumetric strains gradually decreases with rising temperature. This characteristic reflects that there exists an obvious thermal damage threshold for rock mechanical properties within a specific temperature range. 5.2. Analysis of the Particle Effect of Sandstone The size of mineral particles and the distribution and arrangement of cementation between mineral particles have an important influence on the rock failure mechanism. Sandstone is mainly cemented by sand grains, and sand grains with different shapes and sizes exert different effects on its fracture behavior. Regarding the particle effect analysis [ 15, 16, 17, 18], Wang et al. (2018) suggested that under the same loading condition, sandstone with a larger particle size is more prone to failure with more intense fracture behavior [ 15]. Wang et al. (2023) pointed out that increasing heterogeneity of mineral elastic modulus leads to unsynchronized damage of adjacent mineral particles, enhancing the nonlinear characteristics of rock deformation [ 16]. The tangential modulus and compressive strength decrease linearly, accompanied by reduced crack initiation stress and damage stress. The macroscopic failure mode transforms from shear failure to splitting failure. However, under the same heterogeneity of mineral elastic modulus, different spatial distributions of mineral particles result in excessive elastic modulus differences between adjacent grains. During compression, incompatible deformation between adjacent particles forms “weak contact surfaces” in mechanical parameters, promoting the initiation, propagation and coalescence of mesoscopic cracks [ 17]. Stage 1: Due to the mechanical property discrepancy between particles and cement, grain interfaces become relatively weak regions. When stress exceeds cementation strength, new cracks preferentially initiate and propagate along grain boundaries. A large number of intergranular cracks form in this stage, with crack networks distributed along grain contours, which macroscopically corresponds to the late period of rock compaction and linear elastic stages. Stage 2: With increasing stress, cracks propagating along grain boundaries gradually coalesce to form localized deformation bands. As the intergranular crack network develops, the stress transfer path reconstructs. Grains in partially high-stress concentration zones bear stress exceeding their inherent strength, driving cracks to extend from grain boundaries into grain interiors, namely the transformation from intergranular failure to transgranular fracture. This stage acts as a critical transition from stable deformation to unstable failure. Macroscopically, the stress–strain curve deviates from linearity, accompanied by prominent nonlinear characteristics and volumetric dilatancy. Stage 3: The full coalescence of intragranular and transgranular cracks eventually forms macroscopic fracture surfaces. The interlocking effect between grains is substantially weakened, leading to a sharp decline in bearing capacity, which corresponds to the stress drop stage macroscopically. 5.3. Thermal Effect The temperature enhancement effect of sandstone is analyzed from the perspectives of thermal strain and negative strain energy. As shown in Figure 13, thermal strain generally rises with increasing temperature. It increases rapidly within 100–180 °C and tends to stabilize at 180–250 °C, indicating thermal expansion of quartz, calcite, plagioclase, clay minerals and other constituents during heating. When thermal stress induced by temperature rise does not exceed intergranular bonding strength, sandstone properties will not degrade. Instead, thermal expansion compresses internal pores and elevates the effective contact degree between mineral particles. Continuous accumulation of negative strain energy can be observed in Figure 14. Such accumulated negative strain energy offsets partial external work under axial loading, thereby boosting bearing capacity and optimizing mechanical properties to a certain extent. 5.4. Statistical Damage Constitutive Model Sandstone contains numerous randomly distributed defects such as pores, microcracks and joints, and thus can be regarded as a porous medium. Affected by pores and other defects, the strength of rock mesoscopic elements presents random variations. The two-parameter Weibull distribution function exhibits superior descriptive capability and can well characterize the variation characteristics of rock element strength. Accordingly, the Weibull distribution is adopted to establish the constitutive model from the perspective of statistical damage. According to damage mechanics, the process of a material from the initiation of damage to failure is continuous. Therefore, it is assumed that the material is composed of isotropic elements that obey the generalized Hooke’s law, and the strength of each element follows the Weibull distribution, whose probability density function P(F) is given by: Density function: F ( k ) = 1 − exp − ( k F ) m (6) where m and f are the shape parameter and scale parameter of the Weibull function, which correspond to the homogeneity and peak strength of concrete, respectively. k represents the strength of rock mesoscopic elements ( k = α 0 I 1 + J 2 ). Under the combined action of temperature and pressure, the meso-elements continue to fracture, resulting in rock damage. Assuming that the number of failed meso-elements is Nf and the total number of meso-elements is N, the statistical damage variable D is defined as: D = Nf/N (7) At the stress level of f( σ), the number of damaged rock elements Nf is: N f = ∫ 0 f σ N f σ d σ = N ∫ 0 f σ f σ d σ (8) Substitute Equation (8) into Equation (7), and the damage variable D is: D = N f / N = N ∫ 0 f σ f σ d σ / N = ∫ 0 f σ f σ d σ = 1 − exp − f σ F m (9) The Drucker–Prager criterion is introduced as the failure criterion, namely: f σ − k = 0 (10) Substituting Equation (10) into Equation (9), and considering σ2 = σ3 in the triaxial test, the constitutive model is expressed as follows: σ 1 = E T ε 1 exp − ( α 0 I 1 + J 2 F ) m + 2 μ σ 3 (11) Substitute the peak point ( ɛc, σc) into Equation (11), yielding: σ c = E T ε c exp − ( α 0 I 1 + J 2 F ) m + 2 μ σ 3 (12) By partially differentiating Equation (12), the first derivative at the peak point is zero. Substitution yields: ∂ σ 1 ∂ ε 1 | ε = ε c = E T exp − ( α 0 I 1 + J 2 F ) m + E T ε c exp − ( α 0 I 1 + J 2 F ) m ୍ଠ − m ( α 0 I 1 + J 2 F ) m − 1 ୍ଠ α 0 σ c + 2 σ 3 E T σ c − 2 μ σ 3 + σ c − σ 3 E T 3 σ c − 2 μ σ 3 F = 0 (13) Rearranging Equations (12) and (13) gives: m = 1 ln E T ε c σ c − 2 μ σ 3 F = α 0 σ c + 2 σ 3 + 3 3 σ c − σ 3 E T ε c σ c − 2 μ σ 3 ln E T ε c σ c − 2 μ σ 3 1 m (14) After parameter solving ( Table 4) (Gao et al., 2018; Zhang et al., 2021; Gao et al., 2024) [ 21, 22, 23], the experimental parameters are substituted into the constitutive equation to obtain the theoretical constitutive curve. The rationality of the constitutive model is verified by comparison with the experimental curves. Figure 15 shows the comparison between the experimental and theoretical results of the stress–strain curves of sandstone. As shown in Figure 15, when the stress–strain curve of the specimen develops from the damage stage to the post-peak stage, the stress growth rate gradually slows down, and the stress drops rapidly after the peak, showing obvious brittle failure characteristics. The theoretical curve and the experimental curve basically coincide with good matching characteristics. It can be seen that the constitutive model established based on statistical damage can accurately describe its damage evolution law and deformation characteristics, and is more consistent with the actual failure law of rock. 5.5. Implications for Rockburst Prevention and Control Many adverse geological problems encountered in tunnel engineering in sandstone strata are closely related to the inherent brittleness of sandstone. As a typical brittle material, sandstone exhibits a Type II failure characteristic in its stress–strain curve ( Figure 16). Rockburst is essentially a catastrophic phenomenon induced by energy evolution during the crack initiation and brittle fracture process of the tunnel surrounding rock. In recent years, with the implementation of a series of major engineering projects in Western China, a large number of deep-buried long and large tunnels have emerged. However, Western China is located in the orogenic belt formed by the compression of the Indian Plate and the Eurasian Plate. The mutual collision and convergence of crustal plates have resulted in a complex continental crustal convergence—a chimeric tectonic setting. In particular, since the Quaternary period, the Y-shaped tectonic belt has been reactivated under the intracontinental collision and compression between the Qinghai–Tibet Plate and the Yangtze Plate, forming a complex geological environment characterized by the coupling of high in situ stress and high geotemperature. Such a complicated geological environment inevitably exerts a significant impact on engineering construction in this region. For example, more than 200 rockbursts of varying intensities occurred successively during the construction of the Erlangshan Tunnel on National Highway 318 ( Figure 17), distributed across 15 sections with a total length of 1776 m. The lithology is dominated by hard and brittle sandstone, sandy mudstone, and quartz sandstone [ 24]. Meanwhile, among the 13 engineering geological rock groups along the under-construction CZ Railway in Western China, as many as seven contain sandstone ( Table 5), indicating its wide distribution and high proportion. At present, investigations into the energy evolution characteristics and fracture mechanism of sandstone under thermo-mechanical coupling can provide effective technical support for the prevention and control of geological hazards such as rockbursts in sandstone strata along the CZ Railway. The study reveals that the increase in confining pressure can significantly enhance the strength properties of sandstone, and temperature rise within a certain range (100–180 °C) can also improve its strength. This indicates that a high-temperature and high-stress environment may be conducive to the occurrence of rockbursts. In the preliminary engineering demonstration stage, sections prone to rockbursts under high ground temperature and high in situ stress should be avoided as far as possible. Meanwhile, during the construction of deeply buried tunnels with high ground temperature, such as the CZ Railway tunnels, it is necessary to reasonably control the stress concentration degree and construction temperature of surrounding rocks. This measure can mitigate thermal shock induced by temperature difference and instability caused by stress concentration, thereby reducing sudden rockburst disasters and corresponding engineering risks. 6. Conclusions In this paper, triaxial compression tests and acoustic emission monitoring were carried out to explore the deformation and failure characteristics, mechanical parameters, acoustic emission features, and energy evolution laws of sandstone under confining pressures of 10–30 MPa and temperatures of 100–250 °C. The sensitivities to confining pressure and temperature, as well as the particle effect, were discussed. A statistical damage constitutive model was established, and implications for rockburst prevention and control in tunnel engineering were revealed. Considering that each parameter combination was only tested once without repeated trials and statistical analysis, the preliminary conclusions are presented as follows: (1) The deformation of sandstone generally exhibits the characteristics of compaction, linear elasticity, crack initiation and propagation, stable crack propagation stage, accelerated crack propagation stage, and stress drop stage. The fracture angle ranges from 60° to 90°, representing typical brittle failure. The peak strength and damage strength increase with the rise in confining pressure and temperature. The elastic modulus increases with increasing confining pressure. (2) It can be inferred from the sandstone test results that the damage point of the rock may serve as the critical point for energy conversion and acoustic emission (AE) activities. After damage, the work done by an external force is mainly converted into dissipated energy. Acoustic emission activities rise markedly at the damage stress and reach the maximum at peak strength. Both cumulative AE ring-down counts and cumulative energy increase slowly before the peak stress and grow rapidly after the peak stress. The discreteness of elastic strain energy and dissipated energy is relatively slight under different temperature conditions, while it becomes more prominent under various confining pressures. (3) The fracture mechanism considering the particle effect of sandstone is described as follows: cracks preferentially initiate along grain boundaries, and incompatible deformation between particles promotes the formation of transgranular cracks. The connection and coalescence of these cracks eventually lead to specimen failure. A thermal–mechanical statistical damage constitutive model for sandstone was established. The theoretical curves agree well with the test curves, which effectively verifies the rationality of the model. The model can accurately describe the damage evolution and deformation characteristics and is more consistent with the actual rock failure mechanism. (4) Within a certain range, the elevation of temperature and confining pressure can enhance the bearing capacity of sandstone, indicating that a high-temperature and high-stress environment may be conducive to the occurrence of rockbursts. In engineering practice, sections prone to rockbursts induced by high ground temperature and high in situ stress should be avoided as far as possible. During construction, reasonable regulation of surrounding rock stress concentration and temperature can effectively mitigate thermal shock caused by temperature difference and instability induced by stress concentration, thereby reducing sudden rockburst disasters and engineering risks. It is further pointed out that rockburst occurrence is affected by numerous factors, including rock lithology, in situ stress, geological structures, groundwater, seismic activity and geotemperature. Combined with the geological characteristics of high ground temperature up to 150 °C and burial depth ranging from 1000 m to 3000 m in Kangding, Sichuan Province, this study conducted sandstone tests under temperatures of 100–250 °C and confining pressures of 10–30 MPa. The temperature effect was preliminarily analyzed from the perspectives of rock lithology, confining pressure and temperature, which serves as a pilot study. The research findings can provide references and guidance for subsequent relevant investigations. Nevertheless, only one specimen was tested under each temperature and confining pressure condition, so the statistical regularity of the obtained results remains to be verified. Accordingly, further systematic research will be carried out by the research group to clarify the influences of medium-low temperature (room temperature to 250 °C) and confining pressure on the mechanical properties, fracture mechanisms and rockburst propensity of sandstone, so as to draw universally applicable conclusions. Author Contributions M.G.: Conceptualization, data analysis and original draft. M.H. and R.C.: Tests and literature search. S.Q. and F.Z.: Data analysis and literature search. Y.Z. and T.L.: Conceptualization, review and editing. All authors have read and agreed to the published version of the manuscript. Funding This work was funded by the National Natural Science Foundation of China (42130719), Humanities and Social Sciences Research Project of Ministry of Education (23YJCZH051), the Opening fund of State Key Laboratory of Geohazard Prevention and Geoenvironment Protection (Chengdu University of Technology) (SKLGP2025K023), and the Opening Foundation of Key Laboratory of Landslide Risk Early-warning and Control, Ministry of Emergency Management (Chengdu University of Technology) (KLLREC2022K003), for which the authors are grateful. Institutional Review Board Statement Not applicable. Informed Consent Statement Not applicable. Data Availability Statement The data that support the findings of this study are available from the corresponding author upon reasonable request. Conflicts of Interest The authors declare no conflicts of interest. References Figure 1. Typical adverse geological phenomena in sandstone stratum tunnels. ( a) Sandstone tunnel. ( b) Spalling of primary support. ( c) Collapse. ( d) Rockburst. Adapted from Ref. [ 4]. Figure 1. Typical adverse geological phenomena in sandstone stratum tunnels. ( a) Sandstone tunnel. ( b) Spalling of primary support. ( c) Collapse. ( d) Rockburst. Adapted from Ref. [ 4]. Figure 2. IRSM-THM-1500 multi-field coupling testing system. ( a) RSM-THM-1500 testing equipment. ( b) Muffle furnace. ( c) Acoustic Emission testing system. Figure 2. IRSM-THM-1500 multi-field coupling testing system. ( a) RSM-THM-1500 testing equipment. ( b) Muffle furnace. ( c) Acoustic Emission testing system. Figure 3. Stress–strain curves and failure patterns of sandstone under different temperatures and confining pressures. Figure 3. Stress–strain curves and failure patterns of sandstone under different temperatures and confining pressures. Figure 4. Variation in stress characteristics of sandstone with confining pressure and temperature. ( a) Variation in stress characteristics with confining pressure (150 °C). ( b) Variation in stress characteristics with temperature (30 MPa). Figure 4. Variation in stress characteristics of sandstone with confining pressure and temperature. ( a) Variation in stress characteristics with confining pressure (150 °C). ( b) Variation in stress characteristics with temperature (30 MPa). Figure 5. Variation in deformation parameters of sandstone with confining pressure and temperature. ( a) Variation in elastic modulus and Poisson’s ratio with confining pressure (150 °C). ( b) Variation in elastic modulus and Poisson’s ratio with temperature (30 MPa). Figure 5. Variation in deformation parameters of sandstone with confining pressure and temperature. ( a) Variation in elastic modulus and Poisson’s ratio with confining pressure (150 °C). ( b) Variation in elastic modulus and Poisson’s ratio with temperature (30 MPa). Figure 6. Relationship between stress and acoustic emission ringing count over time under different confining pressure and thermal conditions. Figure 6. Relationship between stress and acoustic emission ringing count over time under different confining pressure and thermal conditions. Figure 7. Relationship between stress and energy over time under different confining pressure and thermal conditions. Figure 7. Relationship between stress and energy over time under different confining pressure and thermal conditions. Figure 8. Statistical analysis of energy at each stage for sandstone specimens. Figure 8. Statistical analysis of energy at each stage for sandstone specimens. Figure 9. Variation in energy with confining pressure and temperature. Figure 9. Variation in energy with confining pressure and temperature. Figure 10. Sensitivity analysis diagram. ( a) Sensitivity to confining pressure; ( b) Sensitivity to temperature. Figure 10. Sensitivity analysis diagram. ( a) Sensitivity to confining pressure; ( b) Sensitivity to temperature. Figure 11. Schematic diagram of sandstone failure mechanism considering particle effect (modified 2024 [ 18]). Figure 11. Schematic diagram of sandstone failure mechanism considering particle effect (modified 2024 [ 18]). Figure 12. Mechanical parameters of sandstone under different confining pressures after heat treatment (Yu et al., 2015) [ 19]. Figure 12. Mechanical parameters of sandstone under different confining pressures after heat treatment (Yu et al., 2015) [ 19]. Figure 13. Thermal-strain curve under different temperatures. Figure 13. Thermal-strain curve under different temperatures. Figure 14. Strain-energy curve of the heating process. Figure 14. Strain-energy curve of the heating process. Figure 15. Experimental and theoretical stress–strain curves. Figure 15. Experimental and theoretical stress–strain curves. Figure 16. Failure types of rock under uniaxial compression. Figure 16. Failure types of rock under uniaxial compression. Figure 17. Typical failure signs of rockburst in the Erlangshan Tunnel on National Highway 318 [ 24]. Figure 17. Typical failure signs of rockburst in the Erlangshan Tunnel on National Highway 318 [ 24]. Table 1. Sandstone specimens and experimental scheme. Table 1. Sandstone specimens and experimental scheme. No. Mass/g (Before Heating) Mass/g (After Heating) Mass Loss Rate/% Volume/cm 3Initial Density/g·cm −3Test Conditions Typical Specimen Photos Temperature/°C Confining Pressure/MPa S-2 396.5 393.5 0.76% 190.3 2.08 150 10 S-3 403.5 400.0 0.87% 191.7 2.11 150 20 S-4 397.5 394.5 0.75% 192.4 2.07 150 30 S-6 400.0 396.0 1.00% 192.8 2.07 100 30 S-7 408.5 403.0 1.35% 192.8 2.12 180 30 S-8 406.5 403.0 0.86% 192.4 2.11 250 30 Table 2. Results of X-ray diffraction test and polarized microscope thin section analysis of sandstone specimens. Table 2. Results of X-ray diffraction test and polarized microscope thin section analysis of sandstone specimens. Mineral Proportion (%) Particle Size (mm) Particle Structure Photomicrograph of Sandstone Quartz 53 0.2~0.5 Particle crushing ( Q) Calcite 16 0.5~1.0 Distinct twinkling ( Cal) Plagioclase 14 0.4~0.6 Well-developed polysynthetic twins ( Pl) Clay minerals 17 0.3~0.5 Flaky Table 3. Correspondence between macro and micro-fracture characteristics of sandstone. Table 3. Correspondence between macro and micro-fracture characteristics of sandstone. Mechanical Stage Microscopic Macroscopic Compaction stage (OA) Initial pore closure Concave-up stress–strain curve with nonlinear deformation Linear elastic stage (AB) Elastic compression of grains and load bearing by cement Linear stress–strain relationship with uniform volumetric contraction Stable crack propagation stage (BC) Initiation and stable propagation of intergranular cracks Deviated linear stress–strain curve and initial dilatancy Accelerated crack propagation stage (CD) Coalescence of intragranular and transgranular cracks Stress reaches peak strength, and volumetric strain shifts from compression to dilation Stress drop stage (DE) Grain slippage Stress drop, residual strength dominated by intergranular friction Table 4. The values of constitutive model parameters for each sample. Table 4. The values of constitutive model parameters for each sample. NO. σc/MPa εcE/GPa μ F/MPa m SY-2 19.7 0.010488 2.15 0.19 25.8 0.5 SY-3 22.5 0.010730 2.51 0.17 45.1 3.1 SY-4 20.0 0.010392 2.23 0.20 23.9 1.2 SY-6 20.0 0.010130 2.31 0.24 22.2 1.0 SY-7 26.3 0.011008 2.89 0.17 91.2 4.7 SY-8 24.3 0.010619 2.83 0.21 38.0 1.5 Table 5. List of engineering geological rock masses along and adjacent to the CZ Railway. Table 5. List of engineering geological rock masses along and adjacent to the CZ Railway. No. Engineering Geological Rock Mass Area (km 2) Proportion (%) 1 Hard, thick-bedded sandstone rock mass 17,835.7 1.6 2 Medium-hard to hard medium-thick bedded sandstone intercalated with conglomerate, mudstone and slate rock mass 114,246.3 10.3 3 Medium-thick bedded sandstone and mudstone with alternating soft and hard layers, intercalated with limestone and argillaceous limestone, as well as their interbedded rock mass 203,712.2 18.4 4 Weak to medium-hard thin to medium-thick bedded interbedded sandstone, mudstone, conglomerate and argillaceous rock mass 67,185.8 6.1 5 Weak thin-bedded mudstone and shale rock mass 70,239.2 6.3 6 Hard, medium-thick bedded limestone and dolomite rock mass 35,793.8 3.2 7 Medium-hard thin- to medium-thick bedded limestone and argillaceous limestone rock mass 33,039.3 3.0 8 Medium-hard to hard medium-thick bedded limestone and dolomite rock mass intercalated with sandstone, mudstone, phyllite and slate 60,239.2 5.4 9 Medium-hard to hard thin- to medium-thick bedded interbedded rock mass of slate, phyllite and metamorphic sandstone 73,724.0 6.7 10 Weak to medium-hard thin- to medium-thick bedded phyllite and schist intercalated with limestone, sandstone and volcanic rock mass 140,566.2 12.7 11 Massive basalt-dominated hard rock mass 20,639.4 1.9 12 Hard massive rock mass of granite, andesite and diorite 170,171.5 15.4 13 Soft, loose structure rock mass 100,085.6 9.0 Disclaimer/Publisher’s Note: The statements, opinions and data contained in all publications are solely those of the individual author(s) and contributor(s) and not of MDPI and/or the editor(s). MDPI and/or the editor(s) disclaim responsibility for any injury to people or property resulting from any ideas, methods, instructions or products referred to in the content. © 2026 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license. Share and Cite MDPI and ACS Style Li, T.; Qiu, S.; Han, M.; Chang, R.; Zeng, F.; Zhang, Y.; Gao, M. Study on the Energy Evolution Law of Sandstone and Its Implications for Rockburst Prevention Considering Particle Effect Under Thermal Action. Appl. Sci. 2026, 16, 5813. https://doi.org/10.3390/app16125813 AMA Style Li T, Qiu S, Han M, Chang R, Zeng F, Zhang Y, Gao M. Study on the Energy Evolution Law of Sandstone and Its Implications for Rockburst Prevention Considering Particle Effect Under Thermal Action. Applied Sciences. 2026; 16(12):5813. https://doi.org/10.3390/app16125813 Chicago/Turabian Style Li, Tianbin, Shuhao Qiu, Mengting Han, Ruichi Chang, Feng Zeng, Yan Zhang, and Meiben Gao. 2026. "Study on the Energy Evolution Law of Sandstone and Its Implications for Rockburst Prevention Considering Particle Effect Under Thermal Action" Applied Sciences 16, no. 12: 5813. https://doi.org/10.3390/app16125813 APA Style Li, T., Qiu, S., Han, M., Chang, R., Zeng, F., Zhang, Y., & Gao, M. (2026). Study on the Energy Evolution Law of Sandstone and Its Implications for Rockburst Prevention Considering Particle Effect Under Thermal Action. Applied Sciences, 16(12), 5813. https://doi.org/10.3390/app16125813 Note that from the first issue of 2016, this journal uses article numbers instead of page numbers. See further details here. Article Metrics Article metric data becomes available approximately 24 hours after publication online.
