Degradation Behavior and Damage Evolution Model of Sandstone under Coupled Stress-Temperature-Chemical Action

Abstract

Seepage from water-rich strata and persistent roof water inflow during coal mining can substantially weaken the mechanical properties of coal and rock masses. Elevated in situ stress and geothermal temperature in deep roadways further accelerate deterioration and increase the risk of engineering instability. In this study, sandstone, a common coal-seam roof rock, was selected as the test material. Immersion and uniaxial compression tests were conducted under coupled thermal–alkaline water conditions. Scanning electron microscopy and X-ray diffraction analyses were used to clarify the strength degradation mechanism, and a uniaxial compressive strength characterization model accounting for thermal–chemical–stress damage was developed. The results show that immersion extends the compaction stage and reduces the elastic modulus and peak stress; these effects become more pronounced with increasing temperature and solution alkalinity. The uniaxial compressive strength decreases linearly with temperature and exponentially with pH, and temperature, pH, and their interaction all have significant effects on the uniaxial compressive strength of sandstone (p < 0.001). The strength degradation rate gradually declines as alkalinity increases, whereas higher temperature accelerates strength deterioration. The most pronounced deterioration occurs at 60 °C and pH = 12, where the uniaxial compressive strength and elastic modulus decrease to 37.724 ± 1.094 MPa and 1.260 ± 0.046 GPa, respectively, corresponding to reductions of 58.50% and 58.25% relative to the dry specimens at the same temperature. Microscopically, sandstone damage evolves from local crack development and fragment spalling to lamellar delamination, edge curling, and propagation of internal defects with increasing alkalinity. The net increase in SiO₃ ^2– concentration rises from 5.694 to 14.235 mg/L, indicating that the dominant water–rock interaction progressively shifts from wetting-induced softening and hydrolysis to alkaline dissolution. The proposed segmented damage constitutive model can describe the compaction stage, pre-peak damage evolution, and mechanical response near the peak. Three-fold leave-one-out validation yields mean relative errors of 6.17–12.89%, with an overall mean error of 9.63%. These findings provide a theoretical basis for evaluating and controlling the stability of surrounding rock in deep mines under elevated geothermal and water-temperature conditions.

1. Introduction

As coal resource development continues to extend to greater depths, mine roadway engineering must not only address traditional geological engineering hazards such as large deformation of surrounding rock, roof collapse, and water inrush caused by high in situ stress, but also face special challenges induced by high geothermal temperature, high water temperature, and water–rock interactions. Under multi-field coupling effects, the difficulty of stability control for rock mass engineering in deep mine roadways has increased significantly. − Groundwater in water-rich strata can seep toward roadways through pores, bedding planes, and mining-induced fractures in the rock mass. Persistent roof water inflow and water–rock interactions weaken the cementation between mineral grains and promote the development of pores and fractures, thereby reducing the strength, stiffness, and load-bearing capacity of coal and rock masses. Numerous studies have shown that under coupled thermal-mechanical-chemical actions, roadway surrounding rock is highly prone to sudden instability and failure, seriously threatening the safe operation of deep roadway engineering and the reliability of support systems. , Accurately understanding the degradation laws of rock mechanical parameters under coupled thermal-mechanical-chemical actions and quantitatively characterizing rock damage are of great research significance for timely evaluating the degradation state of surrounding rock in deep roadways and ensuring the safety of deep coal mining.

Sandstone, as a typical deep brittle-hard rock, has become a research hotspot in rock mechanics regarding its mesoscopic fracture mechanisms and mechanical response characteristics under conditions of high in situ stress, high temperature, and chemical erosion. − It is widely accepted that rock strength degrades under multi-field coupling conditions. Generally, high in situ stress can cause compression or propagation of preexisting fractures within the rock mass, leading to the accumulation of initial damage. − Water–rock interactions can alter the morphology of mineral particles and weaken intergranular cementation through physical dissolution or chemical erosion, resulting in the degradation of the mechanical properties of the rock mass. − Abnormal environments characterized by high geothermal temperature and high water temperature can induce high-temperature and high-humidity conditions, thereby accelerating water–rock interactions and further weakening the structural integrity and load-bearing capacity of the rock mass. − Related studies using CT scanning, mercury intrusion porosimetry, and other techniques have revealed that microcrack propagation and coalescence, increased pore fractal dimension, and pore-structure remodeling are the intrinsic causes of the degradation of sandstone mechanical properties. − In addition, some researchers, from the perspective of energy evolution, have demonstrated through uniaxial compression tests combined with acoustic emission monitoring that temperature and chemical erosion alter the energy dissipation pathways and energy release rates during sandstone failure. , Overall, stress primarily affects crack compaction and propagation as well as the load-bearing structure of the rock mass; water directly alters mineral particles and their cementation state; and temperature further amplifies rock deterioration by accelerating water–rock interactions.

In terms of theoretical model research, existing studies have mainly focused on constitutive models describing the entire process of rock deformation and failure under complex environments, which can be roughly classified into three categories. The first category involves statistical damage constitutive models based on macroscopic damage variables, which introduce environmental degradation factors such as temperature effects, acid erosion, or high-temperature action to describe the relationship between rock damage evolution and stress–strain response. − The second category includes crack propagation models considering mesoscopic mechanisms, such as equivalent crack propagation mesomechanical models and elastoplastic constitutive models for sandstone, which reveal crack evolution, stiffness degradation, and nonlinear deformation characteristics under chemical action. − The third category encompasses time-dependent rheological damage models, such as true triaxial creep constitutive models considering water-chemical damage and sandstone rheological damage constitutive models, which analyze the long-term deformation and damage accumulation process of rock under water-chemical environments. , Furthermore, in terms of describing the full-process response under uniaxial compression, some studies have established a full-process damage constitutive model for layered sandstone based on the logistic function, reflecting the continuous evolution process of rock from compaction and elastic deformation to damage development and post-peak failure.

Existing studies have investigated the mechanical deterioration and failure behavior of sandstone from the perspectives of thermal–hydraulic–mechanical–chemical coupling, alkaline erosion, and damage constitutive modeling. However, most existing thermal–hydraulic–mechanical–chemical studies have focused on rock deformation, fracturing, and seepage responses under multi-field coupling conditions, whereas studies following the loading path of uniaxial compression after thermal–alkaline water treatment remain relatively limited. Previous studies on alkaline erosion have revealed the effects of alkaline solutions on rock strength and microstructure, but the enhancement of alkaline erosion by temperature and the interaction between these two factors still lack quantitative understanding. In terms of damage characterization, existing models generally incorporate environmental deterioration into the stress–strain relationship as a single damage factor, without clearly distinguishing the initial damage induced by environmental treatment before loading from the stress-induced damage generated during subsequent loading. Therefore, it is necessary to investigate the mechanical deterioration of roof sandstone after thermal–alkaline water treatment by considering the in situ water-temperature and alkalinity conditions, and to separately characterize the initial environmental damage and subsequent loading-induced damage.

In view of this, this study takes the medium-grained roof sandstone from Zhaolou Coal Mine in Heze City, which is characterized by deep burial, high horizontal tectonic stress, and high-temperature alkaline roof water inflow, as the research object. The experimental conditions were designed with reference to the temperature and alkalinity characteristics of the in situ roof water. Uniaxial compression tests were conducted on sandstone specimens after immersion in simulated alkaline mine-water solutions with different temperatures and pH values. The effects of temperature and pH on the full stress–strain curves of sandstone were analyzed, and the relationships of peak strength, elastic modulus, and peak strain with temperature and pH were examined. Subsequently, scanning electron microscopy (SEM) and X-ray diffraction (XRD) analyses were employed to elucidate the deterioration mechanisms of sandstone under thermal–chemical effects from the perspectives of microstructural evolution of mineral particles and changes in mineral composition. Finally, based on damage mechanics theory, a segmented damage constitutive model considering coupled thermal–chemical–stress damage was developed, and its applicability was validated against the experimental data. In addition, representative in situ conditions were considered to interpret the engineering implications of strength and stiffness degradation of roof sandstone subjected to high-temperature alkaline water inflow. This study aims to provide a theoretical basis for the control of mining-induced surrounding rock in deep mines under high-temperature alkaline-water erosion conditions.

2. Methods

2.1. Specimen Preparation

The engineering background of this study was the Zhaolou Coal Mine of Yankuang Group, located in Heze City, Shandong Province, China. The comprehensive stratigraphic column of the mine strata is presented in Figure a. The No. 3 coal seam, which was the main mining seam in the No. 5 mining district, had an average thickness of 6.35 m, an average burial depth of approximately 930 m, and a maximum burial depth of 1100 m. In situ stress measurements indicated that the geological tectonic stress in this mining district was dominated by horizontal tectonic stress, with the maximum horizontal principal stress reaching 47.5 MPa and a lateral pressure coefficient of 1.5, exhibiting typical characteristics of deep mining. The transportation roadway of the 5305 working face was a rectangular entry driven along the floor of the No. 3 coal seam, with a net width of 5800 mm and a net height of 4000 mm. The roadway roof was supported by high-strength threaded steel bolts (φ = 22 mm × 2400 mm). The coring location of the sandstone specimens is shown in Figure b. The medium-grained sandstone layer in the coal seam roof, which was unaffected by mining disturbance, was selected for coring. The borehole diameter was 113 mm, and the single borehole depth was 15 m. In the laboratory, the cores were processed into standard cylindrical specimens (φ = 50 mm × 100 mm) using dry machining. After measuring the geometric dimensions, mass, end-surface nonparallelism, axial deviation, and P-wave velocity of each specimen, a total of 45 rock specimens with relatively concentrated wave velocity and density and satisfying the machining-accuracy requirements were selected for uniaxial compression tests. All specimens were prepared using the same sampling, machining, end-surface treatment, and screening criteria. The 45 specimens were assigned to 15 test conditions comprising five environmental conditions (dry, deionized water, pH = 7, pH = 10, and pH = 12) and three temperature levels (20, 40, and 60 °C), with three independent replicate specimens for each condition.

1.

Stratigraphic column and specimen preparation.

During the excavation of the 5305 transportation roadway within a range of 50–200 m from the southern No.1 auxiliary haulage roadway, as well as during the subsequent working face extraction, significant water inflow (30 m³/h) occurred from the roof. This water inflow primarily originated from the medium-grained sandstone aquifer of the immediate roof. Water quality analysis results showed that the pH value of the water sample from the roof sandstone aquifer ranged from 9.5 to 10.3, with a water temperature of 38.6 °C. The average concentrations and proportions of the main ions are listed in Table . To avoid inconsistencies in experimental conditions caused by variations in water quality due to differences in field collection time, location, and volume, an alkaline mine water simulation solution was prepared in the laboratory based on the mean values of key ions and pH of the groundwater solution collected in the field. The main mineral components of the dry sandstone were determined by X-ray diffraction, as shown in Figure c: 57.63% quartz, 15.52% kaolinite, 12.75% albite, 8.76% potassium feldspar, 3.11% muscovite, and 2.23% clinochlore.

1. Major-Ion Composition of Mine Water from Zhaolou Coal Mine.

pH	Parameter	K+ + Na+	Ca2+	Mg2+	Cl–	SO4 2–	HCO3 –	Other ions
9.5∼10.3	Ion concentration (mg L–1)	1157.67	169.78	61.53	318.80	2338.76	220.66	4.34
	Proportion(%)	27.10	3.97	1.44	7.46	54.75	5.17	0.11

2.2. Experimental Design

To investigate the deterioration behavior of sandstone under the combined effects of temperature and chemical environment, immersion tests were designed under aqueous environments with different temperatures and pH values, as illustrated in Figure . The experimental conditions were established with reference to the average temperature (approximately 38.6 °C) and pH value (approximately 9.9) of the roof water inflow measured in situ in the 5305 transportation roadway. Based on these in situ hydrothermal–chemical conditions, the temperatures were set at 20, 40, and 60 °C. Among them, 40 °C was close to the measured in situ water temperature, 20 °C represented ambient-temperature conditions, and 60 °C was selected to investigate the deterioration response of sandstone at a relatively elevated temperature. The solution pH values were set at 7, 10, and 12, where pH = 10 approximated the in situ mine-water condition, pH = 7 represented a neutral hydrochemical environment, and pH = 12 served as a strongly alkaline condition beyond the measured field range. In addition, a deionized-water group was included as a control, together with a dry group as an unimmersed reference. The environmental treatment duration was uniformly set to 60 h for all test conditions. Specimens in the immersion groups were completely submerged in the corresponding solutions, and the prescribed temperatures were maintained using a constant-temperature device. The dry control specimens were not exposed to any solution and were maintained at 20, 40, and 60 °C, respectively, for 60 h. Except for solution exposure, the dry and immersed groups were subjected to the same target temperatures, treatment durations, specimen-handling procedures, and subsequent uniaxial loading conditions.

2.

Experimental workflow.

After immersion, the solutions from different experimental groups were collected for ion concentration testing to analyze the ion migration pattern during the water–rock interaction. Upon reaching the preset immersion time, the sandstone specimens were removed, wiped dry to remove surface moisture, and subjected to surface cleaning and end surface trimming. Subsequently, uniaxial compression tests were conducted on the sandstone specimens under different immersion conditions using an MTS-810 servo-hydraulic loading system to obtain the complete stress–strain curves, peak strength, and peak strain. After the mechanical tests, typical fragments of failed specimens were selected for scanning electron microscopy (SEM) and X-ray diffraction (XRD) analyses to reveal the deterioration mechanism of sandstone from the perspectives of microstructural evolution and mineral composition changes.

3. Results and Discussion

3.1. Basic Mechanical Properties

To minimize the influence of the natural variability of sandstone on the experimental results, three independent replicate specimens were prepared for each temperature–hydrochemical condition. Based on the uniaxial compression stress–strain curves of each specimen, the uniaxial compressive strength, elastic modulus, and peak strain were extracted, and their mean values and standard deviations were calculated. The statistical results are presented in Table .

2. Mechanical Parameters (Mean ± SD) of Sandstone under Different Temperature and Solution Conditions.

Condition	Temperature/°C	UCS/MPa	Elastic modulus/GPa	Peak strain/%
Dry	20	92.713 ± 1.205	3.204 ± 0.058	3.650 ± 0.055
Dry	40	91.924 ± 1.287	3.129 ± 0.058	3.722 ± 0.060
Dry	60	90.901 ± 1.454	3.018 ± 0.060	3.782 ± 0.064
DI water	20	81.849 ± 1.391	2.728 ± 0.039	3.678 ± 0.066
DI water	40	72.027 ± 1.369	2.264 ± 0.061	3.899 ± 0.078
DI water	60	62.997 ± 1.323	2.044 ± 0.053	4.046 ± 0.085
pH = 7	20	63.425 ± 1.269	2.013 ± 0.047	4.045 ± 0.081
pH = 7	40	56.067 ± 1.233	1.737 ± 0.042	4.329 ± 0.095
pH = 7	60	42.792 ± 1.070	1.547 ± 0.045	3.952 ± 0.095
pH = 10	20	54.396 ± 1.142	1.820 ± 0.050	3.561 ± 0.071
pH = 10	40	49.303 ± 1.134	1.650 ± 0.061	3.696 ± 0.081
pH = 10	60	39.693 ± 1.072	1.420 ± 0.043	3.275 ± 0.082
pH = 12	20	49.386 ± 1.086	1.650 ± 0.049	3.014 ± 0.063
pH = 12	40	46.520 ± 1.116	1.480 ± 0.040	3.181 ± 0.073
pH = 12	60	37.724 ± 1.094	1.260 ± 0.046	3.127 ± 0.086

As shown in Table , the coefficients of variation of the uniaxial compressive strength, elastic modulus, and peak strain ranged from 1.30% to 2.90%, 1.43% to 3.70%, and 1.51% to 2.75%, respectively, indicating good repeatability and stability of the experimental results. The mechanical parameters of the dry specimens varied only slightly within the temperature range of 20–60 °C. After immersion treatment, the uniaxial compressive strength and elastic modulus of sandstone generally decreased with increasing temperature and solution alkalinity.

3.2. Stress–Strain Curve Characteristics

Figure presents the complete stress–strain curves of sandstone specimens under different immersion conditions. The curves can be divided into four stages: the compaction stage, elastic stage, yield stage, and post-peak failure stage. For dry sandstone, the strain corresponding to the compaction stage is relatively small, the slope of the elastic stage is steeper, and the peak stress is higher, followed by pronounced brittle failure after the peak. In contrast, after immersion in solutions with different temperatures and pH values, the compaction stage is generally prolonged, while both the slope of the elastic stage and the peak stress decrease to varying degrees. These results indicate that water–rock interaction increases the internal pore volume of sandstone, resulting in greater compaction deformation during the initial loading stage and a reduction in the overall stiffness and load-bearing capacity.

3.

Complete stress–strain curves of sandstone under different soaking conditions.

The relationship surface of uniaxial compressive strength versus temperature and pH value is shown in Figure a. It can be seen that the compressive strength of sandstone decreased with increasing temperature and pH value. Taking 20 °C as an example, under deionized water, pH = 7, pH = 10, and pH = 12 conditions, the compressive strengths of sandstone were 81.85, 63.43, 54.39, and 49.39 MPa, respectively. Under the same pH immersion environment, for example at pH = 12, the uniaxial compressive strengths of sandstone at 20, 40, and 60 °C were 49.38, 46.52, and 37.72 MPa, respectively. The relationship surface of peak strain versus temperature and pH is shown in Figure b. It can be observed that as the pH value increased, the strain corresponding to the peak stress of sandstone gradually decreased. Based on Figures and , it can be concluded that when temperature and alkaline solution acted together, a synergistic deterioration effect was exhibited. At the same temperature, increasing alkalinity primarily reduced the peak strength and enhanced pre-peak nonlinear deformation. Under the same solution condition, increasing temperature mainly reduced the peak stress. When high temperature and strong alkaline environment were superimposed, the above changes were simultaneously intensified, and the reductions in peak stress and peak strain both exceeded those under the action of a single factor. This indicated that elevated temperature further intensified the damage accumulation effect of alkaline solution on sandstone.

4.

Variations in UCS and peak strain under different temperature and pH conditions.

The variation curves of the percentage reduction in the uniaxial compressive strength of sandstone with pH and temperature are shown in Figure . Under the same temperature condition, the percentage reduction in sandstone strength generally increased with increasing pH, although the rate of increase gradually slowed at higher alkalinity. Taking 20 °C as an example, compared with the dry specimens at the same temperature, the compressive strengths of sandstone under DI water, pH = 7, pH = 10, and pH = 12 conditions decreased by 11.72%, 31.59%, 41.33%, and 46.73%, respectively. Under the same solution condition, the percentage reduction in sandstone strength increased with increasing temperature. For example, under the pH = 12 condition, the compressive strengths at 20, 40, and 60 °C decreased by 46.73%, 49.39%, and 58.50%, respectively, relative to the corresponding dry specimens at the same temperatures. These results indicate that increasing temperature significantly promotes the strength deterioration of sandstone, and that the temperature sensitivity of sandstone strength varies among different hydrochemical environments.

5.

Reduction in the uniaxial compressive strength of sandstone.

The specific experimental values of uniaxial compressive strength of sandstone under different immersion conditions are listed in Table . To quantitatively characterize the individual influence of temperature or pH value on the compressive strength of sandstone, the uniaxial compressive strength of sandstone in solutions with the same pH value was fitted (Figure ). It can be seen that the UCS–temperature variation curve could be approximately expressed by eq . That is, in the same immersion environment, the compressive strength of sandstone decreased approximately linearly with increasing temperature, and the fitting parameters are listed in Table . Among these, under the pH = 7 condition, the absolute value of the slope of the fitted straight line was the largest, indicating that temperature further promoted the chemical reaction.

$${\sigma }_c=aT+b$$ 1

where σ _c is the uniaxial compressive strength of sandstone (MPa); T is the temperature (°C); and a and b are fitting parameters.

6.

Relationship between UCS and temperature under different solution conditions.

3. Fitting Parameters for UCS–Temperature Relationships in Different Soaking Solutions.

Soaking solution	a	b	Correlation coefficient
DI water	–0.4713	91.1430	0.9994
pH = 7	–0.5158	74.7277	0.9733
pH = 10	–0.3676	62.5003	0.9695
pH = 12	–0.2916	56.2053	0.9207

The fitting curves between uniaxial compressive strength and pH value under the same temperature condition are shown in Figure . It can be seen that UCS and solution pH value exhibited a good negative exponential relationship, and the fitting parameters are listed in Table . The deionized water group served as a blank control and was not included in the pH exponential fitting analysis. Table indicates that at a constant temperature, the compressive strength of sandstone exhibited an exponential decay characteristic with increasing pH value. The exponential parameter B decreased with increasing temperature, indicating that although the compressive strength of sandstone continued to decline with increasing pH under high-temperature environments, the decay rate gradually diminished.

$${\sigma }_c=A{e}^{-Bp}$$ 2

where σ _c is the uniaxial compressive strength of sandstone (MPa); p is the pH of the soaking solution; and A and B are fitting parameters.

7.

Variation in UCS with pH.

4. Fitting Parameters for UCS–pH Relationships of Sandstone at Different Temperatures.

T/°C	A	B	Correlation coefficient
20	90.0039	0.05013	0.9998
40	72.7167	0.03777	0.9908
60	51.0530	0.02520	1.0000

To quantitatively evaluate the effects of temperature, pH, and their interaction on the uniaxial compressive strength of sandstone, a two-way analysis of variance (ANOVA) was performed on the experimental data obtained at pH = 7, 10, and 12, with temperature and pH treated as fixed factors and UCS as the response variable. The results are presented in Table . The dry group was not subjected to solution treatment, and the DI-water group did not belong to the prescribed pH levels; therefore, these two groups were excluded from the analysis. The effect of temperature on UCS was significant, F­(2, 18) = 444.286, p < 0.001, partial η² = 0.980. The results indicate that, within the experimental range, both temperature and pH are important factors affecting the UCS of sandstone. Moreover, the effect of temperature on UCS varies with pH, while the effect of pH is also dependent on temperature.

5. Two-Way ANOVA of the Effects of Temperature and pH on Sandstone UCS.

Source of variation	df	SS	MS	F	p	Partial η2
T	2	1149.036	574.518	444.286	<0.001	0.980
pH	2	424.419	212.209	164.106	<0.001	0.948
T × pH	4	63.105	15.776	12.200	<0.001	0.731
Error	18	23.276	1.293			
Total	26	1659.836				

In summary, after immersion for 60 h in DI water and solutions with pH values ranging from 7 to 12 at temperatures of 20–60 °C, the compressive strength of sandstone decreases approximately linearly with increasing temperature and exhibits an exponential decay with increasing pH. The temperature sensitivity is strongest at pH = 7. As the pH further increases, the sandstone strength continues to decrease, but the rate of strength degradation gradually slows. Overall, temperature and alkaline water do not act independently; elevated temperature significantly intensifies the mechanical deterioration of sandstone induced by the alkaline aqueous environment, and their coupled effects further weaken the load-bearing stability of the deep surrounding rock.

3.3. Microstructure

The SEM images of sandstone specimens after immersion in different solutions at 20 °C for 60 h at a magnification of ×3000 are presented in Figure . With increasing alkalinity, significant differences were observed in the surface microstructure of sandstone, which was generally characterized by gradual development of pores and cracks, roughening of grain boundaries, and weakening of intergranular cementation. As shown in Figure a, the local structural plane of the original sandstone specimen was relatively intact, the mineral grain boundaries were relatively smooth, abundant fine debris was attached to the surface, and only a few pores and cracks were developed between grains, indicating a relatively intact overall microstructure. After immersion in the solution with pH = 7, as shown in Figure b, secondary cracks and pores appeared on the specimen surface, accompanied by local fragment exfoliation, layered distribution, and grain accumulation, suggesting the onset of loosening of the surface structure. When the alkalinity of the solution was increased to pH = 10, as shown in Figure c, the surface damage of sandstone was further intensified, manifested as flaky delamination, increased pores and cracks, curling of local grain edges, and surface roughening. At pH = 12, as shown in Figure d, the development of internal cracks became more evident, the number of pores and microcracks further increased, and scattered stacking of angular fragments was locally observed. The strongly alkaline water environment significantly dissolved the cementing materials inside the rock, destroyed the grain cementation system, and induced structural damage of the rock mass.

8.

Microstructural changes in sandstone after soaking in different alkaline solutions.

In general, as the pH value of the solution increased, the microstructure of sandstone gradually evolved from local crack propagation and fragment exfoliation at the early stage to flaky delamination, edge curling, surface roughening, and internal crack propagation. Alkaline water continuously weakened the intergranular cementation strength by dissolving mineral cements and softening clay components, leading to continuous development of internal defects in the rock mass.

It should be noted that the SEM analysis in this study was primarily used to qualitatively characterize the microstructural deterioration of sandstone under different alkaline conditions. Systematic quantitative analyses of parameters such as pore–fracture area fraction, crack density, and surface roughness were not conducted. Future work will combine standardized SEM image acquisition with quantitative image analysis to further establish quantitative relationships between microstructural parameters and the reduction in uniaxial compressive strength of sandstone, and to investigate the associated damage evolution mechanisms in greater depth.

3.4. Mineral Composition

Figure shows the relative contents of the main mineral components in sandstone after immersion in different solutions for 60 h. The water–rock chemical reactions occurring after immersion are expressed in eqs –. Compared with the deionized water group, the relative quartz content decreased from 57.63% to 48.69% under the pH = 7 condition, while the kaolinite content increased by 7.28%. The contents of albite and muscovite decreased slightly. When the pH increased to 10, the quartz content increased to 54.42%, the kaolinite content decreased to 19.77%, K-feldspar was no longer detected, and the albite content increased to 13.58%. When the pH further increased to 12, the quartz content increased to 56.90%, the kaolinite content decreased to 18.52%, and the variations in some mineral components became less pronounced. Overall, the mineralogical response of sandstone exhibited a stage-dependent evolution with increasing alkalinity: the dominant processes gradually shifted from initial wetting-induced softening and mineral hydrolysis to the combined action of hydrolysis and alkaline dissolution, and finally to alkaline-dissolution-dominated deterioration. Combined with the SEM results discussed above, the sandstone microstructure evolved from local cracking and fragment spalling to lamellar delamination, surface roughening, and the accumulation of angular fragments as the pH increased, indicating a progressive loss of structural integrity.

9.

Changes in the mineral composition of sandstone after soaking in different alkaline solutions.

The water–rock chemical reactions of sandstone after immersion in different solutions are expressed in eqs –.

$${\mathrm{Al}}_4[{\mathrm{Si}}_4{\mathrm{O}}_{10}]{(\mathrm{OH})}_8+4{\mathrm{H}}_2\mathrm{O}\to {\mathrm{Al}}_4[{\mathrm{Si}}_4{\mathrm{O}}_{10}]{({\mathrm{OH}}_1)}_8·4{\mathrm{H}}_2\mathrm{O}$$ 3

$${\mathrm{SiO}}_2+2{\mathrm{H}}_2\mathrm{O}\to {\mathrm{H}}^{+}+{\mathrm{H}}_3{\mathrm{SiO}}_4^{-}$$ 4

$${2\mathrm{NaAlSi}}_3{\mathrm{O}}_8+2{\mathrm{H}}_2{\mathrm{CO}}_3+9{\mathrm{H}}_2\mathrm{O}\to {\mathrm{Al}}_2{\mathrm{Si}}_2{\mathrm{O}}_5{(\mathrm{OH})}_4+4{\mathrm{H}}_4{\mathrm{SiO}}_4+2{\mathrm{Na}}^{+}+2{\mathrm{HCO}}_3^{-}$$ 5

$${4(\mathrm{K},\mathrm{Na})[\mathrm{AlSi}}_3{\mathrm{O}}_8{]+6\mathrm{H}}_2\mathrm{O}\to {\mathrm{Al}}_4[{\mathrm{Si}}_4{\mathrm{O}}_{10}]{(\mathrm{OH})}_8+8{\mathrm{SiO}}_2+4(\mathrm{K},\mathrm{Na})\mathrm{OH}$$ 6

$${\mathrm{KAl}}_2{[\mathrm{AlSi}}_3{\mathrm{O}}_{10}{](\mathrm{OH})}_2\to {\mathrm{K}}_{1\sim \mathrm{n}}{\mathrm{Al}}_2[{\mathrm{AlSi}}_3{\mathrm{O}}_{10}]{(\mathrm{OH})}_2·{\mathrm{H}}_2\mathrm{O}$$ 7

$${\mathrm{SiO}}_2+2{\mathrm{OH}}^{-}\to {\mathrm{SiO}}_3^{2-}+{\mathrm{H}}_2\mathrm{O}$$ 8

$${(\mathrm{K},\mathrm{Na})\mathrm{AlSi}}_3{\mathrm{O}}_8+7{\mathrm{OH}}^{-}\to (\mathrm{K},\mathrm{Na}){\mathrm{OH}+\mathrm{Al}(\mathrm{OH})}_4^{-}+3{\mathrm{SiO}}_3^{2-}+{\mathrm{H}}_2\mathrm{O}$$ 9

To further analyze the water–rock chemical interactions associated with the observed changes in mineral composition, the concentrations of the major ions were measured before immersion and after 60 h of immersion. The results are presented in Table .

6. Changes in Ion Concentrations after Sandstone Immersion (mg/L).

Ion	DI water	pH = 7	pH = 10	pH = 12
K+ + Na+	0 → 12.233	1157.670 → 1154.090	1157.670 → 1161.970	1157.670 → 1163.262
	+12.233	–3.580	+4.300	+5.592
Ca2+	0 → 0.300	169.782 → 65.991	169.782 → 68.981	169.782 → 51.469
	+0.300	–103.792	–100.802	–118.314
Mg2+	0 → 0.200	61.530 → 20.510	61.530 → 16.781	61.530 → 0
	+0.200	–41.020	–44.749	–61.530
Al3+	0 → 15.099	0 → 11.802	0 → 11.209	0 → 6.692
	+15.099	+11.802	+11.209	+6.692
Fe3+	0 → 11.269	0 → 9.072	0 → 8.254	0 → 5.086
	+11.269	+9.072	+8.254	+5.086
SiO3 2–	0 → 2.904	0 → 5.694	0 → 11.872	0 → 14.235
	+2.904	+5.694	+11.872	+14.235

As shown in Table , after immersion in DI water, the concentrations of Al³⁺, Fe³⁺, and SiO₃ ^2– in the solution increased by 15.099, 11.269, and 2.904 mg/L, respectively, indicating that aluminosilicate minerals and Fe-bearing components in the sandstone underwent a certain degree of hydrolysis and dissolution. Under the pH = 7 condition, the net increases in Al³⁺, Fe³⁺, and SiO₃ ^2– were 11.802, 9.072, and 5.694 mg/L, respectively. These changes correspond to the decreases in the relative contents of albite and muscovite and the increase in kaolinite, reflecting the hydrolysis of feldspar and mica as well as the hydration of kaolinite.

As the pH increased to 10 and 12, the net increase in SiO₃ ^2– further rose to 11.872 and 14.235 mg/L, respectively. Meanwhile, K-feldspar was no longer detected and the relative content of kaolinite decreased, indicating that strongly alkaline conditions intensified the dissolution of the Si–O and Al–O frameworks in quartz, feldspar, and clay minerals. The marked decreases in Ca²⁺ and Mg²⁺ concentrations in the alkaline solutions further suggest that the components released by mineral dissolution underwent redistribution through processes such as precipitation, adsorption, and ion exchange.

Figure schematically illustrates the deterioration process of sandstone under the effects of temperature and pH. Increasing temperature intensifies the differential thermal deformation between mineral grains and the matrix, resulting in enlarged intergranular spacing and loosening of grain-contact boundaries. Increasing alkalinity weakens the cementing materials and promotes matrix dissolution, thereby inducing surface roughening, lamellar delamination, and the accumulation of angular fragments. When temperature and alkaline solution act together, thermally induced loosening and crack propagation provide more favorable pathways for solution migration, while chemical erosion further amplifies the initial defects. These combined effects ultimately promote the expansion of local pores, crack connectivity, and the progressive loss of structural integrity.

10.

Schematic diagram of the deterioration mechanism of sandstone under thermal–alkaline water treatment.

4. Damage Constitutive Model

4.1. Development of the Damage Constitutive Model

To characterize the effects of temperature and alkaline-water exposure on the damage evolution of sandstone under uniaxial compression, the total damage of sandstone was divided into two components: temperature–chemical damage and stress-induced damage. Temperature–chemical damage was used to characterize the initial deterioration of the material caused by temperature and alkaline-water exposure, whereas stress-induced damage was used to describe the damage evolution associated with microcrack propagation during uniaxial compression. According to the experimental procedure adopted in this study, the sandstone specimens were first subjected to thermal–alkaline water treatment for 60 h and were subsequently tested under uniaxial compression. Therefore, the temperature–chemical damage was generated prior to loading, whereas the stress-induced damage continued to evolve in the material that had already undergone initial deterioration. By regarding (1–D_c) and (1–D_m) as the residual integrity coefficients of the material after temperature–chemical treatment and during subsequent loading, respectively, the overall residual integrity after the two-stage damage process can be expressed as (1–D_c) (1–D_m). Accordingly, the total damage variable can be written as eq .

$${\mathrm{D}=1-(1-\mathrm{D}}_{\mathrm{c}}{)(1-\mathrm{D}}_{\mathrm{m}})$$ 10

where D is the total damage variable; D_c is the temperature–chemical damage variable; and D_m is the stress-induced damage variable. D, D_c, and D_m are all dimensionless scalar damage variables ranging from 0 to 1.

Compared with the direct additive form D = D_c + D_m, eq contains the interaction term −D_cD_m, which reflects that subsequent stress-induced damage further weakens only the residual load-bearing structure remaining after environmental treatment, thereby avoiding repeated accounting of the environmental damage during mechanical loading. Meanwhile, when 0 ≤ D_c, D_m ≤ 1, eq ensures that the total damage variable always satisfies 0 ≤ D ≤ 1. When either damage component is zero, the total damage naturally reduces to the other single damage variable. Therefore, this multiplicative form is consistent with the experimental path of “environmental treatment followed by mechanical loading” and also avoids the repeated damage calculation and nonphysical result of D > 1 that may arise from simple addition.

It should be noted that this coupling rule is a scalar phenomenological representation and is applicable to cases in which specimens are first subjected to temperature–chemical treatment and subsequently loaded monotonically under uniaxial compression without considering damage recovery. For conditions involving simultaneous variations in temperature, chemical action, and stress, cyclic loading, pronounced anisotropy, or long-term time-dependent effects, further extensions incorporating path-dependent evolution equations or tensorial damage variables are required. The parameter calibration and validation of the present model are limited to temperatures of 20–60 °C, DI water and solutions with pH values of 7–12, an environmental treatment duration of 60 h, and monotonic uniaxial compression. Applications beyond these ranges require further experimental validation.

Considering the varying degrees of elastic modulus degradation under different temperature and solution conditions, the elastic modulus of dry, unimmersed sandstone is taken as the reference value. The temperature–chemical damage is quantified by the degree of elastic modulus degradation, as expressed in eq .

$$D_c=1-\frac{E_{T,p}}{E_0}$$ 11

where E₀ is the average initial elastic modulus of sandstone in the dry state, MPa; and E _T,p is the elastic modulus after exposure to a given temperature T and solution condition p, MPa.

After the compaction stage, internal microcracks begin to propagate stably, and the sandstone gradually enters the stages of damage accumulation and unstable failure. Assuming that the strength of rock microelements follows a Weibull distribution, the stress-induced damage variable can be expressed as eq .

$$D_m=1-\exp [-{\left(\frac{\epsilon -{\epsilon }_c}{F_0}\right)}^m],\epsilon \ge {\epsilon }_c$$ 12

where ε is the axial strain; ε _c is the strain at the end of the compaction stage; and F ₀ and m are model parameters.

According to the strain equivalence principle, the damage constitutive relation after the compaction stage can be expressed as eq .

$$\sigma =E_0(1-D_c)(1-D_m)(\epsilon -{\epsilon }_c),\epsilon \ge {\epsilon }_c$$ 13

where σ is the axial stress, MPa.

By substituting eqs and into eq , the constitutive equation for the elastic–brittle stage can be derived, as given in eq .

$$\sigma =E_{T,p}(\epsilon -{\epsilon }_c)\exp [-{\left(\frac{\epsilon -{\epsilon }_c}{F_0}\right)}^m],\epsilon \ge {\epsilon }_c$$ 14

Because the compaction stage becomes more pronounced after temperature–alkaline water treatment, a power-function empirical model is adopted to describe the curve characteristics associated with microcrack closure, as expressed in eq .

$$\sigma =a{\epsilon }^n,0\le \epsilon \le {\epsilon }_c$$ 15

where a and n are fitting parameters for the compaction stage.

The parameters F ₀ and m in eq can be determined using the peak conditions. Let the peak stress and peak strain be denoted by σ _p and ε _p , respectively. Since the peak point satisfies ∂σ/∂ε = 0, the following expression can be obtained:

$$\sigma ={\sigma }_p,\frac{d\sigma }{d\epsilon }=0$$ 16

By combining eq with the peak conditions, the model parameters can be derived as follows:

$$m=\frac{1}{\ln \left[\frac{E_{T,p}({\epsilon }_p-{\epsilon }_c)}{{\sigma }_p}\right]}$$ 17

$$F_0=({\epsilon }_p-{\epsilon }_c)m^{1/m}$$ 18

In summary, the segmented damage constitutive model for sandstone under combined stress–temperature–chemical effects can be expressed as follows:

$$\sigma =\{\begin{array}{ll}a{\epsilon }^n,\hfill & 0\le \epsilon \le {\epsilon }_c\hfill \\ E_{T,p}(\epsilon -{\epsilon }_c)\exp [-{\left(\frac{\epsilon -{\epsilon }_c}{({\epsilon }_p-{\epsilon }_c)m^{1/m}}\right)}^m],\hfill & \epsilon >{\epsilon }_c\hfill \end{array}$$ 19

where the compaction stage is governed by a, n, and ε _c , whereas the elastic–brittle stage is jointly determined by E _(T,p), σ _p , and ε_p .

The segmented damage constitutive model developed in this study considers both temperature–chemical damage and loading-induced dynamic damage, with separate formulations for the compaction and elastic–brittle stages. It can be used to describe the stress–strain response of sandstone from initial compaction and elastic deformation to the vicinity of the peak under different thermal–alkaline water conditions. Because post-peak brittle instability is strongly affected by crack localization, rapid coalescence of the failure surface, and the randomness of sudden stress drops, the present model still has limited capability for quantitatively describing the post-peak brittle failure stage.

4.2. Model Fitting and Validation

To evaluate the applicability and accuracy of the proposed model, the uniaxial compression curves of sandstone specimens after 60 h of immersion under different temperature and solution conditions were fitted in a segmented manner, and the model curves were compared with the experimental curves. The model parameters were determined as follows: the elastic modulus E _T,p , peak stress σ_p , peak strain ε_p , and strain at the end of the compaction stage ε _c were directly extracted from the experimental curves, whereas the compaction-stage parameters a and n and the Weibull shape parameter m were determined by inverse fitting. For each test condition, the model parameters were taken as the average values obtained from the two calibration specimens in each round. Without using any mechanical parameters of the validation specimen, the calibrated parameters were used to calculate its stress–strain response, which was then compared with the corresponding experimental curve. This procedure was repeated for three rounds, and the three leave-one-out validation results for each condition were used to evaluate the predictive capability of the model under the same test condition.

As shown in Figure , the model curves calculated using the parameters obtained from the calibration specimens generally agree well with the experimental curves of the validation specimens that were not involved in parameter identification. The model adequately reproduces the nonlinear deformation in the compaction stage and the stress increase from the elastic stage to the vicinity of the peak, indicating that the proposed model has a certain predictive capability for independent replicate specimens under the same temperature–solution condition. Relatively pronounced local deviations are observed in the post-peak stage, mainly because of the randomness associated with the location of brittle failure, crack coalescence paths, and the stress-drop process in sandstone. Therefore, the quantitative applicability of the present model is limited to the pre-peak stage and the vicinity of the peak, and the post-peak brittle instability process is not intended to be predicted precisely.

11.

Comparison of experimental and predicted stress–strain curves under different temperature and solution conditions.

The mean relative error was calculated using the experimental data from the onset of loading to the peak point to quantitatively evaluate the validation accuracy of the model for the pre-peak stress–strain response of the held-out specimens. The calculation is expressed as follows:

$$\delta =\frac{1}{\mathrm{N}}\sum _{i=1}^{\mathrm{N}}\left|\frac{{\sigma }_i-{\sigma }_i^{\prime }}{{\sigma }_i}\right|\times 100\%$$ 20

where δ is the mean relative error, %; N is the total number of data points; ${\sigma }_i^{\prime }$ is the experimental stress, MPa; and σ_i′ is the model-predicted stress, MPa.

To evaluate the model’s ability to describe specimens that were not involved in parameter calibration, three-fold leave-one-out validation was performed separately for the 12 temperature–solution conditions. Each condition contained three independent replicate specimens. In each fold, one specimen was selected as the validation specimen, while the remaining two specimens were used for model parameter calibration. This procedure was repeated three times so that each specimen served once as an independent validation specimen. Model performance was evaluated using the mean relative error between the experimental stress and the model-predicted stress in the pre-peak stage. The three-fold validation results are presented in Table .

7. Three-Fold Leave-One-Out Validation Errors under Different Temperature and Solution Conditions.

condition	Temperature/°C	Fold 1 error/%	Fold 2 error/%	Fold 3 error/%	Mean error ± SD/%
DI water	20	12.84	13.27	12.56	12.89 ± 0.36
pH = 7	20	8.41	8.93	8.67	8.67 ± 0.26
pH = 10	20	10.74	11.29	10.88	10.97 ± 0.28
pH = 12	20	9.83	10.47	10.16	10.15 ± 0.32
DI water	40	9.76	10.34	10.11	10.07 ± 0.29
pH = 7	40	6.48	7.02	6.71	6.74 ± 0.27
pH = 10	40	10.19	10.87	10.54	10.53 ± 0.34
pH = 12	40	11.24	11.91	11.56	11.57 ± 0.34
DI water	60	10.63	11.38	10.93	10.98 ± 0.38
pH = 7	60	5.87	6.45	6.18	6.17 ± 0.29
pH = 10	60	7.31	7.96	7.68	7.65 ± 0.33
pH = 12	60	8.72	9.51	9.09	9.11 ± 0.40

As shown in Figure and Table , the mean relative errors from the three-fold leave-one-out validation ranged from 6.17% to 12.89% across the different test conditions, with an overall mean error of 9.63% for the 12 conditions. The sample standard deviations of the three validation errors ranged from 0.26% to 0.40%. The model-predicted curves generally agreed well with the curves of the held-out specimens that were not involved in parameter calibration in the compaction stage, elastic stage, and vicinity of the peak. This indicates that the model is not limited to reproducing the calibration curves used for parameter determination, but also exhibits a certain predictive capability for independent replicate specimens under the same temperature–solution conditions. The temperature–chemical damage characterizes the initial stiffness degradation induced by environmental treatment, whereas the stress-induced damage describes the accumulation of loading-induced damage associated with microcrack propagation after the compaction stage. Together, these two damage components govern the pre-peak deformation and evolution of the load-bearing capacity of sandstone. The relatively larger validation deviations in the post-peak stage indicate that the model still has limitations in describing the stochastic brittle instability process.

Although the model can reasonably describe replicate specimens under the same test condition that were not involved in parameter identification using parameters obtained from the calibration specimens, indicating a certain adaptability to the natural variability among specimens, its applicability to other rock types, long-term environmental exposure, and complex stress paths remains to be further validated.

5. Conclusions

To investigate the mechanical deterioration and damage evolution mechanisms of sandstone under coupled stress–temperature–chemical effects, roof sandstone from the No. 3 coal seam of Zhaolou Coal Mine in Heze, China, was selected as the research material. Water–rock interaction and uniaxial compression tests were conducted under different temperature and solution conditions. Scanning electron microscopy and X-ray diffraction analyses were further performed to examine the microscopic deterioration mechanisms. Based on the experimental and modeling results, a segmented damage constitutive model incorporating temperature–chemical damage and stress-induced damage was established. The main conclusions are as follows:

• 1)Coupled thermal–alkaline water effects significantly alter the deformation characteristics of sandstone under uniaxial compression. With immersion, increasing temperature, and increasing alkalinity, the specimens exhibit an extended compaction stage, a reduced elastic modulus, decreased peak stress, and enhanced pre-peak nonlinear deformation. The interaction between temperature and alkalinity is significant, substantially weakening the load-bearing capacity and structural stability of sandstone. Under the condition of 40 °C and pH = 10, which is close to the in situ roof-water environment, the sandstone UCS is 49.303 MPa, representing a reduction of 46.37% relative to the dry-state reference value of 91.924 MPa. The most severe deterioration occurs under the intensified condition of 60 °C and pH = 12, where the UCS decreases to 37.724 MPa, corresponding to a maximum reduction of 58.50%.
• 2)After immersion for 60 h in DI water and solutions with pH values ranging from 7 to 12 at temperatures of 20–60 °C, the compressive strength of sandstone decreases linearly with increasing temperature and exponentially with increasing solution pH. The temperature sensitivity is strongest at pH = 7 and gradually decreases with increasing alkalinity, while the rate of strength degradation tends to slow in the highly alkaline range. Two-way ANOVA shows that temperature, pH, and their interaction all have significant effects on the compressive strength of sandstone (p < 0.001), indicating that the temperature effect varies with pH and that increasing temperature further modifies the degree of strength degradation induced by alkaline water.
• 3)The microscopic deterioration of sandstone exhibits a stage-dependent evolution. At pH = 7, mineral hydrolysis and wetting-induced softening are dominant; at pH = 10, hydrolysis and alkaline dissolution act synergistically; and at pH = 12, alkaline dissolution becomes dominant. The net increase in SiO₃ ^2– concentration in the immersion solution rises from 5.694 to 14.235 mg/L. Combined with the XRD-detected changes in the relative contents of feldspar, muscovite, and kaolinite, these results indicate that increasing alkalinity promotes the dissolution of aluminosilicate minerals and the migration of mineral components. SEM observations of particle spalling, crack propagation, and lamellar delamination further demonstrate that mineral dissolution and destruction of the cementation structure jointly promote the continuous development of internal defects in sandstone, ultimately resulting in macroscopic strength degradation.
• 4)The segmented temperature–chemical damage–stress-induced damage constitutive model established based on damage mechanics can characterize the compaction stage, pre-peak damage evolution, and mechanical response near the peak of sandstone. Three-fold leave-one-out validation shows that the mean relative errors for different test conditions range from 6.17% to 12.89%, with an overall mean error of 9.63%. The model exhibits good capability in describing the pre-peak response of replicate specimens under the same test condition that were not involved in parameter calibration. The model is applicable to the characterization of sandstone damage responses within the experimental range considered in this study, namely 20–60 °C, DI water and pH = 7–12 solutions, and an immersion duration of 60 h. Its extrapolation capability across different rock types and environmental conditions requires further validation.
• 5)The strength and stiffness degradation induced by thermal–alkaline water exposure indicates that roof sandstone in deep roadways may have already accumulated initial environmental damage before being subjected to mining-induced loads. Therefore, surrounding-rock stability assessment and support-parameter design should account for the reduction in mechanical properties caused by the temperature and alkalinity of roof water inflow, together with monitoring of water temperature, pH, and surrounding-rock deformation. On this basis, future research will further investigate sandstone damage evolution under long-term thermal–alkaline water exposure and complex stress paths to improve the damage model and verify its engineering applicability.

The datasets generated and/or analyzed during the current study are available from the corresponding author on reasonable request.

This work was funded by the National Key Research and Development Program of China (2024YFC3909304) and the National Natural Science Foundation of China (52574177).

The authors declare no competing financial interest.