Introduction

As precious relics of human history and culture, the relics of the cave temples carry with them a wealth of historical information and artistic value. Limestone artifacts, the main component of which is calcium carbonate, are susceptible to chemical reactions under acidic conditions. This leads to various types of deterioration such as surface weathering, cracking, and mineral dissolution, which compromise the integrity of the appearance and the lasting preservation of stone cultural relics1,2,3. The Longmen Grottoes in Luoyang, China, a representative example of limestone cave temple heritage, have undergone prolonged exposure to natural environmental conditions. Direct contact with rainfall, solar radiation, and atmospheric pollutants has contributed to observable surface weathering and mineral dissolution processes4,5. As shown in Fig. 1.

Fig. 1: Surface diseases of Longmen Grottoes.
Fig. 1: Surface diseases of Longmen Grottoes.
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(The photos were taken by the author; the picture is made by Microsoft PowerPoint).

The accelerated progression of global industrialization has been associated with heightened levels of environmental pollution, particularly in the form of atmospheric pollutants. This, in turn, has contributed to an increased frequency and intensity of acid rain events in numerous regions6,7. When acid rain is retained on the surfaces of stone cultural relics rather than being rapidly drained, it may induce leaching processes. This can result in the dissolution of surface minerals and contribute to structural deterioration of the relics8,9. Previous studies have established that acid rain represents a significant environmental threat to stone cultural relics. The mechanisms of damage and the deterioration effects of acid rain on carbonate cultural relics, such as limestone, have garnered considerable attention. Acid rain not only accelerates the dissolution and surface erosion of limestone—resulting in phenomena such as surface powdering and spalling—but also contributes to the formation of black hard shells, pores, and pits on the rock surface. Additionally, it alters the microstructure of the surface layer while reducing the roughness of joint surfaces10,11,12. Following the dissolution of carbonate minerals, their byproducts are likely to precipitate from the rock surface, further exacerbating mass loss and pore development within samples12,13. Prolonged immersion in an acid rain solution adversely affects the mechanical properties of carbonate rocks. As immersion time increases, both elastic modulus and compressive strength exhibit an exponential decline14. Furthermore, there is a positive correlation between immersion duration in acid rain and corrosion severity; with extended exposure time leading to intensified deterioration in limestone’s surface morphology alongside an increase in precipitation levels for calcium, magnesium, and other ions15,16. The internal structure of the stone became loosened, with a concomitant increase in porosity. Correspondingly, the key mechanical properties, including compressive and tensile strength, exhibited a declining trend. These observations indicate that the long-term pooling of acidic water at the base of the grottoes not only to the dissolution of surface material but also to a progressive degradation of the stone’s mechanical performance. Such latent damage constitutes a non-negligible factor for structural stability. Consequently, it is necessary to analyze the dissolution mechanism induced by acid rain based on the petrological characteristics of the relics. This analysis aims to establish reference thresholds for the conservation of water-affected zones at the grotto base.

Moreover, given the irreplaceable nature of stone cultural relics, obtaining a sufficient quantity of samples for experimental analysis is often impractical17,18. Consequently, traditional mechanical testing methods are limited in their ability to systematically investigate the long-term degradation patterns of the material and the underlying leaching mechanisms under acid rain exposure19,20,21,22. Nanoindentation technology serves as a prominent method for microscale mechanical testing, enabling measurements with nanometric resolution. This technique is applicable for assessing the mechanical properties of both centimeter-scale rock samples and individual mineral components23,24,25,26. For instance, Yin et al.26 employed nanoindentation to validate the uniformity of the mechanical properties of bricks from a Han Dynasty tomb. José et al.27 performed nanoindentation experiments to analyze the micromechanical properties of zircon-glass composites. Buchner et al.28 employed nanoindentation to investigate the microstructural and mechanical properties of fired clay bricks, demonstrating its capability for quantitative assessment even with limited sample availability. These studies collectively indicate that the nanoindentation method offers a reliable approach for evaluating the mechanical properties of masonry materials with considerable precision.

In summary, the systematic investigation into the degradation mechanisms affecting the mechanical properties of limestone relics under prolonged acid rain leaching, utilizing appropriate testing and analytical methods, provides valuable insights for both the preventive conservation of stone cultural relics and the formulation of atmospheric pollutant control policies in the heritage areas. However, there is currently insufficient research into the acid rain leaching mechanism and the mechanical degradation patterns of limestone cultural remains under long-term leaching. The purpose of this study is to systematically reveal the mechanism of mechanical deterioration of limestone cultural remains under long-term acid rain. By immersing scattered fragments of limestone cultural relics in acidic solutions of different pH values for a long time, the long-term erosion effect of acid rain is simulated. The nanoindentation testing method is employed to obtain the micro-mechanical properties of the samples after dissolution. An integrated approach incorporating scanning electron microscopy (SEM), uniaxial compression tests and binary image analysis was employed. This enabled a cross-scale investigation into the coupled deterioration of limestone cultural relics under acid rain dissolution, focusing on the relationship between the microstructure evolution (pores and cracks) and the deterioration of mechanical properties (elastic modulus and compressive strength). It provides a basis for the prevention and control of diseases of limestone cultural relics and the supervision of atmospheric pollutant emissions in the surrounding areas of similar cultural relics.

Methods

Test materials and sample preparation

The test materials comprised surface limestone fragments collected from the Leigu Tai site in the eastern section of the Longmen Grottoes, China. Prior to sampling, preliminary non - destructive testing evaluation of the parent rock was performed using a rebound hammer, a thermal imaging camera and a Lee hardness tester. Sampling locations exhibiting comparable physical properties were identified, and representative fragments from these areas were retrieved for analysis.

A subset of the collected limestone fragments was processed to produce non-standard cylindrical specimens (25 mm in diameter ×50 mm in height, giving a height-to-diameter ratio of 2) for uniaxial compressive strength testing. Another subset was trimmed and polished into specimens measuring 15 × 15 × 5 mm. These prisms were then embedded in epoxy resin (mixed at a resin-to-hardener ratio of 2:1), followed by successive grinding, polishing, and cleaning steps to produce specimens suitable for nanoindentation testing.

The remaining materials after cutting were dried, ground, and passed through a 0.15 mm sieve. An X - ray diffraction pattern was obtained using a Bruker D8 Advance X - ray diffractometer from Germany (Fig. 2a). In their natural state, limestone samples are primarily composed of calcite (CaCO₃) and dolomite (CaMg(CO₃)₂), with respective contents of 84.3% and 12.9%. The integration of XRD quantitative analysis and energy-dispersive spectroscopy (EDS) confirmed that the matrix of the sample consists of calcite, whereas the fine surface-adhering crystals, characterized by significantly elevated Mg content, were identified as dolomite. The samples were characterized by scanning electron microscopy (SEM; Zeiss Sigma 300). Observations revealed that the calcite within the samples exhibited a blocky morphology with well-defined edges. Relatively large pores were observed at the grain boundaries, occupying a considerable proportion of the area. As shown in Fig. 2b, dolomite was found attached to the calcite surfaces, covering a comparatively smaller area.

Fig. 2: The scanning electron microscope image and XRD diffraction pattern of the sample.
Fig. 2: The scanning electron microscope image and XRD diffraction pattern of the sample.
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a XRD diffraction pattern (b) Scanning electron microscope image. (Figure created using Origin Pro and Microsoft PowerPoint).

Simulation of long-term erosion by acid rain

According to the atmospheric precipitation monitoring data from the Luoyang region of China, acid rain in this area is primarily of the sulfuric acid type, with contributions from nitric acid and hydrochloric acid, and the pH values range from 4.38 to 7.80. The annual average precipitation exceeds 700 mm, concentrated mainly in July and August, readily causing water to accumulate at the base of the cave temples29. This experiment used an increased solution pH value to simulate the accelerated effects of acid rain erosion11,14. Based on the chemical composition and pH monitoring data of acid rain from the Luoyang region, the corresponding simulated acid rain solution was prepared to reproduce the proportion characteristics of the main anions (SO₄²⁻, NO₃⁻, Cl⁻) in the local acid rain and the corresponding H+ synergistic corrosion effect13. A mixed-acid stock solution was first prepared by adding 6 mL of H₂SO₄ (60%), 3 mL of HNO₃ (30%), and 1 mL of HCl (10%) to 500 mL of deionized water. This stock solution was then diluted with distilled water to obtain acid rain simulation solutions with nominal pH values of 3.0 (Extreme acid rain type), 5.0 (Typical acid rain type), and 7.0 (Control group) as acid rain simulation solutions30,31. The pH of all solutions was verified using a calibrated pH meter with a resolution of 0.01 and the preparation error was controlled within ±0.02. To simulate the long-term corrosive effects of acid rain, limestone samples were placed in acidic solutions of different pH values, with pH = 7 (distilled water) as the control group, as shown in Fig. 3.

Fig. 3: Test flow chart.
Fig. 3: Test flow chart.
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(Figure composed and annotated using Microsoft PowerPoint).

Testing methods for macro and micro mechanical properties

The micro-mechanical properties of the samples after acid solution erosion were tested using an Agilent G200 nano - indenter from the United States. Before the nanoindentation test, the dried nanoindentation samples were closely attached to the base of the instrument, and the upper surface of the samples was kept parallel. During the test, the indenter was configured to approach the sample surface at a velocity of 10 nm/s. Nanoindentation tests were performed in the CSM mode with the following parameters: a frequency of 45 Hz, a displacement amplitude of 2 nm and a strain rate of 0.05 s−1. The maximum indentation depth was controlled between 2000 and 2200 nm. After reaching the peak load, a 10 s holding period was implemented, followed by unloading at a specified rate. To avoid potential interference between adjacent measurement points, a minimum spacing 20 μm.

By systematically recording the load and displacement data during the loading, holding, and unloading phases of the indenter, a comprehensive load-displacement curve was generated (Fig. 4). The elastic modulus, hardness, and other pertinent mechanical parameters of the sample were calculated using Fig. 5 in conjunction with Eqs. (1) to (5).

Fig. 4: Schematic diagram of load-displacement curve.
Fig. 4: Schematic diagram of load-displacement curve.
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(Figure composed and annotated using Microsoft PowerPoint).

Fig. 5: Indentation profile of nanoindentation.
Fig. 5: Indentation profile of nanoindentation.
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(Figure composed and annotated using Microsoft PowerPoint).

Hardness is a performance index that represents the resistance of a material to indentation, as shown in Formula (1)32.

$$H=\frac{F\,\max }{A{\rm{c}}}$$
(1)
$$A{\rm{c}}=24.5{({h}_{\max }-{\varepsilon }\frac{{F}_{\max }}{S})}^{2}$$
(2)

Fmax is the maximum load (mN); Ac is the projected contact area (Eq. (2)) (nm²); hc is the contact depth at the maximum load (nm); hmax is the maximum displacement (nm).

Contact stiffness S indicates the ability of two contact surfaces to resist deformation, (nN/nm). As illustrated in Fig. 4, the slope of the tangent line at the initial vertex of the maximum load during the unloading phase of the test (Eq. (3)) signifies the contact stiffness.

$$S={(\frac{dF}{dh})}_{h={h}_{\max }}$$
(3)

The reduced modulus Er represents the overall mechanical properties of the indenter and the sample, as illustrated in Eq. (4).

$${E}_{{\rm{r}}}=\frac{\sqrt{{\rm{\pi }}}}{2\beta }\frac{S}{\sqrt{{A}_{{\rm{c}}}}}$$
(4)

\({\beta }\) is a constant related to the geometric shape of the indenter. When using a Berkovich indenter, \({\beta }\) =1.03433.

The true modulus of the sample (E) is the elastic modulus, (GPa), as shown in Eq. (5).

$$E=\frac{1-{{\nu }}^{{2}}}{\frac{1}{{E}_{{\rm{r}}}}-\frac{1-{{\nu }}_{{\rm{i}}}^{2}}{{E}_{{\rm{i}}}}}$$
(5)

\({\nu }\) is the Poisson’s ratio, dimensionless \({\nu }_{i}\) is the Poisson’s ratio of the indenter, dimensionless; \({E}_{i}\) is the elastic modulus of the indenter, GPa; When using a Berkovich indenter, so \({E}_{i}=1141\)GPa, \({{\nu }}_{{\iota }}=0.07\) 33,34;

The single-axis compression test was performed using a microcomputer-controlled electronic pressure testing machine, which regulates the loading method based on displacement. The loading was performed at a rate of 0.02 mm/min until specimen failure. Following the test, the compressive strength and elastic modulus of the non-standard specimens were determined. The test results for specimens with varying height-to-diameter ratios were adjusted using conversion formula (6), as presented in Table 1.

$${\sigma }_{{\rm{c}}}={{\sigma }_{{\rm{c}}}}^{\text{'}}\cdot {K}_{({\rm{h}}/{\rm{d}})}$$
(6)
Table 1 Correction coefficient for the height-diameter ratio in uniaxial compressive strength testing36
Full size table

In the formula, \({\sigma }_{{\rm{c}}}\) is the compressive strength of the standard specimen, MPa; \({{\sigma }_{{\rm{c}}}}^{\text{'}}\) is the compressive strength of the non-standard specimen, MPa K(h/d) is the height-to-diameter ratio correction factor.

Macro and micro mechanical property testing plan

Before conducting macro and micro mechanical property tests on limestone samples, place them in a drying oven to dry and weigh the dried sample mass m0. The 15 nanoindentation samples were divided into three groups based on pH value differences, with each group containing five samples. Nine single-axis compression specimens were divided into three groups based on differences in pH values, with each group containing three valid specimens. It is worth noting that due to the variability of single-axis compression tests, each valid sample is the average value of three parallel samples. As shown in Table 2.

Table 2 The micro-mechanical property testing
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Ion concentration changes and microstructural testing

Given that relevant studies have indicated a more pronounced erosive effect of acidic solutions on limestone with lower pH values, the present investigation selected an acidic solution with a pH of 3 as the representative. Following immersion periods of 360 h, 1080 h, and 1800h, the concentrations of Ca²⁺ and Mg²⁺ ions released into the solution were quantified using ion chromatography (ICS-5000). The microstructure evolution of the limestone samples after these leaching intervals was examined by scanning electron microscopy (Zeiss Sigma 300). Prior to SEM observation, all samples were freeze - dried in liquid nitrogen and sputter - coated with a thin gold layer.

Variation of solution pH and sample mass

The PH values of the acidic solutions with different PH levels were measured using a portable pH meter, the Qi Wei PHB-4, with an interval time of 36 h. The measurement range of the instrument was 0-14.00 pH, with a resolution of 0.01 pH and an accuracy of 0.01 pH.

During the acid solution immersion process, the mass loss of the samples can indirectly reflect the degree of ion exchange of the limestone in the acidic environment. Therefore, the samples after acid solution immersion were dried and compared with their original dried mass. The mass loss rate of the samples was calculated using Eq. (7).

$$M{\rm{C}}=\frac{m0-mn}{m0}\times 100 \%$$
(7)

In the equation, m0 denotes the initial dried mass of the sample (g), and mn represents the dried mass of the sample after immersion in the acid solution for n hours (g).

Results

The variation law of solution PH value and sample mass

As illustrated in Fig. 6a, the pH values of the acidic solutions with different initial pH values changed significantly when the immersion time of the samples was 36 h. At this point, the PH values of the initial acidic solutions with pH = 3.0, pH = 5.0, and pH = 7.0 became 7.40, 8.50, and 9.70, respectively. With the increase of the immersion time, the pH values of the acidic solutions with different initial PH values first increased rapidly and then decreased, tending to stabilize when the immersion time was 1080 h. The pH values of the solutions with initial pH values of 3, 5, and 7 eventually stabilized at 3.50, 5.20, and 7.30, respectively. Analysis indicates that during the initial phase of soaking, calcite (CaCO₃) and dolomite (CaMg(CO₃)₂) rapidly react with H⁺ ions present in the acid rain solution, resulting in the formation of HCO₃⁻ and CO₃²⁻. These ions subsequently undergo hydrolysis, leading to a continuous production of OH⁻ ions, which significantly elevates the pH of the solution; notably, this increase is more pronounced at higher initial pH levels. As the reaction progresses, the availability of carbonate for dissolution gradually diminishes, causing a corresponding decline in the generation rate of HCO₃⁻/CO₃²⁻. Concurrently, atmospheric CO₂ interacts with the system, which slows down H+ consumption. Ultimately, this results in a gradual decrease in pH as it approaches a state of dynamic equilibrium.

Fig. 6: The variation law of solution pH value and sample mass.
Fig. 6: The variation law of solution pH value and sample mass.
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a The variation law of pH value with soaking time (b) Variation law of mass loss. (Figure created using Origin Pro and Microsoft PowerPoint).

As illustrated in Fig. 6b, the mass loss rate of limestone samples immersed in acidic solutions with varying initial PH values exhibited a rapid increase. When the immersion time exceeded approximately t = 1080 h, the rate of mass loss began to decrease and gradually approached a plateau. Throughout the prolonged immersion, the samples underwent progressive dissolution, accompanied by the formation of white particulate precipitates in the solution. When the solution pH was 3 and the immersion time was 1800h, the number of white mineral particles was the highest, which corresponded to a measured mass loss rate of 4.16%. The mass loss rates of the samples after 1800h of immersion in solutions with pH = 5.0 and pH = 7.0 were 1.79% and 1.02%, respectively. Throughout the immersion period, the mass loss rate of the sample in the PH = 3 solution remained higher than those observed in the pH=5.0 and pH=7.0 solutions. This trend demonstrates that the lower solution pH corresponds to a greater extent of dissolution in the limestone cultural relics.

Micromechanical properties of limestone cultural relics

Following acidic solution immersion, the load-displacement curves of the limestone fragments, acquired via nanoindentation, displayed similar overall shapes. However, the maximum indentation load was significantly influenced by both the pH level of the solution and the duration of soaking, as shown in Fig. 7. For a given immersion duration, the maximum indentation load of the sample increases with the PH value of the solution. Conversely, under a constant solution pH value, the maximum indentation load exhibits a decreasing trend with prolonged immersion time.

Fig. 7: The Load-displacement curve after dissolution.
Fig. 7: The Load-displacement curve after dissolution.
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(Figure created using Origin Pro and Microsoft PowerPoint).

Under the extreme conditions of solution pH = 3 and soaking time of 1800 h, the maximum indentation load of the sample decreased sharply from 265.72 mN in the natural state to 76.71 mN. This represents the most substantial degree of mechanical degradation observed among the tested conditions. In contrast, under the condition of PH = 7.0 with an immersion time of 360 h, the sample exhibited the least deterioration, retaining the maximum indentation load of 231.85 mN. These results suggests that the lower the pH of the initial soaking solution, the more fully the high concentration of H+ reacts with the mineral composition in the sample, the higher the degree of damage to the internal structure of the sample, and the mechanical properties decrease significantly. Prolonged immersion extends the duration of the acidic reaction, leading to progressively greater internal damage and more pronounced deterioration of the limestone.

As shown in Fig. 8a, when the limestone sample is immersed for the same duration, the elastic modulus of the sample gradually decreases with the decreases in the PH value of the soaking solution. The elastic modulus of the natural state limestone samples was 65.75 GPa. The elastic modulus of the samples immersed in acidic solutions of varying pH values exhibited a gradual decrease as the soaking time increased, concomitantly, the loss rate of the elastic modulus progressively rose. Among them, during the soaking time of 0–720 h, the elastic modulus of the sample decreased rapidly, the loss rate of elastic modulus increased rapidly, and the deterioration effect of the sample was obvious. After soaking in acidic solution for more than 1080 h, the elastic modulus of the sample decreased, but the decrease slowed down and tended to be stable. The degree of deterioration in the microscopic elastic modulus of the limestone sample becomes more pronounced with increasing acidity of the soaking solution and extended soaking duration.

Fig. 8: The deterioration trend of microscopic elastic modulus and hardness.
Fig. 8: The deterioration trend of microscopic elastic modulus and hardness.
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a Microscopic elastic modulus and corresponding loss rate of samples. b Hardness variation and corresponding loss rate of samples. (Figure created using Origin Pro and Microsoft PowerPoint).

As shown in Fig. 8b, under a given solution pH value, sample hardness decreased with prolonged immersion time. Conversely, for a fixed immersion duration, the hardness of the samples increased progressively with higher pH value of the acidic solution. The untreated natural limestone exhibited a reference hardness of 2.4 GPa. For samples immersed in acidic solutions of varying pH values, the elastic modulus and hardness both exhibited a decreasing trend with prolonged immersion time, accompanied by an increase in the rate of hardness loss. Notably, during the initial 0–720 h period, both hardness decrease and hardness loss rate accelerated markedly, coinciding with the formation of white precipitates in the solution. After more than 1080 h of immersion in acidic solution, the hardness of the sample showed a gradual decline and eventually approached a plateau. Furthermore, the degradation of microhardness was enhanced by both higher acidity and longer exposure time.

Macroscopic mechanical properties of limestone cultural relics

The macroscopic elastic modulus (Fig. 9a) and uniaxial compressive strength (Fig. 9b) of the limestone samples are consistent with the degradation patterns of the micro-mechanical properties of the samples. For the same pH value of the acidic solution, the compressive strength and macroscopic elastic modulus of the samples decrease with the increase of the immersion time. At the same immersion time, the compressive strength and macroscopic elastic modulus increase gradually with the increase of the pH value of the acidic solution. After 1080 h of immersion in the acidic solution, the rate of decline in the compressive strength and macroscopic elastic modulus diminished, with both properties gradually approaching a plateau. Additionally, the extent of degradation in these mechanical properties increased with higher solution acidity and longer immersion duration.

Fig. 9: Macroscopic mechanical properties of the specimen.
Fig. 9: Macroscopic mechanical properties of the specimen.
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a Macroscopic elastic modulus and loss rate (b) Uniaxial compressive strength and loss rate. (Figure created using Origin Pro and Microsoft PowerPoint).

Investigation into the deterioration mechanism of mechanical properties in limestone cultural heritage

The primary constituents of the limestone samples utilized in the experiment were calcite (CaCO₃, 84.3%) and dolomite (CaMg(CO₃)₂, 12.9%). During the immersion in acidic solution, the primary mineral calcite is dissolved in the acid-rock reaction, generating Ca²⁺. Therefore, in the solution the total concentration of Ca²⁺ is always higher than that of Mg²⁺. As shown in Fig. 10, with the increase of the immersion time, the concentrations of Ca²⁺ and Mg²⁺ in the solution are continuously increasing. Among them, during the period of 0-360 h of immersion, the rate of change of Ca²⁺ and Mg²⁺ concentrations in the solution are the greatest, indicating the most intense reaction. After 1080 h of immersion, the rate of change of Ca²⁺ and Mg²⁺ concentrations in the solution slows down, indicating that the acid-rock chemical reaction begins to slow down until it reaches chemical equilibrium. The acidic solution enters the interior of the limestone through its natural fractures, further increasing the degree of damage to the cultural relics and causing a decline in their mechanical properties. Furthermore, with prolonged immersion, the width and depth of the fractures within the limestone increased, leading to of extensive, continuous zones of damage their progressive interconnection and the formation. The chemical reaction mechanism between acidic solutions and limestone samples explains the deterioration of their macro-mechanical and micro-mechanical properties.

Fig. 10: The long-term erosion process of acid rain and the changes in ion concentration.
Fig. 10: The long-term erosion process of acid rain and the changes in ion concentration.
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(Figure created using Origin Pro and Microsoft PowerPoint).

A comparison and analysis with the SEM images of the natural state limestone samples reveals that the size, shape, number, and dimensions of the surface mineral grains of the limestone samples immersed in acidic solutions with different PH values have undergone significant changes35, as shown in Fig. 11a. Based on microstructural observations, the degradation process can be categorized into three stages. Flat and Dense Stage. In their natural state, the limestone samples displayed a relatively flat and compact microstructure. The mineral grains were predominantly round and flat, with a uniform and closely packed distribution. No significant pores or fractures were observed at this stage. Pore Development Stage. As the immersion time of the limestone samples in the acidic solution increases (1080 h), the number of pores on the sample surface gradually increases, and the pore size enlarges. Some areas exhibit a “honeycomb” structure. Compared to the natural state, the surface clastic particles of the samples begin to decrease, with evident signs of erosion. The pores between mineral grains expand, dissolution cavities emerge, and the structure becomes progressively more porous and loose. Fracture development stage. Following 1800 h of immersion in acidic solution, the surface microstructure of the limestone underwent pronounced alteration. Most of the clastic particles are dissolved. The dense structure is transformed into loose and porous. It can also be seen that the pores between mineral grains significantly increase in size and number. Small pores, fractures, and cracks gradually expand and interconnect to form large cavities. In localized regions, this process led to the development of interconnected through-cavities, accompanied by the partial collapse and destabilization of the primary mineral framework.

Fig. 11: Changes in the microstructure of the sample.
Fig. 11: Changes in the microstructure of the sample.
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a SEM image of the sample (b) Binary image. (Figure created using Origin Pro and Microsoft PowerPoint).

The SEM images were converted from RGB to 8 - bit grayscale images. Then, the brightness and background of the images were adjusted, and the images were subjected to uniform grayscale distribution and uniform blurring. Finally, under the determined threshold T = 46 (0 ≤ T ≤ 225), the SEM images of the samples under different PH values of acid rain solution were binarized, transforming the SEM images into either black or white colors. As shown in Fig. 11b, the statistical analysis of the defect area of the SEM image of the limestone sample after the acid solution immersion was carried out. The white part is the defect area (loose/porous structure), and the black part is the limestone matrix (dense structure). As the soaking time increases, the dissolution holes between the minerals of the limestone sample gradually grow and expand until they connect, increasing the size of the defective area. The greater the acidity, the more significant the effect.

Statistical analysis was carried out on the binarised images. It was found that the area of surface defects of the limestone gradually increased with the length of time spent immersed in acidic solutions with varying PH values. The higher the acidity, the greater the increase in the proportion of defective areas on the surface of the sample during the immersion period. If the immersion time is at or above 1800h, the fraction of defective areas on the sample surface is tends to stabilize.

The relationship between the macro-compressive strength and macro-elastic modulusand micro-elastic modulus of limestone samples and the proportion of defective areas after immersion in acidic solutions is shown in Fig. 12a–c. The macro-compressive strength and macro-elastic and micro-elastic modulus of limestone samples are basically negatively correlated with the proportion of defective areas in a linear manner. This shows that the main factor causing deterioration of macro- and micro-mechanical properties is the increase in the proportion of microstructural defects. The physical degradation of limestone cultural remains by acid rain leaching is essentially due to the dissolution and destruction of their microstructures.

Fig. 12: The relationship between defect areas and macro and micro mechanical properties.
Fig. 12: The relationship between defect areas and macro and micro mechanical properties.
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a The change of macroscopic elastic modulus with the defect area. b The change of uniaxial compressive strength with the defect area. c The change of micro elastic modulus with the defect. (Figure created using Origin Pro and Microsoft PowerPoint).

Discussion

In this study, dispersed limestone fragments from the Longmen Grottoes served as the research objects. The long-term dissolution effects of acid rain were simulated by immersing samples in acidic solutions of varying pH values. The resulting changes in surface morphology and the deterioration patterns of mechanical properties were investigated. The micromechanical properties were characterized via nanoindentation test. Furthermore, the degradation mechanism was analyzed across scales by integrating scanning electron microscopy (SEM), uniaxial compression testing, and Image analysis technology.

The long-term dissolution process induced by acid rain exhibits distinct stages. During the initial stage (0–360 h), the H+ from the acidic solution reacts violently with calcite and dolomite. This leads to a rapid rise in the pH of the solution, substantial mass loss of the sample, and a leachate in which the Ca2+ concentration exceeds that of Mg2+. In the intermediate stage (360–1080 h), the reaction rate decreased and the measured parameters (e.g., pH, ion concentration) gradually stabilized. In the later stage ( >1080 h), the system approached a state of dynamic equilibrium, where the rates of mineral dissolution and secondary precipitation became comparable. Throughout this process, the microstructure of the stone evolved from an initially dense state to a porous one, ultimately developing interconnected fractures. This microstructural degradation showed a linear negative correlation the mechanical properties, indicating that structural damage is the primary driver of mechanical deterioration. Both microscale (elastic modulus, micro hardness) and macroscale (uniaxial compressive strength, elastic modulus) properties of the samples decreased with prolonged acid rain corrosion time. The rate of this decrease diminished after approximately 1080 h, with the properties gradually approaching a stable plateau. The mechanical properties exhibited a consistent deterioration trend across both macro and micro scales. By applying the Mori-Tanaka model to scale the microscopic mechanical parameters, the predicted results showed close agreement with experimental macroscopic data. This approach offers a viable method for assessing property degradation while mitigating the challenge of obtaining large samples from cultural relics.

This study offers relevant insights for the conservation of limestone cultural relics, particularly those located in regions experiencing frequent acid rain or affected by persistent water accumulation at their base. It is recommended that key parameters, such as the PH value and precipitation chemistry of local rainfall, be monitored continuously in critical conservation areas. Furthermore, given the marked attenuation of mechanical properties and the pronounced degradation of surface morphology induced by prolonged acid rain dissolution, the establishment of effective drainage system is advised to mitigate water-related deterioration. Compared with previous studies, this work addresses the practical limitations of obtaining large samples from cultural relics by utilizing dispersed fragments for testing. It systematically simulates and analyzes the evolution of surface morphology and the deterioration of mechanical properties in limestone relics under t prolonged acid rain exposure. Furthermore, the findings derived from this cross-scale analytical approach provide supportive evidence for established theories of acid rain corrosion on carbonate stone. However, this study has several limitations. First, it primarily examined the effects of H⁺ concentration (pH) and exposure time, while differences among specific acid anions (e.g., SO₄²⁻, NO₃⁻) were not treated as independent variables. In actual acid rain, each anion may potentially influence the microstructure and mechanical properties of the stone through the formation of calcium salts and secondary products with differing solubilities. Second, the experimental approach relied on an accelerated acid immersion test under controlled laboratory conditions, which represents a simplification of complex natural environments. Finally, the use of dispersed fragments, though practical, may limit the full representativeness of the samples with respect to in situ relic materials. Future research should investigate the combined effects of diverse pollutants and environmental factors present in real-world acid rain. Employing field-based or environmental chamber aging tests would yield data more representative of actual degradation processes. Expanding the research to include a wider variety of lithic materials would enhance the generalizability of the findings. Such work is essential for developing more robust conservation strategies and supporting the long-term preservation of stone cultural heritage.