Chemical weathering records in Yungang Formation, North China: implications for stone heritage conservation

Abstract

The Yungang Grottoes located in Datong area, North China, have experienced extensive surface and structural damage. Previous studies have recognized the importance of temperature and water during weathering, but the quantitative evaluation on both the physical and chemical weathering remains absent. Here we conducted geochemical analyses on the sculpture-hosting sedimentary rocks of Shiku Member in Jurassic Yungang Formation. The results reveal that feldspar dissolution is predominant during chemical weathering, while the effects caused by other factors like calcic cement and sulphate are minor. The estimated chemical weathering rate of feldspar is 7.84 × 10⁻²¹ - 2.7 × 10⁻¹⁸ mol·cm^-2·s⁻¹, with an average cumulative chemical weathering amount of 1.46 × 10⁻¹¹ mol·cm^-2·y⁻¹. The mass loss caused by chemical weathering is about 0.000061% per year and the annual mass loss rate is approximately 0.00015%–0.00018% when the effect of physical weathering is considered. The damage (5% mass loss) of Yungang Grottoes (450–520 AD) began in ca. AD 800 and all grottoes will be destroyed in the upcoming 4,000–5,000 years without protection. As the chemical weathering of feldspar is controlled by local temperature change, the grottoes should be accommodated in relatively constant low-temperature environment through adding eaves and air conditioners.

1 Introduction

Grottoes are common stone heritages that provide valuable records of the contemporaneous social environment, production activities, transformation and utilization of nature, religious customs and other social conditions (Gomez-Heras and McCabe, 2015; Li et al., 2014; Ponziani et al., 2012). The diverse grottoes hold crucial clues to explore historical truths and preserving unique historical, scientific, cultural, social, economic, and artistic values (Guo and Bai, 2024).

The Yungang Grottoes, located on Wuzhou Mountain in Datong area of Shanxi Province, have existed for 1,500 years and attract thousands of tourists every year (Shao et al., 2024). Historical records suggest that there might be 100,000 stone Buddhas across the Yungang Grottoes (Wang et al., 2014). However, since the grottoes are large and difficult to move, they have been significantly affected by natural environments and human activities over a long period (Zhang et al., 2022), resulting in surface weathering and structural damage, e.g., cracking, collapse and shedding (Figure 1) (Guo and Jiang, 2014). Thousands of statues have been lost due to increasing damage by natural weathering, making it necessary for immediate protection.

FIGURE 1

The weathering processes include physical and chemical weathering. On the one hand, physical weathering refers to the process of rock disintegration and fragmentation into debris and particles of various sizes due to physical and mechanical forces. There has been significant damage caused by physical weathering in the Yungang Grottoes. Cracks in the grottoes have been detected using various methods since the last century (Huang and Zhang, 1998), which provide a pathway for rainwater infiltration, posing a significant obstacle to the preservation efforts of the Yungang Grottoes. The local climate is characterized by concentrated rainfall in summer, rainwater is also within the category of physical weathering (Camuffo, 1995). In addition, frequent and cyclic temperature variations induce the development and expansion of pores and cracks, thereby accelerating the degradation and weathering processes of rock in the grotto temples (Vlcko et al., 2009; Xia et al., 2024). When the temperature decreases, condensation water forms and leads to the degradation of the Yungang Grottoes (Huang et al., 2022). Furthermore, dust deposition and black soot stains appear in multiple grottoes, significantly affecting the weathering resistance and aesthetic value (Liu et al., 2011). Finally, the southern flanks of grottos, more frequently exposed to sunlight, show greater intensity of weathering than the northern flanks (Ren et al., 2019). On the other hand, chemical weathering refers to the process in which rocks undergo compositional change and form new substances under the influence of various factors such as water, carbon dioxide, SO₂ and oxygen. Destruction caused by chemical weathering, such as salt crystallization, calcite deposition and kaolinization of feldspar (Fu et al., 2009; Yuan and Feng, 2004), is also commonly observed, including Grottoes No. 41 and No. 45 (Liu et al., 2011).

Previous studies have widely recognized that temperature and water play crucial roles in both the physical and chemical weathering processes of grottoes (Becherini et al., 2010; Li et al., 2019; Paradise, 2002; Ponziani et al., 2012; Warscheid and Braams, 2000; Yan et al., 2007). For instance, temperature and humidity influence the formation of condensation water, freeze-thaw cycles, and ice wedging (Ponziani et al., 2012; Xia et al., 2024; Yang et al., 2018; Zhou et al., 2023). Moreover, low pH value of water accelerates the chemical weathering in the Yungang Grottoes (Bastien et al., 2016; Zhang et al., 2009). Nevertheless, the quantitative evaluation of both physical and chemical weathering on the Yungang Grottoes remains absent, making it difficult to accurately implement protection measures and extend the life of these stone heritages. The dissolution rate of minerals (such as feldspar and calcite) in solution can be used to quantitatively estimate the intensity and timescale of chemical weathering (Burch et al., 1993; Crundwell, 2015a; Crundwell, 2015b; Steefel and Cappellen, 1990). The Yungang Grottoes are just engraved on the sedimentary rocks (mainly feldspar-quartz sandstones) of Shiku Member (here Member refers to a lithostratigraphic unit) in the Jurassic Yungang Formation and show extensive chemical weathering. We therefore conduct geochemical analyses (mineralogy and chemical compositions) on 19 samples of sedimentary rocks from the Shiku Member (lithostratigraphic unit). The aims of this study are focused on the main factors influencing the chemical weathering and estimation of the weathering rate in accordance with the local climate data. The results have potential for developing targeted recommendations and evaluating protection strategies, and for reducing the weathering of the Yungang Grottoes.

2 Methods and materials

2.1 Material sampling

The Yungang Grottoes are located in the southern foothills of Wuzhou Mountain, about 16 km west of Datong City, Shanxi Province, North China, with a geographical location of 113°20′E and 40°04′N. The Datong area has a temperate continental monsoon climate, with average annual rainfall of 330 mm (Yuan and Feng, 2004). The grottoes are excavated on the sandstones of Shiku Member (lithostratigraphic unit) of Yungang Formation (Figure 2) (Fan et al., 2014; Shao et al., 2024). The mineral composition of Yungang grottoes mainly includes quartz, feldspar, calcite, with accessory clay minerals and sulfate. The sulfate is usually associated with calcite on the surface of the sandstones, representing the reacted product between the atmospheric SO₂, vapor and calcite (Liu et al., 2011; Zhang et al., 2023). There are 45 main caves and 209 affiliated caves, with a carving area of more than 18,000 square meters. There are more than 1,100 Buddhist niches and more than 59,000 statues (Ma et al., 2005; Zhang et al., 2023).

FIGURE 2

We collected 19 samples (Nos. 19YG-01 to 19YG-19) from bottom to top (Figure 2C) of a profile (113°15′E, 40°11′N) of Shiku Member (lithostratigraphic unit) located about 3 km east of the Yungang Grottoes (Ai et al., 2021). The sedimentary profile exhibits nearly horizontal layers with very low dip angles (<10°, Figure 2C), showing minimal deformation and indicating a relatively tectonically stable setting since the Middle Jurassic (Taherynia et al., 2016; Zhou et al., 2017). The color, grain size, and lithology in the profile are completely identical to those sedimentary strata where the Yungang Grottoes are carved (Figure 2C).

2.2 Analytical techniques

The bulk-rock major and trace element contents were analyzed at Tongwei Analytical Technology Co., Ltd., in Guiyang, China. The fresh samples were cut and finely ground to powders of <200 mesh. For major element analysis, approximately 0.5 g of the powdered sample were dried at 105°C for at least 2 h to remove the adsorbed water, and then these samples were mixed with with 3.6 g of Li₂B₄O₇, 0.4 g of LiF, 0.3 g of NH₄NO₃, and a small amount of LiBr in a platinum crucible. This mixture was then melted in a furnace to create a glass disk. Major oxide concentrations were determined using ARL Perform ‘X 4200 X-ray fluorescence (XRF) spectrometer produced by Thermo Fisher. The standard samples GSR-1 (granite), GSR-2 (andesite), and GSR-3 (basalt) were repeatedly analyzed to obtain consistent results, with analytical errors within 2% (Fan et al., 2004; Wen et al., 2024).

During trace element analysis, approximately 0.1 g powder was digested in a mixture of 1 mL HNO₃ and 0.5 mL HF within high-pressure Teflon bombs. Steel-jacketed bombs were used for the digestion process, being placed in an oven at 195°C for 2 days to ensure complete digestion. Once cooled, the bombs were opened, and the contents were dried on a hotplate. They were then re-dissolved with 5 mL of 15 wt% HNO₃ and 1 mL of Rh internal standard, sealed, and placed in an oven at 150°C overnight. Aliquots of the digested solutions, diluted by a factor of 2000, were nebulized into an Agilent Technologies 7,700x quadrupole ICP-MS for trace element analysis. Repeated analysis of W-2a (diabase) and BHVO-2 (basalt) yields an analysis error of ≤5% (Liu et al., 1996; Wei et al., 2022).

To further determine the mineral compositions of the sedimentary rocks in the Shiku Member (lithostratigraphic unit), we selected 1-3 samples from each lithology for X-ray diffraction (XRD) analysis (Li et al., 2018; Li et al., 2019). The XRD analyses were also conducted at Guangzhou Tuoyan Testing Co., Ltd. About 0.5 g sample powder is set into the groove of microprobe slide and then is analyzed by a D8ADVANCE X-ray diffractometer (Bruker, Germany) at room temperature with a relative humidity of 50%. The test adheres to the SY/T 5163–2010 standard. The instrumental conditions include a Cu target, a voltage of 40 kV and a current of 100 mA for the X-ray tube, scanning width to 0.02° (2θ), and a step time of 1 s. The original data of XRD analyses are listed in Supplementary Table S1.

The particle size of the sample was investigated using a polarizing microscope. The grain size of terrigenous debris was determined according to the Udden-Wentworth grain size standard. Moreover, alizarin red S was used for staining to enhance the observations (the calcite shows red).

3 Results and discussion

3.1 Mineral compositions of the Shiku Member

The studied samples (from 19YG-01 to 19YG-19) are mainly composed of quartz (Qtz), plagioclase (PL), K-feldspar, calcite (Cal) and clay minerals (Figure 3) with a small amount of accessory dolomite and hematite. These minerals have angular shapes, showing the characteristics of near-source deposition (Kovach et al., 2023).

FIGURE 3

As illustrated in Figure 4, the XRD results (Table 1) obtain the main mineral components of the 10 samples in the Shiku Member (Figures 5B–E). The lithology of the sample (Figure 5A) is strongly correlated with the particle size. The main minerals of sandstone include quartz (35.2%–48.1%, average of 42.0%), K-feldspar (13.2%–25.0%, average of 18.1%), plagioclase (11.7%–20.8%, average of 14.1%), calcite (3.9%–23.5%, average of 13.4%) and clay minerals (7.0%–12.8%, average of 9.7%). The mineral phases of mudstone are obviously different from those of sandstone, including quartz (34.3%–56.2%, average of 46.1%), K-feldspar (0%–22.0%, average of 11.6%), plagioclase (5.1%–11.7%, average of 7.3%), and clay minerals (14.6%–30.3%, average of 23.4%), with little or even no carbonate found. The whole section contains very little dolomite and hematite.

FIGURE 4

FIGURE 5

3.2 Chemical weathering index of the Shiku Member

The chemical index of alteration (CIA) is extensively utilized to assess the weathering intensity of samples (Nesbitt and Young, 1982). The CIA is calculated based on the oxide content to assess the degree of transformation from feldspar minerals to clay minerals. The formula for CIA is as Equation 1:

The oxide contents used in the calculations are derived from the XRF results. CaO^* represents the Ca content in the silicate component (excluding nonsilicate materials such as carbonates and phosphates). McLennan et al. (1993) proposed an indirect method to calculate CaO^*. They introduced a parameter of CaO_Residual = CaO - (10/3 × P₂O₅); if CaO_Residual < Na₂O, then CaO^* = CaO_Residual; if CaO^* > Na₂O, then CaO^* = Na₂O (McLennan et al., 1993). All oxides are expressed as molar fractions during the calculation.

According to Formula 1, the CIA values of the Shiku Member (lithostratigraphic unit) range from 59.7 to 85.9, with an average of 68.7 (Figure 5F). Notably, there is a significant CIA shift between 19YG-12 and 19YG-13, which corresponds to a change in grain size and lithology. Most of these samples from 19YG-01 to 19YG-12 are sandstones, which exhibit lower CIA values (59.7–68.8, with an average of 64.1), while the samples from 19YG-13 to 19YG-19 are mostly mudstones, which have higher CIA values (69.4–86, with an average of 77.4). Based on the weathering intensity indicated by the CIA value, we roughly subgroup the profile into sandstone section and mudstone section. The sandstone section includes the samples from 19YG-01 to 19YG-12 and the samples of 19YG-13 to 19YG-19 in the mudstone section. It should be noted that there are sandstones interbedded in the mudstone section; similarly, some mudstones are interbedded in the sandstone section.

3.3 The elemental migration trends

represents the weight percentage of the mobile element i in the protolith, while ​ indicates the weight percentage of the mobile element i remaining in the weathered (or altered) product (Ng et al., 2001). According to this formula, when X_gpi is greater than 0, it indicates elemental migration in, and vice versa. We plot the change of X_gpi in Figures 5G–J. The X_gpi values in the sandstone section decrease strongly, e.g., X_gpi-Na changes from 31.55 to −55.26, K decreases from 20.5 to −56, X_gpi-Al decreases by 80, and X_gpi-Si also decreases from 31.7 to −49. In contrast, the X_gpi values for the mudstone section exhibit less variations (Figures 5G–J): the X_gpi-Na is about −25.9, X_gpi-K is approximately −48.6, X_gpi-Al is close to −39.5, and X_gpi-Si is nearly −39.5.

FIGURE 6

However, almost no sulphate has been identified in our studied samples from the Shiku Member profile, suggesting that the role of acid rainfall was insignificant during the chemical weathering of the sandstones. Possible reasons include: (1) the road was built when the atmospheric SO₂ was at low levels, and/or (2) the mudstone section acted as a shielding layer and blocked the penetration of acid rainfall into the sandstone section.

3.4 Chemical weathering rate of the Yungang Grottoes

It has been well acknowledged that temperature and pH significantly influence the feldspar dissolution rate (Bastien et al., 2016; Ponziani et al., 2012; Zhou et al., 2023). To quantify their impacts, several equations have been proposed to calculate the dissolution rate, including the linear transition state theory (L-TST) rate law (Aagaard and Helgeson, 1982), the nonlinear transition state theory (TST) rate law (Steefel and Cappellen, 1990), the parallel rate equation (Burch et al., 1993), the rate law of the step wave model (Lasaga and Luttge, 2001), and the partial equilibrium law (Crundwell, 2015a; Crundwell, 2015b). Considering that reactions typically occur far from equilibrium under natural conditions, we adapt the L-TST rate equation (Equation 7) to estimate the dissolution rate of feldspar:

In this equation, m is the mineral index. In this paper, we do not consider anorthite to be a major phase during chemical weathering of the Yungang Grottoes, as indicated by petrographic observations, so m represents only albite and K-feldspar. r_m expresses the chemical weathering rate (mol·cm^-2·s^-1), k_m denotes the reaction rate constant at temperature T (mol·cm^-2·s^-1), A represents the specific surface area (cm²/g), signifies the hydrogen ion activity, and n is the empirical reaction order. In this study, the reaction order of albite is 0.572, that of K-feldspar is 0.823 (Palandri and Kharaka, 2004), ΔG_m is the change in the Gibbs free energy (kJ·mol⁻¹) of the reaction, and σ stands for the Temkin’s average stoichiometric number (Matylda et al., 2022). In the dissolution reaction of albite and potassium feldspar, Temkin’s number is 3 because in 1 mol of albite and K-feldspar, the stoichiometric coefficient of Si is 3 (Matylda et al., 2022). R is the gas constant with a value of 8.314 J/kcal·mol, and T is the Kelvin temperature.

k_m can usually be calculated according to the reaction rate constant at 25°C under far-from-equilibrium conditions and the derivation of the van’t Hoff Equation 8:k_25,m is the reaction rate constant (mol·cm^-2·s⁻¹) at 25°C, and Ea_m is the activation energy (KJ/mol). During the calculation, the reaction rate constants of albite and K-feldspar are 1 × 10⁻¹⁵ mol·cm^-2·s⁻¹ (Knaus and Wolery, 1986) and 1 × 10⁻¹⁶ mol·cm^-2·s⁻¹ (from the PHREEQC thermodynamic database), respectively. The activation energies of albite and orthoclase used in the calculations under alkaline conditions are 71 kJ/mol and 94.1 kJ/mol, respectively (Palandri and Kharaka, 2004; Yuan et al., 2019).

A can be calculated using Formula 9 proposed by Brantley and Mellott (2000):

In Equation 9, b = 5.2 ± 0.2, m = −1.0 ± 0.1, and d is the particle diameter (μm).

According to the Gibbs free energy equation, ΔG_m is:

Here, ΔH_m represents the standard molar enthalpy of formation (KJ/mol), T represents the Kelvin temperature, and ΔS_m signifies the standard molar entropy of formation (J/Kcal·mol). According to thermodynamic data (Huang et al., 2009), the ΔH_Ab of the albite dissolution reaction is −77.57 kJ/mol, the ΔS_Ab is 0.91 J/kcal·mol, and the ΔH_Or and ΔS_Or of the K-feldspar dissolution reaction are −21.52 kJ/mol and 1.27 J/kcal·mol, respectively.

Combining Equations 8–10, we can obtain the chemical weathering rate:

The α_Ab is the proportion of the albite component.

Previous studies have demonstrated notable discrepancies in feldspar dissolution rate between laboratory and field conditions, which are attributed to variables such as temperature, pH, and mineral surface reactivity (Gruber et al., 2014; Reeves and Rothman, 2013; White and Brantley, 2003). To address these variations, all parameters employed in this study were exclusively derived from site-specific data of the Yungang Grottoes. Although thermodynamic parameters originate from laboratory measurements, they represent intrinsic characteristics and are thus independent of experimental or natural conditions. For instance, based on the sandstone composition of the grottoes, characterized by particle sizes ranging from 0.063 to 2 mm, we calculated a specific surface area of 153.71 cm²/g using Equation 9. Field data collection focused on the hydrogeochemical parameters in the Datong region during 2022. The temperature in Yungang area ranged from 255.65 K (−17.5°C) to 301.15 K (28.0°C), with a mean value of 280.75 K (7.6°C). The pH of groundwater changed little, with the lowest pH of 7.91 and an average pH of 8.23. Detailed groundwater pH and temperature profiles are presented in Figure 7 (Panels A and B, respectively), with complete datasets archived in Supplementary Table S2. The shaded colorful fields in Figures 7, 8 represent the calculation error bars, which are derived from the difference between the average temperature and the maximum or minimum of multiple measured values per day; and they are same for the pH value of groundwater (one measurement for every 4 h).

FIGURE 7

FIGURE 8

According to Formula 11, we explored the relationships between chemical weathering rate and pH and temperature (Figure 7). In Figure 7C, the average temperature of 280.75 K is fixed to show the influence of pH on the chemical weathering of feldspar. The pH shows a mirror relationship with the chemical weathering rate of feldspar, with the lowest pH (7.91) corresponding to the highest weathering rate (3.43 × 10⁻¹⁹ mol·cm^-2·s⁻¹) and the highest pH (8.51) corresponding to the lowest weathering rate (1.55 × 10⁻¹⁹ mol·cm^-2·s⁻¹). In Figure 7D, the average pH (8.23) is fixed to show the influence of temperature. A positive correlation exists between the chemical weathering rate and temperature, with the highest temperature of 301.15 K (28.0°C) corresponding to the highest weathering rate (1.78 × 10⁻¹⁸ mol·cm^-2·s⁻¹) and the lowest temperature of 255.65 K (−17.5°C) corresponding to the lowest weathering rate (1.14 × 10⁻²⁰ mol·cm^-2·s⁻¹). Our calculation results agree with prior studies on feldspar-fluid interactions, indicating that an increase in temperature elevates the fraction of activated molecules, while a decrease in pH enhances the availability of H⁺, thereby facilitating the reaction (Bastien et al., 2016; Zhou et al., 2023).

The chemical weathering rate of feldspar caused by the temperature change is much greater than that caused by the pH shift (Figures 7C,D). When the pH changed (Figure 7C), the maximum (3.43 × 10⁻¹⁹ mol·cm⁻²·s⁻¹) and minimum (1.55 × 10⁻¹⁹ mol·cm⁻²·s⁻¹) weathering rates were only about 2 times different. While, when the temperature changes (Figure 7D), the maximum chemical weathering rate is 1.78 × 10⁻¹⁸ mol·cm^-2·s⁻¹, the minimum chemical value is 1.14 × 10⁻²⁰ mol·cm^-2·s⁻¹, and the difference is approximately 150 times greater. In the Shiku Member (lithostratigraphic unit), the effect of temperature on the chemical weathering rate is more obvious than that of pH. This difference in weathering rate is probably attributed to the greater variation in temperature than in groundwater pH (Figures 7A, B).

The daily weathering amount (A_d, mol·cm^-2·day^-1) and annual cumulative weathering amount (A_c, mol·cm^-2·year^-1) are estimated by the following Equations 12, 13:

According to the calculation results (Figure 8A), the chemical weathering rate in summer is faster (0.3–2.3 × 10⁻¹³ mol·cm⁻²·day^-1), while that in winter is the lowest (close to 0). The chemical weathering rate in spring and autumn is moderate, ranging from 0.1–0.3 × 10⁻¹³ mol·cm⁻²·day⁻¹.

The cumulative weathering amount (Figure 8B) can more intuitively reflect the chemical weathering process within a year. In spring and autumn, the cumulative weathering amount is about 0.2–0.3 × 10⁻¹¹ mol/cm², while in summer, it reaches around 9.2 × 10⁻¹² mol/cm². The weathering amount in summer accounts for approximately 62.8% of the annual weathering value.

3.5 Implications for the protection of Yungang Grottoes

It is crucial to determine the chemical weathering rate that helps estimate the timescale for structural damage of the Yungang Grottoes when protective measures are absent. The annual percentage of chemical weathering can be calculated by R_c with the following formula:

Here, η represents the annual chemical weathering percentage; α represents the mineral component content, and M is the molar mass of the corresponding mineral. In accordance with Equation 14, the chemical weathering percentage of Yungang Grottoes in 2022 is approximately 0.000061%.

Although the roles of physical weathering processes, such as precipitation, cracks, dust deposits, black smoke, condensation water (Qin et al., 2016) and salt crystallization (Zhang et al., 2013), have been identified, whereas the quantitative evaluation of physical weathering on the Yungang Grottoes remains absent.

In accordance with the estimation method proposed by Gabet and Mudd (2009), there is a quantitative relationship of about 1.5–1.9 times between physical and chemical weathering in tectonically stable regions such as the Datong area, North China. Accordingly, we can estimate that the amount of weathering (chemical + physical weathering) of the Yungang Grottoes is approximately 0.00015%–0.00018%.

According to Cai (2022), when the mass loss ratio of sandstone reaches about 5%, cracks, collapses or block shedding begin to occur. Therefore, it may take approximately 300 years (=5% ÷ 0.00015%–0.00018% years) for the mass loss to reach 5%. Assuming that the initial construction of the Yungang Grottoes occurred 1,500 years ago (AD 450–520), the carved sandstones were fresh; if no protective measures and/or artificial destruction were applied, the Yungang Grottoes began to destruct in ca. AD 800 (equivalent to the Tang Dynasty). Moreover, the Yungang Grottoes will be destroyed in the coming 4,000–5,000 years (=100% ÷ 0.00015%–0.00018% - 1,500) under natural conditions.

We collected the annual average temperatures from 1971 to 2021 in the Datong area (Figure 9a) (He, 2011). The results show an increasing annual average temperature after the onset of industrialization in China, with an increase of approximately 0.5°C per decade. Because of the implementation of energy conservation and emission reduction policies since 2007, the annual average temperature kept relatively stable in recent years. At the same time, the stable pH value of groundwater is also likely to be related to the low level of SO₂ content in the air after these policies (Xuan et al., 2021; Zhang et al., 2023). As shown in Figure 9, the continuous increase in annual average temperature also accelerates the weathering rate, leading to more rapid structural and morphological damage of the grottoes during 1971–2007.

FIGURE 9

Collectively, it is essential to specifically address temperature fluctuations before protective measures are implemented to reduce weathering intensity at the Yungang Grottoes. If possible, we should reduce the impact of extreme temperature fluctuations on the grottoes by controlling the surrounding temperature. For example, we can use air conditioners to stabilize the ambient temperature. Alternatively, we can reduce direct exposure to sunlight by constructing shading structures or planting trees, which may lower surface temperature fluctuations. We may also apply appropriate protective coatings to the surface of the grottoes to help mitigate the impact of temperature changes on the interior. Regular monitoring of temperature changes inside and outside the grottoes will help to adjust protective measures. Raising awareness of environmental protection among the public and tourists will also reduce unnecessary human-induced temperature fluctuations. Finally, reducing carbon emission is also significant to decrease annual chemical weathering rate and to decelerate the damage of stone cultural relics (Figure 9).

4 Conclusion

While current estimations require refinement due to uncertainties in physical weathering intensity, our results provide a novel approach to quantitative assessment of weathering in the Yungang Grottoes.

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