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Article

The Process and Mechanisms of Freezing and Thawing Deterioration of Petroglyphs under Snowmelt and Rainfall Infiltration

Key Laboratory of Disaster Prevention and Mitigation in Civil Engineering of Gansu Province, Department of Geotechnical Engineering, Lanzhou University of Technology, 287 Langongping Road, Lanzhou 730050, China
*
Author to whom correspondence should be addressed.
Coatings 2023, 13(3), 543; https://doi.org/10.3390/coatings13030543
Submission received: 8 December 2022 / Revised: 15 February 2023 / Accepted: 22 February 2023 / Published: 2 March 2023
(This article belongs to the Special Issue Coatings for Cultural Heritage: Cleaning, Protection and Restoration)

Abstract

:
Freeze–thaw cycles under the conditions of snowmelt and rainfall infiltration in winter are triggers for petroglyph weathering. Rock samples from the Helan Mountains were subjected freeze–thaw cycles under various conditions in laboratory testing, and the mass, elastic wave velocity and unconfined compressive strength were tested. The results show that the mass loss rate, wave velocity and compressive strength decreased. In addition, according to XRD analyses, the content of calcite and feldspar in the samples decreased, and according to SEM analyses, the microscopic pores grew. Considering the mass, mineral content and micro-voids, the variation decreases in the order: snowmelt group, rainfall infiltration group, normal freeze–thaw group. However, for wave velocity and compressive strength, the opposite results were observed. This research contributes to a better understanding of the weathering processes and mechanisms of petroglyphs in the Helan Mountains in winter.

1. Introduction

Over 5500 single petroglyphs have been found on the slopes and floodplain fans outside Helan Pass in Ningxia’s Helan Mountains (Figure 1a), with the themes of animals, plants, human bodies, human faces and symbols (Figure 1b). Many of the petroglyphs incised in the rock of the Helan Mountains are famous for their rich expression and profound cultural connotations [1]. However, some deterioration such as erosion, flake buckling, peeling etc. occurs and the rock is seriously weathered when exposed to the open air for a long time [2]. Especially in recent years, due to drastic environmental changes, the weathering process of the rocks has accelerated, leading to the danger that the petroglyphs will disappear. Therefore, it has become an urgent issue to study the weathering mechanisms of petroglyph carriers caused by environmental factors and formulate scientific conservation measures. In addition, the unique climatic characteristics of Helankou mean that snowmelt, rainfall infiltration and common freeze–thaw weathering are important factors that cannot be ignored in the process of rock weathering of petroglyphs [3].
A lot of research has been carried out on the effects on rocks under the action of freeze–thaw cycles, and informative research results have been obtained. It is universally accepted that temperature, moisture content and rock type are the main factors causing rock damage [4,5,6]. The importance of temperature conditions, such as minimum temperature and cooling rate, have been investigated in a number of studies [7], and moisture content has also been reported as a significant factor leading to rock failure following F–T cycles [8]. Rock properties including initial porosity, pore size distribution and mineral content also affect the likelihood of rock failure [9,10,11]. Nicholson [12] conducted a comparative analysis of the mass changes in different sedimentary rocks under different freeze–thaw cycles, and the results showed that the mass loss was greater with increasing numbers of cycles and relatively smaller for sedimentary rocks with high strength. Tan [13] studied the freeze–thaw cycles of sandstone in the temperature range of −40 °C to 40 °C and concluded that the compressive strength of sandstone deteriorates with an increase in the number of cycles. Zhang Jizhou [14] conducted a systematic experimental study on the freeze–thaw damage mechanisms and mechanical characteristics of specimens after freeze–thaw cycling for three types of rocks (mudstone, gabbro and dolomite), and the results showed that rock freeze–thaw damage is influenced by multiple factors, among which environmental factors are significant. Keping Zhou [15] et al. conducted a comparative study on the macroscopic properties and microscopic characteristics of granite after freeze–thaw cycles. They concluded that the physical properties of granite gradually decreased with the increase in cycles. The granite changed from medium to strongly weathered with the increase in freeze–thaw cycles because the internal pores of the rock were continuously damaged and expanded and the porosity increased [16].
In recent years, some scholars have considered the impact of snowfall on earth sites and rock sites. Pu [17] pointed out that the coupled effect of freeze–thaw cycles and salinity due to snowfall is a highly important driver for the development of soil sites in Qinghai-Tibet. Cui [18] simulated the freeze–thaw cycle process in soils in different temperature ranges in indoor tests. Cui [19] also study the deterioration mechanisms of rock art in the Helan Mountains under freeze–thaw cycles and different salinity conditions. Previous studies did not take into account the fact that the water recharge of snow into rock is slow as a result of the melting of snow, and does not occur uniformly throughout the snow layer [20]. The process of water infiltrating into the soil is slow with the snow melting, and the water added into the soil is not uniform or immediate [21]. The contact surface between the snow layer and the rock also produces a freezing-sticky effect, which affects the rock’s integrity. This effect is a unique property of the overlying snow, which should also be a major focus for study [22].
In summary, scholars have studied the damage processes and mechanisms of sandstone, mudstone, tuff and other sedimentary rocks under the action of freezing and thawing. The research ideas and methods are becoming more mature. However, the carriers of petroglyphs in the Helan Mountains are meta-sandstones, and the rock carriers located on the cliff face and on the slope of the flood fan experience different types of freezing and thawing during the long winters in the area. However, little research has been reported on the weathering of these petroglyphs. Based on previous studies, in this paper, freeze–thaw tests are carried out on rock specimens under snowmelt and rainfall infiltration considering the actual environmental conditions of the Helankou petroglyph carrier in the Helan Mountains. A combined qualitative and quantitative analysis of the cumulative damage mechanisms of the specimens is conducted to provide some reference for the formulation of scientific conservation measures for the Helankou petroglyphs.

2. Study Background

The geographical coordinates of the Helan Mountains are 38°21′ N~39°22′ N and 105°49′ E~106°42′ E. The Yinchuan Plain and Alxa Plateau are on the east and west sides, respectively, with an altitude of about 2000~3000 m. The area belongs to the moderate-temperate arid, semi-arid plateau climate zone. According to survey data, the annual average temperature of the Helan Mountains is −0.9 °C, and the temperature range is large, with the annual extreme temperature reaching 25 °C and the lowest being −33 °C. Precipitation occurs during 62% of the year, and the annual average evapotranspiration is 1230 mm. The winter lasts for 5 months with a frost-free period of about 122.6 days, and the annual average wind speed is 7.7 m/s.
In recent years, human activities and environmental changes have intensified, and the destruction of Helankou petroglyphs has accelerated, with flaking, buckling and peeling, resulting in shallow and blurred carvings (Figure 2). According to survey statistics, about 660 petroglyphs were distributed within the 570-m-long petroglyph key reserve from the mouth of Helankou to the south bank of “Shuiguan”. Among them, 173 petroglyphs showed flaking, buckling and peeling, accounting for 26.2% of the petroglyphs in this area, and 419 petroglyphs showed shallow and blurry carving marks, accounting for 63.4% of the petroglyphs in this section [23]. In addition, related studies have shown that flaking, buckling and spalling are mainly caused by physical weathering, while the shallow layer of the indentation is mainly due to chemical weathering of the erosion by aqueous chemical solutions [24]. Flaking, buckling and spalling refer to the deformation and uplift of the weathered crust on the surface of the rock mass and separation from the host rock, which results in a cavity area between the host rock the weathered crust that has not yet completely peeled off. Weathering refers to the phenomenon that the notches of the rock painting gradually become lighter until they disappear.

3. Samples and Methods

Thin section identification tests were carried out to understand the mineral composition, grain size, and structure of the samples. The results showed that the rock consists of clastic and filler, and the rock is modified by metamorphic recrystallization. The debris content of the rock sample is 81%, which is composed of 57% quartz and 24% feldspar. The filler portion is 19%, which is composed of 12% mud matrix, 4% siliceous material, and 3% calcium.
Fresh and complete rock samples were taken from the Helankou petroglyph area. According to the “Engineering Rock Mass Test Method Standard” [26], the specimen was processed into a square with 70.7 mm sides and polished smooth. First, the rock specimens with obvious defects or appearance differences were rejected. Then the RSM-SY5 intelligent acoustic detector was used to measure the wave velocity of the specimen and the specimens with similar wave speeds were selected. The specimens were dried at 105 °C for 48 h until a constant weight was reached. After cooling, the samples were equilibrated at room temperature and the dried samples were saturated using suitable vacuum venting equipment.
Group X (Figure 3) (snow melt) were samples covered with a snow layer weighing 53.5 g [22]. To avoid over-melting of the snow, the rock samples were placed in a 5 °C environment for 12 h before the freeze–thaw cycle began. Group Y (rainfall infiltration) were samples sprayed from above with snow water of equal quality. The Group Z samples were not covered with snow or rain. The tests were carried out in accordance with the Code for Rock Test of Water Conservancy and Hydropower Engineering (DL/T 5368-2007, China). The rock samples were repeatedly saturated in distilled water at ambient temperature and then frozen in a refrigerator at about −30 °C. Referring to the average winter temperatures of Helankou since 2010, −30 °C was selected as the freezing temperature, 5 °C as the melting temperature, and 24 h as the freeze–thaw cycle. The freeze–thaw time was 12 h.
Each set of test samples was divided into 5 groups of 5 samples each, which were subjected to 0, 15, 30, 45, and 60 F–T cycles, respectively. The mass loss rate and wave propagation velocity of the sample were recorded, and uniaxial compression experiments were carried out to study the mechanisms of mechanical change. In addition, X-ray diffraction (XRD) and scanning electron microscopy (SEM) analyses were performed to investigate the weathering mechanisms, mineral changes and micromorphology in the samples subjected to snowmelt and rainfall infiltration.

4. Results

4.1. Changes in Mass

The mass test of the samples was based on the test methods of rock for highway engineering (JTG E41-2005, China) specifications. The samples subjected to the snow melting and rainfall infiltration showed more significant changes in mass (Figure 4). The mass loss rate of samples was determined using the formula given in JTG E41-2005 Part 5 (Test methods of rock for highway engineering, 2005) as follows:
Δ m = m s m f m s
where Δ m is the mass loss rate (%); m s is the quality of saturated specimens before the test (g); and m f is the quality of saturated specimens after the test.
As the weathering cycle progressed, the rate of rock mass loss increased slowly before the 15th cycle, with the treatment groups ordered as follows: Z, Y, X. Then, it decreased significantly after the 15th F–T cycle in the following order: X, Y, Z.

4.2. Changes in Wave Velocity

An RSM-SY5 intelligent acoustic detector was used to test the wave velocity of each group of samples. The results showed that wave velocity decreased in all experimental treatments (Figure 5). The wave velocity of the samples in Group X decreased by 21.44%, the samples in Group Y decreased by 19.89%, and the samples in Group Z decreased by 17.53%.

4.3. Variation in Uniaxial Compression

In order to determine the strength of rock under snowmelt, rainfall infiltration and freeze–thaw treatments, uniaxial compression tests were performed and the coefficient of freezing resistance was calculated by Equation (2):
K f = R f R s
where K f is the coefficient of freezing resistance; R f is the compressive strength of the saturated specimens after F–T treatment (MPa); and R s is the compressive strength of the saturated specimens before F–T treatment (MPa).
For Group X, the coefficient of freezing resistance decreased slowly in the freeze–thaw series, from 1.0 to 0.996 before the 15th cycle. After that, it changed faster, almost linearly, i.e., it decreased from 0.982 to 0.961 and, finally, to 0.931 by the 30th, 45th, and 60th cycles, respectively. Overall, the Group X sample strength decreased by 6.9%. For Group Y, the coefficient of freezing resistance decreased slowly before 30th cycle and quickly after that; overall, the Group Y sample strength decreased by 10.7%. However, unlike the X and Y groups, the change law of the frost resistance coefficient of Group Z almost conformed to the linear law, and decreased by 12.1% (Figure 6).

4.4. Features of Stress–Strain Curves

After conducting uniaxial compression experiments on three different rock samples, it was revealed that the stress–strain curves of the specimens showed a common character. The four main stages of the process were defined as compaction, elastic deformation, yield and failure. The gradients of the stress–strain curves of all of the group samples declined, showing that their modulus of deformation decreased significantly in all three freeze–thaw cycle treatments. Moreover, the length of the compaction–deformation stage became longer with an increasing number of weathering cycles, whereas the elastic and yield stages were both shortened. Finally, the yield strength and ultimate strength of the samples decreased with an increasing number of weathering cycles (Figure 7).
The stress–strain curves of the three treatment groups (snowmelt (X), rainfall infiltration (Y) and freeze–thaw cycles (Z)) showed obvious differences. In all experiments, the modulus of deformation, yield strength and ultimate strength decreased in the following order: X, Y, Z. The yield and failure stages of Group X exhibited distinct ductility features. Conversely, the Group Y samples showed no obviously distinct yield and failure stages, but did exhibit distinct rigidity features.

4.5. XRD Analysis

XRD analysis was conducted on rock samples of the petroglyphs to investigate changes in the mineralogical composition in the snow melting, rain infiltration and freeze–thaw treatments. A sample of 50 g was collected from the contact surface between the rock and snow, rock and rain and the arbitrary surface of rock in the freeze–thaw treatments, respectively. The samples were passed through a 0.075 mm sieve and different treatments (i.e., air-drying, heating and glycolation) were applied for the XRD tests. A Philips PW 3710 diffractometer was used for XRD analysis of the three slides. The diffraction patterns were determined using Cu–Kα radiation with a Bragg angle (2θ) range of 3–30°, running at a rate of 0.05°/s.
Figure 8 shows that quartz, clay, feldspars and calcite were the main minerals, with the clay containing kaolinite with a little illite. The mineral content of the unweathered sample is also shown in Figure 8b. Since quartz hardly reacts at low temperature, the results show that the content of clay increased while the content of feldspar, plagioclase, and calcite decreased during the snow melting, rain infiltration and freeze–thaw process. We also found the mineral content changed more dramatically in the snow melting group than in the others, e.g., the content of calcite decreased from 12% to 2% in the snow melting group versus 4% in the rain filtration group and up to 9% in the freeze–thaw group. In addition, the decrease in the calcite content was faster in the early stage of the snowmelt group and rain filtration group. It then became slower, and the changes in the feldspar and plagioclase content show the opposite trend.

4.6. Microstructural Features

To investigate changes in the microstructure, SEM analysis was conducted on rock samples subjected to snow melting, rain infiltration and freeze–thaw treatments. The observation surfaces were selected on the contact surface between the rock and snow, and the rock and rain in the snow melting and rain infiltration treatments and on the arbitrary surface of the rock in the freeze–thaw treatment.
PCAS software of Nanjing University was applied in analysing the SEM images to calculate the particle size, porosity and pore width of samples.
Changes in the surface microstructure of the rock samples were manifested by the development, addition, expansion and interconnection of holes and linear gaps. The surface of the unweathered rock was smooth (Figure 9a). After snowmelting treatment, a large number of holes and increased linear porosity were found in the SEM images (Figure 9b). The rainwater filtration treatment led to increased porosity, but no linear porosity (Figure 9c). Compared with the test above, Figure 9d shows that the sample surface only became rough after the freeze–thaw treatment. In addition, evidence of calcite and feldspar corrosion and the increase and agglomeration of clay was found in the SEM images at 1000× magnification (Figure 9e–g). The parameters of porosity and pore width for the three freeze–thaw cycle treatments are detailed in Table 1.

5. Discussion

The main visual weathering forms of the petroglyph were erosion (76.6%), peeling (12.7%), biological growth (9.5%) and man-made damage (1.1%). The weathering damage including granular disintegration and rounding/notching to make petroglyph lines is difficult to distinguish in natural light. The snowmelt, rainfall infiltration, and freeze–thaw processes are the critical causes of rock weathering in this area. The experiments found that the grains in the surface of the petroglyph corrode in snowmelt and rainfall infiltration form granular disintegration and notching [27]. In addition, the tests also detected that the strength of rock of petroglyph is easily affected by snowmelt, rainfall infiltration, and freeze–thaw possesses, which results in the production of cracks and peeling.
Mass loss, wave velocity and uniaxial compression tests were applied to study the processes in the rocks of petroglyph subjected to snowmelt, rainfall infiltration, and freeze–thaw processes. These tests show that the mass, wave velocity and compressive strength decrease with the number of F–T cycles. The associated parameters (determined by weathering index, wave velocity, stress-strain curve and compressive strength) of rocks in the snowmelt group were smaller than those of the other groups, and parameters for the rainwater infiltration group were smaller than those of the freeze–thaw group [28,29]. However, the rate of mass change shows the opposite pattern, i.e., the mass change is greatest in snowmelt group, which was confirmed by the SEM analysis. After the three treatments, the roughness of the rock surface between snow, rain and rock was obviously large, with the greatest roughness in the snowmelt group, followed by the rainwater infiltration group and freeze–thaw group. It turns out that snowmelt mainly affects the rock surface, making it rougher. Additionally, the mineral changes also provide clear evidence, i.e., the corrosion of calcite and feldspar and increase in clay are the main reasons for the increase in voids resulting a decrease in mechanical strength. The XRD analyses also indicate that calcite is highly susceptible to freeze–thaw action. The calcite content decreased significantly in the early stages of the tests, with the snowmelt group declining the fastest. However, the feldspar content decreased slowly in the all experiments, and was stable in freeze–thaw group for it may be associated with the type of ion and its content in snow and rain [19].
In these experiments, it is difficult to collect and store the snow and rain from the Helan Mountains and process many specimens for mechanical testing. For example, the specimens for the mass, velocity, SEM and XRD tests could be reused, but the specimens for testing mechanical strength were required in large quantities and were damaged by testing. As a consequence, the authors attempted to determine the relationships between the mass change rate, velocity change rate, and uniaxial compression between the snowmelt group and rainfall infiltration group with data from the freeze–thaw group. For each regression, the coefficients of fit and determination are shown in Figure 10. These graphs demonstrate that, in all situations, lineal and logarithmic regression curves were judged to be the most accurate representations of the relationships, which indicates that good linear and logarithmic correlations were obtained, especially among mass change rate, wave velocity change range and uniaxial compressive strength in group Y and group Z. The equations for the correlations are shown in Table 2 below.
The t test calculated with SPSS was performed among the produced equations to examine the validity of the regression equations used in this study (Equations (3)–(8)). The results show that there is a real correlation between the mass change, wave velocity change and the intensity of the snowmelt group and the rainfall infiltration group and the corresponding parameters of the freeze–thaw group, which can be used at least for the preliminary evaluation of the weathering process of snowmelt and rainfall infiltration.

6. Conclusions

(1)
The mass, wave velocity, stress–strain curve, compressive strength, mineral content, and microstructure were altered clearly in response to snowmelt and rainfall infiltration processes. Meanwhile, the variation in mass, particle size, porosity and pore width in the snowmelt group was greater than in the rainfall infiltration group, and the values for the rainfall infiltration group were greater than those in the normal freeze–thaw group. However, the wave velocity and uniaxial compression strength followed the reverse trend.
(2)
The ordinary freeze–thaw treatment had a greater effect on the physical and mechanical properties of the petroglyph rocks than the snowmelt and rainwater treatments, as shown in the mass change, XRD and SEM tests. However, calcite and feldspar are prone to corrosion in the early stage of the snowmelt and rainfall infiltration processes. Thus, snowmelt and rainfall infiltration mainly affected the rock surface, making it rougher.
(3)
Our study showed that the uniaxial compressive strength after normal freeze–thaw cycles had good accuracy for estimating the uniaxial compressive strength after snowmelt and rainfall infiltration, thus making it possible to assess the other two kinds of freeze–thaw processes. As a result, performing a freeze–thaw tests with snowmelt or rainfall infiltration could be avoided, which are laborious, time-consuming and difficult to realize.
This study conducted preliminary research on the distribution and characteristics of damage to petroglyphs in the Helan Mountains. The deterioration of petroglyphs is a long process, which is undoubtedly a great challenge to scientific researchers. The protection of petroglyphs is difficult. Therefore, approaches to protect and reinforce the petroglyphs still need to be explored.

Author Contributions

Conceptualization, G.W. and K.C.; methodology, G.W.; validation G.W. and X.Y.; formal analysis, C.G.; investigation, G.W.; resources, G.W.; data curation, X.Y.; writing—original draft preparation, G.W.; writing—review and editing, G.W. and C.G.; visualization, X.Y.; supervision, K.C.; project administration, G.W.; funding acquisition, G.W. All authors have read and agreed to the published version of the manuscript.

Funding

This study was supported by National Natural Science Foundation of China (Grant No. 42107206), the Program for Changjiang Scholars and Innovative Research Team at the University of the Ministry of Education of China (No. 2017IRT17051), the National Natural Science Foundation of Gansu (Grant No. 22JR5RA292) and the “Hongliu Excellent Young” Talents Support Program of Lanzhou University of Technology.

Institutional Review Board Statement

Not applicable.

Informed Consent Statement

Not applicable.

Data Availability Statement

Not applicable.

Conflicts of Interest

The authors declare no conflict of interest.

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Figure 1. Location of the Helan Mountains petroglyphs: (a) the study site; (b) distribution of petroglyphs at study site; and (c) snow at study site.
Figure 1. Location of the Helan Mountains petroglyphs: (a) the study site; (b) distribution of petroglyphs at study site; and (c) snow at study site.
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Figure 2. The main weathering types of the Helan Mountains petroglyphs [25]: (a) distribution of petroglyph weathering in Helankou; (b) peeling; (c) erosion; and (d) line drawing of petroglyph corresponding to (c).
Figure 2. The main weathering types of the Helan Mountains petroglyphs [25]: (a) distribution of petroglyph weathering in Helankou; (b) peeling; (c) erosion; and (d) line drawing of petroglyph corresponding to (c).
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Figure 3. Samples. (a) Results of thin section identification test. (Pl: Plagioclase, Q: Quartz, Si: siliceous). (b) Samples for melting snow treatment.
Figure 3. Samples. (a) Results of thin section identification test. (Pl: Plagioclase, Q: Quartz, Si: siliceous). (b) Samples for melting snow treatment.
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Figure 4. Mass change rate curve of three freeze–thaw cycle treatments.
Figure 4. Mass change rate curve of three freeze–thaw cycle treatments.
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Figure 5. Wave velocity curve of three freeze–thaw cycle treatments.
Figure 5. Wave velocity curve of three freeze–thaw cycle treatments.
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Figure 6. Compressive strength curve of three freeze–thaw cycle treatments.
Figure 6. Compressive strength curve of three freeze–thaw cycle treatments.
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Figure 7. Stress–strain curve of three freeze–thaw cycle treatments at (a) 15 cycles; (b) 30 cycles; (c) 45 cycles; and (d) 60 cycles.
Figure 7. Stress–strain curve of three freeze–thaw cycle treatments at (a) 15 cycles; (b) 30 cycles; (c) 45 cycles; and (d) 60 cycles.
Coatings 13 00543 g007aCoatings 13 00543 g007b
Figure 8. X-ray diffraction (XRD) scans of rock for three F–T cycle treatments. (a) XRD spectrogram (1—quartz, 2—clay, 3—feldspar, 4—plagioclase, 5—calcite). (b) Mineral content variation after three F–T cycle treatments. (c) Mineral content variation in snowmelt group. (d) Mineral content variation in rain infiltration group.
Figure 8. X-ray diffraction (XRD) scans of rock for three F–T cycle treatments. (a) XRD spectrogram (1—quartz, 2—clay, 3—feldspar, 4—plagioclase, 5—calcite). (b) Mineral content variation after three F–T cycle treatments. (c) Mineral content variation in snowmelt group. (d) Mineral content variation in rain infiltration group.
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Figure 9. SEM photographs of rock after 60 F–T cycles for three treatments: (a) untreated samples (500×); (b) snowmelt (500×); (c) rain infiltration (500×); (d) normal F–T (500×); (e) corrosion of feldspar (1000×); (f) corrosion of calcite (1000×); and (g) increase in clay (1000×).
Figure 9. SEM photographs of rock after 60 F–T cycles for three treatments: (a) untreated samples (500×); (b) snowmelt (500×); (c) rain infiltration (500×); (d) normal F–T (500×); (e) corrosion of feldspar (1000×); (f) corrosion of calcite (1000×); and (g) increase in clay (1000×).
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Figure 10. Correlation after X and Y with Z. (a) Correlation between the mass change rates. (b) Correlation between the velocity change rates. (c) Correlation between the uniaxial compressive strengths.
Figure 10. Correlation after X and Y with Z. (a) Correlation between the mass change rates. (b) Correlation between the velocity change rates. (c) Correlation between the uniaxial compressive strengths.
Coatings 13 00543 g010aCoatings 13 00543 g010b
Table 1. SEM parameters of the samples.
Table 1. SEM parameters of the samples.
GroupsNumber of CyclesParticle Size (μm)Porosity (%)Pore Width (μm)
X04–1010–151–3
156–1012–202–6
306–1215–254–8
4510–1815–258–12
6015–20>25>10
Y04–1010–151–3
156–1012–202–6
306–1012–202–6
458–1515–255–10
6010–1815–258–12
Z04–1010–151–3
156–1010–151–3
308–1015–252–6
4510–1515–252–6
6012–1815–255–10
Table 2. The analyses results by t test.
Table 2. The analyses results by t test.
Equation NumberRegression EquationDetermination Coefficient (R2)t Test
Calculated ValueTabulated Value
(3) Δ m X = 0.0039 + 1.2767 Δ m Z   0.99518.153±1.35
(4) Δ m Y = 0.0127 + 1.896 Δ m Z 0.97419.238±1.53
(5) Δ V _ X = 11.32 E X P ( V _ Z / 17.55 11.32 0.99918.762±1.25
(6) Δ V _ Y = 12.81 E X P V _ Z / 19.93 12.59 0.99918.531±1.28
(7) UCSX = 184.83 2.62 E 8 lnUCSZ 0.99718.319±1.31
(8) UCSY = 184.16 4.95 E 8 lnUCSZ 0.99918.256±1.29
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MDPI and ACS Style

Wu, G.; Cui, K.; Ge, C.; Yu, X. The Process and Mechanisms of Freezing and Thawing Deterioration of Petroglyphs under Snowmelt and Rainfall Infiltration. Coatings 2023, 13, 543. https://doi.org/10.3390/coatings13030543

AMA Style

Wu G, Cui K, Ge C, Yu X. The Process and Mechanisms of Freezing and Thawing Deterioration of Petroglyphs under Snowmelt and Rainfall Infiltration. Coatings. 2023; 13(3):543. https://doi.org/10.3390/coatings13030543

Chicago/Turabian Style

Wu, Guopeng, Kai Cui, Chengrui Ge, and Xiangpeng Yu. 2023. "The Process and Mechanisms of Freezing and Thawing Deterioration of Petroglyphs under Snowmelt and Rainfall Infiltration" Coatings 13, no. 3: 543. https://doi.org/10.3390/coatings13030543

APA Style

Wu, G., Cui, K., Ge, C., & Yu, X. (2023). The Process and Mechanisms of Freezing and Thawing Deterioration of Petroglyphs under Snowmelt and Rainfall Infiltration. Coatings, 13(3), 543. https://doi.org/10.3390/coatings13030543

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