Introduction

China is located in the middle and low latitudes of the northern hemisphere. Seasonal frozen soil accounts for more than half of Chin’s territory. The rock mass in cold regions is subject to significant environmental weathering1. The long-term freeze–thaw cycle process may cause damage to the rock microstructure in the region, thus affecting the engineering properties of the rock mass. In recent years, with the steady progress of ‘the Belt and Road’ construction, the problem of engineering catastrophe caused by freeze–thaw action of red-bed sandstone in Urumqi area has become increasingly prominent. Therefore, it is of great significance to study the macro and micro structural damage characteristics of red-bed sandstone in Urumqi area under the action of freeze–thaw cycle to guide the construction of seasonal frozen soil area.

The study of the evolution law of physical and mechanical properties of rock under freeze–thaw cycles is an important part of the field of rock freeze–thaw mechanics, which provides a basis for the study of frozen rock mechanism. By testing the compressive and tensile properties of frozen rock, Winkler2 analyzed the law of phase change expansion of water ice in rock. Through the uniaxial compression test and triaxial compression test of Sirahama sandstone in Japan after freeze–thaw cycles, Yambae et al.3found that the uniaxial compressive strength of rock is inversely proportional to temperature and freeze–thaw cycles during freeze–thaw cycles. Sondergld et al.4summarized the evolution of physical parameters such as compression coefficient, shear rate and resistance coefficient of sandstone during freeze–thaw cycles through basic physical tests and mechanical tests. Yavuz et al.5analyzed the evolution of macroscopic physical and mechanical properties of andesite under different freeze–thaw cycles through basic physical and mechanical tests. Bayram6, Martínez-Martínez et al.7studied the strength damage law of rocks in cold regions under different freeze–thaw cycles by means of mechanical testing and ultrasonic testing. Then, based on the theory of damage mechanics and material mechanics, the uniaxial compression strength prediction model of limestone after freeze–thaw cycles was established. Ruedrich et al.8carried out long-term freeze–thaw tests on four kinds of natural building stones in 1400 freeze–thaw cycles to compare the behavior of rocks in weathering tests. Dehghani et al.9studied the crack initiation, propagation and fracture modes of marble specimens under the action of freezing cooling (F–C), heating cooling (H-C), freezing cooling heating (F–C-H) and heating cooling saturated freezing (H-C-F(sat)).

With the development of science and technology, the trend of multidisciplinary research and the emergence of a large number of advanced scientific instruments, the observation and analysis of rock freeze–thaw damage characteristics have gradually changed from focusing on macroscopic physical and mechanical properties to focusing on microstructure. Under the background of this research, fruitful results have been achieved in the analysis of freeze–thaw damage of rock microstructure. Luo et al.10, Zhang et al.11analyzed the damage evolution mechanism of ordinary concrete to ultra-high performance concrete composite materials and asphalt under extreme salt freezing conditions by X-ray diffraction technology and atomic force microscope (AFM), respectively. Tian et al.12used the combination of X-ray computed tomography (X-ray CT) technology and U-Net image segmentation method to accurately quantify the effect of freeze–thaw damage on the microstructure of concrete. Based on continuous damage mechanics (CDM), the damage evolution model was established and its validity was verified, which provided a new method for evaluating the freeze–thaw damage of hydraulic concrete.Yang et al.13focused on the emulsified asphalt cold recycled mixture (CRME), obtained the two-dimensional cross-section of the specimen by X-ray computed tomography (X-ray CT) scanning, and constructed an accurate two-dimensional discrete element model (DEM) after pretreatment. The CRME micro DEM modeling method based on X-ray computed tomography (X-ray CT) cross-section is proposed to study the micro damage of the mixture under freeze–thaw cycles, which provides a theoretical basis for pavement stability control and performance evaluation in seasonal frozen areas. Park et al.14used artificial weathering simulation in the laboratory to carry out freeze–thaw cycle experiments on diorite, basalt and tuff under saturated conditions. With the help of X-ray computed tomography (X-ray CT) and scanning electron microscope (SEM), they observed the internal microstructure changes of rocks and measured physical properties. The results show that different rocks are affected by freeze–thaw to different degrees. The tuff deteriorates rapidly due to loose structure, the diorite changes little, and the basalt is between the two. This experimental method can be used to evaluate the frost resistance of various rocks and provide reference for engineering construction in cold regions. Zhong et al.15studied the meso-damage characteristics of hydrophobic modified geopolymer composites (HM-GC) under freeze–thaw cycles based on Computed Tomography (CT) scanning technology, compared the damage degree and distribution characteristics before and after modification, quantitatively studied the meso-damage of HM-GC under freeze–thaw cycles, compared the damage differences before and after modification, and analyzed the damage gradient distribution characteristics, which provided reference for the application of geopolymer in cold regions. Zhang et al.16carried out different freeze–thaw cycles on sandstone, and used nuclear magnetic resonance (NMR), SEM and split Hopkinson pressure bar (SHPB) to test the P-wave velocity and porosity of sandstone, and carried out dynamic fracture test. The results show that the freeze–thaw cycle deteriorates the microstructure of sandstone and affects its dynamic fracture mode and toughness, and the dynamic fracture toughness is negatively exponentially correlated with the freeze–thaw damage factor. The freeze–thaw damage factor is defined to reveal its relationship with the dynamic fracture toughness, which provides a basis for the optimization of rock mass engineering parameters and stability analysis in cold regions or high altitude areas.

In addition, due to the limitation of experimental means, theoretical basis and other factors, most of the research still stays in the macro stage of rock freeze–thaw damage, and there are few studies on the evolution characteristics of rock microscopic characteristics under the influence of freeze–thaw cycle. Therefore, in order to study the evolution law of microscopic characteristics of red-bed sandstone in Urumqi area under the action of freeze–thaw cycle, this paper takes the red-bed sandstone of Bainiaohu Station of Urumqi Metro Line 4 as the research object, and studies the evolution law of macroscopic and microscopic characteristics of red-bed sandstone in this area under the action of freeze–thaw cycle through overburden pressure porosity and permeability test, X-ray diffraction test (XRD), CT non-destructive testing technology and uniaxial compression test, the research method is shown in Fig. 1. It is of great significance to guide the construction of red-bed sandstone projects in this area.

Fig. 1
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Research approach.

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Test scheme

Sample preparation

The red-bed sandstone sample was taken from the complete red-bed sandstone at the Bainiaohu Station of Urumqi Metro Line 4 (Fig. 2 (a)). The surface was red, and the average dry density of the block was 2.335 kg/m3.After cutting and end grinding, it was processed into Φ50 mm × 100 mm and Φ25 mm × 50 mm cylindrical standard samples. The allowable error edge of the diameter and height is 0.3 mm17(Fig. 2 (b)). The samples with obvious appearance defects were removed, and the rock samples with similar P-Wave velocity were selected by acoustic velocity measurement method for freeze–thaw test. Among them, a red-bed sandstone sample with a size of Φ50 mm × 100 mm was selected for CT scanning experiments after different freeze–thaw cycles. Three red-bed sandstone samples with a size of Φ25 mm × 50 mm were used for the pore-permeability test after different freeze–thaw cycles. A total of 28 red-bed sandstone samples with a size of Φ50 mm × 100 mm were used for uniaxial compression experiments after different freeze–thaw cycles.

Fig. 2
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Freeze–thaw cycle experiment time design.

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Experimental design of freeze–thaw cycle

All the red bed sandstone samples were put into a High-temperature blast drying oven for 24 h to ensure that the samples were in a completely dry state, and then the dried samples were put into a Low temperature freeze–thaw constant temperature experimental box (Fig. 4(a)). According to the meteorological and hydrological conditions in the study area, the freeze–thaw cycle experiment was carried out by means of air freezing and water thawing.In this study, the freezing and thawing time and temperature setting in the freeze–thaw cycle experiment are mainly based on the climate temperature and related standards17 of the study area in the past 5 years. The freezing temperature is -20 ℃, and the melting is 20 ℃. The freezing time of this experimental design is 12 h, and the melting time is 12 h. The specific time arrangement is shown in Fig. 3 to ensure that the sample can reach the state of complete freezing and complete melting. The number of freeze–thaw cycles was 0, 3, 5, 10, 15, 20, 25 times, respectively. After each group of freeze–thaw cycles, the rock samples of two sizes were tested and analyzed following standard experimental procedures. Specifically, the Φ25 mm × 50 mm specimen was utilized for the overburden pore-structure test, while the Φ50 mm × 100 mm specimen was subjected to X-ray diffraction analysis, CT scanning, and uniaxial compression testing.

Fig. 3
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freeze–thaw cycle experiment time design.

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Micro test experiment design

In order to observe the evolution of microscopic characteristics of red bed sandstone samples in Urumqi area under the condition of freeze–thaw cycle, the porosity and permeability of freeze–thaw rock samples were measured by AP-608 type porosity and permeability instrument. Because the red bed sandstone area in Urumqi area was deteriorated under the action of freeze–thaw cycle, the AP-608 type porosity and permeability instrument was set up to test without confining pressure.(Fig. 4(b)). The phase composition of red-bed sandstone samples under different freeze–thaw cycles was determined by D8 ADVANCE series X-ray powder diffractometer (Fig. 4(c)). The German Diondo d2 universal micro-nano CT system (Fig. 4(d)) was used to perform CT scanning tests on red-bed sandstone samples with different freeze–thaw cycles.160 layers were scanned in each sample, and the layer interval was 0.625 mm to obtain the modeling data of freeze–thaw rock samples.

Fig. 4
figure 4

Laboratory equipment. (a) Low temperature freeze-thaw constant temperature experiment box; (b) AP-608 type porosity and permeability instrument; (c) D8 ADVANCE series X-ray powder diffractometer; (d) The German Diondo d2 universal micro-nano CT system; (e) MTS E45.605 mine rock mechanical property test system.

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Macro test experiment design

In this study, MTS E45.605 mine rock mechanical property test system(Fig. 4(e)) was used to carry out uniaxial compression test on each group of samples after freeze–thaw cycles . The rock sample was loaded at a loading rate of 0.5 KN/s until the sample was destroyed17,18. Each test group contains 4 rock samples, a total of 28 red- test.

Experimental result analysis

Evolution characteristics of microscopic parameters

(1) Permeability and porosity test.

In this study, the permeability and porosity of red-bed sandstone samples under different freeze–thaw cycles were measured. Through the previous measurement, three samples with similar permeability and porosity were selected for subsequent freeze–thaw cycle samples, and the permeability and porosity were measured after the corresponding freeze–thaw cycles were completed. The permeability and porosity of the samples under different freeze–thaw cycles are shown in Table 1, and the changes of permeability and porosity of the samples under freeze–thaw cycles are shown in Fig. 5 and Fig. 6.

Table 1 Changes in porosity and permeability of red-bed sandstone after freeze–thaw cycles.
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According to Fig. 5, it can be seen that with the increase of freeze–thaw cycles, the average porosity of the sample shows a gradual increase. It can be divided into three stages: rapid increase stage of porosity, slow increase stage of porosity and stable stage of porosity.When the number of freeze–thaw cycles is less than 5 times, the porosity increases rapidly, and the average porosity change rate of the sample increases rapidly. The average porosity change rate of the sample is between 0 and 10.86%. When the number of freeze–thaw cycles is between 5 and 20 times, the porosity increases slowly. At this stage, the average dry mass change rate of the sample gradually slows down, and the average porosity change rate of the sample is between 10.86% and 14.27%. When the number of freeze–thaw cycles is more than 20 times, the porosity is stable. At this stage, the average porosity change rate of the sample gradually tends to be stable, and the average porosity change rate of the sample is between 14.27% and 14.65%.

Fig. 5
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Porosity change under freeze–thaw cycles.

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According to Fig. 6, it can be seen that with the increase of freeze–thaw cycles, the average permeability of the sample shows a gradual increase. It can be divided into three stages: rapid increase stage of permeability, slow increase stage of permeability and stable stage of permeability. When the number of freeze–thaw cycles is less than 5 times, the permeability increases rapidly, and the average permeability of the sample increases rapidly.. The average permeability change rate of the sample is between 0 and 24.06%. When the number of freeze–thaw cycles is between 5 and 20 times, the permeability increases slowly. At this stage, the average dry mass change rate of the sample gradually slows down, and the average permeability change rate of the sample is between 24.06% and 42.11%. When the number of freeze–thaw cycles is greater than 20 times, the permeability is stable. At this stage, the average permeability change rate of the sample gradually tends to be stable, and the average permeability change rate of the sample is between 42.11% and 43.98%.

Fig. 6
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Permeability change under freeze–thaw cycles.

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In the process of freeze–thaw cycles, the evolution of permeability is intrinsically related to the amplitude and shape of porosity development. When the average porosity increased by 14.65% ( from 7.92% to 9.08% after 25 cycles ), the average permeability increased by 43.98 ( from 0.266 mD to 0.383 mD after 25 cycles ), indicating that the change of pore connectivity dominated the increase of permeability.

(2) Analysis of CT scan test results.

Through CT scanning of red bed sandstone samples, the scanning data of red bed sandstone under each number of freeze–thaw cycles were obtained, the single-layer raw scan data are shown in Fig. 7(a). The Avizo software was used to reconstruct the model of red bed sandstone samples19,20. The reconstructed sample model is shown in Fig. 7(c).

Fig. 7
figure 7

Digital image processing. (a) CT Scan Section; (b) Threshold division section; (c) Three-dimensional reconstruction of specimen; (d) Three-dimensional reconstruction of pore.

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After completing the reconstruction of the red-bed sandstone sample model, the threshold is divided by the Interactive Thresholding module of Avizo software. By adjusting the threshold, the pores in the model are selected, and then the pore distribution in the sample model is obtained (Fig. 7(b), Fig. 7(d)). After that, the obtained model pores and the overall model are calculated by the Volume Fraction module to obtain the pore volume, material volume, overall volume and porosity of the sample. The analysis results are shown in Table 2.

Table 2 Statistics of pore distribution of red-bed sandstone samples.
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According to Fig. 8, it can be seen that in the process of increasing the number of freeze–thaw cycles, the pore volume of red-bed sandstone samples shows a gradual upward trend, and the pore volume can be divided into three stages according to its upward trend. When the number of freeze–thaw cycles is between 0 ~ 15 times, it is the first stage. In this stage, the pore volume gradually increases, and the pore volume is between 12,514 mm3 ~ 18,445.4 mm3. When the number of freeze–thaw cycles is between 15 and 20, it is the second stage. In this stage, the pore volume shows a sharp upward trend, and the pore volume is between 18,445.4 mm3 and 24,271.4 mm3. When the number of freeze–thaw cycles is between 20 and 25, it is the third stage, and the pore volume rising trend is gradually gentle, and the pore volume is between 24,271.4 mm3 and 24,806.1 mm3.

Fig. 8
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Red-bed sandstone pore volume line chart.

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According to Fig. 9, it can be seen that with the increase of freeze–thaw cycles, the material volume of red-bed sandstone samples shows a gradual downward trend, and the material volume can be divided into three stages according to its downward trend. When the number of freeze–thaw cycles is between 0 and 15, it is the first stage. At this stage, the volume of the material decreases steadily, and the volume of the material is between 185,405 mm3 and 176,046.7 mm3. When the number of freeze–thaw cycles is between 15 and 20, it is the second stage. At this stage, the material volume shows a sharp downward trend, and the material volume is between 176,046.7 mm3 and 169,978.8 mm3. When the number of freeze–thaw cycles is between 20 and 25, it is the third stage. At this stage, the material volume decreases gradually, and the material volume is between 169,978.8 mm3 and 169,356.8 mm3.

Fig. 9
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Red-bed sandstone material volume line chart.

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According to Fig. 10, it can be seen that with the increase of freeze–thaw cycles, bulk volume of red-bed sandstone samples shows a gradual downward trend, and the total volume can be divided into three stages according to its downward trend. When the number of freeze–thaw cycles is between 0 and 3, it is the first stage. At this stage, the total volume decreases steadily, and bulk volume is between 197,919 mm3 and 197,521.1 mm3. When the number of freeze–thaw cycles is between 3 and 10 times, the second stage is the second stage. In this stage, bulk volume shows a sharp downward trend, and bulk volume is between 197,521.1 mm3 and 195,013 mm3. When the number of freeze–thaw cycles is between 10 and 25, it is the third stage. Bulk volume of this stage gradually decreases, and the total volume is 195,013 mm3 ~ 194,162.9 mm3.

Fig. 10
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Red-bed sandstone bulk volume line chart.

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According to Fig. 11, it can be seen that with the increase of the number of freeze–thaw cycles, the porosity of red-bed sandstone samples shows a gradual upward trend, and the porosity can be divided into three stages according to its upward trend. When the number of freeze–thaw cycles is between 0 and 15, it is the first stage. At this stage, the porosity gradually increases, and the porosity is between 6.32% and 9.48%. When the number of freeze–thaw cycles is between 15 and 20, it is the second stage. At this stage, the porosity shows a sharp upward trend, and the porosity is between 9.48% and 12.49%. When the number of freeze–thaw cycles is between 20 and 25, it is the third stage. At this stage, the porosity increases gradually, and the porosity is between 12.49% and 12.78%.

Fig. 11
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Red-bed sandstone porosity line chart.

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Evolution characteristics of phase composition

In this study, Jade 5.0 software was used to qualitatively and quantitatively process the X-ray diffraction test data of red-bed sandstone under freeze–thaw cycles. The percentage of phase content of red-bed sandstone under different freeze–thaw cycles was obtained, so as to analyze the deterioration mechanism of red-bed sandstone under freeze–thaw cycles from a microscopic point of view. The qualitative analysis results and quantitative analysis results of red-bed sandstone samples under different freeze–thaw cycles are shown in Fig. 12.

Fig. 12
figure 12figure 12

XRD test results of red-bed sandstone under freeze–thaw cycles.

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The main components of red-bed sandstone in Urumqi area include Quartz (SiO2), Analcime (NaAlSi2O6·H2O), Albite (Na2O·Al2O3·6SiO2), Calcite (CaCO3), Kaolinite (Al2H4O9Si2), Muscovite (KAl2(AlSi3O10)(OH)2) and Montmorillonite (Al2O9Si3). The percentage content of each component obtained by quantitative analysis of XRD data is shown in Table 3.

Table 3 Phase composition of red-bed sandstone under freeze–thaw cycles(%).
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In rocks, the role of each phase composition is not the same. According to its role in rocks, it can be divided into two categories: rock skeleton and cement21,22. In this study, the main phase compositions of the rock skeleton in the red-bed sandstone samples are Quartz, Albite and Calcite. The main phase compositions of the cements are Analcime, Kaolinite, Muscovite and Montmorillonite. According to the above classification, the percentage of phase content of red-bed sandstone samples under different freeze–thaw cycles in this study was re-counted, as shown in Table 4.

Table 4 Phase composition of red-bed sandstone skeleton and cement under freeze–thaw cycles.
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According to Fig. 13, the internal phase composition of red-bed sandstone samples is divided into two categories: rock skeleton and cement. It can be analyzed that the change of phase composition in red-bed sandstone samples during freeze–thaw cycles can be divided into four stages. When the number of freeze–thaw cycles is less than 3 times, it is the first stage. In this stage, the content percentage of rock skeleton shows a sharp upward trend, and the content percentage of cement shows a sharp downward trend. The loss of material in the sample is mainly based on the loss of cement, and the loss of rock skeleton is low. When the number of freeze–thaw cycles is 3 ~ 5 times, it is the second stage. In this stage, the content percentage of rock skeleton shows a sharp downward trend, and the content percentage of cement shows a sharp upward trend. The material loss in the sample is mainly the loss of rock skeleton, and the damage degree of cement is low.When the number of freeze–thaw cycles is 5 ~ 20 times, it is the third stage. In this stage, the percentage change of rock skeleton and cement content is relatively stable, and the damage degree of rock skeleton and cement in this stage is similar. When the freeze–thaw cycle is 20 ~ 25 times, it is the fourth stage. In this stage, the percentage of rock skeleton content again shows a sharp downward trend, and the percentage of cement content again shows a sharp upward trend. The material loss in the sample is mainly based on the loss of rock skeleton, and the damage degree of cement is low.

Fig. 13
figure 13

Red-bed sandstone skeleton and cement phase composition content diagram.

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Evolution characteristics of macroscopic mechanical parameters

(1) Stress–strain curve.

The stress–strain curves of the samples with different freeze–thaw cycles are shown in Fig. 14, which can be divided into four stages: pore fracture compaction stage (OA stage), elastic deformation to micro-elastic fracture stable development stage (AB stage), progressive fracture stage (BC stage), and post-fracture stage (CD stage)23,24.

Fig. 14
figure 14figure 14

Sample stress–strain curve.

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It can be seen from Fig. 14 that with the increase of the number of freeze–thaw cycles, the most obvious difference in the stress–strain curve of the red-bed sandstone sample lies in the progressive fracture stage (BC stage) and the post-fracture stage (CD stage)25. The peak stress of the sample shows a significant downward trend with the increase of the number of freeze–thaw cycles. At the same time, the number of the maximum points on the curve also increases with the increase of the number of freeze–thaw cycles. The more the maximum points are, the more serious the damage degree of the sample under the load is, and the failure form gradually changes from the overall failure to the local failure.

In order to further analyze the damage mechanism of red-bed sandstone under freeze-thaw cycles, the strain bandwidth of each stage of the stress-strain curve after different freeze-thaw cycles is statistically analyzed. The strain bandwidth of each stage is shown in Fig. 15.

Fig. 15
figure 15

Strain bandwidth line chart of red bed sandstone samples under freeze–thaw cycles.

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The size evolution of the stress–strain stage provides important theoretical support for the fracture mode. With the increase of freeze–thaw cycles, there are three key strain transformations:

①OA stage: the strain bandwidth of the pore fracture compaction stage increased from 0.0023 ( 0th cycle ) to 0.0051 ( 25th cycle ). With the increase of the number of freeze–thaw cycles, the strain of sandstone under certain stress conditions gradually increased, and the axial strain variation range became larger, that is, the compaction stage of red bed sandstone became more obvious. This is because the higher number of freeze–thaw cycles causes the increase of internal pores, and gradually forms a connection with the original pores. Finally, the proportion of the compaction stage is also increasing.

② AB stage: the strain bandwidth of the elastic deformation to micro-elastic fracture stable development stage of micro-elastic fracture decreases from 0.0115 ( 0th cycle ) to 0.0020 ( 25th cycle ). The number of freeze–thaw cycles increases, the elastic deformation stage gradually shortens, and becomes less and less obvious on the whole process curve, which means that the deterioration effect of freeze–thaw cycle on rock is increasing. Because the freeze–thaw cycle causes the number of pores to increase and the volume to increase, the bonding degree between the mineral particles inside the rock is reduced. After the internal pores are closed, new cracks are generated after a short period of elastic deformation and enter the next stage.

③BC stage: the strain bandwidth of the progressive fracture stage increases from 0.0030 ( the 0th cycle ) to 0.0042 ( the 25th cycle ). In the progressive failure stage, the microcracks and pores in the frozen-thawed sandstone are further developed under the axial load, and new fine cracks begin to form, and the rock deformation shows plastic characteristics. As the number of freeze–thaw cycles gradually increases, especially after increasing to 10 times, the proportion of this stage gradually increases, becoming more and more obvious, and the stress at the peak point also decreases, indicating that the freeze–thaw cycle has a greater impact on the curve characteristics of this stage.

(2) Evolution characteristics of mechanical parameters.

The statistical results of the mechanical properties of red-bed sandstone under freeze–thaw cycles are shown in Table 5. The relationship between the peak stress and the number of freeze–thaw cycles is shown in Fig. 16, and the relationship between the elastic modulus and the number of freeze–thaw cycles is shown in Fig. 17.

Table 5 Statistical table of mechanical properties of red-bed sandstone under freeze–thaw cycles.
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Fig. 16
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Relation curve between peak stress and freeze–thaw cycles.

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Fig. 17
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Curve of the relationship between elastic modulus and freeze–thaw cycles.

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It can be seen from Fig. 16 that with the increase of freeze–thaw cycles, the peak stress of the sample shows a gradual decline, which can be divided into three stages: rapid failure stage, slow failure stage and re-failure stage. When the number of freeze–thaw cycles is less than 5 times, it is a rapid failure stage. In this stage, the peak stress of the sample shows a sharp downward trend, and the peak stress of the sample is between 89.4 MPa and 67 MPa. When the number of freeze–thaw cycles is between 5 ~ 20 times, it is a slow failure stage. In this stage, the decreasing trend of the peak stress of the sample slows down, and the peak stress of the sample is between 67 MPa ~ 47.1 MPa ; when the number of freeze–thaw cycles is more than 20 times, it is the rapid failure stage again. At this stage, the peak stress of the sample decreases again, and the peak stress of the sample is between 47.1 MPa and 37.8 MPa.

It can be seen from Fig. 17 that during the freeze–thaw cycle of the sample, the elastic modulus of the sample gradually decreases with the increase of the number of freeze–thaw cycles. According to the decreasing trend of the elastic modulus, it can be divided into three stages: rapid failure stage, slow failure stage and rapid failure stage again. When the number of freeze–thaw cycles is less than 5 times, it is a rapid failure stage. In this stage, the elastic modulus of the sample shows a sharp downward trend, and the elastic modulus of the sample is between 7.663 GPa and 6.777 GPa. When the number of freeze–thaw cycles is between 5 and 20 times, it is a slow failure stage, and the decrease trend of the elastic modulus of the sample in this stage is slowed down. The elastic modulus of the sample is between 6.777 GPa and 6.033 GPa ; when the number of freeze–thaw cycles is more than 20 times, it is the rapid failure stage again, and the elastic modulus of the sample decreases again, and the elastic modulus of the sample is between 6.033 GPa and 4.758 GPa.

Analysis of CT scan test based on fractal dimension theory

Evolution characteristics of macroscopic mechanical parameters

The Box-counting Dimension of the sample is calculated by using the Fractal Dimension module in Avizo software, and the fractal dimension of the pores after threshold treatment is calculated. In the calculation, the overall fractal dimension and the section fractal dimension of the sample can be selected for statistical analysis. In this study, in order to further analyze the variation characteristics of the internal structure of the sample under the action of freeze–thaw cycles, and the development characteristics of the internal pores of the sample, the overall fractal dimension and the section analysis dimension of the sample scan are counted separately.

Through the above method, the CT scan image of the red bed sandstone sample is analyzed, the fractal dimension of the red bed sandstone sample is obtained, and the degradation law of the red bed sandstone sample under the action of freeze–thaw cycle is analyzed. The overall fractal dimension of red-bed sandstone samples is shown in Table 6.

Table 6 Statistics of pore distribution of red-bed sandstone samples.
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Fractal dimensionis a quantitative indicator of geometric complexity, where higher FD values reflect more tortuous and irregular pore morphologies. As shown in Fig. 18, the progressive increase in fractal dimension (from 2.518 to 2.642 after 25 cycles) reveals intensified structural heterogeneity within the specimen. This correlates directly with freeze–thaw-induced alterations in pore geometry, including increased irregularity of pore boundaries and enhanced interconnectivity of microcracks.The fractal dimension of the red-bed sandstone sample increases gradually with the increase of the number of freeze–thaw cycles, and the upward trend is stable, which basically conforms to the linear trend. Therefore, it can be inferred that with the increase of the number of freeze–thaw cycles, the damage of the internal structure of the red-bed sandstone is more obvious, and the freeze–thaw cycle is the main influencing factor of the internal structure damage of the red-bed sandstone.

Fig. 18
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Point-line diagram of fractal dimension of body.

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In order to further study the main position of internal structure damage of fractal red-bed sandstone samples under freeze–thaw cycles, the analysis dimension of different XY layers of red-bed sandstone samples under CT scanning was counted in this study (Fig. 19).

Fig. 19
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surface fractal dimension curve diagram.

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According to the surface fractal dimension point line diagram of the red-bed sandstone sample in Fig. 19, it can be seen that the surface fractal dimension of the red-bed sandstone sample can be divided into five parts. The sample is calculated from the top, and the length of the sample is 0 mm ~ 6.25 mm is the first part. The fractal dimension of this part is relatively stable and has no large change. The fractal dimension is basically around 0.85, and does not change significantly with the increase of the number of freeze–thaw cycles. The length of the sample is 6.25 mm ~ 13 mm, which is the second part. The fractal dimension of this part shows a sharp increase trend, and the peak fractal dimension of this stage increases obviously with the increase of the number of freeze–thaw cycles. The peak value of fractal dimension is between 1.5 ~ 1.6; the sample length of 13 mm ~ 87 mm is the third part. The fractal dimension of this part has a small change trend and shows a downward trend. When the number of freeze–thaw cycles increases gradually, the fractal dimension of this part is still fluctuating, but the whole tends to be stable. The length of the sample is 87 mm ~ 93.25 mm, which is the fourth part. The fractal dimension of this part shows a sharp downward trend, and the peak value of this part shows an upward trend with the increase of the number of freeze–thaw cycles. The peak value of fractal dimension is between 1.38 and 1.6 ;The length of the sample is 93.25 mm ~ 100 mm, which is the fifth part. The fractal dimension of this part is relatively stable and has no significant change. The fractal dimension is basically around 0.85, which does not change significantly with the increase of freeze–thaw cycles.

Through the comprehensive analysis of the above contents, it can be found that the pore part of the red-bed sandstone sample is mainly distributed in the middle part of the sample, and the pore distribution at both ends is less. With the increase of the number of freeze–thaw cycles, the fractal dimension at both ends does not change significantly, indicating that the part of the pore increases less. With the increase of the number of freeze–thaw cycles, the fractal dimension of the middle section of the sample increases to a certain extent, and the fractal dimension of the middle section of the sample changes from uneven to uniform gradually. It can be seen that with the increase of the number of freeze–thaw cycles, the pores of each layer inside the red-bed sandstone show an increasing trend. During the freeze–thaw cycle, the water ice phase transition and the uneven shrinkage and expansion of minerals lead to the expansion and penetration of pores in the rock sample, and the area with less pore distribution in the sample is destroyed. Finally, the overall pore distribution shows a uniform distribution trend. The expanded pores are sufficient to accommodate the volume expansion of the water ice phase transition in the freeze–thaw cycle at this stage, so the surface fractal dimension tends to be stable in the later stage of the freeze–thaw cycle26,27.

Analysis of damage rate of mechanical properties of red-bed sandstone under freeze–thaw cycle

In order to evaluate the effect of freeze–thaw cycles on the mechanical properties of red bed sandstone samples, the damage rate (DRX) was used to evaluate the mechanical parameters28,29. Formula (1) is the calculation formula of damage rate (DRX).

$$DR_{X} = (1 - \frac{{X_{{\text{n}}} }}{{X_{0} }}) \times 100$$
(1)

In the formula, Xn represents the mechanical parameters after n freeze–thaw cycles, and X0 represents the mechanical parameters of the sample at 0 freeze–thaw cycles.

When the damage rate of a parameter shows a single increase or decrease trend with the increase of the number of freeze–thaw cycles, it can be explained that the freeze–thaw cycle is the main influencing factor of the parameter change ; when a certain parameter shows an irregular increase and decrease trend with the increase of the number of freeze–thaw cycles, it can be explained that there are many main influencing factors affecting the change of this parameter. Table 7 is the calculation of the damage rate of each physical and mechanical parameter, and Fig. 20 is the point line diagram of the damage rate of each physical and mechanical parameter.

Table 7 Damage rate of mechanical parameters of red-bed sandstone under freeze–thaw cycles.
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According to Fig. 20(a), the damage rate of elastic modulus shows a gradual upward trend with the increase of freeze–thaw cycles. When the number of freeze–thaw cycles is 25, the damage rate of elastic modulus reaches a peak of 37.91%. According to the change of elastic modulus damage rate, it can be inferred that the main reason for the change of elastic modulus is the influence of freeze–thaw action.

Fig. 20
figure 20

Point-line diagram of damage rate of mechanical parameters.

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According to Fig. 20(b), the damage rate of peak stress increases gradually with the increase of freeze–thaw cycles. When the number of freeze–thaw cycles is 25, the damage rate of peak stress reaches 57.72%. According to the change of peak stress damage rate, it can be inferred that the main reason for the change of peak stress is the influence of freeze–thaw action.

In summary, under the influence of freeze–thaw cycles, the elastic modulus and peak stress damage rate of red-bed sandstone samples increase with the increase of freeze–thaw cycles, and the parameters show a significant decreasing trend. Therefore, the influence of freeze–thaw cycle on the physical and mechanical properties of red-bed sandstone is very significant, which is the main influencing factor of the change of mechanical properties of samples.

Analysis of damage mechanism of red-bed sandstone samples under freeze–thaw cycles

In order to study the macro and micro evolution law of red-bed sandstone under freeze–thaw cycle, this paper analyzes the evolution law of macro and micro characteristics of red-bed sandstone under freeze–thaw cycle by means of micro test and macro mechanics experiment. The evolution law of macro and micro characteristics of red-bed sandstone under freeze–thaw cycle is shown in Fig. 21.

Fig. 21
figure 21

Damage evolution mechanism of red-bed sandstone under Freeze–Thaw cycles.

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In the process of freeze–thaw cycle, the thermophysical properties of the three-phase medium (water, air and rock) of red bed sandstone are inconsistent in the process of freeze–thaw cycle. During the freezing process, the pore water in the rock freezes and expands in volume, and the rock particles shrink when they freeze. The interaction between the two causes frost heaving force in the rock, resulting in damage to the internal structure of the rock ; when the rock melts, the ice inside the rock melts into water to bring out the falling particles inside the rock, which further aggravates the damage of the rock30,31.

The phase composition analysis (Table 3–4, Fig. 13) reveals that the dynamic redistribution of rock skeleton (quartz, calcite) and cementing materials (analcime, kaolinite, muscovite) governs the damage evolution during freeze–thaw cycles. When rock skeleton dominates material loss (3 ~ 5 and 20 ~ 25 cycles), structural integrity deteriorates rapidly due to the primary load-bearing role of quartz and calcite. This leads to abrupt increases in porosity (10.86% to 14.65%) and permeability (24.06% to 43.98% change rates), precipitating severe mechanical decline in peak stress (25.06% to 57.72% damage rate). Conversely, when cement dissolution prevails, the relatively elastic cement network partially buffers stress redistribution, resulting in slower porosity growth (7.58% to 14.27%) and milder strength degradation (e.g., 19.57% vs. 57.72% DRσ at 3 vs. 25 cycles). Stabilization of phase content ratios (5 ~ 20 cycles) correlates with reduced porosity/permeability gradients (Fig. 5,6) and attenuated mechanical deterioration (40.72% to 47.32% DRσ). This dual-phase interaction framework elucidates the non-linear mechanical degradation observed in stress–strain curves (Fig. 14), validating the necessity of tracking chemical composition shifts to decode macroscopic damage patterns.

Through the test in this paper, the deterioration process of frozen-thawed rock can be described as follows: the freezing stage freezes the pore water inside the rock and expands the volume, while the solid medium shrinks when it encounters cold, resulting in the generation of frost heaving force, resulting in the development of primary pores and cracks inside the rock, and the generation of new pores and the destruction of cements in the rock. In the melting stage, the ice inside the rock melts into water, and migrates in the rock to form a fracture channel and take away the cemented material and particles after failure, which further increases the porosity of the rock and leads to the damage of the rock. With the increase of freeze–thaw cycles, the microscopic damage at the water accumulation area gradually develops into macroscopic damage.

Conclusion

In this study, the microscopic parameters, phase composition and mechanical parameters of red-bed sandstone under freeze–thaw cycles were tested by a combination of macro and micro tests, and the macro and micro damage evolution characteristics of red-bed sandstone were analyzed. The results are as follows:

(1)The phase composition evolution characteristics of red-bed sandstone under freeze–thaw cycles were analyzed by X-ray diffraction test. The red-bed sandstone in the study area is mainly composed of quartz (SiO2), analcime (NaAlSi2O6·H2O), albite (Na2O·Al2O3·6SiO2), calcite (CaCO3), kaolinite (Al2H4O9Si2) and muscovite (KAl2(AlSi3O10)(OH)2). Among them, quartz, albite and calcite can be divided into rock skeleton, and analcime,, kaolinite, muscovite and montmorillonite can be divided into cements. When the number of freeze–thaw cycles is 3 ~ 5 times and 20 ~ 25 times, the rock skeleton material is the main loss material. At this stage, the rock structure is destroyed and the mechanical properties of the rock are obviously deteriorated.

(2)The microstructure changes of red-bed sandstone under freeze–thaw cycles were analyzed by CT scanning and fractal dimension theory. With the increase of the number of freeze–thaw cycles, the pore volume and porosity of the red-bed sandstone samples show an increasing trend, and the material volume and total volume show a decreasing trend. The pore part of the red-bed sandstone sample is mainly distributed in the middle part of the sample, and the pore distribution at both ends is less. With the increase of the number of freeze–thaw cycles, the maximum fractal dimension of the middle part of the sample gradually increases, and with the increase of the number of freeze–thaw cycles, the fractal dimension of the middle part of the sample changes from uneven to uniform.

(3)The evolution characteristics of mechanical parameters of red-bed sandstone samples under freeze–thaw cycles were studied by uniaxial compression experiments. Under the action of freeze–thaw cycles, the mechanical properties of red bed sandstone samples show a gradual downward trend. When the number of freeze–thaw cycles is 0 ~ 5 times, the mechanical properties of red bed sandstone samples are in a sharp decline stage ; when the number of freeze–thaw cycles is 5 ~ 20 times, the downward trend of mechanical properties of red-bed sandstone samples gradually slows down ; when the number of freeze–thaw cycles is 20 ~ 25 times, the mechanical properties of red-bed sandstone samples decrease sharply.