1 Introduction

Since rock has a complex porous medium structure, its pore characteristics are the main factors affecting the physical properties (Liu et al. 2017; Li et al. 2017) and macro mechanical properties (Dehestani et al. 2020; Tianshou and Chen 2014). The rock mass in the subsidence zone of the reservoir bank is often in an environment of periodic water invasion and water loss alternation due to the reciprocal rise and fall of the reservoir water level. This will lead to the changes in the rock meso-structure under the action of different water invasion cycles, which will then cause displacement failure and slope collapse at the macro-level (Zhou et al. 2017; Liu et al. 2016). It is therefore of great engineering significance to study the degradation of the rock meso-structure during different cycles of water invasion for slope disaster prevention.

In recent years, many testing methods, such as the capillary pressure curve method (Du and Zhang 2019), thin section casting analysis (Zhang et al. 2018), nuclear magnetic resonance (Zhou 2016), scanning electron microscope (SEM) analysis (Kassab and Weller 2015), uniaxial compression tests (Gkceolu et al. 2000; Hale2003), triaxial compression tests (Shao et al. 2021), creep tests (Deng et al. 2016) and Brazil split tests (Wen et al. 2015), amongst others have been used by researchers to conduct in-depth research on the influence of water invasion on physical and mechanical properties of various rocks. The changes in the characteristics of rock physical and mechanical properties during different water invasion cycles were revealed through the changes of porosity, compressive strength, shear strength, and other parameters (Ramandi et al. 2016; Ma et al. 2020). With the development of CT technology, the quantitative characterization of meso-three-dimensional structures in rocks can be achieved (Liu et al. 2020; Moslemipour and Sadeghnejad 2021). Salek et al. (2023) investigated the effect of CT imaging parameters on pore connectivity and surface area quantification of sandstone samples with different compositions. Li et al. (2023) proposed an effective method to analyse the microstructure of loaded rocks by using fractal theory and computed tomography (CT), and established the relationship between the microstructural properties of sandstone porosity, fractal dimension and loading stress. Zhou et al. (2023) conducted a study utilizing CT scanning of fractures, to analyze the brittleness characteristics of various types of sandstone at different coring angles under formation confining pressure, as well as studying the law of fracture propagation. Song et al. (2023) employed nano-CT scanning technology to examine how the micro-pore structure of tight sandstone reservoirs influences the presence of tight oil. Du et al. (2023) utilised computed tomography scanning technology to examine the micro-heterogeneity of the conglomerate reservoir and its impact on seepage. The researchers discovered considerable micro-heterogeneity in the distribution of matrix minerals and pore throat size within the reservoir. However, studies on the meso-pore structure of rocks mostly focus on the analysis of original rock samples, and there are still minimal studies on the meso-pore structure damage of rocks during water invasion cycles.

In this paper, with yellow sandstone taken as the study object, the rock samples were scanned by CT to explore the changes in the pore structure of the sandstone under the different water invasion cycles. The pore parameter damages of rock samples during water invasion cycles were quantitatively characterized to reveal the changes in the rock parameters and damage to the pores of the rocks during water invasion.

2 Experimental setup

2.1 Micro-CT test system

The cross-scale core scanning imaging system (nanoVoxel-3502E) was used to scan the rock samples to obtain their meso-pore structure. The system is composed of a motorized X-ray source, a sample stand, a detector, and a computer system for motion control and data acquisition. When the X-ray e passed through the sample, the absorption coefficient of each component to the X-ray diffraction line was different (Tiwari et al. 2013; Wildenschild and Sheppard 2013). As the sample rotates at a certain rate, a series of attenuation projection profiles were obtained (Fig. 1). The X-ray tube of the nanoVoxel-3502E cross-scale core imaging scanning system uses an open directional high-power microfocus X-ray tube with a minimum spatial resolution of 700 nm and a maximum sample diameter of 300 mm.

Fig. 1
figure 1

Principles of CT imaging

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2.2 Sample preparation and experimental procedure

The study focuses on yellow sandstone, a rock commonly found in water-wading slopes. The chosen sample of yellow sandstone exhibits a natural uniaxial compressive strength exceeding 35 MPa, classified as high strength yellow sandstone. It can be inferred from the data that the sandstone has a compact internal structure and small pores. As a result, there will be no failure or collapse caused by erosion during cyclic water intrusion, thereby ensuring excellent integrity. Further details of the samples are available in Table 1.

Table 1 Basic physical properties of rocks
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Considering the detection range of the CT scanning equipment, the influences of sample size on the penetration rate of the X-ray beam, the distance between the detector and the sample, and the final imaging resolution, the cubic yellow sandstone sample of 100 mm × 100 mm × 100 mm were selected for water invasion cycles and CT scanning experiment. The test on water invasion cycles underwent two processes, including immersion and drying. Firstly, the rock sample was completely immersed in pure water for 24 h. Secondly, the rock sample was dried to a constant weight at 105 °C ± 5 °C for no less than 24 h. Each immersion-drying process was treated as a complete water invasion cycle and the above steps were repeated several times according to the needs of the experiment. The original rock sample without immersion and drying treatment was considered to have undergone 0 water invasion cycles (N = 0). The CT scanning experiment was carried out at the end of 0, 1, 5, and 10 times of implementing the water invasion cycle test. 1600 16-bit gray image slices were obtained by scanning the sandstone each time. The specific scanning parameters are shown in Table 2.

Table 2 Micro-CT scanning configuration parameters
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2.3 Image processing

The original two-dimensional CT image was processed by three-dimensional reconstruction and image segmentation to quantitatively analyze the meso-pore structure in the rock sample. FEI Avizo software was used for three-dimensional image reconstruction and image segmentation. This process is based on the practical experience in literature (Dong and Blunt 2009; Yi et al. 2017; Yang et al. 2019) to realize the identification and segmentation of pores and rock matrixes in rocks. By observing the gray histogram of pores and rock matrixes in meso-structure, the optimal threshold segmentation point was determined. The region of interest (ROI) was extracted after the 3D rendering of the rock sample structure, with the ROI voxels of 80 × 180 × 180. The ROI was used to extract and analyze the meso-pore structure parameters, and to obtain the pore radius, volume, area, and other related parameters of the sandstone sample. The image segmentation followed the following process (Li et al. 2023; Yang et al. 2018):

  1. (1)

    Denoise the image by the median filter denoising method.

  2. (2)

    Binarise the image by the Otsu method.

  3. (3)

    Segment the image by the region growth method.

Finally, the three-dimensional pore structure of the rock sample was assessed under different water invasion cycles. The image processing process is showed in Fig. 2.

Fig. 2
figure 2

The process of the imaging analysis procedure

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2.4 Identification and segmentation of pore structure

To study the meso-pore structure changes of the ROI under different water invasion cycle states, it is necessary to accurately obtain the size and spatial position of each pore and pore throat of the sandstone sample. The rock sample has many connected pores, as shown in Fig. 3, so a reliable method is needed to separate the pores and pore throat structures. The pore network model was used in this paper to quantitatively characterize the meso-pore structure of the rock sample under different water invasion cycles. The following steps were followed to separate the pore and pore throat structures (Fig. 4):

  1. (1)

    Identify the routes connecting the pores and find the corresponding joint points between pores and pore throats.

  2. (2)

    Skeletonize the pore structure and characterize the pore structure by "sphere plus line" form.

  3. (3)

    Mark each pore and pore throat in pore structure and calculate the geometric distance and volume.

Fig. 3
figure 3

Pore structure in the ROI of different water invasion cycles

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Fig. 4
figure 4

Separation steps of pore and pore throat structures

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To facilitate the description of the pore structure, it is now defined as follows:

  1. (1)

    The pore radius represents the sphere radius under the equivalent volume.

  2. (2)

    The pore throat radius represents the equivalent cylinder radius.

  3. (3)

    The coordination number represents the number of pores connected to a given pore.

3 Results and discussion

3.1 Pore structure characterization under different water invasion cycles

The pore network model of rock samples under different water invasion cycles is shown in Fig. 5. The pores and pore throats are equivalent to spheres and cylinders, respectively. The sizes and positions of the spheres and cylinders reflect the sizes and positions of the pores and pore throats. This model makes it easier to quantitatively characterize pore size changes within the space of the ROI.

Fig. 5
figure 5

Pore network Model in the ROI of different water invasion cycles

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Through the above steps, the connectivity of the pore structure in the ROI of the rock sample was gradually strengthened with each increase in the number of water invasion cycles. A pore throat mainly exists between large pores, while the connectivity of smaller pores is weaker than that of large pores.

To further characterize the variation in the characteristics of the pore structures under different numbers of water invasion cycles, the pore radius and pore throat radius of the rock samples were statistically analyzed. The distribution of the pore radius under a varying number of water invasion cycles is shown in Fig. 6a. The results from Fig. 6a are as follows: (1) More than 50% of the pore radiuses are distributed to be below 6 μm, and the pores are mainly small. (2) After 10 water invasion cycles, the proportion of pores with a radius below 10 μm decreased from 81 to 76%, and the proportion of large pores increased. (3) The peak value of pore radius distribution is concentrated in the range of 2–6 μm, and with an increase in the number of water invasion cycles, the peak value of pore radius distribution transitions from the range of 2–4 μm to that of 4-6 μm. (4) The pores with a radius greater than 10 μm increased with an increase in the number of water invasion cycles, and the changes were the most significant between the first and the fifth water invasion cycles. Figure 6b shows the distribution of pore throat radiuses under different numbers of water invasion cycles. Compared with the change in the pore radius distribution, the pore throat radius changed relatively little with an increase in the number of the water invasion cycles. The results from Fig. 6b are as follows: (1) More than 50% of the pore throat radiuses are less than 6 μm and the pore throats are mainly small pore throats. (2) After 10 water invasion cycles, the proportion of pore throats with a radius below 10 μm decreased from 82 to 72%. The proportion of larger pore throats increased and the pore connectivity was enhanced. (3) The peak distribution of pore throat radiuses was in the range of 4–6 μm. (4) The pore throat radius change was the most obvious between the first and the fifth water invasion cycles. The proportion of pore throats with a radius of less than 10 μm in the ROI decreased from 78 to 73%.

Fig. 6
figure 6

Pore structure statistics under different water invasion cycles. a Pore equivalent radius statistics; b Throat equivalent radius statistics

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3.2 Quantitative analysis of microstructure damage

To quantitatively characterize the damage of pore structure parameters in the ROI during the different water invasion cycles, the distributions of the maximum, minimum, and average values of equivalent pore radius, equivalent pore throat radius, coordination number, and pore volume for each of the different water invasion cycles are shown in Fig. 7. The maximum values of the pore radius (Fig. 7a) and the pore throat radius (Fig. 7b) are randomly distributed, and the maximum values of coordination number (Fig. 7c) and pore volume (Fig. 7d) increase with the increase in the number of water invasion cycles. The average value of all the parameters with an increase in the number of water invasion cycles according to the exponential function relationship. It can be found that the distribution of pores and pore throats was the same in the initial water invasion cycle (N = 0 and N = 1). The pore structure began to be damaged significantly when N = 5 and pore structure damage showed a weakening trend with an increasing number of water invasion cycles (N = 5 ~ 10). Therefore, it can be concluded that as the number of cycles increases, the development and expansion of pores and microcracks caused by the alternating dry–wet action will gradually develop slowly, and the dry–wet cyclic action will not cause greater damage to the rock, and the degree of damage will gradually tend towards a fixed value.

Fig. 7
figure 7

Relationship between pore structure parameters and cycle times. a Relationship between pore equivalent radius and cycle times; b Relationship between throat equivalent radius and cycle times; c Relationship between coordination number and cycle times; d Relationship between pore volume and cycle times

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To more intuitively characterize the damage of water invasion on the meso-pore sandstone structure, based on the damage mechanics theory, this study introduced the damage variable \(F_{D}\) to quantitatively characterize the sandstone damage caused by the water invasion cycle process. When the pore structure parameter values are the average values for each of the water invasion cycles, the damage variable \(F_{D}\) can be calculated by the following formula (Shi et al. 2021):

$$F_{D} { = }\frac{\Delta D}{{D_{0} }} = \frac{{D_{N} - D_{0} }}{{D_{0} }} \times 100{\text{\% }}$$
(1)

where \(F_{D}\) represents the damage variable; \(\Delta D\) represents the difference of the pore structure parameters for rock sample under the state of water invasion cycle time N; \(D_{N}\) represents the pore structure parameter when the water invasion cycle time is N; \(D_{0}\) represents the pore structure parameter of the rock sample in the natural state.

When the pore structure damage of the rock sample under the action of water invasion in the natural state is not considered, \(F_{D} { = 0}\) is found in the natural state (N = 0). At the same time, the damage variable values of each parameter under each of the different water invasion cycles are calculated and shown in Table 3. The variation of pore structure parameters with each of the water invasion cycles is shown in Fig. 8. Through nonlinear regression analysis, the objective function for each parameter conforms to the exponential function change and \(R^{2} > 0.99\). The form of the regression equation is as follows:

$$F_{D} = A_{1} \exp ( - N/t_{1} ) + y_{0}$$
(2)

where \(A_{1}\), \(t_{1}\) and \(y_{0}\) all denote the fitting coefficient, and N denotes the water invasion cycle times.

Table 3 Damage variables of pore structure parameters under different water invasion cycles
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Fig. 8
figure 8

Relationship between damage variables and cycle times

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The damage variables of each parameter increase with an increase in the number of water invasion cycles, as can be seen from Fig. 8. However, the increase in the degree of damage for each parameter is different, shown by the slope of each fitting curve. Of these, the pore volume damage is the most obvious, and the maximum damage variable is as high as 41.44%. The coordination number damage is the least obvious and the maximum damage variable is only 5.80%. The degree of damage to the pore throats is larger than that of the pores themselves. The maximum amount of damage occurs between the first and the fifth water invasions for all of the parameters. This phenomenon is consistent with the distribution of pore radius and pore throat radius, indicating that the degree of damage to the meso-pore structure of rock samples is obvious between the first and the fifth water invasion cycles.

4 Conclusions

With the help of micro-CT imaging equipment, the microscopic pore structure of sandstone under different water invasion cycles was characterized and analyzed. Pore structure parameters of the ROI were obtained and the damage of water invasion on the pore structure parameters of rock samples was studied. The following conclusions are drawn:

  1. (1)

    A pore network model was established by FEI Avizo to quantitatively characterize the meso-pore structure of the rock samples during the different water invasion cycles. It is found that the deterioration rate of the pore structure initially increases and then slows as the number of water invasion cycles increases, and is most obvious between 1 and 5 water invasion cycles.

  2. (2)

    Based on the statistics on the distribution of the pores structure, the size and distribution form of the pores and pore throats of rock samples changed with water each invasion cycle, and the change of the pores was more obvious. After 10 water invasion cycles, the peak range of pore radius distribution transitioned from the initial range of 2–4 μm to the range of 4–6 μm, and the proportion of pore throats with a radius less than 10 μm decreased from 82 to 72%. The results show that the interpore connectivity is enhanced significantly by cyclic water intrusion, which leads to the continuous increase in rock permeability.

  3. (3)

    The mean values of the pore structure parameters all increased with an increase in the number of water invasion cycles, indicating that the damage variables for each parameter all increased to a certain extent. By introducing the damage variables to define the degree of damage to each parameter, it was found that the maximum damage of pore volume was 41.44% after 10 water invasion cycles and the minimum damage variable of the coordination number was only 5.80%. The parameter that is most affected by an increase in the number of water invasion cycles is the pore volume.

Finally, it is important to acknowledge that the CT imaging equipment utilized in the experiment has a resolution of 10 μm, which is insufficient to display the evolution of minuscule pores below 10 μm. Therefore, the next phase should focus on enhancing the resolution to further analyze the progression of pore damage. Additionally, the experiment was limited to only ten repetitions of cyclic water intrusion, neglecting the long-term scenario, water intrusion pressure, water chemical environment, and other related factors. In future research, it is recommended that additional cyclic water intrusion scenarios are examined to investigate the coupling mechanism of damage.