2.1 Materials

The mudstone of this research was taken from the side slopes of the S210 provincial highway in southern Guangxi Zhuang Autonomous Region, China. The region is in a subtropical monsoon climate with an average annual rainfall of 1674 mm. Mudstone is mainly distributed at the slope height of 3.5-6.5 m. Moreover, the mudstone surface is not covered by vegetation and directly exposed to the atmosphere. The collapsed part of the sampling slope after WD is mainly concentrated in the area where the mudstone layer is located [24].

The diffraction spectrum of the powder and the results of quantitative analysis are shown in Figure 1 and Table 1. The main mineral compositions in the mudstone can be divided into three groups: quartz (53.8%), illite (29.9%), and feldspar minerals (16.3% in total). The feldspar group of minerals includes both microcline and albite.

Figure 1全屏查看

XRD pattern of mudstone sample

2.2 Test procedure

A large mudstone sample was cut and polished into a cylinder with the diameter of 5 mm and height of 20 mm. The Xradia 510 Versa 3D CT scanner (micro-CT) produced by Zeiss Company was used in this experiment with its limit resolution of 0.9 μm, and the minimum recognizable voxel size of 70 nm. The CT scanning system consisted of an X-ray emission source, an X-ray detector and a rotary table. The overall schematic diagram of the testing procedure is shown in Figure 2. First, micro-CT was used to scan the original mudstone cylinder. Next, the sample was kept in water for 24 h until the saturated water content was reached. Then, the sample was dried at 105 ℃ until the sample mass no longer changed, and the second CT scan was performed. The experimental parameters used for the two CT scans in this study, including the size and position of the REV, and the greyscale values used in segmentation process were all consistent.

Figure 2全屏查看

Instruments, samples, and procedures for the micro-CT scans

In this test, 1000 grayscale slices with a resolution of 1.2 μm were obtained in each scan. As X-ray passed through the test sample, materials with different densities had different attenuation coefficients, and finally these materials appeared as different grayscale values [22]. Figure 3 illustrates the CT slices and grayscale distribution maps of the mudstone. After deconvolution of the grayscale distribution, the CT slices of mudstone can be divided into three components. Combined with the XRD results and according to the different gray thresholds corresponding to the three compositions, the pore, clay matrix, and quartz in the mudstone samples can be segmented separately.

Figure 3全屏查看

Grayscale slice for CT test: (a) Mudstone slice and original grayscale image; (b) Grayscale distribution map

A cube with a side length of 500 mm×500 mm×500 mm voxels at the center of the sample was selected as the representative volume element (RVE) for the analysis. The selection of this RVE not only eliminated the effect of irregular sample boundaries, but also effectively reduced the memory capacity of the computer and speeded up the operation [25, 26]. In addition, because the disintegration of mudstone under WD effect occurs from the outside to the inside [27], selecting the central area of the mudstone sample as the RVE for CT test can effectively reduce the impact of sample disintegration.

In order to prove that the selected cube met the requirements of RVE, a texture characterization method called the gray-level size-zone matrix (GLSZM) proposed by SINGH et al [28] was used. According to the GLSZM method, REV can be determined by calculating the porosity by increasing the cube domain size from the center of the sample. It has been proved that the method can accurately determine the size of RVE dimensions of Bentheimer sandstone and fieldstone with good analytical accuracy [29, 30].

From the RVE center point to the eight vertices of the cube, the porosity change was calculated, and the results are shown in Figure 4. As the voxel size increased, the porosity calculated along the eight vertices tended to a consistent value, and the rate of change of porosity tended to converge. Thereby, it can be concluded that the cube with a side length of 500 voxels at the center position can be used as the RVE in this research. Based on the different grayscale values of the various compositions in the mudstone, the AVIZO software (FEI Co., USA) was used to perform a grayscale threshold segmentation and a 3D reconstruction.

Figure 4全屏查看

Caluculated porosity vs RVE dimension (voxels)

The overall 3D reconstruction of RVE is shown in Figure 5(a). Three different fractions were then extracted, and Figures 5(b)-(d) show the quartz particles, clay matrix, and pore network in the mudstone, respectively.

Figure 5全屏查看

3D reconstruction of the mudstone after threshold segmentation: (a) RVE; (b) Quartz particles; (c) Clay matrix; (d) Pore network

It can be seen that the overall pore network of the mudstone was very complex, and a large number of them were distributed at the joints of the clay particles. The pore size varied greatly. There were both isolated small pores and interconnected large pores, so it was necessary to classify these two types of pores for subsequent quantitative analysis. The quartz particles are relatively large in size, and they are relatively distributed in the clay particles.

3.1 Porosity and fractal dimension analysis

A large number of studies regard rock as a porous medium with a large number of fractures and pores. CT can be used for 3D reconstruction and quantitative analysis of parameters such as porosity and fractal dimension [31-33]. The porosity of the mudstone samples used in this study can be calculated as follows:

(1)

where is the calculated porosity; V_pore is the single pore volume; and V_voxel is the total volume of the REV. Fractal theory uses the perspective of continuous dimensions to describe the properties and states of objects, and then quantifies the diversity and complexity of objects. The fractal dimension is one of the important parameters for describing the complexity of an object [34]. The determination of the fractal dimension in this research based on the box-counting method [35]. This method uses boxes with different radii to cover whole the mudstone in the image. When the size of the selected boxes is different, the number is also different. Assume that the radius of the small box is and the number of boxes is . Choose different values of and assume that both satisfy:

(2)

where A and B are fitting parameters. By deforming the formula, we have:

(3)

where , , and is the box-counting dimension.

Depending on the value of , a series of data pairs of “grids” with different sizes and corresponding “grid coverage numbers” can be obtained, that is, data pairs. The data pairs are then plotted in a double logarithmic coordinate system and fitted to a primary function using least squares to obtain the slope , whose opposite number is the box counting dimension of the image [36].

Based on formula (3), the porosity and fractal dimension of each slice before and after WD are quantified and the results are shown in Figure 6.

Figure 6全屏查看

Slice porosity and fractal dimension analysis (Notes: P_i and P′_i are the porosities of each slice before and after WD, respectively. F_i and F′_i are the fractal dimension of each slice before and after WD, respectively)

Preliminary analysis revealed that the porosity and fractal dimension of the slices increased significantly after WD, and the values of the two parameters fluctuated significantly. Furthermore, the calculation results of porosity and fractal dimension are characterized through the box plot, which is shown in Figure 7. The average value of porosity in the original RVE was 0.23, which rose to 0.30 after WD. There were relatively small fluctuations in porosity of slices in the original sample, mainly in the range 0.21-0.27. The minimum slice porosity after WD was about 0.22 and the maximum was 0.42, with a variation ratio of 90.9%, which was much higher than that of the original sample. This indicated that the WD led to the rapid growth of pores in each slice of the sample and affected the homogeneity of the pore distribution. Similar to porosity, the fractal dimension of each slice of the sample after WD increased not only in value, but also in the range of fluctuation. This suggested that WD led to a more complex structure of the mudstone due to the generation of a large number of pores and cracks.

Figure 7全屏查看

Box statistics about the fractal dimension and porosity of the slices: (a) Porosity; (b) Fractal dimension

3.2 Quantitative analysis of pore size

RVE can be used to conduct quantitative analysis and statistical analysis on the geometric parameters of the pore structure. In this section, the equivalent radius of pores was taken as the main index to quantify the pore size. The equivalent radius can be given as follows:

(4)

In order to simplify the collective topological relationship of pores in mudstone, the pores of RVE before and after WD were simplified into a pore network structure which was composed of pores and pore throats. And its pore network model (PNM) was generated. As shown in the Figure 8, the sphere represents the hole, and the connecting line between the holes represents the throat [37]. It should be noted that the PNM can only characterize connected pores and pore throats, and all the isolated pores still needed to be extracted and analyzed separately.

Figure 8全屏查看

RVE and PNM before and after WD: (a) PNM wrapped by REV of original sample; (b) PNM of original sample; (c) PNM wrapped by REV after WD; (d) PNM after WD

The statistical results of the equivalent radius of connected pores and pore throats in PNM before and after WD are shown in Figure 9. In the original state, the radii of connected pores in the RVE were mainly concentrated 30-40 μm. The number of connected pores increased from 962 to 1891 after WD. The average connected pore radius decreased from 34.85 μm to 30.59 μm. This is mainly because the clay matrix produced more connected micro pores under the effect of WD. Among them, the number of pores with an equivalent radius of 15-20 μm increased by 236%, and the growth rate was the highest among all ranges. Followed by the pores with equivalent radius of 20-25 μm, the number of such pores increased by 138%. Gaussian distribution has been used to describe the pore spacing of natural rock, which has achieved good effects [38]. The distribution of connected and isolated pores and pore throats in a mudstone sample before and after WD can be achieved through Gaussian distribution of Eq. (5).

(5)

Figure 9全屏查看

Frequency distribution of equivalent radius of connected pores and pore throats: (a) Connected pores; (b) Pore throats

In the equation, , x_c and are the fitting parameters of the Gaussian distribution.

The values of the specific parameters are also indicated in the related figures. By comparing the Gaussian distribution curves with the frequency distributions of the pore radius and the pore throat radius, it can be found that by adjusting the parameters of the Gaussian distribution, a better fit between the two can be achieved, and R² was kept above 81%.

The pore throat radius of the sample is mainly concentrated 1-7 μm, and the number of pore-throats with such radius in the original sample accounts for 87.1%. The number of pore throats in the RVE increased from 7329 to 8496 after WD, which was much higher than that of the connected pores. This indicated that the pore throat network in mudstone samples was very complex, and one pore was often connected with multiple pore throats. Similar to the variation of connected pores, the average pore throat radius in the RVE decreased after WD. The main reason was that the number of micro pore throats, especially those with the radius of less than 2 μm, increased significantly. The number of micro pore throats increased from 1508 to 1806 after WD, which showed the highest increase among all radii.

Similarly, quantitative analysis of isolated pores showed that the equivalent radius of isolated pores in the original sample was significantly smaller than that of connected pores, as shown in Figure 10. Its average equivalent radius was only 1.64 μm, much smaller than the 34.85 μm of connected pores. The number of pores with an equivalent radius of less than 1.5 µm accounts for 56.25% of the total number. After WD, the number of isolated pores in the sample increased significantly. According to the growth ratio of each interval, the largest increase was in the 1.5-2 μm interval, which increased from 29.45% to 32.59%. Although there had also been significant growth in the total number of other intervals, their proportions to the total number remained stable. The large increase in this interval was mainly due to the large number of micro pores with a radius of less than 1.5 μm having been further cracked because of WD. It is important to note that the analysis of micro pores using CT was limited by the ultimate resolution of the CT (the ultimate resolution of the CT used here was 0.9 μm). In fact, some pores in this sample smaller than the resolution were also identified in the interval of 1-1.5 µm. Therefore, if micro-CT was used to subdivide the aperture with an equivalent radius of less than 1 μm, errors will often occur, which should be avoided in practical operation.

Figure 10全屏查看

Frequency distribution of equivalent radius of isolated pores

Gaussian distribution was used in this study to describe the distribution of the three types of pores in the mudstone, and they all show a unimodal type. Therefore, the representative pore radius is the value of the horizontal coordinate corresponding to the Gaussian peak. The representative pore size obtained from the Gaussian distribution is more accurate compared to the most probable pore size or average pore size used as a characterization index in previous studies [39, 40].

The representative equivalent radius of the connected pores, which can be found in Figure 9, decreases from 25.25 μm to 21.01 μm after the first cycle of WD. Intriguingly, there was a decrease in the representative radius of connecting pores after WD, which can be attributed to the significant increase in the number of connecting pores in the mudstone after wet and dry interaction. In addition, the increment in the number of connected pores after WD was mainly concentrated on smaller pores with radii in the range of 10-40 µm. The representative radius of the pore throats increased from 3.01 μm to 3.34 μm. The representative radius of the isolated pores shown in Figure 10 increased from 1.49 μm to 1.67 μm, which was an increase of 12.1%.

3.3 Pore morphology analysis

3.3.1 Pore shape factor

The irregularity of the pore space was described by the shape factor G. This parameter influenced the way and speed of fluid transport and was one of the important parameters in the PNM. The pore space of real rocks was irregular, which had great influence on the seepage. If the pore shape was represented by a regular circular capillary, multiphase flow cannot be performed because multiphase fluids cannot coexist in this shape. Therefore, it is necessary to use cylinders of different cross-sectional shapes to represent the shape of pores or throats, and the shape factor G was defined as [41]:

(6)

In the formula, V is the pore volume; R is the equivalent radius of the pore; A_s is the pore surface area. All three variables can be extracted from the results of CT.

In the PNM, both the pore and throat used irregular shapes to represent their section shapes. The commonly used shapes were triangles, squares, circles, etc. The degree of irregularity of different shapes was defined by the shape factor G. The smaller the shape factor, the more irregular it was. Figure 11 shows several common section shapes and their corresponding magnitude ranges of shape factors. In this study, we assumed that each representative shape factor corresponded to an interval, and the flatter the shape, the lower the G value. While the larger the G value was, the more regular the section shape was. The shape factor interval corresponding to the triangle was (0, 0.048], (0.048, 0.0625] for the square and circle was (0.0625, 0.0796]. Pore structure of actual rock is very irregular, which cannot be fully represented by simple shape. However, the definition of shape factor G can make it reflect to the complexity of the actual pore structure as much as possible.

Figure 11全屏查看

Definition of shape factor in pore network

The shape factor was essentially of the irregularity of the pore section. When the pore size was too small, the accuracy was easily affected by the CT resolution. In order to eliminate the impact, the analysis of this part would only apply to areas larger than 10 μm². The analysis and statistics on the shape factor are shown in Figure 12. The statistical results of the number of pores in triangle, square, and circle intervals before and after WD are shown in Figure 13. In all statistical intervals, the relative frequency corresponding to each interval increased with the shape factor value, mainly in the circular interval of (0.0625, 0.0796]. This suggested that the pore shapes in the mudstone samples were mostly regular and can be approximated as circular pores. After WD, the proportion of pores in the circular section further increased, in contrast to a decrease in the proportion of pores belonging to the triangular interval. Quantitatively, although the number of pores in all three intervals increased after WD, the number of pores in the triangular interval increased by only 24.3% and the number of pores in the circular interval increased by 86.9%. This is mainly due to two reasons. On the one hand, the WD makes the clay matrix at the corners of the irregular pores further fall off and decompose, thus forming more regular, circular-like pores. On the other hand, clay minerals in mudstone have good expansibility [42, 43], the expansion of clay minerals causes the corners and tips of pores to be covered or partially covered, thus forming new relatively regular pores between clay particles.

Figure 12全屏查看

Relative frequency statistics of shape factors of three representative cross-sections

Figure 13全屏查看

Frequency statistics of shape factors of three representative sections

3.3.2 Pore sphericity analysis

Sphericity referred to the degree to which the spatial structure of the pore was close to a sphere. The shape factor characterized the shape of the two-dimensional cross-section of the pore and had nothing to do with the height of the pore. The closer a pore was to a sphere in space, the closer the it is sphericity was to 1. Conversely, the more the sphericity deviated from 1, the more irregular and narrow the pore was. The pore sphericity was calculated according to the following formula [44].

(7)

In order to further refine the sphericity distribution of pores, the sphericity was divided into two parts: less than 1 and more than 1 for statistical analysis. The frequency and relative frequency of each statistical interval are shown in Figure 14 and Table 2.

Figure 14全屏查看

Frequency of pores with sphericity in the range of 0.2-0.9

Table 2全屏查看

Statistics of number and relative frequency of pores with sphericity more than 1

Sphericity range	Frequency
	Before WD	After WD
1-3	6993	14148
3-5	698	946
5-7	186	224
7-9	66	82
9-11	25	22
11-13	14	14
13-15	6	9
15-17	11	0
17-19	6	5
19-21	2	1
21-23	2	2
23-25	0	0
25-27	0	2
27-29	1	0
29-31	0	1

展开更多

In terms of quantity, the sphericity in the initial sample was mainly concentrated in 0.2-0.3, with a proportion of 61.36%, and the number of pores in this range reached 54089. However, the corresponding relative frequency decreased to 58.05%, which indicated that the sphericity value of the overall pores was getting larger. The overall average sphericity after WD was 0.49, and the maximum value reached 28.10. Similar to the change of the shape factor, the average sphericity of the pores after WD decreased to 0.46, and the maximum value decreased to 25.60, which meant that the pore space structure after WD tended to be more spherical. For the pores with sphericity greater than 1, the sphericity distribution was mainly concentrated in the 1-3 interval, indicating that the spatial structure of most pores in the sample was close to the sphere. After WD, the number of pores with sphericity between 1 and 3 increased from 6993 to 14148, and the corresponding relative frequency increased from 87.30% to 91.53%. It can be found that the WD process transformed the originally angular and flat pores into round and regular pores. In order to analyze whether the sphericity was related to pore size, a sphericity-pore radius scatter diagram was drawn, as shown in Figure 15.

Figure 15全屏查看

Relationship between pore radius and sphericity in RVE before and after WD: (a) Before WD; (b) After WD

It can be seen from the figure that the sphericity value before and after WD was positively correlated with the equivalent radius of the pores, which approximately satisfied the distribution of a quadratic equation in one variable. After WD, the sphericity distribution of the sample was more intensive, and the number of discrete points decreased. Pore radius and sphericity distribution in mudstone were relatively concentrated, mainly distributed in areas with sphericity less than 15 and pore radius less than 8. This also suggested that the micro pores in the mudstone were mostly close to spheres, and as the equivalent radius of the pores increased, the shape of the pores was closer to sheet and columnar.

Pores with representative sphericity values were extracted and reconstructed, as shown in Figure 16. It can be found that the pores with smaller equivalent radii were closer to a sphere. As the radius increased, the pore structure would be elongated and the pore height would decrease. With the further increase of radius and sphericity, almost no isolated large pores can be seen, and more pores were formed by a large number of small pores. In general, the walls of these pores consisted of a large number of small pores, and densely distributed with small protrusions. As the number and distribution of pore clusters were arbitrary, the shape of the pores was even more irregular. Finally, when the sphericity was greater than 30, the pore throats radii were further decreased, the spatial structure was further elongated, and the basic characteristics of pore disappeared, and its geometric characteristics was closer to a crack.

Figure 16全屏查看

Pore morphology with different spherical degree: (a) Sphericity=4.81; (b) Sphericity=11.59; (c) Sphericity=21.37; (d) Sphericity=31.09