Introduction

Deep soft rocks in coal mines are relatively intact, hard, and have good mechanical properties in their natural state1. The roof and floor of coal seams usually contain soft rock layers2,3, such as mudstone. Disturbance in coal mining can lead to the destruction of overlying rock structure and integrity4, as well as water resource migration, which results the interaction between water and rock. And this interaction process changes the micro-structure, mineral composition, and fracture development morphology of the rock mass, which weaken the mechanical properties of coal rock mass, and easily causes deformation and instability of the engineering rock mass5,6.

Mudstone contains abundant mineral components, and its mechanical properties significantly deteriorate when exposed to water7 – 11. Moreover, the higher the moisture content, the more significant the decrease in mechanical properties of mudstone12. The interaction between mudstone and water can cause changes in some physical properties of mudstone rock mass13,14. That is, the influence of water on the mechanical properties of soft rocks is mainly reflected in changing its structural properties15 –17. Mudstone has strong hydrophilicity and is easy to absorb water when in contact with water. Water entering the pore structure of mudstone disrupts the bonding between clay and minerals, leading to a decrease in the mechanical strength of mudstone18,19. The phenomenon of mudstone deteriorating in properties when encountering water seriously increases the difficulty of engineering construction and may cause damage to existing engineering facilities20,21.

In recent years, numerous scholars have conducted extensive research on the mechanical properties of mudstone containing water22 –26. These studies all indicate a common feature that the presence of water in mudstone deteriorates its mechanical properties to varying degrees. With moisture content of mudstone increasing, the uniaxial compressive strength decreases negatively exponentially or negatively linearly27 –29. The experimental results of Erguler et al.30 showed that the mechanical strength of mineral rich mudstone with moisture content decreased by more than 60%. The experimental results of Lu et al.31 indicate that water not only affects failure mode and creep characteristics of mudstone, but also reduces its short-term mechanical properties. Its compressive strength decreases exponentially with the increase of moisture content. For mudstone saturated with water, its compressive strength and cohesive force have decreased by 56%, and its elastic modulus has also decreased by 28%32. Xu et al.33 analyzed the macroscopic and microscopic mechanisms of water in mudstone and pointed out that the strength of mudstone is negatively correlated with water content. Yun et al.34 proposed a nonlinear prediction model for the mudstone softening strength by analyzing the triaxial test results of mudstone with different moisture contents and confining pressures. The above research mainly focuses on the mechanical properties of mudstone with moisture content, and there are few reports on the structural evolution characteristics of mudstone under isotropic and equal pressure loading. Therefore, Numerous scholars have analyzed the microstructure characteristics of mudstone samples under different moisture contents provided by CT scanning technology, thereby deepening the understanding of the microscopic mechanism of water-weakening mudstone21,35–37.

In this paper CT scanning technology is utilized to obtain CT number (Me) of mudstone during loading. And the structural parameters with clear concepts and simple forms are proposed, which can accurately describe the structural evolution characteristics of hydrous mudstone. Through real-time CT scanning of mudstone samples under isotropic and isobaric loading, the macroscopic mechanical parameters during the loading process are linked to the microscopic structural parameters during the scanning process. The structural evolution law during the loading process can be clarified, and the damage evolution equation during the loading process of hydrous mudstone can be established, providing reference for further establishing structural models of mudstone considering structure.

Materials and methods

Test materials

The mudstone used in this experiment was taken from the coal roof of Wucaiwan No.1 mine (with a burial depth of about 300 m), which has a low rock strength and collapses due to wet swelling in water. The mudstone blocks (as shown in Fig. 1a) were transported to the laboratory, and then a HZ-15 electric coring machine was used to core the original mudstone blocks (with a diameter of 25 mm, as shown in Fig. 1b). The rock column was cut and polished using a TCHR-II cutting mill to produce a 50 mm long sample (Fig. 1b). The original moisture content of mudstone is 1.20%, the density is 2.22 g/cm3, and the porosity is 13.26% .

Fig. 1
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Production of mudstone specimens.

Preparation of mudstone samples with moisture content

Experimental equipment

In order to study the yield performance of hydrous mudstone, it is necessary to prepare hydrous mudstone samples with different moisture contents. The conventional soaking method is to immerse the sample in a container filled with water, which can easily lead to sample disintegration and destruction38,39. Therefore, appropriate and effective methods need to prepare different hydrous mudstone samples with uniform water distribution. Therefore, the Aquadyne DVS-2 water absorption analyzer (Fig. 2) is used to measure the weight increase of mudstone with increasing relative humidity (RH) using the gravimetric method. According to Lewis Greenspan’s research results, the relative humidity values of saturated salt solutions at 40℃ are shown in Table 1.

Fig. 2
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Schematic illustration of a dynamic water vapor adsorption instrument.

Table 1 Relative humidity of saturated salt solution.
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Experimental process

During the experiment, the static gravimetric method was used to measure the water vapor adsorption capacity of mudstone samples at different relative humidity. The main experimental process of the water vapor adsorption process of mudstone samples is as follows:

(1) The mudstone samples are placed in a drying oven (set at 105 ℃ for 24 h) to dry the samples.

(2) The dried mudstone samples are sealed and stored for future use.

(3) The different saturated salt solutions are configured and the corresponding humidity for each solution is shown in Table 1. Then, the saturated salt solution sealed and stored at a constant temperature (30℃).

(4) The measured mudstone sample is placed on the bracket connected to microbalance, and it is equilibrated at the set temperature for about 3 days. To ensure long-term stability during the experiment, an independent temperature of 40 ℃ was used to maintain the equilibrium environment.

(5) During the initial 24 h of the experiment, measurements were made every 2 h, and then every 6 h, a balance with an accuracy of 0.0001 g was used to weigh the mudstone sample until the quality remained basically unchanged.

(6) The temperature stability and relative humidity resolution of the sample room reach 0.1℃ and 1%/min, respectively. Water balance under low humidity conditions is performed and gradually increased to relative humidity.

(7) After the test is completed, the new mudstone sample and saturated salt solution are replaced, and the test steps (3) to (6) is repeated until all the tests are completed.

An electronic balance is used to measure the mass change of mudstone sample at different times, which is considered as the water vapor adsorption capacity. By calculating the difference between the mass of the adsorbed water vapor mudstone sample and the initial mudstone sample mass, the change in moisture content of the mudstone sample at different times is calculated according to Eq. (1), and the formula for calculating moisture content (θ) can be expressed as:

$$\theta =\frac{{m - {m_{dry}}}}{{{m_{dry}}}} \times 100\%$$
(1)

Where, m is the mudstone sample mass at different times; mdry is the quality of the mudstone sample under dry conditions; θ is the moisture content.

In Fig. 3, water vapor adsorption capacity by mudstone sample under different relative humidity conditions is transformed into a curve of moisture content over time. From Fig. 3, it can be seen that the moisture content of mudstone samples has the same variation pattern with time under different relative humidity, that is, the moisture content of mudstone samples increases sharply in the initial stage, then slowly increases, and finally remains basically stable. Moreover, as the relative humidity increases, the moisture content of sample also increases. When water vapor adsorption capacity reaches to be stable at different relative humidity, the moisture content of mudstone are 5.86, 13.38, and 21.19% respectively.

Fig. 3
Fig. 3
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Comparison of moisture content of mudstone samples with time.

Isobaric loading and CT scanning test system

The experimental system consists of two parts: mudstone sample loading system and industrial CT scanning system (Fig. 4). Isobaric loading system for hydrous mudstone samples mainly includes the loading system and data collection part. The industrial CT scanning system is mainly composed of X-ray sources, turntables, X-ray detectors, and computer data processing units.

Fig. 4
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Isobaric loading and CT scanning system.

The four mudstone samples have moisture contents of 1.20% (protolith), 5.86, 13.38, and 21.19%, respectively, with corresponding sample numbers of M1, M2, M3, and M4. Isotropic loading (totaling 8 levels of load) applied to four mudstone samples, and effective stress σes is at 0, 2, 4, 6, 8, 10, 15, and 20 MPa respectively.

Step-by-step loading method

After assembling the sample, firstly, the confining pressure is applied and maintained the net confining pressure unchanged. For the burial depth of the rock layer is about 300 m, the confining pressure is set at 7.5 MPa. Secondly, the mudstone sample is loaded slowly by the servo press at the set loading force, as the volumetric strain of the mudstone sample reaches stability, the data are recorded. Thirdly, the next level of load is applied until the end of the test. During the test, the stability should meet the requirements for mudstone sample volumetric strain, that is, within 2 h, the mudstone sample volumetric strain should be less than 0.001.

Effective stress (σes) in triaxial stress state can be represented by Eq. (2):

$${\sigma _{es}}=\frac{{{\sigma _1}+2{\sigma _3}}}{3} - p$$
(2)

Where, σes is the effective stress, MPa; σ1 and σ3 are the major and minor principal stresses, MPa; p is the pore water pressure, MPa.

The volumetric strain is an important mechanical parameter for studying sample deformation, and the calculation formula is as follows:

$${\varepsilon _v}=\frac{{\Delta V}}{{{V_0}}} \times 100\%$$
(3)

Where, ΔV and V0 respectively represent the volume change and the initial volume of the sample, cm3; εv is the volumetric strain of the sample, %, and εv is related to void ratio (e) of rock, that is,

$$e=(1+{e_0}) \times (1 - {\varepsilon _v}) - 1$$
(4)

Where, e0 is the initial void ratio, which is equal to the ratio of the pore volume of the initial sample to the volume of its solid matrix.

The relationship of specific volume of rock sample v=(1 + e) and volumetric strain (εv) is as following:

$$v=(1+{e_0}) \times (1 - {\varepsilon _v})={v_0}(1 - {\varepsilon _v})$$
(5)

Where, v0 is the initial specific volume of the rock sample, cm3/g.

CT scanning and metering method

Based on previous experience in rock mass scanning image analysis, a unified set is window width of 400 and a window level of 1050, which can ideally distinguish the changes in the internal structure of mudstone samples in loading process. The size of window level affects the brightness of the image (resulting in a red and blue color after processing). When window level is smaller, the image brightness is blue, and when window level is larger, the image brightness is red. Different window widths and levels do not affect the CT scan data of the sample, but have an impact on the clarity of the image.

The CT scanning position is selected as the middle section of the sample, as shown in Fig. 5. The effective stresses corresponding to each scan are 0, 2, 4, 6, 8, 10, 15, and 20 MPa, totaling 8 times. A total of 32 CT images were obtained from the experiments of mudstone samples under four different moisture contents.

Fig. 5
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Schematic diagram of CT scanning positions for mudstone samples.

When X-rays penetrate the scanned object, a series of complex physical processes occur. Through CT scanning, the CT number Me and variance SD of each material point in the mudstone cross-section can be obtained. Me reflects the average density in the selected area. A larger Me indicates a larger density, which can be calculated using the following equation:

$$\operatorname{Me} =\frac{{\mu - {\mu _w}}}{{{\mu _w}}} \times 1000$$
(6)

Where, µ and µw are the attenuation coefficients of material and water respectively.

The attenuation coefficient µ is a physical quantity that changes with the X-ray energy E and the material properties of the object itself. When the voltage is below 200 kV, the attenuation coefficient can be determined by the following equation:

$$\mu =\rho (a+9.8 \times {10^{ - 24}}{Z^{3.8}}/{E^{3.2}})$$
(7)

Where, ρ is the material density, Z is the atomic number, a is the Kline Nishina coefficient, and E is the X-ray energy.

In addition, through statistical calculations, the degree of density difference of material points in the selected area can be obtained within a certain confidence interval, which can be represented by variance SD (dimensionless). The size of SD reflects the non-uniformity of density in selected area. The larger the SD, the higher the degree of unevenness in density; On the contrary, the smaller the density and the lower the degree of unevenness.

Test results and analysis

Yield characteristics

During the step-by-step loading process, mudstone samples will undergo deformation after each level of load stabilizes. The specific volume (v) according to Eq. (5) can be obtained corresponding to each level of net confining pressure, which are plotted in Fig. 6. The volumetric strain increases gradually with the effective stress increasing. In order to better reflect the yield characteristics of the mudstone sample during the loading process, the effective stress is used semi logarithmic coordinates, as shown in Fig. 6. For each mudstone sample, there is a turning point in the relationship curve of v-lgσes, where there is a significant change in specific volume before and after the turning point. By fitting the v and lgσes with linear functions before and after the turning point, these two fitted lines have a point of intersection, and the effective stress corresponding to the intersection point can be regarded as the yield stress40. In Fig. 6, the slope of the straight line before and after the yield point under each moisture content can be obtained through linear segmented fitting, and the slope can be used as a compression index for hydrous mudstone samples. Taking the yield point as the dividing point, the straight line slope before and after yield are showed in Table 2, which are represented by the symbol Cc1 and Cc2. And the yield stress corresponding to each moisture content is obtained through linear fitting, which is listed in Table 2. Table 2 shows that the yield stress of mudstone sample decreases with moisture content increasing. It can be seen that the moisture content plays an important role in the yield characteristics.

Fig. 6
Fig. 6
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Relationship curve between specific volume and effective stress.

Table 2 Key mechanical index during loading test.
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CT real-time scanning

After each level of load is applied and the deformation reaches the stable standard, the mudstone sample cross-section is scanned according to the scanning position in Fig. 5. The entire scanning cross-section is taken as the analysis object, and the CT number Me and variance SD on the cross-section are recorded. Due to the small difference in CT number and variance of the cross-section, both the CT number Me and variance SD are taken as averages to represent the microstructural changes of the entire mudstone sample under each level of load.

Figure 7 shows the CT scan images of mudstone sections of M1 ~ M4 samples at effective stresses of 0, 2, 4, 6, 8, 10, 15, and 20 MPa, respectively. The red part in the figure represents the low-density area of the mudstone sample, mainly composed of primary larger pores and holes. The blue part represents the high-density area, where the rock mass is relatively dense, without large pores and holes. When scanning at 0 MPa, the red area in the image is clearly distributed, which also indicates the non-uniformity of the original mudstone structure with large pores and holes inside. As the load gradually increases, the red area decreases and the blue area increases, indicating that the original mudstone structure is gradually destroyed, new structures are gradually generated, and the density gradually tends to be more uniform. During the process of applying effective stress, irregular large pores and holes become more regular pores, but small pores are difficult to compress and close.

Fig. 7
Fig. 7
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CT images of cross section of different mudstone samples under loading process.

Figure 8 shows the variation curves of CT number Me and variance SD with effective stress for four mudstone samples during loading. As the effective stress increases, the CT number Me gradually increases, while the variance SD gradually decreases, which indicate a gradual increase in density and a decrease in non-uniformity. The corresponding CT scan image in Fig. 7 shows a process of gradually darkening from brighter. In addition, the CT number Me varies regularly with the load, while the variance SD is more sensitive, but the overall decreasing trend remains unchanged. The reason for the sensitivity of variance SD changes may be related to the significant differences in statistical regional density.

Fig. 8
Fig. 8
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Variation of scanning data with each level of load during hydrostatic triaxial compression test CT (a) Values Me and effective stress (b) Square deviation and effective stress.

The different Me values of the initial scanning cross-section in Fig. 8a reflect the uneven spatial distribution of the initial mudstone structure. The moisture content of mudstone sample has a significant impact on the CT number, and as moisture content increases, Me shows a regular change. With moisture content increasing, the Me value of mudstone sample decreases. Under the same effective stress level, the CT number of sample with larger moisture content increases more slowly. The larger the moisture content, the smaller the density of the sample after its deformation stabilizes. Density and moisture content play a key role in affecting the CT number Me. Therefore, the larger the moisture content, the weaker the ability of mudstone structure to resist external loads.

Discussion

Effect of mudstone structure on yield characteristics

From the previous experimental results (Fig. 6; Table 2), it can be seen that mudstone has a distinct structure, which has a certain impact on its mechanical deformation characteristics and can withstand external loads to a certain extent. As moisture content is larger, the structure influence of mudstone on its mechanical characteristics is relatively smaller. On the contrary, when the moisture content is smaller, the structural effect on resisting external loads is greater. The water film interaction between mudstone particles corresponding to larger moisture content is obvious, while the interaction between mudstone matrices is significantly reduced. When the moisture content is smaller, the water film interaction between the particles in the mudstone matrix is weaker, and the interaction between the mudstone matrices is stronger, which results in larger mechanical properties.

Before the yield of mudstone, the structural properties can play a good role. As the applied effective stress increases, the structural properties are also subjected to varying degrees of damage and gradually reduce their contribution to mechanical characteristics. But after yielding, the mudstone enters the plastic hardening stage and undergoes significant plastic deformation. At this point, the structural effect decreases and the structural damage increases.

From the CT scan image (Fig. 7), it can be seen that the pores and holes inside the sample will decrease after applying effective stress, but they will not close. It can be said that the original pores and holes in the mudstone matrix are difficult to completely close under external load. Only under greater external forces these internal pores and holes can be completely closed. That is because that the original structure becomes dense and forms a new structure after the sample yields, which can better resist external loads.

Comparing with the curves of Me-σes (Fig. 8a) and v-lgσes (Fig. 6), the change of Me value can clearly reflect the mudstone yield behavior, therefore, the curve of Me-σes can also serve as an effective method for determining yield stress. When a load is applied to mudstone sample M1, the curve of Me-σes in Fig. 8a can be divided into two straight segments, and 8.5 MPa can be used as the yield stress of mudstone sample M1 through least squares fitting. The other mudstone samples M2, M3, and M4 also exhibit this typical feature with yield stresses approximately equal to 7.0 MPa, 6.0 MPa, and 4.5 MPa, which is consistent with the yield stresses obtained in Fig. 6; Table 2. In addition, as shown in Fig. 8a, before the mudstone yields, the small curve variation in the Me-σes curve indicates that the mudstone structure has the ability to resist external loads. However, when the external load increases and the structure is no longer sufficient to resist the external load, the mudstone undergoes significant deformation and enters the plastic hardening stage, and the curve of Me-σes shows a linear growth trend (Fig. 8a) .

Structural damage evolution characteristics during isotropic loading process

During the loading process, the original structure of mudstone samples gradually damages, which results in structural damage. The CT number Me can reflect the mudstone density and the arrangement and distribution of matrix particles, which can reflect the structural characteristics of mudstone. The CT scan data obtained from the experiment can be used to define the structural parameters of mudstone, and based on these data, the structural damage evolution law of mudstone can be studied under simple compression state. In addition, due to the sensitivity of variance SD during the loading process, the variation pattern is not very obvious (Fig. 8b), so the CT number Me is the main tool for studying the damage evolution law in this paper.

Structural parameters

The mudstone without loading is considered as a complete structure, and its corresponding CT number is represented by Me0. However, during the loading process, although the mudstone sample structure undergoes changes or damage, it is considered as a relatively complete rock sample, and the corresponding CT number is represented by Me. The mudstone sample with significant structural damage at the end of loading can be considered as a completely damaged sample. The corresponding CT number is represented by Mef, and the structural parameter (m) of a certain mudstone sample during any loading process is defined as:

$$m=\frac{{{{\operatorname{Me} }_f} - \operatorname{Me} }}{{{{\operatorname{Me} }_f} - {{\operatorname{Me} }_0}}}$$
(8)

The structural parameters determined by Eq. (8) are actually a relative value. Without loading, the mudstone sample has not undergone damage or failure, with Me = Me0 and the structural parameter m = 1. After loading is completed, the mudstone sample undergoes complete structural failure due to external load, with Me = Mef and structural parameter m = 0. The transition of structural parameters from 1 to 0 also indicates a gradual weakening and disappearance of the structure.

Taking the data in Fig. 8a as the analysis object, the initial Me value of sample M4 with moisture content of 21.19% is equal to 934.44 HU, while the Me value of sample with moisture content of 1.20% is 1396.18 HU when the effective stress is applied to 20 MPa. All other Me values are between these two data. In fact, the structural parameters range from 1 to 0, which also indicates that the disappearance of the structure is a relative process. Therefore, in order to facilitate calculation and prevent special situations where the structural parameter is 0, Me0 is taken as 930 HU and Mef is taken as 1400 HU. The values of Me0 and Mef have a certain impact on the values of structural parameters, but they do not have a significant impact on the characteristics of structural evolution.

According to Eq. (8), the structural parameter (m) of mudstone sample can be obtained at a certain time during the loading process, as shown in Fig. 9. As the effective stress increases, the structural parameters gradually decrease from 1 to 0, indicating that the structure is gradually disappearing. Moreover, before the mudstone sample yields, the disappearance of structural parameters is relatively small, while the disappearance of structural parameters increases after yielding, which is more consistent with Figs. 6 and 7. This also indicates that the reduction of structure is closely related to external loads, and structural parameters only rapidly decrease when the external load exceeds the yield stress. After yielding, it also indicates the emergence of a stage of rapid disappearance of structure.

Fig. 9
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Variation of structural parameters and effective stress.

Structural damage evolution equation

The structure of mudstone gradually decreases under external loads, which indicates an increase in damage to the original structure. The generation of damage is closely related to the macroscopic performance of the mudstone sample. From the Eqs. (6) and (7), it can be seen that the change in CT number is closely related to the density change. The density change is caused by the occurrence of volumetric strain under external loads. Therefore, the damage evolution of the structure is closely related to the volumetric strain (εv) of the mudstone sample.

During the loading process, the original structure of mudstone samples disappears and gradually damages. In order to clarify the evolution law of structural damage during the loading process, a structural damage variable D is defined, and its expression is:

$$D=\frac{{{m_0} - m}}{{{m_0}}}$$
(9)

Where, m0 and m respectively represent the structural parameters at the initial state and any loading state of the mudstone sample. m0 is determined by the state when the effective stress is equal to 0 MPa (Fig. 9 ), which is the initial state after the stable loading confining pressure. The structural damage variable will gradually transition from 0 to 1, indicating that the structural damage will gradually increase during the loading process until the sample is completely destroyed and no longer has structural characteristics.

According to Eq. (9), the structural damage variables of four types of mudstone samples can be calculated and related to the volumetric strain of the mudstone samples during the loading process. The relationship between the damage variables and the volumetric strain is shown in Fig. 10. In Fig. 10, as the the volumetric strain increases, the damage variable shows a power function growth trend. And moisture content is larger, the structural damage is smaller under the same volumetric strain, which indicates that moisture content has a significant impact on structural damage. At the same moisture content, the greater the volumetric strain (the effective stress), the greater the structural damage value. When the volumetric strain is the same, the higher the moisture content, the smaller the structural damage value.

Fig. 10
Fig. 10
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Variation of damage variable and volumetric strain.

Based on Fig. 10, the relationship between damage variables and volumetric strain during the loading process of mustone samples can be obtained, which basically conforms to Eq. (10). The fitting parameters are listed in Table 3, and the correlation coefficient reaches above 0.99.

$$D=\exp (\alpha {\varepsilon _v}) - 1$$
(10)
Table 3 Fitting parameter.
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Where, α is an empirical parameter that is related to the moisture content of the sample, and is fitted by fitting α (Fig. 11) can be represented as,

Fig. 11
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α value fitting.

$$\alpha =0.0599 - 0.0027\theta +\begin{array}{*{20}{c}} {5.9785 \times {{10}^{ - 5}}{\theta ^2}} \end{array}({R^2}=0.9592)$$
(11)

Where, θ is the moisture content, %.

By combining Eqs. (10) and (11), it can be concluded that:

$$D=\exp [(0.0599 - 0.0027\theta +\begin{array}{*{20}{c}} {5.9785 \times {{10}^{ - 5}}{\theta ^2}} \end{array}){\varepsilon _v}] - 1$$
(12)

The damage variable D of mudstone under different moisture contents obtained the test results and the damage variable calculated from Eq. (12) are shown in Fig. 12. If the two calculation results are equal, they should be on the 45° line in the figure. From Fig. 12, it can be seen that the damage variables from test results and the damage variables calculated using Eq. (12) are both near the 45o line. It can be seen that the calculated values obtained from Eq. (12) basically reflect the influence of volumetric strain on structural damage. Equation (12) is simple, clear, and highly practical, providing a reference for establishing structural constitutive models of mudstone.

Fig. 12
Fig. 12
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Relationship between damage variable and its calculated value.

The study of damage variable D in the constitutive model of mudstone is of great significance for potential applications, mainly reflected in the following aspects:

Firstly, the damage variable D can quantitatively describe the degree of damage to mudstone. In the constitutive model of mudstone, the damage variable D is used to characterize the development and accumulation of internal defects in the material during the loading process, thereby reflecting the degree of damage to the material. By introducing the damage variable D, the mechanical behavior of mudstone under loading conditions can be more accurately described, especially under cyclic loading and long-term loading, the damage evolution characteristics of mudstone can be quantitatively analyzed in more detail.

Secondly, the damage variable D is conducive to to establish a more accurate constitutive model. In the constitutive model of mudstone, by defining and calculating the damage variable D, a damage constitutive model can be constructed to reflect the entire stress-strain process of mudstone. This method can not only comprehensively analyze the strength evolution characteristics of mudstone under uniaxial compression, but also monitor the damage evolution characteristics and degree of mudstone in real time, which provides reference for maintaining the stability of underground goaf.

In addition, the damage variable D has significant value in engineering applications. The damage theory is considered as an effective research method to study mudstone materials containing initial defects. By introducing the damage variable D, we can better understand the failure mechanism of mudstone under loading, optimize design parameters, and improve the stability and safety of engineering structures.

In summary, the application of damage variable D in the constitutive model of mudstone not only helps to quantitatively describe the degree of damage of mudstone, but also establishes more accurate constitutive models and provides important reference basis in engineering practice, which has significant theoretical and practical value.

Conclusion

Through stepwise isobaric loading tests and CT scanning technology, the relationship between macroscopic mechanical indicators and microscopic scanning data is obtained for mudstone samples with four kinds of moisture contents, which can be used to study the structural evolution of hydrous mudstone during loading process. The main conclusions include:

(1) The structure of mudstone has a significant impact on its stress-strain curve before and after yielding. Before the mudstone yields, the growth of Me is slow, indicating that the structure can resist external loads to a certain extent. After yielding, Me shows a linear growth trend, and the mudstone enters the plastic hardening stage with a significant decrease in structural effects.

(2) Degree of structural action is closely related to mudstone water content. The structure of mudstone is closely related to its moisture content. As moisture content in mudstone is larger, the structural influence on its mechanical characteristics is relatively smaller. On the contrary, as moisture content in mudstone is smaller, the structural effect on resisting external loads is significantly enhanced.

(3) From the CT images, it can be seen that after applying effective stress to the mudstone, the internal pores and holes will decrease, but will not close. After applying a larger load, the original structure undergoes damage, accompanied by the formation of a new structure that can withstand external loads.

(4) According to the scanning CT number Me, the structural parameters and structural damage variables were defined, and the relationship expression was established between structural damage variables and volumetric strain during the loading process. The established structural evolution equation has a simple form and strong practicality, which can better reflect the impact of solid phase changes on the structural damage of mudstone. At the same time, it provides a reference for establishing a constitutive model suitable for the structure of mudstone.