Study on Uniaxial Mechanical Behavior and Damage Evolution Mechanism of Water-Immersed Mudstone

Abstract

The existence of mudstone weak interlayers has a significant impact on the stability of open-pit coal mine slopes. Under the combined influence of rainfall and groundwater, the mechanical properties of the mudstone of weak interlayers deteriorate, leading to a local loss of bearing capacity of the slope and further accelerating the overall instability of the slope. In order to investigate the changes of macroscopic and mesoscopic structures, mechanical failure behavior, and the damage evolution mechanism of water-immersed mudstone, non-destructive water immersion experiments and uniaxial compression experiments were conducted. The results indicate that the main causes of macroscopic structure failure of water-immersed mudstone are the initiation, propagation, and mutual penetration of micro cracks. The mesoscopic structure characteristics of water-immersed mudstone are primarily manifested by increased surface smoothness, increased occurrence of small-scale pores, the presence of a dense network of fissures on the surface, and fusion of mineral unit boundaries. With the increasing immersion time, the quality, relative water content, and peak strain increase, while the uniaxial mechanical parameters and energy parameters decrease. In addition, a statistically damaged constitutive model for mudstone considering the coupling damage of water immersion and low-stress loading was established, and the model is consistent with experimental results. Finally, the water-softening characteristics of mudstone are caused by the propensity of clay minerals to expand and disintegrate upon water contact, changes in pore structure, variations in mineral types and distributions, and the presence of pore water pressure. This study provides valuable insights into the water–rock deterioration mechanism of mudstone and the stability of slopes containing weak interlayers.

1. Introduction

Coal, as a traditional major source of energy, plays a critical role in the stable development of the economy, society, and environment. However, the impact of water immersion on mudstone in the weak interlayer during open-pit coal mining, leading to instability in open-pit mine slopes, cannot be underestimated in terms of its implications for sustainable resource development. The presence of weak interlayers primarily composed of mudstone increases the probability of slope instability and landslides in open-pit coal mines. These weak interlayers have a loose internal structure and weak bonding forces between particles. Due to the softening effect of water and the swelling characteristics of mudstone in water, the mechanical properties of the weak interlayers are significantly reduced under the influence of rainfall and groundwater, which is prone to rapid disintegration and failure, leading to accelerated instability of the slope rock mass. Such weak interlayers often become the dominant failure surfaces that contribute to slope sliding [1,2,3]. Therefore, it is of significant engineering importance to study the mechanism of immersion degradation of mudstone in weak interlayers. Gaining a comprehensive understanding of the variations in mudstone under water immersion conditions can significantly enhance the assessment and prediction of potential geological hazards during coal mining, effectively reducing safety risks associated with mining operations. Concurrently, these research findings can offer vital insights for optimizing coal mining schemes and resource utilization, contributing to the reduction in resource wastage and environmental impact, and propelling the coal industry towards a more sustainable direction.

There has been extensive research on the interaction between water and rocks, focusing primarily on the following aspects: microstructural evolution of rocks under water–rock interactions [4,5,6,7], the static mechanical behavior of rocks under water–rock interactions [8,9,10,11], the dynamic behavior of rocks under water–rock interactions [8,12,13], and the physical and chemical interaction mechanisms between water and rocks [2,14,15]. It can be concluded that the presence of water to some extent disrupts the macroscopic and mesoscopic structure of rocks, weakening the mechanical properties.

The softening effect of water on mudstone is closely related to the characteristics of the internal clay mineral composition, as well as the presence of inherent defects such as pores and cracks. Scholars have conducted relevant research from different scales to investigate the relationship. At the microscopic scale, the clay minerals in mudstone exhibit strong water molecule adsorption behavior in aqueous solutions, leading to significant expansion of the crystal lattice in the stacking direction [16]. Additionally, clay particles as a whole carry fixed negative charges, and the surfaces of clay particles in water solutions often form a diffuse double-layer structure, causing the clay mineral particles to repel each other [17,18]. Consequently, the presence of clay minerals serves as the material basis for the softening of mudstone. Moreover, the strength of swelling characteristics of mudstone is closely related to the types of clay minerals. Kuang and Oueslati [18,19] quantitatively analyzed the relationship between water content and interlayer spacing in montmorillonite and kaolinite using X-ray diffraction and neutron scattering, as well as the formation of hydration shells and the difficulty of binding water molecules in illite interlayers. Based on the analysis of the physical properties of crystal structures, Li et al. [20] pointed out that the hydration expansion of these three clay minerals could be ranked from highest to lowest as follows: montmorillonite, illite, and kaolinite. At the mesoscopic scale, the influence of water on mudstone is primarily studied using techniques such as scanning electron microscopy (SEM), X-ray CT scanning technology, and optical microscopy. These techniques allow researchers to investigate the effects of water on mudstone at a fine-scale level. Huang et al. [21] investigated the influence of pore structure on the adsorption and desorption behavior of mudstone using water vapor physical adsorption. He pointed out that the moisture absorption of mudstone was mainly controlled by micro fractures rather than pore structure, and the hydration fractures serve as the main pathways for capillary water absorption, controlling the capillary water absorption coefficient and height in mudstone. Huang et al. [22] developed a three-dimensional mesoscale finite element model of concrete based on in-situ X-ray computed tomography (XCT) images and conducted simulations of three-dimensional uniaxial tensile tests on concrete. The study revealed that the internal inhomogeneity of the mesostructure, resulting from the multi-phase random spatial distribution, has a significant impact on the macroscopic behavior of concrete. Furthermore, the distribution of voids plays a crucial role in influencing the tensile strength and crack mode of the material. Feng et al. [23] observed the microstructure and morphological changes of mudstone after water immersion. The results indicated that the nonhomogeneous strain of mudstone led to the expansion between adjacent clay mineral aggregates and particle clusters, resulting in the reduction in or disappearance of pores, which causes a decrease in the number of large-diameter pores and an increase in the number of small-diameter pores in the internal pores of mudstone. At the macroscopic scale, the effect of water on mudstone primarily involves investigating the expansiveness. Zhou and Zhong [24,25] conducted expansion experiments on mudstone from the Chuanzhong red beds; the results showed that the uneven expansion caused by variations in water absorption capacity and the distribution of clay minerals led to swelling and cracking in mudstone. The water absorption and expansion process of mudstone could be divided into three stages: rapid expansion in the initial short period, continuous expansion with decreasing expansion rate, and stabilization with almost no further expansion deformation.

The weakening effect of water on the mechanical properties of mudstone is primarily studied through experimental means. Liu et al. [26] conducted uniaxial compression experiments, Brazilian splitting experiments, and triaxial compression experiments on mudstone samples with different water contents. They found that, as the water content increased, the elastic modulus, uniaxial compressive strength, tensile strength, triaxial compressive strength, and cohesion of the mudstone samples all decreased to varying degrees, while the peak strain initially decreased and then increased, and the internal friction angle remained almost unchanged. Yang et al. [27] investigated the influence of water content on the mode I fracture toughness of mudstone; the results showed that with the increasing immersion time, the fracture toughness of the mudstone samples exhibited a decreasing trend, accompanied by a significant increase in the degree of anisotropy, and the failure mechanism of the mudstone gradually shifted from brittle failure to ductile failure. Liu and Zhang [28,29] studied the mechanical properties and energy evolution mechanism of mudstone under different water immersion. It was found that the influence on the mechanical properties of saturated mudstone was characterized by the decrease in characteristic strength, the weakening of brittle deformation, the enhancement of plastic deformation, and the obvious difference of each deformation section. The influence on the energy evolution of mudstone was characterized by the weakening of energy absorption and release properties of rock after saturation, the enhancement of energy dissipation properties, and the different energy distribution rules of each stage. In summary, scholars have conducted research on the impact of soaking conditions on the mechanical properties of mudstone and have gained a better understanding of the macro-scale mechanism of mudstone weakening in water. However, there are relatively few studies that comprehensively investigate the weakening mechanism of mudstone under soaking conditions, taking into account the changes in macro- and meso-structure, mechanical properties, and energy evolution of mudstone.

After being exposed to water, fissures in mudstone significantly proliferate and expand, while internal microstructures and micropores exhibit pronounced development [30]. When the external force is subsequently applied to the rock, the combination of water-induced fissures and cracks initiated by loading gradually expands, leading to the formation of macroscopic cracks, which ultimately causes the structural failure of the rock, resulting in the loss of its load-bearing capacity [31,32,33]. This process influences the mechanical properties of the rock and represents an accumulation of damage on the macroscopic scale. Cao et al. [34] introduced the concept of a damage threshold, suggesting that rock damage does not occur immediately upon loading but rather when the stress or deformation reaches a certain level. Yang et al. [35] used CT scanning technology to study the damage characteristics of rocks; the results indicated that under low stress levels, the degree of compaction of the holes in the rock was greater than the degree of compaction of most initial defects such as micro cracks and pores and the degree of the expansion of main cracks. The introduction of the concept of rock damage threshold can provide a better explanation for the phenomenon of elastic deformation occurring in rocks at low stress levels. For the description of the damage process in rocks under loading, scholars generally believe that rock damage follows a Weibull distribution, so statistical damage constitutive models have been widely recognized as effective tools for describing damage [36,37,38,39,40]. The internal structure of mudstone is loose, the internal cracks increase after immersion, and the bearing capacity is further reduced, so there is a possibility of failure and instability under low stress levels. Therefore, it is necessary to establish a statistical damage constitutive model of mudstone considering immersion damage and low-stress loading.

In this paper, a comprehensive study was conducted to investigate the weakening mechanism of mudstone under different water immersion times. The research started by quantitatively analyzing the mineral composition of the mudstone. Subsequently, non-destructive water immersion experiments were carried out on the mudstone, and the macroscopic and mesoscopic structural changes were monitored at different water immersion times. Following this, uniaxial compression strength (UCS) experiments were performed on the mudstone samples subjected to different immersion times to determine their mechanical failure characteristics and energy evolution patterns. Through these experimental observations and analyses, the weakening mechanism of mudstone under different water immersion times was revealed by considering the changes in macro- and mesostructure, mechanical properties, and energy evolution patterns. Additionally, based on the concepts of damage mechanics and damage threshold, a statistical damage constitutive model for mudstone was developed, which takes into account the coupling damage of immersion and low-stress loading, and the accuracy and effectiveness were validated through further experiments and analysis.

2. Methodology

2.1. Engineering Background

Based on field investigations in the eastern part of Inner Mongolia province, China, a prominent weak interlayer was identified in the slope of a specific open-pit mine. The rock type of this weak interlayer is mudstone, characterized by a high content of clay minerals and strong water absorbency, which is prone to swelling and disintegration when in contact with aquifers [30]. Moreover, the mine’s location has a temperate semi-arid continental monsoon climate, with an annual precipitation of 294.74 mm, and the rainfall is concentrated during specific seasons, with approximately 70% of the annual precipitation occurring in the summer. In addition, the mine is also in close proximity to a river, and there are multiple sets of pore phreatic water and fractured confined aquifers in the stratum, resulting in substantial water inflow to the mining area. Under the influence of water, mudstone is susceptible to the weakening of its macro- and microstructure as well as mechanical properties, which subsequently impacts the slope stability. Therefore, samples were obtained from the weak layer, and experimental research was conducted. The geographical location, weak interlayer condition, and climatic conditions of the mine are illustrated in Figure 1.

2.2. Sample Preparation

The mudstone was taken from the weak interlayer of the open-pit mine. Following the recommendations of the International Society for Rock Mechanics (ISRM) [41], standard cylindrical samples with a diameter of 50 mm and a height of 100 mm were prepared. To ensure the accuracy of the uniaxial compression experiments, samples with significant visual defects were removed, and samples with no apparent defects on the surface were selected for the experiments. To observe the mesoscopic structural changes of the mudstone during the water immersion, fresh rock samples were processed into cubes with a side length of less than 1 cm. Additionally, to determine the mineral composition of the mudstone, the dried samples were ground using agate mortars to obtain a powder with a particle size of less than 45 μm.

2.3. Determination of Water Immersion Method

The conventional method for water immersion involves directly submerging the mudstone samples in a water-containing container. In order to preliminarily judge the influence of water on the surface structure of mudstone, the rock samples were cut into 2 × 2 × 1 cm³ blocks and placed in a transparent vessel. Pure water was added until the water covered the top surface of the samples. The process of surface structure change after the interaction between the sample and water was observed.

The whole process of the mudstone sample disintegration in water is illustrated in Figure 2. After 5 s, a large number of bubbles appeared in the water and the surface of the rock sample reacted rapidly with the water, forming a honeycomb-like structure. After 55 s, significant particles and massive disintegration were generated on the rock surface. After 480 s, there were no apparent large-volume blocks on the external surface of the sample, but a cluster of bubbles was floating on the water surface. At 660 s, a large internal block in the upper-left corner of the sample disintegrated, and thereafter, there were no significant large blocks inside or outside the sample. The disintegration rate noticeably decreased. After being left undisturbed for 1200 s, the disintegration process was complete, and the water became turbid.

Hence, it can be inferred that the conventional water immersion method would cause significant soaking damage to the mudstone studied in this research. Therefore, a non-destructive water immersion method was employed to treat the mudstone. The non-destructive water immersion device consists of an air humidifier and a closed container, as shown in Figure 3. The air humidifier provides a constant temperature and humidity water environment, immersing the mudstone in the form of water mist, thus avoiding the disintegration of the rock samples inside the sealed box.

2.4. Composition

The material composition of rocks is closely related to their mechanical properties, and mudstone is a typical clay-bearing soft rock whose moisture absorption capacity depends on its clay mineral content, exhibiting a positive correlation between the two [29,42]. In order to obtain the composition and content of the mudstone, especially the content of hydrophilic clay minerals such as montmorillonite, illite, and kaolinite, X-ray diffraction (XRD) analysis was conducted on the processed powder. The XRD instrument used is the Rigaku D/MAX-2600 from Japan, with a diffraction angle range of 5° to 80° and a scanning speed of 2°/min. The composition and content of the mudstone are shown in Figure 4. The results indicate that mudstone is a heterogeneous rock composed of clay minerals and mineral fragments. The major constituents include quartz, illite, albite, kaolinite, montmorillonite, and clinochlore. Quartz particles dominate the fragmental minerals, exhibiting high hardness and low water absorption, making it a mineral with stable physical and chemical properties. The clay minerals, comprising illite, clinochlore, montmorillonite, and kaolinite, account for 39.5% of the composition. The presence of a high content of clay minerals contributes to the low strength and water-induced softening and disintegration characteristics of the rock sample. Therefore, the mudstone used in this experiment possesses the material basis for water-induced softening.

2.5. Test Scheme

To investigate the influence of water on the macroscopic and mesoscopic structures as well as the mechanical behavior of the mudstone, a non-destructive immersion device was used to pretreat the mudstone. The device was set at 26 °C and 90% humidity. To visually observe the development and propagation of macroscopic cracks in the rock due to water immersion, three standard cylindrical mudstone samples were selected for the same immersion tests of 0 h, 12 h, 24 h, 36 h, 48 h, and 72 h. In order to characterize the mesoscopic structure characteristics of the mudstone, scanning electron microscopy (SEM) experiments were conducted using the ZEISS Gemini 300 scanning electron microscope. The experiments involved scanning the surface of the same sample at different immersion times to observe and analyze the microstructure. The immersion times were 0 h, 12 h, 24 h, 36 h, and 48 h. The quality and appearance of the rock samples were monitored and recorded. Lastly, due to the significant amount of detachment on the surface of the shale after being soaked for 72 h, further mechanical experiments cannot be carried out. Therefore, 15 standard cylindrical shale samples are finally selected and evenly divided into 5 groups for immersion experiments of 0 h, 12 h, 24 h, 36 h, and 48 h. These 5 groups of samples were subjected to UCS tests with a displacement loading rate of 0.2 mm/min. The main testing scheme is illustrated in Figure 5.

3. Results

3.1. Deterioration of Macrostructure and Mesostructure of Water-Immersed Mudstone

3.1.1. Macrostructure Deterioration

The relative water content $w_t$ of each sample was defined based on the increase in rock mass relative to the mass of the sample in the natural state to assess the degradation of mudstone due to water immersion.

$$w_t=\frac{m_t-m_0}{m_0}$$

(1)

where $m_0$ and $m_t$ represent the mass of the rock in the natural state and the mass of the rock after t hours of water immersion, respectively.

Figure 6 shows the curve of the variation in mass and relative water content of the samples within 72 h of water immersion. It can be observed that the mass and relative water content of the mudstone exhibit a concave-upward trend with the increasing immersion time. According to the fitting results, the mass and relative water content of the mudstone roughly follow an exponential function with the increasing immersion time. Based on the concept of limits, it is considered that when the time approaches infinity, the mass and relative water absorption rate of the mudstone will tend to a stable value, indicating that the rock is in a water-saturated state. The relative water content of the samples exhibits an overall growth trend of “fast first and then slow”, with the maximum change occurring within the initial 12 h, and then the growth rate began to decline.

The changes in surface cracks of the mudstone under different immersion times are depicted in Figure 7. It can be observed that at 0 h of water immersion, there are no apparent cracks on the rock’s surface. After 12 h of immersion, longitudinal tensile cracks appear in the middle of the surface, with a length of about 3.5 cm and a width of approximately 0.2 mm. By the 24th hour of immersion, these longitudinal cracks further develop and expand at an angle of around 70°, reaching a length of about 4 cm. Additionally, two small longitudinal cracks emerge on the upper part of the rock, with lengths ranging between 1 and 1.5 cm. These cracks are horizontally distributed and not fully connected, indicating relatively good overall stability of the sample. When the immersion time reaches 36 h, a transverse tensile crack with an angle of 135° forms and extends in the upper part of the sample, with a length of about 4 cm and a width of approximately 0.2 mm. After 48 h of immersion, the surface cracking intensifies, and the crack width and length increase. The longitudinal tensile cracks gradually extend towards the cross-section of the rock at a specific angle of around 70° but do not fully penetrate it. Finally, at 72 h of water immersion, the longitudinal tensile cracks on the surface propagate along the 70° angle, forming macroscopic through-cracks with significantly increased lengths, widths, and depths compared to 48 h. Cracks in the sample exhibit an interwoven distribution both horizontally and vertically.

From the process of crack propagation in the water-immersed mudstone described above, it can be inferred that water immersion gradually induces the development of surface cracks. The macroscopic failure process of the immersed mudstone is primarily characterized by the initiation, development, propagation, and through-penetration of micro cracks, leading to localized damage and ultimately overall fracturing instability of the sample. Among these observations, the presence of longitudinal tensile cracks propagating along specific angles may be attributed to the existence of original defects within the rock.

3.1.2. Mesostructure Deterioration

The mesoscopic structural changes of the mudstone under different water immersion times were observed through SEM scanning. The SEM images at various magnifications are shown in Figure 8.

(1) Surface smoothness: At 500 times magnification, it can be seen from Figure 8a that the mudstone surface in the natural state appears rough, with abundant and closely packed mineral grains. After 12 h of water immersion, the mudstone exhibits a significant reduction in surface roughness. By 24 h of immersion, large relatively flat areas appear on the mudstone surface, indicating an increase in surface smoothness after water immersion.

(2) Porosity: At 5000 times magnification, the intergranular pore size of the mudstone in the natural state varies between 2 and 10 μm. After 12 h of immersion, the intergranular pore size reduces to approximately 1 to 2 μm. This reduction is due to the strong hydrophilicity of clay minerals such as illite and chlorite. Water entering the rock’s pores and fissures causes uneven volume expansion, leading to the dilution and dissolution of some cementing materials, resulting in the fragmentation of particles and an increase in the proportion of small voids [30,43,44]. By 48 h of immersion, the mudstone surface shows increased structural looseness, with a significant increase in small pores, indicating a continuous refinement and fragmentation of irregular-shaped coarse particles, resulting in changes in the arrangement of particle structures. From this, it can be seen that after water immersion, the surface of the mudstone exhibits the structural characteristic of a reduction in large-scale pores and an increase in small-scale pores.

(3) Number of cracks: At 5000 times magnification, in the natural state, the basic units of the mudstone are platy aggregates with curled and flake-like edges. The arrangement of particles is disordered, and the connections between them are tight. After 24 h of immersion, a large number of platy aggregates appear, and the connections between particles weaken, resulting in the presence of numerous cracks. By 36 h of immersion, the distance between irregular hexagonal platy aggregates further increases, forming a dense network of cracks on the surface. From this, it can be observed that after water immersion, the surface of the mudstone exhibits the structural characteristic of a decrease in bonding ability and a significant increase in cracks.

(4) Surface smoothness: At 5000 times magnification, in the natural state, the surface of the mudstone units is rough. After 24 h of immersion, the units’ contours become clearer, presenting a hexagonal flake-like shape. By 48 h of immersion, the contours of many hexagonal flake aggregates become blurred, and the surface shows the fusion of hexagonal aggregates, forming large smooth regions. The flake-like petal-shaped structures undergo significant damage. From this, it can be observed that after water immersion, the surface of the mudstone exhibits the structural characteristic of decreased surface smoothness, and the appearance of fused boundaries where unit aggregates detach and collapse.

The above observations suggest that the mesoscopic morphological characteristics of the mudstone after immersion can be described as follows: improved surface smoothness, increased presence of small pores, interwoven cracks, and fusion of the boundaries of flake units.

3.2. Uniaxial Compression Experiments

3.2.1. Mechanical Parameters

The uniaxial compression stress–strain curve of the rock sample can reflect the failure process to some extent. The variations of the uniaxial compression stress–strain compression curve of the mudstone are illustrated in Figure 9. In addition the uniaxial strength (UCS), elastic modulus (E), and peak strain (${\epsilon }_p$) of the mudstone with different immersion times are shown in

Table 1. Uniaxial mechanical parameters of different samples.

Immersion Time/h		Sample Number	${\mathit{w}}_{\mathit{t}}$/%		E/MPa		UCS/MPa		${\mathit{\epsilon }}_{\mathit{p}}$/%
				Mean		Mean		Mean		Mean
0	4	0	0	516.08	540.55	5.82	5.75	1.22	1.24
	21	0		623.91		5.71		1.26
	28	0		481.66		5.73		1.24
12	3	1.62	1.47	176.21	177.95	2.37	2.30	1.81	1.66
	7	1.31		210.65		2.18		1.53
	10	1.47		146.99		2.36		1.65
24	2	2.72	2.80	125.30	131.67	2.15	2.01	1.83	1.70
	5	2.73		112.62		1.86		1.53
	41	2.96		157.10		2.01		1.74
36	6	4.63	4.81	86.32	104.11	1.42	1.47	1.87	1.75
	8	4.77		129.90		1.32		1.24
	9	5.03		96.11		1.67		2.15
48	12	6.97	6.71	83.19	63.35	1.55	1.16	2.36	2.11
	13	6.72		58.26		0.91		1.97
	32	6.43		48.60		1.03		2.00

. The results show that the evolution of the stress–strain curves during uniaxial compression of the mudstone under different immersion times exhibits consistency and can be divided into four stages: compaction stage, elastic stage, plastic stage, and post-peak failure stage.

With the increase in immersion time, the softening characteristics of mudstone become significant, the range of compaction stage and plastic stage of mudstone is expanded, the elastic modulus and compressive strength of mudstone are reduced to varying degrees, and the peak strain and relative water content exhibit an increasing trend. It is found that the physical and mechanical parameters decrease the most in the first 12 h, the elastic modulus decreases by 66.98%, the compressive strength decreases by 60%, and the peak strain increases by 33.87%, which indicates that the weakening effect of water on mudstone is the most significant at this stage and the changes in physical and mechanical parameters exhibit a “fast first and then slow” trend. Among them, the elastic modulus and compressive strength have a strong sensitivity to water immersion.

3.2.2. Macroscopic Failure Characteristics

The common modes of uniaxial failure in rocks vary depending on the rock type and can be classified into three types: tensile failure, shear failure, and tensile–shear mixed failure. Figure 10 shows the uniaxial compression failure mode of mudstone after different immersion times (0 h, 12 h, 24 h, 36 h, 48 h). It can be observed that in the natural state, the mudstone primarily exhibits a mixed mode of tensile–shear failure, with a distinct tensile crack initially transitioning into shear cracks at an angle of approximately 50°. After 12 h of water immersion, the number of failure cracks slightly increases and penetrates each other, with tensile failure being the dominant mode of failure. After 24 h of water immersion, there is a significant increase in the number of tensile cracks, and the side surface shows fragmentation and spalling, resulting in a rough surface. After 36 h of water immersion, the mudstone exhibits significant shear dilation characteristics, and a localized bulging on the surface leads to fragmentation and spalling of the rock mass. After 48 h of water immersion, two occurrences of bulging and spalling of rock blocks are observed on the side surface due to shear dilation. Additionally, there is an increase in the number of small-scale cracks, and the cracks intersect vertically and horizontally.

Compared to the natural rock sample with a relatively low density of cracks, the immersed samples exhibit a higher density of initial cracks distributed both longitudinally and transversely. The number of cracks is significantly greater than in the natural state, accompanied by swelling phenomena, which exacerbates the structural damage of the samples. The analysis suggests that with the increasing immersion time, the ingress of water further triggers the disintegration effect in the mudstone, resulting in the continuous development and expansion of micro cracks, with an increase in their number, length, and width. Under the applied loads, the cracks are more prone to generate and propagate, leading to the interconnection and eventual failure of transverse and longitudinal cracks. The combined effect of internal and external fracture surfaces results in the overall fragmentation and collapse of the rock, leading to a decrease in structural integrity and a weakening of load-bearing capacity, ultimately leading to a reduction in the mechanical properties of the rock.

Based on the internal structural damage characteristics and uniaxial failure mode of water-immersed mudstone, it can be observed that for mudstone with high clay mineral content, crack propagation is the main failure mode after water immersion. Furthermore, when clay minerals exist in the form of weak interlayers, such as in shale, compared to non-clay mineral interlayered shale, the mechanical properties of layered shale with clay mineral interlayers are more susceptible to the effects of hydration. The hydration of clay mineral interlayers in layered shale leads to expansion, making it prone to the development of tensile cracks, resulting in the disruption of the rock structure [45,46]. Therefore, for engineering projects involving rock formations with high clay mineral content or layered rocks, the hydration effects of water are a critical factor that requires special attention.

4. Energy Evolution Law of Mudstone

4.1. Strain Energy Calculation Method

In order to fully reveal the failure mechanisms of mudstone under uniaxial compression under different water immersion times, an explanation can be provided from an energy perspective [47,48]. During the uniaxial compression process, the work done by the external environment on the rock sample represents the total input energy. Neglecting energy losses in a closed thermodynamic system, all the energy is absorbed by the rock sample and transformed into elastic energy and dissipated energy. The elastic energy represents the strain energy stored in the rock itself, while the dissipated energy is closely associated with the closure, propagation, and interconnection of cracks within the rock. During the post-peak failure stage of the rock, the stored strain energy is released, leading to crack interconnection and instability in the internal structure of the rock. The theoretical energy evolution process during the loading of the rock is illustrated in Figure 11. The relationship between energy and compression in mudstone can be expressed as follows [49]:

$$u=u^e+u^d$$

(2)

$$u={\displaystyle {\int }_0^{{\epsilon }_1}{\sigma }_1\mathrm{d}{\epsilon }_1}+{\displaystyle {\int }_0^{{\epsilon }_2}{\sigma }_2\mathrm{d}{\epsilon }_2}+{\displaystyle {\int }_0^{{\epsilon }_3}{\sigma }_3\mathrm{d}{\epsilon }_3}$$

(3)

$$u^e=\frac{{\sigma }_1^2+{\sigma }_2^2+{\sigma }_3^2-2\nu \left({\sigma }_1{\sigma }_2+{\sigma }_1{\sigma }_3+{\sigma }_2{\sigma }_3\right)}{2E}$$

(4)

where $u$, $u^e$, and $u^d$ are the total input energy density, elastic energy density, and dissipated energy density of the rock sample, respectively, and $E$ and $\nu$ are the elastic modulus and Poisson’s ratio of rock material, respectively. ${\sigma }_1$, ${\sigma }_2$, and ${\sigma }_3$ are the principal stress in three directions of the material, respectively; ${\epsilon }_1$, ${\epsilon }_2$, and ${\epsilon }_3$ are the principal strain in three directions of the material, respectively.

Under uniaxial stress state, ${\sigma }_2={\sigma }_3=0$, the relationship of energy can be simplified as

$$u={\displaystyle {\int }_0^{{\epsilon }_1}{\sigma }_1\mathrm{d}{\epsilon }_1}$$

(5)

$$u^e=\frac{{\sigma }_1^2}{2E}$$

(6)

4.2. Characteristics of Energy Evolution

The evolution law of input energy density, elastic energy density, and dissipation energy density during uniaxial compression of mudstone under different immersion times and the change trend of pre-peak dissipation energy ratio under different immersion conditions are calculated by using Equations (5) and (6), as shown in Figure 12. In order to quantitatively analyze the energy evolution law of immersed mudstone, the pre-peak energy characteristic parameters of mudstone under different immersion times are counted, and the results are shown in

Table 2. Statistics of pre-peak energy evolution parameters of mudstone with different immersion times.

Immersion Time/h	u/KJ·m−3	ue/KJ·m−3	ud/KJ·m−3
0	35.56	34.03	1.53
12	21.59	18.98	2.61
24	19.67	16.64	3.03
36	14.71	11.73	2.98
48	10.34	6.32	4.02

.

From Figure 12a–c, it can be observed that the mudstone exhibits significant degradation due to water immersion. With the increasing water immersion time, the input energy density and elastic energy density of the mudstone show varying degrees of reduction, while the dissipated energy density gradually increases. The numerical analysis of the characteristic energy parameters before the peak, as presented in Table 2, reveals that the input energy density of the samples undergoes the greatest variation within the initial 12 h, which decreased by 39.29%, followed by a slower decrease after 12 h, which indicates that the most severe deterioration and damage occur within the early stages of water immersion, and with the continuous effect of immersion factors, the internal damage of rock is aggravated.

Taking the evolution process of input energy density, elastic energy density, and dissipated energy density of the mudstone without water immersion as an example, it can be observed that the input energy continuously increases under the action of external load. The evolution process of elastic energy within the mudstone sample is essentially consistent with the stress evolution process. In the pre-peak stage, the input energy is primarily converted into internal elastic strain energy, indicating that the mudstone mainly stores elastic energy internally. The dissipated energy is almost negligible and shows a small increment in the pre-peak stage, where a small amount of input energy is consumed for closure of initial cracks and friction between crystal particles, which is transformed in the form of dissipated energy. As the loading process progresses, cracks within the mudstone continuously initiate, propagate, and coalesce. In the post-peak stage, the internally stored elastic energy is released, and the dissipated energy sharply increases, exhibiting a steep linear-like increase. This ultimately leads to the formation of macroscopic fracture surfaces and the occurrence of unstable failure in the mudstone sample. Figure 12d shows the proportion of dissipated energy in the total energy at the peak point of mudstone under different immersion times. It can be found that the proportion of dissipated energy increases with the increasing immersion time, there is a nonlinear relationship, and the growth rate shows a trend of “first increase, then decrease, then increase”.

5. Mechanical Damage Behavior of Water-Immersed Mudstone

5.1. Geometric Damage Model

Based on the assumption of strain equivalence, a geometric damage constitutive model for the interaction of water immersion and loading was established. The model divides the infinitesimal element into four parts: the undamaged region, the immersed damage region, the loaded damage region, and the immersion–load damaged region, as shown in Figure 13. The nominal stress and total area of the infinitesimal element are denoted as ${\sigma }_1$ and S, respectively. The effective stress and area of the undamaged region are denoted as ${\sigma }_1^{\ast }$ and S₁, respectively. The areas of the immersed damage region, loaded damage region, and immersion–load damaged region are denoted as S₂, S₃, and S₄, respectively.

According to the force balance of the micro unit, it can be seen that:

$${\sigma }_{1}S={\sigma }_1^{\ast }{S}_1$$

(7)

where $S=S_1+S_2+S_3-S_4$.

The immersion damage variable of mudstone D₁:

$$D_1=\frac{S_2}{S}$$

(8)

The mudstone after immersion is further damaged under load, and the load damage variable D₂ can be expressed as

$$D_2=\frac{S_3-S_4}{S-S_2}$$

(9)

The damage variable D of the combined action of immersion and load of mudstone can be expressed as

$$D=\frac{S_2+S_3-S_4}{S}$$

(10)

Substitute Equation (10) into Equation (7) to obtain

$${\sigma }_1={\sigma }_1^{\ast }(1-D)$$

(11)

The damage variable D can be expressed as

$$D=D_1+D_2-D_1{D}_2$$

(12)

According to the generalized Hooker theorem,

$${\sigma }_1^{\ast }=E_0{\epsilon }_1+\nu ({\sigma }_2+{\sigma }_3)$$

(13)

where $E_0$ and $\nu$ are the elastic modulus and Poisson’s Ratio after immersion, respectively; ${\epsilon }_1$, ${\sigma }_2$, and ${\sigma }_3$ are the nominal strain and confining pressure of rock, respectively.

In the uniaxial state

$${\sigma }_1^{\ast }=E_0{\epsilon }_1$$

(14)

Substituting Equation (14) into Equation (11) to obtain

$${\sigma }_1=E_0{\epsilon }_1(1-D)$$

(15)

5.2. Damage Constitutive Model

Defining the immersion damage variable D₁ in terms of the degree of degradation of the elastic modulus

$$D_1=1-\frac{E_n}{E_0}$$

(16)

where $E_0$ and $E_n$ represent the elastic modulus of the mudstone after 0 h and n hours of water immersion, respectively.

In the initial stage of loading, the pores and initial micro cracks within the rock tend to close under the influence of pressure, and no internal damage occurs, exhibiting elastic deformation. As the stress or deformation further increases, the micro cracks inside the rock begin to grow, accompanied by the generation of new cracks, leading to continuous damage in the rock. Assuming that the load damage variable D₂ in the rock is a function of axial strain ${\epsilon }_1$, and the damage threshold is denoted as ${\epsilon }_{1d}$, where ${\epsilon }_{1d}$ represents the strain corresponding to the elastic limit, when the axial strain is less than ${\epsilon }_{1d}$, the rock undergoes elastic deformation, and the damage D₂ is equal to 0. It is considered that the failure of rock micro units is random, and Weibull distribution is used to describe the damage evolution law of rock.

When $\epsilon >{\epsilon }_{1d}$, rock damage begins to occur, and the density function of the load damage variable D₂ is given by:

$$\phi ({\epsilon }_1)=\frac{m}{{\epsilon }_0}\left(\frac{{\epsilon }_1-{\epsilon }_{1d}}{{\epsilon }_0}\right)\exp \left[-{\left(\frac{{\epsilon }_1-{\epsilon }_{1d}}{{\epsilon }_0}\right)}^m\right]$$

(17)

where ${\epsilon }_1$ is the axial strain; m and ${\epsilon }_0$ are the shape parameter and scale parameter of the three-parameter Weibull distribution, respectively.

The load damage D₂ can be expressed as an integral of the density function, which is

$$D_2={\displaystyle {\int }_0^{{\epsilon }_1}\phi \left({\epsilon }_1\right)\mathrm{d}{\epsilon }_1}$$

(18)

Substituting Equation (17) into Equation (18), the evolution law of the load damage D₂ with respect to the axial strain ${\epsilon }_1$ can be obtained. The expression is

$$D_2=\{\begin{array}{l}0\hspace{1em}{\epsilon }_1\le {\epsilon }_{1d}\\ 1-\exp \left[-{\left(\frac{\epsilon -{\epsilon }_{1d}}{{\epsilon }_0}\right)}^m\right]\hspace{1em}{\epsilon }_1>{\epsilon }_{1d}\end{array}$$

(19)

Substitute Equations (16) and (19) into Equation (12) to obtain

$$D=\{\begin{array}{l}1-\frac{E_n}{E_0}\hspace{1em}{\epsilon }_1\le {\epsilon }_{1d}\\ 1-\frac{E_n}{E_0}\exp \left[-{\left(\frac{\epsilon -{\epsilon }_{1d}}{{\epsilon }_0}\right)}^m\right]\hspace{1em}{\epsilon }_1>{\epsilon }_{1d}\end{array}$$

(20)

Under different confining pressures, the stress–strain curve of rock satisfies the following conditions:

$${\epsilon }_1={\epsilon }_c,{\sigma }_1={\sigma }_c;{\epsilon }_1={\epsilon }_c,\frac{\mathrm{d}{\sigma }_1}{\mathrm{d}{\epsilon }_1}=0$$

where ${\sigma }_c$ is the peak strength; ${\epsilon }_c$ is the peak strain.

The model parameters are obtained by solving

$$m=-\frac{{\epsilon }_c-{\epsilon }_{1d}}{{\epsilon }_c\ln \left(\frac{{\sigma }_c}{E_0{\epsilon }_c}\right)}$$

(21)

$${\epsilon }_0={\left[m{\epsilon }_c{({\epsilon }_c-{\epsilon }_{1d})}^{m-1}\right]}^{\frac{1}{m}}$$

(22)

5.3. Damage Evolution Law of Immersed Mudstone

By using Equations (21) and (22), the model parameters are obtained and substituted into Equation (15) to obtain the damage constitutive model of rock samples, and the damage constitutive model parameters of mudstone under different immersion times are obtained, as shown in

Table 3. Parameters of damage constitutive model of mudstone with different immersion times.

Immersion Time/h	${\mathit{E}}_{\mathit{n}}$/MPa	${\mathit{\epsilon }}_{1\mathit{d}}$/%	${\mathit{\epsilon }}_{\mathit{c}}$/%	${\mathit{\sigma }}_{\mathit{c}}$/MPa	$\mathit{m}$	${\mathit{\epsilon }}_0$
0	481.66	0.812	1.24	5.73	8.256	0.006
12	146.99	0.713	1.65	2.36	20.806	0.011
24	125.30	1.601	1.83	2.15	1.952	0.009
36	86.32	1.202	1.87	1.42	2.795	0.014
48	58.26	1.150	1.97	0.91	1.793	0.019

.

The evolution of damage variables of water-immersed mudstone under uniaxial loading is illustrated in Figure 14. It is evident that the initial value of the immersion damage variable, D₁, gradually increases with the increasing immersion time. Furthermore, the overall total damage, D, exhibits a characteristic “S”-shaped trend.

Figure 15 presents the damage evolution process of mudstone in the natural state under uniaxial loading, demonstrating the model’s ability to effectively reflect the mechanical response of rock under uniaxial compression. Upon specific analysis of the damage evolution under uniaxial loading, the process can be divided into three stages, which are described as follows:

(1) Initial damage retention stage: the generation of damage is very slow. Apart from the immersion damage, there is almost no new load damage, resulting in a nearly horizontal evolution curve of damage. It is believed that micro cracks gradually close without extending, and no new damage is generated. This stage corresponds to the elastic stage in the stress–strain curve.

(2) Subsequent damage generation stage: the damage evolution curve exhibits a concave upward trend, and the damage variable increases rapidly, gradually reaching a value of 1. It is considered that weak interfaces and elements within the rock start to fracture, leading to the formation of new cracks that stably propagate and penetrate, resulting in macroscopic fractures. Irreversible plastic deformation occurs, and the material progressively yields and rapidly fails. In the stress–strain curve, this stage is characterized by the rock yielding as strain increases until reaching peak strength, followed by a sudden drop in stress and rapid failure.

(3) Residual damage stage: the damage variable reaches a plateau and stabilizes at 1. During this stage, macroscopic cracks have formed, and the internal structure of the rock is completely disrupted. The rock is unable to maintain its original shape under external loading.

The comparison between the theoretical and experimental curves of uniaxial compression for different immersion times of the mudstone is shown in Figure 16. It can be observed that the proposed uniaxial compression model in this study effectively describes the stress–strain relationship of immersed mudstone, which validates the correctness and rationality of the model proposed in this study. However, it should be noted that the theoretical model cannot reproduce the compaction stage and the residual stage during the loading process.

5.4. Immersion Deterioration Mechanism of Mudstone

Based on the X-ray mineral composition analysis and macroscopic and mesoscopic structural observations, it can be observed that the mudstone exhibits significant softening characteristics after immersion. The softening process of the mudstone after immersion can be attributed to four stages: the clay mineral expansion stage, mineral fracture and disintegration stage, pore filling stage, and structural damage stage.

(1) Clay mineral expansion stage: The internal defects (fissures, pores, etc.) within the mudstone provide pathways for water molecules to infiltrate, as observed in the disintegration experiment depicted in Figure 2. It can be seen from Figure 4 that there is a high content of hydrophilic clay minerals in the mudstone. The invasion of water molecules will quickly interact with clay minerals and cause the volume expansion of the rock. The main component of clay minerals in mudstone studied in this paper is illite. The illite crystal structure unit in mudstone is a three-layer structure cell composed of two layers of silicon sheets and a layer of aluminum sheets. There are counterions between the cells. In the process of interaction between illite clay minerals and water, counterions continue to escape, and the binding force between the cells gradually decreases. Water molecules fill the crystal, and the lattice expands, which will cause the original volume of the rock to increase by 50~60% [43,50]. The chemical reaction can be described as follows:

$${\mathrm{K}}_{0.9}{\mathrm{Al}}_{2.9}{\mathrm{Si}}_{3.1}{\mathrm{O}}_{10}{\left(\mathrm{OH}\right)}_2+n{\mathrm{H}}_2\mathrm{O}\to {\mathrm{K}}_{0.9}{\mathrm{Al}}_{2.9}{\mathrm{Si}}_{3.1}{\mathrm{O}}_{10}{\left(\mathrm{OH}\right)}_2\cdot n{\mathrm{H}}_2\mathrm{O}$$

(23)

(2) Mineral fracture and disintegration stage: On the one hand, there are different clay minerals and non-hydrophilic minerals in mudstone, and the expansion capacity of different mineral types varies [20]. Additionally, the distribution and structure of minerals in mudstone are not uniform, leading to uneven volume expansion of the mudstone and the generation of uneven stress within it. This uneven stress causes non-coordinated deformation around mineral particles, resulting in the generation of numerous micro cracks. With the gradual expansion and interconnection of these micro cracks, macroscopic fractures are further formed, as shown in Figure 7, which is also one of the reasons for the fracture and disintegration of mineral components in the mudstone. On the other hand, based on scanning electron microscopy (SEM) analysis, it is observed that coarse mineral particles such as quartz, albite, and other coarse-grained minerals are embedded in the clay mineral matrix, forming a cementitious connection. When water molecules infiltrate, the clay minerals adsorb water molecules and form a hydration film, causing the clay cementation to transform into water cementation. This deterioration of the bond strength between clay minerals and coarse mineral particles promotes the fracture and disintegration of rock minerals.

(3) Pore filling stage: On the one hand, when the volume of clay minerals expands to a certain extent, the initial cracks and pores present in the mudstone are filled by the expanded clay minerals, leading to a reduction in pore size. On the other hand, due to the fluidity of pore water, larger pores and fractures within the rock gradually get filled with fragmented particles, resulting in an increased proportion of smaller voids, which leads to an improvement in the surface smoothness of the rock and a gradual loosening of its structure.

(4) Structural damage stage: With the continuous infiltration of water molecules, the mechanical effects resulting from the expansion deformation and fracture of minerals within the mudstone accumulate, leading to the progressive accumulation of structural damage, and ultimately leading to the overall destruction of the mudstone’s structure.

The deterioration of the microstructural features of mudstone during water–rock interaction weakens the bond strength between mineral particles, reduces frictional forces, and increases pore water pressure. The stress concentration at the tips of fractures promotes the initiation and propagation of the fracture, ultimately resulting in the disruption of the internal structural system of mudstone. This phenomenon is macroscopically manifested as a softening of the physical and mechanical properties, which explains the significant decrease in elastic modulus and UCS of the mudstone after 48 h of immersion (reduced by 88.84% and 79.83% respectively), as shown in Table 1.

From the energy perspective, the absorption and release of energy are the driving forces behind the initiation, development, and propagation of micro cracks in rocks. As mentioned in Section 4.2, compared to the samples in the natural state, the energy storage and dissipation capacities of water-immersed mudstone decrease, while the energy dissipation capacity increases. Based on the scanning electron microscopy (SEM) results of water-immersed mudstone shown in Figure 8, it is evident that the easy disintegration characteristic of mudstone when exposed to water leads to a looser structure. According to the results in Table 1, the mechanical properties of the mudstone are significantly weakened. Water–rock interaction is believed to reduce the fracture toughness of the original micro pore tip in the mudstone, and the presence of pore water pressure causes stress concentration near primary defects and new cracks. These effects contribute to the initiation of new cracks in water-immersed mudstone, resulting in an increase in energy dissipation at the macroscopic level [28]. In addition, the increase in axial load promotes the development, connectivity, and cumulative damage of micro cracks, weakening the supporting capacity of the rock framework. This is manifested macroscopically by a decrease in elastic strain energy and an increase in the surface energy required for crack propagation and extension. The physical softening and chemical damage caused by water weaken the bond strength between mineral particles and disrupt the mechanical structure of the mudstone, driving the rock towards a state of minimum energy.

In conclusion, the water-softening characteristic of mudstone can be attributed to the propensity of clay minerals to expand and disintegrate upon water contact, changes in pore structure, variations in mineral types and distributions, and the presence of pore water pressure.

To comprehensively understand the mechanism of mudstone weakening in water, a combination of laboratory testing and numerical simulation methods can be employed. In addition to laboratory testing, the finite element method and discrete element method can be utilized to simulate the evolution of internal particles and pore structure of the immersed mudstone, which allows for a more accurate depiction of microscopic structural changes within the mudstone. Considering the inherent complexity and randomness of the mudstone’s internal structure, the use of random field modeling [51] offers distinct advantages in simulating the spatial randomness of the mudstone, enabling a more authentic representation of its structural evolution when encountering water.

By integrating experimental data and numerical simulation results, the mechanism of mudstone weakening in water can be comprehensively explored from multiple perspectives, which provides valuable theoretical support and practical guidance for the field of geological engineering, contributing to enhanced safety and reliability of geological engineering practices.

6. Conclusions

In order to investigate the macroscopic and mesoscopic structural changes, mechanical failure behavior, and damage evolution mechanism of mudstone under different water immersion times, the degradation characteristics of mudstone were observed under different water immersion times, and the degradation mechanism of water–rock interaction was explored. UCS experiments were conducted on mudstone samples immersed for different times to obtain the mechanical and energy evolution characteristics under uniaxial compression. Based on the results, a constitutive model considering the coupling damage of water immersion and low-stress loading was established and validated in mudstone.

(1) Based on the analysis of X-ray mineral composition and macro-microstructural observations, the main cause of macroscopic failure in water-immersed mudstone is the initiation, propagation, and interconnection of micro cracks. The microstructural characteristics of water-immersed mudstone include improved surface smoothness, reduced large-scale pore–crack networks, the appearance of dense crack networks on the surface, and fusion of unit boundaries.

(2) With the increase in immersion time, the mass and relative water content of the mudstone increase and the uniaxial mechanical parameters and energy parameters decrease, and the deterioration of the physical and mechanical properties of the mudstone is more severe during the early stage of immersion. Lastly, the proposed statistical damage constitutive model for mudstone considering the coupling damage of water-immersion and low-stress loading can effectively describe the stress–strain evolution during uniaxial compression of immersed mudstone.

(3) The water-softening characteristic of mudstone can be attributed to the propensity of clay minerals to expand and disintegrate upon water contact, changes in pore structure, variations in mineral types and distributions, and the presence of pore water pressure.