Microstructure, Deformation Characteristics and Energy Analysis of Mudstone under Water Absorption Process

Abstract

In geological engineering, a series of safety problems caused by expansive mudstone are common, such as slope instability and roadbed up-arch. In this paper, the mineral composition of mudstones in the Xining area was analyzed by X-ray diffraction (XRD), and the microstructural and morphological changes of mudstones after water absorption were observed by scanning electron microscopy (SEM) test to analyze the internal factors and microstructural evolution patterns of water absorption and swelling of mudstones. Based on the microstructural units, the mudstones were defined into two categories, one is N-type mudstone with flat sheet-like stromatolite units, and the other is SN-type mudstone with more clastic particle units. Water absorption experiments were conducted on the rock samples to study the microstructure of these two types of mudstones under different water absorption conditions. The pore characteristics of the mudstones were analyzed by using Image-Pro Plus to reveal the water absorption mechanism. The results show that the pore area of N-type mudstone is smaller, as well as the distribution of pore diameter. The pore area of N-type mudstone develops rapidly, in the early stage of water absorption, lots of pores are produced, and the pore area of SN-type mudstone shows an overall decreasing trend. The pore area and the number of SN-type mudstones are at a low level after full water absorption. Under the condition of full immersion, water enters the pores rapidly and soluble salts are dissolved in large quantities. The change of water absorption rate of mudstone with time can be divided into the stage of sudden increase, decrease and stability of water absorption rate. Then, based on the stress theory, the relationship between the macroscopic expansion process and the microstructure of mudstone was analyzed. Finally, the energy basis of mudstone water absorption is discussed. In the swelling of mudstone, the energy gradually turns into swelling strain energy.

1. Introduction

Mudstone is one rock formed by the physical and chemical solidification of mud and clay. As a clay rock with no obvious bedding, the composition of mudstone is complex, and it is mainly composed of clay minerals (hydromica, kaolinite, montmorillonite, etc.), which are followed by clastic minerals (quartz, feldspar, mica), metaminerals (epidote, chlorite, etc.), ferric manganese and organic matter [1,2,3,4]. The texture of mudstone is soft, as the degree of consolidation is weaker than shale. Compared with other rocks, mudstone absorbs water easily in the water environment and expands so that deformation occurs. This causes it to exhibit characteristics such as water absorption, expansion, and disintegration, which will cause various engineering geological disasters [5,6].

The dry and wet changes in nature and the lithology of mudstone are important factors leading to disintegration [7]. Most researchers believe that humidity change is an important reason for mudstone weathering [8]. The disintegration of mudstone is due to the loss of water in mudstone under the action of light and heat, thus obtaining higher surface energy. Then, energy dissipates and works in different forms under wet conditions. The binding energy formed when water is absorbed on the mudstone surface, the chemical energy formed by mineral dissolution, and the impact of mudstone expansion cause the mudstone collapse to produce new surfaces which encounter the same process and continue to collapse. In this process, the role of different factors can lead to the transmission and dissipation of energy. Energy plays a decisive role in mudstone disintegration [9,10].

The expansion of mudstone is usually considered to be mainly intergranular and lattice expansion. The former mainly occurs when the surface of clay particles absorbs water in the aqueous medium under the action of electrostatic attraction, and the swelling of soil is caused by the increase in the thickness of the water film. The expansion of the crystal layer (lattice), that is, the expansion of the expansive mineral, is due to the fact that under the action of water or in a humid environment, water enters the mineral as a part of mineral composition or lattice, resulting in the significant expansion of mineral volume [11,12]. The mudstone pores are mainly intergranular, interlayer pores, and fractures of clastic mineral particles extending in the plane direction. The adsorption of water can not only cover the entire surface of the micropores and microcracks, but can also produce a wedging, causing the further development of pores, which results in the decrease in the strength, leading to inflation [13,14]. The main causal factors of mudstone swelling are its chemical composition and microstructure. The microstructure of rock, especially the pore structure, can seriously affect its water absorption. After it absorbs the water, the microstructure of the rock is damaged [15,16,17]. In addition, different hydrochemical environments also have important effects on the expansion and contraction of mudstone, including temperature, pH value, and ion concentration [18,19]. According to the microscopic observation of pores and fissures in previous studies, it is concluded that the softening and disintegration failure of mudstone is caused by the adsorption within micropores and fissures [20,21]. Through computed tomography (CT), Videolab, scanning electron microscope (SEM), and other analysis methods, researchers use IPP and Matlab to quantify structural parameters. Nowadays, the combination of quantitative structure and engineering problems is not close enough, and the practical value of structural research results should be improved. At present, the research mainly focuses on the mechanical properties of rocks after water absorption and softening. However, the deformation properties of mudstone during water absorption are mainly improved based on the soil settlement method.

For further study of the microstructure and deformation properties of that mudstone during water immersion, SEM and water absorption tests were used to investigate the changes in microstructure and deformation properties of mudstone after water absorption. The mudstone of the Xining area in China was taken as the main object of study. The mineral composition and microstructure of the mudstone were analyzed, and the water absorption and deformation characteristics of the mudstone were revealed through the water absorption and deformation tests. This paper analyzes the water absorption mechanism of mudstone microstructure and expounds on the water absorption deformation mechanism of mudstone. Finally, this paper studies the mechanism of energy accumulation and release in the process of mudstone deformation and fracture.

2. Materials and Methods

2.1. Materials

The samples were taken from Xining, Qinghai, China. The mudstones in this area are divided into two main categories according to the characteristics of the units: one is mudstone containing mainly flat-sheeted stromatolite units (N-type mudstone); the other is that containing mainly clastic grains (SN-type mudstone). Two samples of each type were selected, named N-1, N-2, and SN-1, SN-2, respectively.

The mineral composition of mudstone samples was analyzed, and the mineral composition table of mudstone in the Xining area was obtained, as shown in

Table 1. Mineral composition of samples (according to the X-ray diffraction analysis of the sample).

	Serial Number	Quartz	Clay Mineral			Feldspar	Calcite	Dolomite	Analcite	Siderite
			Illite	Chlorite	Kaolinite
Mudstone	N-1	40.71	20.47	8.76		15.57	1.99			0.44
	N-2	43.98	21.02		5.82	17.12	7.06	2.87	2.13
Sandy mudstone	SN-1	41.34	20.12	5.76		20.18	10.62			1.98
	SN-2	47.93	16.13		7.82	10.13	10.53	3.52	3.94

. It is worth mentioning that they are saturated. The rock samples were cut, then ground, and made into a cylinder with a basic size of φ50 mm × 50 mm according to the standard ATSM D4543 [22].

2.2. Methods

2.2.1. X-ray Diffractometer (XRD)

X-rays are electromagnetic waves with short wavelengths (about 20 to 0.06 nm) that can penetrate substances of a certain thickness and cause fluorescent substances to glow. Bombarding a metal target with an electron beam produces X-rays with specific wavelengths corresponding to various elements in the target, called characteristic (or identification) X-rays. The formula Bragg’s law is the basis of crystal diffraction. When X-rays are incident on an atomic surface with d dotted planar spacing at a Bragg angle θ, a set of diffraction lines enhanced by superposition is obtained in the direction of reflection as the Bragg equation is satisfied [23,24].

2.2.2. Scanning Electron Microscopy (SEM)

The principle of scanning electron microscopy is the very fine high-speed deflection of the electron beam to scan the surface of the gold-sprayed rock samples, the sample surface and electron interaction, the formation of a variety of electrical signals, these signals are processed and imaged on the fluorescent screen. Scanning electron microscope image resolution is high for the pore boundary morphology, and connectivity in rock samples and clay mineral type analysis provides a good medium.

2.2.3. Water Absorption

The device shown in Figure 1 is used to simulate the water absorption process of mudstone samples. Since the device is based on the principle of water absorption test with a U-shaped tube, the water surface of the water storage tank and the water contactor shall be consistent before the test. The rock sample is placed in the water contactor to absorb the water in the water contactor under the action of the capillary. Water reduced by the water storage tank is equal to the water absorbed by the rock sample. The reduction rate of the water storage tank is read into the computer through an electronic balance, and the micrometer is used to measure the deformation of mudstone during water absorption.

2.2.4. Pore Characteristic Analysis

The specific steps of pore structure analysis are as follows: SEM images with the magnification of 2000 times were selected as the analysis objects. The image is preprocessed. Firstly, contrast enhancement and background correction are carried out on the SEM image, and some isolated points affecting the results are removed by morphological methods. Then, use the HIS color separation selection method to determine the segmentation threshold of the image, and quantitative processing, using the ruler of the SEM image for space calibration, after calibration, select measurement parameters, and perform the measurement.

The pore characteristics were analyzed through image-Proplus (IPP) image analysis. IPP is the United States Media Cybernetics that develops professional image processing, and analysis software for medical, industrial and other professional fields [25,26]. The physical significance of these parameters is as follows:

(1)

Pore area: pore area is the estimated area occupied by pores in SEM image, affecting mechanical stability, and the total area of the SEM image is 300 μm².

(2)

Face rate: this refers to the visible porosity of the rock under the microscope (excluding micropores), and is the percentage of the pore area in the total area of the observation field of view.

(3)

Pore diameter: the pore morphology of mudstone varies greatly and is irregular. For the convenience of quantifying the pore size, the equivalent diameter is used to represent the pore diameter.

(4)

Pore fractal dimension: fractal dimension can evaluate the complexity and heterogeneity of pore structure.

(5)

Roundness: the pore cross-section is close to the theoretical circle, the closer it is to the circle, the closer the value is to 1.

3. Results and Discussion

3.1. Development Characteristics of Microstructure

3.1.1. Development Characteristics of Clay Minerals

The characteristics of the state of clay minerals before and after water absorption reflect the water absorption mechanism of mudstone. During water absorption, the clay mineral surface adsorbs, infiltrates, and absorbs water by osmosis. From the analysis of XRD test results, the clay minerals of mudstone in the Xining area are mainly illite, and chlorite. Previous researchers conducted dehumidification and humidification tests on four single minerals: montmorillonite, illite, kaolinite, and chlorite. The results showed that the water absorption of the single mineral montmorillonite produced fissures during humidification, while the single minerals kaolinite, chlorite and illite did not produce fissures after water absorption, but only swelled outward [27,28,29,30]. According to this preliminary inference, the mudstone clay minerals in the Xining area mainly swell in volume during water absorption and do not produce fissures inside the minerals.

Below are selected SEM images of mudstone before and after water absorption at low magnification (2000×) (Figure 2) and high magnification (10,000×) (Figure 3). The N-type mudstones change their overall structure from dense to loose, and the pore size became larger as well as the number of pores. Additionally, the clay minerals became separated into layers after absorbing water. The SN-type mudstone was more structurally intact and the volume of clay minerals increased.

From Figure 3, it can be seen that after water absorption, the pores will become larger due to the loss of fillers in the pores and on the boundary of the pores. Meanwhile, the pores and fissures will be gradually squeezed with the effect of mineral volume expansion, resulting in the reduction in fissures and pores between mudstone minerals and minerals. Additionally, with the expansion of lamellar minerals, the water-absorbing film between mineral layers thickens, leading to the increase in spacing, resulting in the separation between layers. Then, the whole structure is destroyed.

N-type mudstone has a compact structure with few pores visible before water absorption. The expansion of clay minerals is mainly manifested in two aspects. Firstly, the adsorption of bound water causes the expansion of the crystal basal spacing. The expansion is continuous, the water film thickens, the interlayer connection force weakens and the separation between layers occurs. Secondly, the expansion is also caused by the inhomogeneous strain between the adjacent particles and particle groups of clay mineral aggregates. SN-type mudstone has a loose structure and more pores before water absorption; after that, the clay minerals mainly expand, and the increase in volume squeezes the pores and fissures, making them smaller or even closed. Both types of mudstones will dissolve and lose pore fillers after water absorption while developing micropores. These pores provide water-conducting channels from the surface to the inner parts of the mudstone sample, creating the necessary conditions for water migration.

3.1.2. Development Characteristics of Pores

To explore the changes in the microstructure of mudstone under different water absorption conditions, the pore characteristics of N-1 are shown in Figure 4.

The structure of the mudstone changed from a tightly ordered to a loosely disordered state as the water content increased. The water content of 4% was the natural state of mudstone when the mudstone unit body was in a relatively close structural state whose pore size was small. When the water content increased from 4% to 7%, the pore size became large. As it increased further, the pores were further developed. After the moisture content reached its maximum, 12%, the samples clearly exhibited layer by layer separation and outward expansion.

Table 2. Pore structure parameters of N-1 mudstone samples.

Rate of Water Content (%)	4	7	12	16	18
Total void area (μm2)	21.01	319.60	172.93	175.80	251.37
Average pore diameter (μm)	2.48	2.36	2.81	2.26	2.49
Number of pores	6	92	36	59	67
Max pore diameter (μm)	8.12	9.59	9.59	7.66	11.94
Roundness	1.65	1.85	1.89	1.93	1.98
Minimum pore diameter (μm)	0.71	0.64	0.66	0.72	0.55
Fractional dimension	1.13	1.09	1.09	1.10	1.09

shows the pore structure parameters of the mudstone N-1 samples quantified by IPP software. In the case of no water absorption, the pore area was small, while after water absorption, a large number of pores developed. When the water content was low, the filling material of the original pores of the mudstone was dissolved, and more pores appeared for 7% of the water content. As the pore area of the mudstone increased, the water content increased with the absorption process. The clay minerals of the mudstone absorb water and expand, and the expansion volume begins to squeeze the pores in the mudstone, resulting in the reduction in the pore area of the mudstone.

The distribution pattern of the pore area is seen in Figure 5a. When the water content grew to 7%, the mudstone derived pores of other grain sizes. The mudstone pores studied in this paper mostly belong to clay matrix pores, microporous type, and the pore ranged are all between 1–9 μm. No sudden appearance of large pores occurred during the whole water absorption process. With water content increasing, the pore size of large grains slightly decreased, which was due to the expansion of clay minerals and the filling of pores by the expansion volume. At 18%, the pore range was further expanded, which was then due to the thickening of the water film of clay minerals, the possibility of further enlarging the pore size between pores, and the derivation of new pores.

Figure 5b shows that after absorption, the pore number of sudden growth. Water infiltration caused a spurt of the pore number, and derived some new pore sizes, mainly concentrated between 1–3 μm, these pores were mainly caused by the dissolution of soluble substances. When increased to 12%, the pore range shrank from 1–8 μm to 1–7 μm, and the number of pores with the same particle size also decreased. This is because the clay minerals begin to expand and fill the pores with the continuous entry of water. With the further increase in the water content to 16%, the number of pores increased slightly, because the dissolution of soluble substances and the expansion of clay minerals occurred together. The dissolution of soluble substances played a dominant role, resulting in many new small pores. When the water content is from 16% to 18%, the pore size and number of mudstones do not change significantly, which was related to the complete dissolution of soluble materials and the saturation of clay minerals with water absorption.

It can be seen from Figure 6 that the mudstone SN-1 contains more clastic particle units, and its pore development characteristics are quite different from those of N-1. When SN-1 is at an initial water content of 3%, the pore space is more developed. Based on the measurement results extracted by IPP, the pore conformation parameters are shown in

Table 3. Pore structure parameters of SN-1 mudstone samples.

Rate of Water Content (%)	3	8	10	12	15
Total void area (μm2)	92.44	121.90	236.03	196.75	71.17
Average pore diameter (μm)	2.03	2.28	2.76	2.30	2.27
Number of pores	33	39	40	60	23
Max pore diameter (μm)	6.64	8.55	10.35	5.39	8.89
Roundness	1.59	1.92	1.80	1.85	1.91
Minimum pore diameter (μm)	0.73	0.65	0.91	0.77	0.55
Fractional dimension	1.08	1.09	1.08	1.11	1.10

.

During the water content of the mudstone from 3% to 8%, the mudstone did not produce pores with the new particle of different sizes, mainly because SN-1 contains more clastic particle units. When the water content increased to 10%, the swelling of clay minerals and the dissolution of soluble substances took place, the dissolution of soluble substances in the pores generating new small pores. In the process of water absorption, the filling pores due to the expansion of clay minerals caused the large particle size to become smaller.

Figure 7 shows that after the water content increased to 8%, the number of pores in the mudstone did not change much. When the water content of the mudstone increased to 10%, the number of large-size pores increased due to the dissolution of soluble material around the pores, making the pore size large. The clay minerals started to swell with the entry of water, and the swelling volume squeezed the pores at the water content of 12%, and the number of large-size pores decreased. The clay minerals continue to swell and squeeze the pores, thus reducing the number of pores.

Figure 8 shows the main pore characteristics parameters of N-type and SN-type mudstones under different water absorption conditions. N-type mudstone has a lot of pores at low water content. The structure of N-type mudstone is loose after water absorption, and the pore area and quantity are high. When the water content is low, the pore area and the number of SN mudstone are small and increase with the increase in water content. In terms of roundness, the trend of N-type mudstone and SN-type mudstone was the same, both tend to be close to 2. This is because, with the water absorption, the clay minerals continued to expand and squeeze the pores.

3.2. Water Absorption and Deformation Characteristics

3.2.1. Water Absorption Characteristics

The water absorption was plotted against time, and the water absorption characteristic curves of the mudstone samples N-1, N-2, SN-1, and SN-2 were obtained by fitting as shown in Figure 9. The R² of samples N-1, N-2, SN-1, and SN-2 were 0.9859, 0.987, 0.998 and 0.9996, respectively, indicating a good fitting effect.

From Figure 9, in the initial stage of water absorption, the variation of water absorption (dQ/dt) of the rock sample is large and the rate of water absorption is faster. However, as time passes, the increasing trend of water absorption gradually slows down and becomes stable, indicating that the water absorption almost reaches saturation and the rate of water absorption is unchanged. Roughly, the water absorption process of mudstone is divided into two stages: nonlinear decelerated water absorption and constant velocity water absorption. Non-linear deceleration absorption stage: the water absorption rate of mudstone decreases gradually in this stage, which can be derived from the trend of the slope of the curve, and the duration of this process is very long, reaching about 3000 min. Constant velocity water absorption stage: the water absorption curve of mudstone in this stage is relatively flat, and the slope of the curve is maintained at a constant value, and the water absorption of mudstone is close to saturation at this time.

3.2.2. Deformation Characteristics

The water absorption deformation curve of mudstone is shown in Figure 10. It can be divided into three stages, which are the rapid growth stage, the slow growth stage, and the stabilization stage.

(1) Rapid growth stage: in the initial stage of water absorption of the rock, the initial expansion potential of clay minerals is larger, and the growing amount of deformation with time is also larger, and the change of deformation amount of rock samples (dL/dt) is larger.

(2) Slow growth stage: after the initial period of water absorption, the expansion and deformation capacity of clay minerals after water absorption is weakened, and the change of deformation of rock samples (dL/dt) is smaller.

(3) Stabilization stage: at this stage, the mudstone is close to saturation, and the clay minerals no longer expand and deform, so the deformation reaches the stabilization stage.

From Figure 10, we can see that the changing trend of water absorption deformation (dL/dt) of N-type mudstone is larger than those of SN-type mudstone. The clay mineral content of N-type mudstone is high, which expands and deforms more for the same rock surface area.

3.3. Relationship between Microstructure and Deformation

3.3.1. Relationship between Clay Mineral Content and Deformation

The volume of clay minerals will increase significantly after water absorption, for example, illite will increase the original volume by 50~60% after water absorption, so the influence of the amount of clay minerals on water absorption and deformation cannot be ignored [29,30]. The relationship between clay mineral content and final water absorption and final deformation at the end of experiments is shown in Figure 11a.

The relationship between clay mineral content and water absorption shows that the more clay minerals are present, the more water is absorbed by the mudstone. This is because, for the same volume, there is a positive correlation between the clay mineral particles and the water absorbed through hydration. The trend of clay mineral content and deformation volume is less obvious, which indicates that the influence of clay mineral content on deformation volume is relatively weak. From Figure 11b, the trend of clay mineral content and water absorption rate of mudstone indicates that the higher the clay mineral content, the higher the water absorption potential, and when in contact with water, the clay minerals absorb water molecules rapidly with a higher absorption rate. The clay mineral content is not the main influencing factor of the deformation rate.

3.3.2. Relationship between Pore Structure Characteristics and Mudstone Water Absorption Deformation

From Figure 12a, a greater connection between pore area and water absorption and deformation of mudstone exists, leading to larger water absorption. Then, the clay particles can fully absorb water molecules, and the water film thickens, resulting in larger particle-to-particle spacing and larger deformation.

The pore area of mudstone has a greater connection with water absorption rate and deformation rate, showing that rock samples with small pore areas have large water absorption rate and large deformation rate (Figure 12b). After the rock sample with small pore area is exposed to water, the pore area will develop rapidly, providing water conduction area for water absorption and deformation when the reaction rate is positively correlated with the water conduction area.

3.4. Deformation Mechanism after Water Absorption

The swelling of mudstone is closely related to its internal plate structure, the size and the density of pores, and hydrophilic clay minerals [31,32]. A schematic diagram of the interaction between mineral grains of mudstone and between the grains and the boundary is shown in Figure 13.

The mudstone swelling by water absorption is given by the following equation developed by Equation (1) [33,34]:

$$\overline{{\sigma }_{ij}}=\frac{1}{V}({\displaystyle \sum _{P\in V}{\displaystyle \sum _{c\in P}{v}_i{}^{P_c}{f}_j{}^{P_c}}}+R_{ij}{}^P)$$

(1)

where $f_i{}^{P_C}$ is the expansion force on particle P at point c. $R_{ij}{}^P$ is the part considered as the rolling action between particles [35]. The change process and influencing factors of macroscopic swelling stress of mudstone can be explained from the microscopic perspective of particle mechanics. The water absorption and expansion of clay mineral particles is the material basis of the swelling stress $f_i{}^{P_C}$. With the increase in the water absorption degree the expansion force on the clay mineral particles, $f_i{}^{P_C}$ will increase continuously. The existence of bedding, pores, and cracks provides channels to increase the contact surface, reinforcing the reaction between clay mineral particles and water. As the aqueous solution enters the rock sample from the bedding, pores, and cracks, the number of mineral particles in contact with water increases, so the effect of swelling by water absorption increases.

At the beginning of water solution immersion, the adsorption of clay mineral surface makes the mineral particle volume at the water rock interface expand. With the passage of time, due to the defects of mudstone, such as pores and cracks, water enters the interior of the rock sample through the mudstone bedding and cracks. That results in the expansion and uplift of the internal clay mineral particles due to water absorption, causing swelling stress, and strain. The expansion of internal mineral particles reduces the bonding force, increases the crack on the surface of the rock sample, and promotes contact between the aqueous solution and internal minerals. The clay particles involved in the expansion continue to increase, and the double sum continues to increase, showing that the macroscopic expansion continues to increase, but the growth rate decreases until the expansion disappears. This is consistent with the deformation characteristics of mudstone discussed in Section 3.2.2.

After the swelling disappears, the rock samples are still in the aqueous environment, and the water–rock physicochemical interaction will continue. During the whole expansion process, the internal pores of mudstone increase, and the volume increases. The inner part of the sample becomes loose, which leads to the reduction in the inner bonding force of mudstone. The collapse in the process of expansion will inevitably lead to particle shedding and dissolution of clay mineral content. On the macro level, after the expansion force reaches the peak value, it becomes slightly smaller, and finally, it is in a dynamic equilibrium state.

3.5. Mechanism of Energy Accumulation and Release

In the long-term geological tectonic process, the underground rock volume has accumulated a lot of energy and is in a certain equilibrium state [36]. If the original energy balance is broken under the action of internal and external forces, it will lead to the rapid release of rock mass energy, thus causing various geological disasters [37,38]. Therefore, it is of great significance to study the mechanism of energy accumulation and release in the process of mudstone fracture for disaster reduction and prevention.

This paper assumes that the brittle failure of mudstone is dominant, so its plastic deformation is not considered. Under the action of external force work, the elastic strain energy stored and energy consumed in mudstone are different in different deformation and failure stages. To simplify the analysis, it is assumed that mudstone is in the linear elastic deformation stage before the crack initiation point, and only elastic strain energy is stored in mudstone at this stage. Once the crack initiation point is exceeded, the existing crack will expand. Driven by elastic energy, along with crack propagation, part of the stored elastic strain energy will be converted into dissipative energy, such as surface energy, frictional heat energy, acoustic emission radiation energy, etc., while the rest will be left in mudstone. Later, with the growth of existing cracks or the generation of new cracks, some of the required elastic strain energy will also be converted into dissipative energy, leading to the gradual increase in the total dissipative energy.

Based on the law of conservation of energy and the above analysis, it can be confirmed that the dissipated energy is the result of partial elastic strain energy conversion. This shows that elastic strain energy is the root cause of rock damage and fracture. The total elastic strain energy (Ea) accumulated in the rock sample is equal to the elastic strain energy (Er) currently retained in the rock sample plus the total dissipated energy (Ed) [39,40]. The detailed derivation process is as follows.

Once the crack initiation point is exceeded, the crack will expand. After the first crack propagation, the energy balance conditions in the rock sample are:

$$E_{a1}-E_{a0}=\Delta E_{r1}{+E}_{d1}$$

(2)

where E_a0 is the accumulated elastic strain energy of rock sample before the crack initiation point, E_a1 is the current cumulative elastic strain energy of rock sample after the first crack propagation, $\Delta E_{r1}$ is the retained elastic strain energy in the rock sample after the first crack propagation, E_d1 is the dissipated energy corresponding to the first crack growth.

Similarly, during the second crack propagation, there are:

$$E_{a2}-E_{a1}=\Delta E_{r2}{+E}_{d2}$$

(3)

By analogy, when crack propagation is n, there are:

$$E_{an}-E_{a(n-1)}=\Delta E_{rn}{+E}_{dn}$$

(4)

According to Equations (2)–(4), there are:

$$E_{an}=E_{a0}+[\Delta E_{r1}+\Delta E_{r2}+\cdots \Delta E_{rn}]+[\Delta E_{d1}+\Delta E_{d2}+\cdots \Delta E_{dn}]=\Delta E_r{+E}_d$$

(5)

The expression of the law of conservation of energy: energy can neither be generated nor disappear in vain, but can only be transferred from one object to another, and the forms of energy can also be converted to each other. The law of conservation of energy is one of the universal basic laws in nature. Based on this law and the above analysis, it can be confirmed that the dissipated energy is the result of partial elastic strain energy conversion, that is, the dissipated energy is provided by elastic energy. This also shows that elastic strain energy is the root cause of rock damage and fracture. Dissipated energy does not disappear, but is consumed in the formation of damage and plastic deformation inside mudstone, that is, the change of internal structure state conforms to the trend of entropy increase. Mudstone expansion is equivalent to doing work, which is a process of energy release. At the beginning of water absorption, the expansion of mudstone should first overcome the interaction between particles in the mudstone. The strength of the interaction between particles is reflected in its structural strength, which is described by the structural strain energy. As the internal structure is damaged due to the continuous water absorption of mudstone, the structural strain energy decreases, and the remaining energy is converted into the expansion strain energy generated by work performed externally. At this point the clay particles begin to expand. With the expansion process of water absorption, the expansion strain energy of mudstone increases. When the internal structure of mudstone is destroyed, the energy is completely converted to expansion strain energy.

4. Conclusions

The internal law of mudstone disintegration and the relationship between disintegration characteristics are obtained through microscopic testing. This is of great significance for improving the safety of project construction under rainfall environment and reducing a series of geological disasters such as water and soil loss, landslide, and collapse caused by rock degradation. Based on the in-depth study of mineral composition and microstructure of mudstone, experimental study of water absorption characteristics is conducted to reveal the macroscopic water absorption and deformation law of mudstones in the Xining area, with a view to establishing a mathematical model between microstructure and water absorption and deformation characteristics of mudstone. The main conclusions of this paper are as follows:

(1)

The development characteristics of clay minerals after encountering water are mainly shown in two aspects. The uneven strain produces expansion between adjacent particles and particle groups of clay mineral aggregate, making the pores smaller or causing them to disappear. Clay minerals easily adsorb bound water, resulting in the mutual separation of clay mineral layers.

(2)

The pore development characteristics of N-type mudstone are as follows: N-type mudstone has rapid pore development, lots of pores are produced in the early stage of water absorption, and the pore area and the number of pores suddenly increase, and then slightly decrease in the late stage of water absorption. With the progress of water absorption, the pore area and number of pores are reduced in the later stage, and the overall trend is decreasing.

(3)

There are some correlations between clay mineral content, pore area, and water absorption and deformation of mudstone, among which the correlation between clay mineral content and water absorption rate of mudstone is stronger, and the correlation with deformation volume and deformation rate is weaker. This paper analyzes the relationship between the microstructure and disintegration characteristics of mudstone in the Xining area and concludes that the mudstone with low clay mineral content and large pore area has stronger disintegration. Through the deduction of the formula, the elastic strain energy is the root cause of mudstone damage and fracture in the process of mudstone disintegration.