Characteristics of Load-Bearing Rupture of Rock–Coal Assemblages with Different Height Ratios and Multivariate Energy Spatiotemporal Evolution Laws

Abstract

The destabilizing damage of rock structures in coal beds engineering is greatly influenced by the bearing rupture features and energy evolution laws of rock–coal assemblages with varying height ratios. In this study, we used PFC3D to create rock–coal assemblages with rock–coal height ratios of 2:8, 4:6, 6:4, and 8:2. Uniaxial compression simulation was then performed, revealing the expansion properties and damage crack dispersion pattern at various bearing phases. The dispersion and migration law of cemented strain energy zoning; the size and location of the destructive energy level and its spatiotemporal evolution characteristics; and the impact of height ratio on the load-bearing characteristics, crack extension, and evolution of multiple energies (strain, destructive, and kinetic energies) were all clarified with the aid of a self-developed destructive energy and strain energy capture and tracking Fish program. The findings indicate that the assemblage’s elasticity modulus and compressive strength slightly increase as the height ratio increases, that the assemblage’s cracks begin in the coal body, and that the number of crack bands inside the coal body increases as the height ratio increases. Also, the phenomenon of crack bands penetrating the rock through the interface between the coal and rock becomes increasingly apparent. The total number of cracks, including both tensile and shear cracks, decreases as the height ratio increases. Among these, tensile cracks are consistently more abundant than shear cracks, and the proportion between the two types remains relatively stable regardless of changes in the height ratio. The acoustic emission ringing counts of the assemblage were not synchronized with the development of bearing stress, and the ringing counts started to increase from the yield stage and reached a peak at the damage stage (0.8${\sigma }_{\mathrm{c}}$) after the peak of bearing stress. The larger the rock–coal height ratio, the smaller the peak and the earlier the timing of its appearance. The main body of strain energy accumulation was transferred from the coal body to the rock body when the height ratio exceeded 1.5. The peak values of the assemblage’s strain energy, destructive energy, and kinetic energy curves decreased as the height ratio increased, particularly the energy amplitude of the largest destructive energy event. In order to prevent and mitigate engineering disasters during deep mining of coal resources, the research findings could serve as a helpful reference for the destabilizing properties of rock–coal assemblages.

1. Introduction

China has comparatively abundant coal resources but limited oil and natural gas reserves, and it will take some time for renewable energy to overtake fossil fuels as the primary energy source. As a result, coal is expected to continue to play a significant role in China’s energy consumption structure for some time to come. The need for deep coal resource mining is rising in tandem with the depletion of coal resources in the shallow parts of mines. The characteristic “three highs and one strong disturbance” of deep mining makes it a major danger to the safe and effective production of mines and causes dynamic disasters that will only become worse over time [1,2,3]. Numerous domestic and international studies have noted that deep shock catastrophes are basically the concentrated expression of the gradual accumulation of damage and abrupt instability of the “rock–coal body” composite structure under intricate stress pathways. Strong mining disturbances ultimately cause structural instability, which manifests as a dynamic effect [4,5,6]. Therefore, conducting in-depth research and revealing the law of crack development and energy co-evolution throughout the entire life cycle of rock–coal combinations, from “fracture → crack propagation → instability of the combination”, is of great significance for grasping the bearing characteristics and instability failure features of rock–coal combinations.

The current experimental studies on rock–coal assemblages primarily involve extracting coal and rock samples using a drilling coring machine, followed by grinding and bonding processes. Subsequently, the acoustic emission and loading system are employed to investigate the assemblage’s mechanical behavior, including its load-bearing capacity and failure characteristics [7,8,9]. Zuo Jianping et al. [10] conducted uniaxial compression experiments on rock–coal assemblages to analyze the evolution of elastic energy density in both coal and rock components. They further proposed a differential energy instability model for the rock–coal assemblage, highlighting the correlation between the degree of assemblage failure and energy distribution. Chen Shaojie et al. [11] conducted uniaxial compression tests on five groups of roof sandstone–coal pillar structural bodies with different height ratios based on acoustic emission and digital camera video recording systems, revealing the mechanism of the influence of the strength and height of the combined units on the macroscopic mechanical properties and progressive damage of the combined bodies. Liu Jie et al. [12] investigated the mechanical behavior and acoustic emission characteristics of various rock–coal composite media under uniaxial compression, elucidating the impact of rock strength on the macroscopic strength and fracture patterns of the composite structure. Chen Guangbo et al. [13] carried out axial loading tests on five types of rock–coal composite specimens with varying fracture lengths and fracture angles to investigate the influence of through fractures on the mechanical behavior of the rock–coal system.

However, due to the limitations in monitoring the accuracy of current laboratory equipment, a major drawback of conducting combined body compression tests in the laboratory is the significant difficulty in tracking internal stress within the samples and accurately identifying rupture events. This limitation has hindered in-depth research on the complete life cycle of crack development and energy evolution in rock–coal combination bodies, particularly the sequence from “rupture → crack propagation → combined body instability.” On the other hand, discrete element numerical simulation offers a viable solution to overcome this limitation. Guo Weiyao et al. [14] employed PFC2D simulation software to investigate the fracture characteristics of the composite body, the impact energy index, and variations in its ultimate compressive strength and elastic modulus. Additionally, they examined the effects of the rock–coal strength ratio and height ratio on the mechanical properties of the rock–coal composite. Yang Zhen et al. [15] employed FLAC3D to develop a composite rock–coal model, aiming to investigate the variation patterns of the stress–strain relationship during loading failure for coal sample thickness, the rock–coal composition ratio, coal seam parameters, and the lithology of the roof and floor strata. Based on acoustic emission monitoring experiments, and in conjunction with PFC2D discrete element software, Yang Jiangkun et al. [16] analyzed the evolution characteristics of acoustic emissions in rock under uniaxial compression, as well as the energy variation patterns during the progressive failure process.

Currently, existing research primarily centers on the macroscopic mechanical properties and failure evolution mechanisms of rock–coal combinations. The precision of acoustic emission spatial positioning technology is constrained by several factors, including sensor layout density, wave velocity anisotropy, and diffusion effects [17,18,19,20]. Although recent advanced studies have predominantly employed sophisticated algorithms for noise reduction, the resulting improvements remain limited in effectiveness [21,22]. Consequently, accurately characterizing the distribution and spatiotemporal evolution patterns of rupture events in three-dimensional space remains a significant challenge. At the microscopic level, research has mostly focused on PFC2D. Especially in previous studies, the core indicators of particle strain energy or overall dissipation energy have been used to characterize the fracture mechanism [23,24,25,26,27]. This can only indirectly reflect the energy storage and failure state and cannot directly and precisely quantify the cumulative damage of the cemented structure, resulting in an ambiguous identification of the failure mechanism.

Specifically, existing research has yet to clarify describe (1) the quantitative correlation between the height ratio and the spatial distribution characteristics of cracks from initiation to coalescence in rock–coal combination bodies under three-dimensional conditions; (2) the zonal migration patterns of cementation strain energy within the rock–coal combination body and their quantitative correlation with the height ratio remain unestablished; (3) precise quantification methods for the energy-level localization and spatiotemporal evolution characteristics of fracture energy within three-dimensional space; and (4) the influence of the height ratio, based on three-dimensional models, on the synergistic evolution mechanism of multiple energies (strain energy, fracture energy, and kinetic energy). The lack of clarity on these key scientific questions impedes a comprehensive understanding of the instability mechanism in rock–coal combination bodies.

With this in mind, we adopted PFC3D 6.0 software to construct three-dimensional rock–coal body models with different rock–coal height ratios and thoroughly studied the crack propagation and internal fracture characteristics of rock–coal combinations at different stress levels under uniaxial compression, revealing crack development and multi-energy evolution laws throughout the entire life cycle of “fracture → crack propagation → instability of the combination”. By independently developing strain energy and cementation failure energy, the Fish program was used to quantify the migration law of strain energy zones with height ratios and the spatiotemporal evolution characteristics of failure energy. The results of our research can provide useful references for a deeper understanding of the bearing characteristics and instability failure features of rock–coal combinations throughout their entire life cycle, thereby facilitating the prediction and prevention of disasters in deep composite structures.

2. Model Construction and Parameter Calibration

2.1. Selection of Research Methods

This study used PFC3D 6.0 to simulate the crack propagation and energy evolution of rock–coal composite bodies for the following reasons:

The finite element method (FEM) has excellent accuracy in simulating continuous medium problems, but it faces limitations when dealing with materials with significant discontinuities, such as rocks. During the crack propagation process in rock–coal composite bodies, there is often strong material discontinuity and complex fracture patterns at the interface between rocks and coal, which greatly increases the simulation time and computational load, making it difficult to accurately depict the dynamic evolution of internal cracks in rock–coal composite bodies [28]. Although the extended finite element method (XFEM) has made progress in simulating crack propagation problems, it is difficult to use it to accurately represent the complex mechanical behaviors between different phases such as coal and rock. Moreover, due to its strong dependence on the mesh, if the crack propagation path is complex or variable, it often requires frequent mesh redivision, resulting in a large computational cost [29]. UDEC/3DEC is good at simulating the mechanical behavior of discontinuous media such as jointed rock masses, treating rock masses as a collection of discrete blocks and focusing on the interaction between blocks. However, its ability to simulate the microscopic details of crack propagation in rock–coal composite bodies is relatively weak, so it cannot simulate these micro-features as deeply and precisely as PFC3D. Compared with traditional finite element and discrete element methods, PFC3D has unique advantages in simulating the propagation of microscopic cracks and energy evolution. Especially in the dynamic evolution of crack propagation and the precise assessment of energy distribution, it can accurately track the spatiotemporal evolution characteristics of strain energy and failure energy.

The particle flow code (PFC) is a mesoscopic mechanics program based on an explicit difference algorithm and discrete element theory. It uses microscopic particles to form macroscopic objects and updates the positions of walls and particles via Newton’s second law. The contact force between particles is updated by the force–displacement criterion, ultimately enabling the model to reach a balanced state or undergo damage and failure [30]. The contact between particles adopts a linear parallel cementation model, which can transmit both force and moment. When the cementation between particles exceeds the strength limit under tensile and shear stress, it breaks and degenerates into a linear model. Its working principle is shown in Figure 1. The calculation formulas for normal stress and tangential stress during contact are shown in Equation (1).

$$\overline{\sigma }={\displaystyle \frac{{\overline{F}}_{\mathrm{n}}}{\overline{A}}}+\overline{\beta }{\displaystyle \frac{‖{\overline{M}}_{\mathrm{b}}‖\overline{R}}{\overline{I}}}\dots \overline{\tau }={\displaystyle \frac{‖{\overline{F}}_{\mathrm{s}}‖}{\overline{A}}}+\overline{\beta }{\displaystyle \frac{\left|{\overline{M}}_{\mathrm{t}}\right|\overline{R}}{\overline{J}}}$$

(1)

In the above formula, ${\overline{F}}_{\mathrm{n}}$ is the parallel bonding normal force; ${\overline{F}}_{\mathrm{s}}$ is the parallel bonding shear force; ${\overline{M}}_{\mathrm{t}}$ is the bonding bending moment; ${\overline{M}}_{\mathrm{b}}$ is the torque; A is the parallel bonding contact area (in PFC3D, the contact is circular); $\overline{J}$ and $\overline{I}$ are the moment of inertia and the moment of extreme inertia at the contact point, respectively; $\overline{R}$ is the parallel bonding contact radius; $\overline{\beta }$ is the coefficient of moment of inertia, with a default value of 1.0.

2.2. Construction of Numerical Model

A columnar diagram of the 3–1 coal seam borehole and a schematic diagram of the coal mining face in a specific mine in Inner Mongolia are shown in Figure 2. The thickness of the rock and coal seams varies in different sections of the same mining field. The occurrence of rock–coal dynamic disasters (such as rock burst and roof fall) in mining engineering is essentially an energy instability process affecting the rock–coal combination under the combined action of geological structure and occurrence conditions. Research shows that such disasters are not only related to the impact tendency of rock–coal bodies but also controlled by the nonlinear characteristics of complex structural parameters (such as rock–coal height ratio), the distribution features of mineral components, and their energy evolution laws [31]. Based on this, uniaxial compression numerical simulation experiments were carried out to compare and analyze the progressive failure characteristics of different rock–coal height ratio combinations. By establishing the correlation relationship between the rock–coal height ratio, energy evolution, and failure mode, such analyses provide useful references for early warnings of deep rock–coal composite structure disasters.

Research shows [14,32,33] that when the rock–coal height ratio is within the range of 2:8 to 8:2, the distribution of the particle contact force chain and the failure mode have significant differences, and the stability of the calculation results is relatively high. Therefore, this study adopts a similar ratio to facilitate direct comparison with related research results and verify the rationality of the model parameters. The author used PFC3D to establish four groups of rock–coal composite body models with rock–coal height ratios of 2:8, 4:6, 6:4, and 8:2, with lengths × widths × heights of 50 mm × 50 mm × 100 mm, as shown in Figure 3. During loading, a planar wall was added at the top and bottom of the sample to simulate the loading plate for uniaxial compression. According to the recommendations of the PFC manual, a quasi-static process should be approached through a low loading rate. Therefore, a displacement loading method was adopted, and the upper and lower loading plates moved towards each other at a speed of 0.3 mm/min, which was consistent with the rate range of similar studies [32,33]. We stopped loading when the combination broke apart.

2.3. Calibration of Simulated Material Parameters

The core samples with dimensions of 50 mm × 50 mm × 100 mm, consisting of full coal and full rock, were extracted from drill holes in the mining face of the 3–1 coal seam. These samples were processed and tested using the MTS 816 electro-hydraulic servo rock mechanics testing system at the National Key Laboratory of Deep Earth Engineering, Intelligent Construction, and Health Maintenance at the China University of Mining and Technology, as shown in Figure 4. A uniaxial compression test was performed with displacement control, and the strength curves for both coal and rock samples were obtained. The corresponding strengths were 26.05 MPa for coal and 39.52 MPa for rock, as depicted in Figure 5c.

DING et al. [34] found through PFC3D simulation that the ratio of model feature size to particle size (L/d) has a significant impact on the discreteness of the simulation results. When L/d ≥ 25, it can effectively suppress the particle size effect. Therefore, in order to balance computational efficiency and suppress the particle size effect, particles with a radius of 1.0–1.5 mm (corresponding to L/d ≥ 25) were adopted, which was within the same range as the particle size used in reference [35]. A numerical model of the full coal and full rock samples containing 23,490 spherical particles and 114,170 contact bonds was established, as shown in Figure 5a,b, and physical and mechanical parameter calibration was carried out. By ensuring alignment with the macroscopic mechanical parameters, such as the uniaxial compressive strength and elastic modulus obtained from laboratory experiments, parameter calibration was achieved through a trial-and-error approach. Model parameters were repeatedly adjusted to make the numerical simulation results as consistent as possible with the experimental results. After each parameter adjustment, the fitting quality was evaluated by calculating the root mean square error (RMSE) between the numerical simulation results and the experimental results. When the RMSE was less than 5%, the fitting result was considered to be within the acceptable error range. Additionally, the standard deviation (σ) was used to assess the fluctuation degree of the numerical results and the experimental data, and the standard deviation between the two could not exceed 2%. Finally, we determined the parameters of the simulated material. In addition, considering that the rock–coal interface is a weak link in mechanics and its strength is lower than that of coal and the rock itself, in order to fully take into account the effect of the rock–coal interface, special settings were applied for the interface parameters. Based on the results derived from research on the mechanical properties of the combined rock–coal interface [36,37,38], and in combination with the simulation requirements, the interface parameters were set. The contact elastic modulus of the interface was set to 80% of the rock stiffness, the parallel bonding tensile strength was set to 70% of the coal parallel bonding tensile strength, and the parallel bonding cohesion strength was set to 70% of the coal parallel bonding cohesion strength in order to reflect the mechanical characteristics of “weak cementation and easy damage” at the interface, as shown in

Table 1. Mesoscopic parameters used in numerical models.

Type	$R_{\min }/\mathrm{mm}$	$R_{\max }/\mathrm{mm}$	$E_{\mathrm{c}}/\mathrm{GPa}$	$\mu$	$\overline{k_n}/\overline{k_s}$	${\overline{\sigma }}_c/\mathrm{MPa}$	$\overline{C}/\mathrm{MPa}$	$\overline{\varphi }/°\mathrm{C}$	$\rho /({\mathrm{kg}·\mathrm{m}}^{-3})$
Rock	1.0	1.5	1.3	0.577	1.0	5.5	9.9	30	2500
Coal			0.78	0.235	1.0	3.7	6.11	17	1340
Interface			1.04	0.3	1.0	2.59	4.29	-	-

Note: $R_{\min }$ represents the minimum particle radius; $R_{\max }$ represents the maximum particle radius; $E_{\mathrm{c}}$ represents the contact elastic modulus; $\mu$ represents the coefficient of friction; $\overline{k_n}/\overline{k_s}$ represents the parallel bonding stiffness ratio; ${\overline{\sigma }}_c$ represents the parallel bonding tensile strength; $\overline{C}$ represents the parallel bonding cohesion strength; $\overline{\varphi }$ represents the friction angle; $\rho$ represents particle density.

.

The laboratory coal and rock monomer samples and the corresponding numerical simulation fracture states are shown in Figure 5a,b. By comparison, it is found that the macroscopic failure fracture morphology of the coal and rock monomer physical experiments is similar to that calculated via numerical simulation, and macroscopic fracture surfaces at the same angle appear. Figure 5c shows the laboratory strength curve and the corresponding simulation curve. Due to the presence of primary micro-fissures in the coal and rock samples during the indoor tests, the stress–strain curve enters the initial compaction stage. However, the numerical model does not contain primary micro-fissures and thus does not have this stage. Therefore, in reference [30], it is stated that “the inclined straight line section of the indoor test stress–strain curve is extended and intersects with the X-axis.” The parameter calibration method consists of subsequently moving the entire unit to the left of the origin. It can be determined that the stress–strain curves can be well matched under the two methods. It can also be found that the relative error between the test and simulated strength values in Figure 5c is approximately 0.05%. This comprehensively indicates that the model established in this paper can accurately reflect the mechanical properties and fracture morphology of the single coal and rock specimens.

3. Bearing Characteristics and Crack Development of Rock–Coal Composite Bodies

3.1. Strength Characteristics of Rock–Coal Composites

Figure 6a shows the stress–strain curves of rock–coal composites with different height ratios during uniaxial compression, presenting the characteristics of different stages: the elastic stage, microelastic cracks’ stable development stage, the yield stage, and the post-peak failure stage [39,40,41]. Take the combination body with a height ratio of 2:8 as an example. A to B4 represents the first stage, at which point the stress and strain change in a linear proportional relationship. Point B4 represents the yield point, where the corresponding stress is approximately two-thirds of the peak strength. The phase from B4 to C4 is referred to as the “yield stage,” during which the axial stress continues to increase, albeit at a decreasing rate, until reaching the ultimate compressive strength at point C4. In the third stage (C4~), the axial stress drops sharply, approaching but not completely dropping to zero, and the combined body basically loses its load-bearing capacity.

The compressive strengths of the combinations with rock–coal height ratios of 2:8, 4:6, 6:4, and 8:2 are 26.15 MPa, 26.36 MPa, 26.9 MPa, and 27.64 MPa, respectively, as shown in Figure 6a. From the perspective of the strength differences among the four combined body samples, as shown in Figure 6b, the errors are only −2.35%, −1.54%, −0.51%, and 3.91%, respectively, indicating that the rock–coal height ratio of the combined body samples has little effect on the compressive strength of the combined body. This is consistent with the results obtained in references [14,42,43]. Moreover, it can be seen from this that the compressive strength and deformation capacity of the combined body specimens are mainly controlled by the coal samples. Compared with the individual coal samples, the values slightly increase but are far lower than those for the strength of the rocks. In addition, it can be seen from

Table 2. Simulation results of coal and rock masses with different height ratios.

		Rock–Coal Height Ratio
	0:10	2:8	4:6	6:4	8:2	10:0
Compressive strength/MPa	26.05	26.15	26.36	26.9	27.64	39.52
Elastic modulus/GPa	0.577	0.9	1	1.11	1.19	1.11

that the elastic modulus of the combined specimen increases with an increase in the height ratio, indicating that the load-bearing capacity and deformation resistance of the combined body are enhanced. However, the strain corresponding to the peak strength decreases with an increase in the rock–coal height ratio, indicating that the stiffness of the combined body increases and the ductility decreases. This indirectly proves that, compared with coal roadways, semi-coal–rock roadways with a “rock mass–coal body” combined structure have higher stability and are conducive to disaster prevention and control.

Based on the simulated data for the composite body, the relationship between the rock proportion x and the compressive strength y of the composite body was fitted, and Equation (2) and relationship Figure 7 were obtained:

$$\mathrm{y}=0.034\times e^{({\displaystyle \frac{\mathrm{x}}{0.167}})}+26.016(R^2=0.96)$$

(2)

According to Equation (2), the rock proportion x of the composite body is directly proportional to the strength of the composite body, and it increases with an increase in the rock proportion. This indicates that the contribution of the rock part to the strength of the composite body gradually increases. According to the fitting model, the increase in the rock proportion has a relatively small contribution to the strength improvement in the initial stage, but as the rock proportion approaches 1, the contribution of the rock part significantly enhances, leading to a rapid increase in the strength of the composite body.

3.2. Counting of Acoustic Emission Ringing in Rock–Coal Composite Bodies

In rock mechanics, acoustic emission (AE) is a physical phenomenon characterized by the radiation of transient elastic waves resulting from the rapid release of strain energy during microcrack initiation, propagation, and frictional sliding along structural planes when materials undergo loading deformation leading to failure [44]. As a key technique for capturing the dynamic evolution of internal damage, AE not only enables real-time tracking of crack formation and propagation processes but also allows for the inference of spatial distribution and intensity characteristics of damage through signal analysis [31,45]. Core AE characteristic parameters include ring-down counts, event counts, energy, amplitude, and pulse duration. Among these, ring-down counts and event counts directly quantify the number and activity level of cracks, while energy and amplitude correlate with the severity of crack propagation. Pulse duration can indirectly reflect crack dimensions.

The present model employs a self-developed real-time AE monitoring program written in the Fish language. This program treats each crack formation as an AE pulse [46,47]. By recording the number of cracks (i.e., ring-down counts) in composite specimens with varying rock–coal height ratios during uniaxial compression, the model processes the data to simulate the temporal evolution patterns of AE events. Although numerical simulation cannot directly acquire frequency band information, the rationality of the model can be validated by comparing the temporal characteristics of AE events between simulations and physical experiments [48].

The strain corresponding to the peak intensity is not consistent with that corresponding to the peak of the AE count. The variation pattern of the AE ringing count is coordinated with the stress–strain curve, as shown in Figure 8. According to the trend and rate of acoustic emission changes, the AE ringing count changes in the combined body are divided into four periods, namely, the “Quiet Period”, “Steady Increase Period”, “Rapid Increase Period”, and “Decline Period”, corresponding to the three stages of the stress–strain curve.

The first stage is the “Quiet Period”. At this stage, the AE ringing count is relatively small, and the axial stress is not significant enough to cause damage between mesospheric particles. Only when approaching the yield point B4 do a few minor fractures occur, and accordingly, a small number of acoustic emission signals appear, corresponding to the elastic stage and the stable development stage of microcracks in Figure 6a of the combined body sample.

The second stage is the “Steady Increase Period”. With an increase in stress and strain, the number of AE events gradually increases. This is because the combination changes from volume compression to expansion, and the axial strain and volume strain rates increase, causing the stress between particles in a local range to exceed the contact strength and resulting in cracks. This stage corresponds to the yield stage, and the degree of failure shows a gradually increasing trend. The AE ringing count also presents similar characteristics.

The third stage is the “Rapid Increase Period”. The stress decreased, and the AE ringing count increased sharply, reaching its peak when the axial stress was close to 0.8 times the residual strength of the specimen. This indicates that the crack is developing and expanding rapidly, causing a sharp drop in the stress of the combined body, corresponding to the “post-peak fracture stage”.

The fourth stage, the “Decline Period”, is the period during which the stress continues to decrease as the strain increases. The AE ringing count starts to gradually decrease from the maximum value but ultimately does not reach zero. This indicates that at this point, due to the formation of the macroscopic fracture surface, the coal sample of the combined body gradually loses its load-bearing capacity, the load-bearing object gradually shifts to the rock, and the acoustic emission signal gradually weakens.

From the coordinate points D4 to D1 in Figure 8a–d, it is found that the number of acoustic emissions of different height ratio combinations varies greatly. The maximum values of AE ringing count are 1581, 1359, 1270, and 635, respectively. As the rock-to-coal height ratio increases, the maximum AE ringing count value decreases, reflecting the increasing difficulty of microcrack formation and propagation within the material. Under conditions in which the proportion of rock is high, the hardness and strength of the material increase, the formation of microcracks is difficult, and the AE signal weakens. In contrast, when the proportion of coal is high, the coal’s quality is soft and prone to cracking, and the activity of AE is enhanced. Meanwhile, the strain corresponding to the peak AE ringing count decreases accordingly, indicating that the compressive variable of the combined body is mainly concentrated in the coal part, which determines the compressible potential and deformation capacity of the entire combined body.

3.3. Dynamic Crack Propagation Process of the Rock–Coal Composite Body

Figure 9, Figure 10, Figure 11 and Figure 12 show the crack evolution process of the combined bodies with different rock–coal height ratios under different stress levels. The compressive strength of the combined body specimens is presented in the figures. The principle for selecting the stress level is to take the peak strength of the stress–strain curve as the dividing point. The different stress levels are as follows: Before the peak, it is 0.9 ${\sigma }_c$. After the peak, it is 0.9${\sigma }_{\mathrm{c}}$, 0.8 ${\sigma }_{\mathrm{c}}$, 0.7 ${\sigma }_{\mathrm{c}}$, and 0.6 ${\sigma }_{\mathrm{c}}$, as shown in in Figure 9, Figure 10, Figure 11 and Figure 12.

When the rock–coal height ratio is 2:8, cracks develop from the rock–coal contact surface and the bottom boundary of the coal body towards the central area, presenting two segments: Q1 → Q2 and Q3 → Q2. Eventually, an inclined crack band at a 45-degree angle to the horizontal plane is formed, as shown in Figure 9c. When the height ratio is 4:6, the cracks mainly accumulate at the corners of the coal body, and there are also sporadic distributions inside. The aggregation areas present two development zones, M1 → M2 and M1 → M3, as shown in Figure 10b. Then, the initial development zone of the cracks forms a macroscopic crack band “from the surface to the inside” along the 46-degree inclined plane, as shown in Figure 10e.

When the height ratio is 6:4, the cracks accumulate at the bottom edge angles L1 to L3 and the top N1 of the coal seam. The cracks continue to develop and expand along the 45-degree inclined planes determined by L2N4 and L2L3 and the 46-degree inclined planes determined by L2N4 and L2L1. Eventually, they successively connect to form two macroscopic crack zones, as shown in Figure 11c,d. Meanwhile, the cracks gathered at N1 spread and penetrate both sides along N1 → N2 and N1 → N3, forming a horizontal crack band composed of the contours formed by the connections of each vertex from N1 to N4.

When the height ratio is 8:2, no obvious crack inclination surface is formed inside the coal body. Instead, a large amount of contact and fragmentation occur at the bottom and top corners of the coal body, and it expands and develops “from the outside to the inside”, eventually leading to complete fragmentation of the coal body part, especially at the rock–coal interface; the fragmentation of the coal body part is more severe than that of the 6:4 combination.

In addition to the macroscopic crack bands, a considerable number of microcracks also emerge in the combined body. The formation of these microcracks exacerbates the instability of the composite body. As the height ratio of coal to rock increases, the internal fragmentation of the coal body intensifies, forming more crack zones. These crack zones continuously expand and penetrate under the load, leading to an increase in the degree of internal damage to the rock, as shown in the yellow elliptical marked parts in Figure 9d–f, Figure 10d–f, Figure 11d–f and Figure 12d–f. The reason for this phenomenon lies in the fact that, under the action of external loads, the initial cracks inside the coal body gradually expand into macroscopic crack bands. The increase in the height ratio leads to an increase in the number of crack zones in the coal body, while the stress concentration effect at the crack tip intensifies, promoting the crack zones to extend to the rock part and intensifying the rock’s damage.

3.4. Development Law of Crack Quantity in Rock–Coal Composite Bodies

In the parallel bonding model of PFC3D, the bonding strength between particles is jointly determined by the normal and tangential contact strengths. During the compression process, if the normal or tangential stress exceeds the corresponding bonding strength, the contact bonds between particles will break, resulting in either tensile or shear failure. Thus, recording the failure types associated with contact bond breakage can effectively address the challenge of distinguishing between tensile and shear failures in current laboratory tests.

Figure 13 illustrates the variation curves of crack numbers during the loading process of rock–coal composite bodies with different height ratios. As shown in the figure, the crack evolution trends across all height ratios are generally consistent, each comprising four distinct stages. Stage I: During the initial loading phase, the stress level remains relatively low and has not yet reached the material’s failure threshold; consequently, no cracks are initiated. Stage II: As loading progresses and the stress gradually approaches the compressive strength of the material, a limited number of cracks begin to form, exhibiting a linear increase in crack count. Stage III: With the continuous initiation and propagation of cracks, macroscopic fracture zones progressively develop within the composite body, resulting in a sharp increase in crack numbers. However, the rate of increase gradually diminishes. This stage corresponds to the “rapid increase and subsequent decline phase” observed in acoustic emission studies, indicating a period of rapid internal damage accumulation followed by stabilization. Stage IV: Once the macroscopic fracture zones are fully established, the number of cracks stabilizes, signifying that the composite body has reached a state of failure and structural equilibrium. This study quantifies the cracks of the composite body numerically, which correspond to the acoustic emission change stages mentioned earlier.

Notably, during Stage III, the number of tensile cracks gradually surpasses that of shear cracks, a trend that becomes more pronounced and stabilizes in Stage IV. This phenomenon can be attributed to the Poisson effect under uniaxial compression, which induces transverse tensile stress. Given the relatively low tensile strength of coal, tensile cracks are more readily generated. In contrast, the formation of shear cracks requires overcoming higher shear resistance.

Figure 14 presents the statistical distribution of internal microcracks across composite bodies with varying rock-to-coal height ratios. As illustrated in the figure, with an increase in the rock-to-coal height ratio, the total number of cracks, as well as the total number of tensile and shear cracks, exhibit a decreasing trend. This phenomenon can be attributed to the rock’s relatively stable mechanical properties and higher strength, and as the rock proportion increases, crack initiation and propagation are effectively constrained. Consequently, the presence of rock enhances the structural stability of the composite body and improves its resistance to damage.

Furthermore, the analysis reveals that tensile cracks dominate throughout the entire failure process, with their quantity being approximately 1.9 times greater than that of shear cracks. Specifically, under different height ratios, the proportions of tensile cracks are 66.1%, 65.8%, 67.2%, and 64.4%, while those of shear cracks are 33.9%, 34.2%, 33.8%, and 35.6%, respectively. The variation in these proportions is minimal, indicating that changes in the rock-to-coal height ratio have a limited effect on the relative distribution of crack types. This finding suggests that, despite potential differences in composition and structure within coal-bearing strata, the failure mechanisms under uniaxial compression exhibit certain common characteristics. These insights provide a valuable reference for predicting and mitigating rock mass instability failures in practical engineering applications.

4. The Law of Multi-Energy Co-Evolution in Rock–Coal Composite Bodies

Energy evolution is an important indicator for characterizing the internal fracture state of a specimen. The PFC 6.0 simulation software provides the monitoring and tracking function of the energy module and fully considers the influence of various factors, defining multiple energies, which are divided into two major parts: body energies and contact energies. Mechanical energy is the energy related to the motion of an object itself, including local damping energy, boundary work, and kinetic energy. Contact energy is the energy defined by the contact model, including the energy dissipated by the damper between contacts, bonding strain energy, and sliding friction energy, etc. This paper researches bonding strain energy, bonding failure energy, kinetic energy, etc. During the compression process, the bonding strain energy continuously accumulates. When the contact overload fails, the stored bonding strain energy is gradually released in the form of bonding failure energy. The calculation method is shown in Equation (3):

$${\overline{E}}_k={\displaystyle \frac{1}{2}}({\displaystyle \frac{{\overline{F}}_n^2}{{\overline{k}}_n\overline{A}}}+{\displaystyle \frac{{‖{\overline{F}}_s‖}^2}{{\overline{k}}_s\overline{A}}}+{\displaystyle \frac{{\overline{M}}_t^2}{{\overline{k}}_s\overline{J}}}+{\displaystyle \frac{{‖{\overline{M}}_b‖}^2}{{\overline{k}}_n\overline{I}}})$$

(3)

In the formula, ${\overline{E}}_k$ is the bonding strain energy at the contact point; ${\overline{F}}_n$ is the parallel bonding normal force; ${\overline{F}}_s$ is the parallel bonding shear force; ${\overline{M}}_t$ is the bonding torque; ${\overline{M}}_{\mathrm{b}}$ is the bonding bending moment; ${\overline{k}}_n$ is the normal stiffness; ${\overline{k}}_s$ is the shear stiffness; $\overline{J}$ and $\overline{I}$ are the moment of inertia and the extreme moment of inertia at the contact point, respectively.

4.1. Characteristics of Multi-Energy Evolution of Combined Bodies

Figure 15 shows the multi-energy evolution diagram of rock–coal composite bodies with different height ratios. It reflects the energy storage state of the composite body during the force application process through the trend in strain energy variation. The special introduction of cementation failure energy to characterize the magnitude of the energy radiated outward when the sample fails is consistent with the use of acoustic emission energy by researchers conducting experiments to characterize the failure features of the sample, and its energy magnitude is more accurate. The principle is as follows: The energy released at each cementation rupture is extracted in real time through Fish language and then accumulated and visualized. According to the changes in velocity characteristics during the evolution of strain energy, the energy evolution is divided into four stages for analysis and research. The energy variation trends in various combinations with different height ratios are the same. Taking a height ratio of 2:8 as an example, we note the following steps:

(1)

The Slow Accumulation Stage (A to E4): The cemented strain energy starts to increase in a “downward convex” trend from 0, and the growth rate gradually decreases. This is the initial strain energy accumulation stage. This is because, during the initial loading stage, the microstructure and stress inside the material begin to adjust, which slows down the strain energy growth rate. The corresponding cementation failure energy and kinetic energy are very small, corresponding to the stable development stage of elastic and microelastic cracks during the stress–strain process and the “Quiet Period” in acoustic emission counting.

(2)

The High-Speed Growth Stage (E4–F4): At this stage, the strain energy growth rate remains relatively stable but reaches its maximum value at this stage, and the cemented strain energy accumulates rapidly. Near the F4 point, the growth rate gradually decreases, and it becomes 0 at F4. The corresponding cemented strain energy reaches the maximum value, and the kinetic energy and cemented failure energy curves gradually rise. This indicates that at this stage, the partial contact of the combined body begins to break and release energy, resulting in relatively active particles, but the overall state remains in an energy accumulation state, corresponding to the yield stage in the stress–strain process and the “Steady Increase Period” in the acoustic emission count.

(3)

The Rapid Release Stage (F4–I4): After reaching a maximum energy accumulation state at point F4, the combined body is on the verge of instability. The cemented strain energy decreases with the sharp drop in stress, while the kinetic energy and cemented failure energy increase rapidly. This is due to the large number of acoustic emission events at this stage, which cause the kinetic energy and cemented failure energy to rise sharply and reach a maximum value at about 1.25% of the strain, corresponding to the post-peak failure stage in the stress–strain process and the “Rapid Increase Period” in the acoustic emission count.

(4)

The Slow Dissipation Stage (I4~): At this stage, energy begins to dissipate slowly, and the rate of decline in cementation strain energy and the rate of increase in cementation failure energy gradually decrease, but they do not reach zero. Kinetic energy began to drop sharply from its peak and approach zero. At this point, the coal part loses its load-bearing capacity, while rocks gradually become new carriers. The entire system tends to stabilize, and the energy conversion process becomes slow.

It can be seen from Figure 15a–d that, as the rock–coal height ratio increases, the maximum values of cemented strain energy, failure energy, and kinetic energy all decrease. This is because the coal body is the main controller of the energy evolution of the composite body. A decrease in the coal body proportion leads to a reduction in the cemented strain energy storage capacity and the number of acoustic emission events, and when the particles break, the kinetic energy and dissipated energy also decrease accordingly. This reflects the co-evolutionary mechanism of the interaction among energies. The energy evolution law here is consistent with the crack quantity evolution law in the previous text, revealing that the essence of specimen fracture is the transformation of energy. This indicates that the system’s energy storage capacity under sudden loads decreases, and its ability to accumulate a large amount of elastic potential energy weakens, thereby reducing the risk of severe shock damage caused by excessive energy. Meanwhile, the energy release process becomes more gentle, avoiding the intense dynamic response (such as support failure, coal–rock ejection, etc.) caused by the concentrated and instantaneous energy release when the proportion of coal is too high (height ratio 2:8). Conversely, the higher the proportion of coal, the more likely the system is to experience rapid energy accumulation and sudden release under emergency loading, posing a greater threat to the stability of the project. The curves of cemented failure energy all show a steady increase at first, followed by a sharp rise in the strain energy “rapid release stage” before remaining unchanged. This feature reflects the damage evolution law of cemented structures during the stress process; in other words, in the initial stage, the cemented bonds gradually break, and energy accumulates slowly. When the critical state is reached, a large number of cemented bonds break, and energy is rapidly released and remains unchanged. At the same time, it can be observed that the corresponding strain when each energy reaches its peak is also decreasing, which is consistent with the results shown in Figure 6, indicating that the elastic modulus of the combined body sample increases with the increase in the rock–coal height ratio. In engineering applications, this may imply that, as the rock–coal height ratio increases, the overall stiffness of the material improves, enabling it to more effectively resist external impact loads and thereby enhancing its impact resistance and deformation toughness.

4.2. Characteristics of Cemented Strain Energy Zoning

To better study the failure mechanism of the combined body, a Fish program was independently developed to traverse the particle contact of the coal and rock parts in real time. The energy of the coal and rock in the combined body was statistically studied in a zonal manner. The strain energy accumulated during the contact was recorded and visualized. Finally, the strain energy zonal evolution curves of the combined rock–coal body samples with different height ratios were drawn, as shown in Figure 16. From this figure, it can be found that the variation trend regarding the strain energy zones is the same as that of the combined strain energy in Figure 15, with both showing phased characteristics of first aggregating and then releasing.

The difference lies in the fact that, as the height ratio increases, the maximum strain energy of the coal gradually decreases, while that of the rock gradually increases. The ratio of the two maximum values continuously decreases in the following order: 6.81 → 2.50 → 1.13 → 0.41.

This is mainly due to the increase in the proportion of rock and the decrease in the volume of coal, which leads to the transfer of the external load from coal to rock. The strain energy of the combined body obtained from Section 4.1 also decreases with the increase in the height ratio. Both indicate that the decrease rate of the strain energy of the coal body is greater than the increase rate of the strain energy of the rock, further confirming that the coal body is the main carrier affecting the accumulation of the strain energy of the combined body and the fracture of the combined body. By comparing Figure 16a–d, it can be found that only when the rock–coal height ratio is greater than 1.5 does the rock become the main body of energy accumulation in the combination.

5. Spatiotemporal Distribution and Evolution Characteristics of Composite Body Fracture Events Based on Cementation Failure Energy

To make up for the spatial resolution deficiency of the traditional acoustic emission energy integration method, and to clarify the magnitude and location of the destructive energy level and its spatiotemporal evolution characteristics, this study independently developed a Fish program for capturing and tracking destructive energy. The principle is as follows: Based on the contact model response mechanism of PFC3D, when the cemented bond undergoes tensile/shear failure, the failure energy and its spatial coordinates at the contact fracture are captured in real time through the built-in Fish interface function and exported to a table. Then, the OriginPro 2021 plotting software was used for positioning and drawing. The spatial positioning and quantitative tracking of mesoscopic-scale destruction energy have been achieved, enabling energy analysis to delve from “macroscopic total” to “mesoscopic local”. Figure 17, Figure 18, Figure 19 and Figure 20 show three-dimensional spatial location diagrams of the cementation failure energy of the composite body at different stress levels. The size of the spatial position in the figure is consistent with the size of the combined body sample. The size and color of the particles indicate the amount of energy released by the fracture event at this contact position. The larger the particle size and the darker the color (purple-red represents small energy events, and cyan represents large energy events), the greater the cementation failure energy. The light red plane in the middle of the scatter plot represents the rock–coal contact interface.

When the rock–coal height ratio is 2:8, the cementation failure energy is mainly released at the corners and edges of the coal body and the rock–coal contact interface first. When the axial stress level reaches the peak strength, the cementation failure energy accumulates at the corners and edges, as shown in Figure 17a,b, indicating that the corresponding corners and edges have been completely damaged at this time. Subsequently, the failure energy of the sample is gradually released along the plane where Q1Q2 and Q1Q4 are located and the two regions of Q3 → Q2 in the line segment in Figure 17c at an angle of approximately 45 degrees to the horizontal plane.

When the rock–coal height ratio is 4:6, the energy generated is first released at the corners of M1 to M3 before being released from the corners towards the interior on the 45-degree inclined plane where the line segments M1M2 and M1M3 are located, corresponding to the crack morphology in Figure 10b. When the height ratio is 6:4, the release of failure energy is distributed along the three major crack bands described in 3.3, as illustrated in Figure 11d and Figure 19d. When the height ratio is 8:2, as shown in Figure 20, an energy release zone is formed on the outer layer of the coal body of the combined body, and it continuously advances inward, which is consistent with the evolution trend of the crack zone in Figure 12.

By comparing the color scale changes representing the failure energy in Figure 17, Figure 18, Figure 19 and Figure 20, it can be found that the range of the failure energy is from 0 to 0.009 J. During contact, the majority of failure the energy is mostly released at the corners of the coal body part, and with an increase in the height ratio, the maximum failure energy during contact continuously decays from 0.00876 → 0.00796 → 0.00676 → 0.00482. In addition, from the previous analysis, it is known that the steady increase period of acoustic emission can be used as precursor information before the failure of the composite body, when the cementation failure energy begins to show a significant nonlinear growth trend. Therefore, the threshold of the significant energy event of the maximum failure energy is located at the moment before the peak, at a value of 0.9. This moment corresponds to the turning stage of the composite body crack, from stable expansion to accelerated expansion. The maximum failure energy values of the four proportional combinations are 0.00125 J, 0.00125 J, 0.00077 J, and 0.00089 J. The threshold is taken as the average value (0.00104J), which can provide a reference value for disaster early warning and protection. The energy released by failure in the rock is relatively small, and the energy distribution mainly extends upward along the concentrated area of partial failure energy in the coal body. Moreover, as the rock–coal height ratio increases, the energy release area of the rock also expands, as shown in Figure 20c–f.

6. Discussion

Figure 6a shows the strength evolution characteristics of different height ratio combinations. It is found that the strength of the combination lies between that of coal and rock monomers. Moreover, as the height ratio increases, the strength and elastic modulus of the combination increase, while the strain corresponding to the strength decreases. This is consistent with the strength laws of the different height ratio combinations studied in references [11,14,23,31,49,50]. Figure 8 shows the acoustic emission characteristics of rock–coal combinations at different height ratios. Through comparison, it is found that the ringing count begins to increase from the yield stage and reaches the peak at the failure stage (0.8) after the load-bearing stress peak, and the number of acoustic emission events shows a first increasing and then decreasing trend, which is consistent with the conclusion in reference [31]. In reference [16], it was proposed that the energy dissipation in the simulation was mainly due to the cracking caused by the fracture of the bond, and the energy accumulated in the pre-peak stage of the compression process dissipated significantly in the post-peak stage. This study is consistent with these rules. At the same time, thisanother paper mentions that the energy dissipation is mainly due to the cracking caused by the fracture of bonds. However, this study evidences the evolution of multiple energy sources (strain energy, failure energy, and kinetic energy) of different height ratio combinations under uniaxial compression conditions [23,24,25,26,27] (Figure 15), resulting in the dissipated energy previously observed in concrete.

In addition to the consistency of the above conclusions, this study differs from others. Firstly, by means of the self-developed Fish program for capturing and tracking failure energy and strain energy, the regional distribution characteristics and migration laws of cemented strain energy were clarified, as shown in Figure 16. In particular, the bonding failure energy is introduced to characterize the magnitude of the energy radiated outward when the specimen fails, rather than using the particle strain energy or overall dissipation energy as core indicators to characterize the fracture mechanism as in other studies [23,24,25,26,27], directly and precisely quantifying the cumulative damage of the cemented structure. Finally, three-dimensional spatial positioning diagrams of the bonding failure energy under different stress levels are presented in Figure 17, Figure 18, Figure 19 and Figure 20. Compared with traditional acoustic emission positioning, three-dimensional spatial positioning is more accurate and can visually reflect the initial position, propagation direction, energy release, and evolution process of the crack in the composite body, as well as the surface morphology of the crack propagation, providing reference values for disaster early warning and protection.

It is worth noting that Figure 13 reveals the evolution of the number of cracks in different height ratio combinations. The proportion of tensioning cracks and shear cracks is less affected by the height ratio, which may be due to the significant differences in mechanical properties between rocks and coal. Coal is more prone to tensioning cracks, while rocks are more likely to develop shear cracks. So even if the height ratio changes, the inherent properties of these materials still dominate the distribution of crack types, and thus, the proportion of crack types changes relatively little, or it could be that, within the height ratio range of this study, the stress distribution did not undergo any changes sufficient to cause a variation in the crack type.

7. Conclusions

The strength of the combined body lies between that of coal and rock units. Moreover, as the height ratio increases, the strength and elastic modulus of the combined body increase, while the strain corresponding to the strength decreases. The AE ringing count goes through the “Quiet Period”, “Steady Increase Period”, “Rapid Increase Period”, and “Decline Period”. The peak of the count appears at 0.8${\sigma }_{\mathrm{c}}$ after the intensity peak. As the height ratio increases, the peak of the AE event gradually decreases and appears earlier. Among them, the steady increase period can be used as a warning before the destruction of the combination.

The cracking of the combined body mainly occurs in the coal body part, extending and penetrating along the inclined plane at about 45 degrees from the horizontal plane, except for the height ratio of 8:2. Due to the large degree of fragmentation, the coal body expands and extends inward from the outer layer without a distinct inclination angle. Moreover, as the height ratio increases, the number of crack zones inside the coal mass increases, resulting in deeper rock fractures.

With an increase in the height ratio, the total number of cracks in the composition, the number of tensioning cracks, and the number of shear cracks all show a downward trend. Among them, the number of tensioning cracks is about 1.9 times that of shear cracks, and their proportion is not affected much by the height ratio. In particular, the number of tensile cracks and shear cracks is very close at the initial stage of specimen loading. When the combined strength approaches the bearing capacity of the specimen, the difference between the two gradually increases and eventually stabilizes.

The peak values of the strain energy, failure energy, and kinetic energy curves of the combined body all decrease with an increase in the height ratio. The maximum value of the kinetic energy of the combined body remains very low at all times. The cemented failure energy first steadily increases before increasing sharply in the “rapid release stage” of strain energy and remaining unchanged. When the rock–coal height ratio exceeds 1.5, the main body of strain energy accumulation migrates from the coal body to the rock mass. Through the quantitative means of failure energy localization, it was found that the energy amplitude of the maximum failure energy event during contact also decreases with an increase in the height ratio. This method can clearly show the initial position of the crack in the combination body, the propagation direction, and the size and evolution of the energy released by the crack. All these provide important references for optimizing the structural design of rock–coal combinations and improving their load-bearing capacity and stability.