Research on the Mechanical Properties and Failure Mechanism of Lignite Affected by the Strain Rate Under Static and Dynamic Loading Conditions

Abstract

Coal seams, as critical components of open-pit mine slopes, are subjected to both quasi-static and dynamic loading disturbances during mining operations, with their mechanical properties directly influencing the slope stability. Consequently, to clarify the mechanical properties and failure mechanisms of coal seams affected by the strain rate under the static–dynamic loading conditions, the mineral composition and meso-structural characteristics of lignite were analyzed in this study, and uniaxial compression tests with different quasi-static loading rates and dynamic compression tests with different impact velocities were conducted. The results indicate that there is an obvious horizontal bedding structure in lignite, which leads to differences in mechanical response and failure mechanism at different strain rates. Under the quasi-static loading, lignite exhibits significantly lower strain-rate sensitivity than compared to dynamic impact conditions. The Poisson’s ratio difference between the bedding matrix and the lignite will produce interfacial friction, which gradually decreases with the increase in the distance from the interface, thus promoting the transformation of lignite from multi-crack tensile shear mixed fracture to single-crack splitting failure. Under the dynamic impact conditions, low-impact velocities induce stress wave reflection at bedding interfaces due to wave impedance disparity between the matrix and lignite, generating tensile strains that result in bedding-plane delamination failure; at higher velocities, incomplete energy absorption by the rock specimen leads to fragmentation failure of lignite. These findings are of great significance for the stability analysis of open-pit slopes.

1. Introduction

Slope stability is a critical concern for safe mining operations in open-pit mines. As fundamental structural components of slopes, the mechanical properties of coal seams directly influence both slope stability and disaster resistance capacity [1,2,3,4]. During the open-pit mining operations, the coal seams are subjected to the quasi-static and dynamic load disturbances. On the one hand, the quasi-static loading (strain rate of 10⁻⁵~10⁻² × s⁻¹) under long-term gravitational stress and slow unloading is characterized by progressive stress accumulation and damage evolution [5], with the low strain rates and small amplitudes [6]. On the other hand, the dynamic loading (with a strain rate of 100~10³ × s⁻¹) generated by the blasting propagates through stress waves [7], exhibiting high strain rates and large amplitudes [8]. These two loading mechanisms exhibit significant differences in strain-rate levels and energy-transfer pathways, leading to distinct mechanical responses in coal-rocks [9,10,11]. Therefore, investigating the mechanical behavior of coal rock under quasi-static loading and dynamic impact conditions is significant to reveal their failure mechanisms under static–dynamic loading and ensure safe, efficient mining practices in open-pit operations.

The mechanical properties of coal rock exhibit significant strain-rate dependence, with distinct variations in strength, deformation, and failure characteristics across different strain-rate regimes [12,13,14,15,16]. To address the high strain rates that are testing demands for dynamic impacts, the split Hopkinson pressure bar (SHPB) system has been widely employed to investigate the dynamic strength, energy dissipation, and damage evolution in brittle materials such as coal, rock, and concrete [17,18,19,20,21]. Jiang et al. [22] studied the damage characteristics of the soft coal rock composites under the dynamic disturbances, revealing that the dynamic loading significantly degrades composite strength and exacerbates damage, with the tensile crack propagation dominating failure while shear cracks play a secondary role. Gao and Zheng et al. [23,24] analyzed the mechanical behavior and fragmentation fractal characteristics of coal rock under dynamic strain rates, finding that the fractal dimensions increase while the average fragment sizes decrease with rising strain rates. Strain-rate regime classification critically influences the rock deformation mechanisms, so Li et al. [25] defined 10⁻⁵~10⁻¹ × s⁻¹ as the quasi-static loading range. The coal-rock mechanics display notable strain-rate sensitivity [26]. Liu and Liang et al. [27] investigated the strain-rate strengthening effects on coal strength, non-monotonic elastic modulus trends, and tensile–shear failure modes. Munoz and Pan et al. [28,29] observed progressive strain localization in granite and sandstone, with quasi-static strength correlating linearly to meso-structural parameters. During the mining operations, the coal rock experiences complex failure mechanisms due to the coupled disturbances from excavation, unloading, and stress redistribution [30,31,32,33]. Jing and Liu et al. [34,35] identified the weak interfaces as dominant controls in coal rock composites, with failure transitioning from tensile to tensile–shear modes under the dynamic loading. Dai et al. [36] explored energy evolution and damage mechanisms of fractured granite under combined static–dynamic loading, demonstrating that the rock-burst propensity correlates closely with static stress levels. Wang et al. [37] characterized the compressive-shear failure in sandstone, showing the confining pressure’s superior crack suppression effect.

The existing research on the mechanical behavior of coal-rock strain rate mainly focuses on single dynamic impact, quasi-static loading, and dynamic–static coupling. There is relatively little research on the comparative analysis of the mechanical behavior and failure mechanism of coal rock under quasi-static loading and dynamic impact. In this paper, the mineral composition and microstructure characteristics of lignite were analyzed by XRD-XRF test, SEM, and thin slice analysis. Then, based on the AG-X250 universal test machine and SHPB test system, the quasi-static different loading rates uniaxial compression tests and dynamic impact tests under different impact velocities were conducted on lignite to comparatively analyze the mechanical behavior characteristics and progressive failure characteristics of lignite under different strain rates. Finally, the failure mechanism of lignite under quasi-static and dynamic impact is clarified, respectively. The research results are of great significance to the stability analysis of open-pit slopes.

2. Methodology

2.1. Sample Preparation

The rock specimens were taken from the open-pit lignite in Inner Mongolia. To preserve the sample’s original characteristics, the deep lignite was excavated by bucket, and the target coal blocks were selected for preservation film storage and then transported to the laboratory. In these quasi-static loading and dynamic impact tests, lignite was processed into short cylindrical specimens with a height and diameter of 50 mm according to the method recommended by the International Society for Rock Mechanics and Rock Engineering (ISRM). After cutting and polishing, the roughness and non-parallelism at both ends of each specimen do not exceed 0.05 mm and 0.02 mm, respectively. The size and machining accuracy of the specimen meet the test standards [38].

2.2. Test System and Experimental Procedure

The plan of the quasi-static loading test for lignite is shown in Figure 1a. Firstly, the coal rock samples collected on site were crushed and ground, using an agate mortar, into a powdered form with particle sizes smaller than 48 µm. Subsequently, the mineral composition and content characteristics of the lignite were obtained using the XRD and XRF techniques. Additionally, the collected lignite rock samples were processed into cube specimens with edge lengths smaller than 1 cm and observed under the ZEISS Gemini SEM 300 scanning electron microscope (The ZEISS Gemini SEM 300 scanning electron microscope was from Carl Zeiss (Shanghai) Management Co., Ltd., Shanghai, China) from high to low magnification. Meanwhile, the thin section specimens parallel to the bedding planes of lignite were prepared to observe the interlayer structures of lignite using microscopy (Microscopic analysis was performed using equipment from Carl Zeiss, Oberkochen, Germany.). Following this preparation, the speckle pattern was made on the lateral surface of the cylindrical rock specimen, and the strain field of lignite was monitored using the DIC technique. Finally, the test was loaded at a rate of 1 mm/s, 0.1 mm/s, 0.01 mm/s, and 0.001 m/s using displacement control, and the loading force was 0.5 kN/s. In order to reduce the influence of discreteness on the tests, three parallel tests were conducted for each loading rate, and the parameters were statistically analyzed after the tests. The dynamic impact testing system for lignite is shown in Figure 1b. The dynamic mechanical properties of lignite under different impact velocities were systematically investigated in this study by using the split Hopkinson pressure bar (SHPB) test device (The split Hopkinson pressure bar (SHPB) tests were conducted using a system from Shandong University of Science and Technology, Qingdao, China). Structurally, the testing device consists of core components, including a dynamic loading unit, impact assembly, stress wave transmission system, and data acquisition module. The stress wave transmission system comprised a 3 m long incident bar, a 3 m long transmission bar, and a 1.5 m long energy-absorbing bar. To ensure controlled stress wave generation, the special bullet was used as the loading device, and a waveform shaper was installed in the front end of the incident rod to minimize the dispersion effect during the propagation of the stress wave. During the testing, the high-precision DH8302 laser velocimeter (The high-precision DH8302 laser velocimeter was manufactured by Jiangsu Donghua Test Technology Co., Ltd., Taizhou, China) was employed to monitor the impact velocity in real-time, with a measurement accuracy of up to 10⁻⁵ m/s. Meanwhile, the failure process of the specimen was recorded in real-time using a Vision Research V410L ultra-high-speed camera system(), which features a sampling frequency of 57,000 frames per second. In order to obtain the strain information during the propagation of the stress wave, dynamic strain gauges were equidistantly arranged on the incident and transmission rods, and the data were recorded in real time through a high-speed data acquisition system. Moreover, to facilitate observation of the progressive failure characteristics of the specimen under impact loading, a black and white speckle pattern for DIC analysis was pre-made on the lateral surface of the specimen.

2.3. The Principle of the SHPB Test

In studying the dynamic mechanical properties of materials using the SHPB test, it is necessary to satisfy the one-dimensional stress wave assumption and the uniformity of stress–strain assumption [39]. Based on the one-dimensional stress wave theory in the classic SHPB testing technology, the average stress ${\sigma }_s(t)$, average strain rate $\dot{\epsilon }(t)$, and average strain ${\epsilon }_s(t)$ of the tested material could be obtained from Equation (1) [40]:

$$\left\{\begin{array}{l}{\sigma }_s(t)={\displaystyle \frac{E{A}_0({\epsilon }_1+{\epsilon }_R+{\epsilon }_T)}{2A_s}}\\ \dot{\epsilon }(t)={\displaystyle \frac{C_0\left({\epsilon }_I-{\epsilon }_R-{\epsilon }_T\right)}{L_s}}\\ {\epsilon }_s(t)={\displaystyle \frac{C_0}{L_s}}{\displaystyle {\int }_0^t\left({\epsilon }_I-{\epsilon }_R-{\epsilon }_T\right)}dt\end{array}\right.$$

(1)

where ${\epsilon }_1$, ${\epsilon }_R$, and ${\epsilon }_T$ are the strain of the incident, reflected, and transmitted waves at time $t$, respectively; $A_s$ and $L_s$ are the cross-sectional area and initial length of the test specimen, respectively; $A_0$ and $E$ are the cross-sectional area and the Young’s modulus of the pressure rod, respectively; $C_0$ is the propagation velocity of the one-dimensional stress wave within the rod.

To ensure the accuracy of the experimental data, the stress equilibrium state between the incident and transmitted rods before the specimen fails must be confirmed. Therefore, before conducting the analysis of experimental data, it is necessary to verify the stress equilibrium state of the impact specimen. The equilibrium verification curve is shown in Figure 2, where the sum of the incident stress and the reflected stress is approximately equal to the transmitted stress, indicating that the specimen ends have reached the stress equilibrium condition, and the test results are valid.

3. Composition and Mesoscopic Structure Analysis of Lignite

3.1. Mineral Composition

The mineral composition and content distribution of lignite are presented in Figure 3, with carbon accounting for 75.6% of its content, and the main minerals include quartz, orthoclase, muscovite, kaolinite, and pyrite, with percentages of 7%, 6.2%, 6%, 3.6%, and 1.6%, respectively.

3.2. Micro-Morphology

Figure 4 shows the micro-morphology of lignite samples under different magnifications. Figure 4a shows the internal structural characteristics of lignite under 500 times magnification. The lignite surface exhibits a rough texture. Particles are densely packed with uniform size distribution, and no observable pores or fractures are detected. Figure 4b shows the internal structural characteristics of lignite under 1000 times magnification, where the lignite matrix exhibits a compact skeleton with distinct pits left by particle detachment. The clear cementation lines between particles and localized small-sized pores are observed. These results indicate that lignite possesses a well-integrated micro-morphology with low development of the pores and fractures.

3.3. Meso-Structure Features

The observation results of the thin slice samples of lignite prepared along the parallel bedding direction are presented in Figure 5. At the macro scale, the rock samples exhibit a typical horizontal bedding structure, characterized by uniform radial faces with no discernible local undulations. Microscopic observations reveal the development of multi-level stratification interfaces along the axial direction of the samples, with significant heterogeneity in the composition of matrix minerals between the layers. During the preparation of the thin-sections, the rock samples consistently exhibit distinct cracks between the layers, indicating the low strength and ease of separation of interlayer materials. Overall, it can be concluded that the lignite rock samples display a distinct horizontal bedding structure, and there are significant differences in the strength characteristics of the matrix in different bedding layers. The unique structure of the lignite may have a certain impact on its mechanical response properties.

4. Mechanical Characteristics of Lignite Under Quasi-Static Loading and Dynamic Impact

4.1. Stress–Strain Curve

Figure 6a shows the stress–strain curves of lignite at different loading rates under quasi-static conditions. Although there are significant differences in the strength of rock samples under different loading rates, the stress–strain curves show a high degree of similarity and show an obvious progressive failure process. There is a fracture compaction stage, a linear elastic stage, a plastic yield stage, and a post-peak failure stage in the compression process. After the rock sample reaches the peak strength, the stress–strain curve drops sharply, indicating that the rock sample has obvious brittle failure characteristics under quasi-static loading. When the loading rate increases from 0.001 mm/s to 0.01 mm/s, the mechanical parameters of the rock sample are significantly reduced. The reason for this phenomenon may be that the softening phenomenon caused by the defect development during the loading process of the rock sample and the hardening phenomenon caused by the structural compaction are competing with each other. When the loading rate is 0.001 mm/s, the lignite is slowly compressed, the internal bedding structure is gradually denser, and the interior of the rock sample gradually tends to be complete. At this time, the hardening process of the rock sample dominates. When the loading rate is 0.01 mm/s, the compaction process of rock sample bedding is also accompanied by the significant development of defects, which weakens the strength of the structure to a certain extent. With the increase in loading rate, the strain rate-strengthening effect of rock samples is significantly enhanced, which leads to a further increase in the mechanical parameters of rock samples.

Figure 6b presents the stress–strain curves of lignite under dynamic loading at impact velocities ranging from 4.26 to 14.04 m/s. As the impact velocity increases, the curve characteristics evolve markedly. Notably, the initial elastic stage slope and elastic modulus increase sharply, demonstrating lignite’s strain rate-strengthening effect, where high strain rates delay the microcrack initiation, thereby requiring higher stress levels for deformation. Two distinct stress peaks are observed during the loading process, with the peak stress gradually exhibiting a significant increase with the impact velocity. Upon reaching the peak stress, the curve drops abruptly, accompanied by marked reductions in stress and residual strength.

Through further calculation and analysis of the experimental data, the average mechanical parameters of lignite under different strain rates were obtained, as shown in

Table 1. Statistical analysis of mechanical parameters of lignite under quasi-static loading and dynamic impact conditions.

Number	Loading Rate/Impact Velocity /(m/s)	Strain Rate /s−1	Uniaxial/Dynamic Compressive Strength /MPa	Elastic Modulus /GPa	Peak Strain /%
C-1	1 × 10−6	1 × 10−5	18.49~20.25	0.652~0.687	3.65~3.93
			19.65	0.672	3.78
C-2	1 × 10−5	1 × 10−4	15.66~17.20	0.613~0.687	3.01~3.51
			16.63	0.660	3.26
C-3	1 × 10−4	1 × 10−3	21.40~21.67	0.641~0.665	4.10~4.71
			21.54	0.652	4.50
C-4	1 × 10−3	1 × 10−2	20.66~22.48	0.523~0.532	4.38~4.67
			21.57	0.528	4.57
D-1	4.33	9.90	9.47	25.78	3.01 × 10−2
D-2	5.73	13.23	12.70	38.47	3.58 × 10−2
D-3	7.03	15.10	14.47	53.67	4.73 × 10−2
D-4	8.32	19.33	18.53	57.11	7.29 × 10−2
D-5	9.38	20.73	19.83	60.80	9.09 × 10−2
D-6	11.69	26.23	25.17	75.13	9.73 × 10−2
D-7	13.95	31.60	30.27	82.94	10.90 × 10−2

. Under quasi-static loading conditions, in general, the uniaxial compressive strength of lignite at higher loading rates is significantly higher than that of samples with lower loading rates. At the loading rate of 0.001 mm/s, lignite is slowly compressed, and the internal stratified structure gradually becomes denser, with the rock sample becoming gradually complete, and the hardening process dominating at this time. At the loading rate of 0.01 mm/s, the development of defects within the rock samples is concurrent with the compaction of their stratified structure, resulting in a certain degree of weakening in the structural integrity. When the loading rate is increased further, the strain rate-strengthening effect of the rock samples is significantly enhanced, resulting in a further increase in the mechanical parameters of the rock. Additionally, the elastic modulus of the rock samples exhibits a gradual decrease as the strain rate increases, indicating that the possibility of achieving sufficient compaction in the stratified structure of the samples diminishes with progressively higher loading rates. Under dynamic impact conditions, the mechanical parameters of lignite show a more significant strain-rate sensitivity. The compressive strength exhibits a nonlinear strengthening trend with increasing strain rate, increasing from 9.47 MPa to 30.27 MPa, indicating that dynamic impact significantly enhances the bearing capacity of coal rock by inhibiting the propagation of microcracks. The growth rate of the elastic modulus is greater than the uniaxial compressive strength, increasing from 25.78 MPa to 82.94 MPa; the peak strain increases from 3.01% to 10.9%.

In order to further investigate the differences in the mechanical behavior of lignite under different strain-rate conditions, a comparative analysis of the mechanical parameters of lignite under quasi-static and dynamic impact loading was conducted, resulting in the fitting curves shown in Figure 7.

During the dynamic impact, the mechanical parameters of lignite demonstrated less scatter in linear fitting and exhibited a linearly increasing trend with an increase in strain rate. Under the quasi-static loading, the internal stratification and defects of lignite lead to a certain degree of dispersion in the linear fitting curves. However, the uniaxial strength and peak strain exhibit a slow upward trend with the increase in loading rate, while the elastic modulus shows a decreasing trend. The research results indicate that there are differences in the mechanical properties of lignite under quasi-static and dynamic impact conditions. Under dynamic impact, the mechanical sensitivity of lignite is enhanced, and as the strain rate increases, the strain rate-strengthening effect becomes more pronounced. In contrast, when subjected to quasi-static loading, the mechanical behavior of lignite is less sensitive to the loading rate, and the magnitude of its mechanical property changes is significantly less than under dynamic impact conditions.

4.2. Macroscopic Failure

The macroscopic failure characteristics of lignite are shown in Figure 8. Under quasi-static loading, the failure characteristics of lignite are influenced by bedding plane weakness, presenting the progressive interlayer fracture. Macroscopically, the coal exhibits large-scale delamination with tensile–shear composite fracture morphology. During failure, cracks primarily propagate along bedding planes, inducing interlayer shear slip and tensile splitting, resulting in large fragments with smooth edges. Under low-strain-rate conditions, the propagation speed of cracks is slow, and within the coal, the interconnection between pores and microcracks gradually occurs, resulting in the dissipation of energy through the stable extension of primary cracks, with the residual structure retaining a degree of integrity. With the increase in loading rate, although the failure mode is still predominantly controlled by bedding plane, a small number of secondary cracks may appear locally, and the size of the fragments slightly decreases. Overall, the quasi-static failure process is consistent with the brittleness characteristics of the stress–strain curve.

Under dynamic impact conditions, lignite mainly exhibits fractures along bedding planes at low-impact velocities; however, at high-impact velocities, its destructive characteristics transition to large-scale fragmentation with a randomly distributed orientation of the failure surfaces, indicating that the control role of the weak bedding planes is suppressed by the dynamic inertial effect. With the impact velocity increasing, the degree of coal fragmentation intensifies, generating a large amount of irregular and fine debris, with the size of the fragments being significantly smaller than under quasi-static conditions. This phenomenon is manifested in the decrease in compressive strength and residual strength of the specimens, reflecting the rapid energy release of lignite under instantaneous high-energy input and resulting in large-scale crushing of lignite.

4.3. Energy Evolution

Under external load, the deformation and failure of solid materials essentially involve a series of complex evolutionary processes involving energy input, accumulation, and dissipation. Assuming no heat exchange with the external environment, according to the first law of thermodynamics, the energy input from the external environment is converted into elastic strain energy and dissipated energy. The total energy input upon external unloading $W$ can be expressed as follows [41,42]:

$$W=W_s+W_d$$

(2)

where $W$ is the total input strain energy, kJ/m³; $W_s$ is the elastic strain energy, which is the energy that can be released by the rock during the loading process, kJ/m³; $W_d$ is the dissipated strain energy, with a magnitude equal to the area enclosed by the stress–strain curve and the unloading elastic modulus $E_d$, kJ/m³. Equation (2) can be derived as follows:

$$W={\displaystyle \int \sigma d}\epsilon ={\displaystyle \sum _{i=1}^{n-1}{\displaystyle {\int }_{{\epsilon }_i}^{{\epsilon }_i+1}{\sigma }_i}}d\epsilon ={\displaystyle \sum _{i=1}^{n-1}\frac{{\epsilon }_{i+1}-{\epsilon }_i}{2}}\left({\sigma }_{i+1}+{\sigma }_i\right)$$

(3)

$$W_s={\displaystyle \frac{1}{2}}{\sigma }_i\left({\epsilon }_i-{\epsilon }_d\right)={\displaystyle \frac{{{\sigma }_i}^2}{2E_d}}\approx {\displaystyle \frac{{{\sigma }_i}^2}{2E}}$$

(4)

where ${\epsilon }_i$ is the strain value at ${\sigma }_i$; ${\epsilon }_d$ is the remaining strain when the ${\sigma }_i$ unloads to 0; $E$ is the slope of the straight-line segment of the loading curve.

Figure 9 shows the strain energy evolution of lignite under the quasi-static loading at different loading rates. With increasing loading rates, the energy evolution exhibits progressive damage characteristics, where elastic energy plays a dominant role in the energy distribution. The input energy shows a non-linear increasing trend with the increase in loading rate. With the loading rates moving from 0.001 to 0.01 mm/s, the slope of the input energy curve is relatively flat, indicating that the energy is gradually dissipated through pore compaction and bedding slip. However, when the loading rates reach 0.1 to 1 mm/s, the rate of increase in input energy accelerates significantly, especially in the late stage of strain, revealing the enhanced strain-rate effect of lignite. The elastic energy proportion gradually decreases with the increase in loading rate. With the loading rates from 0.001 to 0.01 mm/s, the elastic-stored energy is dominant, reflecting the elastic deformation capacity of lignite; when the loading rates reach 1 mm/s, the elastic energy proportion decreases, indicating that high strain rates inhibit elastic storage capacity and significantly increase coal-rock brittleness. The dissipated energy and elastic energy exhibit a complementary relationship, with the proportion of dissipated energy gradually increasing with higher loading rates. With the loading rates increasing from 0.001 to 0.01 mm/s, the rate of increase in dissipated energy is relatively slow, corresponding to pore closure and the initiation of microcracks. With the loading rates increasing from 0.1 to 1 mm/s, the onset of dissipated energy occurs earlier, and the rate of increase accelerates, reflecting the increase in the number of crack bifurcations and accompanied by secondary fracturing. Under the quasi-static loading, the dynamic balance of energy allocation in lignite reveals a transition from “elastic energy storage-progressive damage” to “brittle energy dissipation-instantaneous instability”.

Figure 10a–d show the evolution law of the strain energy of lignite under different impact speeds. To reflect the differences in the evolution of strain energy under dynamic impact at different speeds, four representative impact velocities with distinct failure characteristics were selected from seven tested groups by 4.26 m/s, 7.04 m/s, 9.39 m/s, and 14.04 m/s, respectively. The energy evolution of lignite exhibits significant sensitivity to dynamic strain rates. With the impact speed increasing, both the input energy and dissipated energy of the coal samples show non-linear growth. The critical strain of the dissipated energy lags behind the input energy, but their peak values are similar. Within the 4.26~7.04 m/s velocity range, the elastic energy initially increases and then decreases, showing a non-monotonic trend, indicating that the elastic energy storage and crack propagation compete with crack propagation during the initial stress-wave propagation stage. Within the velocity range of 9.39–14.04 m/s, the elastic energy increases gently with strain at the initial low-strain stage. As the strain continues to grow, the elastic energy experiences a slight decline. Subsequently, it resumes an upward trend with a further increase in strain. However, as the strain approaches its maximum, the elastic energy begins to decrease gradually. Although the variation in elastic energy exhibits fluctuations under high-impact velocities, it demonstrates an overall increasing trend with increasing strain. This overall increase suggests enhanced elastic deformation, which results from greater energy absorption at higher impact velocities. However, as strain accumulates, the proportion of elastic energy within the total energy decreases significantly, while dissipated energy gradually becomes dominant. This shift can be attributed to the accelerated deformation and intensified fragmentation of coal under high-velocity impacts, which reduce the storage of elastic strain energy and promote the release of dissipated energy.

Figure 11 shows the evolution of the peak strain energy in lignite under quasi-static and dynamic impact conditions. Under both loading conditions, the peak strain energy increases with the increasing loading rate; however, lignite under the dynamic impact exhibits a more significant strain-rate effect. Furthermore, under both conditions, the peak dissipated energy increases with the increase in loading speed, dominating the energy transformation.

4.4. Strain Field Evolution

The surface deformation field of lignite specimens under quasi-static loading was analyzed using DIC technology, and the strain field results are shown in Figure 12. There are significant differences in the evolution of the principal strain and the progressive failure modes under different loading rates. At the loading rate of 0.001 mm/s, the strain field during the compaction stage already exhibits localized characteristics. However, when the stress reached 100% of the Unconfined Compressive Strength (UCS), the strain concentration area still maintained a dispersed distribution, eventually forming a multi-crack shear failure mode, indicating that the internal bedding of the coal body plays a dominant role in energy distribution regulation under low-speed loading. At the loading rate of 0.01 mm/s, a distinct strain concentration zone appears at the mid-section of the specimen only when the stress level reaches 60% UCS. By the 80% UCS stage, the strain accumulation range expands, but does not become fully connected. The final failure mode exhibits a synergistic interaction between horizontal tensile cracks at the mid-section and lateral shear cracks. At the loading rate of 0.1 mm/s, the maximum principal strain concentrates at the mid-section and propagates axially through the specimen at the 60% UCS stage. By the 80% UCS stage, the strain field bifurcation and spreading led to a combined shear–tensile failure mode, reflecting the competitive mechanism of energy dissipation pathways. At the loading rate of 1 mm/s, the tensile-dominated strains exhibit diffuse distribution on the specimen surface when the stress level reached 10% UCS, with a peak strain of 0.05%. As the stress increases to 60% UCS, the tensile strain concentration zones are formed at the upper, middle, and lower sections, showing clear coalescence trends. By the 80% UCS stage, the local strain concentration areas converge to form an axial tensile crack, resulting in a splitting tensile failure mode.

As shown in Figure 8, the macroscopic failure characteristics of lignite under dynamic impact reveal that, at lower impact velocities, the lignite exhibits fracture failure of layered joints, showing the large-scale fragmentation oppositely. To investigate the influence of the internal horizontal bedding of lignite accounting for the failure mechanism, the lignite sample with 7.81 m/s impact velocity was selected as the research object. The strain evolution of lignite specimens during impact compression was analyzed using DIC technology, as shown in Figure 13.

When the compressive stress wave propagates to the first layered-joint weak plane, a significant compressive strain appears in this area, reaching a peak of 0.03, accompanied by the tensile strain concentration. In addition, the compressive–tensile composite strain field leads to interlayer failure at the joint interface, and the new compressive-strain concentration zone shows on the soft interlayer by the stress-wave propagation. The compressive strain in this region accumulates progressively to 0.03, while the strain values in the rear region remain at a low level, indicating that the matrix material in the soft interlayer exhibits higher compressive toughness, which enables energy absorption through plastic deformation. When the compressive strain of the soft interlayer increases to 0.04, new cracks appear at the lower part of the coal sample. The strain field results show that the reflection effect of the stress wave at the joint interface triggers the concentration of tensile strain, which is the main reason leading to the failure of layered joints.

5. Failure Mechanism of Lignite Under Quasi-Static Loading and Dynamic Impact

From the above analysis, it can be concluded that under dynamic impact, the strain rate effect of lignite is significantly stronger than under quasi-static conditions. Under dynamic impact, lignite undergoes layered failure at low velocities and fragmental failure at elevated velocities, with dissipated energy dominance; the reflection effect of stress waves at the joint plane causes the concentration of tensile strain, which is the main reason leading to the fracturing of layered joints. Under the quasi-static loading, the cracks in lignite mainly propagate along the bedding weak planes, causing inter-layer shear slip and tensile splitting, and energy is gradually dissipated through the stable propagation of the main cracks, with elastic energy dominating; the strain field results show that the failure mode of lignite changes from mixed tensile–shear failure of multiple cracks to single-crack splitting failure. Meanwhile, combined with the analysis of the microstructure of lignite in this paper, it is found that there are obvious horizontal bedding characteristics within the lignite rock samples, and they are prone to interlayer fractures with low strength, which has a certain impact on the failure behavior of lignite rock samples. Therefore, this section comprehensively discusses the failure mechanisms of lignite under quasi-static loading and dynamic impact conditions.

Due to the presence of distinct horizontal bedding characteristics within the lignite rock samples, according to the Mohr–Coulomb yield criterion, static equilibrium, and Hooke’s Law, the uniaxial compressive strength of the bedding matrix ${\sigma }_1^b$ at the two interfaces can be expressed as follows [43,44]:

$${\sigma }_1^b={\displaystyle \frac{{\sigma }_b}{1+{\delta }_b\frac{{\lambda }_1}{\lambda }}}$$

(5)

Equation (5):

$${\lambda }_1=u_b\left({\displaystyle \frac{E_c}{E_b}}-{\displaystyle \frac{{\mathrm{u}}_{\mathrm{c}}}{u_b}}\right)\left[u_b\left({\displaystyle \frac{E_c}{E_b}}+{\displaystyle \frac{u_c}{u_b}}\right)+{\displaystyle \frac{E_c}{E_b}}+1\right]$$

(6)

$$\lambda ={\left({\displaystyle \frac{E_c}{E_b}}+1\right)}^2-{u_b}^2{\left({\displaystyle \frac{E_c}{E_b}}+{\displaystyle \frac{u_c}{u_b}}\right)}^2,{\delta }_b={\displaystyle \frac{1+\sin {\varphi }_b}{1-\sin {\varphi }_b}}$$

(7)

where $E_b$ and $E_c$ are the elastic modulus of bedding matrix and lignite, respectively, GPa; $u_b$ and $u_c$ are the Poisson’s ratio of bedding matrix and lignite, respectively; ${\varphi }_b$ is the internal friction angle of lignite bedding matrix, °; ${\sigma }_b$ is the uniaxial compressive strength of the bedding matrix of lignite far from the interface, which is equivalent to the uniaxial compressive strength of lignite ${\sigma }_c$, MPa.

Consequently, the inferior strength of the bedding matrix leads to $E_b<E_c$, $u_b>u_c$. Through the combination of Equations (5)–(7), the following formulation is established:

$$\mathsf{\Delta }\sigma ={\sigma }_c-{\sigma }_1^b<0$$

(8)

Equation (8) demonstrates that the bedding matrix in lignite exhibits significantly lower uniaxial compressive strength compared to the lignite itself. This mechanical parameter disparity between lignite and the bedding matrix affects the interfacial mechanical properties, thereby further influencing the failure characteristics of lignite. Figure 14 illustrates the failure mechanism of lignite under quasi-static loading. Under the uniaxial compressive stress $\sigma$, the difference in Poisson’s ratio between the bedding matrix and lignite generates interfacial friction directed toward the interface center. For the bedding matrix, this friction manifests as compressive stress; while, for lignite, the frictional force appears as tensile stress, placing the interfacial rock in a triaxial compressive–tensile stress state and reducing its strength [45]. During the initial quasi-static loading, the bedding plane is first subjected to tensile failure, while frictional forces trigger interlayer shear slip and tensile splitting. Subsequently, the internal cracks initiate and propagate along the weak bedding planes, forming a tensile–shear composite fracture pattern. As the frictional effect diminishes progressively with increasing distance from the interface, the failure mode transitions from the multi-crack tensile–shear hybrid fractures to single-crack splitting, macroscopically observed as large-scale layered spalling.

Under the condition of normal incidence of stress waves, when propagating from one material $A$ to material $B$, if there is a difference in the wave impedances of the two materials, wave energy will undergo transmission and reflection at the interface, with the refractive effect being negligible. In this phenomenon, the amplitude of stress of the transmitted and reflected waves can be quantitatively characterized by theoretical equation [46], with the mathematical expression given as follows:

$$\begin{array}{l}{\sigma }_R=F{\sigma }_1\\ {\sigma }_T=T{\sigma }_1\end{array}$$

(9)

where ${\sigma }_1$, ${\sigma }_{\mathrm{R}}$, and ${\sigma }_{\mathrm{T}}$ are the incident stress wave, reflected stress wave, and transmitted stress waves, respectively; $F$ and $T$ are the reflectance coefficient and transmittance coefficient, respectively, which can be derived from Equation (9) as follows:

$$\begin{array}{l}F=(1-n)/(1+n)\\ T=2/(1+n)\\ n={(\rho c)}_A/{(\rho c)}_B\end{array}$$

(10)

where $n$ is the wave impedance ratio; $\rho$ is the material density; $c$ is the wave velocity in the material; $A$ and $B$ are the materials $A$ and materials $B$, respectively.

Figure 15 illustrates the failure mechanism of lignite under dynamic impact. The prominent horizontal bedding features within lignite enable its structure to be characterized as a binary system composed of alternating thin low-wave-impedance bedding planes and thick high-wave-impedance bedrock. As derived from Equation (10), during dynamic impact, stress waves propagating through lignite undergo transitions from high-wave-impedance bedrock (Material $A$) to low-wave-impedance bedding planes (Material $B$). At this moment, $n>1$, $F$ < 0, resulting in the reflection wave and incident wave having opposite signs, and a reflection unloading phenomenon occurs, with the amplitude of the transmitted wave being less than that of the incident wave. In the initial stage of the dynamic impact, the bedding planes are initially damaged. Subsequently, the stress waves rapidly reflect and transmit across the bedding interfaces, causing the primary cracks to penetrate the bedding planes and secondary cracks to branch out radially. Throughout this process, the reflection effect induces local tensile stress concentrations at the bedding interfaces, resulting in interlayer fracturing failure within the lignite. The failure mechanisms of lignite under the two strain rates are significantly different. Under the dynamic impact conditions, due to the instantaneous nature of energy input and the reflection of stress waves, multiple cracks develop and expand within the coal and rock, leading to the fragmentation failure of lignite. Under the quasi-static loading, the failure of lignite is primarily governed by the Poisson’s ratio disparity between bedding planes, manifesting as progressive splitting dominated by weak bedding interfaces.

6. Conclusions

In order to study the mechanical failure behavior and mechanism of lignite under quasi-static and dynamic loading, the mineral composition and meso-structure of lignite were analyzed in this paper. Uniaxial compression tests with different quasi-static loading rates and dynamic compression tests with different impact velocities were carried out, and then the failure mechanism of lignite under quasi-static and dynamic impact was illustrated. This study provides a theoretical basis for the stability analysis of lignite slopes in open-pit mines. The key conclusions are as follows:

(1)

The mineral composition analysis shows that the main minerals in lignite are quartz, orthoclase, muscovite, kaolinite, and pyrite. The lignite possesses a relatively intact microstructure with low porosity and fracture development, though localized small-sized pores are observed. Additionally, distinct horizontal bedding structures are identified within the lignite, with significant differences in strength characteristics among different bedding matrices.

(2)

In terms of mechanical behavior, lignite shows significant strain-rate sensitivity under dynamic loading, with strengthening effects escalating at higher rates, and the failure mode transitions from stratified fractures at low velocities to fine-grained fragmentation at high velocities. In contrast, quasi-static responses exhibit lower rate dependency, marked by tensile–shear delamination and slow crack propagation along bedding planes, generating large fragments.

(3)

Under the quasi-static loading, the surface of lignite is dominated by tensile strain and shows a significant trend of penetration with the increase in loading speed. Under the dynamic impact, the lignite forms a compressive–tensile composite strain field at the weak surface of the bedding, resulting in interlayer fracture failure of the lignite.

(4)

Under the quasi-static loading, the energy evolution analysis reveals that lignite exhibits progressive damage characteristics with the elastic energy dominating the energy allocation. The failure mode transitions from tensile–shear hybrid failure with multiple cracks to single-crack splitting failure. Under the dynamic impact conditions, the proportion of elastic energy progressively diminishes while the dissipative energy becomes predominant.

(5)

The horizontal bedding structure of lignite leads to different failure mechanisms under quasi-static loading and dynamic impact. Under the quasi-static loading, the interfacial friction arising from the different Poisson’s ratios between the bedding matrix and lignite constituents governing the progressive splitting failure dominated by bedding plane weakness. The layered failure of lignite under the dynamic impact is fundamentally attributed to the reflection phenomena of stress waves at bedding interfaces, which arise from the wave impedance disparity between the bedding matrix and coal constituents. Therefore, to ensure the stability of the lignite slope in the open-pit mine, the slope bedding should be specifically strengthened to prevent slope instability resulting from bedding plane failure.