Experimental and Numerical Study of Damage Evolution and Fracture Characteristics of Three-Layer Composite Rocks Under Dynamic Loading

Abstract

In order to study the damage evolution and fracture characteristics of rock with different composite modes in three layers under dynamic loading, rock specimens with different composite modes were made by using three materials: sandstone, marble and granite. The dynamic fracture impact test was carried out by using the Hopkinson pressure bar impact loading system, the voltage signal on the Hopkinson pressure bar was calculated and processed, and the crack propagation mode of the specimen was captured by using a high-speed camera, and the stress wave characteristics, stress time–history relationship and energy change characteristics of rocks with different composite modes were studied. At the same time, combined with Distinct Lattice Spring Model numerical simulation, the fracture process of the specimen was inverted, and the changes in stress intensity factor, stress change and load–displacement change in monitoring point were analyzed to compare the dynamic fracture behavior differences between different composite rocks. The results show that the dynamic fracture process captured by the high-speed camera has a good fit with the crack propagation process simulated by numerical simulation. When marble is used as the upper material, the energy transmittance is larger, and the transmission energy ratio between sandstone and granite is basically the same due to the large difference in hardness. When the comprehensive hardness of the specimen is the same, the smaller the hardness of the material at the cracking position, the faster the cracking will be, and the smaller the hardness of the second layer of the specimen at the cracking position, the faster the cracking speed of the specimen. In terms of dynamic fracture toughness, for specimens with little difference in hardness, when the impact end material is sandstone, the dynamic fracture extreme value of the specimen is lower, and when the sandstone material is used as the impact end material, it is more likely to crack. When the first layer of material is the same, the dynamic fracture toughness of the specimen with less hardness of the second layer of material is smaller, and the easier the crack development is.

1. Introduction

The rapid advancement of economic development has led to an expansion in the scale of geotechnical engineering works covering both surface and subsurface projects, resulting in increasingly complex and varied rock mechanics challenges [1]. These engineering issues are closely related to rock instability under impact loads and the propagation characteristics of stress waves in flawed rocks, which are pertinent to activities such as shaft excavation, mining operations, engineering blasting, dam foundation construction, and refuge excavation [2]. As a natural material susceptible to temperature fluctuations, weathering, tectonic movements, and other factors, rock formations inherently possess certain natural defects [3,4]. These defects can manifest as cracks, laminations, joints, and other irregularities, contributing to the inhomogeneity and anisotropy of the rock material [5]. Consequently, this leads to complex deformation behaviors and mechanisms of failure. Failure to accurately identify the defects in the mechanical properties of rocks may hinder efforts to prevent and manage rock-related disasters, complicating the assurance of long-term stability in underground engineering structures [6,7,8,9,10,11,12]. Thus, it is crucial to investigate the mechanical properties and characteristics of rocks with bedding defects. Current research works predominantly focus on the overall damage mechanisms of rock and the damage mechanisms associated with pre-existing fissures within the rock body. However, there is a notable lack of studies addressing the damage mechanisms of rock materials under various composite conditions, particularly in multi-layered contexts. Therefore, efforts to study the dynamic mechanical properties of three-layer composite rocks under dynamic loading conditions hold an immense value and relevance for both academic and engineering applications.

The research works on the static mechanical properties of composite rock materials were conducted by some scholars. Ding [13] investigated the modal transformation of stress waves at the interfaces of layered composite rocks. This process was reproduced through finite element analysis, and the progression of crack development was also examined. Regarding the sandstones and mudstones from deep dense reservoirs, layered composite rocks were created using similar material modeling tests. Uniaxial compression tests were performed, supplemented by an acoustic emission (AE) system and a digital image correlation (DIC) system, to determine the strength, elastic modulus, and other physical-mechanical parameters of the layered composite rocks. Xu Ke [14] studied the influence of fracture position on the mechanical properties of layered composite rocks under different confining pressures. A numerical model of composite rock samples with prefabricated single fractures was established using the particle flow software PFC2D, and the stress–strain, volume change, and related stress thresholds of the composite rock samples were analyzed. The study found that the increase in confining pressure changes the dominant factor of rock sample failure from fracture position to confining pressure, and the fracture in hard rock weakens the rock sample strength the least. Dong [15] carried out uniaxial compression tests on two varieties of rock-like specimens with differing layer counts. The evolution of the apparent strain field in these specimens was analyzed using digital image correlation (DIC). By applying energy dissipation theory and a damage evolution model, acoustic emission technology was employed to investigate the damage evolution process of the specimens. Park et al. [16] investigated gypsum-like composite rocks with three closed fractures via uniaxial compression, noting that wing (tensile) and secondary (shear) cracks initiate from fracture tips, with their initiation stress increasing with fracture inclination, spacing, and overlap rate, and coalescence modes linked to geometric parameters. Sagong et al. [17] tested rock-like composites with 3 and 16 fractures, finding crack types consistent with fewer-fracture specimens; multi-fracture specimens showed lower crack initiation and coalescence stress, with coalescence mostly in a “columnar” mode dependent on geometric parameters.

The research works on the dynamic mechanical properties of composite rock materials were conducted by some scholars. Li Jin [18] transformed raw materials from deep rock formations into various types of layered composite rock specimens in consideration of the acidic environment and the effects of different angles at the interface layers, leading to experimental investigations into the mechanical properties and damage mechanisms of these layered composite rocks. Zhao Guoyan [19] employed a split Hopkinson pressure bar (SHPB) to perform impact tests on composite sandstone featuring non-penetrating fractures of varying counts and depths. This research established correlations between dynamic peak stress, dynamic modulus of elasticity, damage modes, fractal dimensions of the damaged specimens, energy dissipated per unit volume, and the energy absorption rate in relation to the fissure characteristics. Additionally, Li Dejian [20] employed the finite element method-discrete element method (FDEM) for simulating Brazilian disc splitting experiments on composite coal rock specimens with beddings. The study identified four distinct splitting damage modes that emerged with increasing angles of the laminations and analyzed the tensile strength and energy dissipation values. Guéry et al. [21] established a micromechanical model of three-phase composite geomaterials composed of clay matrix, calcite and quartz, considering the non-associated dilatant elastoplasticity of clay matrix and elastic damage of calcite (including microcrack closure effect). Through nonlinear homogenization, they revealed the regulatory mechanism of mechanical properties of each component on the dynamic response of composite materials.Bikong et al. [22] proposed a micro-macro model of clay rock, pointing out that subcritical propagation of anisotropic microcracks in clay matrix is the key mechanism for its time-dependent deformation. Using two-step homogenization and considering microcrack interaction and mineral inclusions, they found that mineral composition and microcrack distribution significantly affect the dynamic creep characteristics of composite rocks.

At present, most existing research works focus on the overall rock failure mechanism and the failure mechanism of pre-fissured rock masses in defective rocks; however, there are relatively few studies on the failure mechanism of rock materials under different multi-layer composite modes. Therefore, the basic and applied research on the dynamic mechanical properties of three-layer composite rocks under dynamic loading holds significant research value and engineering significance. In this work, a Hopkinson pressure bar impact loading system was operated to conduct dynamic fracture impact tests on three-layer composite rock specimens. A high-speed camera was used to capture the crack propagation patterns of the specimens. The research aims to investigate the characteristics of stress waves, the relationship between stress and time, and the energy variations in the rock under various composite modes. Through the numerical simulation using DLSM, efforts were made to invert the fracture process of the specimens and analyze the variations in the stress intensity factor, the stress changes at monitoring points, and the load–displacement changes. This further facilitated a comparison of the difference in dynamic fracture behavior among different composite rocks, and a study of the damage evolution and fracture characteristics of three layers of rocks with different composite modes under dynamic loading.

2. Test Program and Fabrication of Specimens

2.1. Test Programand Apparatus

A split Hopkinson pressure bar (SHPB) system (Figure 1) was adopted, which has widely recognized reliability in dynamic loading tests. The system consists of four parts: a loading drive system, a pressure bar system, a data acquisition system, and an image acquisition system. The functions and parameters of each part are as follows:

(1)

Loading drive system: including launch chamber, high-pressure gas chamber, pressure control valve, high-pressure nitrogen cylinder, etc.

(2)

Pressure bar system: composed of impact bar, incident bar, transmission bar, absorption device, etc.

(3)

Data acquisition system: composed of strain gauges, junction box, ultra-dynamic strain gauge, oscilloscope, computer, etc.

(4)

Image acquisition system: high-speed camera, supplementary lighting device, etc.

Figure 1. SHPB test system.

Figure 1. SHPB test system.

The elastic bars in the pressure bar system are made of high-strength alloy steel. Taking the bar made of 40rC alloy steel as an example, its elastic limit can reach 800 MPa, and under an impact pressure of 800 MPa, an impact velocity of 40 m/s can be achieved. To ensure the smooth transmission of stress pulses at the contact surfaces, the two end faces of the elastic bars were polished to make the contact surfaces flat, smooth, and well-contacted. The bar ends are shown in Figure 1. To meet the requirement of fixing the pressure bar and replacing elastic bars of different diameters and materials at any time, a support frame as shown in Figure 1 is mostly used. Figure 1 shows the high-speed camera for recording the test process, with a maximum frame rate of 100,000 frames per second. Higher resolution requires higher lighting conditions. Due to the limited power of the supplementary lighting device, in this study, when using a professional high-speed camera, the image resolution was set to VGA (896 × 848) and the shooting speed was 100,000 frames per second.

To explore the dynamic fracture characteristics of the three-layer composite specimen, six unique experimental programs were prepared. Figure 2 presents a physical depiction of the three-layer composite rock specimen, whereas Figure 3 gives a schematic representation of the same. For example, the specimen illustrated in Figure 2c is referred to as the sandstone-marble-granite (SDH) which consists of an upper layer of sandstone, a middle layer of marble, and a lower layer of granite. This configuration incorporates various rock materials in each layer, with the two layers adhered together using epoxy resin. The beddings are aligned at an angle of 0°, with the lower beddings spaced 6 mm from the tip of cut seam, and the space between the two layers also measuring 6 mm. The corresponding schematic for this physical specimen is depicted in Figure 3c, where the diagonal area represents sandstone, the square area denotes marble, and the grid area denotes marble, while the white area denotes granite.

Each specimen was subjected to loading in the direction of the incident bar impacting the specimen while in a clamped state, with the contact point located at the top of the half disk. Given that the transmissive bar end of the SHPB system utilized in the experiment is a conventional plane, it would not be feasible to directly apply loading via three-point bending. Therefore, a specially designed three-point bending support was affixed to the end of the transmissive bar to accommodate the loading requirements of the Notched Semi-Circle Bending (NSCB) specimen.

2.2. Fabrication of Specimens

Following the extraction of the cylindrical core from the rock, the core was shaped into a standard disc specimen in accordance with the dimensions recommended by the International Society for Rock Mechanics for disc experiments, specifically maintaining a diameter-to-thickness ratio of 2:1 [23]. The dimensions of the disc specimen measured 50 mm in diameter and 25 mm in thickness. Subsequently, the half-disc specimen was prepared with pre-existing cracks and transformed into the NSCB specimen, as illustrated in Figure 1. Each half-disc specimen was then cut at the bottom center. The bottom center of each half-disc was processed through cutting, with a prefabricated crack of 4 mm in depth located along the centerline of the half-disc, forming a reasonable ratio with the specimen’s diameter and thickness. This configuration not only ensures that the crack tip can effectively initiate the propagation of the main crack but also avoids excessive reduction in the overall strength of the specimen due to an overly deep cut. The crack had a width of 0.3 mm, and its tip was sharpened using a diamond wire saw, ensuring that the width of the crack tip was precisely controlled to 0.1 mm. The fundamental physico-mechanical parameters of the three types of rock materials are set out in

Table 1. Physical and mechanical parameters of test materials.

Rock Material	Density (kg/m3)	Poisson’s Ratio	Elastic Modulus (GPa)	Protodyakonov’s Hardness	UCS (MPa)
Marble	2500	0.3	3.0	8	90.5
Sandstone	2600	0.24	4.6	6	62.3
Granite	3000	0.2	18.4	12	150.1

.

3. Test Results and Analysis

3.1. Analysis of Specimen Damage Process

Figure 4a–f illustrate the dynamic fracture expansion graphs of six groups of three-layer composite specimens captured by a high-speed camera. The fracture processes of these groups exhibit remarkable similarity; specifically, cracks initiate at the tip of cut seam and expand vertically upward. The cracks display only minor lateral displacements, influenced by variations in hardness across the laminar surfaces, which cause changes in the direction of crack propagation before reverting to the original direction for continued expansion. The three-layer composite specimens exhibit two modes of damage: crack propagation and localized extrusion. Additionally, both primary and secondary cracks emerge at the pre-existing cracks and at the interfaces of the interlayer structure. Figure 4a depicts the marble-sandstone-granite composite specimen (DSH), while Figure 4f presents the granite-sandstone-marble composite specimen (HSD). A notable similarity between these specimens is the presence of sandstone as the intermediate layer. However, the materials at the incident and exit ends differ, with one specimen featuring marble and the other granite. A comparative analysis of the damage forms reveals variations from the bottom to the top of the specimens. Within the three layers, the width of the cracks varies from the initiation point to the crack tip, with both sandstone specimens being susceptible to slight deviations in crack direction at the material interface. This phenomenon is attributed to the differing hardness of the two rock types, resulting in a minor degree of stress concentration at the bedding surface.

A comparison of the damage duration of the specimens reveals that the total duration for crack propagation is greater in HSD than in DSH. Furthermore, the initiation of cracks occurs earlier in HSD compared to DSH. This can be attributed to the presence of the same weak surface of bedding in both specimens. At this stage, the propagation of cracks is influenced by the material properties beyond the weak surface of bedding. The overall extent of material damage can be assessed by examining the destruction of the upper and lower layers, which also experiences an additional stress concentration effect due to material hardness, ranked in a descending order: Granite > Marble > Sandstone. Consequently, the greater hardness of the HSD bedding surface results in a more pronounced offset damage effect. This principle is similarly applicable to specimens with identical interlayer materials, such as HDS and SDH, as well as SHD and DHS. When the interlayer material remains constant, a higher hardness at the incident end correlates with an increased duration of crack extension and an earlier onset of crack initiation.

3.2. Stress Wave Characterization

Figure 5 and Figure 6 illustrate the stress waveform curves of the three-layer composite specimens. The incident waveforms for the six composite specimens exhibit a high degree of similarity. Notably, the DSH and DHS specimens demonstrate a slower response during the initial phase of the descending section, while the remaining specimens show comparable behavior in this segment. The ascending sections of all six specimens are also largely consistent. By observing the transmitted waveforms, the SDH, DSH, and DHS specimens show resembling waveforms, characterized by smooth sine curves that align closely, with their peaks nearly equating. In contrast, the transmitted wave forms of the other three specimens exhibit greater irregularity, featuring more fluctuations and higher peaks compared to the first three specimens. Regarding the transmitted wave forms, the peak value of the SDH specimen is lower than that of the DSH specimen. When marble is utilized as the impacted end material for the composite specimen, it results in improved wave impedance matching, generating a greater number of transmitted waves [24]. Similarly, the peak value of the HSD specimen is less than that of the SHD specimen, indicating that the wave impedance effect of sandstone surpasses that of granite. Consequently, the wave impedance matching of the composite specimen with marble is superior to that of the specimen using granite as the impacted end material. This leads to the conclusion that among the three materials, marble exhibits the highest wave impedance effect, while granite has the lowest, implying that the DHS specimen has a larger peak value than the HDS specimen. From the perspective of inherent material properties, differences in elastic modulus also contribute to the aforementioned variations in stress wave characteristics. As shown in Table 1, the elastic moduli of the three rock types follow the order: granite > sandstone > marble. The elastic modulus directly affects the propagation velocity of stress waves in materials, while wave impedance, a key indicator of stress wave transmission efficiency, has a matching degree that depends on wave velocity differences between materials. The ascending segments of the incident wave curves for the six specimen groups are nearly overlapping, indicating consistent initial transmission laws of stress waves at the interface between the pressure bar and the specimen during the initial impact stage. However, the early descending segments of DSH and DHS are gentler, reflecting that the lower elastic modulus of marble results in a more gradual attenuation rate of stress waves.

3.3. Analysis of Stress Characteristic Curve and Peak Intensity Change

Figure 7 illustrates the time–history curve of the stress intensity factor for the three-layer composite specimen. The overall trend of the stress intensity factor is consistent across the six specimens, beginning at a value of zero. Initially, the curve fluctuates around this zero value before gradually increasing over time, reaching a peak after approx. 100 μs of fluctuation, followed by a decline back to zero after a certain period of time. Among the various specimen combinations, the SDH specimen demonstrates the earliest rise and peak, indicating that it achieves fracture toughness first. This phenomenon can be attributed to the order of material impact on the specimen: sandstone, marble, and granite, arranged from lowest to highest hardness (hardness: sandstone < marble < granite). The SHD specimen follows closely behind the SDH specimen in the ascending phase, with the curves of SDH and SHD positioned to the left of the curves of the other specimens, suggesting that, when the overall hardness of the specimens is equivalent, a lower hardness at the crack location results in faster cracking. Furthermore, the SDH specimen is positioned to the left of the SHD curve, indicating that when both the overall hardness and crack location are the same, a lower hardness in the second layer of the specimen leads to quicker cracking initiation. This trend is also observed in the other groups of specimens.

3.4. Analysis of Dynamic Fracture Toughness

Table 2. Dynamic fracture toughness of three-layer composite laminates.

Test Specimen	Dynamic Fracture Toughness/MPa·m1/2
SDH	0.67605
DSH	0.92144
DHS	0.83249
HDS	0.77472
SHD	0.78014
HSD	0.69563

presents the dynamic fracture toughness values of the specimens, which are derived from the curve illustrated in Figure 5 and plotted as the dynamic fracture toughness curve for the three-layer composite specimens in Figure 8. A comparison of the data reveals that the dynamic fracture toughness of the SDH and SHD specimens is lower. This suggestis that when the impact section material is sandstone, the dynamic fracture extremum of the specimen decreases. This indicates that sandstone materials are more prone to fracturing when utilized as impact section materials, particularly in respect of hardness. When comparing the SDH and SHD specimens, both of which feature sandstone as the impact end material, it is noted that the dynamic impact toughness of the SDH specimen is lower than that of the SHD specimen. The hardness of the two-layer materials follows the order: SDH < SHD. When the first layer of material remains constant, a decrease in the hardness of the second layer correlates with reduced dynamic fracture toughness, facilitating crack propagation. This trend is also observed in the remaining groups of combined specimens. However, the data for the HSD specimen deviates from this pattern. According to the aforementioned pattern, the dynamic fracture toughness of the HSD specimen should rank second. However, the significant hardness disparity between granite and sandstone leads to increased susceptibility to damage at the interface of these materials. Consequently, the specimens with substantial hardness differences are not covered by the aforementioned pattern.

3.5. Characterization of Energy Evolution in the Impact Process

The propagation and energy dissipation characteristics of stress waves in rocks under dynamic impact loading are crucial for revealing the dynamic response mechanisms of composite rocks. According to the energy transmission law when stress waves pass through rock joints, the energy during impact can be divided into incident energy E_I, reflected energy E_R, transmitted energy E_T, and dissipated energy E_D, which satisfy the energy conservation relationship:

E_I = E_R + E_T + E_D

(1)

For three-layer composite rocks, different material combinations and bedding interface properties significantly affect the efficiency of energy transmission and dissipation.

Table 3. Energy-to-energy ratio of composite specimen.

Specimen Type		Incident Energy EI/J	Reflected Energy ER/J	Transmitted Energy ET/J	Dissipated Energy ED/J	ER/EI	ET/EI	ED/EI
Three-layer composite	SDH	30.79	6.75	8.99	15.04	21.93%	29.19%	48.86%
	DSH	40.08	9.90	16.13	14.04	24.71%	40.23%	35.04%
	SHD	31.03	7.23	8.58	15.22	23.30%	27.64%	49.04%
	HSD	33.04	7.73	9.36	15.94	23.40%	28.35%	48.24%
	DHS	36.57	9.06	12.65	14.86	24.77%	34.58%	40.63%
	HDS	31.12	6.97	8.86	15.29	22.39%	28.47%	49.13%

presents the energy parameters of six three-layer composite specimens (SDH, DSH, SHD, HSD, DHS, HDS) during impact, including specific values of incident energy, reflected energy, transmitted energy, and dissipated energy, as well as their proportions relative to the incident energy.

Figure 9 illustrates the energy ratio curves for the three-layer composite specimens. Firstly, regarding the reflected energy ratio, all specimens maintain a relatively consistent level, due to the fact that the six specimens are constructed from the same three materials, with variations only in the arrangement of the upper, middle, and lower layers. As a result, there are only minor differences in the reflected energy ratio. In terms of the transmittance energy ratio, the specimen composed of marble-sandstone-granite (DSH) exhibits a higher value compared to the sandstone-marble-granite (SDH), sandstone-granite-marble (SHD), and granite-sandstone-marble (HSD) specimens. Notably, there is no significant difference between the sandstone-granite-marble (SHD) and granite-sandstone-marble (HSD) specimens. Furthermore, the marble-granite-sandstone (DHS) specimen demonstrates a greater transmittance than the granite-marble-sandstone (HDS) specimen. This indicates that when marble is used as the impacting material, the transmittance energy is enhanced. The transmittance energy ratios for sandstone and granite are largely similar due to their comparable hardness. Regarding the dissipated energy ratio, the sandstone-marble-granite (SDH) specimen surpasses the marble-sandstone-granite (DSH) specimen, while no significant difference is observed between the sandstone-granite-marble (SHD) and granite-sandstone-marble (HSD) specimens. Additionally, the granite-marble-sandstone (HDS) specimen exhibits a higher dissipated energy ratio than the marble-granite-sandstone (DHS) specimen.

4. DLSM Numerical Simulation Analysis of Stress Wave Transmission and Stress Damage in Three-Layer Composite Rock Materials

4.1. Modeling

DLSM numerical simulation reproduces the discontinuous failure characteristics of rock materials through the particle discrete element method, while incorporating the finite element concept to handle stress wave propagation problems. The model of the three-layer composite specimen is illustrated in Figure 10. Initially, a straight-cut groove half-disc model identical to the overall dimensions of the test specimen was constructed [25]. The model measures a diameter of 50 mm and a thickness of 25 mm, with the diameter of the spherical particles set at 25 mm. The prefabricated cut seam measures 4 mm in length and 0.5 mm in width. To simulate the beddings present in the test specimen, a layer of spherical particles with varying parameters of the rock matrix was set, with a thickness of 0.5 mm. The parameters of the rocks were selected from the data measured in the actual experiment, as shown in Table 1. Parameters such as particle stiffness and bond strength refer to the conventional values used in discrete element simulations of rock-like materials.

The boundary conditions of the model are depicted in Figure 11, illustrating the clamped and strained conditions of the specimen on the Hopkinson bar during testing. Since the transmissive bar was not secured when the incident bar struck the specimen, the boundary conditions for the left and right supports were established as velocity loads with a value of 0. The boundary conditions at the loading point correspond to the dynamic load experienced by the specimen due to the impact of the incident bar, which was measured using the velocity acquisition instrument of the Hopkinson bar during the test. Based on the impact velocity recorded by the Hopkinson rod velocity acquisition instrument, the boundary condition at the loading point is also defined as a velocity load. To standardize the simulated dynamic loading conditions, all models with varying bedding spacing are set to 6000 mm/s, with reference to the average impact velocity observed in the test.

To examine the impact of varying layer spacing on the stress and energy evolution characteristics of the rock matrix situated between two beddings, five monitoring points were established within this interval. The relevant stress and strain parameters for these monitoring points were derived from numerical simulations [26]. It is important to note that the positions of the monitoring points remain consistent across different layer spacing models, with the coordinates for each monitoring point given in

Table 4. Coordinates of monitoring points.

Coordinate	X	Y	Z
Monitoring Point 1	5	13	12.5
Monitoring Point 2	15	13	12.5
Monitoring Point 3	25	13	12.5
Monitoring Point 4	35	13	12.5
Monitoring Point 5	45	13	12.5

.

4.2. Dynamic Fracture Process Analysis

Figure 12 illustrates the fracture simulation process of the three-layer composite specimen. Initially, a comparative analysis of the test and simulation of the fracture process reveals that the sandstone-marble-granite (SDH) specimen exhibits a relatively similar crack propagation pattern in both scenarios. The crack initiates at the tip of cut seam and extends vertically upward. Upon reaching the bedding, the crack continues to propagate along the bedding in an upward direction. After a specific distance, the crack expands once more in the direction vertical to the bedding until it reaches the top of the specimen. A notable distinction is that the crack in the simulated specimen appears smoother, with fewer “jagged teeth” along its edge. In contrast, the edge of the crack in the test specimen is rougher and features more counts of jagged teeth. This discrepancy arises from the heterogeneous nature of the actual test specimen, whereas the simulated specimen is composed of homogeneous material, which does not produce jagged cracks during the tearing process of spherical particles. In comparison to the simulated results, the test and simulation results for the marble-sandstone-granite (DSH) specimen also demonstrate a high degree of similarity. In this case, the cracks do not initiate from the tip of cut seam, but rather begin at the lower end of the bedding and propagate upward along the bedding, ultimately penetrating perpendicularly near the upper end of the bedding and expanding to the top of the specimen. The difference between the two lies in the later stages of crack development. The test results indicate that the cracks initially expand in a straight line before abruptly bending upward, while the simulated results show a bending upward of propagation. Significant discrepancies were found when comparing the test and simulation results of sandstone-granite-marble (SHD) specimens. Firstly, in the experimental results, the cracks did not propagate from the tip of cut seam; instead, they initiated damage directly from the lower end of the bedding. In contrast, the simulation results indicated that cracking initiated at the tip of cut seam. Secondly, there is a notable difference in the location of the cracks that penetrate the upper end of the bedding. The experimental results showed penetration occurring from the centerline of the specimen, whereas the simulation results indicated penetration from a position closer to the upper end of the bedding.

4.3. Analysis of Crack Propagation Displacement Fitting Curve

Figure 13 illustrates the displacement load curve resulting from the simulation of the three-layer composite specimen. It is evident that the slope of the ascending section of the curve remains consistent when the upper material is identical. Notably, the steepest slope is observed when the upper material is granite, while the shallowest slope is observed with sandstone as the upper material. Regarding the peak load, there is no significant distinction between the SDH and SHD configuration. Specifically, when the upper material is sandstone, the slope of the ascending section remains unchanged. Although the peak load does not exhibit considerable variation with changes in the middle- and lower-layer materials, the specimen with the highest peak load is identified as HSD, followed by HDS (which is slightly lower), and DSH which is slightly higher than DHS. This outcome contradicts the earlier assumptions regarding the behavior of the previous two specimen groups, where it was anticipated that the peak load would be greater with sandstone as the middle layer compared to marble or granite.

This deviation is mainly related to the synergistic effect of the mechanical properties of the upper layer material and the hardness difference between layers. On one hand, since the elastic modulus and hardness of granite are significantly higher than those of sandstone and marble, when granite is used as the upper layer material, its high strength can significantly enhance the overall stiffness of the specimen, resulting in generally higher load peaks for HSD and HDS. This “bearing-dominant effect” of the upper layer material outweighs the influence of the middle layer material properties on the load peak. On the other hand, the middle layer of HSD is sandstone, with granite and marble as the upper and lower layers, respectively, and the interlayer hardness difference is relatively moderate, leading to weak stress concentration effect and difficulty in early failure of the bedding interface, thus supporting a higher load peak. In contrast, the upper layers of DSH and DHS are marble, whose hardness is lower than that of granite, resulting in lower overall stiffness. Even if the middle layer is sandstone, it is difficult to offset the impact of insufficient strength of the upper layer material, leading to their load peaks being lower than that of HSD. In addition, although there is a hardness difference between granite and sandstone in HSD, the high strength of the upper granite can inhibit early interface instability, further enhancing its bearing capacity, which ultimately leads to the deviation from the expected law.

4.4. Analysis of Stress–Strain Characteristics at Monitoring Points

Figure 14 presents the stress and strain curves obtained from numerical simulations at monitoring point 3. Monitoring points 1 and 5 are positioned symmetrically relative to the midline of cut seam, resulting in nearly equal forces on both sides. Consequently, the stress and strain curves for these points are largely similar. The average stress and strain values for points 1 and 5 are calculated to derive their respective curves, and a similar approach is applied to obtain the stress and strain curves for points 2 and 4. The stress and strain time–history curves for points 2 and 4 are derived using the same method [27].

Figure 14a illustrates the stress and strain curves recorded at point 3, where the initial layer consists of sandstone in the simulation. The stress-time curve begins to increase gradually around 12 μs, indicating that the stress wave has penetrated through layer II and is accumulating energy within the rock matrix situated between the two layers. At approx. 25 μs, the stress curve experiences a rapid ascent, with the combined curves of the two layers exhibiting varying rates of ascending. Notably, the curve corresponding to a 6-mm spacing between the layers shows the least steep rise, suggesting that the pore space between the layers is being densified at a faster rate. Once the layers reach their densification limit, the underlying rock matrix begins to experience stress, resulting in an increase in pressure at the monitoring point. As the bedding attains the compaction threshold, the stress on the rock matrix below escalates swiftly. The curves for the specimens with two different material combinations reached their respective stress peaks at 43 μs and 45 μs, measuring 18.20 MPa and 19.80 MPa, respectively, with a change ratio of 8.79% as observed in relation to the order of the marble-granite combination.

The strain-time curve depicted in the figure is categorized into three stages. In the initial stage, spanning from 0 to 25 μs, the impact load begins to exert force on the tip of the specimen, primarily affecting the densification of bedding II. During this period, the stress conduction is relatively poor, resulting in a gradual increase in the strain curve. As the bedding is compacted to the strain limit, the curve transitions into the second phase. In the course of simulation, once each section of the specimen attains the compaction limit, stress conduction becomes more uniform, leading to a rapid increase in strain at monitoring point 3. As the spacing between the beddings widens, bedding II approaches the end of the impact load, allowing for a more rapid compaction due to the dynamic load. This process drives elastic strain into the rock matrix situated between the two beddings, causing the upward slope of the curve in phase II to rise in correlation with the increased spacing of the bedding. The rate of increase in the curve gradually diminishes in the later stages, then transitions into phase III, where cracks begin to propagate near the monitoring point. This results in the rapid destabilization of the rock matrix between the beddings, the elastic deformation capacity approximates the limit. The two sets of curves reach their respective strain peaks at 48 μs and 50 μs, respectively, measuring 0.013 × 10⁻³ and 0.014 × 10⁻³. The observations indicate that both the peak stress and peak strain at monitoring point 3 exhibit similar patterns of change, with their peak values and the time points of these peaks showing consistent trends over time. The peak stress point is identified at the moment when crack propagation reaches monitoring point 3. At this point, which is situated near the rock matrix, significant compression pushes the material to its elastic deformation limit. This results in the formation of numerous fine cracks and damage, leading to a maximum bearing capacity, after which the stress begins to decline rapidly. The greater spacing of the bedding causes bedding Ⅱ to endure earlier compression due to the impact load, so the rock matrix between the beddings becomes crushed. Consequently, the overall strength of this section is more susceptible to premature failure. The strain peak value observed at monitoring point 3 exhibits a clear relationship with the bedding material. If the first layer is composed of sandstone, a minimal difference in hardness between the first and second layers results in an earlier appearance of the stress–strain peak value, particularly when the hardness of the second or third layers is lower. This phenomenon occurs because the initial impact load is more effectively absorbed by the first layer, leading to damage in the bedding matrix. The lower the hardness of the material, the less energy is required for its destruction. Additionally, when the bedding surfaces are in close proximity, the impact load can drive the two laminar rock substrates to fail prematurely, thereby diminishing the overall strength of the section. The time required for cracks to penetrate bedding Ⅰ is reduced, allowing cracks to reach the monitoring point more swiftly [28], which destabilizes the rock matrix in that area and results in reduced strain under identical stress conditions.

The stress–strain characteristics of the three-layer composite bedding specimen are influenced by the overall hardness of the materials utilized. This specimen comprises three materials, and it is observed that a lower hardness in the material located near the impact end results in a reduced overall hardness of the specimen. Consequently, this leads to a diminished peak stress–strain value, with the time taken to achieve peak stress and strain occurring earlier. Additionally, the time to reach peak strain and peak stress is also influenced by the differences in material hardness. In the case where the first layer is granite, followed by marble, the aforementioned trend is followed. However, when the first layer consists of sandstone, the significant disparity in hardness between sandstone and granite, along with the brittleness of granite, results in the peak SHD occurring earlier than the SDH. This can be attributed to the contrasting hardness and the inherent brittleness of granite.

Figure 15a–c illustrate the time–history curves of stress and strain for sandstone monitoring points 2 and 4 in the course of simulation. The stress curves initially exhibit a gradual loading phase, followed by a rapid increase after 25 μs, ultimately reaching a peak stress. This peak coincides with the moment when the crack propagates to bedding II, resulting in destructive separation between bedding II and the rock matrix situated between the two beddings. Consequently, the internal bonding force diminishes, leading to a reduction in stress transmission from the loading point to the section, and a rapid decline in stress commences. In comparison to Figure 15d–f, under identical material conditions, the stress and strain peaks at monitoring points 2 and 4 are elevated by 13.13% and 14.77%, respectively, when compared to monitoring point 1. Additionally, the stress peaks at monitoring points 1 and 5 are increased by 22.82% and 23.63% relative to those at monitoring points 2 and 4. This indicates that the farther a monitoring point is from the centerline, the higher the peak stress that can be attained at that location. The ratio of peak stress increase relative to the integrated hardness of the specimen is most evident at monitoring point 3, while the correlation between peak stress and integrated hardness diminishes as the distance from the centerline of the cut seam increases. The maximum stress observed at the monitoring point is associated with the residual strength at that location. A lower integrated hardness of the specimen facilitates the susceptibility of bedding II to the compressive effects of the impact load, which can lead to the failure of the rock matrix situated between the beddings. Additionally, as the distance from the centerline increases, the overall strength of the rock matrix near the monitoring point is less influenced by the damage caused by extrusion, allowing for a higher peak stress to be attained. The curve exhibits a gradual increase during stage I. In comparison to the curve at monitoring point 1, the duration of stage II for each curve is extended, indicating that the peak strain point occurs later. When the crack propagates to monitoring point 1, monitoring points 2 and 4 remain intact, and their residual strength enables the strain to continue increasing. As the crack reaches bedding II, the rock matrix between the two beddings progressively loses its bond with bedding II, which coincides with further degradation of the specimen. The rock matrix near monitoring points 2 and 4 ultimately loses its load-bearing capacity and attains the peak strain point. A closer examination of Figure 15a–c indicates that the peak strain at monitoring points 1 and 5 occurs later than at the first two points, suggesting that the farther one is from the centerline, the slower the destruction rate of the adjacent rock matrix and the greater the residual strength.

5. Conclusions

(1)

The fracture mechanism of the composite specimen primarily initiates at the tip of cut seam, subsequently propagating along the upper surface and penetrating the bedding structure. When marble is utilized as the impact end material, it tends to generate secondary cracks due to stress concentration rather than originating from the tip of cut seam. Furthermore, the fracture morphology observed in the three-layer composite specimens exhibits a notable similarity, without significant distinctions.

(2)

When subjected to identical impact conditions, the incident wave forms across various composite specimens are nearly identical. However, the peak value of the transmitted wave varies with the position switch of each layer. It has been observed that marble demonstrates superior wave impedance matching when utilized as the material subjected to the impact. The ratio of reflected energy in the three-layer composite specimens remains relatively constant, while the transmitted energy ratio indicates that when marble serves as the upper material, the energy transmission ratio is greater. In contrast, the transmitted energy ratios for sandstone and granite are largely comparable due to their substantial hardness differences.

(3)

When the integrated hardness of a specimen remains constant, a lower hardness at the crack initiation site leads to a more rapid onset of crack initiation. If the crack initiation site is identical, a reduced hardness in the second layer of the specimen results in quicker crack propagation. Regarding dynamic fracture toughness, specimens exhibiting minimal hardness variation demonstrate that when the impact material is sandstone, the dynamic fracture peak value is diminished, causing these specimens more susceptible to cracking. For specimens where the first layer material is uniform, those with a softer second layer material exhibit lower dynamic fracture toughness, facilitating crack expansion. Conversely, specimens with a significant hardness disparity experience faster damage, which deviates from this observed trend.

(4)

The dynamic fracture behavior simulated by DLSM aligns closely with experimental findings. The load–displacement curve indicates that the peak load for specimens with granite as the upper layer is significantly greater than that of other specimens. Among specimens sharing the same upper material, variations in peak load are evident. Specifically, when the lower material is marble or granite, the peak load surpasses that of specimens with sandstone as the lower layer. However, when the upper material is either marble or granite, no substantial difference is observed between these specimens and those with sandstone as the lower layer. Notably, the three-layer composite specimen exhibiting the highest peak load is HSD, followed closely by HDS, while DSH exhibits a slight increase over DHS.

(5)

The stress–strain characteristics of the three-layer composite laminated specimen are influenced by the overall hardness of the material. Specifically, a lower hardness in the material composition located near the impact end results in a reduced overall hardness of the specimen, which in turn leads to a diminished peak stress–strain value and a delayed time to achieve peak stress and strain. The time to reach peak strain and peak stress is also contingent upon the differences in material hardness. Where the first layer is composed of granite, followed by marble, the aforementioned trend is followed. However, when the first layer consists of sandstone, the significant hardness disparity between sandstone and granite, along with the brittleness of granite, alters this dynamic. Consequently, the time to reach the peak for the sandstone layer occurs prior to that of the granite layer.

(6)

The findings of this study hold significant application prospects for practical engineering. In geotechnical engineering involving dynamic loading such as tunnel excavation, mine blasting, and hydraulic engineering, for composite rock masses composed of multiple layers of different rocks, their damage evolution and fracture characteristics under impact loading can be predicted based on the properties (e.g., hardness, elastic modulus) of each layer of rock. This provides a theoretical basis for optimizing engineering design and formulating reasonable construction schemes.