The rock sample investigated was obtained from the mudstone-siltstone interlayer roof of coal seam No. 31 in Renlou Coal Mine, located at the intersection of Suixi County, Huaibei City and Mengcheng County, Bozhou City, Anhui Province. In order to ensure the authenticity of the simulation test, a rock sample collected from the site was meticulously cut and polished into a standardized specimen measuring Ф50 mm × 100 mm, followed by comprehensive physical and mechanical property testing. The detailed results of these tests are presented in Table 1.

Based on extensive research conducted by scholars (Wang et al., 2006; Wang et al., 2024) and in conjunction with the precise measurement of mechanical properties of roof rock from seam No. 31 in Renlou Coal Mine, the proportion of the composition of the corresponding rock-like material produced by mixing is shown in Table 2. Subsequently, the analogous materials were fabricated using the established mix ratio. The static mechanical properties of the rock-like materials were evaluated using the electronic universal testing machine located at the School of Civil Engineering, Anhui Jianzhu University. The specimen dimensions were Ф50 mm × 100 mm. The comprehensive static mechanical properties were systematically documented in Table 3. The mold used in this test has an internal size of Ф70 mm × 35 mm, and the resulting specimens are suitable for direct use in impact testing, as depicted in Figure 1.

The test was conducted at the National-local joint Engineering Laboratory of building health monitoring and disaster prevention technology, Anhui Jianzhu University. The SHPB equipment (model: ZLKJ-SHPB-75) as shown in Figure 2 (Zuo et al., 2022). The incident rod, transmission rod, and bullet have lengths of 3000mm, 2500mm, and 500 mm respectively; their diameter is 75 mm. Additionally, the elastic modulus is measured as 206 GPa with a density of 7820 kg/m³ and Poisson ratio of 0.29.

The SHPB impact test fulfills the assumptions of one-dimensional stress wave propagation and uniform stress distribution. The voltage signal acquired from the strain gauge is converted into a strain signal, and using the three-wave method (as Formulas 1–3) to calculate the stress σ t , strain ε t , and strain rate ε ˙ t of specimen (Zhu et al., 2009). σ t = A E A s ε t t (1) ε t = − 2 C O L S ε r t (2) ε ˙ t = − ∫ 0 t 2 C O L S ε r t d t (3) where E represents the elastic modulus of the bar material; A represents the cross-sectional area of the bar material; C _o represents the longitudinal wave velocity of the bar material, and C O = E / ρ ; L _s represents the thickness of the sample; and t represents the stress wave loading time during the test.

The SHPB impact test adheres to the assumption of one - dimensional stress waves. Specifically, it is assumed that the propagation speed of stress waves in each rod remains constant. However, in the experiment, a significant issue arises: low - frequency stress waves propagate at a relatively faster rate compared to high - frequency stress waves. This phenomenon results in oscillations in the stress - strain curves obtained during the experiment. As a consequence, accurately evaluating the mechanical properties of materials becomes challenging, a phenomenon known as the dispersion effect.

To mitigate wave dispersion and maintain a state of constant strain rate deformation in the specimen, a wave shaper made of rubber is affixed to the end of the incident rod where it is struck by the bullet. Moreover, researchers uniformly apply a layer of vaseline at the interface between the specimen and the rods. This vaseline layer serves as a lubricant, effectively reducing the adverse influence of end - friction effects on the experimental results (Wang X. et al., 2022). Simultaneously, the specimens we fabricated have dimensions of Ф70 mm × 35 mm, with the ratio of length to radius being 2:1. This ratio is close to the optimal length - to - diameter ratio ( 3 / 2 )) for specimens used in SHPB impact tests, enabling the minimization of end - friction effects and inertial effects (Wang X. et al., 2022).

The test involved the selection of five different impact pressure levels, namely, 0.10MPa, 0.13MPa, 0.15MPa, 0.18 MPa and 0.20MPa, for impacting similar specimens of mudstone and siltstone. Each group underwent three replicate experiments. After identifying and excluding outliers, a representative test value was selected from the remaining dataset.

The strain rate at the plateau is determined as the mean strain rate of the rock in this test, when the strain rate-time curve reaches a steady state (Wu J. H. et al., 2024). The data processing method is illustrated in Figure 3, and the final test results are presented in Table 4.

The dynamic stress-strain curve of the weakly cemented rock-like material specimen is depicted in Figure 4. For both mudstone-like material and siltstone-like material, the general trend of the curve follows an initial rise, reaching a peak, and then declining. During the initial stage of stress growth, the majority of curve segments exhibit linear elastic behavior, indicating a certain degree of positive correlation between them. The specimen also attains a state of uniform stress and strain. However, at this juncture, the stress level is insufficient to induce crack expansion in the rock specimen; instead, it can only propagate minimally along existing micro-cracks. The elastic modulus observed during this stage can serve as an appropriate dynamic elastic modulus for mudstone and siltstone. With the escalation of stress, micro-cracks progressively propagate and new cracks emerge, which are not interconnected with the primary cracks, leading to a transition into plastic deformation. As stress continues to intensify, crack propagation accelerates rapidly and microcracks link up with the main crack. During this stage, there is a change in slope on the stress-strain curve indicating a non-linear relationship until reaching peak stress. Subsequently, the slope of the stress-strain curve decreases due to macroscopic failure caused by rock cracking, resulting in diminished load-bearing capacity.

Compared to the curves of siltstone-like material and mudstone-like material, the stress interval of siltstone-like material is larger, indicating its superior hardness and dynamic impact resistance compared to mudstone. This trend becomes more pronounced with increasing speed. Additionally, the stress flattening stage of mudstone is brief and immediately declines after reaching its peak, whereas siltstone exhibits a prolonged period of stress flattening following the peak. Moreover, the flattening stage in siltstone shows a significant increase and gentler decline compared to that observed in mudstone. These observations can be attributed to the fact that siltstone does not undergo immediate destruction after reaching its stress peak, highlighting its higher yield strength when compared to mudstone.

The dynamic compressive strength of rocks directly reflects their resistance to external impact loads. Figure 5 and Table 5 illustrate the relationship between the dynamic compressive strength of specimens and the strain rate. It is observed that weakly cemented materials tend to harden at higher strain rates, exhibiting exponential growth beyond a certain threshold.

The two materials exhibit distinct disparities. The dynamic compressive strength of mudstone demonstrates a gradual and relatively stable growth trend with an increase in strain rate, owing to its soft nature and limited strength. Conversely, siltstone material displays an overall growth pattern that is notably faster, as evidenced by the transition of the relationship function’s B value from negative to positive.

The bullet impacts the incident bar with a specific velocity, resulting in the transfer of impact kinetic energy carried by the bullet, as follows: W b = 1 2 m v 0 2 (4) where W b represents the impact kinetic energy of a bullet, J; m represents the mass of the bullet, kg; and v 0 represents the impact velocity, m/s.

The energy carried by the incident stress wave is as follows: W = A e E e C e ∫ 0 t ε 2 t d t (5) where A e represents the cross-sectional area of the press bar, m ² ; E e represents the elastic modulus of bar; C e represents the longitudinal wave velocity; and ε t represents the strain corresponding to the stress wave during the loading time.

The calculation formula for incident energy W _I , transmitted energy W _T , and reflected energy W _R during the test is as follows: W I = A e E e C e ∫ 0 t ε I 2 t d t (6) W R = A e E e C e ∫ 0 t ε R 2 t d t (7) W T = A e E e C e ∫ 0 t ε T 2 t d t (8) where ε I t represents the incident wave; ε R t represents the reflected wave; and ε T t represents the transmission wave of strain.

Dissipation energy of the test specimen equals incident wave energy minus reflected and transmitted wave energies, as follows: W D = W I − W R + W T (9)

The incident energy, reflected energy, and dissipated energy of the two rocks were computed using formulas 4–9, and the corresponding results are presented in Table 6.

The dissipated energy of rocks exhibits a velocity-dependent effect on impact. As the impact velocity increases, the dissipated energy of rocks also increases. A strong quadratic linear correlation exists between the dissipated energy of mudstone and siltstone and the impact velocity. This can be attributed to the fact that both the development and penetration of internal micro-cracks during specimen impacts require energy consumption, with higher energy consumption observed during crack generation compared to their subsequent development and penetration processes. Consequently, when subjected to low external impacts, minimal energy is generated resulting in tiny cracks within the specimen. At this stage, both absorbed energy by the specimen and its degree of damage remain low. However, as impact velocity rises, so does the generated energy which activates cracks requiring more substantial amounts of energy until complete fracture occurs in specimens (as depicted in Figure 6).

The failure morphology of the specimen under different impact velocities is illustrated in Figure 7. As can be seen from the figure, the mudstone specimen has been completely broken under the impact pressure of 0.10MPa, with uneven distribution of fragments. The siltstone specimen was completely broken under the impact pressure of 0.13MPa, and the fragment distribution was relatively uniform, which was basically large particle size and larger than mudstone. When the impact pressure increased to 0.18MPa, there were almost no large particle size fragments, and small particle size fragments began to appear in a large area. Compared with mudstone and siltstone, the fragmentation degree of siltstone is stronger than that of mudstone under similar impact strength.

The failure mode of rock changes from tensile failure to tension-shear coupling failure with the increase in impact velocity. In order to analyze the impact of velocity on the degree of damage in mudstone and siltstone, a statistical analysis of rock fragments was conducted following the impact test. Building upon Wang Chun’s method (Gao et al., 2024) for measuring rock fragment size, it is noted that when fragmentation is minimal, its statistical significance becomes less pronounced. Therefore, a standard length greater than 35 mm was adopted for broken rock fragments and subsequent counting. The relationship between the number of damaged rock blocks, the maximum length of rock blocks, and the impact velocity is illustrated in Figure 8.

The analysis of Figure 8 reveals that the number of rock blocks with a block size greater than 35 mm exhibits a quadratic relationship with increasing impact velocity. Simultaneously, the maximum length of broken rock blocks demonstrates a quadratic decrease as impact velocity increases, indicating a reduction in rock failure block size with higher impact velocities. At lower impact speeds, only minimal energy is sufficient to cause slight fragmentation in the rock sample. However, as impact velocity rises, the degree of fragmentation intensifies and multiple occurrences of tensile shear failure result in the formation of macroscopic fracture surfaces. This further enhances the level of fragmentation within the rock samples and ultimately leads to decreased block sizes post-failure.

The fractal characteristics of rocks can provide insights into the fracture mechanism of rocks. To investigate the fracture mechanism of sandstone under varying impact rates, we employed a particle size classification method to conduct an in-depth analysis of the experimental observations. Specifically, we statistically measured the longest edge of broken rock fragments and weighed the accumulated mass of fragments across different particle sizes, establishing a relationship between these two variables. The fragmentation distribution patterns for mudstone and siltstone under different impact velocities are illustrated in Figure 9, while Figure 10 depicts the ln M R / M T − l n R curve for a representative rock specimen. Additionally, we calculated the fractal dimension using formulas 10, 11 (Wu J. H. et al., 2024). b = ln M R M T l n R (10) D = 3 − b (11) where b represents the slope of the fitting function in the double logarithmic coordinate system of ln M R / M T − l n R ; M R represents the particle size less than R accumulated debris quality; M T represents the sample quality; and D represents the fractal dimension of the sample fragments.

The fractal dimension of rock fragments increases as a quadratic function with the increase of impact velocity, as shown in Figure 11, indicating that the fragmentation degree of mudstone and siltstone also increases correspondingly. Based on the macroscopic morphology analysis of typical rock breakage under different impact velocities, it can be concluded that higher impact velocities result in increased load and energy absorption by the rock sample, leading to enhanced crushing degree. Therefore, fractal dimension serves as a quantitative index for describing fracture characteristics and reflecting the extent of rock sample fractures. Through advanced drilling sampling and SHPB test analysis, the anticipated fractal dimensions of fractures in the roof rocks across various sections ahead of the roadway can be determined. Subsequently, by differentiating these fractal dimensions, support designs tailored to specific roof sections can be developed. This approach enables a more scientific alignment with the rock mass conditions, thereby achieving an optimal balance between safety and economic efficiency.

The relationship between the fractal dimension of rock sample fragments and dissipated energy exhibits an exponential pattern, as illustrated in Figure 12. As dissipated energy increases, the fractal dimension of rock progressively rises due to the absorption of energy during crack formation. Moreover, escalating impact velocity intensifies rock damage, necessitating a greater amount of absorbed energy for crack propagation until complete failure.