Cumulative damage characteristics of rock samples under cyclic low energy inclined plane impact | Scientific Reports

Scientific Reports volume 14, Article number: 25656 (2024) Cite this article

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The ore pass wall in underground mines is often damaged by the impact and wear caused by unloaded ores. Studying the mechanisms of rock damage and failure under different impact angles can provide technical insights for the design and maintenance of the ore passes. This study employed an inclined impact experimental device along with a drop hammer loading test machine to perform cyclic low-energy impact tests on sandstone samples at five different inclined plane angles. The porosity of the rock samples was measured using a nuclear magnetic resonance (NMR) detection system, which provided data on porosity, T2 spectrum distribution, and NMR images of the samples after different numbers of impacts at different slope angles. The results indicate that: (1) Under cyclic inclined plane impact loading, an increase in the inclination angle, leads to reduced damage to the rock sample. The rock sample impacted at a 45° inclined plane exhibited the most severe damage. Rock samples with large inclination angles are more prone to experience rupture fractures at the tip of the inclined plane, primarily due to shear-tensile failure. The porosity changes dramatically at initially slope angles, resulting in greater damage. (2) As the number of impacts increases, the porosity of the samples first decreases, then increases, and subsequently decreases again. This progression corresponds to the closure of large pores following the first impact, followed by the expansion of micropores into macropores after 5 impacts, ultimately leading to gradual degradation of the samples until failure. (3) As the number of impacts increases, new cracks form within the rock sample and small cracks expand. Despite an increase in the number of micropores, the macropores still exert a significant influence on the rock samples, with the macropore spectrum area accounting for over 95%.

Rocks, as naturally occurring heterogeneous materials, often form with initial defects such as bedding planes and micro-cracks during their forming process1. In the development and utilization of underground spaces, rocks are inevitably subjected to original rock stress and secondary disturbance stress resulting from excavation activities. These initial damages, exacerbated by impact and compressive loads, can evolve further, leading to extensive rock failure. For instance, in underground mine ore passes, the surrounding rock mass experiences both rock pressure and disturbances from blasting. Notably, during the ore unloading process in the mine ore pass, collisions between ore blocks and the walls can cause impact abrasion, potentially leading to an increase in the ore pass diameter or even its collapse2. This issue has become a significant bottleneck in the transportation of ore within underground mining operations. Therefore, the research on the damage evolution process of rocks under impact loading is crucial for ensuring safe construction and disaster prevention in underground engineering.

Numerous scholars have combined theoretical analysis, physical experiments, and numerical simulation methods to investigate the dynamic fracturing and damage patterns of rocks3,4,5,6. The macroscopic impact failure process of rock samples can be categorized into three stages: initial damage, cumulative damage, and macroscopic failure7. Currently, most studies focus on analyzing the dynamic mechanical properties of rocks through impact tests. Commonly utilized equipment for examining the dynamic mechanical properties of materials in engineering includes the Split Hopkinson Pressure Bar (SHPB) system and drop hammer test devices. A wealth of research has been dedicated to understanding the mechanical responses of rocks under dynamic conditions, including various impact loading speeds, energies, and constraint conditions8. Some scholars have also analyzed the shear characteristics of rocks under combined static-dynamic loads using physical experiments and numerical simulation methods9,10. With the continuous development of detection technologies, investigating microscopic damage within rocks under dynamic loads has emerged a prominent research focus. Techniques such as computed tomography (CT) scanning11, scanning electron microscopy (SEM)12, acoustic emission testing, and nuclear magnetic resonance (NMR) detection13 have proven effective in analyzing and elucidating the microscopic damage characteristics of rocks. In recent years, NMR detection technology has found widespread application in fields such as medicine, geotechnical engineering, and materials science. In geotechnical engineering, parameters such as porosity, permeability, and free fluid index inside specimens can be measured using NMR technology, offering an intuitive description of the microscopic damage in materials14. This has spurred the development of NMR relaxation theories aimed at studying the damage of porous mediums in rocks15,16. For example, Weng et al.17 utilized NMR technology to investigate the microscopic damage characteristics of pre-cut opening in rocks under static-dynamic combined loading, while Fu et al.18 analyzed the dynamic process of capillary water imbibition in sandstone samples using NMR technology.

While numerous studies have explored the cyclic impact failure mechanisms of various rock materials, most investigations have centered on axial impacts on rock samples. However, in practical engineering scenarios, the phenomenon of inclined plane impacts occurs frequently where the force is not perpendicular to the impacted surface2. This is particularly observable in metal mines during the ore unloading process; ore rocks do not always strike the ore pass walls vertically. Instead, most ore rocks move along an inclined parabolic path, resulting in collisions at various angles, which significantly influences the extent of wall damage. From an engineering perspective, Jiang et al.19 combined theoretical analysis and numerical simulation to study the impact abrasion behaviour of ore rocks on ore pass walls in steeply inclined mine ore passes. Similarly, Esmaieli et al.20 utilized numerical calculation methods to demonstrate that such impacts lead to localized damage and hasten the failure of these structures. Beyond general impacts, specific studies have also assessed the mechanical and and damage characteristics of layered rocks7, rocks with different fracture surfaces21, and coal-rock combinations with different slope angles22. In mining contexts where specific rock mass conditions and stress environments prevail, the predominant cause of ore pass wall failure is often impact and wear. The nature of this impact-related failure correlates with the angle between the branch ore passes and the main ore pass, that is, the direction of the impact between the unloaded ore and the ore past wall. Wu et al.23 analyzed the damage characteristics attributable to different inclined plane angles using an experimental device specifically designed for inclined plane impacts. However, impact failure is not instantaneous but a progressive deterioration, underlining the importance of understanding the rock damage process across various impact frequencies. From a microscopic standpoint, the mechanisms of rock damage due to inclined impacts necessitate further in-depth investigation to improve preventive strategies and enhance the structural integrity of mining infrastructure.

In summary, significant progress has been made in understanding the dynamic characteristics and damage evolution mechanisms of rock impacts, actively promoting the safety and efficiency of underground engineering productions. However, research gaps remain concerning inclined impacts, especially under different frequency impact conditions, and the microscopic damage evolution process of rocks. Therefore, this study aims to utilize an improved drop hammer impact test device and NMR technology to investigate the cumulative damage characteristics of sandstone samples under cyclic inclined impact loads. By conducting impact tests at different frequencies on rock samples with five inclination angles and analyzing changes in porosity, NMR images, and T2 distribution properties, we can gain insights into the crack propagation process before and after impacts and further reveal the damage process of inclined rock samples.

As illustrated in Fig. 1, the testing apparatus comprises two primary components: a loading mechanism and a rigid force transmission device. The JZ-5011 drop hammer impact testing machine serves as the test loading device, incorporating components such as the main frame, guide rod, drop hammer, anti-secondary impact device, and electric control box. The impact force exerted by the drop hammer is adjusted through modifications to the weight of the hammerhead, the drop hammer counterweight, the height from which the hammer is dropped, and the thickness of the collision pad layer. The range of the testing hammer’s mass varies from 0.25 to 15.0 kg, with a radius of 2–50 mm, and an impact height of 0–2000 mm. The rigid force transmission device consists of a steel column with an inclined end surface that ensures full contact with the inclined surface of the rock sample, maintaining a consistent inclination angle throughout the experiment.

Testing equipment of drop hammer inclined plane impact.

The rock sample’s porosity and pore size distribution before and after impact testing are assessed using NMR technology15. As depicted in Fig. 2, the sample detection was conducted utilizing a large-bore NMR analyzer and imaging analysis system (MacroMR12-150 H-I) developed by Niumai Analytical Instrument Co., Ltd. Suzhou, China. The system includes a temperature control system, industrial computer, analysis software, radio frequency unit, and a rare earth neodymium iron boron permanent magnet. This equipment is designed to assess the porosity and pore size distribution of rock cores and cuttings, measure permeability and fluid saturation, and provide two-dimensional imaging from various angles across multiple layers. The NMR analyzer and imaging analysis system enables detailed measurements of porosity, the transverse relaxation time T2 spectrum curve, and internal pore distribution images of the specimen, facilitating a comprehensive analysis of rock sample characteristics under dynamic impact conditions.

Nuclear magnetic resonance imaging analyzer.

NMR testing offers the advantages of being non-destructive, repeatable, safe, and rapid. The fundamental principle of NMR detection involves the interaction between hydrogen nuclei and an external magnetic field. This interaction begins when a specific radio frequency pulse is introduced within the magnetic field, causing the hydrogen nuclei to resonate with the field and absorb energy from the pulse. Once the radio frequency pulse ends, the absorbed energy is gradually released by the hydrogen nuclei. The process whereby a hydrogen nucleus transitions from a high-energy state to a low-energy state is known as relaxation. The transverse relaxation time T2, a critical parameter in NMR testing, is directly related to the pore structure of the rocks being analyzed. The transverse relaxation time T2 is measured by detecting the energy release process and inverting the digital transmission signal. Importantly, The ratio of the surface area to the volume of the rock pores determines the NMR relaxation time T2, allowing it to serve as an intuitive indicator of the microscopic structural changes inside rock samples at different stages of impact24.

Prior to NMR detection, it is necessary to saturate the samples with water to enhance the visibility of their internal structures. This saturation is achieved using the ZYB-II vacuum saturation pressure device, which can apply a vacuum saturation pressure of up to 60 MPa, ensuring thorough saturation of the samples for accurate NMR analysis.

For the experiments, cylindrical sandstone samples were utilized, each with a diameter of 50 mm and a uniaxial compressive strength of 77 MPa. Reflecting the typical inclination angle of branch ore passes in underground mines, which is generally around 50°, the experiment was designed to accommodate five sets of rock samples, each set varying by 5° in inclination angle. This setup ensured a comprehensive range of angles to simulate various stress scenarios encountered in mining operations. Each set consisted of 5 samples, culminating in a total of 25 samples. The distance (h) between the lower edge of the inclined surface and the bottom of the sample was maintained at 30 mm to standardize the testing conditions across all samples. The specific dimensions, shape, and inclination angles of the samples are detailed in Table 1 and illustrated in Fig. 3. Figure 4 displays the sandstone samples prepared with the respective inclination angles, ready for the impact testing phase.

Sketch map of a test sample.

Sandstone samples with different inclination angles.

The experimental process involves a series of steps designed to evaluate the changes in porosity and other characteristics of the rock samples using NMR technology during impact tests. The specifics of the experimental methodology, as illustrated in Fig. 5, are outlined below:

Firstly, immerse the sample in water for 12 h. Following this, place it in the ZYB-II vacuum saturation device to undergo vacuum saturation for an additional 12 h, maintaining a pressure of 20 MPa. After saturation is complete, remove the sample, gently wipe off any excess surface water, and securely wrap it in cling film to prevent moisture loss.

Position the sample within the low magnetic field NMR rock core analysis measurement system to assess its porosity, T2 spectrum, and obtain internal pore NMR imaging.

Following the imaging, remove the cling film and transfer the sample to a drying oven. Set the temperature to 105 °C and allow the sample to dry for 2 h.

Once dry, affix the sample to the inclined loading device to assemble the impact body, and perform impact tests using the JZ-5011 drop hammer impact testing machine.

Upon completion of each test, systematically record the test data. Repeat steps (1) to (4) for each of the 6 planned impact tests and NMR detections, measuring the sample’s porosity after each impact to monitor changes over the course of the testing.

Test flow chart.

Porosity in rocks is indicative of the ratio of internal defects, pores, and fractures to the total volume of rocks, directly influencing the physical and mechanical properties of the material. While porosity measurement can be direct or indirect, the drainage method is a common direct measurement technique25. However, this method is not applicable to rocks containing components that easily dissolve in water. In this study, the indirect measurement method of NMR detection was employed. NMR technology provides both qualitative and quantitative insights into the pore distribution characteristics within rocks by measuring the relaxation time of fluids in pores. During the experimental phase, porosity measurements were conducted on rock samples after varying numbers of impacts. Figure 6 illustrates the relationship curve between the porosity of sandstone samples at various angles and the number of impacts, all under the same impact energy. Overall, the porosity decreases initially and then increases as the number of impacts grows.

Porosity curves of rock samples at different angles under cyclic impact.

For rock samples inclined at angles of 40° and 45°, porosity patterns exhibit a distinctive trend: they are minimal following the initial impact and peak after the fifth impact. Following the sixth impact, a slight reduction in porosity occurs alongside observable local damage within the rock samples. In contrast, samples with inclination angles of 55° and 60° display porosity variations characterized by an initial decrease, then a subsequent increase following impacts. The porosity reaches its lowest after the second impact and its highest after the sixth. Initially, porosity diminishes, indicating compression of some pores and a decrease in total pore volume.

Nevertheless, as impacts accumulate, porosity progressively increases. This phenomenon results from the cumulative effects of multiple impact-induced compression waves and the reflected transmission waves, which persistently alter the internal structure of the pores and fractures within the samples. As a result, micropores enlarge into more substantial cavities, and new, small fissures form, thereby augmenting the porosity.

As illustrated in Table 2, the variation in porosity across different inclination angles, reveals that samples with smaller inclination angles exhibit a more significant change in porosity under identical cyclic impact load. Specifically, the rate of porosity change diminishes as the slope angle increases. For instance, in a sample with a 40° inclination angle, the porosity was recorded at 10.18% before impact, increasing to 10.90% after six impacts, which corresponds to a porosity change rate of 7.1%. In comparison, a sample with a 60° inclination angle displayed porosity values of 8.27% before impacts and 8.80% afterward, respectively, resulting in a change rate of 6.4%. Notably, the sample with the highest porosity change rate is the one inclined at 45°. In this case, the porosity change rate after 5 impacts reached 17.4% compared to the original sample. A fundamental mechanical analysis indicates that as the slope angle increases, the normal force component acting on the inclined surface diminishes under the same impact force. This reduction leads to decreased impact damage to the rock samples.

The T2 spectrum curve represents the transverse relaxation response of 1 H protons in completely water-saturated rock samples, obtained using the Carr-Purcell-Meiboom-Gill (CPMG) pulse sequence. This curve reflects the variation in the quantity and size of the pores within the samples. According to the transverse relaxation time T2, the pores in rock samples can be classified into three groups: macropores (T2 > 100ms), mesopores (10ms < T2 < 100ms), and micropores (T2 < 10ms)13. Alternatively, some scholars have also simplified this classification into two main types based on the critical value of 10ms: macropores (T2 > 10ms) and micropores (T2 < 10ms). This study primarily adopts the latter classification approach. According to empirical methods, a transverse relaxation time of 10 ms corresponds to a pore size of approximately 300 nm24.

Figure 7 illustrates the T2 spectrum curves of inclined plane samples at five different inclinations subjected to the same cyclic impact load. The horizontal axis of the figure represents the T2 relaxation time, where times greater than 10 ms correlate with macropores, indicating larger pore sizes. The vertical axis quantifies the number of pores, with higher values indicating a greater prevalence of pores of corresponding sizes.

Distribution of T2 spectrum under cyclic impact load of rock samples at different inclination angles.

The T2 spectrum curves of the rock samples show consistent changing trends, characterized by two distinct peaks representing different pore sizes: the first peak for micropores and the second for macropores. Notably, the amplitude of the first peak is significantly higher than that of the second, suggesting a predominance of micropores over macropores. Comparative analysis of the T2 spectrum curve before impact (No.0) and post-impact reveals that both peaks decrease after the first two impacts, indicating a decrease in the internal pore numbers and an overall decrease in porosity. Subsequent impacts lead to a notable increase in the amplitude of the first peak, while the second peak continues to decrease, implying an increase in micropores and the compaction of macropores, with an overall upward trend in porosity. Additionally, the horizontal shift of the curve to the left after the third impact indicates a general reduction in pore size across the samples.

Focusing on the T2 spectrum curve for a rock sample with a 45° inclination, there is no significant lateral displacement in the curve after the initial two impacts, and the total relaxation time remains under 1000ms, indicating stable pore sizes. After the first impact, the amplitude of the first peak in the T2 spectrum curve remains unchanged, whereas the second peak decreases slightly, reflecting some compaction of macropores without affecting micropores. Following the second impact, the first peak decreases and the second peak increases, suggesting a transformation of some micropores into macropores. The most significant changes occur after the third impact, with both peaks shifting leftward, indicating a reduction in overall pore size. Furthermore, the first peak’s amplitude significantly increases and the second peak’s decreased, suggesting an increase in micropores and a slight reduction in macropores. After the fourth to sixth impacts, the peaks exhibit minor lateral shifts but fluctuate in value, indicating ongoing transformations between micropores and macropores. Overall, these dynamics suggest a gradual increase in total porosity, with no substantial changes in the conversion dynamics between micropores and macropores after the third impact.

As shown in Tables 3 and 4, the calculations of the peak values for the T2 spectrum curves of rock samples at five different inclination angles after six impact cycles of impact are detailed. The data reveal that the first peak’s value remains relatively stable after the first two impacts but increases significantly after the third impact. For instance, in the 45° rock sample, the first peak value was approximately 1286 prior to the second impact and surged to 1740 following the third impact, highlighting a notable increase in the number of micropores. In addition, the relaxation time corresponding to the first peak value shifted from 0.64 ms before the impact to 0.4 ms after the third impact, indicating a leftward shift in the first peak of Fig. 7 and a slight increase in micropores. According to the results in Table 4, the second peak’s value shows a minor decrease after six impacts, suggesting a slight reduction in the number of macropores. The relaxation time for the second peak decreased from 29.33 ms to 19.34 ms after the third impact, and the leftward shift of the second peak signifies an increase in relatively smaller pores within the macropores category. A comparative analysis of the peak values from the T2 spectrum curve reveals that the first peak values for the rock samples inclined at different angles increased by 34.23%, 30.34%, 39.54%, 34.30%, and 19.89%, respectively. Conversely, the second peak values showed changes of -16.97%, -13.62%, -21.61%, -14.66%, and 4.45%, respectively. These changes confirm the overall trend where the number of micropores increases and the number of macropores decreases after 6 impacts.

Therefore, as the impact count increases, the first peak primarily exhibits vertical shifts, with only the third impact resulting in a significant leftward movement. In contrast, the second peak exhibits both vertical and horizontal changes throughout the impact process, indicating that alterations in the number of micropores are more pronounced in sandstone under cyclic impact conditions. Concurrently, the size and quantity of macropores also exhibit variations. Additionally, the larger the inclination angle of the plane, the greater the signal amplitude of the peak values observed in the T2 spectrum curve.

The area enclosed by the T2 spectral curve, defined in relation to the horizontal axis is referred to as the T2 spectrum area. This area correlates directly with the fluid content within the rock and can serve as a critical parameter reflecting changes in rock pore structure16,24. As depicted in Table 5, the NMR spectral area and macroscopic pore ratio of sandstone samples with different inclined planes after 6 impacts were calculated. The total spectral area for these sandstone samples ranges from 90,000 to 300,000. The spectral area attributed to micropores constitutes less than 4%, whereas the area for larger-sized pores accounts for over 96%. These figures indicate that while the rock samples contain numerous micropores and a limited amount of macropores, it is the macropores that predominantly influence porosity. This finding aligns with the observed trends in porosity changes, which are consistent with variations in the spectral area of macropores.

When comparing the changes in the proportions of macro and micro and micropores across different impact counts on five types of rocks, it is found that the pore alterations are more significant in samples with small inclination angles, while those with larger inclinations exhibit subtler changes. For instance, considering the micro-pore proportion, after six impacts, the sample with a 40° inclination saw a 7.27% increase in micropores. In contrast, the sample with a 60° inclination displayed its highest increase in micropore proportion after the third impact, with a rise of 4.64% compared to the value after the second impact.

NMR imaging provides a crucial visual representation of the spatial distribution and development status of internal pores within rock samples, which is crucial for studying rock damage. Figure 8 displays the NMR images of sandstone samples at inclination angles of 45° and 60°, both before and after six impacts. These images provide cross-sectional images at a distance of 20 mm from the bottom surface. In these images, green spots represent micropores, while the yellow and red spots represent macropores.

NMR images of rock samples before and after cyclic impact.

Taking the image of a 45° inclined plane rock sample as an example, the pre-impact image displays a homogeneous distribution of green spots, indicating small and uniformly sized pores within the rock. After the first impact, the porosity is at its minimum, and there is a noticeable reduction in spots along the right edge of the cross-section, with a concentration of spots mainly on the left side. Additionally, a few yellow and red spots emerge, suggesting that some micropores have expanded into macropores. Following the fifth impact, when porosity peaks, there is a significant increase in the number of spots across the cross-section, and numerous yellow and red spots appear, indicating an increase in macropores.

After the sixth impact, the number of spots decreased slightly. However, there are obvious striped spots, indicating potential penetration of some pores and the formation of a few cracks. In contrast, the images of the 60° inclined plane rock sample show no significant change in the number of spots throughout the impact process. The distribution of spots remains uniform without the emergence of obvious yellow, red, or striped spots. This suggests that a larger inclination angle reduces the extent of damage caused by impacts to the rock sample, illustrating the influence of structural orientation on the mechanical behavior of rock under cyclic impacts.

As illustrated in Fig. 9, the impact surface of the sample adopts an elliptical shape influenced by the slope of the inclined plane. The size of the long semi-axis size gradually varies with the inclination angle of the inclined plane. Defining the major and minor axes of the ellipse as a and b, respectively. The geometric relationships can be expressed as follows: b = acosα = d/2, the inclined plane area A = πd2/ 4cosα. During the impact of a falling hammer, the rock sample experiences both vertical compression stress and horizontal shear force, with the vertical force having a greater impact on the sample. The impact force F from the falling hammer can be decomposed into normal force FN (Fτ = P) and tangential force Fτ, with the vertical force exerting a more significant impact on the sample.

where, σx and σz are the horizontal stress and vertical stress exerted on the inclined plane, measured in Pascals (Pa); P denotes the normal impact force impacting the inclined plane, expressed in Newtons (N); F indicates the total force exerted by the falling hammer, also in Newtons (N); d refers to the diameter of the sample and is given in millimeters (mm); α represents the inclination angle. The coefficients “K1” and “K2” are used to describe the component coefficients for the horizontal and vertical directions, respectively. As illustrated in Fig. 10, as the angle of the inclined plane increases, the horizontal stress component initially increases, reaches a maximum at an angle of 35°, and then decreases. Conversely, the vertical stress component gradually decreases as the inclination angle increases. At an inclination of 45°, the horizontal stress component and the vertical stress component are equal.

Analysis of impact force at the moment of impact.

Component coefficient curve of inclined impact force.

In summary, when compared to traditional vertical impact, the impact of inclined plane loading on rock samples introduces not only vertical compressive stress but also damage and deformation caused by horizontal forces. The extent of damage and failure is significantly influenced by the inclination angle of the sample. As the inclination angle increases, with the same drop height, the vertical stress decreases while the horizontal stress increases. This shift results in reduced damage at the lower part of the sample, altering the overall impact dynamics and structural response of the rock.

To delve deeper into the internal damage and destruction sustained by rock samples under different inclined plane impact frequencies, a damage variable D is introduced. This damage variable D is mathematically defined as a function of internal porosity as follows:

where, n0 represents the natural porosity of the rock sample, and nt represents the porosity of the rock sample after the t-th impact.

As depicted in Table 6, the damage variables for samples with different inclination angles can be calculated by inserting the measured porosities before and after impact (Fig. 6) into Eq. (2).

According to the result presented in Table 6, the damage variable is negative for impact counts fewer than 2, indicating that the first two impacts compress the pores within the rock samples. From the third impact onward, except for the 55° rock samples, the damage variables become positive. The highest values of the damage variable typically occur during the fifth or sixth impact, with an order of increasing maximum values across different angles being 45° > 50° > 40° > 55° > 60°. Notably, the 45° rock sample experiences the highest damage variable during the fifth impact. Under the same number of impacts, the 45° rock sample consistently shows the highest degree of damage, whereas the 60° rock sample exhibits the lowest. This finding has practical implications for the design of ore passes in underground mines. To mitigate impact damage, it is advisable to minimize the angle between branch ore passes and the main ore pass, reducing the impact angle. Additionally, maintaining a certain height of ore material accumulation in the ore pass to reduce impact damage to the ore pass wall.

As depicted in Fig. 11, after six cycles of inclined plane impact with consistent energy, different types of cracks have manifested in the upper part of the samples. The failure mode observed in samples with inclination angles ranging from 45°~60° is characterized by the presence of only one crack. However, the 40° inclined plane sample exhibited multiple cracks and significant detachment at the bottom of the sample. The crack positions are all located within 20 mm of the upper end of the sample and are parallel to the bottom surface, indicative of shear-tensile failure, as illustrated in Fig. 12. This pattern of failure can be attributed to the sample’s sharp corners being relatively thin, which, coupled with the lateral forces generated by the inclined plane impacts, leads to the upper part of the rock sample failing first. The angle of the inclined plane significantly influences the impact damage and failure patterns of rock samples. A smaller inclination angle results in a decreased transverse force and an increased longitudinal force, shifting the failure from a single transverse crack to multiple cracks.

Failure modes of rock samples.

Failure modes of 45° rock samples.

Physical experiments were carried out on samples with five inclined end faces under different frequencies of impact by using a drop hammer testing machine and an inclined plane impact test device. NMR detection was utilized to analyze the damage degradation process of the samples before and after impact. The findings are summarized as follows:

Under the same impact load, the sample’s damage mode is significantly influenced by the inclination of the plane. Samples with larger angles exhibit less damage and require more impacts to fail. The order of samples with the maximum damage variable, showing the most severe impact results, is as follows: 45° > 50° > 40° > 55° > 60°. Failures tend to occur at the sharp corners of the inclined planes, predominantly as shear-tensile failures, with smaller slope angles showing more intense variations in porosity.

The porosity of the rock samples initially decreases, then increases, and finally decreases again as the number of impacts increases. The smallest porosity is observed during the first impact, with the largest after the fifth impact. This pattern is due to the closure of macropores after the first impact, with the rock sample experiencing the most severe damage after 5 impacts, leading to failure after the 6th impact.

Before and after rock sample impacts, the number of micropores in the rock samples is greater than that of macropores. As the number of impacts increases, new micropores are generated, increasing the number of micropores, although changes in the number of macropores are not significant. The proportion of macropore spectrum area remains above 95%, indicating that macrospores still significantly impact the rock samples. With increasing impacts, new cracks appear, and existing cracks continue to propagate, ultimately leading to the damage and destruction of the rock sample.

All data generated or analyzed during this study are included in this published article.

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The authors acknowledge the financial support of the National Natural Science Foundation of China (Grant Nos. 51774176, 52304087) and the General project of Education Department of Liaoning Province (Grant No. LJKMZ20220661). The authors are very grateful for the financial contributions and convey their appreciation to the organizations for supporting this basic research.

School of Mining Engineering, University of Science and Technology Liaoning, Anshan, 114051, China

Xinrong Wang & Zeng-xiang Lu

Xiadian Gold Mine, Zhaojin Mining Industry Co., Ltd., Zhaoyuan, 265400, Shandong, China

Xu Zou

Anshan Iron and Steel Labor Research Institute Technology Co., Ltd., Anshan, 114000, Liaoning, China

Xiao-xu Wu

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Conceptualization, X.R.W. and Z.X.L; Methodology, X.R.W. and X.Z.; Collection, Testing and analysis, Writing–Original Draft Preparation, X.Z. and X.U.W.; Writing–Review & Editing, X.R.W. and Z.X.L. All authors reviewed the manuscript.

Correspondence to Zeng-xiang Lu.

The authors declare no competing interests.

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Wang, X., Zou, X., Lu, Zx. et al. Cumulative damage characteristics of rock samples under cyclic low energy inclined plane impact. Sci Rep 14, 25656 (2024). https://doi.org/10.1038/s41598-024-77159-2

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Received: 02 July 2024

Accepted: 21 October 2024

Published: 27 October 2024

DOI: https://doi.org/10.1038/s41598-024-77159-2

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