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

Cumulative damage characteristics of rock samples under cyclic low energy inclined plane impact | Research Square window.SnipcartSettings = { analytics: { enabled: false } }; (function() { var accessVector = localStorage.getItem('access_vector') || ''; window.dataLayer = window.dataLayer || []; if (accessVector) { window.dataLayer.push({ user: { profile: { profileInfo: { snid: accessVector } } } }); } })(); (function(w,d,s,l,i){w[l]=w[l]||[];w[l].push({'gtm.start':new Date().getTime(),event:'gtm.js'});var f=d.getElementsByTagName(s)[0],j=d.createElement(s),dl=l!='dataLayer'?'&l='+l:'';j.async=true;j.src='https://www.googletagmanager.com/gtm.js?id='+i+dl;f.parentNode.insertBefore(j,f);})(window,document,'script','dataLayer','GTM-K279D39R'); Browse Preprints In Review Journals COVID-19 Preprints AJE Video Bytes Research Tools Research Promotion AJE Professional Editing AJE Rubriq About Preprint Platform In Review Editorial Policies Our Team Advisory Board Help Center Sign In Submit a Preprint Cite Share Download PDF Article Cumulative damage characteristics of rock samples under cyclic low energy inclined plane impact Xinrong Wang, Xu Zou, Zeng-xiang Lu, Xiao-xu Wu This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-4674701/v1 This work is licensed under a CC BY 4.0 License Status: Under Review Version 1 posted 10 You are reading this latest preprint version Abstract To investigate the cumulative damage characteristics and unstable failure mechanism of rock samples under cyclic inclined plane impact loads, an experimental device simulating inclined plane impact, and a drop hammer loading test machine were used to conduct cyclic low-energy impact tests on sandstone samples with five inclined plane angles. The porosity of the sandstone samples was measured using a low magnetic field nuclear magnetic resonance (NMR) detection system, obtaining the porosity, T 2 spectrum distribution, and NMR images of the samples after different numbers of impacts at different slope angles. Under the action of cyclic inclined plane impact loads, the larger the slope angle, the smaller the extent of sample damage. The rock samples with a large inclined angle is more inclined to rupture at the tip of the inclined plane, mainly primarily characterized by shear-tensile failure. The porosity of the small slope angle changes sharply, resulting in greater damage. Under the same impact energy, as the number of impacts increases, the porosity of the samples first decreases, then increases, and then decreases again. This is manifested by large porosity closure after the first impact, followed by small pore expansion into large pores after 5 impacts, leading to gradual degradation of the samples until failure. The main factor affecting the rock samples is the presence of large-sized pores with a spectral area of over 95%. As the number of impacts increases, the quantity of small pores decreases, while the size and quantity of large pores both increase, indicating continuous deterioration of rock sample. Earth and environmental sciences/Natural hazards Physical sciences/Engineering/Civil engineering Physical sciences/Engineering/Energy infrastructure Inclined plane impact NMR T2 spectrum distribution Porosity Cyclic impact Figures Figure 1 Figure 2 Figure 3 Figure 4 Figure 5 Figure 6 Figure 7 Figure 8 Figure 9 Figure 10 Figure 11 Figure 12 1. Introduction Rock, as widely existing natural heterogeneous materials in nature, form with initial defects such as bedding planes and micro-cracks during the forming process 1 . In the development and utilization of underground spaces, rocks are inevitably subjected to original rock stress and secondary disturbance stress induced by excavation. Accompanied by impact and compression loads, initial damages will further evolve, leading to extensive rock failure. Taking underground mine ore passes as an example, the surrounding rock mass of the ore pass is affected by both rock pressure and blasting disturbances. More importantly, during the ore unloading process in the mine ore pass, collisions between ore blocks and the wall of the ore pass will inevitably cause impact abrasion on the wall, potentially resulting in the enlargement of the ore pass diameter or even collapse of the ore pass 2 . It has become a bottleneck in underground mining ore transportation. Therefore, conducting research on the damage evolution process of rocks under impact loading is of great significance for the safe construction and disaster prevention of underground engineering. Many scholars have combined theoretical analysis, physical experiments, and numerical simulation methods to study dynamic fracturing and damage patterns of rocks 3–6 . Rock specimens' macroscopic impact failure process can be divided into initial damage, cumulative damage, and macroscopic failure 7 . Currently, most studies analyze the dynamic mechanical properties of rocks through impact tests. Common equipment used to study the dynamic mechanical properties of materials in engineering includes the Split Hopkinson Pressure Bar (SHPB) system and drop hammer test devices. Numerous studies focus on the mechanical responses of rocks under dynamic conditions, including various impact loading speeds, energies, and constraint conditions 8 . Some scholars have analyzed the shear characteristics of rocks under combined static-dynamic loads using physical experiments and numerical simulation methods 9,10 . With the continuous development of detection technologies, the study of microscopic damage inside rocks under dynamic loads has become a recent research hotspot. Techniques such as computed tomography (CT) scanning 11 , scanning electron microscopy (SEM) 12 , acoustic emission testing, and nuclear magnetic resonance (NMR) detection 13 can effectively analyze and understand the microscopic damage characteristics of rocks. In recent years, NMR detection technology has been widely used in medicine, geotechnical engineering, and materials. In geotechnical engineering, parameters such as porosity, permeability, and free fluid index inside specimens can be measured using NMR technology to describe the microscopic damage of materials14 intuitively 14 . This has led to the development of NMR relaxation theories to study the damage of porous mediums in rocks 15,16 . Weng et al. 17 used NMR technology to study the microscopic damage characteristics of pre-cut opening in rocks under static-dynamic combined loading. Fu et al. 18 analyzed the dynamic process of capillary water imbibition in sandstone samples using NMR technology. There are many studies on the cyclic impact failure mechanism of different rock materials. However, most rock impact tests involve axial impact on rock samples. In practical engineering, the phenomenon of inclined plane impacts where the impact force is not perpendicular to the impacted surface is also common. For example, when unloading ore in mine ore passes, the collision between ore rocks and the ore pass wall is not always a normal impact. Most ore rocks move in an inclined parabolic trajectory in the ore pass. When ore blocks collide with the wall, the angle between the direction of impact force and the ore pass wall also affects 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 highly inclined mine ore passes. Esmaieli et al. 20 used numerical calculation methods to determine that the impact of ore rocks on ore pass walls leads to localized damage and accelerates failure. In terms of rock inclined plane impact, scholars have also conducted preliminary studies on the mechanical characteristics and damage characteristics of layered rocks 7 , rocks with different fracture surfaces 21 , and coal-rock combinations with different slope angles 22 . Wu et al. 23 analyzed the impact damage characteristics of different inclined plane angles based on an inclined plane impact experimental device. However, from a microscopic perspective, the mechanism of rock damage caused by inclined impact still needs further in-depth research. In summary, significant progress has been made in understanding the dynamic characteristics and damage evolution mechanisms of rock impacts, which have actively promoted the safety and efficiency of underground engineering production. However, there are still many gaps in research on inclined impacts where the impact force is not perpendicular to the impacted surface, such as rock impacts on mine ore pass walls and wind-blown impacts on building surfaces. 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. 2. Materials and Experimental Methods 2.1 Experimental Setup As shown in Fig.1, the testing equipment consists of two main components: a loading mechanism and a rigid force transmission device. The JZ-5011 drop hammer impact testing machine is used 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 generated by the drop hammer can be adjusted by varying the weight of the hammer head, the drop hammer counterweight, the height of the drop hammer, and the thickness of the collision pad layer. The testing hammer used ranges in mass from 0.25 to 15.0 kg, with a radius of 2-50mm, and an impact height of 0-2000 mm. The rigid force transmission device comprises a steel column with an inclined end surface that fully contacts the inclined surface of the rock sample, maintaining a consistent inclination angle throughout. The rock sample's porosity and pore size distribution before and after impact testing are assessed using NMR technology 15 . As shown in Fig.2, the sample detection was conducted utilizing a large-bore NMR analyzer and imaging analysis system (MacroMR12-150H-I) developed by Niumai Analytical Instrument Co., Ltd. Suzhou, China. The equipment consists of a temperature control system, industrial computer, analysis software, radio frequency unit, and rare earth neodymium iron boron permanent magnet. It is capable of determining the porosity and pore size distribution of rock cores and cuttings, permeability, and fluid saturation, as well as providing two-dimensional imaging at various angles and multiple layers. Through a NMR analyzer and imaging analysis system, measurements of porosity, transverse relaxation time T 2 spectrum curve, and internal pore distribution images of the specimen can be obtained. NMR testing offers the benefits of being non-destructive, repeatable, safe, and rapid. The underlying principle of NMR detection lies in the interaction between hydrogen nuclei and an external magnetic field. By introducing a specific radio frequency pulse within the established magnetic field, the hydrogen nuclei resonate with the external magnetic field and absorb the energy from the radio frequency pulse. Following the cessation of the radio frequency pulse, the absorbed energy is gradually released by the hydrogen nuclei. The process in which a hydrogen nucleus transitions from a high-energy state to a low-energy state is called relaxation, where the transverse relaxation time T 2 is related to the pore structure of rocks. The transverse relaxation time T 2 can be obtained by detecting the energy release process and inverting the digital transmission signal. The ratio of surface area to volume of rock pores determines the NMR relaxation time T 2 . Therefore, the transverse relaxation time T 2 can intuitively reflect the microscopic structural changes inside rock samples at different stages of impact 24 . Prior to NMR detection, the sample needs to be saturated with water. The ZYB-II vacuum saturation pressure device is used to vacuum saturation the samples with a maximum vacuum saturation pressure of 60 MPa. 2.2 Preparation of rock samples The cylindrical sandstone sample used in the experiment had a diameter of 50 mm and a uniaxial compressive strength of 77 MPa. The rock samples were categorized into five groups according to the inclination angle α , with 5 samples in each group, totaling 25 samples. The distance ( h ) between the lower edge of the inclined surface and the bottom of the sample was 30 mm. The shape, size, and inclination angle of the samples are shown in Table 1 and Fig. 3. Figure 4 shows the sandstone samples with varying inclination angles. Table 1. Shape and size of the sample Group Inclination angle α /° Diameter d /mm Distance from the lower edge of the inclined surface to the bottom of the sample h/mm 1 40 50 30 2 45 3 50 4 55 5 60 2.3 Experimental method and procedure As shown in Fig. 5, during the impact test, it is necessary to determine the porosity and its variations using NMR during the experiment. In the drop hammer impact test, the hammer's mass is 9.5 kg, and the lifting height of the hammer is 2 m. The specific experimental steps are as follows: (1) Firstly, immerse the sample in water for 12 hours, then place it in the ZYB-II vacuum saturation device for vacuum saturation for 12 hours, with the pressure controlled at 20 MPa. After saturation, remove the sample, wipe off excess surface water, and wrap it with cling film. (2) Place the sample in the low magnetic field NMR rock core analysis measurement system to measure the sample porosity, T 2 spectrum, and internal pore NMR imaging. (3) Remove the cling film from the sample and place it in a drying oven at 105°C for 2 hours until the sample is dry. (4) Combine the sample with the inclined loading device to form an impact body and conduct impact tests on the JZ-5011 drop hammer impact testing machine. (5) Save the test data, repeat steps (1) to (4), and measure the sample porosity again after each impact. A total of 6 impact tests and 6 NMR detections were conducted. 3. Results and discussion 3.1 Damage characteristics 3.1.1 Variation of porosity after impact on rock samples with different inclined faces Rocks porosity reflects the ratio of internal defects, pores, and fractures to the total volume of rocks. The size of porosity directly affects the physical and mechanical properties of rocks. NMR technology enables a qualitative and quantitative description of the pore distribution characteristics in rocks by measuring the relaxation time of fluids in pores. Porosity measurements were carried out on rock samples after different numbers of impacts during the experiment. As shown in Fig. 6, the relationship curve between the porosity of sandstone samples at various angles and the number of impacts under the same impact energy is presented. Overall, the porosity decreases first and then increases with the increase in the number of impacts. For rock samples with incline angles of 40° and 45°, the porosity is the lowest after the first impact and the highest after the fifth impact. The porosity slightly decreases after the sixth impact, and some damage is observed in the rock samples. For samples with incline angles of 55° and 60°, the variation characteristics of porosity curves after impact are similar, demonstrating an initial decrease followed by an increase. The minimum porosity value is observed after the second impact, while the maximum value occurs after the sixth impact. The minimum porosity value is observed after the second impact, while the maximum value occurs after the sixth impact. Following the initial impact, a decline in porosity is noted, suggesting compression of certain pores and a reduction in the overall pore volume. Nevertheless, with successive impacts, the porosity gradually rises. This can be attributed to the multiple impact compression waves and reflected transmission waves causing ongoing alterations within the internal pores and fractures of the samples. Consequently, small pores expand into larger ones while new minor cracks emerge, leading to an increase in porosity. By comparing the variation of porosity under different inclinations, it can be observed that the porosity change is greater in samples with smaller inclination angles under the same cyclic impact load. In other words, the rate of change of porosity decreases as the slope angle increases. For a sample with a 40° inclined angle, the porosity was 10.21% before impact and increased to 10.92% after six impacts, resulting in a porosity change rate of 7.0%. In comparison, for a sample with a 60° inclined angle, the porosity before and after impacts were 8.25% and 8.80%, respectively, with a porosity change rate of 6.6%. A basic mechanical analysis indicates that as the slope angle increases, under the same impact force, the normal force component on the inclined surface decreases, resulting in reduced impact damage to the rock. 3.1.2 T 2 distribution of the rock samples The T 2 spectrum curve is the transverse relaxation response of 1H protons in completely water-saturated rock samples under the Carr-Purcell-Meiboom-Gill (CPMG) pulse sequence, reflecting the variation in the quantity of pores of different sizes. According to the transverse relaxation T 2 , the pores in rock samples can be classified into large pore size (T 2 >100ms), medium pore size (10ms<T 2 <100ms), and small pore size (T 2 10ms) and microscopic pores (T 2 <10ms). This study primarily adopts the second type of classification method. According to empirical methods, a transverse relaxation time of 10 ms corresponds to a pore of approximately 300nm in size 24 . Figure 7 illustrates the T 2 spectrum curves of inclined plane samples with five different inclined angles under the same cyclic impact load. The horizontal axis in the figure is T 2 relaxation time, with larger pores corresponding to greater values on the T 2 spectrum curve. The vertical axis indicates the quantity of pores, with higher values representing more pores of that size. The changing trends of each curve in the figure are similar. There are mainly two obvious spectrum peaks on the curve, and the signal amplitude of the first peak is significantly higher than that of the second peak. Compared with the T 2 spectrum curve before impact (No.0), the peak values of both peaks decreased to varying degrees after the first two impacts, indicating a reduction in the number of internal pores in the sample and an overall decrease in porosity. From the third impact to the sixth impact, the curves shift to the left overall, suggesting a gradual decrease in pore size. In terms of peak changes, the peak value of the first peak increases significantly with the number of impacts, while the peak value of the second peak gradually decreases. This means that the number of small pores within the rock sample increases while the large pores are compacted and the number of large pores decreases. The overall porosity shows an increasing trend. Taking the T 2 spectrum curve of a rock sample with a 45° inclined plane as an example, there is no significant lateral displacement in the curve after the first two impacts, and the total relaxation time was within 1000ms. This means that there has been no significant change in pore size. After the first impact, the peak value of the first peak in the T 2 spectrum curve remains unchanged, while the peak value of the second peak slightly decreases, indicating compaction of some large pores within the sample and no change in small pores. After the second impact, the first peak value decreases while the second peak value increases, indicating that some small pores have expanded into larger pores. The number of small pores decreases while the number of large pores increases. After the third impact, the curve undergoes the most significant changes, with both peaks shifting to the left, indicating an overall reduction in pore size. In addition, the first peak value significantly increased and the second peak value decreased, suggesting an increase in the number of small pores and a slight decrease in the number of large pores. After the fourth to sixth impacts, compared to after the third impact, there is no significant lateral shift in the two peaks, but their values fluctuate up and down, indicating a conversion between small and large pores. The overall change is not significant, and the total porosity gradually increases. Therefore, as the number of impacts increases, the first peak mainly shows changes in the vertical direction, with only the third impact causing a leftward shift. The second peak exhibits both vertical and horizontal changes during the impact process, indicating that under cyclic impact loads, the changes in the number of small pores within sandstone are predominant. At the same time, both the size and quantity of large pores also undergo variations. Additionally, the larger the inclination angle of the plane, the greater the signal amplitude corresponding to the peak values in the T 2 spectrum curve. The area enclosed by the T 2 spectral curve and the horizontal axis is referred to as the T 2 spectrum area, which is directly proportional to the amount of fluid in the rock and can serve as an important parameter reflecting changes in rock pore structure 16,24 . The NMR spectral area and macroscopic pore ratio of sandstone samples with different inclined planes after 6 impacts were calculated, as shown in Table 2. The total spectral area of the sandstone samples ranges from 90000 to 30000, with small pore spectral areas accounting for more than 65% and large pore spectral areas accounting for below 35%. This indicates that smaller-sized pores are more prevalent within the sandstone samples, while large-sized pores are less numerous. It can be seen from the T 2 spectrum curve that the signal values of small-sized pores are significantly higher. However, the overall trend of porosity changes aligns with variations in the spectrum areas of large-sized pores. Although there are many small-sized pores in the rock samples, large-sized pores are the main factor affecting porosity. Table 2. T 2 spectral area of rock samples with different angles under different impact frequency Inclination angle α /° Impact frequency T 2 spectral area Microscopic porosity ratio /% Macro porosity ratio /% 40 0 71064.12 66.27% 33.73% 1 67912.69 68.03% 31.97% 2 68917.37 67.47% 32.53% 3 75487.26 72.38% 27.62% 4 78139.86 72.41% 27.59% 5 80995.81 69.45% 30.55% 6 75905.19 73.54% 26.46% 45 0 73091.29 66.55% 33.45% 1 69220.40 68.17% 31.83% 2 70131.16 67.90% 32.10% 3 76396.46 73.54% 26.46% 4 79887.10 72.99% 27.01% 5 79414.97 73.01% 26.99% 6 78284.60 72.30% 27.70% 50 0 76463.04 68.27% 31.73% 1 73298.52 67.94% 32.06% 2 78592.57 70.84% 29.16% 3 83903.35 73.53% 26.47% 4 83699.35 73.46% 26.54% 5 82660.79 73.93% 26.07% 6 77644.57 72.40% 27.60% 55 0 75779.54 72.75% 27.25% 1 72609.12 72.06% 27.94% 2 74475.02 70.93% 29.07% 3 81043.59 76.57% 23.43% 4 84252.80 74.47% 25.53% 5 86304.48 75.02% 24.98% 6 84798.75 75.23% 24.77% 60 0 84607.31 71.21% 28.79% 1 80278.67 70.33% 29.67% 2 82366.63 69.94% 30.06% 3 84395.17 74.58% 25.42% 4 87590.64 72.94% 27.06% 5 87685.22 72.66% 27.34% 6 88250.83 70.92% 29.08% Comparing the changes in macro and micro pore proportions after different numbers of impacts on samples of five types of rocks, it is found that the pore changes are more significant in samples with small inclinations, while samples with larger inclination angles show minor changes. Taking the change in micro-pore proportion as an example, after 6 impacts, the micro-pore proportion increased by 7.27% for the 40° inclined plane sample, and the maximum micro-pore proportion for the 60° inclined plane sample occurred after the third impact, with a 4.64% increase compared to the second impact. 3.1.3 NMR imaging NMR imaging provides a visual representation of the spatial distribution and development status of internal pores in rock samples, which is crucial for studying rock damage. Figure 8 shows the NMR images of sandstone samples with inclination angles of 45 ° and 60 ° before and after six impacts. These images are cross-sectional images at a distance of 20mm from the bottom surface. The green spots in the images represent small-sized pores, while the yellow and red spots represent large-sized pores. Taking the image of a 45 ° inclined plane rock sample as an example, the image of the sample before impact is mainly composed of relatively uniform distributed green spots, indicating that the pore size in the rock sample is small and uniform. After the first impact, the porosity is the smallest. The spots on the right edge of the cross-section were significantly reduced, and the distribution of the spots is mainly concentrated on the left side. At the same time, a small amount of yellow and red spots appear, indicating that some small pores have expanded into large pores. After the fifth impact, the porosity is the highest. The number of spots on the cross-section is significantly increased, and a large number of yellow and red spots appear, indicating an increase in the number of macro-pores. After the sixth impact, the number of spots decreased slightly. However, there are obvious striped spots, indicating that some pores may have penetrated and formed a small number of cracks. Compared with the images of the 60 ° inclined plane rock sample, there is no obvious change in the number of spots on the cross-section during the impact process. The distribution of spots is relatively uniform, without obvious yellow, red, or striped spots appearing. It can be seen that if the inclination angle is too large, the damage degree to the rock sample caused by impact decreases. 3.2 Failure mechanism 3.2.1 Mechanical analysis of the inclined plane impact As shown in Fig. 9, the impact surface of the sample is elliptical due to the slope influence. The size of the long semi-axis size gradually changes with the inclination angle of the inclined plane. Assuming that the major and minor axes of the inclined plane are a and b , respectively. According to the geometric relationship, it can be obtained that b = a cosα= d /2, the inclined plane area A = π d 2 / 4cosα. Under 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 of the falling hammer can be decomposed into normal force F N ( F τ = P ) and tangential force F τ . The stress on the inclined plane can be decomposed into where, σ x and σ z are the horizontal stress and vertical stress on the inclined plane, Pa; P is the normal impact force on the inclined plane, N; F is The impact force of the falling hammer, N; d is the diameter of the sample, mm; α is the inclined angle. " K 1 " and " K 2 " are the component coefficients of horizontal and vertical directions, respectively. As shown in Fig. 10, as the angle of the inclined plane increases, the horizontal stress component first increases and then decreases, reaching its maximum value at an angle of 35°. The vertical stress component gradually decreases as the inclination angle increases. When the inclination angle is 45 °, the horizontal stress component and the vertical stress component are equal. In summary, compared to traditional vertical impact, the impact of inclined plane loading on rock samples induces not only vertical compressive stress but also damage and deformation caused by horizontal forces. Both the damage and failure are influenced by the inclination angle. With increasing inclination angle, under the same drop height, the vertical stress decreases while the horizontal stress increases, resulting in reduced damage at the lower part of the sample. 3.2.2 Quantitative analysis of damage To further investigate the internal damage and destruction of rock samples under different inclined plane impact frequencies, a damage variable D is introduced. The damage variable D is defined as a function of internal porosity as follows: where, n 0 represents the natural porosity of the rock sample, and n t represents the porosity of the rock sample after the t-th impact. As shown in Table 3, the damage degree of samples with different inclined angles after 6 impacts was calculated. Table 3. Statistical Table of damage variables Impact frequency 40° 45° 50° 55° 60° 1 -0.51% -0.58% -0.44% -0.89% -0.48% 2 -0.40% -0.09% -0.06% -0.87% -0.51% 3 0.92% 1.26% 1.51% 0.06% -0.05% 4 1.48% 1.77% 1.54% 0.46% 0.32% 5 1.89% 1.75% 1.38% 0.70% 0.31% 6 1.06% 1.55% 0.55% 0.52% 0.34% According to the result in Table 3, it can be seen that when the number of impacts is less than 2, the damage variable is negative. This indicates that under the first two impacts, the interior of the sample shows a state of pore compression. Since the third impact, except for the 60° rock samples, the damage variables have been positive. The maximum value of the damage variable occurs in the fourth or fifth impact, and the order of the maximum values of the damage variables at each angle is 40° > 45° > 50° > 55° > 60°. The maximum value of the damage variable occurs in the 40° rock sample of the fifth impact, and the minimum value appears in the 60° rock sample of the third impact. Under the same number of impacts, the damage degree of the 45° rock sample is generally the highest, while the damage degree of the 60° rock sample is the lowest. 3.2.3 Failure mode As shown in Fig. 11, after six cycles of inclined plane impact with the same energy, different types of cracks appeared in the upper part of the sample. The failure mode of the 45°~60° inclined plane sample is similar, with only one crack. However, the 40° inclined plane sample showed multiple cracks and a large amount of detachment at the bottom of the sample. The crack positions are all located within 20 mm of the upper end of the sample and parallel to the bottom surface of the sample. The failure type is a shear-tensile failure, as shown in Fig. 12. It is because the sharp corners of the sample are relatively thin, and the lateral force generated by the inclined plane impact causes the upper part of the rock sample to fail first. The impact damage and failure of rock samples on inclined planes are greatly affected by the angle of the inclined plane. The smaller the angle of the inclined plane, the smaller the transverse force and the larger the longitudinal force. The rock sample failure changes from a single transverse crack to multiple cracks. Therefore, the rock sample with a 40 ° inclined plane angle is the most severely damaged. 4. Conclusions Through drop hammer testing and inclined plane impact testing, experiments were conducted on samples at five different slope angles under varying numbers of impact loads. The damage degradation process of the samples before and after impact was analyzed using nuclear magnetic resonance detection, resulting in the following conclusions: (1) Under the same impact load, the sample's damage mode is significantly influenced by the slope angle. The larger the angle, the less the rock damage, requiring more impacts for failure, with the damage being more inclined towards the acute corner of the slope and characterized by shear-tensile failure. Smaller slope angles exhibit more intense porosity variations and greater rock damage. (2) Under the same energy of inclined impact, as the number of impacts increases, the sample's porosity first decreases, then increases, and then decreases again. The porosity is at its minimum after the first impact and reaches its maximum after the 5th impact. This is due to notable closure of large pores after the first impact, with the rock sample suffering the most severe damage after 5 impacts and ultimately failing after the 6th impact. (3) Under inclined impact, the significant influence on the sandstone samples remains the presence of large-sized pores, with large pore area ratios exceeding 95%. With an increasing number of impacts, the quantity of small pores decreases while the size and quantity of large pores both increase, indicating continuous deterioration of the rock with an increasing number of impacts. Declarations Competing interests The authors declare that there is no potential conflicts of interest. Author Contribution 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. Acknowledgement 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. Data Availability All data generated or analyzed during this study are included in this published article. References Wang, H. K. et al. Mechanical properties and damage evolution characteristics of composite rock mass with prefabricated fractures. Comput Part Mech , https://doi.org/10.1007/s40571-024-00719-w (2024). Salmi, E. F., Phan, T., Sellers, E. J. & Stacey, T. R. A review on the geotechnical design and optimisation of ultra-long ore passes for deep mass mining. Environmental Earth Sciences 83 , 301, https://doi.org/10.1007/s12665-024-11616-z (2024). Zhang, Q. B. & Zhao, J. 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Microscopic damage and dynamic mechanical properties of rock under freeze–thaw environment. Transactions of Nonferrous Metals Society of China 25 , 1254-1261, 10.1016/s1003-6326(15)63723-2 (2015). Rios, E. H., Ramos, P. F. D., Machado, V. D., Stael, G. C. & Azeredo, R. B. D. Modeling rock permeability from NMR relaxation data by PLS regression. Journal of Applied Geophysics 75 , 631-637, 10.1016/j.jappgeo.2011.09.022 (2011). Weng, L., Wu, Z. & Li, X. Mesodamage Characteristics of Rock with a Pre-cut Opening Under Combined Static–Dynamic Loads: A Nuclear Magnetic Resonance (NMR) Investigation. Rock Mechanics and Rock Engineering 51 , 2339-2354, https://doi.org/10.1007/s00603-018-1483-4 (2018). Fu, T. F. et al. Analysis of capillary water imbibition in sandstone via a combination of nuclear magnetic resonance imaging and numerical DEM modeling. Engineering Geology 285 , 106070, https://doi.org/10.1016/j.enggeo.2021.106070 (2021). Jiang, L. C., Ji, H. Y. & Xue, L. L. Shaft Wall Damage to High-Depth Inclined Ore Passes under Impact Wear Behavior. Appl Sci-Basel 13 , 13065, 10.20944/preprints202310.2038.v1 (2023). Esmaieli, K. & Hadjigeorgiou, J. Selecting Ore Pass-Finger Raise Configurations in Underground Mines. Rock Mechanics and Rock Engineering 44 , 291-303, 10.1007/s00603-010-0128-z (2011). Li, D. Y., Han, Z. Y., Zhu, Q. Q., Zhang, Y. & Ranjith, P. G. Stress wave propagation and dynamic behavior of red sandstone with single bonded planar joint at various angles. International Journal of Rock Mechanics and Mining Sciences 117 , 162-170, https://doi.org/10.1016/j.ijrmms.2019.03.011 (2019). Xia, Z. G. et al. Mechanical Properties and Damage Characteristics of Coal-Rock Combination with Different Dip Angles. Ksce Journal of Civil Engineering 25 , 1687-1699, 10.1007/s12205-021-1366-1 (2021). Wu, X. X., Lu, Z. X., Zou, X., Deng, Z. & Cao, P. Variation characteristics and mechanical mechanism of porosity of sandstone specimens under oblique impact. Journal of Central South University(Science and Technology) 53 , 4514-4522 (2022). Liu, C., Deng, H., Chen, X., Xiao, D. & Li, B. Impact of Rock Samples Size on the Microstructural Changes Induced by Freeze–Thaw Cycles. Rock Mechanics and Rock Engineering 53 , 5293-5300, https://doi.org/10.1007/s00603-020-02201-4 (2020). Additional Declarations No competing interests reported. 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Also discoverable on Platform About Our Team In Review Editorial Policies Advisory Board Help Center Resources Author Services Accessibility API Access RSS feed Manage Cookie Preferences © Research Square 2026 | ISSN 2693-5015 (online) Privacy Policy Terms of Service Do Not Sell My Personal Information {"props":{"pageProps":{"initialData":{"identity":"rs-4674701","acceptedTermsAndConditions":true,"allowDirectSubmit":false,"archivedVersions":[],"articleType":"Article","associatedPublications":[],"authors":[{"id":331880180,"identity":"c027076d-4986-4fa2-bbe4-e3526c484fff","order_by":0,"name":"Xinrong Wang","email":"","orcid":"","institution":"University of Science and Technology Liaoning","correspondingAuthor":false,"prefix":"","firstName":"Xinrong","middleName":"","lastName":"Wang","suffix":""},{"id":331880181,"identity":"2d838850-e131-4f98-886b-08d73aac7a28","order_by":1,"name":"Xu Zou","email":"","orcid":"","institution":"Zhaojin Mining Industry 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impact\u003c/p\u003e","description":"","filename":"1.png","url":"https://assets-eu.researchsquare.com/files/rs-4674701/v1/31e476b69184a2afc07417a0.png"},{"id":61356966,"identity":"ed765268-0435-4b7a-812e-c28c3d6831c3","added_by":"auto","created_at":"2024-07-29 21:08:00","extension":"png","order_by":2,"title":"Figure 2","display":"","copyAsset":false,"role":"figure","size":104093,"visible":true,"origin":"","legend":"\u003cp\u003eNuclear magnetic resonance imaging analyzer\u003c/p\u003e","description":"","filename":"2.png","url":"https://assets-eu.researchsquare.com/files/rs-4674701/v1/abff87c3c635df46ffdb2724.png"},{"id":61356973,"identity":"cca06b5e-d4f9-4302-87ab-f76f3dff1ca2","added_by":"auto","created_at":"2024-07-29 21:08:00","extension":"png","order_by":3,"title":"Figure 3","display":"","copyAsset":false,"role":"figure","size":5581,"visible":true,"origin":"","legend":"\u003cp\u003eSketch map of a test sample\u003c/p\u003e","description":"","filename":"3.png","url":"https://assets-eu.researchsquare.com/files/rs-4674701/v1/77699c2143f1b895337c5f7f.png"},{"id":61358839,"identity":"0d27b0c8-0a8b-49cd-a362-fae8f1ef0bc0","added_by":"auto","created_at":"2024-07-29 21:24:00","extension":"png","order_by":4,"title":"Figure 4","display":"","copyAsset":false,"role":"figure","size":159401,"visible":true,"origin":"","legend":"\u003cp\u003eSandstone samples with different inclination angles.\u003c/p\u003e","description":"","filename":"4.png","url":"https://assets-eu.researchsquare.com/files/rs-4674701/v1/5b57379a1c63aa7c55338636.png"},{"id":61358095,"identity":"fc6f8cff-af8d-4f0d-bbeb-d98f8305ba20","added_by":"auto","created_at":"2024-07-29 21:16:00","extension":"png","order_by":5,"title":"Figure 5","display":"","copyAsset":false,"role":"figure","size":39624,"visible":true,"origin":"","legend":"\u003cp\u003eTest flow chart\u003c/p\u003e","description":"","filename":"5.png","url":"https://assets-eu.researchsquare.com/files/rs-4674701/v1/8df265d481e5943ccf2ce2bf.png"},{"id":61356968,"identity":"9efc4ab5-5d9c-460a-8f2c-b381af73a21f","added_by":"auto","created_at":"2024-07-29 21:08:00","extension":"png","order_by":6,"title":"Figure 6","display":"","copyAsset":false,"role":"figure","size":12515,"visible":true,"origin":"","legend":"\u003cp\u003ePorosity curves of rock samples at different angles under cyclic impact\u003c/p\u003e","description":"","filename":"6.png","url":"https://assets-eu.researchsquare.com/files/rs-4674701/v1/19eb8598244e97f55a3f9bbd.png"},{"id":61356976,"identity":"ac865450-09e3-47e5-a005-17b9fd8afb4a","added_by":"auto","created_at":"2024-07-29 21:08:00","extension":"png","order_by":7,"title":"Figure 7","display":"","copyAsset":false,"role":"figure","size":273252,"visible":true,"origin":"","legend":"\u003cp\u003eDistribution of T\u003csub\u003e2\u003c/sub\u003e spectrum under cyclic impact load of rock samples at different angles\u003c/p\u003e","description":"","filename":"7.png","url":"https://assets-eu.researchsquare.com/files/rs-4674701/v1/3f35f65754880815978d1afe.png"},{"id":61356975,"identity":"315a9c10-27d7-4a18-82c6-ee9713d255df","added_by":"auto","created_at":"2024-07-29 21:08:00","extension":"png","order_by":8,"title":"Figure 8","display":"","copyAsset":false,"role":"figure","size":328468,"visible":true,"origin":"","legend":"\u003cp\u003eNMR images of rock samples before and after cyclic impact\u003c/p\u003e","description":"","filename":"8.png","url":"https://assets-eu.researchsquare.com/files/rs-4674701/v1/71f8b51564b60a316fc25ead.png"},{"id":61356971,"identity":"503c82c0-52d5-4824-ba63-0e79271ac60d","added_by":"auto","created_at":"2024-07-29 21:08:00","extension":"png","order_by":9,"title":"Figure 9","display":"","copyAsset":false,"role":"figure","size":18992,"visible":true,"origin":"","legend":"\u003cp\u003eAnalysis of impact force at the moment of impact\u003c/p\u003e","description":"","filename":"9.png","url":"https://assets-eu.researchsquare.com/files/rs-4674701/v1/4230ad54364d53bba708d553.png"},{"id":61356972,"identity":"58e4ee54-314f-4f7c-827c-2698a0536c8f","added_by":"auto","created_at":"2024-07-29 21:08:00","extension":"png","order_by":10,"title":"Figure 10","display":"","copyAsset":false,"role":"figure","size":12097,"visible":true,"origin":"","legend":"\u003cp\u003eComponent coefficient curve of inclined impact force\u003c/p\u003e","description":"","filename":"10.png","url":"https://assets-eu.researchsquare.com/files/rs-4674701/v1/1e771d5bacebbf2ccfb455fc.png"},{"id":61358098,"identity":"cea1e583-1fbd-4117-a00e-fefeae98eeeb","added_by":"auto","created_at":"2024-07-29 21:16:00","extension":"png","order_by":11,"title":"Figure 11","display":"","copyAsset":false,"role":"figure","size":98169,"visible":true,"origin":"","legend":"\u003cp\u003eFailure modes of rock samples\u003c/p\u003e","description":"","filename":"11.png","url":"https://assets-eu.researchsquare.com/files/rs-4674701/v1/521d5f155008e049721117bc.png"},{"id":61358097,"identity":"f92f060d-3f90-495e-a5b7-b46aaeffdd03","added_by":"auto","created_at":"2024-07-29 21:16:00","extension":"png","order_by":12,"title":"Figure 12","display":"","copyAsset":false,"role":"figure","size":112012,"visible":true,"origin":"","legend":"\u003cp\u003eFailure modes of 45° rock samples\u003c/p\u003e","description":"","filename":"12.png","url":"https://assets-eu.researchsquare.com/files/rs-4674701/v1/c56ffc0fc40f6f9149546cad.png"},{"id":61359169,"identity":"d85876ec-b9f6-4ad9-9c8c-71f607030a38","added_by":"auto","created_at":"2024-07-29 21:32:01","extension":"pdf","order_by":0,"title":"","display":"","copyAsset":false,"role":"manuscript-pdf","size":2105273,"visible":true,"origin":"","legend":"","description":"","filename":"manuscript.pdf","url":"https://assets-eu.researchsquare.com/files/rs-4674701/v1/187fc88e-115d-4ea2-83c4-6231acc4b5c7.pdf"}],"financialInterests":"No competing interests reported.","formattedTitle":"Cumulative damage characteristics of rock samples under cyclic low energy inclined plane impact","fulltext":[{"header":"1. Introduction","content":"\u003cp\u003eRock, as widely existing natural heterogeneous materials in nature, form with initial defects such as bedding planes and micro-cracks during the forming process\u003csup\u003e1\u003c/sup\u003e. In the development and utilization of underground spaces, rocks are inevitably subjected to original rock stress and secondary disturbance stress induced by excavation. Accompanied by impact and compression loads, initial damages will further evolve, leading to extensive rock failure. Taking underground mine ore passes as an example, the surrounding rock mass of the ore pass is affected by both rock pressure and blasting disturbances. More importantly, during the ore unloading process in the mine ore pass, collisions between ore blocks and the wall of the ore pass will inevitably cause impact abrasion on the wall, potentially resulting in the enlargement of the ore pass diameter or even collapse of the ore pass\u003csup\u003e2\u003c/sup\u003e. It has become a bottleneck in underground mining ore transportation. Therefore, conducting research on the damage evolution process of rocks under impact loading is of great significance for the safe construction and disaster prevention of underground engineering.\u003c/p\u003e \u003cp\u003eMany scholars have combined theoretical analysis, physical experiments, and numerical simulation methods to study dynamic fracturing and damage patterns of rocks\u003csup\u003e3\u0026ndash;6\u003c/sup\u003e. Rock specimens' macroscopic impact failure process can be divided into initial damage, cumulative damage, and macroscopic failure\u003csup\u003e7\u003c/sup\u003e. Currently, most studies analyze the dynamic mechanical properties of rocks through impact tests. Common equipment used to study the dynamic mechanical properties of materials in engineering includes the Split Hopkinson Pressure Bar (SHPB) system and drop hammer test devices. Numerous studies focus on the mechanical responses of rocks under dynamic conditions, including various impact loading speeds, energies, and constraint conditions\u003csup\u003e8\u003c/sup\u003e. Some scholars have analyzed the shear characteristics of rocks under combined static-dynamic loads using physical experiments and numerical simulation methods\u003csup\u003e9,10\u003c/sup\u003e. With the continuous development of detection technologies, the study of microscopic damage inside rocks under dynamic loads has become a recent research hotspot. Techniques such as computed tomography (CT) scanning\u003csup\u003e11\u003c/sup\u003e, scanning electron microscopy (SEM)\u003csup\u003e12\u003c/sup\u003e, acoustic emission testing, and nuclear magnetic resonance (NMR) detection\u003csup\u003e13\u003c/sup\u003e can effectively analyze and understand the microscopic damage characteristics of rocks. In recent years, NMR detection technology has been widely used in medicine, geotechnical engineering, and materials. In geotechnical engineering, parameters such as porosity, permeability, and free fluid index inside specimens can be measured using NMR technology to describe the microscopic damage of materials14 intuitively\u003csup\u003e14\u003c/sup\u003e. This has led to the development of NMR relaxation theories to study the damage of porous mediums in rocks\u003csup\u003e15,16\u003c/sup\u003e. Weng et al.\u003csup\u003e17\u003c/sup\u003eused NMR technology to study the microscopic damage characteristics of pre-cut opening in rocks under static-dynamic combined loading. Fu et al. \u003csup\u003e18\u003c/sup\u003e analyzed the dynamic process of capillary water imbibition in sandstone samples using NMR technology.\u003c/p\u003e \u003cp\u003eThere are many studies on the cyclic impact failure mechanism of different rock materials. However, most rock impact tests involve axial impact on rock samples. In practical engineering, the phenomenon of inclined plane impacts where the impact force is not perpendicular to the impacted surface is also common. For example, when unloading ore in mine ore passes, the collision between ore rocks and the ore pass wall is not always a normal impact. Most ore rocks move in an inclined parabolic trajectory in the ore pass. When ore blocks collide with the wall, the angle between the direction of impact force and the ore pass wall also affects the extent of wall damage. From an engineering perspective, Jiang et al. \u003csup\u003e19\u003c/sup\u003e combined theoretical analysis and numerical simulation to study the impact abrasion behaviour of ore rocks on ore pass walls in highly inclined mine ore passes. Esmaieli et al. \u003csup\u003e20\u003c/sup\u003e used numerical calculation methods to determine that the impact of ore rocks on ore pass walls leads to localized damage and accelerates failure. In terms of rock inclined plane impact, scholars have also conducted preliminary studies on the mechanical characteristics and damage characteristics of layered rocks\u003csup\u003e7\u003c/sup\u003e, rocks with different fracture surfaces\u003csup\u003e21\u003c/sup\u003e, and coal-rock combinations with different slope angles\u003csup\u003e22\u003c/sup\u003e. Wu et al. \u003csup\u003e23\u003c/sup\u003e analyzed the impact damage characteristics of different inclined plane angles based on an inclined plane impact experimental device. However, from a microscopic perspective, the mechanism of rock damage caused by inclined impact still needs further in-depth research.\u003c/p\u003e \u003cp\u003eIn summary, significant progress has been made in understanding the dynamic characteristics and damage evolution mechanisms of rock impacts, which have actively promoted the safety and efficiency of underground engineering production. However, there are still many gaps in research on inclined impacts where the impact force is not perpendicular to the impacted surface, such as rock impacts on mine ore pass walls and wind-blown impacts on building surfaces. 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.\u003c/p\u003e"},{"header":"2. Materials and Experimental Methods","content":"\u003ch2\u003e2.1 Experimental Setup\u003c/h2\u003e\n\u003cp\u003eAs shown in Fig.1, the testing equipment consists of two main components: a loading mechanism and a rigid force transmission device. The JZ-5011 drop hammer impact testing machine is used 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 generated by the drop hammer can be adjusted by varying the weight of the hammer head, the drop hammer counterweight, the height of the drop hammer, and the thickness of the collision pad layer. The testing hammer used ranges in mass from 0.25 to 15.0 kg, with a radius of 2-50mm, and an impact height of 0-2000 mm. The rigid force transmission device comprises a steel column with an inclined end surface that fully contacts the inclined surface of the rock sample, maintaining a consistent inclination angle throughout.\u003c/p\u003e\n\u003cp\u003eThe rock sample\u0026apos;s porosity and pore size distribution before and after impact testing are assessed using NMR technology\u003csup\u003e15\u003c/sup\u003e. As shown in Fig.2, the sample detection was conducted utilizing a large-bore NMR analyzer and imaging analysis system (MacroMR12-150H-I) developed by Niumai Analytical Instrument Co., Ltd. Suzhou, China. The equipment consists of a temperature control system, industrial computer, analysis software, radio frequency unit, and rare earth neodymium iron boron permanent magnet. It is capable of determining the porosity and pore size distribution of rock cores and cuttings, permeability, and fluid saturation, as well as providing two-dimensional imaging at various angles and multiple layers. Through a NMR analyzer and imaging analysis system, measurements of porosity, transverse relaxation time T\u003csub\u003e2\u003c/sub\u003e spectrum curve, and internal pore distribution images of the specimen can be obtained.\u003c/p\u003e\n\u003cp\u003eNMR testing offers the benefits of being non-destructive, repeatable, safe, and rapid. The underlying principle of NMR detection lies in the interaction between hydrogen nuclei and an external magnetic field. By introducing a specific radio frequency pulse within the established magnetic field, the hydrogen nuclei resonate with the external magnetic field and absorb the energy from the radio frequency pulse. Following the cessation\u0026nbsp;of the radio frequency pulse, the absorbed energy is gradually released by the hydrogen nuclei. The process in which a hydrogen nucleus transitions from a high-energy state to a low-energy state is called relaxation, where the transverse relaxation time T\u003csub\u003e2\u003c/sub\u003e is related to the pore structure of rocks. The transverse relaxation time T\u003csub\u003e2\u003c/sub\u003e can be obtained by detecting the energy release process and inverting the digital transmission signal. The ratio of surface area to volume of rock pores determines the NMR relaxation time T\u003csub\u003e2\u003c/sub\u003e. Therefore, the transverse relaxation time T\u003csub\u003e2\u003c/sub\u003e can intuitively reflect the microscopic structural changes inside rock samples at different stages of impact\u003csup\u003e24\u003c/sup\u003e.\u003c/p\u003e\n\u003cp\u003ePrior to NMR detection, the sample needs to be saturated with water. The ZYB-II vacuum saturation pressure device is used to vacuum saturation the samples with a maximum vacuum saturation pressure of 60 MPa.\u003c/p\u003e\n\u003ch2\u003e2.2 Preparation of rock samples\u003c/h2\u003e\n\u003cp\u003eThe cylindrical sandstone sample used in the experiment had a diameter of 50 mm and a uniaxial compressive strength of 77 MPa. The rock samples were categorized into five groups according to the inclination angle \u003cem\u003e\u0026alpha;\u003c/em\u003e, with 5 samples in each group, totaling 25 samples. The distance (\u003cem\u003eh\u003c/em\u003e) between the lower edge of the inclined surface and the bottom of the sample was 30 mm. The shape, size, and inclination angle of the samples are shown in Table 1 and Fig. 3. Figure 4 shows the sandstone samples with varying inclination angles.\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003eTable 1.\u003c/strong\u003e Shape and size of the sample\u003c/p\u003e\n\u003cdiv align=\"center\"\u003e\n \u003ctable border=\"1\" cellspacing=\"0\" cellpadding=\"0\" width=\"100%\"\u003e\n \u003ctbody\u003e\n \u003ctr\u003e\n \u003ctd width=\"10.309278350515465%\"\u003e\n \u003cp\u003eGroup\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"23.711340206185568%\" style=\"width: 28.269%;\"\u003e\n \u003cp\u003eInclination angle \u003cem\u003e\u0026alpha;\u003c/em\u003e /\u0026deg;\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"20.61855670103093%\" style=\"width: 13.3247%;\"\u003e\n \u003cp\u003eDiameter \u003cem\u003ed\u003c/em\u003e /mm\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"45.36082474226804%\" style=\"width: 30.0672%;\"\u003e\n \u003cp\u003eDistance from the lower edge of the inclined surface to the bottom of the sample\u0026nbsp;h/mm\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd width=\"10.309278350515465%\"\u003e\n \u003cp\u003e1\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"23.711340206185568%\" style=\"width: 28.269%;\"\u003e\n \u003cp\u003e40\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"20.61855670103093%\" rowspan=\"5\" style=\"width: 13.3247%;\"\u003e\n \u003cp\u003e50\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"45.36082474226804%\" rowspan=\"5\" style=\"width: 30.0672%;\"\u003e\n \u003cp\u003e30\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd width=\"30.303030303030305%\"\u003e\n \u003cp\u003e2\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"69.6969696969697%\" style=\"width: 28.269%;\"\u003e\n \u003cp\u003e45\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd width=\"30.303030303030305%\"\u003e\n \u003cp\u003e3\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"69.6969696969697%\" style=\"width: 28.269%;\"\u003e\n \u003cp\u003e50\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd width=\"30.303030303030305%\"\u003e\n \u003cp\u003e4\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"69.6969696969697%\" style=\"width: 28.269%;\"\u003e\n \u003cp\u003e55\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd width=\"30.303030303030305%\"\u003e\n \u003cp\u003e5\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"69.6969696969697%\" style=\"width: 28.269%;\"\u003e\n \u003cp\u003e60\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003c/tbody\u003e\n \u003c/table\u003e\n\u003c/div\u003e\n\u003ch2\u003e2.3 Experimental method and procedure\u003c/h2\u003e\n\u003cp\u003eAs shown in Fig. 5, during the impact test, it is necessary to determine the porosity and its variations using NMR during the experiment. In the drop hammer impact test, the hammer\u0026apos;s mass is 9.5 kg, and the lifting height of the hammer is 2 m. The specific experimental steps are as follows:\u003c/p\u003e\n\u003cp\u003e(1) Firstly, immerse the sample in water for 12 hours, then place it in the ZYB-II vacuum saturation device for vacuum saturation for 12 hours, with the pressure controlled at 20 MPa. After saturation, remove the sample, wipe off excess surface water, and wrap it with cling film.\u003c/p\u003e\n\u003cp\u003e(2) Place the sample in the low magnetic field NMR rock core analysis measurement system to measure the sample porosity, T\u003csub\u003e2\u003c/sub\u003e spectrum, and internal pore NMR imaging.\u003c/p\u003e\n\u003cp\u003e(3) Remove the cling film from the sample and place it in a drying oven at 105\u0026deg;C for 2 hours until the sample is dry.\u003c/p\u003e\n\u003cp\u003e(4) Combine the sample with the inclined loading device to form an impact body and conduct impact tests on the JZ-5011 drop hammer impact testing machine.\u003c/p\u003e\n\u003cp\u003e(5) Save the test data, repeat steps (1) to (4), and measure the sample porosity again after each impact. A total of 6 impact tests and 6 NMR detections were conducted.\u003c/p\u003e\n\u003cp\u003e\u003cbr\u003e\u003c/p\u003e"},{"header":"3. Results and discussion","content":"\u003ch2\u003e3.1 Damage characteristics\u003c/h2\u003e\n\u003ch3\u003e3.1.1 Variation of porosity after impact on rock samples with different inclined faces\u003c/h3\u003e\n\u003cp\u003eRocks porosity reflects the ratio of internal defects, pores, and fractures to the total volume of rocks. The size of porosity directly affects the physical and mechanical properties of rocks. NMR technology enables a qualitative and quantitative description of the pore distribution characteristics in rocks by measuring the relaxation time of fluids in pores. Porosity measurements were carried out on rock samples after different numbers of impacts during the experiment. As shown in Fig. 6, the relationship curve between the porosity of sandstone samples at various angles and the number of impacts under the same impact energy is presented. Overall, the porosity decreases first and then increases with the increase in the number of impacts.\u003c/p\u003e\n\u003cp\u003eFor rock samples with incline angles of 40\u0026deg; and 45\u0026deg;, the porosity is the lowest after the first impact and the highest after the fifth impact. The porosity slightly decreases after the sixth impact, and some damage is observed in the rock samples. For samples with incline angles of 55\u0026deg; and 60\u0026deg;, the variation characteristics of porosity curves after impact are similar, demonstrating an initial decrease followed by an increase. The minimum porosity value is observed after the second impact, while the maximum value occurs after the sixth impact. The minimum porosity value is observed after the second impact, while the maximum value occurs after the sixth impact. Following the initial impact, a decline in porosity is noted, suggesting compression of certain pores and a reduction in the overall pore volume.\u003c/p\u003e\n\u003cp\u003eNevertheless, with successive impacts, the porosity gradually rises. This can be attributed to the multiple impact compression waves and reflected transmission waves causing ongoing alterations within the internal pores and fractures of the samples. Consequently, small pores expand into larger ones while new minor cracks emerge, leading to an increase in porosity.\u003c/p\u003e\n\u003cp\u003eBy comparing the variation of porosity under different inclinations, it can be observed that the porosity change is greater in samples with smaller inclination angles under the same cyclic impact load. In other words, the rate of change of porosity decreases as the slope angle increases.\u003c/p\u003e\n\u003cp\u003eFor a sample with a 40\u0026deg; inclined angle, the porosity was 10.21% before impact and increased to 10.92% after six impacts, resulting in a porosity change rate of 7.0%. In comparison, for a sample with a 60\u0026deg; inclined angle, the porosity before and after impacts were 8.25% and 8.80%, respectively, with a porosity change rate of 6.6%. A basic mechanical analysis indicates that as the slope angle increases, under the same impact force, the normal force component on the inclined surface decreases, resulting in reduced impact damage to the rock.\u003c/p\u003e\n\u003ch3\u003e3.1.2 T\u003csub\u003e2\u003c/sub\u003e distribution of the rock samples\u003c/h3\u003e\n\u003cp\u003eThe T\u003csub\u003e2\u003c/sub\u003e spectrum curve is the transverse relaxation response of 1H protons in completely water-saturated rock samples under the Carr-Purcell-Meiboom-Gill (CPMG) pulse sequence, reflecting the variation in the quantity of pores of different sizes. According to the transverse relaxation T\u003csub\u003e2\u003c/sub\u003e, the pores in rock samples can be classified into large pore size (T\u003csub\u003e2\u003c/sub\u003e\u0026gt;100ms), medium pore size (10ms\u0026lt;T\u003csub\u003e2\u003c/sub\u003e\u0026lt;100ms), and small pore size (T\u003csub\u003e2\u003c/sub\u003e\u0026lt;10ms) \u003csup\u003e13\u003c/sup\u003e. Some scholars have also classified the pores in rocks into two main types based on the critical value of 10ms, namely macroscopic pores (T\u003csub\u003e2\u003c/sub\u003e\u0026gt;10ms) and microscopic pores (T\u003csub\u003e2\u003c/sub\u003e\u0026lt;10ms). This study primarily adopts the second type of classification method. According to empirical methods, a transverse relaxation time of 10 ms corresponds to a pore of approximately 300nm in size\u003csup\u003e24\u003c/sup\u003e.\u003c/p\u003e\n\u003cp\u003eFigure 7\u0026nbsp;illustrates the T\u003csub\u003e2\u003c/sub\u003e spectrum curves of inclined plane samples with five different inclined angles under the same cyclic impact load. The horizontal axis in the figure is T\u003csub\u003e2\u003c/sub\u003e relaxation time, with larger pores corresponding to greater values on the T\u003csub\u003e2\u003c/sub\u003e spectrum curve. The vertical axis indicates the quantity of pores, with higher values representing more pores of that size.\u003c/p\u003e\n\u003cp\u003eThe changing trends of each curve in the figure are similar. There are mainly two obvious spectrum peaks on the curve, and the signal amplitude of the first peak is significantly higher than that of the second peak. Compared with the T\u003csub\u003e2\u003c/sub\u003e spectrum curve before impact (No.0), the peak values of both peaks decreased to varying degrees after the first two impacts, indicating a reduction in the number of internal pores in the sample and an overall decrease in porosity. From the third impact to the sixth impact, the curves shift to the left overall, suggesting a gradual decrease in pore size. In terms of peak changes, the peak value of the first peak increases significantly with the number of impacts, while the peak value of the second peak gradually decreases. This means that the number of small pores within the rock sample increases while the large pores are compacted and the number of large pores decreases. The overall porosity shows an increasing trend.\u003c/p\u003e\n\u003cp\u003eTaking the T\u003csub\u003e2\u003c/sub\u003e spectrum curve of a rock sample with a 45\u0026deg; inclined plane as an example, there is no significant lateral displacement in the curve after the first two impacts, and the total relaxation time was within 1000ms. This means that there has been no significant change in pore size. After the first impact, the peak value of the first peak in the T\u003csub\u003e2\u003c/sub\u003e spectrum curve remains unchanged, while the peak value of the second peak slightly decreases, indicating compaction of some large pores within the sample and no change in small pores. After the second impact, the first peak value decreases while the second peak value increases, indicating that some small pores have expanded into larger pores. The number of small pores decreases while the number of large pores increases. After the third impact, the curve undergoes the most significant changes, with both peaks shifting to the left, indicating an overall reduction in pore size. In addition, the first peak value significantly increased and the second peak value decreased, suggesting an increase in the number of small pores and a slight decrease in the number of large pores. After the fourth to sixth impacts, compared to after the third impact, there is no significant lateral shift in the two peaks, but their values fluctuate up and down, indicating a conversion between small and large pores. The overall change is not significant, and the total porosity gradually increases.\u003c/p\u003e\n\u003cp\u003eTherefore, as the number of impacts increases, the first peak mainly shows changes in the vertical direction, with only the third impact causing a leftward shift. The second peak exhibits both vertical and horizontal changes during the impact process, indicating that under cyclic impact loads, the changes in the number of small pores within sandstone are predominant. At the same time, both the size and quantity of large pores also undergo variations. Additionally, the larger the inclination angle of the plane, the greater the signal amplitude corresponding to the peak values in the T\u003csub\u003e2\u003c/sub\u003e spectrum curve.\u003c/p\u003e\n\u003cp\u003eThe area enclosed by the T\u003csub\u003e2\u0026nbsp;\u003c/sub\u003espectral curve and the horizontal axis is referred to as the T\u003csub\u003e2\u003c/sub\u003e spectrum area, which is directly proportional to the amount of fluid in the rock and can serve as an important parameter reflecting changes in rock pore structure\u003csup\u003e16,24\u003c/sup\u003e. The NMR spectral area and macroscopic pore ratio of sandstone samples with different inclined planes after 6 impacts were calculated, as shown in Table 2. The total spectral area of the sandstone samples ranges from 90000 to 30000, with small pore spectral areas accounting for more than 65% and large pore spectral areas accounting for below 35%. This indicates that smaller-sized pores are more prevalent within the sandstone samples, while large-sized pores are less numerous. It can be seen from the T\u003csub\u003e2\u003c/sub\u003e spectrum curve that the signal values of small-sized pores are significantly higher. However, the overall trend of porosity changes aligns with variations in the spectrum areas of large-sized pores. Although there are many small-sized pores in the rock samples, large-sized pores are the main factor affecting porosity.\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003eTable 2.\u003c/strong\u003e T\u003csub\u003e2\u003c/sub\u003e spectral area of rock samples with different angles under different impact frequency\u003c/p\u003e\n\u003cdiv align=\"center\"\u003e\n \u003ctable border=\"1\" cellspacing=\"0\" cellpadding=\"0\"\u003e\n \u003ctbody\u003e\n \u003ctr\u003e\n \u003ctd width=\"19.09547738693467%\"\u003e\n \u003cp\u003eInclination angle \u003cem\u003e\u0026alpha;\u003c/em\u003e /\u0026deg;\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"19.09547738693467%\"\u003e\n \u003cp\u003eImpact frequency\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"14.57286432160804%\"\u003e\n \u003cp\u003eT\u003csub\u003e2\u003c/sub\u003e spectral area\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"23.366834170854272%\"\u003e\n \u003cp\u003eMicroscopic porosity ratio /%\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"23.86934673366834%\"\u003e\n \u003cp\u003eMacro porosity ratio /%\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd width=\"19.09547738693467%\" rowspan=\"7\"\u003e\n \u003cp\u003e40\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"19.09547738693467%\"\u003e\n \u003cp\u003e0\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"14.57286432160804%\"\u003e\n \u003cp\u003e71064.12\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"23.366834170854272%\" valign=\"top\"\u003e\n \u003cp\u003e66.27%\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"23.86934673366834%\" valign=\"top\"\u003e\n \u003cp\u003e33.73%\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd width=\"23.60248447204969%\"\u003e\n \u003cp\u003e1\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"18.012422360248447%\"\u003e\n \u003cp\u003e67912.69\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"28.88198757763975%\" valign=\"top\"\u003e\n \u003cp\u003e68.03%\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"29.503105590062113%\" valign=\"top\"\u003e\n \u003cp\u003e31.97%\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd width=\"23.60248447204969%\"\u003e\n \u003cp\u003e2\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"18.012422360248447%\"\u003e\n \u003cp\u003e68917.37\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"28.88198757763975%\" valign=\"top\"\u003e\n \u003cp\u003e67.47%\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"29.503105590062113%\" valign=\"top\"\u003e\n \u003cp\u003e32.53%\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd width=\"23.60248447204969%\"\u003e\n \u003cp\u003e3\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"18.012422360248447%\"\u003e\n \u003cp\u003e75487.26\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"28.88198757763975%\" valign=\"top\"\u003e\n \u003cp\u003e72.38%\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"29.503105590062113%\" valign=\"top\"\u003e\n \u003cp\u003e27.62%\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd width=\"23.60248447204969%\"\u003e\n \u003cp\u003e4\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"18.012422360248447%\"\u003e\n \u003cp\u003e78139.86\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"28.88198757763975%\" valign=\"top\"\u003e\n \u003cp\u003e72.41%\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"29.503105590062113%\" valign=\"top\"\u003e\n \u003cp\u003e27.59%\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd width=\"23.60248447204969%\"\u003e\n \u003cp\u003e5\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"18.012422360248447%\"\u003e\n \u003cp\u003e80995.81\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"28.88198757763975%\" valign=\"top\"\u003e\n \u003cp\u003e69.45%\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"29.503105590062113%\" valign=\"top\"\u003e\n \u003cp\u003e30.55%\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd width=\"23.60248447204969%\"\u003e\n \u003cp\u003e6\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"18.012422360248447%\"\u003e\n \u003cp\u003e75905.19\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"28.88198757763975%\" valign=\"top\"\u003e\n \u003cp\u003e73.54%\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"29.503105590062113%\" valign=\"top\"\u003e\n \u003cp\u003e26.46%\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd width=\"19.09547738693467%\" rowspan=\"7\"\u003e\n \u003cp\u003e45\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"19.09547738693467%\"\u003e\n \u003cp\u003e0\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"14.57286432160804%\"\u003e\n \u003cp\u003e73091.29\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"23.366834170854272%\" valign=\"top\"\u003e\n \u003cp\u003e66.55%\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"23.86934673366834%\" valign=\"top\"\u003e\n \u003cp\u003e33.45%\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd width=\"23.60248447204969%\"\u003e\n \u003cp\u003e1\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"18.012422360248447%\"\u003e\n \u003cp\u003e69220.40\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"28.88198757763975%\" valign=\"top\"\u003e\n \u003cp\u003e68.17%\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"29.503105590062113%\" valign=\"top\"\u003e\n \u003cp\u003e31.83%\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd width=\"23.60248447204969%\"\u003e\n \u003cp\u003e2\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"18.012422360248447%\"\u003e\n \u003cp\u003e70131.16\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"28.88198757763975%\" valign=\"top\"\u003e\n \u003cp\u003e67.90%\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"29.503105590062113%\" valign=\"top\"\u003e\n \u003cp\u003e32.10%\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd width=\"23.60248447204969%\"\u003e\n \u003cp\u003e3\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"18.012422360248447%\"\u003e\n \u003cp\u003e76396.46\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"28.88198757763975%\" valign=\"top\"\u003e\n \u003cp\u003e73.54%\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"29.503105590062113%\" valign=\"top\"\u003e\n \u003cp\u003e26.46%\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd width=\"23.60248447204969%\"\u003e\n \u003cp\u003e4\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"18.012422360248447%\"\u003e\n \u003cp\u003e79887.10\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"28.88198757763975%\" valign=\"top\"\u003e\n \u003cp\u003e72.99%\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"29.503105590062113%\" valign=\"top\"\u003e\n \u003cp\u003e27.01%\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd width=\"23.60248447204969%\"\u003e\n \u003cp\u003e5\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"18.012422360248447%\"\u003e\n \u003cp\u003e79414.97\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"28.88198757763975%\" valign=\"top\"\u003e\n \u003cp\u003e73.01%\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"29.503105590062113%\" valign=\"top\"\u003e\n \u003cp\u003e26.99%\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd width=\"23.60248447204969%\"\u003e\n \u003cp\u003e6\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"18.012422360248447%\"\u003e\n \u003cp\u003e78284.60\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"28.88198757763975%\" valign=\"top\"\u003e\n \u003cp\u003e72.30%\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"29.503105590062113%\" valign=\"top\"\u003e\n \u003cp\u003e27.70%\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd width=\"19.09547738693467%\" rowspan=\"7\"\u003e\n \u003cp\u003e50\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"19.09547738693467%\"\u003e\n \u003cp\u003e0\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"14.57286432160804%\"\u003e\n \u003cp\u003e76463.04\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"23.366834170854272%\" valign=\"top\"\u003e\n \u003cp\u003e68.27%\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"23.86934673366834%\" valign=\"top\"\u003e\n \u003cp\u003e31.73%\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd width=\"23.60248447204969%\"\u003e\n \u003cp\u003e1\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"18.012422360248447%\"\u003e\n \u003cp\u003e73298.52\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"28.88198757763975%\" valign=\"top\"\u003e\n \u003cp\u003e67.94%\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"29.503105590062113%\" valign=\"top\"\u003e\n \u003cp\u003e32.06%\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd width=\"23.60248447204969%\"\u003e\n \u003cp\u003e2\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"18.012422360248447%\"\u003e\n \u003cp\u003e78592.57\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"28.88198757763975%\" valign=\"top\"\u003e\n \u003cp\u003e70.84%\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"29.503105590062113%\" valign=\"top\"\u003e\n \u003cp\u003e29.16%\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd width=\"23.60248447204969%\"\u003e\n \u003cp\u003e3\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"18.012422360248447%\"\u003e\n \u003cp\u003e83903.35\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"28.88198757763975%\" valign=\"top\"\u003e\n \u003cp\u003e73.53%\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"29.503105590062113%\" valign=\"top\"\u003e\n \u003cp\u003e26.47%\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd width=\"23.60248447204969%\"\u003e\n \u003cp\u003e4\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"18.012422360248447%\"\u003e\n \u003cp\u003e83699.35\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"28.88198757763975%\" valign=\"top\"\u003e\n \u003cp\u003e73.46%\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"29.503105590062113%\" valign=\"top\"\u003e\n \u003cp\u003e26.54%\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd width=\"23.60248447204969%\"\u003e\n \u003cp\u003e5\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"18.012422360248447%\"\u003e\n \u003cp\u003e82660.79\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"28.88198757763975%\" valign=\"top\"\u003e\n \u003cp\u003e73.93%\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"29.503105590062113%\" valign=\"top\"\u003e\n \u003cp\u003e26.07%\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd width=\"23.60248447204969%\"\u003e\n \u003cp\u003e6\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"18.012422360248447%\"\u003e\n \u003cp\u003e77644.57\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"28.88198757763975%\" valign=\"top\"\u003e\n \u003cp\u003e72.40%\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"29.503105590062113%\" valign=\"top\"\u003e\n \u003cp\u003e27.60%\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd width=\"19.09547738693467%\" rowspan=\"7\"\u003e\n \u003cp\u003e55\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"19.09547738693467%\"\u003e\n \u003cp\u003e0\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"14.57286432160804%\"\u003e\n \u003cp\u003e75779.54\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"23.366834170854272%\" valign=\"top\"\u003e\n \u003cp\u003e72.75%\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"23.86934673366834%\" valign=\"top\"\u003e\n \u003cp\u003e27.25%\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd width=\"23.60248447204969%\"\u003e\n \u003cp\u003e1\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"18.012422360248447%\"\u003e\n \u003cp\u003e72609.12\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"28.88198757763975%\" valign=\"top\"\u003e\n \u003cp\u003e72.06%\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"29.503105590062113%\" valign=\"top\"\u003e\n \u003cp\u003e27.94%\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd width=\"23.60248447204969%\"\u003e\n \u003cp\u003e2\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"18.012422360248447%\"\u003e\n \u003cp\u003e74475.02\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"28.88198757763975%\" valign=\"top\"\u003e\n \u003cp\u003e70.93%\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"29.503105590062113%\" valign=\"top\"\u003e\n \u003cp\u003e29.07%\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd width=\"23.60248447204969%\"\u003e\n \u003cp\u003e3\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"18.012422360248447%\"\u003e\n \u003cp\u003e81043.59\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"28.88198757763975%\" valign=\"top\"\u003e\n \u003cp\u003e76.57%\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"29.503105590062113%\" valign=\"top\"\u003e\n \u003cp\u003e23.43%\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd width=\"23.60248447204969%\"\u003e\n \u003cp\u003e4\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"18.012422360248447%\"\u003e\n \u003cp\u003e84252.80\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"28.88198757763975%\" valign=\"top\"\u003e\n \u003cp\u003e74.47%\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"29.503105590062113%\" valign=\"top\"\u003e\n \u003cp\u003e25.53%\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd width=\"23.60248447204969%\"\u003e\n \u003cp\u003e5\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"18.012422360248447%\"\u003e\n \u003cp\u003e86304.48\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"28.88198757763975%\" valign=\"top\"\u003e\n \u003cp\u003e75.02%\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"29.503105590062113%\" valign=\"top\"\u003e\n \u003cp\u003e24.98%\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd width=\"23.60248447204969%\"\u003e\n \u003cp\u003e6\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"18.012422360248447%\"\u003e\n \u003cp\u003e84798.75\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"28.88198757763975%\" valign=\"top\"\u003e\n \u003cp\u003e75.23%\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"29.503105590062113%\" valign=\"top\"\u003e\n \u003cp\u003e24.77%\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd width=\"19.09547738693467%\" rowspan=\"7\"\u003e\n \u003cp\u003e60\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"19.09547738693467%\"\u003e\n \u003cp\u003e0\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"14.57286432160804%\"\u003e\n \u003cp\u003e84607.31\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"23.366834170854272%\" valign=\"top\"\u003e\n \u003cp\u003e71.21%\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"23.86934673366834%\" valign=\"top\"\u003e\n \u003cp\u003e28.79%\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd width=\"23.60248447204969%\"\u003e\n \u003cp\u003e1\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"18.012422360248447%\"\u003e\n \u003cp\u003e80278.67\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"28.88198757763975%\" valign=\"top\"\u003e\n \u003cp\u003e70.33%\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"29.503105590062113%\" valign=\"top\"\u003e\n \u003cp\u003e29.67%\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd width=\"23.60248447204969%\"\u003e\n \u003cp\u003e2\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"18.012422360248447%\"\u003e\n \u003cp\u003e82366.63\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"28.88198757763975%\" valign=\"top\"\u003e\n \u003cp\u003e69.94%\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"29.503105590062113%\" valign=\"top\"\u003e\n \u003cp\u003e30.06%\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd width=\"23.60248447204969%\"\u003e\n \u003cp\u003e3\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"18.012422360248447%\"\u003e\n \u003cp\u003e84395.17\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"28.88198757763975%\" valign=\"top\"\u003e\n \u003cp\u003e74.58%\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"29.503105590062113%\" valign=\"top\"\u003e\n \u003cp\u003e25.42%\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd width=\"23.60248447204969%\"\u003e\n \u003cp\u003e4\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"18.012422360248447%\"\u003e\n \u003cp\u003e87590.64\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"28.88198757763975%\" valign=\"top\"\u003e\n \u003cp\u003e72.94%\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"29.503105590062113%\" valign=\"top\"\u003e\n \u003cp\u003e27.06%\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd width=\"23.60248447204969%\"\u003e\n \u003cp\u003e5\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"18.012422360248447%\"\u003e\n \u003cp\u003e87685.22\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"28.88198757763975%\" valign=\"top\"\u003e\n \u003cp\u003e72.66%\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"29.503105590062113%\" valign=\"top\"\u003e\n \u003cp\u003e27.34%\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd width=\"23.60248447204969%\"\u003e\n \u003cp\u003e6\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"18.012422360248447%\"\u003e\n \u003cp\u003e88250.83\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"28.88198757763975%\" valign=\"top\"\u003e\n \u003cp\u003e70.92%\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"29.503105590062113%\" valign=\"top\"\u003e\n \u003cp\u003e29.08%\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003c/tbody\u003e\n \u003c/table\u003e\n\u003c/div\u003e\n\u003cp\u003eComparing the changes in macro and micro pore proportions after different numbers of impacts on samples of five types of rocks, it is found that the pore changes are more significant in samples with small inclinations, while samples with larger inclination angles show minor changes. Taking the change in micro-pore proportion as an example, after 6 impacts, the micro-pore proportion increased by 7.27% for the 40\u0026deg; inclined plane sample, and the maximum micro-pore proportion for the 60\u0026deg; inclined plane sample occurred after the third impact, with a 4.64% increase compared to the second impact.\u003c/p\u003e\n\u003ch3\u003e3.1.3 NMR imaging\u003c/h3\u003e\n\u003cp\u003eNMR imaging provides a visual representation of the spatial distribution and development status of internal pores in rock samples, which is crucial for studying rock damage. Figure 8 shows the NMR images of sandstone samples with inclination angles of 45 \u0026deg; and 60 \u0026deg; before and after six impacts. These images are cross-sectional images at a distance of 20mm from the bottom surface. The green spots in the images represent small-sized pores, while the yellow and red spots represent large-sized pores.\u003c/p\u003e\n\u003cp\u003eTaking the image of a 45 \u0026deg; inclined plane rock sample as an example, the image of the sample before impact is mainly composed of relatively uniform distributed green spots, indicating that the pore size in the rock sample is small and uniform. After the first impact, the porosity is the smallest. The spots on the right edge of the cross-section were significantly reduced, and the distribution of the spots is mainly concentrated on the left side. At the same time, a small amount of yellow and red spots appear, indicating that some small pores have expanded into large pores. After the fifth impact, the porosity is the highest. The number of spots on the cross-section is significantly increased, and a large number of yellow and red spots appear, indicating an increase in the number of macro-pores.\u003c/p\u003e\n\u003cp\u003eAfter the sixth impact, the number of spots decreased slightly. However, there are obvious striped spots, indicating that some pores may have penetrated and formed a small number of cracks. Compared with the images of the 60 \u0026deg; inclined plane rock sample, there is no obvious change in the number of spots on the cross-section during the impact process. The distribution of spots is relatively uniform, without obvious yellow, red, or striped spots appearing. It can be seen that if the inclination angle is too large, the damage degree to the rock sample caused by impact decreases.\u003c/p\u003e\n\u003ch2\u003e3.2 Failure mechanism\u003c/h2\u003e\n\u003ch3\u003e3.2.1 Mechanical analysis of the inclined plane impact\u003c/h3\u003e\n\u003cp\u003eAs shown in Fig. 9, the impact surface of the sample is elliptical due to the slope influence. The size of the long semi-axis size gradually changes with the inclination angle of the inclined plane. Assuming that the major and minor axes of the inclined plane are \u003cem\u003ea\u003c/em\u003e and \u003cem\u003eb\u003c/em\u003e, respectively. According to the geometric relationship, it can be obtained that \u003cem\u003eb\u003c/em\u003e=\u003cem\u003ea\u003c/em\u003ecos\u0026alpha;=\u003cem\u003ed\u003c/em\u003e/2, the inclined plane area \u003cem\u003eA\u003c/em\u003e= \u0026pi;\u003cem\u003ed\u0026nbsp;\u003c/em\u003e\u003csup\u003e2\u003c/sup\u003e/ 4cos\u0026alpha;. Under 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 \u003cem\u003eF\u003c/em\u003e of the falling hammer can be decomposed into normal force \u003cem\u003eF\u003csub\u003eN\u003c/sub\u003e\u003c/em\u003e \u003cem\u003e\u003csub\u003e\u0026nbsp;\u003c/sub\u003e\u003c/em\u003e(\u003cem\u003eF\u003csub\u003e\u0026tau;\u0026nbsp;\u003c/sub\u003e\u003c/em\u003e= \u003cem\u003eP\u003c/em\u003e) and tangential force \u003cem\u003eF\u003csub\u003e\u0026tau;\u003c/sub\u003e\u003c/em\u003e.\u0026nbsp;The stress on the inclined plane can be decomposed into\u003c/p\u003e\n\u003cp\u003e\u003cimg 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\"\u003e\u003c/p\u003e\n\u003cp\u003ewhere, \u003cem\u003e\u0026sigma;\u003csub\u003ex\u0026nbsp;\u003c/sub\u003e\u003c/em\u003eand \u003cem\u003e\u0026sigma;\u003csub\u003ez\u003c/sub\u003e\u003c/em\u003e are the horizontal stress and vertical stress on the inclined plane, Pa; \u003cem\u003eP\u003c/em\u003e is the normal impact force on the inclined plane, N; \u003cem\u003eF\u003c/em\u003e is The impact force of the falling hammer, N; \u003cem\u003ed\u003c/em\u003e is the diameter of the sample, mm; \u003cem\u003e\u0026alpha;\u003c/em\u003e is the inclined angle. \u0026quot;\u003cem\u003eK\u003c/em\u003e\u003csub\u003e1\u003c/sub\u003e\u0026quot; and \u0026quot;\u003cem\u003eK\u003c/em\u003e\u003csub\u003e2\u003c/sub\u003e\u0026quot; are the component coefficients of horizontal and vertical directions, respectively. As shown in Fig. 10, as the angle of the inclined plane increases, the horizontal stress component first increases and then decreases, reaching its maximum value at an angle of 35\u0026deg;. The vertical stress component gradually decreases as the inclination angle increases. When the inclination angle is 45 \u0026deg;, the horizontal stress component and the vertical stress component are equal.\u003c/p\u003e\n\u003cp\u003eIn summary, compared to traditional vertical impact, the impact of inclined plane loading on rock samples induces not only vertical compressive stress but also damage and deformation caused by horizontal forces. Both the damage and failure are influenced by the inclination angle. With increasing inclination angle, under the same drop height, the vertical stress decreases while the horizontal stress increases, resulting in reduced damage at the lower part of the sample.\u003c/p\u003e\n\u003ch3\u003e3.2.2 Quantitative analysis of damage\u003c/h3\u003e\n\u003cp\u003eTo further investigate the internal damage and destruction of rock samples under different inclined plane impact frequencies, a damage variable \u003cem\u003eD\u003c/em\u003e is introduced. The damage variable \u003cem\u003eD\u003c/em\u003e is defined as a function of internal porosity as follows:\u003c/p\u003e\n\u003cp\u003e\u003cimg src=\"data:image/png;base64,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\"\u003e\u003c/p\u003e\n\u003cp\u003ewhere, \u003cem\u003en\u003c/em\u003e\u003csub\u003e0\u003c/sub\u003e represents the natural porosity of the rock sample, and \u003cem\u003en\u003c/em\u003e\u003csub\u003et\u003c/sub\u003e represents the porosity of the rock sample after the t-th impact.\u003c/p\u003e\n\u003cp\u003eAs shown in Table 3, the damage degree of samples with different inclined angles after 6 impacts was calculated.\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003eTable 3.\u003c/strong\u003e Statistical Table of damage variables\u003c/p\u003e\n\u003cdiv align=\"Left\"\u003e\n \u003ctable border=\"1\" cellspacing=\"0\" cellpadding=\"0\"\u003e\n \u003ctbody\u003e\n \u003ctr\u003e\n \u003ctd width=\"26.073619631901842%\" colspan=\"2\"\u003e\n \u003cp\u003eImpact frequency\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"11.349693251533742%\"\u003e\n \u003cp\u003e40\u0026deg;\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"15.644171779141104%\"\u003e\n \u003cp\u003e45\u0026deg;\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"15.644171779141104%\"\u003e\n \u003cp\u003e50\u0026deg;\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"15.644171779141104%\"\u003e\n \u003cp\u003e55\u0026deg;\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"15.644171779141104%\"\u003e\n \u003cp\u003e60\u0026deg;\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd width=\"21.165644171779142%\"\u003e\n \u003cp\u003e1\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"16.257668711656443%\" colspan=\"2\"\u003e\n \u003cp\u003e-0.51%\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"15.644171779141104%\"\u003e\n \u003cp\u003e-0.58%\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"15.644171779141104%\"\u003e\n \u003cp\u003e-0.44%\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"15.644171779141104%\"\u003e\n \u003cp\u003e-0.89%\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"15.644171779141104%\"\u003e\n \u003cp\u003e-0.48%\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd width=\"21.165644171779142%\"\u003e\n \u003cp\u003e2\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"16.257668711656443%\" colspan=\"2\"\u003e\n \u003cp\u003e-0.40%\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"15.644171779141104%\"\u003e\n \u003cp\u003e-0.09%\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"15.644171779141104%\"\u003e\n \u003cp\u003e-0.06%\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"15.644171779141104%\"\u003e\n \u003cp\u003e-0.87%\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"15.644171779141104%\"\u003e\n \u003cp\u003e-0.51%\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd width=\"21.165644171779142%\"\u003e\n \u003cp\u003e3\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"16.257668711656443%\" colspan=\"2\"\u003e\n \u003cp\u003e0.92%\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"15.644171779141104%\"\u003e\n \u003cp\u003e1.26%\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"15.644171779141104%\"\u003e\n \u003cp\u003e1.51%\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"15.644171779141104%\"\u003e\n \u003cp\u003e0.06%\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"15.644171779141104%\"\u003e\n \u003cp\u003e-0.05%\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd width=\"21.165644171779142%\"\u003e\n \u003cp\u003e4\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"16.257668711656443%\" colspan=\"2\"\u003e\n \u003cp\u003e1.48%\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"15.644171779141104%\"\u003e\n \u003cp\u003e1.77%\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"15.644171779141104%\"\u003e\n \u003cp\u003e1.54%\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"15.644171779141104%\"\u003e\n \u003cp\u003e0.46%\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"15.644171779141104%\"\u003e\n \u003cp\u003e0.32%\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd width=\"21.165644171779142%\"\u003e\n \u003cp\u003e5\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"16.257668711656443%\" colspan=\"2\"\u003e\n \u003cp\u003e1.89%\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"15.644171779141104%\"\u003e\n \u003cp\u003e1.75%\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"15.644171779141104%\"\u003e\n \u003cp\u003e1.38%\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"15.644171779141104%\"\u003e\n \u003cp\u003e0.70%\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"15.644171779141104%\"\u003e\n \u003cp\u003e0.31%\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd width=\"21.165644171779142%\"\u003e\n \u003cp\u003e6\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"16.257668711656443%\" colspan=\"2\"\u003e\n \u003cp\u003e1.06%\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"15.644171779141104%\"\u003e\n \u003cp\u003e1.55%\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"15.644171779141104%\"\u003e\n \u003cp\u003e0.55%\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"15.644171779141104%\"\u003e\n \u003cp\u003e0.52%\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"15.644171779141104%\"\u003e\n \u003cp\u003e0.34%\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003c/tbody\u003e\n \u003c/table\u003e\n\u003c/div\u003e\n\u003cp\u003eAccording to the result in Table 3, it can be seen that when the number of impacts is less than 2, the damage variable is negative. This indicates that under the first two impacts, the interior of the sample shows a state of pore compression. Since the third impact, except for the 60\u0026deg; rock samples, the damage variables have been positive. The maximum value of the damage variable occurs in the fourth or fifth impact, and the order of the maximum values of the damage variables at each angle is 40\u0026deg; \u0026gt; 45\u0026deg; \u0026gt; 50\u0026deg; \u0026gt; 55\u0026deg; \u0026gt; 60\u0026deg;. The maximum value of the damage variable occurs in the 40\u0026deg; rock sample of the fifth impact, and the minimum value appears in the 60\u0026deg; rock sample of the third impact. Under the same number of impacts, the damage degree of the 45\u0026deg; rock sample is generally the highest, while the damage degree of the 60\u0026deg; rock sample is the lowest.\u003c/p\u003e\n\u003ch3\u003e3.2.3 Failure mode\u003c/h3\u003e\n\u003cp\u003eAs shown in Fig. 11, after six cycles of inclined plane impact with the same energy, different types of cracks appeared in the upper part of the sample. The failure mode of the 45\u0026deg;~60\u0026deg; inclined plane sample is similar, with only one crack. However, the 40\u0026deg; inclined plane sample showed multiple cracks and a large amount of detachment at the bottom of the sample. The crack positions are all located within 20 mm of the upper end of the sample and parallel to the bottom surface of the sample. The failure type is a shear-tensile failure, as shown in Fig. 12. It is because the sharp corners of the sample are relatively thin, and the lateral force generated by the inclined plane impact causes the upper part of the rock sample to fail first. The impact damage and failure of rock samples on inclined planes are greatly affected by the angle of the inclined plane. The smaller the angle of the inclined plane, the smaller the transverse force and the larger the longitudinal force. The rock sample failure changes from a single transverse crack to multiple cracks. Therefore, the rock sample with a 40 \u0026deg; inclined plane angle is the most severely damaged.\u003c/p\u003e"},{"header":"4. Conclusions","content":"\u003cp\u003eThrough drop hammer testing and inclined plane impact testing, experiments were conducted on samples at five different slope angles under varying numbers of impact loads. The damage degradation process of the samples before and after impact was analyzed using nuclear magnetic resonance detection, resulting in the following conclusions:\u003c/p\u003e\n\u003cp\u003e(1) Under the same impact load, the sample's damage mode is significantly influenced by the slope angle. The larger the angle, the less the rock damage, requiring more impacts for failure, with the damage being more inclined towards the acute corner of the slope and characterized by shear-tensile failure. Smaller slope angles exhibit more intense porosity variations and greater rock damage.\u003c/p\u003e\n\u003cp\u003e(2) Under the same energy of inclined impact, as the number of impacts increases, the sample's porosity first decreases, then increases, and then decreases again. The porosity is at its minimum after the first impact and reaches its maximum after the 5th impact. This is due to notable closure of large pores after the first impact, with the rock sample suffering the most severe damage after 5 impacts and ultimately failing after the 6th impact.\u003c/p\u003e\n\u003cp\u003e(3) Under inclined impact, the significant influence on the sandstone samples remains the presence of large-sized pores, with large pore area ratios exceeding 95%. With an increasing number of impacts, the quantity of small pores decreases while the size and quantity of large pores both increase, indicating continuous deterioration of the rock with an increasing number of impacts.\u003c/p\u003e"},{"header":"Declarations","content":"\u003cp\u003e \u003ch2\u003eCompeting interests\u003c/h2\u003e \u003cp\u003eThe authors declare that there is no potential conflicts of interest.\u003c/p\u003e \u003c/p\u003e\u003ch2\u003eAuthor Contribution\u003c/h2\u003e\u003cp\u003eConceptualization, X.R.W. and Z.X.L; Methodology, X.R.W. and X.Z.; Collection, Testing and analysis, Writing\u0026ndash;Original Draft Preparation, X.Z. and X.U.W.; Writing\u0026ndash;Review \u0026amp; Editing, X.R.W. and Z.X.L. All authors reviewed the manuscript.\u003c/p\u003e\u003ch2\u003eAcknowledgement\u003c/h2\u003e \u003cp\u003eThe 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.\u003c/p\u003e\u003ch2\u003eData Availability\u003c/h2\u003e\u003cp\u003eAll data generated or analyzed during this study are included in this published article.\u003c/p\u003e"},{"header":"References","content":"\u003col\u003e\n\u003cli\u003eWang, H. 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Impact of Rock Samples Size on the Microstructural Changes Induced by Freeze\u0026ndash;Thaw Cycles. \u003cem\u003eRock Mechanics and Rock Engineering\u003c/em\u003e \u003cstrong\u003e53\u003c/strong\u003e, 5293-5300, https://doi.org/10.1007/s00603-020-02201-4 (2020).\u003c/li\u003e\n\u003c/ol\u003e"}],"fulltextSource":"","fullText":"","funders":[],"hasAdminPriorityOnWorkflow":false,"hasManuscriptDocX":true,"hasOptedInToPreprint":true,"hasPassedJournalQc":"","hasAnyPriority":false,"hideJournal":false,"highlight":"","institution":"","isAcceptedByJournal":true,"isAuthorSuppliedPdf":false,"isDeskRejected":"","isHiddenFromSearch":false,"isInQc":false,"isInWorkflow":false,"isPdf":false,"isPdfUpToDate":true,"isWithdrawnOrRetracted":false,"journal":{"display":true,"email":"[email protected]","identity":"scientific-reports","isNatureJournal":false,"hasQc":true,"allowDirectSubmit":false,"externalIdentity":"scirep","sideBox":"Learn more about [Scientific Reports](http://www.nature.com/srep/)","snPcode":"","submissionUrl":"","title":"Scientific Reports","twitterHandle":"","acdcEnabled":true,"dfaEnabled":true,"editorialSystem":"stoa","reportingPortfolio":"Scientific Reports","inReviewEnabled":true,"inReviewRevisionsEnabled":true},"keywords":"Inclined plane impact, NMR, T2 spectrum distribution, Porosity, Cyclic impact","lastPublishedDoi":"10.21203/rs.3.rs-4674701/v1","lastPublishedDoiUrl":"https://doi.org/10.21203/rs.3.rs-4674701/v1","license":{"name":"CC BY 4.0","url":"https://creativecommons.org/licenses/by/4.0/"},"manuscriptAbstract":"\u003cp\u003eTo investigate the cumulative damage characteristics and unstable failure mechanism of rock samples under cyclic inclined plane impact loads, an experimental device simulating inclined plane impact, and a drop hammer loading test machine were used to conduct cyclic low-energy impact tests on sandstone samples with five inclined plane angles. The porosity of the sandstone samples was measured using a low magnetic field nuclear magnetic resonance (NMR) detection system, obtaining the porosity, T\u003csub\u003e2\u003c/sub\u003e spectrum distribution, and NMR images of the samples after different numbers of impacts at different slope angles. Under the action of cyclic inclined plane impact loads, the larger the slope angle, the smaller the extent of sample damage. The rock samples with a large inclined angle is more inclined to rupture at the tip of the inclined plane, mainly primarily characterized by shear-tensile failure. The porosity of the small slope angle changes sharply, resulting in greater damage. Under the same impact energy, as the number of impacts increases, the porosity of the samples first decreases, then increases, and then decreases again. This is manifested by large porosity closure after the first impact, followed by small pore expansion into large pores after 5 impacts, leading to gradual degradation of the samples until failure. The main factor affecting the rock samples is the presence of large-sized pores with a spectral area of over 95%. As the number of impacts increases, the quantity of small pores decreases, while the size and quantity of large pores both increase, indicating continuous deterioration of rock sample.\u003c/p\u003e","manuscriptTitle":"Cumulative damage characteristics of rock samples under cyclic low energy inclined plane impact","msid":"","msnumber":"","nonDraftVersions":[{"code":1,"date":"2024-07-29 21:07:55","doi":"10.21203/rs.3.rs-4674701/v1","editorialEvents":[{"type":"communityComments","content":0},{"type":"decision","content":"Revision requested","date":"2024-09-25T05:22:22+00:00","index":"","fulltext":""},{"type":"editorInvitedReview","content":"","date":"2024-09-24T19:35:21+00:00","index":"hide","fulltext":""},{"type":"editorInvitedReview","content":"","date":"2024-09-19T12:08:05+00:00","index":"hide","fulltext":""},{"type":"reviewerAgreed","content":"305287241280539075502855733534531327756","date":"2024-09-04T19:04:29+00:00","index":"hide","fulltext":""},{"type":"reviewerAgreed","content":"169187191933883846201627611033073304670","date":"2024-09-04T05:16:08+00:00","index":"hide","fulltext":""},{"type":"reviewersInvited","content":"","date":"2024-09-02T18:53:41+00:00","index":"","fulltext":""},{"type":"editorAssigned","content":"","date":"2024-09-02T18:32:03+00:00","index":"","fulltext":""},{"type":"editorInvited","content":"","date":"2024-07-08T06:10:39+00:00","index":"","fulltext":""},{"type":"checksComplete","content":"","date":"2024-07-04T04:47:59+00:00","index":"","fulltext":""},{"type":"submitted","content":"Scientific Reports","date":"2024-07-02T13:48:15+00:00","index":"","fulltext":""}],"status":"published","journal":{"display":true,"email":"[email protected]","identity":"scientific-reports","isNatureJournal":false,"hasQc":true,"allowDirectSubmit":false,"externalIdentity":"scirep","sideBox":"Learn more about [Scientific Reports](http://www.nature.com/srep/)","snPcode":"","submissionUrl":"","title":"Scientific Reports","twitterHandle":"","acdcEnabled":true,"dfaEnabled":true,"editorialSystem":"stoa","reportingPortfolio":"Scientific Reports","inReviewEnabled":true,"inReviewRevisionsEnabled":true}}],"origin":"","ownerIdentity":"96d811ff-ac0d-4028-845e-6cfe68c85c42","owner":[],"postedDate":"July 29th, 2024","published":true,"recentEditorialEvents":[],"rejectedJournal":[],"revision":"","amendment":"","status":"under-review","subjectAreas":[{"id":35142117,"name":"Earth and environmental sciences/Natural hazards"},{"id":35142118,"name":"Physical sciences/Engineering/Civil engineering"},{"id":35142119,"name":"Physical sciences/Engineering/Energy infrastructure"}],"tags":[],"updatedAt":"2024-10-21T05:23:45+00:00","versionOfRecord":[],"versionCreatedAt":"2024-07-29 21:07:55","video":"","vorDoi":"","vorDoiUrl":"","workflowStages":[]},"version":"v1","identity":"rs-4674701","journalConfig":"researchsquare"},"__N_SSP":true},"page":"/article/[identity]/[[...version]]","query":{"redirect":"/article/rs-4674701","identity":"rs-4674701","version":["v1"]},"buildId":"qtupq5eGEP_6zYnWcrvyt","isFallback":false,"isExperimentalCompile":false,"dynamicIds":[84888],"gssp":true,"scriptLoader":[]}