1 INTRODUCTION

Energy/resource development and underground engineering construction are gradually moving toward greater depths (Fan & Sun, 2015; Gong & Wang, 2022; Wang et al., 2024). In terms of energy development, the depth of oil and gas drilling has exceeded 12 km (Trckova et al., 2008), and the depth of geothermal development has exceeded 5 km (Reinecker et al., 2021). In terms of resource extraction, the depth of metal mines has exceeded 4 km (Tibane & Mamba, 2023), and the depth of coal mines has exceeded 1500 m (Wang, Jiang, et al., 2020). In terms of underground space utilization, deep underground laboratories are buried at depths exceeding 2400 m (Chen et al., 2023), and radioactive waste is stored at depths greater than a kilometer (Zhang et al., 2020). However, the surrounding rock of deep underground engineering is subjected to the combined effects of high geostress static loads, blasting construction, mechanical rock drilling and other cyclic disturbance loads, which simultaneously cause static load damage, dynamic load damage and fatigue damage, increasing the probability of overall failure, instability and dynamic disasters such as rock bursts and impact ground pressure (Du, Dai, et al., 2020; Li et al., 2018; Luo et al., 2023). Therefore, studying the damage and failure mechanism of prestressed statically loaded rock in the cyclic impact process is highly important for safe construction and stable operation of deep underground engineering.

The key to studying rock dynamic characteristics is the strain rate effect. The strain rate represents the strain change rate of the test object over time, measured in s−1. The physical meaning of strain rate is used to characterize the speed of deformation during dynamic loading. Under low strain rates (10−2–100 s−1), the rock mechanical response characteristics are close to static. At medium strain rates (100–102 s−1), the inertia effect and strain rate strengthening effect of rocks begin to emerge. At high-strain rates (102–104 s−1), strain waves mainly propagate inside the rock, and the rock exhibits brittle fracture.

Strain rate is a bridge connecting rock deformation and time scale. Its essence is the rate dependence of rock dynamic response characteristics under dynamic loading. Obtaining the rock dynamic characteristics under different strain rates is crucial for predicting and preventing underground engineering dynamic disasters induced by disturbance loads. The strain rate effect in rocks is widely recognized (Akdag et al., 2020; Qian et al., 2024). On this basis, scholars worldwide have conducted in-depth research from the perspective of dynamic and static loads with different strain rates and have gradually discovered the promoting effects of dynamic and static loads on rock damage and failure (Jiang et al., 2024; Wang et al., 2017; Xie et al., 2022).

In terms of preloading with low-strain rate cyclic impact, Chu et al. (2023), Luo et al. (2020), Yu et al. (2022), and others reported that rock strain increases sharply under cyclic disturbance loads and that the cumulative plastic strain evolves in an S shape with increasing number of cycles. Jiang, Feng, et al. (2021), Li et al. (2017), Miao et al. (2021), and others reported that under weak dynamic disturbances, preloaded rocks exhibit more local tensile splitting cracks, and the damage and fracture process can be divided into stable and accelerated stages. Wu and Gong (2021), Wu, Gong, and Jiang (2022), and others believe that preloading is the prerequisite and dominant factor for rock damage weakening, whereas disturbance loads mainly induce failure and increase the degree of weakening. He, Wang, et al. (2023), Wu, Gong, et al. (2022), Dong et al. (2023), and others reported that rock deformation under static dynamic superposition conditions is positively correlated with preapplied static loads, and that preapplied static loads significantly decrease rock fracture toughness. Du, Song, et al. (2020) studied the effects of peak disturbance loads on rock strength, deformation characteristics, energy dissipation, and fracture laws. Gong et al. (2020) reported that the peak strength and ultimate deformation of preloaded rocks significantly decrease with increasing disturbance frequency. Jiang, Su, et al. (2021) reported that the damage caused by disturbance loads in the direction of σ2 is greater than that caused by disturbance loads in the direction of σ1.

In terms of preloading and high-strain rate cyclic impact, Wang, Liu, et al. (2023), Han et al. (2022), Wang, Luo, et al. (2020), and others explored the influence of the number of cyclic impacts of Hopkinson pressure bars on the dynamic damage, failure mode, and energy evolution of preloaded rock under static loading. The dynamic strength of rock is negatively correlated with the number of cyclic impacts. Fan et al. (2023) reported that as the strain rate increases, the rock failure mode gradually transitions from mode I to mixed mode I−II and gradually shifts from tensile failure to tensile shear failure. Zhang et al. (2022) reported that as the crack inclination angle increases, the dynamic deformation modulus and dynamic strength of preloaded rock under cyclic impact first increase but then decrease. In addition, Ma et al. (2023), He, Ding, et al. (2023), Gong et al. (2023), and others believe that cyclic disturbances accelerate the unsteady-state fracture process of jointed rocks and enhance the shear fracture weakening effect. Bai et al. (2022) studied the creep behavior of fractured rock masses under dynamic disturbances and reported that dynamic disturbances have a significant strengthening effect on the creep rate and failure strain during the accelerated creep stage.

In terms of rock dynamics models under preloaded static loads and cyclic impacts, Xie et al. (2020) proposed the concept of engineering disturbance rock dynamics and established a three-dimensional rock dynamics theory. Yang et al. (2022), Zhu et al. (2022), and others revealed the mechanical behavior of rocks under the combined action of preapplied static loads and impact loads from the perspectives of time, space, and energy through damage theory models. Zhou et al. (2022), Feng et al. (2023), and others established a dynamic cyclic loading damage constitutive model and reported that the impact resistance of rocks is negatively correlated with the number of dynamic cycles. Jia et al. (2022) determined the order of influence of disturbance intensity, frequency, and time on the deformation of surrounding rock and the development of plastic zones through numerical simulations. Yang et al. (2021) studied the uncertainty parameters of internal fractures in rock masses via theoretical analysis and reported that the more cyclic disturbances there are, the greater the degree of engineering safety hazard.

In summary, significant achievements have been made in the study of rock damage and failure characteristics under the combined effects of preloading and cyclic impact. However, the cyclic impact loads applied in relevant experiments are mainly low-strain rate hydraulic pulse loads (10−2−100 s−1) or high-strain rate Hopkinson pressure bar impact loads with poor continuity (102−104 s−1). There is relatively little research on rock damage and failure mechanisms under the superposition of medium-strain rate cyclic impact loads and preapplied static loads, such as mechanical rock drilling and roof fracture. Moreover, a medium strain rate (100−102 s−1) is an important stage for rocks to transition sensitively in terms of strain rate effects (Li et al., 2021). Moreover, limited by experimental methods, existing research considers only cyclic impact loads as a stage-specific damage-inducing factor and does not address the damage and failure laws of preloaded rock during cyclic impact until failure, which differs from the actual situation of surrounding rock instability induced by continuous disturbances at engineering sites.

This study uses a self-developed multistrain rate dynamic static superposition rock mechanics test system. It conducts rock mechanics tests on the superposition of medium-strain rate cyclic impact loads and preadded static loads. The mechanical damage evolution law and macroscopic damage evolution characteristics of rock during continuous impact until failure were obtained. With the logistic inverse function as the core, a damage accumulation evolution model that comprehensively considers preadded static loads, impact peak values, impact frequencies, and impact times was established, and the theoretical model was compared and verified with experimental data.

2 MECHANICAL TESTING OF MEDIUM-STRAIN RATE DYNAMIC AND STATIC LOAD SUPERPOSITION

2.1 Mechanics testing system

The experiments were conducted via a self-developed multistrain rate dynamic–static superposition rock mechanics testing system (Wang, Wang, Wang, et al., 2023), as shown in Figure 1. The experimental system is centered on a gas‒liquid composite dynamic−static loading cylinder, which can be combined to apply creep loads (<10−4 s−1), hydraulic quasistatic loads (10−4–10−2 s−1), hydraulic pulse dynamic loads (10−2–100 s−1), and drop hammer cyclic impact loads (100–102 s−1). The dynamic process of strain energy accumulation and release can be simulated through gas compression and expansion.

By installing springs in the cyclic impact device, during the hammer lifting stage, the springs can be compressed and accumulate elastic energy. During the hammer-falling stage, the elastic energy inside the spring can be released, loading the hammer and increasing its acceleration. When there is a spring, the hammer-falling acceleration a is shown in Equation ( 1), and the hammer-falling time t fall is shown in Equation ( 2).

$$$$ (1)

$$$$ (2)

where g is the gravity acceleration, m is the falling hammer mass, and h is the lifting height; k is the spring stiffness, and x is the spring compression amount.

The strain rate range that can be applied by this rock mechanics testing system is 10−6–102/s−1. The creep load application ability, hydraulic static load application ability, pulse dynamic load application ability, and hammer impact application ability of the system are respectively 200, 300, 300, and 30 kN. The maximum impact dynamic load application frequency is 10 Hz. The maximum impact energy is 100 J.

This mechanical testing system can achieve force and displacement loading, where force loading is achieved by dynamically adjusting the hydraulic pressure through a servo valve. The principle is to collect the force signal of the load sensor in real time and compare it with the preset target value through feedback. The proportional-integral-derivative algorithm is used to control the opening of the servo valve, so as to accurately maintain or change the loading force at the set rate, with a control accuracy of ±0.5%. Load according to displacement by controlling the piston position, dynamically adjusting the oil pump flow rate, and servo valve status based on the piston position information feedback from the displacement sensor, ensuring that the piston is pushed to the designated position at the predetermined speed, with a control accuracy of ±0.2%.

2.2 Mechanical test scheme

Fresh and intact red sandstone blocks buried approximately 800 m deep in Kangding, Ganzi, Sichuan, China. The selected red sandstone minerals are mainly composed of quartz and feldspar, with a dense block structure, high brittleness, and low permeability characteristics. The rock sampling site has active tectonic movements, high seismic intensity, and a complex geostress field. During the construction process, rockburst phenomena have been recorded multiple times. The mechanical conditions of the surrounding rock at the rock sampling site are consistent with the superposition test conditions of preadded static load and cyclic impact in this paper.

The red sandstone blocks were selected, and standard samples with diameters of 50 mm × 100 mm were prepared for testing. All the samples were taken from the same rock block. The sample surface was polished to achieve a flatness of ±0.05 mm or less, with an ultrasonic velocity and amplitude dispersion within 5%. According to relevant testing standards, the uniaxial compressive strength measured for this batch of samples was 50 MPa.

The experimental variables are the preapplied static load (Fs), impact peak value (Fm), and impact frequency (f). A total of 12 sets of experiments were set up, and the experimental parameters are shown in Table 1. To ensure the reliability of the test results and patterns, each group of experiments was repeated three times.

Table 1. Experimental parameters.

Group	Fs (MPa)	Fm (MPa)	f (Hz)	Impact times
1	27.5	8	1.0	Continuously apply impact loads until destroyed
2	32.5	8	1.0
3	37.5	8	1.0
4	42.5	8	1.0
5	37.5	6	1.0
6	37.5	8	1.0
7	37.5	10	1.0
8	37.5	12	1.0
9	37.5	8	0.5
10	37.5	8	1.0
11	37.5	8	1.5
12	37.5	8	2.0

The experimental procedure is shown in Figure 2a. First, the target static load is applied to the sample via hydraulic pressure, and the cyclic impact load of the target peak value and frequency is continuously applied until the sample fails. Mechanical parameter monitoring is shown in Figure 2b. Vertical high-ductility strain gauges are attached to the surface of the sample to monitor the axial strain, with a testing accuracy of ±0.1% and a deformation elongation rate of up to 15%. The piezoelectric impact force sensor is placed at the bottom of the sample to monitor the axial stress at a sampling frequency of 20 kHz. The piezoelectric impact force sensor has a load collection accuracy of 0.2% F.S. and a maximum response frequency of 200 kHz. The monitoring of failure characteristics is depicted in Figure 2c, and a high-speed camera system is used to monitor the process of crack development (1080 × 1080) at 1080@8000 fps. The fragmentation degree of the sample is obtained through screening and weighing.

3 ANALYSIS OF ROCK DAMAGE AND FAILURE LAW DURING THE CYCLIC IMPACT PROCESS

3.1 Analysis of the mechanical damage evolution law

This study mainly studies the damage and failure laws under the combined action of preloading and cyclic impact and does not analyze the relevant laws during the preloading stage. The stress/strain time history curve is shown in Figure 3, and the results indicate that the stress/strain evolution trend is generally consistent with different preapplied static loads, impact peak values, and impact frequencies. During the cyclic impact process, the axial strain continues to increase until failure occurs. According to the inflection point of the strain values, the deformation and failure process of rock can be divided into three stages:

• 1.

  Stage I of crack compaction and closure: During the initial cyclic impacting of preloaded rock, the existing microcracks or interfaces inside are further compacted and closed, and the axial strain shows a nonlinear evolution trend of gradually slowing.

• 2.

  Stage II of the smooth development of cracks: Under the continuous action of dynamic and static superposition, the existing microcracks inside the rock continue to develop steadily, and new small cracks grow. The plastic strain under impact loading linearly increases.

• 3.

  Stage III of high-speed crack propagation: When damage accumulates to a certain threshold, the internal cracks in the rock increase in size significantly, expand and connect, and the axial strain gradually increases nonlinearly until macroscopic failure occurs.

The deformation evolution law of rocks under the above dynamic and static superposition conditions is basically consistent with that of the static load test, but the initial stage of static loading with crack compaction and closure repeatedly occurs in the initial dynamic and static superposition stage, reflecting the special characteristics of rock mechanical damage under dynamic and static superposition conditions. In addition, the smaller the preapplied static load and impact peak value are and the higher the impact frequency is, the more times that impact occurs, the more likely rock failure is, and the more obvious the division of the three deformation stages mentioned above. The combination of the preapplied static load (42.5 MPa) and impact load (8.0 MPa) in Group 4 exceeded the rock static load strength (50.0 MPa), and failure occurred only after seven cycles of impact, reflecting the strain rate strengthening effect of the rock.

The strain curve of the cyclic impact process for Group 4 is enlarged, as shown in Figure 3d. The impact load is applied for approximately 0.3 ms, and the instantaneous strain during impact is approximately 1490 με. The plastic strain after impact is approximately 425 με, and the instantaneous strain rate is approximately 4.97/s, which verifies that the experiment involves medium-strain rate cyclic impact.

The cumulative impact frequency and axial strain at the final failure of the rock change synchronously, as shown in Figure 4, both of which can be used as quantitative characterization parameters for the rock damage evolution mechanism. Assuming that the damage to the rock at the final failure stage is 1, if the cumulative number of impacts is n, the average damage per impact is 1/n. Therefore, the greater the number of cumulative impacts is, the smaller the average damage per impact. The cumulative impact times are exponentially negatively correlated and exponentially positively correlated with the preapplied static load, impact peak value, and impact frequency, respectively. Among them, Group 3 and Group 6 both have a static load of 37.5 MPa plus an impact load of 8 MPa, with 11/12 cumulative impacts and axial strains of 7791/7844 με, confirming the homogeneity of the samples and the reliability of the results.

The core parameter of rock damage under different preapplied static loads and with different impact peak values is the magnitude of the load value. On the basis of previous experience, it can be analyzed from the perspective of statistical damage strength theory. Under the assumption that the strength of microelements inside rock follows a Weibull distribution (Chen et al., 2022), the larger the values of the dynamic and static superimposed loads are, the greater the degree of damage to microelements caused by a single impact and the greater the degree of damage caused by a single impact. Considering that rock mechanics damage is induced mainly by stress concentrations in macroscopic pores and fractures, and that there is a rate effect on the development of rock damage, impact frequency damage can be analyzed at the microscale and in terms of energy. As the impact frequency increases, some of the impact energy cannot be dissipated in a timely manner at the tip of the primary pore crack and is transmitted to the interface of the microscale matrix or crystal particles, thereby inducing microscale fatigue cracks. However, such cracks have relatively little impact on the macroscopic mechanical damage to rocks, reflecting the rule that the larger the impact frequency is, the less damage is caused by a single impact.

3.2 Analysis of macrodamage evolution characteristics

The rock failure process is shown in Figure 5. As the preapplied static load and impact peak decrease or the impact frequency increases, the rock failure mode becomes more complex, and the failure process becomes more severe. The evolution trend of the main failure mode progresses from single shear failure (Groups 4, 8, and 9) to conjugate shear failure (Groups 3 and 7), followed by local burst failure (Groups 2, 6, 10, and 11), and ultimately transitions to overall burst failure (Groups 1, 5, and 12). As the number of impacts increases, microcracks inside the rock continue to emerge and expand, and the nonuniformity and discontinuity of the rock gradually increase, causing the main crack propagation path through the rock to become more tortuous and ultimately making the failure mode more complex. From an energy perspective, as the cumulative number of impacts increases, the axial strain synchronously increases, indicating that elastic strain energy accumulates inside the rock. The release of strain energy during the rock failure process leads to more severe failure and a more pronounced dynamic effect.

Rock failure process quantitative analysis is conducted using cracks fractal dimension and fragment fractal dimension. Cracks fractal dimension is a quantitative indicator that characterizes the surface fracture complexity and irregularity. The fragment fractal dimension is a quantitative indicator that characterizes the fragmentation degree and dynamic characteristics.

The calculation method for fractal dimension of the cracks is as follows (Hou et al., 2019): By using the box dimension method to perform fractal analysis on the evolution characteristics of rock fractures, a calculation program is used to obtain the number of squares required to cover all fractures under different sizes of squares. The relationship between the size and number of squares is shown in Equation ( 3).

$$$$ (3)

where, N( δ) is the number of squares; α c is a proportionality constant of cracks' fractal dimension; δ is the size of squares, and D c is the fractal dimension.

Obtain an array of multiple square sizes and their corresponding square quantities, and the absolute value of the slope of the fitted line is the cracks' dimension Dc of the rock fracture evolution stage. The larger the cracks' dimension, the denser the fractures, and the higher the degree of rock damage.

The calculation method for the fractal dimension of fragments is as follows (Peng et al., 2020): According to relevant research, the particle size of rocks after being loaded and broken exhibits fractal characteristics. Therefore, assuming that the rock fragmentation follows the Gate-Gardin-Schuhmann distribution, the particle size distribution of fragments satisfies the relationship in Equation ( 4).

$$$$ (4)

where k is the mass fraction with a diameter less than r; M( r) is the cumulative mass of fragments with a diameter less than r; M T is the total mass of the fragments; r is the maximum size of the fragment; rm is the rock fragments maximum size; and α is a distribution parameter.

By taking the derivative of Equation ( 5):

$$$$ (5)

The incremental relationship between the quantity of fragments and the mass of fragments is as follows:

$$$$ (6)

The fractal dimension D f shown in Equation ( 7) can be obtained from Equations ( 4) to ( 6). The larger the fractal dimension, the more severe the rock fragmentation and the smaller the fragments particle size.

$$$$ (7)

The cracks' fractal dimension and fragment fractal dimension are shown in Figure 6. The crack images were uniformly selected from high-speed camera system monitoring images taken 20 ms after macroscopic crack initiation. The synchronous evolution of two fractal dimensions can be obtained under different experimental conditions, and the fractal dimension of fractures is slightly greater than that of fragments, indicating the synchronous development of fractures on the rock surface and inside. Moreover, the rock surface experiences the generation and expansion of fractures, resulting in a relatively high fracture density. The smaller the preapplied static load and impact peak value are, the higher the impact frequency, and the larger the fractal dimensions are, the more developed the fractures and the smaller the fragments during the rock failure process, indicating more severe damage.

The comparison between the cumulative impact frequency and the duration of the macroscopic damage process is shown in Figure 7, where the duration of damage is taken as the ratio of the number of photos N taken by the high-speed camera system from the time that the initial crack forms to the time the final damage stage is reached at frame rate f. The smaller the duration of the damage, the more severe the damage. As the preloaded static load and impact peak value decrease and the impact frequency increases, the number of cumulative impacts gradually increases as the failure duration decreases. This trend is consistent with the evolution laws of rock mechanical damage and macroscopic failure mentioned earlier, thereby further verifying the reliability and rationality of the test results and the analysis presented in this paper.

4 DAMAGE ACCUMULATION MODEL OF PRELOADING STATIC ROCK DURING THE CYCLIC IMPACT PROCESS AND ITS VERIFICATION

Equation (8) calculates dependent experimental data, which has limitations in its application. This study uses theoretical analysis and mathematical calculations to establish a universal preloaded static rock damage accumulation model for cyclic impact processes and compares its results with the calculation results of Equation (8) to verify its reliability. This article only considers the damage evolution law under the combined action of cyclic impact and preapplied static loading and does not study the damage generated during the early stage of static load application.

4.2 Cyclic impact damage Dd

The deformation speed of preloaded rock during cyclic impact, according to previous experiments, exhibits an inverted S-shaped development pattern characterized by rapid rise, followed by gentle development, and culminating in another rapid rise. The evolution laws of parameters such as axial strain, cumulative impact times, fractal dimension, and duration of failure are consistent. Consequently, the axial strain throughout the cyclic impact process is selected as the characterization parameter for cyclic impact damage. To model the inverted S-shaped evolution process, the logistic inverse function shown in Equation ( 12) serves as the theoretical basis (Wang, Wang, Zhang, et al., 2023), with considerations for factors such as shock frequency, peak value, and cumulative shock frequency

$$$$ (12)

where α and β are characteristic parameters related to the impact frequency and peak value, N is the cumulative number of impacts at final failure, and n is the nth impact.

The α value controls the size of the damage value at the damage evolution model curve center. The larger the α value, the relatively larger the accumulated damage formed in the initial stage of the damage evolution process. Based on this, α is defined as the initial stage damage accumulation rate factor. The physical meaning of β is to characterize the slope of the low-speed phase curve. Based on this, β is defined as the accumulation rate factor of damage in the low-speed phase.

As shown in Figure 8, the logistic inverse function can better characterize the inverse S-shaped evolution trend of the damage factor during the cyclic impact process. The expression forms of each parameter in Equation (12) are further determined below.

4.2.1 Accumulated number of impacts N

As shown in Figure 4, the cumulative number of impacts at the final failure stage of the rock is exponentially related to the impact frequency and peak value. Therefore, on the basis of the exponential function, two parameters, impact frequency and peak value, are introduced for planning and solving, and the prerequisite of N >  n is set to obtain the evolution equation of cumulative number of impacts N, as shown in Equation ( 13).

$$$$ (13)

where f is the impact frequency, and F m is the peak impact value.

A comparison between the cumulative impact times obtained via Equation (13) and the experimental results is shown in Figure 9, indicating a good correlation between the two.

By combining Equations ( 9)–( 13), a preloaded static rock damage accumulation model for the cyclic impact process can be obtained, as shown in Equation ( 14).

$$$$ (14)

4.2.2 Characteristic parameters α and β

The design includes different forms of alpha and beta functions for preloading (Fs), impact frequency (f), and impact peak value (Fm), as shown in Table 2, with the initial coefficients set to 1. Different alpha and beta functions are combined with actual experimental parameters and substituted into Equation (14) to obtain the theoretical value of the superimposed damage factor D; simultaneously, Equation (8) and axial strain test data are used to obtain the dynamic and static superposition damage factor Dt on the basis of the test data, and the sum of the variances M of the two damage factors D and Dt is calculated. Planning and solving are carried out to obtain the minimum value of M, with the constraint of D ≤ 1. The constants are optimized and adjusted in different forms of α and β functions, and the mathematical models and related constant values with the minimum value of M are ultimately selected.

Table 2. Candidate functions of α and β.

Number	Parameter	Function	Functional form	Parameter	Function	Functional form	Constant
1	α	Linear		β	Linear		All constants have an initial value of 1
2					Exponent
3					Logarithm
4		Exponent			Linear
5					Exponent
6					Logarithm
7		Logarithm			Linear
8					Exponent
9					Logarithm

Group 5 is taken as an example to conduct the above analysis and comparison. The optimized function form, M min, and the evolution trends of the two damage factors D and D t are shown in Figure 10, where D and D t exhibit good synchronization.

$$$$ (15)

The final representation of the characteristic parameters α and β shown in Figure 10 is selected, where α is based on an exponential function and β is based on a linear function. By combining with Equation (14), the final form of the preloaded static rock damage accumulation model D for the cyclic impact process is obtained as shown in Equation (15).

4.3 Damage model validation

To verify the reliability and universality of Equation (15), compare the damage evolution data obtained from all experiments with the theoretical damage evolution trend under the same conditions. Comparison found that when there are more impact cycles (>10), the evolutionary trends of the theoretical damage and experimental damage are basically consistent. As shown in Figure 11, the damage factor at the time of final failure is approximately 1; the greater the cumulative number of impacts is, the closer the evolution laws of D and Dt. But when the impact cycles are small (≤10), the evolutionary trend deviates. Analysis suggests that the preloaded static rock damage accumulation model in the cyclic impact process shown in Equation (15) is solved via the inverted S-shaped logistic inverse function as the core. When the impact cycle is small, the damage caused by a single impact is significant. When the initial impact is applied, the rock damage develops rapidly, and the deformation stage and inverted S-shaped evolution trend are not obvious, resulting in a deviation between theoretical and experimental results. The above comparison results also indicate the limitations of the model under the condition of smaller cycle impact times.

5 DISCUSSION

The purpose of the experiments in this study is to continuously apply a drop hammer-type medium-strain rate cyclic impact load under preloading conditions until rock failure occurs. These experiments differ significantly from conventional methods such as hydraulic low-strain rate fatigue tests (Li et al., 2023), Hopkinson pressure bar multiple impact tests (Wang et al., 2019), and staged impact disturbance damage tests, which involve a sequence of preloading, followed by impact, and culminating in static load failure (Xing et al., 2024). The results of this study can provide theoretical insights and empirical data for investigating the instability and failure mechanisms of underground engineering surrounding rock, as well as stability control technologies under continuous disturbance actions such as blasting excavation and mechanical rock drilling. Experiments have shown that rock damage is positively correlated with preapplied static loading and peak impact, and rocks exhibit a strain rate-dependent strengthening effect. The above law is now widely accepted in rock mechanics research. The experimental results also revealed a negative correlation between rock damage and impact frequency. This study analyzed the mechanism of impact frequency on the evolution of rock damage from a microscopic perspective and reported that the higher the impact frequency is, the greater the amount of impact energy transmitted and dissipated at the interface of the microscopic matrix or crystal particles and the smaller the degree of damage to the macroscopic mechanical parameters. However, owing to limitations in research methods and techniques, quantitative data for related analyses are lacking. The next step is to conduct in-depth research from a multiscale perspective that combines macro- and microperspectives.

In the experiment, the impact load is transmitted in the form of stress waves along the rock and the loading device. The stress waves are dispersed into transmitted and reflected waves at multiple interfaces, and during the cyclic impact process, the stress waves overlap, resulting in waveform oscillations in the stress‒strain test data, which have a certain impact on the test results. Subsequent research can draw on the stress wave transmission structure of the separated Hopkinson pressure bar, optimize the high-frequency impact load application device in this paper, and, on the basis of the stress wave transmission theory, refine the analysis of the entire process of stress wave damage and failure to preloaded rock during cyclic impact.

In addition, the lithology of rocks and the strain rates range applied can also have a significant impact on the dynamic characteristics of rocks. By comparing and analyzing the research results of this article with previous studies (Qi et al., 2009; Song et al., 2024), some influence patterns can be preliminarily obtained.

When subjected to low strain rate cyclic loading, rocks exhibit distinct viscoelastic plastic characteristics and damage evolution showing a three-stage progressive development. When subjected to medium strain rate impact cyclic loading, rock dynamic damage exhibits typical strain rate sensitivity characteristics. The inverted S-shaped damage accumulation curve essentially originates from the evolution process of dynamic crack nucleation and propagation. When the strain energy accumulation rate exceeds the critical threshold for crack propagation, the damage evolution undergoes periodic transitions. When subjected to high strain rate impact cyclic loading, nonequilibrium phase transition zones may form, and the damage mode may shift from macroscopic cracks to microstructural fragmentation.

Fine-grained rocks (such as basalt) are more likely to form a uniform microcrack field during the preloading stage, and the dissipation of impact energy is mainly due to intergranular slip. Porous media (such as sandstone) undergo particle rearrangement during the preloading stage, and the impact damage threshold is significantly reduced. Layered rock masses (such as shale) have significant anisotropy, and the angle between the preloading direction and the bedding plane will dominate the selection of damage modes. Rocks containing weak mineral components (such as gypsum or limestone) may undergo dynamic phase transitions during cyclic impacts, leading to strengthening of macroscopic mechanical parameters during damage.

6 CONCLUSIONS

CONFLICT OF INTEREST STATEMENT

The authors declare no conflict of interest.