Introduction

The waste dump slope is an inevitable product of open-pit mining, and its stability is directly related to the safe and efficient mining of the mine1,2. Unlike rocky slopes, waste dump slopes are loose media accumulators, and the distribution of the loose medium has discreteness and disorder, At the same time, the internal bonding force of the loose medium is weak, and the tensile strength is small3. Therefore, as a hazardous source with high potential energy and anthropogenic accumulation4, once a landslide occurs, the waste dump slope will lead to a series of disasters, which seriously affects the safety production of the mining area. For example, in 2008, a landslide occurred in the South Discharge Site of Jianshan Iron Mine, which resulted in 45 deaths and a direct economic loss of more than 30 million yuan5, and a large-scale landslide occurred in the Hong’ao Discharge Site of Guangming District, Shenzhen City, China in 2015, in which several enterprises and buildings were damaged, resulting in 77 deaths and direct economic losses of more than 800 million yuan6. 56 collapses and 28 landslides occurred in Huadu District of Guangzhou City as of 20177, which were systematically analyzed and corresponding management measures were proposed by ZENG8 as well as HU9 using the finite element limit analysis software OptumG2. Therefore, ensuring the stability of the loose accumulation of the waste dump slope is of great significance for the safe and efficient mining of mines. At the same time, how to scientifically and rationally carry out the monitoring and prediction of the stability of the waste dump slope has become one of the major problems that need to be solved urgently in the industry.

In recent years, with the cross and integration between disciplines, the slope surface displacement monitoring technology has shown diversified development, and automated total station monitoring network10,11, laser ranging and scanning technology 12, synthetic aperture radar interferometry technology 13,14, global positioning system (GPS) monitoring technology15, digital imaging monitoring technology16,17, and geographic information system (GIS) monitoring technology18 have been widely used in the monitoring of slope surface displacements. Compared to acoustic emission monitoring, these traditional monitoring techniques are more focused on the measurement of macroscopic surface displacements and large-scale, long-term monitoring, and are suitable for capturing displacement changes and their spatial distribution over larger areas. However, due to the fluidity of the loose medium in the waste dump slope, the traditional monitoring system cannot fully reflect the misalignment and slippage between the loose media inside the waste dump slope, and therefore it is also difficult to capture the precursor information of the slip of the waste dump slope19.

The essence of the instability of waste dump slopes is that the internal loose medium gradually slides or breaks under the action of gravity or external factors to form a macroscopic deformation and damage process, and the mutual friction and breakage of the loose medium will produce acoustic emission phenomena20,21. Therefore, it is feasible to carry out the stability monitoring of the waste dump slope through acoustic emission technology, which can reflect the dynamic process of the waste dump slope from local sliding to macroscopic destabilization damage. Compared with traditional monitoring technology, acoustic emission is characterized by high sensitivity and high precision, which can capture the tiny cracks, sliding, and initial instability signals inside the slope, and it is especially suitable for early warning and detailed dynamic monitoring. Many experts and scholars have already made a lot of arguments about its applicability.

Michlmayr22 et al. measured precursor acoustic emissions prior to landslide release in an inclined inclined channel using smart distributed sensor technology and evaluated the potential of acoustic emission technology as a landslide early warning, and concluded that fiber-optic acoustic emission detection technology based on smart distributed acoustic emission sensors can be an early warning tool for large-scale monitoring of shallow land-slides and other rapid mass movements; Shiotani23 argued that acoustic emission, as a cutting-edge technology providing critical information on various fracture behaviors, is capable of accurately acquiring elastic waves due to deformation and proposed a method for installing acoustic emission sensing in rocky slopes; Yang24 et al. investigated the anomalies in the evolution of acoustic emission parameters before and after wet subsidence damage in loess through waveguide rod modeling tests and determined the optimal parameters for the use of active waveguide rods; Dixon et al25 proposed a method to assess landslides using an acoustic real-time monitoring system (ALARMS) using the Hollin Hill landslide in North Yorkshire, UK, as an engineering background, and compared and analyzed it with the traditional method of monitoring surface displacement of slopes, which provided new insights into landslide monitoring. Smith et al26 verified the feasibility of active waveguide acoustic emission monitoring of landslides by means of full-size active waveguide physical experiments, and the results of the study showed that active waveguide acoustic emission monitoring not only monitors the dynamic development of the landslide shear surface, but also quantifies the dynamic development of the landslide process. Deng et al27 reproduced the three-stage deformation process of soil slope sliding through modeling experiments and believed that the landslide process has a gradual nature, and the landslide velocity can be quantified through acoustic emission monitoring, and the acoustic emission-related parameters can be used as the discriminating index of progressive landslides. Deng Lizheng et al28,29 elaborated on the method of quantifying the deep behavior of landslides using acoustic emission data, established an acoustic emission-dominated early warning model for the landslide process and verified the feasibility of the model.

Existing studies have shown that the application of acoustic emission monitoring technology has been validated as an effective early warning tool in the monitoring and early warning techniques of landslides and earth slopes, especially in different types of landslides and earth slope deformations. The acoustic emission parameters and empirical formulas can realize the quantitative analysis of landslide hazards to a certain extent, which can further improve the accuracy, timeliness, and effectiveness of landslide warnings. However, there is still a lack of research on the changes in acoustic emission parameters and their correlation with slope failure modes in the process of dynamic destabilization of waste dump slopes. Therefore, this paper starts from the characteristics of acoustic emission parameters in the process of slope dynamic instability of waste dump slope, and explores the change rule of acoustic emission parameters in the process of dynamic instability and the sudden change of the parameters when sliding by constructing the physical model of waste dump slope, aiming to study the feasibility of the application of acoustic emission technology in the monitoring and prediction of dynamic instability of waste dump slope, to achieve the accurate prediction of the dynamic instability of waste dump slope and the timely warning.

Based on engineering and testing plans

Engineering background

The supporting project is located in Xinzhou City, Shanxi Province. The waste dump in the mining area is located on the south side of the excavation site, the main constituents of the waste dump body are sandy mudstone, siltstone, mudstone, and loess above the roof of the stripped coal seam, the height of the discharge is about 112 m, and the angle of the side slopes is 21°. The foundation of the waste dump is the coal seam floor, mainly composed of mudstone and local clay, the overall strength is high, but the mudstone is easy to expand and disintegrate in contact with water, leading to a reduction in the strength. The material discharged from the lower part of the waste dump slope is sand and gravel from early mining, with a thickness of about 37 m. Due to the enhancement and expansion project of the waste dump carried out in the later stage of the mining area, a large number of cracks appeared on the 1019 step surface on the side of the empty face of the waste dump under the influence of frequent blasting vibration and transportation machinery equipment vibration, with cracks extending up to several meters in length (Fig. 1).

Fig. 1
figure 1

Geographical location of the mining area and the current situation of the collapse of the 1019-step surface.

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Testing system

The loose slope dynamic instability coupling test system is mainly composed of test bench system, dynamic loading system, and acoustic emission monitoring system. Among them, the dynamic loading system mainly adopts a ZW-3.5 type vibrator, whose maximum excitation frequency is 50 Hz and maximum excitation force is 3.5kN, and it is also equipped with V0007M1 frequency converter to realize the controllable adjustment of vibration frequency. The main equipment of the acoustic emission monitoring system is the fully digital PCI-II acoustic emission monitoring system, the maximum signal amplitude of the monitoring system is 100 dB, which has a built-in 18-bit A/D converter and processor, which can be applied to low amplitude, low threshold (17 dB) of the acoustic emission signal capture and real-time analysis of the sampling, and has a higher precision of the signal processing. Waveguide rods are also used to safely, reliably, and efficiently transmit the waveform signal to the acoustic emission sensor. The material and size of the waveguide rod have an important influence on the signal strength received by the acoustic emission sensor. According to the relevant30 tests carried out in the literature and combined with the size of similar models in the field, the steel waveguide rod with a length of 1 m and a diameter of 18 mm is selected in this study to obtain the acoustic emission signals in the process of dynamic instability of waste dump slope. The test system and model are shown in Fig. 2.

Fig. 2
figure 2

Experimental system and model diagram.

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In this study, to comprehensively monitor the dynamic destabilization process of the waste dump slope model, three waveguide rods were finally determined to be deployed in the lower, middle, and upper parts of the model through repeated multiple tests. The lower waveguide is located near the foundation layer of the model, the middle waveguide is located in the middle region of the model, and the upper waveguide is located in the top region of the model. This arrangement can fully capture the acoustic emission signals from the bottom to the top, ensuring that the dynamic response of the slope model in each region under different vibration frequencies can be accurately reflected. In addition, this layout also provides sufficient experimental data for the subsequent experimental analysis, which helps to understand the different levels of deformation and damage characteristics of the slope destabilization process.

Model construction and experimental plan

The particle size of the loose medium has an important influence on the stability of the waste dump slope, so the reasonable selection of similar experimental simulation materials can accurately reflect the dynamic instability process of the prototype. Based on the principles of geometric similarity and mechanical property similarity of the prototype, six groups of particle size ranges were set up, and the percentage of each group of particle size is shown in Table 1. Taking the soft substrate as the dividing line, two kinds of particle gradation were set up respectively. Among them, the soft substrate contains more large gravel, the average particle size is larger, and the overlying waste material contains less large gravel; the geometric similarity ratio CL between the model and the prototype is 1:330, so the established model has a height of 36 cm and a horizontal length of 100 cm.

Table 1 Particle size distribution of similar model loose media.
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To minimize the influence of the initial moisture of similar materials on the test results, in the actual operation, the weighed similar materials are firstly put into the drying oven for constant temperature drying. Subsequently, the materials and a certain amount of water are put into the mixing equipment for uniform mixing according to the proportion, to ensure that the materials with different particle sizes can be fully mixed to form a homogeneous geotechnical media layer. After mixing, the mixed materials were laid into the model frame layer by layer according to the predetermined thickness, and compacted layer by layer to simulate the actual compaction and interlayer bonding status of the prototype slope. To minimize the interlayer sliding and enhance the interlayer bonding force, the thickness and compaction density were checked layer by layer during the laying process to ensure that the model construction accurately meets the experimental design requirements. To more clearly observe the destabilizing damage characteristics of the model under dynamic action, a layer of white paint was uniformly sprayed on the surface of the model after laying, to more intuitively demonstrate the dynamic evolution of surface cracks and deformation during the damage process of the model, and to more accurately record the form of damage and the evolution process of the various regions of the slope.

Combining the actual situation of mining in the mining area and the China Seismic Intensity Scale, the sinusoidal wave in the Z direction was applied to the model in a progressively increasing manner according to the time-similarity condition. According to the mining process of the Hequ open pit mine, the duration of each blasting operation is 3.6 s. Assuming 300 days of mining in a year, the total time that the waste dump slope is affected by blasting vibration is about 1080 s. n order to ensure the similarity between the test design and the actual engineering environment, the time similarity ratio Ct = 18 was adopted. According to the time similarity ratio, the test set the duration of vibration effect on the slope model of the earth discharge site at each stage to be 60 s. Considering the influence of different vibration frequencies corresponding to the actual engineering scenarios and frequent engineering activities, the experiment adopts a frequency scheme of step-by-step loading. The experiment started with an initial frequency of 10 Hz and increased by 5 Hz in each stage until 40 Hz, and the whole test lasted for 7 min. The applied sinusoidal wave satisfies the following equation, and the values of each parameter for different test stages are shown in Table 2:

$$y = y_{0} + A\sin \left[ {\left( {x - x_{0} } \right)\pi /\omega } \right]$$
(1)
Table 2 Parameter values for each experimental stage.
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Analysis of experimental results

Analysis of dynamic instability process of waste dump slope

To analyze the entire process of dynamic instability of waste dump slope, similar model states at different stages were obtained using high-speed cameras, as shown in Fig. 3, where 0 Hz is the initial state of the model.

Fig. 3
figure 3

The state of waste dump slope under different vibration frequency conditions.

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It can be analyzed from Fig. 3, when the vibration frequency is 10 Hz, the slope did not occur obvious slip damage, mainly manifested as the sliding of small particles on the slope surface and the gravel of soft substrate for an extremely short distance, which is difficult to capture with the naked eye; When the vibration frequency is 15 Hz, at the end of the stage, a small transverse shallow crack was produced on the right side of the 3rd step of the slope model, and the particles in the lower part of the crack slid for a short distance; When the vibration frequency is 20 Hz, the aforementioned micro cracks further expand and develop into small-scale "V"-shaped landslides, and very small horizontal micro cracks appear on the slope surface of the 3rd step; When the vibration frequency is 25 Hz, the right side of the 3rd step of the slope model is further damaged and expands laterally along the step surface, and small-scale sliding failure begins to appear on the right side of the first and second steps; When the vibration frequency is 30 Hz, the damage range of the slope model continues to develop, in which a large number of transverse cracks are formed in the middle of the 3rd step, and a piece of obvious slip body is formed on the slope of the 2nd step; When the vibration frequency is 35 Hz, a large number of cracks and sliding bodies of different sizes are formed on the 3rd step of the slope, the slip range on the right side of the 1st step is further expanded, and small micro-cracks begin to appear on the 4th and 5th steps; When the vibration frequency is 35 Hz, a large number of cracks penetrating the slope surface appeared in the3rd step of the slope, and slip bodies of varying sizes were formed. The slip range on the right side of the 1st step further expanded, and small micro-cracks began to appear in the 4th and 5th steps; When the vibration frequency is 40 Hz, the slope model is damaged in a large area, and the damage scope involves the whole slope surface, in which the 3rd step is the most serious damage, on the left side of the 1st step at the foot of the slope model has formed a large piece of slip body, and the small-sized slip body formed on the right side in the previous stage has been covered, and obvious large cracks have appeared in the 4th and 5th steps at the top of the slope, and localized slippage has been generated.

Analysis of acoustic emission characteristics of dynamic instability of waste dump slope

Acoustic emission signals are released by the interaction of the loose medium of the slope in the waste dump under vibration, which is macroscopically manifested as the dynamic destabilization damage of the waste dump slope. By extracting the characteristic parameters of the acoustic emission signals for quantitative analysis, the acoustic emission parameter characteristics during the dynamic instability of the waste dump slope in the discharge field can be effectively characterized, and the instability evolution law can be further revealed. This study focuses on the in-depth analysis of the acoustic emission ring counts, energy rate, and amplitude. The ringing counts can sensitively reflect the microcracks and local damages of the slope under external vibration or pressure, and the amplitude of the acoustic emission is not affected by other conditions, which can more directly reflect the real situation of the internal slippage evolution of the slope in the slope of the earth dis-placement site.31. The acoustic emission parameters of the whole process of dynamic destabilization of the waste dump slope are shown in Fig. 4.

Fig. 4
figure 4

Evolution law of acoustic emission parameters for dynamic instability of waste dump slopes.

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Analyzing Fig. 4(a), it can be seen that with the continuation of the vibration continues, the acoustic emission ringing count in the process of the dynamic instability of the waste dump slope shows obvious stage characteristics, and according to the distribution characteristics of the acoustic emission ringing counts and the changing trend of cumulative acoustic emission ringing counts, the dynamic instability of the waste dump slope can be roughly classified into five stages.

  1. (1)

    First stage: vibration compaction stage (0 ≤ t ≤ 90 s). At this stage, the vibrating table inputs vibration energy with low frequency and high amplitude, which leads to the rearrangement and interaction of the loose medium inside the slope model, and then generates acoustic emission signals, and the degree of compaction of the waste dump slope also gradually increases and tends to the limit. In the process of vibration wave transmission from the soft substrate to the top of the slope by a certain damping effect, resulting in continuous energy attenuation, although not enough to cause large-scale landslides, but enough to cause some of the small particles on the slope surface as well as the gravel of the soft substrate to occur in small displacements, but also produces a small number of acoustic emission signals. Therefore, the degree of acoustic emission activity in this stage is relatively high, and there are high energy rate points in the initial stage, and the acoustic emission amplitude is relatively large.

  2. (2)

    Second stage: vibration equilibrium stage (90 s < t ≤ 207 s). In this stage, the acoustic emission activity decreases, and the acoustic emission energy rate and amplitude also decrease significantly. In this stage, the vibration energy input from the vibration table is further increased, and the continuous vibration causes the interaction between the loose media to be closer, but the compaction of the loose media in the previous stage has reached a high level, and the media are in a relatively stable state. However, the increase in vibration energy led to an increase in the energy transferred to the slope surface, which in turn caused the stability of some areas to exceed their limits. Therefore, small displacements of some particles on the surface of the slope model occurred and small tension cracks were formed on the slope surface.

  3. (3)

    Third stage: landslide initiation stage (207 s < t ≤ 315 s). In this stage, the acoustic emission activity increases, and the acoustic emission energy rate and amplitude increase compared with the previous stage. The further increase in vibration frequency in this stage leads to a further increase in vibration energy, and the vibration effect between the loose media on the waste dump slope is more frequent and stronger, increasing the possibility of the loose media sliding. In addition, the tension cracks formed in the previous stage developed further, forming small-scale slip bodies and new cracks in unstable areas.

  4. (4)

    Fourth stage: localized destabilization stage (315 s < t ≤ 360 s). At this stage, the acoustic emission activity increases further, the acoustic emission amplitude increases significantly, and the energy rate appears at a higher point. The vibration frequency in this stage reaches a high degree, and the high-frequency vibration causes the friction between particles to be greatly reduced, which is macroscopically manifested in the further increase of the damage range of the waste dump slope, almost covering the middle step of the waste dump slope.

  5. (5)

    Fifth stage: large-scale destabilization stage (360 s < t ≤ 420 s). This stage has the highest acoustic emission activity, and the acoustic emission amplitude and energy rate increase greatly, indicating that a large amount of energy has been stored inside the waste dump slope in the previous stage, and the energy inside the slide is released in a large amount under the action of vibratory perturbation, which causes large-scale destruction of the slope of the earth discharge site, and the intensity of acoustic emission is also much larger than that in other stages, and the cumulative acoustic emission ringing count curve rises sharply.

According to the above analysis, it can be seen that in the process of dynamic destabilization of the waste dump slope, the acoustic emission ringing counts show obvious stage characteristics, and the cumulative acoustic emission ringing counts show a trend of continuous increase, which reflects the key changes in the process of dynamic destabilization of the waste dump slope. With the increase of vibration frequency, the waste dump slope shows the stage characteristics of “vibration compaction → vibration equilibrium → dynamic instability”. Among them, the vibration compaction stage is manifested as the rearrangement and densification of the loose medium inside the waste dump slope, the mutual friction and collision between particles are more frequent, and the acoustic emission activity is relatively active; the vibration equilibrium stage is manifested as the internal loose medium of the slope tends to be stabilized under the effect of continuous vibration, the slip and collision between particles are reduced, and the acoustic emission activity is decreased, but still maintains a certain degree of fluctuation, which reflects the existence of local instability; while in the dynamic instability, the vibration frequency is increased. In the dynamic instability stage, with the further increase of vibration frequency, the stability of the slope is destroyed, large-scale sliding and cracking occur, and the acoustic emission activity increases significantly, and its amplitude and frequency are obviously elevated, which shows the drastic changes within the system.

Analysis of the entire process characteristics of dynamic instability of waste dump slope

It has been shown that the rock damage process has obvious fractal characteristics, and the change of correlation dimension D can reflect the internal damage characteristics of rock specimens, and the correlation dimension of the acoustic emission parameters is superior in the evaluation index of rock body instability32. Byun33 proposed the concept of ∑N/∑E ratio, which is the ratio between the cumulative number of acoustic emission events and the cumulative acoustic emission energy, and the ∑N /∑E ratio can reflect the magnitude of rock damage. However, whether the landslide process of waste dump slope has fractal characteristics, whether the change of correlation dimension and the size of ∑N/∑E ratio can reveal the dynamic destabilization process of the waste dump slope needs further study.

Calculation of correlation dimension

In this paper, the G-P algorithm is selected to solve the correlation dimension in the process of dynamic instability of the waste dump slope to explore the fractal characteristics of the acoustic emission signals in the process of dynamic instability of the waste dump slope.

Assuming that there exists a time-series of data {xk|k = 1, 2, 3,…, N} representing the dynamic behavior of the model, selecting a time delay value τ, constructing an m-dimensional space, a vector set J(m) can be obtained as34:

$$X_{n} \left( {m,\tau } \right) = \left( {x_{n} ,x_{n + \tau } , \cdots ,x_{n + (m - 1) \times \tau } } \right)$$
(2)

In the above equation, n = 1, 2, 3, …, Nm, the time delay amount τ = k∆t, ∆t is the length of two neighboring sampling times, k takes an integer, Nm = N-(m-1)τ, and m is the embedding dimension, and the geometric features of the original attractor can be reproduced when m ≥ 2d + 1 (d is the dimension of the original state space attractor). Further, a reference point Xi is randomly selected from the Nm points, and the spacing between the remaining points and Xi is:

$$r_{ij} = d\left( {X_{i} ,X_{j} } \right) = \left[ {\sum\limits_{m - 1}^{i = 0} {\left( {x_{i + lr} - x_{j + lh} } \right)^{2} } } \right]^{1/2}$$
(3)

In the above equation, j = 1, 2, 3, …, Nm, the correlation function C(r) is:

$$C_{\left( r \right)} = \frac{2}{{N_{m} \left( {N_{m} - 1} \right)}}\sum\limits_{i,j}^{{N_{m} }} {H\left( {r - r_{ij} } \right)}$$
(4)

In the above equation, H is the Heaviside function, H = 1 when x > 0 and vice versa H = 0. The correlation function C(r) characterizes the ratio of the number of pairs of points with a distance less than r in the phase space to the number of all possible pairs of points, as well as the degree of dispersion of the phase points. Therefore, when m is sufficiently small and r < m, the correlation integral equation can be calculated by the following equation:

$$\ln C_{{\left( {\begin{array}{*{20}c} r \\ \end{array} } \right)}} = \ln C - D_{{\left( {\begin{array}{*{20}c} m \\ \end{array} } \right)}} \ln r$$
(5)

Furthermore, it can be concluded that the correlation dimension of the set J(m) in m-dimensional space is:

$$D_{{\left( {\begin{array}{*{20}c} m \\ \end{array} } \right)}} = - \mathop {\lim }\limits_{m \to 0} \frac{{\partial \ln C_{{\left( {\begin{array}{*{20}c} r \\ \end{array} } \right)}} }}{\partial \ln r}$$
(6)

The phase space dimension D2 is obtained when Dm tends to a stable value with the increase of the phase space dimension m.

To ensure the reliability of the correlation dimension estimated by linear regression, after determining the value of m, the received acoustic emission parameters are reconstructed in phase space according to Eq. (1), and the phase spacing rij of each point is calculated by Eq. (2), then ∆r can be further calculated:

$${\Delta }r = \frac{{r_{{ij\left( {\max } \right)}} - r_{{ij\left( {\min } \right)}} }}{k}$$
(7)

Further, the logarithm is taken for rij as well as C(r), and a fitting curve is plotted with ln rij as the x-axis and ln C(r) as the y-axis, and the slope of the resulting fitting curve is the correlation dimension D2 of the segment.

Determination of m value and determination of fractal characteristics of acoustic emission parameters

As mentioned before, the phase space dimension m has an important influence on the calculation of the correlation dimension. In this paper, 30 acoustic emission time series data are taken as a unit, the time spacing △t between two neighboring samples is taken as 3, the value of k is 15, and the corresponding acoustic emission correlation dimension value can be calculated by Eq. (5). Taking the acoustic emission ringing count time series as an example, the correlation dimension values when m is 2 – 8 are calculated respectively, as shown in Fig. 5. From Fig. 5, it can be seen that when the value of m lies in the interval of 1 – 4, the correlation dimension D shows an obvious linear change, so the optimal value of m can be determined as 3.

Fig. 5
figure 5

Correlation curve between phase space dimension m and correlation dimension D.

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In order to further determine whether the acoustic emission parameters of the dynamic instability damage process of the waste dump slope have fractal characteristics, 30 acoustic emission data at the final stage of the test were analyzed, and the correlation dimensions of the ringing counts, amplitude, and energy rate were calculated. The relationship curves of lnr versus lnC(r) obtained from the calculation of each parameter are shown in Fig. 6. From Fig. 6, it can be seen that there is a good linear relationship between the curves of acoustic emission amplitude and energy rate and the fitted curves of lnr and lnC(r) during the dynamic instability process of the waste dump slope, the correlation coefficients are all above 0.95, while the correlation coefficient of the ringing counts is 0.82 only. Therefore, it can be considered that the acoustic emission amplitude as well as the energy rate series have obvious fractal characteristics in the time domain during the dynamic instability process of the waste dump slope.

Fig. 6
figure 6

Relationship curve between acoustic emission parameter lnr and lnC(r).

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Analysis of the correlation dimension of acoustic emission for dynamic instability of waste dump slope

According to the above analysis, it can be seen that the acoustic emission amplitude as well as the energy rate during the dynamic instability process of the waste dump slope has obvious fractal characteristics. Therefore, the phase space dimension m is taken as 3, and 30 acoustic emission time series data are used to calculate the correlation dimension. To reduce the computation time of the correlation dimension of acoustic emission and avoid the truncation phenomenon of data selection, the acoustic emission data were screened when calculating the correlation dimension of each section. At the same time, the correlation dimension was grouped in accordance with a certain step, and the average value of the correlation dimension within the step was calculated, so that the correlation dimension change curves of the acoustic emission amplitude and energy rate were obtained and plotted as shown in Fig. 7.

Fig. 7
figure 7

Changes in the correlation dimension of acoustic emission amplitude and energy efficiency.

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Analyzing Fig. 7, it can be seen that the correlation dimension of the acoustic emission amplitude and energy rate during the dynamic instability process of the waste dump slope shows multi-peak variations, and the correlation dimension of energy rate is obviously larger than the correlation dimension of amplitude. On the whole, the correlation dimension of the acoustic emission amplitude and energy rate shows a phased characteristic of decreasing and then increasing. Combined with the experimental phenomena, it can be further analyzed that the model can be divided into two states according to the damage characteristics of the model at different stages and the characteristics of the acoustic emission parameters, in which the first state is the vibration compaction stage and the vibration equilibrium stage, and the second state is the landslide initiation stage, the localized destabilization stage, and the large-scale destabilization stage.

When the model is in the first state, the correlation dimension of the acoustic emission amplitude as well as the energy rate shows an overall decreasing trend. When the vibration frequency is at 10 Hz, the initial correlation dimension is large and shows a decreasing trend of fluctuation. When the vibration frequency is increased to 15 Hz, there is a small increase in the correlation dimension, but the value is smaller than the initial value, and then it decreases again and continues until the end of the vibration equilibrium stage (t = 207 s). When the model enters into the second state, the vibration frequency is 25 Hz, the model slip starts, and the correlation dimension of acoustic emission amplitude and energy rate increases significantly compared with the previous stage, along with the time and the vibration frequency increase, when the vibration frequency is 40 Hz, the correlation dimension reaches the maximum, and then the model undergoes large-scale destabilization damage.

In the first state stage, the correlation dimension of the acoustic emission amplitude and energy rate shows a fluctuating downward trend, especially at the end of the state, the correlation dimension of some nodes is 0. It is analyzed that the slope model is in the vibration equilibrium stage in the state, the internal activities are less, and the crack extension and slip phenomenon have not yet occurred significantly, at this time, the acoustic emission signal is relatively simple, which results in the correlation dimension close to zero. With the increase of vibration frequency, the microcracks inside the slope gradually expand, the slip phenomenon gradually intensifies, the acoustic emission signal becomes more complex, and the correlation dimension begins to rise.

Therefore, there is a close correlation between the correlation dimension of the acoustic emission parameters and the dynamic destabilization of the waste dump slope. In the process of slope destabilization, with the increasing vibration action, the stress and deformation inside the slope gradually increase, and microcracks and slip phenomena accumulate. These changes are reflected by the acoustic emission signals, and the correlation dimension of the acoustic emission signals effectively characterizes the complexity and irregularity of the signals. Generally, in the slope stabilization stage, the correlation dimension of the acoustic emission signals is low and shows a more regular and simple pattern; however, as the slope gradually enters into the dynamic instability stage, especially when the cracks and slips increase, the acoustic emission signals become more complex and irregular, and the correlation dimension increases significantly. Especially when the slope enters into the stage of large-scale destabilization and damage, the correlation dimension of the acoustic emission parameters reaches the peak, reflecting the precursor of increased instability and large-scale damage within the slope.

Therefore, by analyzing the correlation dimension of the acoustic emission parameters, the dynamic destabilization process of the waste dump slopes can be further quantified and the potential damage risk can be identified in advance. The correlation dimension of the acoustic emission parameters can be used as an important indicator in slope stability monitoring, which has a significant early warning effect.

Analysis of ∑N/∑E value characteristics of dynamic instability of waste dump slope

Based on the literature findings33, the ∑N/∑E ratio is denoted as NE. where ∑N is the cumulative number of acoustic emissions events and ∑E is the cumulative energy. The acoustic emission data obtained from the dynamic instability test of the waste dump slope were processed and the value of NE during the dynamic instability of the model was calculated and plotted as shown in Fig. 8.

Fig. 8
figure 8

Changes in acoustic emission event rate and NE value.

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Analyzing Fig. 8, it can be seen that the number of acoustic emission events shows a multi-peak phenomenon during the dynamic instability process of the waste dump slope, and the rate of acoustic emission events increases sharply when the model undergoes localized as well as large-scale destabilization, and its activity is high. At different stages, the acoustic emission signals are different due to the differences in the loose medium interaction, so the NE value shows a fluctuating downward trend. Among them, When the model undergoes localized as well as large-scale destabilization, the NE value curve will experience a "cliff-like" decline.

Based on further analysis of experimental phenomena, it can be seen that when the model is in the first stage (0 ≤ t ≤ 90 s), due to the initial stage of the vibration table input frequency is not enough to cause the model damage, but will cause the compaction effect of the loose medium, the mutual friction between loose media and the sliding of small particles on the surface will generate weak acoustic emission signals, so this stage will produce a small number of acoustic emission events. When t = 60 s, the vibration frequency increases to cause a further increase in the interaction of the loose medium, so the number of acoustic emission events will be enhanced, and the degree of compaction of the loose medium tends to limit; in this stage, the number of acoustic emission events accompanied by a certain amount of energy, but because of its small energy, so the NE value of this stage is at a high level. When the model is in the second stage (90 s < t ≤ 207 s), the vibration frequency increases in the first and middle stages of the stage, and the degree of particle transport of the model surface increases, but it is still not enough to cause model damage, and thus a small number of acoustic emission events are generated; in the late stage of the stage, due to the further increase in the vibration frequency, which causes the model to produce small tensile crack in the local area, the number of acoustic emission events increases, and at the same time, due to the increased energy input from the vibration table in this stage, the NE value decreases compared to the previous stage. With the increase of time, the tiny cracks generated in the previous stage further expanded, forming a small-scale slip body, and the model slip began to initiate (207 s < t ≤ 315 s), and the energy input from the vibration table further increased in this stage, and the small-scale slip generated some acoustic emission signals, and the NE value further decreased. With the further increase of vibration frequency, the model enters the localized destabilization stage (315 s < t ≤ 360 s), and the increase of vibration frequency and time causes the increase of the model’s damaged slip body, which generates a locally high number of acoustic emission events, and the high energy and high number of events lead to a "cliff-like" drop of the NE value. When the vibration frequency increases to 40 Hz, the model experiences a large-scale destabilization stage (360 s < t ≤ 420 s), and the damage range of the model is further increased at this stage, and the number of acoustic emission events is further increased, and the energy is larger. Therefore, the NE value has a "cliff-like" drop again.

In summary, there is a certain correlation between the change in NE value and the active degree of acoustic emission. Overall, the NE value shows a "step-like" change, and when the model is damaged, the NE value will experience a "cliff-like" decline. Therefore, according to the change of NE value, the dynamic instability prediction of the waste dump slope can be achieved.

Discuss

Through the analysis of the acoustic emission parameters during the dynamic instability process of the waste dump slope model, it is found that the acoustic emission activities of the waste dump slope show an obvious correlation with its instability process. Based on the distribution characteristics of the acoustic emission ringer counts and the trend of the cumulative acoustic emission ringer counts, the dynamic instability process of the waste dump slope can be divided into five stages to explore the destabilization mechanism more deeply.

  1. (1)

    The vibratory compaction stage describes the initial arrangement of loose media and acoustic emission activation, marking the early stage of waste dump slope response to vibration energy;

  2. (2)

    The vibration equilibrium stage emphasizes the equilibrium state of the interaction between the vibration energy and the loose medium, at which the acoustic emission activity range and amplitude are relatively reduced, reflecting a relatively stable state;

  3. (3)

    The landslide initiation stage describes the initial signs of slope dynamic instability, including the formation of small-scale slip bodies and the appearance of new cracks, and the acoustic emission activity and energy rate begin to increase;

  4. (4)

    The localized destabilization stage is a critical period of further decline in slope stability, and the significant increase in acoustic emission amplitude indicates further expansion of slope damage;

  5. (5)

    The large-scale instability stage is the most serious instability stage, and the acoustic emission activity reaches a peak, indicating that the energy accumulated inside the slope has been released, leading to large-scale damage.

In addition, the research results further demonstrate the potential value of the correlation dimension of the acoustic emission parameters as well as the NE values in predicting the dynamic instability of waste dump slopes. With the increase of vibration frequency and time, the correlation dimension and NE values of the acoustic emission amplitude and energy rate show a stage change, which is consistent with the damage characteristics of the slope model. Especially in the localized destabilization stage and large-scale instability stage, the correlation dimension of the acoustic emission amplitude and energy rate increases significantly, and the high energy and high event number acoustic emission signals lead to a "cliff-like" drop in the NE value.

In summary, in the process of increasing the vibration frequency and time, the sliding force of the waste dump slope model gradually increases, and the interaction of the loose medium inside the model changes, showing the dynamic process of "vibration compaction → vibration equilibrium → dynamic instability". Through the comprehensive analysis of the acoustic emission parameters, it is believed that the sudden increase of the correlation dimension of the acoustic emission amplitude and energy rate, and the "cliff-like" decline of the NE value can be used as a precursor of the dynamic instability damage of the waste dump slopes, and thus be used to carry out the monitoring of the stability of the project.

Therefore, the acoustic emission technique has unique advantages in waste dump slope monitoring, especially in the early detection of microcracks and localized slip inversions. It can sensitively capture subtle changes within the slope and is particularly suitable for highly sensitive dynamic instability detection. In addition, the acoustic emission technique has obvious advantages for monitoring in a non-destructive, real-time, and high spatial resolution of slope.

In the future, the development trend of acoustic emission technology should focus on integration with other monitoring technologies, such as combining with ground displacement monitoring, laser scanning, and remote sensing technology to form a multi-technology synergistic monitoring system. This will improve the comprehensiveness and accuracy of monitoring and further promote the improvement of intelligent early warning systems. At the same time, the combination of big data and artificial intelligence analysis methods will improve data processing efficiency and prediction accuracy, and realize early warning and intelligent management of slope instability.

Conclusion

  1. (1)

    With the increase of vibration frequency, the damage mode of the waste dump slope model gradually changed from the sliding of small particles to large-scale landslides, and showed the dynamic process of "vibration compaction → vibration equilibrium → dynamic instability";

  2. (2)

    Under the condition of low frequency and high amplitude, the slope model mainly manifested as the short distance sliding of small particles and base crushed stones; when under the condition of high frequency and low amplitude, the slope steps are damaged to different degrees, and with the continuous increase of vibration frequency, the damage range is gradually expanded, which directly affects the stability of the whole slope;

  3. (3)

    Strong acoustic emission signals accompanied the dynamic instability process of the waste dump slope, and the changes of the acoustic emission characteristic parameters revealed to some extent the evolution process of the internal state and its stage characteristics during the dynamic instability process of the waste dump slope;

  4. (4)

    The acoustic emission amplitude and energy rate show obvious fractal characteristics in the time domain during the dynamic instability process of the waste dump slope. When the waste dump slope model is close to destruction, the correlation dimension of the acoustic emission amplitude and energy rate will change significantly, and the NE value will experience a "cliff-like" decline, which can be regarded as a precursor of the destruction of the dynamic instability of the waste dump slope.