1 Introduction

With the continuous development of tunneling to large depths and high-stress directions, rockburst disasters began to appear frequently. Rockburst is a kind of excavation process in the rock mass of the energy stored in the sudden release, resulting in rock burst, spalling, ejection, and other phenomena of geological hazards, with a strong suddenness, randomness, and harm (Li et al. 2019; Liang et al. 2020c; Du et al. 2022). The earliest recorded rockburst incident took place in England at the Leipzig Coal Mine (Kaiser et al. 1996). Subsequently, rockburst of varying magnitudes has occurred in tunnels, shafts, caves, and mines worldwide (Wang et al. 2018b, 2019; Tao et al. 2019). Rockbursts have occurred in China’s Qinling Tunnel(Wang et al. 2023b), Yuyangshan Tunnel(Wu et al. 2021), the Hanjiang River to Weihe River diversion tunnel (Liu et al. 2019), the Jinping II Hydroelectric Power Station diversion tunnel(Gong et al. 2012), as well as Canada's Cigar Lake Uranium Mine(Morgenroth et al. 2022), resulting in significant economic losses and casualties. Today, achieving precise rockburst prediction remains a significant challenge. Therefore, how to accurately and efficiently make predictions about rockbursts has become one of the many research hotspots.

Studies have shown that whether or not a rockburst occurs depends on the stability of the rock mass, which depends on the mechanical properties of the rock (e.g. strength, stiffness, and modulus of elasticity, etc.) and external conditions (e.g. dynamic disturbance, magnitude of in situ stresses and geological structure, etc.) (Liu et al. 2013; Meng et al. 2017). Currently, scholars have established a large number of static parameters based on factors such as rock mechanical properties and strain energy evolution, including the rock mass integrity coefficient Kv, buried depth in the tunnel H, maximum ground stress in the surrounding rock before excavation \({\sigma }_{0}\), maximum tangential stress \({\sigma }_{\theta }\), etc. Consequently, empirical index guidelines, exemplified by the Turchaninov criterion (Turchaninov et al. 1972), Barton criterion (Barton et al. 1974), Roussens criterion (Russenes 1974), Hoek and Brown criterion (Hoek and Brown 1997), Tao criterion (Tao 1988), strain energy storage index Wet (Kidybiński 1981), peak intensity strain energy storage index \({{\text{W}}}_{{\text{et}}}^{{\text{p}}}\) (Gong et al. 2019), residual elasticity energy index Cef (Gong et al. 2021) and five-factor criterion (Zhang et al. 2011) have been formulated as rockburst prediction criteria. In the construction stage, with the geological structure and rock stress state and other related static data gradually determined, the accuracy of trend prediction of rockburst disasters through the use of empirical methods has been significantly improved. However, for the higher risk of strong rockburst or very strong rockburst, the trend prediction of rockburst using empirical methods may have a lag phenomenon. The empirical method is mainly through indoor testing to obtain static parameters of rock samples, which can not reflect the real situation of the rock mass. It can not meet the requirements of real-time dynamic early warning at the construction site (He et al. 2021).

The emergence of surveillance systems and monitoring equipment has gradually transformed indicators from static to dynamic, making real-time dynamic early warning possible (Du et al. 2021). By monitoring the dynamic signals generated before and after rock ruptures, such as strain energy, elastic waves, electromagnetic radiation, and rock surface temperature, a diverse set of dynamic indicators has been established. These indicators encompass apparent stress, apparent volume, microseismic energy density, acoustic emission energy, ringer counts, electromagnetic radiation pulse counts, and infrared temperature jump rates (Wang et al. 2011; Dou et al. 2018; Ding et al. 2022; Hao et al. 2022). Consequently, A range of rockburst field monitoring techniques, including microseismic monitoring method (Tang et al. 2021), acoustic emission method (Becker et al. 2010), electromagnetic radiation method (Rabinovitch et al. 2002), infrared thermal imaging method (Liu et al. 2023b), micro-gravity method(Adoko et al. 2013) and drilling cutting method (Zhou et al. 2012), etc., has been developed based on these dynamic indicators. Empirical methods and on-site monitoring methods have avoided casualties and economic losses to a certain extent. However, static and dynamic indicators are more difficult to obtain, and there are outstanding problems such as data outliers and difficulties in data processing. Thus limiting the predictive accuracy of empirical methods and field monitoring methods. Rockburst is the result of the combined effect of a variety of influencing factors, and the high degree of non-linear relationship between the factors so that empirical methods and field monitoring methods are difficult to realize the integrated prediction of multiple indicators, to a certain extent, reducing the prediction efficiency (Ma et al. 2018).

Advances in science and technology, as well as algorithmic modeling, have led to an extension of the application fields for machine learning approaches in recent years. Several academics have been devoted to the investigation of machine learning methods since Feng and Wang (1994) deployed neural network learning and adaptive recognition approaches for rockburst prediction. Four static indicators—rockburst ground stress, uniaxial compressive strength of rock mass, uniaxial tensile strength, and strain energy storage index—were employed by Dong et al. (2013) as input data for the random forest algorithm model for predicting rockbursts. Meanwhile, Ghasemi et al. (2019) used four static metrics, namely Stress coefficient, rock brittleness coefficient, strain energy storage index, and maximum tangential stress, as input data for the C5.0 decision tree algorithm, which explicitly showed the relationship between inputs and outputs. Dealing with non-linear relationships, high dimensionality, and small sample database problems is characteristic of the support vector machine algorithm model (Zhao et al. 2007). Zhou et al. (2023) used six dynamic metrics, namely angular frequency ratio, p-wave to s-wave energy ratio, cumulative microseismic energy, apparent stress, radius of concavity, and seismic moments, as input data to the support vector machine to perform rockburst prediction. Machine learning approaches have been shown in studies to be effective in dealing with static and dynamic index data, as well as non-linear connections between indicators, offering a vital tool for complete multi-indicator forecasting (Zhou et al. 2023).

Currently, rockburst prediction methods based on static and dynamic indicators are shown in Fig. 1. They mainly include empirical methods (Zhao et al. 2017; Gong et al. 2018a), experimental tests (Cai 2016), numerical modeling(Xue et al. 2021), machine learning method (Shirani Faradonbeh et al. 2020; Li et al. 2023c) and geophysical method (Feng et al. 2015; Meng et al. 2016; Wang et al. 2021a). Geophysical methods also include the microseismic monitoring method, acoustic emission method, hydraulic support pressure method, electromagnetic radiation method, infrared radiation method, microgravity method, and drill chip method. These methods can be categorized into two types: short-term prediction and long-term prediction (Pu et al. 2019a). Short-term rockburst prediction mainly refers to on-site monitoring of a localized area, such as microseismic monitoring and electromagnetic radiation, etc., with a shorter test cycle. Long-term prediction is a comprehensive assessment of the rockburst potential and site conditions, such as based on the mechanical properties of the rock and site conditions proposed by a variety of indicators of the method. Because it has a more intuitive appearance and is widely used in the field of rockburst prediction (Zhou et al. 2018a; Afraei et al. 2019). However, there is no article to systematically summarize the rockburst prediction methods from the perspective of static and dynamic indicators. Therefore, it is necessary to analyze the application of static and dynamic indicators in rockburst prediction methods.

Fig. 1
figure 1

Schematic diagram of rockburst prediction methods

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Based on the numerous rockburst prediction methods demonstrated in Fig. 1, this paper aims to analyze four rockburst prediction methods, namely empirical methods, microseismic monitoring, acoustic emission, and machine learning, which are commonly used nowadays, from the perspectives of static and dynamic indicators. First, the importance of various rockburst prediction methods is analyzed based on Citespace software. Then, the application of static and dynamic indicators in the four rockburst prediction methods is analyzed. Finally, the advantages and disadvantages of static and dynamic indicators in rockburst prediction methods and their problems are discussed. The possible future development direction is proposed to provide a useful reference for the rockburst prediction research.

2 Analysis of the importance of rockburst prediction methods

The topic of rockburst prediction is exceedingly complicated, and no mature and full theory and technology exists. Since the beginning of the rockburst disaster, numerous scholars have created a series of study outcomes based on static and dynamic indicators of rockburst prediction research. A scientometric analysis of rockburst prediction methods is required to better grasp the existing area of knowledge and investigate the value of various rockburst prediction methods.

Citespace, as one of the scientometric analysis software, has the advantage of tracking the research frontiers (Liang et al. 2020a), In this chapter, Citespace software is used to visualize and analyze the rockburst prediction methods.

The keyword co-occurrence network is shown in Fig. 2. The size of the keyword in the figure reflects the frequency of that keyword, i.e., the larger the keyword, the more frequently it appears. The blue bar graph in Fig. 3 reflects the specific frequency size of the keyword. From Figs. 2 and 3, it can be found that mechanism, energy, stress, numerical simulation, model, and classification are the keywords with a relatively high frequency of occurrence. Among them, mechanisms appeared 68 times, and energy and stress appeared 63 times. It indicates that the study of the evolution of energy and stress in the process of rock damage using model tests and numerical analysis is the main way to understand the mechanism of rockburst occurrence (Zhao et al. 2021; Cui and Wong 2023; Su et al. 2023). At the same time, it shows that the rockburst mechanism is closely integrated with rockburst prediction. The ultimate goal of understanding the rockburst mechanism is to accurately predict rockburst hazards, and rockburst prediction can be implemented more effectively by exploring the rockburst mechanism.

Fig. 2
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Keyword co-occurrence map for rockburst prediction for the period 2007–2023

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Fig. 3
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Frequency of occurrence of the first 20 keywords and their centrality

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Acoustic emission, machine learning, and microseismic monitoring appear frequently, indicating that the research for rockburst prediction mainly focuses on the three methods of acoustic emission, machine learning, and microseismic monitoring. Centrality refers to the mediating role played by a keyword in the transmission of information, reflecting the academic importance of that keyword (Fu et al. 2022). Figure 2 shows the centrality of the top 20 keywords. The orange bars reflect the magnitude of the centrality of the keywords. (The values in the graph are actual centrality × 103). The results show generally high centrality of acoustic emission, machine learning, and microseismic monitoring. It indicates a crucial transfer value in the field of rockburst prediction. For example, microseismic monitoring can be directly used for field prediction, while the dynamic data it generates can be used as input data for machine learning methods, furthermore, microseismic monitoring has a similar working principle to acoustic emission. There are many other cases where a keyword radiates to two or more keywords, and the centrality can be used to understand the range and intensity of a keyword's radiation. The number of occurrences of index in the figure is low and the centrality is not high. It shows that the use of various indicators for direct rockburst prediction is relatively less used, such as empirical methods.

3 Rockburst prediction methods based on static indicators

In the case of the rockburst mechanism has not been studied clearly (Liu et al. 2022), scholars have established a large number of static indicators based on engineering experience and rockburst influence factors. It is also known as the empirical method of rockburst prediction, which is widely used in practical engineering. At present, the empirical methods are mainly divided into empirical methods with single indicators and empirical methods with multi-index indicators (Wu et al. 2019).

3.1 Empirical methods with a single indicator

For the prediction problem of rockburst susceptibility, a large number of single evaluation indicators have been established from the perspective of a series of theories such as strength, energy, deformation, and stiffness. Among them, the majority of judgment indicators are in terms of stress and energy (Liu et al. 2013; Zhou et al. 2018a; He et al. 2021). This section summarises the empirical methods developed based on static indicators from the energy and stress perspectives.

3.1.1 Stress methods

The stress method has a variety of physical metrics that characterize the rock features. These include key factors such as the geometrical and mechanical parameters of the intact rock, the pathological stresses, and the magnitude of the induced stresses. Evaluation indicators based on these factors have been validated for rockburst prediction (Gong and Li 2007). Table 1 summarises the empirical methods based on strength theory that have emerged in recent years, along with their associated judgments and rockburst classification. However, there is no generalized rockburst criterion that can fully encompass all practical engineering conditions. Previously, a large number of criterion guidelines have been proposed based on the \({\sigma }_{1}/{\sigma }_{c}\), \({\upsigma }_{\uptheta ,\mathrm{ max}}/{\upsigma }_{{\text{c}}}\) and \(\left({\sigma }_{\uptheta }+{\sigma }_{{\text{L}}}\right)/{\sigma }_{c}\) indices, such as Barton's criterion, Tao's criterion, Hoek and Brown's criterion, Russenes' criterion and Turchaninov's criterion, etc. However, the application of rockburst discrimination criteria based on a certain index was found to be unsatisfactory, and it resulted in large prediction deviations, despite the advancement of engineering technology. For instance, Zhou et al. (2018b) tried to adopt these guidelines to discriminate the rockburst class of the Gaoligongshan tunnel. It was found that the various guidelines were independent of each other and applied to different engineering conditions. To establish the connectivity between indices \({\sigma }_{1}/{\sigma }_{c}\), \({\upsigma }_{\uptheta ,\mathrm{ max}}/{\upsigma }_{{\text{c}}}\) and \(\left({\sigma }_{\uptheta }+{\sigma }_{{\text{L}}}\right)/{\sigma }_{c}\), Zhou et al. proposed a rockburst discrimination criterion based on these three indices, as shown in Table 1. However, there is still a lack of research on combining multiple discriminant indices for rockburst intensity classification.

Table 1 Summary of rockburst criteria based on strength theory and assessment of qualitative indicators for rockburst grading
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By analyzing Table 1, it was found that the evaluation indexes established based on the maximum tangential stress of surrounding rock \({\sigma }_{\theta }\), uniaxial compressive strength \({\sigma }_{c}\), uniaxial tensile strength \({\sigma }_{t}\) and Stress coefficient \({\sigma }_{\theta }/{\sigma }_{c}\) are the majority. It indicates that the mechanical properties of the rock have a great influence on the occurrence of rockbursts. However, it should be noted that the stress method established based on strength theory ignores the dynamic characteristics of rockburst. It is easy to confuse general brittle damage with rockburst (He et al. 2023).

The occurrence of rockbursts is related to the mechanical properties of the surrounding rock and the stress transfer path (Liu et al. 2021c). Therefore, the empirical method that only considers the mechanical properties is not comprehensive. Some scientists consider the role of the stress gradient in the surrounding rock based on the stress–strength ratios criterion. They are establishing a new criterion based on stress–strength ratios and surrounding rock stress gradient, namely the SR-SG criterion (Liu et al. 2023c). The advantage of the SR-SG criterion is to improve the accuracy of prediction while overcoming the problem of inhomogeneity in the grading interval of traditional criterion indicators. Table 2 gives the application of the SR-SG criterion in rockburst intensity grading.

Table 2 Rockburst grading criteria based on the SR-SG criterion (Liu et al. 2023c)
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3.1.2 Energy methods

The rock mass generates strain energy in a plateau state of locational stress or a low-stress state of external disturbance. Accumulation of strain energy is generally recognized as the main energy source of rockburst, and the strain energy stored in the rock largely determines the intensity level of the rockburst (Li et al. 2007; He et al. 2023).

Figure 4 shows the general process of energy evolution inside the rock mass under external perturbation. Various external perturbation loads act on the rock body, resulting in the generation of corresponding stresses inside the rock body to resist the external action. According to the law of conservation of energy, mechanical energy is input into the rock body's interior and stored. When the energy stored inside the rock reaches the threshold of rockburst, the energy is actively released to the outside world. Once the crack is created afterward, some of the energy is converted into kinetic energy of the fragments, causing the rocks around the crack to be violently ejected and the rockburst occurs (Liu et al. 2013; Li et al. 2023b). Scholars have established a large number of rockburst evaluation indexes based on the energy evolution process. One of the most widely used indexes is the Wet index, which evaluates rock hardness, brittleness, and susceptibility to bursting.

Fig. 4
figure 4

General process of typical energy evolution

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Table 3 presents the empirical methods based on energy theory that have emerged in recent years, along with their associated discriminant and rockburst classifications. The rockburst phenomenon occurs when the external force acting on the rock reaches the limit of what the rock body can withstand. This phenomenon is observed both in the engineering field and in indoor tests. Therefore, studying the proportionality between the elastic strain energy density and the dissipated strain energy density at the peak intensity of a rock specimen may facilitate the assessment of rockbursts. Gong et al. (2019) proposed the \({W}_{ET}^{P}\) index for rockburst intensity classification in this context, as shown in Table 3. The advantage of using the \({W}_{ET}^{P}\) index is that it no longer calculates the strain energy density at the point of 80–90% of the peak intensity, making the index more suitable for actual use. Additionally, several scholars have proposed or improved the theoretical discriminant for the Wet index (Zhang et al. 2011; Wang et al. 2021d). Further in-depth research is needed to improve the accuracy of the rock burst criterion based on the energy theory.

Table 3 Summary of rock burst criteria based on energy theory and assessment of qualitative indicators for rockburst grading
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The establishment of different energy methods is mainly based on the energy density and energy release rate at different stages of the rock fracture process. On the one hand, it confirms that energy evolution is an important factor in determining the magnitude of the rockburst intensity. On the other hand, it reflects that the energy methods consider the dynamic behavior of the energy evolution, such as the local energy release rate, while considering the static quantitative indicators. Gong et al. (2020) further verified that the energy methods have better predictive performance by comparing 20 tendency evaluation indices such as the strain energy storage index, the energy impact index, the potential energy of elastic strain, the rockburst energy index, the deformation brittleness index, the brittleness index of rockburst proneness, the deformation modulus and the lag time ratio index, etc. However, the difficulty in determining and measuring the stress and strain fields has led to limitations in the use of energy methods in practice.

3.2 Empirical methods with multi-index indicators

Figure 5 summarises some of the factors that influence the occurrence of rockbursts. Some scholars have discussed the influence of size effect, rock material (rock type, rock properties, and structural planes), mechanical conditions (stress state, loading/unloading rate, and dynamic perturbations), and environmental conditions (moisture content and temperature) on rockburst by considering some of the influencing factors. It is shown that rockbursts are the result of a combination of factors (He et al. 2023). Therefore, the single indicator evaluation method developed by considering only factors such as rock mechanical properties or rock energy evolution has limitations. It is easy to apply different evaluation indicators to the same rock samples when the results of the dispersion of the situation.

Fig. 5
figure 5

Factors affecting rockburst (Modified according to Kaiser and Cai (2012) and Keneti and Sainsbury (2018))

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The advantage of the comprehensive evaluation index is that multiple factors affecting rockburst are used as control factors for rockburst prediction. Breakthrough the single indicator evaluation method only considers the limitations of a single factor. Thus, the prediction accuracy and reliability of the empirical index method have been further improved.

Some scholars have carried out research by combining the mechanical properties of rocks and the evolution process of strain energy. The elastic modulus damage index (EMDI) based on peak stress dissipation energy Ud, peak stress total strain energy U, elastic modulus E, and peak strength \({\sigma }_{p}\) is established by considering both strength theory and energy theory (Khan et al. 2022). EMDI is defined as in Eq. (1). When the EMDI value is less than 0.91 for no rockburst, greater than 1.93 for strong rockburst, between the middle range for weak rockburst. From the properties of the indicator, this approach has the distinctive feature of energy-feeding stress. The rockburst prediction is improved by combining the advantages of the energy methods with the disadvantages of the stress methods.

$${\text{EMDI}} = \left( {\lambda /E} \right) \cdot \left( {{\text{U}}_{{\text{d}}}/{\text{U}}} \right) \cdot \left( {\sigma_{r} /\sigma_{p} } \right)$$
(1)

At present, the methods that are used more in the comprehensive evaluation method for the assignment of each indicator include the fuzzy comprehensive evaluation method (FCE), principal component analysis (PCA), analytic hierarchy process (AHP), and quantitative evaluation method (QEM).etc. (Du et al. 2021). The advantage of these methods is that the weights of the indicators can be assigned scientifically. This makes the prediction results more accurate and reliable than single indicator evaluation methods. Zhang et al. (2020c) scientifically assigned weights to five indexes, namely uniaxial compressive strength \({\sigma }_{c}\), stress coefficient \({\sigma }_{\theta }/{\sigma }_{c}\), brittleness coefficient of rock Bi, elasticity energy index \({{\text{W}}}_{{\text{et}}}\) and rock mass integrity coefficient Kv, by adopting a comprehensive weight evaluation method combining AHP and variation coefficient methods, which comprehensively considered the factors of pathological stresses, lithological properties and energy conditions. A comprehensive index evaluation method based on the five indexes was established. Zhu et al. (2022) used a combination of AHP and FCE methods, considering the geodynamic environment, and geological and mining factors. A comprehensive evaluation index system was established based on 15 influencing factors, such as the dip angle of the tectonic depression, the ratio of the tectonic stress to the vertical stress, the vertical movement velocity of fault blocks, the influence zone of fault structure, the mining depth, the thickness variation coefficient of the coal seam, the uniaxial compressive strength and the collapse degree of overlying strata, and so on. The weights of the factors are scientifically determined, and the prediction results are more in line with the actual situation.

Once the tunnel is excavated, the rockburst evolution process manifests itself as a gradual release of radial stress and a gradual increase in tangential stress, forming a tangential stress concentration and inducing rock fragment ejection (Pan et al. 2020). On this basis, Hoek and Brown (1980) proposed a criterion for the stress-intensity ratio. However, a large number of evaluation indexes do not take into account the radial radius of the tunnel and the radius of the plastic zone. Later, a new comprehensive evaluation index ζ based on the stress-strength ratio criterion was proposed by Yang et al. (2022), which takes into account the radial stress \({\sigma }_{r}^{p}\), tangential stress \({\sigma }_{\theta }\), tunnel radius r0, plastic zone radius rp, and uniaxial compressive strength \({\sigma }_{c}\).

In recent years, some scholars have incorporated geological conditions and site construction status into the comprehensive evaluation system. A multi-indicator evaluation method based on in-situ stress, rock brittleness, elastic deformation energy, maximum storage elastic strain energy, rock integrity, groundwater condition, section design size, and site construction status was established by considering five aspects: rock mechanical properties, strain energy evolution, geological conditions, tunnel design parameters, and site construction conditions. Verified by engineering examples, the predicted results are in general agreement with the actual occurrence of rockburst (Qu et al. 2022).

With the continuous deepening of the theoretical study of rock burst prediction, from a single stress method or energy method to the comprehensive consideration of mechanical properties and strain energy evolution of the comprehensive method, and then to the establishment of the mechanical properties of the rock, the evolution of strain energy, geological conditions, tunnel design parameters and construction conditions of the site of the integrated evaluation system, the comprehensive indicators of the evaluation method has been gradually improved. Its prediction performance is gradually improved. It should be noted that although the weighting problem of each indicator is considered, the problem of nonlinear relationships between multiple indicators is not effectively solved. To a certain extent, this limits the predictive performance of the comprehensive indicator evaluation method. In addition, the evaluation indicators should be selected according to specific problems and data characteristics, while weighing them against the requirements of practical applications.

4 Rockburst prediction methods based on dynamic indicators

In recent years, the focus of research has shifted from static indicators to dynamic indicators. The reason for this is that static indicators have to be obtained manually from indoor tests or field measurements. The process is relatively complicated and lacks continuity and timeliness. Dynamic indicators are obtained in real-time by the monitoring system and monitoring equipment, which has the advantages of data integrity, continuity, and timeliness (Du et al. 2021). microseismic monitoring (MS) and acoustic emission (AE) are the main in-situ monitoring methods for the common rockburst problems in tunneling (Moganedi and Stacey 2019; Cheng et al. 2020).

4.1 Microseismic monitoring method

The MS monitoring technique has the advantages of low cost, wide monitoring range, high immunity to interference, no impact on on-site construction, and can relatively accurately determine the location and timing of rock microfracture events (Ma et al. 2016; Tian et al. 2022; Yang et al. 2023). Figure 6 shows a diagram of the microseismic monitoring system. The MS monitoring technology has gradually become one of the most effective tools in the field of rockburst monitoring since it was first introduced in China in 1959 for impact trend monitoring at the Mentougou coal mine (Li et al. 2007; Tang et al. 2015; Ma et al. 2016).

Fig. 6
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Topology of the microseismic monitoring system. (Zhang et al. 2021)

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Tunneling causes disturbances in the surrounding rock mass (manifested as microseismic events, also known as rock fracture events). This causes a redistribution of stresses within the rock mass. The altered stress paths cause localized microcracking and damage to the rock close to the working face. This causes some of the internal energy to be released outwards in the form of elastic waves (Zhang et al. 2018, 2020d). The frequency characteristics of various waves are shown in Fig. 7. MS system sensors receive a large number of signals simultaneously. These include MS signals (e.g., p-wave and s-wave) and noise signals such as electric current, knocking, rock drill, and locomotive whistle. Monitoring data is voluminous and complex, requiring effective processing and interpretation by professionals. The results are heavily influenced by environmental noise and interference. The MS signals are retained by the denoising process. Then, they are converted into electrical signals and uploaded to the analysis and warning center step by step. The analysis and warning center further analyze the source parameters and spatial distribution pattern of MS events to obtain rockburst precursor information. Finally, it is sent to the terminal to realize the effective prediction of rockburst (Mousavi and Langston 2016; Iqbal et al. 2018).

Fig. 7
figure 7

Frequency characteristics of various waves (modified according to Su et al. 2017)

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By analyzing the received elastic waves, a large number of microseismic source parameters (dynamic indicators) can be obtained, such as apparent stress (\({\sigma }_{A}\)), apparent volume (\({V}_{A}\)), p-wave arrival time, seismic energy density, microseismic event density, energy index (EI), 3S (stress accumulation, stress shadow and stress transfer) index, b value (b), and number of energetic tensile damage events (Cai et al. 2014; Dou et al. 2018; Ma et al. 2020; Yu et al. 2022). etc. Apparent stress, apparent volume, energy index, and microseismic energy (E) are commonly used dynamic warning indicators. Among them, the apparent volume reflects the size of cracks in the rock mass. The energy index reflects the pressure level of the rock mass. Microseismic energy reflects the intensity of microseismic events. The use of these indicators can effectively explain the state of cracks in the rock mass for real-time early warning of a rockburst. Xue et al. (2020a) proposed that lgN/b can be used as a new indicator for rockburst warning based on the number of microseismic events and b value. The larger the value of lgN/b, the more serious the rockburst. Zhang et al. (2021) quantitatively analyzed the average release energy, apparent volume, b value, and s value to propose a new index the energy rockburst warning (ERW) index. Table 4 summarizes the early warning situation for selected indicators.

Table 4 Real-time dynamic early warning discriminations for selected microseismic indicators
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As mentioned above, each dynamic indicator has its theoretical formula. The differences between the indicators show that the development state of rock fracture can be interpreted from different aspects. Therefore, the comprehensive use of more source parameters to avoid the one-sidedness and limitation of a few indicators is an effective way to improve the accuracy of real-time warning (Feng et al. 2015; Wang et al. 2021e).

Analyzing the cloud map of microseismic spatiotemporal distribution characteristics is another way to obtain information on rockburst precursors. Figure 8 shows the cloud map of spatio-temporal distribution characteristics of microseismic events in a section of the Qinling tunnel. From June 20 to 29, 2018, microseismic event density gradually increased. A red risk signal appeared on the 26th, with a high risk of rockburst. As of the 29th, the rockburst risk reached 90%, revealing that a rockburst is imminent (Ma et al. 2022b). Khan et al. (2023) proposed four microseismic precursor characterization indices, namely cumulative frequency, cumulative energy, energy deviation, and frequency deviation, from the time dimension. The spatial distribution of each microseismic precursor warning index is obtained from spatially distributed cloud density maps. A temporally and spatially integrated warning method is established based on the time and spatial dimensions to predict the probability of rockburst occurrence in a short period.

Fig. 8
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Spatial and temporal distribution of microseismic events. a Density cloud map of microseismic events. b Map of microseismic events (Ma et al. 2022b)

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It should be noted that MS signals in field monitoring are mostly analyzed and processed based on individual subjective experience. To a certain extent, this can cause the deviation of rockburst precursor characteristics in time and space. Therefore, by further combining microseismic and artificial intelligence technologies to establish a more objective MS signal processing system, the predictive performance of rockburst precursor characteristics in time and space can be effectively improved.

4.2 Acoustic emission monitoring methods

AE is the phenomenon of transient elastic wave emission resulting from the rapid release of energy within a material. It allows monitoring of the surrounding rock before internal cracks propagate to the surface of the material (Zhang et al. 2015). Accurately localizing microcracks and stress changes within rock formations is crucial for assessing rock stability and fracture conditions. However, interpreting monitoring data requires experienced professionals and the accuracy and reliability of the results are affected by the operator's level of expertise. Figure 9 shows the topology of the AE system. According to the acoustic emission theory, the AE technique has a similar working principle to the MS technique. The difference is that the sensor receives acoustic signals rather than vibration signals generated by microcracks in the rock (Zhang et al. 2014). Since the AE technique was first applied to the study of rock damage in 1962 (Kiyoo 1962), the technique has achieved a large number of research results in fields such as coal mining and rock bursting. It has been widely used in geotechnical monitoring (Browning et al. 2017; Xiao et al. 2019; Tan et al. 2022).

Fig. 9
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AE monitoring system topology

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In the paper on AE field monitoring methods, acoustic emission parameters, and waveform characterization are the main analysis methods. All AE signals can be covered by these two analysis methods, and AE dynamic indicators can be obtained (Li et al. 2017a). The AE parameter metrics include AE hit count, AE energy, ringer count, energy count, decay count, rise time, peak amplitude, b value, and number of acoustic emission rings (Ban et al. 2020; Ding et al. 2022; Dong et al. 2022). Among them, the AE hit count reflects the density and intensity of AE activities inside the rock mass, and the AE energy can accurately capture the fine fracture behavior inside the rock mass. The ring count reflects the crack width. b value changes reflect the trend of cracks inside the rock mass. The AE ring count can reflect the damage to the rock mass to a certain extent. Based on the above parameters, the stability of the rock during loading can be further investigated to analyze the precursor characteristics of rock explosion.

Hu et al. (2018) explored the rockburst process in the borehole by analyzing the AE hit count and AE energy. As shown in Fig. 10. Before the rockburst occurs, there is a quiet period in the AE hit count curve. This period has the remarkable characteristics of a sharp decrease in the AE hit count and a sharp increase in the AE energy. Therefore, the quiet period can be used as a precursor signal for the occurrence of a rockburst. Zhai et al. (2020) performed true triaxial compression experiments on granitic syenite to further validate the reasonableness of the quiet period as a warning signal for rockburst.

Fig. 10
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Time series characterization of AE hit counts and AE energy. a Complete process. b The process of debris spalling to the occurrence of rockburst (Modified according to Hu et al. 2018)

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Wang et al. (2022) performed true triaxial compression tests on granite. Comparative analysis of AE impact counts, ringing counts, and AE energies revealed that the accelerated release characteristics of AE energies better reflect the precursor information of rockburst.

Ren et al. (2023) used marble rock samples to simulate static-driven rockburst, pulse-disturbance rockburst, and period-disturbance rockburst. On the one hand, it is proposed that the trend of multiple fractal parameter curves increasing and then decreasing near the peak intensity can be used for rockburst warning for long-term monitoring. The inflection point is used to calculate the warning time, and the higher the rockburst intensity, the shorter the warning time. On the other hand, it is verified that the stress drop can be used for short-term monitoring of rockburst warning.

The significant decrease in b value can be used as a precursor feature of rockburst, and the softening effect of water can significantly reduce the incidence of rockburst (Zhang et al. 2020e; Dong et al. 2022).

The above analysis of rockburst precursor characteristics from the perspective of AE parameters belongs to the time domain parameter analysis. Differently, the frequency domain waveform analysis explains the dynamic damage characteristics of microcracks inside the rock mass by mapping the AE waveform signal from the time domain to the frequency domain.

Mei et al. (2019) conducted uniaxial compression experiments on marble rock samples. The AE dominant frequency characteristics were analyzed for the entire rockburst process (dominant frequency is the frequency of the maximum amplitude in the two-dimensional spectrum, which is usually obtained by the fast Fourier transform (FFT)). As shown in Fig. 11, the two red dashed lines indicate the beginning and the end of the rockburst. The results show that the migration of the dominant frequency density region from the low-frequency domain to the relatively high-frequency domain, as well as the density of the dominant frequency distribution in the high-frequency domain before and after the rockburst can be used as a rockburst precursor characteristic signal.

Fig. 11
figure 11

Scattering density plot of AE full-time domain main frequency characteristics. a N5 sample. b N7 sample. (Modified according to Mei et al. 2019)

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Information entropy can effectively characterize information about the source of rupture within a rock mass. It is useful for research on rockburst prediction(Zhou and Li 2012). Figure 12 shows the main frequency entropy distribution of granite rock samples. The results show that the peak point A point before the sharp decrease of entropy can be used as a characteristic point for rockburst prediction.

Fig. 12
figure 12

Distribution of dominant frequency entropy of granite rock samples (Wang et al. 2021b)

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As mentioned above, AE hit counts, AE energy, AE ringing counts, and primary frequency are the main dynamic indicators for conducting rockburst early warning. It should be noted that the differences in the degree of internal fracture of the rock are reflected by different indicators, resulting in inconsistency in the information proposed based on different indicators of rockburst precursors. It is prone to prediction misjudgment and prediction delay phenomenon. Therefore, the further establishment of a multi-indicator synergistic prediction method can significantly improve the accuracy of rockburst prediction. In addition, due to the limitations of AE sensors and the influence of the test environment at the current stage, the AE dynamic parameters cannot reflect the essential characteristics of rock damage (Chai et al. 2018). The waveform signal contains all the information on mechanical properties and structural state inside the rock mass, which can better reflect the evolution of microcracks. Therefore, the rockburst precursor signal based on frequency domain waveform analysis is more reliable (Zhou et al. 2019; Zhu and Deng 2023).

Combined consideration of time domain parameters and waveform characteristics. To a certain extent, the combination of AE parameter signals and AE waveform signals to jointly implement rockburst precursor warning can avoid the errors caused by using one type of signal alone. Gao et al. (2023) verified that AE energy, AE ringing counts, and AE main frequency can be used as rockburst precursor signals. At the same time, they were defined as the key disaster-causing factors of rockbursts, to establish a comprehensive early warning method for brittle rockbursts. The initial warning point and key warning point of rock explosion were further obtained. As shown in Fig. 13.

Fig. 13
figure 13

Integrated rock burst warning method based on key causative factors of acoustic emission signals. a rock sample 1. b rock sample 2 (Gao et al. 2023)

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5 Machine learning methods

Machine learning methods have the characteristic of discovering the change rule from a large amount of data and extracting the corresponding features (Marsland 2015). It can effectively extract the features related to the occurrence of rockburst from static and dynamic index data. For example, geological structure, stratum lithology, stress state, seismic activity, surface deformation, and so on. In addition, machine learning methods can make predictions based on real-time monitoring data. It can respond to rock changes and stress accumulation on time. It has a wide application potential in real-time rockburst prediction and monitoring systems. With the rapid development of big data science, the use of machine learning methods for rockburst prediction is gradually becoming a popular way (Pu et al. 2019b).

In recent years, numerous machine learning methods have been developed that use static and dynamic indicators as data inputs. Table 5 summarizes the use of static indicators as input data for machine learning methods in rockburst intensity classification in recent years. The table shows that \({\sigma }_{\theta }\), \({\sigma }_{c}\), \({\sigma }_{t}\), and Wet are the earliest major static indicators used for machine learning in rockburst prediction, with prediction accuracies above 90%. The text suggests that the tangential stress, uniaxial compressive strength of rock, tensile strength of rock mass, and strain elasticity energy index Wet are advantageous in predicting rockburst and are highly applicable to certain algorithms. The field of rockburst prediction has seen the introduction of various new algorithmic models with the development of computer engineering. It was determined that using only \({\sigma }_{\theta }\), \({\sigma }_{c}\), \({\sigma }_{t}\), and Wet as input data did not yield satisfactory results for predicting rockburst. Therefore, scholars added the brittleness index \({\sigma }_{c}/{\sigma }_{t}\) and stress concentration factor \({\sigma }_{\theta }/{\sigma }_{c}\) to the existing \({\sigma }_{\theta }\), \({\sigma }_{c}\), \({\sigma }_{t}\), and Wet index to improve the prediction accuracy.

Table 5 Machine learning methods using static indicators as input data
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The machine learning methods use maximum tangential stress \({\sigma }_{\theta }\), compressive strength \({\sigma }_{c}\), tensile strength \({\sigma }_{t}\), brittleness index \(\frac{{\sigma }_{c}}{{\sigma }_{t}}\mathrm{Stress coefficient}{ \sigma }_{\theta }/{\sigma }_{c}\) and elastic energy index Wet as common static inputs. \({\sigma }_{\theta }\) reflects the characteristics of the ground stress. Rocks are dense inhomogeneous bodies, and their lithological characteristics are reflected by \({\sigma }_{c}\mathrm{ and}{ \sigma }_{t}\). Accumulation of strain energy is generally recognized as the main energy source of rockburst, Wet can reflect the ability of the rock to store strain energy. \({\sigma }_{c}/{\sigma }_{t}\) and \({\sigma }_{\theta }/{\sigma }_{c}\) also have a close relationship with the intensity level of rockburst (Li et al. 2023a). Therefore, these indicators are more representative in explaining rockburst than other static indicators such as tunnel burial depth H and stress concentration factor SCF. Li and Jimenez (2017) and Li et al. (2022b) analyzed and found that Wet is always the most important indicator for rockburst prediction. As shown in Fig. 14.

Fig. 14
figure 14

Importance analysis of static indicators (Li et al. 2022b)

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Table 6 summarizes the use of dynamic metrics as input data for machine learning methods for rockburst intensity classification in recent years. The table shows that the machine learning method based on dynamic parameters can carry out rockburst warning, signal identification, crack identification, microseismic source localization, and p-wave first arrival time pickup. The dynamic parameter-based machine learning method offers greater degrees of freedom, as reflected to a certain extent. Currently, machine learning methods primarily utilize microseismic energy, seismic moment, cumulative number of events, cumulative apparent volume, and apparent stress as the main dynamic input indicators. Microseismic energy reflects the intensity of microseismic events to some extent. Seismic moment reflects the magnitude of the earthquake. Cumulative event count indicates the number and density of microfractures occurring within the rock mass. Cumulative apparent volume reflects the size of the cracks in the rock mass. Apparent stress indicates the degree of stress release (Liu et al. 2021b; Yin et al. 2021b).

Table 6 Machine learning methods using dynamic indicators as input data
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The establishment of the indicator database is mainly based on the static and dynamic indicators obtained from global rockburst cases, rock indoor tests, numerical simulations, or field monitoring. At present, scholars have carried out the following studies to address the problems of the original database (Zhang et al. 2020b; Yin et al. 2021c; Zhou et al. 2021):

  1. (1)

    The number of rockburst cases in each class is disproportionate, causing the model to focus too much on the larger number of classes.


    There are two main approaches to solving such problems. One is to oversampling, undersampling, or mixedsampling the data. The other is to replace algorithmic models that are insensitive to unbalanced data sets (Gnip et al. 2021). Xue et al. (2022) The Copula-MC oversampling algorithm is proposed based on Copula theory and Monte Carlo simulation. Through the validation of six machine learning models, the Copula-MC oversampling algorithm performs better than the synthetic minority oversampling algorithm (SMOTE) in dealing with unbalanced datasets, and the accuracies of each model are shown in Fig. 15. The Copula-MC oversampling algorithm significantly reduces the impact of unbalanced datasets on machine learning.

    Fig. 15
    figure 15

    Radar plot of different model predictions (Xue et al. 2022)

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    Li et al. (2022b) used the SMOTETomek algorithm to process the unbalanced dataset. Meanwhile, the BO-SMOTETomet-FNN model was established by combining bayes optimization (BO) and feedforward neural network (FNN). After engineering validation, the rockburst prediction accuracy reached 90.4%.

  2. (2)

    The model ignores other valuable information in the prediction process and overly relies on certain metrics. This leads to a decrease in the model's ability to predict new data.


    The t-distributed Stochastic Neighborhood Embedding (t-SNE) (Van der Maaten and Hinton 2008) is a dimensionality reduction technique that effectively reduces the dependency between the parameters of each indicator. Pu et al. (2019b) combined the t-SNE technique and k-mean clustering with a support vector classifier (SVC). An SVC model based on the t-SNE technique and k-mean clustering was developed. And tenfold cross-validation was used to optimize the accuracy of this model to avoid overfitting. The results show that the model predicts well while reducing the indicator dependency. Feng et al. (2019) used a mean influence value algorithm (MIVA) to reduce indicator dependence and established a probabilistic neural network model for rockburst early warning.

  3. (3)

    Data Outliers. Data outliers are currently handled in three ways, namely removal, replacement, and transformation.


    The Yeo-Johnson transform (He and Zheng 2018) preserves anomalous data. Reduces the impact of anomalous data on the overall prediction results and avoids the destruction of the original characteristics of the data when removing and replacing outliers. Sun et al. (2022) first used Yeo-Johnson transform to solve the outlier problem. Then k-mean SMOTE algorithm is used for oversampling to solve the unbalanced dataset problem, and PCA dimensionality reduction is used to reduce the indicator dependency problem.

  1. (4)

    Incomplete dataset due to missing data.


    Liu et al. (2023a) proposed a histogram gradient boosting tree (HGBT) model for incomplete datasets. The model separates the samples from the missing values based on the potential gain at the point after finding the segmentation point, thus processing the missing values. By comparing seven models such as random forest (RF), K-nearest neighbors (KNN), extreme gradient boosting (XGBoost), support vector machines (SVM), and artificial neural network (ANN), the results show that the HGBT model has 77.78% prediction accuracy. The prediction performance is better compared to other models as shown in Fig. 16.

    Fig. 16
    figure 16

    Comparison of incomplete database models. Missing data is populated by the following values: a 0; b Average value; c Median value; d Common value (Liu et al. 2023a)

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  2. (5)

    The issue of weighting of indicators.


    Li et al. (2023c) used Tent chaotic mapping and the crossover and mutation operators in the genetic algorithm (GA) to improve the Harris Hawk (HHO) algorithm to obtain the IHHO algorithm, which is capable of assigning weights to indicators more objectively. By comparing with optimization algorithms such as GA and HHO, the IHHO algorithm has higher search efficiency and faster convergence accuracy. The extreme learning machine (ELM) model built based on the IHHO algorithm has better prediction performance.

Machine learning methods require a large amount of data to participate in training and testing, but the data sets used in machine learning are generally small at present, which reduces the robustness of the algorithmic model to a certain extent. Decision tree (DT) and naïve bayes (NB) models have better applicability to small samples, but the generalization performance is poor and cannot fundamentally eliminate the limitations of small samples (Li et al. 2017b; Ghasemi et al. 2019). In the future, there is a need to build a larger number of databases with higher quality and from a wider range of sources.

Machine learning methods show significant advantages in integrating multiple metrics and data processing, but they are susceptible to model limitations. For example, SVM algorithms are sensitive to sample perturbations, and the presence of high variance and low bias makes the prediction results lack generalization and robustness. For small samples, logistic regression (LR) is more prone to transition fitting. Ensemble learning methods can significantly improve the accuracy, stability, and robustness of prediction by integrating multiple algorithmic models. To a certain extent, it can make up for the shortcomings of single machine learning methods (Sagi and Rokach 2018; Zhang et al. 2020a). For example, Zhang et al. (2020b) used static indicators as input data and combined seven classifiers such as back propagation neural network (BPNN), support vector machine, decision tree, k-nearest neighbors, logistic regression, multiple linear regression (MLR) and naïve bayes to build an integrated BPNN-SVM-DT-KNN-LR-MLR-NB model. Liang et al. (2021) developed an integrated LR-NB-GP-MLPNN-SVM-DT model that combines six basic classifiers, namely logistic regression, naïve bayes, Gaussian process (GP), multilayer perceptron neural network (MLPNN), support vector machine and decision tree, using dynamic indicators as input data. The results all show that the prediction performance of the integrated classifier is better than the six basic classifiers.

Deep learning methods are mainly based on the concept of artificial neural networks, which simulate the workings of the human brain through a multilevel network of neurons (Strawn 2022). Deep learning models can make full use of the information and patterns in the data by training and learning from large-scale data, thus improving the accuracy and generalization of predictions. Commonly used deep learning models include multilayer perceptron (MLP), deep forests (DF), convolutional neural networks ( CNN), temporal convolutional networks (TCN), recurrent neural networks (RNN), and long-short-term memory networks (LSTM). CNN can effectively deal with the temporal and spatial dependencies in the dataset. Therefore, it is widely used in microseismic monitoring. Yu et al. (2019) used microseismic raw waveform data as CNN input data to realize adaptive denoising. Song et al. (2020) used a CNN model to extract microseismic signals from blasting vibration signals to improve microseismic source localization accuracy. Peng et al. (2021) added Inception structures to the CNN model to form a deep CNN-Inception model for recognizing effective microseismic signals.

Attention is drawn to the fact that TCN models can handle the entire time series simultaneously, thus saving computational time. In addition, the TCN model can effectively deal with the long-term dependence among indicators by capturing the time dependence of different ranges. Therefore, the application of TCN models in the field of rockburst prediction should be enhanced in the future.

6 Limitations and prospects

Empirical methods, microseismic monitoring, acoustic emission, and machine learning are four widely used methods for rockburst prediction. However, due to the complexity of the rockburst mechanism and the uncontrollability of the influencing factors, some aspects of them have some shortcomings and need to be improved in the future.

The empirical methods are a typical traditional rockburst prediction method. Its prediction process relies heavily on the criterion formula established by static indicators, which leads to at least two limitations of the empirical methods. For static parameters, a large number of single-indicator criteria consider only two or three factors, while the occurrence of rockburst is the result of a combination of factors, involving the mechanical properties of the rock mass, geological structure, digging methods, groundwater conditions, tunnel size and depth, etc. It is still unclear which factors are the most important. Thus the criterion formulae established by considering only a small number of factors have serious prediction errors. Even with the comprehensive indicator evaluation method considering multiple factors, the nonlinear relationship between the factors is difficult to determine. In the future, we should further study which factors play a dominant role in the process of rockburst occurrence, and at the same time consider more factors in the establishment of rockburst criterion. What is the relationship between rock tectonic properties, such as rock mineral composition, original pore state and texture orientation, and rockburst still needs to be further explored. In terms of criteria, each criterion formula has its rockburst grading standards. Therefore, the use of different criteria for the prediction of the same rockburst is prone to different rockburst grades, and a large number of criteria are uneven grading interval, resulting in rockburst intensity level imbalance. To a certain extent, this has increased the difficulty of accurate prediction of rockburst. In the future, the establishment of indicators should focus on how to build a uniform grading interval. The establishment of a unified and common rockburst criterion is still a long way to go.

Microseismic monitoring and acoustic emission are the two main field monitoring methods. A large number of waveform signals are often released before and after a rockburst. Whether the waveform signals received by the sensors are generated by the corresponding rupture event, or whether the sensors can segment the signals after receiving them overlapped together. Taking acoustic emission as an example, the overlapping of elastic wave signals leads to a decrease in the AE hit rate, but the cumulative AE counts and energy are increasing exponentially. This anomaly reduces the accuracy of AE monitoring to some extent. Therefore the problem of elastic wave signal overlap needs further study by scholars. A large number of dynamic indicators can be obtained by analyzing the elastic wave signals, such as p-wave arrival time, microseismic energy density, energy index, 3S index, b value, energy counts, decay counts, rise time, and peak amplitude. How to quantify the sensitivity of these indicators to rockburst warning needs further study. Source parameter warning and spatial–temporal distribution warning in microseismic monitoring, as well as time-domain parameter warning and frequency-domain feature warning in acoustic emission are the main methods of rockburst warning. Regardless of the warning method, the warning time obtained through rockburst precursor characteristics is not always reliable. This is related to the strong randomness of the rockburst, while specific rockburst intensity levels cannot be obtained. This makes it difficult to effectively implement graduated prevention and control at a later stage. The current field application is usually based on the energy release characteristics to estimate the rockburst intensity level, which increases the bias caused by individual subjectivity. In the future, we should pay attention to the issue of rockburst warning time, and at the same time consider combining it with related intelligent devices to further study how to determine the rockburst intensity level more objectively through the trend of dynamic parameters such as energy release characteristics. In short, the development of a rockburst disaster whole process recording equipment to assist the site monitoring will greatly improve construction efficiency and safety.

Both microseismic monitoring and acoustic emission monitoring by receiving elastic wave signals. However, the difference is that microseismic monitoring is non-contact monitoring by monitoring and analyzing the seismic waves released by microseismic events to understand the state of underground rocks or geological structures. Acoustic emission is to understand the deformation, rupture or stress release of rocks or structures by monitoring and analyzing the tiny acoustic waves generated inside them, which belongs to contact monitoring. This determines that microseismic monitoring has a wider range and can monitor the location and energy of rockbursts in real time. On the contrary, in acoustic emission monitoring, although the positioning accuracy is higher, the monitoring range is much smaller, resulting in less satisfactory results when applied individually to practical engineering. Based on the characteristics of microseismic monitoring and acoustic emission monitoring, early warning relying only on certain indicators or a certain method of each is not comprehensive. Therefore, in the future, the joint early warning technology of multi-methods and multi-indicators should be further established and enriched. In addition, due to the large number of dynamic indicators and strong correlation, which combinations of indicators can be more effective for rockburst early warning needs to be further studied.

Machine learning methods have shown good predictive ability in comprehensive multi-indicator prediction, and they can effectively deal with the problem of non-linear relationships between multiple indicators. Therefore, it has been widely used in recent years. In terms of input data, the static input indicators of the machine learning methods focus on maximum tangential stress \({\sigma }_{\theta }\), compressive strength \({\sigma }_{c}\), tensile strength \({\sigma }_{t}\), brittleness index \({\sigma }_{c}/{\sigma }_{t} ,\, \mathrm{Stress coefficient}{ \sigma }_{\theta }/{\sigma }_{c}\) and elastic energy index Wet, Dynamic input indicators focus on Microseismic energy, seismic moment, cumulative event count, cumulative apparent volume and apparent stress. Although the above indicators are representative, they cannot cover the effects of tunnel depth and stress drop on rockburst. In general, the more input indicators, the better the model classification effect, so the future should be combined with more indicators to improve the rockburst prediction ability. For example, combining MS raw wave data and parametric data can significantly improve the prediction performance (Ji et al. 2020). In addition, the high prediction accuracy of current machine learning methods is still dominated by small sample datasets. For machine learning methods, small sample datasets limit the prediction performance of machine learning methods to a certain extent. Therefore, the establishment of larger databases in the future is necessary to improve the prediction performance.

It is worth noting that rockburst data have a family resemblance structure, which may affect the original nature of the data indicators when processing the data. For example, the elimination and replacement of outliers may destroy the original characteristics of the indicators, leading to a reduction in the objectivity of the data. Therefore, how to minimize the damage to the original rockburst data and how to quantify the degree of impact on the rockburst prediction of the change in the original characteristics of the indicators after data processing needs to be considered by scholars.

At the level of algorithmic structure, traditional shallow machine learning methods generally suffer from catastrophic forgetting. One of the main reasons is that a large number of algorithmic models assume that the data distribution is steady and the samples are independently and identically distributed, so that the algorithmic models can repeatedly learn data with the same constructive features. There are unsteady data distributions in static and dynamic data, such as microseismic raw signal waveform data, which are not only unsteady but also a continuous data stream. Incremental learning in deep learning can effectively solve the catastrophic forgetting problem. However, there are not many incremental learning algorithms used for rockburst prediction, so further research on incremental learning should be carried out in the future to broaden its scope of application in the field of rockburst prediction.

Ensemble learning synthesizes multiple basic classifiers, and its prediction performance is better than that of a single basic classifier. Currently, ensemble learning uses either static or dynamic indicators as input indicators to the integrated model. In the future, is it possible to consider establishing hybrid indicators based on static and dynamic indicators? Its feasibility needs further research.

7 Conclusions

This paper presents a systematic review of rockburst prediction methods based on static and dynamic indicators from the nature of indicators. First, the importance analysis of rockburst prediction methods was conducted based on Citespace software. The results show that microseismic monitoring, acoustic emission, and machine learning have the highest degree of importance. Through the scientometric analysis, the rockburst prediction methods were focused on four methods: empirical methods, microseismic monitoring, acoustic emission, and machine learning. Then, the application of the four prediction methods is analyzed and summarized from the perspective of static and dynamic indexes, and the following conclusions are obtained:

  1. (1)

    The stress method's parameters are static quantitative indicators, while the energy method's parameters consider the dynamic behavior of the rock system. The latter method, based on energy indicators, better reflects the tendency of rockburst and has a more accurate prediction effect. The comprehensive index evaluation method can predict a variety of static indicators jointly, with energy feedback stress characteristics, showing better prediction performance than single-indicator methods. In the future, research should focus on the non-uniformity of the criterion formula and the problem of non-uniformity of the grading interval.

  2. (2)

    Microseismic monitoring has a main defect in that it has a prediction delay effect and cannot predict the specific time and intensity level of rockburst occurrences. The accuracy and validity of spatio-temporal distribution of characteristic cloud maps are significantly affected by MS signal processing. The introduction of artificial intelligence technology into MS signal processing is a future trend.

  3. (3)

    Acoustic emission monitoring techniques developed for indoor testing have not yet been applied in the engineering field. Further research is needed to determine how to transition from indoor testing to field monitoring. Although prediction miscalculation and prediction hysteresis have less influence on the time domain waveform warning, they remain a key research topic. The integration of time domain parameters and waveform characteristics into early warning methods is expected to become a mainstream trend.

  4. (4)

    Machine learning methods for indicators face several challenges, including missing data, unbalanced datasets, anomalous data values, indicator dependency, indicator assignment, and small sample databases. To minimize damage to the original features of the indicator data, the focus should be on data processing. Further research on advanced algorithmic structures to increase the intensity of data processing and expand the database is key to solving these problems.

No matter which prediction method, it has its advantages and shortcomings, no one method can be used to predict the rockburst activity of all projects. The key to the selection of the best model for rockburst prediction lies in the accuracy and applicability of static and dynamic indicators.