As one of the most dangerous disasters in underground coal mines, water inrush is commonly encountered in the process of tunnel excavation and mining working face advancing (Bagci et al. 2014; Wu et al. 2011a). Once water inrush occurs, groundwater rapidly flows through rock fissure and enters the mining space from the aquifer under the action of water pressure. If the water inflow exceeds the drainage capacity of mine facilities within a short time, the mining space will be flooded (Ma et al. 2020a; Wang et al. 2020a; Zhang and Yang 2021). Water inrush occurring in the tunnel will threaten personnel safety, and large deformation caused by water inrush will disable the tunnel (Golian et al. 2021; Li et al. 2013). Water inrush occurring in the working face will lead to the mining interruption and abandonment of mining equipment (Gao et al. 2018; Hu et al. 2019). In some cases, water inrush will be accompanied by a large amount of solid mud into the space, which not only increases the difficulty of cleaning but also causes the roof collapse, floor heave, and other structural instability disasters (Ma et al. 2021b; Xu et al. 2016; Zhao et al. 2021a). Finally, a large amount of groundwater enters the mining space and the acid mine drainage is produced, resulting in the severe loss and pollution of groundwater and irreparable damage to the environment (Fan and Ma 2018; Kefeni et al. 2017; Wu et al. 2011b; Zhang and Peng 2005).

As the largest consumer and producer of coal in the world, China has consumed about 4 billion tons of coal in 2020, accounting for 56.8% of the total energy consumption (National Bureau of Statistics 2020). Among the consumption of coal, more than 90 percent of coal was produced domestically; in 2020, about 4,700 coal mines were put into operation, producing 3.9 billion tons of coal (China Coal Industry Association 2021; National Bureau of Statistics 2020). At the same time, China has the most complex mine hydrogeological conditions in the world: nearly 60% of the mining areas are carboniferous coal-bearing strata, and about 900 coal mines have a high risk of water inrush (Fig. 1) (Sun et al. 2016; Wu et al. 2019c; Zhao et al. 2020). As a result, a large number of water inrush accidents can be caused. According to incomplete statistics, 1,196 severe water inrush accidents occurred in China in the past 20 years, resulting in 4,775 death and missing (Ma et al. 2018c; State Administration of Coal Mine Safety 2014; Sun et al. 2016) and it also brought the direct economic loss exceeded 1 billion CNY (Yang et al. 2018c). For example, on March 28, 2010, in the construction process of No. 20101 working face of the Wangjialing Coal Mine, when the ventilating tunnel was connected with the old goaf above, a large-scale water inrush accident was triggered, which trapped 153 miners and caused a direct economic loss of nearly 50 million CNY (Cui et al. 2018). On January 30, 2015, in the mining process of the 866-1 working face of the Zhuxianzhuang Coal Mine, water-conducting pathways were connected to the aquifer above the roof under the influence of mining disturbance, water inrush was caused from the working face roof. This accident resulted in 7 deaths, working face abandonment, and a direct economic loss of 12 million CNY (Xue et al. 2021). On April 10, 2021, during the excavation of the B4W01 ventilating tunnel of Fengyuan Coal mine, the groundwater in old goaf broke through the water barrier, causing flooding of the main and secondary inclined shafts, pit bottom and other areas, which resulted in 21 deaths and a direct economic loss of 70 million CNY. (National Mine Safety Administration 2021). In the above accidents, due to the lack of understanding about the seepage mechanics mechanism of rock mass in the coal mine, reasonable measures could not be taken to prevent the occurrence and further development of disasters. Therefore, it is necessary to study the rock seepage mechanics mechanism of water inrush in coal mines for safety production.

Distribution of coal mines with the high risk of water inrush in China. Note: XPCC refers to Xinjiang Production and Construction Corps, data from Sun et al. (2016)

Figure 2 shows the typical water inrush from the roof and floor. In these cases, water source and water-conducting pathway are two main factors inducing the water inrush (Zhao et al. 2020). However, due to the difficulty and the unfavorable consequence (e.g. destroying aquifer) of controlling water source (Ma et al. 2021c), studying the formation mechanism and control method of the water-conducting pathway is the main approach to preventing and controlling water inrush in the coal mine (Liu et al. 2018a). The seepage mechanism in the water-conducting pathway is undoubtedly the most critical link in this issue. It is proved that the stress field and seepage field in rock mass changes dramatically simultaneously in the process of water inrush. At the same time, the nonlinear characteristics of fluid seepage rise sharply with the evolution of mechanical and hydraulic characteristics of rock mass medium. All these phenomena indicate that the seepage mechanism of water inrush in the coal mine is a complicated topic and deserved to be investigated thoroughly.

Different types of water inrush and their main influencing factors

According to the evolution characteristics of water inrush from different views, the seepage mechanism in the process of water inrush is summarized into the following three main aspects: stress-seepage coupling mechanism, flow regime transformation mechanism and rock erosion mechanism. A large number of studies have been conducted through modeling, numerical analysis and experimental investigation from the three aspects, providing scientific guidance for the prevention and control of coal mine water inrush. This review aims to summarize the latest results of rock seepage mechanics of water inrush from these three aspects and propose the future research direction of seepage mechanics mechanism of water inrush in the rock mass.

As mentioned in the above section, researchers mainly focus on three aspects of the stress-seepage coupling mechanism, flow regime transformation mechanism, and rock erosion mechanism in revealing the seepage mechanism of the water inrush.

Many researchers believe that the process of water inrush is a mutation process in which the seepage field and stress field couples and develops towards an unstable state in the rock mass (Pang et al. 2014; Wu et al. 2017c; Yin et al. 2015). Under the influence of mining disturbance, the surrounding rock of the mining space (tunnel, working face) undergoes stress redistribution, causing the damage, large deformation, and fracture development in the rock mass eventually (Chen et al. 2020). The propagation of fractures in rock mass promotes the improvement of rock permeability. At the same time, with the groundwater entering the rock fractures, the rock strength is significantly decreased. Under the combined action of seepage and stress, the water-conducting pathway in the rock mass is gradually connected, then groundwater is forced to enter the mining space at a high velocity (Zhang and Shen 2004; Zhu et al. 2014). In this process, since the stress field and the seepage field constantly couple with each other and change with time, it is difficult to quantitatively analyze the temporal and spatial evolution law (Meng et al. 2016; Yin et al. 2016). In addition, due to the inhomogeneity of rock mass, the fractured and weakly cemented areas such as discontinuities and faults in rock mass become potential seepage channels inside rock mass. Since mechanical properties of the water-conducting pathway present obvious plastic characteristics and seepage properties of the water-conducting pathway present the nonlinear characteristics (Ma et al. 2016b; Sun et al. 2019), the study on the water-conducting pathway of rock materials is extremely complicated.

Another issue is the transformation of the fluid flow regime during water inrush. Ever since H. P. G. Darcy proposed his famous law of linear flow in 1856, the interest in the fluid motion in rock media has never waned. It is generally believed that the fluid movement in the aquifer is a linear laminar flow regime, that is, the fluid pressure and velocity have a linear relation (Layton et al. 2002; Shahbazi et al. 2021). However, the groundwater flow in the mining space is turbulent after the occurrence of water inrush. This means that the relation between water pressure and velocity is non-linear, and the multiplied water pressure often does not get the multiplied flow (Chen et al. 2015c; Zhao et al. 2021b). Therefore, it is of great engineering significance to identify the fluid motion state and study its transformation mechanism for evaluating the water inrush disaster and forecasting the water inrush quantity. Due to the diversity of rock media, the flow pattern transformation in fractured or porous rock mass media is extremely complicated, and the temporal and spatial characteristics of flow regime transformation are difficult to be broken through (Kong et al. 2021; Zhang et al. 2021b).

Under the action of water pressure, some fine particles in rock mass migrate out with water, which has a disastrous effect on the evolution of the water inrush process. The migration of rock particles causes the increase of porosity in the rock mass, which further increases the permeability of rock mass and causes more groundwater to flow out (Ma et al. 2019a; Wang et al. 2019b). At the same time, the loss of rock particles causes damage to the rock structure and induces the instability failure of rock mass (Ma et al. 2021a; Zhao et al. 2021c). Since Vardoulakis et al. (Papamichos et al. 2001; Stavropoulou et al. 1998; Vardoulakis et al. 1996) proposed the erosion constitutive model of rock and soil materials, the phenomenon of rock erosion in rock mass has always been highly concerned by researchers. To explore the migration law of fine particles in the rock mass and its influence on the process of water inrush, a large number of experimental instruments have been developed (Liu et al. 2019a; Ma et al. 2017a; Wang et al. 2020b). However, due to the complexity of the interaction between water and rock mass, it is difficult to intuitively obtain the formation and migration of fine particles, as well as to solve the influence mechanism of rock mass damage, deformation and instability caused by rock erosion.

In the following sections, a large number of studies on different seepage mechanisms are summarized from the aspects of the numerical and experimental approach in the last 30 years. The similarities and differences, merits and limitations of these studies are compared and analyzed to outline the overall picture of this research field.

In the process of the water inrush, the seepage and stress field couples together. First of all, the redistribution of the stress field results in the damage and breakage of rock mass, thus increasing its hydraulic properties. At the same time, the seepage in the rocks also changes the pore pressure and structure strength, so as to change its mechanical behavior. Therefore, the coupling mechanism of seepage and stress fields should be studied to analyze the evolution of water inrush disasters.

3.1 Modelling and numerical study

The study of the interaction between rock mass and fluid began within soil mechanics. Terzaghi (1923) proposed the effective stress theory. It is reported that the total stress \(\sigma\) acting in the saturated soil is borne by the pore pressure \(\sigma_{\text{p}}\) and the effective stress on the soil framework \(\sigma_{\text{eff}}\), that is:

After this, Biot (1941) revised the effective stress theory and proposed the concept of the effective stress coefficient. Since then, more and more researchers have investigated the fluid–structure interaction, established the coupling models, and conducted numerical simulations.

To explore the water inrush phenomenon in the intact floor/roof under the seepage-stress coupling action, a series of modeling and simulation research has been conducted. In these models, fracture initiation and propagation continuously occur in the surrounding rocks under the coupling action of seepage-stress fields, leading to the occurrence of water inrush.

For most models, the initial and expansion of fractures are regarded as the main reason for the increase of permeability in the roof/floor strata. Based on the RFPA^2D, Zhang et al. (2009) conducted a coupling analysis on the evolution of hydraulic characteristics and fractures propagation in the process of water inrush through a flow-stress-damage model. Their results showed that the water inrush in the strata is caused by the connection of a large number of vertical fractures in the fracture zone. To clarify the relationship between permeability and stress during water inrush, Meng et al. (2016) proposed a three-dimensional coupling model of stress and permeability based on the complete stress–strain and permeability curves of different rock samples. The simulation results showed that, as the mining progresses, the fractures in the roof and floor are first compacted; when the stress reaches the rock strength, the fractures develop and expand gradually. The permeability evolution with the stress can be divided into three stages, including the decline stage, growth stage and recovery stage. Based on the analysis of fracture and permeability properties of different rock strata, Liu et al. (2018c) established a seepage-stress coupling model of the coal seam floor. The simulation results show that with the increase of water pressure, the confining pressure decreases, while the permeability of the floor increases, and the fractures’ penetration and water inrush occur at the stress change position. Wang et al. (2021) established a numerical model and analyzed the fracture and hydraulic properties of fractured specimens. It is found that the permeability of floor strata is closely related to the horizontal stress after coal mining, and the longitudinal propagation of wing fractures contributes to the formation of water inrush pathways.

With the increase of mining depth, rock strata are under the environment of high in-situ stress, elevated water pressure, and intensive mining disturbances, there will be more severe water inrush from the roof/floor (Hou et al. 2020; LaMoreaux et al. 2014; Liu et al. 2021; Ma et al. 2022c; Shen et al. 2012). To this end, the mechanism of water inrush in deep mines should be revealed comprehensively. Shen et al. (2012) set up an anisotropic flow model to study the mechanism of water inrush in deep mines, and obtained the failure depth of the floor and the effective protection layer thicknesses in the deep mine according to their simulation results. Guo et al. (2017) analyzed the stress variation and pore pressure distribution characteristics of rock mass at different depths using a fluid–solid coupling model. In line with the equivalent continuum theory, combining the non-linear dynamic module and seepage module of FLAC, Li and Bai (2019) simulated the water inrush process under the influence of the dynamic and static stress superposition disturbance and the pore pressure (This is a typical environment for the deep floor under the high-strength mining). Based on a numerical study by the FLAC^3D, Zhang (2021a) found that water inrush from the deep floor may be attributed to the expansion effect of rock strata after the stress relief.

The above studies focus on the coupling action of seepage stress in intact strata. However, in the process of coal mining, some water-conducting structures such as fault and karst collapse pillar (KCP) are commonly encountered (Kong and Wang 2018b; Lu and Wang 2015; Ma et al. 2015; Shi et al. 2018a). Due to their broken and loose internal structure, these water-conducting structures are easily deformed under the coupling action of seepage and stress, leading to a higher permeability of the structures. These water-conducting structures are regarded as potential water inrush channels (Li et al. 2017; Mu et al. 2020; Yu et al. 2020), which significantly shorten the distance between the mining space and aquifer (Lu et al. 2009; Wu et al. 2017b). Therefore, through theoretical modeling and numerical simulation, many researchers have focused on the evolution of mechanical and hydraulic characteristics of water-conducting structures under the seepage-stress coupling action (Ma et al. 2015, 2018a; Wu et al. 2019b).

KCP is widely distributed in limestone and is formed by the long-term dissolution of groundwater. The interior of KCP is composed of rock blocks of various sizes, between which clay is mainly filled and cemented. In order to analyze the seepage-stress coupling mechanism in KCP, on the basis of variable mass and nonlinear dynamics, Bai et al. (2013) established a plug model to describe the relation between the seepage velocity and KCP mass. The seepage velocity in KCP was regarded as the key factor for water inrush in their study. Ma et al. (2016b) analyzed the influence of coal mining on the instability of seepage and stress fields, and obtained the evolution of mechanical and hydraulic properties when the working face is advanced before and after the penetrated KCP (See Fig. 3). Liu et al. (2018a) considered the influence of the KCP height, floor strength and water pressure on the risk of water inrush. Based on micromechanics theories, Lu et al. (2020) proposed a stress-seepage-damage coupling method to simulate the fracture evolution and the groundwater flow in KCP. The effectiveness of the proposed method is verified by ultra-high precision micro-seismic monitoring, and the method can directly reflect the connectivity of the water-conducting pathway. By establishing a FLAC^3D numerical model, Lin et al. (2021) obtained the evolution law of the plastic zone and the seepage field, and used the affected width of KCP as a criterion of water inrush, that is, if the width reaches a critical value, the aquifer is connected with the floor fracture zone, and then water inrush can be caused.

Damage zone and seepage vectors evolution when the working face is advanced before and after the penetrated KCP,

The fault is formed by the crust fracture under the action of tectonic stress. The activation phenomenon of faults under the coupling action of seepage-stress is considered as the main symptom of the occurrence of water inrush in fault. Through the simulation of the working face advancement, Sun et al. (2019) studied the evolution of stress and flow velocity near the fault, and pointed out that, there is a high risk of water inrush if the flow velocity in the fault is much higher than that in the floor. Li and Wu (2019) further analyzed the coupling of displacement, stress and seepage fields, and summarized the precursory characteristics of water inrush. Considering the softening influence of dewatering on fault permeability, Mu et al. (2020) simulated the mechanical and seepage characteristics of nature and disturbed fault rocks. The results show that the positive feedback effect between the fault rocks’ strength and their permeability is the main inducement for water inrush in the fault zone.

An obvious delay phenomenon of water inrush is reported in Mu et al. (2020)’s research, in fact, many researchers have claimed the lag effect of water inrush in the fault (Bai et al. 2021; Li and Bai 2019). This phenomenon presents a critical opportunity for field workers: if this interval is used for rapid evacuation, personnel and equipment will be protected (Li et al. 2015); if not handled properly, a serious safety accident can be triggered. Therefore, it is essential to understand the seepage-stress coupling mechanism in the lag phenomenon of the water inrush process (Wu et al. 2011a). It is widely believed that the occurrence of delayed effect is the coupling result of the fluid and deformation, which is closely related to the permeability of the fracture zone (Yu et al. 2021).

In recent years, to effectively reveal the seepage-stress coupling principle of water inrush, researchers have tried to analyze the water inrush mechanism from the perspectives of some novel mechanical and mathematical methods, including elastic mechanics methods (Tang et al. 2011), elastoplastic mechanics methods (Zhu et al. 2014), micromechanics methods (Lu and Wang 2015), fracture mechanics methods (Li et al. 2019c) and damage mechanics methods (Zhou et al. 2020).

From the perspective of elasticity mechanics methods, Tang et al. (2011) established a mathematical model of water inrush in KCP and deduced the formula of critical water pressure. It is concluded that the bearing capacity of the waterproof layer is mainly affected by the thickness and strength, and the critical water inrush pressure of KCP depends not only on the relative thickness of the water barrier, but also on its absolute thickness. Lu et al. (2013) and Lu and Wang (2015) combined the continuous damage model with the pore elasticity model and proposed the loss-flow coupling simulation method. Through numerical simulation, the fracture development, permeability change, water inrush channel formation and water flow process of floor strata in the process of mining are reproduced. By combining the brittle fracture criterion in fracture mechanics and the limited equilibrium condition of shear failure in rock mechanics, Li et al. (2019c) found the critical water pressure condition for the instability of waterproof strata, and proposed a confined water pressure-based mechanical criterion of the water inrush.

With the expansion of fractures, a high-permeability damage zone is generated; as the scope of the damage zone further expands, it will eventually cause a water inrush accident. Therefore, studying the damage mechanism of coal and rock mass in the mining process is also beneficial to enriching the seepage-stress coupling mechanism of water inrush. Yuan et al. (2015) used the continuous-discrete element method to obtain the movement of the roof and the damage properties of the floor. It is found that the risk index of water inrush grows with the goaf area, and it approaches the maximum value at the maximum caving interval. Xue et al. (2018a) established a seepage-stress-damage coupling model and discussed the mechanical and hydraulic properties of pre-peak and post-peak periods. By simulating the whole process of coal from microscopic damage to macroscopic fracture, this research concluded that the rupture starts from randomly distributed internal damage points, and then expands to a macroscopic rupture zone with stress loading. In order to reveal the creep failure properties of mudstone, Zhou et al. (2020) developed the hydraulic-mechanical coupling damage creep model of soft rock, which can clearly reflect the deformation characteristics of mudstone in different creep stages. Different from the above researchers who only focused on damage changes under the seepage action, Yang et al. (2007) innovatively linked the accumulation of damage to the evolution of permeability, and proposed a fully coupled flow-stress-damage model to predict the time, location and path of water inrush. On the basis of the seepage-stress coupling theory, Zhang (2014) analyzed the evolution of the damage characteristics and the flow vector in the floor, and divided the rock formation between the mining space and the aquifer into four different areas. Besides, the water inrush is attributed to the connection of “mining damage area” and “water-conducting area”.

However, the rock mass is assumed to be isotropic in the above studies, and the influence of anisotropy of rock mass on the water inrush is not considered. Liu et al. (2012b) employed seepage-stress coupling theory and anisotropic seepage model to simulate the process of floor inrush, analyzed the anisotropic permeability characteristics of floor strata, and proposed that grouting reinforcement in the broken zone and setting up protective coal pillars are effective measures to prevent floor inrush. Considering the cross-coupling effect of seepage and stress fields, Yang et al. (2014) established an anisotropy model and analyzed the anisotropy characteristics of the fractured rock mass. The study has shown that the anisotropy of fractured rock mass has a great influence on the distribution and size of stress field, seepage field and damage zone (Fig. 4). Lu and Wang (2015) introduced the concept of heterogeneity in stress-seepage simulation, and investigated the influence of uniformity index and confined water pressure on water inrush process of heterogeneous floor strata.

Anisotropy fracture model and its simulation result. a Fracture network around 3D tunnel; b Stress and seepage boundary conditions. c Pressure gradient distribution under different fracture angles,

In summary, the effect of expansion, fracture connection in the intact rock, and the activation of water-conducting structure on water inrush in the coal mine have been throughout discussed. The water inrush in the deep coal mine as well as its lagging phenomenon also have been increasingly emphasized. With the development of mathematical methods, a lot of novel mechanical methods (e.g., fracture mechanics methods, micromechanics methods, elastoplastic mechanics methods and damage mechanics methods) have also been applied in this subject, and the anisotropy characteristics of rock media have been concerned as well. These methods are helpful to understand the mechanism of water inrush and are effective methods to prevent the occurrence of water inrush disasters.

3.2 Experimental study

In addition to modeling and simulation methods, experimental research and field measurement are also important methods to study the seepage-stress coupling mechanism of the water inrush process.

Laboratory experimental research refers to the use of mature or self-designed equipment in the laboratory to conduct experiments on rock mechanics, seepage and similar simulations. The external variables and experimental environment can be accurately controlled in laboratory experiments with good flexibility. At the same time, laboratory experiments can also be used to verify the correctness of the theoretical analysis and numerical simulation to facilitate the correction of the theory. However, experimental research also has problems such as difficulty in fully simulating the on-site situation, and the results obtained may deviate from engineering practice. According to the different experimental materials and test methods, experimental research is mainly classified into complete rock experiments, similar material simulation experiments and seepage experiments of the broken rock mass.

In recent years, with the continuous enrichment of seepage-stress coupling test equipment and test methods, researchers have carried out a series of intact rock stress–strain-permeability experiments (Souley et al. 2001; Wang and Park 2002) to analyze the mechanical and seepage characteristics of roof and floor strata. Figure 5 shows the principle of the classic seepage-stress coupling experiment. The rock sample is under the axial compression stress \(P_{1}\), the confining pressure \(P_{2}\) and pore pressures on the upper and bottom of the sample \(P_{3}\) and \(P_{4}\). Due to the pore pressure difference \(\Delta P\), the water flows from upper to bottom. The axial deformation and the variation of pressure difference are recorded in real time for the subsequent calculation of the rock permeability. A large number of test results (Jiang et al. 2013; Pang et al. 2014; Xiao et al. 2020; Zhou et al. 2020) has shown that during the elastic compression stage, the permeability of the sample decreases with the increase of the axial stress. This is caused by the compaction and closure of some small fractures in the rock. As the stress further increases, the sample enters the yield stage; the fractures are gradually generated and developed, contributing to the increase of the permeability. When the rock fractures intensify, the permeability gradually reaches its peak.

Stress–strain-permeability test schematic, After Zhang (2021b)

It is no doubt that different rock samples have different variations in stress–strain-permeability characteristics. Zhang (2021b) compared the stress–strain-permeability of four lithologic rocks. According to the experimental results, the permeability peak generally appears in the stress softening stage. Based on the testing data, a series of quantitative indicators are put forward to assess this seepage-stress coupling process in different lithologic rocks. Through the micro-fracture test of limestone, Feng and Ding (2007) studied the fracture development characteristics of fractured limestone samples with the coupling effects of stress and seepage field. Based on the experimental determination on the strength of the mixed rock, Wu et al. (2017a) proposed to use the critical water inrush coefficient as an indicator to judge the occurrence of water inrush. By improving the traditional test equipment, other researchers (Li et al. 2008b; Xu et al. 2012; Zhao et al. 2009) also established different complete rock seepage-creep coupling test systems and methods, and tested the rock creep and permeability characteristics under long-term seepage-stress coupling. These studies have obtained the characteristics of rock creep failure and the law of permeability evolution.

Due to the difficulty of in-situ sampling of some rock materials, the seepage-stress coupling experiment in similar materials is also a major focus of researchers. Zhang et al. (2017a) used similar materials to simulate the coal seam floor, and dyed the fluid to observe the flow trajectory. The periodic variation of the stress and seepage characteristics of the floor under the mining disturbance and high-pressure water was obtained in this research. In another research (Zhang et al. 2017b), a similar material model of the floor with concealed faults was developed to analyze the interaction between the floor and the fault, which can realize the observation and analysis of the whole process of floor fracture formation and concealed fault activation. To study the water inrush from the floor and the stress evolution during coal mining, Li et al. (2018) established a new type of similar experimental model with good airtightness. The gas pressure was employed to compensate for pressure instability and frequent shutdowns. However, restricted by the size and strength of the equipment, the simulation of rock depth is limited, which cannot meet the simulation of complex geological conditions. Based on the experimental simulation of the whole process of water inrush from the floor, Liu et al. (2019b) adopted the thin plate theory to analyze the distribution of water inrush position, which can realize the prediction of water inrush position.

In order to simulate the process of water inrush from faults and KCP fracture zone, researchers conducted a series of seepage-stress coupling tests on broken rock samples. By means of the MTS815 system and other self-designed components, Ma et al. (2016a; 2019b) carried out a variety of experiments to study the compaction and seepage characteristics of broken rocks. Li et al. (2016) conducted a seepage-creep experiment to illustrate the seepage characteristics of the rock, and used the rate of change of porosity to express the creep characteristics of broken rocks. Wu et al. (2019b) studied the seepage mechanism of fractured sandstone under axial stress, and the results showed that the permeability coefficient of fractured sandstone is related to the axial stress and particle size. Li et al. (2019a; 2019b) performed compaction and seepage experiments of broken coal under different stress conditions. The results indicated that there are differences in compaction characteristics, seepage characteristics and elastic energy storage between a single coal body and a mixed coal body. Liu and Li (2020) obtained the permeability characteristics of coal gangue and fly ash under different stress levels. It is reported that the changes in axial stress and increase in fly ash content can be used as important indicators to characterize water inrush and mud inrush.

Field experiments refer to experiments conducted on the engineering site, which is generally used to collect test samples, obtain in-situ data and verify relevant conjectures and mathematical models. The observed phenomena of field experiments can guide the progress of engineering practice and prevent safety problems in advance. However, the field experiment also has problems such as complicated experiment environment and difficult operation.

To obtain the seepage-stress coupling properties, researchers have conducted many in-situ experimental studies and obtained some interesting conclusions. Through actual measurement and theoretical analysis, Yin et al. (2015) proposed that the destruction of the aquifer and hydraulic fracture caused by water pressure and mining is the main causes of water inrush (See Fig. 6a). From the perspective of fracture mechanics, Li et al. (2015) summarized that there is a hysteresis effect in the compression and shear propagation of water-containing fractures in the face of a karst tunnel, and proposed a "two-zone" theory and a calculation method of minimum safe thickness based on drilling and blasting engineering. Liang et al. (2015) obtained the waterproof characteristics of the normal fault fracture zone by a novel dual-hole pressure test. In order to better understand the hydraulic characteristics of deep fractured rocks under high groundwater pressure and stress, Huang et al. (2016; 2018b) explored the hydraulic response evolution and permeability changes of naturally fractured rocks through a series of high-pressure injection tests (See Fig. 6b). The results show that the injection rate increases non-linearly with the increase of injection pressure, and the fractures show a higher permeability after several water injection cycles. Based on experimental results of the field water injection (See Fig. 6c), Zhu and Zhang (2018) analyzed the relation between waterproof properties of floor and the pore pressure of the aquifer, which provides a risk assessment method for water inrush. Through the existing theory of water inrush and detailed analysis of mine site data, Zhang and Yang (2021) built a parameters system of factors affecting water inrush.

Field tests on the seepage-stress coupling properties of rocks. a Principle of rock failure and under the seepage-stress coupling effect, after Yin et al. (2015); b Layout of high-pressure injection test, after Huang et al. (2018b); c The evolution of water pressure and injection volume during injection test, after Zhu and Zhang (2018)

In summary, researchers have modified the classical fluid–structure coupling test device in different ways, and conducted sufficient studies on the stress-seepage characteristics of intact rocks, similar materials and broken rock masses. Various influencing factors of water inrush are analyzed and different evaluation methods of water inrush are put forward. A series of field tests have provided relevant parameters of seepage-stress characteristics and verification methods for laboratory tests and numerical simulation, providing an important reference for the prevention and control of water inrush.

During water inrush, the water flow in aquifers, mine rock masses and working spaces show different motion properties, and the analysis of flow regime transformation mechanism plays an important role in the mechanism research of water inrush. This section intends to summarize the current research status of the flow regime transformation mechanism in the process of water inrush disasters.

4.1 Modelling and numerical study

According to variable resistance of the fluids in different media, the flow regime can be divided into three forms: laminar flow, transitional flow and turbulent flow (Bear 1988; Yang et al. 2008). The groundwater flow in the aquifer conforms to the Darcy's law, and the flow regime in the mining space belongs to the free turbulent flow, while the flow regime in the water-conducting media (which connects the aquifer and mining space) is between the above two states and represents the nonlinear laminar flow (transition flow) properties.

Zhao et al. (2014) studied the water inrush in confined karst caves. It is believed that the fluid experiences a nonlinear seepage stage before the instability of strata; when waterproof rock columns are unstable, the water state is transformed into pipeline flow (a kind of transitional flow). By analyzing water–rock interaction under different Reynolds numbers, Kundu et al. (2016) characterized different flow regimes in porous media, including three main states (pre-Darcy, Darcy and Forchheimer flow regimes) and two transition states (Darcy transition and weak inertia flow regime) (See Fig. 7).

Streamline and velocity distribution at different Reynolds numbers: a Streamline; b Velocity distribution,

To describe the flow regime at each stage of water inrush, scientists have established various mathematical equations. In 1856, Darcy established the linear relation between fluid flow and head gradient, which is known as Darcy's Law (Chaudhary et al. 2011).

where, u is the flow velocity; μ is the viscosity; k is the permeability; p is the water pressure; ρ is the water density; g is the gravity acceleration; Z is the position head of water.

Later, researchers discovered that the relationship between flow rate and the hydraulic gradient is not always linear. Wood and Hazra (2017) first found that the flow of oil in fractured media shows a non-linear relation between flow rate and hydraulic gradient. In hydraulic engineering, similar nonlinear relations are commonly encountered (Hosseinejad et al. 2019). In the process of water inrush of underground engineering, such non-Darcy characteristics often appear in the high-speed seepage of non-uniform porous media.

Although non-Darcy flow is commonly employed in geotechnical engineering, unfortunately, no equation can accurately describe the nonlinear flow under high Reynolds numbers. The discussion of a single constitutive relation of non-Darcy seepage in the process of water inrush has continued until today. At present, there are two empirical formulas for nonlinear seepage: the Lzbash equation and the Forchheimer equation.

Lzbash equation (Sedghi-Asl et al. 2014) is an empirical formula, and the specific form is:

where, α is the empirical parameter; \(\eta\) is the non-Darcy index (1 ≤ \(\eta\) ≤ 2).

The value of the non-Darcy index depends on the flow pattern of the fluid. When the flow pattern is the linear flow and \(\eta\) = 1, then the equation is degraded to the Darcy equation. When the flow pattern is turbulent flow, \(\eta\) = 2 is used in this equation. If 1 < \(\eta\) < 2, the flow pattern is non-Darcy flow, which is between the linear flow and turbulent flow. Many researchers have made extensive research on the value of the coefficient of this equation and provided a lot of modifications. In general, these empirical equations are obtained through a large number of experimental data.

In 1901, Forchheimer established an equation to describe the nonlinear relation between hydraulic slope and seepage velocity under large Reynolds number, and the specific equation is (Briggs et al. 2017):

where β is the non-Darcy factor. The first and second terms of the right part of Eq. (4) represent the inertial action and the viscous action of fluid, respectively. If the flow velocity is slow and the inertia force can be ignored, the fluid is mainly affected by the viscous force and presents a laminar flow regime. The equation is transformed into the Darcy equation. If the flow velocity is faster, the fluid is mainly affected by inertia force and presents the nonlinear Darcy flow.

When water enters the mining space and presents free turbulent flow, Navier–Stokes equations can be used (Shi et al. 2016):

where f is the body force, t is the time.

The above studies illustrate the motion modes under different flow regimes, but how the fluid motion states change is still unknown. Some researchers have proposed the idea of the critical number to distinguish between Darcy flow and non-Darcy flow. Chilton and Colburn first proposed the critical Reynolds number Re_c for non-Darcy flow in porous media and defined the Reynolds number Re as (Yang et al. 2016):

where, D_p is the medium particle diameter; Re increases with the increase of water velocity u, if Re is beyond the critical Reynolds number Re_c, it is considered that the fluid is changed into the non-Darcy seepage state.

The critical Reynolds number has been widely used to judge the start of the nonlinear flow. The critical Reynolds numbers have a wide range and are summarized in Table 1.

After this, the theoretical model of non-Darcy flow and its internal parameters in different media have been fully investigated. With the continuous innovation of computer technology, researchers can comprehensively consider various factors during flow regime transformation through numerical simulation. By means of mathematical software, analysis results can be visualized more intuitively. For the significant differences of different seepage media (e.g., single rock fracture, rock fracture networks media and broken rock media) in the process of water inrush, different models with various parameters have been established by means of various numerical simulations.

For the fractured rock media, Chen et al. (2015b) analyzed the test results of fractured rock permeability under high water pressure, and obtained the non-Darcy characteristics during hydraulic fracturing by establishing two mathematical models based on Forchheimer theory and Izbash theory. Chaudhary et al. (2011) believed that the characteristics of Forchheimer flow (a kind of non-Darcy flow) are caused by the increase of eddy currents in the pore of material; the hydraulic conductivity coefficient K_a decreases as a result of the water-conducting pathway shrinking caused by the eddy growth. Zhou et al. (2016) proposed a new non-Darcy seepage model considering friction effects. It is recovered that fluid states of the Forchheimer flow and fully turbulent flow are more likely to occur in the rough fracture due to the larger friction coefficient in this media.

Zhang et al. (2017c) established a non-Darcy flow model in the single rough fracture from the pore scale. A critical Reynolds number was added to describe the relation between local permeability and flow rate. Due to the non-uniformity of fluid flow, the macroscopic flow was considered to be linear and turbulence only occurred locally (See Fig. 8). The degree of nonlinear deviation increases gradually with the increase of flow rate. By solving Navier–Stokes equations, Liu et al. (2020; 2016) numerically simulated fracture intersection and plugging effects, and discussed the effect of fluid flow regime transformation on fracture networks in detail.

Flow, velocity and the Reynolds number distribution of fluid in rock fractures a Fluid flow distribution; b Velocity vector distribution; c Reynolds number distribution,

For the study of broken rock media, Dukhan et al. (2014) studied the water flow in two types of porous media filled with spheres in different sizes and metal foams, and obtained the different permeabilities in different flow regimes. The experimental data were fitted by Forchheimer and Ergun relations, and the most suitable characteristic lengths for determining Reynolds number and friction coefficient were obtained. Bagci et al. (2014) also explored the water flow in filled spherical media with two different diameters and determined the coefficient of the Ergun formula. Since the previous studies are concentrated on the evolution of the coefficient in a specific flow regime, the influence of the transformation of the flow regime in the whole flow process is ignored. In line with a traditional power-law equation (Lzbash equation), Banerjee et al. (2019) built a predicted model for flow velocity during the entire flow regime transformation (from laminar to turbulent seepage), in which the size and porosity of the medium were known.

To understand the mining disturbance-induced water inrush, some researchers (Shi et al. 2016; Yang et al. 2018a, 2008) established a conceptual model in broken rock media. In this model, the unfavorable geological body (e.g., KCP (Yang et al. 2017) and fault (Shi et al. 2018a)) was considered as the main water-conducting pathway, and three different seepage modes (i.e., the Darcy laminar flow in the aquifer, the Forchheimer flow in the broken rock media and the Navier–Stokes flow in mining space) were integrated. Based on this conceptual model, Xue et al. (2018b) found that the Forchheimer flow is affected by both the viscous resistance and inertial resistance, and this inertial resistance increases with the increase of flow velocity. Considering the KCP as a transition area between aquifer and tunnel, Yang et al. (2008) developed a nonlinear seepage model. The calculation results show that, if the supply water pressure keeps stable, the seepage velocity changes significantly after entering the water-conducting pathway. Coupling with three different seepage regime equations, Hou et al. (2018) argued that the water flow in the unfavorable geological body obeys the Forchheimer equation and belongs to an intermediate seepage state between linear flow and turbulent flow. Xue et al. (2019) quantitatively described the nonlinear behavior of groundwater flow in fault by the Forchheimer equation. A multi-field coupled flow model was established to analyze the effect of different physical factors on the non-Darcy flow.

Scientists (Huang et al. 2018a; Kundu et al. 2016; Zhang et al. 2021b) also studied the seepage state transformation in the broken rock media from the perspective of parameter variation. Kundu et al. (2016) regarded broken rocks as a kind of isotropic media with different porosity, and discussed the transform point of seepage state based on the parameter evolution. By the numerical analysis of the seepage system in broken coal media, Zhang et al. (2021b) concluded that the water inrush disaster from KCP can be indicated by the mutation of the seepage parameter, and demarcated the limited value of the non-Darcy coefficient β_c. It is summarized that when this coefficient is less than β_c, any slight variation of parameters may lead to water inrush.

In summary, according to the results of the existing research, the process of water inrush is considered to be a transition process from linear laminar flow (Darcy flow) through nonlinear laminar flow (Forchheimer flow) to turbulent flow. Different seepage equations for different flow regimes have been proposed. Some indicators, such as the Reynolds number, are widely used in identifying flow regime transitions. Based on these equations, a series of numerical studies have been carried out to systematically study the evolution of various seepage parameters (permeability, non-Darcy factor, Reynolds number, etc.) in fractured media and porous media. Besides, unfavorable geological bodies (faults, KCP, etc.) have been regarded as the main medium of transition flow (Forchheimer flow) due to their unique fracture/porous structure. These studies contribute to the discovery of the formation and development of water inrush.

4.2 Experimental study

Due to the limitation of experimental instruments, the number of experimental research on flow regime transformation is less than that of theoretical and numerical research. In the past 30 years, the experimental research on flow regime transformation in rock water inrush mainly focused on the testing and analysis of flow characteristics of seepage transition section (i.e., Non-Darcy flow) in different media (including broken rocks media and fractured rocks media).

Lots of researchers have evaluated the non-linear seepage behavior during water inrush through tests on broken rock media. Li et al. (2008a) conducted a series of non-Darcy seepage tests on different lithologies with different particle sizes under different porosities. The results show that the non-Darcy factor may be negative in the sample with a high crush ratio. Sedghi-Asl et al. (2014) discussed the non-Darcy properties of six kinds of broken rock materials, and evaluated several classic seepage equations by testing data. It is found that particle size has an important influence on the parameter of seepage equations. Improving the seepage media by steel balls within variable diameters, Bagci et al. (2014) conducted experiments to study the seepage state transformation mechanism. Several different flow regime characteristics (pre-Darcy flow, Darcy flow, Forchheimer flow and turbulent flow) were obtained through their experimental observations. To investigate the influence of rock erosion on non-linear seepage characteristics of broken rocks, Ma et al. (2019a) introduced the Forchheimer factor in their testing result analysis. It is found that both fluid velocity and rock porosity can affect the non-linear seepage characteristics simultaneously (See Fig. 9). Based on a self-designed device, Shi et al. (2020) researched the non-Darcy seepage properties of broken limestone under different porosities. Through a series of steady-state seepage experiments, an empirical relation among inertia coefficient, hydraulic conductivity and porosity was proposed, and the seepage state and critical velocity were quantitatively studied by using the Reynolds number and Forchheimer number in this study.

Test results of non-linear hydraulic properties of broken rock samples: a The evolution of Forchheimer coefficient; b Effect of seepage velocity and porosity on Forchheimer coefficient,

The above studies mainly focus on the evolution of flow regimes by changing the properties of rock materials (e.g., distribution of particle size, porosity and lithology). In recent years, some studies have found that the stress and pore pressure states of the material also have a great influence on the motion state of the fluid. Using the independently developed experimental system, Zhang et al. (2020b) carried out constant water pressure loading and gradient loading on the media in the fault fracture zone, and revealed the flow regime transformation law under the action of high osmotic pressure. It is found that there is a critical hydraulic gradient under the gradient loading condition, which transforms the seepage state of the medium. Ma et al. (2018b; 2021c) and Liu et al. (2019a) conducted experimental studies on the evolution of non-Darcy seepage in fractured rock mass under confined compression and triaxial compression respectively. The results show that the flow velocity decreases with time while the non-linear properties of flow increase gradually under the compression effect.

Obviously, the non-Darcy seepage properties in the broken rock media have been thoroughly analyzed. For fractured media, researchers are more interested in the judgment of critical conditions of flow regime transformation in the process of water inrush, although most of these studies are also concentrated on the value assessment of physical parameters in the nonlinear seepage process, such as porosity, permeability and non-Darcy factors. Through a hydraulic test on the fractured parallelepiped rock samples under variable water heads (See Fig. 10), Cherubini et al. (2012) verified the validity of the Forchheimer equation in fracture media, and found the essential role of tortuosity in the seepage of fractured rocks. Zhou et al. (2015) studied the nonlinear seepage characteristics of coarse wall fractures at low Reynolds numbers under different confining stresses, and quantitatively describe the initiation time of nonlinear seepage by a critical Reynolds number equation. Zhang et al. (2020d) conducted a sequence of seepage tests on fractured rock specimens under different confining stresses through a self-developed test system. Based on the experimental data, the hydraulic evolution during the flow regime transformation process was analyzed. Zhang et al. (2020c) used a self-designed triaxial seepage test system to measure the permeability of cemented fractured coal rocks. It is found that the severe fluctuation in the magnitude of the non-Darcy coefficient indicates the flow regime transformation, leading to the water inrush.

Schematic diagram of the medium test device for fractured rock mass, after Chaudhary et al. (2011)

In conclusion, studies on the flow regime transformation in the fractured rocks and broken rocks media have been extensively performed in recent years. However, limited by the test conditions, most of the studies only focus on the non-Darcy flow (transition flow) to obtain the precursory law of water inrush disasters. To ensure the stability and reliability of the results, most of the studies rely on self-designed systems. These studies consider the influence of medium properties (particle size, lithology, fracture morphology, etc.) and external conditions (stress state and water pressure, etc.), providing valuable experimental support for the study of flow regime transformation mechanisms in the process of water inrush.

During the water inrush disaster from fractured and broken media, under the action of water flow, some of the solid particles migrate with the fluids, forming the solid–liquid two-phase flow. This rock erosion phenomenon contributes to the increase of hydraulic properties as well as the decrease of rock mass stability, which finally results in water inrush hazards. Therefore, it is essential to study the rock erosion mechanism during water inrush to investigate the precursor information of water inrush.

5.1 Modelling and numerical study

Numerical analysis is considered as an important method for the research of rock erosion mechanisms. The current studies are mainly divided into two categories: (1) studies on the generation and motion characteristics (e.g., pore pressure, particle content and the velocities of fluid and solid particles) of the two-phase flow; (2) studies on the evolution of hydraulic properties (e.g., porosity and permeability) and mechanical properties (e.g., stress, strain and deformation) of media under the action of the two-phase flow.

For the research on the motion properties of two-phase flow, the results show that the threshold velocity of the motion of the particles is affected by their sizes (Yang et al. 2020; Zhang et al. 2021a). Considering the aggregation effect of particles under the interparticle adhesion, Wang et al. (2019b) simplified the fractured sand-stone samples. Based on the two motion modes (i.e., particle movement and collision), the rock erosion process was simulated under different particle sizes, initial flow rates and adhesion forces. Constructing a water–sediment two-phase flow resistance model, Ma et al. (2020b; 2022b) studied the effects of different factors on the water–sediment inrush. It is found that the friction between the sediment grains and the fracture surface is the main source of the drag force on the sediment grains (see Fig. 11). Moreover, based on the Lagrange algorithm, Kong and Wang (2020) established a relation between particle loss mass and particle migration mass. The particle loss ratio can be employed as a water inrush index, and a high loss value indicates a high possibility of seepage instability (see Fig. 12).

a Resistance model of water–sediment mixed flow; b The two-phase flow velocity distribution under variable Fracture width; c Fracture inclination angle and d Fracture bending angle, after Ma et al. (2020b)

Rock erosion process in the broken rocks: a Original sample; b Mass migration and loss; c Water inrush channel forms,

The instability of fine particles on the surface of the rock mass skeleton is a critical reason for seepage water inrush (Liu et al. 2017; Wu et al. 2021). According to the stress characteristics of particles, it is shown that there are two instability conditions in water inrush: sliding instability and rolling instability. Many works (Bong et al. 2016; Kothyari and Jain 2008; Prancevic et al. 2014) studied the instability of particles from the stress characteristics of microscopic particles and calibrated the critical velocity of particle migration under two different instability forms. The relation between the initial velocity \(u_{0}\) and the critical velocity (including the sliding velocity \(u_{\text{s}}\) and the rolling velocity \(u_{\text{r}}\)) is shown in Table 2.

Liu et al. (2017) established a moment equilibrium equation (Eq. 7) for the particles rolling instability through force analysis of particles in granite water-inrush passage.

where, \(F_{\text{D}}\) is the dragging force of water flow; \(F_{\text{C}}\) is the cohesive force; \(F_{\text{U}}\) is the uplift force; \(G\) is the effective gravity; \(D\) is the particle diameter; \(\gamma\) and \(\theta\) are the geometry parameters. Based on Eq. (7), Liu et al. (2017) characterized the starting velocity of particles with different particle sizes and exposure degrees and reported that particle size has a significant influence on the starting velocity. However, this research ignored the water pressure of the two-phase fluid.

Based on the consideration of water pressure in the water-mud inrush disaster, Wu et al. (2021) obtained a moment balance equation (Eq. (8)) for the rolling instability of particles on the surface of the rock mass skeleton and established a sliding instability equation (Eq. (9)).

where, \(F_{\text{S}}\) is the seepage force; \(\varphi\) is the internal friction angle between particles; \(\chi\) is the angle between seepage force and the inclined plane; \(\gamma\) and \(\theta\) are geometry parameters that are the same as defined in Eq. (7).

In the above studies, the effects of particle size and the migration quality on seepage characteristics of the two-phase fluid in the process of water inrush were analyzed. However, the variation of the hydraulic properties (e.g., permeability and porosity) of rocks caused by rock erosion was not involved.

Many works considered the hydraulic evolution of rock media during the water inrush by modeling and simulation as well. Concerning the porosity evolution caused by rock erosion, researchers built many permeability evaluation models and obtained the evolution function of the ratio of original permeability to arbitrary time permeability (Lee et al. 1996; Li and Logan 1997; Veerapaneni and Wiesner 1996). Yao et al. (2018a) established a Warren-Root micro-element model of KCP, which included a mass conservation equation of solid particles and water, an evolution equation of fracture aperture and porosity, and a water seepage equation. Besides, the interaction among permeability evolution, water seepage and rock erosion were studied (Fig. 13).

Coupling process among different physics (Note: b is fracture aperture; q is the mixed fluid velocity; Φ is the porosity; C is the concentration of solid particle),

Other researchers noticed the relation between the Non-Darcy flow and the rock erosion (Ma et al. 2019a; Shi and Yang 2020; Yang et al. 2021). Taking fully weathered granite as the research object, Liu et al. (2018b) obtained the influence of particle erosion on porosity and pore pressure in the evolution process of water inrush by coupling the mass balance equation of fluidized particles with the porosity evolution equation. Yang et al. (2021) built a rock erosion model coupling Darcy, non-Darcy and turbulent seepage regimes, to reveal the evolution law of seepage field during water inrush.

These studies provide a valuable theoretical basis for the mechanism of rock erosion in the process of water inrush from the perspective of numerical analysis. However, in recent years, many researchers (Douglas et al. 2018; Hicher and Chang 2009; Zhang et al. 2017b) believe that in the process of water inrush, the rock mass is more prone to instability failure due to the impact of rock erosion on the structural strength of rock mass, and this failure can induce a larger scale of water inrush.

The study of the effect of rock erosion on the structural strength of geotechnical materials started from soil erosion. The change of mechanical property caused by the migration and loss of particles has been studied in soil mechanics for a long time. It is shown that soil erosion leads to the degradation of soil structure, and finally leads to the deformation and instability of soil structure on the macro scale (Golay and Bonelli 2011; Horikoshi and Takahashi 2015; Hunter and Bowman 2018).

The research on soil erosion provides a reference for studying the change of rock mass structure and mechanical properties caused by rock erosion. Vardoulakis et al. (1996) proposed a mathematical model of erosion dynamics to expound on the relation between rock mass damage and rock erosion. It is pointed out that local damage caused by stress concentration in rock mass increases the concentration of loose particles in the fluid, and the erosion of particles further leads to rock failure. Based on the rock erosion law in the fracture zone, derived a relation between permeability and volumetric strain in the broken rock mass, which has been successfully employed in simulating the variation of stress field under mining disturbance. Based on the non-Darcy law of seepage and water inrush in the fractured rock mass, Wang et al. (2020c) deduced the functional relation between rock eroded mass and sample strain in the seepage process.

By the combination of CFD and DEM methods, Shi et al. (2018b) established a seepage erosion model in coarse particle media and determined that the failure of granular soil particles is attributed to the particle flow under the high pore pressure. Qiu et al. (2019) found that in the seepage process of rock and soil, the liquefied fine particles and water often belong to non-Newtonian fluids instead of Newtonian fluids. Moreover, the increase of the stress caused by the migration of the fine particles will finally result in the instability of the orebody structure.

In conclusion, according to theoretical analysis and numerical simulation, the above research mainly expounds on the change of fluid characteristics and permeability and strength of water inrush media which is caused by rock erosion in the process of water inrush. Based on the force state of the particles, researchers considered various particle instability states such as sliding and rolling and studied the starting characteristics of solid particles from a numerical perspective. Considering the influence of rock erosion on the porosity of rock mass, a series of porosity–permeability relations are proposed, and then the evolution law of hydraulic characteristics in different media under different flow regimes is simulated. On the basis of the research results of erosion in soil mechanics, researchers established a model to describe the relation between rock mass damage and strain and rock erosion. The loss of fine particles caused a sudden change in the distribution of the internal stress field in the rock mass, which is considered as the main cause of water inrush and rock mass instability.

5.2 Experimental study

Experimental research is also an important approach to exploring rock erosion. Many studies have reproduced the process of water inrush under rock erosion flow in the laboratory by providing large pressure and setting particle outlets. By measuring fluid velocity, water pressure, particle concentration, and porosity (although most of the time indirectly), a detailed analysis of rock erosion mechanisms during water inrush can be conducted.

In order to study the evolution law of fluid characteristics, researchers have carried out a large number of laboratory tests of solid–liquid two-phase flow in the process of seepage. Zhang et al. (2014) first developed a fault water inrush testing system, in which the water was injected from the lower inlet and gushed out with solid particles from the upper outlet through the water inrush channel. By conducting seepage tests, Yang et al. (2019) obtained the characteristics of water–sediment seepage through a V-shape fracture. The result showed that the pore water pressure is proportional to fracture angle. Zhang et al. (2021a) carried out a water–sand flow test on a self-designed system. Based on the test curves, an empirical relation among the migration quality of aeolian sand, flow velocity and porosity was summarized.

Unfortunately, all the above rock erosion processes in rock mass could not be visualized, as these experimental studies were carried out in a closed opaque seepage experimental device. To this end, using breaking rods and tubes of borosilicate glass to simulate irregular seepage pathways, Hunter and Bowman (2018) carried out visualized permeability tests under different hydraulic gradients and different particle sizes with planar laser-induced fluorescence experimental means (Fig. 14). Some other works (Yang et al. 2018b; Zhang et al. 2017a) also recorded visually the rock erosion and the fracture connection process during water inrush by the special design in the seepage system.

The approach and results of visualized permeability tests: a Breaking rods and Tubes of Borosilicate glass simulate irregular rock particles; b Composition of the experimental system; c The variation of pore structure and seepage velocity with hydraulic gradient, after Hunter and Bowman (2018)

The velocity of the two-phase fluid is taken as the seepage velocity in all of the above research, which means the water flow and particle share the same velocity during seepage. On the basis of the original seepage experimental system, a new experimental system with a water–sand separation velocimeter was established by Yang et al. (2020). The flow velocity of sand and water was calculated by mass displacement theory, suggesting that the disintegration and migration of small particles are the main reasons for the expansion and permeability increase of the fractured zone.

In recent years, the evolution of hydraulic characteristics of rock mass caused by rock erosion during water inrush has also been researched by different experimental methods. Various erosion tests have been carried out under different fracture distributions (Yang et al. 2019), particle size ratios (Kong et al. 2013; Ma et al. 2017b), mineral composition (Ma et al. 2014) and loading mode (Bendahmane et al. 2008; Richards and Reddy 2010) to study the water inrush mechanism under erosion effects. The results showed that rock erosion are significant reasons for the change of pore structure and permeability of rock mass. (Kong and Wang 2018a; Wang and Kong 2018; Wang et al. 2020b, 2019a, 2020c).

Nevertheless, this study only considered the effect of certain fracture characteristics, in fact, fracture distribution in rock mass often changed under the action of mining stress. Zhang et al. (2020a) made a 3D physical simulation test system on the water–sand inrush. Compared with the previous experiment, this system had a high impermeability and provided a constant-speed excavation without suspending of coal mining simulation. By means of this system, the overall process of water–sand inrush disaster from working face was reproduced.

Some other works reported that the particle size ratio and mineral composition are important factors affecting rock erosion. Wang et al. (2017) invented an injection flow method to ensure constant pressure during the erosion test (See Fig. 15a), obtained the erosion characteristics of fractured mudstone, and defined three types of water inrush channel (i.e., surface cavity, internal cavity and thin pipes) during the unstable seepage phase. To simulate the natural state of rock mass, Feng et al. (2018) conducted an erosion test on the rocks with continuous size distribution. According to the hydraulic evolution, the erosion process during water inrush is divided into three phases: initial seepage, mutation seepage and stable seepage (See Fig. 15b). Ma et al. (2022a; 2017a) analyzed the erosion characteristics of broken sandstones with different granular size distributions, and the results indicate that more significant erosion effects occurred in samples with a higher content of fine granules, and the permeability in these samples increase rapidly. (See Fig. 15c). Furthermore, Wu et al. (2019a) introduced the genetic algorithm into the analysis of the seepage test data. The results showed that particle size distribution has a negative correlation with permeability under the erosion condition. Liang et al. (2008) investigated the hydraulic behavior of salt rock during dissolution. The outcomes indicated that fine particles in the salt rock are gradually dissolved with the increasing leaching time, and the permeability of the orebody grows gradually due to the formation of complex channels on the surface (See Fig. 15d).

Experimental investigations on the erosion properties of rock samples: a Schematic of the erosion test system,

In the above experimental research, the variation law of hydraulic properties caused by rock erosion was characterized. However, the effects of the mechanical field during water inrush were neglected in these experiments. It is no doubt that the migration of particles in the process of seepage inrush first changes the distribution of fracture channels in the rock mass, and then impresses the seepage characteristics of the rock mass. At the same time, with rock erosion, the structural stability of the rock mass is damaged, resulting in the failure of the rock mass. Existing experimental studies have shown that the development and extension of fractures caused by rock erosion have a great influence on the strength of rocks (Zhou et al. 2018, 2019).

As a fact, a large number of seepage experiments under different loading modes have been conducted to evaluate the hydraulic evolution of the media under different stress states (Chen et al. 2021; Liu et al. 2012a; Tomlinson and Vaid 2000). Based on a transient seepage test under compress effect (Zhang et al. 2016), it is found that the internal structure of KCP becomes looser under the influence of mining disturbance, so that the fine particles are more easily migrated.

Based on the seepage test of fracture propagation under rock erosion, Dunning et al. (1994) discovered that water–rock reaction can increase the expansion capacity of fractures in faults and the crushing capacity of mudstones in faults. Ma et al. (2016c) found that the particles in the fractured rock mass were rearranged under the effect of erosion, and the structure of the rock mass structure was changed, leading to the instability of the ore body finally. Yao et al. (2018b) carried out seepage experiments in the different PH of aqueous solutions. It is found that water–rock chemical reactions result in the separation of fine rock particles, which reduces the strength of ore bodies. Based on the study on fractured rock mass, Kong et al. (2020) conducted seepage experiments under different operating environment conditions. The experimental results show that in the process of water–rock interaction, the physical and chemical reactions of water, carbon dioxide and acid or alkali with rock erode the mineral particles on the rock surface; as a result, the distribution of rock particles, the structure and strength of rock mass are changed, and the instability of rock mass is finally caused.

All in all, researchers have carried out a series of experimental studies to explore the evolution of two-phase flow characteristics, hydraulic characteristics and mechanical characteristics of the medium caused by rock erosion. First, by simulating the water inrush channel in the laboratory, the process from the start of the two-phase flow to the migration was reproduced, and the relation between the rock erosion rate, flow velocity, water pressure and other physical quantities were obtained. Interestingly, part of the experiment also visually observed the migration process of the two-phase flow through the visual design of the equipment. Second, based on a series of erosion tests in broken/fractured rock masses, the evolution law of hydraulic characteristics of rock mass media during erosion was obtained. The different stages of erosion-induced water inrush and the types of the water-conducting pathway are divided. Finally, some researchers have considered the mechanical field in the erosion test, so as to study the relation between rock erosion and rock mass failure under the action of seepage stress. These test results show that under the action of stress, more fine particles will leave the rock mass, causing more serious erosion and further deterioration of rock mass.

In this study, we summarized the studies of rock seepage mechanics mechanism of coal mine water inrush disaster from three aspects: fluid–structure coupling mechanism, flow regime transformation mechanism and rock erosion mechanism. The main conclusions and recommendations for further research are as follows.

The stress-seepage coupling mechanism is considered as an important research direction in the process of water inrush in coal mines. Through numerical methods and experimental analysis, the evolution law of stress field and seepage field in the process of water inrush has been fully studied. Many mathematical methods, such as fracture mechanics methods, micromechanics methods and elastoplastic mechanics methods have been applied to the research of this topic. Through various fluid–structure coupling test devices, a series of experimental data of stress-seepage coupling water inrush have been obtained, which provided good support for the theoretical model. For the research in this direction, there are still the following questions to be solved:

1. (1)

   At present, some mesoscopic seepage-stress coupling models have been built to research the stress-seepage coupling mechanism during water inrush. However, due to the complexity of the parameters and calculation of these models, its verification process is still limited in laboratory-scale problems, and it is difficult to accurately describe the engineering-scale water inrush process.

2. (2)

   For the field research, the existing forecasting methods of water inrush in coal mines are mainly based on the assessment of mechanical characteristics of the strata, e.g., analysis of the development characteristics of collapse zone and hydraulic fracture zone. The precursor information analysis related to the seepage field evolution needs to be further studied.

3. (3)

   There is still a lack of understanding of the evolution of other physical fields such as chemical field, thermodynamic field and electromagnetic field. The study of chemical and thermodynamic fields is of great significance to the study of water inrush in specific geological structures, and the study of the earth electromagnetic field before and after water inrush may play a positive role in the detection and prediction of water inrush.

For the mechanism of flow regime transformation in the process of water inrush, researchers have a clear understanding of fluid motion characteristics under different flow regimes. In recent years, a series of numerical and experimental studies have specifically analyzed the evolution of nonlinear hydraulic characteristics of the fluid in the process of water inrush. Especially, researchers have emphasized the non-Darcy flow in fractured and porous rock mass media. For the research in this direction, there are the following problems:

1. (1)

   For flow regime transformation in different rock media, most of the existing studies are based on empirical or semi-empirical formulas, which means that a large number of on-site and indoor studies are required to conduct calibration studies. Considering the heterogeneity of rock mass media, the accuracy of parameter acquisition is greatly reduced.

2. (2)

   Existing studies have not been able to accurately explain the direct connection between the transformation process of the flow regime and the occurrence of water inrush. Most studies failed to put forward a clear judgment standard for the occurrence of water inrush through the transformation of the flow regime.

3. (3)

   Considering the complexity of flow regime transformation, some studies have introduced artificial intelligence algorithms for research, which will be an important trend in this field. It is a challenging task to ensure that artificial intelligence methods can effectively identify flow regime transformation characteristics in the process of water inrush.

Researchers have carried out many numerical and experimental studies on rock erosion in the process of coal mine water inrush. These studies have generally proved the law of particle initiation and migration in the process of water inrush, and have fully studied the influence of rock erosion on the hydraulic and mechanical characteristics of media. The following challenges remain:

1. (1)

   For the existing erosion model, the calibration and verification are usually on the basis of laboratory tests. However, considering the complexity of fracture zone boundary and the inhomogeneity of internal media, the existing models are still difficult to accurately describe the erosion phenomenon in the engineering rock mass.

2. (2)

   At the same time, most of the existing erosion models regard rock mass as the continuous elastic medium. It lacks a discussion on the relation between rock erosion, rock mass damage and microcrack propagation at the meso-mechanical scale. In addition, these models lack the analysis of the influence of stress field in rock mass on particle initiation and migration.

3. (3)

   Due to the limitations of experimental devices and materials, most of the current experimental studies fail to achieve intuitive observation of the rock erosion process. For the evolution of the seepage field (including water pressure and seepage velocity), rock erosion (e.g., particle starting position and migration path) and the medium characteristics (e.g., the spatial distribution of water pressure and porosity) under complex conditions remain to be further studied.