Evolution of hydraulic property and crack propagation of mine roof strata during bending-splitting deformation

Abstract

To explore the mechanism of water inrush from the mine roof strata, a series of seepage-acoustic emission (SAE) experiments on red sandstone disc samples were carried out. The effects of the height to diameter ratio (H/D) and pore pressure on the mechanical, hydraulic and crack propagation properties of red sandstones were investigated. Test results show that, the peak load of rock samples declines with the decreasing H/D and increasing pore pressure. The seepage process can be divided into three phases, i.e., lower permeability stage, and permeability fluctuation stage and high permeability stage. The crack propagation mainly appears near and after the peak load. In addition, in the low permeability stage, fluid mainly flows through the pores of rock. With the deformation and crack propagation, the fluid enters the cracks, causing fluctuations in permeability. When penetrating cracks forms, a large amount of fluid passes through the cracks, causing a rapid increase in permeability. In the case of high H/D, the water inrush phenomenon obviously lags behind the rock failure, and this lagging phenomenon becomes more significant as the water pressure decreases. The critical displacement (the displacement corresponding to the time of water inrush) can be used to characterize the risk of water inrush. The lower the H/D, the greater the water pressure and the higher water inrush risk. Therefore, it is necessary to control the distance from the working face to the overburden aquifer and reduce the groundwater pressure, so as to reduce the risk of water inrush from the roof.

Introduction

Water inrush disaster has posed a great challenge in the safe production of underground mines^1–3. With the increase of mining depth and expansion of the mining scale, the mining disturbance becomes one of the causes of water inrush disasters^4,5. For example, under the action of mining stress, the roof strata will be bent and split^6,7. As the deformation intensifies, the water-conducting cracks in the rock strata are highly developed. Once the cracks are connected to the confined aquifer or the aquifer in the abandoned goaf, it will cause water inrush from the roof⁸ (Fig. 1). Therefore, it is of great significance to study the hydraulic properties and crack propagation of roof strata under the action of bending and splitting deformation for preventing and controlling roof water inrush.

Fig. 1.

Principle of water inrush from roof strata and the simplification of the roof stress state: (a) Water inrush principle (b) Beam model (c) Disc sample model.

The bending-splitting deformation of the mine roof under mining stress has attracted extensive attention from scholars. A large number of studies^9–12 had shown that the central part of the roof is the key point to control the surrounding rock. In order to prevent the serious deformation of the roof, it is necessary to control the width of the coal pillar and the driving time. Jiang et al.¹³ analyzed the force state of the roof under the front support pressure, and obtained a continuous curve of the front support pressure, deflection, bending moment and bending strain energy density distribution of the roof. Zhu et al.¹⁴ studied the bending deformation characteristics of the roof under different coal pillar width-to-height ratios, and divided the deformation and failure process of the roof into two stages, i.e., stable deformation and failure expansion. During the failure expansion, the crack propagation and penetration will occur in the roof. However, the variation of hydraulic characteristics caused by roof damage was not discussed in the above researches. In fact, variation in the hydraulic characteristics of the roof often cause the formation of high-permeability channels, thereby inducing water inrush disasters¹⁵.

To investigate the hydraulic properties of roof strata, many scholars had conducted a series of testing and numerical studies. Studies had shown that the strata under different stress states reveal different hydraulic characteristics. Under the unconfined condition, the permeability of strata decreases with the increase in confined water pressure^1,16; Under the triaxial stress condition, with the increase of confined water pressure, the rock’s permeability increases, and the failure mode is gradually transformed from tensile failure into shear failure^17,18. Based on the previous seepage test result, the risk of water inrush from strata is closely related to the pore pressure^19,20, damage accumulation^21,22 and stress redistribution²³. Li et al.² carried out true triaxial model tests, and the sensitivity priority of precursor information for water inrush disaster is ordered as stress, strain and pore pressure. In addition, some scholars have also carried out numerical simulation studies on the hydraulic evolution of intact rock strata. Yang et al.²⁴ established a seepage-stress coupling anisotropic model, and the influence of rock mass anisotropic properties on the stress distribution and hydraulic conductivity coefficient is analyzed by the purposed model. Based on a coupled seepage-damage-plasticity model of saturated porous media, Chen et al.^25,26 derived the coupled stress-seepage constitutive equations and obtain porosity–permeability evolution. From these studies, it can be found that the variation of the stress field leads to the redistribution of the seepage field, the unstable changes of the seepage field will herald the occurrence of water inrush disasters.

In the above researches, the failure of the rock was considered as the compression-shear failure. In fact, as mentioned in the first paragraph of this section, the bending-splitting deformation of mine roof strata induce the water inrush frequently. Wang et al.⁶ carried out the seepage tests of red sandstone with bending-splitting deformation. However, limited by the test equipment, the relationship between crack propagation and permeability evolution was not researched. And the size factor of rock samples in water inrush was also ignored in this research. Many researches^27–29 had shown the rock roof thickness is a vital factor for the occurrence of rock roof water inrush. Based on the multi-field coupling theory, Shen et al.³⁰ analyzed the depth of the destroyed floor in normal area and fault fractured zone, and predicted the effective protection layer thickness. It has shown that the minimum safety thickness of the rock strata resisting water inrush is closely related to the buried depth, water pressure and surrounding rock mass³¹, and it increases with the increasing strata pressure and decreases with the increasing hydraulic pressure³². Therefore, it is necessary to investigate the impact of the rock roof size ratio on the water inrush disaster.

To investigate the water inrush mechanism of roof strata, the mechanical, hydraulic and crack propagation properties of red sandstone samples under the bending-splitting deformation were investigated by laboratorial tests. First, a series of water seepage-acoustic emission (SAE) tests under variable height to diameter ratio (H/D) and pore pressure are conducted. Then, based on the test results, the effect of mechanic and cracking behaviors on the hydraulic properties were analyzed. Finally, the water inrush mechanism under bending-splitting deformation was discussed.

Testing details

Simplification of roof stress state

In the process of roof water inrush, the influence of mining stress on roof strata is so complicated. Therefore, it is necessary to simplify the roof stress state before test. As shown in Fig. 1, the stress state of the roof during the water inrush process is simplified to the bending-splitting model of the beam, and it is subjected to pore pressure on the compressed side (Fig. 1b). In order to ensure the effective application of pore pressure, a disc sample was used in the test to perform the bending-splitting deformation (Fig. 1c). The midpoint of the upper surface of the disc sample is subjected to a downward point load, and the edge of the lower surface is supported by hinged support. At the same time, the pore pressure acts evenly on the upper surface.

Testing system and material

Testing system

To conduct the bending-splitting SAE experiments, a test system was designed and assembled. As shown in Fig. 2, the test system consists of four parts: the axial loading system I, the pore pressure supply system II, the AE system III, and the bending-splitting seepage system IV.

Fig. 2.

SAE test system.

The axial loading system I is composed of the material test machine and data acquisition instrument. The material test machine provides axial stress. The bending-splitting seepage system IV is installed on the material test machine, and the data acquisition instrument can record the data such as load and displacement at each moment.

The pore pressure supply system II consists of the water pump, oil pump, hydraulic cylinder, pressure gauge, flow meter and data acquisition system of pore pressure and water flow. The water pump, oil pump, and hydraulic cylinder can provide sustained and steady pore pressure. The pressure gauge monitors the pore pressure valve and the flow meter records the flow value. The data acquisition system collects pore pressure and water flow data.

The AE system III consists of the AE probe, signal amplifier and acquisition instrument. AE probe receives AE signals from the rock sample, the signal amplifier amplifies and transmits AE signals, and the acquisition instrument collects and processes AE signals.

The bending-splitting seepage system IV consists of a piston, a fixed plate, a conical base plate and a cylinder. By loading the piston, point stress can be applied to the midpoint of the sample. The inner diameter of the fixed plate is slightly smaller than the diameter of the rock sample, which restricts the surrounding of the rock sample. The water inlet and outlet of the system is connected to the pore pressure supply system and water tank, respectively. AE probes are attached around the rock sample and connected to the signal amplifier through wires. To ensure the sealability during the water seepage process, the sealing material is filled between the piston, fixed plate and the rock sample.

Testing material

In this study, red sandstones were selected as experimental materials. The original red sandstone was collected from the floor rock strata of Woxi mining in Hunan province. The buried depth of the roof strata at the sampling site reaches 950 m. The local mining area is rich in confined water, and the pore pressure in the local area is 2.7 MPa.The original rock was manufactured into the disc-shaped rock samples with a diameter of 50 mm and height of 10 mm, 15 mm, 20 mm, 25 mm, and 30 mm, respectively (as shown in Fig. 3). The physical and mechanical properties of rock samples were obtained as follows: density ρ = 2650 kg/m³; uniaxial compressive strength: 76 MPa; Young’s modulus E = 37.6 GPa; Poisson’s ratio μ = 0.201. The porosities of samples are measured and list in Table 1.

Fig. 3.

Disc red sandstone samples and their sizes: (a) Rock samples; (b) Diameter = 50 mm; (c) Height = 10 mm; (d) Height = 15 mm; (e) Height = 20 mm; (f) Height = 25 mm; (g) Height = 30 mm.

Table 1.

H/D and pore pressure design of SAE test.

Sample number	Porosity (%)	Height (mm)	Diameter (mm)	H/D	Pore pressure(MPa)
S0.0–0.2	9.01	10	50	0.2	0
S0.0–0.3	9.12	15		0.3
S0.0–0.4	9.32	20		0.4
S0.0–0.5	9.44	25		0.5
S0.0–0.6	9.45	30		0.6
S0.5–0.2	9.14	10	50	0.2	0.5
S0.5–0.3	9.06	15		0.3
S0.5–0.4	9.17	20		0.4
S0.5–0.5	9.25	25		0.5
S0.5–0.6	9.27	30		0.6
S1.0–0.2	9.36	10	50	0.2	1.0
S1.0–0.3	9.05	15		0.3
S1.0–0.4	9.17	20		0.4
S1.0–0.5	9.09	25		0.5
S1.0–0.6	9.55	30		0.6
S1.5–0.2	9.58	10	50	0.2	1.5
S1.5–0.3	9.42	15		0.3
S1.5–0.4	9.60	20		0.4
S1.5–0.5	9.23	25		0.5
S1.5–0.6	9.19	30		0.6
S2.0–0.2	9.29	10	50	0.2	2.0
S2.0–0.3	9.38	15		0.3
S2.0–0.4	9.26	20		0.4
S2.0–0.5	9.15	25		0.5
S2.0–0.6	9.30	30		0.6
S2.5–0.2	9.18	10	50	0.2	2.5
S2.5–0.3	9.46	15		0.3
S2.5–0.4	9.50	20		0.4
S2.5–0.5	9.54	25		0.5
S2.5–0.6	9.33	30		0.6

Testing scheme and procedure

In the SAE test, the pore pressure and H/D are non-negligible factors. As shown in Table 1, 25 sets of bending-splitting seepage tests were designed. The range of H/D was: 0.2 ≤ H/D ≤ 0.6, and the gradient was 0.1. The range of pore pressure was: 0.5 MPa ≤ P ≤ 2.5 MPa, and the gradient was 0.5 MPa. In addition, there were 5 sets of blank contrast experiments without pore pressure.

Before the test, to ensure the stability of SAE experiments seepage test, the loading mode with displacement control was adopted, and the loading rate was set at 0.1 mm/min. The AE signals were collected at the acquisition frequency of 30 MHz, and a threshold value of 30 dB was set to eliminate environment noises. The sample is placed in the bending-splitting seepage system, and the bending-splitting seepage system is connected to the other three systems.

When the test starts, the pore pressure is provided for the top surface of the disc rock sample. At the same time, the material test machine applies the load on the piston, and the loading is transmitted from the piston to the sample. Under the point load on the upper and the axial restrain on the lower of the rock sample, the bending-splitting deformation is generated along the radial direction. With the process of test, cracks propagate gradually inside the rock sample, and the high-pressure water penetrates the crack until the rock sample failures. The water flow is collected in the water tank through the conical base plate hole. During the test, the load, displacement, pore pressure, water flow, and the AE signals are recorded by acquisition instruments.

Calculated principle of parameters

Calculation of permeability

In the process of bending-splitting SAE experiments, the continuous crack propagation inside the rock sample leads to the change of the permeability. In this paper, the seepage in the rock cracks is considered as non-Darcy flow. The Forchheimer equation³³ can well describe the non-linear relationship between pressure gradient and flow velocity as follows:

1

where is the pore pressure gradient; is the dynamic viscosity of water; is the permeability; is the water flow velocity; is the non-Darcy coefficient; is the water density.

The height of all rock samples in this study is no more than 25 mm. Considering that the height of rock samples is relatively low, the hydraulic pressure drop is regarded as varying uniformly with height. Therefore, the pore pressure gradient is obtained as:

2

where is the pore pressure; is the height of rock samples.

The flow velocity is calculated by the flow volume and cross-sectional area. And water flow velocity satisfies the following relationship:

3

where is the flow volume; is the diameter of rock samples.

Pascal³⁴ proposed an empirical correlation relationship between permeability and non-Darcy coefficient :

4

Combined with the above four equations, the permeability of the rock sample in the bending-splitting SAE experiments can be calculated according to the water flow volume , the diameter of the rock sample D and pore pressure .

Processing of AE signals

Each AE signal contains all information about an AE event, including sound frequency F, signal duration T, and AE energy W. AE power p is defined as the ratio of energy and signal duration, that is:

5

The crack propagation and structural damage can be reflected by the effective AE event (AE events with dominant-frequency or secondary dominant-frequency). From the frequency-power spectrum, the dominant-frequency and the secondary dominant-frequency can be determined by the maximum power and second-high power.

Test results

Mechanical properties evolution of rock samples

Figure 4 shows the displacement-load curves of rock samples within variable H/D and pore pressure. In all curves, the load decreases sharply after reaching the peak value, indicating the occurrence of the brittle failure of rock samples. In the comparison of the curves under the same H/D, it is obvious that the peak load of the rock sample decreases with the increasing pore pressure. Comparing Figs. 4(a)-(e), it is found that the peak load of the rock sample increases with the increase of H/D.

Fig. 4.

The displacement-load curves of rock samples under different H/Ds: (a) H/D = 0.2; (b) H/D = 0.3; (c) H/D = 0.4; (d) H/D = 0.5; (e) H/D = 0.6.

Figure 5 shows the rock sample failure displacement (i.e., the displacement corresponding to the peak load) of rock samples under different pore pressures and H/Ds. Figure 5(a) shows the evolution of on with pore pressure. When H/D ≤ 0.3, first increases and then decreases with the increase of pore pressure. When H/D > 0.3, monotonously decreases with the increase of pore pressure. When H/D ≤ 0.3, the rock sample primarily undergoes bending deformation, with pore water pressure acting uniformly on the surface of the sample. Under low pore pressure, the pore pressure partially offsets the point load, inhibiting sample failure. However, under high pore water pressure, the coupling of bending deformation and seepage promotes the failure of the rock sample. When H/D > 0.3, the sample predominantly experiences splitting failure. External loads cause damage and crack formation in the sample, while an increase in pore pressure exacerbates the damage, accelerating the sample failure. Figure 5(b) shows the evolution of within variable H/D. With the increase of the H/D, increase rapidly. When H/D ≥ 0.4, of samples under different pore pressure reveals obvious difference, while of different samples are close when H/D < 0.4. This result means the pore pressure has a great effect on in the samples with a high H/D. It was It is worth noting that the growth rate of with H/D was significantly higher than the growth (or decrease) rate of with pore pressure, indicating that H/D had a greater impact on the rock failure displacement than pore pressure.

Fig. 5.

The evolution of failure deformation with different factors: (a) Pore pressure; (b) H/D.

Hydraulic properties evolution of rock samples

Figure 6 shows the permeability evolution of different rock samples. According to the permeability evolution curves, the rock seepage process under bending-splitting deformation can be divided into three stages, i.e., low permeability stage, permeability fluctuation stage, and high permeability stage. A rapid increase in permeability (RIP) appeared between the second and third stages, and this increase in permeability is considered a sign of water inrush. The results also show that the H/D and pore pressure affects the permeability evolution. In most cases, as the H/D of the rock decreases and the pore pressure increases, the permeability fluctuations in the second stage are more significant, and the RIP phenomenon appears earlier.

Fig. 6.

The permeability evolution curves of rock sample under different H/Ds: (a) H/D = 0.2; (b) H/D = 0.3; (c) H/D = 0.4; (d) H/D = 0.5; (e) H/D = 0.6

The permeability after RIP () is also an important hydraulic characteristic, which reflects the permeability of the rock mass after failure. When is high, it means that large amounts of groundwater will influx after the water inrush occurs, which will endanger the safety of underground engineering. Figure 7 plots within the variable H/D and pore pressure. As shown in Fig. 7(a), it can be found that gradually decreases with the increasing H/D, which suggests the rock sample with lower H/D can cause more water to flow in. It can be seen from Fig. 7 (b), with the increase of pore pressure, grows rapidly. This result means that under the action of large pore pressure, there will be a larger-scale water inrush.

Fig. 7.

The evolution of k_R with different factors: (a) H/D; (b) Pore pressure.

Crack propagation behavior of rock sample

Figure 8 shows the frequency-power spectrum of AE events within different H/Ds. The dominant-frequency and secondary dominant-frequency of these rock samples are marked in this figure. Figures 8 and 9 only showed the AE power spectrum and the distribution of AE events under certain pore pressure conditions. Similar patterns were observed under other pore pressure conditions. The dominant-frequency corresponding to rock samples within different H/Ds (H/D = 0.2, 0.4, 0.6 and P = 1.5 MPa) is 285 kHz. The secondary dominant-frequency is 15 kHz, 85 kHz, and 95 kHz, respectively.

Fig. 8.

Frequency-power spectrum of AE events within different H/Ds (P = 1.5 MPa): (a) H/D = 0.2; (b) H/D = 0.4; (c) H/D = 0.6.

Fig. 9.

Time-load curves and AE events scatter within different H/Ds (P = 1.5 MPa): (a) H/D = 0.2; (b) H/D = 0.4; (c) H/D = 0.6.

Figure 9 shows the time-load curves and AE events scatter within different H/Ds and pore pressures. As shown in Fig. 9, each blue dot represents the specific AE event, the dominant frequency zone and secondary dominant-frequency zone are also denoted in the figure. It is found that the effective AE events (blue dots in the dominant-frequency and secondary dominant-frequency zones) are concentrated near and after the peak load. It is indicated that the crack propagation mainly appears near and after the peak load. In addition, the density of effective AE events increases with the increasing H/D, which suggests that more intense crack propagation appears in these samples.

Discussions

The effect of mechanic and cracking behaviors on the hydraulic properties

To further quantify the crack propagation, the number of AE events in the two effective frequency zones was counted. The AE events in the two frequency zones during the entire experiment were counted as the total AE event count C_t The accumulated AE events in the two frequency zones at each moment were counted as the current AE event count C_a. Then, the degree of crack propagation D_c can be expressed as follow³⁵:

6

where D_c belongs to (0, 1), The larger the D_c, the more cracks appear in the rock sample.

Figures 10,11,12,13,14 show the relationship among load, permeability and degree of crack propagation under different factors. Form these figures, it can be found that the degree of crack growth first slowly increases, after a while, it increases exponentially and finally reaches 1. At the same time, it can be found that the degree of crack growth increases rapidly, the destruction of the rock and RIP occur in the same period. This shows that these three processes are mutually induced. The influence mechanism of crack propagation and mechanic properties on different seepage stages can be analyzed as follows.

1. Low permeability stage: In this stage, the permeability of the rock is very low. The permeability is kept around . This permeability value is the same as the permeability of intact red sandstone. Therefore, at this stage, the fluid mainly flows through the pores inside the rock. In addition, the permeability of different samples is very similar, because each sample has similar porosity (see Table 1).

2. Permeability fluctuation stage: In this stage, the permeability of the rock fluctuates slightly. This is because cracks are formed in the rock under the action of deformation, and some fluid will flow out through these cracks, causing a sudden increase in permeability. With further deformation, these cracks will be closed again, making the rock permeability return to the value of the first stage. Combined with the analysis in Sect. “Hydraulic properties evolution of rock samples”, it can be considered that the greater the pore pressure and the smaller the H/D, a more violent crack propagation process occurred in the specimens, which led to violent fluctuations in the permeability of these specimens at this stage.

3. High permeability stage: After a period of fluctuation, the permeability has risen by a large margin (RIP phenomenon), which indicates that there has been at least a through crack in the rock, and a large amount of fluid quickly flows out from the through cracks. This seepage phase is often accompanied by structure failure of the rock sample. Combined with the analysis in Sect. “Hydraulic properties evolution of rock samples” it can be obtained that the larger the pore pressure, the smaller the H/D specimens, the wider the penetrating cracks appear, which leads to the more significant RIP phenomenon in these specimens. At the same time, because the destruction process is more severe, the permeability of these samples after RIP is higher.

Fig. 10.

The load-crack-permeability evolution curves of rock samples with H/D = 0.2: (a) P = 0.5 MPa; (b) P = 1.0 MPa; (c) P = 1.5 MPa; (d) P = 2.0 MPa; (e) P = 2.5 MPa.

Fig. 11.

The load-crack-permeability evolution curves of rock samples with H/D = 0.3: (a) P = 0.5 MPa; (b) P = 1.0 MPa; (c) P = 1.5 MPa; (d) P = 2.0 MPa; (e) P = 2.5 MPa.

Fig. 12.

The load-crack-permeability evolution curves of rock samples with H/D = 0.4: (a) P = 0.5 MPa; (b) P = 1.0 MPa; (c) P = 1.5 MPa; (d) P = 2.0 MPa; (e) P = 2.5 MPa.

Fig. 13.

The load-crack-permeability evolution curves of rock samples with H/D = 0.5: (a) P = 0.5 MPa; (b) P = 1.0 MPa; (c) P = 1.5 MPa; (d) P = 2.0 MPa; (e) P = 2.5 MPa.

Fig. 14.

The load-crack-permeability evolution curves of rock samples with H/D = 0.6: (a) P = 0.5 MPa; (b) P = 1.0 MPa; (c) P = 1.5 MPa; (d) P = 2.0 MPa; (e) P = 2.5 MPa.

The leading and lagging phenomenon of the water inrush

In this study, the RIP phenomenon in the experiment is regarded as a sign of water inrush. From the previous researches on the water inrush mechanism on the rock floor, it is recognized water inrush lags behind the rock failure^36,37. In order to study the mechanism of water inrush under bending-splitting deformation, the temporal relationship between rock failure and water inrush is studied. The time interval between the water inrush and rock failure is obtained by:

7

where and is the moment of water inrush and rock failure (the moment RIP occurred), respectively. If  > 0, the water inrush lags behind the occurrence of rock bending-splitting failure, and vice versa.

The failure moment, water inrush moment, time intervals between the rock failure and water inrush are listed in Table 2. Based on Table 2, the time interval between the failure and water inrush under different pore pressures and H/Ds is plotted and shown in Fig. 15. As shown in Fig. 15, the water inrush may be ahead of or delayed from the bending-splitting failure of the rock sample. If H/D ≤ 0.3, it can be found that the time of water inrush is earlier than the time of rock failure. If H/D > 0.3, the water inrush lagged behind the rock sample failure. And as the pore pressure drops, this hysteresis becomes more obvious. The above results show that the water inrush of thin roof rocks may occur before the rock formation failure, which is worthy of attention. In addition, when the pore pressure is high, the hysteresis of water inrush is not obvious enough, which easily leads to the sudden occurrence of water inrush accident.

Table 2.

Time intervals and critical displacement of different samples.

Sample number	Failure moment (s)	Water inrush moment (s)	Time interval (s)	Critical displacement (mm)
S0.5–0.2	104.74	95.25	-9.49	0.171
S0.5–0.3	149.89	149.27	-0.62	0.251
S0.5–0.4	230.22	270.62	40.40	0.456
S0.5–0.5	456.75	571.94	115.19	0.951
S0.5–0.6	593.87	735.85	141.98	1.226
S1.0–0.2	114.29	108.91	-5.38	0.198
S1.0–0.3	155.48	151.75	-3.74	0.255
S1.0–0.4	223.76	264.54	40.77	0.442
S1.0–0.5	424.69	472.05	47.36	0.774
S1.0–0.6	560.45	632.40	71.95	1.047
S1.5–0.2	118.47	112.77	-5.70	0.201
S1.5–0.3	160.15	158.90	-1.25	0.264
S1.5–0.4	205.15	227.98	22.82	0.376
S1.5–0.5	414.32	431.40	17.07	0.712
S1.5–0.6	503.02	580.22	77.20	0.965
S2.0–0.2	103.45	106.07	2.62	0.172
S2.0–0.3	144.52	140.21	-4.31	0.234
S2.0–0.4	194.06	200.54	6.48	0.333
S2.0–0.5	412.14	424.81	12.67	0.695
S2.0–0.6	457.25	494.07	36.82	0.824
S2.5–0.2	77.44	80.24	2.81	0.131
S2.5–0.3	135.42	139.88	4.46	0.232
S2.5–0.4	189.93	188.47	-1.46	0.317
S2.5–0.5	391.94	402.76	10.82	0.662
S2.5–0.6	405.35	407.01	1.67	0.698

Fig. 15.

The time interval of water inrush for rock failure under different pore pressures and H/Ds (+ denotes water inrush lags behind rock failure, and vice versa).

The water inrush risk assessment

Many studies have shown that the thickness of key rock strata plays a key role in the seepage resistance or water inrush resistance of water-rich roadway^38–40. According to the analysis in Sects. “Test results” and “The effect of mechanic and cracking behaviors on the hydraulic properties”, the roof and floor rocks gradually deform after being subjected to bending-splitting. As the deformation gradually increases, the cracks expand and penetrate, resulting in water inrush. The literature also shows that the rock strata deformation tends to be an important factor for water inrush and structure failure^41,42. This section takes the critical displacement (the displacement of sample at the time of water inrush) as an indicator of the risk of water inrush. A rock formation water inrush criterion based on pore pressure, rock roof size and rock critical displacement is constructed, which provides a new method for roof water inrush prediction.

The critical displacement μ_c under different pore pressures and H/Ds are listed in Table 2. When the μ_c value is larger, it means that the rock needs to undergo greater deformation when it reaches the water inrush, which means the lower the risk of water inrush. The evolution of μ_c under variable pore pressure and H/D is shown in Fig. 16. It is concluded from Fig. 15(a) that the pore pressure has little effect on the μ_c when 0.2 ≤ H/D ≤ 0.4; μ_c obviously decreases with the increasing pore pressure when 0.4 < H/D ≤ 0.6. As shown in Fig. 16(b), μ_c monotonously increases with the increase of H/D. In samples with high H/D, the μ_c under variable pore pressure shows obvious difference, which suggests pore pressure has a significant impact on the μ_c in these samples.

Fig. 16.

The evolution of with different factors: (a) Pore pressure; (b) H/D.

The pore pressure, H/D and μ_c are fitted to solve a three-dimensional critical surface S_c of water inrush (See Fig. 17). The low value of μ_c suggests the rock sample is more likely to appear structure instability, and the water inrush is prone to occur. S_c can be applied as a criterion to assess the risk of water inrush, if the rock deformation is over the S_c, the water inrush occurs. From Fig. 17, it can be found that the decrease of H/D and the increase of pore pressure will increase the risk of water inrush, and the impact of H/D on water inrush is more significant. Therefore, the distance from the aquifers to the mining face must be controlled, and the pore pressure should be reduced using drainage, thereby reducing the risk of water inrush disasters. In engineering practice, the strain or displacement sensors are arranged in multiple directions in the rock layer with high risk of water inrush. The displacement of rock strata in the bending and splitting direction can be obtained through theoretical calculation. According to the critical displacement criterion proposed by this manuscript, the precursor information of water inrush disaster can be identified, and a certain evacuation time can be provided for workers and equipment.

Fig. 17.

Critical surface of water inrush from roof strata.

Conclusions

To investigate the mechanism of water inrush from roof strata, a series of bending-splitting SAE experiments were conducted within variable H/D and pore pressure. The mechanical, hydraulic and crack propagation properties of red sandstone samples under the bending-splitting deformation were analyzed. The main conclusions are listed as follows.

1. It is concluded that the rock has undergone brittle failure under the action of bending and splitting. The peak load of rock samples increases with the increasing H/D and the decreasing pore pressure. In the sample with low H/D, the failure deformation first increases and then decreases; while the failure deformation monotonously decreases in other samples. And the pore pressure has a great effect on failure deformation in the samples with a high H/D.

2. During the whole experiment, the evolution of permeability can be divided into three stages, i.e., low permeability stage, permeability fluctuation stage, and high permeability stage. There is a RIP that appeared between the second and third stages. Permeability after RIP decreases gradually with the growth of H/D and the decline of pore pressure.

3. The crack propagation and structural damage can be reflected by the AE event with dominant-frequency or secondary dominant-frequency, and crack propagation mainly appears near and after the peak load, and the density of effective AE events increases with the increasing H/D.

4. The rapid growth of crack growth, rock destruction and RIP occurred at the same time, and rock mechanics and crack propagation characteristics have a great influence on its permeability evolution. In the low permeability stage, the fluid mainly flows through the pores inside the rock. With the process of test, cracks are formed in the rock under the action of deformation, and some fluid will flow out through these cracks, resulting in the fluctuation of permeability. When the deformation reaches a certain degree, through cracks are formed in the rock, and a large amount of fluid quickly flows out from the through cracks, resulting in the occurrence of RIP phenomenon.

5. In the samples with low H/D, the water inrush occurred slightly earlier than the rock failure, while the water inrush lagged behind the rock sample failure in samples with large H/D. As the pore pressure drops, the lagging phenomenon of the water inrush becomes more obvious.

6. The critical displacement of the sample at the time of the occurrence of water inrush is used as an indicator of the risk of water inrush. The decrease of H/D and the increase of pore pressure will increase the risk of water inrush, and the influence of rock layer size on water inrush is more significant. Therefore, the distance from the overburden aquifer to the working face should be controlled, and the drainage should be conducted to reduce the pore pressure, so as to mitigate the risk of water inrush disasters.

Author contributions

Jiajun Wang: Investigation, Methodology, Writing- Original draft preparation. Jiangzhan Chen: Investigation, Writing—Review & Editing. Jiacheng Lin: Investigation, Data acquisition. Jiangtao Ren: Test scheme design, Investigation. If you have any queries or requirement of data, please feel free to contact Jiangzhan Chen, and his email is jiangzhanchen@csu.edu.cn.

Funding

The National Nature Science Foundation of China, 52304165, The Natural Science Foundation Project of Hunan Province, 2024JJ6505, Postgraduate Scientific Research Innovation Project of Hunan Province,CX20230380,Fundamental Research Funds for Central Universities of the Central South University,2023ZZTS0311

Data availability

The datasets used and/or analysed during the current study available from the corresponding author on reasonable request.

Declarations

Competing interests

The authors declare no competing interests.