Energy evolution mechanism of hard roof of working face adjacent to goaf after hydraulic fracturing and application

Abstract

To solve the unclear energy evolution mechanism and uncertain fracturing effects in hydraulic fracturing of coal seams adjacent to goafs, this study explored hydraulic fracturing’s influence on roof energy release via theoretical analysis, proposed the optimal fracturing location to mitigate inter-roof energy transfer, and clarified fractures’ regulatory effects on key strata through particle flow numerical simulation. Combined with field tests, it revealed the fractured roof energy evolution law: key stratum movement triggers energy release, and hydraulic fracturing promotes the phased subsidence of key strata by generating directional fractures. The elastic potential energy accumulated during this process is converted into gravitational potential energy in phases, and the specific conversion efficiency depends on the spatial distribution of the fracture network. Calculations show energy release is reduced by 95% (to 35,133.16 J) versus the unfractured condition. The optimal fracturing location is within 31.2 m of the return air roadway. Numerical simulation and field data confirm hydraulic fracturing promotes fracture development, alters stratum movement, reduces abutment pressure and high-energy microseismic events, and alleviates stress concentration, ensuring safe and efficient coal mine production.

Introduction

In recent years, coal mining has gradually evolved into deeper reservoirs. With the increase of burial depth, the elastic energy contained in the roof of working face increases and the accumulated energy greatly enhances the occurrence of underground disasters, which seriously restricts the safe and efficient mining of coal resources^1,2. Hard roof is one of the key factors causing the disasters. Due to its high strength, strong integrity and difficulty in natural collapse, hard roof tends to form a large overhanging structure during mining, which increases the stress concentration in the caving area. In addition, its sudden failure and instability instantaneously release a large amount of accumulated elastic energy, which often causes mine disasters and poses a great threat to the safe production of the working face³. Moreover, when the working face adjacent a goaf is caved, the hard roof of the adjacent goaf also increases the energy accumulation in the working face. The working face caving will involve a larger area of strata in the movement, which increases the energy released by the roof failure, and thus further expands the risk and range of disaster⁴. In recent years, significant progress has been made in the research on mechanical models of hydraulic fracturing. Based on the fluid–solid coupling theory, Huang et al.⁵ established a dynamic model of fracturing crack propagation, which provides a theoretical basis for the fracturing design of hard roofs.

Currently, the energy release associated with roof failure has garnered extensive attention from the perspective of energy dissipation^6,7,8,9,10. Zhang et al.¹¹ quantitatively characterized the damage and failure of overlying strata by defining a damage index based on the energy transmission mechanism, though their analytical scope was relatively limited. Employing the split Hopkinson pressure bar (SHPB) combined with the principles of energy dissipation and fractal theory, Jiang et al.¹² revealed the influence of internal fractures on the dynamic properties and energy dissipation of rock masses; however, this study lacked an investigation into the effects of hydraulic fractures on energy dissipation. Through field surveys and measurements, Tan et al.¹³ and Song et al.¹⁴ identified that both the key stratum itself and the underlying load-bearing coal seam accumulate substantial elastic energy. By analyzing the energy release characteristics of hard roof failure, Wang et al.¹⁵ found that the energy released during the failure of hard strata induces microseismic activity. Jiang et al.¹⁶ further analyzed the microseismic events generated by mining-induced overlying strata failure and clarified the release and transfer laws of accumulated elastic energy during the mining-induced failure of hard roofs.

In terms of coal structure research, Wang et al.¹⁷ conducted two-dimensional (2D) and three-dimensional (3D) investigations, confirming a positive correlation between porosity and fractal dimension, and revealing the variation of coal matrix deformation with these two parameters-this provides a precise microscale basis for seepage control and deformation prevention in high-temperature coal seam mining. Utilizing computed tomography (CT)-based 3D simulations, Wang et al.¹⁸ overcame the research challenges posed by coal heterogeneity and conducted in-depth investigations into its deformation laws and water transport characteristics. Additionally, Wang et al.¹⁹ clarified the effects of fracture angle and shape on seepage velocity, addressing the limitations of traditional homogeneous models and offering new practical guidance for parameter optimization in artificially fractured coalbed methane extraction. Hard roof control technology has continuously advanced in recent years. Pan et al. proposed the artificial destress layer technology, which effectively reduces the risk of rock bursts through directional hydraulic fracturing²⁰; Lin et al. investigated the influence law of hydraulic fracturing at the gateway of unmined areas on strata behavior⁴. Building on this, this study focuses on the energy evolution mechanism of the roof under the condition of gob-side working faces.

Many studies have shown that the energy accumulation in the hard roof of working face is a key factor causing mine disasters, and the hard roof management is crucial for preventing mining-induced instability^{21,22,23,24,25}. To this end, extensive studies have been conducted, and various techniques, such as pre-splitting blasting and surface well fracturing, have been proposed^5,26,27. Yet these methods are costly and have limited capabilities of controlling adjacent roofs. Furthermore, limited by research and service life, current hydraulic fracturing treatment of hard roof still faces problems, such as unclear fracturing locations and difficulty in achieving the expected fracturing effects^{20,28,29,30,31}.

To address these technical challenges, we examined the sources of energy accumulation in the 3407 working face of the Gaojiapu Coal Mine and the impacts of roof structure changes after fracturing on the movement of overlying strata and energy release by theoretical analysis and proposed a method for determining the fracturing location to block the energy transmission between adjacent roofs. The theoretical analysis results were verified by numerical simulations. Multiple targeted field measurements were conducted by long-hole segmented hydraulic fracturing, which ensured the fracturing area covering the working face roof and weakened the integrity and strength of the hard roof plate.

Theoretical study on energy regulation of working face roof adjacent to roof in hydraulic fracturing

Roof energy release characteristics after fracturing

The movement mode of roof is one of the key factors affecting the amount of energy release^32,33. The modes of roof movement during working face caving can be divided into four types: initial fracture, periodic fracture, rotational instability, and slip instability. The initial fracture and periodic fracture are characterized by the instantaneous release of a large amount of accumulated elastic energy after reaching the limit, which is transferred to the working face as shock waves. Rotational instability and slip instability, on the other hand, convert the accumulated energy to gravitational potential energy^34,35,36. After hydraulic fracturing, new fractures are generated in the key stratum or the original fractures are connected, which breaks the original energy storage structure. Some of the accumulated elastic energy is released in advance as the formation of fractures and some is in the form of gravitational potential energy of rotational slip settlement, which changes the movement mode of roof to release energy. The nonlinear damage model proposed by Zhang et al.³⁷ can more accurately describe the rock mass energy evolution process, and its constitutive relation lays the foundation for subsequent research.

Before fractured, the stratum is under triaxial stress, and the unit elastic energy is numerically equal to the work done by the external force. Under linear elastic conditions, the strain energy density under spatial stress is:

$$\begin{aligned} v_\varepsilon = \frac{1}{2}\left( \sigma _1\varepsilon _1 + \sigma _2\varepsilon _2 + \sigma _3\varepsilon _3\right) \end{aligned}$$

(1)

where $v_\varepsilon$ is the strain energy density; $\sigma _1$, $\sigma _2$ and $\sigma _3$ are the triaxial stresses; and $\varepsilon _1$, $\varepsilon _2$ and $\varepsilon _3$ are the triaxial strains. Substituting the generalized Hooke’s theorem into Eq. (1), we get:

$$\begin{aligned} v_\varepsilon = \frac{1}{2E}\left[ \sigma _1^2 + \sigma _2^2 + \sigma _3^2 - 2\mu \left( \sigma _1\varepsilon _1 + \sigma _2\varepsilon _2 + \sigma _3\varepsilon _3\right) \right] + \Delta v_{nl} \end{aligned}$$

(2)

Herein, $\Delta v_{nl}$ denotes the nonlinear correction term, which accounts for the damage evolution of rock mass:

$$\begin{aligned} \Delta v_{nl} = \frac{1}{2}D\left( \frac{\sigma _1 + \sigma _2 + \sigma _3}{3}\right) ^2 \end{aligned}$$

(3)

D denotes the damage variable, which is calibrated via laboratory triaxial tests, with a value range of 0.1–0.3.

The elastic energy accumulated in an intact key stratum under triaxial stress before fracturing can be expressed as:

$$\begin{aligned} U = \frac{V}{2E}\left[ \sigma _1^2 + \sigma _2^2 + \sigma _3^2 - 2\mu \left( \sigma _1\varepsilon _1 + \sigma _2\varepsilon _2 + \sigma _3\varepsilon _3\right) \right] + V\Delta v_{nl} \end{aligned}$$

(4)

where U is the elastic energy accumulated in the intact key stratum under triaxial stress before fracturing; V is the volume of the intact key stratum; and $\mu '$ is Poisson’s ratio.

After segmented fracturing, the intact key stratum can be approximated as the segments divided by the fracturing intervals. The high pressure generated by hydraulic fracturing drives the formation of new fractures in each segment or the connection of original ones, which provides a channel for the accumulated elastic energy release. Therefore, the elastic energy accumulated in each segment of the key stratum can be expressed as:

$$\begin{aligned} U_c^1 + U_c^2 + \dots + U_c^w \le U \end{aligned}$$

(5)

where $U_c^w$ is the elastic energy of a single fractured segment; and w is the number of segments, which is related to the fracturing interval and the fracturing range.

Elastic strain energy Formulas (1)–(4) are based on the linear elasticity assumption and applicable to energy estimation under small deformation conditions. Since actual rock masses exhibit nonlinear behavior, the model has certain limitations under high pressure, high temperature, or fluid–structure interaction conditions.

To determine the influences of energy release from the hard roof after long-hole segmented hydraulic fracturing, a model was established to estimate the energy release from the key stratum after fracturing and the disturbance stress generated by the released energy.

The fracturing of the key stratum is approximated as the segments divided by the fracturing intervals, and its movement is characterized by rotation, slippage, and subsidence, which are mainly manifested as the gravitational potential energy of each rock segment^38,39.

$$\begin{aligned} W=G\Delta h=x_c h_c \gamma \Delta h \end{aligned}$$

(6)

According to the law of conservation of energy and the exponential decay model³⁸, the remaining energy transmitted to the caving area by the overlying strata movement can be expressed as:

$$\begin{aligned} U_x = \eta W e^{-\lambda _d S_d} = \eta x_c h_c \gamma \Delta h e^{-\lambda _d S_d} \end{aligned}$$

(7)

where W is the gravitational potential energy; $x_c$ is the distance along the stratum fracture direction, which is controlled by the fracturing interval; $h_c$ is the height of the key stratum; $\gamma$ is the average unit weight of the stratum; $\Delta h$ is the roof subsidence and $\Delta h=x_c \sin \theta$; $\lambda _d$ is the energy propagation attenuation coefficient of each segment of the key stratum; $S_d$ is the distance from the key stratum to the working face, m; and $\eta$ is the seismic wave release efficiency during the movement of each segment of the key stratum.

Based on the elastic wave theory³⁸, the additional disturbance stress generated by the residual energy at the stope is obtained as:

$$\begin{aligned} \Delta \sigma _x = \rho _b V_m \sqrt{\frac{2 p U_x}{\rho _j}} \end{aligned}$$

(8)

where $U_x$ is the residual energy transmitted to the working face by the movement of overlying strata J; $\Delta \sigma _x$ is the additional disturbance stress generated by the residual energy on the working face, MPa; $\rho _s$ is the average density of the coal and rock mass, kg/m$\vphantom{0}^{3}$; $V_m$ is the propagation velocity of the seismic wave, m/s; and p is the coefficient of energy release from the movement of overlying strata.

By combining the above equations, the estimation equation of the dynamic load disturbance stress after the roof movement mode changes can be obtained as:

$$\begin{aligned} \Delta \sigma _x = V_m \sqrt{2 p \rho _b x_c h_c \gamma \Delta h e^{-\lambda _d S_d}} \end{aligned}$$

(9)

According to geological and mining data, the average caving height of the 3407 working face in Gaojiabao Coal Mine is 5 m, and its length (L) is 180 m, and average burial depth is 890 m. Based on the inversion of field microseismic monitoring data (monitoring period: January 2023–June 2023; 1256 valid events), the attenuation coefficient $\lambda =5.8\pm 0.3\%$ (mean ± standard deviation) was obtained via least squares fitting, seismic wave transfer velocity $V_m=3000$ m/s, coefficient of energy release $P=1\%$, stratum movement angle $\alpha =79^\circ$, the average unit weight of roof $\gamma =27\, {\text{kN/m}}^3$, the fracture angle $\theta =5^\circ$, and the fracturing interval $x_c=24\, {\text{m}}$. The calculation results suggest that the energy released by the overlying stratum movement is reduced from 702,663.2 to 35,133.16 J after fracturing, a decrease of about 95%. The theoretical additional disturbance stress generated by the residual energy at the stope is reduced from 6.73 to 1.32 MPa, a  80% decrease.

Influence of changes in static load on overlying strata after fracturing

A plane rectangular coordinate system is established with the intersection of the goaf and the working face as the origin. Based on the coordinate system, a model for estimating the abutment pressure on the working face after fracturing is constructed^40,41. Figure 1 shows the mechanical model of the overlying stratum structures in different caving zones.

Fig. 1

Mechanical models of overlying structure in different caving zones.

The abutment pressure of the target fracturing working face consists of four parts, the self-weight load of the overlying stratum ($\sigma _0$), the stress transmitted from the fracturing of the overlying stratum below the key stratum $\sigma _{\text{I}}$, the stress transmitted by the fracturing of the key stratum$\sigma _{\text{II}}$, and the stress transmitted by the fracturing of stratum above the key stratum, that is:

$$\begin{aligned} \sigma _H = \sigma _0 + \sigma _{\text{I}} + \sigma _{\text{II}} + \sigma _{\text{III}} \end{aligned}$$

(10)

The abutment pressure of the target fracturing working face is $\sigma _H$.

As compared with the overlying structure of the stope without fractured, after the long-hole segmented fracturing, The strike structure of key stratum changes from a long cantilever to a short cantilever. The range of key stratum and the area of the bearing structure are expanded and the thickness of the overlying stratum above the key stratum is reduced, which lowers the stress peak and shifts it deeper into the coal seam; The strength and integrity of the hard roof are broken, which causes the premature release of a large amount of accumulated elastic energy. The overhang area ($S_{DEFG}$) of the overlying stratum decreases, which reduces the static stress of the coal seam; The stress transmission coefficient $k_1$ is positively correlated with the abutment stress $\sigma _H$ of the fracturing working face. Hydraulic fracturing can generate new fractures or break through the original fractures in the key stratum, which changes the original structure of the stratum, decreases the stress transmission coefficient, and thus reduces the transmission efficiency of the roof load to the working face.

Determination of hydraulic fracturing location under goaf-adjacent conditions

Due to the instability and large deformation mechanism of the surrounding rock in roadways, it should be ensured that the fracturing location is outside of the roadways^42,43. Figure 2 is a schematic diagram of the changes in the hard roof of the adjacent goaf after hydraulic fracturing. Hydraulic fracturing reduces the impact of dynamic caving stress on the stability of the surrounding rock of the 3407 return air trough, slows down the energy release rate of the hard top plate.

Fig. 2

Schematic diagram of the changes in the hard roof of adjacent goaf after hydraulic fracturing.

Assuming the self-weight of the suspended roof and its overlying load are uniformly distributed on the coal pillars, the three-dimensional model can be simplified to a two-dimensional model along the width of the coal pillar^44,45. Figure 3 shows the schematic diagram of stress distribution on the coal pillars. There is shear stress $\tau _{xy}$ at the interface with the coal seam floor, and abutment stress $P_x$ from the anchor bolts of coal pillars near the goaf. In the vertical direction, the coal pillar is subjected to the maximum vertical stress $\sigma _{vmax}$ and overlying load of the roof and $x_1$ is the width of the ultimate plastic zone of the coal pillar near the goaf. Therefore, the coal pillars as a whole are in a stress equilibrium state.

Fig. 3

Schematic diagram of stress on coal pillars.

Figure 4 shows the unit stress within the limit equilibrium zone of coal pillar where the roadway height is $h_0$.

Fig. 4

Force analysis of a unit within the limit equilibrium zone of coal pillar.

Taking a unit within the limit equilibrium zone for stress analysis, the resultant force of the unit in the horizontal direction is:

$$\begin{aligned} h_0\left( \sigma _x + d\sigma _x\right) - h_0\sigma _x - 2\tau _{xy} dx = 0 \end{aligned}$$

(11)

At the coal–rock interface, the normal stress $\sigma$ and the shear stress $\tau _{xy}$ satisfy the equilibrium equation:

$$\begin{aligned} \tau _{xy} = \left( \sigma _y \tan \varphi + C\right) \end{aligned}$$

(12)

where $\varphi$ is the internal friction angle of the coal-rock interface, $\vphantom{0}^\circ$; and C is the cohesion of the coal–rock interface, MPa.

Combining the above two equations, we get:

$$\begin{aligned} d\sigma _x = \frac{2\left( \sigma _y \tan \varphi + C\right) dx}{h_0} \end{aligned}$$

(13)

According to the limit equilibrium theory, we get:

$$\begin{aligned} \frac{d\sigma _y}{dx} - \left( \frac{1+\sin \varphi }{1-\sin \varphi }\right) \frac{2\tan \varphi }{h_0}\sigma _y = \left( \frac{1+\sin \varphi }{1-\sin \varphi }\right) \frac{2C}{h_0} \end{aligned}$$

(14)

Then:

$$\begin{aligned} \sigma _y = B_0 e^{\frac{2\tan \varphi }{h}x{\frac{1+\sin \varphi }{1-\sin \varphi }}} - \frac{C}{\tan \varphi } = B_0 e^{\frac{2\xi \tan \varphi }{h_0}x} - \frac{C}{\tan \varphi } \end{aligned}$$

(15)

where $B_0$ is an undetermined coefficient.

If x equals the width of the limit plastic zone $x_1$, the vertical stress $\sigma _y$ reaches the maximum value $\sigma _{y\max }$.

$$\begin{aligned} \sigma _y = \left( \frac{C}{\tan \varphi } + \xi q_x\right) e^{\frac{2\xi \tan \varphi }{h_0}x_1} - \frac{C}{\tan \varphi } = \sigma _{y\max } \end{aligned}$$

(16)

Therefore, the width of the limiting plastic zone of coal pillar near the goaf is:

$$\begin{aligned} x_1 = \frac{h_0 \cot \varphi }{2\xi } \ln \left( \frac{\sigma _{y\max } + C \cot \varphi }{\xi q_x + C \cot \varphi }\right) \end{aligned}$$

(17)

The fracturing location should ensure that the affected area covers the range from 0 to $x_1$; and the roof of the adjacent goaf should be broken to reduce the static load on the coal pillar before the coal pillar reaches its ultimate plasticity. Based on the site conditions, the height of the stratum below the key stratum $H_1=50$ m; the height of the key stratum $H_2=30$ m; the height of the stratum above the key stratum $H_3=810$ m; roof elastic modulus $E= 17.8$ GPa; the coal–rock lateral stress coefficient $k=1$; the internal friction angle $\varphi = 29^\circ$; the stress concentration factor $Kt=3.8$; the support resistance applied to coal pillar $p_x=0.3$ MPa; the resistance of goaf gangue to coal pillar $q_x=0.4$ MPa; the coal cohesion $c_0=5.8$ MPa; the fracture angle $\theta = 5^\circ$; the caving length $S=300$ m; the rock fracture size $l = 24$ m; the Poisson’s ratio of the fracturing stratum is 0.2; the distance between the return air roadway and the intermediate roadway is 170 m. The value of $x_1$ is then calculated to be 2.2 m. Based on the fracturing process and formation conditions, the average influence range of fracturing is 70 m and the width of coal pillar is 6 m. Therefore, the distance between the fracturing site and the return air roadway should be shorter than 31.2 m.

Simulation study of hydraulic fracturing

Model construction

Based on the hydraulic fracturing construction of the 3407 working face in the Gaojiabao Coal Mine and the comprehensive formation parameters of the regional borehole, the fractured model and the unfractured model were constructed using the PFC^2D numerical simulation software for the numerical simulation of coal seam caving. The main difference between the two models is that the fractured model contains 12 prefabricated fractures in the key stratum to simulate the main fractures generated by segmented fracturing. The fracture interval is set based on the on-site segmented fracturing spacing. The size of the model is 500 m L $\times$ 890 m W, the minimum particle size is 1 m and the porosity is 0.18. There are a total of 15 layers in the model, and the 4th coal seam with the thickness of 5 m is the caving coal seam. The thickness of the key stratum is determined to be 30 m based on the average vertical influence range of fracturing obtained by on-site microseismic monitoring. The macroscopic mechanical parameters of the rock and soil layers of the model were measured on-site, and the microscopic mechanical parameters were inverted using the empirical formula³⁹. The microscopic parameter inversion adopts a three-stage calibration method: (1) Laboratory tests: Field cores were collected to fabricate standard specimens ($\varphi$50 $\times$ 100 mm), and unconfined/triaxial compression tests were conducted to obtain macroscopic mechanical parameters; (2) Preliminary calibration: Based on the Parallel Bond Model (PBM), the trial-and-error method was used to align the trend of the numerically simulated stress–strain curves with that of the experimental results; (3) Refined optimization: The response surface methodology (RSM) was employed to optimize combinations of microscopic parameters, ensuring the peak strength error < 5% and elastic modulus error < 3%. The results are shown in Table 1.

Table 1 Mechanical parameters of simulated stratum.

To evaluate the error of the two-dimensional (2D) simulation, a simplified three-dimensional (3D) verification model (dimensions: 50 $\times$ 50 $\times$ 50 m) was established. The comparison results show that the 2D model has an error of 18.3% in predicting the number of fractures, while its consistency with the 3D model in terms of fracture propagation trends reaches 92%. The main error stems from the simplification of lateral constraints, and future work will involve adopting true 3D simulations for further optimization.

Figure 5 shows the schematic diagram of the simulation models. The total stoping length is determined based on the length of the on-site hydraulic fracturing test to be 300 m for both models, which is achieved by 6 stopings, with each of 50 m. The main fractures of hydraulic fracturing are 2 cm wide, and the spacing between fractures is determined to be 25 m based on the on-site fracturing interval. Six measurement points are arranged in the key stratum to monitor its displacement, and three measurement points are arranged at the coal seam to monitor the changes in the abutment pressure of working face. The distances between the measurement points are 60 m for both sets (D1–D6 monitor key stratum displacement; S1–S3 monitor working face vertical stress).

Fig. 5

Schematic diagram of simulation models.

Numerical simulation results

Characteristics of fracture development in stope

Figure 6 illustrates the fracture development of two models at different caving distances. For the first 100 m, their fracture development is similar, both progressing from bottom to top. As caving advances, differences emerge: the fractured model (with hydraulic fracturing-induced main fractures) penetrates the key stratum at 150 m, while the unfractured model only fully penetrates it at 250 m. The unfractured model shows an obvious plateau effect, with key stratum fracturing lagging about 100 m and forming a large overhanging structure. Fracture development height above the key stratum also differs significantly-Fig. 6f shows the fractured model has a much more affected upper stratum, with a moving segment  230% larger than the unfractured model.

Fig. 6

Schematic diagram for the fracture development characteristics in the two the unfractured and fractured models at different caving distances.

In addition to the number of fractures, the uniformity index of the spatial distribution of fractures is calculated:

$$\begin{aligned} U_f = 1 - \frac{\sum _{i=1}^{n} \left| N_{f,i} - \overline{N_f} \right| }{2n\overline{N}_f} \end{aligned}$$

(18)

Herein, $N_{f,i}$ is the number of fractures in the i-th statistical unit, and $\overline{N_f}$ is the mean value. For the fractured model, $U_f=0.82$, which is significantly higher than that of the un-fractured model (0.61).

Caving completion: Hydraulic fracturing-induced main fractures facilitate fracture network formation in the key stratum and surrounding rocks, accelerate propagation, and enhance fracture development in the stope’s overlying stratum. The fractured model’s fracture development height is  112 m (31 m higher than the unfractured model). Figure 7 compares simulated fracture counts at different caving distances: totals are similar within 50–100 m, but differences grow with caving advance-final fracture count of the fractured model is 2.26 times that of the unfractured model.

Fig. 7

Comparison of the numbers of fractures developed in the unfractured and fractured models at different caving distances.

To objectively evaluate the fracture development degree, the fracture density index is defined as $D_f = N_f / V_f$, where $N_f$ is the number of fractures and $V_f$ is the statistical volume. The calculation results show that the final fracture density of the fractured model is 3.26 fractures/m$\vphantom{0}^{3}$, which is significantly higher than that of the un-fractured model (1.44 fractures/m$\vphantom{0}^{3}$).

Comparison of fracture development in the two models shows hydraulic fracturing boosts stope fracture development without forming large overhanging roofs. Energy from the key stratum’s initial fracture converts into gravitational potential energy of rotation, slipping and subsidence.

Lateral abutment pressure characteristics of working face

Figure 8 compares lateral abutment pressures at each stress measurement point of the two models under different caving distances. The pressures show similar evolution trends, but the fractured model has smaller or equal initial abutment pressure that decreases earlier. This is due to local fracturing in the key stratum, which releases accumulated elastic energy and reduces abutment pressure. Additionally, the fractured model features faster, more extensive fracture development and quicker key stratum breaking/subidence, driving the working face’s abutment pressure to equilibrium sooner. Each of the three measurement points experiences two stress concentration and release events: the first is speculated to result from fractures reaching the key stratum (reducing collapse stress), and the second from fractures extending to the upper stratum (causing its fracture). To verify the optimal fracturing position obtained from theoretical calculations (31.2 m from the return air roadway), three control groups were set in the simulation: Position A (25 m), Position B (31 m), and Position C (40 m). The results show that Position B exhibits the maximum reduction in abutment pressure (17.6%), with a deviation of only 1.3% from the theoretical prediction.

Fig. 8

Comparison of the abutment pressures at each stress measurement point of the two models at different caving distances.

Figure 9 compares the peak abutment pressures at each measurement point. The fractured model’s peak pressure is lower than the unfractured model’s at corresponding points: maximum reduction is 6.41 MPa ($\approx$ 17.6%), average reduction 4.12 MPa ($\approx$ 13.7%). Hydraulic fracturing-induced main fractures damage the key stratum’s integrity, reduce the overlying stratum’s overhang area above the coal seam, and avoid large-area hard roof overhang, thus lowering the fractured model’s working face abutment pressure.

Fig. 9

Comparison of peak abutment pressures at each measurement point.

Collapse displacement characteristics of key stratum

As shown in Fig. 10, the unfractured model exhibits key characteristics at different caving distances: no fractures penetrate the key stratum and no key stratum displacement is detected at 100 m; slight subsidence initiates at 150 m with a maximum displacement of approximately 0.19 m; the key stratum’s collapse range expands and the maximum displacement increases to approximately 1.96 m at 200 m; further subsidence occurs at 300 m, with the maximum subsidence reaching approximately 3.71 m.

Compared to the unfractured model, the fractured model exhibits earlier key stratum displacement and more significant subsidence. The key stratum begins to subside at a caving distance of 50 m, approximately 50 m earlier than that in the unfractured model. Under the influence of hydraulic fracturing-induced main fractures, the entire key stratum slips, with the displacement of measurement point D2 reaching 0.71 m at 150 m of caving. As caving advances to 200 m, the segments monitored by D2 and D3 subside further, with their displacements increasing to 2.06 m and 2.22 m respectively. When caving reaches 300 m, the entire key stratum starts to move and the already subsided segments collapse, with the maximum displacement of 4.97 m observed at measurement point D3.

Fig. 10

Comparison of stratum collapse displacements at different measurement points in the unfractured and fractured points.

Comparison of key stratum collapse displacements between the two models shows that hydraulic fracturing alters the key stratum’s movement mode to overall rotation, slipping and subsidence, with energy release shifting to gravitational potential energy. The fractured model’s key stratum subsides nearly 50 m earlier and exhibits greater displacement at the same caving distance.

Field application

Hydraulic fracturing construction plan

Based on the fracturing range defined in “Determination of hydraulic fracturing location under goaf-adjacent conditions” section and considering the actual site conditions, the fracturing zone was determined as an area of 1034 m $\times$ 1334 m in front of the open-off cut of the 3407 working face Fig. 11. Hydraulic fracturing operations were controlled by constant pressure water injection, with the pressure maintained at 30 ± 2 MPa and the flow rate controlled within the range of 50–60 L/min. Stage spacing was dynamically adjusted based on real-time microseismic monitoring to ensure sufficient fracture propagation without excessive interweaving.

Fig. 11

Schematic diagram of hydraulic fracturing operation.

Field hydraulic fracturing effect

Macroscopic characteristics of mining pressure on working face

Figure 12 presents pressure cloud maps of brackets in different mining areas. In the unfractured zone, pressure shows distinct periodic and continuous characteristics. In the fractured zone, pressure intensity drops sharply, periodicity vanishes, pressure intervals lengthen, and pressure duration shortens. Pressure fluctuations near the two roadways are smaller, mostly remaining at low to medium levels. A large high-pressure red area exists adjacent to the return air roadway in the unfractured zone, which reduces by over 80% when caving advances to the fractured zone. These results indicate that hydraulic fracturing damages the hard roof’s integrity and high strength, releases substantial accumulated elastic potential energy, and promotes timely roof collapse. This prevents large-area overhang formation, reduces stress and energy concentration from continuous pressure, weakens stress transmission from the goaf, lowers bracket pressures in the two roadways, and improves their safety during mining.

Fig. 12

Cloud map of pressures on the brackets in different caving zones.

Spatiotemporal evolution characteristics of microseismic events in different caving zones

• (1) Migration characteristics of microseismic events

Microseismic events within a 200 m radius (100 m each in the fractured and unfractured zones) were selected, and their spatiotemporal evolution is shown in Fig. 13. Dots of different colors represent different energy levels: green (0–102 j), blue (102–103 j), and yellow (103–104 j).

In the unfractured zone, caving induced numerous microseismic events, mostly in front of the working face; in the fractured zone, fewer events occurred, mainly in the goaf. The distribution of microseismic events in different zones is consistent with the working face’s abutment pressure distribution. As caving advanced from the unfractured to the fractured zone, microseismic activity decreased significantly, and high-energy events continued to decline. In both zones, more microseismic events occurred on the return air roadway side than the transportation roadway side, with the number of total and high-energy events on both sides gradually decreasing after entering the fractured zone. Although the fractured zone still had more high-energy events near the return air roadway than the transportation roadway, the count was much lower than that in the unfractured zone.

The distribution of microseismic events and occurrence of high-energy events are closely related to roof treatment. Hydraulic fracturing fully fractures the working face’s overlying roof, prematurely releasing accumulated elastic energy, thereby reducing high-energy events and microseismic activity. It also weakens the roof connection between Working Faces 3407 and 3406, effectively alleviating stress concentration on the return air roadway side and reducing high-energy microseismic events.

Fig. 13

Distribution of microseismic events in different caving zones of the working face.

• (2) Microseismic energy and total frequency

The sliding window method (window width: 7 days, step size: 1 day) was used to process the microseismic data (As shown in Fig. 14). The daily average event frequency in the un-fractured area was 38 ± 6 events/day (mean ± standard deviation, n = 45 days), with an energy of 14,648 ± 2356 J; the corresponding values in the fractured area were 41 ± 5 events/day and 4326 ± 892 J. Statistical tests indicated a significant decrease in energy ($t=15.32$, $p<0.001$), and the total daily energy reaches the peak of 32,240 J as the working face advanced to 973 m. In the fractured zone, the average daily total frequency of microseismic events is 41, similar to that in the unfractured zone. However, the total daily energy is greatly reduced to the value of 4326 J, indicating that during fracturing, a large number of new fractures are formed, or the original fractures were connected in the stratum, and the accumulated elastic energy is released prematurely. In addition, segmented fracturing breaks the integrity and strength of the rigid roof, which prevents the accumulation of elastic energy over a large area and the sudden release of energy through rupture, and thus reduces the activity of microseismic events. With reference to the Coal Mine Safety Regulations, the microseismic energy is classified into three safety levels: $< 10^3$ J (safe zone), $10^3$–$10^4$ J (early warning zone), and $> 10^4$ J (dangerous zone). After hydraulic fracturing, the proportion of dangerous events decreased from 23.5 to 4.8%, and the safety level was upgraded by one grade.

Fig. 14

Daily total energy and total frequency of microseismic events.

Conclusions

Through integrated theoretical analysis, numerical simulation, and field validation, this study systematically reveals the energy evolution mechanism of hard roof adjacent to goaf after hydraulic fracturing. The principal findings are:

• (1) Energy conversion mechanism: Hydraulic fracturing transforms the movement pattern of key stratum from instantaneous fracture to segmented rotational subsidence. This converts accumulated elastic energy into gravitational potential energy, reducing the dynamic energy transmitted to the working face by 95% (from 702,663.2 to 35,133.16 J) and lowering additional disturbance stress by 80% (from 6.73 to 1.32 MPa).

• (2) Fracturing location optimization: Theoretical calculations determine the optimal fracturing position within 31.2 m from the return air roadway. Field verification confirms this location effectively blocks energy transmission from adjacent goaf while ensuring roadway stability.

• (3) Fracture development characteristics: Numerical simulation demonstrates that hydraulic fracturing significantly enhances fracture network density. The fractured model exhibits 2.26 times more fractures than the unfractured model, with fracture development height increased by 31 m (from 81 to 112 m).

• (4) Engineering application effects: Field monitoring shows hydraulic fracturing reduces bracket pressure intensity by over 80%, eliminates pressure periodicity, and decreases high-energy microseismic events ($\ge 10^3$ J) from 23.5 to 4.8%, significantly improving working face safety.

Despite the comprehensive findings, this study has several limitations:

• (1) Model dimensionality constraint: The PFC2D simulation, while effective for trend analysis, cannot fully capture three-dimensional stress distribution and fracture spatial characteristics. Complex geological structures such as faults and folds were simplified in the current model.

• (2) Parameter Assumptions: Certain empirical parameters (e.g., attenuation coefficient $\lambda =6$%) were derived from limited field data. The assumption of homogeneous rock properties may not fully represent actual geological heterogeneity.

Based on the current limitations, future studies should focus on:

Advanced numerical modeling: Develop true 3D simulation models incorporating anisotropic in-situ stress conditions. Utilize discrete fracture network (DFN) methods to better represent complex fracture systems.