⚡ electrical engineering

Numerical study on roadway stress control of surrounding rock through hydraulic fracturing-induced cracks in gob-side roof based on phase-field theory

This study employs a phase-field model to demonstrate that optimizing hydraulic fracturing parameters to maximize fracture network connectivity is crucial for effectively controlling roadway stress and mitigating stress concentration in gob-side coal mine roadways.

Original authors: Xin Yu, Huaidong Liu, Changyou Liu, Fengfeng Wu, Yiqi Chen, Zhenhua Chen, Haolie Li, Shibao Liu, Hanrui Zhang

Published 2026-08-18

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CC BY 4.0

Original authors: Xin Yu, Huaidong Liu, Changyou Liu, Fengfeng Wu, Yiqi Chen, Zhenhua Chen, Haolie Li, Shibao Liu, Hanrui Zhang

Original paper licensed under CC BY 4.0 (https://creativecommons.org/licenses/by/4.0/). ✨ This is an AI-generated explanation of the paper below. It is not written or endorsed by the authors. For technical accuracy, refer to the original paper. Read full disclaimer

Deep beneath the earth's surface, where coal is extracted to power cities, the rock surrounding the tunnels faces a constant, crushing squeeze. As miners remove a layer of coal, the weight of the mountains above shifts, concentrating immense pressure onto the narrow strips of rock left behind to support the tunnel roofs. This pressure causes the rock to deform, crack, and sometimes collapse, making the tunnels dangerous and difficult to maintain. To keep these pathways open, engineers have long used a technique called hydraulic fracturing. This involves pumping fluid into the rock to create cracks, which act like pressure valves, allowing the rock to relax and the stress to redistribute away from the tunnel. However, predicting exactly how these cracks will grow and how much they will relieve the pressure is incredibly difficult, especially in the complex, shifting environment of a mine.

A team of researchers from the China University of Mining and Technology has developed a new way to simulate this process with high precision. Instead of guessing where cracks might form, they built a sophisticated computer model that watches the rock break in real-time, step by step. Their work focuses on a specific and challenging scenario: the "gob-side" roadway, which is the tunnel running right next to the area where coal has already been removed. In this zone, the rock is subjected to a unique and violent mix of forces. The researchers used a method called phase-field theory, which treats the rock not as a solid block that suddenly snaps, but as a material that gradually weakens and breaks, allowing the computer to track the birth and growth of every tiny crack without needing to know exactly where the break will happen beforehand.

To test their model, the team recreated the conditions of the 15108 working face of a real coal mine, where the rock is buried about 400 meters deep. They simulated a scenario where the rock above the tunnel is thick and strong, prone to forming a heavy, wedge-shaped structure that hangs over the empty space and presses down on the tunnel. The researchers programmed their model to mimic a staged hydraulic fracturing process. This involves drilling a series of holes and injecting water in three separate stages, moving backward along the tunnel. The goal was to slice through the hanging rock on one side to let it fall safely, while simultaneously creating a network of cracks on the other side to soften the pressure on the tunnel walls.

The simulations revealed that the behavior of the cracks is a delicate dance between the natural pressure of the earth and the new cracks created by the water. When the pressure from the surrounding rock was moderate, the cracks tended to spread out horizontally, linking up to form a wide, interconnected web. This web successfully transferred the heavy load away from the tunnel, reducing the stress on the rock walls by nearly 20 percent. However, as the researchers increased the simulated pressure to more extreme levels, the cracks changed their behavior. Instead of spreading out, they began to shoot straight up and down. This vertical growth prevented the cracks from connecting with one another, leaving gaps where the high pressure could still build up. In these high-pressure conditions, the stress relief became much less effective, with the rock walls seeing only a tiny reduction in pressure.

The study also introduced a new way to measure the quality of the crack network. The researchers found that having a vast number of cracks or a very complex, tangled pattern did not necessarily mean better results. In fact, the most important factor was simply how well the cracks connected to each other. If the cracks formed a continuous path, the pressure could flow away easily. If they were isolated or blocked by the intense stress of the surrounding rock, the pressure relief failed. The team discovered that the best results came when the cracks formed a well-connected network under moderate stress conditions, rather than a chaotic mess under extreme stress.

By mapping out exactly how these cracks grow and interact, the researchers have provided a clear guide for engineers designing these safety measures. They showed that the success of hydraulic fracturing depends heavily on the specific stress conditions of the mine. If the pressure is too high, the cracks will not link up properly, and the technique will struggle to protect the tunnel. The findings suggest that engineers must carefully adjust their drilling angles and injection timing to encourage the formation of connected cracks, ensuring that the rock can safely release its built-up energy. This work offers a more reliable way to predict how the ground will behave, helping to make underground mining safer and more stable.

Technical Summary: Numerical Study on Roadway Stress Control via Hydraulic Fracturing in Gob-Side Roofs

Problem Statement
Coal mine gob-side roadways are subjected to severe deformation and support difficulties due to prolonged high-stress environments caused by lateral roof loading from adjacent panels and mining-induced disturbances. While hydraulic fracturing (HF) is a recognized active stress-relief technique, the coupling mechanism between fracture network evolution and surrounding rock stress relief remains unclear, particularly under the complex, heterogeneous, and asymmetric stress conditions of gob-side roadways. Existing numerical approaches often rely on predefined fracture geometries or weakened regions, which limits their ability to accurately capture the dynamic propagation behavior of hydraulic fractures and the resulting stress-relief mechanisms in such complex environments.

Methodology
This study develops a phase-field numerical model to simulate segmented roof hydraulic fracturing in gob-side roadways. The methodology integrates the following components:

Phase-Field Framework: A coupled poroelastic model is established where fracture interfaces are represented implicitly by a continuous phase-field variable ( $\phi$ ). This approach avoids explicit crack tracking, enabling the simulation of crack initiation, propagation, branching, and coalescence without mesh dependency. The model accounts for rock deformation, fracture damage, and fluid flow.
Stress Environment Implementation: To replicate the mining-induced stress redistribution of a gob-side roadway, a piecewise linear stress function is prescribed at the model boundaries. This function is derived from limit-equilibrium theory to reproduce the characteristic distribution of abutment pressure, including plastic and elastic zones adjacent to the goaf.
Simulation Setup: The study utilizes COMSOL Multiphysics to couple the Solid Mechanics, Darcy's Law, and phase-field modules. A case study is conducted on the 15108 working face, featuring a 15 m wide coal pillar and a 4.6 m thick coal seam. The simulation employs a segmented backward hydraulic fracturing scheme with dual boreholes (inclined at 60° and 75°) and three fracturing stages per borehole.
Quantitative Evaluation: Four quantitative indices are introduced to characterize the fracture networks and assess pressure-relief performance:
1. Fracturing Range ( $X_1$ ): The overall spatial extent of the fracture network.
2. Fracture Density ( $X_2$ ): The ratio of fractured cells to the total reference domain.
3. Fractal Dimension ( $X_3$ ): A measure of the network's geometric complexity.
4. Fracture Connectivity ( $X_4$ ): The horizontal distance between unconnected fracture tips from opposing boreholes.

Key Results
The numerical simulations reveal several critical findings regarding fracture evolution and stress control:

Fracture Propagation Mechanisms: Fracture propagation is jointly governed by the in-situ stress field, pre-existing fractures, and stress interference from adjacent boreholes. The first-stage fractures are primarily driven by the mining-induced stress field, while subsequent stages are dominated by interactions between neighboring fractures.
Stress Evolution: During the fracturing process, stress concentration initially increases on the roadway ribs (up to 30% in the third stage) before transforming into a large-scale low-stress zone upon fracture compaction. The final stress reduction on the roadway ribs reaches 19% and 34% respectively.
Impact of Stress Concentration Factor (SCF):
- Low SCF (1.2–1.4): Fractures propagate predominantly horizontally, forming a well-connected network that creates superimposed low-stress zones. While the average stress in the surrounding rock (RSR) shows reductions of approximately 20% in this range, the peak stress reduction in the coal pillar exhibits a different trend, reaching a minimum value of -0.5% at an SCF of 1.4.
- High SCF (≥1.5): Fracture propagation on the coal-pillar side shifts from horizontal to vertical. Strong inter-stage inhibition occurs, and third-stage fractures fail to connect. This leads to a deterioration in pressure-relief performance. Specifically, when the SCF equals 1.6, the pressure-relief effect is the poorest, with peak stress reductions on the two roadway ribs limited to 6.66% and 5.64%.
Correlation with Performance: A multivariate linear regression analysis ( $R^2 = 0.976$ ) establishes that fracture range, density, and fractal dimension are negatively correlated with stress reduction effectiveness. Conversely, fracture connectivity shows a positive correlation. This indicates that a highly complex network does not guarantee better performance; rather, a well-connected network is essential for effective stress relief.

Significance and Claims
The paper claims to provide a robust numerical framework for investigating hydraulic-fracturing pressure relief under complex mining conditions. By incorporating a boundary stress function and utilizing the phase-field method, the study offers a more accurate representation of fracture evolution compared to methods requiring predefined geometries.

The primary significance lies in the establishment of a quantitative relationship between fracture network characteristics and stress-relief performance. The authors assert that these findings provide practical guidance for hydraulic fracturing design, suggesting that engineers should prioritize the formation of well-connected fracture networks under site-specific stress conditions. Specifically, the study advises adjusting process parameters (such as borehole orientation, duration, and spacing) to maximize connectivity and avoid the negative effects of high stress concentrations that inhibit fracture coalescence. The work aims to improve the stability of gob-side roadways by optimizing the stress environment of the surrounding rock through targeted hydraulic fracturing.

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