Stability of surrounding rock in roadways with fractured rock mass: mechanisms and effects of layout optimization

Abstract

The stability of surrounding rock in coal mine roadways remains a fundamental concern in underground engineering. Rational roadway layout is essential to prevent strength degradation from fracture coalescence and reduce instability risks. Laboratory tests on single-fracture rock specimens, integrated with UDEC Voronoi-based numerical simulations, were conducted to quantify the effects of fracture inclination and confining pressure on crack propagation and failure mechanisms. Validated numerical models of closely spaced roadways were further used to analyze the relationships among the plastic zone, fracture evolution, and roadway spacing. Results indicate that fracture propagation at 30°-60° inclinations is strongly controlled by pre-existing fracture orientation, with crack initiation angles decreasing from 95° to 70° as inclination increases. Higher confining pressures localize crack growth near closed fractures, forming a distinct V-shaped strength distribution. Maintaining roadway spacing greater than five times the roadway radius effectively enhances stability. Elevated in-situ and mining-induced stresses are identified as the main drivers of fracture propagation and plastic zone deepening in the surrounding rock. These findings provide a scientific basis for optimizing roadway layout and assessing stability in coal mines and similar underground engineering environments.

Introduction

Against the backdrop of China’s rapidly advancing economic development, the pace of engineering construction ranks among the fastest in the world. As the primary load-bearing medium in underground projects such as mines and tunnels, rock mass plays a decisive role in the stability of geotechnical engineering^1,2,3. The presence of weak structural planes, such as joints and fractures, significantly influences rock stability, particularly under the combined effects of mining-induced stress, tectonic stress, and engineering disturbances, which can promote the propagation and interconnection of these discontinuities. In coal mining operations, the rational layout of roadways is particularly critical, as it directly affects production efficiency, personnel safety, and spatial stability of the mine^4,5,6,7,8. As a key design parameter, roadway spacing not only governs the distribution of fractures and stress in the surrounding rock but also determines excavation workload, service life, and long-term maintenance costs. Therefore, a scientific analysis of the fracture evolution patterns in surrounding rock is essential for safe and efficient roadway design in coal mines^9,10,11.

In recent years, extensive scientific investigations have been conducted to explore the fracture propagation, evolution, and mechanical properties of rock masses in underground engineering. Wang et al.¹² using the discrete element method combined with in-situ engineering tests, elucidated the mechanism of asymmetric large deformation in coal mine roadways excavated within gently dipping fractured rock masses. The findings indicate that elevated concentrations of maximum principal stress drive the initiation, progressive propagation, and eventual coalescence of shear fractures. When the stress concentration exceeds the load-bearing capacity of the surrounding rock, stress release zones emerge in the shallow rock and gradually extend deeper. Yu et al.¹³ observed that, subsequent to roadway excavation, the surrounding rock surface along the σ₃ direction exhibits a pronounced tendency toward instability and failure, where the initiation of cracking is predominantly governed by inherent weak structural planes in combination with excavation-induced stress redistribution. Huang et al.¹⁴ utilized 3D-printed rock specimens with different excavation geometries to demonstrate that horseshoe-shaped roadways possess superior load-bearing capacity, where pronounced fluctuations in shear strain and strain rate during loading mark the initiation of cracks and act as early indicators of impending rock failure. He et al.¹⁵ employed a digital panoramic borehole imaging system for extended field monitoring of roadway excavation, facilitating high-resolution visualization and accurate quantification of the spatiotemporal evolution of macroscopic fracture morphology and associated parameters within the surrounding rock mass. Li et al.¹⁶ conducted an in-depth investigation using physical similarity modeling combined with PFC^2D simulations to examine the entire failure process of semi-arched roadway sections in fractured rock masses, highlighting dominant failure modes involving roof crack coalescence and collapse, accompanied by tensile cracking along the sidewalls. Cheng et al.¹⁷ developed a DFN-DEM numerical model based on the discrete element method to analyze the mechanical behavior of fractured rock masses with varying sizes and rotation angles. Their findings reveal that rotation angles of 30° and − 60° enhance roadway stability, whereas shear-slip failure along joints represents the primary mechanism driving rock mass instability. The strength exhibits a nonlinear trend, decreasing as the dip angle rises from 0° to 45°, reaching a minimum, and subsequently increasing as the dip angle continues to grow from 45° to 90°. Hu et al.¹⁸ characterized joint density through the fracture fractal dimension and revealed a negative correlation between the density of intermittent fractures and the load-bearing capacity of the surrounding rock, underscoring that fracture density and its spatial distribution are critical determinants of roadway failure behavior. Xu et al.¹⁹ employed PFC simulations to investigate the fracture evolution of roadway surrounding rock, elucidating the coupled interaction between roof fracture propagation and stress release throughout the retreat mining process. Zhou et al.²⁰ used PFC^3D to investigate the key factors influencing the mechanical behavior of fractured rock masses, emphasizing that lithology and the degree of fracture propagation are the predominant controls on rock strength. Sun et al.²¹ analyzed the evolution of roadway roof fractures to determine optimal breaking positions and roof geometries under varying cutting angles, thereby achieving a reduction in roadway deformation. These findings, together with related studies, collectively indicate that fracture propagation and evolution processes, coupled with strength degradation mechanisms, are the primary factors governing rock mass instability. In underground engineering, the fracture development and failure behavior of surrounding rock are more appropriately investigated using discrete element–based numerical approaches. This characteristic enables effective simulation of jointed or highly fractured surrounding rock conditions in underground roadways, allowing systematic analysis of tensile and shear fracture development as well as the expansion and coalescence of fracture networks. Furthermore, DEM provides a robust framework for linking meso-scale fracture structure evolution with macro-scale mechanical strength degradation. Ultimately, this approach offers critical insights into the complex problem of controlling the extent of plastic zones in surrounding rock of coal mine roadways.

The stability of surrounding rock in underground roadway engineering has long been a critical focus of geotechnical research. Within complex and interconnected roadway networks, the rational design and layout of roadways serve as essential prerequisites for mitigating large-scale deformation and subsequent instability, thereby motivating extensive and in-depth studies by numerous researchers. Dong et al.²² integrated analytical methods, parameter reduction techniques, and the equivalent rock mass approach to investigate the distribution of plastic zones in roadway surrounding rocks under different GSI values and burial depths. This analytical framework enables rapid and accurate estimation of plastic zone volumes, thereby providing a robust basis for evaluating the stability of fractured rock masses surrounding roadways. Wang et al.²³ employed elastoplastic theory and yield strength criteria to establish a comprehensive damage zoning model for surrounding rock. Stress-strain, displacement, and radius relationships for the crushed failure zone, plastic softening zone, plastic fracture zone, and elastic deformation zone were rigorously derived, offering a robust quantitative framework for characterizing the progressive failure mechanisms of surrounding rock. Shan et al.²⁴ determined the optimal placement of gas drainage roadways during construction through an analysis of stress deviation distribution. The reliability of these selected roadway locations was subsequently validated by assessing the variations in surrounding rock stress deviation observed during the extraction of underlying coal seams. Wang et al.²⁵ leveraged in situ monitoring data to delineate optimal layout ranges for retreat mining roadways across varying inter-seam distances. This approach effectively mitigates the risk of surrounding rock damage by avoiding zones of elevated stress concentration. W. Wang et al.²⁶ introduced a lining support approach based on the CGP-FDEM algorithm, employing deformation and fracturing characteristics of the surrounding rock as critical indicators of roadway failure. The study demonstrated that the application of lining support in confined roadway environments exacerbates rock mass compression, inducing pronounced cracking and fragmentation, with the ultimate surface failure characterized by a combination of tensile and tensile-shear fractures. Niu et al.²⁷ performed a parametric investigation of a proposed FDM-DFN coupled numerical model, revealing that fracture density exerts a substantial influence on the deformation and failure behavior of roadway rock masses, thereby establishing fracture density as a critical parameter newly incorporated into the model. Gao et al.²⁸carried out uniaxial compression tests on physical similarity models of roadways with varying spatial configurations, revealing that doubling the horizontal spacing between two roof roadways enhances their load-bearing capacity by about 25%. Xiao et al²⁹. employed a Monte Carlo model to generate a variety of crack configurations on a two-dimensional plane and investigated the influence of crack orientation, length, and spacing on the deformation behavior of the surrounding rock. The findings indicate that, although roadway geometry has a negligible effect on the distribution of principal stress differences, the equivalent excavation radius plays a dominant role in determining the extent and spatial configuration of the plastic zone within the surrounding rock. Wang et al.³⁰ examined the influence of fault dip angles and cavity geometries on the mechanical response of dual roadways. Their results demonstrate that, from the perspective of underground engineering, the stability of surrounding rock fundamentally depends on pre-existing discontinuities and the development of fractures induced by excavation and mining disturbances. The discrete element method (DEM) provides a more physically representative approach for investigating underground excavation problems. This approach encompasses, but is not limited to, excavation-induced fracture propagation, stress transfer between fractured zones, and the formation of failure-controlled loosened regions. It is well suited for analyzing the stability of fractured surrounding rock under complex in-situ stress conditions and excavation disturbances, and offers clear advantages in revealing the mechanical mechanisms governing roadway instability.

Building upon existing studies on the mechanical behavior of fractured rock masses and roadway stability, this study further advances the understanding of fracture evolution and spacing optimization in closely spaced coal mine roadways through a systematic multi-scale framework. Unlike previous research that primarily focused on either laboratory experiments or numerical simulations in isolation, this work first establishes a rigorously validated UDEC–Voronoi discrete element model by directly comparing uniaxial compression simulations of single-fracture rock specimens with corresponding physical experimental results. This validation enables a detailed investigation of fracture initiation, propagation, and coalescence mechanisms. In addition, by incorporating confining pressure into the numerical framework, the analysis of fracture evolution is extended to conditions representative of deep underground environments. The effects of varying confinement levels on fracture propagation patterns, strength characteristics, and fracture sensitivity to inclination angle are systematically examined. Finally, by integrating numerical results with field borehole imaging observations from closely spaced roadways, the study interprets fracture development and plastic zone evolution under realistic in-situ and mining-induced stress conditions. Through this integrated approach, the study provides a mechanism-based evaluation of roadway spacing effects and offers a quantitative basis for identifying a more stable spacing range in deep coal mine engineering.

Experimental and modeling methods

Preparation of fractured rock specimens

Utilizing natural rock with prefabricated fractures frequently induces secondary damage^31,32, thereby complicating and limiting the reliability of the preparation process. Therefore, physical modeling with similar materials was adopted. In accordance with the Standard for Test Methods of Engineering Rock Mass (GB/T50266-2013), the selected materials were required to exhibit mechanical properties closely matching those of the original rock. When cylindrical specimens could not be prepared, prismatic specimens were recommended, maintaining a height-to-width ratio between 2.0 and 2.5. In this experiment, standard sand was selected as the aggregate and 325-grade cement as the binder, with a water-to-cement-to-sand ratio of 1:5:10 to produce the concrete specimens. Plastic spacers of varying thicknesses were inserted during casting to produce specimens with controlled fractures. The fabricated specimens incorporated fractures at inclination angles of 0°, 15°, 30°, 45°, 60°, 75°, and 90°, with an aperture of 3.0 mm and overall dimensions of 50 mm × 100 mm × 20 mm (length × width × thickness).

An ultrasonic testing device was utilized, positioning the transmitting and receiving transducers at opposite ends of the specimen. Vaseline served as a coupling agent to facilitate effective acoustic transmission. The travel time of the ultrasonic wave through the specimen was measured, and the corresponding propagation velocity was subsequently determined using the following formula:

$$v=\frac{l}{t}$$

(1)

where v represents the propagation velocity of the ultrasonic wave within the specimen; l denotes the propagation path; t refers to the wave travel time.

To ensure the integrity and homogeneity of the specimens, aside from the prefabricated fractures, the samples were cured in a dry environment for 28 days and subsequently examined using a non-metallic ultrasonic nondestructive testing device. Each specimen was divided into three regions: upper, middle, and lower. The upper and lower regions remained intact, while the middle region contained the prefabricated fracture. Ultrasonic testing was performed four times for each region, and the average travel time was calculated. The wave velocity was then derived according to Eq. (1), with the ultrasonic testing results summarized in Table 1.

Fig. 1

Preparation of rock-like test samples for ultrasonic testing.

Table 1 The ultrasonic testing results of the experimental samples.

As illustrated in Fig. 1, ultrasonic testing of rock specimens with prefabricated fractures of varying apertures and inclination angles revealed that the wave velocity in the central fractured region was markedly lower than that in the upper and lower intact regions. Specifically, the velocities in the central fractured zones ranged from 2915.45 to 3184.71 m/s, whereas those in the intact rock mass was 3322.26 m/s. Although minor variations in homogeneity were observed among the specimens due to external influences during specimen preparation and curing, the ultrasonic testing results suggest that these differences were negligible, and the structural integrity of the non-fractured regions remained well preserved.

Establishment of numerical model for fractured rock masses

The Voronoi polygon model provides an accurate representation of the mesoscopic structure of rock, offering distinct advantages in replicating the damage processes observed in laboratory experiments^33,34. In this model, the rock mass is conceptualized as an assembly of discrete, deformable Voronoi polygon blocks, where internal joints naturally develop and promote crack initiation and separation during failure. The deformation response of the blocks is primarily controlled by the bulk modulus K and shear modulus G, while the mechanical behavior of the contact surfaces is regulated by the normal stiffness k_n and shear stiffness k_s. The strength properties of these interfaces are determined by the internal friction angle φ and cohesion C. The interactions between blocks can be classified into three fundamental types—tensile separation, compressive deformation, and shear slip—as illustrated in Fig. 2.

The k_n of the contact interfaces exerts a dominant influence on compressive failure. In this context, Δσn and Δun denote the stress and displacement increments perpendicular to the contact surfaces. Compressive deformation is primarily characterized by interlocking constraints between blocks, which progressively intensify until specimen failure occurs. The ultimate tensile strength σt of the contact surface dictates the tensile separation failure mechanism. Once the tensile stress between contact interfaces exceeds this critical threshold, tensile failure is initiated within the rock mass. Shear slip along the contact surfaces is triggered when the tangential stress surpasses the load-bearing capacity determined by the shear stiffness. As described in Eqs. (2)–(4), the tangential stress τ is primarily influenced by the internal friction angle φ and cohesion C, with shear failure initiating once this stress exceeds its critical threshold.

$$\Delta {\sigma _n}= - {k_n}\Delta {u_n}$$

(2)

$$\left| \tau \right| \leqslant C+{\sigma _n}\tan \varphi$$

(3)

$$\Delta \tau = - {k_s}\Delta {u_s}$$

(4)

where Δσ_n and Δu_n represent the stress and displacement increments perpendicular to the block contact surfaces; k_n and k_s denote the normal and shear stiffness of the contact surfaces; τ represents the tangential stress along the contact surfaces; φ is the internal friction angle; C is the cohesion.

Fig. 2

Model failure criteria and stress-displacement monitoring process.

The uniaxial compression numerical simulation was performed using a two-dimensional rock mass model measuring 50 mm × 100 mm. To construct the numerical model, the UDEC–Voronoi approach was applied to automatically generate tessellated polygonal blocks, whereby the specified domain was discretized into randomly distributed polygonal elements. During the Voronoi tessellation process, a fixed random number generator seed was imposed to ensure consistency of the numerical base models. An isotropic elastic constitutive model was assigned to the specimen blocks, while a Coulomb slip constitutive model was adopted for the contacts between polygonal blocks. Parameter calibration was performed based on laboratory mechanical tests on fractured rock specimens. The strength characteristics of the intact rock were first determined through uniaxial compression tests, followed by calibration of joint-related parameters using an iterative trial-and-error approach. During this process, numerical simulations were repeatedly conducted by adjusting joint stiffness, cohesion, and friction parameters, and the resulting peak strength and failure modes under different fracture inclination conditions were systematically compared with the laboratory test results. The parameter set that provided the best overall agreement in terms of mechanical response and fracture development characteristics was finally adopted, and the calibrated parameter values are listed in Table 2. A constant loading rate was maintained by simultaneously applying equal force and displacement to the top and bottom boundaries of the model, with the loading rate precisely controlled at 0.2 mm/min as specified in the simulation setup. As UDEC’s default monitoring commands are unable to directly capture stress-strain data during uniaxial compression, a customized monitoring loop was programmed using the built-in FISH language, as illustrated in Fig. 2. Similarly, the number of cracks generated in fractured rock masses under uniaxial compression can be continuously monitored, allowing the cumulative stress, strain, and crack count data to be simultaneously recorded and output for comprehensive analysis of fracture propagation, its evolutionary processes, and the corresponding strength characteristics of the rock mass. This model was employed to simulate uniaxial compression tests of rock masses subjected to varying fracture conditions.

Table 2 Mechanical parameters of fractured rock masses and contact surfaces.

Crack propagation and strength characteristics of fractured rock mass

Crack propagation of single fractured rock mass

Prior to the rock mechanics experiments, a baseline strength assessment was conducted on intact rock specimens, yielding a uniaxial compressive strength of 30.44 MPa. Due to variations in the duration of uniaxial compression for the fractured rock specimens, direct comparisons of crack propagation at equivalent time intervals could not be performed. This section provides a detailed analysis of the strength, propagation trajectories, and ultimate failure modes of single-fracture rock specimens.

Yang et al³⁵. performed uniaxial compression tests on brittle rocks containing a single fracture and, based on the geometric characteristics and propagation mechanisms of the cracks, classified them into nine distinct fracture types. Under axial loading conditions, the tips of prefabricated cracks in fractured rock masses tend to initiate both primary and secondary cracks as a result of tensile and shear mechanisms. Depending on their propagation patterns, these cracks are commonly classified into tensile wing cracks, shear cracks, and far-field cracks, among other types. As illustrated in the failure images of fractured rock specimens in Fig. 3, when the fracture inclination angles are 0° or 15°, the fractures are nearly perpendicular to the loading direction. Under these conditions, cracks initiate at the tips of the prefabricated fractures, generating tensile wing cracks at both ends. The initiation and propagation trajectories are oriented at approximately 90° to the fracture plane, with the final crack propagation direction becoming aligned with the loading axis. At an inclination angle of 30°, tensile wing cracks initiate at both ends of the prefabricated fracture. At the lower tip, the crack initiates almost perpendicular (90°) to the fracture plane, while at the upper tip, the initiation angle is approximately 70°. These cracks subsequently evolve into shear wing cracks that propagate predominantly parallel to the loading direction. At an inclination angle of 45°, tensile wing cracks develop at both tips of the prefabricated fracture, accompanied by secondary shear-sliding cracks forming parallel to the fracture plane. As loading progresses, the propagation of all cracks becomes approximately parallel to the loading direction, and the specimen ultimately fails due to the coalescence of the tensile wing cracks at the upper and lower tips. At an inclination angle of 60°, tensile wing cracks initiate at both tips of the prefabricated fracture. As the applied load increases, anti-tensile cracks emerge at the upper tip. The interaction and subsequent coalescence between the upper tensile wing cracks ultimately result in specimen failure. At an inclination angle of 75°, tensile wing cracks initiate at the upper tips of the prefabricated fracture, with initiation angles of approximately 30°. A shear crack parallel to the prefabricated fracture also develops at the upper tip. With increasing load, the upper tensile wing cracks, shear cracks, and anti-tensile cracks interact and coalesce, ultimately causing specimen failure. At an inclination angle of 90°, the prefabricated fracture is oriented parallel to the loading direction, leading to distinct compressive-shear failure. At the lower tip, secondary shear cracks propagate parallel to the prefabricated fracture, whereas at the upper tip, secondary cracks intersect the fracture plane at relatively shallow angles. Additional secondary cracks form within the intact regions, nearly parallel to the loading direction, and eventually coalesce with the primary fracture, culminating in specimen failure.

Fig. 3

Type of failure and crack propagation in single fissured rock mass.

As demonstrated by the UDEC-Voronoi numerical simulation results in Fig. 4, in rock specimens with a fracture inclination of 0°, crack initiation and propagation do not occur along the prefabricated fracture plane. Instead, internal cracks progressively evolve within the specimen under increasing uniaxial compression. The failure behavior is predominantly governed by shear-slip mechanisms, with tensile failure playing a secondary role. The experimentally measured strength is 28.12 MPa, closely matching the simulated strength of 27.95 MPa, corresponding to a relative error of just 0.6%. In specimens with a fracture inclination of 15°, crack initiation and propagation are closely associated with the prefabricated fracture. Downward-propagating cracks develop from the lower tip, while upward-propagating cracks originate from the upper tip. Throughout the loading process, shear-slip cracking predominates, resulting in a failure mode that remains primarily governed by shear mechanisms. The experimental strength is 25.64 MPa, while the simulated strength is 25.11 MPa, corresponding to a relative error of 2%. In specimens with a 30° fracture inclination, crack initiation and propagation are oriented nearly parallel to the axial loading direction, with cracks extending from both ends of the primary fracture toward their respective tips. The failure mechanism is dominated by shear failure. The experimentally measured strength is 23.81 MPa, closely matching the simulated strength of 24.11 MPa, corresponding to a relative error of 1.2%. In specimens with a fracture inclination of 45°, cracks primarily propagate along the axial direction. The initial phase of crack development is dominated by shear failure, but during the post-peak phase, tensile failure in the central region induces a rapid reduction in strength, leading to a coupled tensile-shear failure mode. The experimental strength is 21.44 MPa, closely matching the simulated strength of 21.66 MPa, with a relative error of 1%. In specimens with a 60° fracture inclination, crack initiation and propagation primarily follow the prefabricated fracture plane. The early stage of crack development is governed by shear failure, whereas tensile failure becomes the dominant mechanism during the post-peak phase. The experimental strength is 24.16 MPa, closely matching the simulated strength of 23.71 MPa, corresponding to a relative error of 1.8%. In specimens with a 75° fracture inclination, crack initiation and propagation predominantly follow the prefabricated fracture plane, with tensile failure serving as the principal failure mechanism. The experimental strength of 24.22 MPa closely matches the simulated strength of 24.07 MPa, corresponding to a relative error of 0.6%. In specimens with a 90° fracture inclination, crack initiation and propagation are absent at the tips of the prefabricated fracture. Instead, internal cracks progressively evolve with increasing uniaxial compression. The failure mechanism is predominantly governed by shear-slip behavior, with tensile failure acting as a secondary mode. The experimental strength is 27.21 MPa, closely matching the simulated strength of 27.25 MPa, corresponding to a relative error of 0.1%. According to Eqs. (5)–(8), a comparative analysis of the theoretical, experimental, and numerical simulation values of crack initiation angles for fractured rock masses at varying inclination angles is provided in Table 3.

Fig. 4

Numerical simulation and experimental results of compression failure characteristics of single fissured rock mass. (a) 0°, (b) 15°, (c) 30°, (d) 45°, (e) 60°, (f) 75°, (g) 90°.

$$\left\{ \begin{gathered} \sigma _{n} = \sigma _{1} \cos \alpha \hfill \\ \tau _{n} = \sigma _{1} \sin \alpha \hfill \\ \end{gathered} \right.$$

(5)

$$\left\{ \begin{gathered} K_{{\text{I}}} = \mathop {\lim }\limits_{{r \to 0}} \sqrt {\pi a} \sigma _{n} \cos \alpha \hfill \\ K_{{{\text{II}}}} = \mathop {\lim }\limits_{{r \to 0}} \sqrt {\pi a} \tau _{n} \cos \alpha \hfill \\ \end{gathered} \right.$$

(6)

$$\left\{ \begin{gathered} \sigma _{r} = \frac{{K_{{\text{I}}} }}{{2\sqrt {\pi a} }}(3 - \cos \theta )\cos \frac{\theta }{2} + \frac{{K_{{{\text{II}}}} }}{{2\sqrt {\pi a} }}(3\cos \theta - 1)\sin \frac{\theta }{2} \hfill \\ \sigma _{\theta } = \frac{{K_{{\text{I}}} }}{{2\sqrt {\pi a} }}(1 + \cos \theta )\cos \frac{\theta }{2} - \frac{{3K_{{{\text{II}}}} }}{{2\sqrt {\pi a} }}\sin \theta \cos \frac{\theta }{2} \hfill \\ \sigma _{{\theta r}} = \frac{{K_{{\text{I}}} }}{{2\sqrt {\pi a} }}\sin \theta \cos \frac{\theta }{2} + \frac{{K_{{{\text{II}}}} }}{{2\sqrt {\pi a} }}(3\cos \theta - 1)\cos \frac{\theta }{2} \hfill \\ \end{gathered} \right.$$

(7)

$$K_{{\text{I}}} \sin \theta + 3K_{{{\text{II}}}} (3\cos \theta - 1) = 0$$

(8)

where σ₁ represents the axial loading stress; σ_n and τ_n are the normal and shear stress components of the axial stress resolved along the fracture plane; α denotes the fracture inclination angle; σ_r is the radial normal stress; σ_θ is the circumferential normal stress; τ_θr is the shear stress in the polar coordinate system; r is the radial distance; θ is the angle between the radial line and the horizontal axis; K_I and K_II are the Mode I and Mode II stress intensity factors.

Table 3 Fracture initiation angle of rock mass with different fracture dip angle.

Crack propagation of single fracture rock mass under different confining pressures

Compression tests of single-fracture rock masses were simulated under confining pressures of 0, 5, 10, and 15 MPa to investigate the evolution of crack propagation and the corresponding strength characteristics of the rock mass under different confinement conditions. As summarized in Table 4, with increasing confining pressure, the crack propagation pattern transitions from extensive cracking throughout the rock mass under unconfined conditions at 0 MPa to localized tensile-shear damage concentrated near the fracture. The extent of the fracture propagation zone progressively decreases, with this trend being most pronounced in specimens exhibiting fracture inclinations between 30° and 60°. As illustrated in Fig. 5, the compressive strength of the rock specimens exhibits a steady increase with rising confining pressures. Across all confining pressure levels, the strength of specimens with varying fracture inclinations consistently follows a characteristic V-shaped distribution. In summary, with increasing confining pressure, the extent of micro-crack development within the rock mass decreases, damage becomes increasingly localized around closed fractures, the rock matrix becomes denser, and the failure mechanism transitions toward a more dominant compressive-shear mode.

Table 4 Crack propagation law of rock mass at different dip angles under different confining pressures.

Fig. 5

Strength distribution of rock mass with various dip angles under different confining pressures.

Observation and evaluation analysis of fractures in the surrounding rock of closely spaced roadways

Using the layout of a main roadway in a coal mine in Shandong as a case study, the initial roadway cross-section was designed to be 6× 4 m and situated within a siltstone stratum. The engineering evaluation aimed to determine the optimal roadway positions corresponding to horizontal offsets of 5 m, 10 m, and 15 m. Building on prior research, numerical simulations were conducted under surrounding rock stress conditions of 10 MPa, 20 MPa, and 30 MPa to assess roadway displacement and the extent of the fracture zone. The simulation outcomes were subsequently utilized to determine the most suitable layout configuration for the main roadway.

As shown in Fig. 6, an increase in surrounding rock stress leads to a progressive escalation in the peak deformation of the roadway surrounding rock, with corresponding displacement values of approximately 12 mm, 30 mm, and 50 mm. The maximum deformation consistently occurs at the roadway roof. When compared under the same graphical scale, it becomes evident that increasing the spacing between roadways leads to a modest reduction in deformation magnitude. As illustrated in Fig. 7, monitoring the central intersection point of the roadway indicates that each 10 MPa increase in surrounding rock stress results in an approximate doubling of the surrounding rock deformation. As illustrated in Fig. 8, the extent of the plastic zone and fracture propagation increases under high-stress conditions, primarily attributed to the limited intrinsic strength of the siltstone. At 10 MPa, the fracture zone within the surrounding rock ranges from 0.8 to 1.6 m; at 20 MPa, it expands to 2.0–2.6 m; and at 40 MPa, it further extends to 2.1–3.0 m. Furthermore, when the roadway spacing is increased to 15 m, the extent of the plastic zone becomes notably smaller. At surrounding rock stress levels of 20 MPa and 30 MPa, a reduction in roadway spacing to 5 m leads to the interconnection of fracture zones within the surrounding rock, substantially undermining the overall stability of the rock mass. Therefore, considering the safety of the surrounding rock, preliminary analysis indicates that a roadway spacing greater than 15 m yields a more stable configuration.

Fig. 6

Displacement of the roadway surrounding rock under different spacing and stress conditions. (a) 5 m, 10 MPa, (b) 10 m, 10 MPa, (c) 15 m, 10 MPa, (d) 5 m, 20 MPa, (e) 10 m, 20 MPa, (f) 15 m, 20 MPa, (g) 5 m, 30 MPa, (h) 10 m, 30 MPa, (i) 15 m, 30 MPa.

Fig. 7

Displacement of roadway surface under different spacing and stress environment.

Fig. 8

Distribution of plastic zone of roadway surrounding rock under different spacing and stress environment.

Using the − 750 m level main roadway of a coal mine as a case study, the horizontal spacing between the return air, rail transport, and belt transport roadways ranges from 15 to 30 m, while in some sections an intermediate roadway is positioned with a spacing of less than 15 m. Throughout its service period, the roadway system has been significantly affected by adjacent roadway excavation and coal face retreat, with deformation of the surrounding rock progressively intensifying, particularly during the retreat operations of working faces on both flanks. On-site borehole imaging was conducted to delineate the current distribution characteristics of fracture zones in the surrounding rock of the roadway network. The main monitoring points are arranged as illustrated in Fig. 9.

Fig. 9

Locations of the main monitoring points.

Figure 10 presents the borehole imaging results obtained from the three designated roof observation points. As illustrated in Fig. 10(a), the central section of the belt transport roadway roof exhibits pronounced fracturing within the 0–0.5 m depth range. Evidence of delamination is observed between 1.9 m and 2.3 m, longitudinal fractures are present between 3.0 m and 3.4 m, and annular fractures are detected between 5.8 m and 6.3 m. The surrounding rock beyond these depths remains largely intact. As illustrated in Fig. 10(b), the roof surrounding rock of the return air roadway exhibits noticeable fracturing within the 0–0.5 m depth range. Between 1.3 m and 1.8 m, partial delamination accompanied by well-developed fractures is observed, while minor longitudinal fractures are detected at approximately 6.5 m. The surrounding rock beyond these zones retains good structural integrity. As illustrated in Fig. 10(c), the roof surrounding rock of the rail transport roadway exhibits significant fracturing within the 0–0.3 m depth range. Annular fractures are distinctly observed between depths of 1.0 m and 2.0 m, along with a few minor fractures at depths of 3.1 m to 3.5 m. The rock mass beyond these depths maintains relatively good integrity.

Fig. 10

Borehole imaging results of cracks in surrounding rock of roadway. (a) Belt haulage roadway, (monitoring point 1), (b) Return airway, (monitoring point 2), (c) Rail haulage roadway, (monitoring point 3).

Discussion

Application of the discrete element method in analyzing the mechanical behavior of fractured surrounding rock in coal mine roadways

As coal resource extraction intensifies and underground space development advances, deep rock engineering faces increasingly complex geological conditions, in which the mechanical behavior of fractured rock masses exerts a pivotal influence on the stability of the surrounding rock. Fractured rock masses, comprising intact rock interwoven with pre-existing fractures, exhibit significant heterogeneity and complex mechanical behaviors, shaped by site-specific environmental factors and the nature and magnitude of external disturbances. Through an integrated approach of physical experimentation and numerical simulation, this study elucidates the failure mechanisms and crack propagation behaviors of fractured surrounding rock in coal mine roadways subjected to varying fracture inclinations and confining pressure conditions. Utilizing a discretized Voronoi model, this study establishes a robust integration between experimental and numerical scales, enabling the identification of a V-shaped distribution in strength responses across different fracture inclinations and providing a quantitative assessment of variations in mechanical strength and fracture propagation density under diverse confining pressure conditions. Although this methodology provides a coherent analytical framework and effectively elucidates the fundamental strength degradation mechanisms of fractured rock masses, it remains limited in its ability to capture the impact of large-scale, spatially discrete distributions of primary and secondary fractures on the load-bearing performance of surrounding rock at the roadway scale. It should be noted that the UDEC–Voronoi simulations adopted in this study are inherently two-dimensional and therefore represent a simplified approximation of the intrinsically three-dimensional fracture processes occurring in underground rock masses. The crack propagation and deformation characteristics obtained from the numerical models should be interpreted as dominant in-plane fracture evolution mechanisms, rather than as direct three-dimensional predictions of fracture geometry or stress interactions. Consequently, this study extends its application to the engineering context of closely spaced roadway layouts, leveraging comparisons between roadway-scale numerical simulations of deformation and plastic zone distribution and field borehole imaging to provide meaningful insights for optimizing roadway spacing. Looking forward, the integration of advanced numerical modeling techniques and more sophisticated constitutive models will enable higher accuracy and efficiency in analyzing complex engineering scenarios, thereby enhancing the robustness and reliability of engineering assessments and validations.

Relationship between optimal roadway spacing and the fracture-plastic zone

The configuration of closely spaced roadways in coal mines constitutes a pivotal technical challenge in deep mining operations, efficient coal recovery, and the implementation of reliable ground support systems. This study focuses on the spacing design of major roadways in coal mines, offering insights that are equally applicable to optimizing the spacing of retreat roadways. In this engineering case, the plastic zone surrounding the return air and rail transport roadways is slightly narrower than that observed in the belt transport roadway. This discrepancy arises because roadway deformation is governed not only by factors such as burial depth, cross-sectional geometry, and the degree of pre-existing fracture development but also by the pronounced effects of mining-induced stresses. Roadways situated closer to longwall retreat faces are particularly prone to significant expansion of the plastic zone. Borehole imaging of the main roadway roof reveals significant deterioration in the shallow rock mass, characterized by localized collapse, contraction deformation, and a dense network of fractures, while the deeper sections of the rock mass remain largely intact and structurally stable. Disturbances induced by longwall retreat operations lead to circumferential cracking within the 4–6 m depth range, extending well beyond the plastic zone and the damage extent anticipated under uniform stress conditions. The progressive increase in the number and density of fractures extending into deeper rock layers not only advances the understanding of stress concentration and crack propagation mechanisms but also provides critical guidance for developing effective field support strategies. These methods include employing rock bolts, cables, and grouting to stabilize deep-seated fractured rock masses and improve their structural integrity. Reinforcement achieved through high-prestress crack arrest and grouting consolidation restores the load-bearing performance of the rock-support system, providing effective resistance to large-scale deformation of the surrounding rock over extended periods. Therefore, from the perspective of roadway spacing, a reduction in the distance between adjacent roadways leads to localized stress superposition, which promotes fracture coalescence within the surrounding rock. Under such conditions, fracture propagation tends to evolve from localized cracking into interconnected fracture networks, thereby increasing the extent of the plastic zone and the associated instability risk. In contrast, larger roadway spacing effectively weakens stress-induced fracture development between adjacent excavation zones, resulting in more localized surface cracking and relatively independent deformation of the surrounding rock. An appropriate roadway spacing should therefore be determined by jointly considering the extent of the plastic zone and engineering economic factors, in order to enhance the long-term stability of roadway surrounding rock.

Conclusion

• 1. The uniaxial compression simulations of single-fracture rock masses, conducted using the UDEC Voronoi model, were rigorously validated against physical experimental data, exhibiting strong concordance and reinforcing the model’s robustness in capturing the mechanical behavior of fractured rock masses. Fracture propagation and coalescence were strongly influenced by the orientation of pre-existing fractures at inclination angles of 30°−60°, and the crack initiation angle, which ranged from 70° to 95°, decreased and aligned more closely with the pre-existing fracture direction as the inclination angle increased.

• 2. Confining pressure applied during the compression process enabled the analysis of crack propagation patterns in fractured rock masses under varying pressure gradients. As confinement increased, the extent of crack propagation diminished, concentrating near closed fractures, while the formation of tensile microcracks became more pronounced. Fractures with inclinations of 30°−60° exhibited a stronger dependence on confining pressure, and the overall strength distribution demonstrated a characteristic V-shaped pattern.

• 3. By integrating numerical simulations with field borehole imaging, this study investigates the fracture distribution characteristics of surrounding rock in closely spaced roadways. From a roadway stability perspective, preliminary findings indicate that a spacing exceeding five times the roadway radius offers more favorable stability conditions. Elevated in-situ stresses, coupled with mining-induced stresses, are identified as the dominant factors driving fracture propagation and the progressive deepening of the plastic zone within the surrounding rock mass.