Study on roof partition fracture based on dominant primary fracture

Abstract

As the length of the open-off cut increases, the roof pressure in the advancing direction of the working face exhibits distinct zoning characteristics, with prolonged pressure duration and challenging predictability. Based on the influence of primary fractures on roof fracture morphology, the concepts of dominant incidence and dominant position of primary fractures are introduced. Dominant primary fractures are considered the main factor leading to zonal roof breakage, while non-dominant ones act as weakening factors. Under the effect of dominant primary fractures with specific occurrence conditions, zonal fracture patterns and criteria for the first roof weighting are established. The study reveals: (1) Multiple zonal fracture models involving primary fractures, such as “double O-X”, “X-Y”, “X-Y-Y”, “Y-X-Y”, “OX-OX”, and “three O-X”, are derived, along with their fracture propagation processes. (2) Using the “double O-X” model as an example, the influence of the roof’s length-span ratio and crack length on fracture toughness and stress intensity factor is analyzed, yielding influence coefficients for internal and external forces during roof bending. Criteria for crack initiation, propagation, and instability under dominant primary fractures are established based on bound theorems and fracture mechanics. (3) PFC3D simulations and three-dimensional physical modeling validate the theoretical fracture patterns, showing good agreement with numerical and experimental results. These findings help explain roof zonal fracture mechanisms and provide a basis for ground control and disaster prediction in super-long working faces.

Introduction

A number of high-intensity mining working faces that reflect China’s enhanced production capability have evolved in recent years as a result of advancements in mining equipment and management. These working faces often exhibit super-long working faces (working face length of more than 350 m), super-large mining heights (up to 9 m), and rapid mining speeds (daily propulsion greater than 15 m)^1,2,3. The frequency of surrounding rock disasters in the stope increases significantly as a result of high-intensity mining, and disaster prediction and control become increasingly challenging. The roof pressure exhibits distinct features from traditional mining, which is susceptible to the phenomena of partition breaking, particularly with the ongoing extension of the working face. The extended duration and high degree of unpredictability associated with this type of roof partition breakdown make prediction work extremely challenging.

One of the most significant topics in coal mining is the investigation of roof failure characteristics of super-long working faces. Numerous research have been conducted on various topics to fully comprehend the law of roof collapse and offer theoretical justification and useful advice for coal mine safety production. In the study of roof failure mode and mechanical mechanism: To address the issue of surface subsidence in western coal mines, researchers examined the control effect of key strata on surface subsidence, talked about the failure modes of main roofs of varying thicknesses using test devices they had designed themselves, and developed a theoretically based mechanical model to determine the critical conditions of fracture and the partition of failure modes⁴. Researchers have examined how roofs of varying thicknesses behave mechanically when subjected to uniform loads. The fracture mode and the development law of the maximum primary stress are determined using bonding element technology, and the method by which the thickness-span ratio of the roof influences the fracture mode is disclosed⁵. Researchers investigated the failure behavior of roofs with varying thicknesses by conducting loading tests on them using the self-created three-dimensional roof fracture experimental platform⁶. The roof’s progressive failure process is examined using the UDEC-Voronoi method, and the influencing factors and failure mechanisms are examined. The field measurement and the numerical modeling findings correspond well⁷. Researchers have developed a model for roof cracking and examined the variables influencing roof fracture and control strategies using field observations and tests⁸. Through numerical modeling and experimentation, researchers examine the propagation law of fracture morphology, identify the primary determinants of fracture parameters, and offer guidance for fracturing design⁹. Researchers created a mechanical model, examined the link between roof parameters and deformation, stress, and its impact on overburden pressure, and investigated the features of roof movement and instability against the background of shallow thin coal seam widening mining¹⁰. Researchers have developed a mechanical analysis model for super-long working faces based on hydraulic support and immediate roof bearing characteristics. They have also examined and validated the link between working face length, stability, and roof deflection¹¹. Through numerical modeling, researchers have demonstrated the impact of roof support distribution on long wall work stability and the relationship between rock mass strength characteristics and active roof support¹². To guarantee stability, researchers have examined the longwall top coal caving face’s supporting force, supporting stress, and roof failure characteristics. They have also proposed a pre-filling plan for abandoned roadways¹³.

The essence of roof failure lies in rock mechanics, and studying different types of rock failure mechanisms can contribute to understanding the fracture behavior of coal mine roof strata. Fu et al. conducted experimental and numerical investigations on the mechanical properties of rock specimens with varying notch sizes, analyzing acoustic emission characteristics and crack propagation patterns^14,15,16. Sarfarazi et al.^17,18,19 examined crack development features and shear failure mechanisms of brittle rocks under high-temperature conditions. The distribution of pre-existing fractures in intact rock formations is governed by geological structures and tectonic movements, resulting in a complex genesis that contributes to the highly intricate nature of roof failure mechanisms in coal mines^20,21,22. In conclusion, it is still challenging to create a universal roof fracture model that is comparable to the “O-X”. Thus, it is very important to categorize and investigate the features of initial fractures before elucidating the morphology of roof fractures under different primary fracture circumstances. The paper examines the dominant occurrence and dominant location of the primary fracture, simplifies the primary fracture reasonably, and thoroughly examines the morphology of roof fractures under various fracture environments. The goal is to uncover the roof fracture law of the super-long working face and achieve precise roof disaster prediction by offering crucial theoretical underpinnings and useful practical advice. This has significant theoretical and practical implications.

Dominant occurrence and location of primary fracture in main roof

The primary causes of rock breaking, structural instability of the main roof, and breaking structures are the major causes of mine pressure in the working face. These factors are also the main focus of mine pressure research in stope. Thus, the main aim of this research is to analyze how major fractures in the middle of a main roof affect roof breaking. Additionally, the overlaying rock strata may have one or more key strata that influence the mine pressure behavior of the working face to varying degrees. This research focuses on the main roof breaking in the near field, but the essential rock layer in the far field may also be studied using the same research methodology.

Dominant occurrence of primary fractures

The main roof’s strength, stress distribution properties, and caving morphology are all significantly impacted by the major and secondary fractures. The main fracture in this area is thought to be a naturally occurring fracture that was created before coal mining by tectonic activity, diagenesis, and stress fields. Only the principal fractures created by the action of the stress field are taken into consideration here to make the study easier. Tensile fractures are used to investigate the presence of primary fractures since the main roof is often brittle. Tensile fractures often form parallel to the direction of the highest primary stress, according to fracture mechanics. Without considering diagenesis and tectonism, the primary fracture in the roof has a dominant occurrence, that is, the direction of the maximum principal stress. When the main roof breaks for the first time, it is primarily caused by the primary cracks; the location and occurrence of the cracks will determine the initial breaking form of the main roof. At the same time, numerous field measurements also demonstrate that there are dominant occurrences of primary fractures. Figure 1 shows the measured occurrences of primary fractures in the Kouzidong Coal Mine. The data indicates that the initial fracture’s dip angle and propensity follow either a normal or skewed distribution. The primary fracture’s prominent occurrence in the site’s roof is confirmed by the mean value, which may be regarded as the primary fracture’s dominant occurrence.

Fig. 1

Measured occurrence of roof fractures in Kouzidong Coal Mine²³.

Dominant location of primary fracture

Further considering the position distribution of the main roof under the condition of the dominant occurrence of the primary fracture, assuming that the stress field is constant before the coal seam mining, the spatial position of the fracture should be subject to random distribution. However, due to the limited range of the main roof overhang, the fracture density distributed at different positions of the working face may be different. In the position where the number of fractures is concentrated, the deterioration of the roof strength is significant, and the area with the largest fracture density can be used as the dominant position. As shown in Fig. 2, the main roof rock is divided into 7 modules along the long side, in which the red dotted line is the primary fracture, and the number of fractures contained in each module is different. Let the density of the primary fracture in the module be ρ, the fracture density in the dominant development position is ρ’, then there are:

$$\rho^{\prime } = \rho_{\max } \left\{ {\rho_{a} ,\rho_{b} ,\rho_{c} ...\left. {\rho_{{\text{g}}} } \right\}} \right.$$

(1)

Fig. 2

Schematic diagram of the dominant position of primary fractures.

Study on the partition attribute of the primary fracture of main roof

The dominant primary fracture has a great influence on the roof fracture. Therefore, only the dominant primary fracture is considered when analyzing the boundary conditions. The dominant primary fracture divides the complete roof into several hinged thin plates. The thin plates can be simplified as simply supported edges, and the non-dominant primary fracture simplifies it as a deterioration factor for the roof strength^24,25,26,27.

Analysis of the first weighting of the main roof with one dominant primary fracture

The model depicted in Fig. 3a serves as the basis for the analysis conducted during the research on roof fracture morphology. The main dominant fracture is thought to occur at a 90° angle before the first mining face’s primary fracture, and its dominant location is in the center of the working face. This divides the roof into two plates with identical secondary fracture densities, with the center of the working face serving as the boundary. The fracture initially starts to spread in the middle of the roof when the first mining face is impacted by the initial pressure because of the primary dominant fracture there. The fracture expands to the long side and then stops as the expanding process continues. At this point, a thin plate structure with three clamped edges and one simply supported edge is produced, consisting of two thin plates with unique boundary conditions. Additionally, the two thin plates are attached and share a simply supported edge. Two thin plates, designated A and B, respectively, are assumed in this model. ρ_A = ρ_B indicates that the two thin plates have roughly identical strengths. The two thin plates exhibit identical fracture propagation and failure mechanism characteristics under these conditions. The two plates’ combined length is set to 2b, while their width is set to a. The thin plate theory states that fracture propagation follows a certain law for thin plate structures with three clamped edges and one simply supported edge. First, as seen in Fig. 3b, cracks will start to show on the fixed branch’s long side and spread out. Fractures will also appear in the middle of the fixed support’s short side due to the ongoing action of stress. As seen in Fig. 3c, these fractures keep growing and finally pierce, creating two thin plates with four edges that are simply supported. The fractures between the two thin plates that are only supported are still growing in the last stage. As time and tension build up, the fractures widen and eventually pierce all the way through, creating a “double O-X” breaking form. Figure 3d provides a good illustration of the particular procedure. The entire roof and fracture development process is illustrated in Fig. 3, which offers a clear foundation for understanding the roof’s fracture mechanism in certain scenarios.

Fig. 3

Schematic diagram of “double O-X” breaking fracture expansion.

However, the initiation and propagation of cracks should be used to evaluate the fracture morphology of the stope roof. The long side of the plate initially approaches the crack initiation condition as the roof stress increases, and the short side thereafter exhibits the crack initiation phenomena, which corresponds to the fracture initiation criteria. The cracks start to expand following crack initiation, which is in accordance with the fracture propagation criterion around the plate since the energy needed for expansion is less than the energy needed for crack initiation when the cracks are formed around the plate. Then, by the cracking criterion of the cracks between the plates, the center of the plate meets the cracking condition to form cracks. After the fractures between the plates develop, the crack propagation phenomenon happens instantly, which corresponds to the crack propagation criteria between the plates. When the crack widens and penetrates, the overlaying load of the roof exceeds its ultimate carrying capacity, and the roof is unstable, which matches the instability criterion. Since the two plates are identical, one of them is examined to investigate the conditions for the start, spread, and roof instability of the O-shaped and X-shaped plate fractures.

The stress component at the fracture end and the stress intensity factor K_I have a linear relationship, making K_I a physical quantity that may represent the stress intensity at the fracture end. The fracture spreads erratically when K_I reaches a crucial threshold K_IC. The K criteria is a result.

When the long edge of the fixed support cracks, the fracture toughness K_IC is determined using the rock fracture toughness test data provided by the International Society of Rock Mechanics Test Method Committee. After taking into account the plastic zone adjustment, the stress intensity factor K_I is expressed as follows:

$$K_{I} = \lambda \gamma \sigma_{1} \sqrt {\pi \left( {l + r_{\gamma } } \right)}$$

(2)

where σ₁ is the maximum principal stress at the end of the crack, γ is the geometric shape factor, r_γ is the half length of the plastic zone, l is the crack length, and λ is the compression-shear ratio coefficient in crack propagation.

The crack initiation criterion of the long side and short side in the roof O-shaped fractures can be solved as follows:

$$\left\{ \begin{gathered} K_{IL} = \lambda \gamma \sigma_{1} \sqrt {\pi \left( {l + r_{\gamma } } \right)} \ge K_{IC} \hfill \\ K_{IS} = \lambda \gamma \sigma_{1} \sqrt {\pi \left( {l + r_{\gamma } } \right)} \ge K_{IC} \hfill \\ \end{gathered} \right.$$

(3)

where K_IC is the fracture toughness when the crack initiates, K_IL and K_IS are the stress intensity factors of the long and short sides of the plate, respectively.

According to the theory of elasticity, it is known that:

$$\left\{ \begin{aligned} \sigma_{xx} = & - \frac{Ez}{{1 - \mu^{{2}} }}\left( {\frac{{\partial^{2} \omega }}{{\partial x^{2} }} + \mu \frac{{\partial^{2} \omega }}{{\partial y^{2} }}} \right) \\ \sigma_{yy} = & - \frac{Ez}{{1 - \mu^{{2}} }}\left( {\frac{{\partial^{2} \omega }}{{\partial y^{2} }} + \mu \frac{{\partial^{2} \omega }}{{\partial x^{2} }}} \right) \\ \tau_{xy} = & - \frac{Ez}{{1 + \mu }}\frac{{\partial^{2} \omega }}{\partial x\partial y} \\ \sigma_{1} = & \frac{{\sigma_{xx} + \sigma_{yy} }}{2} + \sqrt {\left( {\frac{{\sigma_{xx} - \sigma_{yy} }}{2}} \right)^{2} + \tau_{xy}^{2} } \\ \end{aligned} \right.$$

(4)

where E is the elastic modulus, and μ is the Poisson’s ratio, ω is the deflection.

To study the influence of length-span ratio n, fracture length l, and fracture position on the initial fracture characteristics of the “double O-X” model, the length-span ratio n is set as the ratio of length to width of the plate 2b/a, the elastic modulus E, thickness h, Poisson’s ratio μ and load q_r of the main roof are 35 GPa, 5 m, 0.33 and 0.2 MPa, respectively, the working face length 2b, span a, the compression-shear ratio coefficient λ of the rock and the geometric shape factor of the fracture end are 50 nm, 50 m, 2 and 5, respectively.

The correlation between fracture length, length-span ratio, and stress intensity component is depicted in Fig. 4. The graphic illustrates how the stress intensity factor progressively rises with fracture length. There is a threshold value for the length-span ratio, meaning that as the ratio grows, the stress intensity factor initially falls and then rises. The roof is difficult to shatter when the length-span ratio is 2, meaning that the stress intensity factor is lowest when both plates are square.

Fig. 4

Influencing factors of four-sided crack propagation stage.

Below is a study of the plate’s four sides’ expansion criteria. The plate’s four sides are reduced to four beams. Each beam’s fracture point is identified by taking a portion of it perpendicular to the plate’s edge. The fracture toughness K_IC of the plate’s four sides may be found using Eq. (5) if the microcrack tip is assumed to be a rectangular portion.

$$K_{IC} = \frac{{4q_{r} }}{{S_{W} }}l_{a}^{\frac{1}{2}} \times f\left( \alpha \right)$$

(5)

where l_a is the crack length, q_r is the overlying strata load of the roof, S_w is the cross-sectional area of the fracture end, α is the thickness-span ratio, and f(α) is the correction coefficient.

When 0 < α ≤ 0.6, according to ASTM-1972 specification²⁸, the effective value of f(α) is:

$$f\left( \alpha \right) = 2.9 - 4.6\alpha + 21.8\alpha^{2} - 37.6\alpha^{3} + 38.7\alpha^{4}$$

(6)

If the conditions in the specification are satisfied, the stress intensity factor is equal to the fracture toughness. The expansion criterion of the long and short edges of the O-shaped fracture is:

$$\left\{ \begin{gathered} K_{IL} \ge K_{IC} ^{\prime} = \frac{{4q_{r} }}{{S_{W} }}l_{a}^{\frac{1}{2}} \times f\left( \alpha \right) = \frac{{4q_{r} \left( {2.9 - 4.6\alpha + 21.8\alpha^{2} - 37.6\alpha^{3} + 38.7\alpha^{4} } \right)}}{{S_{W} }}l_{a}^{\frac{1}{2}} \hfill \\ K_{IS} \ge K_{IC} ^{\prime} = \frac{{4q_{r} }}{{S_{W} }}l_{a}^{\frac{1}{2}} \times f\left( \alpha \right) = \frac{{4q_{r} \left( {2.9 - 4.6\alpha + 21.8\alpha^{2} - 37.6\alpha^{3} + 38.7\alpha^{4} } \right)}}{{S_{W} }}l_{a}^{\frac{1}{2}} \hfill \\ \end{gathered} \right.$$

(7)

where K_IC’ is the fracture toughness of crack propagation.

The relationship between fracture toughness and length-span ratio and fracture length in the four-edge extension criterion is shown in Fig. 5. The fracture toughness decreases with the increase of length-span ratio n and increases with the increase of fracture length, but the sensitivity of length-span ratio to fracture toughness is higher, indicating that the length-span ratio plays a decisive role in K_IC′. When the length-span ratio is 2, the fracture toughness decreases sharply, indicating that the roof is not easy to crack propagation.

Fig. 5

Influencing factors of K_I and K_IC in the four-sided crack propagation stage.

Keep examining the X-shaped roof fractures crack start criteria. The failure phenomena brought on by the roof fracture start to move to the center of the plate once the long and short edges have been ruined. The four fixed borders of the rectangular roof become just supported boundaries as a result of the roof’s integrity being compromised. The final bending moment of the rock mass is less than the maximum bending moment between the plates as a result of mining. Cracks start to appear in the middle of the roof and spread out to both ends in an X pattern. For analytical purposes, the stress condition of the fracture end can also be reduced to a unit hexahedron. Under bending moment, the stress intensity factor is:

$$K_{MI} = \frac{{3MS_{W} \sigma_{x} }}{{2h^{2} }}\sqrt {\pi l}$$

(8)

To obtain the initiation criterion of the roof center, the roof center is simplified as a three-point bending beam model concerning “Rock and Concrete Fracture Mechanics”^29,30,31. According to the “Stress Intensity Factor Manual”^32,33,34,35 and the “double K criterion”^36,37,38, the crack initiation criterion of the roof center is obtained:

$$K_{MI} \ge K_{Ic}^{ini} { = }\frac{{3q_{r} b}}{{8h^{2} }}\sqrt l S_{W} \sigma_{x} \left( \frac{l}{2h} \right)$$

(9)

where $K_{Ic}^{ini}$ is the initiation toughness of the central crack of the plate.

When considering the crack propagation in the micro-fracture model, to facilitate the calculation, the model can be simplified into a beam. According to the three-point beam theory in “Rock and Concrete Fracture Mechanics”, the fracture toughness of O-shaped fracture propagation is obtained as follows:

$$K_{IC} = \frac{{4q_{r} }}{br\left( \theta \right)}\alpha^{\frac{1}{2}} \times f\left( \alpha \right) = \frac{{4q_{r} }}{br\left( \theta \right)}\alpha^{\frac{1}{2}} \times \left( {2.9 - 4.6\alpha + 21.8\alpha^{2} - 37.6\alpha^{3} + 38.7\alpha^{4} } \right)$$

(10)

Since the crack is mainly caused by tensile stress, the micro-crack model is established according to the maximum normal stress criterion. Substituting σ₁ into Eq. (2), the expansion criterion of X-crack between plates is obtained as follows:

$$K_{{{\text{I}} M}} \ge K_{IC} = \frac{{4q_{r} }}{{S_{W} }}\alpha^{\frac{1}{2}} \times f\left( \alpha \right) = \frac{{4q_{r} \left( {2.9 - 4.6\alpha + 21.8\alpha^{2} - 37.6\alpha^{3} + 38.7\alpha^{4} } \right)}}{br\left( \theta \right)}\alpha^{\frac{1}{2}}$$

(11)

where r(θ) is the size of the crack end area in the center of the plate.

Without considering the strain caused by it, the solution can be simplified to a plane strain problem for analysis, that is, the subsidence effect of the plastic zone can be ignored during the crack propagation process, and only the influence of the crack propagation direction and the load on the crack size is considered, to obtain the expression of the crack end size based on the micro-crack region model under the plane strain state, and the size of each crack end at different positions between the plates is obtained by substituting Eq. (11) into Eq. (12).

$$r\left( \theta \right) = \frac{1}{2\pi }\left( {\frac{{K_{IM} }}{{f_{1} }}} \right)^{2} \left[ {\cos \frac{\theta }{2}\left( {1 + \sin \frac{\theta }{2}} \right)} \right]^{2}$$

(12)

where f₁ is the tensile strength, θ is the angle between the crack and the horizontal direction of the neutral plane, which is obtained by the criterion given by the maximum normal stress.

The relationship between K_IC, K_IM, length-span ratio, and crack length l in X-shaped crack propagation is shown in Fig. 6. For X-shaped cracks, after the expansion of the transverse cracks from the middle, there will be a phenomenon of expansion along the four corners of the plate, that is, when the cracks expand to a certain length, K_IC/K_IM will suddenly increase/decrease, and K_IM will also decrease sharply when the length-span ratio is 2.

Fig. 6

Influencing of X-shaped crack expansion stage.

The ultimate bearing capacity of the roof is the ultimate load of the roof instability. Under the action of the overburden load and the self-weight of the main roof, several cracks are formed during the breaking process. The left side forms the plate A1A2A3A4, in which the cracks develop to form the triangular plate A1A4F_E1 and A₂A₃F_E2, and the middle of the working face forms the trapezoidal plate A1A2F_E2F_E1 and F_E1F_E2A₃A₄. For edges A₁A₂, A₁A₄, A₄A₃, and A₂A₃ are formed in the process of fracture propagation, and the sinking amount is 0 in the process from fixed support to simple support. It is assumed that the sinking amount of the fracture line F_E1F_E2 is Δ₁, the fracture line F_E1’F_E2’, and the sinking amount is Δ₂. If only considering the influence of F_E1F_E2 sinking in the original plate, the rotation angle of the trapezoidal plate in the fracture line A₁A₂ and A₄A₃ is 2Δ₁/a, and the rotation angle of B₁B₂ and B₄B₃ is 2Δ₂/a. The rotation angle of the triangular plate at the fracture line A₁A₄ is Δ₁/m, and the rotation angle at B₂B₃ is Δ₂/m. Figure 7 is the double “O-X” breaking model diagram.

Fig. 7

“Double O-X” breaking model diagram.

The following explanation is given for the determination of the roof subsidence Δ: affected by the uniform load, the plate A1A2A3A4 first generates a fracture extension from the middle of F_E1F_E2 to form a fracture line. Since the C_LO shear force at the midpoint of the line F_E1F_E2 is 0, the C_LO point can be determined as the optimal position for the determination of the subsidence. Therefore, F_E1′′F_E2′′ is made perpendicular to F_E1F_E2, and a point C_LO′′ of F_E1F_E2 is taken to make C_LOC_LO′′ equal to the subsidence Δ₁. The failure mode at the C_LO point is determined by the maneuvering method and sinks at this point. According to the above conditions, the dissipation work of the internal force on the fracture surface during the initial fracture of the main roof can be obtained by Eq. (13-a), and the external force work caused by the dead weight and the follow-up load on the trapezoidal plate and the triangular plate is shown in Eq. (13-b).

The upper bound condition of the main roof’s O-X-shaped fracture is established by applying the upper bound theorem. The internal force dissipation energy formula and the outward force energy formula are identical. Equation (13-c) illustrates the link between the length of the working face and the advancing distance and the final bearing capacity R_si1 of the main roof before the initial weighting:

$$\left\{ {\begin{array}{*{20}l} {E_{d} = 4M_{S} \Delta _{1} \left( {2\frac{b}{a} + \frac{a}{m}} \right)} \hfill & {(a)} \hfill \\ {W = R_{{si}} a\left( {\frac{1}{2}b - \frac{m}{3}} \right)\Delta _{1} } \hfill & {(b)} \hfill \\ {R_{{si1}} = 24M_{s} \frac{{2bm{\text{ + }}a^{2} }}{{ma^{2} \left( {3b - 2m} \right)}}} \hfill & {(c)} \hfill \\ \end{array} } \right.$$

(13)

where E_d is the dissipation energy of the internal force of the main roof, J; W is the advance distance of the working face before the first weighting, m; δ₁ is the subsidence of the fracture line EF, m; M_s is the ultimate bending distance of the main roof, N·m; R_si is the ultimate bearing capacity of the main roof during the first weighting of the working face, MPa.

The relationship between the length of the working face and the advancing distance and the main roof’s final bearing capacity may be found using Eq. (13-c). The ultimate bearing capacity of the main roof will decrease as the working face’s length and advancing distance increase, as illustrated in Fig. 8, and the working face’s advancing distance is more sensitive to the main roof’s ultimate bearing capacity.

Fig. 8

The relationship between the ultimate bearing capacity of the roof and the advancing distance and the length of the working face.

The following analysis of the two plate crack density is different. Assuming that the crack density of the left plate is greater than the crack density of the right plate, the left plate will crack before the right side, and first form the “O-X” fracture morphology. At this time, the left boundary condition of the right plate becomes a free edge, and the “X-Y” fracture morphology shown in Fig. 9 will be formed. In the formation process of the “X-Y” partition fracture model, for the crack initiation and propagation and unstable fracture law of the plate during the advancement of the working face, plate A and plate B are cracked and expanded at the four edges; x-shaped crack initiation and propagation occurred between plate A. With the penetration of X-shaped cracks, plate A was unstable and broken. After the fracture, the boundary condition of plate B became three-sided simply supported and one side free. From the periodic fracture morphology of the plate, it can be seen that the crack initiation position between plate B occurs on the free edge and expands into the plate.

Fig. 9

Roof “X-Y” shape breaking process.

Analysis of the first weighting of the main roof with two dominant primary cracks

For the two plates divided by one dominant primary fracture, the identity or difference between the two plates determines the partition fracture model formed after the working face advances. Similarly, for the main roof with two dominant primary cracks, the identity or difference of the three plates will form different partition fracture models.

Under the condition that the three plates are approximately the same, the size of the plate and the crack density are equal. The three plates will almost simultaneously occur the phenomenon of crack initiation and expansion and instability, forming the fracture morphology of the “three O-X” in Fig. 10. When the crack density of plate A and plate C is greater than that of plate B, plate A, and plate C will crack before plate B and take the lead in “O-X” fracture. After the formation of the surrounding cracks, the boundary condition of plate B becomes simply supported on the opposite side, and the other two sides are free. Finally, a crack will occur in the middle of plate B along the long side direction, and a crack will be formed after it is connected with plates A and C, and the “OX-OX” morphological fracture model is formed. Plate B fractures “O-X” first, followed by plates A and C forming a boundary condition with three sides simply supported and one side free, assuming that the initial fracture density of plate B was higher than that of plates A and C. The initial failure happens because the plate next to the free edge fracture has no supporting effect and the distortion is greater than in other places. Ultimately, the instability of plates A and C results in the Y-shaped fracture, creating a “Y-X-Y” fracture model. The plate with weak bearing capacity at the plate’s edge will first break “O-X” fracture under the influence of mining when the crack density of any one of the two plates at either end is higher than that of the other two plates. After that, the adjacent plate’s boundary condition will become free edge. Elastic mechanics shows that when a plate has three simply supported sides and one free side, its expansion speed is quicker, resulting in a Y-shaped fracture. The plate then starts to crack and expand from the free surface, eventually producing an “X-Y-Y” fracture model.

Fig. 10

Comparison of different main roof models with two dominant primary fractures.

It should also be noted that the partition fracture morphology shown above only applies to one or two prominent main fractures; 90° being the dominant occurrence. The roof may have many prominent primary fractures that split it into multiple hinged plates as the working face’s length progressively rises. The breaking procedure is no longer overly discussed because it is comparable to the analysis above.

Verification of partition breaking model

By reducing the dominant primary fracture to a simply supported boundary condition, the aforementioned study theoretically demonstrates that there is a phenomenon of roof partition breaking in the super-long working face. Simplifying the dominant primary fractures in the roof site to just supported boundary conditions has certain restrictions, though, and only applies if the roof breaks before the coal wall. This is because the various roof fracture locations will result in varying limitations on the surrounding rock mass in the area of the dominant fracture. The roof becomes embedded in the solid coal and the surrounding rock mass when it breaks before the coal wall. This constraint force from the surrounding rock mass can be reduced to a local simply supported boundary condition, creating an inflection point of fracture propagation close to the dominant fracture and leading to zonal fracture. The fracture expansion will pass through the dominant fracture position and produce the “O-X” fracture as a whole when the roof fracture location is close to the coal wall because the front coal body cannot offer a significant binding force close to the dominant fracture.

Numerical simulation

PFC3D is based on the core concept of the Discrete Element Method (DEM), and its numerical approach employs an explicit time-stepping scheme for simulating granular flow^39,40,41. This method discretizes materials into independent spherical or clustered particle units and defines the constitutive contact models between particles (such as linear contact or bonding models) through force–displacement laws. At each time step, the software first calculates contact forces based on the overlap between particles, then applies Newton’s second law to update the velocity and displacement of each particle. By continuously iterating this process, the dynamic evolution of the system is simulated. This approach starts from the microscopic interactions between particles and naturally characterizes complex macroscopic mechanical behaviors such as material fracture, large deformation, and flow. It is particularly suitable for simulating the fracture and movement of granular assemblies like rocks and soils. In PFC3D, crack propagation is not governed by a pre-defined macroscopic fracture law. Instead, it is an emergent behavior resulting from the initiation, growth, and coalescence of numerous micro-cracks at the contact points between particles. The fundamental model controlling this process is the parallel bond model (PBM), which we utilized to represent the cemented or intact rock material. The PBM can be visualized as a finite-sized, brittle cementitious material of a specified stiffness and strength that is deposited on the contact point between two particles. It transmits both forces and moments between particles. Fracture occurs when the stresses acting on the parallel bond exceed its strength limits. A micro-crack is recorded when a parallel bond breaks. The breakage occurs if the maximum tensile stress exceeds pb_ten or the maximum shear stress exceeds pb_coh. The mode of the crack (tensile or shear) is also recorded based on which criterion was violated first.

A PFC3D numerical model was created to investigate the impact of roof breaking location on partition breaking in more detail. First, the Kouzidong 140,502 working face’s roof specifications are adjusted by trial and error. Table 1 displays the final mesoscopic parameters. The actual rock and simulation data are shown in Table 2. The results show that the chosen mesoscopic parameters can replicate the mechanical behavior of the field rock since the strength and elastic modulus derived from the simulation are comparable to those of the genuine rock. To study the roof fracture morphology of the main roof under the involvement of the primary dominating fracture, a simple main roof model is developed based on the parameters that were acquired.

Table 1 Numerical model parameters.

Table 2 Comparison of primary rock with simulated data.

The main roof’s surrounding border is secured before the first crack. To simulate the stress on the roof under various dominant primary fracture situations, the PFC software fixes the displacement and rotation angle of the surrounding boundary ball and applies a uniform load to the top portion of the roof via the wall. A hard boundary condition for the roof will cause the roof to fracture along the coal wall. The location of the advanced coal wall breaking is influenced by the mechanical characteristics of the rock and coal around the main roof. If the boundary condition of the roof is elastic, the roof will break before the coal wall. As a result, as seen in Fig. 11, two roof models with rigid and elastic boundary conditions are created, respectively. The roof fracture morphology for various boundary circumstances is displayed in Fig. 12. It is discovered that the “O-X” shape is the roof fracture morphology under various boundary circumstances. In accordance with the current theory, the roof fracture location under rigid boundary conditions is at the coal wall, while the roof fracture position under elastic boundary conditions occurs before the coal wall. A Z-direction force is applied to the top layer of particles, and due to their small size relative to the roof model, this can be approximated as a uniform load. The load q (Eq. 14) was incrementally increased until a significant reduction in roof loading occurred.

$$q = {1}00000 + {1}0*{\text{step}}$$

(14)

Fig. 11

Simplification diagram of roof model.

Fig. 12

Roof fracture pattern diagram.

The model is built with a prominent location in the center of the working face and the dominant occurrence of the primary fracture at 90°. The normal distribution model is used in the model to create the random fracture, and Fig. 13 illustrates how the numerical simulation model is set up. Eleven survey lines are aligned from left to right, and the dip angle and tendency of the primary fracture are extracted from the model to create the rose diagram. As seen in Fig. 14, the fracture distribution in the roof is acquired from survey line 6, which corresponds to the center of the working face. The model is found to be in good agreement with the 90° dominating occurrence. The two plates outside of the dominant position have almost comparable fracture densities, whereas the dominant position is situated in the center of the working face.

Fig. 13

Numerical model of roof considering dominant primary cracks.

Fig. 14

Cracks distribution.

The fracture morphology of various roof breaking points is displayed in Fig. 15. It is discovered that the traditional “O-X" fracture will form when the roof breaking position is close to the coal wall. However, the position of the fracture inflection point appears earlier than Fig. 15a, and the lateral span is larger, indicating that a larger rock mass has formed at the end of the fractured roof’s working face. This will also increase the support resistance at both ends of the working face. Because the fractured roof is weaker than the intact roof, the crack inflection point is reached sooner when the transversely penetrating cracks start to enlarge. This is because the rigid boundary conditions at both ends of the working face have a stronger constraint on the plate cracks.

Fig. 15

Fracture morphology at different breaking positions.

The “double O-X” partition fracture will develop when the ceiling fractures before the coal wall. This is because the surrounding rock mass around the dominant fracture will be subject to varying limitations due to the roof’s various fracture locations. The roof becomes entrenched in the solid coal and the surrounding rock mass when it fractures before the coal wall. To simplify the dominant fracture position to the local simply supported boundary condition, the surrounding rock mass will provide a binding force. This will create the inflection point of fracture propagation close to the dominant fracture, which will ultimately result in the formation of the “double O-X" fracture. The fracture expansion will pass through the dominant fracture position and produce an “O-X” fracture as a whole when the roof fracture location is close to the coal wall because the front coal body cannot offer a significant binding force close to the dominant fracture. This is compatible with the previous theoretical component and demonstrates that the phenomena of partition fracture will emerge after the roof is damaged before the coal wall and the dominant primary fracture is taken into consideration. The majority of working faces now experience roof breaking before the coal wall. Only when the advancing speed of the working face is too fast, the roof will break near the coal wall, so the site generally conforms to the precondition of partition fracture. The “double O-X” shape fracture also generates an insignificant broken rock block close to the dominant fracture, as shown in Fig. 15b. The main roof broken rock block and the overlaying follow-up load supply the majority of the roof pressure for the working face support. The pressure of the support will unavoidably decrease as the broken rock block decreases, deviating from the traditional working face’s distribution characteristics of “large in the middle and small at both ends".

Similar simulation

The roof partition-breaking procedure was examined using a three-dimensional identical simulation test to further confirm the partition-breaking’s accuracy⁴². Based on the coal seam columnar section (Fig. 16), field measurement data, and previous research findings⁴³, combined with similarity theory, the similar simulation material ratio was determined as shown in Table 3. The experimental setup is illustrated in Fig. 3. The platform measures 2800 mm × 2000 mm × 400 mm. The mixture was uniformly laid inside the platform according to the specified material ratio and allowed to air-dry naturally. A water bladder was then used to apply load on the roof until fracture occurred, enabling observation of the roof’s failure pattern. This water-bladder loading method not only simulates the uniformly distributed load from overlying strata but also facilitates clear observation of roof failure. To maintain a consistent mining height during simulated extraction, stroke limiters were placed in the coal seam simulation device according to the simulated coal seam height. After the water surface stabilized, the electro-hydraulic control system was activated, and image acquisition began. The iron plates simulating the coal seam were lowered sequentially, allowing the fracture behavior of the roof to be observed through the water-loading layer.

Fig. 16

Composite coal seam columnar section.

Table 3 Similar simulation material ratio.

A complete main roof model and a fragmented main roof model are set out, respectively. The process for creating the fractured roof is as follows: Layers are laid sequentially according to the material proportion table for the similarity simulation experiment. The water content for Layers 1, 2, and 3 was 10% of the dry weight. For Layer 4, the water content was increased to 18% of the dry weight. After Layer 4 was completed, the process was paused, and the surface was heated to accelerate moisture evaporation. Once dried, cracks formed in Layer 4 as shown in Fig. 17a. Layer 5 was then applied with the water content restored to 10% of the dry weight. The entire assembly was compacted and allowed to dry naturally. The underlying mechanism is that increasing the water content in Layer 4 allows the similar materials to mix more uniformly and enhances the binding effect of lime as a cementitious material. As the surface layer loses moisture rapidly, the lower layer remains relatively moist. This results in higher tensile stress in the surface layer compared to the layer beneath, leading to the formation of cracks in Layer 4 under the combined influence of gravity and tensile stress. The complete main roof is shown in Fig. 17b

Fig. 17

Complete main roof and fractured main roof.

As shown in Fig. 18, the initial fracture under the condition of a complete main roof forms a typical O-X fracture morphology, which is consistent with Fig. 15a. The main roof model with fissures is divided into three stages during the first weighting. The first stage is the formation of an O-X fracture at the end of the working face, and then the boundary conditions of the adjacent roof become free edges, forming two Y-shaped fractures. Finally, the “X-Y-Y” fracture is formed, which is consistent with the failure mode of Fig. 10, which further confirms the spatial and temporal characteristics of partition and migration of fissure roof pressure.

Fig. 18

Roof breakage form under different main roof conditions.

Analysis of microseismic data in working face

The 150,402 working face’s roof activity is measured by the microseismic monitoring equipment. Figure 19 displays the layout of the station and the components of the microseismic monitoring system. There are six stations spread throughout the two mining roads. The stations are separated by 100 m. The high preloaded full-length bolt is hammered into the station’s location. The working face is 200 m forward of the first pair of geophones. A communication wire connects the geophone to the monitoring base station. The major roadway is where the power supply and base station are situated. To ascertain the quantity, position, timing, and energy of microseismic occurrences, the data is sent from the base station to the ground for real-time analysis.

Fig. 19

Microseismic monitoring system and measuring station layout.

Figure 20 displays the microseismic data findings in the working face’s length direction. The microseismic events and energy at both ends of the working face often exhibit an M-shaped distribution, as shown in the figure, suggesting that the roof activities at both ends are more active. This is because, in the case of a super-long working face roof and relatively developed roof cracks, the roof is more likely to form partition fractures in the inclined direction. Microseismic events and energy less than the two ends result from the formation of a small rock block in the middle of the working face, which further confirms the existence of partition fracture of the roof by producing the characteristics of support resistance “large at both ends and lower in the middle."

Fig. 20

Microseismic distribution in the length direction of the working face.

Conclusions

• (1) The roof of the working face readily exhibits the features of partition fracture because of the presence of primary fractures. The roof is thought of as a thin plate with primary fractures dividing it into a finite number of interactions. It is suggested that primary fractures predominate in terms of both incidence and location. The non-dominant primary cracks are reduced to destruction factors of roof strength, whereas the dominant primary fractures are reduced to simply supported boundary conditions.

• (2) According to distinct dominant primary fractures, a variety of zonal fracture models are developed, and the zonal fracture models of “double O-X”, “X-Y”, “X-Y-Y”, “Y-X-Y”, “OX-OX” and “three O-X” are generated. The initiation criteria, fracture criterion, and instability criterion of several zonal fracture models are produced using upper and lower bound theorem and fracture mechanics knowledge theory.

• (3) Taking “double O-X” as an example, the relationship between the length-span ratio of the roof and the length of the crack on the fracture toughness and the stress intensity factor was studied, and the influence coefficient of the internal force and external force of the self-plate on the adjacent plate during the roof subsidence process was analyzed.

• (4) The “O-X” and “double O-X” fractures were created by simulating the fracture morphology using PFC3D under the conditions of a complete roof and a roof with initial fractures. It is determined that the foundation of zonal fracture is the presence of dominating primary fractures and the roof leading coal wall fracture. Simultaneously, the “O-X” fracture of the whole roof and the partition fracture phenomena of the broken roof were obtained from the same simulation test. The theoretical derivation, which demonstrates that the roof would be divided under the intervention of the dominant primary fracture, is supported by numerical calculations and comparable simulation findings.