1 Introduction

The gob-side entry driving, having no or less influence on regular production, has been developing for decades in China to save the coal resource. Based on the theoretical analysis and structural model, the existence of the initial stress area, stress-concentrated area, and stress-relaxed area of the original rock under the condition of goaf excavation has been verified continuously (He et al. 2017; Shi et al. 2020). In general, through mechanical analysis, the roof pressure of the short-arm beam could be calculated which can be regarded as the roof-breaking criterion (Ma et al. 2022). The results of mechanical analysis showed that the primary mechanism of roof pressure release is to weaken the integrity of the roof, thereby reducing the ultimate bending moment of the rock stratum (Zhu et al. 2022). The deformation law of the single roof and floor of the gob side entry can be characterized and explained by the beam deflection curve based on the reciprocity theorem (Lu et al. 2016), and the floor failure depth after the upper coal seam could be calculated according to the elastic–plastic theory (Liu et al. 2022). The surrounding rock stress, plastic zone and deformation characteristics brought by gob side entry driving under the isolated island working face are different from those under general conditions (Liu and Han 2021; Zhang et al. 2018). Based on the pressure relief of roof cutting along the gob side entry, combined with different roof cutting schemes, the rules of the six stress zones of gob side entry can be refined (Guo et al. 2021). With the increasing complexity of the accompanying conditions of the gob side entry, the research connotation of the gob side entry is constantly enriched. However, the traditional theoretical analysis and physical simulation methods have been significantly limited, and it is difficult to give the engineering limited solution conveniently and accurately.

After establishing the dynamic mechanical model of the roof structure, the roof structure’s stress state and deformation failure mechanism of the gob side entry heading along the working face were studied and the central part of the roof was the main point that controlled the surrounding rock (Bai et al. 2015; Han et al. 2018), and the rotation and subsidence of roof key block lead to severe deformation of roadway (Luan et al. 2018). Xu and Shen (2018) established a mechanical calculation model based on the elastoplastic theory to study the distribution law of abutment pressure and concluded that the vertical stress distribution and plastic zone appear asymmetrical characteristics. (Ma et al. 2020) analyzed the stress distribution characteristics of the narrow coal pillar through numerical simulation, field monitoring, and theoretical analysis, and proposed a method to determine the reasonable width of the coal pillars of gob-side entry with top coal. Wu et al. (2020) analyzed the plastic zone of the surrounding rock, the serious damage area, the degree and scope of the damage, and the dynamic evolution process of the surrounding rock of the gob-side entry retaining through theoretical analysis, numerical simulation, and on-site tests. Based on numerical simulation and theoretical calculation, the obvious asymmetric failure characteristics of the roof and solid coal and the inverse correlation between the width of the coal pillar and failure depth of the roadway bottom were founded through the research on the distribution and evolution of plastic zone and vertical stress of surrounding rock at different locations of goaf roadway (Shan et al. 2021; Wang et al. 2020; Wu et al. 2023; Xie et al. 2020; Zhang et al. 2020). Zhang et al. (2022) studied the stress evolution characteristics of the coal at the side of the goaf under the double-key stratum roof cutting structure through numerical simulation. Zha et al. (2017) studied the surrounding rock deformation characteristics of gob-side entry driving with narrow coal pillar based on the geological condition of 10,416 working face tail entry in Yangliu Coal Mine. Based on numerical simulations, Zhou et al. (2017) employed an innovative model that incorporates a stress equilibrium equation, and the distribution law of displacement and stress and gas pressure in the solid coal on both sides of the gob was determined. Through FLAC3D modeling, the stable damage accumulation of rib at a certain working face position can be predicted, and the surrounding rock environment, vertical stress, and vertical deformation of the backfill body at the side of the goaf approach under different roof pre-splitting angles can be analysed (Ren et al. 2019; Sinha and Walton 2020; Zhang et al. 2016). Moreover, based on discrete element UDEC modeling, the deformation and failure mechanism of the main roof of gob side entry is studied (Li et al. 2022), as the mechanism of roof crack propagation and evolution at different distances from the working face (Yang et al. 2019), the fracture and rotation characteristics of roof strata were confirmed (Yang et al. 2012), and the main failure of coal pillar is the tension-shear crack (Wu et al. 2019).

Though previous studies have confirmed the existence of a stress reduction zone and taken it as a strong basis for the layout of the gob side entry through finite element analysis and discrete element simulation, the overall state of surrounding rock before and after roadway excavation was ignored. Therefore, PFC2D is used to construct a large-scale particle flow model of the surrounding rock structure in the stope, which can monitor the dynamic migration and stress evolution of surrounding rock and display and monitor the global fracture state completely. This study aims to study the influence of main roof failure on the surrounding rock state through PFC simulation and analyze the cause of instability and large deformation in the gob-side entry. Overlying main roof breaking characteristic and its effect on the stability of gob-side entry.

2 On-site description

The Dongtan coal mine is located in Jining city, Shandong province in China, where the XX07 rail crossheading is an inverted trapezoidal roadway tunneling along coal #3 floor which is also a gob-side entry near XX06 gob separated by a 3.5 m-width coal pillar, as shown in Fig. 1. The thickness of coal #3 is 6.8–9.75 m, and its depth is about 660 m below the ground surface. The roof and floor are both siltstones, and more details about the rock strata and geological description of the XX07 rail crossheading are provided in Fig. 2. The relevant rock strata physical and mechanical properties, including density, compressive strength (σc), elastic modulus (E), tensile strength (σt), and Poisson’s ratio (μ), are shown in Table 1.

Fig. 1
figure 1

Working face layout plan

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Fig. 2
figure 2

Rock strata and geological description of the XX07 rail crossheading

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Table 1 Stratigraphic physical and mechanical properties
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3 Methodology and pre-test

3.1 Research method

In order to figure out the reason why the entry driven along the gob-side had such a big deformation, PFC2D was used to simulate the state of the surrounding rock at its location. The entry was buried 650 m under the surface with 40 strata, which would result in the process of modeling being complicated and running being difficult. Therefore, the size of the model was simplified in vertical and horizontal directions as follows:

  • The number of rock strata was reduced vertically. Only the strata directly related to the basic roof and coal seam were taken, and the other overlying strata were replaced by a cluster of equivalent weight according to the result of the primary rock stress test which is as Table 2 shows.

  • The working face size was reduced horizontally. The loading model of the main roof could be constructed, and the minimum length that the main roof was inclined to break could be obtained through limit analysis. According to this, the working face width could be shortened to reduce the overall length of the model.

Table 2 Result of primary rock stress test
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As for the ideal elastoplastic simply supported beam, the basic information could be got in Eqs. (1), (2), and (3).

$$J = h^{3} /12$$
(1)
$$\sigma = \left( {12My} \right)/h^{3}$$
(2)
$$M_{\max } = - \left( {qL^{2} /8} \right)$$
(3)

where J is the moment of inertia; h is the thickness of the beam; σ the normal stress of any point; M is the bending moment of section at any point; y is the distance of any point from the neutral axis; Mmax the maximum bending moment; q the load brought by the upper strata; and L the length of the beam.

When the tensile stress exceeds its tensile strength, it would tend to break. And according to Eqs. (1), (2), and (3), the limited length of the beam could be calculated by

$$L_{\max } = 2h\sqrt {\frac{{\sigma_{t} }}{3q}}$$
(4)

where LB is the limit breaking length or the minimum breaking length; h the thickness of the main roof, h = 20.68 m; σt the tensile strength, σt = 8.61 MPa; and q the load brought by the upper strata, which could be calculated by

$$(q_{n - x + 1} )_{x} = \frac{{E_{x} h_{x}^{3} (\gamma_{x} h_{x} + \gamma_{x - 1} h_{x - 1} + \cdots + \gamma_{1} h_{1} )}}{{E_{x} h_{x}^{3} + E_{x - 1} h_{x - 1}^{3} + \cdots + E_{1} h_{1}^{3} }}(1 \le x \le n)$$
(5)

Where (qn − x+1)x is the load brought by No. (n − x + 1) stratum and suffered by No.x stratum; Ex is the elastic modulus of the No.x stratum; hx is the thickness of the No.x stratum; and γx is the unit weight of the No.x stratum. All the parameters could be found in Table 1.

Equation (5) should be calculated first to analyze where the main roof is by comparing the value. When the \(\left( {q_{n - x} } \right)_{x} \, > \,(q_{n - x + 1} )_{x}\), the No.n−x stratum is the main roof because it bears a larger amount of pressure. After calculation, the medium sandstone (5#) was the key stratum and the least length of it was about 81 m then it would tend to break.

The calibrated parameters were assigned to each rock layer of the model. The measurement circles were arranged and the data recording type was designed, so that the real-time evolution image of cracks, stress, porosity changes, and other data were automatically generated, which were prepared for the analysis of the causes of entry’s large deformation, the rationality of its location, and the key points of surrounding rock control. Lastly, we mined the working face and started running the model to the end.

3.2 Model design and pre-test

To minimize the influence of the boundary, 58 m are retained on the left side of the gob-side entry and 58 m right side of the working face. The size of the model is 236 m × 51.5 m, containing 5 strata and a layer of the cluster, in which the wall is the boundary of the model as shown in Fig. 3.

Fig. 3
figure 3

Model size description

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A linear parallel bond model is chosen to apply between particles to simulate the rock materials. As for the linear parallel bond model, contact stiffness and bonding stiffness together form the macroscopic stiffness, as shown in Fig. 4. The normal stiffness (kn) and shear stiffness (ks) are provided between particles with different radius (R & r), and the normal and shear stiffness of parallel bonding (\(\overline{k}_{n}\) & \(\overline{k}_{s}\)) are also provided. When the normal force (Fn) and shear force (Fs) exceed the set limit, the bonding between particles will be destroyed. Bond failure can directly lead to the reduction of macroscopic stiffness, so the mechanical properties of the material can be consistent with those of rock-like materials during tensile or shear failure.

Fig. 4
figure 4

Sketch map of parallel bond model (Wu et al. 2017)

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The setting of porosity is 0.01 and the radius is between 0.24 and 0.36 m. The particles achieve balance in the initial setting where gravity is 9.81 N/kg. After deleting the extra particles, various groups are set and given parameters separately. Attribute force to the side walls of the model, run, and set the limit that it will not balance until the unbalanced force of the model is below 10–5. There are altogether 3 groups of measuring circles with a diameter of 5 m in the model, 47 in each group above and below the coal seam, and 11 on the left side of the coal seam, as shown in Fig. 5.

Fig. 5
figure 5

Grouping and measurement circle arrangement

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Before the simulation, the mesoscopic parameters of each rock layer should be calibrated, and the trial-and-error iteration method should be used to calibrate the mesoscopic parameters of each rock layer (Hou et al. 2020; Wu et al. 2017). Through the iterative method, the microscopic mechanical parameters are adjusted continuously to achieve the maximum matching degree between the macroscopic parameters such as elastic modulus, peak stress, and Poisson's ratio obtained by the numerical test and those obtained by the laboratory test. Calibration results are shown in Table 3.

Table 3 Calibration results of mesoscopic parameters and macroscopic parameters
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Too many measurement circles are set in the model and if all monitoring data are exported and involve too many curves, it will appear excessively redundant to display in the same data graph, which will affect information extraction and analysis. Considering that the whole model is symmetric, the left half or the right half can be selected for data extraction. The left stress circle is selected here for data extraction and analysis.

As shown in Fig. 6 for stress monitoring, it is not difficult to find that in the initial balance, each rock layer was basically under the action of dead weight. After debugging, the vertical stress stability values obtained from each measuring circle were relatively concentrated in both upper and lower measuring circles, and approximately in accord with the measured values. Excavation could be carried out and the model could continue running.

Fig. 6
figure 6

Stress state at the time of balance

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4 Result

4.1 Fracture evolution

The failure of the overlying rock mass in the gob touches the floor was taken as the standard to stop the operation. The time-step operation was divided into 0.25 time-step for each operation, and the state was stored. At 2.5 time-step, when the bending deformation of the overlying rock mass in the gob touches the bottom, the model tended to be stable, and the operation was stopped. Figure 6 shows the different states of the model at the time step 0.5 and 2.5.

Referring to Fig. 7, the crack development could be observed clearly in the surrounding rock around the gob after excavation. At the beginning of the evolution, the fracture appeared in the coal seam, especially concentrating on the sides close to the gob. In the meantime, the immediate roof began to damage and fractures showed up in the parts above the coal walls, while the main roof retained an integrated state. As for running, the immediate roof and main roof got into the situation of rotation and subsidence, and their bending state changed their stress state, the tensile stress concentration for the bulge where just several apparent cracks crossed the strata, and the compressive stress concentration for the depression which resulted in cracks flocked together. In addition, more cracks formed and expanded to the deeper coal seam. In the final state, when the main roof was broken up, a number of irregular cracks gathered and formed three plastic zones while a few breaking fissures went through the main roof.

Fig. 7
figure 7

The initial (left) and final (right) states during the main roof-breaking process

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4.2 Stress change

According to the vertical stresses obtained by different measuring circles in the main roof, main floor, and coal seam during the whole process, the stress variation of the different places can be drawn as shown in Fig. 8.

Fig. 8
figure 8

Stress state of the main roof, main floor, and coal seam at the time of termination

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As shown in Fig. 8, the obvious stress redistribution characteristics could be observed in the main roof, main floor, and coal seam with the model running. The distribution range of stress reduction area, stress increase area, and original rock stress area could be distinguished. The distribution range of stress zones in the main roof, coal seam, and main floor was slightly different but roughly similar.

As the goaf appeared, the stress reduction area in three strata could be determined within 10 m close to the gob. Meanwhile, the distance within the range from 10 to 30 m could be regarded as a stress increase area where the vertical stress had a process of fluctuation and stayed in a relatively high stage finally. The specific figures, 27 MPa on the main roof, 18.5 MPa on the main floor, and 23.5 MPa on the coal seam, were relatively higher than the stress of primary rock. When the place was over the distance of 30 m, it could be named the original rock stress area, and vertical stress in that area was roughly equal to or slightly less compared to the stress of primary rock. The existence of the stress reduction area meant that the selection of entry’s location within this range should be reasonable.

4.3 Displacement

According to simulation results, the coal and rock mass within the stress reduction zone almost showed a state of complete fragmentation. After the displacement state of the model was cleared to zero, the entry excavation was carried out. After the entry was excavated, the displacement state of the surrounding rock is shown in Fig. 9.

Fig. 9
figure 9

The deformation of surrounding rock in simulation and reality

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As can be seen from Fig. 9, the surrounding rocks on both sides of the entry showed an inward migration trend. The displacement of coal mass on both sides was close to 1 m, and the horizontal displacement of the coal pillar was greater than that of the solid coal side. However, the overall displacement of the entry roof and the floor was not obvious. The floor almost did not change, and the rock mass of the roof even showed a small upward movement trend.

From the above, it could be seen that the surrounding rock deformation of the gob-side entry was mainly concentrated on the two sides of the roadway, and the deformation of the roof and floor was small. Therefore, attention should be paid to the control of the coal body on the two sides of the roadway, especially the coal pillar.

4.4 Porosity variation

During the movement of the strata structure, various kinds of surrounding rock states, such as fracture evolution, stress environment, and deformation, were changing. To indicate the degree of rock fragmentation in a different area, the porosity rate was introduced and its monitoring data is shown in Figs. 10 and 11.

Fig. 10
figure 10

Porosity variation of coal seam

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Fig. 11
figure 11

Porosity variation of the main roof

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As shown in Fig. 10, the porosity of the coal seam changed greatly at the positions of measuring circles No.152 and No.153 within the range of 10 m to the coal wall. Though they fluctuated all the time, they almost kept the rising state after they began to change and finally reached a high rate of porosity, especially in the range of 5 m where the pillar was located the porosity rate reached 0.39.

The porosity variation of the main roof’s bottom is shown in Fig. 11. The curves in yellow of measuring circles No. 72–80 which were located out of the range of 10 m to the coal wall, almost keep the same rate as it used to be all the time. The red curves were obtained through the measuring circles which were above the coal body that was in or close to the range of 10 m to the coal wall. They indicated that the closer the gob was, the higher the porosity was. The highest porosity was 0.23 located at measuring circle No.83 which was the boundary of the gob and coal body. The blue curves originated from the rest measurement circles from the main roof above the gob. It can also be seen that the closer the coal wall was, the higher the porosity change was.

5 Discussion

5.1 Cause of fracture state changes of the surrounding rock

As for the final breaking state of the surrounding rock. the cracks could be divided into two categories: block-shaped cracks near the central part of the main roof and the coal bodies on both sides of the gob, and linear cracks inside the main roof. The fractures in the immediate roof were tensile cracks, and the top area of the main roof was also dominated by tensile fractures. The linear fractures in the main roof were mixed with shear fractures and tensile fractures. The failure process of the main roof was different from that described by the ideal elastoplastic simply supported beam.

The ideal elastoplastic model considers that when the section completely enters plasticity, the distribution of the plastic zone is shown in Fig. 12a. Two plastic zones, the blue for compressive failure and the red for tensile failure, above and below the mid-span section formed a connected area. And the position of the support point of the beam structure formed by default is fixed.

Fig. 12
figure 12

Comparison diagram of simply supported beams in ideal and actual elastoplastic rock mass

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According to the simulation results and after analysis, the breaking process of the main roof strata is mainly elastoplastic, but it is different from the ideal elastoplastic model. The specific situation is shown in Fig. 12b.

The first and most obvious point of differentiation is the division of the plastic zone. Three obvious plastic zones are formed in the actual rock beam fracture. One is the plastic zone located in the middle section of the span, which is similar to the ideal elastic–plastic distribution. The other two plastic zones are distributed above the support point, which is almost symmetric. When the neutral surface is taken as the boundary, the reasons for the formation of the plastic zone in the upper and lower parts are different. The convex part of the buckling is mainly the plastic zone filled by tensile cracks caused by tensile failure, while the depression is the plastic zone filled by shear and tensile cracks caused by compression failure.

The characteristic resulted from the cause that the actual supporting points of the beam structure were not fixed in the horizontal direction. Due to the relatively low strength of the coal body, in the process of bending and sinking the main roof, the shallow part of the coal wall constantly loses its bearing capacity, and the deep part of the coal body gradually plays the main supporting role, and the supporting point continues and slowly transfers to the deep part. This means that the support point of the actual beam structure is semi-fixed. That could be supported by the phenomenon of the breaking process and the data on stress and rock porosity. The abnormal change of components, the support points, in the mechanics model brought in the unusual breaking state of the main roof.

5.2 Reason for the continuous deformation of surrounding rock

The traditional position of gob roadway excavation is based on the lateral abutment pressure distribution after excavation, and the preferred location is the stress reduction area near the gob. According to the simulation results, the stress reduction area can be determined within 10 m close to the coal wall.

The traditional method, reserving a 3.5 m coal pillar, can make the entry driven along the gob-side located in the stress reduction zone, which is reasonable in considering the stress environment. As for this situation, the support system of the entry and coal pillar has to hold the force from the broken roof stratum, which was accorded to the situation of the ideal and abnormal elastic–plastic simply supported beam.

However, this position is also the most fractured part of the coal body. The distribution of cracks and the variation of porosity showed that the integrity of the rock mass was at a relatively low level, which was not good for its stability. In addition, though the stress within the range of 0–10 m was greatly reduced and the influence of stress was transferred to the deeper part of the coal body, the coal body was still squeezed by the roof and the final vertical stress still existed. The coal pillar in the fragmented state could not keep itself immobile while suffering stress even though it was at a low level. The stress transformed into the power to force the pillar to deform towards the free space.

Therefore, in the stress redistribution zone where the lower stress doesn’t mean better integrity. The traditional selection of the location of entry driven along the gob-side is based on the stress reduction area as the first choice, and it is believed that the control of the surrounding rock of gob-side roadway excavation can achieve better results under the low-stress environment. However, the problem of the high fracture degree of coal and rock in stress reduction areas is also relatively prominent (Additional file 1).

When deciding on a gob-side entry location should not just consider the advantages of the stress reduction zone but also pay more attention to the state of the surrounding rock. Except for that, how to improve the integrity and bearing capacity of broken surrounding rock effectively should be the focus when the location of entry driven along the gob-side has been determined in the stress reduction zone.

6 Conclusion

This paper presented a particle flow model of deep strata in PFC2D to study the state of surrounding rock near the gob to analyze the reason why the entry driven along the gob-side showed such a continuous and large deformation after being reinforced and supported. The following conclusions could be obtained.

  1. 1.

    After proper simplification, PFC can be used to model and analyze the deep rock structure. Through reducing the needless strata replaced by a layer of cluster given specific parameters that were equivalent to the measured in site stress. In addition, the width of the working face was lessened properly according to the minimum length of the beam to break. It was successful to simplify the model in those two ways so that the process of model running was efficient.

  2. 2.

    The change of structure of strata, main roof breaking, resulted in the redistribution of stress, especially an indeed range close to the gob in coal seam showed the influence by low stress, which was the stress reduction zone.

  3. 3.

    The broken rock stratum was different from the ideal elastic–plastic simply supported beam in that two more plastic zone appeared on both sides of the beam that included the stress reduction zone while supporting points moved into the deep coal body when the shallow coal body was destroyed.

  4. 4.

    The coal body and rock mass were completely broken in the stress reduction zone of the coal seam and the main roof from the final state of the model and field test results, meanwhile measured porosity in those zones was very high. That was rarely mentioned in the procedure of entry excavation design which had a strong impact on later roadway support or surrounding rock control.