Structure of Overlying Rock Strata and Advanced Abutment Stress Evolution in Deep Filling Mining

Abstract

Filling mining is one of the feasible methods to prevent rock burst in coal mining, which is a research significance topic in the field. In this paper, we first described the filling mining effect based on “equivalent mining height” and analyzed the evolution of overlying rock strata. It was found that time-space hysteresis occurred during the movement of overlying rock strata in filled working face. On this basis, the mechanical relationship of dynamic transformation among “filling rate–strata movement–abutment stress” was obtained by analyzing the coal stress characteristics. Then, an advanced abutment stress estimation model of filled working face in deep coal mine was established. Finally, the C5301 working face of Yunhe coal mine was taken as the engineering background, and example calculation and field monitoring were carried out. The results showed that the influence range of the advanced abutment stress is 91–97 m, and the peak value is 41.1 MPa, which is 21–50 m away from the working face. In addition, large pressure steps and long interval time were the characteristics of time-space hysteresis in the filled working face. This study could provide guidance and reference for deep filling mining under the same or similar conditions.

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1. Introduction

Filling mining is a method widely used in coal mining field. It plays an important role in preventing subsidence, protecting the environment, and digesting waste gangue [1–4]. In recent years, filling mining has gradually been used as a feasible method to prevent rock burst [5–7]. Nevertheless, occasional rock burst events in the filled working faces indicate that there remain significant uncertainties in effectively controlling rock bursts through filling mining. In addition, the stress distribution and evolution within the coal-rock body are dictated by the structural and evolutionary characteristics of the overlying rock strata. Therefore, it is of great significance for revealing the movement characteristics of overlying rock strata and the evolution of advanced abutment stress.

In recent years, scholars at home and abroad have carried out many research studies on the movement of overlying rock strata in filling working face. Jiang et al. [8, 9] revealed the mechanism of rock burst around the separation zone of key strata in deep strip mining. The mechanical model of key stratum separation is established. It is pointed out that the load above the key stratum is transmitted to the surrounding area of the key stratum separation zone, which leads to a significant increase in stress concentration and induces impact. Zhang et al. [10] established a mechanical model of the key block of the main roof of the filling fully mechanized mining face. The internal law of compaction characteristics and time correlation of gangue filling body is studied. An equivalent mining height model for analyzing the mining pressure law of gangue filling mining is proposed. Sun et al. [11] established a mechanical model of overlying rock strata in open super-high water filling mining. The stress and deformation failure mechanism of the working face roof is revealed. Wang et al. [12] established the interaction model between filling body and the immediate roof. The law of roof bending and subsiding process of paste filling working face is analyzed. The calculation equations of deflection increment and bending moment distribution during roof periodic weighting are established. Jiang et al. [13] carried out discrete element numerical simulations of caving mining and filling mining under extremely thick magmatic rocks. The control effect of filling mining on magmatic rock migration and mining stress is analyzed. Zhang et al. [14] studied the control mechanism of overlying rock strata in super high water material filling mining. It is proposed that there are “queuing phenomenon” and “catch-up phenomenon” in the activities of several groups of weak rock strata in the overlying rock strata of the stope. It is revealed that the control of the key strata of the main roof is the key to the success of the filling mining technology. Chang et al. [15] established a mechanical model of roof rock beams during paste filling mining. The calculation equations of limit filling step distance and safe filling step distance are given. It is found that the filling step distance is proportional to the thickness of the roof rock beam. It increases with the increase of rock strength and the thickness of the immediate roof. Guo et al. [16] established a mechanical model of roof stability of strip coal pillar working face with paste filling replacement. It is found that the paste exhibits typical plastic strengthening characteristics under low confining pressure. From the completion of filling to the stability of overlying rock strata movement,the stress of filling the body is a process of gradually increasing and tending to be stable. Yavuz [17] proposed a method for estimating the distance to return of the cover pressure and the stress distribution in the goaf of flat-lying longwall panels where the caving is bulking controlled. Jena et al. [18] dealt with a preliminary analysis of strata control monitoring in an Indian underground coal mine, and the basic objective of the study is to apprehend strata movements so that subsequent preventive measures can be initiated against any sudden situation relating to roof and sides.

However, the above research results were obtained mainly based on the traditional mining experiences, which was rarely involved in the evolution of overlying rock structure and the mechanism of rock burst under filling mining conditions. The influence of goaf filling on the movement of overlying strata and the distribution characteristics of advance abutment stress has not been deeply studied. On this basis, this paper revealed the influence of equivalent mining height on the structure and evolution of overlying rock strata. Then, the theoretical model of the three-zone structure loading model was established under the condition of filling mining, and the distribution characteristics of advanced abutment stress were analyzed under different overlying rock strata structures. Finally, the example calculation and field monitoring were carried out for verification.

2. Structure Characteristics of Overlying Rock Strata

2.1. Equivalent Mining Height

With the continuous mining, the goaf was enriched as the immediate roof fully collapsed. The main roof deflected, broke, and rotated under the action of its own weight and the load of overlying rock strata. This was the provenance of advanced and lateral abutment stresses. This instance the reason for roof subsidence, two-side displacement, floor heave, and other mining pressure manifestations was the effect of coal body at the edge of the goaf on vertical and horizontal stress.

Filling mining make the filling body timely fill the remaining goaf space left by the coal mining, thereby reducing the maximum height of the direct subsidence movement of the roof rock strata. The separation and fracture of the main roof and overlying rock strata were delayed [19]. In fact, the process of roof subsidence and filling body compression was a dynamic balance process of stress. Following the subsidence of the roof strata, the filling body underwent compression and deformation under the influence of compressive stress. Consequently, as the filling rate and compressive strength augmented, the filling body’s supportive effect on the roof correspondingly intensified. When the support force of the filling body was less than the settlement compressive stress of the roof, the roof would continue to subside, the filling body continued to compress and deform, and the filling rate increased gradually. When the two forces reach equilibrium, the roof strata subsidence is stable, and the filling bodyhas reached its maximum compression deformation, no longer undergoing new deformation. There was a mutual feedback and repeated action relationship between the compression deformation of the filling body and the subsidence movement of the roof.

The evolution of roof movement for filling mining can be studied by using the theory of equivalent mining height. The filling body occupies the space of the original coal seam in the goaf, effectively reducing the mining height. This effect is similar to that observed in extremely thin coal seam mining [20]. When the filling method was used, the compressive deformation of the filling body increased with the increase of the working face mining distance. The compressive deformation of the filling body increases with the increase of the working face mining distance and the mining distance is larger when the roof stops settling. That was the difference between filling method and caving method to manage the roof, as shown in Figure 1.

[figure(s) omitted; refer to PDF]

The mining distance was the result of the accumulation of the mining speed with time. Assumed that the mining rate remains constant, the influence of roof span length on the compression deformation of the filling body in goaf could be expressed by the coordinate relationship between the compressive deformation of the filling body and the time t.

Under a specific mining geological condition, the advancement speed of the working face is encapsulated in the time variable t. The compression deformation of the filling body, which is frequently observed in the actual production process, is also considered a function of time. In addition, the movement of mutual occlusion and rotation between rock strata also experienced the state of instability–temporary equilibrium–reinstability–limit equilibrium when the overlying rock strata are broken. The change of advanced abutment stress of coal was related to time parameters and the fracture process of surrounding rock under compression was also the same. As a result, the equivalent mining height of the working face, when using the filling method, can be viewed as a function of the time parameter.$$\begin{array}{}\text{(1)}& h_{e}t=h_0-h_{c}t,\end{array}$$where $h_{e}t$ is the equivalent mining height of filling working face. $h_0$ is mining height. $h_{c}t$ is the height of the filling body after compression.

During the compaction process of the filling body, there exists a substantial variation in the movement amplitude and duration of the roof strata between areas near the open-off cut and the coal wall. The movement of roof strata within the goaf exhibits pronounced regional and temporal characteristics.

The filling body exerts a controlling influence on the roof of goaf, closely tied to its height and abilities for compressive deformation. The control effect that the filling body has on the movement of the overlying rock strata can be intuitively represented by the equivalent mining height. Figure 2 illustrates the movement of overlying rock strata under varying conditions of equivalent mining height. When this height was small, the subsidence movement amplitude of the goaf roof was also small, the immediate roof remained intact, and the overlying rock strata in the goaf mainly underwent a bending subsidence movement. As the equivalent mining height increased, the immediate roof experienced periodic fracturing as the working face advanced. Owing to the expansibility of the collapsed rock strata, the main roof and upper strata only underwent a certain degree of bending subsidence without fracturing, thus reducing the strength and range of roof strata movement above the goaf. A further increase in equivalent mining height led to an increase in the limit height of free subsidence movement of roof strata. This resulted in the collapse of the immediate roof alongside the mining of the working face, followed by the fall of main roof. Under corresponding equivalent mining height conditions, the roof strata exhibited the phenomenon of first weighting and periodic pressure. Ultimately, the overlying rock strata movement of the working face with the filling method extended further to the high-level strata. At this point, there is little difference in the mine pressure of the working face between the filling mining and traditional caving mining.

[figure(s) omitted; refer to PDF]

2.2. Time-Space Hysteresis

Unlike the caving management roof, the main roof range and movement evolution of the filling working face are influenced not only by the vertical height of the rock strata and the coal seam floor, the thickness of the immediate roof, and the expansion coefficient but also by the height changes of the filling body.

In the mining direction, the roof of goaf bends and subsides under the action of its own weight and the load of the overlying rock strata. Throughout the compression deformation process, the filling body offers resistance to the roof strata, thereby controlling the vertical and velocity displacement of the roof strata. As previously mentioned, the compaction process of the filling body is closely tied to the mining degree of working face. The progression shows that only after the working face is mined to a certain phase can it be fully enriched. At this point, the roof halts its movement, and the force balance between the roof and the filling body is achieved. To investigate the relationship between the subsidence movement of the goaf roof and the height of filling body, the roof movement process is divided into three stages:

• Stage 1: During the initial mining of the working face, the rock beam span length of immediate roof is $l_1$. The roof of the goaf was regarded as a beam with fixed ends, supported by the coal walls at the working face and behind the open-off cut. Consequently, the roof of the goaf was only capable of bending and subsiding. The development height of roof crack in the goaf is $h_{f1}$ at this time. The immediate roof exerts minimal extrusion pressure on the filling body. Consequently, the height of filling body is at its maximum and its compactness is at its worst, as depicted in Figure 3(a).

• Stage 2: As the mining of the working face continues, the span length of rock beam increases, enhancing the bending moment and the bending subsidence of the end of rock beam. This results in a new compressive deformation of the filling body, which changes dynamically in tandem with the mining activities of working face. The motion state of the immediate roof is determined by the load of overlying rock strata, the support force of filling body, and its own strength. According to the fixed beam calculation model, the maximum bending moment of rocking beam occurs at the end of beam. If this bending moment is less than its ultimate bending moment, the immediate roof maintains continuous integrity. However, if the bending moment at the end of the rock beam exceeds its ultimate bending moment, the tensile failure will cause the immediate roof to break. This is evidenced by the initial fracture of the immediate roof, leaving room for the bending subsidence and breaking movement of higher-level roof, as shown in Figure 3(b).

• Stage 3: In the direction of the working face mining, the height of filling body continually changes with the position of the coal wall in the working face. When the working face is mined to a specific phase, the constraint of goaf plane size on the overlying rock strata movement is minimized, and the compressive stress applied to the filling body by the roof of goaf reaches its maximum. After mutual feedback and repeated action, the filling body and the roof achieve mechanical balance. The filling body no longer produces new compression deformation, and its compression deformation reaches its maximum, as depicted in Figure 3(c).

[figure(s) omitted; refer to PDF]

The process of the roof strata compressing the filling body is also a process in which the compressive deformation capability of the filling body gradually increases. This is demonstrated by the stepwise increase in the compressive deformation of the filling body as the working face advances to a certain point. Considering the mechanical action mechanism between the roof strata and the filling body, it can be viewed as a dynamic equilibrium mechanical system with mutual feedback. The deformation of the filling body exhibits obvious hysteresis. When the work face is square, the constraint of goaf size on roof movement is minimal. At this point, the compressive deformation of the filling body has not yet peaked, and its compressive deformation will continue to rise. As the working face continues to advance to a certain position, a balance is struck between the mechanical effect of the roof strata and the filling body, and the compressive deformation of the filling body reaches its maximum. Unlike the movement of overlying rock strata in the caving mining face, the amplitude and speed of roof movement in the filling working face are affected by the filling effect of the goaf. The compression of the filling body is a slow process, and the overlying rock strata and its evolution in a filling working face exhibit clear time-space hysteresis.

To accurately describe the height change process of the filling body after it enters the goaf, a filling rate is defined as the ratio of the height of filling body after compressive deformation under the compressive stress of the overlying rock strata to the height of the coal cutting. This rate is represented by η. The filling rate changes dynamically with the movement state of the overlying rock strata. The initial filling rate, represented by ${\eta }_0$, is defined as the ratio of the initial filling height to the coal cutting height when the filling body first enters the goaf. This rate can only reflect the initial filling height of the filling body in the goaf. The final filling rate, represented by ${\eta }_f$, is defined as the ratio of the final filling height to the cutting height of the filling body when the overlying rock strata reach a stable state. This rate can reflect the final state of the roof after movement, but it is not suitable for analyzing the process of roof movement.$$\begin{array}{}\text{(2)}& \eta =\frac{h_{c}t}{h_0},\text{(3)}& {\eta }_0=\frac{h_c{t}_0}{h_0},\text{(4)}& {\eta }_f=\frac{h_c{t}_f}{h_0},\text{(5)}& \Delta h_c=h_c{t}_0-h_c{t}_f,\text{(6)}& \Delta t=t_f-t_0,\end{array}$$where $t_0$ is the time when the filling body is just filled into the goaf. $t_f$ is the time when the filling body reaches the maximum compressive deformation. $h_c{t}_0$ is the initial filling height when the filling body is just filled into the goaf. $h_c{t}_f$ is the final height of the filling body after the overlying rock strata move steadily in the goaf. $\Delta h_c$ is the cumulative compression amount from the filling body self-filling into the goaf to the roof movement stability. $\Delta t$ is the time from the filling body filling into the goaf to the stability of the roof movement.

The compression deformation process of the filling body that was regarded as a special rock mass with low strength under roof stress was analyzed by the Kachanov creep damage theory [21]. The calculation model of compression deformation of the filling body was obtained:$$\begin{array}{}\text{(7)}& \dot{T}=C{\frac{\sigma }{1-T}}^n,\end{array}$$where $\dot{T}$ is the change rate of filling body damage factor. T is the damage factor of filling body. C, n is the inherent parameter of the material, taken as a constant.σ​ is stress.

Take time 0∼t and damage factor 0∼T. Take change rateas 1, separate (1-T) and Cσ and integrate them on both sides (7).$$\begin{array}{}\text{(8)}& {{\displaystyle \int }}_0^{t}C{\sigma }^{n}dt={{\displaystyle \int }}_0^T{1-T}^{n}dT,\text{(9)}& T=1-{1-Ctn+1{\sigma }^n}^{1/n+1}.\end{array}$$

When the damage factor T = 1, the compression deformation of the filling body reaches the maximum. This event $t_f$ was defined as the critical time for the filling body to reach the maximum compressive deformation, which could be expressed as$$\begin{array}{}\text{(10)}& t_f=\frac{1}{Cn+1{\sigma }^n}.\end{array}$$

From equations (1)–(10), the compressive deformation of the filling body was affected by the compressive stress applied by the roof and its own physical and mechanical properties. The greater the compressive stress applied to the roof, the shorter the time to reach the maximum compression deformation. The equivalent mining height was the difference between the height of the filling body and the mining height. The equivalent mining height was a state variable varying with the height of the filling body when the mining height of the coal seam was constant. Compared with the caving mining face, the time required for the overlying rock strata movement of the filling working face to reach a stable state was greater than that of the caving mining face. The overlying rock strata movement of the filling method working face showed a certain hysteresis.

3. Advanced Abutment Stress Evolution Based on Three-Zone Structure Loading Model

3.1. Three-Zone Structure Loading Model Division

The equivalent mining height of the filling working face determines the strength and range of overlying rock strata movement. In addition, it determines the distribution characteristics and variation evolution of advanced abutment stress on the working face. Based on the shape of the overlying rock strata after strata movement, the traditional three zones of strata are categorized. These zones focus on researching the structural characteristics of overlying rock strata once the strata reach a stable state of motion. Primarily, they are used for surface subsidence control, prevention and control of water and gas, etc. The theory of a three-zone structure loading model, proposed by Prof. Jiang [22, 23], categorizes the stress loading mode of coal bodies by rock structure and evolution. This theory focuses on the time effect of overburden structure type and the evolution of coal seam abutment pressure. It is mainly used for the prevention and control of dynamic disasters such as rock bursts. Based on the state of rock strata movement and the timeliness of applying stress to the coal body, the overlying rock strata are divided into an instant loading zone (ILZ), a delayed loading zone (DLZ), and a static loading zone (SLZ).

Numerous engineering practices have indicated that overlying thick and hard rock strata are prone to breakage and induce dynamic load impact during the mining of the working face. Therefore, researching the distribution evolution of advanced abutment stress before and after squaring the working face is crucial for guiding the prevention and control of rock bursts. As the working face advances, the scope of the goaf expands further. When the working face is pushed to the square position, the short side of the goaf extends to the oblique length of working face and remains constant. The limiting effect of goaf size on the fracture development of overlying rock strata is minimized, and the fracture movement of overlying rock strata continues to develop upward. Above the ILZ, new deflection and fracture gradually appear in the rock strata, and separation occurs between the strata. A part of the rock above the ILZ moves slowly over a long period of time and gradually applies stress to the coal body of the working face. The peak value and influence range of advanced abutment stress increase, marking the formation of the stress-affected zone of the DLZ. At this time, the rock strata structure is a three-zone structure consisting of “ILZ + DLZ + SLZ,” as shown in Figure 4.

[figure(s) omitted; refer to PDF]

Based on previous analysis, it was observed that when the supportive stress from the filling body and the compressive stress applied by the roof were in equilibrium, the compression deformation of the filling body reached its peak value. Consequently, the rock bed separation and fracture height also reached their maximum. This separation and fracture resulted in a noncontact state between adjacent rock strata, thereby blocking the downward direct load transmission pathway of the upper rock strata. Typically, the stratum of bed separation is higher than that of the fracture. For ease of analysis, the position of the rock strata separation was utilized as a reference point for determining the height of the DLZ.

To simplify the analysis, the rock strata extending from the key stratum to the coal seam floor were treated as a single group of strata. Given that the compaction of the filling body is a gradual process, the movement of these rock strata would significantly influence the structural characteristics of the three-zone structure loading model of the filling working face. Upon completion of the coal mining and back filling at the working face, the low roof of goaf started to bend and subside, applying compressive stress to the filling body. The movement of these rock strata would immediately manifest at the working face:$$\begin{array}{}\text{(11)}& H_{\text{ILZ}}^0=\frac{h_e}{K_A-1},\end{array}$$where $H_{\text{ILZ}}^0$ is the ILZ height of the filling working face. $h_e$ is the equivalent mining height of a filling working face. $K_A$ is the bulking coefficient of low rock in goaf.

The value of $K_A$ was 1.1–1.3 when calculating the thickness of the caving zone. The ILZ not only included the part of rock strata in the definition of caving zone in reference [24] but also included the mining along with the working face. In a short time, it could break and rotate and form a rock strata group with a bearing structure. The range was larger than the caving zone. Here the value of $K_A$ was 1.1 [25]:$$\begin{array}{}\text{(12)}& M_{\text{ILZ}}^0=H_{\text{ILZ}}^0\approx 10h_e,\end{array}$$where $H_{\text{ILZ}}^0$ was the rock thickness of the ILZ of the filling working face.

Contrary to the caving mining face, the subsidence movement of the roof strata in the filling mining face was regulated by the filling body in the goaf. The ultimate subsidence height of the immediate roof in the goaf matched the equivalent mining height. Consequently, the thickness of the ILZ was intimately linked to the effectiveness of the goaf filling. The better the filling effect, the smaller the equivalent mining height, leading to more moderate roof strata movement. Conversely, if the filling effect was less effective, the movement of the roof strata was more intense.

If the goaf is entirely filled by the ILZ, the upper strata cannot initially bend, fracture, or subside due to the absence of caving space. However, as the filling body gradually compacts, some space is freed up, and a new subsidence area is provided for the upper strata. The separation and fracture of the upper strata continue to propagate upwards until the compression deformation of the filling body ceases to increase. This is a gradual and prolonged process that accompanies the continuous mining of the working face. The timing and spatial characteristics of roof strata movement primarily involve the caving movement of the lower rock strata near the filling body in the early stages, followed by the separation movement of the upper rock strata in the later stages.

Based on the foregoing analysis, the separation height of the overlying rock strata in the goaf is influenced by several factors: the positioning of the key strata, the filling rate of the goaf, the thickness of the coal seam, and the comprehensive expansion coefficient of the key strata relative to the strata between the coal seams. Hence, the height of the DLZ can be expressed as follows:$$\begin{array}{}\text{(13)}& H_{\text{DLZ}}^0=h_{fi}=\frac{h_{0}1-{\eta }_i}{K_i-1},\end{array}$$where $H_{\text{DLZ}}^0$ is the thickness of the DLZ of the filling working face.

According to the definition of static load zone, the rock strata group located above the DLZ until the surface range was the static load zone:$$\begin{array}{}\text{(14)}& M_{\text{SLZ}}^0=H-M_{\text{DLZ}}^0-M_{\text{ILZ}}^0,\end{array}$$where $M_{\text{SLZ}}^0$ is the thickness of the rock strata in the static load zone. H is the mining depth of the coal seam.

3.2. Estimation Method of Advanced Abutment Stress

According to the three-zone structure loading model theory, the rock strata in the ILZ undergo periodic deflection, rupture, and collapse over a short period as the working face advances. This forms a supporting structure in the goaf with the resultant stress appearing immediately in the coal wall of working face. This stress dynamically moves forward with the mining and forms a dynamic advanced abutment stress. The DLZ and its overlying rock strata transfer the stress to the peripheral area of separation zone and impact the coal seam in the form of a static load. The advanced abutment stress of the coal body in front of the working face is composed of the self-weight stress, the increment of rock transfer stress in the ILZ, and the increment of rock transfer stress in the DLZ and the SLZ.$$\begin{array}{}\text{(15)}& {\sigma }_J={\sigma }_q+{\sigma }_{\text{ILZ}}+{\sigma }_{\text{DLZ}},\end{array}$$where ${\sigma }_{\mathrm{q}}$ is self-weight stress. ${\sigma }_{\text{ILZ}}$ is the stress increment of ILZ rock transfer. ${\sigma }_{\text{DLZ}}$ is the stress increment of rock strata transfer in the DLZ and SLZ.

The height of separation and deformation of the overlying rock strata relative to the filling body was analyzed based on the three-zone structural loading model. Subsequently we established an estimation model for the advanced abutment stress of the filling working face. The thicknesses of the ILZ, DLZ, and SLZ were denoted as MILZ, MDLZ, and MSLZ, respectively. The boundary line OB, between the coal wall of the working face and the outer end of the separation area, was called the boundary line of rock movement. The angle α with the horizontal direction indicated the rock strata movement angle. The mining length of the working face was represented by “l,” and “L” denoted the total length of the working face. The dotted line AD was the center line of the goaf. A rectangular coordinate system xoy was established, with the boundary point O of the goaf and the coal wall serving as the origin. This model was used to calculate the vertical stress of the coal body in front of the working face.

1. Instant loading with rock transfer stress increment

  The source of the stress increment in the ILZ could be approximately regarded as the weight of the rock strata in the OAB range in Figure 4. For the filling goaf, the height of the rock strata in this part was affected by the filling rate of the goaf, that is:$$\begin{array}{}\text{(16)}& {\delta }_{\text{ILZ}}=\frac{5L{h}_e\gamma }{2}.\end{array}$$

  The peak stress of rock transfer in ILZ can be expressed as$$\begin{array}{}\text{(17)}& {\sigma }_{\text{ILZmax}}=\frac{L\gamma \tan \alpha }{2},\end{array}$$

  where ${\delta }_{\text{ILZ}}$ is the load of immediate loading with strata transfer. ${\sigma }_{\text{ILZ}\max }$ is the peak value of rock transfer stress in the ILZ.

  The stress increment of this part of rock strata transfer was approximately considered to be a triangular distribution within the allowable precision range of engineering:$$\begin{array}{}\text{(18)}& {\sigma }_{\text{ILZ}}=\begin{array}{cc}\frac{{\sigma }_{\text{Imax}}\tan \alpha }{5h_e}x,& 0,\frac{5h_e}{\tan \alpha },\\ 2{\sigma }_{\text{Imax}}-\frac{{\sigma }_{\text{Imax}}\tan \alpha }{5h_e}x,& \frac{5h_e}{\tan \alpha },\frac{10h_e}{\tan \alpha },\\ 0,& \frac{10h_e}{\tan \alpha },\infty .\end{array}\end{array}$$

  According to equations (16)–(18), the stress expression of immediate loading rock transfer is as follows:$$\begin{array}{}\text{(19)}& {\sigma }_{\text{ILZ}}=\begin{array}{cc}\frac{L\gamma {\tan }^2\alpha }{10h_e}x,& 0,\frac{5h_e}{\tan \alpha },\\ L\gamma \tan \alpha -\frac{L\gamma {\tan }^2\alpha }{10h_e}x,& \frac{5h_e}{\tan \alpha },\frac{10h_e}{\tan \alpha },\\ 0,& \frac{10h_e}{\tan \alpha },\infty .\end{array}\end{array}$$

2. Stress increment of delayed loading with strata transfer

  The height of the DLZ in the filling working face is determined by whether the key stratum separates from the weak rock strata below after its final bending deformation stabilizes. If separation occurs, the height of the DLZ extends from the roof of the coal seam to the topmost part of the key stratum in the bending separation state. Therefore, the thick and hard rock strata (subcritical strata) among the overlying rock strata of the working face function as the skeleton of the rock mass structure. These strata usually exhibit a low degree of crack development or maintain an overall bending and subsiding movement, thus keeping pace with a key stratum above the slow separation stratum. The weight of the rock strata is conveyed to the coal and rock mass outside the separation zone in the manner of a cantilever beam.$$\begin{array}{}\text{(20)}& {\delta }_{\text{DLZ}}=\frac{\gamma H_{\text{DLZ}}‐10h_{e}L\tan \alpha +H_{\text{DLZ}}+10h_e}{2\tan \alpha }.\end{array}$$

  The peak value of rock transfer stress increment in the DLZ could be determined by the following equation:$$\begin{array}{}\text{(21)}& {\sigma }_{\text{DLZmax}}=\frac{\gamma H_{\text{DLZ}}‐10h_{e}L\tan \alpha +H_{\text{DLZ}}+10h_e}{H_{\text{DLZ}}+10h_e}.\end{array}$$

  The transfer stress increment of rock strata in a DLZ could be expressed as$$\begin{array}{}\text{(22)}& {\sigma }_{\text{DLZ}}=\begin{array}{cc}\frac{{\sigma }_{\text{Dmax}}2\tan \alpha }{H_{\text{DLZ}}+10h_e}x,& 0,\frac{H_{\text{DLZ}}+10h_e}{2\tan \alpha },\\ {2\sigma }_{\text{Dmax}}-\frac{{\sigma }_{\text{Dmax}}2\tan \alpha }{H_{\text{DLZ}}+10h_e}x,& \frac{H_{\text{DLZ}}+10h_e}{2\tan \alpha },\frac{H_{\text{DLZ}}+10h_e}{\tan \alpha },\\ 0,& \frac{H_{\text{DLZ}}+10h_e}{\tan \alpha },\infty .\end{array}\end{array}$$

  According to equations (20)–(22), the expression of the transfer stress increment of the rock strata in the DLZ could be obtained:$$\begin{array}{}\text{(23)}& {\sigma }_{\text{DLZ}}=\begin{array}{cc}\frac{2\gamma \tan \alpha H_{\text{DLZ}}‐10h_{e}L\tan \alpha +H_{\text{DLZ}}+10h_e}{{H_{\text{DLZ}}+10h_e}^2},& 0,\frac{H_{\text{DLZ}}+10h_e}{2\tan \alpha },\\ \begin{array}{c}\frac{2\gamma H_{\text{DLZ}}‐10h_{e}L\tan \alpha +H_{\text{DLZ}}+10h_e}{H_{\text{DLZ}}+10h_e}\\ -\frac{2\gamma \tan \alpha H_{\text{DLZ}}‐10h_{e}L\tan \alpha +H_{\text{DLZ}}+10h_e}{{H_{\text{DLZ}}+10h_{\mathrm{e}}}^2}x\end{array},& \frac{H_{\text{DLZ}}+10h_e}{2\tan \alpha },\frac{H_{\text{DLZ}}+10h_e}{\tan \alpha },\\ 0,& \frac{H_{\text{DLZ}}+10h_e}{\tan \alpha },\infty .\end{array}\end{array}$$

3. The transfer stress increment of strata in the static load zone

  The range of rock strata in the static load zone was the key stratum from the curved bed separation state to the surface and the dead weight of the static load zone was transmitted to the coal and rock mass on both sides of the separation zone through the DLZ. The calculation method was consistent with the transfer stress increment of rock strata in the DLZ. The calculation equation was as follows:$$\begin{array}{}\text{(24)}& {\delta }_{\text{SLZ}}=\frac{M_{\text{SLZ}}\gamma L\tan \alpha +2H_{\text{DLZ}}}{2\tan \alpha },\text{(25)}& {\sigma }_{\text{SLZmax}}=\frac{M_{\text{SLZ}}\gamma L\tan \alpha +2H_{\text{DLZ}}}{H_{\text{DLZ}}+10h_e},\text{(26)}& {\sigma }_{\text{SLZ}}=\begin{array}{cc}\frac{{\sigma }_{S\max }2\tan \alpha }{H_{\text{DLZ}}+10h_e}x,& 0,\frac{H_{\text{DLZ}}+10h_e}{2\tan \alpha },\\ 2{\sigma }_{S\max }-\frac{{\sigma }_{S\max }2\tan \alpha }{H_{\text{DLZ}}+10h_e}x,& \frac{H_{\text{DLZ}}+10h_e}{2\tan \alpha },\frac{H_{\text{DLZ}}+10h_e}{\tan \alpha },\\ 0,& \frac{H_{\text{DLZ}}+10h_e}{\tan \alpha },\infty ,\end{array}\end{array}$$

  where ${\sigma }_{\text{SLZ}}$ is the load of rock strata transfer in a static load zone. ${\sigma }_{\text{ILZ}\max }$ is the peak value of transfer stress increment in the static load zone.

According to equations (24) and (26), the expression of the transfer stress increment of the rock strata in the static load zone could be obtained:$$\begin{array}{}\text{(27)}& {\sigma }_{\text{DLZ}}=\begin{array}{cc}\frac{2\gamma M_{\text{SLZ}}\tan \alpha L\tan \alpha +{2H}_{\text{DLZ}}}{{H_{\text{DLZ}}+10h_e}^2}x,& 0,\frac{H_{\text{DLZ}}+10h_e}{2\tan \alpha },\\ \begin{array}{c}\frac{2\gamma M_{\text{SLZ}}L\tan \alpha +{2H}_{\text{DLZ}}}{H_{\text{DLZ}}+10h_e}-\\ \frac{2\gamma M_{\text{SLD}}\tan \alpha L\tan \alpha +{2H}_{\text{DLZ}}}{{H_{\text{DLZ}}+10h_e}^2}x\end{array},& \frac{H_{\text{DLZ}}+10h_e}{2\tan \alpha },\frac{H_{\text{DLZ}}+10h_e}{\tan \alpha },\\ 0,& \frac{H_{\text{DLZ}}+10h_e}{\tan \alpha },\infty .\end{array}\end{array}$$

In summary, the equation for calculating the advanced abutment stress of the filled working face could be obtained by equations (19), (23), and (27):$$\begin{array}{}\text{(28)}& {\sigma }_J=\begin{array}{cc}\frac{{L\gamma \tan }^2\alpha }{10h_e}x+\frac{2\gamma \tan \alpha L\tan \alpha H_{\text{DLZ}}-10h_e+M_{\text{SLZ}}+H_{\text{DLZ}}^2-{100h}_e^2+2H_{\text{DLZ}}{M}_{\text{SLZ}}}{{H_{\text{DLZ}}+10h_e}^2}x,& 0,\frac{5h_e}{\tan \alpha },\\ L\gamma \tan \alpha -\frac{{L\gamma \tan }^2\alpha }{10h_e}x+\frac{2\gamma \tan \alpha L\tan \alpha H_{\text{DLZ}}-10h_e+M_{\text{SLZ}}+H_{\text{DLZ}}^2-{100h}_e^2+2H_{\text{DLZ}}{M}_{\text{SLZ}}}{{H_{DLZ}+10h_e}^2}x,& \frac{5h_e}{\tan \alpha },\frac{10h_e}{\tan \alpha },\\ \frac{2\gamma \tan \alpha L\tan \alpha H_{\text{DLZ}}-10h_e+M_{\text{SLZ}}+H_{\text{DLZ}}^2-{100h}_e^2+2H_{\text{DLZ}}{M}_{\text{SLZ}}}{{H_{\text{DLZ}}+10h_e}^2}x,& \frac{10h_e}{\tan \alpha },\frac{H_{DLZ}+10h_e}{2\tan \alpha },\\ \begin{array}{c}\frac{2\gamma LH\tan \alpha +H_{\text{DLZ}}^2+2H_{\text{DLZ}}{M}_{\text{SLZ}}-{100h}_e^2‐10L{h}_e\tan \alpha }{H_{\text{DLZ}}+10h_e}\\ -\frac{2\gamma \tan \alpha L\tan \alpha H_{\text{DLZ}}-10h_e+M_{\text{SLZ}}+H_{\text{DLZ}}^2-{100h}_e^2+2H_{\text{DLZ}}{M}_{\text{SLZ}}}{{H_{\text{DLZ}}+10h_e}^2}x,\end{array}& 1\frac{H_{\text{DLZ}}+10h_e}{2\tan \alpha },\frac{H_{\text{DLZ}}+10h_e}{\tan \alpha },\\ \gamma H,& \frac{H_{\text{DLZ}}+10h_e}{\tan \alpha },\infty .\end{array}\end{array}$$

3.3. Advanced Abutment Stress Calculation

In accordance with the actual conditions of the C5301 goaf, the mining height ($h_0$) was 3.5 m. The comprehensive expansion coefficient of roof strata in various layers above the coal seam could be determined by referencing the measured results in reference [26]. The critical filling rate of the goaf, based on the bending contact of the key stratum, is depicted in Figure 5. The first subcritical stratum above the coal seam consisted of medium sandstone with a thickness of 25.2 m; its distance from the coal seam height ($h_{f1}$) was 20.1 m. The comprehensive expansion coefficient of the fractured and deformed rock strata between the key stratum and the floor of the coal seam ($K_1$) was 1.027. Substituting these values into equation (11), the critical filling rate (${\eta }_{f1}$) was found to be 77.5%. This is in line with the state where the key stratum is in bending contact with the gangue. In other words, when the height of the compacted filling body exceeds 77.5% of the mining height of the coal seam, the filling body in the goaf and the fractured and deformed rock strata above can fill the separation space beneath the first subcritical stratum, enabling the first subcritical stratum to reach a state of bending contact.

[figure(s) omitted; refer to PDF]

The C5301 working face employed the bag filling mining method, utilizing super-high water material bag mining and filling. The working face was equipped with a new filling support system. A separate filling space was created through the combination of partitions formed by several filling supports. Each filling space contained a filling bag; after the filling support was advanced, the filling bag was refilled between the bag and the roof. Based on site conditions, apart from the roof subsidence before filling, the goaf is generally filled by the filling body. According to data measured from super-high water material bag filling goaf in recent years, the filling rate (η) is 80% [17].

According to the geological mining conditions of C5301 working face, mining depth H = 677 m, L = 60 m, $h_0$ = 3.5 m, α = 78°, β = 0.893, ω = 14, $v$ = 2 m/d, $q_1$ = 2.5 MPa, γ = 25 kN/m³, $l_2$ = 25 m, $f_1$ = 0.1, $l_3$ = 20 m, $l_4$ = 20 m, $h_1$ = 25.1 m, ${\eta }_f$ = 80%, and $h_0$ = 3.2 m. Substituting the parameters into equation (28), the expression of the advanced abutment stress distribution of the C5301 working face was as follows:$$\begin{array}{}\text{(29)}& {\sigma }_{Z-\mathrm{C}5301}=\begin{array}{cc}\begin{array}{c}2.4x,\\ \begin{array}{c}7.6-0.22x,\\ 1.09x,\\ 10.2-0.61x,\end{array}\\ 0.835x,\end{array}& \begin{array}{c}0,3,\\ \begin{array}{c}3,6,\\ 6,20,\\ 20,40,\end{array}\\ 40,49,\end{array}\\ \begin{array}{c}64.8-0.485x,\\ 16.9x,\end{array}& \begin{array}{c}49,98,\\ 98,\infty .\end{array}\end{array}\end{array}$$

The distribution of the advanced abutment stress of the working face is shown in Figure 6. Theoretical calculations showed that the influence range of the advanced abutment stress on the C5301 working face was 98 m. The maximum static stress of 41.1 MPa, transferred by rock in the DLZ and SLZ, was located 49 m from the coal wall of the working face. The advance abutment stress curve exhibited a turning point 20 m from the coal wall, corresponding to the advance abutment stress of 22.5 MPa. This was due to the cumulative effect of dynamic stress and static stress transmitted by rock strata movements under instant loading. Within the 0–20 m range, the dynamic stress increased, resulting in a greater stress disparity within the coal in this area. This, in turn, heightened the inclination toward impact instability induced by significant stress differences.

[figure(s) omitted; refer to PDF]

4. Engineering Applications

4.1. Engineering Overview

The Yunhe coal mine is situated in the northern outcrop area of the Jibei coal field and Tangkou exploration area in Jining City, Shandong Province. A significant amount of coal is overlaid by ground structures, which led to the adoption of strip mining in the early stages of the mine. Consequently, abundant dull coal resources have been generated within the mine field. In particular, to safely recover these leftover coal pillars and ensure the sustainable development of mine, the Yunhe coal mine has undertaken systematic research on coal pillar replacement through filling.

The C5301 working face was the first to employ solid filling in Yunhe coal mine. The working face had an inclined length of 72 m and propulsion length of 260 m. The C5301 working face had a coal seam thickness ranging from 2.8 m to 8.0 m, averaging 6.6 m. The dip angle of the coal seam varied from 4° to 20° in the crossheading, with an average of 12°. The mining depth of the working face varied from 617 to 737 m, with an average of 677 m. The C5301 working face implemented a comprehensive mechanized inclined longwall retreat mining method with stratum as the mining bottom and a mining height of 3.5 m. The super-high water bag full filling method was applied to manage the roof of the goaf. The layout of the C5301 working face is illustrated in Figure 7.

[figure(s) omitted; refer to PDF]

On October 20, 2019, the C5301 working face had mined to 120 m. On that same day, four microseismic events of 10⁴ J energy level were monitored, with the maximum energy recorded being 6.03 × 10⁴ J. The plane location of the large energy microseismical event is depicted in Figure 8. A significant coal burst occurred on the working face. The floor heaved 300–400 mm within a 20 m range ahead of the track roadway. There was obvious convergence in the roadway section within the 50–74 m area of the coal wall of north wing head gate, resulting in varying degrees of roof damage. Some sections even experienced a slight roof fall, as illustrated in Figure 9.

[figure(s) omitted; refer to PDF]

4.2. Field Monitoring and Verification

4.2.1. Coal Stress Monitoring Analysis

Stress measurement points were set up in the mining gateway of the C5301 working face, and a stress online monitoring system was employed to real-time monitor the two sides of the belt roadway, the track roadway, and the north wing head gate. The stress meters were installed during excavation and calibrated before mining on the working face. Each group of stations installed two sets of measurement points at different depths (8 and 14 m), spaced 1.0–1.5 m apart. The initial pressure setting of the stress meter was no less than 4 MPa. The stress meters were arranged before the mining began of working face. The historical monitoring curves of specific measurement points (17# and 19# in the track roadway trough and 13# and 16# in the belt roadway trough) were selected, as shown in Figure 10.

[figure(s) omitted; refer to PDF]

As shown in Figure 10, the monitoring value of stress meter started to rise due to the impact of the advanced abutment stress. The influence range of the advanced abutment stress on the track roadway was 92–94 m. The stress monitoring data of belt roadway showed that the influence range of the advanced abutment stress on the working face was 91–97 m. A positive correlation was found between the influence range of the advanced abutment stress and the distance from the stress gauge station to the open-off cut. In other words, a greater mining range of the working face resulted in an increased distance from the roof movement to the stress transfer in front of the working face [27].

The monitoring value of stress meter entered a phase of accelerated growth when the working face advanced to a distance of 36–50 m from the stress meter, indicating that the stress meter had entered the significant influence range of the advanced abutment stress. As the gap between the stress meter and the coal wall of the working face further decreased, the monitoring value of stress meter experienced some fluctuations. This suggests that the super-high water material underwent compression deformation under the roof load of the goaf. The distribution pattern of advanced abutment stress in a filling working face differed from that in a traditional caving working face. The support of roof from the filling body and its mechanical properties are crucial factors that affect the subsidence movement of roof and the advanced abutment stress distribution.

When the stress meter was 9–32 m away from the coal wall of the working face, the monitoring value reached its peak. Moreover, the monitoring values of some stress meters continued to increase as the distance from the working face further decreased, even exceeding the red warning of stress value in some cases. This indicates that stress concentration due to mining has taken place within the coal body ahead of the coal wall in the working face.

4.2.2. Working Resistance Analysis of Hydraulic Support

Four stress measurement lines were arranged at 10 #, 20 #, 30 #, and 40 # hydraulic support in the early stage of mining. When the working face was mined to 110 m later, measurement lines were arranged every 5 hydraulic support from 5 # to 40 #. A total of 8 measurement lines were arranged. In order to analyze the influence of roof movement on the support efficiency of hydraulic support in filling working face during the whole mining period [28], the change in the data collection method for the working resistance of the support is used as a time division line to represent the variation of the support working resistance with the advancement distance of the working face in the form of a stress cloud map. In the first stage (0–110 m), the advancement distance is taken as the horizontal coordinate, and the average value of the actual working resistance data of the support is taken as the vertical coordinate, as shown in Figure 11. In the second stage (110–260 m), the advancement distance is taken as the horizontal coordinate, and the working resistance data of the support fed back by the roof monitoring system are used as the basis to draw the corresponding relationship between the support’s cycle-end resistance and the advancement distance, as shown in Figure 12.

[figure(s) omitted; refer to PDF]

The overall working resistance of hydraulic support in working face was low, when the working face first saw the square [29]. When the working face was pushed to 80 m, the working resistance of the support was locally increased to more than 20 MPa, and the continuous distance was about 20 m. It showed that the low roof of goaf was broken for the first time, and the first pressure step of working face was about 80–100 m. It was 20–30 m larger than the caving mining face in the same mining area. When the working face advanced to 190–210 m, the working resistance of the hydraulic support increased in a large range for the first time, and the peak was close to the rated working resistance of the hydraulic support. The first breaking step of roof and the advancing distance corresponding to the maximum development height of fracture were larger than those of caving mining face. It showed that the roof movement of coal mining face with filling method has obvious time-space hysteresis [30].

4.2.3. Spatial Distribution Characteristics of Microseismical Events

The fracturing of thick and hard rock strata on the working face often leads to large energy microseismical events [31]. The comprehensive histogram of the borehole and the local borehole histogram should be combined to evaluate the distribution evolution of section. Figure 13 displays the projection of microseismical events along the strike of the C5301 working face during production [32].

[figure(s) omitted; refer to PDF]

Based on the microseismical monitoring location map analysis, the C5301 working face was mined following the coal seam floor, with the average dip angle of coal seam being 12°. The elevation shift of the working face was gradual, with the average elevations in September, October, and November being −683, −665, and −647 m, respectively. The microseismical events during mining recorded average elevations of −655, −652, and −637 m, being 28, 13, and 10 m above the operational face, respectively. This equates to an average of 17 m, which is 23.6% of the working face length, significantly lower than the height of microseismical events during traditional caving mining.

As for the 4th-order microseismical events, their average elevations were −665, −656, and −640 m, respectively, during the mining. They were 18, 9, and 7 m above the working face, respectively, with an average of 11 m. These high-energy microseismical events primarily occurred within a 20 m range above the roof strata. They were likely caused by fractures in the 0–4 m dirt band, 0–4.5 m top coal, 0.4–1.1 m mudstone, 4.33–7.1 m siltstone, and 1.57–6.8 m fine sandstone above the working face. These events suggest that the high-energy microseismical events at the roof of the working face mainly occurred in the bottom coal and low rock strata.

From a broad perspective, the microseismical events above the working face showed a linear distribution, indicating a relatively consistent fracture height in the roof strata. Initially, due to the slow mining speed, in September, microseismical events were mainly concentrated at the same height above the working face. In October and November, as the mining speed increased to 4 m/d, the microseismical events displayed a stepped distribution, reflecting the forward movement of the rupture of roof in line with the advancement of operational face. This suggests that the rupture movement of roof maintained a relatively stable height drop as mining progressed, resulting in a distinct boundary effect in the rock strata movement range, significantly influencing the advanced abutment stress distribution of the working face [33].

5. Conclusion

1. The structure characteristics of overlying rock strata in deep filling mining were revealed. A method to determine the boundary of overlying rock strata movement by “equivalent mining height” was introduced, which can also be applied to analyze the surrounding rock stress characteristics of working face. The roof movement strength of the filled operational working face was influenced by the filling body height and the slow compression process of the filling body, leading to obvious time-space hysteresis in the overlying rock strata and its evolution.

2. The overlying rock strata were divided into an ILZ, DLZ, and SLZ based on the three-zone structure loading model, considering the rock strata movement state and the stress application timeliness to the coal body. The characteristics and division method of each zone in the three-zone structure loading model of the filling working face were acquired. An estimation method for static stress in the filling working face was introduced, and an analytical expression of the three-zone structure loading model stress distribution was derived.

3. The theoretical calculations and field monitoring validation were conducted in the C5301 filling working face of the Yunhe coal mine. The results showed that the influence range of the advanced abutment stress was 98 m, with a peak value of 41.1 MPa at 49 m. The coal stress monitoring results indicated an influence range of 91–97 m and a peak distance of 21–50 m. Microseismical events were concentrated within 17 m above the coal seam, suggesting that the first key stratum remained unbroken. Compared to the caving method, the pressure step distance in the filled working face was significant, and the interval time was long, showing an evident time-space hysteresis.

Disclosure

The preprint was accidentally published at the time of submission to the journal. Compared with the preprint, the manuscript has modified the technical vocabulary and word order. We have added a reference to the preprint in the references of the manuscript.

Author Contributions

Conceptualization, Deyuan Fan and Xuesheng Liu; methodology, Deyuan Fan and Xuesheng Liu; validation, Yang Chen and Xikui Sun; formal analysis, Xikui Sun and Chunyu Dong; investigation, Yang Chen and Peng Gu; resources, Guoying Li and Hao Wang; writing–original draft preparation, Chunyu Dong and Peng Gu; writing–review and editing, Yu Zhang and Chuancheng Liu; supervision, Yu Zhang and Hao Wang; project administration, Chuancheng Liu and Guoying Li; and funding acquisition, Xuesheng Liu.

Funding

This research was funded by the Taishan Industrial Experts Program (No.tscx202408130), the Major Science and Technology Innovation Project in Shandong Province (No. 2019SDZY02), Shandong Energy Group Unveiled Leading Project (No. SNKJ2022BJ01-R27), National Natural Science Foundation of China (Nos. 52174122, 52074168, and 52374218), Excellent Youth Fund of Shandong Natural Science Foundation (No. ZR2022YQ49), and Taishan Scholar in Shandong Province (Nos. tspd20210313 and tsqn202211150).

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