1. Introduction
Longwall mining can seriously disturb surrounding rock masses. After mining out the coal seam, deformation, cracking, movement, and caving of overlying strata can occur with the formation of a continuous deformation zone, surface cracking zone, fractured zone, and caved zone (termed the “four zones” [
1,
2]; see
Figure 1). In general, there are many fissures developed in the rock masses of the fractured zone and the caved zone. If the fractured zone develops completely through the upper aquifer, the water in the aquifer can inflow into the mined-out area, which could lead to water inrush. Moreover, if the fractured zone is connected with the surface cracking zone, air leakage channels could be formed and destroy the underground ventilation circulation, which may further lead to the spontaneous combustion of coal seams [
3,
4,
5,
6,
7]. Therefore, it is essential to study and predict the development characteristics of the “four zones” induced by longwall mining to guarantee mining safety.
Several methods have been employed to study the development characteristics of the four zones in overlying strata, such as field measurements [
5,
8,
9], physical modeling [
4,
10,
11], and numerical modeling [
3,
6,
7,
12,
13,
14]. Numerical modeling can be considered a promising and effective tool to reflect the overburden movement process and predicting the heights of disturbed zones in longwall mining. Various examples of numerical modeling have been reported in the literature. Researchers have used different numerical modeling methods, including the finite element method (FEM) [
12], finite difference method (FDM) [
7,
10], discrete element method (DEM) [
3,
6], and mesh free method (MFM) [
13].
There are several types of zoning methods introduced in the literature. The commonly used zoning methods are outlined below.
In the first method, rock masses are considered elastoplastic materials while employing a strain-softening model, and the process of caving is simulated after determining the parameters in the strain-softening model when rock masses fail using an empirical formula [
12,
15]. As the failed rock masses freely fall from the roof during caving, Ghabraie et al. assumed that the stresses of the rock masses suddenly drop to almost zero after failure [
12]. After satisfying the yielding condition, the material fails, and its properties are updated to those of the damaged material. In this method, the differences in the mechanical characteristics of roof rock masses before and after caving are considered, and it is feasible to simulate strata caving by adjusting the mechanical characteristics of failed rocks. However, this method considers rock mass yielding as the caving criterion without clearly defining the scope of the caved zone, which may lead to a misjudgment of the scope.
In the second method, the heights and shapes of the caved zone and fractured zone are calculated according to an empirical formula, and then the scopes of the two zones above the mined-out area and the corresponding mechanical parameters are determined before conducting a simulation of longwall mining. Tajduś [
16] assumed that the caved zone existed with a height
hz and a shape similar to a trapezoid above the mined-out area. Moreover, the fractured zone existed with a height
hs and a shape similar to a half-ellipse above the caved zone. The heights depended on the mechanical properties of the rock mass layers and the thickness of the excavation. The parameters of the two zones were determined with laboratory tests and the GSI (geological strength index). In this method, the differences between different zones are considered, and the scope of disturbed rock masses is clearly determined. However, the determination of the scope of the caved zone and the fractured zone is strongly impacted by expert judgments, and the roof strata development process from the elastic-plastic deformation stage to the cracking and falling stage is ignored.
In the third method, the height of the caved zone is determined according to the empirical bulking factor, and in the simulation, if the strain or displacement of the falling rock mass reaches the caving criterion, it is considered a new loose material. Shabanimashcool and Li used the principal plastic strain to identify the caving boundary and the bulking factor to determine whether the roof strata of the panel entirely filled the mined-out area. After the caving process stops, the mechanical properties of caving materials are changed to a double-yield model [
17,
18]. In this method, the caving criterion is used to determine whether the surrounding rock falls in a mining simulation, which avoids misjudging the yielded noncaving rock as caved rock. The roof strata development process from elastic-plastic deformation to cracking and caving can be dynamically reflected. Moreover, the change in mechanical parameters of caved rock can also be well reflected. However, in this method, the empirical formula is used to pre-set the maximum height of the caved zone, which may be strongly affected by human intervention.
In the fourth method, caving criteria are established according to experience. In the simulation of the mining process, the boundary of the caved zone is determined dynamically according to the caving criterion, and the mechanical parameters of the rock masses in the caved zone are adjusted according to experience. Singh and Singh thought that failure of the strata was the preliminary requirement for its caving [
19,
20,
21]; therefore, the criterion for caving of the failed strata (failure in tension) to occur in the model was a maximum shear strain of 0.25 or a downwards displacement of 1 m. Then, the cohesion value of caved materials was set to zero. This method does not need to pre-set the height of the caved zone; thus, it can avoid the calculation error caused by human intervention. However, the zoning criteria also have limitations. In reality, the critical shear strain is strongly site-dependent, and the vertical displacement of the caved rock masses is associated with the size of the mined-out area.
In most of the currently used methods for zoning simulation, specific attention is usually paid to modeling the process of roof rock falling and the adjustment of caved rock mass parameters, while in contrast, the strength deterioration of rock masses in other zones is neglected. Although the rock masses in the fractured zone, continuous deformation zone, and surface cracking zone are not broken or collapsed, the strength deterioration of rock masses varies with the extent of damage. In addition, the four zones are developed during the mining process, and the mechanical properties in different regions correspondingly differ. The dynamic zoning characteristics of disturbed rock masses should not be neglected; otherwise, inexact numerical results may be achieved.
In this paper, an FDM-based dynamic zoning method for disturbed rock masses above a longwall mining panel is proposed. This method is mainly composed of four stages: (1) establishing the simplified complete stress-strain curve; (2) determining the zoning criteria; (3) adaptively adjusting the mechanical parameters of disturbed rock masses; and (4) numerically modeling longwall mining based on the FDM. To demonstrate the effectiveness of the proposed dynamic zoning method, a numerical application case is presented with the use of FLAC
3D software. FLAC
3D is inherently capable of solving nonlinear and large-strain problems; in particular, it can be well applied to modeling the distribution patterns of the stress, strain, and displacement of surrounding rock masses in underground mining [
22].
2. The Dynamic Zoning Method
2.1. Overview of Our Method
During the underground mining of coal seams, the overlying disturbed rock mass undergoes all or part of the four stages of elastic-plastic deformation, cracking, caving, and caved material deformation. Correspondingly, we simplify the complete stress-strain curve of the disturbed rock mass into four stages: the elastic deformation stage (Stage I), post-peak softening stage (Stage II), residual strength stage (Stage III), and caved material deformation stage (Stage IV).
According to the deformation and failure characteristics of the rock mass in different stages, the zoning criteria of the rock mass are established: the rock mass in the elastic deformation stage and post-peak softening stage belongs to the continuous deformation zone; the rock mass in the residual strength stage belongs to the fractured zone or the surface cracking zone; and the rock mass in the caved material deformation stage belongs to the caved zone.
According to the simplified complete stress-strain curve, the mechanical parameters of the disturbed rock mass are adaptively adjusted: the parameters are maintained in Stage I, reduced in Stage II, adjusted to satisfy the residual state in Stage III, and adjusted to satisfy the condition of loose deposits in Stage IV.
According to the damage evolution process of rock mass deformation in actual underground mining, by considering the mining process simulation, rock mass zoning criteria, and adaptive adjustment of rock mass mechanical parameters, the simulation of a longwall mining process is conducted based on the FDM.
By exploiting the abovementioned four stages, the dynamic zoning of the disturbed rock masses can be realized (
Figure 2).
2.2. Establishing the Simplified Complete Stress-Strain Curve
In general, there are several common characteristics for rock mass complete stress-strain curves [
23,
24,
25] (
Figure 3). (1) Before reaching the peak strength, the rock mass is in the elastic deformation stage, and the deformation at this stage gradually develops with increasing stress. (2) After reaching the peak strength, the rock mass is in the softening stage. With increasing deformation, the strength of the rock mass gradually decreases. (3) After reaching the residual strength, the rock mass is in the residual strength stage. With the continuous development of plastic deformation, the strength of the rock mass remains at a residual value. (4) With increasing confining pressure, the peak strength and residual strength of the rock mass gradually increase, and the peak strain and residual strain increase correspondingly.
On the basis of the above characteristics, this paper simplifies the complete stress-strain curve of the overlying disturbed rock mass into four stages (
Figure 4b). Stage I (Section OA) is the elastic deformation stage, i.e.,
; Stage II (Section AB) is the post-peak softening stage, i.e.,
; Stage III (Section BC) is the residual strength stage, i.e.,
; and Stage IV (Section CD) is the caved material deformation stage, i.e.,
. More details are shown in
Figure 4.
(1) Elastic deformation stage (Stage I): Before the rock mass yields, its strain develops linearly with increasing stress; see Section OA of the simplified complete stress-strain curve (
Figure 4a).
(2) Post-peak softening stage (Stage II): After the rock mass yields, internal cracks gradually develop, expand, and coalesce. With increasing rock mass strain, the strength of the rock mass degenerates; see Section AB of the simplified stress-strain curve (
Figure 4a). The corresponding strength of Point A is the peak strength
, and the corresponding strain is the maximum elastic strain
; the corresponding strength of Point B is the residual strength
, and the corresponding strain is
. See Equation (1):
For any point M located on Section AB (
Figure 4a), its strain should satisfy Equation (2):
In addition, when subjected to different confining pressures, both the complete stress-strain curves and their simplifications are different. With increasing confining pressure, the peak strength
and residual strength
of the rock mass gradually increase, and the corresponding peak strain
and residual strain
also increase gradually (
Figure 4a).
represents the threshold plastic strain of the rock mass from the post-peak softening stage to the residual strength stage, which depends on the property and stress state of the rock mass, and it is difficult to obtain the value of
directly. As
and
change with increasing confining pressure (
Figure 4a), the critical value of the plastic principal strain
also changes with the confining pressure.
Assuming that the relationship between
and the confining pressure is piecewise linear (
Figure 5), the critical value of the plastic principal strain
subjected to a certain confining pressure can be determined according to the simplified complete stress-strain curve. The continuous relation curve of
can be gained by simply connecting two adjacent points with a straight line, and thus the critical values of the plastic principal strain under different confining pressures can be calculated.
(3) Residual strength stage (Stage III): The rock mass cracks and reaches the residual strength, but it can remain in the layered form. With the continuous development of deformation, the rock mass strength remains at the residual value; see Section BC of the simplified complete stress-strain curve (
Figure 4a).
(4) Caved material deformation stage (Stage IV): When the rock mass completely fails and breaks into caved material, i.e., the rock mass is in the stage of caved material deformation, the strength of the caved material is slower than the residual strength of the rock mass and assumed to be unchanged; see Section CD of the simplified stress-strain curve (
Figure 4a). The corresponding strength of Point C is the strength of the caved material
, and the corresponding strain is
, which satisfies Equation (3):
represents the critical plastic strain of the rock mass from being in the residual strength stage to the caved material deformation stage. The strains at which strength loss occurs are derived based on an investigation of parameters used for the modeling of similar problems in the literature [
17,
18,
19,
20,
26]. It can be summarized that the cohesion and friction properties of rock mass are assumed to drop to a minimum residual value at a plastic shear strain larger than 0.05 (5% strain), and the tensile strength falls to a residual value of zero at a plastic tensile strain larger than 0.01 (1% strain).
2.3. Determining the Zoning Criteria
In the process of underground mining, the deformation and failure characteristics of the overlying disturbed rock masses are different, which corresponds to the different stages of the simplified complete stress-strain curves. The rock masses in the continuous deformation zone undergo elastic-plastic deformation, and they are in the elastic deformation stage (Stage I) or post-peak softening stage (Stage II). The rock masses in the surface cracking zone and the fractured zone go through the process including elastic-plastic deformation and cracking, and they are in the residual strength stage (Stage III). After the process of elastic-plastic deformation, cracking, and caving, rock masses in the caved zone fill the mined-out area; the caved rocks are in the caved material deformation stage (Stage IV).
According to the simplified complete stress-strain curve, the zoning criteria are established by considering the deformation and failure characteristics, as well as the location of the overlying disturbed rock masses.
The parameter , which represents the plastic strain of the rock mass, is one of the major metrics for dynamic zoning, while denotes the total strain of the disturbed rock mass. Details of the zoning criteria are listed as follows.
(1) and .
This means that the rock mass is in the elastic deformation stage, and if the rock mass is located above the fractured zone, it will be classified into the continuous deformation zone.
(2) .
This means that the rock mass is in the post-peak softening stage, and if the rock mass is located above the fractured zone, it will be classified into the continuous deformation zone.
(3) .
This means that the rock mass is in the residual strength stage. If the rock mass is located above the caved zone, it will be classified into the fractured zone, whereas if the rock mass is located near the ground surface, it will be classified into the surface cracking zone.
(4) .
This means that the rock mass is in the caved material deformation stage, and if the rock mass is located above the mine mined-out area, it will be classified into the caved zone.
It should be noted that in general, a rock mass is of low tensile strength, and if the rock mass is subjected to tensile failure, it should be considered to be in the residual strength stage.
2.4. Adaptive Adjustment of Mechanical Parameters of Disturbed Rock Masses
In the process of underground mining, the deformation and failure characteristics of the overlying rock masses dynamically vary, and the mechanical properties correspondingly change. With the mining of the coal seam, at first, the overlying disturbed rock mass undergoes small deformation, and the rock mass is in the elastic deformation stage. After the rock mass yields, internal fissures occur, and the rock mass gradually loses continuity, but it can still maintain the layered form. At this time, the rock mass is in the post-peak softening stage, and the strength parameters (cohesion c and friction angle φ) are gradually reduced. The cohesion c and friction angle φ tend to stabilize until the rock masses reach the residual strength stage. When the coal-seam roof begins to cave and fill into the mined-out area, the rock masses are in the caved material deformation stage, and the cohesion c and friction angle φ reduce to the parameters of the caved materials.
According to the simplified complete stress-strain curve, the adaptive adjustment of the mechanical parameters of rock masses at different stages is as follows:
(1) Elastic deformation stage (Stage I): the mechanical parameters of rock masses in this stage remain unchanged.
(2) Post-peak softening stage (Stage II): the mechanical parameters of rock masses in this stage need to be reduced.
The principles of damage mechanics are employed to interpret the characteristics of the post-peak softening stage of the disturbed overlying strata. More specifically, the formation, expansion, and coalescence of cracks in rock masses can be considered a damage process of the mechanical properties of rock masses. That is, the post-peak softening stage of the coal-seam roof can be regarded as a progressive damage process along with the development of plastic strains.
In the post-peak softening stage, with increasing plastic strain , the cohesion c decreases from an initial value to a residual value , and the friction angle φ decreases from an initial value to a residual value .
More specifically,
can be determined according to the confining pressure
(
Figure 5); thus, the linear softening curves of cohesion
c and friction angle
φ are determined (
Figure 6). According to the
of any point in the post-peak softening stage, the corresponding cohesion
and friction angle
can be achieved.
(3) Residual strength stage (Stage III): the mechanical parameters of rock masses in this stage are adjusted to those parameters in the residual state (i.e., and ).
In the residual strength stage, with increasing plastic strain, the cohesion
c and friction angle
φ remain at residual values of
and
, respectively (
Figure 6).
(4) Caved material deformation stage (Stage IV): the mechanical parameters of rock masses in this stage are adjusted to those parameters of the caved materials (i.e., and ).
When the roof rock masses fall and break into irregular blocks, the cohesion of the rock mass decreases significantly, while the friction angle changes little. In some studies [
17,
18,
19,
20], the cohesion of the caved material is reduced to zero, and the friction angle is not changed or is maintained at the residual value. In this paper, it is assumed that
and
(
Figure 6).
2.5. Numerical Modeling of Longwall Mining Based on the FDM
The four zones are developed during the actual mining process, and the mechanical properties in different zones correspondingly change. Therefore, the proposed dynamic zoning method considers the mechanical parameter adaptation of disturbed rock masses in the progressive mining process. More specifically, according to the simplified complete stress-strain curve, the zoning criteria are established by considering the deformation and failure characteristics of the disturbed rock masses, and the mechanical parameters of the disturbed rock masses are adaptively adjusted. On those bases, the dynamic zoning of the disturbed rock mass in the mining process is simulated, and the dynamic development characteristics of the four zones are obtained.
This paper simulates the underground longwall mining process with FLAC
3D by means of step-by-step excavation. More details of the simulation process are introduced as follows (
Figure 7):
Step 1. Mining with a distance of L in each step.
L is determined according to the actual mining schedule; in this paper, L = 10 m.
Step 2. Adaptively adjusting the parameters of the overlying disturbed rock masses and dynamically zoning by looping over all the elements of the computation model.
For each element, it is first necessary to determine whether the element yields. If not, then the element is in the elastic deformation stage; otherwise, the element needs to be further checked according to the failure type and plastic strain of the element to determine which stage it is in (the post-peak softening stage, the residual strength stage, or the caved material deformation stage). Second, by exploiting the principles of adaptively adjusting the mechanical parameters of rock masses in different stages, the cohesion c and the friction angle φ of the element are adjusted correspondingly. Finally, by following the zoning criteria, it must be determined which zone the element belongs to.
Step 3. Checking whether the numerical computation reaches computational balance after N iterations (in this paper, N = 100).
If the computation is balanced (i.e., the maximum unbalanced force ratio is less than 1 × 10−5), then it should further conduct mining with distance L and repeat Step 2; otherwise, it needs to repeat Step 2 directly until the computation is balanced.
Step 4. Proceeding to the next step of mining and repeating Steps 1–3.
The mechanical parameters of the disturbed rock masses are dynamically adjusted, and the scope of the four zones is updated in real time until the end of the mining.
The program code of the algorithm (
Figure 7) is written by using the FISH language in FLAC3D software, and it is embedded in the numerical simulation calculation process to realize the dynamic adjustment of the mechanical parameters of the disturbed strata. See
Appendix A for the algorithm code.
Additionally, the following methods are used to simulate coal-seam mining: first, before FLAC3D simulation mining, the interfaces are set at the contact surface between the coal seam and the roof, which can avoid the dragging effect on the contact surface when the coal seam is mined, and prevent the distortion of the grid displacement data near the interface, so as to realize the full collapse of the coal-seam roof and the natural collapse to the floor and ensure the numerical simulation effect. Then, according to the coal-seam mining step, the coal-seam units within the step are emptied (that is, set to null model) to simulate the coal-seam excavation in the current step. Finally, it is iterated to the equilibrium state (the maximum unbalance ratio is less than 1 × 10−5), the calculation model is saved, and the next mining step according to the above method is then simulated until the coal-seam excavation of the working face is completed.
4. Discussion
The four zones of overlying disturbed rock strata are dynamically developed during the mining process, and the mechanical properties in different zones are correspondingly changed. The dynamic zoning characteristics of disturbed rock masses should not be neglected. Otherwise, the numerical simulation will lead to deviations from the actual results. To predict the dynamic development characteristics and the height of the four zones more accurately, an FDM-based dynamic zoning method for the disturbed rock masses above the longwall mining panel is proposed. The proposed method is applied to the Taixi coal mine, and the dynamic development characteristics of the four zones of overlying disturbed rock masses are analyzed and predicted according to the dynamic zoning results.
The coal-seam roof above the mined-out area does not fall immediately with the advancement of the excavation face but caves periodically during the mining process. When the excavation face advances a short distance, the coal-seam roof can be considered a cantilever beam (cantilever plate), and bending deformation occurs due to gravity. When the excavation face advances to 30 m, the coal-seam roof caves for the first time. With the advance of
Lp (
Lp = 10~30 m), the coal-seam roof caves periodically until the end of mining. The periodic caving characteristics of the coal-seam roof conform to the caving phenomenon in actual mining [
2] and other research work [
3]. More specifically, Gao et al. [
3] used UDEC to reveal the progressive caving of strata above a longwall panel. Their numerical results indicated that the immediate roof acts like beams and collapses periodically. The features of progressive caving fit reasonably well with the field observations in the Ruhr coalfield. Wang et al. [
11] conducted a physical modeling experiment to simulate the overlying strata destruction induced by mining and revealed the different roof failure zones. Their results showed that the overburden failure evolution was accompanied by periodic collapse in the layer group and that the developing height of fractures discontinuously jumps.
The formation of the four zones is a dynamic process and strongly relevant to coal-seam roof caving. With the advancement of the excavation face, the coal-seam roof periodically caves, and the four zones will also periodically expand upwards and forwards. When the mined-out area reaches a certain extent, the heights of the four zones are nearly constant at maximum, and then the four zones will only develop along the mining direction. The development characteristics of the four zones are in accordance with results in the literature [
6,
14,
27].
After finishing the entire mining process, the heights of the caved and fractured zones are 12 m and 102.8 m, respectively. By using the empirical formula [
1] to calculate the maximum heights of the caved and fractured zones, the calculated maximum heights are 7~28 m and 105~175 m, which are consistent with the numerical modeling results.
After the completion of mining, the final subsidence basin can be roughly divided into three subzones, i.e., the central zone, the compressive zone, and the tensile zone. The maximum surface subsidence is approximately 2.86 m, and the subsidence coefficient is 0.82 (Equation (4)). As the Taixi coal mine has not yet been mined, the measured surface subsidence cannot be obtained. There are several coal mines close to the Taixi coal mine with similar geological conditions, including the Yanzhou coal mine (80 km away from the Taixi coal mine in the southeast), Zaozhuang coal mine (140 km away from the Taixi coal mine in the southeast), and Fengfeng coal mine (180 km away from the Taixi coal mine in the west). The subsidence coefficients of these neighboring coal mines are in the range of 0.78~0.88 (
Table 2). Compared with the settlement coefficient obtained from several neighboring mines in Shandong Province (
Table 2), the settlement coefficient calculated by Taixi Coal Mine is reasonable:
where
Wcm is the maximum value of subsidence,
M is the mining thickness,
q is the surface subsidence coefficient, and
is the dip angle of the coal seam.
The above comparison shows that the numerical simulation results obtained by this work, such as the periodic caving of the coal-seam roof and the dynamic development characteristics of the four zones, are consistent with the observed distributions and other research results. The heights of the caved and fractured zones are basically consistent with the empirical formula. The calculated subsidence coefficient is similar to the measured subsidence coefficients of neighboring coal mines. Thus, the dynamic zoning method is capable of analyzing and predicting the dynamic development characteristics of the four zones.
Compared with other zoning methods, the dynamic zoning method proposed in this paper specifically considers the dynamic zoning characteristics of disturbed rock masses in the longwall mining process to achieve more precise numerical results. More specifically, in the proposed method, the complete stress-strain curves of the disturbed rock mass are first simplified into four stages. Then, according to the simplified complete stress-strain curves, the zoning criteria are established by considering the deformation and failure characteristics of the disturbed rock masses, and the mechanical parameters of the disturbed rock masses are adaptively adjusted. Finally, the dynamic zoning of the disturbed rock masses in the mining process is effectively simulated on those bases, and the dynamic development characteristics of the four zones are obtained.
The influence of deformation and failure of the overlying disturbed rock masses on the mechanical parameters are considered, which improves the numerical modeling precision. However, it should be noted that in the proposed method, only the cohesion and internal friction angle of the disturbed rock masses are adjusted during the longwall mining process. Therefore, future work has been planned to adjust the elastic modulus and Poisson’s ratio by considering the effect of deformation and failure of disturbed rock masses.
5. Conclusions
This paper proposes an FDM-based dynamic zoning method for disturbed rock masses above a longwall mining panel. This method is mainly composed of four stages: (1) establishing a simplified complete stress-strain curve; (2) determining the zoning criteria; (3) adaptively adjusting the mechanical parameters of the disturbed rock mass; and (4) numerically modeling the longwall mining based on the FDM.
To demonstrate the effectiveness, the proposed method has been applied to simulate underground mining in the Taixi coal mine. It has been concluded that (1) the coal-seam roof above the mined-out area does not fall immediately with the advancing of the excavation face but caves periodically; (2) the “four zones” of overlying strata are dynamically developed during the mining process and are strongly related to the roof-caving process; and (3) during the mining process, there is a high probability that the fissures in the fractured zone at the south side of the panel would connect with the fissures in the surface cracking zone, which needs careful attention and specific treatments (for example, by bulldozer rolling) in the actual longwall mining process.
The numerical simulation results obtained in this work, such as the periodic caving of coal-seam roof and the dynamic development characteristics of the four zones, are consistent with the observed distribution and other research results. This indicates that the proposed dynamic zoning method is capable of effectively analyzing and predicting the dynamic development characteristics of the four zones.
In the proposed method, only the cohesion and the internal friction angle of disturbed rock masses are adjusted during the longwall mining process. Future work will be focused on estimating and adjusting the elastic modulus and Poisson’s ratio of disturbed rock masses.