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Article

A Comparative Case Study on Stress Redistribution due to Extraction of Conventional and Split-Level Longwall Panels in Deep Inclined Coal Seams

by
Pengfei Wang
1,*,
Peng Zhao
2 and
Yang Cao
3
1
College of Mining Engineering, Taiyuan University of Technology, Taiyuan 030024, China
2
Ordos Wulan Coal (Group) Co., Ltd., Ordos 017200, China
3
Ma Jiliang Mine, Datong Coal Mine Group Co., Ltd., Datong 034099, China
*
Author to whom correspondence should be addressed.
Processes 2023, 11(11), 3201; https://doi.org/10.3390/pr11113201
Submission received: 23 September 2023 / Revised: 28 October 2023 / Accepted: 30 October 2023 / Published: 9 November 2023
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Abstract

:
Through field observations, theoretical analysis, and a calibrated numerical model, a study of stress redistribution due to the extraction of longwall panels at depths ranging from 580 to 660 m with a 30° dip angle at Tangshan coal mine is presented in this paper. Conventional and new split-level longwall layouts are compared regarding their stress redistributions. The height of the caved zone is 21.7 m; angles of break of 55.6° on the left and 54.2° on the right side of the gob are observed using cross-measure boreholes. Structural models as well as numerical models are constructed based on the above field data to make the geometry of the gobs closer to the in situ situation and more realistic. Compared with the conventional layout, the theoretical analysis shows that the overall influence of the elevated split-level longwall gob on the lowest intact stratum increases by more than 5.07%, meaning that the split-level longwall layout is more likely to maintain the stability of the overlying strata. This is also corroborated by numerical modeling. Conventional longwall panels and split-level longwall panels with and without considering the gob are all simulated using FLAC3D. Instead of only backfilling the height of the coal seam or the height of the coal seam and the immediate roof, as in many numerical modeling studies in the past, in this study, the whole caved zone is backfilled with “double-yield” material. It is found that along the floor, the split-level longwall gob assumes 23.4% more load than the conventional longwall gob, and the split-level longwall abutment bears 6.2% less load than the conventional longwall abutment; stress arches are developed within the gob; concave-down stress beddings are more evident at higher locations of the gob; a self-supporting structure develops within the gob and surrounding rock mass around the lower end of the gob, forming a protective localized intact destressed zone around the location where the split-level tailgate is situated; the yield zone in the floor of the curved section tends to extends toward the center of the curved part, where the curvature is the maximum; the upper stress concentration zone is within the coal seam, while the lower one is above the coal seam; the upper one is more concentrated.

1. Introduction

The extraction of underground ore bodies causes disturbances in the pre-mining stress field until a new equilibrium is reached. Stress redistribution due to underground mining is one of the major concerns for geomechanical researchers. Inclined or dipping coal seams are widespread in China and all over the world as a result of the depositional environment, tectonic movements, or other related geological factors [1,2,3,4,5,6]. With the depletion of easily minable coal seams, the ability to mine such inclined coal seams economically is important to ensure energy supplies [7,8]. Mining inclined coal seams at depth (>500 m) using the longwall mining method may face safety problems such as bursts, large deformation of the gate road, overturning of shields, downhill sliding of the shearer and armored face conveyor (AFC), etc., which can affect the productivity of mines and the safety of miners [9].
Aleman et al. [10] presented a methodology for subsidence prediction in steeply inclined coal seam mining. Aside et al. [11] proposed a profile function for surface subsidence over a longwall panel in the inclined seams and compared it to field measurements. Based on comparison between AE data and in situ testing results, Ren et al. [12] analyzed acoustic emission (AE) patterns (energy rate, total events) of coal samples from the No. 5 coal seam at Huating coal mine, which extracted a steeply inclined, extra thick coal seam where rock instabilities occurred frequently. Sun et al. [13] investigated the dynamic failure depth of an inclined coal seam floor by continuously monitoring AE events within the floor. Using the FLAC2D software, Ma et al. [14] studied the stress and displacement changes in the overburden strata caused by extraction of a steeply inclined coal seam with a fault. Through digital graphics technology and fractal theory, combined with physical modeling, Wei et al. [15] studied the distribution of mining-induced cracks in the overburden strata of an inclined coal seam, and a relationship between the fractal dimension of the fracture network and the pressure in the overburden strata was suggested. Xin et al. [16] analyzed the characteristics of roof movement when mining top coal of an inclined coal seam, and established a mechanical model of support and the surrounding rock’s stability. Considering the plastic softening nature of coal and the inclined coal seam, Gao [17] analyzed the stress–strain deformation and stability of a strip coal pillar using the limiting equilibrium method, and performed a verification case study. He concluded that the width of the non-elastic zone in the strip pillar is markedly affected by the coal seam’s inclination. Luo [5,18] studied the distribution of the final surface subsidence basin induced by longwall operations in an inclined coal seam and developed an influence function. Liu et al. [19] noted that one of the keys to safely and efficiently mining a steeply inclined coal seam under water-filled strata is to control the structural integrity of the roof. Wang et al. [20] proposed criteria for support stability by taking into account the asymmetric characteristics of stratum movement and interaction between supports in the mining of steeply inclined thick coal seams. The mechanical effects of the supporting force and the role of the curved section on the stability of all supports at the face were also discussed. Su et al. [21] experimentally investigated the risk of spontaneous coal combustion in steeply inclined longwall gobs and proposed a practical method to determine the risk. Sun et al. [22] developed a model for an inclined coal seam floor with linearly increasing water pressure based on key strata theory. Xin et al. [23] successfully carried out a field trial of underground coal gasification (UCG) with the shaft method at a coal mine in China to recover abandoned steeply inclined thin coal seams. Li et al. [24] studied the stability of the roof structure and hydraulic supports in steeply inclined coal seams using a physical simulation and theoretical analysis. Wang et al. [9] investigated a strategy with the potential to mitigate problems such as coal bursts and bumps associated with high ground pressure at great depth.
In spite of the extensive research outlined above, the flow or diversion of stress from the overburden into the abutment and the gob after the extraction of inclined panels is not well understood, which may result in devastating disasters if an improper panel layout is employed due to this lack of knowledge. Many rock burst disasters have proved the above statement. The gob stacking characteristics as well as the strata breakage and movement are different from those in the extraction of flat panels [25,26]. Research on stress redistribution due to the extraction of deep inclined longwall panels is unfortunately rare, which may make it hard for mine engineers to guide the longwall system design in these circumstances. In addition, in many numerical modeling studies [27,28,29], only the height of the coal seam or coal seam and immediate roof were backfilled with gob material. Moreover, the angle of break was not taken into account either. However, the height of the caved zone varies greatly depending on the properties of the roof strata. The mining height in longwall top coal caving (LTCC) is particularly large, and the height of the caved zone must be larger. Treating only the height of the coal seam or coal seam and immediate roof as the gob height (caved zone) is not reasonable.
Therefore, the objective of this paper is to fill that gap with a study based on field observation, theoretical analysis, and numerical modeling of the Y294 longwall panel at the Tangshan coal mine. In this study, the height of the caved zone as well as the angle of break were measured in field observations using cross-measure boreholes and then incorporated into the numerical models, which was closer to the in situ situation and more realistic. The findings of the study can provide a reference for mining engineers to choose better longwall layout plans when designing panels in order to better cope with the high stress encountered underground.

2. Engineering Background

Tangshan coal mine is located in Tangshan City, Hebei Province, China (Figure 1). The mining district is 14.55 km long and 3.50 km wide, with a total mineable area of 54.60 km2 [30]. It is the most important coal mine for the Kailuan Group, the oldest coal corporation in China, with a history of over 120 years.
The mine has used a conventional longwall panel layout in the past and has been experiencing severe ground control problems for more than a decade due to a large cover depth and coal seam inclination.
The thickness of the integrated coal seam of No. 8 and No. 9 is 8–11 m. The dip angle varies from 28° to 32°, which contributes to the instability of the longwall equipment at the working face. The Y294 longwall panel selected for this study sits at the No. 11 level in Yuexu District. The overburden depth is over 600 m and the panel is 90 m wide in the dip direction and 1028 m long in the strike direction. Figure 2a shows the layout of the Y294 panel and the adjacent Y292 and Y296 panels. A conventional longwall panel layout was used for the Y292 panel; a split-level single-entry longwall layout [31,32] was employed for the Y294 panel and is also being used for the Y296 panel (Figure 2b). The mine uses a retreating longwall top coal caving method with natural roof caving in the gob for all panels. The cutting height and top coal thickness are 3 m and 6 m, respectively. The web cut width is 0.6 m. The caved top coal is drawn out onto the rear mounted AFC every two web cuts. The height and width of all gate roads are 4 m and 3 m. Cable bolts and rock bolts were used to support the Y292 and Y294 panel headgates and tailgates. The Y296 headgate also uses cable bolts and rock bolts, while the Y296 tailgate uses “I”-shaped yielding steel sets spaced at 1.2 m for support, to match with the triple-section mining operation (TSMT) in the split-level longwall system [9,33]. The layout of the shields at the working face of the Y294 panel is shown in Figure 2c.
The roof rock strata of the Y294 panel consisted mainly of siltstone and medium-grained sandstone, while the floor strata below the coal seam consisted of siltstone, fine-grained sandstone, and siltstone, in descending order (Figure 3), based on the Yue-29 core log (a core log located in the Y294 panel (Figure 2a)). The uniaxial compressive strengths of the immediate roof and floor strata are 63–95 MPa, and for the main roof strata they vary between 84 and 137 MPa.

3. Field Observations

Field observations were used to obtain the necessary data for constructing structural and numerical models. Structural models were then used for the theoretical analysis in the later section.
It is known that coal seam gas represents a potentially significant risk to the safety and productivity of underground mines [34,35]. In order to ensure safe production for the Y294 and Y296 panels, cross-measure boreholes were drilled in the gate roads to drain accumulated gas in the upper corner of the gob. The gas was tapped, achieving simultaneous recovery of coal and gas, which makes reasonable use of energy resources and prevents gas disasters [36]. The cross-measure boreholes were drilled deep into the main roof towards the face from a location by the face, as shown in Figure 4 and Figure 5. With the retreating longwall face, an increasing portion of the hole intercepted the fracture system with increased gas flows.
In order to fully utilize the boreholes, they were also used as exploration holes to observe roof fractures and movement, and to assess the caved zone. Each of these multi-functional exploration boreholes was started with a 127 mm diameter core bit and drilled to a depth of 6 m. The remainder of the hole was drilled with a 75 mm diameter bit. Nine stations were installed, with the first one 105 m away from the set-up room. For the first three stations, the interval between stations was 95 m, while for the remaining six stations the interval was 65 m (Figure 4a). There were two boreholes for each station. The borehole variables (Table 1) included hole length, inclination, and azimuth (the acute angle made by the hole and the long axis of the longwall).
Through these drill cores from the boreholes, structural and physical properties, as well as the quality and integrity of the roof strata, were able to be determined. Key parameters have been annotated in Figure 4b. Then, using some simple knowledge of geometry, the height of the caved zone and the value of the angle of break could be determined. α, β, and γ have been given, L1, L2, and L3 can be obtained from a drill rod inserted into the borehole supplemented with the drill cores. Some photos of the drill cores from the boreholes provided by the coal mine are presented in Figure 4c.
In fact, several parameters can be used to determine the boundaries of the gob. First, as the drilling proceeded, drill parameters including the feed pressure, thrust, torque, rotary speed, penetration rate, rotation pressure, delivery and return water pressures, and flows, etc., were able to be recorded using the method of measurement while drilling (MWD). A borehole camera can also be used to obtain a circumferential image of the hole, showing the quality change along the hole’s length. In addition to borehole filming, during the extraction of the gas, the gas concentration, the volume of gas, the gas volumetric flow rate, and atmospheric pressure can also be monitored. These parameters change with the increase in the borehole depth.
The final results show that the caved zone above the coal seam was about 21.7 m, reaching 4.0 m into the medium sandstone (Figure 4b). Through these borehole samples, the angles of break (defined as the acute angle formed by the caving line and the line parallel to the coal seam) were also obtained, with 55.6° on the left and 54.2° on the right (Figure 6). According to the field measurement of the surface subsidence carried out by the surveying and geologic department of the coal mine, no big surface cracks were found, and no evident structural damage was observed although the thickness of the coal seam reaches over 9 m. Therefore, the panel width is subcritical, or super-subcritical. A great cover depth may be a contributing factor for the subcritical width of extraction.
A conceptual structural model was developed based on the obtained data, as shown in Figure 6a. For comparison, a structural model for a conventional longwall system was also established, as shown in Figure 6b. The two models were then used for the theoretical analysis in the later section.
Note that potential uncertainty existed during the field observations. Sometimes, when the drill bit reached the caved zone, where the integrity of the borehole was poor and rocks may have been fragmented, a borehole was sheared into several parts by fractures, drilling tool jamming, and loss of the drill bit occurred, which caused the bit to block and the drill to stall. Normally, it was best to stop the drilling when the rotation pressure decreased dramatically or when spikes in the rotary speed and torque traces and local steps in the penetration trace were encountered. However, by using the technique developed by the coal mine (patented technique that has not been published), drilling was able to continue deep into the caved zone although one drill bit was lost. The drilling speed was about 20–25 m per hour.

4. Theoretical Analysis

In order to further understand the meaning behind the observed field data, the stability of the model (Figure 6) incorporating the data is analyzed in depth in this section.

Theoretical Analysis of Interaction between Gob and Surrounding Rock Mass

Longwall gob development is a volume-controlled process that influences the stress distribution both within the gob and the surrounding rock mass. Coal extraction produces a large void in the gob and disturbs the equilibrium conditions. Roof strata cave in when the excavated area (or gob) increases to a sufficiently large size. Caving stops when a self-supporting stratum is reached or the overlying strata are fully supported by the caved fragments. The overhanging strata then no longer cave, but bend and rest on the underlying caved rocks and broken strata [37]. The caved rock mass is compacted until an equilibrium is reached when no roof strata subsidence occurs [27]. Three zones are developed due to extraction of a longwall panel, they are: the caved zone, the fractured zone, and the continuous bending (deformation) zone. The strata in the caved zone not only lose their continuity completely, but also lose their stratified beddings; caved rocks in this zone pile up irregularly. Within the fractured zone, strata break and lose continuity, but the stratified beddings remain. For the continuous bending zone, strata between the fractured zone and the surface bend downward without breaking and their continuity, and thus, the original stratigraphic features, remains [5,38,39].
Uniformly distributed pre-mining stress is redistributed after coal extraction, resulting in gob pressure and side abutment pressures. The gob and surrounding rock mass will interact to reach a new stress equilibrium. The integral of the vertical stress (only the vertical stress acting on the floor, shear stresses between broken blocks are not considered) of the surrounding rock mass after extraction plus the stress of the extracted coal must equal the integral of the vertical stress acting on the floor before any extraction. The interaction is influenced by many factors including the panel geometry, mining height, and cover depth, etc. The gob pressure is mainly due to the compaction of the caved rock fragments.
For a flat coal seam, the gob pressure increases toward the center of the mined panel, where the gob is more compacted and stiffer. The maximum gob pressure occurs when the gob takes the full load of the overburden weight and the consolidation of the gob reaches the maximum [27,40,41]. Whether the gob pressure has attained the pre-mining stress level depends highly on the panel width [38]. If the panel is too narrow, the upper unbroken strata may be bridged by the side abutments, resulting in the gob pressure being more or less the weight of the rock fragments under the unbroken strata. During the gob consolidation process, the stress–strain behavior of the gob follows the Salamon equation [42], which was proved later in laboratory testing by Pappas and Mark [43]. The Salamon equation is expressed as follows:
σ = E 0 ε 1 − ( ε / ε m )
where E 0 = 1.039 σ c 1.042 b 7.7 , ε m = b − 1 b , b = H c + m H c , σ is the stress applied to the gob materials, ε is the volumetric strain under the applied stress, E0 is the initial tangential deformation modulus and εm is the maximum volumetric strain, σc is the compressive strength of the rock pieces, b is the bulking factor, Hc is the height of the caved zone, and m is the mining height [29].
For an inclined coal seam, such as the one in this case study, the split-level longwall layout yields a different stress distribution from conventional layouts because the load-bearing characteristics of the gob are related to the gob configuration or geometry, that are determined by the panel layout, and different panel layouts lead to different roof strata failure, fracture, and displacement modes [44]. A large inclination induces the sliding of caved rock fragments downhill. In some cases at Tangshan mine where inclinations are large (say more than 45°), wire mesh has to be placed on top of the shields throughout the working face to prevent fatalities and injuries caused by sliding, rolling, and even flying rocks. Workers must work behind the mesh to ensure safety, which, however, reduces productivity. Due to the large inclination, more gob material accumulates at the lower end of the gob, as shown in Figure 6. The characteristics of the stacking of the gob rocks parallel to the coal seam become more evident with the increase in depth of a location within the gob. This is going to be demonstrated in the numerical modeling. Unlike the stress distribution in flat longwall gobs, asymmetrical inclined gobs result in asymmetrical gob compaction and abutment stresses.
Based on the field observations, an analysis of the simplified structural model (Figure 6) for the stability of the lowest intact stratum is presented here by assuming the strata are isotropic [45,46]. The deflection of the lowest intact strata has to be obtained to determine its stability. Note that the analysis is for the final state, when the gob and overlying strata settle and equilibrium is reached. According to the theory of key strata [22,47,48], the structural model of the inclined lowest intact stratum is established as shown in Figure 7.
Due to the curved section at the lower end of the split-level panel, the elevation of the split-level longwall gob (Figure 6a) is higher than the conventional longwall gob (Figure 6b), the void on the top of the gob in the case in Figure 6a is, therefore, smaller. Through simple geometry, as shown in Figure 8, it was calculated that the total area of the gob was 2308.7 m2 for the split-level longwall gob. The area of the triangular-like solid coal at the lower end is 123.3 m2. For the conventional longwall layout, the gob area is 2308.7 + 123.3 = 2432 m2. Therefore, the triangular-like solid coal pillar accounts for 5.07% of the total gob volume, in other words, 5.07% of the total gob volume is reduced. As the gob at the bottom is more compacted and it is less compacted on the top, the overall influence of the gob on the lowest intact stratum compared with the conventional one increases by more than 5.07%. From the gravity backfilling point of view, the gob in Figure 6a has a higher backfilling rate, indicating that the gob exerts more force over a larger area on the lowest intact stratum. Therefore, the lowest intact stratum, when employing the conventional longwall system, would be higher than with the split-level longwall system. In other words, the split-level longwall layout is more likely to maintain the stability of the overlying strata.

5. Numerical Modeling Studies

Numerical modeling studies can show some detailed observations that are very difficult to be seen. Therefore, in this section, numerical modeling is performed to supplement the theoretical analysis and field observations.

5.1. Model Development

The FLAC3D code was employed for the numerical modeling as stress distribution in this software is more explicitly visible compared to in other software [49,50]. Small faults that only influence the geological conditions locally were not considered. Figure 9 shows the FLAC3D model constructed for the Y294 panel based on the stratigraphic column shown in Figure 3. The model zone sizes were not even, they graded from small around material boundaries to large at the center of a material domain by virtue of the CAD method proposed by Beer et al. [51]. A suitably fine zone resolution was used in the vicinity of the coal seam unit, the gob, and the gate roads for improved accuracy of progressive yielding and deformation [52]. The dimensions of the model were 460 m wide, 1500 m long, and 200 m high, as shown in Figure 9. The generation of the mesh was random, i.e., we neither manually intervened in the generation of the mesh, nor pre-set the mesh generation. The mesh we used had tetrahedral-shaped elements. There were four quadrature points per element. This has a better force transmission property in FLAC3D. The model had 614,888 grid points and 1,187,900 zones in total. A significant distance to the lateral boundaries and bottom boundary was required to minimize model boundary effects.
A uniform stress of 400 m × 0.025 MN/m3 = 10 MPa was applied to the top of the model, corresponding to 400 m of overburden strata, by assuming the overlying unit weight was 0.025 MN/m3 and the gravitational force was applied. The side boundaries were roller-constrained and the bottom boundary was fixed both horizontally and vertically. Based on pre-mining stress measurements in the mine, a ratio of horizontal to vertical stresses (K) of 0.8 in both the model’s in-plane and out-of-plane directions was input (Figure 9a) (Wang et al. [30]).
In addition, discontinuous model interfaces, representing bedding planes, capable of yielding and separating, were built into the model at the contact of each stratum using the FLAC interface logic. The methods and parameters proposed by Wang et al. [53] for interfaces were used to achieve separation between the different units and between the gob and the surrounding rock mass. Beam elements were used to simulate the steel set for the gate road support [54].

5.2. Parameters Used for Numerical Modeling

The physical and mechanical properties of the roof and floor strata were determined from testing samples obtained from the exploration drill cores in the laboratory, supplemented by published data [30], since Wang et al. [30] also carried out a study in the coal mine.
The parameters obtained from the lab testing were then correlated to rock mass parameters using the following empirical equations used in China [55]:
Er = 0.469 Ei
where Er is the elastic modulus of the rock mass and Er is the elastic modulus of intact rock.
σtr = 0.5 σti
where σtr is the tensile strength of the rock mass and σti is the tensile strength of the intact rock.
σcr = 0.284 σci
where σcr is the compressive strength of the rock mass and σci is the compressive strength of the intact rock.
vr = vi
where vr is the Poisson’s ratio of the rock mass and vi is the Poisson’s ratio of the intact rock.
Cr = 0.25 Ci
where Cr is the friction angle of rock mass and Ci is the friction angle of the intact rock.
φr = 0.9 φi
where φr is the cohesion of the rock mass and φi is the cohesion of the intact rock.
After these procedures, the physical and mechanical parameters used for numerical modeling were obtained, as shown in Table 2.

5.3. Gob Modeling

Since the study is highly dependent upon the gob, the gob should be taken into account in the numerical analysis in order to investigate the stress redistribution due to the extraction of deep inclined longwall panels. Three gob modeling methods have been used to date. In the numerical modeling work of Jiang et al. [56] and Wang et al. [30], the gob area was filled with very soft elastic material to approximately simulate the support capability of the fallen rocks from the roof. Song et al. [57] used an artificially pre-set force against the roof, according to a theoretical gob stress distribution, to simulate the support capacity of the gob material, employing the Phase2D 8.0 software. Using the finite element package, ABAQUS, and based on Terzaghi’s model, Morsy and Peng [58] developed a numerical gob model. Esterhuizen et al. [59] used equivalent gob elements that follow the hyperbolic stress–strain curves to model the gob compaction and response and carried out model calibration for the simulation of coal pillars, the gob, and the overburden response. Yavuz [27] and Li et al. [29] used Salamon’s model to simulate the gob and obtained good results.
However, none of the above studies took the angle of break into account, and gobs are commonly treated by replacing only the coal seam or coal seam and immediate roof with the gob material. According to many mining engineers’ and the authors’ field experience and observations, the angle of break is developed after extraction of the coal seam, as demonstrated in Section 3. And fragmented rocks in the caved zone do not come only from the immediate roof. In many cases, several roof strata contribute to the fragmented rocks in the gob of the caved zone. Therefore, instead of replacing only the panel coal seam with double-yield material as in many past studies, a generalized caved zone consisting of several roof strata has been assigned with double-yield material, which is more reasonable, realistic, and scientific, since we have had an in-depth exchange of views on this issue with the general manager, senior engineers, shift bosses, underground laborers, and even contract miners, who have very rich field experience. In addition, to be more realistic with the field situation, the angles of break were incorporated in the numerical models. The caved zone is able to be outlined as the angle of break, the panel width, and the height of the caved zone have been determined. Therefore, when building the model, the angles of break of 55.6° on the left and 54.2° on the right obtained from the field measurements were incorporated into the model shown in Figure 6 and Figure 8. The study focuses mainly on the rock mass response in the dip direction after the movement of the strata ceases, so we backfilled the caved zone by assigning the caved zone with double-yield material as well when building the model.
A built-in double-yield constitutive model in FLAC3D was used to simulate the gob behavior in this study [54] and the cap pressure for the double-yield model was estimated using the Salamon equation, Equation (1). The double-yield model was initially developed to represent the behavior of mine backfill material, for which pre-consolidation pressures are low. It is an extension of the strain-softening model. It is used to simulate irreversible compaction as well as shear yielding. The representative material is lightly cemented granular material in which pressure causes permanent volume decrease, such as hydraulically placed backfill.
As mentioned before, the height of the caved zone was about 21.7 m above the coal seam. Hence, according to Equation (1), the bulking factor, maximum strain, and the initial modulus of the gob materials were calculated as 1.4, 0.29 m/m, and 24.86 MPa, respectively. The cap pressure for the double-yield model is given in Table 3 and is expressed by
σ = 24.86 ε 1 − 3.41 ε
In order to obtain the parameters for the gob and to make sure that the stress–strain relationship agrees with Equation (2), a simple model with dimensions 1 m (length) × 1 m (width) × 2 m (height) was built (in order to display stress and strain contours). The loading was simulated by applying a velocity on the top surface, with the bottom surface fixed vertically and the four side surfaces fixed horizontally. The input parameters were fitted by iterative changes in the bulk and shear modulus, angle of dilation, angle of friction, and density of the gob material. By trial and error, the final properties are given in Table 4. The volumetric strain, vertical stress contours, and stress–strain matching results are given in Figure 10. These show that the numerically obtained data agree very well with Salamon’s equation. Please note that the final set of inputs is not unique, and it is possible that a different combination of input values can equally satisfy Salamon’s equation.
To present the suitability and novelty of this numerical modeling, this work is also compared with relevant previous major numerical modeling studies with the gob considered, as listed in Table 5.

5.4. Validation of the Numerical Modeling

The above parameters were validated using the observed field data. As long as the field data agree well with the numerical modeling using the above-developed parameters, then the reliability of the parameter can be considered to be validated. In fact, the field observations, on the other hand, were used to monitor the performance of the split-level longwall system.
Three variables were considered to validate the numerical model. One was a comparison of the abutment pressure due to extraction of the Y294 panel. One was comparison of the Y296 tailgate convergence. The third was comparison of the gob pressure.
The abutment pressure data were obtained through stress meters installed in stress-monitoring boreholes in the Y296 tailgate. The convergence of the Y296 tailgate was measured. The gob pressure data after extraction of the Y294 panel were collected by monitoring the roof pressure of the Y296 tailgate, since it is located 3–5 m under the gob with only a coal sheet on the top. Figure 11 shows the instrumentation plan for obtaining such data. The measurements included the side abutment pressure within the solid coal of the Y296 panel, the roof pressure, and the roof-to-floor and rib-to-rib convergences of the Y296 tailgate. As the triple-section mining operation (TSMT) has to be employed for the split-level longwall system [9], the Y296 tailgate started to be driven in when the extraction of the Y294 panel was almost finished and the closest distance between the heading and the Y294 working face was about 400 m.
Twelve borehole stress meters were installed in the solid coal mass of the Y296 tailgate (Figure 11b,c). Spaced at 5 m, the stress meters were installed at depths of 3, 5, 7, 9, 11, 13, 15, 18, 21, 24, 27, and 30 m, respectively. The stress meters are shown in Figure 11b. Normal stress transferred from the surrounding rock was measured by balancing the fluid pressure applied to the reverse side of the diaphragm.
The stress data were taken when the stress meter’s reading hardly changed (the system collected data every five minutes).
A total of 30 roof-to-floor and rib-to-rib convergence measurement points were installed within the Y296 tailgate space at 3.6 m (Figure 11a,d). The instruments are shown in Figure 11e. The locations of the measurement points were selected in the middle of the two adjacent steel sets where the roof is clearly exposed and readily marked [9]. Permanent pins (steel nail) were installed (by driving or hammering in) in the roof, floor, pillar rib, and longwall panel rib for each measurement station, respectively (Figure 11d) (Yan et al. [28]). The differences in “AB” and “CD” with respect to their initial values represented the rib-to-rib closure and roof-to-floor convergence, respectively. The rib-to-rib closure was measured using a flexible tape, and the roof-to-floor convergence was measured using a telescoping rod placed between two measuring points firmly fixed to the roof and floor surfaces. The data were collected twice a day.
Roof pressure data were collected using strain boxes (load cell) (Figure 11f) inserted on the top of the steel sets immediately after the steel sets were installed in advance of the gate road heading. Before that, a flat cylinder was chiseled out, whose volume is similar to the load cell. Then, the pressure measured was the pressure of the roof acting on the steel sets. The roof pressure measurement points were located on the top of the steel sets next to the convergence measurement points. The pressure was collected once a day.
As shown in Figure 11g, the steel sets were spaced at 1200 mm in the longitudinal direction of the entry, hence 600 mm of the roof on each side was carried by one set, and 1200 mm of the roof was carried by one set. The roof was 4 m wide (entry width). Since the average stable stress on the top beam of the set was around 1.1 MPa and the flange width of the I-shaped steel was 90 mm. Therefore, the load was 1.1 × 4 × 0.09 = 0.396 MN. So, the weight of rock carried by one set was 39,600 kg. The density of the roof coal was 1400 kg/m3, and the average thickness of the top coal was around 3 m, thus the weight of the solid roof was 4 × 1.2 × 3 × 1400 = 20,160 kg. So, the weight of the gob rock carried by the set was 39,600 – 20,160 = 19,440 kg since the density was 1700 kg/m3. So the volume was 19,440 ÷ 1700 = 11.4 m3. Thus, the height of the caved rock that was carried by one steel set was 11.4 ÷ (4 × 1.2) = 2.4 m. Therefore, gravity loads carried by the support system were limited, meaning that a self-supporting structure must have developed within the gob and the surrounding rock mass.
Continuous monitoring of stress and deformation was carried out during the extraction of the Y294 panel. The obtained data and numerical modeling data are plotted in Figure 12. The stress data are plotted with respect to the distance from the Y296 tailgate in Figure 12a. The modeling data are also plotted and show a good match with the field data. Figure 12b shows a comparison of the convergence data obtained through field measurement and the numerical modeling. They also agree fairly well. The roof pressure comparison (Figure 12c) demonstrates that the numerical modeling is consistent with the field measurements. Overall, the simulated results are in close agreement with the field measurement data. Please note that the magnitude of the modeling data in Figure 12a is significantly larger than the field data. This is due to the property of the borehole stress meter itself, because the pressure change in the stress meter is closely related to the installation pressure. The pressures of all the stress meters were initially set at 3 MPa, which was much lower than the initial vertical stress in the field, especially for the deep ones (for deep ones, the pressure reached as high as 30 MPa). The display showed that the pressure fluctuated (mostly dropped) for the first two hours and then became stable. Therefore, the manufacturers advised comparing the trend rather than the absolute stress values.

6. Modeling Results and Discussion

The modeling results for the two layout approaches are given in Figure 13. Because the gob pressure span is small, the stratified characteristic of the stress distribution within the gob was not evident, so the stress gradient was reduced to reveal such characteristics as shown in the enlarged view of the circled area (Figure 13a). The vectors denote the directions and magnitudes of the gob material displacement. Figure 13a shows the stress distribution for the inclined coal seam and it is asymmetrical. Two evident stress concentration zones are developed within the rock masses on the two sides of the gob. The upper one is within the coal seam, while the lower one is above the coal seam. In addition, the stress of the upper one is more concentrated than the lower one. To more clearly demonstrate the effect of the gob on the stress distribution, a numerical model was constructed without taking the gob into account, i.e., assigning null for the extracted area. The result is shown in Figure 14. It shows that the default equilibrium (1 × 10−5) of the Y294 extraction could not be reached, fluctuating around 6.3 × 10−4, which indicates that the equilibrium is not ideal. In addition, the 90 m overhang of the immediate roof and tensile stress only occurring on the roof is contrary to the field observation. Two stress concentration zones occur within the coal seam and immediate roof or floor (Figure 14), and next to the boundary of the extracted area rather than far from the coal seam or the boundary of the extracted area (Figure 13a). These two zones are concentrated with higher stress values (see the legend). This is due to the elimination of the gob support capacity to the overhanging roof strata. All the roof load is transferred to the abutments, leading to the stress concentration zones with higher stress values seen in Figure 14. While those in Figure 13a are smaller. This demonstrates that the more load the gob bears, the lower the corresponding abutment pressure, and vice versa.
The stress bedding is concave-down, with an obvious stress gradient, which is termed the “gob stress arch” by the authors. The smallest stress is at the top area of the gob, with a value of 0 MPa, and the stress increases with the increase in the depth of the gob, reaching 1 MPa at the bottom. The higher the elevation of an arbitrary point within the gob, the more evident the concave-down characteristic of the stress beddings. The stress value within the gob is highly dependent on the dead weight of the caved-rock pile due to gravity rather than on the load resulting from the overlying strata, as the displacement of the overlying strata (shown by vectors) is quite small, indicating that the panel width is subcritical. In addition, as the load borne by the lower part of the gob is higher, the stress transferred to the surrounding rock mass at the lower abutment of the Y294 panel is smaller although the depth of cover increases. This can also explain the higher intensity of stress at the upper abutment: the upper gob sustains very low loads, resulting from the overlying strata, all the load is transferred to the upper abutment. What is more, the gob displacement vectors indicate that the displacement of the upper part of the split-level longwall gob is smaller than that of the conventional longwall panel, which is demonstrated by the fact that the height of the split-level longwall gob is 58.5 m while that of the conventional longwall gob is 66.3 m. This also suggests that the split-level longwall gob plays a more important role in keeping the overlying strata intact, as discussed in detail in the field-observation-based theoretical analysis in Section 4.
Figure 13b shows the enlarged views of lower parts of the gobs of the two types of longwall panel. It shows that the curved section at the lower end of the panel increases the stability of the rock pile sitting there. The gob stress at the curved section is also more evenly distributed. While the conventional layout leads to the movement trend of rock fragments towards the pointed end of the gob.
Figure 13c indicates that if a 30 m coal pillar is left, the stress concentration on the coal pillar and the peak stress within the surrounding rock mass of the Y296 tailgate reaches 26 MPa, which can lead to ground control difficulties. This is very common and prevailing at Tangshan coal mine, that the conventional longwall layout leads to large gate road deformations and coal bursts, which were discussed in Section 2. The overburden depths of the majority of the longwall panels at Tangshan coal mine exceed the Y294 panel and, due to the rapid increase in cover depth, ground control problems have become increasingly acute. The Y296 split-level longwall tailgate is located within the destressed zone, the stress is far less than the pre-mining stress (also see Figure 12c). In addition, the results of the simulated yield zones for the two longwall systems (Figure 13d) show that the surrounding rock mass of the Y296 tailgate using the conventional longwall system is in the complete yield state, which is unfavorable for gate road maintenance, while the yield zone around the split-level longwall tailgate is much smaller. Figure 13e shows the yield zone before extraction of the split-level Y296 tailgate. Compared with Figure 13d, it is found that the yield zone hardly develops further. The curved section of the working face geometry has a profound influence on the yield zone development. It is deemed from the figure that the yield zone in the floor of the curved section tends to extends toward the center of the curved part, where the curvature is the maximum. The results shown in Figure 13d,e are unexpected and surprising. The mechanism for the localized intact zone around the location where the split-level Y296 tailgate is situated needs further investigation. Therefore, from both the stress and yield zone points of view, the split-level longwall layout, by locating the tailgate within the destressed zone, is better for gate road support and maintenance.
The stress distribution on the coal seam floor was analyzed and is shown in Figure 15. For the case where the gob was assigned null, the floor stress in the gob is zero, and all the overlying strata load is transferred to the abutments, leading to the largest abutment stresses and highest growth rates among the three cases (also see Figure 15b,c). This indicates that the gob has a significant influence on the stress distribution. For the other two cases, the gob stress increases with the increase in depth within the gob. The abutment stress in the split-level longwall system is the smallest. This is because more support is provided on the overlying strata by the split-level longwall gob. Furthermore, the enlarged views on the left show that the gob pressure at the split-level longwall gob edge increases continuously, while a jump discontinuity occurs at the conventional longwall gob edge. This demonstrates that avoiding sharp change in a longwall panel geometry can prevent abrupt changes in the stress distribution that is detrimental to rock mass integrity and stability.

7. Conclusions

An analysis of the stress redistribution due to extraction of the Y294 panel, with a dip angle of 30° and overburden depth over 600 m, through field observation, theoretical analysis, and numerical modeling is presented in this paper.
The field observations were first carried out; these are the foundation on which the latter theoretical analysis and numerical simulations depend. The height of the caved zone and the angle of break were obtained in the field observations, which outlined the profile of the gob. Then, after panel extraction, structural models for both conventional and split-level longwall systems were constructed based on the field data. The models were then used for a theoretical analysis of the strata stabilities for the two cases, with the influences of different gob geometries generated by different longwall panel geometries. Numerical simulations were then established, also based on the field data. Instead of backfilling only the height of the coal seam or the coal seam and immediate roof with gob material, as in many numerical modeling studies in the past, the whole caved zone was backfilled with “double-yield” material in our numerical simulation. And the angles of break that were obtained in the field observations, which were closer to the in situ situation and more realistic, were also incorporated into the numerical models.
The most important scientific findings are as follows: large inclination induces sliding of caved rock fragments downhill leading to an asymmetrical stress distribution within the gob and the surrounding rock mass; a gob stress arch is developed within the gob and the concave-down characteristic of the stress beddings is more evident for higher locations within the gob; the overall influence of the elevated split-level longwall gob on the lowest intact stratum increases by more than 5.07% compared with the conventional layout, meaning that the split-level longwall layout is more likely to maintain the stability of the overlying strata; along the floor line, the split-level longwall gob assumes 23.4% more load than the conventional longwall gob, and the split-level longwall abutment bears 6.2% less load than the conventional longwall abutment; a self-supporting structure develops within the gob and surrounding rock mass around the lower end of the gob, forming a protective localized intact destressed zone around the location where the split-level tailgate is situated; the yield zone in the floor of the curved section tends to extends toward the center of the curved part where the curvature is the maximum; the upper stress concentration zone is within the coal seam, while the lower one is above the coal seam; the upper one is more concentrated; sharp changes in the longwall panel geometry should be avoided to prevent abrupt change in the stress distribution which is detrimental to rock mass integrity and the stability of the pillars as well as the openings.
There are many differences between this manuscript and previous papers [60]. First, the parameters for the geometry of the gob are determined by field-observed data rather than using physical modeling. Second, the numerical modeling code used in the manuscript is FLAC3D (fast Lagrangian analysis of continua) and the gob modeling is further developed by incorporating a double-yield constitutive model. While the previous published paper used Phase2 8.0, which has a lot in common with FLAC3D, the gob was assigned null in Phase2 8.0. What is more, the influence of the gob and the triangular-like solid coal pillar is studied in detail in the manuscript. The interaction of the gob and the surrounding rock is, therefore, carefully investigated. Finally, with the various thicknesses of the coal seams, the stress distributions are different. The different distributions due to different geological conditions will provide some reference or insight for many engineers. This paper also provides some important data to the database for the application of split-level longwall layouts.
This work can guide coal mine engineers to design mine layouts or adjust overall mine designs, or to take remedial measures in mining of inclined and deep coal deposits. It provides convincing theoretical and practical support and validates the scientific foundation of the split-level longwall layout. The method is also a promising solution to the high-stress environment and geological setting of coal seams with large inclinations. The authors hope that the international readers find the potential of the method and spread it to suitable mines all over the world to ensure the safety of our miners. We also hope that the split-level longwall system can stimulate other discussion on alternative mining layouts among researchers, consultants, manufacturers, and mine operators to expedite solutions to ground control problems encountered in mining.
There are some limitations regarding the split-level longwall layout. It is preferable for the extraction to take place sequentially but discontinuously, so as to give more time for the gob to settle. We suggest 0.5 to 1 years. Air leakage and water inrush from adjacent gobs is another concern. Grouting can be used to isolate the gob in this case. Thick top coal can also be left above the gob-side entry to isolate the gob. Please note that the findings of this manuscript are not universally applicable, they are just for this specific case. Different results will be obtained in different geological conditions such as thickness of the coal seam, physical and mechanical properties of the strata, dip angles, cover depths, etc.

Author Contributions

Conceptualization, P.W.; Investigation, P.W.; Writing—original draft, P.W.; Writing—review & editing, P.Z. and Y.C. All authors have read and agreed to the published version of the manuscript.

Funding

This research was funded by the National Natural Science Foundation of China, General Program Fund (No. 52274092).

Data Availability Statement

Data available on request.

Conflicts of Interest

The authors declare no conflict of interest.

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Figure 1. Location of the study area.
Figure 1. Location of the study area.
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Figure 2. Split-level single-entry longwall system for Y294 and Y296 panels. (a) Plan view; (b) section view (gray parts denote shields); (c) configuration of shields.
Figure 2. Split-level single-entry longwall system for Y294 and Y296 panels. (a) Plan view; (b) section view (gray parts denote shields); (c) configuration of shields.
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Figure 3. Stratigraphic column at the test site.
Figure 3. Stratigraphic column at the test site.
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Figure 4. Multi-purpose cross-measure borehole layout. (a) Gas drainage borehole system (not to scale). (b) Schematic of coring scheme and gas drainage for upper corner of the gob where gas concentrates.
Figure 4. Multi-purpose cross-measure borehole layout. (a) Gas drainage borehole system (not to scale). (b) Schematic of coring scheme and gas drainage for upper corner of the gob where gas concentrates.
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Figure 5. In situ drainage stations, boreholes, and equipment.
Figure 5. In situ drainage stations, boreholes, and equipment.
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Figure 6. Conceptual structural models developed from field data. (a) Split-level longwall layout; (b) conventional longwall layout.
Figure 6. Conceptual structural models developed from field data. (a) Split-level longwall layout; (b) conventional longwall layout.
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Figure 7. Theoretical structural model for the inclined lowest intact stratum (q0 is the stress from the overlying strata. qg is the stress from the gob acting on the overlying strata. A, B are the end points rigidly clapped. O is the origin point, X is the X-coordinate, Y is the Y-coordinate, Z is the Z-coordinate, θ is the inclination, G is the gravity, GZ is the component force acting on the stratum perpendicular to the stratum due togravity).
Figure 7. Theoretical structural model for the inclined lowest intact stratum (q0 is the stress from the overlying strata. qg is the stress from the gob acting on the overlying strata. A, B are the end points rigidly clapped. O is the origin point, X is the X-coordinate, Y is the Y-coordinate, Z is the Z-coordinate, θ is the inclination, G is the gravity, GZ is the component force acting on the stratum perpendicular to the stratum due togravity).
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Figure 8. Simple geometry calculation depicting the influence of the triangular-like solid coal pillar for split-level longwall gob compared with conventional longwall layout.
Figure 8. Simple geometry calculation depicting the influence of the triangular-like solid coal pillar for split-level longwall gob compared with conventional longwall layout.
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Figure 9. Numerical model for Y294 panel. (a) Oblique view. (b) Cross-sectional view.
Figure 9. Numerical model for Y294 panel. (a) Oblique view. (b) Cross-sectional view.
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Figure 10. Iteratively fitted results. (a) Stress contour; (b) volumetric contour; (c) matching between numerical data and Salamon’s equation data.
Figure 10. Iteratively fitted results. (a) Stress contour; (b) volumetric contour; (c) matching between numerical data and Salamon’s equation data.
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Figure 11. Field measurements and instruments used. (a) Instrumentation plan when the Y294 panel was about to finish mining (not to scale). (b) Stress meters and accessories (the data were collected every five minutes). (c) Schematic of stress meter installation. (d) Cross measurement method. (e) Flexible tape and telescoping rods used for convergence measurement. (f) Load cell. (g) Schematic of the size of each part of the steel set (mm).
Figure 11. Field measurements and instruments used. (a) Instrumentation plan when the Y294 panel was about to finish mining (not to scale). (b) Stress meters and accessories (the data were collected every five minutes). (c) Schematic of stress meter installation. (d) Cross measurement method. (e) Flexible tape and telescoping rods used for convergence measurement. (f) Load cell. (g) Schematic of the size of each part of the steel set (mm).
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Figure 12. Comparison of field data and modeling data (maximum value when an equilibrium was reached, i.e., the monitoring variables hardly changed). (a) Comparison between field data and modeling data of side abutment pressure at Y294 panel lower end (the red axis corresponds to the red curve and the blue axis corresponds to the blue curve). (b) Comparison between field data and modeling data of roof-to-floor and rib-to-rib convergences. (c) Comparison between field data and modeling data of roof pressure of Y296 tailgate.
Figure 12. Comparison of field data and modeling data (maximum value when an equilibrium was reached, i.e., the monitoring variables hardly changed). (a) Comparison between field data and modeling data of side abutment pressure at Y294 panel lower end (the red axis corresponds to the red curve and the blue axis corresponds to the blue curve). (b) Comparison between field data and modeling data of roof-to-floor and rib-to-rib convergences. (c) Comparison between field data and modeling data of roof pressure of Y296 tailgate.
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Figure 13. Numerical results employing conventional longwall layout and split-level longwall layout. (a) Stress distribution due to extraction of Y294 panel (left: conventional layout; right: split-level layout). (b) The gob material movement (left: conventional layout; right: split-level layout). (c) Stress distribution after extraction of Y296 tailgate (left: conventional layout; right: split-level layout). (d) Yield zone development after extraction of Y296 tailgate (left: conventional layout; right: split-level layout). (e) Yield zone development before extraction of Y296 tailgate (split-level layout).
Figure 13. Numerical results employing conventional longwall layout and split-level longwall layout. (a) Stress distribution due to extraction of Y294 panel (left: conventional layout; right: split-level layout). (b) The gob material movement (left: conventional layout; right: split-level layout). (c) Stress distribution after extraction of Y296 tailgate (left: conventional layout; right: split-level layout). (d) Yield zone development after extraction of Y296 tailgate (left: conventional layout; right: split-level layout). (e) Yield zone development before extraction of Y296 tailgate (split-level layout).
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Figure 14. Conventional approach without taking gob into account. (a) Stress distribution after extraction of Y294 panel. (b) Stress distribution after extraction of Y296 tailgate.
Figure 14. Conventional approach without taking gob into account. (a) Stress distribution after extraction of Y294 panel. (b) Stress distribution after extraction of Y296 tailgate.
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Figure 15. Gob-edge pressure distribution for the modeled methods. (a) Stress distribution on the floor. (b) Enlarged view of left side. (c) Enlarged view of right side.
Figure 15. Gob-edge pressure distribution for the modeled methods. (a) Stress distribution on the floor. (b) Enlarged view of left side. (c) Enlarged view of right side.
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Table 1. Parameters of the cross-measure boreholes.
Table 1. Parameters of the cross-measure boreholes.
StationHole Length/mInclination/(°)Azimuth/(°)
1#110072
29014.54.5
2#3807.51.5
490155
3#510072
680145
4#711072
8120144.5
5#910072
10130145
6#1111073
12110145
7#1313072
14130144.5
8#1512072
16120145
9#1712072
18120145
Table 2. Physical and mechanical properties of different lithologic units.
Table 2. Physical and mechanical properties of different lithologic units.
LithologyUnit Weight
(g/cm3)		UCS
(MPa)		Bulk Modulus
(GPa)		Shear Modulus
(GPa)		Cohesion
(MPa)		Friction Angle/(°)
Siltstone2.710511.49.54.841
5# Coal1.34185.33.21.228
Siltstone2.65101.310.98.24.238
Siltstone2.7290.310.08.13.635
Siltstone2.7611511.98.73.937
Medium sandstone2.721348.96.22.632
Siltstone2.7278.810.48.53.836
Siltstone2.7212510.88.73.737
Medium sandstone2.721248.96.22.632
Siltstone2.72748.65.32.432
8#, 9# coal1.4195.33.21.228
Siltstone2.7280.410.48.53.836
Fine sandstone2.5510212.610.73.742
Siltstone2.7685.612.310.54.443
Table 3. Cap pressures for the double-yield model.
Table 3. Cap pressures for the double-yield model.
Strain (m/m)Stress (MPa)Strain (m/m)Stress (MPa)
000.157.64
0.010.26 0.168.76
0.020.53 0.1710.06
0.030.83 0.1811.59
0.041.15 0.1913.42
0.051.50 0.215.65
0.061.88 0.2118.41
0.072.29 0.2221.92
0.082.74 0.2326.54
0.093.23 0.2432.91
0.103.77 0.2542.22
0.114.38 0.2657.15
0.125.05 0.2784.97
0.135.81 0.28155.08
0.146.660.29668.99
Table 4. Parameters of gob material.
Table 4. Parameters of gob material.
Density (kg/m3)Bulk Modulus (GPa)Shear Modulus (GPa)Friction (°)Dilation (°)
17000.730.526.25.6
Table 5. Comparison of some major numerical modeling works with gob considered.
Table 5. Comparison of some major numerical modeling works with gob considered.
ItemThis PaperYavuz. (2004) [27]Yan et al. (2013) [28]Li et al. (2015) [29]Esterhuizen et al. (2010) [59]Jiang et al. (2012) [56] and Wang et al. (2013) [30]Morsy and Peng (2002) [58]Song et al. (2017) [57]
SoftwareFLAC3DFLAC3DFLAC3DFLAC3DFLAC3DFLAC3DABAQUSPhase2D
Caved zoneIn situ dataCoal seam and immediate roof heightCoal seam heightAssumed, 2 to 8 times of mining heightCoal seam heightCoal seam and the immediate roof6 times the seam thicknessCoal seam height
Angle of breakIn situ data 90°, vertical90°, vertical90°, vertical90°, vertical90°, vertical90°, vertical90°, vertical
Gob materialDouble-yield constitutive modelDouble-yield constitutive modelVery soft elastic materialDouble-yield modelEquivalent gob elements that follow the hyperbolic stress–strain curvesVery soft elastic materialTerzaghi’s modelBackfill material with varying stiffness with distance to the faceline
Strata materialRock mass properties degraded for lab data followed by China standardElastic modelMohr–Coulomb failure criterionMohr–Coulomb criterion for rock and strain-softening model for coal Peak strength: Hoek–Brown model;
yield: strain-softening and non-associated plastic flow rules		Elastoplastic Mohr–Coulomb model with non-associated flow rulesLinear elastic material propertiesHoek–Brown parameters
InterfacesBedding planes and irregular gob boundaries were all consideredNot mentionedNot mentionedCoal/rock interface was consideredAdequately consideredNot mentionedNot mentionedNot mentioned
Model meshRandom, tetrahedron, graded from small around material boundaries to large at the center of the material domainNot mentionedCuboidal or cubic brickCuboidal or cubic brickCuboidal or cubic brickCubic8-node brick, 6-node tetrahedronTriangular, random, graded from small around material boundaries to large at the center of the material domain
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Wang, P.; Zhao, P.; Cao, Y. A Comparative Case Study on Stress Redistribution due to Extraction of Conventional and Split-Level Longwall Panels in Deep Inclined Coal Seams. Processes 2023, 11, 3201. https://doi.org/10.3390/pr11113201

AMA Style

Wang P, Zhao P, Cao Y. A Comparative Case Study on Stress Redistribution due to Extraction of Conventional and Split-Level Longwall Panels in Deep Inclined Coal Seams. Processes. 2023; 11(11):3201. https://doi.org/10.3390/pr11113201

Chicago/Turabian Style

Wang, Pengfei, Peng Zhao, and Yang Cao. 2023. "A Comparative Case Study on Stress Redistribution due to Extraction of Conventional and Split-Level Longwall Panels in Deep Inclined Coal Seams" Processes 11, no. 11: 3201. https://doi.org/10.3390/pr11113201

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