Subsidence Prediction of Overburden Strata and Surface Based on the Voussoir Beam Structure Theory

,e hard and stiff strata (key strata) bear the overburden load in the form of a voussoir beam structure (VBS) after break.,e VBS affects both the surface subsidence and the stope underground pressure. ,erefore, the reasonable method to predict the surface subsidence is based on the whole subsidence formulae of the VBS. ,is study first establishes the subsidence formulae of the VBS analytically. ,e influence of the block length on the subsidence curve and the VBS level on the zero-subsidence range are then analyzed based on the subsidence formulae of the VBS.,e results show the half-subsidence curve of the VBS is an S-shaped curve. ,e block length hardly affects the S-shaped subsidence curve determined by the width of the undercompacted zone. Furthermore, a greater undercompacted zone width corresponds to a greater offset distance of the inflection point. ,e higher the VBS level, the farther the zero-subsidence range, and the flatter the subsidence curve. ,e subsidence of the highest VBS can approximately represent the surface subsidence when the topsoil is thin enough.


Introduction
Coal mining will lead to overburden fracturing [1,2], groundwater pollution [3][4][5][6], and landslides [7].Moreover, all of the environmental damage relates to the surface subsidence.erefore, it is especially important to study the surface subsidence caused by coal mining.To date, several methods can be used to predict the surface subsidence, including profile function [8], modelling [9], and influence function [10][11][12] methods.Most of these approaches are in light of ground station-based statistics predicting the surface subsidence without considering the control action of the key strata (KS) on the surface subsidence.However, field observations and physical model simulations have shown that the KS dynamically controls the surface subsidence [13][14][15], which means that the KS and the controlled soft rocks obtain synchronous subsidence and subsidence speed. is suggests that in order to accurately predict the surface subsidence, it is necessary to first calculate the KS subsidence within the overburden.e overlying strata are usually divided into a caved zone, a fractured zone, and a continuous deformation zone [16].e KS in different zones will present different characteristics.e KS in a caved zone will collapse after mining while that in a fractured zone will bear the overlying load with the voussoir beam structure (VBS).Meanwhile, the KS in a continuous deformation zone deform like a complete rock beam.e KS controls the surface subsidence in the form of a VBS when the coal seam is not deeply buried.
erefore, the subsidence formulae of the VBS should be determined before predicting the surface subsidence.e deformation mechanisms and the stability of undermined sedimentary rock layers have been studied [17,18], but the influence of the VBS on the overlying strata subsidence was not considered.An enhanced subsurface subsidence prediction model considering overburden stratifications had been derived in the literature [19]. is model equally divides the overburden strata into a finite number of layers and considers the percent of hard rocks in each layer.e subsidence of each layer is then predicted progressively upward based on the in uence function method.e model provides a new method for the subsurface subsidence prediction, but it does not consider the control action of the KS and only divides the overburden strata into several equal parts.e proposal of the "voussoir beam theory" [20] based on eld measurements brought a qualitative leap to the understanding of the stope underground pressure.e mechanical model of the VBS proved that the KS after break was essentially a semiarch structure, despite it looking like a rock beam.e condition was that the key block in the VBS must meet the condition of "S-R" (sliding-rotation) stability.
e voussoir beam theory explained the structure form of the overburden strata after coal seam mining, the reason for the front abutment pressure greater than the rear abutment pressure, and the displacement constraints above "immediate roof supports" [21].e voussoir beam theory could explain most of the stope underground pressure phenomena and guides the control of the stope underground pressure and the prevention of roof accidents.Hence, the Mining and Metallurgy roll of the encyclopedia of China has accepted the "voussoir beam" concept.However, the mechanical model of the VBS only analyzes the force balance and displacement of the breaking blocks and does not provide the whole subsidence formulae, which are the basis for the calculation of overburden strata subsidence and the surface subsidence.
e analytical formulae of the whole VBS subsidence are initially derived and used to analyze the in uence of the VBS level on the zero-subsidence range and the block length on the subsidence curve.Field tests are then utilized to validate the analytical subsidence formulae.
e VBS subsidence can approximately represent the surface subsidence when the topsoil is extremely thin, but it cannot represent the surface subsidence when the topsoil is thick because the topsoil has its own complex movement law.e e ect of the topsoil, if it is thick enough, should not be ignored in predicting the surface subsidence based on the overburden strata subsidence.Moreover, the surface subsidence can be theoretically calculated according to the deformation characteristics of the topsoil and the relationship between the surface and the VBS.Herein, only the VBS subsidence is studied, which will be the basis for the overburden subsidence-based surface subsidence prediction.

Subsidence Formula of the VBS above the
Mined-Out Area e overlying voussoir beam is divided into two parts (i.e., one above the mined-out area and another above the rib side separated by the blue line and represented with capital A and B, respectively, in Figure 1(a)).is is because the breaking blocks above the mined-out area interlock with each other, forming a stable mechanical structure and bearing the overburden load, while the voussoir beam above the rib side deforms in the form of an unbroken beam.Furthermore, di erent external forms of the voussoir beam have di erent mechanical models.One is the continuous mechanical model, and another is the discontinuous mechanical model.
Figure 1(c) presents the simpli ed force diagram involving seven blocks based on Figure 1(a).e stress on the VBS is assumed to be linear from the rst block near the rib to the horizontal block because the rst block and the horizontal block are on the separation zone and the compacted zone, respectively.Structural mechanics de nes the degree of freedom of this VBS to be zero.Hence, this model is a statically determinate problem, and the subsidence of each block can be derived based on the structural relationship of static equilibrium.
Each block has the same length L. R i represents the support forces of each block.Q i denotes the resultant loads calculated with the block central stress multiplying the block length and acting on the block center because stress slightly changes on one block.Δ i is the rock compression at the point of support forces.d i is the relative subsidence of two endpoints of one block, and h is the block thickness.
e rock mass under the voussoir beam comprises the whole caved zone rocks and the partial fractured zone rocks.Figure 2 shows the stress-strain curve of the caved zone rocks in the mined-out area based on Su et al. [22], and this stress-strain curve is similar to that listed in the literature [22].Figure 3 presents the load-displacement curve based on the authors' measured rock core experiments.Figure 2 depicts that the three polynomial fitting degree of the stress-strain curve is very high.e load-displacement relationship of the caved zone rocks can satisfy (2) because the stress-strain relationship can be converted to a loaddisplacement relationship and the overall curve trend is kept unchanged.Figure 3 shows that the load-displacement relationship of the rock cores does not completely satisfy (2), and the correlation coefficient is only 0.73.However, the compression mainly concentrates on the caved zone rocks.Furthermore, the load-displacement relationship of the fractured zone rocks can approximately satisfy (2).erefore, the support forces can be assumed to be proportional to the cube of rock compressions: where k is the proportional coefficient, which can be back calculated with the maximum load and the maximum subsidence of the voussoir beam.e maximum load is the weight of the overlying rock strata [23], including the weight of the voussoir beam itself.e compression can be derived through the following equation because the subsidence of the voussoir beam equals the compression of the rock mass under the voussoir beam: where M is the mining height,  h is the thickness from the coal seam to the voussoir beam, and b is the bulking coefficient.e first block of the VBS is located in the bed separation zone.Hence, no interaction exists between the first block and the underlain soft rocks.Compression starts from the second block of the VBS.e compressions at the position of the support forces are presented as follows according to the geometric relationship of the interlocked blocks: e compressions at the position of the support forces of each block can be calculated by combining (1)(2)(3)(4).e subsidence of each block can then be obtained because the subsidence of each block is equal to the rock compression.Note that the subsidence of each block here is relative.Assignments are made to variables for an intuitive Advances in Civil Engineering understanding of the VBS subsidence above the mined-out area.e overburden weight is 3 MPa, the block length is L � 15 m, the block thickness is h � 5 m, the mining height is M � 3 m, and the thickness from the coal seam to the voussoir beam is  h � 30 m. e bulking coefficient is b � 1.05, and the maximum compression is 1.5, which is calculated using (3).
erefore, the proportional coefficient is k � 13.33 MN • m −3 .e subsidence at each block center is obtained (Figure 4) by combining (1-4) with the assignments.e abovementioned VBS only involves seven blocks, but the number of blocks is variant in different geological conditions because the number of blocks is determined by the width of the undercompacted zone and the block length.Equation ( 5) is provided herein to compute the subsidence of any number of interlocked blocks and facilitate the applications in different geological conditions.e geometrical relationships can also be derived in the same manner as in (4).e subsidence of each block is then calculated in line with the load-displacement relationship. (5)

Subsidence Formula of the VBS above the Rib Side
e voussoir beam above the rib side also subsides, except for the subsidence above the mined-out area.Zone A in Figure 1 is enlarged and shown in Figure 5.According to the limit angle in mining subsidence engineering, the higher the level, the farther the subsidence.In other words, the zerosubsidence point extends further as the VBS level becomes far away from the coal seam.e subsidence of the voussoir beam above the rib side is determined by lithology and stress magnitude.e soft rock mass leads in more compression and more VBS subsidence.e VBS subsidence above the rib side is nonnegligible unless the stress is small and the rock mass is hard.e deformation law of the voussoir beam above the rib side is similar to the elastic beam caused by the absence of failure.erefore, the subsidence can be solved with material mechanics.e friction at the top and bottom surfaces of the voussoir beam is in the opposite direction.
e friction coefficients and the stress on both surfaces are almost the same.Consequently, friction can be ignored.Moreover, ignoring the axial force, the differential equation of the voussoir beam becomes where E is the elastic modulus, I is the cross section moment of inertia, p is the stress on the bottom surface of the voussoir beam, and q is the stress on the top surface of the voussoir beam.Figure 5(a) shows the real stress on the top surface of the voussoir beam and the state of the rock mass under the voussoir beam after the coal seam excavation.e partial rock mass under the voussoir beam is in a plastic state.Hence, there is no analytically effective method of obtaining the voussoir beam subsidence.Assuming the rock mass under the voussoir beam to be in an elastic state is the general approach to acquire the voussoir beam subsidence.
at is, the voussoir beam deforms on an elastic foundation.As for the stress on the top surface of the voussoir beam, basically, all methods suppose that the stress distribution is Weibull or uniformly distributed.A uniformly distributed stress is unreasonable because a uniformly distributed stress simultaneously exists with strata sedimentation and does not cause any subsidence, which is caused by the additional stress transferred from the weight of the overlying strata above the mined-out area.
e Weibull distributed stress results from the fact that the rock mass is overstressed and becomes plastic, and then, stress gradually transfers to a distant rock mass until a new equilibrium is obtained.e Weibull distributed stress is not reasonable because the foundation under the voussoir beam is assumed to be elastic, and Weibull distributed stress is the result of a plastic rock mass.Moreover, the Weibull distributed stress theoretically leads to a significantly small subsidence of the voussoir beam.In fact, if the rock mass of the rib side is forever elastic, the nearest point to the rib can bear all the weight of the rock strata above the mined-out area, and the additional weight will not transfer to a distant rock mass.us, the point load shown in Figure 5(b) should be the actual stress state for the elastic rock mass.Meanwhile, the stress on the bottom surface of the voussoir beam is proportional to the subsidence.Equation ( 6) then becomes 4 Advances in Civil Engineering where k 1 is the coe cient of elastic foundation, namely, the stress to displacement ratio.Many rock strata usually exist under the voussoir beam, including the coal seam.Suppose that there are n layers of the rock beam, numbered 1, . . ., n starting from the coal seam.e elastic modulus of each stratum is E i , while the thickness is h i .e coe cient of elastic foundation can then be presented as Setting β k 1 /EI 4 , the general solution of the fourthorder ordinary di erential in (7) is obtained as y e βx (A cos βx + B sin βx) Four boundary conditions must be considered to determine the four coe cients (i.e., A, B, C, and D) of ( 9). e in nite point of the voussoir beam is a xed boundary, indicating that the subsidence and the rotational angle here are zero.Only the shear force exists in the right boundary of the voussoir beam, and the shear force is equal to the weight of the rock mass above the rst layer of the voussoir beam, including the weight of the voussoir beam itself.Consequently, the boundary conditions are summarized as follows: where l is the horizontal distance from the origin to the right boundary, which can be calculated by the broken angle φ and the distance from the coal seam to the voussoir beam h.Q is the shear force on the right boundary equal to the weight of the rock mass above the rst layer of the voussoir beam, including the weight of the voussoir beam itself.q is zero because the voussoir beam subsidence results from the additional load and not from the stress existing before the coal excavation, which would not cause any subsidence.e magnitude of the additional load is related to the breakage of the voussoir beam and the mining conditions.e weight of the rock mass above the mined-out area will all be borne by the rib side if the voussoir beam above the mined-out area does not break.In supercritical mining, the weight of the rock mass over the undercompacted zone half-transfers to the rib side, but no weight of the rock mass over the compacted zone shifts to the rib side.Let S represent the width of the undercompacted zone and c be the average unit weight of the overburden rock mass.Q is then equal to ScH/2.H is the buried depth of the voussoir beam.
Taking the boundary conditions into the rst, second, and third derivatives of ( 9), the subsidence of the voussoir beam above the rib side becomes e mining height is M � 3 m.e thickness from the coal seam to the voussoir beam is  h � 30 m. e weight of the rock mass on the voussoir beam is 3 MPa, while the width of the undercompacted zone is S � 80 m. e shear force is Q � 120 MN/m.e elastic modulus of the rock mass from the coal seam to the voussoir beam is 7 GPa, while that of the coal seam is 5 GPa and that of the voussoir beam is E � 30 GPa. e voussoir beam thickness is h � 5 m. e breaking angle is φ � 70 °and l � 10.92 m. Figure 6 shows the subsidence of the voussoir beam above the rib side after calculating (11) with assignments.Figure 6 depicts that the subsidence at the right boundary is the maximum.Furthermore, the voussoir beam uplifts in a distance from the right boundary.However, this phenomenon is not obvious.

Half-Subsidence Curve of the VBS and Influence Factors
4.1.Half-Subsidence Curve of the VBS.Combining the VBS subsidence above the mined-out area with that above the rib side results in the half-subsidence curve of the VBS.Its formulae are shown in (12).Taking the previous assignments as an example, Figure 7 shows the half-subsidence curve of the VBS. Figure 7 also illustrates that the half-subsidence curve is an S-shaped curve.Its shape is determined by the block length, block thickness, load, VBS level, and mining height.Note that the VBS subsidence above the mined-out area should add the maximum subsidence of the VBS above the rib side because the VBS subsidence above the mined-out area is relative to a fixed point.e VBS subsidence above the mined-out area obtains a corresponding subsidence when the fixed point subsides.In other words, the subsidence above the mined-out area is relative, whereas that above the rib side is absolute.

Influence of the Block Length and the Width of the
Undercompacted Zone on the VBS Subsidence.e block length is decided by stress on the VBS and its hardness.Small stress has a longer block length, while great hardness provides a short block length.Figure 8 illustrates the influence of the block length on the VBS subsidence.e assignments are the same with those used in Figures 4 and 6, except for the block length.Figure 9 shows that the S-shaped subsidence curve of different block lengths is almost the same.It can then be concluded that the block length hardly affects the subsidence curve shape.erefore, a roughly reasonable block length is suitable for the subsidence calculation.Each block length of the overburden VBS is difficult to determine.Hence, the above conclusion makes the prediction of the overburden subsidence simple and feasible.Figure 9 presents the influence of the width of the undercompacted zone on the VBS subsidence, where the width is shown to affect the subsidence curve shape.e elliptical zone represents the 6 Advances in Civil Engineering o set distance of the in ection point.erefore, the higher undercompacted zone width corresponds a higher o set distance of the in ection point.

In uence of the Level on the VBS Subsidence.
Di erent levels normally involve a variation of other factors, such as load, elastic modulus, and bulking coe cient.e elastic modulus of the rock mass is assumed herein to be unchanged.However, the load changes considering a stress gradient of 2.5 MPa/100 m. e bulking coe cient varies at di erent levels.Hence, only the zero-subsidence range above the rib side is studied.e assignments are the same with those used in Figures 4 and 6, except for the VBS level and load.Figure 10 shows the in uence of the level on the zerosubsidence range of the VBS.e zero-subsidence range increases as the VBS level becomes higher, thereby indicating that the sphere of in uence grows in a high level.Moreover, the subsidence volume is almost ascertained.erefore, the subsidence curve becomes smoother in a higher level.

In uence of the Mining Height on the VBS Subsidence.
e mining height is the main factor in uencing the VBS subsidence.Figure 11 presents the in uence of the mining height on the VBS subsidence in supercritical mining.e assignments are the same with those used in Figures 4 and 6, except for the mining height.shows that the in uence of the mining height on the subsidence above the rib side is negligible but signi cantly a ects the VBS subsidence above the mined-out area.e subsidence increases, and the subsidence curve slope becomes steeper with the higher mining height.

Calculation Steps of the VBS Subsidence.
e physical and mechanical parameters of the rock strata, including the elastic modulus, strata thickness, mining height, density, and tensile strength, and the mining subsidence parameters, including the angle of full subsidence, breaking angle, and bulking coe cient, are needed to calculate the VBS subsidence.e subsidence over the mined-out area and the rib side is then calculated accordingly.Finally, the maximum subsidence above the rib side should be added to each block subsidence above the mined-out area.us, the halfsubsidence curve of the VBS can be obtained.Figure 12 shows the detailed calculation steps.e subsidence parameters can be determined according to either the following methods or eld measurements: (1) e thickness of the overburden strata can be obtained through a geological histogram.e physical and mechanical parameters can be tested with in situ drilling cores in a laboratory.e values from the laboratory tests should be reduced because of the numerous geological structures in the eld rock mass.e elastic modulus of the rock mass is approximately half that tested in the laboratory samples [24].e block length can be calculated by theory of beams xed at two sides.(2) e angle of full subsidence determines the width of the undercompacted zone and the shear force magnitude.Moreover, it decides the number of blocks in the VBS.Whether the caved zone is compacted or not is related to the stress magnitude because stress determines the compaction degree.
Only di erent levels of strata have the same width of compacted zone, and stress in the compacted zone of a level can be kept constant.erefore, the width of the compacted zone in every level is xed for one mining condition.Figure 13 shows the numerical width of the compacted zone in di erent levels (the subsidence magnitude is zoomed), where the width of the compacted zone in six di erent levels is almost the same.Hence, the angle of full subsidence can be obtained through eld measurements.
(3) e angle between the horizontal line and the line connecting the coal rib to the rib near the fracture of each stratum is called the breaking angle.e relationship between the breaking angle and the ratio of compressive strength σ s to tensile strength σ t is expressed as follows [25]: (4) e maximum subsidence of the VBS is closely related to the KS breakage.e stress on the caved and fractured zones increases if the KS breaks.e rock mass compression then extends, and the bulking coe cient decreases.e bulking coe cient barely changes after a critical subsidence.e eld measurements show that the bulking coe cient exponentially decreases upward from the coal seam [26,27] and satis es the following equation: where a and b are the parameters related to geological conditions.e Yangquan Yi coal mine has a and b of 0.017 and 1.083, respectively, whereas the Kongzhuang coal mine has 0.037 and 1.151, respectively.k is the bulking coe cient, and h is the height from the coal seam to the VBS.

Case Study One.
In the 1980s, overburden strata movement observations were conducted in some of the coal mines in China.One of these observations is referenced here to validate the subsidence model proposed in the present study [26].e mining coal seam is Panel 8111 with a mining height of 1.8 m and a dip angle of 25 °-26 °. e width and length of Panel 8111 are 112 m and 452 m, respectively.e mining depth is 221 m with 153 m topsoil.e spacing of coal seams #7 and #8 is 24 m. Figure 14 illustrates the observation boreholes drilled in the roadway of coal seam #7.
e rst VBS is a layer of sandstone with 4.6 m thickness and located 16.8 m away from the mining coal seam, which is the rst layer of sandstone under coal seam #7 presented in the dip cross section in Figure 14. e measured subsidence is represented with a dashed red line in Figure 15.e block length and the width of the undercompacted zone are 15 m and 90 m, respectively.erefore, seven blocks act in the VBS.e topsoil and bedrock densities are 1900 kg/m 3 and 2450 kg/m 3 , respectively.Hence, the uniformly distributed stress on the compacted zone is 4.17 MPa vertical to the coal seam.e shear force at the boundary of the rst VBS above the rib side then becomes 187.7 MN/m.ey are assigned based on the literature as a result of the absence of a real elastic modulus [24].e elastic moduli of the coal seam, voussoir beam, and rock mass between the coal seam and the voussoir beam are 3 GPa, 8 GPa, and 5 GPa, respectively.e bulking coe cient is 1.051 according to (14).Consequently, the load to compression ratio is 79.5 MN/m 3 .e breaking angle is 59.2 °based on the measurements.e solid black line in Figure 15 depicts the theoretical subsidence of the VBS.e subsidence of the measurements and the theoretical calculations agrees well with each other.

Case Study Two.
e subsidence of the upmost VBS can approximately represent the surface subsidence if the topsoil is extremely thin.e surface subsidence observed on Panel 31305 of the Wanli Yi coal mine of the Dongsheng colliery is borrowed here as the second example to verify the subsidence model [28].e mining height is 4.9 m, and the dip angle is 1.5 °-5 °. e width and the length of Panel 31305 are 300 m and 2706 m, respectively.e average mining depth is 145 m with 10 m topsoil (Table 1).
e block length and the undercompacted zone width are 50 m and 100 m, respectively.erefore, three blocks act in the VBS.e elastic modulus of the VBS and the rock mass under the VBS are 0.3 GPa and 1 GPa, respectively.e overburden density is 2600 kg/m 3 .Hence, the uniformly distributed stress is 2.34 MPa on the PKS and is 4.42 MPa on the lowest VBS. e shear force at the boundary of the rst VBS above the rib side then becomes 221 MN/m, while the bulking coe cient is 1.023.Consequently, the load to compression ratio is 3.97 MN/m 3 , and the breaking angle is 90 °based on the measurements.e black line in Figure 16 denotes the theoretical subsidence of the VBS, while the red line is the measured surface subsidence.e subsidence of the measurements and the theoretical calculations agrees well with each other.

Application Analysis of the VBS Formulae
(1) e subsurface subsidence could have a significant in uence on the performance of the gob well degasi cation system [29,30], migration of groundwater [31,32], and subsurface mine structures [33].e KS theory shows that the subsidence of a KS can represent a set of strata displacements and the subsurface subsidence can be predicted by KS subsidence.Moreover, the VBS method is suitable for any VBS in the overburden.( is method is also applicable to dip coal seam by decomposing the gravity into the parallel and vertical directions to the coal seam.e subsidence of VBS is yet perpendicular to the coal seam).
erefore, the subsurface subsidence of any strata can be calculated with the subsidence calculation steps of VBS (Figure 12).
(2) e in uence function method is one of the most commonly used methods for surface subsidence prediction in coal mines.Practices indicate that the overburden thick hard rock strata play an important J 17 J-base point of level theodolite cross section G-base point of survey S-deep base point -155.36 Main return way Hau lage road way  e surface subsidence coe cient is relatively large in the Huaibei mining area of China in which the surface subsidence coe cient of critical mining can be as high as one.In the Haizi coal mine of the Huaibei mining area, there is a thick hard layer in the overburden rock mass.e depth of 600 meters and the width and advancing length of the II 1022 and II 1024 longwall working face reaches 390 m and 560 m, respectively.
ere should be a 2.0-2.5 m surface subsidence according to "Coal Mining Regulations and Coal Pillar Design A ected by Buildings, Water Bodies, Railways and Main Roadways'' of China.However, the measured maximum surface subsidence is only 0.526 m (Figure 17). is result illustrates that the in uence function method has errors in the surface subsidence prediction when there is a typical thick and hard stratum.Nevertheless, the advantage of the VBS method is based on the physical and mechanical parameters of the overburdens, not on the empirical data.e surface subsidence is equivalent to the top VBS subsidence when the topsoil is thin enough because the topsoil and the top KS can be treated as a set of stratum.e surface subsidence can be theoretically calculated according to the deformation characteristics of the topsoil if it is thick [34].In short, the subsidence method of the VBS is a good complement and extension for the existing prediction methods of the surface subsidence.

Conclusions
It is quite important to study the subsidence of overburden and surface caused by coal mining in that water inrush and environmental damage result from the subsidence of the overburden and surface.Although many methods were proposed to predict surface subsidence, most of these methods did not consider the e ect of key strata.However, eld investigations and laboratory experiments indicated  that the key strata control the surface subsidence.When the key strata break, it control the surface with a voussoir beam structure formed.
e subsidence of the voussoir beam occurs above both the mined-out and rib-side area.At present, only the displacement of blocks above the minedout area was studied, and the subsidence line was not an S-shaped curve, which was in contradiction with the field investigations.In addition, the previous calculation formula of blocks displacement was revised and improved in this paper.In a word, the following conclusions are obtained from this study: (1) e overlying VBS is divided into two parts: one above the mined-out area and another above the rib sides.e breaking blocks above the mined-out area interlock with each other, forming a stable mechanical structure.Its subsidence can be obtained by structure mechanics.Meanwhile, the VBS above the rib sides deforms like a complete beam, and its subsidence can be derived by continuum mechanics.
Adding the maximum subsidence of the VBS above the rib side to each block subsidence of the VBS above the mined-out area and combining these two subsidence parts result to the half-subsidence curve of the VBS, which is an S-shaped curve.e theoretical subsidence of the VBS agrees well with the field measurements.(2) e undercompacted zone width, and not the block length, determines the S-shaped subsidence curve.e zero-subsidence range increases as the VBS level becomes higher.e subsidence increases, and the subsidence curve slope becomes steeper with the higher mining height.
(3) e proposed subsidence model is suitable to any VBS layer.e VBS subsidence can approximate the surface subsidence when the topsoil is extremely thin but cannot represent the surface subsidence when the topsoil is thick because the topsoil has its own complex movement law.erefore, only the VBS subsidence is studied herein.e overburden subsidence-based surface subsidence prediction method will be studied next.

Figure 1 :
Figure 1: e mechanical model of the longwall overburden voussoir beam structure.

Figure 5 :
Figure 5: Mechanical state of the voussoir beam above the rib side.(a) Plastic foundation; (b) elastic foundation.

Figure 10 :Figure 11 :
Figure 10: In uence of the level on the subsidence of the voussoir beam structure.

Figure 15 :
Figure 15: Subsidence of the eld measurements and the theoretical calculations of the voussoir beam structure.

Figure 16 :Figure 17 :
Figure 16: Subsidence of the surface measurements and the theoretical calculations.

Table 1 :
Strata thickness and KS location.