A method for predicting support load based on critical state inversion of master control layer

Abstract

The application discloses a kind of filling support load prediction methods based on master control layer critical filling rate inversion, steps include: obtaining the parameters of each rock stratum of overburden rock, based on the equivalent deformation coordination principle of combination beam, overburden rock is divided into multiple bearing groups, determine the lowermost unbroken rock stratum in each bearing group that controls overall stability as master control layer;According to equivalent subsidence space, based on the relationship between the final allowable subsidence and equivalent subsidence space, the master control layer failure state is distinguished for each bearing group, and the overburden rock failure horizon and failure range under different filling rates are obtained;Based on the local static load of the broken rock mass in the failure range of the master control layer and the master control layer failure dynamic load increment coefficient, the master control layer failure dynamic load is calculated, based on the equivalent static load of the broken rock mass in the instability influence range of the masonry beam and the masonry beam instability dynamic load increment coefficient, the masonry beam instability dynamic load is calculated, and the support working resistance prediction result is obtained.The application realizes support working resistance prediction.

Description

Technical Field

[0001] This invention relates to a method for predicting the load of a filling support based on the inversion of the critical filling rate of the master control layer, belonging to the field of coal mine filling mining and mine pressure control technology. Background Technology

[0002] In high-density non-dense backfill mining, the goaf is usually unable to achieve high-density full roof contact before the initial subsidence of the roof due to the influence of backfill equipment performance, mining-backfill cycle time, and fluctuations in gangue supply. There is an initial void between the backfill and the roof, and the backfill itself and the gangue cushion formed by the underlying fractured rock strata have compressible space, causing the fracture of the immediate roof, the old roof, the hard layer, and the key layer to exhibit a progressive evolution characteristic from bottom to top.

[0003] The overburden strata are not independently load-bearing. The lower strata bear the load of the upper strata. After the lower strata fracture, the upper strata have more room to move and may induce fractures at higher strata. However, the fractured lower strata will also support the upper strata due to fragmentation and compaction. Therefore, whether or not fracture will occur depends not only on the strength of the strata themselves, but also on the equivalent sinkable space determined by the final filling rate, mining height, allowable subsidence, and the compensation space of the residual fragmentation of the underlying fractured strata.

[0004] Existing methods for predicting support loads often rely on fixed key layers or empirical periods to determine the step distance. This approach struggles to establish a quantitative relationship between the upward shift of overburden fracture caused by changes in fill rate and the sudden increase in support load. Especially under non-dense filling conditions, the support's working resistance includes not only the continuous elastic static load generated by the initial support and top plate deflection compression, but also the local static load formed by the continuous overburden pressure of rock blocks after strata fracture, and the transient dynamic load generated by the instability of masonry beams after the failure of the main control layer and multiple layers. Without first determining which layer the fracture has reached, it is impossible to accurately calculate the sources of static and dynamic loads and the period to determine the peak value, thus hindering the quantitative calculation from fill rate parameters to the overburden fracture layer and the superimposed static and dynamic load response of the support. Summary of the Invention

[0005] The purpose of this invention is to provide a method for predicting the load of a filling support based on the inversion of the critical filling rate of the main control layer. This method can predict the working resistance of the support and establish a quantitative correlation between the filling rate, the evolution of the overburden structure and the working resistance of the support.

[0006] To achieve the above objectives, this invention provides a method for predicting the load of a filled support based on the inversion of the critical filling rate of the master control layer, comprising the following steps:

[0007] S1. Obtain the thickness, elastic modulus, tensile strength, unit weight, mining height, final filling rate, residual fragmentation coefficient of the underlying fractured rock layer and support stiffness parameters of each overburden layer. Based on the principle of equivalent deformation coordination of composite beam, the overburden is divided into multiple bearing groups, and the lowest unfractured rock layer in each bearing group that plays a controlling role in the overall stability is determined as the main control layer.

[0008] S2. Based on the mining height, final filling rate, and the compensation space of residual fragmentation in the underlying fractured strata, determine the equivalent sinkable space of the goaf that is not compensated by the filling body and residual fragmentation. Based on the relationship between the final allowable sinking amount and the equivalent sinkable space obtained by the joint constraint of the maximum allowable bending sinking amount of the main control layer and the allowable sinking amount of surface protection, determine the fracture state of the main control layer for each bearing group, and obtain the fracture strata and fracture range of the overburden under different filling rates.

[0009] S3. Calculate the dynamic load of the main control layer based on the local static load of the fractured rock blocks within the influence range of the main control layer fracture and the dynamic load increment coefficient of the main control layer fracture. Calculate the dynamic load of the masonry beam instability based on the equivalent static load of the fractured rock blocks within the influence range of the masonry beam instability and the dynamic load increment coefficient of the masonry beam instability. Superimpose the initial support force of the support, the elastic static load of the support-direct top coupling, the local static load of the fractured rock blocks, and the dynamic load to obtain the predicted result of the support working resistance.

[0010] Furthermore, the bearing groups in S1 are divided based on the bending deformation coordination and mechanical response consistency of the overburden composite beam, and continuous rock strata with coordinated deformation characteristics are grouped into the same bearing group; the main control layer is the lowest unbroken rock stratum in each bearing group that is closest to the goaf and first reaches the structural control conditions, and its fracture state determines the overall stability of the corresponding bearing group.

[0011] Furthermore, the equivalent sinkable space of the goaf in S2 Determined according to the following formula:

[0012] ;

[0013] Among them, H c To raise the level; V represents the final fullness rate. exp This refers to the residual compensatory space for the underlying fractured rock strata that remains in the final compaction state;

[0014] The V exp Calculate according to the following formula:

[0015] ;

[0016] in, h is the residual fragmentation coefficient of the underlying fractured rock layer i after being subjected to pressure from the overlying rock layer; iThe thickness of the underlying fractured rock layer is denoted as i; n is the target main control layer.

[0017] The method for determining the failure state of the main control layer is as follows:

[0018] when When this occurs, it is determined that the corresponding main control layer has been broken;

[0019] when When this occurs, it is determined that the corresponding main control layer maintains a continuous and stable state;

[0020] Among them, W a The final allowable settlement is constrained by the maximum allowable bending settlement of the main control layer and the allowable settlement of the surface protection layer.

[0021] The process of obtaining the fullness rate is as follows:

[0022] When the main control layer is in a critical state between failure and stability, the following conditions must be met:

[0023] ;

[0024] The critical fullness ratio is obtained through this inversion:

[0025] ;

[0026] When the calculation result is less than 0 or greater than 1, boundary convergence processing is performed within the range of 0 to 1.

[0027] Furthermore, in S3, the initial support force of the support, the elastic static load coupled between the support and the direct top, and the local static load of the fractured rock block together form the static load of the support, wherein the elastic static load coupled between the support and the direct top F a Obtained by integrating the piecewise stiffness function of the support with the direct top deflection curve:

[0028] ;

[0029] Where L2 and L3 are the effective working lengths of the front and rear support beam regions, respectively; g1(x) and g2(x) are the equivalent distributed stiffness functions of the front and rear support beams, respectively; and ω2(x) and ω3(x) are the deflection functions directly supporting the front and rear support beam regions, respectively.

[0030] The equivalent distributed stiffness functions of the front and rear top beams are the equivalent distributed values ​​of the vertical support stiffness of the support top beam along the length of the top beam, and their expressions are as follows:

[0031] g1(x)=Bk q (x), 0≤x≤L2;

[0032] g2(x)=Bk h (x), 0≤x≤L3;

[0033] Where B is the width of the support; k q (x) is the equivalent vertical foundation stiffness coefficient of the front top beam area; k h (x) is the equivalent vertical foundation stiffness coefficient of the rear top beam area; L2 is the effective working length of the front top beam of the support; L3 is the effective working length of the rear top beam of the support;

[0034] The local static load F of the fractured rock block b Calculate using the following formula:

[0035] ;

[0036] Where B is the width of the bracket; L eff γ is the effective support length of the support frame; r is the number of fractured rock strata involved in local load transfer; i and h i χ represents the unit weight and thickness of the i-th fractured rock layer, respectively; i This is a characteristic function of the rock block state;

[0037] The rock block state indicator function χ i The condition is determined jointly by the rock strata fracture state and the rock-coal load transfer state: when the i-th rock stratum has reached the fracture condition, and its maximum subsidence is sufficient to cross the equivalent free void and form effective contact with the underlying rock cushion or the support-direct roof system, χ i Set to 1; otherwise, set χ. i Set to 0;

[0038] The specific determination is as follows:

[0039] like ,and , then χ i =1; otherwise, χ i =0;

[0040] in, The equivalent free void between the bottom interface of the i-th layer rock block and the underlying infill and residual breccia is determined by the following formula:

[0041] ;

[0042] in, The maximum tensile stress in the i-th rock layer; ω is the tensile strength of the i-th rock layer; i,max This represents the maximum subsidence of the i-th rock layer; For the final fullness rate; H c To raise the level; h is the residual fragmentation coefficient of the underlying fractured rock layer j under the final compaction state; j is the thickness of the underlying fractured rock layer j; j is the number of the underlying fractured rock layer.

[0043] The predicted working resistance of the support is obtained by superimposing the initial support force, the elastic static load of the support-direct top coupling, the local static load of the broken rock block, the dynamic load generated by the failure of the main control layer, and the dynamic load generated by the instability of the masonry beam. Its expression is as follows:

[0044] F = F0 + F a +F b +F d1 +F d2 ;

[0045] Where F is the predicted working resistance of the support; F0 is the initial support force of the support; F a For the support-direct top coupling elastic static load; F b For local static load on fractured rock blocks; F d1 Dynamic load generated by the failure of the master control layer; F d2 For dynamic loads generated by the instability of masonry beams;

[0046] The dynamic load F generated by the failure of the main control layer d1 It is determined by the dynamic load increment coefficient of the main control layer failure and the local static load of the rock block after failure, and its expression is:

[0047] ;

[0048] Among them, K d1 The dynamic load increment coefficient for the failure of the main control layer;

[0049] The dynamic load F generated by the instability of the masonry beam d2 The equivalent static load of the broken rock blocks within the influence range of the masonry beam instability and the dynamic load increment coefficient of the masonry beam instability are determined, and its expression is as follows:

[0050] ;

[0051] Among them, K d2 F is the dynamic load increment coefficient for masonry beam instability; mb The equivalent static load transferred from the broken rock blocks within the range of masonry beam instability to the support;

[0052] The F mb The calculation is as follows:

[0053] ;

[0054] Where, r m The number of fractured rock layers involved in the instability load transfer of the masonry beam; ψ i The function is γ, which represents the instability characteristic function of the masonry beam. It is set to 1 when the fractured rock block of the i-th layer participates in the instability of the masonry beam and transmits the load to the support; otherwise, it is set to 0. i h is the unit weight of the i-th rock layer; iLet be the thickness of the i-th rock layer.

[0055] Furthermore, the main control layer allows a maximum bending sag of W. a Based on the deflection model of the elastic foundation beam with two fixed ends, the following is determined: the nth main control layer and its overlying rock layer undergoing coordinated deformation are equivalent to the elastic foundation beam with two fixed ends, and the underlying infill, fractured rock cushion layer and support system are equivalent to the elastic foundation. The deflection control equation of the main control layer is established:

[0056] ;

[0057] Its boundary conditions are:

[0058] ;

[0059] The above boundary conditions indicate that both ends of the calculation section of the equivalent beam of the nth controlling layer are fixedly constrained. At x = -l / 2 and x = l / 2, the deflection and the first derivative of the deflection function of the equivalent beam of the controlling layer are both zero; where ω n (-l / 2)=0 and ω n (l / 2)=0 indicates that the vertical displacement at both ends of the equivalent beam is zero, ω n′ (-l / 2)=0 and ω n′ (l / 2)=0 indicates that the rotation angle of the equivalent beam's two ends is zero;

[0060] Among them, D n ω is the bending stiffness of the nth master control layer; n (x) is the deflection function of the nth main control layer; x is the coordinate set along the equivalent beam span direction of the main control layer, with the origin located at the midpoint of the equivalent calculation section; k b (x) represents the combined foundation stiffness formed by the underlying infill, fractured rock strata cushion, and support system; q n (x) represents the overlying equivalent load acting on the nth main control layer; l represents the equivalent calculation span of the main control layer; x=-l / 2 and x=l / 2 correspond to the left and right boundaries of the equivalent calculation segment, respectively.

[0061] After obtaining the deflection function of the nth main control layer from the deflection control equation of the main control layer, the maximum tensile stress σ of the nth main control layer is calculated based on the beam moment-curvature relationship and the bending normal stress relationship of the rectangular section. n,max When the maximum tensile stress reaches the tensile strength σ of the nth main control layer t,n When the main control layer reaches a critical fracture state, the corresponding maximum deflection is the critical deflection ω of the main control layer. n , crit That is, satisfying:

[0062] σ n,max =σ t,n ;

[0063] ω n , crit =max|ω n (x)|;

[0064] If the allowable subsidence W for surface protection is also considered s Then the final allowable subsidence amount W a Determine using the following formula:

[0065] W a =min(ω n , crit W s ).

[0066] This invention achieves layered identification of overburden bearing structures through a method for classifying overburden bearing groups based on the collaborative deformation characteristics of composite beams; it enables prediction of overburden fracture locations and fracture ranges under different filling rate conditions by establishing a critical filling rate inversion formula among the maximum allowable bending settlement of the main control layer, mining height, final filling rate, and residual fragmentation compensation space; and it establishes a unified calculation framework for the coupled elastic static load of the support-direct roof, the static load of fractured rock blocks, the dynamic load of the main control layer fracture, and the dynamic load of masonry beam instability, thereby establishing a quantitative relationship between filling rate, overburden fracture location, and support working resistance, and enabling prediction of support working resistance. This provides a theoretical basis for the selection of hydraulic supports and optimization of filling parameters. Attached Figure Description

[0067] Figure 1 This is a flowchart of the present invention;

[0068] Figure 2 This is a schematic diagram of the identification of the main control layer and the inversion result of the critical fullness rate of the 101 working face in an embodiment of the present invention;

[0069] Figure 3 This is a schematic diagram of the identification of the main control layer and the inversion result of the critical fullness rate of the 304 working surface in an embodiment of the present invention. Detailed Implementation

[0070] The invention will now be further described with reference to the accompanying drawings.

[0071] like Figure 1 As shown, a method for predicting the load of a filled support based on the inversion of the critical filling rate of the master control layer includes the following steps:

[0072] S1. Obtain the thickness, elastic modulus, tensile strength, unit weight, mining height, final filling rate, residual fragmentation coefficient of the underlying fractured rock layer and support stiffness parameters of each overburden layer. Based on the principle of equivalent deformation coordination of composite beam, the overburden is divided into multiple bearing groups, and the lowest unfractured rock layer in each bearing group that plays a controlling role in the overall stability is determined as the main control layer.

[0073] S2. Based on the mining height, final filling rate, and the compensation space of residual fragmentation in the underlying fractured strata, determine the equivalent sinkable space of the goaf that is not compensated by the filling body and residual fragmentation. Based on the relationship between the final allowable sinking amount obtained by the joint constraint of the maximum allowable bending sinking amount of the main control layer and the allowable sinking amount of surface protection and the equivalent sinkable space, determine the fracture state of the main control layer for each bearing group, and obtain the fracture strata and fracture range of the overburden under different filling rates.

[0074] S3. Calculate the dynamic load of the main control layer based on the local static load of the fractured rock blocks within the influence range of the main control layer fracture and the dynamic load increment coefficient of the main control layer fracture. Calculate the dynamic load of the masonry beam instability based on the equivalent static load of the fractured rock blocks within the influence range of the masonry beam instability and the dynamic load increment coefficient of the masonry beam instability. Superimpose the initial support force of the support, the elastic static load of the support-direct top coupling, the local static load of the fractured rock blocks, and the dynamic load to obtain the predicted result of the support working resistance.

[0075] Example 1: A mine in Inner Mongolia is mining the 3-1 coal seam at its 101 working face. The average mining height is 5.2m, the working face length is 150m, and the burial depth is 600m. The working face is overlain by multiple thick, hard rock layers, and non-dense solid backfill mining is employed. The columnar structure of the overlying strata is as follows... Figure 2 As shown, the thickness, elastic modulus, unit weight, and tensile strength of each rock layer are listed in Table 1:

[0076] Table 1 Physical and mechanical parameters of rock strata at working face 101

[0077]

[0078] Step 1: Division of Overburden Bearing Groups and Identification of Main Controlling Layers:

[0079] Based on the thickness, elastic modulus, unit weight, and tensile strength parameters of each stratum of the overburden at the working face, and according to the principle of equivalent deformation coordination of composite beams, the overburden at the working face is divided into bearing groups. Through analysis of the cooperative deformation characteristics and bearing relationships of each stratum, the overburden at the working face is divided into three bearing groups:

[0080] Bearing group 1 is the first layer of sandy mudstone above the coal seam;

[0081] Bearing group 2 is the second layer of fine-grained sandstone above the coal seam;

[0082] The bearing group 3 is a combined bearing structure formed by the overlying rock layers from the 3rd to the 14th layer.

[0083] Further identify the lowest unbroken rock strata in each bearing group that is closest to the goaf and controls the overall stability as the main control strata, and denote them as L1, L2 and L3 respectively;

[0084] Step 2: Master Layer Failure Detection and Critical Filling Rate Inversion:

[0085] The equivalent subsidence space of the goaf is determined based on the working face height, final filling rate, and the compensation space for residual fragmentation in the underlying fractured strata. Fault determination is performed using the relationship between the maximum allowable bending subsidence of the main control stratum and the equivalent subsidence space of the goaf, and then... The critical fullness rate corresponding to each master control layer is obtained through inversion.

[0086] The calculation results show that:

[0087] The critical fullness rate of the master control layer L1 is 100.0%;

[0088] The critical fullness rate of the master control layer L2 is 82.2%;

[0089] The critical fullness rate of the master control layer L3 is 58.5%.

[0090] The corresponding results are shown in Table 2:

[0091] Table 2 Critical Filling Rate and Initial Filling Volume of the Main Control Layer of the 101 Working Face Bearing Group

[0092]

[0093] When the actual filling rate is lower than the critical filling rate of the corresponding main controlling layer, the main controlling layer fractures; when the actual filling rate is higher than the critical filling rate of the corresponding main controlling layer, the main controlling layer remains stable. This allows us to obtain the fracture locations and extents of overburden fractures under different filling rate conditions.

[0094] Step 3: Stent Load Prediction:

[0095] Based on the fracture location and fracture range obtained in step two, the working resistance of the support is calculated. The static load of the support consists of the initial support force, the elastic static load formed by the direct bending and sinking compression of the support, and the local static load of the rock block after fracture. When the main control layer fractures, the rock strata within its fracture influence range transmit dynamic loads to the support; when multiple load-bearing main control layers fracture successively and form a masonry beam structure, the masonry beam undergoes rotation or slippage instability, generating dynamic loads for masonry beam instability.

[0096] The working resistance of the 101 working face support is determined by the following formula:

[0097] ;

[0098] In the formula, For the 101 working face at the final fill rate Predicted working resistance of the support under the given conditions; This is the initial support force for the support frame; For the support—direct top coupling elastic static load; For local static load on the fractured rock block; The dynamic load generated by the failure of the control layer; The dynamic load generated by the instability of the masonry beam.

[0099] Among them, elastic static load The stress was obtained by integrating the piecewise stiffness function of the front and rear top beams of the support with the direct top deflection curve; local static load of the fractured rock block. Summing the self-weight of the fractured rock strata participating in load transmission within the effective support area of ​​the support; dynamic load of fracture. Dynamic loads on masonry beam instability The values ​​are determined based on the equivalent static load and the corresponding dynamic load increment coefficient within the corresponding influence range.

[0100] Based on the inversion results of the critical fullness ratio of the main control layers L1, L2, and L3 of the 101 working face, the support load calculation can be divided into the working conditions shown in Table 3:

[0101] Table 3 Calculation conditions for support load under different fill rates at working face 101

[0102]

[0103] The results above show that the load on the support at working face 101 increases in a stepwise manner as the filling rate decreases. When the filling rate is higher than the critical value of the lower-level main control layer, the support mainly bears the initial support force and the elastic static load formed by the continuous bending and settlement of the direct roof. When the filling rate is lower than the corresponding critical value, the corresponding main control layer breaks, and the local static load and dynamic load of the broken rock block are included in the working resistance of the support. When multiple main control layers break continuously and form a masonry beam structure, the dynamic load of masonry beam instability is further superimposed. As the filling rate decreases, the overburden fracture layer gradually develops to a higher level, the periodic compressive dynamic load increases significantly, and the working resistance of the support shows an increasing trend.

[0104] Example 2: In a mine in Shandong, the 304 working face was mined using non-dense backfilling, mining the third coal seam at a height of 3.4m, a length of 260m, and a depth of approximately 931m. The columnar structure of the overlying strata of the working face is as follows... Figure 3 As shown, the physical and mechanical parameters of each rock stratum are listed in Table 4:

[0105] Table 4 Physical and mechanical parameters of rock strata in working face 304

[0106]

[0107] Step 1: Division of Overburden Bearing Groups and Identification of Main Controlling Layers:

[0108] Based on the parameters of the overburden strata at the working face, the overburden was divided into bearing groups according to the method of this invention. The results show that the overburden at the working face can be divided into two bearing groups:

[0109] The main controlling layer of bearing group 1 is L1 fine-grained sandstone;

[0110] The main controlling layer of bearing group 2 is L4 medium-grained sandstone;

[0111] Step 2: Master Layer Failure Detection and Critical Filling Rate Inversion:

[0112] A failure criterion is established by using the maximum allowable bending subsidence of the main control layer and the equivalent subsidence space of the goaf, and then... Inversion yields the critical fullness rate of the master control layer;

[0113] The calculation results show that:

[0114] The critical fullness rate of the master control layer L1 is 100.0%;

[0115] The critical fullness rate of the master control layer L4 is 61.2%.

[0116] The corresponding results are shown in Table 5:

[0117] Table 5 Critical filling rate and initial filling volume of the main control layer of the bearing group in the 304 working face

[0118]

[0119] Based on the above calculation results, the fault positions and extent of the overburden under different filling rates can be obtained. The fault positions of the overburden not only reflect the stability state of the overburden structure, but also determine the static load source, dynamic load source, and range of action of the support.

[0120] Step 3: Stent Load Prediction:

[0121] In this embodiment, the critical filling rate inversion and support load prediction process is the same as in Embodiment 1. The difference is that the coal seam thickness, mining height, roof structure parameters, backfill compaction parameters, and working face geological parameters corresponding to Embodiment 2 are substituted into the above model for calculation to obtain the critical filling rate and support load prediction results under the conditions of this embodiment.

[0122] The results show that as the filling rate decreases, the overburden fracture strata gradually develop to higher levels, the number of rock strata involved in bearing and fracture increases, and the periodic pressure dynamic load on the support continues to increase, leading to an increase in the support's working resistance. Therefore, this invention can not only predict the overburden fracture strata and fracture range, but also further predict the support's working resistance and periodic pressure characteristics, realizing a complete analysis from overburden structure evolution to support load prediction.

[0123] In summary, this invention establishes a quantitative relationship between filling rate, overburden fault position, and support working resistance under non-dense backfilling mining conditions through master layer identification, critical filling rate inversion, and superposition calculation of static and dynamic loads on the support. This method is applicable to support load prediction in high-extraction non-dense backfilling working faces and can also provide technical basis for filling rate design, support selection, and mine pressure disaster prevention under different backfilling purposes.

Claims

1. A method for predicting the load of a filling support based on the inversion of the critical filling rate of the master control layer, characterized in that, Includes the following steps: S1. Obtain the thickness, elastic modulus, tensile strength, unit weight, mining height, final filling rate, residual fragmentation coefficient of the underlying fractured rock layer and support stiffness parameters of each overburden layer. Based on the principle of equivalent deformation coordination of composite beam, the overburden is divided into multiple bearing groups, and the lowest unfractured rock layer in each bearing group that plays a controlling role in the overall stability is determined as the main control layer. S2. Based on the mining height, final filling rate, and the compensation space of residual fragmentation in the underlying fractured strata, determine the equivalent sinkable space of the goaf that is not compensated by the filling body and residual fragmentation. Based on the relationship between the final allowable sinking amount and the equivalent sinkable space obtained by the joint constraint of the maximum allowable bending sinking amount of the main control layer and the allowable sinking amount of surface protection, determine the fracture state of the main control layer for each bearing group, and obtain the fracture strata and fracture range of the overburden under different filling rates. S3. Calculate the dynamic load of the main control layer based on the local static load of the fractured rock blocks within the influence range of the main control layer fracture and the dynamic load increment coefficient of the main control layer fracture. Calculate the dynamic load of the masonry beam instability based on the equivalent static load of the fractured rock blocks within the influence range of the masonry beam instability and the dynamic load increment coefficient of the masonry beam instability. Superimpose the initial support force of the support, the elastic static load of the support-direct top coupling, the local static load of the fractured rock blocks, and the dynamic load to obtain the predicted result of the support working resistance.

2. The method for predicting the load of a filling support based on the inversion of the critical filling rate of the master control layer according to claim 1, characterized in that, The bearing groups in S1 are divided based on the bending deformation coordination and mechanical response consistency of the overburden composite beam, and continuous rock strata with coordinated deformation characteristics are grouped into the same bearing group; the main control layer is the lowest unbroken rock stratum in each bearing group that is closest to the goaf and first reaches the structural control conditions, and its fracture state determines the overall stability of the corresponding bearing group.

3. The method for predicting the load of a filling support based on the inversion of the critical filling rate of the master control layer according to claim 1, characterized in that, The equivalent sinkable space of the goaf in S2 Determined according to the following formula: ； Among them, H c To raise the level; V represents the final fullness rate. exp This refers to the residual compensatory space for the underlying fractured rock strata that remains in the final compaction state; The V exp Calculate according to the following formula: ； in, h is the residual fragmentation coefficient of the underlying fractured rock layer i after being subjected to pressure from the overlying rock layer; i The thickness of the underlying fractured rock layer is denoted as i; n is the target main control layer. The method for determining the failure state of the main control layer is as follows: when When this occurs, it is determined that the corresponding main control layer has been broken; when When this occurs, it is determined that the corresponding main control layer maintains a continuous and stable state; Among them, W a The final allowable settlement is constrained by the maximum allowable bending settlement of the main control layer and the allowable settlement of the surface protection layer. The process of obtaining the fullness rate is as follows: When the main control layer is in a critical state between failure and stability, the following conditions must be met: ； The critical fullness ratio is obtained through this inversion: ； When the calculation result is less than 0 or greater than 1, boundary convergence processing is performed within the range of 0 to 1.

4. The method for predicting the load of a filling support based on the inversion of the critical filling rate of the master control layer according to claim 1, characterized in that, The initial support force of the support, the elastic static load coupled between the support and the direct top, and the local static load of the fractured rock block in S3 together form the static load of the support. Among them, the elastic static load coupled between the support and the direct top is F a Obtained by integrating the piecewise stiffness function of the support with the direct top deflection curve: ； Where L2 and L3 are the effective working lengths of the front and rear support beam regions, respectively; g1(x) and g2(x) are the equivalent distributed stiffness functions of the front and rear support beams, respectively; and ω2(x) and ω3(x) are the deflection functions directly supporting the front and rear support beam regions, respectively. The equivalent distributed stiffness functions of the front and rear top beams are the equivalent distributed values ​​of the vertical support stiffness of the support top beam along the length of the top beam, and their expressions are as follows: g1(x)=Bk q (x),0≤x≤L2; g2(x)=Bk h (x),0≤x≤L3; Where B is the width of the support; k q (x) is the equivalent vertical foundation stiffness coefficient of the front top beam area; k h (x) is the equivalent vertical foundation stiffness coefficient of the rear top beam area; L2 is the effective working length of the front top beam of the support; L3 is the effective working length of the rear top beam of the support; The local static load F of the fractured rock block b Calculate using the following formula: ； Where B is the width of the bracket; L eff γ is the effective support length of the support frame; r is the number of fractured rock strata involved in local load transfer; i and h i χ represents the unit weight and thickness of the i-th fractured rock layer, respectively; i This is a characteristic function of the rock block state; The rock block state indicator function χ i The condition is determined jointly by the rock strata fracture state and the rock-coal load transfer state: when the i-th rock stratum has reached the fracture condition, and its maximum subsidence is sufficient to cross the equivalent free void and form effective contact with the underlying rock cushion or the support-direct roof system, χ i Set to 1; otherwise, set χ. i Set to 0; The specific determination is as follows: like ,and , then χ i =1; otherwise, χ i =0; in, The equivalent free void between the bottom interface of the i-th layer rock block and the underlying infill and residual breccia is determined by the following formula: ； in, The maximum tensile stress in the i-th rock layer; ω is the tensile strength of the i-th rock layer; i,max This represents the maximum subsidence of the i-th rock layer; For the final fullness rate; H c To raise the level; h is the residual fragmentation coefficient of the underlying fractured rock layer j under the final compaction state; j is the thickness of the underlying fractured rock layer j; j is the number of the underlying fractured rock layer. The predicted working resistance of the support is obtained by superimposing the initial support force, the elastic static load of the support-direct top coupling, the local static load of the broken rock block, the dynamic load generated by the failure of the main control layer, and the dynamic load generated by the instability of the masonry beam. Its expression is as follows: F=F0+F a +F b +F d1 +F d2 ; Where F is the predicted working resistance of the support; F0 is the initial support force of the support; F a For the support-direct top coupling elastic static load; F b For local static load on fractured rock blocks; F d1 Dynamic load generated by the failure of the master control layer; F d2 For dynamic loads generated by the instability of masonry beams; The dynamic load F generated by the failure of the main control layer d1 It is determined by the dynamic load increment coefficient of the main control layer failure and the local static load of the rock block after failure, and its expression is: ； Among them, K d1 The dynamic load increment coefficient for the failure of the main control layer; The dynamic load F generated by the instability of the masonry beam d2 The equivalent static load of the broken rock blocks within the influence range of the masonry beam instability and the dynamic load increment coefficient of the masonry beam instability are determined, and its expression is as follows: ； Among them, K d2 F is the dynamic load increment coefficient for masonry beam instability; mb The equivalent static load transferred from the broken rock blocks within the range of masonry beam instability to the support; The F mb The calculation is as follows: ； Where, r m The number of fractured rock layers involved in the instability load transfer of the masonry beam; ψ i The function is γ, which represents the instability characteristic function of the masonry beam. It is set to 1 when the fractured rock block of the i-th layer participates in the instability of the masonry beam and transmits the load to the support; otherwise, it is set to 0. i h is the unit weight of the i-th rock layer; i Let be the thickness of the i-th rock layer.

5. The method for predicting the load of a filling support based on the inversion of the critical filling rate of the master control layer according to claim 3, characterized in that, The main control layer allows a maximum bending subsidence W. a Based on the deflection model of the elastic foundation beam with two fixed ends, the following is determined: the nth main control layer and its overlying rock layer undergoing coordinated deformation are equivalent to the elastic foundation beam with two fixed ends, and the underlying infill, fractured rock cushion layer and support system are equivalent to the elastic foundation. The deflection control equation of the main control layer is established: ； Its boundary conditions are: ； The above boundary conditions indicate that both ends of the calculation section of the equivalent beam of the nth controlling layer are fixedly constrained. At x = -l / 2 and x = l / 2, the deflection and the first derivative of the deflection function of the equivalent beam of the controlling layer are both zero; where ω n (-l / 2)=0 and ω n (l / 2)=0 indicates that the vertical displacement at both ends of the equivalent beam is zero, ω n′ (-l / 2)=0 and ω n′ (l / 2)=0 indicates that the rotation angle of the equivalent beam's two ends is zero; Among them, D n ω is the bending stiffness of the nth master control layer; n (x) is the deflection function of the nth main control layer; x is the coordinate set along the equivalent beam span direction of the main control layer, with the origin located at the midpoint of the equivalent calculation section; k b (x) represents the combined foundation stiffness formed by the underlying infill, fractured rock strata cushion, and support system; q n (x) represents the overlying equivalent load acting on the nth main control layer; l represents the equivalent calculation span of the main control layer; x=-l / 2 and x=l / 2 correspond to the left and right boundaries of the equivalent calculation segment, respectively; After obtaining the deflection function of the nth main control layer from the deflection control equation of the main control layer, the maximum tensile stress σ of the nth main control layer is calculated based on the beam moment-curvature relationship and the bending normal stress relationship of the rectangular section. n,max When the maximum tensile stress reaches the tensile strength σ of the nth main control layer t,n When the main control layer reaches a critical fracture state, the corresponding maximum deflection is the critical deflection ω of the main control layer. n , crit That is, satisfying: s n,max =s t,n ; oh n,crit =max|ω n (x)|; If the allowable subsidence W for surface protection is also considered s Then the final allowable subsidence amount W a Determine using the following formula: IN a =min(ω n , crit ,IN s )。

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