A multi-factor coupling prediction method for void ratio of caved and broken coal rock mass in goaf

Abstract

The application discloses a kind of goaf caving broken coal rock mass porosity multi-factor coupling prediction method, belong to goaf caving broken coal rock mass porosity prediction technical field;Including determining the main control factor of initial in-situ stress of protolith, roof lithology and mining height for influencing goaf broken coal rock mass porosity;Establish the mining height effect model of the geometric form of goaf compaction zone, obtain the evolution law of compaction zone width, compaction zone height and caving angle with working face advancing distance;Establish broken coal rock mass physical mechanics compaction equation, determine the evolution law of transient broken expansion coefficient of different lithology broken rock mass with axial compressive stress;Determine the internal transient compaction stress distribution of goaf, introduce stress recovery coefficient to depict the stress recovery process of goaf from edge to core;Establish the porosity prediction model controlled by initial in-situ stress of protolith, roof lithology, mining height.The application realizes the fine distribution prediction of porosity in the width direction, height direction and advancing direction of goaf three-dimensional space.

Description

Technical Field

[0001] This invention belongs to the technical field of porosity testing of collapsed and fractured coal and rock mass in goaf areas. Specifically, it relates to a multi-factor coupled prediction method for porosity of collapsed and fractured coal and rock mass in goaf areas, which is applicable to the evaluation of overburden stability in coal mine goaf areas, analysis of gas migration channels, assessment of underground reservoir capacity, and prediction of surface subsidence. Background Technology

[0002] After coal seam mining, the overlying strata migrate, fracture, and collapse under mining-induced stress, forming a caving zone dominated by caved and fractured rock masses within the goaf. Under the gradual subsidence of the overlying strata and stress recovery, the fractured coal and rock mass in the caving zone undergoes continuous compressive deformation and recompaction. Porosity, as the core physical parameter for the compaction degree of the fractured coal and rock mass in the caving zone, is directly related to the overlying strata subsidence rate, surface subsidence amplitude, and the residual bearing capacity of the goaf, and is a key basis for goaf stability assessment and disaster prevention.

[0003] Currently, several patent documents have disclosed technical solutions for predicting or testing the porosity of fractured coal and rock masses in goaf areas. Specifically, for example, Chinese patent application CN120763429A discloses a method for predicting the porosity of goaf areas in underground coal mining faces. It divides the goaf area into natural accumulation zones and stress-affected zones based on its stress state, and establishes empirical formulas for porosity prediction in each zone. Chinese patent application CN119757162A discloses a method and apparatus for simulating the porosity of fractured rock masses in goaf areas. It simulates the porosity test of collapsed fractured rock masses in a laboratory setting and introduces a fractal dimension method to ensure test accuracy. Chinese patent application CN120014161A discloses a method and apparatus for refined three-dimensional characterization of goaf porosity. It establishes a coal seam mining model based on the physical and mechanical parameters of the coal and rock mass and the geological map of the working face strata, achieving refined three-dimensional characterization of goaf porosity. Chinese patent application CN120139944A discloses a method for determining the porosity of goaf areas. It utilizes multiple detection methods to obtain the porosity of the goaf, removes outliers through deviation analysis, and then takes the average value to obtain the average porosity. Chinese patent application CN118243498A proposes a simulation method for compacting fractured coal and rock mass in the goaf caving zone, considering particle breakage. It studies the variation law of porosity and breakage during the compaction process using discrete element numerical simulation.

[0004] However, the existing technologies still have the following shortcomings: First, most methods simplify the porosity of the goaf to a one-dimensional distribution prediction along the working face advance direction, or conduct simulation tests at the laboratory scale, lacking a quantitative description of the three-dimensional geometric morphology of the compacted zone in the width and height directions, making it difficult to characterize the fine distribution of porosity in the three-dimensional space of the goaf; Second, existing empirical formulas mostly use the fragmentation coefficient Kp as a single lithological characterization parameter (with a value of 1.3~1.8), without establishing a quantitative correlation between lithological parameters (elastic modulus, compressive strength) and the fragmentation coefficient, nor considering the driving effect of the magnitude of ground stress on the compaction process; Third, existing patented technologies mostly focus on laboratory testing methods or single-factor analysis, failing to comprehensively consider the coupling effect of multiple macroscopic main control factors such as the initial ground stress of the original rock, roof lithology, and mining height (referring to the thickness of the coal seam being mined, i.e., mining thickness) on porosity, and lack a predictive model that effectively couples the geometric characteristics of the elliptical zone of the compaction area with the physical and mechanical compaction equation of the fractured coal and rock mass.

[0005] Therefore, there is an urgent need for a multi-factor coupled prediction method for the porosity of collapsed and fractured coal and rock masses in goaf areas that can comprehensively consider the coupling effects of multiple factors such as the initial ground stress of the original rock, roof lithology, and mining height, and can achieve refined three-dimensional spatial prediction of the porosity of the goaf. Summary of the Invention

[0006] This invention addresses the aforementioned problems and overcomes the shortcomings of existing technologies by providing a multi-factor coupled prediction method for the porosity of collapsed and fractured coal and rock masses in goaf areas.

[0007] To achieve the above objectives, the present invention adopts the following technical solution.

[0008] This invention provides a multi-factor coupled prediction method for the porosity of collapsed and fractured coal and rock mass in goaf areas, comprising the following steps: S1. Based on the strain energy density function during the compaction process of fractured coal and rock mass, the dimensionless energy sensitivity coefficients of the initial ground stress of the original rock and the tangential modulus at the initial stage of compaction to the total strain energy are calculated respectively. The primary and secondary factors are determined by combining the spatial scale characteristic numbers of each factor, and the initial ground stress of the original rock, roof lithology and mining height are determined as the main controlling factors affecting the porosity of fractured coal and rock mass in the goaf. S2. Establish a mining height effect model of the geometric morphology of the compacted zone in the goaf, and obtain the evolution law of the compacted zone width, compacted zone height and caving angle as the working face advances. S3. Establish the physical and mechanical compaction equation for fractured coal and rock mass, and determine the evolution law of transient fragmentation coefficient of fractured rock mass with axial compressive stress for different lithologies; S4. Determine the transient compaction stress distribution inside the goaf and introduce a stress recovery coefficient to characterize the stress recovery process from the edge to the core of the goaf. S5. Couple the mining height effect model of the compaction zone geometry with the physical and mechanical compaction equation and the stress distribution to establish an elliptical zone porosity prediction model controlled by multiple factors such as the initial ground stress of the original rock, roof lithology, and mining height. The elliptical zone porosity prediction model simultaneously includes the three-dimensional geometric boundary conditions of the compaction zone and the physical and mechanical compaction equation of the broken coal and rock mass, and outputs the porosity of spatial points inside the goaf.

[0009] In a preferred embodiment of the present invention, in step S1, the expression for the strain energy density function is: ; in, U c This refers to the elastic strain energy density during the compaction process of fractured coal and rock mass. E 0 represents the tangential modulus at the initial stage of compaction (as a characterization of lithological stiffness). e m For compressive strain, e max The ultimate maximum compressive strain controlled by the initial porosity; the initial in-situ stress of the original rock. s 0 Dimensionless energy sensitivity coefficient to total strain energy S σ and the initial tangential modulus of compaction E 0 Dimensionless energy sensitivity coefficient to total strain energy S E They respectively satisfy: ; Among them, Λ σ and Λ E These are the spatial scale characteristic numbers of the initial geostress of the original rock and the initial tangential modulus of compaction, respectively.

[0010] As another preferred embodiment of the present invention, in step S2, the fitting relationship between the width of the compaction zone and the working face advancement distance and mining height is as follows: L = a 1· L 1+ b 1· M + c 1; among which, L The width of the compaction zone, L 1 represents the working face advance distance. M To extract high, a 1. b 1. c 1 represents the regression coefficient; the goodness of fit of this relationship. R 2 It can reach 0.9830; The fitting relationship between the height of the compaction zone and the working face advance distance and mining height is as follows: H =a 2·l ( L 1)+ b 2. M + c 2; among which, H The height of the compaction zone, L 1 represents the working face advance distance. M To extract high, a 2. b 2. c 2 represents the regression coefficient; the goodness of fit of this relationship. R 2 It can reach 0.91382; The fitting relationship between the collapse angle and the working face advance distance and mining height is as follows: i = a 3·l ( L 1)+ b 3· M + c 3; among which, i For the collapse angle, L 1 represents the working face advance distance. M To extract high, a 3. b 3. c 3 is the regression coefficient.

[0011] In another preferred embodiment of the present invention, in step S2, there is a proportional relationship between the single expansion distance of the compaction zone along the working surface direction and the corresponding periodic compaction step distance of the working surface: b i = c · L i ;in, b i This refers to the distance the compacted zone expands along the working face direction each time. L i For each press step distance, c It is a constant, and its range coefficient is 0.6~0.8. The higher the value, the smaller its value.

[0012] In another preferred embodiment of the present invention, in step S2, the geometry of the compaction zone is simplified to an axisymmetric elliptic parabolic model, and the geometric relationship between the boundary of the compaction zone and the working face advancement direction satisfies: ; in, A 1. A 2 represents the distance from the bottom boundary of the compaction zone to the cut-out and the intake and return airways, respectively. H This refers to the height of the compacted zone.

[0013] In another preferred embodiment of the present invention, in step S3, the evolution law of the transient fragmentation coefficient of the fractured rock mass with axial compressive stress is as follows: ; in, F ( s () is the transient fragmentation coefficient. F 0 is the initial coefficient of fragmentation. F r The residual fragmentation coefficient, s It is axial compressive stress. s c This is the characteristic stress of fragmentation and attenuation.

[0014] As another preferred embodiment of the present invention, the residual fragmentation coefficient F r With rock elastic modulus E and uniaxial compressive strength of rock UCS The quantitative relationship is as follows: ; in, k 1 represents the contact cementation and mechanical attenuation constant between rock blocks. F r，min It is the minimum residual fragmentation coefficient; The characteristic stress of fragmentation attenuation s c Uniaxial compressive strength of rock UCS and fractal dimension after fragmentation D The quantitative relationship is as follows: ; in, k 2 is the characteristic constant of compaction rate.

[0015] As another preferred embodiment of the present invention, in step S4, the transient compaction stress inside the goaf is: s ( x , y )= or ( x , y )· s 0; where, s 0 represents the initial geostress of the original rock. or ( x , y ) is the stress recovery coefficient of the goaf, which is 0.15 at the edge of the goaf and 1.0 in the core compacted area of ​​the goaf.

[0016] As another preferred embodiment of the present invention, in step S5, the elliptic zone porosity prediction model is: ; in, n ( x , y , z ) represents the coordinates of a spatial point within the goaf ( x , y , z The porosity at ( ) is considered in this model, which also takes into account the initial geostress of the original rock. s 0. Size, top lithology (through...) E and UCS Characterization), mining height M and working face advance distance L The coupling effect of 1; By combining the mining height effect model of the compaction zone geometry with the porosity prediction model of the elliptical compaction zone, the porosity within the elliptical compaction zone is determined. n The changes satisfy: ; in,( x , y , z） The coordinates of points within the goaf. A 1. A 2 represents the distance from the bottom boundary of the compaction zone to the cut-out and the intake and return airways, respectively. H This refers to the height of the compacted zone.

[0017] As another preferred embodiment of the present invention, the method further includes a model verification step: verifying the porosity prediction model of the elliptical fracture zone using numerical simulation data or laboratory test data, and determining the reasonable range of values ​​for the model parameters; the verification content includes verification of the influence of mining height on porosity, verification of the influence of roof lithology on porosity, verification of the influence of the initial geostress level of the original rock on porosity, and verification of the spatial distribution characteristics of the mining-induced fracture elliptical fracture zone.

[0018] Compared with the prior art, the present invention has the following beneficial effects: 1. This invention establishes a mining height effect model for the geometric morphology of the compacted zone in the goaf. This model quantitatively describes the evolution of the width, height, and caving angle of the compacted zone with mining height and advance distance using an elliptical parabolic surface. It effectively couples the geometric characteristics of the elliptical parabolic surface of the compacted zone with the physical and mechanical compaction equation of the fractured coal and rock mass, and realizes the three-dimensional spatial refined distribution prediction of porosity in the width, height, and advance directions of the goaf, overcoming the limitations of one-dimensional simplification or laboratory-scale simulation in the prior art.

[0019] 2. This invention establishes a quantitative relationship between the residual swelling coefficient and the ratio of elastic modulus and compressive strength, as well as a quantitative relationship between the swelling attenuation characteristic stress and the ratio of compressive strength and fractal dimension, by introducing the rock elastic modulus and uniaxial compressive strength. This achieves accurate quantitative characterization of roof lithology and overcomes the limitation of existing technologies that only use the swelling coefficient as a single empirical parameter to characterize lithology. At the same time, it introduces the original rock initial geostress and stress recovery coefficient to quantitatively characterize the driving effect of geostress on the compaction process and its gradient distribution characteristics within the goaf.

[0020] 3. This invention quantitatively determines the initial in-situ stress, roof lithology, and mining height as the main controlling factors affecting the porosity of broken coal and rock masses in goaf areas through energy sensitivity analysis. It also couples the mining height effect model of the compaction zone geometry with the physical and mechanical compaction equation and stress distribution to establish an elliptical zone porosity prediction model that comprehensively considers the control of multiple factors such as the initial in-situ stress, roof lithology, and mining height. This provides a scientific basis for the analysis of gas migration channels in goaf areas, the assessment of underground reservoir capacity, and the prediction of surface subsidence. Attached Figure Description

[0021] Figure 1 This is a flowchart illustrating the multi-factor coupled prediction method for porosity of collapsed and fractured coal and rock mass in the goaf area according to the present invention.

[0022] Figure 2 This is a three-dimensional spatial structure diagram of the mining height effect model of the compaction zone geometry of the present invention. Detailed Implementation

[0023] To make the technical problems solved, the technical solutions, and the beneficial effects of this invention clearer, the invention will be further described in detail below with reference to the accompanying drawings and specific embodiments. It should be understood that the specific embodiments described herein are merely illustrative of the invention and are not intended to limit the invention.

[0024] This embodiment takes a coal mine working face as the implementation object and provides a detailed description of the multi-factor coupled prediction method for porosity of collapsed and fractured coal and rock mass in the goaf provided by the present invention.

[0025] Combination Figure 1 As shown, the present invention mainly includes the following steps: Step S1: Determine the main controlling factors; Step S2: Establish a mining height effect model of the geometric shape of the compaction zone in the goaf; Step S3: Establish the physical and mechanical compaction equation of the broken coal and rock mass; Step S4: Determine the transient compaction stress distribution inside the goaf; Step S5: Construct a multi-factor coupled prediction model of porosity and verify it.

[0026] Specifically, the determination of the main controlling factors in step S1 includes: Based on borehole data from the working face and laboratory tests of roof and floor rock samples, three basic parameters were obtained: initial in-situ stress, roof lithology, and mining height. The mining height refers to the thickness of the coal seam being mined, i.e., the mining thickness. In this embodiment, the initial in-situ stress... s 0 takes 15MPa; mining height M Three working conditions were set: 2m (thin coal seam), 4m (medium-thick coal seam), and 6m (thick coal seam); the roof lithology was selected as weak roof (mudstone, elastic modulus). E =1.9GPa, uniaxial compressive strength UCS =15MPa), medium-hard roof (siltstone, elastic modulus = ... E =2.5GPa, uniaxial compressive strength UCS =30MPa) and a hard top plate (fine sandstone, elastic modulus = ... E =3.5GPa, uniaxial compressive strength UCS =60MPa).

[0027] Based on the strain energy density function during the compaction process of fractured coal and rock mass: ; Calculate the initial geostress of the original rock separately s 0 Dimensionless energy sensitivity coefficient to total strain energy S σ and the initial tangential modulus of compaction E 0 Dimensionless energy sensitivity coefficient to total strain energy S E : ; By comprehensively analyzing the spatial scale characteristic numbers and energy sensitivity coefficients of various factors, it was determined that the initial in-situ stress of the original rock, the lithology of the roof, and the mining height are the main controlling factors affecting the porosity of the fractured coal and rock mass in the goaf. In the in-situ environment of a large-scale goaf, the influence range of the initial in-situ stress of the original rock and the rock skeleton covers the entire caving zone, and its spatial scale characteristic number Λ σ and Λ E All are close to 1. (Mining height) M The spatial scale characteristic number Λ directly controls the free space of the initial collapse of the overburden and the upper limit of the integral of the total compaction displacement. M This can be expressed as the ratio of the caving zone's maximum development height to the mining height, typically between 2 and 7. Other factors include fragment size. d In large-scale in-situ working face models, the influence weight of large-scale working face models is significantly reduced due to spatial scale effects.

[0028] Specifically, step S2: establishing a mining height effect model of the geometric morphology of the compacted zone in the goaf, including: Based on field geological exploration data, a mining model of the working face was established using UDEC numerical simulation software. The model boundary conditions were set as follows: horizontal displacement was constrained on both sides, a fixed boundary with full displacement was used at the bottom, and an equivalent uniformly distributed load was applied to the top to simulate the self-weight of the unmodeled overburden. Simulations were conducted for three working conditions with mining heights of 2m, 4m, and 6m. The excavation starting position was set 50m to the left of the model, and the mining response was simulated sequentially when the working face advanced by 10m, 40m, and 150m. The width, height, and caving angle of the compacted zone were obtained through numerical simulation at different advancement distances.

[0029] Among them, the analysis of the mining height effect on the width of the compacted zone shows that the evolution law of the width of the compacted zone with the advancing distance of the working face is as follows: when the working face advances to the same distance, the greater the mining height, the smaller the width of the compacted zone. Under the three mining height conditions, the width of the compacted zone shows a stable linear positive correlation with the advancing distance of the working face.

[0030] The width of the compaction zone L Distance from working face L 1 and mining height M The fitting relationship is as follows: L = a 1· L 1+ b 1· M + c 1; Taking the data in this embodiment as an example, when the sampling height is... M When =2m, the fitting relationship is: y =0.79428 x -2.19776, goodness of fit R 2 =0.99407; when mining height M When m = 4m, the fitting relationship is: y =0.7 x -0.3, goodness of fit R 2 =0.99092; when mining height M When m = 6m, the fitting relationship is: y =0.63388 x +0.35277, goodness of fit R 2 =0.99757. The goodness of fit was obtained by performing a multiple linear fit on the compaction zone width. R 2 It can reach 0.9830.

[0031] There is a clear proportional relationship between the single expansion distance of the compaction zone along the direction of the working face and the corresponding periodic compaction step distance of the working face: b i = c ·L i ;in, b i This refers to the distance the compacted zone expands along the working face direction each time. L i For each press step distance, c It is a constant, and its range coefficient is 0.6~0.8. The higher the value of the compaction zone, the smaller its value is, and the smaller the expansion of the compaction zone width is.

[0032] The analysis of the mining height effect on the compaction zone height reveals the following evolution pattern: As the working face advances, the compaction zone height increases, but this upward trend gradually slows down. With the same advancement distance, a higher mining height corresponds to a greater compaction zone height.

[0033] The height of the compaction zone H Distance from working face L 1 and mining height M The fitting relationship is as follows: H = a 2·l ( L 1)+ b 2. M + c 2; Taking the data in this embodiment as an example, when the sampling height is... M When =2m, the fitting relationship is: y =﹣31.29+24.68l( x -32.66), goodness of fit R 2 =0.99938; when mining height M When m = 4m, the fitting relationship is: y =﹣13.14+13.66l( x -30.67), goodness of fit R 2 =0.99844; when mining height M When m = 6m, the fitting relationship is: y =﹣12.74+11.61log ( x -29.05), goodness of fit R 2 =0.99833. The goodness of fit was obtained by performing a multiple linear fit on the compaction zone height. R 2 It can reach 0.91382.

[0034] Among them, the analysis of the mining height effect of the caving angle: During the formation of the compaction zone, its lateral boundary and the bottom plate of the coal seam will form a characteristic angle, which is called the caving angle in engineering.

[0035] Under different mining heights, the variation of the caving angle with the advancing distance of the working face follows this pattern: the development characteristics of the caving angle are significantly controlled by the mining height. Overall, the lower the mining height, the smaller the corresponding caving angle value, but the greater the variation range with the advancing working face. After each periodic mining pressure manifestation, the caving angle corresponding to the boundary of the newly expanded compacted zone will be smaller than the angle formed in the previous cycle.

[0036] The collapse angle i Distance from working face L 1 and mining height M The fitting relationship is as follows: i = a 3·l ( L 1)+ b 3· M + c 3; Taking the data in this embodiment as an example, when the sampling height is... M When =2m, the fitting relationship is: y =118.93-22.19log ( x -24.64), goodness of fit R 2 =0.99612; when mining height M When m = 4m, the fitting relationship is: y =174.49-27.79log ( x +5.73), goodness of fit R 2 =0.97223; when mining height M When m = 6m, the fitting relationship is: y =92.30-8.60 cc ( x -34.40), goodness of fit R 2 =0.99877.

[0037] Because the collapse angle of the compacted zone boundary decreases layer by layer with the development of the overburden, the lateral boundary of the compacted zone exhibits a natural arc-shaped transition, and its overall shape approximates an elliptical paraboloid. Based on the law that the collapse angle of the compacted zone boundary decreases layer by layer with the development of the overburden, the geometry of the compacted zone is simplified to an axisymmetric elliptical paraboloid model. The geometric relationship between the compacted zone boundary and the working face advancement direction satisfies: ; in, A 1. A 2 represents the distance from the bottom boundary of the compaction zone to the cut-out and the intake and return airways, respectively. H This refers to the height of the compacted zone.

[0038] Since the central compaction zone is generally elliptical, the model can be approximated as axisymmetric. The collapse angle formed by each expansion of the compaction zone satisfies a geometric relationship with the increments in width and height. Once the compaction zone is formed, its subsequent expansion process has obvious inheritance. The expansion of the compaction zone triggered by each cycle of compaction is carried out on the basis of the compaction core formed in the previous cycle.

[0039] Specifically, step S3: establishing the physical and mechanical compaction equation of fractured coal and rock mass includes: obtaining compaction curves of fractured rock masses with different lithologies through indoor lateral compression tests; the test adopts a graded loading method, records strain data under each stress level, and plots stress-strain relationship curves.

[0040] Transient fragmentation coefficient of fractured rock mass in goaf F ( s With axial compressive stress s The increase of exhibits a nonlinear dynamic decay characteristic, and its evolution law is as follows: ; in, F ( s () is the transient fragmentation coefficient. F 0 is the initial coefficient of fragmentation. F r The residual fragmentation coefficient, s It is axial compressive stress. s c This is the characteristic stress of fragmentation and attenuation.

[0041] Residual fragmentation coefficient F r The value of is influenced by the lithology of the rock itself. Hard rocks such as sandstone have high strength and modulus, and easily form a skeleton structure that is extremely difficult to break apart between rock blocks, resulting in large macroscopic residual voids. Soft rocks such as sandy mudstone are prone to secondary fracturing during compaction, and the resulting fine particles fill large pores, leading to a small final fracturing coefficient. Residual fracturing coefficient F r With rock elastic modulus E and uniaxial compressive strength of rock UCS The quantitative relationship is as follows: ;in, k 1 represents the contact cementation and mechanical attenuation constant between rock blocks. F r，min It is the minimum residual fragmentation coefficient.

[0042] Characteristic stress of fragmentation attenuation s cRelated to the rock's inherent strength and the fractal dimension after fragmentation, the lower the rock's inherent strength or the higher the fractal dimension after fragmentation, the more fine particles are produced, promoting rock slippage and reorganization, and resulting in a faster rate of pore volume dissipation during the initial compaction phase. (Characteristic stress attenuation due to fragmentation) s c Uniaxial compressive strength of rock UCS and fractal dimension after fragmentation D The quantitative relationship is as follows: ;in, k 2 is the characteristic constant of compaction rate.

[0043] In this embodiment, for mudstone (weak roof), the initial breccia coefficient is... F 0 = 1.80, residual fragmentation coefficient F r =1.67, characteristic stress of fragmentation attenuation s c =0.265; for siltstone (medium-hard cap), the initial breccia coefficient is... F 0=1.85, residual fragmentation coefficient F r =1.75, characteristic stress of fragmentation attenuation s =0.167; for fine sandstone (hard cap), the initial breccia coefficient is... F 0 = 1.92, residual fragmentation coefficient F r =1.85, characteristic stress of fragmentation attenuation s c =0.125, Inter-block contact cementation and mechanical attenuation constant k 1 = 0.15, minimum residual fragmentation coefficient F r，min =1.60, characteristic constant of compaction rate k 2 = 0.02.

[0044] Specifically, step S4: determining the transient compaction stress distribution inside the goaf, including: During the movement and evolution of the overlying strata in the goaf, the axial compaction stress borne by the fractured coal and rock mass is the main influencing factor driving the nonlinear compressive deformation of the gangue in the caving zone. The local compaction stress within the goaf is related to the initial in-situ stress of the original rock at the depth of the working face. As the working face continues to advance, the fractured rock strata above the goaf undergo nonlinear bending settlement, gradually reapplying the overlying strata load to the lower caving gangue deposit, causing its stress to gradually recover.

[0045] Based on the stress recovery coefficient of the goaf or ( x , y ), determine the coordinates of any spatial plane within the goaf ( x, y Transient compaction stress at point ) s ( x , y )= or ( x , y )· s 0; where, s 0 represents the initial geostress of the original rock. or ( x , y The stress recovery coefficient of the goaf is denoted as . In this embodiment, the stress recovery coefficient at the edge of the goaf is denoted as . or Take 0.15 as the stress recovery coefficient of the fully compacted core area of ​​the goaf. or The value is 1.0. From the edge of the goaf to the core area, the stress recovery coefficient shows a gradient increasing distribution, which represents the stress recovery process inside the goaf from the insufficiently compacted edge area to the fully compacted core area.

[0046] The stress concentration around the stope varies significantly under different initial in-situ stress conditions. Under low in-situ stress conditions, the vertical load on the overlying rock is relatively small, the peak value of the advance support pressure of the working face is low, the compaction driving force of the collapsed rock mass in the goaf is insufficient, and stress recovery is relatively slow. Under high in-situ stress conditions, the peak value of the support pressure in front of the coal face increases significantly, the overlying load in the goaf increases significantly, and the collapsed gangue is subjected to strong compression and compacted rapidly. The increase in initial in-situ stress has a significant promoting effect on the development of the plastic zone of the overlying rock; the greater the in-situ stress, the stronger the compaction driving force of the collapsed rock mass.

[0047] Specifically, step S5: constructing and validating a multi-factor coupled prediction model for porosity (i.e., the elliptic parabolic zone porosity prediction model), includes: The mining height effect model of the compaction zone geometry is coupled with the physical and mechanical compaction equation and stress distribution, combined with the porosity in porous media mechanics. n With the coefficient of fragmentation F Satisfaction Relationship n =1- F A prediction model for the porosity of the elliptical ejecta zone, controlled by multiple factors including the initial in-situ stress, roof lithology, and mining height, was established. ; This formula means: any spatial point within the goaf ( x , y , z porosity at ) n The transient fragmentation coefficient F ( s )Decide, F ( s ) is axial compressive stress s The function, whose value is determined by the transient compaction stress at that location within the goaf. or ( x , y )· s 0 driven, and subject to the rock elastic modulus E and uniaxial compressive strength of rock UCS The influence of lithological parameters, specifically the rock elastic modulus. E and uniaxial compressive strength of rock UCS The residual fragmentation coefficient is determined. F r Size; mining height M and working face advance distance L 1. By influencing the stress recovery coefficient or ( x , y Spatial distribution and initial fragmentation coefficient F 0 indirectly affects the calculation results of porosity.

[0048] The model also takes into account the initial geostress of the original rock. s 0. Size, top lithology (through...) E and UCS Characterization), mining height M and working face advance distance L The coupling effect of 1, and simultaneously includes the three-dimensional geometric boundary conditions of the compacted zone and the physical and mechanical compaction equations of the fractured coal and rock mass. The three-dimensional elliptical band structure of the mining height effect model of the compacted zone geometry in the goaf, such as... Figure 2 As shown; by Figure 2 It can be seen that the three-dimensional geometric boundary of the compacted zone is determined by the height of the compacted zone. H Distance from the bottom boundary to the incision eye A 1 and distance from the intake and return airway A 2. By common definition, the equation of the elliptic paraboloid is satisfied in the spatial coordinate system (x, y, z). Combining the mining height effect model of the compaction zone geometry with the porosity prediction model of the elliptic paraboloid zone, the porosity within the compaction zone of the elliptic paraboloid zone can be obtained. n Changes: ; in,( x , y , z () represents the coordinates of a point within the goaf. A 1. A 2 represents the distance from the bottom boundary of the compaction zone to the cut-out and the intake and return airways, respectively. H This refers to the height of the compacted zone.

[0049] Finally, the elliptic parabolic zone porosity prediction model was validated using numerical simulation data: Verification 1: The effect of mining height on porosity. The lithology was fixed as siltstone, with an initial in-situ stress of 15 MPa and a stress recovery coefficient of 1.0. At a mining height of 2 m, the initial calving coefficient of the caving zone was used in the formula to calculate the residual porosity in the center of the goaf to be approximately 0.45. At a mining height of 4 m, the initial compressible free space of the caving zone increased, and the calculated residual porosity in the center of the goaf was approximately 0.46. With increasing mining thickness, the initial compressible free space of the caving zone increases, the energy required for the overall compaction process increases, and the final residual pore volume is correspondingly larger.

[0050] Verification 2: The Influence of Roof Lithology on Porosity. With a fixed mining height of 4m, an initial in-situ stress of 15MPa, and a stress recovery coefficient of 1.0, the residual porosity of fine sandstone (hard roof) is approximately 0.47 due to its high compressive strength, achieved by selecting a higher residual fragmentation coefficient and a smaller equivalent attenuation coefficient. The residual porosity of siltstone (medium-hard roof) is approximately 0.43, and that of mudstone (weak roof) is approximately 0.39. As the rock strength decreases, the porosity generally shows a decreasing trend.

[0051] Verification 3: The Influence of Initial In-situ Stress Level on Porosity. A fixed mining height of 4m and lithology of siltstone were used, with a stress recovery coefficient of 1.0. Different in-situ stress levels lead to different compaction driving forces. When the initial in-situ stress was 10 MPa, the calculated porosity was approximately 0.45; when the initial in-situ stress was 25 MPa, the calculated porosity was approximately 0.38. The higher the initial in-situ stress, the stronger the driving force for rock compaction, and the lower the final porosity will be as the in-situ stress increases.

[0052] Verification 4: Spatial Distribution Characteristics of Mining-Induced Fracture Elliptical Zones. With a fixed mining height of 4m and lithology of siltstone, the porosity varies from the insufficiently compacted zone at the edge of the goaf (stress recovery coefficient 0.15) to the fully compacted zone at the core (stress recovery coefficient 1.0). The porosity at the edge is approximately 0.64, while the porosity in the fully compacted zone is approximately 0.44. During this transition from the insufficiently compacted zone to the fully compacted zone, the goaf coordinates shift from the periphery towards the center, resulting in a clear gradient distribution of the output porosity.

[0053] Based on the comprehensive verification results, under the existing parameters, when the mining height, roof lithology, and initial in-situ stress of the original rock are taken as physical limits, the porosity of the thin coal seam-weak roof-deep high stress-completely compacted core is 0.41, and the porosity of the thick coal seam-hard roof-shallow low stress-insufficiently compacted edge is 0.67. Based on this, it can be inferred that the porosity of the goaf in coal mines is generally in the range of 0.4 to 0.7.

[0054] The validated model is applied to predict the three-dimensional spatial distribution of porosity in the goaf of the target working face. By inputting the initial geostress of the original rock of the working face, the lithological parameters of the roof and the mining height parameters, the porosity value of any spatial point inside the goaf can be output, providing a basis for the analysis of gas migration channels in the goaf, the assessment of underground reservoir capacity or the prediction of surface subsidence.

[0055] It is understood that the above specific description of the present invention is only for illustrating the present invention and is not limited to the technical solutions described in the embodiments of the present invention. Those skilled in the art should understand that modifications or equivalent substitutions can still be made to the present invention to achieve the same technical effect; as long as the use needs are met, they are all within the protection scope of the present invention.

Claims

1. A multi-factor coupled prediction method for the porosity of collapsed and fractured coal and rock mass in a goaf, characterized in that: Includes the following steps: S1. Based on the strain energy density function during the compaction process of fractured coal and rock mass, the dimensionless energy sensitivity coefficients of the initial ground stress of the original rock and the tangential modulus at the initial stage of compaction to the total strain energy are calculated respectively. The primary and secondary factors are determined by combining the spatial scale characteristic numbers of each factor, and the initial ground stress of the original rock, roof lithology and mining height are determined as the main controlling factors affecting the porosity of fractured coal and rock mass in the goaf. S2. Establish a mining height effect model of the geometric morphology of the compacted zone in the goaf, and obtain the evolution law of the compacted zone width, compacted zone height and caving angle as the working face advances. S3. Establish the physical and mechanical compaction equation for fractured coal and rock mass, and determine the evolution law of transient fragmentation coefficient of fractured rock mass with axial compressive stress for different lithologies; S4. Determine the transient compaction stress distribution inside the goaf and introduce a stress recovery coefficient to characterize the stress recovery process from the edge to the core of the goaf. S5. Couple the mining height effect model of the compaction zone geometry with the physical and mechanical compaction equation and the stress distribution to establish an elliptical zone porosity prediction model controlled by multiple factors such as the initial ground stress of the original rock, roof lithology, and mining height. The elliptical zone porosity prediction model simultaneously includes the three-dimensional geometric boundary conditions of the compaction zone and the physical and mechanical compaction equation of the broken coal and rock mass, and outputs the porosity of spatial points inside the goaf.

2. The multi-factor coupled prediction method for porosity of collapsed and fractured coal and rock mass in a goaf area according to claim 1, characterized in that: In step S1, the expression for the strain energy density function is: ； in, U c This refers to the elastic strain energy density during the compaction process of fractured coal and rock mass. E 0 represents the tangential modulus at the initial stage of compaction. ε m For compressive strain, ε max The ultimate maximum compressive strain is controlled by the initial porosity; Initial geostress of original rock σ 0 Dimensionless energy sensitivity coefficient to total strain energy S σ and the initial tangential modulus of compaction E 0 Dimensionless energy sensitivity coefficient to total strain energy S E They respectively satisfy: ； Among them, Λ σ and Λ E These are the spatial scale characteristic numbers of the initial geostress of the original rock and the initial tangential modulus of compaction, respectively.

3. The multi-factor coupled prediction method for porosity of collapsed and fractured coal and rock mass in a goaf area according to claim 1, characterized in that: In step S2, the fitting relationship between the width of the compaction zone and the working face advance distance and mining height is as follows: L = a 1· L 1+ b 1· M + c 1; in, L The width of the compaction zone, L 1 represents the working face advance distance. M To extract high, a 1. b 1. c 1 represents the regression coefficient; The fitting relationship between the height of the compaction zone and the working face advance distance and mining height is as follows: H = a 2·l ( L 1)+ b 2· M + c 2; among which, H The height of the compaction zone, L 1 represents the working face advance distance. M To extract high, a 2. b 2. c 2 is the regression coefficient; The fitting relationship between the collapse angle and the working face advance distance and mining height is as follows: θ = a 3·l ( L 1)+ b 3· M + c 3; among which, θ For the collapse angle, L 1 represents the working face advance distance. M To extract high, a 3. b 3. c 3 is the regression coefficient.

4. The multi-factor coupled prediction method for porosity of collapsed and fractured coal and rock mass in a goaf area according to claim 1, characterized in that: In step S2, there is a proportional relationship between the single expansion distance of the compaction zone along the direction of the working face and the corresponding periodic compaction step distance of the working face: b i = c · L i ; in, b i This refers to the distance the compacted zone expands along the working face direction each time. L i For each press step distance, c It is a constant.

5. The multi-factor coupled prediction method for porosity of collapsed and fractured coal and rock mass in a goaf area according to claim 1, characterized in that: In step S2, the geometry of the compaction zone is simplified to an axisymmetric elliptic parabolic model, and the geometric relationship between the boundary of the compaction zone and the working face advancement direction satisfies: ； in, A 1. A 2 represents the distance from the bottom boundary of the compaction zone to the cut-out and the intake and return airways, respectively. H This refers to the height of the compacted zone.

6. The multi-factor coupled prediction method for porosity of collapsed and fractured coal and rock mass in a goaf area according to claim 1, characterized in that: In step S3, the evolution law of the transient fragmentation coefficient of the fractured rock mass with axial compressive stress is as follows: ； in, Φ ( σ () is the transient fragmentation coefficient. Φ 0 is the initial coefficient of fragmentation. Φ r The residual fragmentation coefficient, σ It is axial compressive stress. σ c This is the characteristic stress of fragmentation and attenuation.

7. The multi-factor coupled prediction method for porosity of collapsed and fractured coal and rock mass in a goaf area according to claim 6, characterized in that: In step S3, the residual fragmentation coefficient Φ r With rock elastic modulus E and uniaxial compressive strength of rock UCS The quantitative relationship is as follows: ； in, k 1 represents the contact cementation and mechanical attenuation constant between rock blocks. Φ r，min It is the minimum residual fragmentation coefficient.

8. The multi-factor coupled prediction method for porosity of collapsed and fractured coal and rock mass in a goaf area according to claim 6, characterized in that: In step S3, the fragmentation attenuation characteristic stress σ c Uniaxial compressive strength of rock UCS and fractal dimension after fragmentation D The quantitative relationship is as follows: ； in, k 2 is the characteristic constant of compaction rate.

9. The multi-factor coupled prediction method for porosity of collapsed and fractured coal and rock mass in a goaf according to claim 1, characterized in that: In step S4, the transient compaction stress inside the goaf is: σ ( x , y )= η ( x , y )· σ 0; in, σ 0 represents the initial geostress of the original rock. η ( x , y ) is the stress recovery coefficient of the goaf, which is 0.15 at the edge of the goaf and 1.0 in the core compacted area of ​​the goaf.

10. The multi-factor coupled prediction method for porosity of collapsed and fractured coal and rock mass in a goaf area according to claim 1, characterized in that: In step S5, the elliptical zone porosity prediction model is as follows: ； in, n ( x , y , z ) represents the coordinates of a spatial point within the goaf ( x , y , z The model considers the porosity at the location of the original rock, the initial geostress of the original rock, the lithology of the roof, the mining height, and the working face advance distance.

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