Design method for flat plate type artificial dam body of coal mine underground reservoir

Abstract

The invention belongs to the technical field of coal mine underground reservoirs, and particularly relates to a design method for a flat plate type artificial dam body of a coal mine underground reservoir. Comprising the steps that strength parameters of the artificial dam body after performance degradation in the complex hydraulic environment are determined; an artificial dam body three-dimensional thick plate elastic mechanical model is constructed, boundary conditions of the artificial dam body three-dimensional thick plate elastic mechanical model are determined, the mechanical model is solved through an energy variational method, and the internal stress distribution condition of the artificial dam body is determined; constructing an artificial dam body stretching-shearing composite yield criterion; determining an artificial dam body design scheme feasible region based on a stretching-shearing composite yield criterion; and determining a reasonable design depth range of the artificial dam body cutting based on rigidity matching and shear resistance. According to the method, the stress distribution of the artificial dam body of the underground reservoir can be accurately obtained, accurate identification of different damage types can be realized, the reasonable slotting depth can be determined, the coordination and stability of connection between the artificial dam body and surrounding coal and rock masses can be effectively improved, and thus the stability and reliability of the artificial dam body in long-term operation are ensured.

Description

Technical Field

[0001] The invention belongs to the technical field of coal mine underground reservoirs, and in particular relates to a design method for a flat-plate artificial dam body of a coal mine underground reservoir. Background Art

[0002] Currently, the artificial dams used in underground coal mine reservoirs are mostly flat-plate structures, usually arranged in a rectangular shape along the cross-section of the tunnel. The embedded structures at the upper, lower, left, and right ends respectively form a groove-embedded structure with the cutout structure in the surrounding coal and rock mass, thereby achieving the function of sealing and water-isolating the water storage space. Unlike surface reservoir dams, underground reservoir artificial dams must withstand the combined effects of reservoir water pressure and overburden stress. At the same time, the artificial dam body also forms a collaborative load-bearing system with the cutout-embedded structure. In other words, the stress environment of underground reservoir artificial dams is complex. Understanding its stress characteristics is of great significance for analyzing the stability of artificial dams and guiding their design. However, existing artificial dam design methods have obvious shortcomings and limitations, which are mainly manifested in the following aspects.

[0003] (1) The current analysis methods for the stability of artificial dams are highly dependent on numerical simulation methods; such methods can only conduct feasibility assessments for specific design schemes and lack guidance on general design paths.

[0004] (2) Some existing theoretical analysis methods still establish mechanical models based on simplified assumptions such as shear walls or beam structures, which fail to truly reflect the structural complexity and actual load-bearing state of artificial dams, resulting in a large deviation between the analysis results and the actual engineering conditions. The elastic thin plate mechanical model has improved the analysis accuracy to a certain extent, but it still only considers the deflection response of the artificial dam's mid-surface and lacks a true representation of the artificial dam's three-dimensional structure under complex stress states. The part involving the elastic thin plate plastic design method is risky and difficult to meet engineering safety requirements.

[0005] (3) The current design methods generally ignore the strength degradation law of the concrete constituting the artificial dam body under complex hydraulic environment, and still use the initial performance of concrete as the strength assessment standard, which fails to reflect the concrete degradation process under the actual service environment, affecting the long-term stability assessment of the artificial dam body.

[0006] (4) The depth of the cutout between the artificial dam body and the surrounding coal and rock mass is currently mostly determined by empirical methods or numerical simulations. There is a lack of unified theoretical calculation criteria, and the design basis is insufficient, making it difficult to ensure the rationality and engineering adaptability of the cutout embedded structure.

[0007] The above-mentioned deficiencies and limitations seriously restrict the reliability and scientificity of the design and optimization of artificial dams of underground reservoirs. Therefore, it is urgent to establish an artificial dam design method that considers the deterioration law of the hydraulic environment on the strength of the artificial dam, the influence of thickness and concrete strength grade on the yield state of the artificial dam, and the stiffness matching and shear resistance coordination between the artificial dam and the surrounding coal and rock mass, so as to provide a theoretical basis and technical support for the scientific design and safe operation and maintenance of artificial dams. Summary of the Invention

[0008] In response to the above technical problems, the present invention provides a method for designing a flat-plate artificial dam body for an underground water reservoir in a coal mine, which specifically includes the following steps.

[0009] S1: Determine the strength parameters of the artificial dam after performance degradation in a complex hydraulic environment.

[0010] S2: Construct a three-dimensional thick plate elastic mechanical model of the artificial dam and clarify its boundary conditions. Use the energy variation method to solve the mechanical model and determine the internal stress distribution of the artificial dam, and construct the tensile-shear composite yield criterion of the artificial dam.

[0011] S3: Determine the feasible region of the artificial dam design scheme based on the tensile-shear composite yield criterion.

[0012] S4: Determine the reasonable design depth range of the artificial dam cut based on stiffness matching and shear resistance.

[0013] .

[0014] Where, d is the reasonable design depth of the cut, F s is the total shear stress on the boundary surface of the cut, w f is the width of the cut boundary surface, c f is the cohesion of the cut boundary surface, φ f is the internal friction angle of the cut boundary surface; σ n is the normal stress on the boundary surface of the cut; h is the thickness of the artificial dam; E w With μ w are the elastic modulus and Poisson's ratio of the surrounding coal and rock mass respectively; ω a and θ a are the maximum normal displacement and maximum rotation angle allowed on the boundary surface of the cut, respectively; p n is the normal reaction force of the cut boundary surface, m n is the bending moment in the thickness direction of the cut boundary surface.

[0015] Preferably, in step S4, F s By calculating the shear stress τ on each cut boundary surface s Integrate to obtain τ on the top and bottom surfaces s is τ yz , in the coal faces is τ xz ; Width w of top and bottom surfaces f The width of the artificial dam is 2a, the width of the coal seam is w f is the height b of the artificial dam; , , c is the cohesion of the artificial dam, c w is the cohesion of the surrounding coal and rock mass, φ is the friction angle inside the artificial dam, w is the friction angle of the surrounding coal rock, 0.7 is the reduction coefficient; σ n Take σ at the top and bottom surfaces y , take σ at the coal seam surface x .

[0016] Preferably, step S1 includes: subjecting concrete samples to different dry-wet cycles and different moisture content treatments, constructing a concrete sample strength degradation model based on concrete sample mechanical experiments, and converting concrete sample strength parameters into artificial dam strength parameters.

[0017] Preferably, in step S1, the strength parameters of the artificial dam body include elastic modulus E and Poisson's ratio μ, which are the elastic modulus E and Poisson's ratio μ of the concrete sample; and also include the compressive strength R of the artificial dam body. c , .

[0018] The tensile strength R of the artificial dam t , .

[0019] The cohesion of the artificial dam c, .

[0020] The internal friction angle of the artificial dam is φ, .

[0021] Where, α c1 is the conversion factor between the strength of cubic concrete specimens and the strength of prismatic concrete specimens; α c2 is the brittleness reduction coefficient; ζ is the statistical variation coefficient; f c0 is the compressive strength of the concrete specimen without dry-wet cycle and moisture content treatment; is the compressive strength degradation index.

[0022] Preferably, in step S2, the three-dimensional thick plate elastic mechanical model of the artificial dam body is constructed and its boundary conditions are clarified, including: the width of the mechanical model is 2a, the height is b, the thickness is h, the elastic modulus E, the Poisson's ratio μ, and the water storage height H; the origin of the mechanical model coordinate system is established at the center of the top surface of the artificial dam body, and the three spatial coordinates x, y, and z are parallel to the width, height, and thickness directions, respectively, and the positive direction of the coordinates points to the coal side of one of the roadways of the artificial dam body, the bottom rock layer, and the outer surface.

[0023] The actual load and constraint conditions of the artificial dam body are as follows: the top surface y=0 bears the overburden stress p transmitted from the roof rock layer; the inner surface z=-h / 2 bears the reservoir water pressure q(y)=ρg(Hy) linearly distributed along the height of the artificial dam body; the outer surface z=h / 2 is a free boundary; the two coal seam surfaces x=±a and the bottom surface y=b are displacement fixed boundary conditions.

[0024] Preferably, in step S2, the energy variation method is used to solve the mechanical model and determine the stress distribution inside the artificial dam body.

[0025] .

[0026] Where σ is the stress tensor describing the stress state of any point in the artificial dam body, and its spatial stress components include the normal stress component σ x , σ y , σ z and the shear stress component τ xy , τ yz , τ xz ; ; ; δ ij is the Kronecker symbol, which takes the value 1 when i=j and takes the value 0 when i≠j; u i 、u j 、u k represent the i-th, j-th and k-th components of the displacement vector u of any point inside the artificial dam; x i 、x j 、x k They represent the i-th, j-th and k-th components of the coordinate system vector respectively.

[0027] Preferably, in step S2, the tensile-shear composite yield criterion for constructing the artificial dam body is.

[0028] .

[0029] Where: F is the composite yield function, which is a three-dimensional spatial distribution function; the position where F>0 in the artificial dam body indicates that it has entered the yield state; the position where F=0 in the artificial dam body indicates that it has entered the critical state of yield; the position where F<0 in the artificial dam body indicates that the artificial dam body is in an elastic state and has not yielded; F DP is the shear yield function, , α and K are strength parameters related to the cohesion c of the artificial dam and the friction angle φ of the artificial dam body, , ; I1 is the first invariant of the stress tensor σ; J2 is the second deviatoric stress invariant of the deviatoric stress tensor corresponding to the stress tensor σ, , σ1 is the maximum principal stress, σ2 is the intermediate principal stress, and σ3 is the minimum principal stress; FT is the tensile yield function, .

[0030] Preferably, step S3 includes: determining the composite yield function peak cloud map under multiple combinations of concrete strength grades and multiple artificial dam thicknesses, dividing the composite yield function peak cloud map into regions and selecting elastic safety regions, and determining the optimal design scheme based on comprehensive safety and economic constraints.

[0031] Preferably, step S4 includes: calculating the normal reaction force and thickness direction bending moment of each groove boundary surface based on the boundary stress distribution, determining the upper limit of each groove structure depth based on the coal rock support stiffness matching criterion, and determining the lower limit of each groove structure depth based on the boundary surface shear strength.

[0032] Preferably, in step S4, the calculation of the normal reaction force and the thickness direction bending moment of each cut boundary surface based on the boundary stress distribution includes:

[0033] .

[0034] .

[0035] Where dS f is the area element of the cut boundary; Γ f is the integral area of ​​the groove boundary, where the integral range of the top and bottom surfaces is x∈[-a,a], z∈[-h / 2,h / 2], and the integral range of the coal seam surface is y∈[0,b], z∈[-h / 2,h / 2].

[0036] The key technical means and beneficial effects of the present invention are as follows: 1. The present invention introduces a strength attenuation model for the degradation of concrete materials used to make artificial dam bodies in complex hydraulic environments, which can more accurately evaluate the strength and safety margin of artificial dam bodies throughout their service life, and ensure the stability and reliability of artificial dam bodies in long-term operation.

[0037] 2. The present invention constructs a three-dimensional thick plate elastic mechanics model of the artificial dam body and solves it with the help of the energy variation method. It can comprehensively consider the various loads and boundary constraints on the artificial dam body and obtain more accurate displacement and stress distribution results of the artificial dam body.

[0038] 3. The tensile-shear composite yield criterion system constructed in the present invention takes into account the main controlling failure mechanism of the artificial dam body and can accurately identify areas of different failure types (such as tensile failure areas, shear failure areas or tensile-shear failure areas).

[0039] 4. Based on stiffness matching and shear resistance, the present invention quantifies the normal and angular constraint capabilities of the surrounding coal and rock masses on the artificial dam body, as well as the anti-sliding safety performance, and then scientifically determines the cutting depth. This can effectively improve the coordination and stability of the connection between the artificial dam body and the surrounding coal and rock masses, and avoid the risk of local damage caused by stiffness mismatch and insufficient shear resistance. BRIEF DESCRIPTION OF THE DRAWINGS

[0040] The present invention will be further described below with reference to the accompanying drawings.

[0041] Figure 1 This is a schematic diagram of the relationship between the flat-plate artificial dam body, the cutout structure and the surrounding coal and rock mass of the underground reservoir of the present invention.

[0042] Figure 2 It is a schematic structural diagram of the three-dimensional thick plate elastic mechanics model of the flat-plate artificial dam body of the underground reservoir of the present invention.

[0043] Figure 3 Schematic diagram of the division of the yield zone and elastic zone of the artificial dam based on the tensile-shear composite yield criterion.

[0044] In the figure: 11-roof embedded structure, 12-bottom plate embedded structure, 13-coal side embedded structure; 21-roof rock layer, 22-bottom rock layer, 23-coal side of tunnel; 31-roof groove structure; 32-bottom plate groove structure; 33-coal side groove structure; 4-artificial dam body. DETAILED DESCRIPTION

[0045] The technical solution of the present invention is described in more detail below with reference to the accompanying drawings.

[0046] like Figure 1-Figure 3 As shown, the present invention proposes a design method for a flat-plate artificial dam body of a coal mine underground reservoir, which is suitable for the scientific design and engineering optimization of an artificial dam body 4 under complex hydraulic conditions of a coal mine underground reservoir, and specifically includes the following steps.

[0047] Step S1: Determine the strength parameters of the artificial dam after performance degradation in a complex hydraulic environment.

[0048] S11: Preparation of concrete specimens for artificial dams of underground reservoirs.

[0049] The artificial dam body 4 of the coal mine underground reservoir is made of concrete. Therefore, a cubic standard sample with a side length of 150 mm is prepared from concrete, compacted and formed using a vibration table, and cured for 28 days in a standard curing room with a temperature of 20±2°C and a relative humidity of ≥95%. The surface flatness error of the concrete sample is controlled within ±0.5 mm.

[0050] S12: The concrete samples were subjected to different dry-wet cycles and different moisture content treatments.

[0051] In order to simulate the water environment disturbance effect of the artificial dam body 4 of the underground reservoir during long-term service, the concrete specimens were first subjected to multiple dry-wet cycle treatments with different cycles. Each dry-wet cycle includes two stages: the first stage is saturation treatment, in which the concrete specimens are placed in a constant temperature water bath (25±1℃) and immersed for no less than 90 hours to ensure sufficient saturation; the second stage is air-drying treatment, in which the concrete specimens are placed in a light-proof and ventilated environment (25±2℃) and naturally dried for no less than 72 hours; the number of dry-wet cycle cycles is represented by N, and the maximum number of cycles should be greater than 5.

[0052] Then the concrete samples after the dry-wet cycle treatment were treated with different moisture contents. The saturated moisture content W of the concrete samples in the saturated state was used as the s The upper limit is W0, the lowest moisture content in the air-dried state after the dry-wet cycle is W0, and the lower limit is W0. No less than 5 moisture content points are evenly selected in this interval. The concrete samples in the air-dried state after the dry-wet cycle are humidified by a humidifier using atomized steam to obtain concrete samples with different moisture contents W.

[0053] S13: Construct a concrete specimen strength degradation model based on concrete specimen mechanical experiments.

[0054] The uniaxial compression test of concrete specimens was carried out using an electronic servo loading device, the peak load and stress-strain curve were recorded, and the compressive strength f of the concrete specimens was calculated. cu,m , elastic modulus E and Poisson's ratio μ (the compressive strength in this article refers to the uniaxial compressive strength unless otherwise specified); to ensure the stability and statistical reliability of the experimental data, there should be no less than 3 concrete specimens under the same experimental conditions.

[0055] The compressive strength of the concrete sample f cu,m The compressive strength of concrete samples without dry-wet cycle and moisture content treatment is f c0 The ratio of The ratio of the elastic modulus E of the concrete sample to the elastic modulus E0 of the concrete sample without dry-wet cycle and moisture content treatment is defined as the elastic modulus degradation index ; Use data fitting method to obtain compressive strength degradation index and elastic modulus degradation index The expression is as follows.

[0056] (1-1).

[0057] (1-2).

[0058] Where, 、 、 They are respectively the compressive strength dry-wet cycle degradation coefficient, the compressive strength moisture content degradation coefficient, and the compressive strength composite degradation coefficient; 、 、 They are the dry-wet cycle degradation coefficient of elastic modulus, the moisture content degradation coefficient of elastic modulus, and the composite degradation coefficient of elastic modulus.

[0059] Construct the compressive strength of concrete specimens under hydraulic conditions cu,m The degradation model with the elastic modulus E is as follows.

[0060] (1-3).

[0061] (1-4).

[0062] S14: Convert the strength parameters of the concrete specimen into the strength parameters of the artificial dam body.

[0063] With the exception of the elastic modulus E and Poisson's ratio μ of the concrete specimens, the strength parameters of the concrete specimens cannot be directly used as the strength parameters of the artificial dam body 4 and need to be corrected. Taking into account the discreteness of the experimental results that may be caused by factors such as the material heterogeneity of the concrete specimens, differences in dry-wet cycles and moisture content curing conditions, and operational errors, a statistical coefficient of variation ζ is introduced to characterize the variability of the experimental strength results. To ensure the applicability and safety of the strength parameters of the concrete specimens in the design of the artificial dam body 4, and considering that the actual pouring and construction process of the artificial dam body 4 is difficult to achieve strict controllability of the concrete specimen preparation conditions, the actual strength of the artificial dam body 4 is usually lower than the strength of the concrete specimens. To reflect this difference, a correction coefficient α is introduced. s The strength parameters of concrete specimens are reasonably reduced, and the recommended value is 0.88. In addition, because the prismatic specimen can more truly reflect the compressive state of the artificial dam body 4, the conversion coefficient α between the strength of cubic concrete specimens and the strength of prismatic concrete specimens is introduced. c1 At the same time, considering that the failure mode of the artificial dam body 4 is more brittle than that of the concrete specimen during the stress process, the brittleness reduction coefficient α is introduced c2 .

[0064] In summary, the compressive strength of the artificial dam body R c Can be expressed as.

[0065] (1-5).

[0066] According to the conversion relationship between compressive strength and tensile strength, the tensile strength of the artificial dam body R t Can be expressed as.

[0067] (1-6).

[0068] Under the combined conditions of compression and shear, the shear strength parameters cohesion and internal friction angle can be expressed by the compressive strength, based on which the cohesion c and friction angle φ of the artificial dam can be determined.

[0069] (1-7).

[0070] (1-8).

[0071] S21: Determine the geomechanical parameters of the coal and rock mass around the artificial dam of the underground reservoir.

[0072] like Figure 1 As shown, the artificial dam body 4 is constructed in the coal rock mass around the tunnel by means of a groove-cutting embedded structure. Specifically, the artificial dam body 4 is respectively embedded in the roof rock layer 21, the bottom rock layer 22 and the coal sides 23 of the tunnels on both sides by means of a top plate groove-cutting embedded structure, a bottom plate groove-cutting embedded structure and a groove-cutting embedded structure of the tunnel coal sides on both sides; the top plate groove-cutting embedded structure includes a top plate groove-cutting structure 31 formed by grooves in the top rock layer 21 and a top plate embedded structure 11 located at the top of the artificial dam body 4 and embedded in the top plate groove-cutting structure 31; the bottom plate groove-cutting embedded structure includes a bottom plate groove-cutting structure 32 formed by grooves in the bottom rock layer 22 and a bottom plate embedded structure 11 located at the top of the artificial dam body 4 and embedded in the top plate groove-cutting structure 31; The bottom of the artificial dam body 4 is embedded in the bottom plate embedded structure 12 in the bottom plate groove structure 32, and the tunnel coal side groove structure embedded structure includes a coal side groove structure 33 formed by grooves in the tunnel coal side 23 and a coal side embedded structure 13 located on both sides of the artificial dam body 4 and embedded in the tunnel coal side 23; the top plate embedded structure 11, the bottom plate embedded structure 12 and the coal side embedded structure 13 are extensions of the artificial dam body 4 into the surrounding coal rock mass, and are cast and constructed together with the artificial dam body 4, and the entire concrete casting body is also a rectangular flat plate structure like the artificial dam body 4. In this article, for the convenience of research and analysis, the artificial dam body 4 specifically refers to the non-embedded part of the entire concrete casting body.

[0073] Through engineering investigation and field testing, the overburden stress on the artificial dam body 4 and the elastic modulus E of the coal and rock mass around the artificial dam body 4 (the roof rock layer 21, the bottom rock layer 22, and the coal ribs 23 on both sides of the roadway) are determined. w , Poisson's ratio μ w 、Internal friction angle φ w , cohesion c w .

[0074] S22: Construct a three-dimensional thick plate elastic mechanics model of the artificial dam and clarify its stress and displacement boundary conditions.

[0075] like Figure 2As shown, an artificial dam body 4 is selected to construct a three-dimensional thick plate elastic mechanical model of the artificial dam body. Since the thickness and aspect ratio of the artificial dam body 4 exceed the applicable range of the elastic thin plate theory, the mechanical model of the present invention adopts the three-dimensional thick plate theory to more accurately reflect the stress and displacement distribution characteristics inside the artificial dam body 4; the width of the mechanical model is 2a, the height is b, the thickness is h, the elastic modulus is E, the Poisson's ratio is μ, and the water storage height is H; the mechanical model is established on the following basic assumptions: the material is continuous, uniform, and isotropic, follows linear elastic behavior, and the deformation is within a small deformation range; the origin of the mechanical model coordinate system is established at the center of the top surface of the artificial dam body 4, and the three spatial coordinates x, y, and z are parallel to the width, height, and thickness directions, respectively, and the positive coordinates point to one of the roadways coal ridges 23 of the artificial dam body 4, the bottom rock layer 22, and the outer surface (away from the water storage side).

[0076] The actual load and constraint conditions of the artificial dam body 4 are determined as follows: the top surface (y=0) is subjected to the overburden stress p transmitted from the roof rock layer 21; the inner surface (z=-h / 2) is subjected to the reservoir water pressure q(y)=ρg(Hy) linearly distributed along the height of the artificial dam body 4; the outer surface (z=h / 2) is a free boundary; the two coal seam surfaces (x=±a) and the bottom surface (y=b) are constrained by the groove embedded structure, which is a displacement fixed boundary condition.

[0077] S23: Use the energy variation method to solve the mechanical model and determine the internal stress distribution of the artificial dam.

[0078] Construct the total potential energy functional of artificial dam 4 , defined as the elastic energy U of the artificial dam body 4 e Work done with external force W F difference.

[0079] (2-1).

[0080] Where: σ is the stress tensor describing the stress state of any point in the artificial dam body, ε is the strain tensor describing the deformation degree of any point in the artificial dam body, σ:ε represents the double inner product between the stress tensor and the strain tensor; the external force vector includes the body force f and the surface force t, the body force f can be ignored, , the superscript T represents the transpose of the vector; Ω is the overall volume domain of the artificial dam body, dV is the volume element; Γ is the force-bearing boundary surface, including the top and inner surfaces of the artificial dam body, dS is the surface area element of the force-bearing boundary surface, including the top and inner surfaces of the artificial dam body; u is the displacement vector or displacement function of any point inside the artificial dam body, which contains three direction components of x, y, and z, and can be expanded as follows.

[0081] (2-2).

[0082] Where u0 is the displacement vector of the special solution that satisfies the displacement boundary condition; M mnr is a diagonal matrix consisting of unknown coefficients; u mnr is a set of basis function terms that are always zero on the displacement boundary; m, n, r represent the order subscripts of the expansion terms in the x, y, and z coordinate directions.

[0083] The specific form is.

[0084] (2-3).

[0085] (2-4).

[0086] (2-5).

[0087] (2-6).

[0088] Where u1, u2, and u3 are the components of the displacement vector u in the x, y, and z directions; A mnr 、B mnr 、C mnr are the undetermined coefficients of the mth, nth, and rth displacement basis functions in the x, y, and z directions respectively; diag is the constructed diagonal matrix; β mnr is the scalar factor of the basis function, which is a polynomial of x, y, and z. It satisfies the zero displacement boundary condition and can be expressed as: .

[0089] According to the geometric equation and physical constitutive relationship, the strain and stress in the artificial dam body 4 can be expressed by displacement as follows.

[0090] (2-7).

[0091] (2-8).

[0092] Where, ε ij represents the strain component in the strain tensor ε that is located in the i-direction plane and points in the j-direction; σ ij represents the stress component in the stress tensor σ that is located on the i-direction plane and points in the j-direction; δ ij is the Kronecker symbol, which takes the value 1 when i=j and takes the value 0 when i≠j; ε kk represents volume strain; u i 、u j Respectively represent the i-th and j-th components of the displacement vector u; x i 、x jRespectively represent the i-th and j-th components of the coordinate system vector; according to the convention in tensor analysis (vector is a type of tensor, belonging to the first-order tensor), the subscripts i and j range from 1, 2, and 3 to represent the three components of the coordinate system vector, where 1 represents the x-axis direction, 2 represents the y-axis direction, and 3 represents the z-axis direction; λ is the Lame constant, , G is the shear modulus, .

[0093] Substituting Equations (2-7) and (2-8) into Equation (2-1), we can obtain the total potential energy functional expressed in terms of displacement.

[0094] (2-9).

[0095] Where, It is the top surface of the artificial dam. It is the inner surface of the artificial dam.

[0096] According to the principle of minimum potential energy, the static equilibrium state of the artificial dam body 4 under given boundary load conditions corresponds to the minimum value of the total potential energy functional; that is, by varying the displacement vector u so that the total potential energy functional takes the minimum value, the static equilibrium solution of the artificial dam body 4 can be obtained; further, according to the principle of energy variation, the partial derivatives of the total potential energy functional with respect to all unknown coefficients at the extreme point must be zero, so the following conditions should be met.

[0097] (2-10).

[0098] After solving, we get all the unknown coefficients A mnr 、B mnr 、C mnr , back-substitute into the displacement formula (2-2) to obtain the displacement vector of any point inside the artificial dam body 4; further combined with formula (2-8), each spatial stress component of the spatial stress tensor can be calculated.

[0099] (2-11).

[0100] Where, the spatial stress components of the stress tensor σ include the normal stress component σ x , σ y , σ z and the shear stress component τ xy , τ yz , τ xz ;u k represents the kth component of the displacement vector u at any point inside the artificial dam; x kRepresents the kth component of the coordinate system vector. According to the convention in tensor analysis (a vector is a type of tensor and belongs to a first-order tensor), the subscript k ranges from 1, 2, and 3 to represent the three components of the coordinate system vector, where 1 represents the x-axis direction, 2 represents the y-axis direction, and 3 represents the z-axis direction.

[0101] S24: Construct a tensile-shear composite yield criterion for artificial dams.

[0102] In order to determine whether the artificial dam body 4 has reached the yield state, the principal stress of each point in the artificial dam body 4 is solved. The principal stress is the characteristic value of the stress tensor σ and can be obtained by the characteristic equation.

[0103] (2-12).

[0104] Where det represents the determinant operation on the matrix; I is the 3×3 unit matrix; σ is the eigenvalue of the stress tensor σ, that is, the principal stress; I1, I2, and I3 are the first, second, and third invariants of the stress tensor σ, respectively, and their expressions are:

[0105] (2-13).

[0106] By solving equation (2-13), we can obtain three principal stresses σ1, σ2, and σ3, where σ1 is the maximum principal stress, σ2 is the intermediate principal stress, and σ3 is the minimum principal stress. The expression is:

[0107] (2-14).

[0108] Where σ η represents the ηth principal stress solution, η=1, 2, 3; , .

[0109] Since the artificial dam body 4 is mainly subjected to compressive stress and shear stress under operating conditions, and the intermediate principal stress has a significant influence on the yield behavior of the material, the Drucker-Prager strength criterion is used to evaluate the shear stability of the artificial dam body 4.

[0110] (2-15).

[0111] Where, F DP is the shear yield function, α and K are strength parameters related to the cohesion c and the internal friction angle φ of the artificial dam body, , ; J2 is the second deviatoric stress invariant of the deviatoric stress tensor corresponding to the stress tensor σ, .

[0112] At the same time, in order to consider the possible tensile failure of the artificial dam body 4 in the local tensile stress dominant area, the tensile strength R t The tensile yield function F is the basis T .

[0113] (2-16).

[0114] Construct the tensile-shear composite yield criterion of artificial dam body 4.

[0115] (2-17).

[0116] Where: F is the composite yield function, which is a three-dimensional spatial distribution function; the position where F>0 in the artificial dam body 4 indicates that it has entered the yield state; the position where F=0 in the artificial dam body 4 indicates that it has entered the critical state of yield; the position where F<0 in the artificial dam body 4 indicates that the artificial dam body 4 is in an elastic state and has not yielded.

[0117] In the present invention, a composite yield criterion is constructed based on the Drucker-Prager shear yield criterion and the tensile yield criterion. This allows point-by-point determination of whether the artificial dam body 4 has entered a yield state in three-dimensional space, enabling comprehensive identification of yield behavior under tension-compression-shear composite conditions. This criterion is particularly suitable for stability analysis of the artificial dam body 4 under complex working conditions, such as when it is simultaneously subjected to top overburden stress and internal surface reservoir water pressure. The Drucker-Prager criterion can effectively characterize the shear yield characteristics of the material of the artificial dam body 4 under a three-dimensional stress state, and is particularly suitable for describing the shear failure trend caused by the internal surface reservoir water pressure of the artificial dam body 4. To address the potential risk of local tensile stress concentration in the artificial dam body 4 under the action of top overburden stress, a tensile yield function constructed based on the difference between the maximum principal stress and the tensile strength of the artificial dam body is introduced. This effectively identifies possible tensile failure at the restrained positions around the artificial dam body 4, demonstrating good sensitivity to tensile stress yield.

[0118] Step S3: Determine the feasible region of the artificial dam design scheme based on the tensile-shear composite yield criterion.

[0119] The composite yield function F constructed in step S2 can be used to analyze the yield failure distribution characteristics of the artificial dam body 4 under a specific design scheme. It is suitable for a single design scheme and is difficult to support comparison and optimization among multiple design schemes. In order to evaluate the feasibility of multiple artificial dam body 4 design schemes with the composite yield function F, this step is based on elastic design theory to construct a peak cloud diagram of the composite yield function F of the artificial dam body under multiple design schemes, and determine the feasible domain of the design scheme that meets the safety requirements. The design scheme mainly involves the design of the thickness of the artificial dam body and the selection of the concrete strength grade. An evaluation function is further introduced with the goal of improving the convenience of engineering construction and reducing the construction cost, and the thickness of the artificial dam body and the concrete strength grade are jointly optimized, so as to select the artificial dam body 4 design scheme that achieves the best balance between safety and economy. Specifically including.

[0120] S31: Determine the peak cloud diagram of the composite yield function under multiple combinations of concrete strength grades and multiple artificial dam thicknesses.

[0121] Set the concrete strength grade range to C15 to C40, the artificial dam thickness range to 0.5m to 3.0m, and construct multiple design schemes to calculate the composite yield function peak F of the artificial dam body 4 under each design scheme. max The composite yield function peak F max It is used to judge whether there is a risk of damage to the artificial dam body 4 under a certain design scheme. max When <0, the composite yield function F is less than 0 in the entire domain of the artificial dam body 4, and the entire domain of the artificial dam body 4 is in an elastic state; Figure 3 As shown in the figure, the concrete strength grade is set as the horizontal axis and the thickness of the artificial dam body is set as the vertical axis, and a two-dimensional distribution diagram of the composite yield function peak value, that is, the composite yield function peak value cloud diagram, is drawn.

[0122] S32: Divide the composite yield function peak cloud into regions and select the elastic safety region.

[0123] The composite yield function peak cloud map is divided into regions based on the composite yield function peak F max = 0 as the dividing line, the peak value of the composite yield function F max The area below 0 is the elastic safety zone ( Figure 3 In the middle B area, such as [C35, 2.0] and [C30, 2.5]), the artificial dam body 4 is in an elastic working state and is a safe design solution area; the peak value of the composite yield function F max The area where >0 is the yield failure zone, which can be further divided into the shear failure zone according to its yield failure form ( Figure 3 A1 area, such as [C20,2.5]), tensile failure zone ( Figure 3 A2 region, such as [C25,1.0]) and the tensile-shear failure region ( Figure 3 In the shear failure zone, the thickness of the artificial dam body is large but the concrete strength is low, and the shear stress exceeds the strength limit of the concrete material. In the tensile failure zone, the concrete strength is high but the thickness of the artificial dam body is insufficient, and the tensile stress dominates the instability. In the tensile-shear failure zone, both the concrete strength and the thickness of the artificial dam body are underdesigned, and the local tensile stress and shear stress are concentrated, which is manifested as tensile cracks in some areas first, followed by crack expansion inducing shear slip, and finally forming tensile-shear composite failure.

[0124] S33: Determine the optimal design solution based on comprehensive safety and economic constraints.

[0125] Determine the cost objective function of concrete materials required to build artificial dam body 4 , where C represents the concrete strength grade and h represents the thickness of the artificial dam. Under the premise of meeting the safety constraints, the following optimization model is constructed.

[0126] (3-1).

[0127] This optimization model represents finding the cost objective function among all the design solutions that meet the safety constraints. The minimum concrete strength grade C* and artificial dam thickness h* are taken as the optimal design solution. Indicates that the cost objective function is satisfied The values ​​of concrete strength grade C and artificial dam thickness h that reach the minimum value.

[0128] The cost of concrete materials is proportional to the unit price and amount of concrete, based on which the cost objective function can be determined.

[0129] (3-2).

[0130] Where, P C The price per unit volume of concrete of strength grade C.

[0131] The thickness of the artificial dam and the concrete strength grade of the design scheme in the elastic safety zone are calculated and screened item by item, and the cost objective function is selected. The combination of concrete strength grade C* and artificial dam thickness h* (C*, h*) with the minimum value is taken as the design solution.

[0132] Step S4: Determine the reasonable design depth range of the artificial dam body cutout based on stiffness matching and shear resistance.

[0133] like Figure 1As shown, the artificial dam body 4 has a total of 6 boundary surfaces: the top surface is connected to the top plate groove structure 31 and is coplanar with the top plate rock layer 21; the bottom surface is connected to the bottom plate groove structure 32 and is coplanar with the bottom plate rock layer 22; the two coal side surfaces are connected to the coal side groove structure 33 and are coplanar with the roadway coal side 23; the inner surface is located on the side of the water storage space; the outer surface is away from the water storage space; among them, the top surface, bottom surface and coal side surface are groove boundary surfaces; under the combined action of reservoir water pressure and overburden stress, each groove boundary surface bears normal reverse force and bending moment, and is ultimately borne by the surrounding coal and rock masses; therefore, the cutting depth directly affects the supporting performance of the surrounding coal and rock masses on the artificial dam body 4; a deep cutting will lead to a decrease in the supporting stiffness of the surrounding coal and rock masses; although a shallow cutting can increase the stiffness of the surrounding coal and rock masses, the construction is difficult, and the connection reliability and anti-slip ability are insufficient; therefore, it is necessary to select a suitable cutting depth to ensure that the cutting embedded structure has sufficient normal stiffness, angular stiffness and shear resistance, thereby providing stability guarantee for the artificial dam body 4.

[0134] S41: Calculate the normal reaction force and thickness direction bending moment of each cut boundary surface based on the boundary stress distribution.

[0135] Based on the internal stress state of the artificial dam body 4, the normal stress σ on each cut boundary surface is extracted. n , establish the normal reaction force p of the cut boundary surface n Bending moment in thickness direction m n The calculation model is used to clarify the support stiffness requirements of the artificial dam body 4 on the boundary surfaces of each cut; the cut embedded structure should be able to guarantee the reverse support capacity of the coal rock mass to the artificial dam body 4, and ensure that the artificial dam body 4 maintains an elastic working state during its service; specifically, the normal stress σ along the boundary surface of the cut of the artificial dam body 4 n Integrate and calculate the normal reaction force p of the cut boundary surface n Bending moment in thickness direction m n , the integral expression is as follows.

[0136] (4-1).

[0137] (4-2).

[0138] Where, normal stress σ n Take σ on the top and bottom surfaces y , take σ at the coal seam surface x , can be obtained based on formula (2-11); dS f is the area element of the cut boundary surface; Γ f is the integration area of ​​the boundary surface of the groove, where the integration range of the top and bottom surfaces is x∈[-a,a], z∈[-h / 2,h / 2], and the integration range of the coal seam surface is y∈[0,b], z∈[-h / 2,h / 2].

[0139] S42: Determine the upper limit of the depth of each slot structure based on the coal-rock support stiffness matching criterion.

[0140] In order to quantify the reverse support capacity of the surrounding coal and rock mass to the artificial dam body 4, according to the elastic modulus E of the coal and rock mass measured in step S21, w and Poisson's ratio μ w , calculate the normal support stiffness k provided by each cut structure n and the corner support stiffness k θ .

[0141] (4-3).

[0142] (4-4).

[0143] Where, d is the reasonable design depth of the cut, h is the thickness of the artificial dam; w f is the width of the groove boundary surface, the top and bottom surfaces are the width of the artificial dam body 2a, and the coal seam surface is the height b of the artificial dam body.

[0144] As the reasonable design depth d of the cut increases, the stiffness of the coal and rock mass gradually decreases, and the supporting capacity decreases. To ensure reasonable stiffness matching, the following stiffness constraints should be met.

[0145] (4-5).

[0146] (4-6).

[0147] Where, ω a and θ a are the maximum normal displacement and maximum rotation angle allowed on the boundary surface of the cut respectively; in actual engineering, the recommended value is: ω a =1.0×10-3m,θ a =1.0×10-3rad.

[0148] Substituting equations (4-3) and (4-4) into equations (4-5) and (4-6), we can obtain the constraint range of each cut structure depth as follows: , ; Taking the more stringent restriction condition of the two, we can get the upper limit of the depth of each groove structure: .

[0149] S43: Determine the lower limit of the depth of each cut structure based on the shear strength of the boundary surface.

[0150] If the reasonable design depth d of the cut is too small, although the rigidity is sufficient, the shear resistance of the cut boundary surface is reduced due to insufficient contact area, which can easily induce sliding failure of the artificial dam body 4. Therefore, the design must also meet the anti-slip safety requirements.

[0151] (4-7).

[0152] Where, τ f,max is the ultimate shear strength of the cut boundary surface, c f is the cohesion of the cut boundary surface, φ f is the internal friction angle of the cut boundary surface; , , c is the cohesion of the artificial dam, c w is the cohesion of the surrounding coal and rock mass, φ is the friction angle inside the artificial dam, w is the friction angle of the surrounding coal rock mass, and 0.7 is the reduction coefficient.

[0153] In order to meet the anti-sliding safety requirements of the artificial dam body 4, the shear stress at each cut boundary surface should not exceed the ultimate shear strength.

[0154] (4-8).

[0155] Where, F s is the total shear stress on the boundary surface of the cut, which can be obtained by calculating the shear stress τ on each boundary surface of the cut s Integrate to obtain τ on the top and bottom surfaces s is τ yz , in the coal face s is τ xz ; Shear contact area A f The width of the cut boundary surface w f and the reasonable design depth d of the cut, the specific .

[0156] The lower limit of the depth of each cut structure is finally determined as: .

[0157] S44: Determine the depth range of each cut structure of the artificial dam body.

[0158] Based on the above, the lower limit controls anti-slip safety and the upper limit constrains stiffness matching, and finally the depth range of each groove structure can be determined.

[0159] (4-9).

[0160] The present invention is not limited to the above-mentioned optimal implementation mode. Anyone can derive other various forms of methods under the inspiration of the present invention. However, any technical solution that is the same or similar to that of the present application falls within the scope of protection of the present invention.

Claims

1. A design method for a flat-plate artificial dam of a coal mine underground reservoir, characterized in that: The following steps are involved: S1: Determine the strength parameters of the artificial dam after performance degradation under complex hydraulic environment; S2: Construct a three-dimensional thick plate elastic mechanics model of the artificial dam and clarify its boundary conditions. Use the energy variation method to solve the mechanical model and determine the internal stress distribution of the artificial dam, and construct the tensile-shear composite yield criterion of the artificial dam. S3: Determine the feasible region of the artificial dam design scheme based on the tensile-shear composite yield criterion; S4: Determine the reasonable design depth range of the artificial dam cut based on stiffness matching and shear resistance: ； Where, d is the reasonable design depth of the cut, F s is the total shear stress on the boundary surface of the cut, w f is the width of the cut boundary surface, c f is the cohesion of the cut boundary surface, φ f is the internal friction angle of the cut boundary surface; σ n is the normal stress on the boundary surface of the cut; h is the thickness of the artificial dam; E w With μ w are the elastic modulus and Poisson's ratio of the surrounding coal and rock mass respectively; ω a and θ a are the maximum normal displacement and maximum rotation angle allowed on the boundary surface of the cut, respectively; p n is the normal reaction force of the cut boundary surface, m n is the bending moment in the thickness direction of the cut boundary surface.

2. The method for designing a flat-plate artificial dam for an underground reservoir in a coal mine according to claim 1, wherein: In step S4, F s By calculating the shear stress τ on each cut boundary surface s Integrate to obtain τ on the top and bottom surfaces s is τ yz , in the coal face s is τ xz ; Width w of top and bottom surfaces f The width of the artificial dam is 2a, the width of the coal seam is w f is the height b of the artificial dam; , , c is the cohesion of the artificial dam, c w is the cohesion of the surrounding coal and rock mass, φ is the friction angle inside the artificial dam, w is the friction angle of the surrounding coal rock, 0.7 is the reduction coefficient; σ n Take σ at the top and bottom surfaces y , take σ at the coal seam surface x .

3. The method for designing a flat-plate artificial dam for an underground reservoir in a coal mine according to claim 2, wherein: Step S1 includes: subjecting concrete samples to different dry-wet cycles and different moisture content treatments, constructing a concrete sample strength degradation model based on concrete sample mechanical experiments, and converting concrete sample strength parameters into artificial dam strength parameters.

4. The method for designing a flat-plate artificial dam for an underground reservoir in a coal mine according to claim 3, wherein: In step S1, the strength parameters of the artificial dam body include the elastic modulus E and Poisson's ratio μ, which are the elastic modulus E and Poisson's ratio μ of the concrete sample; and the compressive strength R of the artificial dam body. c , ; The tensile strength R of the artificial dam t , ; The cohesion of the artificial dam c, ; The internal friction angle of the artificial dam is φ, ; Where, α c1 is the conversion factor between the strength of cubic concrete specimens and the strength of prismatic concrete specimens; α c2 is the brittleness reduction coefficient; ζ is the statistical variation coefficient; f c0 is the compressive strength of the concrete specimen without dry-wet cycle and moisture content treatment; is the compressive strength degradation index.

5. The method for designing a flat-plate artificial dam for an underground reservoir in a coal mine according to claim 4, characterized in that: In step S2, the three-dimensional thick plate elastic mechanical model of the artificial dam body is constructed and its boundary conditions are clarified, including: the width of the mechanical model is 2a, the height is b, the thickness is h, the elastic modulus E, the Poisson's ratio μ, and the water storage height H; the origin of the mechanical model coordinate system is established at the center of the top surface of the artificial dam body, the three spatial coordinates x, y, and z are parallel to the width, height, and thickness directions, respectively, and the positive coordinates point to the coal side of one of the roadways, the bottom rock layer, and the outer surface of the artificial dam body in sequence; The actual load and constraint conditions of the artificial dam body are as follows: the top surface y=0 bears the overburden stress p transmitted from the roof rock layer; the inner surface z=-h / 2 bears the reservoir water pressure q(y)=ρg(Hy) linearly distributed along the height of the artificial dam body; the outer surface z=h / 2 is a free boundary; the two coal seam surfaces x=±a and the bottom surface y=b are displacement fixed boundary conditions.

6. The method for designing a flat-plate artificial dam for an underground reservoir in a coal mine according to claim 5, characterized in that: In step S2, the energy variation method is used to solve the mechanical model and determine the internal stress distribution of the artificial dam body as follows: ； Where σ is the stress tensor describing the stress state of any point in the artificial dam body, and its spatial stress components include the normal stress component σ x , σ y , σ z and the shear stress component τ xy , τ yz , τ xz ; ; ; δ ij is the Kronecker symbol, which takes the value 1 when i=j and takes the value 0 when i≠j; u i 、u j 、u k represent the i-th, j-th and k-th components of the displacement vector u of any point inside the artificial dam; x i 、x j 、x k They represent the i-th, j-th and k-th components of the coordinate system vector respectively.

7. The method for designing a flat-plate artificial dam for an underground reservoir in a coal mine according to claim 6, wherein: In step S2, the tensile-shear composite yield criterion for constructing the artificial dam body is: ； Where: F is the composite yield function, which is a three-dimensional spatial distribution function; the position where F>0 in the artificial dam body indicates that it has entered the yield state; the position where F=0 in the artificial dam body indicates that it has entered the critical state of yield; the position where F<0 in the artificial dam body indicates that the artificial dam body is in an elastic state and has not yielded; F DP is the shear yield function, , α and K are strength parameters related to the cohesion c of the artificial dam and the friction angle φ of the artificial dam body, , ; I1 is the first invariant of the stress tensor σ; J2 is the second deviatoric stress invariant of the deviatoric stress tensor corresponding to the stress tensor σ, , σ1 is the maximum principal stress, σ2 is the intermediate principal stress, and σ3 is the minimum principal stress; F T is the tensile yield function, .

8. The method for designing a flat-plate artificial dam for an underground reservoir in a coal mine according to claim 7, wherein: Step S3 includes: determining the composite yield function peak cloud map under multiple combinations of concrete strength grades and multiple artificial dam thicknesses, dividing the composite yield function peak cloud map into regions and selecting elastic safety regions, and determining the optimal design scheme based on comprehensive safety and economic constraints.

9. The method for designing a flat-plate artificial dam for an underground reservoir in a coal mine according to claim 8, wherein: Step S4 includes: calculating the normal reaction force and thickness direction bending moment of each cut boundary surface based on the boundary stress distribution, determining the upper limit of each cut structure depth based on the coal rock support stiffness matching criterion, and determining the lower limit of each cut structure depth based on the boundary surface shear strength.

10. The method for designing a flat-plate artificial dam for an underground reservoir in a coal mine according to claim 9, wherein: In step S4, the calculation of the normal reaction force and the thickness direction bending moment of each cut boundary surface based on the boundary stress distribution includes: ； ； Where dS f is the area element of the cut boundary; Γ f is the integral area of ​​the groove boundary, where the integral range of the top and bottom surfaces is x∈[-a,a], z∈[-h / 2,h / 2], and the integral range of the coal seam surface is y∈[0,b], z∈[-h / 2,h / 2].

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