Mine ballast bed and roadway bottom plate vertical rigidity calculation method and verification system

Abstract

The invention provides a method for calculating the vertical rigidity of a mine ballast bed and a roadway bottom plate and a verification system. Compared with an existing method for obtaining the vertical rigidity of the mine ballast bed and the roadway bottom plate according to experience, the calculation method provided by the invention has the advantages that the influence of physical and mechanical property parameters of the ballast bed and the roadway bottom plate on the vertical rigidity can be comprehensively considered; the vertical stiffness of the mine ballast bed and the roadway bottom plate under different laying conditions and different surrounding rock conditions can be analyzed, and more reasonable parameters can be provided for engineering design and dynamic analysis in related fields.

Description

Technical Field

[0001] The invention belongs to the field of coal mine auxiliary transportation, and in particular relates to a method for calculating the vertical stiffness of a mine roadbed and a tunnel floor and a corresponding calibration system. Background Art

[0002] like Figure 1 As shown, the mine track is composed of rails, fasteners, sleepers, ballast and tunnel floor. The ballast is laid on the tunnel floor, the sleepers are located on the ballast, the rails are located on the sleepers, and the rails and sleepers are connected by fasteners. Under the action of load, the ballast and the tunnel floor will deform. In the present invention, the vertical stiffness of the ballast and the tunnel floor refers to the ratio of the pressure on the ballast surface of the mine track to the vertical displacement at that location, including the influence of the physical properties and mechanical properties of the ballast and the tunnel floor on the force and displacement, and characterizes the anti-deformation ability of the ballast and the tunnel floor.

[0003] The vertical stiffness of the ballast and the tunnel floor directly affects the dynamic response characteristics of the narrow-gauge vehicle and the mine track structure, and is a key parameter of the narrow-gauge vehicle-mine track coupling dynamic system. Due to the complex surrounding rock conditions of the mine, this parameter is currently determined mainly based on experience, and the vertical stiffness value taken is often quite different from the actual situation. To this end, the present invention provides a method for calculating the vertical stiffness of the mine ballast and the tunnel floor and a corresponding verification system. Summary of the invention

[0004] The purpose of the present invention is to provide a method for calculating the vertical stiffness of the mine roadbed and tunnel floor and a verification system, so as to provide a basis for the design of the mine track and the analysis of its dynamic characteristics.

[0005] The technical solution of the present invention is a method for calculating the vertical stiffness of the mine track bed and the tunnel floor, which is characterized in that an xOz coordinate system is established in the schematic diagram of the mine track structure, the origin O is located on the track bed surface, the Ox axis is parallel to the track length direction, and the Oz axis is vertically downward. According to the structural characteristics of the track bed, it is regarded as an elastic medium. According to the elasticity theory, the normal stress of the track bed along the x direction and the z direction, and the shear stress are respectively

[0006]

[0007] In the formula, They are The simplified expression of λ is the displacement of a particle with coordinates (x, z) on the track bed along the x and z directions at time t, in units of m; e , μ e is the Lame constant of the ballast, in Pa;

[0008] Along the x-direction and z-direction, the dynamic equations of the track bed are

[0009]

[0010] In the formula, ▽ 2 is the Laplace operator, ρ e is the ballast density, in kg / m 3 ;

[0011] Formula (4) and Formula (5) are derived for x and z respectively, then added and rearranged to obtain

[0012]

[0013] Define the function f(t) and The Fourier transform and inverse transform of time t and frequency Ω are

[0014]

[0015] Perform Fourier transform on equation (6) as shown in equation (7), and we get

[0016]

[0017] Define the function f(x) and The Fourier transform and inverse transform of displacement x and wave number ξ are

[0018]

[0019] Perform Fourier transform on equation (9) as shown in equation (10), and rearrange it to get

[0020]

[0021] Solve the differential equation shown in formula (12) and obtain its general solution:

[0022]

[0023] In the formula, A and B are coefficients determined according to the boundary conditions and continuity conditions of the roadbed and roadway floor.

[0024] Perform Fourier transform on equation (4) as shown in equation (7) and equation (10), and rearrange it to get

[0025]

[0026] Solve the differential equation shown in formula (14) and obtain its general solution:

[0027]

[0028] In the formula, C and D are coefficients determined according to the boundary conditions and continuity conditions of the roadbed and roadway floor.

[0029] Substituting equation (13) into equation (14) and rearranging it, we get

[0030]

[0031] Solving the differential equation (16) in the frequency-wavenumber domain yields

[0032]

[0033] For θ in formula (1) e Perform Fourier transform as shown in equation (7) and equation (10), and we get

[0034]

[0035] Substituting equation (13) and equation (17) into equation (18) and rearranging them, we get

[0036]

[0037] In the formula,

[0038] Perform Fourier transform on equation (1), equation (2) and equation (3) as shown in equation (7) and equation (10), respectively, and we get

[0039]

[0040] Substituting equations (13), (17) and (19) into equations (20), (21) and (22), we can obtain the stress of the roadbed in the frequency-wavenumber domain:

[0041]

[0042] The tunnel floor is regarded as a two-phase saturated porous medium, and its dynamic equation is:

[0043]

[0044] Where, λ and μ are the Lame constants of the solid phase skeleton of the tunnel floor, in Pa; u x 、u z u x (x,z,t) and u z The simplified expression of (x,z,t) means the displacement of the solid skeleton particle of the tunnel floor at the coordinate (x,z) along the x and z directions at time t, in units of m; w x 、w z They are wx (x,z,t) and w z The simplified expression of (x,z,t) is the seepage displacement of the pore fluid in the tunnel floor at the coordinate (x,z) at time t along the x and z directions, in units of m; α is the compressibility coefficient of the solid skeleton of the tunnel floor; M is the compressibility parameter of the pore fluid in the tunnel floor, in units of N·m -2 ; b is the ratio of pore fluid viscosity to tunnel floor permeability coefficient, unit: kg·(m 3 ·s) -1 ;

[0045] ρ=(1-β)ρ s +βρ f , β is the porosity of the tunnel floor, ρ s and ρ f are the densities of the solid matrix and pore fluid of the tunnel floor, in kg / m 3 ; m = ρ f / β;

[0046] According to the saturated porous medium theory, the normal stress and shear stress of the tunnel floor along the x-direction and z-direction are

[0047]

[0048] In the formula, P is a simplified expression of P(x,z,t), which means the excess pore pressure of the pore fluid in the tunnel floor at the coordinate (x,z) at time t, in units of Pa, P = -αMθ-Mθ w ,

[0049] The excess pore pressure expression of the pore fluid in the tunnel floor is obtained as

[0050]

[0051] Substituting equation (33) into equation (26) and equation (27), we get

[0052]

[0053] Perform Fourier transform on equation (34), equation (35), equation (28), and equation (29) as shown in equation (7), and arrange them to obtain

[0054]

[0055] Substitute equation (38) and equation (39) into equation (36) and equation (37) respectively, and rearrange them to obtain

[0056]

[0057] In the formula,

[0058] Formula (40) and Formula (41) are derived with respect to x and z respectively, then added together and rearranged to obtain

[0059]

[0060] Formula (38) and Formula (39) are derived with respect to x and z respectively, then added together and rearranged to obtain

[0061]

[0062] Perform Fourier transform on equation (33) as shown in equation (7), and we get

[0063]

[0064] Substituting equation (44) into equation (43) and rearranging it, we get

[0065]

[0066] From formula (45), we can get

[0067]

[0068] Applying the Laplace operator to equation (45), we get

[0069]

[0070] Substituting equation (42) and equation (46) into equation (47) and rearranging them, we get

[0071]

[0072] In the formula,

[0073]

[0074] Perform Fourier transform on equation (47) as shown in equation (10), and rearrange it to obtain

[0075]

[0076] It can be seen from the actual working conditions that in the z direction, the tunnel floor extends downward from the surface. According to the actual working conditions, the tunnel floor is regarded as a semi-infinite space, so the general solution of the differential equation shown in formula (49) is

[0077]

[0078] In the formula, A1 and A2 are coefficients determined according to the boundary conditions and continuity conditions of the roadbed and roadway floor;

[0079]

[0080] Perform Fourier transform on equation (46) as shown in (10), and we get

[0081]

[0082] Substituting equation (50) into equation (51), we get

[0083]

[0084] In the formula,

[0085] Perform Fourier transform on equation (41) as shown in equation (10), and we get

[0086]

[0087] Substituting equation (50) and equation (52) into equation (53) and rearranging them, we get

[0088]

[0089] Solving the differential equation shown in equation (54) in the frequency-wavenumber domain yields

[0090]

[0091] Where A3 is a coefficient determined based on the boundary conditions and continuity conditions of the roadbed and roadway floor.

[0092]

[0093] The tunnel floor is considered as a semi-infinite space, so,

[0094]

[0095] Perform Fourier transform on θ in equation (30) as shown in equation (7) and equation (10), and we get

[0096]

[0097] Substituting equation (52) and equation (55) into equation (57) and rearranging them, we get

[0098]

[0099] Perform Fourier transform on equations (30), (31) and (32) as shown in equations (7) and (10), respectively, and we get

[0100]

[0101] Substituting equations (50), (52), (55) and (58) into equations (59), (60) and (61), we can obtain the stress of the tunnel floor in the frequency-wavenumber domain:

[0102]

[0103]

[0104] When measuring the vertical stiffness of the ballast and the roadway floor, it is necessary to apply a downward force to the ballast on the sleeper. It can be seen that when z = 0, the boundary condition of the ballast surface is

[0105]

[0106] Where F0 is the pressure applied to the sleeper during the measurement, in N; A0 is the contact area between the sleeper and the ballast, in m 2 ;δ(x) is the Dirac delta function, when x=0,δ(x)=1, when x≠0,δ(x)=0;x j is the horizontal coordinate of the pressure application position in the xOz coordinate system during the measurement process;

[0107] It can be seen from the actual working conditions that the ballast bed and the roadway floor remain continuous at their interface. Therefore, at the interface between the ballast bed and the roadway floor (z = h, h is the ballast bed thickness, unit m), the continuity condition between the bottom surface of the ballast bed and the surface of the roadway floor is

[0108]

[0109] The tunnel floor surface is the permeable boundary, that is,

[0110] P(x,h,t)=0 Formula (71)

[0111] The boundary conditions of the ballast surface and the continuity conditions between its bottom surface and the roadway floor surface are subjected to Fourier transformation as shown in equations (7) and (10), and the frequency-wavenumber domain expression is obtained. Substituting z = 0 into equations (65) and (66), and substituting z = h into equations (67), (68), (69), (70), and (71), we obtain

[0112]

[0113]

[0114] Substituting the mechanical performance parameters and physical performance parameters related to the roadbed and roadway bottom plate into equations (72), (73), (74), (75), (76), (77) and (78) respectively, and solving them jointly, we can obtain the values ​​of coefficients A, B, C, D, A1, A2 and A3;

[0115] Substituting the obtained coefficients A, B, C, and D into equation (19), we obtain The expression of ; Substituting z = 0 into The expression of , and the inverse Fourier transform is performed on it as shown in equations (8) and (11), and the displacement of the point on the surface (z = 0) of the ballast bed in the time-space domain along the z direction is obtained as

[0116]

[0117] In formula (79) is a function of the mechanical and physical properties of the ballast and roadway floor, the surface force F0 of the ballast, and the contact area A0 between the sleeper and the ballast. Extract the common factor about F0, and we get

[0118]

[0119] In the formula, the integrand is includes the mechanical properties parameters and physical properties parameters related to the roadbed and roadway bottom plate; from formula (80), we get

[0120]

[0121] Formula (81) is the value at the measurement position x j The vertical stiffness calculation formula of the roadbed and roadway floor is obtained by substituting the mechanical performance parameters and physical performance parameters related to the roadbed and roadway floor into formula (81). In formula (81), the independent variables of the integrand are ξ and Ω. MATLAB is used to calculate the value of the denominator in formula (81). First, the value range and the number of discretization points of the independent variables ξ and Ω are defined. The linspace function is used to create an equally spaced array. On this basis, the meshgrid function is used to generate a grid. Finally, the fft function of MATLAB is used to solve the numerical solution of the denominator in formula (81) to obtain the vertical stiffness values ​​of the roadbed and the roadway floor.

[0122] Compared with the existing method of obtaining the vertical stiffness of mine roadbed and tunnel floor based on experience, the calculation method provided by the present invention can comprehensively consider the influence of the physical and mechanical performance parameters of the roadbed and tunnel floor on the vertical stiffness, which is conducive to analyzing the vertical stiffness of mine roadbed and tunnel floor under different laying conditions and different surrounding rock conditions, and can provide more reasonable parameters for engineering design and dynamic analysis in related fields. BRIEF DESCRIPTION OF THE DRAWINGS

[0123] Figure 1 It is a schematic diagram of the mine track structure;

[0124] Figure 2 It is the xOz coordinate system established in the mine track structure schematic diagram;

[0125] Figure 3 is a schematic diagram of the test system;

[0126] Figure 4 It is the schematic diagram of data acquisition in the test system;

[0127] Figure 5 It is a schematic diagram of the connection between each sensor and the programmable logic controller PLC and computer in the test system;

[0128] Explanation of the accompanying figures: tunnel floor 1, ballast bed 2, sleeper 3, rail 4, left flat beam 5, left displacement sensor 6, cylinder 7, pressure sensor 8, curved pad 9, piston 10, first valve 11, second valve 12, manual pump 13, third valve 14, fourth valve 15, oil tank 16, right flat beam 17, right displacement sensor 18, pad 19, fastener 20, programmable logic controller PLC 21 (consisting of CPU module and analog module), power supply 22, computer 23. DETAILED DESCRIPTION

[0129] It can be seen from the actual working conditions that the roadbed is composed of ballast with uniform particle size, and the size of the ballast particles is much smaller than that of the roadbed. From the theory of granular mechanics, it can be seen that the roadbed can be regarded as an elastic medium; the tunnel floor is composed of solid rock containing pores and fluid filling the pores. The mine tunnels are buried deep and the floor saturation is usually high, so it can be regarded as a two-phase saturated porous medium.

[0130] The present invention will be described in detail from several aspects below

[0131] 1. Dynamic characteristics of track bed

[0132] When the vehicle is running, the vertical load can easily cause the roadbed and the roadway floor to produce large vertical deformation, and the vertical deformation is much larger than its lateral deformation. Therefore, when calculating the vertical stiffness, the mine track is regarded as a two-dimensional structure. Figure 2The xOz coordinate system is established in the schematic diagram of the mine track structure shown in the figure. The origin O is located on the surface of the track bed, the Ox axis is parallel to the length direction of the track, and the Oz axis is vertically downward. According to the elasticity theory, the normal stress and shear stress of the track bed along the x and z directions are respectively

[0133]

[0134] In the formula, They are The simplified expression of λ is the displacement of a particle with coordinates (x, z) on the track bed along the x and z directions at time t, in units of m; e , μ e is the Lame constant of the ballast, in Pa;

[0135] Along the x-direction and z-direction, the dynamic equations of the track bed are

[0136]

[0137] In the formula, ▽ 2 is the Laplace operator, ρ e is the ballast density, in kg / m 3 ;

[0138] Formula (4) and Formula (5) are derived for x and z respectively, then added and rearranged to obtain

[0139]

[0140] Define the function f(t) and The Fourier transform and inverse transform of time t and frequency Ω are

[0141]

[0142] Perform Fourier transform on equation (6) as shown in equation (7), and we get

[0143]

[0144] Define the function f(x) and The Fourier transform and inverse transform of displacement x and wave number ξ are

[0145]

[0146] Perform Fourier transform on equation (9) as shown in equation (10), and rearrange it to get

[0147]

[0148] Solve the differential equation shown in formula (12) and obtain its general solution:

[0149]

[0150] In the formula, A and B are coefficients determined according to the boundary conditions and continuity conditions of the roadbed and roadway floor.

[0151] Perform Fourier transform on equation (4) as shown in equation (7) and equation (10), and rearrange it to get

[0152]

[0153] Solve the differential equation shown in formula (14) and obtain its general solution:

[0154]

[0155] In the formula, C and D are coefficients determined according to the boundary conditions and continuity conditions of the roadbed and roadway floor.

[0156] Substituting equation (13) into equation (14) and rearranging it, we get

[0157]

[0158] Solving the differential equation (16) in the frequency-wavenumber domain yields

[0159]

[0160] For θ in formula (1) e Perform Fourier transform as shown in equation (7) and equation (10), and we get

[0161]

[0162] Substituting equation (13) and equation (17) into equation (18) and rearranging them, we get

[0163]

[0164] In the formula,

[0165] Perform Fourier transform on equation (1), equation (2) and equation (3) as shown in equation (7) and equation (10), respectively, and we get

[0166]

[0167] Substituting equations (13), (17) and (19) into equations (20), (21) and (22), we can obtain the stress of the roadbed in the frequency-wavenumber domain:

[0168]

[0169] 2. Dynamic characteristics of tunnel floor

[0170] As mentioned above, the tunnel floor is regarded as a two-phase saturated porous medium, and its dynamic equation is:

[0171]

[0172] Where, λ and μ are the Lame constants of the solid phase skeleton of the tunnel floor, in Pa; u x 、u z u x (x,z,t) and u z The simplified expression of (x,z,t) means the displacement of the solid skeleton particle of the tunnel floor at the coordinate (x,z) along the x and z directions at time t, in units of m; w x 、w z They are w x (x,z,t) and w z The simplified expression of (x,z,t) is the seepage displacement of the pore fluid in the tunnel floor at the coordinate (x,z) at time t along the x and z directions, in units of m; α is the compressibility coefficient of the solid skeleton of the tunnel floor; M is the compressibility parameter of the pore fluid in the tunnel floor, in units of N·m -2 ; b is the ratio of pore fluid viscosity to tunnel floor permeability coefficient, unit: kg·(m 3 ·s) -1 ;

[0173] ρ=(1-β)ρ s +βρ f , β is the porosity of the tunnel floor, ρ s and ρ f are the densities of the solid matrix and pore fluid of the tunnel floor, in kg / m 3 ; m = ρ f / β;

[0174] According to the saturated porous medium theory, the normal stress and shear stress of the tunnel floor along the x-direction and z-direction are

[0175]

[0176] In the formula, P is a simplified expression of P(x,z,t), which means the excess pore pressure of the pore fluid in the tunnel floor at the coordinate (x,z) at time t, in units of Pa, P = -αMθ-Mθw ,

[0177] The excess pore pressure expression of the pore fluid in the tunnel floor is obtained as

[0178]

[0179] Substituting equation (33) into equation (26) and equation (27), we get

[0180]

[0181] Perform Fourier transform on equation (34), equation (35), equation (28), and equation (29) as shown in equation (7), and arrange them to obtain

[0182]

[0183] Substitute equation (38) and equation (39) into equation (36) and equation (37) respectively, and rearrange them to obtain

[0184]

[0185]

[0186] In the formula,

[0187] Formula (40) and Formula (41) are derived with respect to x and z respectively, then added together and rearranged to obtain

[0188]

[0189] Formula (38) and Formula (39) are derived with respect to x and z respectively, then added together and rearranged to obtain

[0190]

[0191] Perform Fourier transform on equation (33) as shown in equation (7), and we get

[0192]

[0193] Substituting equation (44) into equation (43) and rearranging it, we get

[0194]

[0195] From formula (45), we can get

[0196]

[0197] Applying the Laplace operator to equation (45), we get

[0198]

[0199] Substituting equation (42) and equation (46) into equation (47) and rearranging them, we get

[0200]

[0201] In the formula,

[0202] Perform Fourier transform on equation (47) as shown in equation (10), and rearrange it to obtain

[0203]

[0204] It can be seen from the actual working conditions that in the z direction, the tunnel floor extends downward from the surface. According to the actual working conditions, the tunnel floor is regarded as a semi-infinite space, so the general solution of the differential equation shown in formula (49) is

[0205]

[0206] In the formula, A1 and A2 are coefficients determined according to the boundary conditions and continuity conditions of the roadbed and roadway floor;

[0207]

[0208] Perform Fourier transform on equation (46) as shown in (10), and we get

[0209]

[0210] Substituting equation (50) into equation (51), we get

[0211]

[0212] In the formula,

[0213] Perform Fourier transform on equation (41) as shown in equation (10), and we get

[0214]

[0215] Substituting equation (50) and equation (52) into equation (53) and rearranging them, we get

[0216]

[0217] Solving the differential equation shown in equation (54) in the frequency-wavenumber domain yields

[0218]

[0219] Where A3 is a coefficient determined based on the boundary conditions and continuity conditions of the roadbed and roadway floor.

[0220]

[0221] As mentioned above, the tunnel floor is regarded as a semi-infinite space, so,

[0222]

[0223] Perform Fourier transform on θ in equation (30) as shown in equation (7) and equation (10), and we get

[0224]

[0225] Substituting equation (52) and equation (55) into equation (57) and rearranging them, we get

[0226]

[0227] Perform Fourier transform on equations (30), (31) and (32) as shown in equations (7) and (10), respectively, and we get

[0228]

[0229] Substituting equations (50), (52), (55) and (58) into equations (59), (60) and (61), we can obtain the stress of the tunnel floor in the frequency-wavenumber domain:

[0230]

[0231] In the present invention, when measuring the vertical stiffness of the ballast and the roadway floor, a downward force needs to be applied to the ballast on the sleeper. It can be seen that when z = 0, the boundary condition of the ballast surface is

[0232]

[0233] Where F0 is the pressure applied to the sleeper during the measurement, in N; A0 is the contact area between the sleeper and the ballast, in m 2 ;δ(x) is the Dirac delta function, when x=0,δ(x)=1, when x≠0,δ(x)=0;x j It is the abscissa of the pressure application position in the xOz coordinate system during the measurement.

[0234] 3. Boundary conditions and continuity conditions of roadbed and roadway floor

[0235] It can be seen from the actual working conditions that the ballast bed and the roadway floor remain continuous at their interface. Therefore, at the interface between the ballast bed and the roadway floor (z = h, h is the ballast bed thickness, unit m), the continuity condition between the bottom surface of the ballast bed and the surface of the roadway floor is

[0236]

[0237] As mentioned above, the roadbed is composed of ballast. The pores between the ballast are much larger than the pores of the solid phase of the roadway floor. The pore fluid of the roadway floor can move on its surface, so the surface of the roadway floor is a permeable boundary, that is,

[0238] P(x,h,t)=0 Formula (71)

[0239] The boundary conditions of the ballast surface and the continuity conditions between its bottom surface and the roadway floor surface are subjected to Fourier transformation as shown in equations (7) and (10), and the frequency-wavenumber domain expression is obtained. Substituting z = 0 into equations (65) and (66), and substituting z = h into equations (67), (68), (69), (70), and (71), we obtain

[0240]

[0241] Substituting the mechanical properties parameters related to the roadbed and tunnel floor (such as Lame constant, compressibility parameters of the solid-liquid two-phase of the tunnel floor) and physical properties parameters (such as density, pore fluid viscosity, porosity) into equations (72), (73), (74), (75), (76), (77) and (78), respectively, and solving them jointly, we can obtain the values ​​of coefficients A, B, C, D, A1, A2, and A3.

[0242] 4. Vertical stiffness calculation

[0243] Substituting the obtained parameters A, B, C, and D into equation (19), we can obtain in the frequency-wavenumber domain: The expression of ; Substituting z = 0 into By performing inverse Fourier transform as shown in equations (8) and (11), the displacement of a point on the surface (z = 0) of the ballast bed in the time-space domain along the z direction can be obtained as

[0244]

[0245] From the above analysis, we can see that in formula (79) is a function of the mechanical properties of the roadbed and roadway floor (e.g., Lame constant, compressibility parameters of the solid-liquid phase of the roadway floor), physical properties (e.g., density, pore fluid viscosity, porosity), the roadbed surface force F0, and the contact area A0 between the sleeper and the roadbed. Extract the common factor about F0, and we get

[0246]

[0247] In the formula, the integrand is It includes mechanical performance parameters and physical performance parameters related to the roadbed and roadway bottom plate.

[0248] From formula (80), we can get

[0249]

[0250] Formula (81) is the value at the measurement position x j The vertical stiffness calculation formula of the roadbed and the roadway floor is obtained by substituting the mechanical properties parameters (such as Lame constant, compressibility coefficient of solid-liquid phase of the roadway floor) and physical properties parameters (such as density, pore fluid viscosity, porosity) related to the roadbed and the roadway floor into formula (81): In equation (81), the independent variables of the integrand are ξ and Ω. Using MATLAB to calculate the value of the denominator in equation (81), first define the value range and number of discretization points of the independent variables ξ and Ω, use the linspace function to create an equally spaced array, use the meshgrid function to generate a grid, and finally, use MATLAB's fft function to solve the numerical solution of the denominator in equation (81) to obtain the vertical stiffness values ​​of the roadbed and roadway floor.

[0251] 5. Vertical stiffness calibration system for roadbed and roadway floor

[0252] In order to verify the vertical stiffness value calculated according to formula (81), the corresponding test system in the present invention is as follows: Figure 3 As shown in Figure 2, the principle of collecting measurement data is as follows: Figure 4 As shown, all components and parts in the test system meet the explosion-proof requirements of coal mines.

[0253] Before measurement, select an appropriate measurement position in the tunnel, remove the fastener 20 between the corresponding sleeper 3 and the rail 4 at the measurement position, place the pad 19 in the middle of the sleeper 3 with the fastener removed, fix one end of the left flat beam 5 and the right flat beam 17 on the side wall of the tunnel near the selected measurement position, install the left displacement sensor 6 (model HG-C1200) and the right displacement sensor 18 (model HG-C1200) on the protruding ends of the left flat beam 5 and the right flat beam 17, adjust the left displacement sensor 6 (model HG-C1200) and the right displacement sensor 18 (model HG-C1200) to the left and right sides of the measuring position, and adjust the left displacement sensor 6 (model HG-C1200) to the right and left sides of the measuring position. ) and the right displacement sensor 18 (model HG-C1200), ensure that their probes are facing the surface of the pad 19, and make the distance between the left displacement sensor 6 (model HG-C1200), the right displacement sensor 18 (model HG-C1200) and the pad 19 less than 200mm, place the cylinder 7 of the hydraulic support in the middle of the pad 19, put the arc surface pad 9 on the top of the piston 10 of the hydraulic support, drive the manual pump 13 (model PL201), when the piston 10 rises, the arc surface pad 9 contacts with the roof of the tunnel.

[0254] like Figure 5 As shown, the positive and negative poles of the 24V power supply 22 are respectively connected to the L pole and M pole of the CPU module (model SIEMENS200Smart T40) of the programmable logic controller PLC21 to supply power to the programmable logic controller PLC21.

[0255] The L and M poles of the left displacement sensor 6 (model HG-C1200) are respectively connected to the positive and negative poles of the power supply 22. The positive and negative poles of the signal output terminal of the left displacement sensor 6 (model HG-C1200) are respectively connected to the 0+ port and 0- port of the programmable logic controller PLC21 analog module (model EM AM06).

[0256] The L and M poles of the right displacement sensor 18 (model HG-C1200) are respectively connected to the positive and negative poles of the power supply 22. The positive and negative poles of the signal output terminal of the right displacement sensor 18 (model HG-C1200) are respectively connected to the 1+ port and 1- port of the analog module (model EM AM06) of the programmable logic controller PLC21.

[0257] The positive pole of the pressure sensor 8 (model MIK-P310) is connected to the positive pole of the power supply 22, the negative pole of the pressure sensor 8 (model MIK-P310) is connected to the 2+ port of the programmable logic controller PLC21 analog module (model EM AM06), and the 2- port of the programmable logic controller PLC21 analog module (model EM AM06) is connected to the negative pole of the power supply 22.

[0258] During measurement, the second valve 12 (model XYF-QFT1-SK) and the fourth valve 15 (model XYF-QFT1-SK) are closed, the first valve 11 (model XYF-QFT1-SK) and the third valve 14 (model XYF-QFT1-SK) are opened, the manual pump 13 (model PL201) is driven steadily, the hydraulic support piston 10 gradually rises, the programmable logic controller PLC21 receives the signals from each sensor, and when the pressure sensor 8 (model MIK-P310 ) shows that the pressure is about 1MPa, the hydraulic prop has compressed the cambered pad 9 and the pad 19, and the roadbed 2 and the roadway bottom plate 1 have been deformed to a certain extent. Continue to drive the manual pump 13 (model PL201) steadily, and the pressure value of the pressure sensor 8 (model MIK-P310) increases accordingly. The stress and deformation of the roadbed 2 and the roadway bottom plate 1 also increase accordingly. When the pressure value of the pressure sensor 8 (model MIK-P310) increases by about 0.5MPa on the original basis, stop driving the manual pump 13 (model PL201). PL201), after the pressure value of the pressure sensor 8 (model MIK-P310) is stabilized, the computer 23 is used to record the current measurement data of the pressure sensor 8 (model MIK-P310), the left displacement sensor 6 (model HG-C1200) and the right displacement sensor 18 (model HG-C1200); then, the manual pump 13 (model PL201) is driven steadily, and when the pressure value of the pressure sensor 8 (model MIK-P310) increases by about 0.5MPa, the manual pump 13 (model PL201) is driven again. The manual pump 13 (model PL201) is temporarily driven, and after the pressure value of the pressure sensor 8 (model MIK-P310) is stabilized, the measurement data of the pressure sensor 8 (model MIK-P310), the left displacement sensor 6 (model HG-C1200) and the right displacement sensor 18 (model HG-C1200) are recorded again using the computer 23. This process is repeated until the pressure value of the pressure sensor 8 (model MIK-P310) is about 4 MPa, and a total of 6 sets of pressure and displacement values ​​are recorded. When the pressure value of the pressure sensor 8 (model MIK-P310) reaches 4 MPa and the last data recording is completed, close the first valve 11 (model XYF-QFT1-SK) and the third valve 14 (model XYF-QFT1-SK), open the second valve 12 (model XYF-QFT1-SK) and the fourth valve 15 (model XYF-QFT1-SK), drive the manual pump 13 (model PL201), and gradually shrink the piston 10 of the hydraulic support into its cylinder 7 to complete the experiment.

[0259] It can be seen from the actual working conditions that the sleepers used in mine tracks are concrete sleepers, which have a large stiffness and the influence on the measurement can be ignored. The vertical stiffness of the roadbed and the roadway floor is calculated using the measured data:

[0260]

[0261] Where P j is the jth measured value of the pressure sensor, in Pa; d is the inner diameter of the hydraulic support cylinder, in m; d lj d rj They are Figure 3 The j-th measurement value of the left displacement sensor 6 and the right displacement sensor 18.

[0262] Comparison test results of the stiffness coefficient k t The calculated stiffness coefficient k f If the relative difference between the two is less than 5%, the calculation result is considered reasonable and can be used for engineering design and related theoretical research; otherwise, it must be recalculated.

Claims

1. A method for calculating the vertical stiffness of mine roadbed and tunnel floor, characterized in that: In the schematic diagram of the mine track structure, the xOz coordinate system is established. The origin O is located on the surface of the track bed. The Ox axis is parallel to the length direction of the track, and the Oz axis is vertically downward. According to the structural characteristics of the track bed, it is regarded as an elastic medium. From the elasticity theory, it can be known that the normal stress of the track bed along the x direction and the z direction, as well as the shear stress are respectively In the formula, They are The simplified expression of λ is the displacement of a particle with coordinates (x, z) on the track bed along the x and z directions at time t, in units of m; e , μ e is the Lame constant of the ballast, in Pa; Along the x-direction and z-direction, the dynamic equations of the track bed are In the formula, ▽ 2 is the Laplace operator, ρ e is the ballast density, in kg / m 3 ; Formula (4) and Formula (5) are derived for x and z respectively, then added and rearranged to obtain Define the function f(t) and The Fourier transform and inverse transform of time t and frequency Ω are Perform Fourier transform on equation (6) as shown in equation (7), and we get Define the function f(x) and The Fourier transform and inverse transform of displacement x and wave number ξ are Perform Fourier transform on equation (9) as shown in equation (10), and rearrange it to get Solve the differential equation shown in formula (12) and obtain its general solution: In the formula, A and B are coefficients determined according to the boundary conditions and continuity conditions of the roadbed and roadway floor. Perform Fourier transform on equation (4) as shown in equation (7) and equation (10), and rearrange it to get Solve the differential equation shown in formula (14) and obtain its general solution: In the formula, C and D are coefficients determined according to the boundary conditions and continuity conditions of the roadbed and roadway floor. Substituting equation (13) into equation (14) and rearranging it, we get Solving the differential equation (16) in the frequency-wavenumber domain yields For θ in formula (1) e Perform Fourier transform as shown in equation (7) and equation (10), and we get Substituting equation (13) and equation (17) into equation (18) and rearranging them, we get In the formula, Perform Fourier transform on equation (1), equation (2) and equation (3) as shown in equation (7) and equation (10), respectively, and we get Substituting equations (13), (17) and (19) into equations (20), (21) and (22), we can obtain the stress of the roadbed in the frequency-wavenumber domain: The tunnel floor is regarded as a two-phase saturated porous medium, and its dynamic equation is: Where, λ and μ are the Lame constants of the solid phase skeleton of the tunnel floor, in Pa; u x 、u z u x (x,z,t) and u z The simplified expression of (x,z,t) means the displacement of the solid skeleton particle of the tunnel floor at the coordinate (x,z) along the x and z directions at time t, in units of m; w x 、w z They are w x (x,z,t) and w z The simplified expression of (x,z,t) is the seepage displacement of the pore fluid in the tunnel floor at the coordinate (x,z) at time t along the x and z directions, in units of m; α is the compressibility coefficient of the solid skeleton of the tunnel floor; M is the compressibility parameter of the pore fluid in the tunnel floor, in units of N·m -2 ; b is the ratio of pore fluid viscosity to tunnel floor permeability coefficient, unit: kg·(m 3 ·s) -1 ; ρ=(1-β)ρ s +βρ f , β is the porosity of the tunnel floor, ρ s and ρ f are the densities of the solid matrix and pore fluid of the tunnel floor, in kg / m 3 ; m = ρ f / β; According to the saturated porous medium theory, the normal stress and shear stress of the tunnel floor along the x-direction and z-direction are In the formula, P is a simplified expression of P(x,z,t), which means the excess pore pressure of the pore fluid in the tunnel floor at the coordinate (x,z) at time t, in units of Pa, P = -αMθ-Mθ w , The excess pore pressure expression of the pore fluid in the tunnel floor is obtained as Substituting equation (33) into equation (26) and equation (27), we get Perform Fourier transform on equation (34), equation (35), equation (28), and equation (29) as shown in equation (7), and arrange them to obtain Substitute equation (38) and equation (39) into equation (36) and equation (37) respectively, and rearrange them to obtain In the formula, Formula (40) and Formula (41) are derived with respect to x and z respectively, then added together and rearranged to obtain Formula (38) and Formula (39) are derived with respect to x and z respectively, then added and rearranged to obtain Perform Fourier transform on equation (33) as shown in equation (7), and we get Substituting equation (44) into equation (43) and rearranging it, we get From formula (45), we can get Applying the Laplace operator to equation (45), we get Substituting equation (42) and equation (46) into equation (47) and rearranging them, we get In the formula, Perform Fourier transform on equation (47) as shown in equation (10), and rearrange it to obtain It can be seen from the actual working conditions that in the z direction, the tunnel floor extends downward from the surface. According to the actual working conditions, the tunnel floor is regarded as a semi-infinite space, so the general solution of the differential equation shown in formula (49) is In the formula, A1 and A2 are coefficients determined according to the boundary conditions and continuity conditions of the roadbed and roadway floor; Perform Fourier transform on equation (46) as shown in (10), and we get Substituting equation (50) into equation (51), we get In the formula, Perform Fourier transform on equation (41) as shown in equation (10), and we get Substituting equation (50) and equation (52) into equation (53) and rearranging them, we get Solving the differential equation shown in equation (54) in the frequency-wavenumber domain yields Where A3 is a coefficient determined based on the boundary conditions and continuity conditions of the roadbed and roadway floor. The tunnel floor is considered as a semi-infinite space, so, Perform Fourier transform on θ in equation (30) as shown in equation (7) and equation (10), and we get Substituting equation (52) and equation (55) into equation (57) and rearranging them, we get Perform Fourier transform on equations (30), (31) and (32) as shown in equations (7) and (10), respectively, and we get Substituting equations (50), (52), (55) and (58) into equations (59), (60) and (61), we can obtain the stress of the tunnel floor in the frequency-wavenumber domain: When measuring the vertical stiffness of the ballast and the roadway floor, it is necessary to apply a downward force to the ballast on the sleeper. It can be seen that when z = 0, the boundary condition of the ballast surface is Where F0 is the pressure applied to the sleeper during the measurement, in N; A0 is the contact area between the sleeper and the ballast, in m 2 ;δ(x) is the Dirac delta function, when x=0,δ(x)=1, when x≠0,δ(x)=0;x j is the horizontal coordinate of the pressure application position in the xOz coordinate system during the measurement process; It can be seen from the actual working conditions that the roadbed and the roadway floor are continuous at their interface, so at the interface between the roadbed and the roadway floor, that is, z = h, h is the roadbed thickness, unit m; the continuity condition between the roadbed bottom surface and the roadway floor surface is The tunnel floor surface is the permeable boundary, that is, P(x,h,t)=0 Formula (71) The boundary conditions of the ballast surface and the continuity conditions between its bottom surface and the roadway floor surface are subjected to Fourier transformation as shown in equations (7) and (10), and the frequency-wavenumber domain expression is obtained. Substituting z = 0 into equations (65) and (66), and substituting z = h into equations (67), (68), (69), (70), and (71), we obtain Substitute the mechanical performance parameters and physical performance parameters related to the roadbed and roadway floor into equations (72), (73), (74), (75), (76), (77) and (78) respectively, and solve them jointly to obtain the values ​​of coefficients A, B, C, D, A1, A2 and A3; Substituting the obtained coefficients A, B, C, and D into equation (19), we obtain The expression of z = 0 is substituted into The expression of , and the inverse Fourier transform is performed on it as shown in equations (8) and (11), and the displacement of the point on the surface (z = 0) of the ballast bed in the time-space domain along the z direction is obtained as In formula (79) is a function of the mechanical and physical properties of the ballast and roadway floor, the surface force F0 of the ballast, and the contact area A0 between the sleeper and the ballast. Extract the common factor about F0, and we get In the formula, the integrand is includes the mechanical properties parameters and physical properties parameters related to the roadbed and roadway bottom plate; from formula (80), we get Formula (81) is the value at the measurement position x j The vertical stiffness calculation formula of the roadbed and roadway floor is obtained by substituting the mechanical performance parameters and physical performance parameters related to the roadbed and roadway floor into formula (81). In formula (81), the independent variables of the integrand are ξ and Ω. MATLAB is used to calculate the value of the denominator in formula (81). First, the value range and the number of discretization points of the independent variables ξ and Ω are defined. The linspace function is used to create an equally spaced array. On this basis, the meshgrid function is used to generate a grid. Finally, the fft function of MATLAB is used to solve the numerical solution of the denominator in formula (81) to obtain the vertical stiffness values ​​of the roadbed and the roadway floor.

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