Inverse calculation method of equivalent wind speed based on failure mode of concrete pole structure under local strong wind

Abstract

The application discloses a kind of equivalent wind speed inversion calculation methods based on local strong wind under concrete pole type structure failure mode, comprising the following steps: step one: determine local strong wind type, obtain the base bending moment and shear force under different wind speeds;Root ultimate resistance R1 is calculated;Step two: with root ultimate resistance R1 as base equivalent bending moment, equivalent wind speed V1 under root fracture failure mode is obtained by inversion calculation;The inclination angle of concrete pole type structure under different wind speeds is calculated, and wind speed-inclination angle curve is obtained;With the limit maximum value of wind speed as the equivalent wind speed V2 under overturning failure mode;The inclination angle and wind speed corresponding to any point on wind speed-inclination angle curve are used as the equivalent wind speed V3 under inclination failure mode when corresponding inclination angle;Step three: the mapping relationship between the characteristic wind speed and the three failure modes of concrete pole type structure is established, and the equivalent wind speed of local strong wind is obtained by inversion calculation combined with the damage situation of concrete pole type structure after disaster.

Description

Technical Field

[0001] This invention belongs to the field of wind load calculation technology, specifically a method for equivalent wind speed inversion calculation based on the failure mode of concrete pole structures under local strong winds. Background Technology

[0002] Localized strong winds are characterized by their small spatial scale, sudden onset, short duration, and high and rapidly changing wind speeds, such as tornadoes and downbursts. Therefore, localized strong winds are difficult to measure or capture with existing anemometers of sufficient strength and observation systems, making wind speed determination extremely challenging. This results in insufficient scientific rigor and objectivity in wind load calculations during structural design and modification, posing significant difficulties for the systematic prevention and control of related problems.

[0003] Post-disaster investigation is an effective technical means to analyze and assess local extreme strong wind fields. Based on the degree of structural damage and failure characteristics within the range of local strong winds, inversion analysis can be used to calculate key information such as the length and width of the local strong wind path, duration, and equivalent wind speed intensity. Concrete pole structures such as power transmission and distribution poles are among the most common disaster indicators under local strong winds. Their failure modes mainly manifest as three characteristics: root fracture, tilting, and overall overturning. Current equivalent wind speed inversion calculations only consider the single failure mode of root fracture and generally assume that the wind speed is uniform along the height direction. However, in reality, the magnitude and direction of local strong winds such as tornadoes and downbursts vary greatly along the height, making it impossible to accurately calculate the magnitude of local strong winds at the disaster site. Therefore, to improve the accuracy of local strong wind equivalent wind speed inversion calculations, a more refined and accurate inversion calculation algorithm needs to be established based on the characteristics of local strong wind loads and the failure modes of pole structures. Summary of the Invention

[0004] In view of this, the purpose of this invention is to provide an equivalent wind speed inversion calculation method based on the failure modes of concrete pole structures under local strong winds. Considering the three failure modes of concrete pole tilting, overall overturning and root fracture, and combining the variation of local strong wind speed in the height direction, the method can effectively improve the accuracy of the equivalent wind speed inversion calculation under local strong winds.

[0005] To achieve the above objectives, the present invention provides the following technical solution:

[0006] An equivalent wind speed inversion calculation method based on the failure mode of concrete pole structures under local strong winds includes the following steps:

[0007] Step 1: Determine the type of local strong wind and establish a mathematical model of wind speed vector distribution. Determine the wind speed at different locations and heights, and obtain the bending moment and shear force of the concrete pole structure foundation under different wind speeds.

[0008] Determine the dimensions and material parameters of the concrete pole structure, and calculate the ultimate resistance R1 at the root of the concrete pole structure;

[0009] Step 2: Calculate the equivalent wind speed of the concrete pole structure under three failure modes.

[0010] Using the ultimate resistance R1 at the root of the concrete pole structure as the equivalent bending moment of the concrete pole structure base, the equivalent wind speed V1 under the root fracture failure mode is obtained by inversion calculation.

[0011] Based on the lower dimensions, burial depth, and soil parameters of the concrete pole structure, the tilt angle of the concrete pole structure under different wind speeds is calculated, and the wind speed-tilt angle curve is obtained.

[0012] The maximum wind speed limit in the wind speed-tilt angle curve is taken as the equivalent wind speed V2 in the overturning failure mode;

[0013] The tilt angle and wind speed corresponding to any point on the wind speed-tilt angle curve are used as the equivalent wind speed V3 at the corresponding tilt angle in the tilt failure mode.

[0014] Step 3: Establish the mapping relationship between the characteristic wind speed at the set height location and the three failure modes of the concrete pole structure. Combined with the post-disaster damage to the concrete pole structure, the equivalent wind speed of the local strong wind is calculated by inversion.

[0015] Furthermore, the bending moment of the concrete pole-type structure foundation is:

[0016]

[0017]

[0018]

[0019] The shear force of the concrete rod-type structure foundation is:

[0020]

[0021]

[0022]

[0023] Where M represents the bending moment of the concrete beam structure foundation; M 切 M represents the base bending moment in the tangential direction of a concrete pole structure. 径 V represents the radial bending moment at the base of the concrete pole structure; V represents the shear force at the base of the concrete pole structure; V 切 V represents the base shear force in the tangential direction of a concrete beam structure. 径The base shear force in the radial direction of the concrete pole structure is represented by ρ, air density, G, and C. f D(z) is the drag coefficient of the concrete pole structure; D(z) is the diameter of the concrete pole structure along its height, where z represents a certain height of the concrete pole structure; H represents the overall height of the concrete pole structure; U 切 Indicates tangential wind speed; U 径 Indicates radial wind speed.

[0024] Furthermore, in step two, the method for constructing the wind speed-tilt angle curve includes the following steps:

[0025] S1: Determine the dimensions of the substructure and soil type of the concrete pole structure, and clarify the basic differential equations for the horizontally loaded pile locations:

[0026]

[0027] Where EI represents the bending stiffness of the pile section; k represents the secant modulus of the py curve at depth x; x represents the depth below the ground; and y represents the displacement of the pile body.

[0028] S2: Divide the concrete pole structure into n segments, each with a length of h. The pile body has n+1 points. The division points of each segment are replaced by the derivatives in the differential equation of the pole's elastic curve using finite difference form, transforming the basic differential equation into a set of algebraic difference equations:

[0029]

[0030] Among them, E sm The modulus of soil reaction is represented by h; the length of the element segment is represented by m = 0, 1, 2, ..., n.

[0031] S3: Determine the initial conditions for the top and bottom of the shaft, and randomly initialize E. sm The value of , where:

[0032] The initial conditions at the top of the shaft are:

[0033]

[0034]

[0035] The initial conditions at the bottom of the shaft are:

[0036] y -2 -2y -1 +2y1-y2=0

[0037] y -1 -2y0+y1=0

[0038] Where M0 represents the base bending moment of the concrete pole structure; V0 represents the base shear force of the concrete pole structure.

[0039] S4: Take advantage of E sm Solving the discrete system of equations yields the solution y. i ,i=-2,-1,0...,n,n+1,n+2;

[0040] S5: p can be calculated from the py curve. i , to obtain new E sm for:

[0041]

[0042] S6: Determine the E calculated in the current iteration step. sm E calculated in the previous iteration step sm Is the absolute value of the difference less than or equal to a set threshold? If yes, proceed to step S7; if no, proceed to step S4.

[0043] S7: Obtain the solution y at each point using discrete equations. m According to y m The value is used to determine the tilt angle at the top of the shaft:

[0044]

[0045]

[0046] Where H represents the height of the pole;

[0047] S8: Gradually increase the wind speed to obtain the wind speed-tilt angle curve of the concrete pole structure.

[0048] Furthermore, in step S5, the equation of the py curve is:

[0049]

[0050] k in =n hmax x

[0051] p u =N g γ s d 2-j (α0+x) j

[0052] Where, k in n is the modulus of ground reaction force; hmax These are parameters determined based on the internal friction angle and soil density; x is the depth from the soil surface; p u For ultimate resistance; N gThe ultimate resistance coefficient is K. p 2 linear function, K p γ is the passive earth pressure coefficient; s α is the soil unit weight; α0 is a constant reflecting the soil resistance or equivalent soil depth; j is the exponent between α0 and x; d is the pile diameter.

[0053] The beneficial effects of this invention are as follows:

[0054] This invention is applicable to the quantitative description of the equivalent wind speed of local strong winds such as downbursts and tornadoes based on post-disaster survey results. It provides a method for inverting and calculating the equivalent wind speed based on the failure modes of concrete pole structures under local strong winds. A mathematical model of wind speed vector distribution is established based on the characteristics of local strong wind types to calculate the root load effect value of the concrete pole structure caused by aerodynamic wind loads. The root resistance R1 is calculated based on the cross-sectional characteristics, geometric dimensions, and material properties of the concrete pole structure. Based on the stress characteristics of an elastic foundation beam model, a basic differential equation for the horizontally loaded foundation is established. Combined with basic information such as the foundation dimensions, soil conditions, and burial depth of the concrete pole structure, iterative solutions are obtained using the finite difference method to obtain the correspondence between the horizontal wind load caused by each level of wind speed and the tilt angle of the pole structure, as well as the critical wind speed V2 under overturning conditions. By progressively increasing the wind speed, a mapping relationship is formed between the characteristic wind speed at a set height and the failure mode of the concrete pole structure. Then, combined with the damage status of the concrete pole structure in the post-disaster survey data, the equivalent wind speed of the local strong winds is inverted and calculated. This invention relates to an equivalent wind speed inversion calculation method for concrete pole structures under localized strong winds. Considering three failure modes—concrete pole tilting, overall overturning, and root fracture—and combining the variation of localized strong wind speed in the height direction, it can effectively improve the accuracy of the equivalent wind speed inversion calculation for localized strong winds. Attached Figure Description

[0055] To make the objectives, technical solutions, and beneficial effects of this invention clearer, the following figures are provided for illustration:

[0056] Figure 1 This is a schematic diagram of the downburst wind profile;

[0057] Figure 2 The aerodynamic bending moment and root resistance of a concrete pole structure under the action of a downburst;

[0058] Figure 3 The wind speed-tilt angle curve of a concrete pole structure under the action of a downburst;

[0059] Figure 4 Here are schematic diagrams of a tornado model; (a) shows the radial wind speed variation curve along height; (b) shows the tangential wind speed variation curve along height.

[0060] Figure 5 The aerodynamic bending moment and root resistance of a concrete pole structure under the action of a tornado;

[0061] Figure 6 This is the wind speed-tilt angle curve of a concrete pole structure under the action of a tornado. Detailed Implementation

[0062] The present invention will be further described below with reference to the accompanying drawings and specific embodiments, so that those skilled in the art can better understand and implement the present invention. However, the embodiments described are not intended to limit the present invention.

[0063] This embodiment is based on the equivalent wind speed inversion calculation method for the failure mode of concrete pole structures under local strong winds, and includes the following steps.

[0064] Step 1: Determine the type of local strong wind and establish a mathematical model of wind speed vector distribution. Determine the wind speed at different locations and heights to obtain the bending moment and shear force of the concrete pole structure foundation under different wind speeds. The specific process is as follows:

[0065] (1) Determine the type of local strong wind;

[0066] (2) Establish a corresponding mathematical model of the vector distribution of local strong wind speed based on the determined local strong wind type;

[0067] (3) Determine the height, upper and lower diameters, concrete thickness, steel bar diameter, number of steel bars, and strength grades of steel bars and concrete for the concrete pole structure;

[0068] (4) Calculate the base bending moment and shear force of the concrete pole structure under different wind speeds based on the mathematical model of local strong wind speed vector distribution. Specifically, the base bending moment of the concrete pole structure is:

[0069]

[0070]

[0071]

[0072] The shear force of the concrete rod-type structure foundation is:

[0073]

[0074]

[0075]

[0076] Where M represents the bending moment of the concrete beam structure foundation; M 切M represents the base bending moment in the tangential direction of a concrete pole structure. 径 V represents the radial bending moment at the base of the concrete pole structure; V represents the shear force at the base of the concrete pole structure; V 切 V represents the base shear force in the tangential direction of a concrete beam structure. 径 The base shear force in the radial direction of the concrete pole structure is represented; ρ is the air density, taken as 1.225 kg / m³; G is the gust factor, which is calculated based on the gust speed over three seconds, taking 1.0, since the wind speed of local strong winds varies drastically with time; C f The drag coefficient of the concrete pole structure needs to consider the influence of the Reynolds number; D(z) is the diameter of the concrete pole structure along its height, where z represents a certain height of the concrete pole structure; H represents the overall height of the concrete pole structure; U 切 Indicates tangential wind speed; U 径 Indicates radial wind speed.

[0077] Determine the dimensions and material parameters of the concrete pole structure, and calculate the ultimate resistance R1 at the root of the concrete pole structure. The specific process is as follows:

[0078] (1) Determine the concrete thickness, steel bar diameter, steel bar quantity, and steel bar and concrete strength grade.

[0079] (2) Calculate the ultimate resistance R1 at the root of the concrete pole structure according to the specifications.

[0080] Step 2: Calculate the equivalent wind speed of the concrete pole structure under three failure modes.

[0081] (1) The root ultimate resistance R1 of the concrete pole structure is used as the equivalent bending moment of the concrete pole structure base, and the equivalent wind speed V1 under the root fracture failure mode is obtained by inversion calculation.

[0082] (2) Based on the lower dimensions, burial depth, and soil parameters (including soil type and foundation soil reaction coefficient) of the concrete pole structure, calculate the tilt angle of the concrete pole structure under different wind speeds to obtain the wind speed-tilt angle curve. Specifically, the steps for constructing the wind speed-tilt angle curve are as follows:

[0083] S1: Determine the dimensions of the substructure and soil type of the concrete pole structure, and clarify the basic differential equations for the horizontally loaded pile locations:

[0084]

[0085] Where EI represents the bending stiffness of the pile section; k represents the secant modulus of the py curve at depth x; x represents the depth below the ground; and y represents the displacement of the pile body.

[0086] S2: Divide the concrete pole structure into n segments, each with a length of h. The pile body has n+1 points. The division points of each segment are replaced by the derivatives in the differential equation of the pole's elastic curve using finite difference form, transforming the basic differential equation into a set of algebraic difference equations:

[0087]

[0088] Among them, E sm The modulus of soil reaction is represented by h; the length of the element segment is represented by m = 0, 1, 2, ..., n.

[0089] S3: Determine the initial conditions for the top and bottom of the shaft, and randomly initialize E. sm The value of , where:

[0090] The initial conditions at the top of the shaft (m=n) are:

[0091]

[0092]

[0093] The initial conditions at the bottom of the shaft (m=0) are:

[0094] y -2 -2y -1 +2y1-y2=0

[0095] y -1 -2y0+y1=0

[0096] Where M0 represents the base bending moment of the concrete pole structure; V0 represents the base shear force of the concrete pole structure.

[0097] S4: Take advantage of E sm Solving the discrete system of equations yields the solution y. i , i=-2,-1,0...,n,n+1,n+2.

[0098] S5: p can be calculated from the py curve. i , to obtain new E sm for:

[0099]

[0100] Specifically, the equation of the py curve is:

[0101]

[0102] k in =n hmax x

[0103] p u =Ng γ s d 2-j (α0+x) j

[0104] Where, k in n is the modulus of ground reaction force; hmax These are parameters determined based on the internal friction angle and soil density; x is the depth from the soil surface; p u For ultimate resistance; N g The ultimate resistance coefficient is K. p 2 linear function, K p The passive earth pressure coefficient is taken as N, based on the non-displacement soil construction method of the foundation. g = (0.55~2.5)K p 2 ;γ s α is the unit weight of the soil; α0 is a constant reflecting the resistance of the ground soil or the equivalent soil depth, which is taken as 0 according to relevant studies; j is the exponent between α0 and x, which is the shape parameter of the ultimate resistance, and is taken as 1.7 according to relevant studies; d is the diameter of the pile.

[0105] S6: Determine the E calculated in the current iteration step. sm E calculated in the previous iteration step sm Is the absolute value of the difference less than or equal to a set threshold? If yes, proceed to step S7; if no, proceed to step S4. The threshold in this embodiment is 0.0001.

[0106] S7: Obtain the solution y at each point using discrete equations. m According to y m The value is used to determine the tilt angle at the top of the shaft:

[0107]

[0108]

[0109] Where H represents the height of the pole.

[0110] S8: Gradually increase the wind speed to obtain the wind speed-tilt angle curve of the concrete pole structure.

[0111] (3) The maximum limit of wind speed in the wind speed-tilt angle curve is taken as the equivalent wind speed V2 in the overturning failure mode, and the tilt angle and wind speed corresponding to any point on the wind speed-tilt angle curve are taken as the equivalent wind speed V3 at the corresponding tilt angle in the tilt failure mode.

[0112] Step 3: Establish the mapping relationship between the characteristic wind speed at a set height (10m in this example) and the three failure modes of the concrete pole structure. Combined with the damage of the concrete pole structure after the disaster, the equivalent wind speed of the local strong wind is calculated by inversion.

[0113] The following section provides a more detailed description of the specific embodiments of the present invention, focusing on two typical types of localized strong winds: downbursts and tornadoes.

[0114] 1. Localized strong winds are downbursts.

[0115] This embodiment is based on the equivalent wind speed inversion calculation method for the failure mode of concrete pole structures under local strong winds, and includes the following steps.

[0116] Step 1: Determine the local strong wind type as a downburst, and calculate the bending moment and shear force of the concrete pole structure foundation under different wind speeds. The specific process is as follows:

[0117] (1) The local strong wind type was determined to be a downburst;

[0118] (2) Based on the determined local strong wind types, establish corresponding mathematical models for the vector distribution of local strong wind speeds, such as... Figure 1 As shown:

[0119]

[0120] Where V represents the wind speed at height z; V max The maximum wind speed is represented by δ; A, B, and C are known parameters. In this embodiment, A = 1.55, B = 1 / 6, and C = 0.7; δ is the height corresponding to the maximum wind speed; and z is the height above the ground.

[0121] (3) The concrete pole structure has a height of 8m, an upper diameter of 0.18 and a lower diameter of 0.24.

[0122] (4) Calculate the base bending moment and shear force of the concrete pole structure under different wind velocities based on the mathematical model of the wind speed vector distribution of downbursts. Specifically, the base bending moment of the concrete pole structure is:

[0123]

[0124] The shear force of the concrete rod-type structure foundation is:

[0125]

[0126] Where M represents the bending moment of the concrete beam structure foundation; M 切 M represents the base bending moment in the tangential direction of a concrete pole structure. 径V represents the radial bending moment at the base of the concrete pole structure; V represents the shear force at the base of the concrete pole structure; V 切 V represents the base shear force in the tangential direction of a concrete beam structure. 径 The base shear force in the radial direction of the concrete pole structure is represented; ρ is the air density, taken as 1.225 kg / m³; G is the gust factor, which is calculated based on the gust speed over three seconds, taking 1.0, since the wind speed of local strong winds varies drastically with time; C f The drag coefficient of the concrete pole structure needs to consider the influence of the Reynolds number; D(z) is the diameter of the concrete pole structure along its height, where z represents a certain height of the concrete pole structure; H represents the overall height of the concrete pole structure; U 切 Indicates tangential wind speed; U 径 Indicates radial wind speed.

[0127] Determine the dimensions and material parameters of the concrete pole structure, and calculate the ultimate resistance R1 at the root of the concrete pole structure. The specific process is as follows:

[0128] (1) The concrete thickness is 0.06 mm, the steel bar diameter is 5 mm, the number of steel bars is 12, the steel bar strength is Q235, the concrete strength is C50, and the concrete cover thickness is 0.02 mm.

[0129] (2) Calculate the ultimate resistance at the bottom of the concrete column structure. The ultimate bending moment of the normal section bearing capacity of the annular section concrete column structure under bending conditions is calculated according to the following formula:

[0130]

[0131] In the formula: R1 is the ultimate resistance at the bottom of the concrete pole structure; f ck f is the standard value of the axial compressive strength of concrete; yk A is the standard value of the tensile strength of the steel reinforcement; A is the area of ​​the annular cross-section; A s r1 is the total area of ​​longitudinal ordinary reinforcing bars; r2 is the inner radius of the annular section; r3 is the outer radius of the annular section; r4 is the total area of ​​longitudinal ordinary reinforcing bars. s α is the distance from the center of the longitudinal reinforcement to the center of the ring of the bar section; α is the ratio of the area of ​​the concrete compression zone to the total cross-sectional area, which can be calculated by the following formula: α=f yk A s / (2.5f yk A s +α1f cu A) α1 is a partial factor, taking 1.0 for strengths below C50 and 0.94 for strengths above C80. For intermediate strength grades, it can be directly interpolated. t α is the ratio of the cross-sectional area of ​​the tensile longitudinal reinforcement to the total cross-sectional area of ​​the longitudinal reinforcement. t =1-1.5α, when α>2 / 3, α t=0. The calculated ultimate bending moment R1 of the concrete beam structure is 11.19 kN·m. Figure 2 As shown.

[0132] Step 2: Calculate the equivalent wind speed of the concrete pole structure under three failure modes.

[0133] (1) The root ultimate resistance R1 of the concrete pole structure is used as the equivalent bending moment of the concrete pole structure base, and the equivalent wind speed V1 under the root fracture failure mode is obtained by inversion calculation.

[0134] (2) The concrete pole structure has a lower diameter of 0.24 mm, a burial depth of 0.8 mm, and uses sandy soil with a foundation reaction ratio of 10000. The inner diameter of the circular cross-section is 0.18 mm, and the passive earth pressure coefficient is 4.7. The tilt angle under different wind speeds is calculated to obtain the wind speed-tilt angle curve. Specifically, the steps for constructing the wind speed-tilt angle curve are as follows:

[0135] S1: Determine the dimensions of the substructure and soil type of the concrete pole structure, and clarify the basic differential equations for the horizontally loaded pile locations:

[0136]

[0137] Where EI represents the bending stiffness of the pile section; k represents the secant modulus of the py curve at depth x; x represents the depth below the ground; and y represents the displacement of the pile body.

[0138] S2: Divide the concrete pole structure into n segments, each with a length of h. The pile body has n+1 points. The division points of each segment are replaced by the derivatives in the differential equation of the pole's elastic curve using finite difference form, transforming the basic differential equation into a set of algebraic difference equations:

[0139]

[0140] Among them, E sm The modulus of soil reaction is represented by h; the length of the element segment is represented by m = 0, 1, 2, ..., n.

[0141] S3: Determine the initial conditions for the top and bottom of the shaft, and randomly initialize E. sm The value of , where:

[0142] The initial conditions at the top of the shaft are:

[0143]

[0144]

[0145] The initial conditions at the bottom of the shaft are:

[0146] y -2 -2y -1 +2y1-y2=0

[0147] y -1 -2y0+y1=0

[0148] Where M0 represents the base bending moment of the concrete pole structure; V0 represents the base shear force of the concrete pole structure.

[0149] S4: Take advantage of E sm Solving the discrete system of equations yields the solution y. i ,i=-2,-1,0...,n,n+1,n+2.

[0150] S5: p can be calculated from the py curve. i , to obtain new E sm for:

[0151]

[0152] Specifically, the equation of the py curve is:

[0153]

[0154] k in =n hmax x

[0155] p u =N g γ s d 2-j (α0+x) j

[0156] Where, k in n is the modulus of ground reaction force; hmax These are parameters determined based on the internal friction angle and soil density; x is the depth from the soil surface; p u For ultimate resistance; N g The ultimate resistance coefficient is K. p 2 linear function, K p The passive earth pressure coefficient is taken as N, based on the non-displacement soil construction method of the foundation. g = (0.55~2.5)K p 2 ;γ s α is the unit weight of the soil; α0 is a constant reflecting the resistance of the ground soil or the equivalent soil depth, which is taken as 0 according to relevant studies; j is the exponent between α0 and x, which is the shape parameter of the ultimate resistance, and is taken as 1.7 according to relevant studies; d is the diameter of the pile.

[0157] S6: Determine the E calculated in the current iteration step.sm E calculated in the previous iteration step sm Is the absolute value of the difference less than or equal to a set threshold? If yes, proceed to step S7; if no, proceed to step S4. The threshold in this embodiment is 0.0001.

[0158] S7: Obtain the solution y at each point using discrete equations. m According to y m The value is used to determine the tilt angle at the top of the shaft:

[0159]

[0160]

[0161] Where H represents the height of the pole.

[0162] S8: Gradually increase the wind speed to obtain the wind speed-tilt angle curve of the concrete pole structure, such as... Figure 3 As shown.

[0163] (3) The maximum wind speed limit in the wind speed-tilt angle curve is taken as the equivalent wind speed V2 in the overturning failure mode. In this embodiment, at a height of 10m, the equivalent wind speed V2 in the overturning failure mode is 31m / s. The tilt angle and wind speed corresponding to any point on the wind speed-tilt angle curve are taken as the equivalent wind speed V3 in the tilt failure mode at the corresponding tilt angle.

[0164] Step 3: Establish the mapping relationship between the characteristic wind speed at a set height (10m in this embodiment) and the three failure modes of the concrete pole structure. In this embodiment, the structure tilts when the wind speed is less than 31m / s, overturns when the wind speed is greater than 31m / s, and the root fracture occurs when the wind speed reaches 52m / s. Based on the damage to the concrete pole structure after the disaster, the equivalent wind speed of the local strong wind is calculated by inversion.

[0165] 2. Localized strong winds were tornadoes.

[0166] This embodiment is based on the equivalent wind speed inversion calculation method for the failure mode of concrete pole structures under local strong winds, and includes the following steps.

[0167] Step 1: Determine the local strong wind type as a tornado, and calculate the bending moment and shear force of the concrete pole structure foundation under different wind speeds. The specific process is as follows:

[0168] (1) The local strong wind type was determined to be a tornado;

[0169] (2) Based on the determined local strong wind types, establish corresponding mathematical models for the vector distribution of local strong wind speeds, such as... Figure 4As shown. The radial and tangential wind speed profiles of a tornado are presented. Based on existing research, the empirical formula for tornadoes is selected as follows:

[0170] The tornado empirical model adopts the 3D Kuo-wen model, as follows:

[0171] Boundary layer thickness:

[0172] δ(r′)=δ0[1-exp(-0.5r 2 )]

[0173] In the formula: r = r′ / r max r′ is the distance from the target point to the center of the tornado. max The radius corresponding to the maximum tangential wind speed is 50m according to the "HAD101-10 Extreme Meteorological Events for Nuclear Power Plant Site Selection" standard; δ0 is the boundary layer thickness of the tornado, which is 457m. The distance between the selected concrete pole structure and the center of the tornado is 20m. In actual inversion, the value can be determined based on the post-disaster investigation.

[0174] Within the boundary layer height (z < δ):

[0175] T(η,r)=f(r)=1.4V max[1.0-exp(-1.256r 2 )]r -1

[0176] R(η, r) = 0

[0177] W(η, r) = 93r 3 exp(-5r)V max

[0178] Within the boundary layer height (z > δ):

[0179] T(η, r) = f(r)[1-e -πη cos(2bπη)]

[0180] R(η, r) = f(r){0.672e -πη sin[(b+1)πη]}

[0181] W(η, r) = 93r 3 exp(-5r)V max [1-e -πη cos(2bπη)]

[0182] Where T(η, r), R(η, r), and W(η, r) are the tangential, radial, and vertical wind speeds, respectively; f(r) represents the tangential wind speed; η = z / δ(r'); r = r' / r max r' is the distance from the target point to the center of the tornado.max The radius corresponding to the maximum tangential wind speed; V max Maximum tangential wind speed;

[0183] (3) The concrete pole structure has a height of 8m, an upper diameter of 0.18 and a lower diameter of 0.24.

[0184] (4) Calculate the base bending moment and shear force of the concrete pole structure under different wind speeds based on the mathematical model of tornado wind speed vector distribution. Specifically, the base bending moment of the concrete pole structure is:

[0185]

[0186]

[0187]

[0188] The shear force of the concrete rod-type structure foundation is:

[0189]

[0190]

[0191]

[0192] Where M represents the bending moment of the concrete beam structure foundation; M 切 M represents the base bending moment in the tangential direction of a concrete pole structure. 径 V represents the radial bending moment at the base of the concrete pole structure; V represents the shear force at the base of the concrete pole structure; V 切 V represents the base shear force in the tangential direction of a concrete beam structure. 径 The base shear force in the radial direction of the concrete pole structure is represented; ρ is the air density, taken as 1.225 kg / m³; G is the gust factor, which is calculated based on the gust speed over three seconds, taking 1.0, since the wind speed of local strong winds varies drastically with time; C f The drag coefficient of the concrete pole structure needs to consider the influence of the Reynolds number; D(z) is the diameter of the concrete pole structure along its height, where z represents a certain height of the concrete pole structure; H represents the overall height of the concrete pole structure; U 切 Indicates tangential wind speed; U 径 Indicates radial wind speed.

[0193] Determine the dimensions and material parameters of the concrete pole structure, and calculate the ultimate resistance R1 at the root of the concrete pole structure. The specific process is as follows:

[0194] (1) The concrete thickness is 0.06 mm, the steel bar diameter is 5 mm, the number of steel bars is 12, the steel bar strength is Q235, the concrete strength is C50, and the concrete cover thickness is 0.02 mm.

[0195] (2) Calculate the ultimate resistance at the bottom of the concrete column structure. The ultimate bending moment of the normal section bearing capacity of the annular section concrete column structure under bending conditions is calculated according to the following formula:

[0196]

[0197] In the formula: R1 is the ultimate resistance at the bottom of the concrete pole structure; f ck f is the standard value of the axial compressive strength of concrete; yk A is the standard value of the tensile strength of the steel reinforcement; A is the area of ​​the annular cross-section; A s r1 is the total area of ​​longitudinal ordinary reinforcing bars; r2 is the inner radius of the annular section; r3 is the outer radius of the annular section; r4 is the total area of ​​longitudinal ordinary reinforcing bars. s α is the distance from the center of the longitudinal reinforcement to the center of the ring of the bar section; α is the ratio of the area of ​​the concrete compression zone to the total cross-sectional area, which can be calculated by the following formula: α=f yk A s / (2.5f yk A s +α1f cu A) α1 is a partial factor, taken as 1.0 for strengths below C50, and 0.94 for strengths above C80. For intermediate strength grades, it can be directly interpolated. t α is the ratio of the cross-sectional area of ​​the tensile longitudinal reinforcement to the total cross-sectional area of ​​the longitudinal reinforcement. t =1-1.5α, when α>2 / 3, α t =0. The calculated ultimate bending moment R1 of the concrete beam structure is 11.19 kN·m. Figure 5 As shown.

[0198] Step 2: Calculate the equivalent wind speed of the concrete pole structure under three failure modes.

[0199] (1) The root ultimate resistance R1 of the concrete pole structure is used as the equivalent bending moment of the concrete pole structure base, and the equivalent wind speed V1 under the root fracture failure mode is obtained by inversion calculation.

[0200] (2) The concrete pole structure has a lower diameter of 0.24 mm, a burial depth of 0.8 mm, and uses sandy soil with a foundation reaction ratio of 10000. The inner diameter of the circular cross-section is 0.18 mm, and the passive earth pressure coefficient is 4.7. The tilt angle under different wind speeds is calculated to obtain the wind speed-tilt angle curve. Specifically, the steps for constructing the wind speed-tilt angle curve are as follows:

[0201] S1: Determine the dimensions of the substructure and soil type of the concrete pole structure, and clarify the basic differential equations for the horizontally loaded pile locations:

[0202]

[0203] Where EI represents the bending stiffness of the pile section; k represents the secant modulus of the py curve at depth x; x represents the depth below the ground; and y represents the displacement of the pile body.

[0204] S2: Divide the concrete pole structure into n segments, each with a length of h. The pile body has n+1 points. The division points of each segment are replaced by the derivatives in the differential equation of the pole's elastic curve using finite difference form, transforming the basic differential equation into a set of algebraic difference equations:

[0205]

[0206] Among them, E sm The modulus of soil reaction is represented by h; the length of the element segment is represented by m = 0, 1, 2, ..., n.

[0207] S3: Determine the initial conditions for the top and bottom of the shaft, and randomly initialize E. sm The value of , where:

[0208] The initial conditions at the top of the shaft are:

[0209]

[0210]

[0211] The initial conditions at the bottom of the shaft are:

[0212] y -2 -2y -1 +2y1-y2=0

[0213] y -1 -2y0+y1=0

[0214] Where M0 represents the base bending moment of the concrete pole structure; V0 represents the base shear force of the concrete pole structure.

[0215] S4: Take advantage of E sm Solving the discrete system of equations yields the solution y. i ,i=-2,-1,0...,n,n+1,n+2.

[0216] S5: p can be calculated from the py curve. i , to obtain new E sm for:

[0217]

[0218] Specifically, the equation of the py curve is:

[0219]

[0220] k in =n hmax x

[0221] p u =N g γ s d 2-j (α0+x) j

[0222] Where, k in n is the modulus of ground reaction force; hmax These are parameters determined based on the internal friction angle and soil density; x is the depth from the soil surface; p u For ultimate resistance; N g The ultimate resistance coefficient is K. p 2 linear function, K p The passive earth pressure coefficient is taken as N, based on the non-displacement soil construction method of the foundation. g = (0.55~2.5)K p 2 ;γ s α is the unit weight of the soil; α0 is a constant reflecting the resistance of the ground soil or the equivalent soil depth, which is taken as 0 according to relevant studies; j is the exponent between α0 and x, which is the shape parameter of the ultimate resistance, and is taken as 1.7 according to relevant studies; d is the diameter of the pile.

[0223] S6: Determine the E calculated in the current iteration step. sm E calculated in the previous iteration step sm Is the absolute value of the difference less than or equal to a set threshold? If yes, proceed to step S7; if no, proceed to step S4. The threshold in this embodiment is 0.0001.

[0224] S7: Obtain the solution y at each point using discrete equations. m According to y m The value is used to determine the tilt angle at the top of the shaft:

[0225]

[0226]

[0227] Where H represents the height of the pole.

[0228] S8: Gradually increase the wind speed to obtain the wind speed-tilt angle curve of the concrete pole structure, such as... Figure 6 As shown.

[0229] (3) The maximum wind speed limit in the wind speed-tilt angle curve is taken as the equivalent wind speed V2 in the overturning failure mode. In this embodiment, at a height of 10m, the equivalent wind speed V2 in the overturning failure mode is 33m / s. The tilt angle and wind speed corresponding to any point on the wind speed-tilt angle curve are taken as the equivalent wind speed V3 in the tilt failure mode at the corresponding tilt angle.

[0230] Step 3: Establish the mapping relationship between the characteristic wind speed at a set height (10m in this embodiment) and the three failure modes of the concrete pole structure. In this embodiment, the structure tilts when the wind speed is less than 33m / s, overturns when the wind speed is greater than 33m / s, and the root fracture occurs when the wind speed reaches 59m / s. Based on the damage to the concrete pole structure after the disaster, the equivalent wind speed of the local strong wind is calculated by inversion.

[0231] The above-described embodiments are merely preferred embodiments provided to fully illustrate the present invention, and the scope of protection of the present invention is not limited thereto. Equivalent substitutions or modifications made by those skilled in the art based on the present invention are all within the scope of protection of the present invention. The scope of protection of the present invention is defined by the claims.

Claims

1. A method for calculating equivalent wind speed inversion based on the failure mode of concrete pole structures under localized strong winds, characterized in that: Includes the following steps: Step 1: Determine the type of local strong wind and establish a mathematical model of wind speed vector distribution. Determine the wind speed at different locations and heights, and obtain the bending moment and shear force of the concrete pole structure foundation under different wind speeds. Determine the dimensions and material parameters of the concrete pole structure, and calculate the ultimate resistance R1 at the root of the concrete pole structure; Step 2: Calculate the equivalent wind speed of the concrete pole structure under three failure modes. Using the ultimate resistance R1 at the root of the concrete pole structure as the equivalent bending moment of the concrete pole structure base, the equivalent wind speed V1 under the root fracture failure mode is obtained by inversion calculation. Based on the lower dimensions, burial depth, and soil parameters of the concrete pole structure, the tilt angle of the concrete pole structure under different wind speeds is calculated, and the wind speed-tilt angle curve is obtained. The maximum wind speed limit in the wind speed-tilt angle curve is taken as the equivalent wind speed V2 in the overturning failure mode; The tilt angle and wind speed corresponding to any point on the wind speed-tilt angle curve are used as the equivalent wind speed V3 at the corresponding tilt angle in the tilt failure mode. Step 3: Establish the mapping relationship between the characteristic wind speed at the set height location and the three failure modes of the concrete pole structure. Combined with the post-disaster damage to the concrete pole structure, the equivalent wind speed of the local strong wind is calculated by inversion.

2. The equivalent wind speed inversion calculation method based on the failure mode of concrete pole structures under local strong winds as described in claim 1, characterized in that: The bending moment of the concrete pole-type structure foundation is: The shear force of the concrete rod-type structure foundation is: Where M represents the bending moment of the concrete beam structure foundation; M 切 M represents the base bending moment in the tangential direction of a concrete pole structure. 径 V represents the radial bending moment at the base of the concrete frame structure; V represents the shear force at the base of the concrete frame structure; V 切 V represents the base shear force in the tangential direction of a concrete beam structure. 径 The base shear force in the radial direction of the concrete pole structure is represented by ρ, air density, and gust factor; C represents the shear force at the base in the radial direction. f D(z) is the drag coefficient of the concrete pole structure; D(z) is the diameter of the concrete pole structure along its height, where z represents a certain height of the concrete pole structure; H represents the overall height of the concrete pole structure; U 切 Indicates tangential wind speed; U 径 Indicates radial wind speed.

3. The equivalent wind speed inversion calculation method based on the failure mode of concrete pole structures under local strong winds as described in claim 1, characterized in that: In step two, the method for constructing the wind speed-tilt angle curve is as follows: S1: Determine the substructure dimensions and soil type of the concrete pole structure, and clarify the basic differential equation for the displacement of horizontally loaded piles: Where EI represents the bending stiffness of the pile section; k represents the secant modulus of the py curve at depth x; x represents the depth below the ground; and y represents the displacement of the pile body. S2: Divide the concrete pole structure into n segments, each with a length of h. The pile body has n+1 points. The division points of each segment are replaced by the derivatives in the differential equation of the pole's elastic curve using finite difference form, transforming the basic differential equation into a set of algebraic difference equations: Among them, E sm The modulus of soil reaction is represented by h; the length of the element segment is represented by m = 0, 1, 2, ..., n. S3: Determine the initial conditions for the top and bottom of the shaft, and randomly initialize E. sm The value of , where: The initial conditions at the top of the shaft are: The initial conditions at the bottom of the shaft are: y -2 -2y -1 +2y1-y2=0 y -1 -2y0+y1=0 Where M0 represents the base bending moment of the concrete pole structure; V0 represents the base shear force of the concrete pole structure. S4: Take advantage of E sm Solving the discrete system of equations yields the solution y. i ,i=-2,-1,0...,n,n+1,n+2; S5: p can be calculated from the py curve. i , to obtain new E sm for: S6: Determine the E calculated in the current iteration step. sm E calculated in the previous iteration step sm Is the absolute value of the difference less than or equal to a set threshold? If yes, proceed to step S7; if no, proceed to step S4. S7: Obtain the solution y at each point using discrete equations. m According to y m The value is used to determine the tilt angle at the top of the shaft: Where H represents the height of the pole; S8: Gradually increase the wind speed to obtain the wind speed-tilt angle curve of the concrete pole structure.

4. The equivalent wind speed inversion calculation method based on the failure mode of concrete pole structures under local strong winds as described in claim 3, characterized in that: In step S5, the equation of the py curve is: k in =n hmax x p u =N g c s d 2-j (α0+x) j Where, k in n is the modulus of ground reaction force; hmax These are parameters determined based on the internal friction angle and soil density; x is the depth from the soil surface; p u For ultimate resistance; N g The ultimate resistance coefficient is K. p 2 linear function, K p γ is the passive earth pressure coefficient; s α is the soil unit weight; α0 is a constant reflecting the soil resistance or equivalent soil depth; j is the exponent between α0 and x; d is the pile diameter.

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