A CRTSII type track slab arching stability discrimination method

Abstract

The application discloses a CRTSII type track slab upwarp stability discrimination method, which comprises the following steps: establishing a two-dimensional numerical calculation model of the CRTSII type track slab; combining different adverse influence factors to form a calculation condition, and calculating the track slab allowable temperature amplitude under the upwarp allowable vector condition of the calculation condition by using the two-dimensional numerical calculation model; establishing a sample database according to the calculation condition and the track slab allowable temperature amplitude, constructing a regression model between the adverse influence factors and the slab body allowable temperature amplitude by using a regression analysis method, and improving the regression model; and judging the CRTSII type track slab upwarp stability according to the improved regression model, the measured value of the adverse influence factors and the actual maximum temperature amplitude of the track slab. The application accurately simulates the adverse influence factors of the CRTSII type track slab, establishes a representative sample database, and improves the accuracy and efficiency of the CRTSII type track slab upwarp stability discrimination through the improved regression model.

Description

Technical Field

[0001] This invention relates to the field of damage, repair and maintenance of ballastless track structures, and specifically to a method for judging the arch stability of CRTSII type track slabs. Background Technology

[0002] CRTSII type slab track is mainly used in high-speed railways such as the Beijing-Tianjin, Beijing-Shanghai, and Shanghai-Hangzhou lines. Currently, the operational mileage of CRTSII type slab track on main lines in my country has reached over 5,000 kilometers. Figure 1 This is a CRTSII type slab track. The ends of adjacent track slabs in the CRTSII type slab track structure are connected by tension locking devices; therefore, this track system is a longitudinally continuous structure. Joints are left between the longitudinally connected CRTSII type track slabs, such as... Figure 2 As shown, the actual construction of the joints between CRTSII type track slabs is that it is wider at the top (called a wide joint) and narrower at the bottom (called a narrow joint). During the construction phase, after the tensioning and locking devices are installed, the joints between the CRTSII type track slabs are filled and compacted with concrete. Due to the longitudinal connection structure of the CRTSII type slab track, it is more significantly affected by ambient temperature compared to other types of ballastless tracks.

[0003] During hot summer weather, CRTSII type track slabs frequently exhibit upward arching. This arching has become the most significant type of damage threatening the safety of high-speed trains during the use of this type of ballastless track. Furthermore, CRTSII type track slab arching is characterized by its high frequency and unpredictability, and its formation mechanism remains unclear.

[0004] Current research on the arching stability of track slabs has shown that, among the five main influencing factors—temperature, joint damage between slabs (including both narrow and wide joint damage), initial bending, and gravity—the other three factors, except for gravity and wide joint damage, are detrimental to maintaining the arching stability of the track slab. Temperature is a direct factor in track slab arching, initial bending is a contributing factor, and narrow joint damage is closely related to track slab arching: almost all arched areas contain narrow joints, and the maximum sag of the arch is located at the narrow joints. The grout concrete at the narrow joints exhibits varying degrees of peeling and spalling. However, currently, it is impossible to construct an accurate simulation model for these adverse factors, thus hindering an efficient and accurate assessment of the arching stability of CRTSII type track slabs. Summary of the Invention

[0005] In view of the above-mentioned shortcomings in the prior art, the present invention provides a method for judging the arching stability of CRTSII type track slabs, which can accurately simulate the adverse influencing factors of CRTSII type track slabs, thereby improving the accuracy and efficiency of judging the arching stability of CRTSII type track slabs.

[0006] To achieve the above-mentioned objectives, the technical solution adopted by this invention is as follows:

[0007] A method for determining the arch stability of a CRTSII type track slab includes the following steps:

[0008] S1. Establish a two-dimensional numerical calculation model for the CRTSII type track slab;

[0009] S2. Combine different adverse influencing factors to form a calculation condition, and use the two-dimensional numerical calculation model in step S1 to calculate the allowable temperature rise of the track slab under the allowable sagittal condition of the upper arch.

[0010] S3. Based on the calculated working conditions and allowable temperature rise of the track slab in step S2, establish a sample database, construct a regression model between adverse influencing factors and allowable temperature rise of the slab using regression analysis, and improve the regression model.

[0011] S4. Based on the improved regression model in step S3, the measured values ​​of adverse influencing factors, and the actual maximum temperature rise of the track slab, determine the arching stability of the CRTSII type track slab.

[0012] Further, step S1 includes the following sub-steps:

[0013] S11. Use beam elements to simulate the track slab to obtain the simulated part of the track slab;

[0014] S12. The initial bending of the track slab is simulated by using nonlinear spring elements uniformly distributed to support beam elements in step S11, thus obtaining the simulation part of the initial bending of the track slab.

[0015] S13. The damage at the narrow joint is simulated using a two-dimensional numerical calculation model with voids to obtain the simulated damage at the narrow joint.

[0016] S14. Determine the simulated width and equivalent thickness of the track slab based on actual measured values;

[0017] S15. The track slab length is simulated by the most unfavorable wavelength of the upper arch of the track slab to obtain the simulated length of the track slab.

[0018] S16. Based on the track slab simulation part in step S11, the track initial bending simulation part in step S12, the damage simulation part at the narrow joint in step S13, the track slab width simulation part and equivalent thickness simulation part in step S14, and the track slab length simulation part in step S15, establish a two-dimensional numerical calculation model of the CRTSII type track slab.

[0019] Furthermore, step S15 includes the following sub-steps:

[0020] S151. Based on the equal wavelength model, determine the arching deformation curve, elastic initial bending deformation curve, and plastic initial bending deformation curve of the track slab under temperature and pressure, as follows:

[0021]

[0022]

[0023]

[0024] Where: y f The curve shows the upward arching deformation of the track slab under temperature and pressure, where f is the upward arching deformation vector, L is the upward arching deformation wavelength, and y... oe f is the deformation curve of the track slab under elastic initial bending. oe Let y be the initial elastic deformation vector of the track slab. op f is the deformation curve of the track slab during initial plastic bending. op This represents the initial plastic deformation vector of the track slab;

[0025] S152. Based on the arching deformation curve of the track slab under temperature and pressure, the deformation curve of the track slab under initial elastic bending, and the deformation curve of the track slab under initial plastic bending in step S151, determine the deformation curves of the track slab under and without temperature and pressure, as follows:

[0026] y T =y f +y oe +y op ;

[0027] y o =y oe +y op

[0028] Where: y T The curve of track slab deformation under temperature and pressure conditions is y. o The deformation curve of the track slab under no temperature or pressure conditions;

[0029] S153. Based on the track slab deformation curves in step S152 with and without temperature and pressure, calculate the arc length change of the track slab under axial pressure, expressed as:

[0030]

[0031] Where: Δl is the change in arc length of the track slab under axial pressure, Δl T y' represents the arc-chord difference after deformation, Δl0 represents the arc-chord difference before deformation, and y' represents the arc-chord difference before deformation. T The deformation curve y of the track slab under temperature and pressure. T Regarding the first derivative of the wavelength L of the upward arch deformation, y'0 is the deformation curve of the track slab under no temperature or pressure conditions. o The first derivative with respect to the wavelength L of the upward arch deformation;

[0032] S154. Based on the arc length change of the track slab under axial pressure in step S153, calculate the compressive deformation energy of the track slab, expressed as:

[0033] A1=P×Δl

[0034] Where: A1 is the compressive deformation energy of the track slab, and P is the critical temperature force at which the track slab arches;

[0035] S155. Based on the upward arching deformation curve of the track slab under temperature and pressure and the deformation curve of the initial elastic bending of the track slab in step S151, calculate the bending strain energy of the track slab, expressed as:

[0036]

[0037] Where: A2 is the bending deformation energy of the track slab, L is the wavelength of the upward arch deformation, and M... f θ represents the newly added internal torque during deformation. f M represents the angle created by the bending of the track slab. oe β is the internal moment of the original elastic bending, E is the elastic modulus of the track slab, J is the moment of inertia of the cross section, and y is the internal moment of the original elastic bending. f "y" represents the upward arching deformation curve of the track slab under temperature and pressure. f Regarding the second derivative of the wavelength L of the upward arch deformation, y oe "y" represents the deformation curve of the track slab during its initial elastic bending. oe The second derivative with respect to the wavelength L of the upward arch deformation;

[0038] S156. The gravitational potential energy of the track slab is calculated based on the upper arch deformation vector and the upper arch deformation wavelength, and expressed as:

[0039]

[0040] Where: A3 is the gravitational potential energy of the track slab, ρ is the density of the track slab concrete; g is the gravitational acceleration; A is the cross-sectional area of ​​the track slab;

[0041] S157. Based on the energy principle, establish the expression for the arch stability of the CRTSII type track slab, which is expressed as:

[0042]

[0043] S158. Substituting the compressive deformation energy of the track slab in step S154, the bending deformation energy of the track slab in step S155, and the gravitational potential energy of the track slab in step S156 into the camber stability expression of the CRTSII type track slab in step S157, we obtain the calculation formula for the critical temperature force of camber on the track slab, which is expressed as:

[0044]

[0045] S159. Using the function extremum solution method, the calculation formula for the critical temperature force of track slab arching in step S158 is differentiated with respect to the deformation wavelength to obtain the most unfavorable wavelength of track slab arching, expressed as:

[0046]

[0047] Where: l is the most unfavorable wavelength for the upward arch of the track slab.

[0048] Furthermore, step S2 includes the following sub-steps:

[0049] S21. Determine the adverse factors affecting the arching stability of the CRTSII type track slab, including initial bending of the track slab, height of narrow joint damage, and width of narrow joint damage.

[0050] S22. Divide the initial bending of the track plate in step S21 into seven different bending states.

[0051] S23. Divide the narrow joint damage height in step S21 into ten different damage levels.

[0052] S24. Divide the width of the narrow seam damage in step S21 into three different damage levels.

[0053] S25. Combine the initial bending of the track slab with the seven different bending states divided in step S22, the damage height of the narrow joint with the ten different damage degrees divided in step S23, and the damage width of the narrow joint with the three different damage degrees divided in step S24 to form the calculation conditions.

[0054] S26. Calculate the allowable temperature rise of the track slab at the allowable sagitta of the upper arch based on the two-dimensional numerical calculation model in step S1.

[0055] Furthermore, step S3 includes the following sub-steps:

[0056] S31. Construct a sample database based on the working conditions and allowable temperature rise of the track slab calculated in step S2;

[0057] S32. Use regression analysis to construct an initial regression model between adverse influencing factors and the allowable temperature rise of the track slab;

[0058] S33. Using the statistical analysis software SPSS, the sample database in step S31 is calculated according to the initial regression model in step S32 to obtain the calculation results of the initial regression model.

[0059] S34. Based on the calculation results of the initial regression model in step S33, determine the significance calculation results of each adverse influencing factor in the initial regression model, and delete the independent variable terms whose significance calculation results of each adverse influencing factor in the initial regression model are greater than the standard value, to obtain the improved regression model.

[0060] Furthermore, in step S32, the initial regression model between the adverse influencing factors and the allowable temperature rise of the track slab is expressed as follows:

[0061] ΔT=a0+a1×w+a2×h+a3×h 2 +a4×f i +a5×f i 2 +ε

[0062] Where: ΔT is the allowable temperature rise of the track slab; a0 is a constant term; a1 is the coefficient for the narrow joint damage width; w is the narrow joint damage width; a2 is the first-order coefficient for the narrow joint damage height; h is the narrow joint damage height; a3 is the second-order coefficient for the narrow joint damage height; a4 is the first-order coefficient for the initial bending; f i Let a5 be the initial curvature, ε be the second-order coefficient of the initial curvature, and ε be the random term.

[0063] Furthermore, step S4 includes the following sub-steps:

[0064] S41. Based on the improved regression model and the measured values ​​of adverse influencing factors in step S34, the predicted value of the allowable temperature rise of the track slab is obtained.

[0065] S42. Determine whether the predicted value of the allowable temperature rise of the track slab in sub-step S41 is greater than or equal to the actual maximum temperature rise of the track slab; if so, determine that the CRTSII type track slab is stable by arching; otherwise, determine that the CRTSII type track slab is unstable by arching.

[0066] The beneficial effects of this invention are as follows:

[0067] (1) The present invention uses a two-dimensional numerical calculation model to simulate the arching stability of the inter-slab joint damage. The modeling difficulty is small, the number of elements is small, and the calculation efficiency is high. Furthermore, the calculation results of the two-dimensional numerical calculation model have been verified by the analytical formula calculation results. Compared with the analytical solution, the two-dimensional numerical calculation model can accurately calculate the temperature rise of the track slab under any damage state and degree, and its application range is wider.

[0068] (2) The method for judging the arch stability of CRTSII type track slab proposed in this invention has established a representative sample database and improved the accuracy and efficiency of judging the arch stability of CRTSII type track slab through an improved regression model. As can be seen from the overall misjudgment rate and detailed misjudgment results, this method has a very high accuracy in evaluating the arch stability of CRTSII type track slab.

[0069] (3) In practical applications, this invention can plot the width and height of narrow joint damage, the initial curvature of the track slab, and the allowable temperature rise under the allowable camber sagitta condition (cambering the track slab by 2mm) corresponding to the width, height, and initial curvature of the narrow joint damage, as well as the allowable temperature rise under the allowable camber sagitta condition. Track inspectors at the railway site only need to use simple measuring tools to first measure the joint damage size and initial curvature sagitta value of the track slab (using a 6.5m chord length). Then, they can quickly obtain the allowable temperature rise corresponding to the actual damage condition through the plotted table. By comparing this allowable temperature rise with the actual maximum temperature rise of the track slab, the camber stability of the CRTSII type track slab under this damage type can be quickly determined, greatly simplifying the judgment process for track camber stability and improving the judgment efficiency. Attached Figure Description

[0070] Figure 1 This is a diagram of the CRTSII type slab track.

[0071] Figure 2 Diagram of the joint between CRTSII type track slabs;

[0072] Figure 3 A flowchart of a method for determining the arch stability of a CRTSII type track slab;

[0073] Figure 4 Figure 1 shows a simulation method for narrow joint damage. Figure 2a is a schematic diagram in which the concrete spalling and powdery area at the damaged narrow joint is regarded as a cavity. Figure 3b is a simulation effect diagram of the bottom damage of the joint between track slabs using beam elements and the Beam Tool toolbar in ANSYS software. Detailed Implementation

[0074] The specific embodiments of the present invention are described below to enable those skilled in the art to understand the present invention. However, it should be understood that the present invention is not limited to the scope of the specific embodiments. For those skilled in the art, various changes are obvious as long as they are within the spirit and scope of the present invention as defined and determined by the appended claims. All inventions utilizing the concept of the present invention are protected.

[0075] like Figure 3 As shown, a method for determining the arch stability of a CRTSII type track slab includes steps S1-S4:

[0076] S1. Establish a two-dimensional numerical calculation model for the CRTSII type track slab.

[0077] In an optional embodiment of the present invention, considering that the track slab mainly exhibits upward arching deformation under temperature and pressure, with almost no tilting in the width direction, it can be assumed that the upward arching deformation characteristics at various positions in the width direction of the track slab are consistent with those at the centerline of the track slab, and that the length of the track slab is much greater than its thickness. Therefore, the present invention employs a two-dimensional numerical calculation model for simulation.

[0078] Two-dimensional numerical calculation models must conform to the actual structural and mechanical response characteristics of the research object. The main problem with the two-dimensional numerical calculation model established in this invention in terms of structural characteristics is the accurate simulation of joint damage between plates, and the main problem in terms of mechanical response characteristics is the accurate simulation of initial bending.

[0079] Step S1 includes the following sub-steps:

[0080] S11. Beam elements are used to simulate the track slab to obtain the simulated part of the track slab.

[0081] Specifically, considering the influencing factors such as shearing and torsion during the arching deformation of the track slab, the present invention uses beam elements to simulate the track slab, thus obtaining the track slab simulation part of the two-dimensional numerical calculation model.

[0082] S12. The initial bending of the track slab is simulated by using nonlinear spring elements to uniformly support the beam elements in step S11, thus obtaining the simulation part of the initial bending of the track slab.

[0083] When performing numerical analysis on a structure using finite element method (FEM) software, the process includes three stages: modeling, loading and solving, and viewing the results. These three stages must be performed in the correct order to complete the analysis. The elastic and plastic initial bending of the track slab must be pre-defined on the beam elements simulating the track slab during the modeling stage. However, gravity loads can only be applied during the loading stage. During the solution process, the gravity load will cause the pre-defined initial bending on the track slab elements to be smaller. This contradicts the fact that the initial bending of the track slab is the deformation after overcoming gravity, thus affecting the accuracy of the numerical model's calculation results.

[0084] Specifically, to ensure that the initial bending in the two-dimensional numerical calculation model matches the actual situation, this invention employs a method of uniformly distributing nonlinear spring elements to support the beam elements. The nonlinear springs only generate pressure, not tension. The working principle of these nonlinear springs is as follows: when the track slab experiences downward displacement under gravity, the nonlinear spring generates pressure to prevent the track slab from sinking; however, when the track slab arches upward under temperature pressure, the nonlinear spring does not generate tension and does not prevent the track slab from arching upward. This achieves the goal of simulating the initial bending of the track slab as deformation after overcoming gravity, while simultaneously not affecting the upward arching of the track slab.

[0085] S13. The damage at the narrow joint is simulated using a two-dimensional numerical calculation model with voids, resulting in the simulated damage at the narrow joint.

[0086] In the study of the arching stability of track slabs, damage to the track slab mainly causes a difference in the bending resistance at the damaged location compared to other parts of the track slab, thus affecting the arching deformation of the slab. Therefore, accurately reflecting the impact of damage on the bending resistance of the track slab is crucial to the correctness of the two-dimensional numerical calculation model in this invention.

[0087] The main forms of damage at narrow joints are concrete powdering, spalling, and chipping. The concrete in the spalled and powdered areas of the narrow joint no longer contributes to the bending resistance of the track slab; this area can be considered non-existent, similar to a "void" at the narrow joint. Figure 4 As shown in Figure a. Therefore, the bending resistance at the narrow joint damage point is the bending resistance of the remaining plate thickness after subtracting the height of the "void" caused by the damage from the track plate thickness. In the numerical model, the impact of the damage on the bending resistance of the plate can be reflected as long as the "void" caused by the damage is accurately simulated.

[0088] Specifically, the two-dimensional numerical calculation model of this invention uses the Offset To option in the Beam Tool toolbar of ANSYS software to simulate the "void" caused by joint damage between plates, such as... Figure 4As shown in b. The specific method is as follows: the width of the "void" is achieved by defining the length of the beam element at the damaged location, and the height of the "void" is achieved by defining the cross-sectional height of the beam element at the damaged location.

[0089] S14. Determine the simulated width and equivalent thickness of the track slab based on the actual measured values.

[0090] Specifically, the two geometric parameters, namely the track slab width and equivalent thickness, as well as the physical property parameters, in the two-dimensional numerical calculation model for the arch stability of the track slab are determined according to the actual situation.

[0091] S15. The track slab length is simulated using the most unfavorable wavelength of the upper arch of the track slab to obtain the simulated length of the track slab.

[0092] Specifically, the magnitude of the critical force for upward camber on the track slab is closely related to the slab's bending resistance and its self-weight within the specified wavelength range. When the allowable deformation vector remains constant, a longer deformation wavelength results in a smaller bending deformation energy and a larger gravitational potential energy for the track slab; conversely, a shorter deformation wavelength results in a larger bending deformation energy and a smaller gravitational potential energy. Therefore, there exists a deformation wavelength that minimizes the critical force for upward camber, at which point the track slab's ability to maintain upward camber stability is weakest. This deformation wavelength represents the wavelength at which upward camber is most likely to occur, i.e., the most unfavorable wavelength for upward camber. In the two-dimensional numerical calculation model, the track slab length should be the wavelength at which upward camber is most unfavorable. Therefore, the track slab length is simulated using the wavelength at which upward camber is most unfavorable, resulting in the simulated length portion of the track slab.

[0093] Step S15 includes the following sub-steps:

[0094] S151. Based on the equal wavelength model, determine the arching deformation curve, elastic initial bending deformation curve, and plastic initial bending deformation curve of the track slab under temperature and pressure, as follows:

[0095]

[0096]

[0097]

[0098] Where: y f The curve shows the upward arching deformation of the track slab under temperature and pressure, where f is the upward arching deformation vector, L is the upward arching deformation wavelength, and y... oe f is the deformation curve of the track slab under elastic initial bending. oe Let y be the initial elastic deformation vector of the track slab. op f is the deformation curve of the track slab during initial plastic bending. op Let be the initial plastic deformation vector of the track slab.

[0099] S152. Based on the arching deformation curve of the track slab under temperature and pressure, the deformation curve of the track slab under initial elastic bending, and the deformation curve of the track slab under initial plastic bending in step S151, determine the deformation curves of the track slab under and without temperature and pressure, as follows:

[0100] y T =y f +y oe +y op ;

[0101] y o =y oe +y op

[0102] Where: y T The curve of track slab deformation under temperature and pressure conditions is y. o This is the deformation curve of the track slab when there is no temperature or pressure.

[0103] S153. Based on the track slab deformation curves in step S152 with and without temperature and pressure, calculate the arc length change of the track slab under axial pressure, expressed as:

[0104]

[0105] Where: Δl is the change in arc length of the track slab under axial pressure, Δl T y' represents the arc-chord difference after deformation, Δl0 represents the arc-chord difference before deformation, and y' represents the arc-chord difference before deformation. T The deformation curve y of the track slab under temperature and pressure. T Regarding the first derivative of the wavelength L of the upward arch deformation, y'0 is the deformation curve of the track slab under no temperature or pressure conditions. o The first derivative of the wavelength L of the upward arch deformation.

[0106] S154. Based on the arc length change of the track slab under axial pressure in step S153, calculate the compressive deformation energy of the track slab, expressed as:

[0107] A1=P×Δl

[0108] Where: A1 is the compressive deformation energy of the track slab, and P is the critical temperature force for the arching of the track slab.

[0109] S155. Based on the upward arching deformation curve of the track slab under temperature and pressure and the deformation curve of the initial elastic bending of the track slab in step S151, calculate the bending strain energy of the track slab, expressed as:

[0110]

[0111] Where: A2 is the bending deformation energy of the track slab, L is the wavelength of the upward arch deformation, and M... f θ represents the newly added internal torque during deformation. f M represents the angle created by the bending of the track slab. oe β is the internal moment of the original elastic bending, E is the elastic modulus of the track slab, J is the moment of inertia of the cross section, and y is the internal moment of the original elastic bending. f "y" represents the upward arching deformation curve of the track slab under temperature and pressure. f Regarding the second derivative of the wavelength L of the upward arch deformation, y oe "y" represents the deformation curve of the track slab during its initial elastic bending. oe The second derivative of the wavelength L of the upward arch deformation.

[0112] S156. The gravitational potential energy of the track slab is calculated based on the upper arch deformation vector and the upper arch deformation wavelength, and expressed as:

[0113]

[0114] Where: A3 is the gravitational potential energy of the track slab, ρ is the density of the track slab concrete; g is the gravitational acceleration; A is the cross-sectional area of ​​the track slab.

[0115] S157. Based on the energy principle, establish the expression for the arch stability of the CRTSII type track slab, which is expressed as:

[0116]

[0117] S158. Substituting the compressive deformation energy of the track slab in step S154, the bending deformation energy of the track slab in step S155, and the gravitational potential energy of the track slab in step S156 into the camber stability expression of the CRTSII type track slab in step S157, we obtain the calculation formula for the critical temperature force of camber on the track slab, which is expressed as:

[0118]

[0119] S159. Using the function extremum solution method, the calculation formula for the critical temperature force of track slab arching in step S158 is differentiated with respect to the deformation wavelength to obtain the most unfavorable wavelength of track slab arching, expressed as:

[0120]

[0121] Where: l is the most unfavorable wavelength for the upward arch of the track slab.

[0122] Specifically, the two geometric parameters and physical property parameters of track slab width and equivalent thickness determined in step S14, as well as the upward arch deformation vector f and the initial elastic vector f of the track slab determined in existing studies, are used. oeSubstituting into the above formula, we can obtain the specific value of the most unfavorable wavelength of the track slab's upward arch. This value is used as the track slab length in the two-dimensional numerical calculation model.

[0123] S16. Based on the track slab simulation part in step S11, the track initial bending simulation part in step S12, the damage simulation part at the narrow joint in step S13, the track slab width simulation part and equivalent thickness simulation part in step S14, and the track slab length simulation part in step S15, establish a two-dimensional numerical calculation model of the CRTSII type track slab.

[0124] After establishing a two-dimensional numerical calculation model of the CRTSII type track slab, this invention provides a method for verifying the correctness of the two-dimensional numerical calculation model. Specifically, under the same initial bending conditions, if the temperature pressure acting on the two-dimensional numerical calculation model, causing its deformation vector to be the upward arch deformation vector f, is equal to the critical temperature pressure calculated by the stability formula under the same deformation vector conditions, i.e., the formula described in step S158, then it indicates that the calculation result of the two-dimensional numerical calculation model is correct. The temperature pressure acting on the two-dimensional numerical calculation model is generated by the temperature rise applied to the track slab element. The relationship between the temperature rise amplitude ΔT of the track slab in the two-dimensional numerical calculation model and the critical temperature force P calculated by the stability formula is as follows:

[0125]

[0126] Where: ΔT is the allowable temperature rise of the track slab, α is the linear expansion coefficient of the concrete material, E is the elastic modulus of the track slab, and A is the cross-sectional area of ​​the track slab.

[0127] Under the same conditions, the critical temperature pressure P calculated by the above formula is compared with the critical temperature force of track slab arching calculated by the formula in step S158 to verify the correctness of the two-dimensional numerical calculation model.

[0128] Since the existing formula for the stability of track slab arching considering damage has been proven to be only applicable to calculating the critical force of track slab arching when the damage height at the joint is no more than 2 cm, the correctness of the numerical model was verified by comparing the results of the analytical solution with those of the two-dimensional numerical calculation model, with the smaller narrow joint damage as the calculation condition.

[0129] S2. Combine different adverse influencing factors to form a calculation condition, and use the two-dimensional numerical calculation model in step S1 to calculate the allowable temperature rise of the track slab under the allowable sagittal condition of the upper arch.

[0130] In an optional embodiment of the present invention, the present invention determines the adverse influencing factors on the arching stability of the CRTSII type track slab, including initial track slab curvature, narrow joint damage height, and narrow joint damage width. Then, it combines narrow joint damage heights and widths of different damage degrees with initial track slab curvatures of different curvature states to constitute a calculation condition. A two-dimensional numerical calculation model is then used to calculate the allowable temperature rise of the track slab under the allowable arching sag condition of the calculation condition, and the data of the calculation condition and the allowable temperature rise of the track slab under the allowable arching sag condition are saved.

[0131] Step S2 includes the following sub-steps:

[0132] S21. Determine the adverse factors affecting the arching stability of the CRTSII type track slab, including initial bending of the track slab, height of narrow joint damage, and width of narrow joint damage.

[0133] S22. Divide the initial bending of the track plate in step S21 into seven different bending states.

[0134] Specifically, the present invention increases the initial bending of the track slab from 4mm to 10mm in increments of 1mm, thus creating a total of seven different bending states.

[0135] S23. Divide the narrow joint damage height in step S21 into ten different damage levels.

[0136] Specifically, the present invention expresses the damage height of narrow joints in terms of bending stiffness coefficients, with a increment of 0.1. There are ten conditions from 1 to 0.1, constituting ten different degrees of damage. The bending stiffness coefficient of an intact narrow joint is 1, and the bending stiffness coefficient of a damaged narrow joint is less than 1.

[0137] S24. Divide the width of the narrow seam damage in step S21 into three different damage levels.

[0138] Specifically, this invention divides the width of narrow seam damage into three conditions: 1cm, 3cm, and 5cm, with a 2cm increment, thus constituting three different degrees of damage.

[0139] S25. Combine the initial bending of the track slab with the seven different bending states divided in step S22, the damage height of the narrow joint with the ten different damage degrees divided in step S23, and the damage width of the narrow joint with the three different damage degrees divided in step S24 to form the calculation conditions.

[0140] Specifically, this invention combines the above three adverse influencing factors to establish a total of 210 sample data for the method of judging the stability of the arch, that is, 210 calculation conditions.

[0141] S26. Calculate the allowable temperature rise of the track slab at the allowable sagitta of the upper arch based on the two-dimensional numerical calculation model in step S1.

[0142] Specifically, based on the 210 calculation conditions in step S25 and the two-dimensional numerical calculation model in step S1, two-dimensional numerical calculation models corresponding to the 210 calculation conditions are established respectively, and the allowable temperature rise amplitude ΔT of the plate body when the allowable upper arch sagitta f = 2 mm is calculated for all two-dimensional numerical calculation models.

[0143] S3. Based on the calculated operating conditions and allowable temperature rise of the track slab in step S2, establish a sample database, construct a regression model between adverse influencing factors and allowable temperature rise of the slab using regression analysis, and improve the regression model.

[0144] In an optional embodiment of the present invention, the accuracy and applicability of the upward arch stability discrimination method are important indicators for determining the quality of this method, and the accuracy and applicability are closely related to the sample data used when establishing this discrimination method. Reasonableness and quantity are two main aspects for measuring the quality of sample data. The database establishment process of the present invention ensures the reasonableness of the sample data and selects a large amount of representative data. Based on this, a sample database is established, and a regression analysis method is used to construct a regression model between adverse influencing factors and the allowable temperature rise of the plate. The regression model is then improved based on the established sample database.

[0145] Step S3 includes the following sub-steps:

[0146] S31. Construct a sample database based on the operating conditions and allowable temperature rise of the track slab calculated in step S2.

[0147] Specifically, to obtain a sufficient number of samples, this invention uses three conditions for narrow joint damage width, ranging from 1cm to 5cm in increments of 2cm; and ten conditions for narrow joint damage height, expressed as the bending stiffness coefficient, ranging from 1 to 0.1 in increments of 0.1. Seven conditions are also considered for the initial bending of the track slab, increasing from 4mm to 10mm in increments of 1mm. After combining these three influencing factors, the total number of sample data for establishing the arch stability discrimination method is 210, which corresponds to the 210 working conditions in step S2 above.

[0148] The present invention establishes a sample database based on the 210 working conditions in step S2 and the allowable temperature rise of the plate under various working conditions when the allowable arch sagitta f = 2 mm.

[0149] S32. An initial regression model is constructed using regression analysis to establish the relationship between adverse influencing factors and the allowable temperature rise of the track slab.

[0150] In step S32, the initial regression model between the adverse influencing factors and the allowable temperature rise of the track slab is expressed as follows:

[0151] ΔT=a0+a1×w+a2×h+a3×h 2 +a4×f i +a5×f i 2 +ε

[0152] Where: ΔT is the allowable temperature rise of the track slab; a0 is a constant term; a1 is the coefficient for the narrow joint damage width; w is the narrow joint damage width; a2 is the first-order coefficient for the narrow joint damage height; h is the narrow joint damage height; a3 is the second-order coefficient for the narrow joint damage height; a4 is the first-order coefficient for the initial bending; f i Let a5 be the initial curvature, ε be the second-order coefficient of the initial curvature, and ε be the random term.

[0153] S33. Using the statistical analysis software SPSS, the sample database in step S31 is calculated according to the initial regression model in step S32 to obtain the calculation results of the initial regression model.

[0154] S34. Based on the calculation results of the initial regression model in step S33, determine the significance calculation results of each adverse influencing factor in the initial regression model, and delete the independent variable terms whose significance calculation results of each adverse influencing factor in the initial regression model are greater than the standard value, to obtain the improved regression model.

[0155] Specifically, the significance calculation results of each adverse influencing factor in the initial regression model, namely the first term of the narrow joint damage width w and the narrow joint damage height h, the second term of the narrow joint damage height h, and the initial bending f in the initial regression model expression in step S32. i Initial bending f i The significance Sig value corresponding to the five independent variables of the quadratic term has a standard value of 0.05. If the significance Sig value calculated by the initial regression model is >0.05, that is, the difference is not significant, the relevant variable fails the test, and the independent variable term needs to be deleted; if the significance Sig value calculated by the initial regression model is <0.05, that is, the difference is significant, the test is passed, and the relevant independent variable term should be considered.

[0156] The improved regression model is expressed as:

[0157] ΔT=180.885-0.179×w-0.003×h 2 -24.405×f i +1.157×f i 2 .

[0158] S4. Based on the improved regression model in step S3, the measured values ​​of adverse influencing factors, and the actual maximum temperature rise of the track slab, determine the arching stability of the CRTSII type track slab.

[0159] In an optional embodiment of the present invention, the measured values ​​of adverse influencing factors are substituted into the improved regression model in step S3 to obtain the predicted value of the allowable temperature rise of the track slab. Then, the predicted value of the allowable temperature rise of the track slab is compared with the actual maximum temperature rise of the track slab to obtain the judgment result of the arch stability of the CRTSII type track slab.

[0160] Step S4 includes the following sub-steps:

[0161] S41. Based on the improved regression model and the measured values ​​of adverse influencing factors in step S34, the predicted value of the allowable temperature rise of the track slab is obtained.

[0162] Specifically, in practical applications, staff can use measuring tools to directly measure the height of the narrow joint damage, the width of the narrow joint damage, and the initial bending sagitta value. Substitute these three values ​​into the improved regression model to calculate the predicted value of the allowable temperature rise of the CRTSII type track slab under this damage condition.

[0163] S42. Determine whether the predicted value of the allowable temperature rise of the track slab in sub-step S41 is greater than or equal to the actual maximum temperature rise of the track slab; if so, determine that the CRTSII type track slab is stable by arching; otherwise, determine that the CRTSII type track slab is unstable by arching.

[0164] Specifically, a method for judging the arch stability of the track slab is established based on the actual maximum temperature rise of the track slab, as follows:

[0165]

[0166] Wherein: ΔT0 is the predicted value of the allowable temperature rise, which is determined by step S41, and 50℃ is the actual maximum temperature rise of the track slab.

[0167] When F(ΔT0) = 1, it means that the allowable temperature rise required for the track slab to reach an allowable camber of 2 mm is greater than or equal to 50℃. In this case, the camber of the CRTSII type track slab is considered stable. When F(ΔT0) = 0, it means that the allowable temperature rise required for the track slab to reach an allowable camber of 2 mm is less than 50℃. In this case, the camber of the CRTSII type track slab is considered unstable.

[0168] Those skilled in the art will recognize that the embodiments described herein are intended to help the reader understand the principles of the invention, and should be understood that the scope of protection of the invention is not limited to such specific statements and embodiments. Those skilled in the art can make various other specific modifications and combinations based on the technical teachings disclosed in this invention without departing from the spirit of the invention, and these modifications and combinations are still within the scope of protection of this invention.

Claims

1. A method for determining the arch stability of a CRTSII type track slab, characterized in that, Includes the following steps: S1. Establish a two-dimensional numerical calculation model for the CRTSII type track slab; S2. Combine different adverse influencing factors to form a calculation condition, and use the two-dimensional numerical calculation model in step S1 to calculate the allowable temperature rise of the track slab under the allowable sagittal condition of the upper arch. S3. Based on the calculated working conditions and allowable temperature rise of the track slab in step S2, establish a sample database, construct a regression model between adverse influencing factors and allowable temperature rise of the slab using regression analysis, and improve the regression model. S4. Based on the improved regression model in step S3, the measured values ​​of adverse influencing factors and the actual maximum temperature rise of the track slab, determine the arching stability of the CRTSII type track slab. Step S1 includes the following sub-steps: S11. Use beam elements to simulate the track slab to obtain the simulated part of the track slab; S12. The initial bending of the track slab is simulated by using nonlinear spring elements uniformly distributed to support beam elements in step S11, thus obtaining the simulation part of the initial bending of the track slab. S13. The damage at the narrow joint is simulated using a two-dimensional numerical calculation model with voids to obtain the simulated damage at the narrow joint. S14. Determine the simulated width and equivalent thickness of the track slab based on actual measured values; S15. The track slab length is simulated by the most unfavorable wavelength of the upper arch of the track slab to obtain the simulated length of the track slab. S16. Based on the track slab simulation part in step S11, the track slab initial bending simulation part in step S12, the damage simulation part at the narrow joint in step S13, the track slab width simulation part and equivalent thickness simulation part in step S14, and the track slab length simulation part in step S15, establish a two-dimensional numerical calculation model of the CRTSII type track slab.

2. The method for determining the arch stability of a CRTSII type track slab according to claim 1, characterized in that, Step S15 includes the following sub-steps: S151. Based on the equal wavelength model, determine the arching deformation curve, elastic initial bending deformation curve, and plastic initial bending deformation curve of the track slab under temperature and pressure, as follows: ； ； ； in: The curve shows the upward arching deformation of the track slab under temperature and pressure. The upward arch deformation sagitta, The wavelength of the upward arch deformation. This represents the deformation curve of the track slab during its initial elastic bending. Let be the initial elastic deformation vector of the track slab. The deformation curve of the track slab during initial plastic bending is shown. This represents the initial plastic deformation vector of the track slab; S152. Based on the arching deformation curve of the track slab under temperature and pressure, the deformation curve of the track slab under initial elastic bending, and the deformation curve of the track slab under initial plastic bending in step S151, determine the deformation curves of the track slab under and without temperature and pressure, as follows: ； in: The curve shows the deformation of the track slab under temperature and pressure. The deformation curve of the track slab under no temperature or pressure conditions; S153. Based on the track slab deformation curves in step S152 with and without temperature and pressure, calculate the arc length change of the track slab under axial pressure, expressed as: in: This represents the change in arc length of the track slab under axial pressure. The difference between the deformed arc and chord. The difference between the arc and chord before deformation. The deformation curve of the track slab under temperature and pressure. Regarding the wavelength of the upward arch deformation The first derivative, The deformation curve of the track slab under no temperature and pressure conditions. Regarding the wavelength of the upward arch deformation The first derivative; S154. Based on the arc length change of the track slab under axial pressure in step S153, calculate the compressive deformation energy of the track slab, expressed as: in: For the compressive deformation energy of the track slab, P The critical temperature force for arching on the track slab; S155. Based on the upward arching deformation curve of the track slab under temperature and pressure and the deformation curve of the initial elastic bending of the track slab in step S151, calculate the bending strain energy of the track slab, expressed as: in: For the bending deformation energy of the track slab, The wavelength of the upward arch deformation. This refers to the newly added internal torque during the deformation process. This refers to the angle created when the track slab is bent. The internal moment of the original elastic bending, This is the conversion factor for track stiffness. The elastic modulus of the track slab. Let the moment of inertia of the cross section be... The curve of the upward arching deformation of the track slab under temperature and pressure. Regarding the wavelength of the upward arch deformation The second derivative, Deformation curve of the track slab under elastic initial bending Regarding the wavelength of the upward arch deformation The second derivative; S156. The gravitational potential energy of the track slab is calculated based on the upper arch deformation vector and the upper arch deformation wavelength, and expressed as: in: The gravitational potential energy of the track slab. The density of the track slab concrete; It is the acceleration due to gravity; The cross-sectional area of ​​the track slab; S157. Based on the energy principle, establish the expression for the arch stability of the CRTSII type track slab, which is expressed as: ； S158. Substituting the compressive deformation energy of the track slab in step S154, the bending deformation energy of the track slab in step S155, and the gravitational potential energy of the track slab in step S156 into the camber stability expression of the CRTSII type track slab in step S157, we obtain the calculation formula for the critical temperature force of camber on the track slab, which is expressed as: ； S159. Using the function extremum solution method, the calculation formula for the critical temperature force of track slab arching in step S158 is differentiated with respect to the deformation wavelength to obtain the most unfavorable wavelength of track slab arching, expressed as: in: l The wavelength that is most unfavorable for the upward arch of the track slab.

3. The method for determining the arch stability of a CRTSII type track slab according to claim 1, characterized in that, Step S2 includes the following sub-steps: S21. Identify the adverse factors affecting the arch stability of the CRTSII type track slab, including initial bending of the track slab, height of narrow joint damage, and width of narrow joint damage. S22. Divide the initial bending of the track plate in step S21 into seven different bending states; S23. Divide the narrow seam damage height in step S21 into ten different damage levels; S24. Divide the narrow joint damage width in step S21 into three different damage degrees; S25. Combine the initial bending of the track slab with the seven different bending states divided in step S22, the damage height of the narrow joint with the ten different damage levels divided in step S23, and the damage width of the narrow joint with the three different damage levels divided in step S24 to form the calculation conditions. S26. Calculate the allowable temperature rise of the track slab at the allowable sagitta of the upper arch based on the two-dimensional numerical calculation model in step S1.

4. The method for determining the arch stability of a CRTSII type track slab according to claim 1, characterized in that, Step S3 includes the following sub-steps: S31. Construct a sample database based on the working conditions and allowable temperature rise of the track slab calculated in step S2; S32. Use regression analysis to construct an initial regression model between adverse influencing factors and the allowable temperature rise of the track slab; S33. Using the statistical analysis software SPSS, the sample database in step S31 is calculated according to the initial regression model in step S32 to obtain the calculation results of the initial regression model. S34. Based on the calculation results of the initial regression model in step S33, determine the significance calculation results of each adverse influencing factor in the initial regression model, and delete the independent variable terms whose significance calculation results of each adverse influencing factor in the initial regression model are greater than the standard value, to obtain the improved regression model.

5. The method for determining the arch stability of a CRTSII type track slab according to claim 4, characterized in that, In step S32, the initial regression model between the adverse influencing factors and the allowable temperature rise of the track slab is expressed as follows: in: The allowable temperature rise range for the track slab. a 0 is a constant term; a 1 represents the coefficient for the width of the narrow seam damage. w is Narrow seam damage width; a 2 is the first-order coefficient for the damage height of narrow seams. h For the height of the narrow seam damage, a 3 is the second-order coefficient for the damage height of narrow seams. a 4 is the first-order coefficient of the initial bending. For the initial bend, a 5 is the second-order coefficient for the initial bending. This is a random item.

6. The method for determining the arch stability of a CRTSII type track slab according to claim 4, characterized in that, Step S4 includes the following sub-steps: S41. Based on the improved regression model and the measured values ​​of adverse influencing factors in step S34, the predicted value of the allowable temperature rise of the track slab is obtained. S42. Determine whether the predicted value of the allowable temperature rise of the track slab in sub-step S41 is greater than or equal to the actual maximum temperature rise of the track slab; if so, determine that the CRTSII type track slab is stable by arching; otherwise, determine that the CRTSII type track slab is unstable by arching.

Images