A method for near-field longitudinal wave velocity inversion of a railway periodic bridge structure

Abstract

The application provides a near-field longitudinal wave velocity inversion method of a railway periodic bridge structure. The method comprises the following steps: constructing a vehicle-bridge-foundation dynamic interaction model according to railway parameters, periodic bridge structure parameters, track irregularity parameters and site soil parameters; theoretically analyzing the vibration response of the railway periodic bridge structure in the near-field foundation soil by using the model, and calculating the theoretical value of the ground vibration velocity response; performing a site vibration test around the actual railway periodic bridge structure, and obtaining the measured value of the ground vibration velocity response; comparing and verifying the theoretical value of the ground vibration velocity response and the measured value of the ground vibration velocity response, performing spectrum analysis, time-frequency analysis and wave velocity inversion according to the comparison and verification result, and obtaining the near-field longitudinal wave velocity of the railway periodic bridge structure. The method is based on the periodic bridge structure vibration theory and the Doppler effect to test the longitudinal wave velocity, and has good time resolution and relatively stable test results.

Description

Technical Field

[0001] This invention relates to the field of soil wave velocity measurement technology, and in particular to a method for inverting near-field longitudinal wave velocity of a periodic railway bridge structure. Background Technology

[0002] With the continuous development of my country's economy and the continuous growth of railway technology, my country's railway construction has achieved remarkable achievements in the past decade, with numerous railway lines emerging. When railway trains run on the tracks, they inevitably cause vibrations in the tracks. These vibrations are transmitted to the bridges through the wheel-rail contact between the train and the tracks, and then to the bridge piers through the supports, thus causing vibrations in the surrounding area and propagating in the form of waves to any location in the near and far fields of the soil.

[0003] Site soil wave velocity measurement has been widely applied in geological exploration and civil engineering. In engineering, shear wave velocity is an important parameter reflecting the dynamic characteristics of soil, often used to determine the thickness of the overburden layer, identify seismic liquefaction of sandy or silty soil foundations, classify building sites, and calculate the dynamic shear modulus of soil. Existing methods for measuring shear wave velocity mainly include the single-hole method, the cross-hole method, the surface wave method, and the bending element method, with the first three being the most commonly used. The single-hole and cross-hole methods require the assumption that seismic waves propagate in a straight line and that the medium is horizontally layered and uniformly distributed, which limits the upper limit of accuracy in solving for shear wave velocity. The surface wave method mainly measures the Rayleigh wave velocity at the surface and then solves for the shear wave velocity based on the functional relationship between the shear wave velocity and the Rayleigh wave velocity. However, this method is affected by other surface waves when measuring Rayleigh waves, resulting in lower accuracy.

[0004] Existing methods are all designed for measuring shear wave velocity and cannot directly and accurately obtain longitudinal wave velocity. Furthermore, measuring soil wave velocity using existing methods requires excavating a deep borehole within the soil area to be measured, allowing the acquisition instrument to be inserted for measurement. Given the increasing scarcity of land resources and stricter environmental protection requirements in recent years, traditional wave velocity measurement methods present significant implementation challenges. Therefore, researching and developing a new wave velocity measurement method is urgently needed.

[0005] Since a railway train can be considered a moving vibration source, and the location of the vibration source changes with the train's operation, a railway bridge with equidistant standard spans can be viewed as an approximately periodic structure. This periodically distributed bridge structure causes the vibration of the surrounding ground caused by the train's operation to exhibit a Doppler effect at the wavefield correlation frequency. Therefore, this invention combines the Doppler effect with the vibration wavefield generated by high-speed railway train operation. Taking into full account factors related to rail transit vibration (track irregularities, train-bridge structure-soil coupling, dynamic interaction between periodic bridge structures and soil), it utilizes the Doppler effect to calculate the wave velocity of the near-field soil vibration response, proposing a method for inverting the soil wave velocity.

[0006] In the existing technology, some scholars have proposed a method to roughly measure the longitudinal wave velocity using the vibration and Doppler effect caused by high-speed trains. However, this method does not take into account track irregularities, train-bridge structure-site soil coupling, periodic bridge structure and site soil dynamic interaction, etc. The correctness and rationality of the inversion results need to be further verified.

[0007] Currently, existing methods for measuring soil wave velocity primarily target shear wave velocity. For longitudinal wave velocity, calculations rely on empirical formulas relating shear and longitudinal waves, with few methods directly providing the longitudinal wave velocity. Furthermore, most existing wave velocity testing methods require excavating a deep borehole within the measured soil area to accommodate the instrument, incurring significant engineering costs for pile driving and drilling. These methods are also susceptible to interference from surrounding noise and vibration, leading to inaccurate wave velocity values. Summary of the Invention

[0008] The embodiments of the present invention provide a method for inverting the near-field longitudinal wave velocity of a railway periodic bridge structure, so as to effectively calculate the longitudinal wave velocity in the soil of the site through which railway trains pass.

[0009] To achieve the above objectives, the present invention adopts the following technical solution.

[0010] A method for inverting near-field longitudinal wave velocity in a periodic railway bridge structure includes:

[0011] A dynamic interaction model of vehicle-bridge-foundation soil is constructed based on railway parameters, periodic bridge structural parameters, track irregularity parameters, and site soil parameters.

[0012] The vibration response of a periodic railway bridge structure at any point in the near-field foundation soil was theoretically analyzed and numerically simulated using the vehicle-bridge-foundation soil dynamic interaction model, and the theoretical value of the ground vibration velocity response was calculated.

[0013] Field vibration tests were conducted around actual railway periodic bridge structures to obtain measured values ​​of ground vibration velocity response.

[0014] The theoretical value of the ground vibration velocity response and the measured value of the ground vibration velocity response are compared and verified. Based on the comparison and verification results, spectrum analysis, time-frequency analysis and wave velocity inversion are performed to obtain the near-field longitudinal wave velocity of the railway periodic bridge structure.

[0015] Preferably, the construction of the vehicle-bridge-foundation soil dynamic interaction model based on railway parameters, periodic bridge structural parameters, track irregularity parameters, and site soil parameters includes:

[0016] The vehicle-bridge-foundation soil dynamic interaction model includes a vertical random vibration analysis model of the vehicle-bridge time-varying system, a frequency domain finite element model analysis model of the periodic bridge structure, and a bridge pile foundation-site soil dynamic interaction analysis model.

[0017] The vertical stochastic vibration analysis model of the vehicle-bridge time-varying system is used to obtain the vertical motion equation of the vehicle-bridge multi-degree-of-freedom system based on structural dynamics and finite element theory. According to the basic principle of virtual excitation method, the track irregularity is equivalent to a series of simple harmonic loads, and the virtual excitation input form of the vehicle-bridge time-varying system is constructed. The motion equation of the vehicle-bridge time-varying system is solved by the separation iteration method to obtain the vertical stochastic dynamic calculation results and wheel-rail dynamic interaction force of the vehicle-bridge coupled system.

[0018] The frequency domain finite element analysis model of the periodic bridge structure is used to derive the frequency domain finite element dynamic equation and frequency domain finite element characteristic equation of the bridge structure based on the infinite periodic structure theory and frequency domain finite element method. It is used to obtain the calculation method of the basic span load spectrum under train load. Based on the dynamic response of the railway train structure and the dynamic wheel-rail force obtained by the vehicle-bridge system calculation, the vertical reaction force generated at the top and bottom of the pier when the railway train passes is calculated.

[0019] The bridge pile foundation-soil dynamic interaction analysis model is used to establish a soil model based on a thin-layer method with an ideal matching layer, and to derive and solve the basic solution of the soil vibration and the soil dynamic response under dynamic load. The bridge pile foundation-soil dynamic interaction model is established using the volume method, and the foundation dynamic impedance function and the foundation-soil vibration frequency response function are derived. The vibration response at any point in the soil is calculated based on the pier bottom reaction force obtained from the frequency domain finite element model of the periodic bridge structure.

[0020] Preferably, the method of using the vehicle-bridge-foundation soil dynamic interaction model to perform theoretical analysis and numerical simulation of the vibration response of a periodic railway bridge structure at any point in the near-field foundation soil, and calculating the theoretical value of the ground vibration velocity response, includes:

[0021] Based on the actual situation, the relevant parameters of the vehicle and the bridge are determined. These parameters include vehicle speed, vehicle body mass, bogie mass, wheelset mass, total number of bridge spans, and single span length. The relevant parameters are input into the vertical stochastic dynamic analysis model of the vehicle-bridge time-varying system. Track irregularities are equivalent to a series of simple harmonic loads, and a virtual excitation input form of the vehicle-bridge system is constructed. The motion equations of the vehicle-bridge system are solved using the separation iteration method to obtain the dynamic stochastic response of the vehicle and the bridge, as well as the dynamic interaction force between the train wheelset and the rail.

[0022] Substituting the dynamic interaction force between the train wheelset and the rail into the periodic bridge structure model established based on the infinite periodic structure theory and the frequency domain finite element method, the frequency domain finite element dynamic equation and frequency domain finite element characteristic equation of the bridge structure are derived, and the vertical reaction force at the top of the pier and the vertical reaction force at the bottom of the pier when the railway train passes are obtained.

[0023] A dynamic interaction model of pile group foundation-soil was established using the thin-layer method and volumetric method with ideal matching layer boundary conditions. A vertical unit harmonic load was applied to the center of the pile cap of the bridge pile group foundation, and the frequency response function of the ground observation points around the railway bridge was derived. The frequency response function was multiplied by the spectrum of the vertical reaction force at the bottom of the pier to obtain the velocity response spectrum of the soil surface around the railway bridge. Then, the time history data of the velocity response was obtained by using inverse Fourier transform, and the theoretical value of the ground vibration velocity response was calculated.

[0024] Preferably, the method of conducting site vibration tests around an actual railway periodic bridge structure to obtain measured values ​​of ground vibration velocity response includes:

[0025] When a railway train passes over an actual railway periodic bridge structure, a series of measuring points are arranged in the near field around the bridge piers, and speed sensors are used to measure the ground vibration velocity response caused by the railway train passing over the bridge structure.

[0026] Preferably, the step of comparing and verifying the theoretical value and the measured value of the ground vibration velocity response, and performing spectral analysis, time-frequency analysis, and wave velocity inversion based on the comparison and verification results to obtain the near-field longitudinal wave velocity of the railway periodic bridge structure includes:

[0027] The theoretical value and the measured value of the ground vibration velocity response are subjected to spectral and time-frequency analysis. The vertical velocity vibration order of magnitude, periodic loading time history trend and attenuation dominant frequency band distribution at each observation point on the ground are compared and verified. The correctness of the theoretical value of the ground vibration velocity response is determined based on the comparison and verification.

[0028] Wavelet transform is performed on the theoretical value of the ground vibration velocity response to obtain the time-frequency diagram of the ground vibration velocity response. Wavelet transform is also performed on the measured value of the ground vibration velocity response to obtain the time-frequency diagram of the ground vibration velocity response. When the Doppler frequency shift phenomenon can be analyzed from both time-frequency diagrams, it is confirmed that the Doppler effect can be found through the vehicle-bridge-foundation soil theoretical model.

[0029] Spectral and time-frequency analyses were performed on the theoretical values ​​of the ground vibration velocity response. The obtained spectra before and after the train passed a certain point on the ground were placed in the same coordinate system. The frequencies ω1 and ω2 received at the observation point when the vibration source position changed were substituted into the wave velocity calculation formula. Where V is the speed of the railway train, the near-field longitudinal wave velocity C is calculated. P .

[0030] As can be seen from the technical solutions provided by the embodiments of the present invention, the longitudinal wave velocity measurement method proposed in this invention directly utilizes a normally operating ordinary train or high-speed train, without requiring a huge engineering project for pile driving, making it simpler and more feasible than previous methods. This method is based on the theory of periodic bridge structure vibration and the Doppler effect to test the longitudinal wave velocity, which has good time resolution and relatively stable test results. It can solve the problem that traditional methods are easily affected by ambient noise and vibration, resulting in inaccurate measurement results, and has good prospects for engineering applications.

[0031] Additional aspects and advantages of the invention will be set forth in part in the description which follows, and will become apparent from the description or may be learned by practice of the invention. Attached Figure Description

[0032] To more clearly illustrate the technical solutions of the embodiments of the present invention, the drawings used in the description of the embodiments will be briefly introduced below. Obviously, the drawings described below are only some embodiments of the present invention. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0033] Figure 1 A flowchart illustrating a method for inverting near-field longitudinal wave velocity in a periodic railway bridge structure, provided in an embodiment of the present invention.

[0034] Figure 2 This is a flowchart illustrating the calculation of the dynamic interaction between a vehicle, a bridge, and the foundation soil, as proposed in an embodiment of the present invention. Detailed Implementation

[0035] Embodiments of the present invention are described in detail below, examples of which are shown in the accompanying drawings, wherein the same or similar reference numerals denote the same or similar elements or elements having the same or similar functions throughout. The embodiments described below with reference to the accompanying drawings are exemplary and are only used to explain the present invention, and should not be construed as limiting the present invention.

[0036] Those skilled in the art will understand that, unless specifically stated otherwise, the singular forms “a,” “an,” “the,” and “the” used herein may also include the plural forms. It should be further understood that the term “comprising” as used in this specification means the presence of the stated features, integers, steps, operations, elements, and / or components, but does not exclude the presence or addition of one or more other features, integers, steps, operations, elements, components, and / or groups thereof. It should be understood that when we say an element is “connected” or “coupled” to another element, it can be directly connected or coupled to the other element, or there may be intermediate elements. Furthermore, “connected” or “coupled” as used herein can include wireless connections or couplings. The term “and / or” as used herein includes any and all combinations of one or more of the associated listed items.

[0037] It will be understood by those skilled in the art that, unless otherwise defined, all terms used herein (including technical and scientific terms) have the same meaning as commonly understood by one of ordinary skill in the art to which this invention pertains. It should also be understood that terms such as those defined in general dictionaries should be understood to have the same meaning as in the context of the prior art, and should not be interpreted in an idealized or overly formal sense unless defined as herein.

[0038] To facilitate understanding of the embodiments of the present invention, the following will provide further explanation and description with reference to the accompanying drawings and several specific embodiments. These embodiments do not constitute a limitation on the embodiments of the present invention.

[0039] This invention addresses the problem that there are few direct measurement methods for longitudinal wave velocity in existing wave velocity measurement methods. It provides a method for inverting the longitudinal wave velocity in the foundation soil around elevated railway lines by utilizing a vehicle-bridge-foundation soil dynamic interaction model and the Doppler effect.

[0040] The method of this invention first uses a vehicle-bridge-foundation soil dynamic interaction model to theoretically analyze and numerically calculate the vibration response of a high-speed railway train at any point in the foundation soil near the ground. Then, it performs spectral analysis and wavelet transform on the ground vibration velocity response. At the same time, it combines the Doppler effect to directly obtain the longitudinal wave velocity in the foundation soil, avoiding the problem of inaccurate longitudinal wave velocity data caused by using shear wave velocity and empirical formulas to convert longitudinal wave velocity.

[0041] The processing flowchart of a near-field longitudinal wave velocity inversion method for a periodic railway bridge structure provided in this invention is as follows: Figure 1 As shown, the processing steps include the following:

[0042] Step S1. Vibration prediction of the site around railway trains and bridges

[0043] The vehicle-bridge-foundation soil dynamic interaction model proposed in this embodiment of the invention consists of the following three parts:

[0044] (1) Vertical random vibration analysis of vehicle-bridge time-varying system

[0045] Based on structural dynamics and finite element theory, the vertical motion equations of the vehicle-bridge system with 10 degrees of freedom are obtained. According to the basic principle of the virtual excitation method, track irregularities are equivalent to a series of simple harmonic loads, constructing the virtual excitation input form of the vehicle-bridge time-varying system. The motion equations of the vehicle-bridge time-varying system are solved using the separation iteration method, yielding the vertical stochastic dynamic calculation results of the vehicle-bridge coupled system.

[0046] (2) Frequency domain finite element model analysis of periodic bridge structures

[0047] Based on the theory of infinite periodic structures and the frequency domain finite element method, the frequency domain finite element dynamic equation and frequency domain finite element characteristic equation of bridge structure are derived, and the calculation method of the basic span load spectrum under train load is obtained. The dynamic response of railway train structure and the dynamic interaction force between wheel and rail obtained from the vehicle-bridge system calculation are substituted into the frequency domain finite element model of periodic bridge structure to calculate the vertical reaction force generated at the bottom of the pier when the railway train passes.

[0048] (3) Analysis of the interaction between bridge pile foundation and site soil dynamics

[0049] A site soil model was established based on the thin-layer method with an ideal matching layer, and the basic solution of site vibration and the dynamic response of site soil under dynamic load were derived and solved. A dynamic interaction model of bridge pile foundation-site soil was established using the volume method, and the dynamic impedance function of the foundation and the vibration frequency response function of the foundation-site soil were derived. The pier bottom reaction force calculated in the frequency domain finite element model of the periodic bridge structure was substituted into the dynamic interaction model of bridge pile foundation-site soil to calculate the vibration response at any point in the site soil.

[0050] Step S2. On-site vibration test

[0051] The calculation process for the dynamic interaction between a vehicle, a bridge, and the foundation soil, as proposed in this embodiment of the invention, is as follows: Figure 2As shown, vibration tests were conducted around an actual periodic railway bridge structure. When a train passed over the bridge, a series of measuring points were set up around the piers, and velocity sensors were used to measure the velocity response of the surrounding soil caused by the train's passage. The velocity response obtained from the actual test was compared with the velocity response obtained through numerical calculation using a vehicle-bridge-soil dynamic interaction model to verify the reliability of the theoretical calculation results used in this invention.

[0052] Step S3. Data Analysis and Wave Velocity Calculation

[0053] S3.1 Wavelet Transform

[0054] The vibration response calculated by the vehicle-bridge-foundation soil dynamic interaction model is decomposed into different spatial and scale components, and time-frequency analysis of the spatial and scale components is performed by wavelet transform. This invention utilizes the continuous wavelet transform in wavelet transform, as shown in formula (1):

[0055]

[0056] In the formula, t represents time, v(t) represents the collected vibration velocity signal of the soil surface at the site, and W... v (a,b) represents the wavelet transform values ​​of v(t), where a is the scale factor variable of the wavelet transform, b is the translation factor variable of the wavelet transform, and f is the sampling frequency. For wavelet mother function, for The conjugate function of .

[0057] S3.2 Wave Speed ​​Calculation

[0058] According to the Doppler effect, when the train vibration source is close to the ground observation point, the frequency received at the observation point is:

[0059]

[0060] Where ω1 is the frequency received by the train vibration source when it is running close to the ground observation point. Let V be the angular frequency of the train's vibration source, V be the train's speed, and C be the angular frequency of the train's vibration source. P The longitudinal wave velocity of the site soil.

[0061] When the train vibration source is far away from the ground observation point, the frequency received at the observation point is:

[0062]

[0063] Where ω2 is the frequency received when the train vibration source is far from the ground observation point.

[0064] Combining equations (2) and (3), we obtain the following formula for calculating the longitudinal wave velocity:

[0065]

[0066] The vibration response in the foundation soil around the railway line is calculated using the vehicle-bridge-foundation soil dynamic interaction model. The response signal is subjected to spectrum analysis and time-frequency analysis. The spectrum diagrams obtained by the analysis before and after the train passes a certain point on the ground are placed in the same coordinate system. The longitudinal wave velocity can be calculated by substituting the frequencies ω1 and ω2 received at the observation point when the vibration source position changes into the wave velocity calculation formula (4).

[0067] In summary, the embodiments of the present invention utilize the structural vibration and Doppler effect generated by the dynamic interaction between railway trains and periodic bridge piers, and use numerical simulation and experimental verification as research methods to invert the longitudinal wave velocity in the soil of the site through which the railway train passes, directly obtaining the longitudinal wave velocity, effectively making up for the shortcoming of existing wave velocity inversion methods that cannot directly invert the longitudinal wave velocity.

[0068] Those skilled in the art will understand that the accompanying drawings are merely schematic diagrams of one embodiment, and the modules or processes shown in the drawings are not necessarily essential for implementing the present invention.

[0069] As can be seen from the above description of the embodiments, those skilled in the art can clearly understand that the present invention can be implemented by means of software plus necessary general-purpose hardware platforms. Based on this understanding, the technical solution of the present invention, or the part that contributes to the prior art, can be embodied in the form of a software product. This computer software product can be stored in a storage medium, such as ROM / RAM, magnetic disk, optical disk, etc., and includes several instructions to cause a computer device (which may be a personal computer, server, or network device, etc.) to execute the methods described in various embodiments or some parts of the embodiments of the present invention.

[0070] The various embodiments in this specification are described in a progressive manner. Similar or identical parts between embodiments can be referred to mutually. Each embodiment focuses on describing the differences from other embodiments. In particular, for apparatus or system embodiments, since they are basically similar to method embodiments, the description is relatively simple; relevant parts can be referred to the descriptions in the method embodiments. The apparatus and system embodiments described above are merely illustrative. The units described as separate components may or may not be physically separate. The components shown as units may or may not be physical units; that is, they may be located in one place or distributed across multiple network units. Some or all of the modules can be selected to achieve the purpose of this embodiment according to actual needs. Those skilled in the art can understand and implement this without creative effort.

[0071] The above description is merely a preferred embodiment of the present invention, but the scope of protection of the present invention is not limited thereto. Any variations or substitutions that can be easily conceived by those skilled in the art within the technical scope disclosed in the present invention should be included within the scope of protection of the present invention. Therefore, the scope of protection of the present invention should be determined by the scope of the claims.

Claims

1. A method for near-field longitudinal wave velocity inversion of a railway periodic bridge structure, characterized in that, The application relates to a method for measuring the near-field longitudinal wave velocity of a railway periodic bridge structure. The method comprises the following steps: a vehicle-bridge-foundation soil dynamic interaction model is constructed according to railway parameters, periodic bridge structure parameters, track irregularity parameters and site soil parameters; theoretical analysis and numerical simulation are conducted on the vibration response of the railway periodic bridge structure at any point in the near-field foundation soil by using the vehicle-bridge-foundation soil dynamic interaction model, and the theoretical value of the ground vibration velocity response is calculated; a site vibration test is conducted around the actual railway periodic bridge structure, and the measured value of the ground vibration velocity response is obtained; the theoretical value of the ground vibration velocity response is compared with the measured value of the ground vibration velocity response, frequency spectrum analysis, time-frequency analysis and wave velocity inversion are conducted according to the comparison result, and the near-field longitudinal wave velocity of the railway periodic bridge structure is obtained. The theoretical analysis and numerical simulation of the vibration response of the railway periodic bridge structure at any point in the near-field foundation soil by using the vehicle-bridge-foundation soil dynamic interaction model to calculate the theoretical value of the ground vibration velocity response comprises the following steps: the related parameters of the vehicle and the bridge are determined according to the actual situation, the related parameters include the vehicle speed, the vehicle body mass, the bogie mass, the wheelset mass, the total span number of the bridge and the single span length, the related parameters are input into the vertical random dynamic analysis model of the vehicle-bridge time-varying system, the track irregularity is equivalent to a series of harmonic loads, the virtual excitation input form of the vehicle-bridge system is constructed, the motion equation of the vehicle-bridge system is solved by using the separation iteration method, and the dynamic random response of the vehicle and the bridge and the dynamic interaction force between the train wheelset and the rail are obtained; the dynamic interaction force between the train wheelset and the rail is substituted into the periodic bridge structure model established based on the infinite periodic structure theory and the frequency domain finite element method, the frequency domain finite element dynamic equation and the frequency domain finite element characteristic equation of the bridge structure are derived, and the vertical reaction force at the top of the pier and the vertical reaction force at the bottom of the pier of the bridge are obtained when the train passes through; 2. The method of claim 1, wherein, a group pile foundation-foundation soil dynamic interaction model is established by using the thin layer method and the volume method with ideal matching layer boundary conditions, a vertical unit harmonic load is applied to the center of the pile cap of the bridge group pile foundation, the frequency response function of the ground surface observation point around the railway bridge is derived, the frequency spectrum of the vertical reaction force at the bottom of the pier is multiplied by the frequency response function to obtain the velocity response frequency spectrum of the ground surface around the railway bridge, and the time history data of the velocity response is obtained by using the inverse Fourier transform, so that the theoretical value of the ground vibration velocity response is calculated. The vehicle-bridge-foundation soil dynamic interaction model comprises a vertical random vibration analysis model of a vehicle-bridge time-varying system, a periodic bridge structure frequency domain finite element model analysis model and a bridge group pile foundation-foundation soil dynamic interaction analysis model. The vertical random vibration analysis model of the vehicle-bridge time-varying system is used to obtain the vertical motion equation of the vehicle-bridge multi-degree-of-freedom system based on structural dynamics and finite element theory, to equivalently convert the track irregularities into a series of harmonic loads according to the basic principle of the pseudo-excitation method, to construct the pseudo-excitation input form of the vehicle-bridge time-varying system, to solve the motion equation of the vehicle-bridge time-varying system by using the separation iteration method, and to obtain the vertical random dynamic calculation results of the vehicle-bridge coupling system and the wheel-rail dynamic interaction force; The periodic bridge structure frequency domain finite element analysis model is used to obtain the calculation method of the basic span load spectrum under the action of the train load based on the bridge structure frequency domain finite element dynamic equation and the frequency domain finite element characteristic equation derived based on the infinite periodic structure theory and the frequency domain finite element method, and to calculate the vertical reaction force generated at the top and bottom of the pier when the train passes through the railway bridge according to the structural dynamic response and the dynamic wheel-rail force of the train calculated by the vehicle-bridge system. The bridge pile group foundation-site soil dynamic interaction analysis model is used to establish the site soil model based on the thin layer method with ideal matching layers, to derive and solve the basic solution of the site vibration and the dynamic response of the site soil under the action of the dynamic load, to establish the bridge pile group foundation-site soil dynamic interaction model by using the volume method, to derive the foundation dynamic impedance function and the foundation-site soil vibration frequency response function, and to calculate the vibration response at any point in the site soil according to the pier bottom reaction force calculated by the periodic bridge structure frequency domain finite element model.

3. The method of claim 1, wherein, The field vibration test around the actual railway periodic bridge structure is performed to obtain the measured value of the ground vibration velocity response, including: When the train passes through the actual railway periodic bridge structure, a series of measuring points are arranged around the pier in the near field, and the velocity sensor is used to measure the ground vibration velocity response caused by the train passing through the bridge structure.

4. The method according to any one of claims 1 to 3, characterized in that, The theoretical value and the measured value of the ground vibration velocity response are compared and verified, the spectrum analysis, the time-frequency analysis and the wave velocity inversion are performed according to the comparison and verification results, and the near-field longitudinal wave velocity of the railway periodic bridge structure is obtained, including: The spectrum analysis and the time-frequency analysis are performed on the theoretical value and the measured value of the ground vibration velocity response, and the comparison and verification are performed through the vertical velocity vibration order of each observation point on the ground, the periodic loading time trend and the distribution of the dominant frequency band in the frequency domain, and whether the theoretical value of the ground vibration velocity response is correct is judged according to the comparison and verification; The wavelet transform is performed on the theoretical value of the ground vibration velocity response to obtain the time-frequency diagram of the ground vibration velocity response, the wavelet transform is performed on the measured value of the ground vibration velocity response to obtain the time-frequency diagram of the ground vibration velocity response, and when the Doppler shift phenomenon can be analyzed from both time-frequency diagrams, it is confirmed that the Doppler effect can be found by the vehicle-bridge-foundation soil theoretical model. The theoretical value of the ground vibration velocity response is subjected to frequency spectrum analysis and time-frequency analysis, the frequency spectrum diagrams obtained by the analysis before and after the train passing through a certain point on the ground are placed in the same coordinate system, and the frequency and into the wave velocity calculation formula where V is the running speed of the railway train, and the near-field longitudinal wave velocity C P is calculated.

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