A method, system, device and medium for simulating Rayleigh surface waves from high-speed railway earthquake sources

Abstract

The present invention relates to a method, system, device and medium for simulating Rayleigh surface waves of a high-speed railway earthquake source, and belongs to the technical field of numerical simulation of earthquake waves. A high-speed train is a moving line source in a fixed direction. Based on the train moving load model, the loads applied by the four pairs of axles of each carriage to the sleepers under the track are taken as point sources, and the moving line source is decomposed into a superposition of a series of point sources. Considering the elastic effect of the track rails, a time function of the high-speed railway earthquake source is constructed based on the Euler-Bernoulli elastic beam theory. Considering the absorption and attenuation of seismic waves by the underground medium, the staggered grid finite difference method is used to solve the Kelvin viscoelastic wave equation, and at the same time, considering the free surface boundary, the wave field of the earthquake Rayleigh surface wave excited by the high-speed railway moving earthquake source is numerically simulated. It provides the basis and data for the subsequent waveform inversion based on the high-speed railway earthquake source and the inversion of the high-speed railway earthquake source surface wave dispersion curve.

Description

Technical Field

[0001] The present invention belongs to the technical field of seismic wave numerical simulation, and in particular relates to a method, system, equipment and medium for simulating Rayleigh surface waves of a high-speed railway earthquake source. Background Art

[0002] With rapid economic development and growing public demand for convenient travel, China has become a global leader in high-speed rail development. By the end of 2023, my country's total high-speed rail mileage exceeded 45,000 kilometers, including trunk lines connecting numerous economically developed regions and major cities. my country's vast territory and complex and diverse topography pose challenges for traditional seismic sources in meeting the needs of geological exploration. During the operation of high-speed trains, the interaction between the axles and the tracks generates tremendous impact forces, which excite seismic waves in the underground medium, thus forming a green seismic source, the high-speed rail seismic source. Given the stability of the high-speed rail network and high-speed train operation, the high-speed rail seismic source is considered a reliable and repeatable artificial seismic source for geophysical exploration and geological structure imaging. Early studies have shown that the seismic signals generated by high-speed rail seismic sources have discrete spectra and broadband characteristics, and can reflect changes in the underground medium, providing an effective tool for underground structure detection.

[0003] Existing techniques typically simulate the wavefield of a high-speed rail moving source consistent with measured high-speed rail seismic signals in an elastic medium, analyze the wavefield, and generate subsequent data based on the high-speed rail seismic signals. Under these medium conditions, the data obtained from numerical simulations of the wavefield excited by the moving source of the high-speed rail and the extracted surface waves are incomplete. However, the actual underground medium is not completely elastic and generates high-energy Rayleigh surface waves when a train passes through it. Existing simulation methods often overlook the generation of Rayleigh surface waves when analyzing the wavefield. Summary of the Invention

[0004] In order to solve the problem that the viscoelastic medium and free surface boundary are not considered in the existing high-speed railway earthquake source Rayleigh surface wave simulation method, the present invention provides a high-speed railway earthquake source Rayleigh surface wave simulation method, system, equipment and medium.

[0005] In order to achieve the above object, the present invention provides the following technical solutions:

[0006] A method for simulating Rayleigh surface waves of a high-speed railway earthquake source comprises the following steps:

[0007] Taking train length parameters, bridge pier structure parameters, and underground three-dimensional viscoelastic medium parameters, and determining the train running state according to the train length parameters and bridge pier structure parameters;

[0008] According to the running state of the train, the load force of the sleeper at each wheel axle position of the high-speed train is obtained, and according to the load force, a time function of the earthquake source excited by the high-speed train during operation is determined;

[0009] constructing a three-dimensional viscoelastic wave equation according to the three-dimensional viscoelastic medium parameters of the underground and based on the Kelvin-Voigt model, solving the three-dimensional viscoelastic wave equation by a staggered grid finite difference method to obtain a three-dimensional viscoelastic wave staggered grid finite difference format equation;

[0010] The free surface boundary is set, and the three-dimensional viscoelastic wave staggered grid finite difference format equation and the source time function are solved by the time domain staggered grid finite difference method. Based on the solution results, the Rayleigh surface wave field of the high-speed railway moving earthquake source is simulated and generated.

[0011] Preferably, the load force at the wheel axle position is obtained by:

[0012]

[0013] Where x represents the position of the sleeper, x i represents the position of the i-th axle on the high-speed train; is the position of the i-th wheel axle at time t, G i is the axle load at the corresponding position, Δx is the sleeper spacing, and the coefficient β=(α / 4EI) 0.25 , E is the elastic modulus of the rail, I is the cross-sectional momentum, α is the ground stiffness under the track, and the total deflection distance x0 = π / β.

[0014] Preferably, the method of determining the source time function of the earthquake excited by the high-speed train during operation according to the acting force specifically includes the following steps:

[0015] Adding up the forces exerted on the sleepers by all axles of each carriage of the high-speed train, the total force on the sleepers is:

[0016]

[0017] Where N is the number of carriages, 4N is the 4N axles under the N carriages of the high-speed train, x is the position of the sleeper, and x is the i represents the position of the i-th axle on the high-speed train; x i t is the position of the i-th wheel axle at time t, G i is the axle load at the corresponding position, Δx is the sleeper spacing, and the coefficient β=(α / 4EI) 0.25 , E is the elastic modulus of the rail, I is the cross-sectional momentum, α is the ground stiffness under the track, and the total deflection distance x0 = π / β;

[0018] The first-order time derivative of the total force acting on the sleeper is used as the time function of the high-speed rail earthquake source:

[0019]

[0020] Where M is the number of piers, d is the spacing between piers, h is the depth of the pier pile foundation buried underground, x0 is the position of the first pier, L is the length of the carriage, and F'(x,t) is the first-order derivative of the total force acting on the sleeper.

[0021] Preferably, a three-dimensional viscoelastic wave equation is constructed based on the three-dimensional viscoelastic medium parameters of the underground and the Kelvin-Voigt model, specifically:

[0022]

[0023] Where, σ xx , σ yy , σ zz , τ yz , τ xz , τ xy is the stress component, v x 、v y 、v z are the velocity components of the particle in different directions,

[0024] μ=ρV s 2 , The three-dimensional viscoelastic medium parameters of the underground include: V p 、V s ,ρ,Q p , Q s , V p is the longitudinal wave velocity of the medium, V s is the shear wave velocity, ρ is the density, Q p , Q s are the quality factors of longitudinal and shear waves, and ω is the circular frequency.

[0025] Preferably, the free surface boundary is specifically:

[0026] The acoustic and elastic medium boundaries are used to approximate the free surface boundaries. The normal stress is set to zero directly at the free boundary, and the shear stress is set to zero. The free boundary parameters are set as follows:

[0027]

[0028] Where, σ zz(x,y,0) , ρ (x,y,0) ,λ (x,y,0) 、μ (x,y,0) represent the normal stress, density and Lame constant on the free surface boundary, respectively; ρ, λ and μ represent the density and Lame constant of the medium below the free surface boundary.

[0029] The present invention also provides a high-speed railway source Rayleigh surface wave simulation system, comprising:

[0030] The parameter input module is used to obtain train length parameters, bridge pier structure parameters and underground three-dimensional viscoelastic medium parameters, and determine the train operation status based on the train length parameters and bridge pier structure parameters.

[0031] The high-speed rail moving earthquake source analysis module is used to obtain the load force of the sleeper at each wheel axle position of the high-speed rail train according to the train operation status, and determine the earthquake source time function excited by the high-speed rail train during operation according to the force.

[0032] The staggered grid finite difference simulation module is used to construct a three-dimensional viscoelastic wave equation based on the three-dimensional viscoelastic medium parameters of the underground and the Kelvin-Voigt model, and solve the three-dimensional viscoelastic wave equation through the staggered grid finite difference method to obtain a three-dimensional viscoelastic wave staggered grid finite difference format.

[0033] The output module is used to set the free surface boundary, solve the three-dimensional viscoelastic wave staggered grid finite difference format and the source time function using the time domain staggered grid finite difference method, and simulate the Rayleigh surface wave field of the high-speed rail moving source based on the solution results.

[0034] The present invention also provides a computer device, comprising a memory, a processor and a computer program stored in the memory, wherein the processor executes the computer program to implement the steps described in the method for simulating Rayleigh surface waves of high-speed railway earthquake sources.

[0035] The present invention also provides a computer-readable storage medium, on which a computer program is stored. When the computer program is loaded by a processor, it can execute the steps described in the high-speed railway source Rayleigh surface wave simulation method.

[0036] The method for simulating Rayleigh surface waves from a high-speed railway earthquake source provided by the present invention has the following beneficial effects:

[0037] Train length parameters, bridge pier structural parameters, and three-dimensional viscoelastic medium parameters are obtained, and their effects on the simulation of high-speed rail moving earthquake sources are considered. The time function of the high-speed rail earthquake source excited by the train during operation is obtained based on the forces acting on it. A three-dimensional viscoelastic wave equation is constructed based on the three-dimensional viscoelastic medium parameters and the Kelvin-Voigt model. Rayleigh surface waves are generated by considering the free surface boundary. The three-dimensional viscoelastic wave equation and the time function of the high-speed rail earthquake source are solved using the staggered-grid finite-difference method in the time domain, resulting in the Rayleigh surface wave field of the moving high-speed rail earthquake source. Under viscoelastic medium conditions, the wave field of the moving high-speed rail earthquake source is simulated, consistent with the measured high-speed rail seismic signal. High-speed rail seismic records containing Rayleigh surface waves are obtained, and the high-speed rail seismic wave field is analyzed, along with the next steps based on the high-speed rail seismic data. This provides a theoretical basis and data for extracting Rayleigh surface wave dispersion curves and performing surface wave inversion using high-speed rail seismic signals. BRIEF DESCRIPTION OF THE DRAWINGS

[0038] To more clearly illustrate the embodiments of the present invention and its design, the following briefly introduces the drawings required for this embodiment. The drawings described below are only some embodiments of the present invention. For those skilled in the art, other drawings can be derived from these drawings without inventive effort.

[0039] Figure 1 A schematic flow chart of a method for simulating Rayleigh surface waves from a high-speed railway earthquake source provided by the present invention.

[0040] Figure 2 This is the train moving load model provided by the present invention.

[0041] Figure 3 This is a three-dimensional pier model when a train runs on a viaduct.

[0042] FIG4 shows the wave field capacity attenuation process of a specific embodiment, wherein FIG4(a) is a two-layer model provided by the present invention; FIG4(b) and FIG4(c) are instantaneous wave field slices at time t=0.375s when the two-layer model is an elastic medium and a viscoelastic medium, respectively.

[0043] Figure 5 shows the high-speed rail source wavelet and its spectrum obtained through the source function, where Figure 5 (a) is the high-speed rail source wavelet excited by the train, and Figure 5 (b) is the high-speed rail source wavelet spectrum corresponding to Figure 5 (a).

[0044] Figure 6 These are instantaneous slices of the seismic wave field excited by a high-speed train in a three-dimensional viscoelastic medium uniform model in an embodiment of the present invention, corresponding to the wave field snapshots at 1s, 5s, 9s, and 12s respectively.

[0045] Figure 7 for Figure 6The instantaneous slices of the 3D seismic wave field correspond to the instantaneous slices of the wave field in the XY plane, which correspond to the snapshots of the wave field at the time of 1s, 5s, 9s, and 12s respectively.

[0046] Figure 8 for Figure 6 The instantaneous slices of the 3D seismic wave field correspond to the instantaneous slices of the wave field in the XZ plane, which correspond to the snapshots of the wave field at 1s, 5s, 9s, and 12s respectively.

[0047] FIG9 is a time profile of earthquake records excited by a high-speed train in a three-dimensional uniform viscoelastic medium model according to an embodiment of the present invention; wherein FIG9(a), FIG9(b), and FIG9(c) correspond to records on the X-direction survey line under the viaduct, 125 m and 250 m away from the railway line, respectively.

[0048] Figure 10 shows the high-speed rail seismic signal received at x = 400m when the train is running on the bridge pier in an embodiment of the present invention. Figure 10 (a), Figure 10 (b), and Figure 10 (c) respectively correspond to the x, y, and z components of the high-speed rail seismic signal and its spectrum received by the detector under the viaduct.

[0049] Figure 11 shows the high-speed rail seismic signal received at x = 400m when the train is running on the bridge pier in an embodiment of the present invention. Figure 11 (a), Figure 11 (b), and Figure 11 (c) respectively correspond to the x, y, and z components of the high-speed rail seismic signal and its spectrum received by the detector 125m away from the railway line.

[0050] Figure 12 is a high-speed rail seismic signal received at x = 400m when the train is running on the bridge pier in an embodiment of the present invention. Figure 12 (a), Figure 12 (b), and Figure 12 (c) respectively correspond to the x, y, and z components of the high-speed rail seismic signal and its spectrum received by the detector 250m away from the railway line.

[0051] Figure 13 Schematic diagram of a device for simulating Rayleigh surface waves of a high-speed railway source in a three-dimensional viscoelastic medium provided by the present invention.

[0052] Figure 14 This is a schematic structural diagram of an embodiment of a device for simulating Rayleigh surface waves of a high-speed railway source in a three-dimensional viscoelastic medium provided by the present invention. DETAILED DESCRIPTION

[0053] In order to enable those skilled in the art to better understand the technical solution of the present invention and to be able to implement it, the present invention is described in detail below with reference to the accompanying drawings and specific embodiments. The following embodiments are only used to more clearly illustrate the technical solution of the present invention and are not intended to limit the scope of protection of the present invention.

[0054] When simulating the high-speed rail moving source wave field that is consistent with the measured high-speed rail seismic signal, the actual underground medium is not a completely elastic body, and the effect of friction within the medium needs to be considered. Mechanical energy will also be converted into other forms of energy. At this time, the proportional relationship between stress and strain no longer holds.

[0055] Based on this, the present invention provides a method for simulating Rayleigh surface waves of high-speed railway earthquake sources, such as Figure 1 As shown, the specific steps include:

[0056] S1. Obtain train length parameters, bridge pier structural parameters, and underground three-dimensional viscoelastic medium parameters. Determine the train's operating status based on the train length and pier structural parameters. When a train runs on a track, it can be considered a moving line source moving in one direction. The track is fixed to the sleepers or ballastless track slabs via fasteners.

[0057] The interaction between the train and the track is simplified into the vertical load of the carriage axle on the sleeper or fastener. These loads continuously excite seismic waves along the track as the train moves. The train moving load model is as follows: Figure 2 As shown. Where L represents the length of each carriage, a and b are the distances between the front and rear axles, G i is the axle load (unit: N), assuming that the load applied to each axle is equal.

[0058] High-speed trains spend most of their time running on viaducts. At this time, the seismic waves are excited by the pile foundations of the bridge piers inserted into the ground, and the earthquake source point changes from the sleepers to the bridge piers. Construct a load model for high-speed trains running on viaducts, such as Figure 3 .

[0059] S2. Based on the train's running status, obtain the load force acting on the sleeper at each axle position of the high-speed train, and determine the source-time function of the earthquake excited by the high-speed train during operation based on the force. Simplify the high-speed train into a moving line source moving on the track, with each sleeper acting as a source point during the movement of the moving line source; based on the Euler-Bernoulli beam equation, calculate the force acting on any sleeper under any axle load on the high-speed train, and determine the force acting on the sleeper under the axle load at any position of the high-speed train as:

[0060]

[0061] Where x represents the position of the sleeper, x i represents the position of the i-th axle on the high-speed train; is the position of the i-th wheel axle at time t, G iis the axle load at the corresponding position, Δx is the sleeper spacing, the coefficient β = (α / 4EI)0.25, E is the elastic modulus of the rail, I is the cross-sectional momentum, α is the ground stiffness under the track, and the total deflection distance x0 = π / β.

[0062] Considering the 4N load on the axle from the train, the total action on the sleeper at x is:

[0063]

[0064] Where N represents the number of carriages, and 4N represents the 4N axles under the N carriages of the high-speed train.

[0065] The first-order time derivative of the total force is used as the time function of the high-speed rail earthquake source:

[0066]

[0067] Where M is the number of piers, d is the spacing between piers, h is the depth of the pier pile foundation buried underground, x0 is the position of the first pier, L is the length of the carriage, and F'(x,t) is the first-order derivative of the total force acting on the sleeper.

[0068] S3. Considering the three-dimensional viscoelastic medium parameters and constructing the three-dimensional viscoelastic wave equation based on the Kelvin-Voigt model, the three-dimensional viscoelastic wave equation is solved by the staggered grid finite difference method to obtain the three-dimensional viscoelastic wave staggered grid finite difference format equation.

[0069] The stress of a medium under elastic deformation consists of two parts, namely the strain part and the strain change rate part. The viscoelastic medium is considered to be composed of two parts, one is a completely elastic medium and the other is a viscoelastic medium. Based on the differential equation of motion of elastic bodies, the relationship between stress and displacement components, and the generalized Hooke's law, the three-dimensional first-order stress-velocity viscoelastic wave equation is obtained:

[0070]

[0071] Where, σ xx , σ yy , σ zz , τ yz , τ xz , τ xy is the stress component, v x 、v y 、v z are the velocity components of the particle in different directions,

[0072] The three-dimensional viscoelastic medium parameters of the underground include: V p 、V s ,ρ,Q p, Q s , V p 、V s , ρ is the medium longitudinal wave velocity, shear wave velocity and density, Q p , Q s are the quality factors of longitudinal and shear waves, and ω is the circular frequency.

[0073] S4. Set the free surface boundary and solve the three-dimensional viscoelastic wave staggered grid finite difference scheme equation and the source time function using the time domain staggered grid finite difference method. Based on the solution results, simulate and generate the Rayleigh surface wave field of the high-speed rail moving earthquake source. The time domain staggered grid finite difference simulation based on the three-dimensional viscoelastic wave staggered grid finite difference scheme and the high-speed rail source wavelet specifically includes:

[0074] The three-dimensional first-order stress-velocity viscoelastic wave equation is solved based on the Kelvin model.

[0075] While considering the continuity of stresses in the transverse direction above and below the free surface boundary, the acoustic and elastic medium boundaries are used to approximate the free surface boundary to simulate and generate Rayleigh surface waves. Instead of directly processing all stress conditions, the normal stress is set to zero at the free boundary. The zero shear stress condition is achieved by setting the physical parameters on the free boundary:

[0076]

[0077] Among them, σ zz(x,y,0) , ρ (x,y,0) ,λ (x,y,0) 、μ (x,y,0) represent the normal stress, density and Lame constant on the free surface boundary, respectively; ρ, λ and μ represent the density and Lame constant of the medium below the free surface boundary.

[0078] A two-layer model was used for testing. The size of the two-layer medium model is 1000m×1000m, where the stratum is located at a depth of 250m, as shown in Figure 4(a). The source uses Ricker wavelet with a main frequency of 30Hz and is located at the center of the surface (five-pointed star). The two geophones (inverted triangles) are 125m and 250m away from the source respectively. When the two-layer model contains elastic medium and viscoelastic medium (Q p =Q s=40), snapshots of the vertical component wavefield at t = 0.375s are shown in Figures 4(b) and 4(c). These include P-waves (P) and S-waves, as well as the high-energy Rayleigh surface waves (R) generated near the surface after adopting a free surface boundary. P-waves passing through the stratum interface generate reflected P-waves (P11) and transmitted P-waves (P12). Comparing (b) and (c), using the same scale range, reveals that the wavefield energy in viscoelastic media is attenuated compared to that in elastic media, and the degree of attenuation increases with propagation distance.

[0079] The rails are treated as Euler-Bernoulli elastic beams, and the total force exerted by the four front and rear axles of each high-speed train car on the sleepers is calculated as the load function. The number of train cars N = 16, the travel speed v = 83.3 m / s (300 km / h), the distances between the front and rear axles a = 2.5 m, b = 17.5 m, the length of each car L = 25 m, and the ground stiffness α = 400 MN / m are assumed. 2 , EI=6.626MN / m 2 The load-time functions obtained are mostly positive, with large energy at zero frequency in the frequency domain. Directly using them as source-time functions will lead to dynamic imbalance in the numerical simulation of seismic waves.

[0080] Taking into account the reaction force exerted by the track slab on the sleeper, and using the first-order time derivative of the load-time function as the time function of the high-speed rail earthquake source, the resulting high-speed rail earthquake source wavelet and its spectrum are shown in Figures 5(a) and (b). In the time domain, the high-speed rail earthquake source wavelet has a clear periodicity corresponding to the number of train cars N. In the frequency domain, the high-speed rail earthquake source wavelet has a distinct discrete spectral characteristic. The frequency corresponding to the first peak line is called the fundamental frequency, and other peak lines appear at integer multiples of the fundamental frequency.

[0081] The three-dimensional viscoelastic wave equation and the time function of the high-speed rail earthquake source are solved using the staggered-grid finite-difference method in the time domain to obtain the Rayleigh surface wave field and seismic records of the high-speed rail moving earthquake source. The axle loads exerted by the wheels on the sleepers during high-speed train operation are obtained based on the Euler-Bernoulli elastic beam theory. The time derivatives of the axle loads are then calculated as the high-speed rail earthquake source wavelets generated by the train during operation.

[0082] Based on the three-dimensional first-order stress-velocity viscoelastic wave equation and the high-speed railway source wavelet, the propagation of seismic waves excited by the high-speed railway moving source in the three-dimensional viscoelastic medium is simulated using the time domain staggered grid finite difference method.

[0083] In the three-dimensional horizontal surface uniform model of viscoelastic medium, the model size is 1000m×1000m×250m, the bridge piers are evenly distributed along the x direction, and the first bridge pier is located at (x=50m,y=500m).p =800m / s, shear wave velocity V s =400m / s, density ρ = 1800kg / m 3 The staggered grid has a spatial step size of Δx = Δz = 2.5 m and a time step size of Δt = 0.5 ms. The high-speed rail earthquake source load is applied to the vertical velocity component, and the simulation duration is 15 s. The model contains 32 bridge piers, with a spacing of 25 m between them.

[0084] Figure 6 Snapshots of the high-speed rail seismic wavefield in a 3D homogeneous viscoelastic medium model at 1s, 5s, 9s, and 12s. As the train moves, the carriages continuously pass over bridge piers, exciting orderly seismic wavefronts that advance as the train advances. At 1s, the train begins to excite seismic waves. As time passes, as the train continues to move forward, more bridge piers excite seismic waves. By 5s, the train has passed multiple bridge piers, and the wavefield becomes more complex. By 9s, the waves excited by different bridge piers produce complex interference phenomena, until 12s, when the train approaches the end of the model.

[0085] Figure 7 Snapshots of the high-speed rail seismic wavefield on the XY plane at 1s, 5s, 9s, and 12s. As the train moves, the wheel axles of the carriages sequentially pass over bridge piers, generating seismic waves that form multiple circular wavefronts that move in the direction of the train's travel. Within the total length of the train, the seismic waves generated by multiple bridge piers superimpose, forming a straight line parallel to the railway line, which propagates outward.

[0086] Figure 8 This is a snapshot of the high-speed rail seismic wavefield in the XZ plane. The black boxes show the seismic waves generated by the four pairs of axles on a single carriage. First, the P and S waves are excited by the front two pairs of axles. Because the distance between these two pairs of axles is very short (2.5 meters), the time difference between the excitations is only 0.03 seconds, causing the P and S waves corresponding to the two pairs of axles to propagate for a certain distance before gradually separating. Next, the R waves excited by these two pairs of axles are generated. Their energy is relatively strong, but they decay rapidly with propagation depth. The rear two pairs of axles also excite P, S, and R waves, with the same excitation pattern as the front two pairs. This excitation process is then repeated for the next carriage until all axles have passed the bridge pier. The train's multiple axles interact with different bridge piers simultaneously, generating seismic waves, increasing the complexity of the wavefield. At the same location, a geophone will simultaneously receive seismic waves excited by different axles and different carriage axles.

[0087] Figure 9 shows the vertical component of high-speed rail earthquake signals recorded along the x-axis at different distances from the railway line. (a), (b), and (c) correspond to the detectors located below the viaduct, 125m, and 250m from the railway line, respectively. The abscissa is x-distance, and the ordinate is time. As distance increases, the high-speed rail seismic signal is no longer confined to the brief period of time during which the train passes, but appears over a longer timeframe.

[0088] Figure 10 shows the three-component high-speed rail seismic signal and its spectrum, received by a ground-based geophone beneath the viaduct. The simulated seismic record exhibits quasi-periodicity in the time domain, corresponding to the number of train cars, and exhibits distinct discrete spectra and broadband characteristics in the frequency domain.

[0089] Figure 11 shows the three-component high-speed rail seismic signals and their spectra received by the ground detector at a distance of 125 m from the railway line.

[0090] Figure 12 shows the three-component high-speed rail seismic signals and their spectra received by the ground detector 250 m away from the railway line.

[0091] As the distance from the railway increases, the amplitude of the high-speed rail seismic signal gradually decreases. The detectors receive seismic waves generated by the bridge piers over a wider area and along a longer propagation path, resulting in a flatter waveform in the time domain. The high-frequency components of the high-speed rail seismic signal gradually decrease, narrowing the overall frequency band, consistent with the characteristics of the measured high-speed rail seismic signal.

[0092] like Figure 14 As shown, the present invention also provides a device for simulating Rayleigh surface waves of a high-speed railway source in a three-dimensional viscoelastic medium. The device 1000 includes a processor 1001 , a memory 1002 and a display 1003 .

[0093] The memory 1002 can be an internal storage unit of the device 1000 for simulating high-speed railway earthquakes with a source of Rayleigh surface waves in a three-dimensional viscoelastic medium, such as a hard disk or memory of the device 1000. The memory 1002 can also be an external storage device of the device 1000, such as a plug-in hard disk, a smart media card (SMC), a secure digital (SD) card, a flash memory card, etc. equipped on the device 1000. The memory 1002 can also include both an internal storage unit and an external storage device of the device 1000. The memory 1002 is used to store application software and various data installed in the device 1000.

[0094] In some embodiments, the processor 1001 may be a central processing unit (CPU), a microprocessor, or other data processing chip, configured to execute program codes or process data stored in the memory 1002, such as a high-speed rail source Rayleigh surface wave simulation method of the present invention.

[0095] In some embodiments, display 1003 can be an LED display, a liquid crystal display, a touch-sensitive liquid crystal display, or an OLED (Organic Light-Emitting Diode) touchscreen. Display 1003 is used to display information about the device 1000 for simulating high-speed rail earthquakes and Rayleigh surface waves in a three-dimensional viscoelastic medium and to display a visual user interface. Components 1001-1003 of the device 1000 for simulating high-speed rail earthquakes and Rayleigh surface waves in a three-dimensional viscoelastic medium communicate with each other via a system bus.

[0096] The embodiment of the present invention does not specifically limit the type of the device 1000 for simulating Rayleigh waves from a high-speed railway earthquake in a three-dimensional viscoelastic medium. The device 1000 can be a mobile phone, a tablet computer, a personal digital assistant (PDA), a wearable device, a laptop computer, etc., including but not limited to simulation devices running iOS, Android, Microsoft, or other operating systems.

[0097] The present invention specifically provides a high-speed railway source Rayleigh surface wave simulation system, such as Figure 13 As shown, the system 900 includes:

[0098] The parameter input module 901 obtains the train length parameters, the bridge pier structure parameters and the underground three-dimensional viscoelastic medium parameters, and determines the train running status according to the train length parameters and the bridge pier structure parameters.

[0099] The high-speed rail moving earthquake source analysis module 902 is used to obtain the load force of the sleeper at each wheel axle position of the high-speed rail train according to the train running status, and determine the earthquake source time function excited by the high-speed rail train during operation based on the force.

[0100] The staggered grid finite difference simulation module 903 is used to consider the parameters of the three-dimensional viscoelastic medium and construct a three-dimensional viscoelastic wave equation based on the Kelvin-Voigt model, solve the three-dimensional viscoelastic wave equation by the staggered grid finite difference method, and obtain a three-dimensional viscoelastic wave staggered grid finite difference format.

[0101] Output module 904 is used to set the free surface boundary, perform a time-domain staggered-grid finite-difference solution on the 3D viscoelastic wave staggered-grid finite-difference scheme and the source-time function, and simulate the Rayleigh surface wave field of the high-speed rail moving earthquake source based on the solution results. The simulated Rayleigh surface wave field and seismic records of the high-speed rail moving earthquake source are output to the corresponding path.

[0102] Each module in the aforementioned high-speed rail source Rayleigh surface wave simulation system can be implemented in whole or in part through software, hardware, or a combination thereof. Each module can be embedded in or independent of a processor in a computer device in the form of hardware, or can be stored in a computer device memory in the form of software, so that the processor can call and execute the corresponding operations of each module.

[0103] The present invention also provides a computer device comprising a memory, a processor, and a computer program stored in the memory. The processor executes the computer program to implement the steps of an embodiment of a method for simulating Rayleigh surface waves from a high-speed railway earthquake source. The specific implementation method can be found in the method embodiment and will not be repeated here.

[0104] Furthermore, the present invention also provides a non-transitory computer-readable storage medium containing instructions, wherein a computer program is stored on the storage medium. For example, a memory containing instructions, wherein the instructions can be executed by a processor of a computer device to perform the above-mentioned method. For example, the non-transitory computer-readable storage medium can be a ROM, a random access memory (RAM), a CD-ROM, a magnetic tape, a floppy disk, and an optical data storage device. When the computer program is executed by the processor, the steps in an embodiment of a method for simulating Rayleigh surface waves of a high-speed railway source can be implemented. The specific implementation method can be found in the method embodiment and will not be repeated here.

[0105] Those skilled in the art will appreciate that embodiments of the present invention may provide methods, systems, or computer program products. Thus, the present invention may take the form of an entirely hardware embodiment, an entirely software embodiment, or an embodiment combining software and hardware aspects. Furthermore, the present invention may take the form of a computer program product implemented on one or more computer-usable storage media (including but not limited to magnetic disk storage, CD-ROM, optical storage, etc.) containing computer-usable program code.

[0106] The present invention is described with reference to flowcharts and / or block diagrams of methods, apparatus (systems) and computer program products according to embodiments of the present invention. It should be understood that each process and / or block in the flowcharts and / or block diagrams, as well as combinations of processes and / or blocks in the flowcharts and / or block diagrams, can be implemented by computer program instructions. These computer program instructions can be provided to a processor of a general-purpose computer, a special-purpose computer, an embedded processor or other programmable data processing device to produce a machine, so that the instructions executed by the processor of the computer or other programmable data processing device generate instructions for implementing the processes in the flowcharts and / or block diagrams. Figure 1 a process or multiple processes and / or boxes Figure 1 A device that provides the functions specified in a block or multiple blocks.

[0107] These computer program instructions may also be stored in a computer readable memory that can direct a computer or other programmable data processing device to work in a specific manner, so that the instructions stored in the computer readable memory produce an article of manufacture comprising an instruction device, which implements the process Figure 1 a process or multiple processes and / or boxes Figure 1 The function specified in one or more boxes.

[0108] These computer program instructions can also be loaded onto a computer or other programmable data processing device so that a series of operational steps are executed on the computer or other programmable device to produce a computer-implemented process, thereby providing the instructions executed on the computer or other programmable device for implementing the process. Figure 1 a process or multiple processes and / or boxes Figure 1 A step that specifies a function in one or more boxes.

[0109] It should be pointed out that the specific implementation methods described above can enable those skilled in the art to understand the invention more comprehensively, but do not limit the invention in any way. Therefore, although the present specification and examples have described the invention in detail, those skilled in the art should understand that the invention can still be modified or replaced by equivalents; and all technical solutions and improvements that do not deviate from the spirit and scope of the invention are included in the scope of protection of the patent for the invention. Any figure mark in the claims should not be regarded as limiting the claims involved. Any simple change or equivalent replacement of the technical solution that can be obviously obtained by any person familiar with the art within the technical scope disclosed in the present invention falls within the scope of protection of the present invention.

Claims

1. A method for simulating Rayleigh surface waves from a high-speed railway earthquake source, characterized in that: The following steps are involved: Obtaining train length parameters, bridge pier structure parameters, and underground three-dimensional viscoelastic medium parameters, and determining the train running state according to the train length parameters and bridge pier structure parameters; According to the running state of the train, the load force of the sleeper at each wheel axle position of the high-speed train is obtained, and according to the load force, a time function of the earthquake source excited by the high-speed train during the running process is determined; constructing a three-dimensional viscoelastic wave equation according to the three-dimensional viscoelastic medium parameters of the underground and based on the Kelvin-Voigt model, solving the three-dimensional viscoelastic wave equation by a staggered grid finite difference method to obtain a three-dimensional viscoelastic wave staggered grid finite difference format equation; A free surface boundary is set, and the three-dimensional viscoelastic wave staggered grid finite difference format equation and the source time function are solved by the time domain staggered grid finite difference method. The Rayleigh surface wave field of the high-speed rail moving source is simulated and generated based on the solution results.

2. The method for simulating Rayleigh surface waves of a high-speed railway earthquake source according to claim 1, characterized in that: The method for obtaining the load force at the wheel axle position is specifically as follows: Where, Indicates the position of the sleeper, Indicates the first i The position of the axles; is the axle load at the corresponding position, is the sleeper spacing, coefficient , E is the elastic modulus of the rail, I is the cross-sectional momentum, α is the ground stiffness under the track, the total deflection distance .

3. The method for simulating Rayleigh surface waves of a high-speed railway earthquake source according to claim 2, characterized in that: Determining the source time function of the earthquake excited by the high-speed train during operation according to the load force specifically includes the following steps: Adding up the forces exerted on the sleepers by all axles of each carriage of the high-speed train, the total force on the sleepers is: Where, Indicates the number of carriages, High-speed train N Under the carriage axles, Indicates the position of the sleeper, Indicates the first i The position of the axles; For t Moment The position of the axles, is the axle load at the corresponding position, is the sleeper spacing, coefficient , E is the elastic modulus of the rail, I is the cross-sectional momentum, α is the ground stiffness under the track, the total deflection distance ; The first-order time derivative of the total force acting on the sleeper is used as the time function of the high-speed rail earthquake source: ； Where, M is the number of bridge piers, d is the distance between bridge piers, h is the depth of the pier pile foundation buried underground, is the location of the first pier, is the length of the carriage, is the first-order derivative of the total force acting on the sleeper.

4. The method for simulating Rayleigh surface waves of a high-speed railway earthquake source according to claim 1, characterized in that: According to the three-dimensional viscoelastic medium parameters of the underground and based on the Kelvin-Voigt model, a three-dimensional viscoelastic wave equation is constructed, specifically: Where, is the stress component, are the velocity components of the particle in different directions, ， , is the circular frequency, and the three-dimensional viscoelastic medium parameters of the underground include: is the longitudinal wave velocity of the medium, is the shear wave velocity, is the density, is the longitudinal wave quality factor, is the shear wave quality factor.

5. The method for simulating Rayleigh surface waves of a high-speed railway earthquake source according to claim 1, characterized in that: The free surface boundary is specifically: The acoustic and elastic medium boundaries are used to approximate the free surface boundaries. The normal stress is set to zero directly at the free boundary, and the shear stress is set to zero. The free boundary parameters are set as follows: Where, and denote the normal stress and density on the free surface boundary respectively; and represents the Lamé constant, represents the density of the medium below the free surface boundary; and represents the Lamé constant.

6. A high-speed railway source Rayleigh surface wave simulation system, characterized in that: include: A parameter input module is used to obtain train length parameters, bridge pier structure parameters, and underground three-dimensional viscoelastic medium parameters, and determine the train running status based on the train length parameters and bridge pier structure parameters; A high-speed rail moving earthquake source analysis module is used to obtain the load force of the sleeper at each wheel axle position of the high-speed rail train according to the train running status, and determine the earthquake source time function excited by the high-speed rail train during operation according to the load force; a staggered grid finite difference simulation module for constructing a three-dimensional viscoelastic wave equation based on the parameters of the underground three-dimensional viscoelastic medium and the Kelvin-Voigt model, and solving the three-dimensional viscoelastic wave equation using a staggered grid finite difference method to obtain a three-dimensional viscoelastic wave staggered grid finite difference format; The output module is used to set the free surface boundary, solve the three-dimensional viscoelastic wave staggered grid finite difference format and the source time function using the time domain staggered grid finite difference method, and simulate and generate the Rayleigh surface wave field of the high-speed rail moving source based on the solution results.

7. A computer device comprising a memory, a processor, and a computer program stored in the memory, characterized in that: The processor executes the computer program to implement the steps of the method according to any one of claims 1 to 5.

8. A computer-readable storage medium having a computer program stored thereon, characterized in that: When the computer program is loaded into a processor, it can execute the steps of the method according to any one of claims 1 to 5.

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