High-speed rail seismic source Rayleigh surface wave simulation method, system, equipment and medium

Abstract

The invention relates to a high-speed rail seismic source Rayleigh surface wave simulation method, system and device and a medium, and belongs to the technical field of seismic wave numerical simulation. A high-speed train is a moving line source in the fixed direction, based on a train moving load model, loads applied by four pairs of wheel shafts of each compartment to sleepers below a rail serve as point seismic sources, and the moving line source is decomposed into superposition of a series of point seismic sources. A high-speed rail seismic source time function is constructed based on an Euler-Bernoulli elastic beam theory by considering the elastic effect of a rail steel rail. The method comprises the following steps of: solving a Kelvin viscoelastic wave equation by adopting a staggered grid finite difference method in consideration of absorption attenuation of an underground medium to seismic waves, and performing numerical simulation on a seismic Rayleigh surface wave field excited by a high-speed rail moving seismic source in consideration of a free surface boundary. And basis and data are provided for subsequent high-speed rail seismic source-based waveform inversion and high-speed rail seismic source surface wave frequency dispersion curve inversion.

Description

Technical Field

[0001] The present invention belongs to the technical field of numerical simulation of seismic waves, 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 the rapid economic development and the growing public demand for convenient travel, China has become a global leader in the development of high-speed railways. By the end of 2023, the total mileage of my country's high-speed railways will exceed 45,000 kilometers, including trunk lines connecting many economically developed regions and important cities. my country has a vast territory and complex and diverse topography, and traditional seismic sources are challenging to meet the needs of geological exploration. During the operation of high-speed trains, the interaction between the train axles and the tracks generates a huge impact force, which excites seismic waves in the underground medium, thus forming a green seismic source, namely the high-speed rail seismic source. Given the stability of the high-speed railway network and the operation of high-speed trains, the high-speed rail seismic source is regarded as a reliable and repeatable artificial seismic source that can be used for geophysical exploration and geological structure imaging. Early studies have shown that the seismic signals generated by the high-speed rail seismic source have the characteristics of discrete spectrum and wide frequency band, and can reflect the changes in the underground medium, providing an effective tool for underground structure detection.

[0003] In the existing technology, most of the methods simulate the high-speed rail moving source wave field consistent with the measured high-speed rail seismic signal under elastic medium, analyze the high-speed rail seismic wave field and the next step based on the high-speed rail earthquake data. Under this medium condition, the data obtained by numerical simulation of the high-speed rail moving source excitation wave field and the extracted surface waves are incomplete. However, the actual underground medium is not a completely elastic body and will generate Rayleigh surface waves with large energy when the train passes. The existing simulation methods often ignore the generation of Rayleigh surface waves when analyzing the wave field. Summary of the invention

[0004] In order to solve the problem that the viscoelastic medium and the 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 force, the source time function excited by the high-speed train during the running process is determined;

[0009] 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, and the three-dimensional viscoelastic wave equation is solved 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. According to the solution results, the Rayleigh surface wave field of the high-speed railway moving source is simulated and generated.

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

[0012]

[0013] In the formula, 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 excited by the high-speed train during operation according to the acting force specifically comprises the following steps:

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

[0016]

[0017] In the formula, N represents the number of carriages, 4N represents the 4N axles under the N carriages of the high-speed train, x represents the position of the sleeper, and x i represents the position of the i-th wheel 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 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 distance 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 on the sleeper.

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

[0022]

[0023] In the formula, 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 longitudinal and transverse wave quality factors, 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, and 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] In the formula, σ zz(x,y,0) , (x,y,0) , (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 running status according to the train length parameters and bridge pier structure parameters.

[0031] The high-speed rail mobile 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 running status of the train, 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 according to the three-dimensional viscoelastic medium parameters of the underground and based on the Kelvin-Voigt model, and solve the three-dimensional viscoelastic wave equation by 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 by the time domain staggered grid finite difference method, and simulate and generate the Rayleigh surface wave field of the high-speed railway moving source based on the solution results.

[0034] The present invention also provides a computer device, including 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 a high-speed railway earthquake source.

[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, the steps described in the high-speed railway source Rayleigh surface wave simulation method can be executed.

[0036] The high-speed railway source Rayleigh surface wave simulation method provided by the present invention has the following beneficial effects:

[0037] The train length parameters, bridge pier structure parameters and three-dimensional viscoelastic medium parameters are obtained, and the effect of three-dimensional viscoelastic medium parameters on the simulation of high-speed rail moving earthquake sources is considered. The time function of the high-speed rail earthquake source excited by the high-speed rail train during operation is obtained according to the force of the train operation. The three-dimensional viscoelastic wave equation is constructed based on the three-dimensional viscoelastic medium parameters and the Kelvin-Voigt model, and 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 time domain staggered grid finite difference method to obtain the Rayleigh surface wave field of the high-speed rail moving earthquake source. The high-speed rail moving earthquake source wave field that is consistent with the measured high-speed rail seismic signal can be simulated under the viscoelastic medium condition, and the high-speed rail seismic record containing Rayleigh surface waves can be obtained. The high-speed rail seismic wave field and the next step based on the high-speed rail seismic data are analyzed. The theoretical basis and data are provided for extracting Rayleigh surface wave dispersion curves and surface wave inversion using high-speed rail seismic signals. BRIEF DESCRIPTION OF THE DRAWINGS

[0038] In order to more clearly illustrate the embodiment of the present invention and its design scheme, the following briefly introduces the drawings required for this embodiment. The drawings described below are only some embodiments of the present invention. For ordinary technicians in this field, other drawings can be obtained based on these drawings without creative work.

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

[0040] Figure 2 The present invention provides a train moving load model.

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

[0042] FIG4 is a diagram showing a wave field capability 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 t=0.375s when the two-layer model is an elastic medium and a viscoelastic medium, respectively.

[0043] Figure 5 is the high-speed rail source wavelet and its spectrum obtained by the source function, wherein 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 the high-speed train in the three-dimensional viscoelastic medium uniform model in the 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 three-dimensional 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 three-dimensional 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 section of earthquake records excited by a high-speed train in a three-dimensional viscoelastic medium uniform model in 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 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 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 is a high-speed rail seismic signal received at x=400m when the train is running on a 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 a 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] Fig.13 A schematic diagram of a high-speed railway source Rayleigh surface wave simulation device in a three-dimensional viscoelastic medium provided by the present invention.

[0052] Fig.14 A schematic structural diagram of an embodiment of a high-speed railway earthquake source Rayleigh surface wave simulation device in a three-dimensional viscoelastic medium provided by the present invention. DETAILED DESCRIPTION

[0054] In order to enable those skilled in the art to better understand the technical solution of the present invention and implement it, the present invention is described in detail below in conjunction with the accompanying drawings and specific embodiments. The following embodiments are only used to more clearly illustrate the technical solution of the present invention, and cannot be used to limit the scope of protection of the present invention.

[0055] 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.

[0056] 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:

[0057] S1. Obtain train length parameters, bridge pier structure parameters, and underground three-dimensional viscoelastic medium parameters, and determine the train running state based on the train length parameters and bridge pier structure parameters. When a train runs on the track, the train can be regarded as a moving line source moving in one direction, and the track is fixed to the sleeper or ballastless track plate by fasteners.

[0058] The interaction between the train and the track is simplified to 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.

[0059] High-speed trains travel on viaducts most of the time. At this time, the seismic waves are excited by the pier pile foundation inserted into the ground, and the source point is changed from the sleeper to the pier. Construct a load model when a high-speed train runs on a viaduct, such as Figure 3 .

[0060] S2. According to the running status of the train, obtain the load force of the sleeper at each axle position of the high-speed train, and determine the source time function of the high-speed train during operation based on the force. Simplify the high-speed train into a moving line source moving on the track, and each sleeper is used as a source point when the moving line source moves; according to the Euler-Bernoulli beam equation, calculate the force on any sleeper under any axle load on the high-speed train, and determine the force on the sleeper under the axle load at any position of the high-speed train as:

[0061]

[0062] In the formula, 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 wheel axle load at the corresponding position, Δx is the sleeper spacing, 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.

[0063] Considering the 4N load on the axle from the train, the total action on the sleeper at x is:

[0064]

[0065] In the formula, N represents the number of carriages, and 4N represents the 4N axles under the N carriages of the high-speed train.

[0066] The first-order time derivative of the total force is taken as the time function of the high-speed rail source:

[0067]

[0068] Where M is the number of piers, d is the distance 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 on the sleeper.

[0069] 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.

[0070] The stress of the medium under elastic deformation consists of two parts, namely the strain part and the strain change rate part. The viscoelastic medium is regarded as consisting of two parts of medium, one is a completely elastic medium and the other is a viscoelastic medium. According to the differential equation of motion of the elastic body, 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:

[0071]

[0072] In the formula, 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,

[0073] 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 longitudinal wave velocity, shear wave velocity and density of the medium, Q p , Q s are the longitudinal and transverse wave quality factors, and ω is the circular frequency.

[0074] S4. Set the free surface boundary, solve the three-dimensional viscoelastic wave staggered grid finite difference format equation and the source time function by 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. The time domain staggered grid finite difference simulation based on the three-dimensional viscoelastic wave staggered grid finite difference format and the high-speed rail source wavelet includes:

[0075] The three-dimensional first-order stress-velocity viscoelastic wave equation is solved based on the Kelvin model.

[0076] At the same time, considering the continuity of the lateral stress on both sides of the free surface boundary, the acoustic and elastic medium boundaries are used to approximate the free surface boundary to simulate the generation of Rayleigh surface waves. Instead of directly processing all stress conditions, the normal stress is directly set to zero at the free boundary, and the condition of zero shear stress is achieved by setting the physical parameters on the free boundary:

[0077]

[0078] Among them, σ zz(x,y,0) , (x,y,0) , (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.

[0079] 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. p =Q s=40), the vertical component wave field snapshot at t = 0.375s is shown in Figure 4 (b) and (c). There are longitudinal waves (P) and transverse waves (S), and after the free surface boundary is adopted, a strong Rayleigh surface wave (R) is generated near the surface. The longitudinal wave generates a reflected P wave (P11) and a transmitted P wave (P12) through the stratum interface. (b) and (c) are compared in the same scale range. It can be seen that the wave field energy in the viscoelastic medium is weakened compared with the elastic medium, and the attenuation degree increases with the increase of the propagation distance.

[0080] The rails are treated as Euler-Bernoulli elastic beams, and the total force of the sleeper load applied by the four front and rear axles of each high-speed train car on the sleepers is calculated as the load function. Set the number of train cars N = 16, the travel speed v = 83.3m / s (300km / h), the distance between the front and rear axles a = 2.5m, b = 17.5m, the length of each car L = 25m, and the ground stiffness α = 400MN / m 2 , EI=6.626MN / m 2 The load-time functions obtained are mostly positive values, with large energy at zero frequency in the frequency domain. Directly using them as source-time functions will lead to dynamic imbalance in numerical simulation of seismic waves.

[0081] At the same time, considering the reaction force exerted by the track plate on the sleeper, the first-order time derivative of the load time function is used as the time function of the high-speed rail source, and the high-speed rail source wavelet and its spectrum are shown in Figure 5 (a) and (b). In the time domain, the high-speed rail source wavelet has obvious periodicity, corresponding to the number of train cars N. In the frequency domain, the high-speed rail source wavelet has obvious discrete spectral characteristics. The frequency value corresponding to the first peak line is called the fundamental frequency, and other peak lines appear at integer multiples of the fundamental frequency.

[0082] The three-dimensional viscoelastic wave equation and the time function of the high-speed rail earthquake source are solved by 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. Based on the Euler-Bernoulli elastic beam theory, the wheel axle load applied by the wheel axle to the sleeper during the operation of the high-speed rail train is obtained, and the time derivative of the wheel axle load is obtained as the high-speed rail earthquake source sub-wave excited by the high-speed rail train during operation.

[0083] 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 by using the staggered grid finite difference method in time domain.

[0084] 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-wave velocity Vp =800m / s, shear wave velocity V s =400m / s, density ρ = 1800kg / m 3 The staggered grid spatial step size Δx = Δz = 2.5m, the time step size Δt = 0.5ms, the high-speed rail source loading is on the vertical velocity component, and the simulation duration is 15s. There are 32 bridge piers arranged in the model, and the spacing between the piers is 25m.

[0085] Figure 6 Snapshots of the high-speed rail seismic wave field at 1s, 5s, 9s and 12s in a three-dimensional viscoelastic medium uniform model. As the train moves, the carriages continuously pass by bridge piers, exciting orderly seismic wavefronts, which continue to advance as the train moves forward. At 1s, the train just starts to excite seismic waves. As time goes by, the train continues to move forward, and more bridge piers excite seismic waves. At 5s, the train has passed multiple bridge piers, and the wave field becomes complex. At 9s, the waves excited by different bridge piers produce rich interference phenomena until 12s, when the train runs close to the end of the model.

[0086] Figure 7 The snapshots of the high-speed rail seismic wave field at 1s, 5s, 9s and 12s on the XY plane surface. As the train moves, the axles of the carriages pass through the bridge piers in turn to excite seismic waves, forming multiple circular wavefronts that move in the direction of the train over time. Within the total length of the train, the seismic waves excited by multiple bridge piers are superimposed to form a straight line parallel to the railway line, which propagates outward.

[0087] Figure 8 This is a snapshot of the seismic wave field of the high-speed railway in the XZ plane. The black box shows the seismic waves generated by the four pairs of axles of a carriage. First, the P waves and S waves are generated by the first two pairs of axles in the carriage. Since the distance between the two pairs of axles is very short (2.5m), the time difference of excitation is only 0.03s, which causes the P waves and S waves corresponding to the two pairs of axles to gradually separate after propagating for a certain distance. Then comes the R waves generated by the two pairs of axles, which have strong energy and decay rapidly with the propagation depth. The two pairs of axles at the back of the carriage also excite P waves, S waves and R waves, and their excitation patterns are consistent with the first two pairs of axles. Subsequently, the next carriage repeats this excitation process until all the axles of the carriage pass through the bridge pier. Multiple axles of the train will interact with different piers at the same time to excite seismic waves, increasing the complexity of the wave field. At the same position, the detector will simultaneously receive seismic waves excited by different piers and axles of different carriages.

[0088] Figure 9 shows the vertical component acquisition records of the high-speed rail earthquake received on the x-direction survey line at different distances from the railway line. (a), (b) and (c) correspond to the detectors under the viaduct, 125m and 250m away from the railway line, respectively. The horizontal axis is the x-direction distance and the vertical axis is time. As the distance increases, the high-speed rail earthquake signal is no longer limited to the short time when the train passes, but appears in a longer time range.

[0089] Figure 10 shows the three-component high-speed rail seismic signals and their spectra received by the ground detector under the viaduct. It can be seen that the simulated seismic records have quasi-periodicity in the time domain, corresponding to the number of train carriages; and show obvious discrete spectrum and wide-band characteristics in the frequency domain.

[0090] Figure 11 shows the three-component high-speed rail seismic signal and its spectrum received by the ground detector at a distance of 125 m from the railway line.

[0091] Figure 12 shows the three-component high-speed rail seismic signal and its spectrum received by the ground detector at a distance of 250 m from the railway line.

[0092] As the distance from the railway line increases, the amplitude of the high-speed rail seismic signal gradually decreases. The detector receives seismic waves excited by the bridge piers in a larger range and the propagation path is longer, resulting in a flatter waveform in the time domain. The high-frequency components of the high-speed rail seismic signal gradually decrease, resulting in a narrower width of the entire frequency band, which is consistent with the measured high-speed rail seismic signal characteristics.

[0093] like Fig.14 As shown, the present invention also provides a device for simulating Rayleigh surface waves of high-speed railway earthquake sources in a three-dimensional viscoelastic medium. The device 1000 includes a processor 1001 , a memory 1002 and a display 1003 .

[0094] The memory 1002 may be an internal storage unit of a high-speed railway source Rayleigh surface wave simulation device 1000 in a three-dimensional viscoelastic medium, such as a hard disk or memory of a high-speed railway source Rayleigh surface wave simulation device 1000 in a three-dimensional viscoelastic medium. The memory 1002 may also be an external storage device of a high-speed railway source Rayleigh surface wave simulation device 1000 in a three-dimensional viscoelastic medium, such as a plug-in hard disk, a smart memory card (Smart Media Card, SMC), a secure digital (Secure Digital, SD) card, a flash card (FlashCard), etc. equipped on a high-speed railway source Rayleigh surface wave simulation device 1000 in a three-dimensional viscoelastic medium. The memory 1002 may also include both an internal storage unit of a high-speed railway source Rayleigh surface wave simulation device 1000 in a three-dimensional viscoelastic medium and an external storage device. The memory 1002 is used to store and install application software and various data of a high-speed railway source Rayleigh surface wave simulation device 1000 in a three-dimensional viscoelastic medium.

[0095] In some embodiments, the processor 1001 may be a central processing unit (CPU), a microprocessor or other data processing chip, used to run program codes or process data stored in the memory 1002, such as a high-speed rail source Rayleigh surface wave simulation method in the present invention.

[0096] In some embodiments, the display 1003 may be an LED display, a liquid crystal display, a touch-sensitive liquid crystal display, an OLED (Organic Light-Emitting Diode) touch device, etc. The display 1003 is used to display information of the high-speed railway source Rayleigh surface wave simulation device 1000 in a three-dimensional viscoelastic medium and to display a visual user interface. The components 1001-1003 of the high-speed railway source Rayleigh surface wave simulation device 1000 in a three-dimensional viscoelastic medium communicate with each other through a system bus.

[0097] The embodiment of the present invention does not specifically limit the type of the device 1000 for simulating Rayleigh waves of high-speed railway earthquake sources in a three-dimensional viscoelastic medium. The device 1000 for simulating Rayleigh waves of high-speed railway earthquake sources in a three-dimensional viscoelastic medium 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 equipped with IOS, Android, Microsoft or other operating systems.

[0098] The present invention specifically provides a high-speed railway source Rayleigh surface wave simulation system, such as Fig.13 As shown, the system 900 includes:

[0099] The parameter input module 901 obtains train length parameters, bridge pier structure parameters and underground three-dimensional viscoelastic medium parameters, and determines the train running status according to the train length parameters and bridge pier structure parameters.

[0100] The high-speed rail mobile 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 according to the force.

[0101] The staggered grid finite difference simulation module 903 is used to consider the three-dimensional viscoelastic medium parameters 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.

[0102] The output module 904 is used to set the free surface boundary, solve the three-dimensional viscoelastic wave staggered grid finite difference format and the source time function by the time domain staggered grid finite difference method, and simulate and generate the Rayleigh surface wave field of the high-speed rail moving source according to the solution results. The simulated Rayleigh surface wave field and seismic records of the high-speed rail moving source are output to the corresponding path.

[0103] Each module in the above-mentioned high-speed railway source Rayleigh surface wave simulation system can be implemented in whole or in part by software, hardware and their combination. The above-mentioned modules can be embedded in or independent of the processor in the computer device in the form of hardware, or can be stored in the memory of the computer device in the form of software, so that the processor can call and execute the operations corresponding to the above modules.

[0104] The present invention also provides a computer device, including a memory, a processor, and a computer program stored in the memory, wherein the processor executes the computer program to implement the steps in an embodiment of a method for simulating Rayleigh surface waves of a high-speed railway source. The specific implementation method can be found in the method embodiment, which will not be described in detail here.

[0105] Furthermore, the present invention also provides a non-temporary computer-readable storage medium containing instructions, and a computer program is stored on the storage medium. For example, a memory containing instructions, the above instructions can be executed by a processor of a computer device to complete the above method. For example, a non-temporary 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, it can implement the steps in an embodiment of a high-speed rail source Rayleigh surface wave simulation method. The specific implementation method can be found in the method embodiment, which will not be repeated here.

[0106] It will be appreciated by those skilled in the art that embodiments of the present invention may provide methods, systems or computer program products. Therefore, the present invention may take the form of a complete hardware embodiment, a complete software embodiment or an embodiment combining software and hardware. Moreover, 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 disk storage, CD-ROM, optical storage, etc.) containing computer-usable program code.

[0107] 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 flowchart and / or block diagram, as well as a combination of processes and / or blocks in the flowchart and / or block diagram, 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 flowchart and / or block diagram. 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.

[0108] These computer program instructions may also be stored in a computer-readable memory capable of directing a computer or other programmable data processing device to operate 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 A function specified in one or more boxes.

[0109] These computer program instructions can also be loaded onto a computer or other programmable data processing device so that a series of operating steps are executed on the computer or other programmable device to produce a computer-implemented process, thereby providing instructions for implementing the process. Figure 1 A process or multiple processes and / or boxes Figure 1 The steps for the functions specified in one or more boxes.

[0110] 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 invention has been described in detail in this specification and embodiments, 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 protection scope 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 technician familiar with the field within the technical scope disclosed in the present invention belongs to the protection scope of the present invention.

Claims

1. A method for simulating Rayleigh surface waves of high-speed railway earthquake sources, characterized in that: The following steps are involved: Acquire train length parameters, bridge pier structure parameters, and underground three-dimensional viscoelastic medium parameters, and determine 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 force, the source time function excited by the high-speed train during the running process is determined; 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, and the three-dimensional viscoelastic wave equation is solved by a staggered grid finite difference method to obtain a three-dimensional viscoelastic wave staggered grid finite difference format equation; 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. According to the solution results, the Rayleigh surface wave field of the high-speed railway moving source is simulated and generated.

2. The method for simulating Rayleigh surface waves of high-speed railway earthquake sources according to claim 1, characterized in that: The method for obtaining the load force at the wheel axle position is specifically as follows: In the formula, 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.

3. The method for simulating Rayleigh surface waves of high-speed railway earthquake sources according to claim 2, characterized in that: Determining the source time function excited by the high-speed train during operation according to the force specifically includes the following steps: Add up the forces exerted on the sleepers by all axles of each carriage of the high-speed train, and the total force on the sleepers is: In the formula, N represents the number of carriages, 4N represents the 4N axles under the N carriages of the high-speed train, x represents the position of the sleeper, and 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; The first-order time derivative of the total force on the sleeper is used as the time function of the high-speed rail earthquake source: Where M is the number of piers, d is the distance 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 on the sleeper.

4. The method for simulating Rayleigh surface waves of high-speed railway earthquake sources according to claim 1, characterized in that: According to the underground three-dimensional viscoelastic medium parameters and based on the Kelvin-Voigt model, a three-dimensional viscoelastic wave equation is constructed, which is specifically: In the formula, 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, ω is the circular frequency, 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 longitudinal and shear wave quality factors.

5. The method for simulating Rayleigh surface waves of high-speed railway earthquake sources 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, and 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: In the formula, σ zz(x,y,0) , (x,y,0) , (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.

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 state according to the train length parameters and bridge pier structure parameters; A high-speed rail mobile 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 running state of the train, and determine the earthquake source time function excited by the high-speed rail train during operation according to the force; A staggered grid finite difference simulation module is used to construct a three-dimensional viscoelastic wave equation according to the three-dimensional viscoelastic medium parameters of the underground and based on the Kelvin-Voigt model, and solve 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; 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 by the time domain staggered grid finite difference method, and simulate and generate the Rayleigh surface wave field of the high-speed rail moving source according to 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.

Images