Vibration response calculation method for site soil and buildings under action of high-speed rail train

Abstract

The invention discloses a method for calculating vibration response of site soil and buildings under the action of a high-speed train. The method comprises the following steps: establishing a high-speed train model, a track model and a wheel-rail contact model, and establishing a train track model according to the high-speed train model, the track model and the wheel-rail contact model; the compression amount generated by wheel-rail contact is obtained, and the rail dynamic counter-force under the action of the high-speed rail train is calculated according to the compression amount generated by wheel-rail contact and the train rail model; and based on the rail dynamic reaction force under the action of the high-speed rail train, calculating the vibration response of the site soil under the action of the high-speed rail train by adopting a Fourier transform method, and calculating the vibration response of the building under the action of the high-speed rail train by adopting a transfer function method. According to the method, the calculation efficiency and accuracy of the vibration response of the site soil and the building under the action of the high-speed rail train can be improved, so that the vibration threat actually suffered by the site soil and the building can be more accurately obtained, and the method is used for later structural transformation and reinforcement work.

Description

Technical Field

[0001] The present invention relates to the field of vibration response detection of site soil and buildings, and in particular to a method for calculating the vibration response of site soil and buildings under the action of a high-speed train. Background Art

[0002] Many high-speed railway foundations and buildings are built on saturated soil. The operation of the railway transportation system will inevitably cause vibration of the site soil and buildings, which may even endanger operational safety in serious cases. Therefore, testing the vibration response of the site soil and buildings under the action of high-speed trains can evaluate the actual vibration threat to the site soil and buildings, so as to be used for later structural transformation and reinforcement work to improve the vibration resistance of existing buildings and make a stronger contribution to improving the safety and reliability of buildings.

[0003] The existing method uses finite element software to predict the vibration response of site soil and buildings. This method takes a long time to calculate, has low prediction efficiency, and there are certain differences between the calculation model and the actual project. Summary of the invention

[0004] In view of the above-mentioned deficiencies in the prior art, the present invention provides a method for calculating the vibration response of site soil and buildings under the action of a high-speed train.

[0005] In order to achieve the above-mentioned object of the invention, the technical solution adopted by the present invention is:

[0006] A method for calculating the vibration response of site soil and buildings under the action of a high-speed train comprises the following steps:

[0007] S1. Establish a high-speed train model, a track model and a wheel-rail contact model, and establish a train track model based on the high-speed train model, the track model and the wheel-rail contact model;

[0008] S2, obtaining the compression amount caused by wheel-rail contact, and calculating the track dynamic reaction force under the action of the high-speed train according to the compression amount caused by wheel-rail contact and the train track model in step S1;

[0009] S3. Based on the track dynamic reaction force under the action of the high-speed train in step S2, the vibration response of the site soil under the action of the high-speed train is calculated using the Fourier transform method, and the vibration response of the building under the action of the high-speed train is calculated using the transfer function method.

[0010] Furthermore, in step S1, a high-speed train model, a track model and a wheel-rail contact model are established, specifically: the nodding and sinking and floating of the car body, the nodding and sinking and floating of the front and rear bogies, and the sinking and floating degrees of freedom of the four wheel sets are considered, and the car body and the bogie, and the bogie and the wheelset are connected by Kelvin units to establish a high-speed train model; based on a two-layer discrete point support model, Eulre-bernoulli beams are used to simulate rails, and mass blocks are used to simulate sleepers. The rails in the length direction are supported on the sleepers by discrete point supports, and each layer is connected by Kelvin units to establish a track model; based on the Hertz contact method, the contact between the wheel and the rail is simplified to a vertical spring to construct a wheel-rail contact model.

[0011] Further, in step S2, according to the compression amount generated by the wheel-rail contact and the train track model in step S1, the track dynamic reaction force under the action of the high-speed train is calculated, including the following steps:

[0012] A1. Calculate the normal force of the wheel-rail contact according to the compression generated by the wheel-rail contact and the train track model in step S1;

[0013] A2. Calculate the equivalent stiffness of the wheel-rail contact according to the normal force of the wheel-rail contact in step A1 and the train track model in step S1;

[0014] A3. Calculate the track dynamic reaction force under the action of the high-speed train based on the equivalent stiffness of the wheel-rail contact in step A2 and the train track model in step S1.

[0015] Further, in step A3, according to the equivalent stiffness of the wheel-rail contact in step A2 and the train track model in step S1, the track dynamic reaction force under the action of the high-speed train is calculated, which is expressed as:

[0016] P ij (t) = k h [z wij (t)-w rij (t)-z rij (t)]

[0017] Where: P ij (t) is the track dynamic reaction force of the jth wheelset of the i-th train under the action of the high-speed train, k h is the equivalent stiffness of wheel-rail contact, z wij (t) is the displacement of the jth wheelset of the i-th train under the action of the high-speed train, w rij (t) is the vertical displacement of the track caused by the load at the jth wheelset of the i-th train under the action of the high-speed train, z rij (t) is the track unevenness at the j-th wheelset of the i-th train under the action of the high-speed train.

[0018] Further, in step S3, based on the track dynamic reaction force under the action of the high-speed train in step S2, the vibration response of the site soil under the action of the high-speed train is calculated by using the Fourier transform method, including the following steps:

[0019] B1. Based on the track dynamic reaction force under the action of the high-speed train in step S2, the vertical simple harmonic load of the rail under the action of the high-speed train is calculated using the Fourier transform method;

[0020] B2. Calculate the vertical displacement of the site soil under the action of the high-speed train according to the simple harmonic load of the rail in the vertical direction under the action of the high-speed train in step B1;

[0021] B3. Superimpose the vertical displacement of the site soil under the action of the high-speed train in step B2 to calculate the vibration response of the site soil under the action of the high-speed train.

[0022] Further, in step B1, based on the track dynamic reaction force under the action of the high-speed train in step S2, the Fourier transform method is used to calculate the vertical simple harmonic load of the rail under the action of the high-speed train, which is expressed as:

[0023]

[0024] Among them: F J (t) is the vertical simple harmonic load at the Jth rail node under the action of the high-speed train at time t, P J (t) is the track dynamic reaction force at the Jth rail node under the action of the high-speed train, which is determined by the track dynamic reaction force under the action of the high-speed train in step S2, t is time, 41 is the total number of track nodes, ω J is the circular frequency of the load at the Jth rail node, θ J is the phase at the Jth rail node;

[0025] Further, in step B2, according to the simple harmonic load of the rail in the vertical direction under the action of the high-speed train in step B1, the vertical displacement of the site soil under the action of the high-speed train is calculated, which is expressed as:

[0026]

[0027] in: u x is the positive displacement of the site soil under the action of the high-speed train, u y is the vertical displacement of the site soil under the action of the high-speed train, u z is the vertical displacement of the site soil under the action of the high-speed train, u z is the normal displacement of the site soil under the action of the high-speed train, w zis the normal displacement of pore water under the action of high-speed train, T is the transposed sign, F is the amplitude of force, ω0 is the circular frequency of load, [K1] is the coefficient matrix, e is the natural logarithm, ξ is the abscissa in wave number domain, and η is the ordinate in wave number domain:

[0028] C1. Calculate the vertical vibration acceleration of the site soil under the action of high-speed trains;

[0029] C2. Calculate the coupling loss coefficient and floor amplification factor of the building under the action of high-speed trains;

[0030] C3, using the transfer function method to calculate the vertical vibration acceleration of the building under the action of the high-speed train based on the vertical vibration acceleration of the site soil under the action of the high-speed train in step C1 and the coupling loss coefficient and the floor amplification coefficient of the building under the action of the high-speed train in step C2;

[0031] C4. According to the vertical vibration acceleration of the building under the action of the high-speed train in step C3, the vibration acceleration level of the building under the action of the high-speed train is calculated to determine the vibration response of the building under the action of the high-speed train.

[0032] Furthermore, in step C1, the vertical vibration acceleration of the site soil under the action of the high-speed train is calculated and expressed as:

[0033]

[0034] Where: a(f) is the vertical vibration acceleration of the site soil with a frequency of f under the action of the high-speed train, is the second-order derivative of the displacement U(f), ω is the circular frequency, and U(f) is the displacement of the site soil with a frequency of f under the action of the high-speed train;

[0035] Further, in step C3, according to the vertical vibration acceleration of the site soil under the action of the high-speed train in step C1 and the coupling loss coefficient and the floor amplification factor of the building under the action of the high-speed train in step C2, the vertical vibration acceleration of the building under the action of the high-speed train is calculated by the transfer function method, which is expressed as:

[0036] a b (f) = a soil (f) C l (f) F a (f)

[0037] Among them: a b (f) is the vertical vibration acceleration of the building with a frequency of f under the action of the high-speed train, a soil (f) is the vertical vibration acceleration of the site soil with a frequency of f under the action of the high-speed train, C l (f) is the coupling loss coefficient of the building at frequency f under the action of the high-speed train, F a(f) is the floor amplification factor of frequency f under the action of high-speed train.

[0038] The present invention has the following beneficial effects:

[0039] The present invention establishes a high-speed train model, a track model and a wheel-rail contact model, and establishes a train track model according to the high-speed train model, the track model and the wheel-rail contact model, then obtains the compression generated by the wheel-rail contact, and calculates the track dynamic reaction force under the action of the high-speed train according to the compression generated by the wheel-rail contact and the train track model, and finally, based on the track dynamic reaction force under the action of the high-speed train, adopts the Fourier transform method to calculate the vibration response of the site soil under the action of the high-speed train, and adopts the transfer function method to calculate the vibration response of the building under the action of the high-speed train, which can improve the calculation efficiency and accuracy of the vibration response of the site soil and the building under the action of the high-speed train, and further more accurately obtains the actual vibration threat suffered by the site soil and the building, so as to be used for the later structural transformation and reinforcement work, so as to improve the vibration resistance of the existing site soil and the building. BRIEF DESCRIPTION OF THE DRAWINGS

[0040] Figure 1 A flow chart of a method for calculating the vibration response of site soil and buildings under the action of a high-speed train;

[0041] Figure 2 It is a schematic diagram of the train track model structure of the present invention. DETAILED DESCRIPTION

[0042] The specific implementation modes of the present invention are described below so that those skilled in the art can understand the present invention. However, it should be clear that the present invention is not limited to the scope of the specific implementation modes. For those of ordinary skill in the art, as long as various changes are within the spirit and scope of the present invention as defined and determined by the attached claims, these changes are obvious, and all inventions and creations utilizing the concept of the present invention are protected.

[0043] like Figure 1 As shown, a method for calculating the vibration response of site soil and buildings under the action of a high-speed train comprises the following steps:

[0044] S1. Establish a high-speed rail train model, a track model and a wheel-rail contact model, and establish a train track model based on the high-speed rail train model, the track model and the wheel-rail contact model.

[0045] In an optional embodiment of the present invention, the present invention establishes a high-speed train model, a track model and a wheel-rail contact model, specifically: considering the nodding and sinking and floating of the car body, the nodding and sinking and floating of the front and rear bogies, and the sinking and floating degrees of freedom of the four wheel sets, the car body and the bogie, the bogie and the wheelset are connected by Kelvin units to establish a high-speed train model; based on a two-layer discrete point support model, Eulre-bernoulli beams are used to simulate rails, mass blocks are used to simulate sleepers, and the rails in the length direction are supported on the sleepers by discrete point supports, and each layer is connected by Kelvin units to establish a track model; based on the Hertz contact method, the contact between the wheel and the rail is simplified to a vertical spring to construct a wheel-rail contact model.

[0046] like Figure 2 As shown, the present invention provides a schematic diagram of the train track model structure, M c is the vehicle mass, J c is the moment of inertia of the vehicle section, c t is the primary spring vertical damping, k t is the vertical stiffness of the primary spring, M t is the bogie mass, J t is the moment of inertia of the bogie section, c w is the secondary spring damping, k w is the secondary spring stiffness, m is the wheelset mass, k H is the equivalent stiffness of the Hertz contact spring, m1 is the mass of the sleeper, c1 is the fastener damping, k1 is the fastener stiffness, c2 is the roadbed damping, and k2 is the roadbed stiffness. These parameters are used to calculate the track dynamic reaction force under the action of the high-speed train through MATLAB.

[0047] S2. Obtain the compression amount caused by wheel-rail contact, and calculate the track dynamic reaction force under the action of the high-speed train based on the compression amount caused by wheel-rail contact and the train track model in step S1.

[0048] In an optional embodiment of the present invention, the present invention calculates the track dynamic reaction force under the action of the high-speed train according to the compression amount generated by the wheel-rail contact and the train track model in step S1, including the following steps:

[0049] A1. According to the compression generated by the wheel-rail contact and the train track model in step S1, the normal force of the wheel-rail contact is calculated and expressed as:

[0050]

[0051] Where: P is the normal force of wheel-rail contact, G is the Hertz contact constant, and δ is the compression generated by wheel-rail contact.

[0052] A2. According to the normal force of the wheel-rail contact in step A1 and the train track model in step S1, the equivalent stiffness of the wheel-rail contact is calculated and expressed as:

[0053]

[0054] Where: k h is the Hertz contact constant.

[0055] A3. According to the equivalent stiffness of the wheel-rail contact in step A2 and the train track model in step S1, the track dynamic reaction force under the action of the high-speed train is calculated, which is expressed as:

[0056] P ij (t) = k h [z wij (t)-w rij (t)-z rij (t)]

[0057] Where: P ij (t) is the track dynamic reaction force of the jth wheelset of the i-th train under the action of the high-speed train, k h is the equivalent stiffness of wheel-rail contact, z wij (t) is the displacement of the jth wheelset of the i-th train under the action of the high-speed train, w rij (t) is the vertical displacement of the track caused by the load at the jth wheelset of the i-th train under the action of the high-speed train, z rij (t) is the track unevenness at the j-th wheelset of the i-th train under the action of the high-speed train.

[0058] Specifically, the present invention calculates the track dynamic reaction force under the action of the high-speed train through MATLAB based on the above formula.

[0059] S3. Based on the track dynamic reaction force under the action of the high-speed train in step S2, the vibration response of the site soil under the action of the high-speed train is calculated using the Fourier transform method, and the vibration response of the building under the action of the high-speed train is calculated using the transfer function method.

[0060] In an optional embodiment of the present invention, based on the track dynamic reaction force under the action of the high-speed train in step S2, the present invention uses the Fourier transform method to calculate the vibration response of the site soil under the action of the high-speed train, including the following steps:

[0061] B1. Based on the track dynamic reaction force under the action of the high-speed train in step S2, the Fourier transform method is used to calculate the vertical simple harmonic load of the rail under the action of the high-speed train, which is expressed as:

[0062]

[0063] Among them: F J(t) is the vertical simple harmonic load at the Jth rail node under the action of the high-speed train at time t, P J (t) is the track dynamic reaction force at the Jth rail node under the action of the high-speed train, which is determined by the track dynamic reaction force under the action of the high-speed train in step S2, t is time, 41 is the total number of track nodes, ω J is the circular frequency of the load at the Jth rail node, θ J is the phase at the Jth rail node.

[0064] B2. According to the simple harmonic load of the rail in the vertical direction under the action of the high-speed train in step B1, the vertical displacement of the site soil under the action of the high-speed train is calculated, which is expressed as:

[0065]

[0066] in: u x is the positive displacement of the site soil under the action of the high-speed train, u y is the vertical displacement of the site soil under the action of the high-speed train, u z is the vertical displacement of the site soil under the action of the high-speed train, u z is the normal displacement of the site soil under the action of the high-speed train, w z is the normal displacement of pore water under the action of high-speed train, T is the transposed sign, F is the amplitude of force, ω0 is the circular frequency of load, [K1] is the coefficient matrix, e is the natural logarithm, ξ is the abscissa in wave number domain, and η is the ordinate in wave number domain.

[0067] Specifically, based on the above calculation formula, the present invention uses the numerical analysis method MATLAB to solve the vertical displacement of the site soil under the action of the high-speed train.

[0068] B3. Superimpose the vertical displacement of the site soil under the action of the high-speed train in step B2 to calculate the vibration response of the site soil under the action of the high-speed train, expressed as:

[0069]

[0070] Among them: U soil is the vibration response of the site soil under the action of the high-speed train, n is, u ij is the vertical displacement of the site soil caused by the simple harmonic load of the jth frequency at the ith rail unit under the action of the high-speed train.

[0071] The present invention adopts a transfer function method to calculate the vibration response of a building under the action of a high-speed train, comprising the following steps:

[0072] C1. Calculate the vertical vibration acceleration of the site soil under the action of the high-speed train, expressed as:

[0073]

[0074] Where: a(f) is the vertical vibration acceleration of the site soil with a frequency of f under the action of the high-speed train, is the second-order derivative of the displacement U(f), ω is the circular frequency, and U(f) is the displacement of the site soil with a frequency of f under the action of the high-speed train.

[0075] C2. Calculate the coupling loss coefficient and floor amplification factor of the building under the action of high-speed trains.

[0076] Specifically, in the present invention, the transmission coefficient between the site soil and the building structure is determined as the coupling loss coefficient of the building, and then the coupling loss coefficient of the building is obtained.

[0077] The present invention calculates the floor magnification factor of a building under the action of a high-speed train, which is expressed as:

[0078]

[0079] Where: {F a} is the column vector of floor amplification factor, [M] is the mass matrix of the building, {I} is a column vector with all row values ​​equal to 1, which is of the same order as the stiffness matrix of the building, ω is the frequency of building vibration, i is the sign of the imaginary number, [K] is the stiffness matrix of the building, and [C] is the damping matrix of the building.

[0080] Specifically, the present invention adopts a known method to construct the mass matrix, stiffness matrix of the same order and damping matrix of the building by the vehicle body mass, vehicle body section inertia moment, primary spring vertical damping, primary spring vertical stiffness, bogie mass, bogie section inertia moment, secondary spring damping, secondary spring stiffness, wheelset mass, Hertz contact spring equivalent stiffness, sleeper mass, fastener damping, fastener stiffness, roadbed damping and roadbed stiffness.

[0081] C3. According to the vertical vibration acceleration of the site soil under the action of the high-speed train in step C1 and the coupling loss coefficient and floor amplification coefficient of the building under the action of the high-speed train in step C2, the vertical vibration acceleration of the building under the action of the high-speed train is calculated by the transfer function method, which is expressed as:

[0082] a b (f) = a soil (f) C l (f) F a (f)

[0083] Among them: a b (f) is the vertical vibration acceleration of the building with a frequency of f under the action of the high-speed train, a soil (f) is the vertical vibration acceleration of the site soil with a frequency of f under the action of the high-speed train, C l(f) is the coupling loss coefficient of the building at frequency f under the action of the high-speed train, F a (f) is the floor amplification factor of frequency f under the action of high-speed train.

[0084] C4. According to the vertical vibration acceleration of the building under the action of the high-speed train in step C3, the vibration acceleration level of the building under the action of the high-speed train is calculated to determine the vibration response of the building under the action of the high-speed train.

[0085] The present invention calculates the vibration acceleration level of a building under the action of a high-speed train, which is expressed as:

[0086]

[0087] Where: VAL is the vibration acceleration level of the building with a frequency of f under the action of the high-speed train, a0 is the acceleration reference value, a0 = 1×10 -6 m / s 2 .

[0088] The present invention is described with reference to flowcharts and / or block diagrams of methods, devices (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 the 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.

[0089] 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.

[0090] 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.

[0091] The present invention uses specific embodiments to illustrate the principles and implementation methods of the present invention. The description of the above embodiments is only used to help understand the method of the present invention and its core idea. At the same time, for those skilled in the art, according to the idea of ​​the present invention, there will be changes in the specific implementation methods and application scope. In summary, the content of this specification should not be understood as a limitation on the present invention.

[0092] Those skilled in the art will appreciate that the embodiments described herein are intended to help readers understand the principles of the present invention, and should be understood that the protection scope of the present invention is not limited to such specific statements and embodiments. Those skilled in the art can make various other specific variations and combinations that do not deviate from the essence of the present invention based on the technical revelations disclosed by the present invention, and these variations and combinations are still within the protection scope of the present invention.

Claims

1. A method for calculating the vibration response of site soil and buildings under the action of high-speed trains, characterized in that: The following steps are involved: S1. Establish a high-speed train model, a track model and a wheel-rail contact model, and establish a train track model based on the high-speed train model, the track model and the wheel-rail contact model; S2, obtaining the compression amount caused by wheel-rail contact, and calculating the track dynamic reaction force under the action of the high-speed train according to the compression amount caused by wheel-rail contact and the train track model in step S1; S3. Based on the track dynamic reaction force under the action of the high-speed train in step S2, the vibration response of the site soil under the action of the high-speed train is calculated using the Fourier transform method, and the vibration response of the building under the action of the high-speed train is calculated using the transfer function method.

2. The method for calculating the vibration response of site soil and buildings under the action of a high-speed train according to claim 1 is characterized in that: In step S1, a high-speed train model, a track model and a wheel-rail contact model are established, specifically: the nodding and sinking and floating of the car body, the nodding and sinking and floating of the front and rear bogies, and the sinking and floating degrees of freedom of the four wheel sets are considered, and the car body and the bogie, and the bogie and the wheel set are connected by Kelvin units to establish a high-speed train model; based on a two-layer discrete point support model, an Eulre-bernoulli beam is used to simulate the rail, a mass block is used to simulate the sleeper, and the rail in the length direction is supported on the sleeper by a discrete point support method, and each layer is connected by a Kelvin unit to establish a track model; Based on the Hertz contact method, the contact between the wheel and rail is simplified into a vertical spring to construct the wheel-rail contact model.

3. The method for calculating the vibration response of site soil and buildings under the action of a high-speed train according to claim 1 is characterized in that: In step S2, the track dynamic reaction force under the action of the high-speed train is calculated according to the compression amount generated by the wheel-rail contact and the train track model in step S1, including the following steps: A1. Calculate the normal force of the wheel-rail contact according to the compression generated by the wheel-rail contact and the train track model in step S1; A2. Calculate the equivalent stiffness of the wheel-rail contact according to the normal force of the wheel-rail contact in step A1 and the train track model in step S1; A3. Calculate the track dynamic reaction force under the action of the high-speed train based on the equivalent stiffness of the wheel-rail contact in step A2 and the train track model in step S1.

4. The method for calculating the vibration response of site soil and buildings under the action of a high-speed train according to claim 3 is characterized in that: In step A3, based on the equivalent stiffness of the wheel-rail contact in step A2 and the train track model in step S1, the track dynamic reaction force under the action of the high-speed train is calculated and expressed as: P ij (t)=k h [z wij (t)-w rij (t)-z rij (t)] Where: P ij (t) is the track dynamic reaction force of the jth wheelset of the i-th train under the action of the high-speed train, k h is the equivalent stiffness of wheel-rail contact, z wij (t) is the displacement of the jth wheelset of the i-th train under the action of the high-speed train, w rij (t) is the vertical displacement of the track caused by the load at the jth wheelset of the i-th train under the action of the high-speed train, z rij (t) is the track unevenness at the j-th wheelset of the i-th train under the action of the high-speed train.

5. The method for calculating the vibration response of site soil and buildings under the action of a high-speed train according to claim 1 is characterized in that: In step S3, based on the track dynamic reaction force under the action of the high-speed train in step S2, the vibration response of the site soil under the action of the high-speed train is calculated using the Fourier transform method, including the following steps: B1. Based on the track dynamic reaction force under the action of the high-speed train in step S2, the vertical simple harmonic load of the rail under the action of the high-speed train is calculated using the Fourier transform method; B2. Calculate the vertical displacement of the site soil under the action of the high-speed train according to the simple harmonic load of the rail in the vertical direction under the action of the high-speed train in step B1; B3. Superimpose the vertical displacement of the site soil under the action of the high-speed train in step B2 to calculate the vibration response of the site soil under the action of the high-speed train.

6. The method for calculating the vibration response of site soil and buildings under the action of a high-speed train according to claim 5 is characterized in that: In step B1, based on the track dynamic reaction force under the action of the high-speed train in step S2, the Fourier transform method is used to calculate the vertical simple harmonic load of the rail under the action of the high-speed train, which is expressed as: Among them: F J (t) is the vertical simple harmonic load at the Jth rail node under the action of the high-speed train at time t, P J (t) is the track dynamic reaction force at the Jth rail node under the action of the high-speed train, which is determined by the track dynamic reaction force under the action of the high-speed train in step S2, t is time, 41 is the total number of track nodes, ω J is the circular frequency of the load at the Jth rail node, θ J is the phase at the Jth rail node.

7. The method for calculating the vibration response of site soil and buildings under the action of a high-speed train according to claim 5, characterized in that: In step B2, according to the simple harmonic load of the rail in the vertical direction under the action of the high-speed train in step B1, the vertical displacement of the site soil under the action of the high-speed train is calculated, which is expressed as: in: u x is the positive displacement of the site soil under the action of the high-speed train, u y is the vertical displacement of the site soil under the action of the high-speed train, u z is the vertical displacement of the site soil under the action of the high-speed train, u z is the normal displacement of the site soil under the action of the high-speed train, w z is the normal displacement of pore water under the action of high-speed train, T is the transposed sign, F is the amplitude of force, ω0 is the circular frequency of load, [K1] is the coefficient matrix, e is the natural logarithm, ξ is the abscissa in wave number domain, and η is the ordinate in wave number domain.

8. The method for calculating the vibration response of site soil and buildings under the action of a high-speed train according to claim 5, characterized in that: The transfer function method is used to calculate the vibration response of the building under the action of the high-speed train, including the following steps: C1. Calculate the vertical vibration acceleration of the site soil under the action of high-speed trains; C2. Calculate the coupling loss coefficient and floor amplification factor of the building under the action of high-speed trains; C3, using the transfer function method to calculate the vertical vibration acceleration of the building under the action of the high-speed train based on the vertical vibration acceleration of the site soil under the action of the high-speed train in step C1 and the coupling loss coefficient and the floor amplification coefficient of the building under the action of the high-speed train in step C2; C4. According to the vertical vibration acceleration of the building under the action of the high-speed train in step C3, the vibration acceleration level of the building under the action of the high-speed train is calculated to determine the vibration response of the building under the action of the high-speed train.

9. The method for calculating the vibration response of site soil and buildings under the action of a high-speed train according to claim 8, characterized in that: In step C1, the vertical vibration acceleration of the site soil under the action of the high-speed train is calculated and expressed as: Where: a(f) is the vertical vibration acceleration of the site soil with a frequency of f under the action of the high-speed train, is the second-order derivative of the displacement U(f), ω is the circular frequency, and U(f) is the displacement of the site soil with a frequency of f under the action of the high-speed train.

10. The method for calculating the vibration response of site soil and buildings under the action of a high-speed train according to claim 8, characterized in that: In step C3, according to the vertical vibration acceleration of the site soil under the action of the high-speed train in step C1 and the coupling loss coefficient and the floor amplification coefficient of the building under the action of the high-speed train in step C2, the vertical vibration acceleration of the building under the action of the high-speed train is calculated by the transfer function method, which is expressed as: a b (f)=a soil (f)·C l (f)·F a (f) Among them: a b (f) is the vertical vibration acceleration of the building with a frequency of f under the action of the high-speed train, a soil (f) is the vertical vibration acceleration of the site soil with a frequency of f under the action of the high-speed train, C l (f) is the coupling loss coefficient of the building at frequency f under the action of the high-speed train, F a (f) is the floor amplification factor of frequency f under the action of high-speed train.

Images