A probabilistic assessment method for vehicle-induced foundation vibration considering spatial variation of soil properties

Abstract

The present invention belongs to the technical field of vibration prediction in rail transit environment, and specifically relates to a method for evaluating the probability of vehicle-induced foundation vibration taking into account the spatial variation of soil properties. First, field measurements are conducted to obtain the measured values ​​of the vibration transfer function from soil to building foundation when the train is running, and a finite element model is established to simulate the vibration transfer from soil to structure when the train passes, and the results are compared and verified with the measured results; a three-dimensional random field sample is generated using the midpoint method based on Cholesky decomposition to describe the spatial variation of soil properties; the three-dimensional random field sample values ​​are assigned to the finite element model to predict the sample values ​​of the vibration transfer function from soil to building foundation. Finally, the sample values ​​of the transfer function are combined with the measured soil vibration acceleration level to obtain the structural foundation vibration acceleration level, and the sample values ​​are fitted with probability distribution to realize the probabilistic evaluation of train-induced structural foundation vibration, filling the gap in the current engineering field for the probabilistic evaluation of train-induced structural foundation vibration.

Description

Technical Field

[0001] The present invention belongs to the field of rail transit vibration prediction, and in particular relates to a vehicle-induced foundation vibration probability assessment method taking into account spatial variations in soil properties. Background Art

[0002] In recent years, in order to solve ground traffic congestion and people's travel needs, rail transit has developed rapidly. At the same time, the integrated development of station-city integration oriented to public transportation has emerged. Making full use of the upper space of rail transit for property development can not only efficiently utilize urban land resources and realize "one land, two uses", but also feed back the operation of the rail system economically, which is one of the important measures to solve the problem of urban land resource shortage. However, the vibration generated by the operation of rail transit trains spreads to the foundation soil through the track structure, and spreads outward through it as a medium. It is transmitted to the upper building structure through dynamic interaction at the building foundation, which can easily cause structural vibration, and then induce secondary radiation noise, which will have a negative impact on the quality of life of residents in buildings along the rail transit.

[0003] Methods for predicting train-induced vibration can be divided into empirical models, analytical or semi-analytical methods, numerical simulation methods, and hybrid methods. However, none of these methods consider the spatial variability of soil properties. Most of the considerations of the randomness of train-induced vibration are focused only on the vibration source, and the site soil is assumed to be uniformly distributed, ignoring the randomness and variability brought by the vibration propagation path. Soil profiles and dynamic parameters control the propagation law of ground vibration caused by trains. The common uniform layered soil model cannot consider the spatial variation of soil properties, nor can it achieve probabilistic evaluation. Summary of the invention

[0004] In view of the problems existing in the background technology, the present invention proposes a probability assessment method for train-induced foundation vibration that takes into account the spatial variation of soil properties. By considering the spatial variation of different soil parameters, the probability distribution of the train-induced building foundation vibration level is obtained. This fills the gap in the current engineering field in the probability assessment of train-induced building foundation vibration, so as to more effectively serve the prediction and design of environmental vibration caused by train vibration.

[0005] The purpose of the present invention is achieved through the following technical solutions.

[0006] A method for evaluating the probability of vehicle-induced foundation vibration considering the spatial variation of soil properties comprises the following steps:

[0007] S1. Obtain the measured value of the vibration transfer function from soil to building foundation during train operation, obtain the dynamic design parameters of soil stratification, obtain the structural design parameters of building foundation, establish a finite element model of train-homogeneous stratified soil-building foundation under the action of simple harmonic uniformly distributed stress on the surface, calculate the vibration transfer function from soil to building foundation induced by the train, generate a large number of random field samples of spatial variation of soil properties and assign them to the finite element model;

[0008] S2. Calculate and obtain the sample value of the building foundation vibration acceleration level;

[0009] S3, fitting the probability distribution of the building foundation vibration acceleration level to obtain a probability density curve of the building foundation vibration acceleration level;

[0010] According to a method for evaluating the probability of train-induced foundation vibration considering the spatial variation of soil properties disclosed in the present invention, preferably, in step S1, the measured train vibration wave propagates outwards with the foundation soil as the medium, and when the vibration wave reaches the building foundation structure, the soil and the foundation structure interact dynamically. Therefore, when evaluating the probability of train-induced building foundation vibration, considering the spatial variation of soil in the propagation path is the key to evaluating the probability of train-induced building foundation vibration.

[0011] Preferably, the calculation formula of the measured value of the vibration transfer function from soil to building foundation when the train is running in step S1 is:

[0012]

[0013] Among them, U C is the measured value of vibration acceleration at the building foundation, U S It is the measured value of the vibration acceleration of the surface soil 0.5m away from the building foundation, and TF is the measured value of the vibration transfer function from the soil to the building foundation when the train is running.

[0014] Preferably, in step S1, the foundation soil is divided into several homogeneous soil layers, and the dynamic design parameters of the homogeneous soil layers include soil density ρ, soil elastic modulus E, soil damping ratio ξ, and soil Poisson's ratio v.

[0015] Preferably, the structural design parameters of the building foundation in step S1 include the length L of the building foundation, the cross-sectional area A of the building foundation structure, and the elastic modulus E of the building foundation material. c and material density ρ c .

[0016] Preferably, step S1 establishes a finite element model of train-homogeneous layered soil-building foundation under the action of simple harmonic uniformly distributed stress on the surface, assuming that the train operation excitation is statistically independent, and simplifies the train excitation to a rectangular simple harmonic uniformly distributed stress of the double wheel pairs in the bogie.

[0017] Preferably, step S1 couples the finite element and the infinite element to analyze each other to prevent vibration wave reflection from affecting the calculation results. The finite element model calculates the train-induced soil-to-building foundation vibration transfer function and compares it with the measured vibration transfer function value, and verifies the established finite element model. If the comparison result is poorly consistent, the model parameters are adjusted until the result comparison is well consistent.

[0018] Preferably, step S1 first establishes a standard normal random field matrix U according to the soil parameters of the finite element model, and then performs Cholesky decomposition on the autocorrelation coefficient matrix R to obtain a lower triangular matrix. The calculation formula of the standard normal random field based on the Cholesky decomposition midpoint method is:

[0019] H=LU

[0020] Assuming that the spatially varying soil parameters follow a log-normal distribution, the degree of soil parameter variation is expressed as:

[0021]

[0022] COV=σ Xi / μ Xi

[0023] Among them, σ Xi and μ Xi are the standard deviation and mean of the standard normal distribution of soil parameters; σ lnXi and lnμ Xi are the standard deviation and mean of the log-normal distribution of soil parameters respectively; COV is the coefficient of variation of soil parameters.

[0024] The theoretical autocorrelation function is used to represent the correlation of soil parameters at two different locations in space:

[0025]

[0026] Among them, τ x ,τ y ,τ z Is the relative distance between two different positions in space. h ,δ v ,δ w is the autocorrelation distance of the random field in the corresponding direction.

[0027] Preferably, step S1 assigns the generated soil property random field sample values ​​to the finite element model unit grid.

[0028] Preferably, step S2 uses the assignment of soil parameters of the finite element model in step S1 to calculate sample values ​​of the soil-to-building foundation vibration transfer function, and adds the measured soil vibration acceleration level to the sample values ​​of the soil-to-building foundation vibration transfer function calculated by the finite element model to obtain a predicted sample value of the train-induced building foundation vibration acceleration level.

[0029] Preferably, step S3 counts the predicted sample values ​​of the train-induced building foundation vibration acceleration level obtained by random finite element calculation, performs probability distribution fitting to obtain a probability density curve, and the calculated sample values ​​of the building foundation vibration acceleration level follow a Gaussian distribution. The probability distribution is determined based on the mean and standard deviation of the distribution, and the probability of a specific value appearing in the distribution is predicted. The Gaussian distribution is expressed by the following formula:

[0030]

[0031] Where f(x) represents the probability density function PDF of the normal distribution, x represents the vibration acceleration level of the building foundation induced by the train at a specific frequency, μ is the mean value of the building vibration acceleration level, and σ is the standard deviation of the building vibration acceleration level.

[0032] Preferably, step S3 obtains the distribution of building acceleration levels induced by trains at different frequencies by analyzing the probability density curve of building vibration acceleration levels.

[0033] It can be seen from the above technical solutions that the advantages and positive effects of the present invention are:

[0034] The present invention provides a vehicle-induced foundation vibration probability assessment method that considers the spatial variation of soil properties, and constructs a train-homogeneous layered soil-building foundation finite element model under the action of simple harmonic uniformly distributed stress on the surface, and the model has a faster calculation speed and more accurate calculation results. Then, a large number of soil property random field samples are generated based on the midpoint method of Cholesky decomposition, and the random field samples are assigned to the finite element grid units. The soil property random finite element model after the assignment can better describe the dynamic behavior of the interaction between the soil and the building foundation under the spatial variation of the soil property; by fitting the probability distribution of the building foundation vibration acceleration level, the probability density curve of the building foundation vibration acceleration level is obtained to realize the probability assessment of the building foundation vibration; the established train-induced building foundation vibration probability assessment method with spatial variation of soil properties is more in line with the working conditions, greatly improving the efficiency of the building foundation vibration probability assessment, and the obtained prediction results are more scientific and reasonable. BRIEF DESCRIPTION OF THE DRAWINGS

[0035] Figure 1 is a flow chart of the steps of the present invention;

[0036] Figure 2 A simplified soil layered cross-section diagram related to an embodiment of the present invention;

[0037] Figure 3 A diagram of a building foundation model involved in an embodiment of the present invention;

[0038] Figure 4 A simplified train excitation model diagram involved in an embodiment of the present invention;

[0039] Figure 5 It is a schematic diagram of a finite element model of a train-homogeneous layered soil-building foundation under the action of simple harmonic uniformly distributed stress on the ground surface according to an embodiment of the present invention;

[0040] Figure 6 It is a comparison curve diagram of the vibration transfer function from soil to building foundation calculated by the finite element model in the embodiment of the present invention and the measured value when the train is running;

[0041] Figure 7 A schematic cloud diagram of a random field sample of three-dimensional soil parameters in an embodiment of the present invention;

[0042] Figure 8 A diagram of the building foundation vibration acceleration level predicted in an embodiment of the present invention;

[0043] Fig. 9 It is a probability density curve of the building foundation vibration acceleration level at 40 Hz fitted in an embodiment of the present invention. DETAILED DESCRIPTION

[0044] In order to make the purpose, features and advantages of the present invention more obvious and understandable, the technical solutions in the embodiments of the present invention will be clearly and completely described below in conjunction with the accompanying drawings in the embodiments of the present invention.

[0045] Obviously, the embodiments described below are only some embodiments of the present invention, not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by ordinary technicians in this field without creative work are within the scope of protection of the present invention.

[0046] like Figure 1 As shown, the present invention provides a method for evaluating the probability of vehicle-induced foundation vibration considering the spatial variation of soil properties, comprising the following steps:

[0047] S1. Obtain the measured value of the vibration transfer function from soil to building foundation during train operation, obtain the dynamic design parameters of soil stratification, obtain the structural design parameters of building foundation, establish a finite element model of train-homogeneous stratified soil-building foundation under the action of simple harmonic uniformly distributed stress on the surface, calculate the vibration transfer function from soil to building foundation induced by the train, generate a large number of random field samples of spatial variation of soil properties and assign them to the finite element model;

[0048] S2. Calculate and obtain the sample value of the building foundation vibration acceleration level;

[0049] S3. Fit the probability distribution of the building foundation vibration acceleration level to obtain a probability density curve of the building foundation vibration acceleration level.

[0050] According to the above embodiment, preferably, the measured train vibration wave in step S1 propagates outwards through the foundation soil as a medium, and when the vibration wave reaches the building foundation structure, the soil and the foundation structure interact dynamically. Therefore, when evaluating the probability of train-induced building foundation vibration, considering the spatial variation of the soil in the propagation path is the key to evaluating the probability of train-induced building foundation vibration.

[0051] Preferably, the calculation formula of the measured value of the vibration transfer function from soil to building foundation when the train is running in step S1 is:

[0052]

[0053] Among them, U C is the measured value of vibration acceleration at the building foundation, U S It is the measured value of the vibration acceleration of the surface soil 0.5m away from the building foundation, and TF is the measured value of the vibration transfer function from the soil to the building foundation when the train is running.

[0054] like Figure 2 As shown, the soil parameters of this embodiment are simplified into three horizontal layers according to the test section drilling data, and the soil parameters are shown in Table 1. The thickness of the first backfill soil layer is 2.4 meters, the thickness of the second clay layer is 11.4 meters, and the thickness of the third granite layer is 8.9 meters.

[0055] Table 1 Homogeneous layered soil parameters

[0056]

[0057] like Figure 3 As shown, the structural design parameters of the building foundation in this embodiment include the building foundation length L, the building foundation structural cross-sectional area A, and the building foundation material elastic modulus E c and material density ρ s .

[0058] like Figure 4 As shown, the actual train of this embodiment is a four-section L-type train, including 4 carriages, 8 bogies and 16 wheel sets. The rectangular shaded area represents the excitation of the surface soil by the wheel-rail force of the double wheel sets in each bogie after the stress diffusion of the track structure, which is simplified to the simple harmonic uniformly distributed stress effect.

[0059] like Figure 5As shown in the figure, a finite element model of train-homogeneous layered soil-building foundation under the action of simple harmonic uniformly distributed stress on the ground surface is established according to the soil parameters and the design parameters of the building foundation. Assuming that the train running excitation is statistically independent, the train excitation is simplified to the rectangular simple harmonic uniformly distributed stress of the double wheel pair in the bogie. The size of each rectangular shadow area is 2.5m×2.5m, and the model size is 100m×100m×22.3m. In order to capture the soil vibration within 80Hz in the backfill soil, the minimum grid size is 0.4m. The soil of the outermost unit of the model is set as an infinite element, and the attenuation formula is introduced on the boundary to simulate the radiation damping of the infinite foundation to gradually attenuate the vibration radiation energy outward to prevent the vibration wave from reflecting and interfering with the finite element model calculation.

[0060] like Figure 6 As shown in the figure, the vibration transfer function from soil to building foundation calculated by the finite element model of train-homogeneous layered soil-building foundation under the action of simple harmonic uniformly distributed stress on the surface is very close to the average measured value of the vibration transfer function from soil to building foundation when the train is running, with a maximum error of only 4dB, which proves the accuracy of the model.

[0061] like Figure 7 As shown in FIG. 1 , a large number of spatially varying random field samples are generated for the elastic modulus, density and damping ratio of the first layer of backfill soil (2.4 m) and the second layer of clay (11.4 m) of this embodiment. The size of the random field model is 100 m×100 m×13.8 m. The depth of the grid color corresponds to different soil property values. The autocorrelation parameter of the random field model adopts a coefficient of variation of 0.2, and the fluctuation length δ h , δ v , δ w They are 20 meters, 20 meters, and 4 meters respectively. According to the soil parameters of the finite element model, the relevant standard normal random field matrix U is established, and then the autocorrelation coefficient matrix R is decomposed by Cholesky to obtain the lower triangular matrix. The calculation formula of the standard normal random field based on the Cholesky decomposition midpoint method is:

[0062] H=LU

[0063] Assuming that the spatially varying soil parameters follow a log-normal distribution, the degree of soil parameter variation is expressed as:

[0064]

[0065] COV=σ Xi / μ Xi

[0066] Among them, σ Xi and μ Xi are the standard deviation and mean of the standard normal distribution of soil parameters; σ lnXi and lnμ Xiare the standard deviation and mean of the log-normal distribution of soil parameters respectively; COV is the coefficient of variation of soil parameters.

[0067] The autocorrelation function describes the autocorrelation of parameters at different spatial locations. It is crucial to accurately capture the spatial relationship and correlation of soil parameters, but determining the autocorrelation function requires a large amount of sample data. The theoretical autocorrelation function can be used to represent the correlation of soil parameters at two different locations in space. This embodiment uses the exponential autocorrelation function:

[0068]

[0069] Among them, τ x ,τ y ,τ z is the relative distance between two different positions in space, i.e., τ x =|x i -x j |,τ y =|y i -y j |,τ z =|z i -z j |. δ h ,δ v ,δ w is the autocorrelation length of the random field in the corresponding direction.

[0070] like Figure 8 As shown, step S2 adds the measured soil vibration acceleration level to the transfer function calculated by the finite element model to obtain the predicted value of the building foundation vibration acceleration level induced by the train.

[0071] like Fig. 9 As shown in the figure, the train-induced building foundation vibration acceleration level values ​​obtained by statistical random finite element calculation are subjected to Gaussian distribution probability fitting to obtain the probability density curve of building foundation vibration acceleration level of different frequencies. The mean and standard deviation of the Gaussian distribution can be used to determine the probability distribution and predict the possibility of a specific value appearing in the distribution. The Gaussian distribution is expressed by the following formula:

[0072]

[0073] Where f(x) represents the probability density function PDF of the normal distribution, x represents the vibration acceleration level of the building foundation induced by the train at a specific frequency, μ is the mean value of the building vibration acceleration level, and σ is the standard deviation of the building vibration acceleration level.

[0074] By analyzing the probability density curve of building vibration acceleration level, the distribution of building acceleration level induced by trains at different frequencies is obtained.

[0075] The above embodiments are only used to illustrate the technical solutions of the present invention, rather than to limit the same. Although the present invention has been described in detail with reference to the aforementioned embodiments, those skilled in the art should understand that the technical solutions described in the aforementioned embodiments may still be modified, or some of the technical features may be replaced by equivalents. However, these modifications or replacements do not deviate the essence of the corresponding technical solutions from the spirit and scope of the technical solutions of the embodiments of the present invention.

Claims

1. A method for evaluating the probability of vehicle-induced foundation vibration considering the spatial variation of soil properties, the characteristics of which include: S1. Obtain the measured value of the vibration transfer function from soil to building foundation during train operation, obtain the dynamic design parameters of soil stratification, obtain the structural design parameters of building foundation, establish a finite element model of train-homogeneous stratified soil-building foundation under the action of simple harmonic uniformly distributed stress on the surface, calculate the vibration transfer function from soil to building foundation induced by the train, generate a large number of random field samples of spatial variation of soil properties and assign them to the finite element model; S2. Using the values ​​assigned to the finite element model in step S1, the sample values ​​of the soil-to-building foundation vibration transfer function are calculated, and the sample values ​​of the soil-to-building foundation vibration transfer function calculated by the finite element model are added together to obtain the predicted sample values ​​of the train-induced building foundation vibration acceleration level; S3, fitting the probability distribution of the building foundation vibration acceleration level to obtain a probability density curve of the building foundation vibration acceleration level; In step S1, the measured value of the vibration transfer function from soil to building foundation when the train is running is calculated according to the following formula: Among them, U C is the measured value of vibration acceleration at the building foundation, U S is the measured value of the vibration acceleration of the surface soil 0.5 m away from the building foundation, and TF is the measured value of the vibration transfer function from the soil to the building foundation when the train is running; In step S1, a large number of random field samples of spatially varying soil properties are generated and assigned to the finite element model, including: establishing a standard normal random field matrix U according to the soil parameters of the finite element model, performing Cholesky decomposition on the autocorrelation coefficient matrix R to obtain a lower triangular matrix, and the calculation formula of the standard normal random field based on the Cholesky decomposition midpoint method is: H=LU; the spatially varying soil parameters follow a log-normal distribution, and the degree of variation of the soil parameters is calculated; the theoretical autocorrelation function is used to represent the correlation of soil parameters at two different positions in space; and the generated soil parameter random field sample values ​​are assigned to the finite element model grid; In step S1, the foundation soil is divided into a plurality of homogeneous soil layers, and the dynamic design parameters of the homogeneous soil layers include soil density ρ, soil elastic modulus E, soil damping ratio ξ, and soil Poisson's ratio v; In step S1, a finite element model of train-homogeneous layered soil-building foundation under the action of simple harmonic uniformly distributed stress on the ground surface is established, including: making the train operation excitation statistically independent, simplifying the train excitation to the rectangular simple harmonic uniformly distributed stress of the double wheel pair in the bogie, thereby calculating the train-induced soil to building foundation vibration transfer function, and comparing the calculated results with the field measured results to adjust the model parameters.

2. A vehicle-induced foundation vibration probability assessment method considering the spatial variation of soil properties according to claim 1, characterized in that: The structural design parameters of the building foundation include the length of the building foundation, the cross-sectional area of ​​the building foundation structure A, and the elastic modulus E of the building foundation material. c and material density ρ c .

3. The method for evaluating the probability of vehicle-induced foundation vibration considering the spatial variation of soil properties according to claim 2 is characterized in that: The variation degree of soil parameters is expressed as: in, and are the standard deviation and mean of the standard normal distribution of soil parameters, respectively; and are the standard deviation and mean of the log-normal distribution of soil parameters, respectively; COV is the coefficient of variation of soil parameters; The theoretical autocorrelation function is used to represent the correlation of soil parameters at two different locations in space: Among them, τ x ,τ y ,τ z is the relative distance between two different positions in space; δ h ,δ v ,δ w is the autocorrelation distance of the random field in the corresponding direction.

4. The method for evaluating the probability of vehicle-induced foundation vibration considering the spatial variation of soil properties according to claim 3 is characterized in that: Step S3 counts the predicted sample values ​​of the train-induced building foundation vibration acceleration level obtained by random finite element calculation, performs probability distribution fitting to obtain a probability density curve, and the calculated predicted sample values ​​of the train-induced building foundation vibration acceleration level follow a Gaussian distribution. The probability distribution is determined based on the mean and standard deviation of the Gaussian distribution, and the probability of a specific value appearing in the Gaussian distribution is predicted; the Gaussian distribution is expressed by the following formula: Where f(x) represents the probability density function of the normal distribution, x represents the train-induced building foundation vibration acceleration at a specific frequency, μ is the average value of the train-induced building vibration acceleration level, and σ is the standard deviation of the building vibration acceleration level.

5. The method for evaluating the probability of vehicle-induced foundation vibration considering the spatial variation of soil properties according to claim 4 is characterized in that: Step S3 obtains the distribution of building acceleration levels induced by trains at different frequencies by analyzing the probability density curve of building vibration acceleration levels.

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