Tunnel wall vibration prediction method and system considering track alignment constraint conditions

Abstract

The application discloses a tunnel wall vibration prediction method and system considering line alignment constraint conditions, and is based on a constructed vehicle-line coupling dynamics, train-track-tunnel (soil body) system vibration integrated analysis model, studies the influence degree of different line parameters such as curve radius, line slope and combinations thereof on the system vibration response, obtains tunnel wall vibration acceleration data in the evaluation section, and further calculates the tunnel wall Z vibration level; based on the probability density distribution and numerical fitting method, the influence function relationship of different line parameters on the tunnel wall vibration level is derived. The application fully considers the objective problem that the influence factors of the existing environmental impact assessment prediction method are not comprehensive, quantifies the corresponding coupling relationship between the line parameters and the tunnel wall Z vibration level, can more systematically determine the prediction and evaluation results of the urban rail transit vehicle-induced tunnel wall vibration, and provides a theoretical basis and an engineering applicable method for realizing tunnel structure vibration prediction and line design optimization.

Description

Technical Field

[0001] This invention relates to the field of track engineering technology, and specifically to a method and system for predicting tunnel wall vibration considering the constraints of the track shape. Background Technology

[0002] In recent years, urban rail transit projects have developed rapidly, facing limitations from the external environment, such as increasingly dense road networks, shrinking available underground space, deteriorating line running conditions, and an increasing number of environmentally sensitive areas such as adjacent to or passing through residential areas and schools. As well as changes in people's demand for a high quality of life, the adverse effects caused by various train operations have become increasingly severe, with vibration and noise complaints being the most prominent issues.

[0003] Train vibrations and noise affect the quality of life and comfort of residents along the line, causing difficulty falling asleep for sensitive individuals, exacerbating the psychological burden on people with underlying diseases, and intensifying the irritability of people commuting to and from the city for work. Reports of problems such as excessive noise inside trains, train swaying, and building vibrations affecting residents' lives are common in urban rail transit systems across the country. The reasons for complaints are complex, and some lines even receive complaints during the trial operation phase.

[0004] The vibration propagation system consists of three parts: first, the vibration source, mainly including the train and track; the system vibration excited by the interaction between the wheel and rail is the most important noise source in rail transit engineering; second, the propagation path, mainly including the foundation and soil beneath the track, which promotes the radial radiation propagation of vibration; and third, the vibrating body, which is the building itself, where vibration is responded to and induces secondary structural noise. Factors affecting vibration noise include multiple factors such as track conditions, track structure type, speed, soil properties, and building foundation type, making it a complex coupled system.

[0005] A crucial step in the environmental impact assessment of train vibration is to evaluate whether the vibration response exceeds the limits specified in relevant standards and specifications. As the source of transmission, the accuracy and breadth of tunnel wall vibration prediction are the primary factors in determining whether the standards are met, and it is directly affected by the train running status and track operating conditions.

[0006] When selecting routes for urban rail transit lines, under the premise of meeting basic requirements, the horizontal and vertical profile parameters such as curve radius, straight section length, and line gradient are determined by combining various factors such as network planning. The horizontal and vertical profile design of the line in a "compliant with the standard" manner can meet the needs of engineering construction and functional positioning, but the service quality cannot be guaranteed and it is difficult to meet the people's high-quality life needs.

[0007] Currently, vibration prediction adopts the chain formula recommended in the "Technical Guidelines for Environmental Impact Assessment of Urban Rail Transit" (HJ453-2018). After obtaining the vibration source strength through on-site measurement and analogy, the vibration prediction value of the ground sensitive point is obtained after correcting the vibration response based on train speed, wheel-rail conditions, tunnel type and distance attenuation.

[0008] Vibration source intensity refers to the magnitude of vibration energy generated at a specific reference point. Measurements are typically taken on straight or flat sections, and vibration intensity predictions for other sections are superimposed and corrected based on this benchmark. However, when correcting vibration response under wheel-rail conditions, only train speed and curve radius are considered. The influence of different line characteristics (parameters such as straight section length and gradient) and their combinations, as well as different track types, on the Z-level of tunnel walls is not considered. A dynamic alignment strategy under the boundary constraints of sensitive point vibration control is lacking. This results in insufficient breadth of vibration prediction, and dynamic control is inadequate to meet the needs of vibration prediction, leading to a degree of uncertainty in the vibration reduction and isolation design of urban rail transit. Summary of the Invention

[0009] This application provides a method and system for predicting tunnel wall vibration considering the constraints of the railway line shape, in order to solve the problem that the existing technology has insufficient breadth for predicting environmental vibration caused by train operation.

[0010] According to a first aspect, one embodiment provides a method for predicting tunnel wall vibration considering route shape constraints, the method comprising:

[0011] Based on the horizontal and vertical profile characteristics of urban rail transit lines, the line parameters affecting the vibration level of tunnel walls in the evaluation section are determined.

[0012] Based on a pre-constructed vehicle-track coupled dynamics analysis model that considers the track shape constraints, the wheel-rail interaction force of a pre-selected single track parameter under different values ​​is obtained through simulation calculation.

[0013] The obtained wheel-rail interaction force is used as a load input to a pre-constructed integrated vibration analysis model of the train-track-tunnel (soil) system. The vibration acceleration of the tunnel wall under different values ​​of the current single line parameters is obtained through simulation calculation.

[0014] Based on the obtained tunnel wall vibration acceleration, the tunnel wall Z-level vibration is calculated under different values ​​of the current single line parameters. Combined with frequency distribution and normal distribution fitting analysis, the predicted value of the tunnel wall Z-level vibration is obtained under different values ​​of the current single line parameters.

[0015] Based on the predicted values ​​of tunnel wall Z-magnitude under different values ​​of the current single line parameters, the functional relationship between the current single line parameters and the predicted values ​​of tunnel wall Z-magnitude is obtained by fitting.

[0016] The functional relationships between different line parameters and the predicted Z-level vibration of the tunnel wall are obtained, and then superimposed and corrected to obtain the final expression for the predicted Z-level vibration of the tunnel wall considering the line shape constraints.

[0017] Furthermore, based on the horizontal and vertical profile characteristics of urban rail transit lines, the line parameters affecting the tunnel wall vibration level in the evaluation section are identified, specifically including:

[0018] The horizontal alignment elements of the railway line include straight lines, circular curves, and transition curves, while the vertical alignment elements include gradient and vertical curves. Circular curves are characterized by length, radius, and superelevation, with superelevation using a semi-superelevation method. Transition curves are cubic parabolic transition curves with straight superelevation and a downward slope. The railway parameters include characteristic parameter information of the horizontal and vertical alignment elements and train information.

[0019] Furthermore, a vehicle-line coupled dynamic analysis model considering the alignment constraints is constructed, specifically including:

[0020] The vehicle-track coupled dynamics analysis model considering the track geometry constraints includes a train model, a wheel-rail relationship model, and a track geometry model; the vehicle is simulated using multibody dynamics, with the car body and bogie connected by a secondary suspension, and the bogie and wheelset connected by a primary suspension.

[0021] Furthermore, based on a pre-constructed vehicle-track coupled dynamics analysis model considering track shape constraints, simulation calculations are performed to obtain the wheel-rail interaction forces under different values ​​of pre-selected single track parameters, specifically including:

[0022] In the simulation calculation, the train is set to travel at a constant speed on the rails. The track irregularity spectrum adopts the US Level 5 spectrum that matches the speed level of urban rail transit or a custom measured track spectrum. The wheel-rail interaction force is characterized by the wheel-rail vertical force, and the wheel-rail vertical force is calculated using Hertzian nonlinear elastic contact theory.

[0023] Furthermore, an integrated vibration analysis model for the train-track-tunnel system considering different ballastless track structural characteristics is constructed, specifically including:

[0024] Based on the spatial vibration analysis theory and finite element analysis theory of train-track system, an integrated vibration analysis model of train-track-tunnel system is constructed, considering different train operating conditions, track geometry conditions and different track structure types. The integrated vibration analysis model of train-track-tunnel system includes rails, fasteners, track bed, tunnel and soil structure. Among them, the rails are simulated using beam elements, the fasteners are simulated using spring-damping elements, and the track bed, tunnel and soil are simulated using solid elements.

[0025] Furthermore, based on the obtained tunnel wall vibration acceleration, the tunnel wall Z-vibration level under different values ​​of the current single line parameters is calculated, specifically including:

[0026] ;

[0027] In the formula, VAL is the Z-level vibration of the tunnel wall; a is the calculated tunnel vibration acceleration value; This is the baseline acceleration value.

[0028] Furthermore, by combining frequency distribution and normal distribution fitting analysis, the predicted values ​​of tunnel wall Z-vibration level under different values ​​of the current single line parameters are obtained, specifically including:

[0029] Using the sample mean or cumulative probability value as the control benchmark, a representative value of the tunnel wall Z-vibration level is selected and used as the predicted value of the tunnel wall Z-vibration level.

[0030] Furthermore, the functional relationships between different line parameters and the predicted Z-level vibration of the tunnel wall are obtained, and these relationships are superimposed and corrected to obtain the final expression for the predicted Z-level vibration of the tunnel wall considering the line shape constraints. Specifically, this includes:

[0031] ;

[0032] In the formula, This is a fitted function expression for the predicted Z-level vibration of the tunnel wall as a function of the line parameter m. To account for the correction amount caused by multiple factors, including the vibration reduction effect of the vibration reduction track bed and the superimposed increment caused by the combination of multiple line parameters, Z is the expression for the predicted value of the tunnel wall Z vibration level obtained by superposition and correction calculation.

[0033] According to a second aspect, one embodiment provides a tunnel wall vibration prediction system considering route shape constraints, the system comprising:

[0034] The line parameter determination module is used to determine the line parameters that affect the vibration level of the tunnel wall in the evaluation section based on the horizontal and vertical characteristics of the urban rail transit line.

[0035] The wheel-rail force calculation module is used to obtain the wheel-rail interaction force under different values ​​of a pre-constructed vehicle-track coupled dynamic analysis model that considers the track shape constraints through simulation calculation.

[0036] The vibration acceleration calculation module is used to input the obtained wheel-rail interaction force as a load into the pre-built integrated vibration analysis model of the train-track-tunnel system, and obtain the tunnel wall vibration acceleration under different values ​​of the current single line parameters through simulation calculation.

[0037] The Z-level calculation module is used to calculate the Z-level of the tunnel wall under different values ​​of the current single line parameters based on the obtained tunnel wall vibration acceleration, and to obtain the predicted value of the Z-level of the tunnel wall under different values ​​of the current single line parameters by combining frequency distribution and normal distribution fitting analysis.

[0038] The fitting module is used to predict the tunnel wall Z-level vibration based on the current single line parameters under different values, and to obtain the functional relationship between the current single line parameters and the predicted tunnel wall Z-level vibration based on the fitting.

[0039] The superposition calculation module is used to obtain the functional relationship between different line parameters and the predicted value of tunnel wall Z-vibration level, and to superimpose and correct the data to obtain the final expression of the predicted value of tunnel wall Z-vibration level considering the line shape constraints.

[0040] Furthermore, the superposition calculation module is specifically used to calculate:

[0041] ;

[0042] In the formula, This is a fitted function expression for the predicted Z-level vibration of the tunnel wall as a function of the line parameter m. To account for the correction amount caused by multiple factors, including the vibration reduction effect of the vibration reduction track bed and the superimposed increment caused by the combination of multiple line parameters, Z is the expression for the predicted value of the tunnel wall Z vibration level obtained by superposition and correction calculation.

[0043] This application provides a method and system for predicting tunnel wall vibration considering the constraints of the tunnel alignment, which has the following advantages:

[0044] 1. The vibration prediction takes into account the influence of different line parameters on tunnel wall vibration, and the vibration prediction is more comprehensive. Compared with the prediction formula recommended in the "Technical Guidelines for Environmental Impact Assessment of Urban Rail Transit" (HJ453-2018), it is more in line with the actual engineering situation.

[0045] 2. Based on the integrated vibration analysis model of the train-track-tunnel system under the line coupling constraint, the corresponding functional relationship between different line parameters (curve radius, straight section length, slope, etc.) and the Z-level vibration of the tunnel wall is obtained. The prediction formula is intuitive and avoids the time cost caused by repetitive modeling calculations.

[0046] 3. The tunnel wall Z-vibration level predicted based on the acceptable level takes into account a certain degree of probability events, fully considers the uncertainties in the environmental vibration prediction system, is easy to operate, has high calculation efficiency, and can provide more comprehensive prediction results for urban rail transit environmental vibration. Attached Figure Description

[0047] Figure 1A flowchart illustrating a method for predicting tunnel wall vibration considering route shape constraints, as provided in one embodiment of the present invention;

[0048] Figure 2 A schematic diagram of the horizontal and vertical profiles of a tunnel wall vibration prediction method considering the route shape constraints provided in an embodiment of the present invention.

[0049] Figure 3 The vertical vibration acceleration waveform of the tunnel wall in the evaluation section is provided in an embodiment of the present invention for a tunnel wall vibration prediction method considering the route shape constraints.

[0050] Figure 4 The image shows the distribution of the Z-level vibration of the tunnel wall in the evaluation section of a tunnel wall vibration prediction method considering the route shape constraints provided in an embodiment of the present invention.

[0051] Figure 5 This is a fitting graph of the probability density function of the maximum Z-level vibration of the tunnel wall in a tunnel wall vibration prediction method considering the route shape constraints provided in an embodiment of the present invention;

[0052] Figure 6 The fitting curve of curve radius to tunnel wall Z-vibration level is provided in a tunnel wall vibration prediction method considering the route shape constraints in an embodiment of the present invention.

[0053] Figure 7 The curve showing the influence of curve radius on the vibration reduction effect in a tunnel wall vibration prediction method considering the route shape constraints provided in an embodiment of the present invention. Detailed Implementation

[0054] The present invention will now be described in further detail with reference to specific embodiments and accompanying drawings. Similar elements in different embodiments are referred to by associated similar element reference numerals. In the following embodiments, many details are described to facilitate a better understanding of this application. However, those skilled in the art will readily recognize that some features may be omitted in different situations, or may be replaced by other elements, materials, or methods. In some cases, certain operations related to this application are not shown or described in the specification. This is to avoid obscuring the core parts of this application with excessive description. For those skilled in the art, detailed description of these related operations is not necessary; they can fully understand the related operations based on the description in the specification and general technical knowledge in the art.

[0055] Furthermore, the features, operations, or characteristics described in the specification can be combined in any suitable manner to form various embodiments. At the same time, the steps or actions in the method description can be rearranged or adjusted in a manner obvious to those skilled in the art. Therefore, the various orders in the specification and drawings are only for the clear description of a particular embodiment and do not imply a necessary order, unless otherwise stated that a particular order must be followed.

[0056] This invention provides a method for predicting tunnel wall vibration considering route shape constraints. The following is a related explanation. Figure 1 Please provide a detailed explanation.

[0057] like Figure 1 As shown, in step S100, based on the planar and longitudinal profile characteristics of the urban rail transit line, the line parameters that affect the vibration level of the tunnel wall in the evaluation section are determined.

[0058] In this embodiment, the schematic diagram of the horizontal and vertical cross-sections of the line is as follows: Figure 2 As shown, where Figure 2 (a) in the diagram is a schematic plan of the railway line. Figure 2 (b) is a schematic diagram of the longitudinal profile of the railway line. The horizontal components of the railway line include straight lines, circular curves, and transition curves. The vertical components include gradient and vertical curves. Circular curves are characterized by length, radius, and superelevation, with superelevation using a semi-superelevation method. Transition curves are cubic parabolic transition curves with straight-line superelevation and a downward gradient. Railway parameters include characteristic parameters of the horizontal and vertical components (curve radius, gradient, length of the straight line between the horizontal and vertical sections, etc.) and train information (train speed, etc.).

[0059] like Figure 1 As shown, in step S200, based on the pre-constructed vehicle-track coupling dynamics analysis model that considers the track shape constraints, the wheel-rail interaction force of the pre-selected single track parameter under different values ​​is obtained through simulation calculation.

[0060] In this embodiment, a vehicle-track coupled dynamic analysis model considering track shape constraints is constructed by establishing a locomotive and rolling stock model, a track model, a wheel-rail contact model, and a track random irregularity model.

[0061] The constructed vehicle-track coupled dynamics analysis model includes a train model, a wheel-rail relationship model, and a track geometry model. The vehicle is simulated using multibody dynamics, and includes a car body, bogies, wheelsets, etc. The car body and bogies are connected by a secondary suspension, and the bogies and wheelsets are connected by a primary suspension.

[0062] In the simulation, the train is set to travel at a constant speed V on the rails. The track irregularity spectrum adopts either the US Level 5 spectrum, which matches the speed level of urban rail transit, or a custom-defined measured track spectrum. The wheel-rail interaction force is characterized by the wheel-rail vertical force, which is calculated using Hertzian nonlinear elastic contact theory. The calculation formula is as follows:

[0063] ;

[0064] In the formula: P(t) is the vertical force between the wheel and the rail; G is the elastic contact constant between the wheel and the rail, in units of: For wheels with worn treads: R is the wheel radius; The relative elastic compression between the wheel and rail is expressed in meters (m); t represents a specific moment.

[0065] The curves of wheel-rail interaction force with the spatial position of the track under different track bed support stiffness conditions were calculated. The support stiffness of different track beds was calculated using the elastic point support beam model listed in the railway track strength verification method. Specifically, the finite element method was used to model the track, discretizing it into multiple beam elements, applying a load F, determining the vertical displacement u of the track, and determining the support stiffness as: K = F / u.

[0066] like Figure 1 As shown, in step S300, the obtained wheel-rail interaction force is input as a load into the pre-constructed integrated vibration analysis model of the train-track-tunnel system, and the tunnel wall vibration acceleration under different values ​​of the current single line parameters is obtained through simulation calculation.

[0067] In this embodiment, based on the spatial vibration analysis theory of train-track systems and the finite element analysis theory, an integrated vibration analysis model of the train-track-tunnel (soil) system considering different ballastless track structural characteristics is established. This integrated vibration analysis model of the train-track-tunnel (soil) system can simulate and consider different train operating conditions, track geometry conditions, and different track structure types.

[0068] The integrated vibration analysis model of the train-track-tunnel (soil) system includes structures such as rails, fasteners, track bed, tunnel, and soil. The track bed can be categorized into general integral track bed, vibration-damping fastener integral track bed, vibration-damping pad integral track bed, and steel spring floating slab integral track bed based on vibration reduction requirements. Specifically, the rails are simulated using beam elements; the fasteners are simulated using spring-damping elements with a fastener node spacing of 595mm; the track bed, vibration-damping pads, tunnel, and soil are simulated using solid elements; dynamic parameters such as elastic modulus and damping are based on design parameters.

[0069] The calculated wheel-rail interaction force is imported into the integrated vibration analysis model of the train-track-tunnel (soil) system as the load curve, and the vibration acceleration of the tunnel wall under different track conditions is obtained by simulation calculation.

[0070] like Figure 1 As shown, in step S400, based on the obtained tunnel wall vibration acceleration, the tunnel wall Z-level vibration of the current single line parameter under different values ​​is calculated, and combined with frequency distribution and normal distribution fitting analysis, the predicted value of the tunnel wall Z-level vibration of the current single line parameter under different values ​​is obtained.

[0071] In this embodiment, the Z-level of the tunnel wall is obtained based on the calculated vibration acceleration of the tunnel wall. The formula for calculating the Z-level of the tunnel wall is as follows:

[0072] ;

[0073] In the formula, VAL is the Z-level vibration of the tunnel wall; a is the calculated tunnel vibration acceleration value; The reference acceleration value is generally taken as... .

[0074] Further, a time history distribution diagram of the Z-level vibration of the tunnel wall in the evaluation section was drawn, the frequency and frequency of different Z-level vibrations were calculated, a frequency distribution histogram and a normal distribution fitting function were drawn, and then the representative value of the Z-level vibration of the tunnel wall in the evaluation section under different reference conditions was obtained using the sample mean or cumulative probability value as the control benchmark. That is, a value that can represent the vibration of the section is selected according to the two benchmarks and used as the predicted value of the Z-level vibration of the tunnel wall in the evaluation section.

[0075] The expression for calculating the predicted vibration magnitude with different cumulative probabilities using integration is as follows:

[0076] ;

[0077] In the formula, Let Z be the tunnel wall vibration level value corresponding to different operating conditions i for a certain line parameter. This corresponds to the predicted vibration level. That is: obtain the probability density function g(x) of the Z-level vibration of the tunnel wall under the baseline conditions, and... For the maximum points, By integrating the probability density function of the tunnel wall Z-level as the lower limit of integration, the tunnel wall Z-level under different cumulative probability values ​​is obtained; where This represents the minimum vibration level in the probability density function curve.

[0078] like Figure 1 As shown, in step S500, based on the predicted values ​​of the tunnel wall Z-vibration level under different values ​​of the current single line parameter, the functional relationship between the current single line parameter and the predicted value of the tunnel wall Z-vibration level is obtained by fitting.

[0079] In this embodiment, based on the tunnel wall Z-vibration level under different cumulative probability conditions, the predicted tunnel wall Z-vibration level for a certain line parameter under a specific value is determined. The predicted tunnel wall Z-vibration level under different line parameter values ​​is then nonlinearly fitted to obtain a fitting formula for the predicted tunnel wall Z-vibration level as a function of the line parameter m. .

[0080] like Figure 1 As shown, in step S600, the functional relationship between different line parameters and the predicted value of tunnel wall Z-vibration level is obtained, and the relationship is superimposed and corrected to obtain the final expression of the predicted value of tunnel wall Z-vibration level considering the line shape constraint.

[0081] In this embodiment, the functional relationships between the fitted different line parameters and the predicted Z-level vibration values ​​of the tunnel wall are superimposed, combined, and corrected, as follows:

[0082] ;

[0083] In the formula, This is a fitted function expression for the predicted Z-level vibration of the tunnel wall as a function of the line parameter m. To account for the correction amount caused by multiple factors, including the vibration reduction effect of the vibration reduction track bed and the superimposed increment caused by the combination of multiple line parameters, Z is the expression for the predicted value of the tunnel wall Z vibration level obtained by superposition and correction calculation.

[0084] Application examples:

[0085] 1. Analyze the influence of curve radius R in the plane parameters of the railway line on tunnel wall vibration.

[0086] Taking a typical integral track bed as an example, using a Type A train with a running speed of 80 km / h, curve radii of 400m, 450m, 500m, 600m, 800m, 1000m, 1500m, 2000m, 3000m and straight sections are selected. The superelevation is taken as the actual superelevation value. The wheel-rail vertical force under different curve radii is calculated through the vehicle-track coupled dynamic analysis model, and the time step is taken as 0.0005s.

[0087] The calculated wheel-rail vertical force was further imported into the integrated vibration analysis model of the train-track-tunnel (soil) system, with a time step of 0.0005 s, to calculate the vertical displacement of the rail and the vibration acceleration of the tunnel wall (e.g., ...). Figure 3 (as shown in the image), etc., are used to indirectly determine the accuracy of the model;

[0088] The Z-level vibration of the tunnel wall is obtained from the tunnel wall acceleration as follows: Figure 4As shown, the histogram of the frequency distribution of the Z-level vibration of the tunnel wall in the evaluation section and the normal distribution curve are plotted, as follows. Figure 5 As shown, taking R=400m as an example, the Z-vibration level of the tunnel wall in the evaluation section follows a normal distribution (79.8, 6.42), with a mean of 79.8dB.

[0089] Furthermore, the same calculation method was used to obtain the predicted values ​​of the tunnel wall Z-vibration level under different curve radii, as shown in Table 1.

[0090] Table 1. Predicted Z-magnitude values ​​of tunnel walls under different curve radii.

[0091] Nonlinear fitting was performed on the predicted values ​​of tunnel wall Z-vibration level under different curve radii conditions in Table 1. Based on the distribution pattern of the calculated values, it was determined that the tunnel wall Z-vibration level data should be fitted in the form of a power function equation.

[0092] ;

[0093] In the formula, Z(R) is the predicted value of the tunnel wall vibration level Z corresponding to the change of curve radius, and R is the curve radius. , , It is a constant.

[0094] The fitting results are as follows Figure 6 As shown, although the calculated values ​​and the power function fitting curve do not completely overlap, they are evenly distributed on both sides of the fitting curve, with a maximum residual of 0.5 dB, indicating a good fit. Therefore, the parameters are determined. =76.04, =5.92, =-0.0014.

[0095] 2. Analyze the influence of train speed V on tunnel wall vibration.

[0096] To further analyze the influence of train speed V on the tunnel wall Z-vibration level, the aforementioned method was used to modify the track conditions and train speed in the vehicle-track coupled dynamic analysis model. The tunnel wall Z-vibration level corresponding to different train speeds in straight sections was calculated, and the frequency distribution histogram and normal distribution curve of the tunnel wall Z-vibration level in the evaluation section were plotted. The mean value of the tunnel wall Z-vibration level corresponding to different train speeds in the evaluation section was obtained, as shown in Table 2.

[0097] Table 2 Predicted values ​​of tunnel wall Z-vibration magnitude under different train speeds

[0098] Nonlinear fitting was performed on the predicted Z-level vibration values ​​of the tunnel wall under different train speeds in Table 2. Based on the distribution pattern of the calculated values, a linear function was determined to fit the tunnel wall Z-level data. After eliminating the constant term, the increment of the tunnel wall Z-level vibration caused by the change in train speed was obtained as follows:

[0099] ;

[0100] In the formula, Z(V) is the predicted value of the tunnel wall vibration level Z corresponding to the change in train speed; For constants, linear operating conditions =0.113; V is the train speed. This is the reference speed.

[0101] Using the same calculation approach, simulations were performed to obtain the changes in the Z-vibration level of the tunnel wall caused by different curve radii and train speeds. After linear fitting, the coefficients under different curve radii were obtained. The values ​​of are shown in Table 3, and it can be seen that the coefficient has a certain functional relationship with the curve radius.

[0102] Table 3. Conditions under different curve radii Value

[0103] Based on the variation pattern in Table 3, the Z-vibration level coefficient of the tunnel wall caused by the change in train speed was determined. Fit the equation using a power function. The expression for the power function fitting is:

[0104] ;

[0105] In the formula, , , The parameters are constants; after fitting the data in Table 3, the parameters are determined. =0.110, =0.087, =-0.0014.

[0106] 3. Analyze the influence of track gradient i on tunnel wall vibration.

[0107] Based on the above application example, using the same analytical calculation method, the functional relationship between the track gradient and the Z-level vibration of the tunnel wall when the train speed is 80 km / h can be obtained, expressed as:

[0108] ;

[0109] In the formula, Z(i) is the predicted value of the tunnel wall vibration level Z corresponding to the change in track gradient; i is the track gradient. The base slope.

[0110] By calculating other operating speed conditions, the results show that there is no significant difference in the slope of the change in Z-vibration level of the tunnel wall caused by different line gradients.

[0111] Furthermore, when the plane curve overlaps with the track gradient, in addition to considering the effect of a single factor, the incremental Z-vibration level of the tunnel wall should be considered according to Table 4 for the superposition effect.

[0112] Table 4. Increment of Z-level vibration of tunnel wall after superposition of plane curve and slope.

[0113] 4. The influence of other single line parameters on tunnel wall vibration

[0114] Based on the above method, the influence of other single line parameter conditions (such as the length of the straight section in the plane and the radius of the vertical curve) on the Z-vibration level of the tunnel wall can be further obtained, and the corresponding prediction formula can be derived. Furthermore, the superimposed increment after the combination of multiple factors is obtained and incorporated into the calculation. parameter.

[0115] 5. Consider the impact of superimposed vibration reduction effect on tunnel wall vibration.

[0116] When considering the superimposed vibration-damping track structure, the track conditions have a coupled influence on the vibration reduction effect of the vibration-damping track structure. The influence of the curve radius on the vibration reduction effect of the vibration-damping track structure is illustrated by example.

[0117] The operating conditions selected were: train speed 80 km / h, integral track bed with vibration damping pads, and superelevation taken according to the actual design; the obtained vibration reduction effect varies with the curve radius as follows: Figure 7 As shown.

[0118] The functional relationship between the overall vibration reduction effect of the vibration damping pad and the curve radius is expressed as follows:

[0119] ;

[0120] In the formula, R represents the vibration reduction effect of the vibration-damping track bed; R is the curve radius. It can be used as a correction factor after deducting the vibration reduction effect and incorporated into the calculation. parameter.

[0121] 5. Superposition and correction of the functional relationship between different line parameters and the predicted value of tunnel wall Z-vibration level

[0122] The expression for the predicted Z-level vibration of the tunnel wall, obtained after superposition and correction, is as follows:

[0123] ;

[0124] In the formula:

[0125] Z(R) is a functional relationship between the curve radius R and the predicted value of the Z-level vibration of the tunnel wall;

[0126] Z(V) is a functional relationship between the train speed V and the predicted value of the tunnel wall vibration level Z;

[0127] Z(i) is a functional relationship between the track gradient i and the predicted value of the tunnel wall vibration level Z;

[0128] Z(λ) is a functional relationship between the length λ of the plane clamping line and the predicted value of the Z vibration level of the tunnel wall;

[0129] Z(R SH ( ) represents the radius of the vertical curve. Functional relationship with the predicted Z-level vibration of the tunnel wall;

[0130] Z(T) is a functional relationship between train type T and the predicted value of tunnel wall vibration level Z, which can be obtained according to the prediction formula recommended in the "Technical Guidelines for Environmental Impact Assessment of Urban Rail Transit" (HJ453-2018).

[0131] The correction amount can include: 1) the superimposed increment after the combination of multiple factors. The functional relationship can be determined based on a large amount of measured data, and the parameter range can also be characterized by the functional relationship. It can be obtained using the aforementioned calculation model and approach. Calculation shows that when the curve radius and slope overlap, its value can reach a maximum of 1dB; 2) the vibration reduction effect of deducting the vibration reduction track bed, which includes, but is not limited to, the corresponding functional relationship between it and the curve radius, as well as the influence relationship of parameters such as slope and speed. All of these can be obtained based on the above theories and methods.

[0132] Corresponding to the tunnel wall vibration prediction method considering the alignment shape constraints disclosed above, this invention also discloses a tunnel wall vibration prediction system considering the alignment shape constraints, which specifically includes:

[0133] The line parameter determination module is used to determine the line parameters that affect the vibration level of the tunnel wall in the evaluation section based on the horizontal and vertical characteristics of the urban rail transit line.

[0134] The wheel-rail force calculation module is used to obtain the wheel-rail interaction force under different values ​​of a pre-constructed vehicle-track coupled dynamic analysis model that considers the track shape constraints through simulation calculation.

[0135] The vibration acceleration calculation module is used to input the obtained wheel-rail interaction force as a load into the pre-built integrated vibration analysis model of the train-track-tunnel system, and obtain the tunnel wall vibration acceleration under different values ​​of the current single line parameters through simulation calculation.

[0136] The Z-level calculation module is used to calculate the Z-level of the tunnel wall under different values ​​of the current single line parameters based on the obtained tunnel wall vibration acceleration, and to obtain the predicted value of the Z-level of the tunnel wall under different values ​​of the current single line parameters by combining frequency distribution and normal distribution fitting analysis.

[0137] The fitting module is used to predict the tunnel wall Z-level vibration based on the current single line parameters under different values, and to obtain the functional relationship between the current single line parameters and the predicted tunnel wall Z-level vibration based on the fitting.

[0138] The superposition calculation module is used to obtain the functional relationship between different line parameters and the predicted value of tunnel wall Z-vibration level, and to superimpose and correct the data to obtain the final expression of the predicted value of tunnel wall Z-vibration level considering the line shape constraints.

[0139] Furthermore, the superposition calculation module is specifically used to calculate:

[0140] ;

[0141] In the formula, This is a fitted function expression for the predicted Z-level vibration of the tunnel wall as a function of the line parameter m. To account for the correction amount caused by multiple factors, including the vibration reduction effect of the vibration reduction track bed and the superimposed increment caused by the combination of multiple line parameters, Z is the expression for the predicted value of the tunnel wall Z vibration level obtained by superposition and correction calculation.

[0142] It should be noted that for a detailed description of the tunnel wall vibration prediction system considering the alignment constraints provided in the embodiments of the present invention, please refer to the relevant description of the tunnel wall vibration prediction method considering the alignment constraints provided in the embodiments of this application, which will not be repeated here.

[0143] In addition, embodiments of the present invention also provide an electronic device, the device comprising: a processor and a memory; the memory for storing one or more program instructions; the processor for executing one or more program instructions to perform the steps of a tunnel wall vibration prediction method considering route shape constraints as described in any of the preceding claims.

[0144] It should be noted that for a detailed description of the electronic device provided in the embodiments of the present invention, please refer to the relevant description of the tunnel wall vibration prediction method considering the line shape constraints provided in the embodiments of this application, which will not be repeated here.

[0145] In addition, embodiments of the present invention also provide a computer-readable storage medium storing a computer program, which, when executed by a processor, implements the steps of a tunnel wall vibration prediction method considering route shape constraints as described in any of the preceding claims.

[0146] It should be noted that for a detailed description of the computer-readable storage medium provided in the embodiments of the present invention, please refer to the relevant description of the tunnel wall vibration prediction method considering the route shape constraints provided in the embodiments of this application, which will not be repeated here.

[0147] Those skilled in the art will understand that all or part of the functions of the various methods in the above embodiments can be implemented by hardware or by computer programs. When all or part of the functions in the above embodiments are implemented by computer programs, the program can be stored in a computer-readable storage medium, which may include: read-only memory, random access memory, disk, optical disk, hard disk, etc., and the program is executed by a computer to achieve the above functions. For example, the program can be stored in the memory of a device, and when the program in the memory is executed by the processor, all or part of the above functions can be achieved. In addition, when all or part of the functions in the above embodiments are implemented by computer programs, the program can also be stored in a server, another computer, disk, optical disk, flash drive, or external hard drive, etc., and can be downloaded or copied to the memory of a local device, or the system of the local device can be updated. When the program in the memory is executed by the processor, all or part of the functions in the above embodiments can be achieved.

[0148] The above examples illustrate the present invention only to aid in understanding it and are not intended to limit the scope of the invention. Those skilled in the art can make various simple deductions, modifications, or substitutions based on the principles of this invention.

Claims

1. A method for predicting tunnel wall vibration considering route shape constraints, characterized in that, The method includes: Based on the horizontal and vertical profile characteristics of urban rail transit lines, the line parameters affecting the vibration level of tunnel walls in the evaluation section are determined. Based on a pre-constructed vehicle-track coupled dynamic analysis model that considers the track shape constraints, the wheel-rail interaction force of a pre-selected single track parameter under different values ​​is obtained through simulation calculation. The obtained wheel-rail interaction force is used as a load input into a pre-constructed integrated vibration analysis model of the train-track-tunnel system. The vibration acceleration of the tunnel wall under different values ​​of the current single line parameters is obtained through simulation calculation. Based on the obtained tunnel wall vibration acceleration, the tunnel wall Z-level vibration is calculated under different values ​​of the current single line parameters. Combined with frequency distribution and normal distribution fitting analysis, the predicted value of the tunnel wall Z-level vibration is obtained under different values ​​of the current single line parameters. Based on the predicted values ​​of tunnel wall Z-magnitude under different values ​​of the current single line parameters, the functional relationship between the current single line parameters and the predicted values ​​of tunnel wall Z-magnitude is obtained by fitting. The functional relationships between different line parameters and the predicted Z-level vibration of the tunnel wall are obtained, and then superimposed and corrected to obtain the final expression for the predicted Z-level vibration of the tunnel wall considering the line shape constraints.

2. The method for predicting tunnel wall vibration considering route shape constraints as described in claim 1, characterized in that, Based on the horizontal and vertical profile characteristics of urban rail transit lines, the line parameters affecting the tunnel wall vibration level in the evaluation section are identified, specifically including: The horizontal alignment elements of the railway line include straight lines, circular curves, and transition curves, while the vertical alignment elements include gradient and vertical curves. Circular curves are characterized by length, radius, and superelevation, with superelevation using a semi-superelevation method. Transition curves are cubic parabolic transition curves with straight superelevation and a downward slope. The railway parameters include characteristic parameter information of the horizontal and vertical alignment elements and train information.

3. The method for predicting tunnel wall vibration considering route shape constraints as described in claim 1, characterized in that, Constructing a vehicle-line coupled dynamic analysis model that considers the alignment constraints, specifically including: The vehicle-track coupled dynamics analysis model considering the track geometry constraints includes a train model, a wheel-rail relationship model, and a track geometry model; the vehicle is simulated using multibody dynamics, with the car body and bogie connected by a secondary suspension, and the bogie and wheelset connected by a primary suspension.

4. The method for predicting tunnel wall vibration considering route shape constraints as described in claim 1, characterized in that, Based on a pre-constructed vehicle-track coupled dynamics analysis model considering track shape constraints, simulation calculations are performed to obtain the wheel-rail interaction forces under different values ​​of pre-selected single track parameters, specifically including: In the simulation calculation, the train is set to travel at a constant speed on the rails, and the track irregularity spectrum is set; the wheel-rail interaction force is characterized by the wheel-rail vertical force, and the wheel-rail vertical force is calculated using Hertzian nonlinear elastic contact theory.

5. The method for predicting tunnel wall vibration considering route shape constraints as described in claim 1, characterized in that, An integrated vibration analysis model for the train-track-tunnel system, considering the structural characteristics of different ballastless tracks, is constructed, specifically including: Based on the spatial vibration analysis theory and finite element analysis theory of train-track system, an integrated vibration analysis model of train-track-tunnel system is constructed, considering different train operating conditions, track geometry conditions and different track structure types. The integrated vibration analysis model of train-track-tunnel system includes rails, fasteners, track bed, tunnel and soil structure. Among them, the rails are simulated using beam elements, the fasteners are simulated using spring-damping elements, and the track bed, tunnel and soil are simulated using solid elements.

6. The method for predicting tunnel wall vibration considering route shape constraints as described in claim 1, characterized in that, Based on the obtained tunnel wall vibration acceleration, the Z-vibration level of the tunnel wall under different values ​​of the current single line parameters is calculated, specifically including: ； In the formula, VAL is the Z-level vibration of the tunnel wall; a is the calculated tunnel vibration acceleration value; This is the baseline acceleration value.

7. The method for predicting tunnel wall vibration considering route shape constraints as described in claim 1, characterized in that, By combining frequency distribution and normal distribution fitting analysis, the predicted values ​​of tunnel wall Z-vibration level for the current single line parameter under different values ​​are obtained, specifically including: Using the sample mean or cumulative probability value as the control benchmark, a representative value of the tunnel wall Z-vibration level is selected and used as the predicted value of the tunnel wall Z-vibration level.

8. The method for predicting tunnel wall vibration considering route shape constraints as described in claim 1, characterized in that, The functional relationships between different line parameters and the predicted Z-level vibration of the tunnel wall are obtained, and then superimposed and corrected to obtain the final expression for the predicted Z-level vibration of the tunnel wall considering the line shape constraints. Specifically, this includes: ； In the formula, This is a fitted function expression for the predicted Z-level vibration of the tunnel wall as a function of the line parameter m. To account for the correction amount caused by multiple factors, including the vibration reduction effect of the vibration reduction track bed and the superimposed increment caused by the combination of multiple line parameters, Z is the expression for the predicted value of the tunnel wall Z vibration level obtained after superposition and correction calculation.

9. A tunnel wall vibration prediction system considering route shape constraints, characterized in that, The system includes: The line parameter determination module is used to determine the line parameters that affect the vibration level of the tunnel wall in the evaluation section based on the horizontal and vertical characteristics of the urban rail transit line. The wheel-rail force calculation module is used to obtain the wheel-rail interaction force under different values ​​of a pre-constructed vehicle-track coupled dynamic analysis model that considers the track shape constraints through simulation calculation. The vibration acceleration calculation module is used to input the obtained wheel-rail interaction force as a load into the pre-built integrated vibration analysis model of the train-track-tunnel system, and obtain the tunnel wall vibration acceleration under different values ​​of the current single line parameters through simulation calculation. The Z-level calculation module is used to calculate the Z-level of the tunnel wall under different values ​​of the current single line parameters based on the obtained tunnel wall vibration acceleration, and to obtain the predicted value of the Z-level of the tunnel wall under different values ​​of the current single line parameters by combining frequency distribution and normal distribution fitting analysis. The fitting module is used to predict the tunnel wall Z-level vibration based on the current single line parameters under different values, and to obtain the functional relationship between the current single line parameters and the predicted tunnel wall Z-level vibration based on the fitting. The superposition calculation module is used to obtain the functional relationship between different line parameters and the predicted value of tunnel wall Z-vibration level, and to superimpose and correct the data to obtain the final expression of the predicted value of tunnel wall Z-vibration level considering the line shape constraints.

10. A tunnel wall vibration prediction system considering route shape constraints as described in claim 9, characterized in that, The superposition calculation module is specifically used for calculation: ； In the formula, This is a fitted function expression for the predicted Z-level vibration of the tunnel wall as a function of the line parameter m. To account for the correction amount caused by multiple factors, including the vibration reduction effect of the vibration reduction track bed and the superimposed increment caused by the combination of multiple line parameters, Z is the expression for the predicted value of the tunnel wall Z vibration level obtained after superposition and correction calculation.

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