A method for analyzing the coupled vibration response of near-fault earthquake-rockfall-vehicle-bridge

Abstract

The present invention belongs to the technical field of bridge safety, and specifically relates to a near-fault earthquake-rockfall-vehicle-bridge coupled vibration response analysis method, comprising: obtaining the near-fault earthquake load, rockfall-bridge interaction load and vehicle-bridge interaction load on the bridge; wherein the rockfall-bridge interaction load is Gaussian distributed; inputting the near-fault earthquake load, rockfall-bridge interaction load and vehicle-bridge interaction load on the bridge into a near-fault earthquake-rockfall-vehicle-bridge coupled vibration model to obtain the dynamic response of the bridge subsystem and the vehicle subsystem; calculating the dynamic response of the bridge subsystem and the vehicle subsystem to evaluate the safety of the bridge structure and the vehicles traveling on the bridge. The present invention significantly improves the safety assessment and protection design capabilities of the bridge structure and the vehicles on it in an earthquake environment by comprehensively analyzing the near-fault earthquake, rockfall and the coupled vibration response of the vehicle and the bridge.

Description

Technical Field

[0001] The invention belongs to the technical field of bridge safety, and in particular relates to a near-fault earthquake-rockfall-vehicle-bridge coupled vibration response analysis method. Background Art

[0002] The unique characteristics of plate tectonic movement in southwest my country have led to the dense development of deep and large active fault zones in the region. The continuous plate compression and collision have caused strong seismic activity and frequent large earthquakes on the eastern edge of the Qinghai-Tibet Plateau. When carrying out bridge construction on major railway trunk lines in southwest my country, the near-fault earthquake effects in the Hengduan Mountains, the huge ups and downs of high and steep mountains, and landslides and rockfall disasters are unavoidable problems. In addition, the near-fault area will produce more destructive velocity pulse-type seismic motions that are different from the far-field area. Compared with the far-field seismic motion, the velocity pulse-type seismic motion has the characteristics of high amplitude and long period, which can cause greater deformation of medium- and long-period structures and increase the risk of structural collapse.

[0003] If the bridge structure near the fault zone suffers large plastic damage under the action of a strong earthquake and cannot be repaired in time, it will cause greater cumulative damage under the action of secondary disasters such as landslides and rockfalls on high and steep mountains, and there is a risk of collapse. Accidents of bridge damage caused by disasters such as landslides and rockfalls are not uncommon, such as the piers of the Chequguan Bridge in Wenchuan being broken by boulders in 2009 and the collapse of the Yaoheba Bridge on the Ya'an-Xichang Expressway in 2020. The above many cases show that the movement ability of earthquake landslides is often stronger than that of non-earthquake landslides. Compared with gravity landslides, earthquake landslides have more complex movement characteristics. As a key lifeline project, mountain bridges may face the intrusion of multiple disasters such as earthquakes and landslides and rolling rocks during the construction and operation stages, especially in the Hengduan Mountain area in the southwest. This problem is more prominent. Studying the working state of bridge structures under the action of earthquake-rockfall chain disasters and proposing protective measures are of great theoretical value and engineering significance for post-earthquake emergency rescue and post-disaster recovery and reconstruction.

[0004] However, most previous studies have focused on studying near-fault earthquakes and rockfall impact separately. Few studies or engineering accident analyses have combined the two to conduct dynamic response analysis of bridge structures under near-fault earthquakes and rockfall collapse. Moreover, evaluating the performance of bridge structures and the safety of trains on bridges under two or more loads is still a very challenging topic. Some existing studies have focused on specific external loads, such as seismic response analysis, rockfall impact response analysis, and coupled vehicle-bridge analysis, but these studies have not yet considered the chain disaster effects of earthquakes, rockfalls, etc. When a bridge is subjected to multiple dynamic loads, the traditional method of calculating the dynamic response of the bridge by superimposing the dynamic response under a single load may also lead to improper estimates of the structural response. Summary of the invention

[0005] The purpose of the present invention is to provide a near-fault earthquake-rockfall-vehicle-bridge coupled vibration response analysis method to overcome the shortcomings of the prior art.

[0006] To achieve the above-mentioned purpose, the technical solution adopted by the present invention is: a near-fault earthquake-rockfall-vehicle-bridge coupled vibration response analysis method, comprising:

[0007] Obtain the near-fault earthquake load, rockfall-bridge interaction load and vehicle-bridge interaction load on the bridge; among which, the rockfall-bridge interaction load presents a Gaussian distribution;

[0008] The near-fault earthquake load, rockfall-bridge interaction load and vehicle-bridge interaction load on the bridge are input into the near-fault earthquake-rockfall-vehicle-bridge coupled vibration model to obtain the dynamic responses of the bridge subsystem and the vehicle subsystem.

[0009] The dynamic responses of the bridge subsystem and the vehicle subsystem are calculated to evaluate the safety of the bridge structure and the vehicles traveling on the bridge.

[0010] Optionally, the near-fault earthquake-rockfall-vehicle-bridge coupled vibration model is constructed in the following way:

[0011] Obtaining the training data of the near-fault earthquake load, the rockfall-bridge interaction load, and the vehicle-bridge interaction load on the bridge;

[0012] The near-fault earthquake-rockfall-vehicle-bridge coupled vibration equation is established based on the vehicle model and bridge model, the near-fault earthquake load training data, the rockfall-bridge interaction load training data, and the vehicle-bridge interaction load training data.

[0013] Solving the near-fault earthquake-rockfall-vehicle-bridge coupled vibration equation to obtain predicted values ​​of dynamic responses of the bridge subsystem and the vehicle subsystem;

[0014] The pre-constructed deep learning neural network is trained using the near-fault earthquake load training data, rockfall-bridge interaction load training data, vehicle-bridge interaction load training data, and the dynamic response prediction values ​​of the bridge subsystem and vehicle subsystem to obtain the near-fault earthquake-rockfall-vehicle-bridge coupled vibration model.

[0015] Optionally, the vehicle model is simulated by forming a mass-spring-damper system by a plurality of rigid bodies, dampers, springs, suspension systems and axles;

[0016] The bridge model is established by the finite element method, the main beam, bridge tower, pier and foundation are simulated by three-dimensional beam units, the inclined cable is simulated by spatial rod units, and the auxiliary structure and the second-phase dead load are simulated by applying mass units;

[0017] The near-fault earthquake loads on the bridge are simulated by the harmonic synthesis method based on the moving average method and the spectrum matching method, and the rockfall and road roughness excitations are simulated by the harmonic synthesis method.

[0018] Optionally, the vehicle-bridge interaction load includes lateral contact force and vertical contact force between the bridge deck and the tire, which can be divided into an excitation force caused by road surface roughness and an additional force caused by bridge deformation;

[0019] The rockfall-bridge interaction load is the rockfall-structure interaction force acting on the bridge substructure taking into account the earthquake effect, including the translational velocity and rotational velocity related to the rockfall velocity;

[0020] The near-fault earthquake load action on the bridge is the near-fault sequence earthquake force on the bridge.

[0021] Optionally, the near-fault earthquake-rockfall-vehicle-bridge coupled vibration equation is expressed as formula (1) and formula (2);

[0022]

[0023] in, and Respectively represent the mass, damping and stiffness matrices of the vehicle subsystem of the i-th vehicle; M b , C b and K b They represent the mass, damping and stiffness matrices of the bridge subsystem, respectively; the superscript i represents the i-th vehicle traveling on the bridge, and the subscripts b and v represent the bridge subsystem and the vehicle subsystem, respectively; and Respectively represent the displacement, velocity and acceleration vector of the i-th vehicle; d b , and denote the displacement, velocity and acceleration vectors of the bridge respectively; and represent the interaction force between the i-th vehicle and the bridge subsystem respectively; represents the gravity on the i-th vehicle; F br F is the rockfall impact force acting on the bridge considering the near-fault earthquake effect; be They represent the equivalent seismic forces acting on the bridge respectively.

[0024] Optionally, the F v i bIt is expressed as formula (3);

[0025]

[0026] in, represents the excitation force on the i-th vehicle caused by the road roughness at the vehicle position at time t; It represents the additional force on the i-th vehicle caused by the deformation of the bridge, which is related to the speed of the i-th vehicle, the speed and displacement of the bridge.

[0027] Optionally, the Expressed as formula (4); the F br Expressed as formula (5); the F be It is expressed as formula (6);

[0028]

[0029] in, represents the excitation force exerted on the bridge deck by the i-th vehicle due to the road roughness at the vehicle position at time t; It represents the additional force exerted on the bridge deck by the i-th vehicle due to the deformation of the bridge, which is related to the speed and displacement of the i-th vehicle and the speed and displacement of the bridge; It represents the rockfall impact force acting on the bridge considering the near-fault earthquake effect, which is related to the acceleration of the rockfall, the acceleration of the bridge structure and the earthquake acceleration; It represents the equivalent seismic force acting on the bridge, which is related to the acceleration, velocity and displacement of the earthquake motion.

[0030] Optionally, solving the near-fault earthquake-rockfall-vehicle-bridge coupled vibration equation to obtain dynamic response prediction values ​​of the bridge subsystem and the vehicle subsystem includes:

[0031] The vibration equations of the bridge subsystem and the vehicle subsystem are solved separately by means of separate iteration using the numerical integration method until the mechanical and geometric coordination relationship between the bridge subsystem and the vehicle subsystem is satisfied.

[0032] Optionally, the separation iterative process is:

[0033] Assume that the dynamic response of the bridge subsystem and the vehicle subsystem is zero at the initial moment, that is, the initial state is a static state; Assume that the calculation time step is Δt, and there are two layers of loop iterations, including an outer loop and an inner loop, where the outer loop is a time step loop and is marked as i, and the inner loop is an iteration loop and is marked as j;

[0034] Step 1: The i-th outer loop determines whether the vehicle has left the bridge deck. If all vehicles have left, the outer loop is exited; this includes:

[0035] According to the vehicle response at time t-Δt and Bridge Response b , and The initial vehicle-bridge interaction force at time t is obtained by combining the external load excitation at time t and Initial rockfall-bridge force F br and the seismic force F acting on the bridge be ;

[0036] Substitute the obtained initial force into the vibration equations of the bridge subsystem and the vehicle subsystem, and use the numerical integration method to obtain the initial response of the vehicle and the bridge at time t;

[0037] Update the vehicle-bridge interaction force and rockfall-bridge force according to the initial responses of the vehicle and bridge at time t;

[0038] Step 2: In the jth inner loop, when j=1, determine whether the difference between the initial vehicle-bridge interaction force, rockfall-bridge force and the updated vehicle-bridge interaction force, rockfall-bridge force related to the response of the bridge subsystem and the vehicle subsystem meets the convergence condition; when j≥2, determine whether the difference between the last updated vehicle-bridge interaction force, rockfall-bridge force and the updated vehicle-bridge interaction force, rockfall-bridge force meets the convergence condition. If not, enter the next inner loop, otherwise exit the inner loop and output the vehicle response at time t. and and bridge response d b , and Among them, include:

[0039] Substitute the updated vehicle-bridge interaction force and rockfall-bridge force into the vibration equations of the bridge subsystem and vehicle subsystem, and use the numerical integration method to obtain the updated responses of the vehicle and bridge at time t.

[0040] The updated responses of the vehicle and bridge are used to obtain the secondary updated vehicle-bridge interaction force and rockfall-bridge force.

[0041] Optionally, the calculating of the dynamic responses of the bridge subsystem and the vehicle subsystem to evaluate the safety of the bridge structure and the vehicles traveling on the bridge includes:

[0042] According to the bridge response d b and the stiffness matrix K of the bridge structure b Calculate the internal force K of the structure b d b , verify the deformation and strength of the bridge through bridge response and structural internal force, and judge the safety of the bridge structure;

[0043] According to the vehicle response and and bridge response d b , and Calculate the forces acting on the vehicle And according to the force on the vehicle Calculate the vehicle's rollover coefficient and determine the vehicle's driving safety.

[0044] The present invention has the following beneficial effects:

[0045] By comprehensively considering the dynamic effects of earthquakes, rockfalls and vehicles, and using models trained with deep learning neural networks, the dynamic responses of bridges and vehicles are simulated and calculated with high precision, and the safety of bridge structures and vehicles is comprehensively evaluated. It is not only applicable to complex situations in actual engineering, but also helps identify potential risks and provides a scientific basis for bridge design and reconstruction, thus playing an important role in preventing and reducing losses from disasters such as earthquakes, and improving the safety and reliability of bridge engineering. BRIEF DESCRIPTION OF THE DRAWINGS

[0046] Figure 1 A schematic flow chart of a method for analyzing near-fault earthquake-rockfall-vehicle-bridge coupled vibration response provided in an embodiment of the present application;

[0047] Figure 2 A schematic diagram of a construction process of a near-fault earthquake-rockfall-vehicle-bridge coupled vibration model provided in an embodiment of the present application;

[0048] Figure 3 A schematic diagram of an arch bridge provided in an embodiment of the present application under the combined effects of earthquakes, rockfalls, and other fields;

[0049] Figure 4 A schematic diagram of the structure of the BP neural network model provided in the embodiment of the present application;

[0050] Figure 5 A schematic diagram of the forward calculation of the BP neural network model provided in the embodiment of the present application;

[0051] Figure 6 A schematic diagram of the structure of a near-fault earthquake-rockfall-vehicle-bridge coupled vibration model provided in an embodiment of the present application;

[0052] Figure 7 A schematic diagram showing the comparison between the predicted value and the actual value of the BP neural network model provided in the embodiment of the present application. DETAILED DESCRIPTION

[0053] The following will be combined with the attached embodiment of the present invention Figure 1-7, the technical solutions in the embodiments of the present invention are clearly and completely described. Obviously, the described embodiments are only part of the embodiments of the present invention, not all of them. Unless otherwise specified, the technical means used in the embodiments are conventional means well known to those skilled in the art.

[0054] It should be noted that, in the absence of conflict, the embodiments of the present invention and the features of the embodiments may be combined with each other.

[0055] It should be noted that similar reference numerals and letters denote similar items in the following drawings, and therefore, once an item is defined in one drawing, further definition and explanation thereof is not required in subsequent drawings.

[0056] Reference Figure 1 , Figure 1 A flow chart of a method for analyzing a near-fault earthquake-rockfall-vehicle-bridge coupled vibration response provided in an embodiment of the present application includes the following steps:

[0057] S100, obtaining the near-fault earthquake load, rockfall-bridge interaction load and vehicle-bridge interaction load on the bridge; wherein the rockfall-bridge interaction load presents a Gaussian distribution;

[0058] It should be noted that bridges can be seen everywhere in life and can be classified according to application scenarios: cross-sea bridges, mountain arch bridges and overpasses, etc. Bridges in different application scenarios are in different environments, so they will be affected by different forces when an earthquake occurs. For example, when a cross-sea bridge encounters an earthquake, it will be affected by the forces of wind, waves, and vehicles, while an arch bridge in a mountain area will be affected by the forces of falling rocks and vehicles. The near-fault earthquake-falling rocks-vehicle-bridge coupled vibration response analysis method provided in an embodiment of the present invention is mainly used to analyze arch bridges in mountainous areas.

[0059] S200, inputting the near-fault earthquake load, rockfall-bridge interaction load and vehicle-bridge interaction load on the bridge into the near-fault earthquake-rockfall-vehicle-bridge coupled vibration model to obtain the dynamic responses of the bridge subsystem and the vehicle subsystem;

[0060] The near-fault earthquake-rockfall-vehicle-bridge coupled vibration model is a model obtained by training based on a deep learning neural network. The training of the model will be discussed in detail later.

[0061] S300, the dynamic responses of the bridge subsystem and the vehicle subsystem are calculated to evaluate the safety of the bridge structure and the vehicles traveling on the bridge.

[0062] In this embodiment, by comprehensively analyzing the impact of near-fault earthquakes, falling rocks and vehicle loads on arch bridges in mountainous areas, the accuracy of bridge safety assessment is significantly improved, thereby playing an important role in preventing and reducing losses from disasters such as earthquakes and improving the safety and reliability of bridge projects.

[0063] It is understandable that based on the dynamic responses of the bridge and the vehicle, we can evaluate the internal force and deformation of the bridge structure, as well as the rollover coefficient of the vehicle, and thus judge the safety of the bridge and the vehicle.

[0064] Alternatively, if Figure 2 As shown in the figure, the near-fault earthquake-rockfall-vehicle-bridge coupled vibration model is constructed in the following way:

[0065] S210, obtaining near-fault earthquake load training data, rockfall-bridge interaction load training data, and vehicle-bridge interaction load training data on the bridge;

[0066] In a specific implementation manner, seismic load data borne by the bridge structure when an earthquake occurs are collected, and these data are usually obtained through seismic monitoring, numerical simulation or physical experiments.

[0067] In a specific implementation manner, load data generated when falling rocks impact a bridge are collected, and these data can be obtained through methods such as on-site monitoring, experimental simulation, etc.

[0068] In a specific implementation manner, load data on the bridge structure generated when a vehicle passes through the bridge is collected, and this data can be obtained through vehicle-mounted equipment monitoring, bridge health monitoring system, and other means.

[0069] S220, establishing a near-fault earthquake-rockfall-vehicle-bridge coupled vibration equation based on the vehicle model and the bridge model, the near-fault earthquake load training data on the bridge, the rockfall-bridge interaction load training data, and the vehicle-bridge interaction load training data;

[0070] Based on the above introduction to bridges, the forces on arch bridges in mountainous areas are roughly the vehicle-bridge interaction load, rockfall-bridge interaction load, and the near-fault strong earthquake force on the bridge (see Figure 3 ), and these three forces are all formed by the interaction between vehicles, bridges and falling rocks. Therefore, it is necessary to use vehicle models and bridge models to simulate the vehicle-bridge interaction load, the rockfall-bridge interaction load and the near-fault earthquake load on the bridge, so as to construct the earthquake-rockfall-vehicle-bridge coupled vibration equation.

[0071] S230, solving the near-fault earthquake-rockfall-vehicle-bridge coupled vibration equation to obtain the predicted values ​​of the dynamic responses of the bridge subsystem and the vehicle subsystem;

[0072] Dynamic response refers to the corresponding movement of particles inside a structure under load. These movements can be described by physical quantities such as displacement, stress, velocity, acceleration, and frequency, which are collectively referred to as dynamic response.

[0073] Specifically, numerical analysis methods (such as finite element analysis, differential method, etc.) are used to solve the near-fault earthquake-rockfall-vehicle-bridge coupled vibration equations. The predicted values ​​of the dynamic responses of the bridge subsystem and the vehicle subsystem are obtained: the responses of the bridge and the vehicle under the coupled vibration, such as displacement, velocity, acceleration, etc., are obtained by solving the equations.

[0074] S240, using the near-fault earthquake load training data, rockfall-bridge interaction load training data, vehicle-bridge interaction load training data and the dynamic response prediction values ​​of the bridge subsystem and the vehicle subsystem, a pre-constructed deep learning neural network is trained to obtain a near-fault earthquake-rockfall-vehicle-bridge coupled vibration model.

[0075] Specifically, the collected load training data and dynamic response prediction values ​​are used as input and output to train the deep learning neural network. The pre-built deep learning neural network is trained to accurately predict the near-fault earthquake-rockfall-vehicle-bridge coupled vibration by adjusting the network parameters. The near-fault earthquake-rockfall-vehicle-bridge coupled vibration model is obtained. After the training is completed, the obtained deep learning neural network is the required coupled vibration model, which can be used for actual engineering prediction and analysis.

[0076] In a specific implementation, the deep learning neural network may be a BP neural network.

[0077] The following is a detailed introduction to the training process of the BP neural network and the near-fault earthquake-rockfall-vehicle-bridge coupled vibration model:

[0078] BP neural network was first proposed by Rumelhart and McCelland in 1986. It is a multi-layer feedforward network that reversely propagates errors to reduce the gradient along the propagation direction. It is currently the most widely used method for predicting impact damage. Its advantages include high fault tolerance and strong ability to map nonlinear relationships.

[0079] BP neural network is mainly composed of input layer, one or more hidden layers and output layer. There is no correlation between neurons in the same layer, and neurons in the previous layer only affect neurons in the next layer. The input layer is mainly used to place training data, while the hidden layer mainly processes the data of the input layer through functional relationships and passes it to the output layer, and finally the output layer obtains the fitting data. The calculation process of BP neural network is mainly divided into two parts: forward calculation and reverse calculation. Its basic structure is as follows Figure 4 shown.

[0080] The output of any neuron in the jth layer of the BP neural network is related to the output of all neurons in the ith layer (i=j-1). The weight between the nth (n≥1) neuron in the ith layer and the mth (m≥1) neuron in the jth layer is denoted by W. nm In order to make the fitting result better, a separate neuron 0 is introduced, and its output is fixed to -1. Its corresponding weight is recorded as θ, which is called bias. The output of the nth neuron in the i-th layer is recorded as Y in , let the output of the mth neuron in the jth layer be Y jm .Y jm It is obtained by multiplying and summing the outputs of all neurons in the i-th layer with their corresponding weights, and finally converting them through the SIGMOID excitation function. The purpose of introducing the excitation function is to consider nonlinear factors and improve the neural network's ability to fit the target. The calculation diagram is as follows Figure 5 shown.

[0081] In the forward calculation, the value output by the output layer is compared with the theoretical value. If the two are equal, the neural network fitting is terminated. If they are not equal, the reverse calculation process is entered. The so-called reverse calculation is actually an iterative process, in which the error between the output value and the theoretical value is used as the input value to propagate backward from the output layer to the input layer. During the propagation process, the error is distributed to all neurons in each layer, and the weight value and bias value corresponding to the output value of the neuron in each layer are modified so that the error gradient decreases along the propagation direction. Finally, iterate repeatedly until the modified weight value can make the output value reach the ideal accuracy. The reverse calculation weight correction formula is shown in the following formula:

[0082] W' nm =W nm -βD im Y (i-1)n

[0083] Where W' nm is the corrected weight value between the mth neuron in the i-th layer and the nth neuron in the i-1th layer, W nm is the weight value before correction between the mth neuron in the i-th layer and the nth neuron in the i-1-th layer, D im is the error gradient of the mth neuron in the i-th layer, Y (i-1)n is the output of the nth neuron in the i-1th layer, and β is the learning efficiency of the neural network ∈(0,1).

[0084] Training on the near-fault earthquake-rockfall-vehicle-bridge coupled vibration model:

[0085] like Figure 6As shown in the figure, the BP neural network used this time has five parts, namely the input layer, the output layer and three hidden layers with different excitation functions. The input data of the input layer are the three parameters of the near-fault earthquake load training data, the rockfall-bridge interaction load training data and the vehicle-bridge interaction load training data. The output data of the output layer are the predicted values ​​of the dynamic response of the bridge subsystem and the vehicle subsystem.

[0086] To evaluate the accuracy of the BP model, the coefficient of determination R was used. 2 , R 2 Expressions such as: Where x i is the FE simulation observation result, is the average value of FE simulation observation results, To predict the results, the R2 value ranges from 0 to 1, and the value close to 1 indicates excellent model performance. Based on the construction of the above BP neural network architecture, the near-fault earthquake-rockfall-vehicle-bridge coupled vibration model was derived.

[0087] To verify the validity of the model, a detailed test was conducted and the test results are shown as follows: Figure 7 As shown in the figure, the prediction accuracy of the model reaches 0.99936. The high-precision numerical value fully proves that the proposed model has excellent accuracy in predicting the response of bridge structures after rockfall impact. The prediction function fits the test samples well, the samples are evenly distributed on both sides of the prediction curve, and the difference between the predicted value and the actual value is very small. Therefore, the prediction function generated by the BP neural network structure used in this paper has a high accuracy.

[0088] In this embodiment, deep learning modeling is used to improve the prediction accuracy of the dynamic response of the bridge under complex loads, providing efficient and accurate support for bridge design and maintenance, and enhancing the bridge safety and disaster prevention capabilities.

[0089] Optionally, the vehicle model is simulated by a mass-spring-damper system composed of several rigid bodies, dampers, springs, suspension systems and axles; the bridge model is established by the finite element method, the main beam, bridge tower, piers and foundation are simulated by three-dimensional beam units, the cable-stayed cable is simulated by spatial rod units, and the auxiliary structure and secondary constant load are simulated by applying mass units; the near-fault earthquake load on the bridge is constructed based on the moving average method and spectrum matching method, and the rockfall and road roughness excitation are simulated by the harmonic synthesis method.

[0090] In this embodiment, the design cost is reduced by establishing a vehicle model and a bridge model and simulating the earthquake, rockfall and road roughness excitations in interaction through the harmonic synthesis method.

[0091] Optionally, the vehicle-bridge interaction load includes the lateral contact force and vertical contact force between the bridge deck and the tire, which can be divided into the excitation force caused by the road surface roughness and the additional force caused by the bridge deformation; the rockfall-bridge interaction load is the rockfall-structure interaction force acting on the bridge substructure taking into account the seismic effect, including the translational velocity and rotational velocity related to the rockfall velocity; the near-fault seismic action load on the bridge is the near-fault sequence seismic force received by the bridge.

[0092] In this embodiment, by further analyzing the vehicle-bridge interaction, rockfall-bridge interaction load and near-fault earthquake load on the bridge, the established earthquake-rockfall-vehicle-bridge coupled vibration equation can more realistically reflect the actual situation.

[0093] Optionally, the near-fault earthquake-rockfall-vehicle-bridge coupled vibration equation is expressed as formula (1) and formula (2);

[0094]

[0095] in, and Respectively represent the mass, damping and stiffness matrices of the vehicle subsystem of the i-th vehicle; M b , C b and K b They represent the mass, damping and stiffness matrices of the bridge subsystem, respectively; the superscript i represents the i-th vehicle traveling on the bridge, and the subscripts b and v represent the bridge subsystem and the vehicle subsystem, respectively; and Respectively represent the displacement, velocity and acceleration vector of the i-th vehicle; d b , and denote the displacement, velocity and acceleration vectors of the bridge respectively; and represent the interaction force between the i-th vehicle and the bridge subsystem respectively; represents the gravity on the i-th vehicle; F br F is the rockfall impact force acting on the bridge considering the near-fault earthquake effect; be They represent the equivalent seismic forces acting on the bridge respectively.

[0096] In this embodiment, by using formula (1), the mass, damping, stiffness matrix, acceleration vector, velocity and displacement of the vehicle subsystem of the i-th vehicle are calculated to obtain the gravity on the i-th vehicle and the interaction force between the vehicle and the bridge subsystem; by using formula (2), the mass, damping, stiffness matrix, displacement, velocity and acceleration vector of the bridge subsystem are calculated to obtain the interaction force between the i-th vehicle and the bridge subsystem, the rockfall impact force on the bridge considering the seismic effect and the equivalent seismic force acting on the bridge, thereby constructing the earthquake-rockfall-vehicle-bridge coupled vibration equation.

[0097] Optionally, It is expressed as formula (3);

[0098]

[0099] in, represents the excitation force on the i-th vehicle caused by the road roughness at the vehicle position at time t; It represents the additional force on the i-th vehicle caused by the deformation of the bridge, which is related to the speed of the i-th vehicle, the speed and displacement of the bridge.

[0100] In this embodiment, by using formula (3), the excitation force, speed, bridge speed and displacement caused by the road roughness at the vehicle position at time t are calculated to obtain the interaction force between the i-th vehicle and the bridge subsystem, thereby ensuring the accuracy of the earthquake-rockfall-vehicle-bridge coupled vibration equation construction process.

[0101] Optionally, Expressed as formula (4); F br Expressed as formula (5); F be It is expressed as formula (6);

[0102]

[0103] in, represents the excitation force exerted on the bridge deck by the i-th vehicle due to the road roughness at the vehicle position at time t; It represents the additional force exerted on the bridge deck by the i-th vehicle due to the deformation of the bridge, which is related to the speed and displacement of the i-th vehicle and the speed and displacement of the bridge; It represents the rockfall impact force acting on the bridge considering the near-fault earthquake effect, which is related to the acceleration of the rockfall, the acceleration of the bridge structure and the earthquake acceleration; It represents the equivalent seismic force acting on the bridge, which is related to the acceleration, velocity and displacement of the earthquake motion.

[0104] In this embodiment, by using formula (4), the excitation force, velocity and displacement of the i-th vehicle on the bridge deck caused by the road surface roughness at the vehicle position at time t and the velocity and displacement of the bridge are calculated to obtain the interaction force between the i-th vehicle and the bridge subsystem; by using formula (5), the acceleration of the falling rock, the acceleration of the bridge structure and the earthquake acceleration are calculated to obtain the rockfall impact force on the bridge considering the earthquake effect; by using formula (6), the acceleration, velocity and displacement of the seismic motion are calculated to obtain the equivalent seismic force acting on the bridge, so as to ensure the accuracy of the construction process of the earthquake-rockfall-vehicle-bridge coupled vibration equation.

[0105] Optionally, the above step S230 may further include the following steps:

[0106] S231, using the numerical integration method to solve the vibration equations of the bridge subsystem and the vehicle subsystem respectively through separate iterations, and separate iterations until the mechanical and geometric coordination relationship between the bridge subsystem and the vehicle subsystem is satisfied.

[0107] In this embodiment, the earthquake-rockfall-vehicle-bridge coupled vibration equation is solved by using a numerical integration method in a separate iterative manner, and the vibration equations of the bridge subsystem and the vehicle subsystem are obtained respectively, thereby solving the problem that the earthquake-rockfall-vehicle-bridge coupled vibration equation cannot be solved due to its complex expression.

[0108] Optionally, the above step S231 may further include the following steps:

[0109] The process of separation iteration is as follows: assuming that the dynamic response of the bridge subsystem and the vehicle subsystem at the initial moment is zero, that is, the initial state is a static state; assuming that the calculation time step is Δt, there are two layers of loop iteration, including an outer loop and an inner loop, where the outer loop is a time step loop and is marked as i, and the inner loop is an iteration loop and is marked as j;

[0110] Step 1: The i-th outer loop determines whether the vehicle has left the bridge deck. If all vehicles have left, the outer loop is exited; this includes:

[0111] According to the vehicle response at time t-Δt and Bridge Response b , and The initial vehicle-bridge interaction force at time t is obtained by combining the external load excitation at time t and Initial rockfall-bridge force F br and the seismic force F acting on the bridge be ;

[0112] Substitute the obtained initial force into the vibration equations of the bridge subsystem and the vehicle subsystem, and use the numerical integration method to obtain the initial response of the vehicle and the bridge at time t;

[0113] Update the vehicle-bridge interaction force and rockfall-bridge force according to the initial responses of the vehicle and bridge at time t;

[0114] Step 2: In the jth inner loop, when j=1, determine whether the difference between the initial vehicle-bridge interaction force, rockfall-bridge force and the updated vehicle-bridge interaction force, rockfall-bridge force related to the response of the bridge subsystem and the vehicle subsystem meets the convergence condition; when j≥2, determine whether the difference between the last updated vehicle-bridge interaction force, rockfall-bridge force and the updated vehicle-bridge interaction force, rockfall-bridge force meets the convergence condition. If not, enter the next inner loop, otherwise exit the inner loop and output the vehicle response at time t. and and bridge response d b , and Among them, include:

[0115] Substitute the updated vehicle-bridge interaction force and rockfall-bridge force into the vibration equations of the bridge subsystem and vehicle subsystem, and use the numerical integration method to obtain the updated responses of the vehicle and bridge at time t.

[0116] The updated responses of the vehicle and bridge are used to obtain the secondary updated vehicle-bridge interaction load and rockfall-bridge force.

[0117] Optionally, the above step S300 may further include the following steps:

[0118] S310, according to the bridge response d b and the stiffness matrix K of the bridge structure b Calculate the internal force K of the structure b d b , verify the deformation and strength of the bridge through bridge response and structural internal force, and judge the safety of the bridge structure;

[0119] S230, according to the vehicle response and and bridge response d b , and Calculate the forces acting on the vehicle And according to the force on the vehicle Calculate the vehicle's rollover coefficient and determine the vehicle's driving safety.

[0120] In this embodiment, the deformation and strength of the bridge are verified through the bridge response and structural internal force to determine the safety of the bridge structure, and the overturning coefficient of the vehicle is calculated by the force acting on the vehicle to determine the driving safety of the vehicle, thereby evaluating the safety of the bridge structure and vehicles traveling on the bridge under the action of sudden earthquakes during the operation stage in mountainous areas.

[0121] The above embodiments are only descriptions of the preferred modes of the present invention, and are not intended to limit the scope of the present invention. Without departing from the design spirit of the present invention, various deformations, modifications, and substitutions made to the technical solutions of the present invention by ordinary technicians in this field should all fall within the protection scope determined by the claims of the present invention.

Claims

1. A near-fault earthquake-rockfall-vehicle-bridge coupled vibration response analysis method, characterized in that: include: Obtain the near-fault earthquake load, rockfall-bridge interaction load and vehicle-bridge interaction load on the bridge; among which, the rockfall-bridge interaction load presents a Gaussian distribution; The near-fault earthquake load, rockfall-bridge interaction load and vehicle-bridge interaction load on the bridge are input into the near-fault earthquake-rockfall-vehicle-bridge coupled vibration model to obtain the dynamic responses of the bridge subsystem and the vehicle subsystem. Calculating the dynamic responses of the bridge subsystem and the vehicle subsystem to evaluate the safety of the bridge structure and vehicles traveling on the bridge; The near-fault earthquake-rockfall-vehicle-bridge coupled vibration model is constructed in the following way: Obtaining the training data of the near-fault earthquake load, the rockfall-bridge interaction load, and the vehicle-bridge interaction load on the bridge; The near-fault earthquake-rockfall-vehicle-bridge coupled vibration equation is established based on the vehicle model and bridge model, the near-fault earthquake load training data, the rockfall-bridge interaction load training data, and the vehicle-bridge interaction load training data. Solving the near-fault earthquake-rockfall-vehicle-bridge coupled vibration equation to obtain predicted values ​​of dynamic responses of the bridge subsystem and the vehicle subsystem; The pre-built deep learning neural network is trained using the near-fault earthquake load training data, rockfall-bridge interaction load training data, vehicle-bridge interaction load training data, and the dynamic response prediction values ​​of the bridge subsystem and the vehicle subsystem to obtain the near-fault earthquake-rockfall-vehicle-bridge coupled vibration model. The vehicle model is simulated by a mass-spring-damper system consisting of a plurality of rigid bodies, dampers, springs, suspension systems and axles; The bridge model is established by the finite element method, the main beam, bridge tower, pier and foundation are simulated by three-dimensional beam units, the inclined cable is simulated by spatial rod units, and the auxiliary structure and the second-phase dead load are simulated by applying mass units; The near-fault earthquake load on the bridge is simulated by the moving average method and the spectrum matching method, and the rockfall and road roughness excitations are simulated by the harmonic synthesis method; The vehicle-bridge interaction load includes the lateral contact force and the vertical contact force between the bridge deck and the tire, which can be divided into the excitation force caused by the road surface roughness and the additional force caused by the bridge deformation; The rockfall-bridge interaction load is the rockfall-structure interaction force acting on the bridge substructure taking into account the earthquake effect, including the translational velocity and rotational velocity related to the rockfall velocity; The near-fault earthquake load action on the bridge is the near-fault sequence earthquake force on the bridge; The near-fault earthquake-rockfall-vehicle-bridge coupled vibration equation is expressed as formula (1) and formula (2); in, and Respectively represent the mass, damping and stiffness matrices of the vehicle subsystem of the i-th vehicle; M b , C b and K b They represent the mass, damping and stiffness matrices of the bridge subsystem, respectively; the superscript i represents the i-th vehicle traveling on the bridge, and the subscripts b and v represent the bridge subsystem and the vehicle subsystem, respectively; and Respectively represent the displacement, velocity and acceleration vector of the vehicle subsystem of the i-th vehicle; d b , and denote the displacement, velocity and acceleration vectors of the bridge subsystem respectively; represents the force exerted by the bridge subsystem on the vehicle subsystem of the i-th vehicle; represents the force exerted by the vehicle subsystem of the i-th vehicle on the bridge subsystem; represents the gravity acting on the vehicle subsystem of the i-th vehicle; F br F is the rockfall-structure interaction force acting on the bridge substructure considering the earthquake effect; be Represents the near-fault sequence earthquake force on the bridge.

2. The near-fault earthquake-rockfall-vehicle-bridge coupled vibration response analysis method according to claim 1 is characterized in that: Said It is expressed as formula (3); in, represents the force exerted by the bridge subsystem on the vehicle subsystem of the i-th vehicle; represents the excitation force on the vehicle subsystem of the i-th vehicle caused by the road roughness at time t; It represents the additional force on the vehicle subsystem of the i-th vehicle caused by the deformation of the bridge, which is related to the speed of the vehicle subsystem of the i-th vehicle, the speed and displacement of the bridge.

3. The near-fault earthquake-rockfall-vehicle-bridge coupled vibration response analysis method according to claim 1, characterized in that: Said Expressed as formula (4); the F br Expressed as formula (5); the F be It is expressed as formula (6); in, represents the force exerted by the vehicle subsystem of the i-th vehicle on the bridge subsystem; represents the excitation force of the vehicle subsystem of the i-th vehicle acting on the bridge deck caused by the road surface roughness at time t; It represents the additional force of the vehicle subsystem of the i-th vehicle acting on the bridge deck caused by the deformation of the bridge, which is related to the speed and displacement of the vehicle subsystem of the i-th vehicle and the speed and displacement of the bridge; It represents the rockfall-structure interaction force acting on the bridge substructure considering the earthquake effect, which is related to the acceleration of the rockfall, the acceleration of the bridge subsystem and the earthquake acceleration; It indicates the near-fault sequence earthquake force on the bridge, which is related to the acceleration, velocity and displacement of the ground motion.

4. The near-fault earthquake-rockfall-vehicle-bridge coupled vibration response analysis method according to claim 1, characterized in that: The near-fault earthquake-rockfall-vehicle-bridge coupled vibration equation is solved to obtain the predicted values ​​of the dynamic responses of the bridge subsystem and the vehicle subsystem, including: The vibration equations of the bridge subsystem and the vehicle subsystem are solved separately by means of separate iteration using the numerical integration method until the mechanical and geometric coordination relationship between the bridge subsystem and the vehicle subsystem is satisfied.

5. The near-fault earthquake-rockfall-vehicle-bridge coupled vibration response analysis method according to claim 4, characterized in that: The process of separation iteration is: Assume that the dynamic response of the bridge subsystem and the vehicle subsystem is zero at the initial moment, that is, the initial state is a static state; Assume that the calculation time step is Δt, and there are two layers of loop iterations, including an outer loop and an inner loop, where the outer loop is a time step loop and is marked as i, and the inner loop is an iteration loop and is marked as j; Step 1: The i-th outer loop determines whether the vehicles have left the bridge deck. If all vehicles have left, the outer loop is exited, including: According to the vehicle response d at time t-Δt i v , and Bridge Response b , and The initial vehicle-bridge interaction force at time t is obtained by combining the external load excitation at time t and Initial rockfall-bridge force F br and the seismic force F acting on the bridge be ; Substitute the obtained initial force into the vibration equations of the bridge subsystem and the vehicle subsystem, and use the numerical integration method to obtain the initial response of the vehicle and the bridge at time t; Update the vehicle-bridge interaction force and rockfall-bridge force according to the initial responses of the vehicle and bridge at time t; Step 2: In the jth inner loop, when j=1, determine whether the difference between the initial vehicle-bridge interaction force, rockfall-bridge force and the updated vehicle-bridge interaction force, rockfall-bridge force related to the response of the bridge subsystem and the vehicle subsystem meets the convergence condition; when j≥2, determine whether the difference between the last updated vehicle-bridge interaction force, rockfall-bridge force and the updated vehicle-bridge interaction force, rockfall-bridge force meets the convergence condition. If not, enter the next inner loop, otherwise exit the inner loop and output the vehicle response at time t. and and bridge response d b , and include: Substitute the updated vehicle-bridge interaction force and rockfall-bridge force into the vibration equations of the bridge subsystem and vehicle subsystem, and use the numerical integration method to obtain the updated responses of the vehicle and bridge at time t. The updated responses of the vehicle and bridge are used to obtain the secondary updated vehicle-bridge interaction force and rockfall-bridge force.

6. The near-fault earthquake-rockfall-vehicle-bridge coupled vibration response analysis method according to claim 1, characterized in that: The calculation of the dynamic response of the bridge subsystem and the vehicle subsystem to evaluate the safety of the bridge structure and the vehicles traveling on the bridge includes: According to the bridge response d b and the stiffness matrix K of the bridge structure b Calculate the internal force K of the structure b d b , verify the deformation and strength of the bridge through bridge response and structural internal force, and judge the safety of the bridge structure; According to the vehicle response and and bridge response d b , and Calculate the forces acting on the vehicle And according to the force on the vehicle Calculate the vehicle's rollover coefficient and determine the vehicle's driving safety.

Images