A Simulation Method and System for Bridge Cable-Modulated Vibration Damping Bearings Based on Flac3D's Built-in Fish Language

Abstract

This invention discloses a method and system for simulating bridge cable-stayed vibration damping bearings based on the Fish language built into Flac3D. This method enables the simulation of bridge vibration damping bearings and the seismic analysis of bridges within Flac3D. The solid elements in Flac3D are further developed using the Fish language, and a simulation program for the bearing elements is written in Fish. By extracting the shear deformation magnitude of the bearing elements under seismic loading in real time, the stage of shear deformation is determined in real time, and the shear stiffness of the bearing elements is adjusted accordingly to ensure that the shear force-shear strain relationship meets the bilinear ideal elastoplastic mechanical characteristics of the bearing elements. This method enables the simulation of bridge cable-stayed vibration damping bearings in Flac3D, and the vibration damping effect of the bearings can be reflected in the seismic analysis of bridges under seismic loading, making the calculation results of bridges under seismic loading more consistent with actual conditions.

Description

Technical Field

[0001] This invention relates to the field of bridge seismic analysis and calculation technology, and in particular to a method and system for simulating bridge cable damping bearings based on the Flac3D built-in Fish language. Background Technology

[0002] Cable-stayed bearings are typically installed at the connection between bridge piers and the structure. These bearings release seismic energy through sliding motion, reducing the structure's seismic response, and the cables effectively limit the relative displacement between the piers and the bridge, preventing beam collapse. Under normal service loads, cable-stayed bearings function similarly to ordinary bearings, meeting the load and displacement requirements of the superstructure. When the bridge structure experiences a design earthquake, the shear pins of the bearings break, transforming the entire system into a seismic isolation system. Subsequently, the cables limit the displacement between the piers and the bridge within a controllable range. Therefore, cable-stayed bearings significantly improve the overall seismic performance of the bridge structure.

[0003] In the numerical analysis of bridge seismic resistance, it is necessary not only to establish a numerical model of the main bridge structure, but also to model the bearing structure and simulate the mechanical properties of the bearing elements to demonstrate the seismic protection function of the bearing structure for the bridge structure. The mechanical model of the cable-stayed bearing consists of two independent elements: the bearing and the cable. The mechanical properties of each element need to be simulated separately, and then they are connected in parallel to form the cable-stayed bearing element. The frictional effect of the cable-stayed bearing can be simulated using bilinear ideal elastoplastic spring elements.

[0004] Existing bridge numerical analysis software, such as Midas Civil, has readily available bilinear spring elements that can be used to simulate the mechanical behavior of cable-stayed bearings. However, when performing seismic analysis on bridges in Midas Civil, only the bridge structural model can be created; the subsurface topography cannot be modeled, thus failing to consider the impact of topographic stability on the bridge's seismic performance under seismic loading. This is especially true for bridges built on steep slopes, where the slope stability under seismic loading significantly affects the bridge's seismic performance. Therefore, for seismic analysis of bridge structures on steep slopes, it is necessary to simultaneously create both the bridge structural model and its subsurface slope model to analyze the combined stability of the bridge and slope under seismic loading.

[0005] Flac3D is a numerical simulation software based on the fast Lagrangian analysis method for continuous media. Due to its mature command-driven mode, it can easily modify and optimize custom models and is widely used in structural and slope stability analysis research. However, the existing constitutive models in Flac3D cannot reflect the bilinear ideal elastoplastic mechanical model of supports. To simulate bridge damping supports and perform seismic simulation analysis of bridges in Flac3D, the mechanical behavior simulation of support elements requires secondary development. Fish is a built-in programming language in Flac3D, and many functions that cannot be achieved by program commands can be implemented through Fish programming. Flac3D sets many variable values ​​internally during calculations; some of these data are based on blocks, some on mesh points, and some on elements. Programming with Fish allows for the retrieval of this information at any time, enabling secondary development and enhancing data processing capabilities, as well as the setting and modification of internal variables. Summary of the Invention

[0006] In view of this, the purpose of this invention is to provide a method for simulating bridge cable damping bearings based on the Fish language built into Flac3D. This method utilizes the Fish language built into Flac3D to perform secondary development on the bridge damping bearing unit, thereby realizing the simulation of the bridge damping bearing structure.

[0007] To achieve the above objectives, the present invention provides the following technical solution:

[0008] This invention provides a method for simulating bridge cable damping supports based on the Flac3D built-in Fish language, comprising the following steps:

[0009] S1: Establish a numerical simulation model;

[0010] S2: Input model parameters;

[0011] S3: Set boundary conditions and perform initial equilibrium calculations;

[0012] S4: Extract the gravity W of the support bearing the superstructure, and calculate the mechanical model of the support unit according to the support model;

[0013] S5: Input seismic load;

[0014] S6: Construct a simulation program unit for the support element. The simulation program unit is used to extract the magnitude of the shear deformation of the support element under seismic loading, determine the stage of the shear deformation of the support in real time, and change the shear stiffness of the support element in real time so that the shear force-shear strain relationship can meet the mechanical characteristics of the bilinear ideal elastic-plasticity of the support element.

[0015] Furthermore, the shear stiffness is set in the following manner:

[0016] The shear deformation process of the support element is divided into different stages based on the horizontal displacement difference between nodes, and the corresponding shear stiffness is set according to the different stages until the seismic load ends.

[0017] Furthermore, the shear deformation of the support is divided into three stages as follows:

[0018] First stage: The shear pins of the support structure are subjected to shear force. In numerical simulation, the support elements in this stage satisfy the shear force-shear strain relationship with shear stiffness G = K1.

[0019] Second stage: As the shear force gradually increases, it reaches the maximum shear force F of the shear pin. max At this time, the shear pin of the support is sheared, there is no shear force transmission or interaction between the bridge and the pier, and the bridge and the pier freely undergo relative displacement; at this time, the support element in the numerical simulation satisfies the shear force-shear strain relationship when the shear stiffness G = 0.

[0020] Third stage: When the relative displacement between the bridge and the piers reaches the maximum allowable value u0, the cables of the support structure begin to function, bearing the shear force caused by the earthquake and limiting the relative displacement between the bridge and the piers; the shear force-shear strain relationship of the support element satisfies the shear stiffness G = K H The linear relationship over time.

[0021] Furthermore, the numerical simulation model is established in the following manner:

[0022] A three-dimensional solid model of the bridge structure was established, and solid elements were created between the transition piers and the bridge to simulate the supports. The solid model was then meshed and imported into Flac3D. According to the requirements of seismic calculation, the maximum mesh size of the model should be less than one-tenth of the earthquake wavelength. The mesh nodes between adjacent surfaces of various bridge components were connected to ensure the continuity of stress and strain between different bridge components.

[0023] Furthermore, the numerical simulation model is set up in the following manner:

[0024] Determine the input model parameters;

[0025] The bridge model and bearing elements are set as linear elastic constitutive models, and the corresponding physical and mechanical parameters are set according to the concrete grade of different bridge components.

[0026] Set boundary conditions and perform initial equilibrium calculations;

[0027] Apply fixed boundary conditions to the bottom of the model, set the gravitational acceleration g, and perform initial equilibrium calculation. In the initial equilibrium calculation process, Flac3D defaults to the calculation converging when the maximum unbalanced force of the model meets the preset conditions, thus completing the initial equilibrium calculation.

[0028] After equilibrium is reached, the compressive stress σ of the support element is extracted. n And based on the cross-sectional area A of the support unit z Calculate the weight W = σ borne by the support element from the superstructure. n ·A z .

[0029] Furthermore, in step S4, the gravity W borne by the support and the superstructure is extracted, and the mechanical model of the support unit is calculated according to the support model. The specific method is as follows:

[0030] The mechanical model consists of two independent units: the support and the cable. The mechanical properties of each unit are simulated separately, and then they are connected in parallel to form a cable damping support unit.

[0031] The frictional effect of the cable-stayed damping bearing is modeled using a bilinear ideal elastoplastic mechanical model. The mechanical model of the bearing element is calculated according to the following formula, and the specific values ​​of each parameter in the mechanical model are calculated based on the type of cable-stayed damping bearing:

[0032]

[0033] In the formula: K1—is the initial stiffness; K H —The horizontal stiffness of the cable component in the cable-stayed damping bearing; u0—The free travel of the cable-stayed damping bearing; x y —The yield displacement of the movable support, taken as the displacement at the critical sliding point of the support; F max — represents the critical sliding friction force of the movable support; F— represents the horizontal shear force acting on the support; u— represents the horizontal displacement of the support;

[0034] in:

[0035] (1) Critical sliding friction force F of movable support max :

[0036] F max =μ d W

[0037] (2) Initial stiffness K1:

[0038]

[0039] Where: μ d —Coefficient of sliding friction; W—Weight of the superstructure borne by the support; x y —The yield displacement of the movable support is taken as the displacement when the support is at its critical sliding point;

[0040] (3) Horizontal stiffness K of the cable member of the cable damping support H :

[0041] K H =4·cos 2 α·K S

[0042]

[0043] In the formula: K S —Axial stiffness of the cable; α —Angle between the cable and the horizontal plane when the cable is taut; E s —Elastic modulus of the cable; A—Calculated cross-sectional area of ​​the cable; L—Total length of a single cable.

[0044] Furthermore, the input of the seismic load in step S5 is performed in the following manner:

[0045] According to the relevant codes for seismic design of bridges, when using the dynamic time history method to analyze the seismic performance of bridges, it is necessary to consider the seismic loads in three directions: longitudinal, transverse, and vertical.

[0046] Therefore, to perform seismic analysis of bridges in Flac3D, it is necessary to convert the seismic wave acceleration time histories in the longitudinal, transverse, and vertical directions into corresponding stress time histories, and simultaneously apply three-dimensional seismic loads at the bottom of the model to analyze the seismic performance of the bridge under the three-dimensional seismic loads.

[0047] Integrating the acceleration time history of the seismic wave yields the velocity time history v(t), which is then used to calculate the corresponding stress time history σ(t) according to equation (6).

[0048] σ n (t)=-2(ρC p )v n (t)

[0049] σ s (t)=-2(ρC s )v s (t)

[0050] In the formula: σ n (t) — represents the longitudinal stress time history of the seismic wave; σ s (t) — the transverse stress time history of the seismic wave; ρ — the density of the rock medium; Cp — the longitudinal propagation velocity of the seismic wave in the medium; Cs — the transverse propagation velocity of the seismic wave in the medium; v n (t) — the longitudinal velocity time history obtained by integrating the longitudinal acceleration time history of the seismic wave; v s(t) — The lateral velocity time history obtained by integrating the lateral acceleration time history of the seismic wave; t — The time when the seismic load acts:

[0051] Among them, Cp and Cs are calculated according to the following formula:

[0052]

[0053] In the formula: E — The elastic modulus of the seismic wave propagation medium; ρ — The density of the seismic wave propagation medium; v — The Poisson's ratio.

[0054] Furthermore, the simulation program unit in step S6 is implemented using the built-in Fish language in Flac3D, and specifically proceeds according to the following steps:

[0055] S61: Traverse the unit grid nodes, and according to the numbers of the support unit grid nodes, locate the position for extracting the grid node displacement information to the nodes of the support unit;

[0056] S62: Respectively extract the displacements d1 and d2 of the node in the horizontal direction;

[0057] S63: Calculate the horizontal displacement difference between the nodes, and take the absolute value of the displacement difference, that is, Δd = |d1 - d2|;

[0058] S64: Judge the magnitude of the horizontal displacement difference Δd, and according to the mechanical model formula (1) of the support unit, obtain the judgment result in the following manner:

[0059] ① If Δd < x y , then set the shear stiffness of the support unit to G = K1;

[0060] ② If x y < Δd < u0, then set the shear stiffness of the support unit to G = 0;

[0061] ③ If u0 < Δd, then set the shear stiffness of the support unit to G = K H ;

[0062] S65: Run the numerical simulation model for a preset number of cycles;

[0063] S66: Judge whether the calculation of the seismic load ends in the following manner:

[0064] ① If the calculation of the seismic load ends, the program calculation terminates and saves the calculation result;

[0065] ② If the calculation of the seismic load has not ended, the program returns to step S62 above for cycling.

[0066] The present invention provides a bridge cable damping bearing simulation system based on Flac3D's built-in Fish language, which includes a memory, a processor, and a computer program stored in the memory and capable of running on the processor. When the processor executes the program, it implements the above-mentioned method.

[0067] The beneficial effects of this invention are as follows:

[0068] This invention provides a method for simulating bridge cable damping bearings based on the Fish language built into Flac3D. It realizes the simulation of bridge damping bearings and the simulation analysis of bridge seismic resistance in Flac3D. The solid elements in Flac3D are further developed using the Fish language, and a simulation program for the bearing elements is written using the Fish language. By extracting the magnitude of shear deformation of the bearing elements under seismic loading in real time, the stage of shear deformation of the bearing is determined in real time, and the shear stiffness of the bearing elements is changed in real time to ensure that the shear force-shear strain relationship can meet the mechanical characteristics of the bilinear ideal elastic-plasticity of the bearing elements.

[0069] This method enables the simulation of bridge cable damping bearings in Flac3D. In the seismic analysis of bridges in Flac3D, the damping effect of the bearings can be reflected, making the calculation results of bridges under seismic loading more consistent with the actual situation.

[0070] Other advantages, objectives, and features of the invention will be set forth in part in the description which follows, and in part will be apparent to those skilled in the art from the following examination, or may be learned from practice of the invention. The objectives and other advantages of the invention can be realized and obtained through the following description. Attached Figure Description

[0071] To make the objectives, technical solutions, and beneficial effects of this invention clearer, the following drawings are provided for illustration.

[0072] Figure 1 This is a mechanical model of a cable-stayed damping pot bearing.

[0073] Figure 2 A flowchart for simulating bridge vibration damping bearings.

[0074] Figure 3 This is a numerical simulation model of the bridge structure.

[0075] Figure 4 This is a schematic diagram of the support unit.

[0076] Figure 5 This represents the relationship between shear force and horizontal displacement of the support element. Detailed Implementation

[0077] The present invention will be further described below with reference to the accompanying drawings and specific embodiments, so that those skilled in the art can better understand and implement the present invention. However, the embodiments described are not intended to limit the present invention.

[0078] Example 1

[0079] The basic principle of the bridge cable damping bearing simulation method provided in this embodiment is as follows:

[0080] The shear deformation of cable-stayed vibration damping bearings under shear force exhibits bilinear ideal elastoplastic mechanical properties. In numerical analysis, the bearing element simulation consists of two independent elements: the bearing and the cable. However, the existing linear elastoplastic constitutive model in Flac3D cannot realize the shear deformation process of cable-stayed vibration damping bearings. Flac3D's built-in Fish language can extract the model's built-in variable information during calculation and incorporate this information into various logical operations. According to elasticity theory, the shear deformation relationship of linear elastic elements in Flac3D satisfies Hooke's Law γ = τ / G, meaning there is a linear relationship between shear stress τ and shear strain γ, with the stress path determined by the shear stiffness G. Based on this, this method uses the Fish language to extract the shear strain magnitude of the bearing element in real time and performs logical operations based on the shear strain magnitude to change the shear stiffness of the element in real time, ensuring that the shear force-shear strain relationship satisfies the bilinear ideal elastoplastic mechanical model of the bearing element, thus enabling the simulation of bridge cable-stayed vibration damping bearings in Flac3D.

[0081] like Figure 1 As shown in the figure, the bridge cable damping support simulation method based on the Flac3D built-in Fish language provided in this embodiment includes the following steps:

[0082] S1: Establish a numerical simulation model

[0083] A three-dimensional solid model of the bridge structure was created, and solid elements were established between the transition piers and the bridge to simulate the supports. After meshing the solid model, it was imported into Flac3D. According to the requirements of seismic calculation, the maximum mesh size of the model should be less than one-tenth of the earthquake wavelength. In addition, during modeling, the mesh nodes between adjacent surfaces of various bridge components should be connected to ensure the continuity of stress and strain between different components of the bridge.

[0084] S2: Input model parameters

[0085] All bridge models adopted linear elastic constitutive models, and corresponding physical and mechanical parameters were set according to the concrete grade of different bridge components. Before the seismic load was input into the model, the support structure only bore the gravity of the superstructure and did not experience shear force; therefore, the support elements also adopted linear elastic constitutive models before the seismic load was input into the model.

[0086] S3: Set boundary conditions and perform initial equilibrium calculations

[0087] A fixed boundary condition is applied to the bottom of the model, and the gravitational acceleration g is set for initial equilibrium calculation. During the initial equilibrium calculation, Flac3D defaults to a condition where the maximum unbalanced force of the model is less than 1 × 10⁻⁶. -5 The calculation converges upon reaching equilibrium, completing the initial equilibrium calculation. After equilibrium is reached, the compressive stress σ of the support element is extracted. n And based on the cross-sectional area A of the support unit z Calculate the weight W = σ borne by the support element from the superstructure. n ·A z The preset condition is that the maximum unbalanced force is less than 1×10. -5 ;

[0088] S4: Extract the gravity W of the support bearing the superstructure, and calculate the mechanical model of the support unit according to the support model;

[0089] The mechanical model of the cable-stayed damping bearing consists of two independent elements: the bearing and the cable. The mechanical properties of each element are simulated separately, and then they are connected in parallel to form the cable-stayed damping bearing element. The frictional effect of the cable-stayed damping bearing follows a bilinear ideal elastoplastic mechanical model, satisfying... Figure 1 The mechanical response relationship is shown, and the mechanical model of the support element is shown in Equation (1). The specific values ​​of each parameter in the mechanical model can be calculated according to the model of the cable damping support.

[0090]

[0091] In the formula:

[0092] K1 — Initial stiffness, kN / m;

[0093] K H —This represents the horizontal stiffness of the cable component in the cable-stayed damping bearing, in kN / m;

[0094] u0—Free travel of the cable-stayed damping bearing, m;

[0095] x y —The yield displacement of the movable support, taken as the displacement at the critical sliding point of the support, in meters; F max — is the critical sliding friction force of the movable support, in kN.

[0096] F—Horizontal shear force on the support, kN; u—Horizontal displacement of the support, m; where:

[0097] (1) Critical sliding friction force F of movable support max :

[0098] F max =μ d W (2)

[0099] (2) Initial stiffness K1:

[0100]

[0101] In the formula:

[0102] μ d —Coefficient of sliding friction;

[0103] W—The weight of the superstructure borne by the support, kN;

[0104] (3) Horizontal stiffness K of the cable member of the cable damping support H :

[0105] K H =4·cos 2 α·K S (4)

[0106]

[0107] In the formula:

[0108] K S —Axial stiffness of the cable, kN / m;

[0109] α—The angle between the cable and the horizontal plane when the cable is taut, in degrees;

[0110] E s —Elastic modulus of the cable, MPa;

[0111] A—Calculated cross-sectional area of ​​the cable, m2;

[0112] L—Total length of a single cable, in meters;

[0113] S5: Input seismic load

[0114] According to relevant codes for seismic design of bridges, the seismic performance analysis of bridges using the dynamic time history method requires simultaneous consideration of seismic loads in three directions: longitudinal, transverse, and vertical. Therefore, in Flac3D, the seismic wave acceleration time histories in the three directions need to be converted into corresponding stress time histories, and three-dimensional seismic loads need to be applied simultaneously at the bottom of the model to analyze the seismic performance of the bridge under these three-dimensional seismic loads. The velocity time histories of the seismic waves are obtained by integrating the acceleration time histories, and the corresponding stress time histories can be obtained by calculating the velocity time histories according to equation (6).

[0115] σ n (t)=-2(ρC p )v n (t)

[0116] σs (t)=-2(ρC s )v s (t) (6)

[0117] In the formula:

[0118] σ n (t) — represents the longitudinal stress time history of the seismic wave, in kPa;

[0119] σ s (t) — represents the transverse stress time history of the seismic wave, in kPa;

[0120] ρ—the density of the rock medium, kg / m3;

[0121] Cp—is the longitudinal propagation velocity of seismic waves in the medium, m / s, which can be calculated according to formula (7);

[0122] Cs—is the transverse propagation velocity of seismic waves in the medium, m / s, which can be calculated according to formula (7);

[0123] v n (t) — the longitudinal velocity time history obtained by integrating the longitudinal acceleration time history of the seismic wave, m / s;

[0124] v s (t) — the transverse velocity time history obtained by integrating the transverse acceleration time history of the seismic wave, m / s;

[0125] t — the time (s) during which the seismic load is applied.

[0126]

[0127] In the formula:

[0128] E—is the elastic modulus of the medium through which seismic waves propagate, in GB / T.

[0129] ρ—the density of the medium through which seismic waves propagate, kg / m³;

[0130] v—is Poisson's ratio, 1.

[0131] S6: Define the Fish function to perform secondary development on the support element and construct the simulation program unit of the support element. The simulation program unit is used to extract the magnitude of the shear deformation of the support element under seismic action, determine the stage of the shear deformation of the support in real time, and change the shear stiffness of the support element in real time so that the shear force-shear strain relationship can meet the mechanical characteristics of the bilinear ideal elastic-plasticity of the support element.

[0132] The shear deformation process of the support element is divided into different stages based on the horizontal displacement difference between nodes, and the corresponding shear stiffness is set according to the different stages until the seismic load ends.

[0133] Set up two mesh nodes on the support element, namely node 1 and node 2, extract the horizontal displacements d1 and d2 of node 1 and node 2 of the support element, and calculate the difference in horizontal displacement Δd between node 1 and node 2.

[0134] Under seismic loads, the support structure between the bridge and the piers will bear shear force, and the relationship between the horizontal shear force and the horizontal displacement of the support structure satisfies... Figure 1 Based on the relationship between the two elements, the shear deformation process of the support element can be divided into three stages.

[0135] The first stage mainly involves the shear pins of the support structure bearing shear force. During numerical simulation, the support elements in this stage satisfy the shear force-shear strain relationship with shear stiffness G = K1.

[0136] Second stage: As the shear force gradually increases, it reaches the maximum shear force F of the shear pin. max At this time, the shear pin of the support is sheared, and there is no shear force transmission or interaction between the bridge and the pier. The bridge and the pier can freely undergo relative displacement. At this time, the support element in the numerical simulation satisfies the shear force-shear strain relationship when the shear stiffness G = 0.

[0137] The third stage occurs when the relative displacement between the bridge and the piers reaches the maximum allowable value u0. At this point, the cables of the support structure begin to function, bearing the shear force caused by the earthquake and limiting the relative displacement between the bridge and the piers. The shear force-shear strain relationship of the support element at this stage satisfies the shear stiffness G = K. H The linear relationship over time.

[0138] Therefore, when simulating the mechanical behavior of the support structure, based on the linear elastic constitutive model, the shear force-shear strain relationship of the support element can be divided into three processes with different shear stiffness G values ​​according to the relative displacement between the bridge and the pier. This allows for the simulation of the bilinear ideal elastoplastic mechanical model of the support element and the restoration of the mechanical properties of the support element during numerical simulation.

[0139] like Figure 4 As shown, node 1 and node 2 are two mesh nodes on the support element. Node 1 is connected to the bridge, and node 2 is connected to the pier. When the support element is subjected to shear force, node 1 and node 2 will generate horizontal relative displacement (i.e., shear strain of the support element). The shear force-shear strain relationship is linear with respect to the shear stiffness G.

[0140] Therefore, by monitoring the relative displacement of node 1 and node 2 of the support element (i.e., the relative displacement between the bridge and the pier), the magnitude of the shear stiffness G of the support element can be changed, thereby simulating the bilinear mechanical behavior of the support element.

[0141] Based on this, the above process is implemented using the built-in Fish language in Flac3D. The specific process of defining the Fish function is as follows:

[0142] (1) Use the element mesh node traversal statement "loop foreach gp gp.list" in the Fish language, and according to the numbers id of the support element mesh nodes 1 and mesh node 2, locate the positions for extracting the mesh node displacement information to nodes 1 and 2 of the support element. The positions of nodes 1 and 2 are as Figure 4 shown;

[0143] (2) Use the statement "gp.disp.x(gp)" to extract the displacements d1 and d2 of nodes 1 and 2 in the horizontal direction respectively;

[0144] (3) Calculate the horizontal displacement difference between nodes 1 and 2, and take the absolute value of the displacement difference, that is, Δd = |d1 - d2|;

[0145] (4) Use the "if" statement to judge the magnitude of the horizontal displacement difference Δd, and according to the mechanical model formula (1) of the support element, the main output has the following several judgment results:

[0146] ① If Δd < x y , then use the "command" command to make the shear stiffness G of the support element equal to K1;

[0147] ② If x y < Δd < u0, then use the "command" command to make the shear stiffness G of the support element equal to 0;

[0148] ③ If u0 < Δd, then use the "command" command to make the shear stiffness G of the support element equal to K H .

[0149] (5) The numerical simulation model runs for 1000 steps;

[0150] (6) Judge whether the calculation of the seismic load is completed. There are mainly two judgment results:

[0151] ① If the calculation of the seismic load is completed, the program calculation terminates and the calculation results are saved;

[0152] ② If the calculation of the seismic load is not completed, the program returns to step (2) for cycling.

[0153] In step (5), when the numerical simulation model runs for 1000 time steps, the specific number of time steps can be adjusted according to the model operation speed and test accuracy requirements.

[0154] Example 2

[0155] As Figure 2 As shown, Figure 2 This is a flowchart of a bridge cable damping support simulation method based on the Flac3D built-in Fish language, which mainly includes the following steps:

[0156] Step 1: Establish a numerical simulation model

[0157] Based on the design drawings and dimensions of a certain bridge, this bridge is a continuous rigid frame bridge with two tracks and spans of 85m + 160m + 85m. A 3D solid model of the bridge structure was created using Rhino 6 software, mainly including four components: the bridge itself, piers, abutments, and pile foundations. According to seismic calculation requirements, the maximum mesh size of the model should be less than one-tenth of the earthquake wavelength. The solid model was meshed according to this requirement and then imported into Flac3D. Figure 3 As shown. The connection between the main pier and the bridge is fixed; therefore, mesh points on adjacent surfaces between the bridge and the main pier need to be treated as shared nodes when building the model. The transition pier is simulated as a support element by creating a solid element with the same cross-section as the pier but a height of 1m, as shown. Figure 4 As shown.

[0158] Step 2: Input model parameters

[0159] In the model, the bridge, piers, abutments, and pile foundations are mainly made of reinforced concrete of different grades, and a linear elastic constitutive model is used for simulation. Based on the concrete grade used in each component of the bridge design drawings, and according to the parameters of different concrete grades in the "Specifications for Design of Highway Reinforced Concrete and Prestressed Concrete Bridges and Culverts," the physical and mechanical parameters of each part of the bridge are set. Before the seismic load is input into the model, the support structure only bears the gravity of the superstructure and not shear force. Therefore, before the seismic load is input into the model, the support elements also use a linear elastic constitutive model for initial equilibrium calculation. The model material parameters are shown in Table 1.

[0160] Table 1 Physical and mechanical parameters of the bridge model

[0161]

[0162] Step 3: Set boundary conditions and perform initial equilibrium calculations

[0163] A fixed boundary condition is applied to the bottom of the model, and the gravitational acceleration g is set to 9.81 m / s². 2 The calculation is performed using the "solve" command. During the initial equilibrium calculation, when the maximum unbalanced force of the model is less than 1 × 10⁻⁶, the calculation is performed. -5 The calculation converges upon reaching equilibrium, completing the initial equilibrium calculation. After equilibrium is reached, the compressive stress σ of the support element is extracted. n And based on the cross-sectional area A of the support unit z Calculate the weight W = σ borne by the support element from the superstructure.n ·A z .

[0164] Step 4: Calculate the theoretical mechanical model of the support element based on the support type.

[0165] The bearing model used in this simulation is a bidirectional movable cable-stayed damping pot bearing (LSPZ6000SX), and the corresponding bearing parameters are shown in Table 2.

[0166] Table 2 LSPZ6000SX type support parameter table

[0167]

[0168] The mechanical model of the cable-stayed damping bearing consists of two independent elements: the bearing and the cable. The mechanical properties of each element are simulated separately, and then they are connected in parallel to form the cable-stayed damping bearing element. The frictional effect of the cable-stayed damping bearing follows a bilinear ideal elastoplastic mechanical model, satisfying... Figure 1 The mechanical response relationship is shown, and the mechanical model of the support element is shown in Equation (1). The specific values ​​of each parameter in the mechanical model can be calculated according to the model of the cable damping support. The specific calculation process is as follows:

[0169] (1) Critical sliding friction force F of movable support max :

[0170] F max =μ d W = 0.02 × 4127.5 = 82.55 (kN)

[0171] In the formula:

[0172] μ d —The coefficient of sliding friction is generally taken as 0.02;

[0173] W—The weight of the superstructure borne by the support, which is 4127.5kN according to the initial equilibrium calculation results;

[0174] x y —The yield displacement of the movable support is taken as the displacement when the support is critically sliding, and is generally taken as 0.003m.

[0175] (2) Initial stiffness K1:

[0176]

[0177] (3) The support height is taken from Table 2 of LSPZ6000SX cable-stayed damping pot bearing dimensions:

[0178]

[0179] L=(B+l)×2=(1.02+0.307)×2=2.654(m)

[0180] The cosine of the angle α between the cable and the horizontal plane when the cable is taut is:

[0181] Neglecting the frictional force at the contact surface between the cable and the support, the relationship between the axial force of the cable and the horizontal force of the support is as follows:

[0182]

[0183] Where l represents the length of the cable when tensioned, in meters; h represents the cable anchorage distance, in meters, taken from the support parameter table 2; B represents the length of the support plate, in meters, taken from the support parameter table 2; P represents the horizontal force of the support, in kN; T Z This indicates the axial ultimate bearing capacity of the cable, in kN;

[0184] Table 2 shows that the ultimate bearing capacity of the cable members in the cable-stayed damping pot bearing (LSPZ6000SX) is 2400kN. According to the "Design Specifications for Highway Reinforced Concrete and Prestressed Concrete Bridges and Culverts," the steel wire rope of the cable member is a steel strand, and its ultimate strength standard value f... ptk =1960MPa, elastic modulus taken as E s =1.10×10 5 MPa, then the axial stiffness K of the cable s Theoretical values ​​can be obtained as follows:

[0185]

[0186] Horizontal stiffness K of cable members in cable-stayed basin bearing H :

[0187] K H =4·cos 2 α·K S =4 × 0.814 2 ×31168=82607(kN / m)

[0188] Finally, substituting the above calculation results into equation (1), we obtain the theoretical mechanical model of the support element as follows:

[0189]

[0190] Where A represents the calculated cross-sectional area of ​​the cable, in meters. 2 E S This represents the elastic modulus of the cable, expressed in MPa.

[0191] Step 5: Input seismic load

[0192] According to relevant codes for seismic design of bridges, the seismic performance analysis of bridges using the dynamic time history method requires simultaneous consideration of seismic loads in three directions: longitudinal, transverse, and vertical. Therefore, in Flac3D, the seismic wave acceleration time histories in the three directions need to be converted into corresponding stress time histories, and three-dimensional seismic loads need to be applied simultaneously at the bottom of the model to analyze the seismic performance of the bridge under these three-dimensional seismic loads. The velocity time histories of the seismic waves are obtained by integrating the acceleration time histories, and the corresponding stress time histories can be obtained by calculating the velocity time histories according to equation (6).

[0193] Step 6: Define the Fish function for secondary development of the support unit.

[0194] Under seismic loads, the support structure between the bridge and the piers will bear shear force, and the relationship between the horizontal shear force and the horizontal displacement of the support structure satisfies... Figure 1 Based on the relationship between the two elements, the shear deformation process of the support element can be divided into three stages.

[0195] The first stage mainly involves the shear pins of the support structure bearing shear force. In the numerical simulation, the support elements in this stage satisfy the shear force-shear strain relationship with shear stiffness G = K1 = 27516 kN / m.

[0196] Second stage: As the shear force gradually increases, it reaches the maximum shear force F of the shear pin. max When the shear stiffness G = 82.55 kN, the shear pin of the support is broken, and there is no shear force transmission or interaction between the bridge and the pier. The bridge and the pier can freely undergo relative displacement. At this time, the support element in the numerical simulation satisfies the shear force-shear strain relationship when the shear stiffness G = 0.

[0197] The third stage occurs when the relative displacement between the bridge and the piers reaches the maximum allowable value u0 = 0.25m. At this point, the cables of the support structure begin to function, bearing the shear force caused by the earthquake and limiting the relative displacement between the bridge and the piers. At this time, the shear force-shear strain relationship of the support element satisfies the shear stiffness G = K. H Linear relationship when = 82607kN / m.

[0198] Therefore, when simulating the mechanical behavior of the support structure, based on the linear elastic constitutive model, the shear force-shear strain relationship of the support element can be divided into three processes with different shear stiffness G values ​​according to the relative displacement between the bridge and the pier. This allows for the simulation of the bilinear ideal elastoplastic mechanical model of the support element and the restoration of the mechanical properties of the support element during numerical simulation.

[0199] like Figure 4As shown, node 1 and node 2 are two mesh nodes on the support element. Node 1 is connected to the bridge, and node 2 is connected to the pier. When the support element is subjected to shear force, node 1 and node 2 will generate horizontal relative displacement, and the relationship between shear force and horizontal displacement is linear with respect to shear stiffness G.

[0200] Therefore, by monitoring the relative displacement of node 1 and node 2 of the support element, the magnitude of the shear stiffness G of the support element is changed, thereby simulating the bilinear mechanical behavior of the support element.

[0201] Based on this, the above process is implemented in Flac3D using the built-in Fish language. The specific flow of the Fish function is defined as follows:

[0202] (1) Using the element mesh node traversal statement "loop foreach gp gp.list" in Fish language, and based on the ID numbers of support element mesh node 1 and mesh node 2, the positions of the extracted mesh node displacement information are located on nodes 1 and 2 of the support element. The positions of nodes 1 and 2 are as follows: Figure 4 As shown;

[0203] (2) Using the statement “gp.disp.x(gp)”, extract the horizontal displacements d1 and d2 of node 1 and node 2 respectively;

[0204] (3) Calculate the horizontal displacement difference between node 1 and node 2, and take the absolute value of the displacement difference, i.e., Δd=|d1-d2|;

[0205] (4) Using the "if" statement, determine the magnitude of the horizontal displacement difference Δd, and based on the mechanical model (1) of the support element, the main outputs are as follows:

[0206] ①If Δd<0.003m, then use the “command” command to make the shear stiffness of the support element G=27516kN / m;

[0207] ②If 0.003m < Δd < 0.25m, then use the “command” command to make the shear stiffness G of the support element = 0;

[0208] ③ If 0.25m < Δd, then use the “command” command to make the shear stiffness of the support element G = 82607kN / m.

[0209] (5) The numerical simulation model was run for 1000 steps;

[0210] (6) There are two main ways to determine whether the seismic load calculation is complete:

[0211] ①If the earthquake load calculation is completed, the program will terminate and the calculation results will be saved;

[0212] ②If the earthquake load calculation is not completed, the program will return to step (2) and loop.

[0213] In step (5), the numerical simulation model is operated for 1000 time steps. The specific number of time steps can be adjusted according to the model operation speed and experimental accuracy requirements.

[0214] Based on the numerical simulation model of this example, the Fish program, which simulates the support elements, is used for seismic calculations. By monitoring the shear force and shear deformation of the support elements, the relationship between the two is as follows: Figure 5 As shown. Simultaneously, the theoretical mechanical model of the support element in this example is calculated according to equation (8) and then imported. Figure 5 The results were compared with those obtained from numerical simulation. The comparison showed that the results calculated according to equation (8) and the mechanical response of the support unit obtained from numerical simulation were in good agreement, indicating that the simulation results of the support unit developed using Fish language were correct and could reflect the mechanical characteristics of the cable damping support.

[0215] This embodiment uses the Fish statement to change the shear stiffness of the support in real time according to the deformation of the support after shear force is applied, so that the support element can meet the bilinear ideal elastic-plastic mechanical properties. The simulation of bridge cable damping support is realized in Flac3D, so that the damping effect of the support can be reflected in the seismic analysis of bridges in Flac3D, and the calculation results of bridges under seismic action are more in line with the actual situation.

[0216] The above-described embodiments are merely preferred embodiments provided to fully illustrate the present invention, and the scope of protection of the present invention is not limited thereto. Equivalent substitutions or modifications made by those skilled in the art based on the present invention are all within the scope of protection of the present invention. The scope of protection of the present invention is defined by the claims.

Claims

1. A method for simulating bridge cable damping bearings based on the built-in Fish language in Flac3D, characterized by: The following steps are involved: S1: Establish a numerical simulation model; S2: Input model parameters; S3: Set boundary conditions and perform initial equilibrium calculations; S4: Extract the gravity W of the support bearing the superstructure, and calculate the mechanical model of the support unit according to the support model; S5: Input seismic load; S6: Construct a simulation program unit for the support unit. The simulation program unit is used to extract the magnitude of the shear deformation of the support unit under seismic action, determine the stage of the shear deformation of the support in real time, and change the shear stiffness of the support unit in real time so that the shear force-shear strain relationship can meet the mechanical characteristics of the bilinear ideal elastic-plasticity of the support unit. The shear deformation of the support unit is divided into three stages as follows: First stage: The shear pins of the support structure are subjected to shear force. In numerical simulation, the support elements in this stage satisfy the shear force-shear strain relationship with shear stiffness G = K1. Second stage: As the shear force gradually increases, it reaches the maximum shear force F of the shear pin. max At this time, the shear pin of the support is sheared, there is no shear force transmission or interaction between the bridge and the pier, and the bridge and the pier freely undergo relative displacement; at this time, the support element in the numerical simulation satisfies the shear force-shear strain relationship when the shear stiffness G = 0. Third stage: When the relative displacement between the bridge and the piers reaches the maximum allowable value u0, the cables of the support structure begin to function, bearing the shear force caused by the earthquake and limiting the relative displacement between the bridge and the piers; the shear force-shear strain relationship of the support element satisfies the shear stiffness G = K H Linear relationship over time; The mechanical model of the support unit is calculated according to the following formula, and the specific values ​​of each parameter in the mechanical model are calculated based on the model of the cable damping support: In the formula: K1—is the initial stiffness; K H —The horizontal stiffness of the cable component in the cable-stayed damping bearing; u0—The free travel of the cable-stayed damping bearing; x y —The yield displacement of the movable support, taken as the displacement at the critical sliding point of the support; F max — represents the critical sliding friction force of the movable support; F— represents the horizontal shear force on the support; u— represents the horizontal displacement of the support.

2. The bridge cable damping support simulation method based on Flac3D's built-in Fish language as described in claim 1, characterized in that: The shear stiffness is set as follows: The shear deformation process of the support element is divided into different stages based on the horizontal displacement difference between nodes, and the corresponding shear stiffness is set according to the different stages until the seismic load ends.

3. The bridge cable damping support simulation method based on Flac3D's built-in Fish language as described in claim 1, characterized in that: The numerical simulation model is established in the following manner: A three-dimensional solid model of the bridge structure was established, and solid elements were created between the transition piers and the bridge to simulate the supports. The solid model was then meshed and imported into Flac3D. According to the requirements of seismic calculation, the maximum mesh size of the model should be less than one-tenth of the earthquake wavelength. The mesh nodes between adjacent surfaces of various bridge components were connected to ensure the continuity of stress and strain between different bridge components.

4. The method for simulating bridge cable damping supports based on the Flac3D built-in Fish language as described in claim 1, characterized in that: The numerical simulation model is set up as follows: Determine the input model parameters; The bridge model and bearing elements are set as linear elastic constitutive models, and the corresponding physical and mechanical parameters are set according to the concrete grade of different bridge components. Set boundary conditions and perform initial equilibrium calculations; Apply fixed boundary conditions to the bottom of the model, set the gravitational acceleration g, and perform initial equilibrium calculation. In the initial equilibrium calculation process, Flac3D defaults to the calculation converging when the maximum unbalanced force of the model meets the preset conditions, thus completing the initial equilibrium calculation. After equilibrium is reached, the compressive stress σ of the support element is extracted. n And based on the cross-sectional area A of the support unit z Calculate the weight W = σ borne by the support element from the superstructure. n ·A z .

5. The bridge cable damping support simulation method based on Flac3D's built-in Fish language as described in claim 1, characterized in that: In step S4, the gravity W borne by the support and the superstructure is extracted, and the mechanical model of the support unit is calculated according to the support model. The specific method is as follows: The mechanical model consists of two independent units: the support and the cable. The mechanical properties of each unit are simulated separately, and then they are connected in parallel to form a cable damping support unit. The parameters in the mechanical model of the support element satisfy the following relationship: (1) Critical sliding friction force F of movable support max : F max =μ d W (2) Initial stiffness K1: Where: μ d —Coefficient of sliding friction; W—Weight of the superstructure borne by the support; x y —The yield displacement of the movable support is taken as the displacement when the support is at its critical sliding point; (3) Horizontal stiffness K of the cable member of the cable damping support H : K H =4·cos 2 a·K S Where: K S —Axial stiffness of the cable; α —Angle between the cable and the horizontal plane when the cable is taut; E s —Elastic modulus of the cable; A—Calculated cross-sectional area of ​​the cable; L—Total length of a single cable.

6. The method for simulating bridge cable damping supports based on the Flac3D built-in Fish language as described in claim 1, characterized in that: The seismic load input in step S5 is performed in the following manner: According to the relevant codes for seismic design of bridges, when using the dynamic time history method to analyze the seismic performance of bridges, it is necessary to consider the seismic loads in three directions: longitudinal, transverse, and vertical. Therefore, to perform seismic analysis of bridges in Flac3D, it is necessary to convert the seismic wave acceleration time histories in the longitudinal, transverse, and vertical directions into corresponding stress time histories, and simultaneously apply three-dimensional seismic loads at the bottom of the model to analyze the seismic performance of the bridge under the three-dimensional seismic loads. Integrating the acceleration time history of the seismic wave yields the velocity time history v(t), which can then be used to calculate the corresponding stress time history σ(t) using the following formula: σ n (t)=-2(ρC p )v n (t) σ s (t)=-2(ρC s )v s (t) In the formula: σ n (t) — represents the longitudinal stress time history of the seismic wave; σ s (t) — the transverse stress time history of the seismic wave; ρ — the density of the rock medium; Cp — the longitudinal propagation velocity of the seismic wave in the medium; Cs — the transverse propagation velocity of the seismic wave in the medium; v n (t) — the longitudinal velocity time history obtained by integrating the longitudinal acceleration time history of the seismic wave; v s (t) — the transverse velocity time history obtained by integrating the transverse acceleration time history of the seismic wave; t — the time of seismic load application: Cp and Cs are calculated according to the following formula: In the formula: E—is the elastic modulus of the seismic wave propagation medium; ρ—is the density of the seismic wave propagation medium; v—is Poisson's ratio.

7. The method for simulating bridge cable damping supports based on the Flac3D built-in Fish language as described in claim 1, characterized in that: The simulation program unit in step S6 is implemented using the built-in Fish language in Flac3D, specifically according to the following steps: S61: Traverse the unit mesh nodes and locate the position of the extracted mesh node displacement information to the node of the support unit according to the number of the support unit mesh node; S62: Extract the horizontal displacements d1 and d2 of the nodes respectively; S63: Calculate the horizontal displacement difference between nodes and take the absolute value of the displacement difference, i.e., Δd=|d1-d2|; S64: Determine the magnitude of the horizontal displacement difference Δd, and obtain the determination result according to the mechanical model (1) of the support element in the following manner: ①If Δd <x y Then the shear stiffness of the support element is set to G = K1; ② If x y <Δd < u0, then set the shear stiffness of the bearing unit to G = 0; ③If u0 < Δd, then set the shear stiffness of the support element as G = K. H ; S65: Preset number of loops for running the numerical simulation model; S66: Determine whether the seismic load calculation is complete using the following method: ①If the earthquake load calculation is completed, the program will terminate and the calculation results will be saved; ②If the earthquake load calculation is not completed, the program will return to step S62 above and loop.

8. A bridge cable damping bearing simulation system based on the Flac3D built-in Fish language, comprising a memory, a processor, and a computer program stored in the memory and executable on the processor, characterized in that, When the processor executes the program, it implements the method described in any one of claims 1 to 7.

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