Method for improving beam falling prevention function of in-service ductile bridge and beam falling prevention device

Abstract

The invention discloses an in-service ductile bridge anti-beam-falling function improving method and an in-service ductile bridge anti-beam-falling device, relates to the technical field of in-service highway bridge anti-seismic property reinforcement and transformation, and provides a method for solving the problems that in-service ductile bridge anti-beam-falling device type selection and parameter determination depend on experience, a system method is lacked, and multi-level performance controllability is difficult to achieve. Comprising the steps of anti-seismic performance evaluation, multi-level fortification standard setting, problem judgment, device model selection and parameter calculation optimization, and by establishing a parallel constraint system of a support and an anti-falling beam device and a series model of the support and a pier, the lateral stiffness requirement is deduced based on force-displacement coordination; the lateral stiffness of the anti-falling beam device is calculated according to E1, moderate earthquake and E2 levels in a grading mode, the maximum value is taken, parameters are iteratively optimized through nonlinear time-history analysis, it is ensured that the damage control target is met, and the method is used for improving the anti-seismic performance of a bridge and preventing support sliding, main beam deviation displacement and falling beam earthquake damage.

Description

Technical Field

[0001] This invention relates to the field of seismic performance reinforcement and retrofitting technology for in-service highway bridges. More specifically, this invention relates to a method and device for improving the anti-falling beam function of in-service ductile bridges. Background Technology

[0002] Once a bridge is damaged by an earthquake or suffers secondary disasters, it not only reduces the safety level of the structure itself, but also significantly affects the safety and smooth flow of regional network traffic, posing a great safety hazard to emergency rescue work, and directly or indirectly causing casualties and significant economic losses.

[0003] For highway bridges in service, especially those constructed in earlier periods, compared to the current "Code for Seismic Design of Highway Bridges" (JTG / T 2231-01-2020), there are issues such as lower seismic fortification standards and weaker seismic forces. Furthermore, as the operational time of bridges increases, the combined effects of climate, operational loads, and environmental factors inevitably lead to performance degradation and functional decline, resulting in reduced seismic resistance or functional failure. In summary, in-service highway bridges face the risk of increased seismic response and structural damage. Given the frequent occurrence of earthquakes, improving the seismic performance of in-service highway bridges is imperative to reduce the risk of seismic damage.

[0004] According to the current "Code for Seismic Design of Highway Bridges" (JTG / T 2231-01-2020), the seismic resistance systems of highway bridges in my country are mainly divided into Class I and Class II. Class I seismic resistance systems refer to bridges where, under seismic loading, the elastoplastic deformation and energy dissipation components are located at the piers. Class II seismic resistance systems refer to bridges where, under seismic loading, the seismic-resistant components are located at the connection members between the superstructure and substructure, including seismic isolation bearings and energy dissipation devices. Generally, Class I bridges adopt ductile seismic design, while Class II bridges adopt seismic isolation design. For bridges constructed in earlier periods, they are usually Class I or ductile system bridges, with ordinary plate rubber bearings and pot bearings as the main bearing types. Through seismic performance assessments of in-service highway bridges, calculation and analysis results show that beam bridges equipped with ordinary plate rubber bearings experience bearing slippage and main beam displacement under seismic loading, which can cause bridge displacement, collisions, beam collapse, and bearing slippage, among other seismic damage. Because the analysis considered the protective effect of bearing sliding on the substructure, the ductile design resulted in less plastic damage to the piers. Without considering bearing sliding with adjacent structures, there is a risk of severe plastic damage to the piers. As the main supporting structural member of a bridge, the pier must ensure that it does not collapse or suffer severe damage under strong earthquakes to meet post-earthquake emergency response and repair needs. Improvements in local seismic performance can affect the seismic response and seismic resistance of adjacent structures or the overall structure; therefore, improving the seismic performance of in-service highway beam bridges should be carried out as a systematic project.

[0005] The current "Code for Seismic Strengthening Design of Highway Bridges" (JTG TJ 22-2008) introduces design methods for pier and foundation strengthening, seismic isolation and damping measures, and anti-falling beam measures based on seismic performance assessment results. However, it does not provide methods for selecting anti-falling beam measures and determining their parameters. In practical applications, empirical judgment is still the primary method, lacking reliable scientific criteria. With the continuous improvement of anti-falling beam structures, different structural types have emerged, such as U-shaped steel plate anti-falling beam structures, steel spring anti-falling beam structures, and steel bar and spring combined anti-falling beam structures. When used for lateral restraint in bridges, anti-falling beam structures are usually anchored to the upper main beam, lower cap beam, or pier. Under seismic action, especially strong earthquakes, they limit the displacement of the main beam and supports. Simultaneously, the increased lateral stiffness of their local restraint system leads to an increase in the seismic force transmitted to the piers. Therefore, it is necessary to scientifically and rationally determine the structural type and technical parameters of lateral restraint anti-falling beams. Summary of the Invention

[0006] The purpose of this invention is to provide a method and device for improving the anti-falling beam function of in-service ductile bridges. In order to scientifically and rationally determine the structural type and technical parameters of the lateral limiting anti-falling beam, this invention focuses on the seismic performance improvement of the widely used in-service ductile beam bridges. In view of the problems of insufficient bearing anti-slip capacity and deformation capacity, and the need to ensure the strength and deformation capacity of the piers, this invention is based on the multi-level and multi-objective seismic design concept, combined with the linear and nonlinear mechanical models of the stop blocks, to form a design method for improving the lateral anti-falling beam function of in-service ductile highway beam bridges.

[0007] To address the aforementioned problems and achieve the objectives and other advantages of this invention, a method for enhancing the anti-falling beam function of in-service ductile bridges is provided, comprising the following steps: S1. Seismic performance assessment and parameter acquisition: After establishing the finite element model of the original bridge, nonlinear time history analysis was performed to obtain the horizontal force F at the top of the support, the eccentric displacement λ of the main beam, the horizontal displacement δ at the top of the support, the sliding displacement X of the support, and the horizontal displacement Δ at the top of the pier. c , Residual displacement of bridge piers △ p Bending moment M at key sections of the foundation p and shear force V p Earthquake demand; Calculate the anti-slip force F of the support s =μR, where μ is the friction coefficient of the support interface, taken as 0.1 to 0.2, and R is the vertical force acting on the support; Calculate the lateral stiffness K of the existing support B0 =G×A / Σt, where G is the shear modulus of the rubber bearing, A is the plane area of ​​the bearing, and Σt is the total thickness of the rubber layer of the bearing; The ultimate displacement Δ of the bridge pier was determined by moment-curvature analysis. u and the horizontal displacement of the pier top yield Δ y and the yield horizontal force F of the pier column y Through K y =F y / △ y Calculate the equivalent yield lateral stiffness of the pier column; S2. Multi-level defense standards and damage control target setting: Establish a multi-level seismic fortification standard that includes minor, moderate, and major earthquakes at the E1 level, and set quantified damage state control targets for supports, main beams, and piers at each level: E1 level minor earthquake control target: Foundation bending moment M p <M pu Shear force V p <V pu M pu V pu Based on the flexural and shear bearing capacities; F < F s The displacement at the top of the support δ < 0.5t f , t f The thickness of the rubber layer of the support; The main beam's offset displacement satisfies λ < 0.5t. f ; Horizontal displacement of pier top △ c <△ y ; The leveling control targets for moderate earthquakes fall into the following two categories: When the support does not slide: F < F s And the displacement δ at the top of the support satisfies 0.5t. f ≤δ<t f ; Support sliding condition: F≥F s The total shear deformation and sliding displacement of the support are less than λ. u For the longitudinal direction of the bridge, λ u For the collision clearance between the pier and the anti-fall beam device, λ is the cross-sectional area of ​​the bridge. u The collision gap between the main beam and the anti-fall beam device; The main beam's offset displacement meets the requirement of 0.5t. f ≤λ<λ u ; The following conditions must be met in both cases: Foundation bending moment M p <M pu Shear force V p <V pu ; The main beam's offset displacement meets the requirement of 0.5t.f ≤λ<λ u ; Horizontal displacement and residual displacement Δ at the top of the pier p Satisfies: 0.005L≤△ p =(△ c -△ e )≤0.01L, where L is the effective height of the pier column, △ e The elastic horizontal displacement at the top of the pier is estimated using a bilinear model or by taking Δ. e =F / K y ; E2 level major earthquake control target: Foundation bending moment M p <M pu Shear force V p <V pu ; F≥F s The displacement at the top of the support δ≥t f And the sliding displacement of the support X ≤ X u X u is the distance from the edge of the pad stone to the edge of the support, and is the allowable sliding displacement limit of the support; Main beam offset displacement λ≥λ u ; Horizontal displacement and residual displacement Δ at the top of the pier p Satisfy: 0.01L < △ p ≤0.015L; S3. Seismic performance issue assessment: If any deformation result does not meet the control target set in S2, it is determined that there is a seismic performance problem, reinforcement is required, and steps S4-S7 are performed. S4. Preliminary selection and parameter definition of anti-falling beam device: Choose a mechanical model that is either linear elastic or bilinear for the anti-fall beam device; Lateral stiffness K LB Determined in S6; Ultimate lateral force F of anti-fall beam structure LB =F LB-1 +K LB-2 ×(χ u –χ2);F LB Used to assess the maximum load-bearing capacity of the device and ensure that it does not fail unexpectedly under a major earthquake; Displacement χ1 when it begins to function: Take χ1 = δ p =F s / K B0 And it must satisfy χ1<λ u This is to ensure that the anti-fall beam device can work in a timely manner before or during the sliding of the support; Design limit displacement χ u Take χ u =λ u ; When selecting the bilinear model, the following parameters are further defined: First stage lateral stiffness K LB-1 Its value is determined in S6; First stage control displacement χ2: Take χ2=min(t) f , λ u ); Second stage lateral stiffness K LB-2 Take K LB-2 =n﹒ K LB-1 where n≥10; The first stage of lateral force control value F LB-1 =K LB-1 ×(χ2-χ1); S5. Calculation and Iterative Optimization of Mechanical Parameters for Anti-Beam Falling Device: A mechanical model is established to form a parallel constraint system consisting of the supports and the anti-falling beam device, and a series structure consisting of the constraint system and the bridge pier. The support and the anti-fall beam device form a parallel constraint system with a lateral stiffness of K. 并 =K LB +K B K LB To improve the lateral stiffness of the anti-fall beam device, K B The lateral stiffness of the support; The constraint system and the bridge piers form a series structure with a lateral stiffness of K. 串 =(K 并 ×K c ) / (K 并 +K c ), K c The lateral stiffness of the bridge pier column; Based on the series model and the force-displacement compatibility relationship, the derivation process is as follows: Under horizontal seismic loading, the total horizontal force F of the series structure is... total =K 串 ×(△ c +δ), this force is equal to the horizontal force F acting on the bridge pier. pier =K c ×△ c ,Right now: K 串 ×(△ c +δ)=K c ×△ c ; K 串 =(K 并 ×K c ) / (K 并 +Kc Substituting into the above formula, we obtain the formula for calculating the lateral stiffness requirement of a parallel constraint system: K 并 =(△ c / δ)×K c ; The lateral stiffness of the anti-fall beam device or the lateral stiffness of the support are analyzed and determined according to the graded calculation method: E1 level minor earthquake calculation: Let K be the required lateral stiffness of the support at this level. B1 The anti-falling beam device does not participate in the operation. LB =0, at this time K 并 =K B1 lateral stiffness K of bridge pier column c =K y , by K 并 =(△ c / δ)×K c The required lateral stiffness K of the support to meet this leveling performance target is derived. B1 =(△ c / δ)×K y The calculated K B1 The existing support stiffness K calculated in S1 B0 Comparison, if K B0 ≥K B1 If the existing support stiffness meets the E1 level requirement; if K B0 <K B1 If the existing support stiffness is insufficient, additional stiffness K needs to be provided by installing an anti-fall beam device. LB =K B1 -K B0 and this K LB The value is recorded as the E1 leveling design reference value K. LB-E1 ; Leveling calculations for moderate earthquakes fall into two categories: a. Set the required lateral stiffness of the support at this level to K. B2 If the support does not slide, the anti-falling beam device will not work. LB =0, at this time K 并 =K B2 Considering the stiffness reduction of the pier after it enters the elastoplastic state, a stiffness reduction coefficient α is introduced for the pier. At this point, the lateral stiffness K of the pier... c =αK y α is taken as 0.5 to 1; considering the increase in pier top displacement, a pier top horizontal displacement increase coefficient β is introduced, at which time the pier top horizontal displacement Δ c =β△ y β is taken as 1 to 3; considering the increase in support displacement, a support displacement increase coefficient γ is introduced, at which point the horizontal displacement at the top of the support is δ = γt. f γ is taken as 0.5 to 1; by K并 =(△ c / δ)×K c The required lateral stiffness K of the support to meet this leveling performance target is derived. B2 =(△ c / δ)×K c =β△ y / (γt f )×αK y =η×(△ y / t f )×K y Where η = αβ / γ; the calculated K B2 The existing support stiffness K calculated in S1 B0 Comparison, if K B0 ≥K B2 Then the existing support stiffness meets the requirements under the condition of no slippage during a moderate earthquake; if K B0 <K B2 If the existing support stiffness is insufficient, additional stiffness K needs to be provided by installing an anti-fall beam device. LB =K B2 -K B0 and this K LB The value recorded is the design reference value K for moderate earthquakes without slippage. LB-M1 ; b. If the support slides, the anti-fall beam device needs to be activated. In this case, K 并 =K LB +K B ; Lateral stiffness K of bridge piers c =αK y α is taken as 0.5 to 1; the horizontal displacement Δ at the top of the pier c =β△ y β is taken as 1 to 3; the horizontal displacement of the top of the support is δ = γt f γ takes values ​​of 1 to 2; determined by K 并 =(△ c / δ)×K c The lateral stiffness of the constrained system is derived to be K. 并 =β△ y / (γt f )×αK y =η×(△ y / t f )×K y Where η = αβ / γ; by K 并 =K LB +K B0 The lateral stiffness K of the anti-fall beam device required to meet this level performance target is derived. LB =η×(△ y / t f )×K y –KB0 and this K LB The value recorded is the design reference value K for sliding during moderate earthquakes. LB_M2 ; E2 level earthquake calculation: At this level, the anti-falling beam device is in operation, and at this time K 并 =K LB +K B ; Lateral stiffness of bridge pier K c =αK y α is taken as 0.2 to 0.5; the horizontal displacement Δ at the top of the pier c =β△ y β is taken as 3 to 4; the horizontal displacement of the top of the support is δ = γt f γ is 2; by K 并 =(△ c / δ)×K c The lateral stiffness of the constrained system is derived to be K. 并 =β△ y / (γt f )×αK y =η×(△ y / t f )×K y Where η = αβ / γ; by K 并 =K LB +K B0 The lateral stiffness K of the anti-fall beam device required to meet this level performance target is derived. LB =η×(△ y / t f )×K y -K B0 and this K LB The value is recorded as the E2 leveling design reference value K. LB_E2 ; Final design value of lateral stiffness K for anti-fall beam device LB Determination: A comprehensive comparison of the design reference values ​​K calculated under all levels. LB_E1 K LB_M1 K LB_M2 With K LB_E2 The maximum value among them is taken as the final design value K of the lateral stiffness of the anti-fall beam device. LB ; S6, Final design value K LB Model of anti-falling beam device: If a linear elastic model is chosen, its lateral stiffness K LB That is, take the final design value; If the bilinear model is chosen, its first-stage lateral stiffness K LB-1 Take this final design value and calculate the second-stage lateral stiffness K accordingly. LB-2 First stage lateral force control value FLB-1 ; F LB-1 K LB-1 K LB-2 , χ1, χ2, χ u Together they are given a bilinear mechanical model; S7. Add the defined anti-falling beam device model to the original bridge finite element model; Repeat S1 and S3; If any deformation result does not meet the control target set by S2, and / or the actual force F of the anti-falling beam device obtained through nonlinear time history analysis LB实 Exceeding its ultimate lateral resistance F LB Then adjust the parameters of the anti-fall beam device, including the lateral stiffness K of the linear elastic model. LB , Displacement χ1 when it begins to function, Design limit displacement χ u Or the first-stage lateral stiffness K of the bilinear model LB-1 The second-stage lateral stiffness K of the bilinear model LB-2 , Displacement χ1 when it begins to function, Design limit displacement χ u Then, the nonlinear time history analysis and result verification of this step are repeated until all quantitative and qualitative control objectives are met.

[0008] An anti-falling beam device is designed and installed based on a multi-level, multi-objective method for improving the anti-falling beam function of in-service ductile bridges. The anti-falling beam device is selected and set according to the mechanical performance parameters calculated and determined by the anti-falling beam function improvement method. The anti-falling beam device is installed on the cap beam or the top of the main beam on the outside of the main beam or on the side of the support. It is used to limit the sliding of the support and the displacement of the main beam under the level of minor and moderate earthquakes, and to prevent the beam from falling under the level of major earthquakes through its own damage.

[0009] Preferably, the anti-fall beam device is a U-shaped steel plate anti-fall beam structure, a steel spring anti-fall beam structure, or a combination of steel bars and springs anti-fall beam structure, installed in the transverse or longitudinal direction of the bridge to limit the lateral or longitudinal displacement of the main beam.

[0010] Preferably, in the aforementioned anti-falling beam device, when the anti-falling beam device adopts a bilinear mechanical model, its second-stage lateral stiffness K LB-2 Compared with the lateral stiffness K of the first stage LB-1 Satisfying the relation: K LB-2 =n﹒ K LB-1 Where n≥10; and the displacement χ1 when the anti-falling beam device starts to function satisfies the condition: χ1=δ p =F s / K B0 This ensures that the anti-fall beam device can intervene in a timely manner when or before the support slides.

[0011] Preferably, in the anti-falling beam device, an initial installation gap is provided between the anti-falling beam device and the restrained main beam or support. The width of the initial installation gap is not less than the displacement value χ1 when the anti-falling beam device begins to function, and not greater than the limit displacement value λ of the main beam. u .

[0012] Preferably, in the aforementioned anti-falling beam device, the anti-falling beam device is a self-resetting stop block, and its mechanical model is a bilinear mechanical model; after a major earthquake, the anti-falling beam device can rely on its own elastic restoring force to reset the main beam to near its initial position.

[0013] Preferably, in the aforementioned anti-falling beam device, the anti-falling beam device is a self-resetting stop block, and its first-stage lateral stiffness K LB-1 The value range is 1.0 × 10. 3 -1.0×10 4 kN / m.

[0014] Preferably, in the aforementioned anti-falling beam device, the connection between the anti-falling beam device and the main structure of the bridge adopts a non-rigid connection method, provided by hinged or flexible connecting elements.

[0015] The present invention has at least the following beneficial effects: This invention realizes the transformation from qualitative design relying on engineering experience to scientific design based on mechanical models and quantitative standards, and provides a systematic and operable design process for improving the anti-falling beam function.

[0016] This invention establishes a multi-level seismic fortification standard that includes E1-level minor earthquakes, moderate earthquakes, and E2-level major earthquakes, and sets quantitative damage state control targets for each component, thereby achieving refined performance control and target management under earthquakes of different intensities.

[0017] This invention establishes a parallel system of supports and anti-fall beam devices and a series structural mechanical model of the support and bridge piers, accurately deriving the lateral stiffness requirements of the constraint system, and providing a reliable theoretical basis and calculation method for determining the parameters of the anti-fall beam devices.

[0018] This invention employs a graded calculation method to determine the lateral stiffness requirements of the anti-fall beam device based on the sliding state of the bearings and the stiffness reduction of the piers under different seismic levels, and takes the maximum value as the final design value, thus ensuring the effectiveness of the device under all expected seismic levels.

[0019] This invention ensures that the final parameters meet all preset quantitative and qualitative control objectives by substituting the designed anti-falling beam device model into the original bridge finite element model for nonlinear time history analysis and iterative verification, thus guaranteeing the accuracy and reliability of the design results.

[0020] This invention effectively balances the deformation requirements of the bridge during normal use with the limiting function under seismic action by precisely controlling the displacement timing when the anti-falling beam device begins to function and setting a reasonable initial installation gap, thus achieving "no disturbance during normal times, effective during earthquakes".

[0021] This invention employs a beam-prevention device with a bilinear mechanical model and self-resetting function, enabling the main beam of the bridge to return to its original position after a major earthquake by relying on the elastic restoring force of the device itself. This significantly reduces residual displacement and improves the bridge's seismic toughness and post-earthquake functional recoverability.

[0022] This invention clarifies that the anti-falling beam device adopts a non-rigid connection method with the main structure of the bridge, so that it only transmits horizontal force and not bending moment, avoiding unnecessary constraints on the free deformation of the structure under normal use and minor earthquakes, thus protecting the main structure.

[0023] The systematic design method provided by this invention effectively avoids the problems of over-strengthening or under-strengthening that may occur in traditional empirical design. It can optimize material usage and improve economy while ensuring seismic safety.

[0024] Other advantages, objectives and features of the present invention will become apparent in part from the following description, and in part from those skilled in the art through study and practice of the invention. Attached Figure Description

[0025] Figure 1 This is a schematic diagram of the anti-falling beam device installation. Figure 1 (a) The anti-falling beam device is installed in the longitudinal direction of the bridge; Figure 1 (b) The anti-falling beam device is installed in the transverse direction of the bridge; Figure 2 It is a linear elastic mechanical model; Figure 3 It is a bilinear mechanical model; Figure 4 This is a schematic diagram of a partial series structure between the constraint system and the bridge pier; Figure 5 This is a graph showing the trend of shear performance changes in rubber bearings; Figure 6 This is a graph showing the trend of horizontal displacement and horizontal force of a reinforced concrete pier column. Figure 7 This is a diagram representing the plastic displacement of the pier column; Figure 8 This is the horizontal force-displacement curve of the support where sliding occurs; Figure 9 This is a graph showing the trend of lateral stiffness variation in the constrained system. Figure 10It is a curve showing the lateral stiffness requirement of a displacement-based constrained system; Figure 11 It is a curve showing the lateral stiffness requirement of the pier column based on displacement; Figure 12 This is a flowchart illustrating the functional improvement process of anti-fall-off devices for in-service ductile bridges. Figure 13 This is a diagram of the finite element numerical model for seismic response analysis of a bridge structure. Figure 14 This is a diagram showing the calculation results of the full curve of bending moment-curvature at the interface of the pier column under vertical and horizontal unidirectional loads. Figure 15 This is a graph showing the calculated results of the horizontal displacement-horizontal force curve of the support under the combined action of horizontal and vertical dead loads. Figure 16 It is a diagram showing the slippage between the top surface of the support and the superstructure, and between the bottom surface and the substructure, under the combined action of horizontal and vertical dead loads. Detailed Implementation

[0026] The present invention will now be described in further detail with reference to the accompanying drawings, so that those skilled in the art can implement it based on the description.

[0027] This invention provides a method for improving the anti-falling beam function of in-service ductile bridges, comprising the following steps: S1. Seismic performance assessment and parameter acquisition: After establishing the finite element model of the original bridge, nonlinear time history analysis was performed to obtain the horizontal force F at the top of the support, the eccentric displacement λ of the main beam, the horizontal displacement δ at the top of the support, the sliding displacement X of the support, and the horizontal displacement Δ at the top of the pier. c , Residual displacement of bridge piers △ p Bending moment M at key sections of the foundation p and shear force V p Earthquake demand; Calculate the anti-slip force F of the support s =μR, where μ is the friction coefficient of the support interface, taken as 0.1 to 0.2, and R is the vertical force acting on the support; Calculate the lateral stiffness K of the existing support B0 =G×A / Σt, where G is the shear modulus of the rubber bearing, A is the plane area of ​​the bearing, and Σt is the total thickness of the rubber layer of the bearing; The ultimate displacement Δ of the bridge pier was determined by moment-curvature analysis. u and the horizontal displacement of the pier top yield Δ y and the yield horizontal force F of the pier column y Through K y =F y / △ y Calculate the equivalent yield lateral stiffness of the pier column; S2. Multi-level defense standards and damage control target setting: Establish a multi-level seismic fortification standard that includes minor, moderate, and major earthquakes at the E1 level, and set quantified damage state control targets for supports, main beams, and piers at each level: E1 level minor earthquake control target: Foundation bending moment M p <M pu Shear force V p <V pu M pu V pu Based on the flexural and shear bearing capacities; F < F s The displacement at the top of the support δ < 0.5t f , t f The thickness of the rubber layer of the support; The main beam's offset displacement satisfies λ < 0.5t. f ; Horizontal displacement of pier top △ c <△ y ; The leveling control targets for moderate earthquakes fall into the following two categories: When the support does not slide: F < F s And the displacement δ at the top of the support satisfies 0.5t. f ≤δ<t f ; Support sliding condition: F≥F s The total shear deformation and sliding displacement of the support are less than λ. u For the longitudinal direction of the bridge, λ u For the collision clearance between the pier and the anti-fall beam device, λ is the cross-sectional area of ​​the bridge. u The collision gap between the main beam and the anti-fall beam device; The main beam's offset displacement meets the requirement of 0.5t. f ≤λ<λ u ; The following conditions must be met in both cases: Foundation bending moment M p <M pu Shear force V p <V pu ; The main beam's offset displacement meets the requirement of 0.5t. f ≤λ<λ u ; Residual horizontal displacement Δ at the top of the bridge pier p Satisfies: 0.005L≤△ p =(△ c -△ e )≤0.01L, where L is the effective height of the pier column, △ eThe elastic horizontal displacement at the top of the pier is estimated using a bilinear model or by taking Δ. e =F / K y ; E2 level major earthquake control target: Foundation bending moment M p <M pu Shear force V p <V pu ; F≥F s The displacement at the top of the support δ≥t f And the sliding displacement of the support X ≤ X u X u is the distance from the edge of the pad stone to the edge of the support, and is the allowable sliding displacement limit of the support; Main beam offset displacement λ≥λ u ; Residual horizontal displacement Δ at the top of the bridge pier p Satisfy: 0.01L < △ p ≤0.015L; S3. Seismic performance issue assessment: If any deformation result does not meet the control target set in S2, it is determined that there is a seismic performance problem, reinforcement is required, and steps S4-S7 are performed. S4. Preliminary selection and parameter definition of anti-falling beam device: Choose a mechanical model that is either linear elastic or bilinear for the anti-fall beam device; Lateral stiffness K LB Determined in S6; Ultimate lateral force F of anti-fall beam structure LB =F LB-1 +K LB-2 ×(χ u –χ2);F LB Used to assess the maximum load-bearing capacity of the device and ensure that it does not fail unexpectedly under a major earthquake; Displacement χ1 when it begins to function: Take χ1 = δ p =F s / K B0 And it must satisfy χ1<λ u This is to ensure that the anti-fall beam device can work in a timely manner before or during the sliding of the support; Design limit displacement χ u Take χ u =λ u ; When selecting the bilinear model, the following parameters are further defined: First stage lateral stiffness K LB-1 Its value is determined in S6; First stage control displacement χ2: Take χ2=min(t) f , λ u ); Second stage lateral stiffness K LB-2 Take K LB-2 =n﹒ K LB-1 where n≥10; The first stage of lateral force control value F LB-1 =K LB-1 ×(χ2-χ1); S5. Calculation and Iterative Optimization of Mechanical Parameters for Anti-Beam Falling Device: A mechanical model is established to form a parallel constraint system consisting of the supports and the anti-falling beam device, and a series structure consisting of the constraint system and the bridge pier. The support and the anti-fall beam device form a parallel constraint system with a lateral stiffness of K. 并 =K LB +K B K LB To improve the lateral stiffness of the anti-fall beam device, K B The lateral stiffness of the support; The constraint system and the bridge piers form a series structure with a lateral stiffness of K. 串 =(K 并 ×K c ) / (K 并 +K c ), K c The lateral stiffness of the bridge pier column; Based on the series model and the force-displacement compatibility relationship, the derivation process is as follows: Under horizontal seismic loading, the total horizontal force F of the series structure is... total =K 串 ×(△ c +δ), this force is equal to the horizontal force F acting on the bridge pier. pier =K c ×△ c ,Right now: K 串 ×(△ c +δ)=K c ×△ c ; K 串 =(K 并 ×K c ) / (K 并 +K c Substituting into the above equation, we get: [(K 并 ×K c ) / (K 并 +K c )]×(△ c +δ)=K c ×△ c ; Divide both sides of the equation by K. c ,have to: [K 并 / (K 并 +K c )]×(△ c +δ)=△ c ; Multiply both sides of the equation by (K) 并 +K c ),have to: K and × (△) c +δ)=△ c ×(K 并 +K c ); Expanding the equation, we get: K 并 ×△ c +K 并 ×δ=△ c ×K 并 +△ c ×K c ; Eliminate the identical terms K on both sides of the equation 并 ×△ c ,have to: K 并 ×δ=△ c ×K c ; Finally, the formula for calculating the lateral stiffness requirement of the parallel constraint system is obtained: K 并 =(△ c / δ)×K c ; The lateral stiffness of the anti-fall beam device or the lateral stiffness of the support are analyzed and determined according to the graded calculation method: E1 level minor earthquake calculation: Let K be the required lateral stiffness of the support at this level. B1 The anti-falling beam device does not participate in the operation. LB =0, at this time K 并 =K B1 lateral stiffness K of bridge pier column c =K y , by K 并 =(△ c / δ)×K c The required lateral stiffness K of the support to meet this leveling performance target is derived. B1 =(△ c / δ)×K y The calculated K B1 The existing support stiffness K calculated in S1 B0 Comparison, if KB0 ≥K B1 If the existing support stiffness meets the E1 level requirement; if K B0 <K B1 If the existing support stiffness is insufficient, additional stiffness K needs to be provided by installing an anti-fall beam device. LB =K B1 -K B0 and this K LB The value is recorded as the E1 leveling design reference value K. LB-E1 ; Leveling calculations for moderate earthquakes fall into two categories: a. Set the required lateral stiffness of the support at this level to K. B2 If the support does not slide, the anti-falling beam device will not work. LB =0, at this time K 并 =K B2 Considering the stiffness reduction of the pier after it enters the elastoplastic state, a stiffness reduction coefficient α is introduced for the pier. At this point, the lateral stiffness K of the pier... c =αK y α is taken as 0.5 to 1; considering the increase in pier top displacement, a pier top horizontal displacement increase coefficient β is introduced, at which time the pier top horizontal displacement Δ c =β△ y β is taken as 1 to 3; considering the increase in support displacement, a support displacement increase coefficient γ is introduced, at which point the horizontal displacement at the top of the support is δ = γt. f γ is taken as 0.5 to 1; by K 并 =(△ c / δ)×K c The required lateral stiffness K of the support to meet this leveling performance target is derived. B2 =(△ c / δ)×K c =β△ y / (γt f )×αK y =η×(△ y / t f )×K y Where η = αβ / γ; the calculated K B2 The existing support stiffness K calculated in S1 B0 Comparison, if K B0 ≥K B2 Then the existing support stiffness meets the requirements under the condition of no slippage during a moderate earthquake; if K B0 <K B2 If the existing support stiffness is insufficient, additional stiffness K needs to be provided by installing an anti-fall beam device. LB =K B2 -K B0 and this K LB The value recorded is the design reference value K for moderate earthquakes without slippage.LB-M1 ; b. If the support slides, the anti-fall beam device needs to be activated. In this case, K 并 =K LB +K B ; Lateral stiffness K of bridge piers c =αK y α is taken as 0.5 to 1; the horizontal displacement Δ at the top of the pier c =β△ y β is taken as 1 to 3; the horizontal displacement of the top of the support is δ = γt f γ takes values ​​of 1 to 2; determined by K 并 =(△ c / δ)×K c The lateral stiffness of the constrained system is derived to be K. 并 =β△ y / (γt f )×αK y =η×(△ y / t f )×K y Where η = αβ / γ; by K 并 =K LB +K B0 The lateral stiffness K of the anti-fall beam device required to meet this level performance target is derived. LB =η×(△ y / t f )×K y –K B0 and this K LB The value recorded is the design reference value K for sliding during moderate earthquakes. LB_M2 ; E2 level earthquake calculation: At this level, the anti-falling beam device is in operation, and at this time K 并 =K LB +K B ; Lateral stiffness of bridge pier K c =αK y α is taken as 0.2 to 0.5; the horizontal displacement Δ at the top of the pier c =β△ y β is taken as 3 to 4; the horizontal displacement of the top of the support is δ = γt f γ is 2; by K 并 =(△ c / δ)×K c The lateral stiffness of the constrained system is derived to be K. 并 =β△ y / (γt f )×αK y =η×(△ y / t f )×K y Where η = αβ / γ; by K 并=K LB +K B0 The lateral stiffness K of the anti-fall beam device required to meet this level performance target is derived. LB =η×(△ y / t f )×K y -K B0 and this K LB The value is recorded as the E2 leveling design reference value K. LB_E2 ; Final design value of lateral stiffness K for anti-fall beam device LB Determination: A comprehensive comparison of the design reference values ​​K calculated under all levels. LB_E1 K LB_M1 K LB_M2 With K LB_E2 The maximum value among them is taken as the final design value K of the lateral stiffness of the anti-fall beam device. LB ; S6, Final design value K LB Model of anti-falling beam device: If a linear elastic model is chosen, its lateral stiffness K LB That is, take the final design value; If the bilinear model is chosen, its first-stage lateral stiffness K LB-1 Take this final design value and calculate the second-stage lateral stiffness K accordingly. LB-2 First stage lateral force control value F LB-1 ; F LB-1 K LB-1 K LB-2 , χ1, χ2, χ u Together they are given a bilinear mechanical model; S7. Add the defined anti-falling beam device model to the original bridge finite element model; Repeat S1 and S3; If any deformation result does not meet the control target set by S2, and / or the actual force F of the anti-falling beam device obtained through nonlinear time history analysis LB实 Exceeding its ultimate lateral resistance F LB Then adjust the parameters of the anti-fall beam device, including the lateral stiffness K of the linear elastic model. LB , Displacement χ1 when it begins to function, Design limit displacement χ u Or the first-stage lateral stiffness K of the bilinear model LB-1 The second-stage lateral stiffness K of the bilinear model LB-2 , Displacement χ1 when it begins to function, Design limit displacement χ u Then, the nonlinear time history analysis and result verification of this step are repeated until all quantitative and qualitative control objectives are met.

[0028] The core challenge currently facing the seismic reinforcement of in-service highway bridges lies in the lack of a systematic design method for preventing bridge collapse. Traditional methods mainly rely on engineering experience to select and determine the parameters of anti-collapse devices, lacking scientific design basis and quantitative standards. This makes it difficult to balance the relationship between normal use and seismic safety, and fails to achieve controllable performance under multi-level seismic loading.

[0029] The closest existing technology mainly relies on the general requirements of the "Code for Seismic Strengthening Design of Highway Bridges" for anti-falling beam design. It typically uses a single type of anti-falling beam device and determines its installation location and stiffness parameters based on experience. This method lacks a systematic seismic performance evaluation process, cannot accurately quantify the damage state of various bridge components under earthquakes of different intensities, and lacks multi-level fortification targets and corresponding damage control indicators for minor, moderate, and major earthquakes. Furthermore, the determination of anti-falling beam device parameters does not consider the mechanical interaction between the device and the structural system composed of supports and piers, making it difficult to precisely control the timing and extent of the device's intervention. This often results in the device either intervening too early, affecting normal use, or intervening too late, failing to effectively prevent beam fall.

[0030] This scheme establishes a complete seismic performance assessment and parameter acquisition process, providing a precise data foundation for anti-falling beam design. It employs multi-level seismic design standards and quantified damage control targets to ensure the bridge reaches its predetermined performance state under minor, moderate, and major earthquakes. Accurate identification of seismic performance issues clarifies the necessity and direction of reinforcement. Based on a mechanical model, the selection and parameter definition of the anti-falling beam device are conducted to ensure that the device performance matches the seismic design objectives. By establishing a parallel constraint system between the supports and the anti-falling beam device, and its series structural model with the piers, the stiffness requirements of the anti-falling beam device are accurately calculated. A graded calculation method is used to determine the device parameters for different seismic levels, and finally, iterative optimization ensures that all design parameters meet the multi-level seismic performance requirements.

[0031] This solution represents a shift from experience-based design to scientific design. Through a systematic process and precise mechanical models, it ensures that the anti-falling beam device does not interfere with structural deformation under normal use, effectively limits displacement under minor and moderate earthquakes, and effectively prevents beam fall under major earthquakes. Furthermore, by controlling multiple fortification targets, it effectively avoids the problems of over-strengthening or under-strengthening, significantly improving the seismic safety performance and functional recoverability of in-service ductile bridges.

[0032] An anti-falling beam device is designed and installed based on a multi-level, multi-objective method for improving the anti-falling beam function of in-service ductile bridges. The anti-falling beam device is selected and set according to the mechanical performance parameters calculated by the anti-falling beam function improvement method. The anti-falling beam device is installed on the outer side of the main beam or on the cap beam or the top of the main beam on the side of the support. It is used to limit the sliding of the support and the displacement of the main beam under the level of minor and moderate earthquakes. Under the level of major earthquakes, it prevents the beam from falling by damaging itself. The superstructure (main beam) and substructure (pier, cap beam) of the bridge are not directly connected by the anti-falling beam device. The anti-falling beam device is selected and set according to the mechanical performance parameters calculated by the anti-falling beam function enhancement method. The anti-falling beam device is installed on the outer side of the main beam or on the top of the cap beam or the support side of the main beam. The installation method of the anti-falling beam device ensures that under normal use, it does not restrict the free relative deformation between the superstructure (main beam) and the substructure (pier, cap beam) of the bridge, so that the upper and lower structures do not form a direct mechanical connection through the anti-falling beam device. The anti-falling beam device is used to limit the sliding of the support and the displacement of the main beam under the level of minor and moderate earthquakes, and to prevent the beam from falling under the level of major earthquakes through its own damage.

[0033] The main problem currently facing the design of anti-falling beam devices for in-service bridges is the insufficient compatibility between the device and the bridge structure. Traditional anti-falling beam devices often adopt standardized designs, and their mechanical performance parameters have not been specifically calculated and optimized for the seismic requirements of specific bridges and the characteristics of existing supports. As a result, the devices either have insufficient restraint effect or excessive restraint that affects the normal use function of the bridge during actual seismic action.

[0034] The closest existing technology is to directly select and install general-purpose anti-girder-falling devices based on experience. These devices are usually fixed to the outside of the main girder or the cap beam of the support, and their design objective is relatively singular, mainly focusing on preventing the main girder from falling under a major earthquake. However, existing technologies lack a link between the device's performance and a systematic multi-level seismic design method. The device's mechanical performance parameters, such as stiffness and ultimate displacement, are not determined through precise calculations, nor are they directly correlated with the overall seismic fortification objectives and damage control indicators of the bridge. This makes it difficult to precisely control the timing and extent of the device's operation during actual earthquakes, and fails to achieve the synergistic goal of effectively limiting displacement under minor and moderate earthquakes and preventing girder fall under major earthquakes.

[0035] The core of the anti-girder-falling device provided by this technology lies in the fact that all its key mechanical performance parameters are calculated and determined through the aforementioned systematic multi-level seismic design method. This ensures that the device's performance is closely matched with the fortification objectives of a specific bridge under E1 level minor, moderate, and E2 level major earthquakes. The device is installed on the outer side of the main girder or on the cap beam or top of the main girder on one side of the support. Its selection and installation directly serve the multi-level performance objectives: under minor and moderate earthquakes, the device can effectively limit the sliding of the support and the displacement of the main girder, preventing irreparable damage to structural components; under E2 level major earthquakes, the device, through its predetermined damage or functional operation, consumes seismic energy and withstands large deformations, thereby providing final protection for the core structural components and ensuring that the bridge does not suffer the catastrophic consequence of girder fall. At the same time, the damage mode of the device itself is controllable and predictable.

[0036] The establishment of the design and installation scheme for this device marks its transformation from an independent, empirically-based structural measure into an integral part of the overall seismic resistance system of the bridge. It ensures that the anti-falling beam function is coordinated with the seismic resistance mechanism of ductile bridges, guaranteeing both the bridge's usability under frequent earthquakes and the safety of lives under rare earthquakes, thus achieving precise and systematic improvement in seismic performance.

[0037] In another embodiment, the anti-falling beam device is a U-shaped steel plate anti-falling beam structure, a steel spring anti-falling beam structure, or a combination of steel bars and springs anti-falling beam structure, installed in the transverse or longitudinal direction of the bridge to limit the lateral or longitudinal displacement of the main beam.

[0038] This technical solution clearly defines the specific structural forms that can be selected for the anti-falling beam device, including U-shaped steel plate anti-falling beam structures, steel spring anti-falling beam structures, and steel bar and spring combined anti-falling beam structures. This limitation connects the abstract mechanical model with a real engineering product, providing designers with a clear and feasible range of choices. Simultaneously, the solution clarifies that these devices can be installed in the transverse or longitudinal direction of the bridge as needed to restrict the lateral or longitudinal displacement of the main beam, respectively. This gives the device a clear functional focus, enabling precise reinforcement of seismic weak points in different directions of the bridge, thus solving the problem that a single functional direction of the device might not match the actual complex seismic vibration requirements.

[0039] By limiting the anti-falling beam device to several specific structural forms that have been proven in engineering, and clarifying its installation direction and function, it is ensured that the design parameters derived from complex calculations can be accurately achieved through mature and reliable engineering products. This effectively bridges theoretical design and engineering practice, guaranteeing both the reliability and predictability of the anti-falling beam device's performance, and improving the efficiency and success rate of design implementation, thus concretizing and successfully realizing the goal of improving the bridge's seismic performance.

[0040] In another embodiment, when the anti-falling beam device adopts a bilinear mechanical model, its second-stage lateral stiffness K... LB-2 Compared with the lateral stiffness K of the first stage LB-1 Satisfying the relation: K LB-2 =n﹒ K LB-1 Where n≥10; and the displacement χ1 when the anti-falling beam device starts to function satisfies the condition: χ1=δ p =F s / K B0 This ensures that the anti-fall beam device can intervene in a timely manner when or before the support slides.

[0041] This technical solution clearly specifies the second-stage lateral stiffness K when the anti-fall beam device adopts a bilinear mechanical model. LB-2 Compared with the first stage lateral stiffness K LB-1 K must be satisfied LB-2 =n﹒ K LB-1 The relationship is defined as follows, and n≥10. This provision ensures that after the device undergoes a relatively soft deformation in the first stage, the second stage can provide a sufficiently large stiffness change, thereby quickly and effectively limiting the displacement of the main beam and supports, preventing unlimited displacement development. Simultaneously, the scheme sets the displacement χ1 at which the device begins to function as equal to the support sliding displacement δ. p , and δ p The bearing anti-slip force F s With support lateral stiffness K B0 The calculations show that the activation timing of the device is strictly linked to the critical sliding state of the support itself, ensuring that the anti-falling beam device works precisely when the support is about to slip or begins to slip, achieving precise coordination between the device and the support behavior.

[0042] By precisely quantifying the core parameters of the bilinear model and directly linking them to the mechanical properties of the supports, the working mechanism of the anti-falling beam device is ensured to be highly compatible with the seismic requirements of the bridge. This not only guarantees that the device can provide a powerful limiting function when needed, effectively controlling structural displacement, but also avoids the risk of excessive additional force on the piers or device failure due to unreasonable parameter settings, significantly improving the controllability and reliability of the anti-falling beam measures.

[0043] In another embodiment, the anti-falling beam device includes an initial installation gap between the device and the restrained main beam or support. The width of this initial installation gap is not less than the displacement value χ1 when the anti-falling beam device begins to function, and not greater than the limit displacement value λ of the main beam. u .

[0044] This technical solution effectively decouples the daily function and seismic function of the anti-falling beam device by explicitly specifying an initial installation gap between the device and the main beam or support it is restrained. The width of this initial installation gap is limited to a calculated and reasonable range: its lower limit is not less than the displacement value χ1 when the anti-falling beam device begins to function, ensuring that the device will not prematurely engage when the structure undergoes normal deformation or minor earthquake deformation less than χ1, thus avoiding interference with daily use; its upper limit is not greater than the ultimate offset displacement limit λ of the main beam. u This ensures that when the main beam displacement develops to a level that may endanger safety, the anti-falling beam device will definitely have already started working and played a limiting role, providing a last reliable barrier to prevent the beam from falling.

[0045] The establishment of this technical feature makes the anti-falling beam device a "smart" seismic-resistant component, achieving the design goal of "no disturbance under normal conditions, effective during earthquakes." It scientifically balances the contradiction between the needs of normal structural use and the needs of seismic safety, ensuring that the performance of the bridge is not affected during long-term operation, while ensuring that the anti-falling beam function can be reliably activated in the event of an earthquake, significantly improving the overall performance of the bridge throughout its entire life cycle.

[0046] In another embodiment, the anti-falling beam device is a self-resetting stop, and its mechanical model is a bilinear mechanical model; after a major earthquake, the anti-falling beam device can rely on its own elastic restoring force to reset the main beam to near its initial position.

[0047] The self-resetting stop employs a bilinear mechanical model, meaning its mechanical behavior under seismic loads is divided into two distinct phases. More importantly, after a major earthquake, the device can use its elastic restoring force to drive the displaced main girder back to its initial position. This self-resetting characteristic allows the bridge to not only avoid girder collapse after a strong earthquake but also significantly reduce the residual displacement of the main girder, enabling the bridge alignment and support system to quickly return to a serviceable state.

[0048] The application of this device has greatly improved the seismic resilience of bridges. It ensures the safety of the structure under strong earthquakes, and at the same time, through the device's self-resetting function, it minimizes permanent damage and residual deformation of the structure after the earthquake. It provides valuable transportation channels for emergency rescue after the earthquake and significantly reduces the difficulty, cost and time of subsequent repairs, achieving a performance leap from simply preventing collapse to ensuring the sustainable functioning after the earthquake.

[0049] In another embodiment, the anti-falling beam device is a self-resetting stop block, whose first-stage lateral stiffness K LB-1 The value range is 1.0 × 10. 3 -1.0×104 kN / m, through this specific stiffness range, enables the main beam to return to its initial position by relying on its own elastic restoring force after a major earthquake.

[0050] This technical solution addresses the first-stage lateral stiffness K of the self-resetting stop. LB-1 Limited to 1.0×10 3 -1.0×10 4 Within a specific range of kN / m, a clear and reliable basis is provided for determining this key design parameter. The establishment of this stiffness range is based on a deep understanding of the interaction between the mechanical properties of the self-resetting stop and the overall response of the bridge. It ensures that the stop has sufficient flexibility during normal operation to avoid unnecessary constraints on the free deformation of the bridge under daily operation and minor earthquakes; simultaneously, this stiffness range guarantees that the stop can accumulate and provide sufficient elastic restoring force, thereby effectively driving the main girder to overcome friction and residual deformation resistance after a major earthquake, restoring it to near its initial position.

[0051] The specific stiffness range defined allows the design of the self-resetting stop to move from concept to precise quantification. This significantly improves the reliability and consistency of the self-resetting function, ensuring that the device can perform its expected reset function after an earthquake, effectively reducing permanent structural displacement, and providing crucial technical support for enhancing the seismic toughness of bridges and achieving rapid functional recovery.

[0052] In another embodiment, the connection between the anti-falling beam device and the main bridge structure is a non-rigid connection provided by hinged or flexible connecting elements, so that the anti-falling beam device only transmits horizontal force and not bending moment, ensuring that the free deformation of the structure is not affected under normal use and minor earthquakes.

[0053] This technical solution fundamentally alters the force transmission path by explicitly specifying a non-rigid connection between the anti-falling beam device and the main bridge structure, specifically through hinged or flexible connecting elements. This connection design ensures that the anti-falling beam device transmits only horizontal forces to the main structure, eliminating the transmission of bending moments. This characteristic guarantees that under normal use conditions and minor earthquakes, the bridge structure can freely deform according to its original stress mechanism. The presence of the anti-falling beam device does not introduce additional constraints, thus completely eliminating interference with the normal functioning of the structure.

[0054] The establishment of this non-rigid connection method allows the anti-fall beam device to purely perform its pre-set seismic resistance function. Like a smart switch, it is "disconnected" from the structure under normal circumstances, allowing for free structural movement; during an earthquake, it quickly "closes" by transmitting horizontal forces, effectively limiting displacement. This design not only protects the main structure from unnecessary additional forces but also simplifies the stress state of the device itself, improving its reliability and durability under seismic loads. It is a key technical measure to achieve a harmonious balance between normal structural use and seismic safety.

[0055] In view of the imperfections in the current seismic reinforcement design and analysis methods and indicators for anti-falling beam measures of highway bridges, this invention provides a design method for improving the transverse anti-falling beam function of in-service ductile highway beam bridges based on multi-level, multi-objective, and displacement.

[0056] To achieve the above objectives, the specific implementation steps are as follows: (1) Seismic performance analysis and evaluation of in-service ductile system bridges This study employs the finite element method (FEM) to analyze the seismic response of in-service ductile bridge systems. Starting with typical seismic damage patterns, it focuses on extracting seismic demand analysis results, including displacement and strength of the main girder, bearings, and piers. Based on the current "Code for Seismic Design of Highway Bridges" (JTG / T 2231-01-2020), theoretical calculations and finite element numerical simulations are comprehensively used to calculate seismic capacity indicators such as bearing strength and shear deformation, and pier strength and displacement. The structural capacity / demand ratio is used to identify any problems in the bridge's seismic performance.

[0057] (2) Establish seismic performance enhancement design standards for in-service bridges that take into account multiple levels and objectives. To address the existing seismic performance issues of in-service bridges, in accordance with the current "Code for Seismic Design of Highway Bridges" (JTG / T2231-01-2020), and based on the seismic design category, importance, owner requirements, and seismic performance improvement level of in-service highway bridges, the seismic design concept of "no damage in minor earthquakes, repairable in moderate earthquakes, and no collapse in major earthquakes" is adopted. Firstly, multi-level, multi-objective seismic fortification standards for improving in-service ductile bridges are determined, i.e., the minimum fortification target requirements, as shown in Table 1. Further, focusing on the fortification targets and structural damage control targets, the seismic performance targets for bridge structures and various types of components are clarified, as shown in Table 2 (including Tables 2-1, 2-2, and 2-3).

[0058] Table 1 Seismic Design Objectives for Improving the Seismic Performance of In-Service Ductile Highway Bridges Table 2-1 Targets for Improving Damage Control of In-Service Ductile Highway Bridge Structures Table 2-2 Targets for Improving Damage Control of In-Service Ductile Highway Bridge Structures Table 2-3 Targets for Improving Damage Control of In-Service Ductile Highway Bridge Structures (3) Installation location of anti-falling beam device To address the issue of insufficient beam restraint in existing bridges, anti-falling beam devices are installed on the outer side of the main girder, on the cap beam of the support side, or on the top of the main girder, without direct connection between the upper and lower structures. The anti-falling beam devices can be installed transversely, longitudinally, or horizontally, as illustrated in the installation diagram below. Figure 1 As shown in (a) and 1(b), Figure 1 In (a) and 1(b), 1-support; 2-main beam; 3-anti-falling beam device; 4-pier or cap beam.

[0059] (4) Selection of anti-fall beam device Anti-fall beam devices are primarily used to control the deformation deviation of supports and main beams to within their damage limits, and to prevent serious damage and functional failure of the devices themselves. Based on the mechanical characteristics of anti-fall beam devices, their typical mechanical models are divided into linear elastic and bilinear models (to accommodate structural strength and deformation requirements under different design flood levels and objectives). To avoid the impact of anti-fall beam device installation on structural deformation requirements under normal operation and minor earthquakes, a gap exists between the device and the restricted object. Therefore, the typical mechanical model of an anti-fall beam device is as follows: Figure 2 and Figure 3 As shown. Figure 2 It is a linear elastic mechanical model. Figure 3 It is a bilinear mechanical model. Figure 2 and Figure 3 middle, F LB To prevent the ultimate lateral force of the beam structure from falling; F LB-1 These are the lateral force control values ​​for the first stage; x 1 represents the displacement when the anti-fall beam structure begins to function; x 2 is the first stage control displacement for the anti-fall beam structure; x u The ultimate displacement of the structure is designed to prevent beam collapse; K LB-1 This represents the lateral stiffness for the first stage. K LB-2 This represents the lateral stiffness in the second stage. K LB To prevent the beam from falling, the effective linear elastic lateral stiffness of the structure is required.

[0060] (5) Mechanical relationship between anti-falling beam device and local structure The anti-falling beam device and the supports together form a restraint system, which, together with the lower piers, forms a series structure. Under horizontal seismic loads, the horizontal force is transferred from the restraint system to the lower piers. The mechanical diagram of the local series structure is shown below. Figure 4 As shown in the figure. The trends in the mechanical properties of the supports and piers under horizontal loads are as follows. Figure 5 and Figure 6 As shown in the figure, K c The lateral stiffness of the pier column; K LB + K B The combined lateral stiffness of the support and anti-fall beam structure; F For horizontal force; △ c This refers to the horizontal displacement of the pier top; d i To control displacement of the superstructure or constraint system; △ i It is the horizontal displacement of the rubber bearing, Δ max It is the horizontal displacement of the pier top when the force reaches its maximum. F max It is the maximum horizontal force at the top of the pier, △ μ It is the ultimate displacement of the pier top. F μ It is the ultimate bearing capacity horizontal force at the top of the pier.

[0061] The support and the anti-fall beam structure form a parallel restraint system with the following lateral stiffness: K 并 = K LB + K B (1) The constraint system and the bridge piers form a series structure with the following lateral stiffness: K 串 =( K 并 . K c ) / ( K 并 + K c (2) According to the principle of force balance: K 串 (△) c + d i )= K 并 d i = Kc △ c (3) Then there is K 并 / K c =△ c / d i (4) From this, we can conclude that: K LB =(△ c / d i )× K c - K B (5) In summary, the lateral stiffness requirements of the anti-fall beam structure and restraint system can be determined based on the limiting displacement of the main beam, supports, piers, etc. under different waterproofing levels.

[0062] (6) Method for determining the mechanical performance parameters of displacement-based anti-fall beam device Based on the multi-level fortification standard requirements, namely "no damage in minor earthquakes, repairable in moderate earthquakes, and no collapse in major earthquakes," and simultaneously meeting the needs of post-earthquake emergency transportation, repairable damage, and restoration of traffic functions, this paper elaborates on the method for determining the mechanical performance parameters of the anti-falling beam device, starting from ensuring the support and constraint functions and capabilities, including controllable bearing sliding and shear deformation, repairable pier damage and no collapse, controllable main beam displacement and deviation, and no failure of the anti-falling beam function.

[0063] ① Minor earthquakes cause no damage Under minor earthquakes, all components of the bridge structure are in the elastic working stage, and the anti-falling beam device does not participate in the operation. According to the fortification target requirements for supports, main beams, piers, foundations, etc., under minor earthquakes as shown in Table 1, the corresponding damage state should meet the requirements of Table 2. During this stage, the displacement of each component should simultaneously meet the following conditions: (a) Pier displacement Horizontal displacement of pier top: △ c <△ y (6) (b) Support deformation Displacement at the top of the support: d i <0.5 t f (7) At the same time, the support did not slide, meaning the support meets the anti-slip force requirement: F < Fs = μR (8) In the formula: m The interfacial friction coefficient is taken as 0.1 to 0.2; R This refers to the vertical force acting on the support; (c) Calculation of lateral stiffness For ordinary plate rubber bearings, the lateral stiffness of the bearing is calculated as follows: K B = F s / d i (9) According to the horizontal displacement-horizontal force variation curve of reinforced concrete pier ( Figure 6 The elastic lateral stiffness of the pier column is calculated as follows: K c = F c / △ c = F y / △ y =K y (10) In the formula: △ c The horizontal displacement at the top of the pier is less than the yield displacement. F c The horizontal force is in the cracked state; △ y This represents the yield horizontal displacement; F y The yield force of the pier column; K y The yield lateral stiffness of the pier column.

[0064] Under minor earthquakes, the pier column is generally in an elastic state, that is, the equivalent yield state is its elastic limit state. Under normal circumstances, to control the pier column to reach the cracking state at this stage, the corresponding horizontal displacement of the pier column is less than the yield displacement.

[0065] (d) Calculation of lateral stiffness of the constrained system During this stage, the anti-fall beam device is not involved in the operation; therefore, the stiffness of the parallel constraint system is equal to the lateral stiffness of the support. K 并 = K B (11) Based on the mechanical relationships of series structures, to meet the design objective requirement that the displacements of supports, main beams, and piers remain in an elastic state under minor earthquakes, the corresponding lateral stiffness requirements of the constraint system or supports are calculated as follows: KB1 =(△ c / d i )× K c =(△ c / d i )× K y =( or △ y / d i )× K y (12) In the formula: or It is generally 0.5-0.7 times the yield displacement, when the bridge pier reaches the ultimate elastic state. or Take 1; d i The displacement at the top of the support (without sliding between the support and adjacent structures, and the displacement developing in a coordinated and synchronous manner) is less than 0.5. t f .

[0066] In summary, the adaptability of the support technical parameters is determined based on the displacement requirements of each component under minor earthquakes.

[0067] ② Moderate earthquakes are repairable Under moderate earthquake loading, bridge structural components are allowed to operate in an elastoplastic state, and anti-falling beam devices can be implemented according to the requirements of bearing sliding or limiting. Based on the fortification target requirements for bearings, main beams, piers, foundations, etc., under moderate earthquake loading (Table 1), the corresponding damage states should meet the requirements of Table 2. During this stage, the displacement of each component should simultaneously meet the following conditions: (a) Pier displacement The horizontal displacement of the pier top must meet the following conditions: △ y ≤△ c <△ max (13) The corresponding residual displacement Δ at the pier top p As shown in equation (14), the residual displacement is characterized as follows: Figure 7 As shown.

[0068] 0.005 L ≤△ p =(△ ci -△ e )≤0.01 L (14) △ c For the horizontal displacement of the pier top, △ ci This refers to the horizontal displacement of the pier top during this stage; (b) Support displacement The displacement at the top of the support must satisfy the following condition: 0.5 t f ≤ d i < t f (15) At the same time, the support did not slide, meaning the support's anti-slip force meets the following requirements: F < F s = μR (16) In the formula: m The interfacial friction coefficient is taken as 0.1 to 0.2; R This refers to the vertical force acting on the support; (c) Lateral stiffness The lateral stiffness of the support is calculated as shown in equation (9).

[0069] According to the horizontal displacement-horizontal force variation curve of reinforced concrete pier ( Figure 6 The lateral stiffness of the pier column is calculated as follows: K c = F c / △ c = αK y (17) In the formula: α The stiffness attenuation coefficient of the pier column is between 0.5 and 1.

[0070] (d) Calculation of lateral stiffness of locally constrained system without considering support sliding Within the controlled displacement, no relative sliding occurs between the support and the adjacent structure. Under the condition of meeting the anti-slip capacity and deformation requirements, the anti-falling beam device does not participate in the operation. Therefore, the stiffness of the parallel constraint system is equal to the lateral stiffness of the support. K 并 = K B (18) Based on the mechanical relationships of a series structure, and considering the performance targets for deformation and strength of piers and supports as shown in Table 2, the lateral stiffness requirement of the supports at this stage is calculated as follows: K B2 =(△ ci / d i )× K ci =( β △ y) / ( gd i )× αK y =( αβ / c )×(△ y / d i )× K y (19) In the formula: △ ci This refers to the horizontal displacement of the pier top during this stage; β This is the factor that increases the horizontal displacement of the pier top, and it is generally between 1 and 3. c This is the support displacement amplification factor, which is generally less than 2; when α =1, β =1, c When =1, K B2 Lateral stiffness of bearings under minor earthquakes K B1 1.3 times that.

[0071] when α =0.5, β=3 , c When =2, K B2 This is the upper limit of the lateral stiffness of the bearing under moderate earthquake loading, and also the upper limit of the lateral stiffness of the bearing under minor earthquake loading. K B1 It is 0.75 times that of the support, which is basically consistent with the lateral stiffness requirement of the pier column when it reaches the cracking state under minor earthquake.

[0072] In summary, the lateral stiffness parameters of the bearings that meet the deformation requirements of the bearings and piers under moderate earthquake loading can be determined.

[0073] (e) Calculation of lateral stiffness of locally constrained system considering support sliding Under moderate earthquake loading, when the bearing slides, an anti-fall beam device should be installed on the side of the bearing to limit the sliding displacement of the bearing to less than the control displacement (rubber layer thickness). First, determine the displacement at which the bearing begins to slide. d p : d p = F s2 / K B (20) 0.5 t f ≤ d p < tf (twenty one) The anti-slip force of the support is calculated as follows: F s2 = μR (twenty two) The horizontal force-displacement relationship of the support where sliding occurs is as follows: Figure 8 As shown, F s1 , F s2 These represent the support anti-slip forces in the first and second stages, respectively. When the support displacement reaches... d p At that time, the anti-fall beam participates in the work, that is, the displacement of the anti-fall beam participates in the work. x 1= d p .

[0074] When the support begins to slide, the sliding is restricted by installing an anti-fall beam device. At this time, the anti-fall beam device and the support form a parallel constraint system, and the corresponding lateral stiffness is calculated as follows: K 并 = K LB + K B (twenty three) Because the anti-falling beam device distributes some of the horizontal force, it reduces the horizontal seismic force on the support and limits the horizontal slippage and shear deformation of the support. However, it may increase the stress and deformation of the lower pier column. Therefore, it is necessary to control the damage to the pier column to a repairable state, and at the same time, control the collision between the main beam and the outer stop block, that is, the sum of the sliding displacement and limited lateral deformation of the main beam should be less than [a certain value]. l u If the shear deformation of the support meets the deformation requirements, then the displacement control value of the anti-fall beam structure at this stage is... x 2.

[0075] The corresponding parallel system lateral stiffness limit is calculated as shown in Equation (24), and the support deformation meets its deformation requirements.

[0076] K 并 =(△ ci / d p )× K ci =( β △ y ) / ( gd i )× αK y =( αβ / c)×(△ y / d i )× K y (twenty four) From the perspective of controlling collision displacement and pier damage, the following calculation is performed based on formula (4) and stiffness requirements: K 并 =(△ ci / l u )× K ci =( β △ y / l u )× αK y = αβ ×(△ y / l u )× K y (25) To meet the limiting requirements after the support slides, the required lateral stiffness of the additional anti-fall beam is calculated as follows: K LB =( ab / c )×(△ y / d i )× K y - K B (26) or K LB = αβ ×(△ y / l u )× K y - K B (27) The displacement value corresponding to the additional anti-falling beam device starting to function is 0.5. t f ≤ x 1 or d p ≤ t f .

[0077] ③ Remains standing even after a major earthquake Under a major earthquake, the bridge structural components are in the elastoplastic working stage. The anti-falling beam device is operational, but does not fail functionally or fall off. The pier top displacement is less than the collapse limit displacement; the supports do not slip. According to the seismic design requirements for supports, main beams, piers, foundations, etc., under earthquake loading in Table 1, the corresponding damage state should meet the requirements in Table 2. During this stage, the displacement of each component should simultaneously meet the following conditions: (a) Pier displacement The horizontal displacement of the pier top must meet the following conditions: △ c ≤△ μ (28) The corresponding residual displacement Δ at the pier top p The following conditions must be met: 0.01 L ≤(△ ci -△ e )≤0.015 L (29) (b) Support displacement The displacement at the top of the support must satisfy the following condition: d i = t f (30) Meanwhile, in order to limit the slippage of the support, anti-slip beam supports are used to meet the anti-slip force requirements: F s = μR (31) In the formula: m The interfacial friction coefficient is taken as 0.1 to 0.2; R This refers to the vertical force acting on the support; (c) Calculation of lateral stiffness The lateral stiffness of a common plate rubber bearing is calculated as follows: K B = F s / d i (32) According to the horizontal displacement-horizontal force variation curve of reinforced concrete pier ( Figure 6 The lateral stiffness of the pier under severe damage limit state is calculated as follows: K ci = F ci / △ ci = αK y (33) In the formula:α This is the stiffness attenuation coefficient of the pier column, which generally corresponds to the section where the bearing capacity decreases, and its value ranges from 0.5 to 0.2.

[0078] (d) Calculation of lateral stiffness of locally constrained system During this stage, when the support displacement or main beam displacement is greater than [a certain value], l u At that time, the anti-fall beam device takes effect and controls its ultimate deformation to reach the specified value. x u Meanwhile, the support meets the deformation requirements, and its mechanical properties change as follows: Figure 9 As shown. Therefore, the stiffness of the parallel constraint system is calculated as follows: K 并 = K LB + K B (34) Based on the mechanical relationships of series structures, the lateral stiffness of the constrained system is calculated as follows: K 并 =(△ u / t f )× K ci =( β △ y ) / ( gd i )× αK y =( αβ / c )×(△ y / d i )× K y (35) In the formula: β This is the factor that increases the horizontal displacement of the pier top, and it is generally between 3 and 4. c This is the bearing deformation amplification factor, relative to the control deformation limit under minor earthquakes or normal conditions, and is generally taken as 2.

[0079] when α =0.2, β =4, c When the value is 2, the upper limit of the lateral stiffness of the parallel system is 0.4 times the upper limit of the initial stiffness (the upper limit of the lateral stiffness under small earthquake action).

[0080] Therefore, based on the deformation ratio of the series structure, the lateral stiffness parameters of the anti-fall beam that meet its deformation requirements under a major earthquake can be calculated as follows: KLB-2 =( αβ / c )×(△ y / d i )× K y - K B (36) (7) Determination of lateral stiffness requirements for multi-level and multi-stage bridge structures Based on the bridge seismic design principle of "no damage in minor earthquakes, repairable in moderate earthquakes, and no collapse in major earthquakes," and considering the multi-level seismic design and performance targets in Tables 1 and 2, and taking into account the stages of operation of the anti-falling beam device, the corresponding displacement-based constraint system and the lateral stiffness requirement curves of the lower ductile pier columns are obtained as follows: Figure 10 and Figure 11 As shown in the figure. ① represents the characteristic displacement and stiffness requirement values ​​during the minor earthquake stage; ② represents the characteristic displacement and stiffness requirement values ​​during the moderate earthquake stage; ③ represents the characteristic displacement and stiffness requirement values ​​during the major earthquake stage.

[0081] To meet the displacement and strength design targets for each component in Tables 1 and 2: In stage ①, the total lateral stiffness of the constraint system (excluding the anti-falling beam device) is primarily determined by the lateral stiffness of the supports. K B The lateral stiffness of the pier column is the equivalent yield stiffness. K y In stage ②, the total lateral stiffness of the constraint system (excluding the anti-falling beam device) is 0.9-1.3 times that of stage ① (related to the horizontal control displacement of the pier top in the first stage), and the lateral stiffness of the pier column is 0.5-1 times the equivalent yield stiffness. In stage ③, the total lateral stiffness of the constraint system (excluding the anti-falling beam device) is 0.4-0.9 times that of stage ①, and the lateral stiffness of the pier column is 0.2-0.5 times the equivalent yield stiffness.

[0082] (8) Determination of mechanical performance requirements for multi-level, multi-stage anti-fall beam devices In summary, under horizontal seismic loading, the mechanical properties of the restraint system and the tandem piers interact. Adding an anti-falling beam device, which participates in horizontal seismic resistance, alters the lateral stiffness of the restraint system. To achieve the bridge seismic design and performance targets in Tables 1 and 2, based on the lateral stiffness requirements of the restraint system and piers under different deformation and damage states shown in the figure, and considering the original support conditions, the lateral stiffness requirements of the additional anti-falling beam device are determined. K LB =(△ c / d i )× K c - KB .

[0083] (9) Determination and optimization of the rationality of mechanical parameters of the anti-falling beam device The finite element method (FEM) numerical analysis was employed. The anti-falling beam mechanical model (linear elastic or bilinear) and lateral stiffness and displacement parameters were input into the original bridge's FEM numerical analysis model. Seismic response analysis of the bridge after the upgrade was conducted. The deformation, displacement, and strength analysis results of the supports, piers, and main beams before and after the upgrade were extracted and compared with the seismic design targets to verify the rationality of the anti-falling beam mechanical parameters and to optimize them.

[0084] Practical application examples Specific implementation process, such as Figure 12 As shown: 1) Seismic response requirements of bridge structure under seismic action in step (1) (excluding anti-fall-beam device) Based on the geometric configuration and structural characteristics of actual bridges, reasonable mechanical constitutive relationships are introduced for piers, bearings, foundations, main beams, and connection measures. A corresponding finite element numerical model of the decoupled bridge structure is then established, such as... Figure 13 As shown, the seismic response results under horizontal seismic loading are obtained, including main beam displacement, support deformation, pier deformation, pier bending moment and shear force, and foundation bending moment and shear force.

[0085] 2) Step (2) Calculation of seismic resistance of components under horizontal load Based on the damage control targets in Table 2, the strength and deformation capacity of the piers and supports are calculated primarily using finite element numerical simulation and theoretical calculation methods. The displacement limit of the main beam is a fixed value. ① Seismic resistance calculation of piers like Figure 14 As shown, the moment-curvature analysis method is applied to calculate the flexural bearing capacity of the bridge pier. M u Yield bending moment M y And the corresponding curvature results.

[0086] By applying the theoretical relationship between bending moment-curvature and horizontal force and displacement, the horizontal force at different characteristic points is obtained. F and horizontal displacement Δ c The horizontal stiffness of the pier column can then be calculated. K c Plastic deformation △ p Yield displacement Δ y Feature points, etc., the results are shown in Table 3.

[0087] Table 3 shows the calculated characteristic points of the piers. ② Calculation of bearing seismic resistance Calculate the lateral stiffness of the supports under vertical and horizontal loads using finite element numerical simulation or theoretical calculation methods. K R Shear deformation d Results such as slippage can be obtained. Based on the displacement deviations between the top surface of the support and the superstructure, and between the bottom surface and the substructure, the slippage state of the support can be determined relatively accurately. The horizontal displacement-horizontal force curve of the support under the combined action of horizontal and vertical dead loads is shown below. Figure 15 As shown, the slippage state between the top surface of the support and the superstructure, and between the bottom surface and the substructure, under the combined action of horizontal and vertical dead loads is as follows: Figure 16 As shown.

[0088] 3) The capacity requirement ratio in steps (3) and (4) is calculated in relation to the selection of anti-fall beams. The comparative conclusions are as follows: Taking the longitudinal horizontal seismic action and the structural capacity demand ratio as an example. (1) Comparison of conclusions ① The maximum bending strength requirement of the pier bottom section is 5390kNm, which is less than the calculated bending moment of 6467kNm under the equivalent yield state. According to the fortification target requirements under E2 seismic action (severe damage is allowed but collapse is not), the bending strength meets the requirements (the requirement is less than the capacity, which means that the capacity meets the requirement). ② The maximum shear force requirement at the top of the pier is 862kN, which is greater than the calculated shear strength of the plastic hinge zone section at the top of the pier, which is approximately 673kN. Therefore, the shear strength at the top of the pier does not meet the requirements (the requirement is greater than the capacity, indicating that the capacity does not meet the requirement). ③ The maximum horizontal displacement requirement at the top of the pier is 49.49 mm, which is greater than the horizontal displacement of 41.9 mm under the equivalent yield state, but less than the horizontal displacement of 72.35 mm under the protective layer concrete spalling state. The displacement capacity of the pier meets the requirements. ④ The effective shear deformation requirement of the bearing is 68.25mm, which does not meet the 55mm thickness requirement for Class B bridge bearings; ⑤ The longitudinal offset displacement requirement at the beam end is 28.25mm, and the support length meets the requirements.

[0089] (2) Selection of anti-fall beam For linear elastic stops, including steel stops and spring stops, their mechanical relationship model is as follows: Figure 2 As shown (in a single horizontal direction), given that steel and concrete retaining blocks are rigid, their lateral stiffness range is generally greater than 1.0 × 10⁻⁶. 6 The lateral stiffness of the spring stop is on the order of kN / m (simulation results of the stop block); the maximum range of lateral stiffness is controlled within 1.0×10. 5 On the order of kN / m.

[0090] To utilize the limit stop with self-resetting function, the stiffness of the adjustable rigid stop can be set to 1.0 × 10⁻⁶. 3 ~1.0×10 4 The mechanical model of this type of stop exhibits a bilinear mechanical relationship, such as... Figure 3 As shown.

[0091] 4) Determination of mechanical parameters of the anti-fall beam device in steps (5) and (6) Take the linear anti-falling beam device as an example; ① Stiffness requirements under minor earthquake conditions: Based on seismic response and demand calculations, it can be concluded that the requirements are met under minor earthquakes, and the bearing does not need to participate in the work. Since the displacement of the support under minor earthquakes is approximately 24mm, which is less than 50% of the support shear deformation, the 50% shear deformation of the corresponding support can be preliminarily defined as... x 1; ② Stiffness requirements under moderate earthquake conditions: Based on the damage control requirements of each component in Table 2, and combined with the seismic capacity calculation results in step (2), the required anti-fall beam stiffness value is calculated using formula (26). ③ Stiffness requirements under major earthquake conditions: Based on the damage control requirements of each component in Table 2, and combined with the seismic capacity calculation results in step (2), the required anti-fall beam stiffness value is calculated using formula (36). The stiffness of the additional anti-fall beam is approximately 79604 kN / m, corresponding to χ μ The limit shear deformation of the support is set at 55 mm.

[0092] 5) Determination of the mechanical model and parameters of the anti-falling beam device in step (7) Taking linear as an example, the displacement of feature points x 1 is 27.5 mm; χ μ It is 55mm; K LB Take 79000 kN / m; 6) Calculation of seismic response requirements and capacity after adding anti-falling beam device in step (8) The determined anti-falling beam mechanical model and parameters are input into the model for seismic response calculation in step (1). The seismic response of the structure is calculated and compared with the seismic resistance capacity. Based on the damage control indicators in Table 2, it is determined whether the target is met. Taking support deformation as an example: Table 4 shows a comparison of the calculated seismic response results for steel blocks and elastic blocks with linear mechanical properties, or self-resetting blocks with nonlinear mechanical characteristics.

[0093] Table 4. Effectiveness Analysis Results of Anti-Falling Beam Stops Based on Support Deformation Results Table 4 shows that the three types of blocks have different effects on the shear deformation of the support. Comparing the damage control indicators, it can be seen that under minor earthquakes, the self-resetting block controls the support deformation to within 50%, and under major earthquakes, it controls the support deformation to within 100%, meeting the requirements. This device can be adopted. In addition, the linear block can control the support deformation to within 100% under major earthquakes, and under minor earthquakes, it can reduce the initial displacement value at which the anti-fall beam functions, achieving the goal of meeting minor earthquake requirements.

[0094] Although embodiments of the present invention have been disclosed above, they are not limited to the applications listed in the specification and embodiments. They can be applied to various fields suitable for the present invention. For those skilled in the art, other modifications can be easily made. Therefore, without departing from the general concept defined by the claims and their equivalents, the present invention is not limited to the specific details and illustrations shown and described herein.

Claims

1. A method for improving the anti-falling beam function of in-service ductile bridges, characterized in that, Includes the following steps: S1. Seismic performance assessment and parameter acquisition: After establishing the finite element model of the original bridge, nonlinear time history analysis was performed to obtain the horizontal force F at the top of the support, the eccentric displacement λ of the main beam, the horizontal displacement δ at the top of the support, the sliding displacement X of the support, and the horizontal displacement Δ at the top of the pier. c , Residual displacement of bridge piers △ p Bending moment M at key sections of the foundation p and shear force V p Earthquake demand; Calculate the anti-slip force F of the support s =μR, where μ is the friction coefficient of the support interface, taken as 0.1 to 0.2, and R is the vertical force acting on the support; Calculate the lateral stiffness K of the existing support B0 =G×A / Σt, where G is the shear modulus of the rubber bearing, A is the plane area of ​​the bearing, and Σt is the total thickness of the rubber layer of the bearing; The ultimate displacement Δ of the bridge pier was determined by moment-curvature analysis. u and the horizontal displacement of the pier top yield Δ y and the yield horizontal force F of the pier column y Through K y =F y / △ y Calculate the equivalent yield lateral stiffness of the pier column; S2. Multi-level defense standards and damage control target setting: Establish a multi-level seismic fortification standard that includes minor, moderate, and major earthquakes at the E1 level, and set quantified damage state control targets for supports, main beams, and piers at each level: E1 level minor earthquake control target: Foundation bending moment M p <M pu Shear force V p <V pu M pu V pu Based on the flexural and shear bearing capacities; F < F s The displacement at the top of the support δ < 0.5t f , t f The thickness of the rubber layer of the support; The main beam's offset displacement satisfies λ < 0.5t. f ; Horizontal displacement of pier top △ c <△ y ; The leveling control targets for moderate earthquakes fall into the following two categories: When the support does not slide: F < F s And the displacement δ at the top of the support satisfies 0.5t. f ≤δ<t f ; Support sliding condition: F≥F s The total shear deformation and sliding displacement of the support are less than λ. u For the longitudinal direction of the bridge, λ u For the collision clearance between the pier and the anti-fall beam device, λ is the cross-sectional area of ​​the bridge. u The collision gap between the main beam and the anti-fall beam device; The main beam's offset displacement meets the requirement of 0.5t. f ≤λ<λ u ; The following conditions must be met in both cases: Foundation bending moment M p <M pu Shear force V p <V pu ; The main beam's offset displacement meets the requirement of 0.5t. f ≤λ<λ u ; Horizontal displacement and residual displacement Δ at the top of the pier p Satisfies: 0.005L≤△ p =(△ c -△ e )≤0.01L, where L is the effective height of the pier column, △ e The elastic horizontal displacement at the top of the pier is estimated using a bilinear model or by taking Δ. e =F / K y ; E2 level major earthquake control target: Foundation bending moment M p <M pu Shear force V p <V pu ; F≥F s The displacement at the top of the support δ≥t f And the sliding displacement of the support X ≤ X u X u is the distance from the edge of the pad stone to the edge of the support, and is the allowable sliding displacement limit of the support; Main beam offset displacement λ≥λ u ; Horizontal displacement and residual displacement Δ at the top of the pier p Satisfy: 0.01L < △ p ≤0.015L; S3. Seismic performance issue assessment: If any deformation result does not meet the control target set in S2, it is determined that there is a seismic performance problem, reinforcement is required, and steps S4-S7 are performed. S4. Preliminary selection and parameter definition of anti-falling beam device: Choose a mechanical model that is either linear elastic or bilinear for the anti-fall beam device; Lateral stiffness K LB Determined in S6; Ultimate lateral force F of anti-fall beam structure LB =F LB-1 +K LB-2 ×(χ u –χ2);F LB Used to assess the maximum load-bearing capacity of the device and ensure that it does not fail unexpectedly under a major earthquake; Displacement χ1 when it begins to function: Take χ1 = δ p =F s / K B0 And it must satisfy χ1<λ u This is to ensure that the anti-fall beam device can work in a timely manner before or during the sliding of the support; Design limit displacement χ u Take χ u =λ u ; When selecting the bilinear model, the following parameters are further defined: First stage lateral stiffness K LB-1 Its value is determined in S6; First stage control displacement χ2: Take χ2=min(t) f , λ u ); Second stage lateral stiffness K LB-2 Take K LB-2 =n﹒ K LB-1 where n≥10; The first stage of lateral force control value F LB-1 =K LB-1 ×(χ2-χ1); S5. Calculation and Iterative Optimization of Mechanical Parameters for Anti-Beam Falling Device: A mechanical model is established to form a parallel constraint system consisting of the supports and the anti-falling beam device, and a series structure consisting of the constraint system and the bridge pier. The support and the anti-fall beam device form a parallel constraint system with a lateral stiffness of K. 并 =K LB +K B K LB To improve the lateral stiffness of the anti-fall beam device, K B The lateral stiffness of the support; The constraint system and the bridge piers form a series structure with a lateral stiffness of K. 串 =(K 并 ×K c ) / (K 并 +K c ), K c The lateral stiffness of the bridge pier column; Based on the series model and the force-displacement compatibility relationship, the derivation process is as follows: Under horizontal seismic loading, the total horizontal force F of the series structure is... total =K 串 ×(△ c +δ), this force is equal to the horizontal force F acting on the bridge pier. pier =K c ×△ c ,Right now: K 串 ×(△ c +δ)=K c ×△ c ; K 串 =(K 并 ×K c ) / (K 并 +K c Substituting into the above formula, we obtain the formula for calculating the lateral stiffness requirement of a parallel constraint system: K 并 =(△ c / δ)×K c ; The lateral stiffness of the anti-fall beam device or the lateral stiffness of the support are analyzed and determined according to the graded calculation method: E1 level minor earthquake calculation: Let K be the required lateral stiffness of the support at this level. B1 The anti-falling beam device does not participate in the operation. LB =0, at this time K 并 =K B1 lateral stiffness K of bridge pier column c =K y , by K 并 =(△ c / δ)×K c The required lateral stiffness K of the support to meet this leveling performance target is derived. B1 =(△ c / δ)×K y The calculated K B1 The existing support stiffness K calculated in S1 B0 Comparison, if K B0 ≥K B1 If the existing support stiffness meets the E1 level requirement; if K B0 <K B1 If the existing support stiffness is insufficient, additional stiffness K needs to be provided by installing an anti-fall beam device. LB =K B1 -K B0 and this K LB The value is recorded as the E1 leveling design reference value K. LB-E1 ; Leveling calculations for moderate earthquakes fall into two categories: a. Set the required lateral stiffness of the support at this level to K. B2 If the support does not slide, the anti-falling beam device will not work. LB =0, at this time K 并 =K B2 Considering the stiffness reduction of the pier after it enters the elastoplastic state, a stiffness reduction coefficient α is introduced for the pier. At this point, the lateral stiffness K of the pier... c =αK y α is taken as 0.5 to 1; considering the increase in pier top displacement, a pier top horizontal displacement increase coefficient β is introduced, at which time the pier top horizontal displacement Δ c =β△ y β is taken as 1 to 3; considering the increase in support displacement, a support displacement increase coefficient γ is introduced, at which point the horizontal displacement at the top of the support is δ = γt. f γ is taken as 0.5 to 1; by K 并 =(△ c / δ)×K c The required lateral stiffness K of the support to meet this leveling performance target is derived. B2 =(△ c / δ)×K c =β△ y / (γt f )×αK y =η×(△ y / t f )×K y Where η = αβ / γ; the calculated K B2 The existing support stiffness K calculated in S1 B0 Comparison, if K B0 ≥K B2 Then the existing support stiffness meets the requirements under the condition of no slippage during a moderate earthquake; if K B0 <K B2 If the existing support stiffness is insufficient, additional stiffness K needs to be provided by installing an anti-fall beam device. LB =K B2 -K B0 and this K LB The value recorded is the design reference value K for moderate earthquakes without slippage. LB-M1 ; b. If the support slides, the anti-fall beam device needs to be activated. In this case, K 并 =K LB +K B ; Lateral stiffness K of bridge piers c =αK y α is taken as 0.5 to 1; the horizontal displacement Δ at the top of the pier c =β△ y β is taken as 1 to 3; the horizontal displacement of the top of the support is δ = γt f γ takes values ​​of 1 to 2; determined by K 并 =(△ c / δ)×K c The lateral stiffness of the constrained system is derived to be K. 并 =β△ y / (γt f )×αK y =η×(△ y / t f )×K y Where η = αβ / γ; by K 并 =K LB +K B0 The lateral stiffness K of the anti-fall beam device required to meet this level performance target is derived. LB =η×(△ y / t f )×K y –K B0 and this K LB The value recorded is the design reference value K for sliding during moderate earthquakes. LB_M2 ; E2 level earthquake calculation: At this level, the anti-falling beam device is in operation, and at this time K 并 =K LB +K B ; Lateral stiffness of bridge pier K c =αK y α is taken as 0.2 to 0.5; the horizontal displacement Δ at the top of the pier c =β△ y β is taken as 3 to 4; the horizontal displacement of the top of the support is δ = γt f γ is 2; by K 并 =(△ c / δ)×K c The lateral stiffness of the constrained system is derived to be K. 并 =β△ y / (γt f )×αK y =η×(△ y / t f )×K y Where η = αβ / γ; by K 并 =K LB +K B0 The lateral stiffness K of the anti-fall beam device required to meet this level performance target is derived. LB =η×(△ y / t f )×K y -K B0 and this K LB The value is recorded as the E2 leveling design reference value K. LB_E2 ; Final design value of lateral stiffness K for anti-fall beam device LB Determination: A comprehensive comparison of the design reference values ​​K calculated under all levels. LB_E1 K LB_M1 K LB_M2 With K LB_E2 The maximum value among them is taken as the final design value K of the lateral stiffness of the anti-fall beam device. LB ; S6, Final design value K LB Model of anti-falling beam device: If a linear elastic model is chosen, its lateral stiffness K LB That is, take the final design value; If the bilinear model is chosen, its first-stage lateral stiffness K LB-1 Take this final design value and calculate the second-stage lateral stiffness K accordingly. LB-2 First stage lateral force control value F LB-1 ; F LB-1 K LB-1 K LB-2 , χ1, χ2, χ u Together they are given a bilinear mechanical model; S7. Add the defined anti-falling beam device model to the original bridge finite element model; Repeat S1 and S3; If any deformation result does not meet the control target set by S2, and / or the actual force F of the anti-falling beam device obtained through nonlinear time history analysis LB实 Exceeding its ultimate lateral resistance F LB Then adjust the parameters of the anti-fall beam device, including the lateral stiffness K of the linear elastic model. LB , Displacement χ1 when it begins to function, Design limit displacement χ u Or the first-stage lateral stiffness K of the bilinear model LB-1 The second-stage lateral stiffness K of the bilinear model LB-2 , Displacement χ1 when it begins to function, Design limit displacement χ u Then, the nonlinear time history analysis and result verification of this step are repeated until all quantitative and qualitative control objectives are met.

2. The anti-falling beam device designed and installed according to the method for improving the anti-falling beam function of in-service ductile bridges based on multi-level and multi-objective methods as described in claim 1, characterized in that, The anti-falling beam device is selected and set according to the mechanical performance parameters calculated by the anti-falling beam function enhancement method. The anti-falling beam device is installed on the cap beam or the top of the main beam on the outside of the main beam or on the side of the support.

3. The anti-falling beam device as described in claim 2, characterized in that, The anti-fall beam device is a U-shaped steel plate anti-fall beam structure, a steel spring anti-fall beam structure, or a combination of steel bars and springs anti-fall beam structure, installed in the transverse or longitudinal direction of the bridge to limit the lateral or longitudinal displacement of the main beam.

4. The anti-falling beam device as described in claim 2, characterized in that, When the anti-falling beam device adopts a bilinear mechanical model, its second-stage lateral stiffness K LB-2 Compared with the lateral stiffness K of the first stage LB-1 Satisfying the relation: K LB-2 =n﹒ K LB-1 Where n≥10; and the displacement χ1 when the anti-falling beam device starts to function satisfies the condition: χ1=δ p =F s / K B0 This ensures that the anti-fall beam device can intervene in a timely manner when or before the support slides.

5. The anti-falling beam device as described in claim 2, characterized in that, An initial installation gap is provided between the anti-fall beam device and the main beam or support it restricts. The width of the initial installation gap is not less than the displacement value χ1 when the anti-fall beam device begins to function, and not greater than the limit displacement value λ of the main beam. u .

6. The anti-falling beam device as described in claim 2, characterized in that, The anti-falling beam device is a self-resetting stop block, and its mechanical model is a bilinear mechanical model; after a major earthquake, the anti-falling beam device can rely on its own elastic restoring force to reset the main beam to near its initial position.

7. The anti-falling beam device as described in claim 2, characterized in that, The anti-falling beam device is a self-resetting stop block, and its first-stage lateral stiffness K LB-1 The value range is 1.0 × 10. 3 -1.0×10 4 kN / m.

8. The anti-falling beam device as described in claim 2, characterized in that, The connection between the anti-falling beam device and the main structure of the bridge is a non-rigid connection, provided by hinged or flexible connecting elements.

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