A method and system for evaluating seismic toughness of railway beam bridges

Abstract

The present invention discloses a method and system for evaluating the seismic toughness of a railway beam bridge, relates to the technical field of bridge engineering structures, and solves the technical problem that the prior art lacks a seismic toughness evaluation method suitable for railway bridges; the present invention comprises establishing a nonlinear finite element model of the entire bridge for vulnerability analysis; according to the vulnerability result, using damage probability weighted quantification of component damage status and traffic function damage status; determining the post-earthquake repair time and function recovery value, obtaining a post-earthquake bridge traffic function recovery curve, and finally obtaining the bridge toughness index and dividing the bridge function status into three levels; the present invention proposes a full-process solution for railway beam bridges of "bridge design parameters-nonlinear time history analysis-probabilistic earthquake demand model-vulnerability analysis-traffic function recovery-toughness index-seismic toughness three levels", providing a reference for pre-earthquake design and post-earthquake emergency repair decisions.

Description

Technical Field

[0001] The invention relates to the technical field of bridge engineering structures, and in particular to a method and system for evaluating the seismic toughness of a railway beam bridge. Background Art

[0002] The existing bridge (structure) seismic fortification concept of "no damage in small earthquakes, repairable in medium earthquakes, and not collapsing in large earthquakes" has put forward requirements for the seismic fortification level of bridges at the macro level. As an important rescue channel, the degree of post-earthquake function loss and the time required for function recovery are crucial to earthquake rescue, especially for the railway transportation network where bridges account for a high proportion. The damage of railway bridges under strong earthquakes will directly affect the traffic function of the entire line. At present, the seismic resilience evaluation method is mainly aimed at building structures, such as GB / T 38591-2020 "Standard for Evaluation of Seismic Resilience of Buildings" and FEMA-P58. The following problems will arise when using the building structure seismic resilience evaluation method to evaluate railway bridges: (1) The building structure is quite different from the bridge structure. The building structure damage and resilience evaluation index cannot describe the characteristics of bridge damage, and the evaluation index system needs to be reconstructed; (2) The function of a bridge is to ensure the safe passage of trains at a certain speed, while the main function of a building is to ensure the safety of personnel and its ancillary functions (such as the function of a hospital building structure to ensure its provision of medical services). The quantification of the post-earthquake function of a railway bridge needs to be redefined; (3) The building resilience level is determined by comprehensively considering the repair cost, repair time and casualties, which is not very suitable for railway bridges. The commonly used comprehensive index resilience index is a normalized quantity that cannot intuitively reflect the post-earthquake traffic function status. Therefore, the above three issues need to be focused on. Summary of the invention

[0003] In order to solve the above problems existing in the prior art, the present invention provides a method and system for evaluating the seismic toughness of railway beam bridges, which solves the technical problem that the prior art lacks a seismic toughness evaluation method suitable for railway bridges.

[0004] A method for evaluating the seismic toughness of a railway beam bridge, comprising:

[0005] Step 1: Establish a nonlinear finite element model of the entire bridge to simulate and output the seismic response of key bridge components. Based on the mapping relationship between the seismic response of key bridge components and the beam-track deformation, calculate the track irregularity. V ,The key components of bridges include piers, bearings and tracks;

[0006] Step 2: Based on the pier analysis results of seismic waves, a logarithmic scatter plot of seismic intensity and pier curvature ductility coefficient is established. Based on the support analysis results of seismic waves, a logarithmic scatter plot of seismic intensity and support displacement is established. Based on the track irregularity analysis results of seismic waves, a logarithmic scatter plot of seismic intensity and track irregularity V is established. The three scatter plots are linearly regressed to establish the response probability seismic demand model of each key bridge component.

[0007] Step 3: Combine the response probability seismic demand model of key bridge components to calculate the damage exceedance probability of key bridge components under different damage states, normalize the damage rate threshold of key bridge components based on the capacity threshold; and calculate the bridge bearing weights based on the damage exceedance probability and damage rate threshold. Q LB , Bridge pier damage rate Q LP and loss of bridge traffic function Q L , establish the loss evolution curve of key bridge components under different earthquake motion intensities;

[0008] Step 4: Loss based on the passing function Q L Obtaining residual traffic function of bridges after earthquake Q r , Calculate the repair time of components after earthquake T rej ( j =1,2,3); calculate the traffic function value of each key bridge component after complete repair Q r1 、Q r2 and Q r3 , and finally establish the post-earthquake traffic function recovery curve;

[0009] Step 5: Calculate the seismic toughness index of the bridge, and then obtain the minimum seismic intensity for the bearings and piers to reach the complete destruction level and the minimum seismic intensity for the track to reach the slight damage level and complete destruction level based on the loss evolution curves of each key bridge component under different seismic motion intensities and the post-earthquake traffic function recovery curve; determine the boundary values ​​of the three levels of seismic toughness of the bridge based on the seismic motion intensity-seismic toughness index curve, namely: normal traffic, speed limit traffic and structural safety.

[0010] Furthermore, the step 1 comprises:

[0011] Step 1.1: Establish a nonlinear finite element model of the entire bridge based on the bridge design parameters;

[0012] Considering the nonlinear mechanical characteristics of key components, the supports are simulated using nonlinear units; the piers are simulated using nonlinear fiber units, and the main beams are simulated using beam units;

[0013] Step 1.2: Determine the target response spectrum curve according to the bridge site conditions;

[0014] Step 1.3: Based on the target response spectrum curve, select no less than 60 seismic waves from PEER and input them into the finite element model to carry out nonlinear time history analysis; the three-way seismic wave input intensity amplitude ratio is transverse bridge direction: longitudinal bridge direction: vertical = 1.0: 0.85: 0.65

[0015] Step 1.4: Output the relative displacement of the main beam end at the expansion joint, the bearing deformation and the curvature of the pier bottom section As the seismic response of the key bridge components, the relative displacement of the main beam end at the expansion joint includes the peak displacement D r and residual displacement D p ;

[0016] Step 1.5: Calculate track irregularity based on beam-track deformation mapping V .

[0017] Furthermore, the calculation formula of the track irregularity V is as follows:

[0018] (1)

[0019] In the formula, D r is the peak displacement, D p is the residual displacement, g 0- g 4 is the calculation of intermediate parameters.

[0020] Furthermore, the step 2 comprises:

[0021] Step 2.1: Analyze the cross section of the pier bottom, establish the cross-sectional strain-curvature curve, and obtain the initial yield curvature corresponding to the yield of the longitudinal reinforcement of the pier. ;

[0022] Step 2.2: Calculate the curvature ductility coefficient of the pier according to the curvature φ of the bottom section of the pier under earthquake action , as shown in formula (2);

[0023] (2)

[0024] Step 2.3: Take the logarithm of the seismic intensity of each ground motion and the deformation of the model support, the curvature ductility coefficient of the bridge pier, and the V value of the track irregularity under its action, and establish a logarithmic scatter plot of the seismic intensity (IM) and the seismic response (EDP);

[0025] Step 2.4: Perform linear regression on the logarithmic scatter cloud to establish the probabilistic earthquake demand model of the bearing, pier and track response, as shown in formula (3);

[0026] (3)

[0027] In the formula, a , b are the regression parameters of the probabilistic earthquake demand model.

[0028] Furthermore, the step 3 comprises:

[0029] Step 3.1: Classify the damage status of each key bridge component into five levels: no damage, slight damage, moderate damage, severe damage and complete destruction, and determine the corresponding control indicators. The control indicator parameters of the pier include longitudinal steel bar strain and concrete strain, the control indicator parameters of the support include support displacement, and the control indicator parameter of the track is track irregularity;

[0030] Step 3.2: The vulnerability analysis calculation is shown in equations (4)-(5);

[0031] (4)

[0032] (5)

[0033] In the formula, S c is the mean value of the seismic capacity of structural components; is the logarithmic standard deviation of the seismic capacity of the components; is the logarithmic standard deviation of the component seismic response; EDP i For the i Seismic response under the action of seismic waves; N is the number of input seismic waves; IM is the earthquake intensity; EDP is the earthquake response; a , b are the regression parameters of the probabilistic earthquake demand model.

[0034] Furthermore, the step 3 also includes:

[0035] Step 3.3: Calculate the damage rate threshold of each key bridge component L 1 i , L 2 i , L3 i , Equations (6)-(8) correspond to the support, pier and track respectively;

[0036] (6)

[0037] (7)

[0038] (8)

[0039] Where: D c is the allowable seismic displacement of the bearing; D i For the support i The support deformation threshold for each damage state; μ i For the bridge pier i The cross-sectional curvature ductility coefficient for each damage state; V d_max Design the maximum speed for the line, V min Design speed for the line; V r The residual speed after the earthquake, is the ductility coefficient threshold of complete destruction;

[0040] Step 3.4: Based on the results of the fragility analysis, the bearing is calculated using the weighted damage exceedance probability ( Q LB )、bridge pier performance loss( Q LP ) and loss of bridge traffic function ( Q L ), refer to equations (9) to (12) for calculation;

[0041] (9)

[0042] (10)

[0043] (11)

[0044] (12)

[0045] Where: P f (i) represents the damage exceedance probability function; P DS1 , P DS2 , P DS3 , P DS4They correspond to the probability of exceeding slight damage, moderate damage, severe damage, and complete destruction respectively;

[0046] Step 3.5: Under a given ground motion intensity, when Q L Exceeds the threshold of the corresponding damage state L i ( i =1,2,3) that is, the corresponding damage state is reached; in particular, it is a conservative estimate of the judgment of the complete destruction state, that is, Q L More than 0.85 L 4 is considered to be completely destroyed.

[0047] Furthermore, the step 4 comprises:

[0048] Step 4.1: Calculate the residual traffic function after the earthquake Q r ;

[0049] (13)

[0050] Step 4.2: Calculate the time required to repair supports, piers and tracks after an earthquake ;

[0051] (14)

[0052] In the formula, represents the damage exceedance probability function, T i is the repair time required for the component to reach the i-th damage state;

[0053] Step 4.3: Calculate the traffic function value after the piers, bearings and tracks are fully repaired Q r1 、Q r2 and Q r3 ;

[0054] (15)

[0055] (16)

[0056] (17)

[0057] Step 4.4: Establish the post-earthquake bridge traffic function recovery curve;

[0058] (18)

[0059] Where Q(t) is the functional recovery function, t represents the time after the earthquake, t0 is the start time of repair, t1 is the completion time of the repair of the first type of components, t2 is the completion time of the repair of the second type of components, and t3 is the completion time of the repair of the third type of components.

[0060] Furthermore, the step 5 comprises:

[0061] Step 5.1: Calculate the bridge seismic resilience index R;

[0062] (19)

[0063] (20)

[0064] In the formula, T re is the total time for post-earthquake repair.

[0065] Step 5.2: Based on the bearing and pier damage evolution curves and the traffic function damage evolution curves, calculate the seismic intensity of the bearing and pier to achieve 85% damage rate as the minimum seismic intensity for structural safety. PGA b4 and PGA p4 ;

[0066] Step 5.3: Based on the bearing and pier damage evolution curves and the traffic function damage evolution curves, the seismic intensity at which the traffic function loss rate reaches slight damage and 85% damage rate is calculated as the driving safety threshold, which are PGA t1 and PGA t4 ;

[0067] Step 5.4: Based on the seismic intensity-seismic resilience index curve, calculate PGA t1 , PGA t4 and min( PGA b4 , PGA p4 ) corresponding to the toughness index R 1. R 2 and R 3. So far, the seismic toughness is divided into three levels and the corresponding seismic toughness index thresholds are obtained.

[0068] A railway beam bridge seismic toughness evaluation system includes: a simulation module, a model building module, a loss evolution analysis module, a function recovery analysis module and an evaluation module.

[0069] The simulation module is used to establish a nonlinear finite element model of the whole bridge to simulate and output the seismic response of key bridge components, and calculate the track irregularity V based on the seismic response of key bridge components and the beam-track deformation mapping relationship. The key bridge components include piers, bearings and tracks;

[0070] The model building module is used to establish a logarithmic scatter plot of seismic intensity and pier curvature ductility coefficient based on the pier analysis results of seismic waves, establish a logarithmic scatter plot of seismic intensity and bearing displacement based on the support analysis results of seismic waves, establish a logarithmic scatter plot of seismic intensity and track irregularity V based on the track irregularity analysis results of seismic waves, and perform linear regression on the above three scatter plots to establish a response probability seismic demand model for each key bridge component;

[0071] The loss evolution analysis module is used to calculate the damage exceedance probability of key bridge components and normalize the damage rate threshold of key bridge components based on the capacity threshold. L1 i , L2 i and L3 i ; Using damage probability weighted calculation to calculate bridge bearings Q LB , Bridge pier damage rate Q LP and loss of bridge traffic function Q L , establish the loss evolution curve of key bridge components under different earthquake motion intensities;

[0072] The function recovery analysis module is used to analyze the loss of traffic function according to the Q L Obtaining residual traffic function of bridges after earthquake Q r , Calculate the repair time of components after earthquake T rej ( j =1,2,3); calculate the bridge traffic function value after each key bridge component is fully repaired Q r1 、Q r2 and Q r3 , based on the above calculations, establish the bridge post-earthquake traffic function recovery curve;

[0073] The evaluation module is used to obtain the minimum seismic intensity for bearings and piers to reach complete destruction level, and the minimum seismic intensity for tracks to reach slight damage level and complete destruction level based on the loss evolution curves of each key bridge component under different seismic motion intensities and the bridge post-earthquake traffic function recovery curve; based on the seismic motion intensity-seismic toughness index curve, determine the boundary values ​​of three levels of seismic toughness of the bridge, namely: normal traffic, speed limit traffic and structural safety.

[0074] The beneficial effects of the present invention include:

[0075] The present invention proposes an evaluation index system for seismic toughness of railway beam bridges, a method for quantifying the damage state of components and traffic functions based on vulnerability, and a three-level classification method for seismic toughness based on toughness index, and establishes a framework and process for seismic toughness evaluation methods. A full-process solution for railway beam bridges, "bridge design parameters-nonlinear time history analysis-probabilistic earthquake demand model-vulnerability analysis-traffic function recovery-toughness index-three-level seismic toughness", is proposed to provide a reference for pre-earthquake design and post-earthquake emergency repair decisions. BRIEF DESCRIPTION OF THE DRAWINGS

[0076] Figure 1 The finite element analysis model of the bridge involved in the embodiment.

[0077] Figure 2 This is the constitutive structure of the fiber material of the pier involved in the embodiment.

[0078] Figure 3 This is the support structure involved in the embodiment.

[0079] Figure 4 This is the constitutive structure of the interaction between the main beam, abutment and block involved in the embodiment.

[0080] Figure 5 Schematic diagram of the target response spectrum curve involved in the embodiment.

[0081] Figure 6 Schematic diagram of 100 natural earthquake wave response spectrum curves involved in the embodiment.

[0082] Figure 7 Schematic diagram of relative displacement of the ends of the main beam in response to earthquakes involved in the embodiment.

[0083] Figure 8 Schematic diagram of support displacement in earthquake response according to the embodiment.

[0084] Fig. 9 is the curvature of the seismic response pier bottom section involved in the embodiment.

[0085] Fig.10 It is a schematic diagram of track irregularity involved in the embodiment.

[0086] Fig.11 Schematic diagram of the cross-sectional strain-curvature curve involved in the embodiment.

[0087] Fig.12 The figure is a logarithmic scatter diagram of the curvature ductility coefficient of the 14m bridge pier involved in the embodiment and a probabilistic earthquake demand model diagram.

[0088] Fig.13 It is a logarithmic scatter diagram of the first span support displacement and the probabilistic seismic demand model diagram involved in the embodiment.

[0089] Fig.14 It is a logarithmic scatter plot of the seismic intensity and track irregularity involved in the embodiment.

[0090] Fig.15 Figure 2 is the fragility curve of the 14m, 12m and 8m piers involved in the embodiment.

[0091] Fig.16 is the first span support fragility curve involved in the embodiment.

[0092] Fig.17 It is the vulnerability curve of the traffic function at the expansion joint of the abutment and pier involved in the embodiment.

[0093] Fig.18 It is the damage evolution curve of the bridge pier involved in the embodiment.

[0094] Fig.19 It is the bearing damage evolution curve involved in the embodiment.

[0095] Fig. 20 It is the evolution curve of the traffic function damage involved in the embodiment.

[0096] Fig.21 The remaining function of the embodiment is Q r Schematic diagram.

[0097] Fig. 22 It is a schematic diagram of the repair time of the bearings, piers and tracks after the earthquake involved in the embodiment.

[0098] Fig.23 It is a schematic diagram of the post-earthquake traffic function recovery curve involved in the embodiment.

[0099] Fig.24 It is a schematic diagram of the seismic toughness index curve involved in the embodiment.

[0100] Fig.25 The present invention is a flow chart of a method for evaluating the seismic toughness of a railway beam bridge according to an embodiment. DETAILED DESCRIPTION

[0101] In order to make the purpose, technical scheme and advantages of the embodiments of the present application clearer, the technical scheme in the embodiments of the present application will be clearly and completely described below in conjunction with the drawings in the embodiments of the present application. Obviously, the described embodiments are only part of the embodiments of the present application, rather than all of the embodiments. Therefore, the following detailed description of the embodiments of the present application provided in the drawings is not intended to limit the scope of the application for protection, but merely represents the selected embodiments of the present application. Based on the embodiments of the present application, all other embodiments obtained by those skilled in the art without making creative work belong to the scope of protection of the present application.

[0102] A method for evaluating the seismic toughness of railway beam bridges, such as Fig.25 As shown, including:

[0103] Step 1: Establish a nonlinear finite element model of the entire bridge to simulate and output the seismic response of key bridge components. Based on the mapping relationship between the seismic response of key bridge components and the beam-track deformation, calculate the track irregularity. V ,The key components of bridges include piers, bearings and tracks;

[0104] Step 2: Based on the analysis results of the bridge piers by seismic waves, establish a logarithmic scatter plot of the seismic intensity and the ductility coefficient of the bridge pier curvature. Based on the analysis results of the bearings by seismic waves, establish a logarithmic scatter plot of the seismic intensity and the bearing displacement. Based on the analysis results of the track irregularity by seismic waves, establish a logarithmic scatter plot of the seismic intensity and the track irregularity. V Logarithmic scatter plot, linear regression is performed on the above three scatter plots to establish the response probability seismic demand model of each key bridge component;

[0105] Step 3: Combine the response probability seismic demand model of key bridge components to calculate the damage exceedance probability of key bridge components under different damage states, normalize the damage rate threshold of key bridge components based on the capacity threshold; and calculate the bridge bearing weights based on the damage exceedance probability and damage rate threshold. Q LB , Bridge pier damage rate Q LP and loss of bridge traffic function Q L , establish the loss evolution curve of key bridge components under different earthquake motion intensities;

[0106] Step 4: Loss based on the passing function Q L Obtaining residual traffic function of bridges after earthquake Q r , Calculate the repair time of components after earthquake T rej ( j =1,2,3); calculate the traffic function value of each key bridge component after complete repairQ r1 、Q r2 and Q r3 , and finally establish the post-earthquake traffic function recovery curve;

[0107] Step 5: Calculate the seismic toughness index of the bridge, and then obtain the minimum seismic intensity for the bearings and piers to reach the complete destruction level and the minimum seismic intensity for the track to reach the slight damage level and complete destruction level based on the loss evolution curves of each key bridge component under different seismic motion intensities and the post-earthquake traffic function recovery curve; determine the boundary values ​​of the three levels of seismic toughness of the bridge based on the seismic motion intensity-seismic toughness index curve, namely: normal traffic, speed limit traffic and structural safety.

[0108] In another embodiment, the step 1 comprises:

[0109] Step 1.1: Establish a nonlinear finite element model of the entire bridge based on the bridge design parameters;

[0110] Considering the nonlinear mechanical characteristics of key components, the supports are simulated using nonlinear units; the piers are simulated using nonlinear fiber units, and the main beams are simulated using beam units;

[0111] In this embodiment, the bridge span is 32×5m, the main beam adopts ballastless double-track precast concrete box beam, the main beam is 11.6m wide and 2.6m high, C50 concrete is used, the second phase of the bridge deck dead load is 120 kN / m, the expansion joint gaps at the piers and abutments are 10cm and 20cm respectively, and the transverse gap between the block and the main beam is 5cm. Four bearing spherical steel bearings are arranged in each span, one side is a longitudinal sliding bearing, and the other side is a fixed bearing. The pier heights are 8, 14, 12, and 8m respectively, and the cross-section round-end solid piers are made of C35 concrete. HRB400 steel bars with a diameter of 25mm are arranged longitudinally, and the stirrups are HRB400 steel bars with a diameter of 12mm.

[0112] The bearings exhibit bilinear mechanical behavior characteristics under earthquake action, which is a bilinear constitutive model. The yield force of the fixed bearing is 750 kN, the yield displacement is 2.5 mm, and the post-bend stiffness is 0.001. The yield force of the sliding bearing is 75 kN, the yield displacement is 2.5 mm, and the post-bend stiffness is 0.001. The bridge piers are simulated by nonlinear fiber elements (Nonlinear Beam-ColumnElement), the concrete adopts the Kent-Part constitutive model, and the steel bars adopt the Steel02 constitutive model. The main beam is simulated by elastic beam-column elements (Elastic Beam-Column Element). The interaction between the main beam and the block and abutment is simulated by elastic-plastic elements with gaps. Nonlinear finite element modeling information reference Figure 1-4, Figure 2 middle f c , ε c , f s , ε s and E s are concrete stress, concrete strain, steel stress, steel strain and steel elastic modulus respectively; Figure 3 middle F and d are the support horizontal force and displacement respectively; Figure 4 middle f , 、gap1、gap2、 f y1 , f y2 , E and E a They are the interaction force between the main beam and the block or the abutment, the deformation of the block or the abutment, the gap between the main beam and the block, the gap between the main beam and the abutment, the yield force of the block, the yield force of the abutment, the stiffness of the block and the stiffness of the abutment.

[0113] Step 1.2: Determine the target response spectrum curve according to the bridge site conditions;

[0114] Refer to Section 5.2 of the Code for Seismic Design of Highway Bridges (JTG / T 2231-01—2020) to calculate the target response spectrum curve, such as Figure 5 As shown;

[0115] Step 1.3: Based on the target response spectrum curve, select no less than 60 earthquake waves from PEER (Pacific Earthquake Engineering Research, PEER) and input them into the finite element model to carry out nonlinear time history analysis;

[0116] In this embodiment, 100 natural earthquake waves are selected, and the earthquake wave response spectrum curve is as follows: Figure 6 Some seismic wave information is shown in Table 1.

[0117] Table 1 Input seismic wave information table (partial)

[0118]

[0119] Step 1.4: Output the relative displacement of the main beam end at the expansion joint, the bearing deformation and the curvature of the pier bottom section As the seismic response of the key bridge components, the relative displacement of the main beam end at the expansion joint includes the peak displacement Dr and residual displacement D p , see Figure 7 , a total of 600 groups of results; since the supports are divided into fixed direction and sliding direction, the horizontal yield force of the fixed direction support is larger, and the seismic capacity value is different from the sliding direction, so the maximum displacement of the fixed direction and sliding direction of each span support is output separately, see Figure 8 , a total of 500 sets of results; record the cross-sectional curvature of the pier bottom in the longitudinal and transverse directions of the 4 piers, see Fig. 9 A total of 400 sets of results.

[0120] Step 1.5: Based on the beam-track deformation mapping relationship, Figure 7 The peak displacement D r and residual displacement D p Substitute the result into formula (1) to calculate the track irregularity V .

[0121] In another embodiment, the calculation formula of the track irregularity V is as follows:

[0122] (1)

[0123] In the formula, D r is the peak displacement, D p is the residual displacement, g 0- g 4 is the calculation of intermediate parameters.

[0124] The peak displacement of 100 seismic waves was obtained by analyzing the nonlinear finite element model. D r and residual displacement D p Substitute into equation (1) to calculate the track irregularity, as Fig.10 shown.

[0125] In another embodiment, the step 2 comprises:

[0126] Step 2.1: Analyze the cross section of the pier bottom, establish the cross-sectional strain-curvature curve, and obtain the initial yield curvature corresponding to the yield of the longitudinal reinforcement of the pier. ;

[0127] In this embodiment, the cross section of the pier bottom is established according to XTRACT, and the vertical force is applied to analyze the cross section of the pier bottom. The cross section strain-curvature curve is established to obtain the initial yield curvature corresponding to the first yield of the longitudinal reinforcement of the pier. , the initial yield curvatures in the longitudinal and transverse directions are 1.36E-03 and 4.48E-04, respectively. Fig.11 As shown, the vertical axis is the strain, which is a dimensionless variable.

[0128] Step 2.2: According to the curvature of the bottom section of the pier under earthquake action , calculate the ductility coefficient of the pier curvature , as shown in formula (2);

[0129] (2)

[0130] Step 2.3: The earthquake intensity of each earthquake and the deformation of the model support, the ductility coefficient of the pier curvature, and the track irregularity under its action are calculated. V The values ​​are taken logarithmically, and the logarithmic scatter plot of ground motion intensity (PGA) and earthquake response (EDP) is established;

[0131] The maximum curvature ductility coefficient of the bottom section of piers #1 to #4 under each seismic wave input is taken as the seismic response value of the pier. Based on the analysis results of the piers of 100 waves, the seismic intensity ( PGA ) and the logarithmic scatter plot of the ductility coefficient of the pier curvature, such as Fig.12 shown, specific Fig.12 Disp in the equation represents the curvature ductility coefficient of the pier. ;

[0132] Based on the support analysis results of 100 waves, the earthquake intensity ( PGA ) and the logarithmic scatter plot of support displacement. Since there are many supports, only the results of the first span support are shown here, such as Fig.13 shown, specific Fig.13 Disp in represents the first cross-branch displacement;

[0133] Based on the track irregularity analysis results of 100 seismic waves, the seismic intensity ( PGA ) and track irregularity V Logarithmic scatter plot, such as Fig.14 As shown;

[0134] Step 2.4: Perform linear regression on the logarithmic scatter cloud to establish the probabilistic earthquake demand model of the bearing, pier and track response, as shown in formula (3);

[0135] (3)

[0136] In the formula, EDP For earthquake response, a , b are the regression parameters of the probabilistic earthquake demand model, IM is the earthquake intensity, IM The earthquake acceleration can be expressed as PGA )、seismic velocity( PGV )、seismic spectrum acceleration( S a ), this embodiment uses PGA .

[0137] Specifically, in this embodiment, the regression model parameters of 5 span supports, 4 bridge piers, and 6 beam joint tracks are shown in Table 2;

[0138] Table 2 Probabilistic earthquake demand model parameters

[0139]

[0140] In another embodiment, the step 3 comprises:

[0141] Step 3.1: Classify the damage status of each key bridge component into five levels: no damage, slight damage, moderate damage, severe damage and complete destruction, and determine the corresponding control indicators. The control indicator parameters of the pier include longitudinal steel bar strain and concrete strain, the control indicator parameters of the support include support displacement, and the control indicator parameter of the track is track irregularity;

[0142] Specifically, the indicators are as follows:

[0143] Table 3 Bridge pier damage standards and control indicators

[0144]

[0145] Remark: ɛ s is the longitudinal reinforcement strain; ɛ c is the concrete strain; μ 1, μ 2, μ 3, μ 4 are the ductility coefficient thresholds for the piers reaching slight damage, moderate damage, severe damage, and complete destruction, respectively.

[0146] Table 4 Bearing damage standards and control indicators

[0147]

[0148] Remark: d For support seat displacement; D 0 is the normal displacement allowed by the support; D C Allowable seismic displacement of the bearing.

[0149] Table 5 Track damage standards and control indicators

[0150]

[0151] With reference to Code for Seismic Design of Railway Engineering (GB 50111-2006 (2009 Edition)), the threshold values ​​of the roughness index are shown in Table 6.

[0152] The support of the implementation example allows normal displacement in the sliding direction and the fixed direction D 0 are 60mm and 3mm respectively, and the bearing allows earthquake displacement D C It is 150mm, referring to the support damage classification standard, and the support damage threshold is shown in Table 6.

[0153] according to Figure 6 The cross-sectional strain-curvature curve is shown in Table 6, with reference to the pier damage classification standard. The curvature ductility coefficient thresholds under various damage states of the pier are shown in Table 6.

[0154] Table 6 Damage standards and thresholds for bearings, piers and tracks

[0155]

[0156] Step 3.2: Vulnerability is the probability of exceeding the seismic capacity value under a given ground motion intensity. P , can be calculated by equations (4) to (5). The mean seismic capacity of structural components S c According to the values ​​in Table 3, the logarithmic standard deviation of the seismic capacity of the components is generally taken as 0.5. EDP are bearing displacement, pier curvature ductility coefficient and track irregularity, and the number of seismic waves N is 100, the vulnerability calculation results under different earthquake motion intensities are as follows Figure 15-17 shown; Fig.15 is the fragility curve of piers with different pier heights; Fig.17 Corresponding to the traffic function vulnerability curves at different beam joints, there are two types of abutment and pier expansion joints, numbered #0, #1, #2, #3, #4, and #5.

[0157] (4)

[0158] (5)

[0159] In the formula, P contains P DS1 , P DS2 , P DS3 , P DS4 , divided into five damage states, with four thresholds corresponding to the damage exceedance probability P DS1 , PDS2 , P DS3 , P DS4 , S c is the mean value of the seismic capacity of structural components; is the logarithmic standard deviation of the seismic capacity of components; is the logarithmic standard deviation of the component seismic response; EDP for earthquake response; EDP i For the i The seismic response under the action of seismic waves ( i =1~100); N is the number of input seismic waves.

[0160] In another embodiment, the step 3 further comprises:

[0161] Step 3.3: Calculate the key components of each bridge in the i The loss rate threshold under the damage state L 1 i , L 2 i , L 3 i , calculation formulas (6)-(8) correspond to the bearing, pier and track respectively;

[0162] (6)

[0163] (7)

[0164] (8)

[0165] Where: Dc is the allowable seismic displacement of the bearing; D i For the support i The support deformation threshold for each damage state; D i (i=1, 2, 3, 4) are D 0 , D C , 2D C , 3.3D C , μ i For the bridge pier i The cross-sectional curvature ductility coefficient for each damage state. V d_max The maximum speed of the line design (this patent is for conventional railways, and the value is 200km / h), Vmin is the line design speed (45km / h); V r Residual speed after earthquake;

[0166] In specific implementation, formula (6) includes:

[0167] Fixed support:

[0168] (6.1)

[0169] Sliding support:

[0170] (6.2)

[0171] Formula (7) includes:

[0172] Pier longitudinal direction:

[0173] (7.1)

[0174] Pier Horizontal:

[0175] (7.2)

[0176] Formula (8) is:

[0177] track:

[0178] (8)

[0179] Step 3.4: Based on the results of the fragility analysis, calculate the bearing weights based on the damage exceedance probability and damage rate threshold ( Q LB )、bridge pier performance loss( Q LP ) and loss of bridge traffic function ( Q L ), the calculation reference equations (9) to (12), the loss evolution curves of bearings, piers and traffic functions (tracks) under different earthquake motion intensities are as follows: Figure 18-20 ,In the figure, DS-1 corresponds to slight damage, DS-2 corresponds to moderate damage, DS-3 corresponds to severe damage, and DS-4 corresponds to complete destruction;

[0180] (9)

[0181] (10)

[0182] (11)

[0183] (12)

[0184] Where: P f (i) represents the damage exceedance probability function; P DS1 , P DS2 , P DS3 , P DS4 They correspond to the probability of exceeding slight damage, moderate damage, severe damage, and complete destruction respectively;

[0185] Step 3.5: Under a given earthquake intensity, when the bearings, piers and traffic functions exceed the threshold of the corresponding damage state, the corresponding damage state is reached.

[0186] In another embodiment, step 4 comprises:

[0187] Step 4.1: When the earthquake intensity PGA = 0.4g, calculate the residual traffic function Q after the earthquake according to formula (13): r , functional residual under other earthquake intensities Qr The calculation results are as follows Fig.21 As shown;

[0188] (13)

[0189] Step 4.2: When the earthquake intensity PGA =0.4g, the repair time of the bearings, piers and tracks after the earthquake is calculated according to formula (14). T rej (j=1,2,3), the component repair time results under other earthquake intensities are as follows Fig. 22 As shown;

[0190] (14)

[0191] In the formula, represents the damage exceedance probability function, T i is the repair time required for the component to reach the i-th damage state;

[0192] Step 4.3: The post-earthquake repair of bridge components is generally carried out in the order of piers-supports-tracks. After the repair of a single type of component is completed, the bridge's traffic function is restored according to a step function. The contributions of piers, supports, and tracks to the restoration of traffic function are 0.7, 0.2, and 0.1, respectively. PGA = 0.4g, calculate the traffic function value after the piers, supports and tracks are completely repaired Q r1 、 Q r2 andQ r3 , as shown in equations (15) to (17), the bridge traffic function recovery value under other earthquake motion intensities can be calculated by referring to this method;

[0193] (15)

[0194] (16)

[0195] (17)

[0196] Step 4.4: When the earthquake intensity PGA =0.3g, the bridge traffic function recovery curve function is as shown in formula (18), and the bridge traffic function recovery curve under other earthquake motion intensities is as follows Fig.23 As shown;

[0197] (18)

[0198] Where Q(t) is the function recovery function, t represents the time after the earthquake, t0 is the start time of repair, t1 is the time when the repair of the first type of components (supports or piers) is completed, t2 is the time when the repair of the second type of components (supports or piers) is completed, and t3 is the time when the repair of the third type of components (tracks) is completed.

[0199] In another embodiment, step 5 comprises:

[0200] Step 5.1: When the earthquake intensity PGA =0.4g, the bridge seismic toughness index is calculated according to formulas (19) to (20). R The value is 0.83. The values ​​of bridge seismic toughness index under other earthquake intensities are as follows: Fig.24 As shown;

[0201] (19)

[0202] (20)

[0203] In the formula, T re is the total time for post-earthquake repair.

[0204] Step 5.2: Based on the bearing and pier damage evolution curves and the traffic function damage evolution curves, calculate the seismic intensity of the bearing and pier to achieve 85% damage rate as the minimum seismic intensity for structural safety. PGA b4 and PGA p4 ;

[0205] Based on the determination of bearings and piers respectively L=The earthquake intensity with a damage rate of 0.85% is taken as the minimum earthquake intensity for structural safety. PGA b4 and PGA p4 They are 1.64g and 1.78g respectively, which means the minimum earthquake intensity for structural safety is 1.64g;

[0206] Step 5.3: Based on the bearing and pier damage evolution curves and the traffic function damage evolution curves, the seismic intensity at which the traffic function loss rate reaches slight damage and 85% damage rate is calculated as the driving safety threshold, which are PGA t1 and PGA t4 ;

[0207] The earthquake intensity at which the loss rate of traffic function reaches slight damage and 85% damage rate is determined as the driving safety threshold. PGA t1 and PGA t4 0.46g and 1.15g respectively;

[0208] Step 5.4: Based on the seismic intensity-seismic resilience index curve, calculate PGA t1 , PGA t4 and min( PGA b4 , PGA p4 ) corresponding to the toughness index R 1. R 2 and R 3. So far, the three levels of bridge seismic toughness are divided and the corresponding seismic toughness index thresholds are obtained;

[0209] like Fig.24 As shown, confirm PGA t1 , PGA t4 and min( PGA b4 , PGA p4 ) corresponding to the toughness index R 1. R 2 and R 3 is 0.78, 0.32 and 0.23. If an earthquake occurs, if the toughness of the bridge after the earthquake is less than 0.23, the structure of the bridge will fail. If the toughness of the bridge after the earthquake is greater than 0.23, the structure of the bridge is considered safe. Under the premise of the safety of the bridge structure, if the toughness of the bridge is greater than 0.32 and less than 0.78, vehicles can pass through the bridge at a limited speed. If the toughness of the bridge is greater than 0.78, vehicles can pass safely on the bridge.

[0210] In another embodiment, a railway beam bridge seismic toughness evaluation system is provided, comprising: a simulation module, a model building module, a loss evolution analysis module, a function recovery analysis module and an evaluation module.

[0211] The simulation module is used to establish a nonlinear finite element model of the whole bridge to simulate and output the seismic response of key bridge components, and calculate the track irregularity based on the seismic response of key bridge components and the beam-track deformation mapping relationship. V ,The key components of bridges include piers, bearings and tracks;

[0212] The model building module is used to establish a logarithmic scatter plot of seismic intensity and pier curvature ductility coefficient based on the pier analysis results of seismic waves, establish a logarithmic scatter plot of seismic intensity and bearing displacement based on the support analysis results of seismic waves, and establish a logarithmic scatter plot of seismic intensity and track irregularity based on the track irregularity analysis results of seismic waves. V Logarithmic scatter plot, linear regression is performed on the above three scatter plots to establish the response probability seismic demand model of each key bridge component;

[0213] The loss evolution analysis module is used to calculate the damage exceedance probability of key bridge components and normalize the damage rate threshold of key bridge components based on the capacity threshold. L1 i , L2 i and L3 i ; Using damage probability weighted calculation to calculate bridge bearings Q LB , Bridge pier damage rate Q LP and loss of bridge traffic function Q L , establish the loss evolution curve of key bridge components under different earthquake motion intensities;

[0214] The function recovery analysis module is used to analyze the loss of traffic function according to the Q L Obtaining residual traffic function of bridges after earthquake Q r , Calculate the repair time of components after earthquake T rej ( j =1,2,3); calculate the bridge traffic function value after each key bridge component is fully repaired Q r1 、Q r2 and Q r3 , based on the above calculations, establish the bridge post-earthquake traffic function recovery curve;

[0215] The evaluation module is used to obtain the minimum earthquake intensity for bearings and piers to reach the complete destruction level, and the minimum earthquake intensity for tracks to reach the slight damage level and the complete destruction level based on the loss evolution curves of each key bridge component under different earthquake motion intensities and the bridge post-earthquake traffic function recovery curve; based on the earthquake motion intensity-seismic toughness index curve, the boundary values ​​of the three levels of bridge seismic toughness are determined, namely: normal traffic, speed limit traffic and structural safety, such as Fig.24 shown.

[0216] The above-mentioned embodiments only express the specific implementation methods of the present application, and the descriptions thereof are relatively specific and detailed, but they cannot be understood as limiting the protection scope of the present application. It should be pointed out that, for ordinary technicians in this field, several variations and improvements can be made without departing from the technical solution concept of the present application, and these all belong to the protection scope of the present application.

Claims

1. A method for evaluating the seismic toughness of a railway beam bridge, characterized in that: include: Step 1: Establish a nonlinear finite element model of the entire bridge to simulate and output the seismic response of key bridge components. Based on the seismic response of key bridge components and the beam-track deformation mapping relationship, calculate the track irregularity V. Key bridge components include piers, bearings and tracks. Step 2: Based on the pier analysis results of seismic waves, a logarithmic scatter plot of seismic intensity and pier curvature ductility coefficient is established. Based on the support analysis results of seismic waves, a logarithmic scatter plot of seismic intensity and support displacement is established. Based on the track irregularity analysis results of seismic waves, a logarithmic scatter plot of seismic intensity and track irregularity V is established. The three scatter plots are linearly regressed to establish the response probability seismic demand model of each key bridge component. Step 3: Calculate the damage exceedance probability of key bridge components under different damage states by combining the response probability seismic demand model of key bridge components, and normalize the damage rate threshold of key bridge components based on the capacity threshold; Weighted calculation of bridge bearings based on damage exceedance probability and damage rate threshold Q LB , Bridge pier damage rate Q LP and loss of bridge traffic function Q L , establish the loss evolution curve of key bridge components under different earthquake motion intensities; Step 4: Loss based on the passing function Q L Obtaining residual traffic function of bridges after earthquake Q r , Calculate the repair time of components after earthquake T rej ; Calculate the traffic function value of each key bridge component after complete repair Q r1 、Q r2 and Q r3 , and finally establish the post-earthquake traffic function recovery curve; Step 5: Calculate the seismic toughness index of the bridge, and then obtain the minimum seismic intensity for the bearings and piers to reach the complete destruction level and the minimum seismic intensity for the track to reach the slight damage level and the complete destruction level based on the loss evolution curves of each key bridge component under different seismic intensities and the post-earthquake traffic function recovery curve; determine the boundary values ​​of the three levels of seismic toughness of the bridge based on the seismic intensity-seismic toughness index curve: normal traffic, speed limit traffic and structural safety; The step 3 comprises: Step 3.1: Classify the damage status of each key bridge component into five levels: no damage, slight damage, moderate damage, severe damage and complete destruction, and determine the corresponding control indicators. The control indicator parameters of the pier include longitudinal steel bar strain and concrete strain, the control indicator parameters of the support include support displacement, and the control indicator parameter of the track is track irregularity; Step 3.2: Perform vulnerability analysis and calculate the damage exceedance probability as shown in equations (4)-(5); ， Where P is the damage exceedance probability, S c is the mean value of the seismic capacity of structural components; is the logarithmic standard deviation of the seismic capacity of the components; is the logarithmic standard deviation of the component seismic response; EDP i For the i Seismic response under the action of seismic waves; N is the number of input seismic waves; IM is the seismic intensity; EDP is the seismic response; a, b are the regression parameters of the probabilistic seismic demand model; Step 3.3: Calculate the damage rate threshold of each key bridge component L 1 i , L 2 i , L 3 i , Equations (6)-(8) correspond to the support, pier and track respectively; ， Where: D c is the allowable seismic displacement of the bearing; D i For the support i The support deformation threshold for each damage state; μ i For the bridge pier i The cross-sectional curvature ductility coefficient for each damage state; V d_max Design the maximum speed for the line, V min Design speed for the line; V r The residual speed after the earthquake, is the ductility coefficient threshold of complete destruction; Step 3.4: Weighted calculation of bearings using damage exceedance probability Q LB , Bridge pier performance loss Q LP and loss of bridge traffic function Q L , refer to equations (9) to (12) for calculation; ， Where: P f (i) represents the damage exceedance probability function; P DS1 , P DS2 , P DS3 , P DS4 They correspond to the probability of exceeding slight damage, moderate damage, severe damage, and complete destruction respectively; Step 3.5: Under a given ground motion intensity, when Q L Exceeds the threshold of the corresponding damage state L i ( i =1,2,3) then it is determined that the corresponding damage state has been reached; The step 4 comprises: Step 4.1: Calculate the residual traffic function after the earthquake Q r ; ， Step 4.2: Calculate the time required to repair bearings, piers and tracks after an earthquake ; ， In the formula, represents the damage exceedance probability function, T i is the repair time required for the component to reach the i-th damage state; Step 4.3: Calculate the traffic function value after the piers, bearings and tracks are fully repaired Q r1 、Q r2 and Q r3 ; ， Step 4.4: Establish the post-earthquake bridge traffic function recovery curve; ， Where Q(t) is the functional recovery function, t represents the time after the earthquake, t0 is the start time of repair, t1 is the completion time of the repair of the first type of components, t2 is the completion time of the repair of the second type of components, and t3 is the completion time of the repair of the third type of components.

2. A railway beam bridge seismic toughness evaluation method according to claim 1, characterized in that: The step 1 comprises: Step 1.1: Establish a nonlinear finite element model of the entire bridge based on the bridge design parameters; Step 1.2: Determine the target response spectrum curve according to the bridge site conditions; Step 1.3: Based on the target response spectrum curve, select the seismic wave input finite element model from PEER to carry out nonlinear time history analysis; Step 1.4: Output the relative displacement of the main beam end at the expansion joint, the bearing deformation and the curvature of the pier bottom section As the seismic response of the key bridge components, the relative displacement of the main beam end at the expansion joint includes the peak displacement D r and residual displacement D p ; Step 1.5: Calculate track irregularity based on beam-track deformation mapping V .

3. A railway beam bridge seismic toughness evaluation method according to claim 2, characterized in that: The calculation formula of the track irregularity V is as follows: ， In the formula, D r is the peak displacement, D p is the residual displacement, g0-g4 are the intermediate parameters for calculation.

4. The method for evaluating seismic toughness of a railway beam bridge according to claim 1, characterized in that: The step 2 comprises: Step 2.1: Analyze the cross section of the pier bottom, establish the cross-sectional strain-curvature curve, and obtain the initial yield curvature corresponding to the yield of the longitudinal reinforcement of the pier. ; Step 2.2: Calculate the ductility coefficient of the pier curvature , as shown in formula (2); ， Where φ is the curvature of the bottom section of the bridge pier under earthquake action, is the yield curvature corresponding to the initial yield of the longitudinal reinforcement of the pier; Step 2.3: Take the logarithm of the seismic intensity of each ground motion and the deformation of the model support, the curvature ductility coefficient of the bridge pier, and the track irregularity V under its action, and establish a logarithmic scatter plot of the seismic intensity IM and the seismic response EDP; Step 2.4: Perform linear regression on the logarithmic scatter cloud to establish the probabilistic earthquake demand model of the bearing, pier and track response, as shown in formula (3); ， In the formula, a , b are the regression parameters of the probabilistic earthquake demand model, IM is the ground motion intensity, and EDP is the earthquake response.

5. The method for evaluating seismic toughness of a railway beam bridge according to claim 1, characterized in that: The step 5 comprises: Step 5.1: Calculate the bridge seismic resilience index R; ， In the formula, T re is the total time for post-earthquake repair; Step 5.2: Based on the bearing and pier damage evolution curves and the traffic function damage evolution curves, calculate the seismic intensity of the bearing and pier that reaches the complete destruction level as the minimum seismic intensity for structural safety. PGA b4 and PGA p4 ; Step 5.3: Based on the bearing and pier damage evolution curves and the traffic function damage evolution curves, the seismic intensity at which the traffic function loss rate reaches the level of slight damage and complete destruction is calculated as the driving safety threshold, which are: PGA t1 and PGA t4 ; Step 5.4: Based on the seismic intensity-seismic resilience index curve, calculate PGA t1 , PGA t4 and min( PGA b4 , PGA p4 ) corresponding to the toughness index R 1. R 2 and R 3, which are the seismic resilience index thresholds corresponding to the three levels of bridge seismic resilience.

6. A railway beam bridge seismic toughness evaluation method according to claim 2, characterized in that: In the nonlinear finite element model of the whole bridge in step 1.1, the supports are simulated by nonlinear units, the piers are simulated by nonlinear fiber units, and the main beams are simulated by beam units.

7. A railway beam bridge seismic toughness evaluation system, characterized in that: A railway beam bridge seismic toughness evaluation method according to any one of claims 1 to 6 is adopted, comprising: a simulation module, a model building module, a loss evolution analysis module, a function recovery analysis module and an evaluation module, The simulation module is used to establish a nonlinear finite element model of the whole bridge to simulate and output the seismic response of key bridge components, and calculate the track irregularity V based on the seismic response of key bridge components and the beam-track deformation mapping relationship. The key bridge components include piers, bearings and tracks; The model building module is used to establish a logarithmic scatter plot of seismic intensity and pier curvature ductility coefficient based on the pier analysis results of seismic waves, establish a logarithmic scatter plot of seismic intensity and bearing displacement based on the support analysis results of seismic waves, establish a logarithmic scatter plot of seismic intensity and track irregularity V based on the track irregularity analysis results of seismic waves, and perform linear regression on the above three scatter plots to establish a response probability seismic demand model for each key bridge component; The loss evolution analysis module is used to calculate the damage exceedance probability of key bridge components and normalize the damage rate threshold of key bridge components based on the capacity threshold. L1 i , L2 i and L3 i ; Using damage probability weighted calculation to calculate bridge bearings Q LB , Bridge pier damage rate Q LP and loss of bridge traffic function Q L , establish the loss evolution curve of key bridge components under different earthquake motion intensities; The function recovery analysis module is used to analyze the loss of traffic function according to the Q L Obtaining residual traffic function of bridges after earthquake Q r , Calculate the repair time of components after earthquake T rej ; Calculate the bridge traffic function value after each key bridge component is fully repaired Q r1 、Q r2 and Q r3 , and finally establish the bridge post-earthquake traffic function recovery curve; The evaluation module is used to obtain the minimum seismic intensity for bearings and piers to reach complete destruction level, and the minimum seismic intensity for tracks to reach slight damage level and complete destruction level based on the loss evolution curves of each key bridge component under different seismic motion intensities and the bridge's post-earthquake traffic function recovery curve; based on the seismic motion intensity-seismic toughness index curve, determine the boundary values ​​of the three levels of seismic toughness of the bridge: normal traffic, speed limit traffic and structural safety.

Images