Method and device for evaluating shock resistance and toughness of lower structure of double-column pier bridge

Abstract

The invention discloses a method and a device for evaluating shock resistance and toughness of a double-column pier bridge substructure. The method comprises the following steps: determining a damage index of a single component; determining the damage probability of a single component through the component damage index; according to the damage probability of a single component, using a Copula function to calculate the vulnerability of a double-column-pier lower structure system; according to the vulnerability of the system, calculating a post-earthquake function loss function of the lower structure of the double-column pier bridge; and calculating the anti-seismic toughness index of the double-column-pier lower structure by using the post-earthquake function loss function and the function recovery function of the double-column-pier bridge lower structure. By the adoption of the technical scheme, the influence of damage correlation and delay time between parts of the lower structure of the double-column pier bridge on the anti-seismic toughness can be considered at the same time, a more appropriate anti-seismic toughness evaluation mode is selected for different bridges, and the anti-seismic toughness index is accurately calculated.

Description

Technical Field

[0001] The invention belongs to the technical field of bridge seismic toughness assessment, and in particular relates to a method and device for assessing the seismic toughness of a substructure of a double-column pier bridge. Background Art

[0002] Traditional bridge structures mainly avoid collapse under strong earthquakes through ductile seismic design, and use the hysteresis energy dissipation capacity of the main structure to consume earthquake energy. After the earthquake, the damaged parts of the bridge are repaired to ensure subsequent normal operation. The substructure of the double-column pier bridge is an over-static structure. When an earthquake occurs along the transverse direction of the bridge, the stress conditions of the piers are relatively complex, and it is very difficult to select appropriate pier damage indicators. At the same time, since the method of structural toughness assessment was proposed not long ago, the influencing factors considered in the toughness assessment process are relatively single, and the results of the toughness assessment are mostly divided into grades, the results are relatively vague, which greatly affects the reliability of the post-earthquake toughness assessment of the bridge. Summary of the invention

[0003] The technical problem to be solved by the present invention is to provide a method and device for evaluating the seismic toughness of the substructure of a double-column pier bridge, which can simultaneously consider the damage correlation between the components of the substructure of the double-column pier bridge and the influence of delay time on the seismic toughness, select a more appropriate seismic toughness evaluation method for different bridges, and accurately calculate the seismic toughness index.

[0004] To achieve the above object, the present invention adopts the following technical solution:

[0005] A method for evaluating the seismic toughness of a double-column pier bridge substructure comprises:

[0006] Step 1: Determine the damage index of a single component;

[0007] Step 2: Determine the damage probability of a single component through the component damage index;

[0008] Step 3: Based on the damage probability of a single component, the Copula function is used to calculate the vulnerability of the double-column pier substructure system;

[0009] Step 4: Calculate the post-earthquake functional loss function of the substructure of the double-column pier bridge according to the system vulnerability;

[0010] Step 5: Use the post-earthquake function loss function and function recovery function of the double-column pier bridge substructure to calculate the seismic toughness index of the double-column pier substructure.

[0011] As a preferred method, the calculation formula for evaluating the damage degree of the pier column is as follows:

[0012]

[0013] Among them, KDX It is an index for evaluating the damage degree of a bridge pier; F j K is the frequency value of a certain axial force at the bottom of a bridge pier; j It is the curvature of the characteristic point on the moment-curvature curve of the pier bottom section corresponding to a certain axial force.

[0014] As a preferred embodiment, in step 3, the Gumbel Copula function is used to calculate the component correlation, and the distribution function expression of the multivariate Gumbel Copula function is:

[0015]

[0016] Among them, α is the relevant parameter, and α∈(0,1),

[0017] By introducing the Copula function, the vulnerability of multiple components to simultaneous damage can be expressed as:

[0018] P(X1X2…X k )=C(P1,P2,…,P k )

[0019] Among them, P k is the vulnerability of a single component; C(P1,P2,···,P k ) is a multivariate Copula function that considers the correlation of multiple components;

[0020] Substituted into the vulnerability expressions of the series system and the parallel system, the vulnerability of the series system P fcl for:

[0021]

[0022] Preferably, in step 4, the system vulnerability taking into account the correlation of components is calculated using the Copula function, and the functional loss of the bridge is calculated according to the exceedance probability of the vulnerability, and the calculation formula is:

[0023]

[0024] Where j is the damage level of the bridge system; C s,j is the repair cost of the structural system under the jth damage level; s Cost of reconstruction after total destruction; is the cost-loss ratio; P j is the destruction probability of a bridge with damage state j under a certain PGA;

[0025] The destruction probability P of the bridge with damage state j under PGA j The calculation formula is:

[0026]

[0027] Among them, P fj is the exceedance probability of each damage state under a certain PGA action.

[0028] Preferably, the function recovery function of the double-column pier bridge after an earthquake includes: a linear function recovery function, an exponential function recovery function and a trigonometric function recovery function.

[0029] The present invention also provides a double-column pier bridge substructure seismic toughness assessment device, comprising:

[0030] The first calculation module is used to determine the damage index of a single component;

[0031] A second calculation module is used to determine the damage probability of a single component according to the component damage index;

[0032] The third calculation module is used to calculate the vulnerability of the double column pier substructure system using the Copula function according to the damage probability of a single component;

[0033] The fourth calculation module is used to calculate the post-earthquake functional loss function of the substructure of the double-column pier bridge according to the system vulnerability;

[0034] The fifth calculation module is used to calculate the seismic toughness index of the double-column pier substructure by using the post-earthquake function loss function and function recovery function of the double-column pier bridge substructure.

[0035] Preferably, the calculation formula of the index used by the first calculation module to evaluate the damage degree of the pier column is as follows:

[0036]

[0037] Among them, K DX It is an index for evaluating the damage degree of a bridge pier; F j K is the frequency value of a certain axial force at the bottom of a bridge pier; j It is the curvature of the characteristic point on the moment-curvature curve of the pier bottom section corresponding to a certain axial force.

[0038] Preferably, the third calculation module uses the Gumb Copula function to calculate the component correlation, and the distribution function expression of the multivariate GumbelCopula function is:

[0039]

[0040] Among them, α is the relevant parameter, and α∈(0,1),

[0041] By introducing the Copula function, the vulnerability of multiple components to simultaneous damage can be expressed as:

[0042] P(X1X2…Xk )=C(P1,P2,…,P k )

[0043] Among them, P k is the vulnerability of a single component; C(P1,P2,···,P k ) is a multivariate Copula function that considers the correlation of multiple components;

[0044] Substituted into the vulnerability expressions of the series system and the parallel system, the vulnerability of the series system P fcl for:

[0045]

[0046] Preferably, the fourth calculation module calculates the system vulnerability taking into account the correlation of components using the Copula function, and calculates the functional loss of the bridge according to the exceedance probability of the vulnerability, and the calculation formula is:

[0047]

[0048] Where j is the damage level of the bridge system; C s,j is the repair cost of the structural system under the jth damage level; s Cost of reconstruction after total destruction; is the cost-loss ratio; P j is the destruction probability of a bridge with damage state j under a certain PGA;

[0049] The destruction probability P of the bridge with damage state j under PGA j The calculation formula is:

[0050]

[0051] in, is the exceedance probability of each damage state under a certain PGA action.

[0052] Preferably, the function recovery function of the double-column pier bridge after an earthquake includes: a linear function recovery function, an exponential function recovery function and a trigonometric function recovery function.

[0053] The present invention can determine the damage probability of each component in the actual project by fitting the existing seismic data; can calculate the system vulnerability of the complex substructure for each component of the double-column pier substructure; and can correct and test the seismic toughness index by considering the delay time and different functional recovery functions. The present invention can evaluate the seismic toughness more accurately and in line with the actual project by considering the influence of the delay time and different functional recovery functions on the seismic toughness index, thereby achieving the purpose of improving the accuracy and reliability of the seismic toughness evaluation results. BRIEF DESCRIPTION OF THE DRAWINGS

[0054] In order to more clearly illustrate the embodiments of the present invention or the technical solutions in the prior art, the drawings required for use in the embodiments or the description of the prior art will be briefly introduced below. Obviously, the drawings described below are only embodiments of the present invention. For ordinary technicians in this field, other drawings can be obtained based on the provided drawings without paying creative work.

[0055] Figure 1 The function-time curve corresponding to the linear functional recovery function;

[0056] Figure 2 The function-time curve corresponding to the exponential recovery function;

[0057] Figure 3 The function-time curve corresponding to the trigonometric recovery function;

[0058] Figure 4 This is the full bridge model diagram;

[0059] Figure 5 It is the stress-deformation diagram of the plate rubber bearing;

[0060] Figure 6 It is the restoring force model of the PTFE slide rubber bearing;

[0061] Figure 7 is the bilinear stress-strain relationship of the steel bar;

[0062] Figure 8 is the stress-strain relationship of ordinary confined concrete;

[0063] Fig. 9 This is the fiber cross-section segmentation diagram of the pier column;

[0064] Fig.10 are the 10 selected seismic wave response spectra;

[0065] Fig.11 is the moment-curvature diagram of the cross section at the bottom of the pier;

[0066] Fig.12 is the probability of occurrence of different damage levels of the bridge structure; (a) is slight damage, (b) is moderate damage, (c) is severe damage, and (d) is complete damage;

[0067] Fig.13 is the repair time of the bridge structure under different earthquake motion intensities; (a) is the longitudinal direction of the bridge, and (b) is the transverse direction of the bridge;

[0068] Fig.14This is the bridge post-earthquake function-PGA-time curve (linear recovery); (a) is the longitudinal direction of the bridge, and (b) is the transverse direction of the bridge;

[0069] Fig.15 This is the bridge post-earthquake function-PGA-time curve (exponential recovery); (a) is the longitudinal direction of the bridge, and (b) is the transverse direction of the bridge;

[0070] Fig.16 This is the bridge post-earthquake function-PGA-time curve (trigonometric function recovery); (a) is the longitudinal direction of the bridge, and (b) is the transverse direction of the bridge;

[0071] Fig.17 is the toughness index of different types of functional recovery functions; where (a) is the longitudinal bridge direction and (b) is the transverse bridge direction;

[0072] Fig.18 This is a flow chart of a method for evaluating the seismic toughness of a double-column pier bridge substructure according to an embodiment of the present invention. DETAILED DESCRIPTION

[0073] The following will be combined with the drawings in the embodiments of the present invention to clearly and completely describe the technical solutions in the embodiments of the present invention. Obviously, the described embodiments are only part of the embodiments of the present invention, not all of the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by ordinary technicians in this field without creative work are within the scope of protection of the present invention.

[0074] In order to make the above-mentioned objects, features and advantages of the present invention more obvious and easy to understand, the present invention is further described in detail below with reference to the accompanying drawings and specific embodiments.

[0075] Embodiment 1:

[0076] like Fig.18 As shown, an embodiment of the present invention provides a method for evaluating the seismic toughness of a substructure of a double-column pier bridge, comprising:

[0077] Step 1: Preliminary determination of damage indicators of individual components

[0078] The damage index of the bearing and tie beam is determined based on the existing database. For the damage index of the pier column, the cracking point, equivalent yield point, maximum moment point and limit point of the moment-curvature curve of the pier bottom section are multiplied by the corresponding frequency to obtain the index for evaluating the damage degree of the pier column. The specific calculation formula is shown below.

[0079]

[0080] Where: K DX It is an index for evaluating the damage degree of a bridge pier; F jK is the frequency value of a certain axial force at the bottom of a bridge pier; j It is the curvature of the characteristic points on the moment-curvature curve of the pier bottom section corresponding to a certain axial force, including the cracking point, equivalent yield point, maximum moment point and limit point.

[0081] Step 2: Determine the damage probability of a single component through the component damage index

[0082] First, multiple seismic waves of different intensities are selected for time history analysis to obtain a series of seismic response data. Then, the seismic response and seismic intensity index are logarithmized, and the probability demand model of the structure is obtained through linear regression. The fitted regression formula is

[0083] ln(μ d )=a+bln(IM) (2)

[0084] Based on reliability theory, the component failure cracking expression is:

[0085]

[0086] When the seismic demand and seismic capacity of the bridge structure both satisfy the log-normal distribution, the logarithmic seismic demand and seismic capacity are substituted into formula (2), and the damage probability of a single component can be obtained as:

[0087]

[0088] Where: φ[] is the standard normal distribution function; β d is the earthquake demand variance; β c is the earthquake capacity variance; μ d is the result of the earthquake response; μ c Damage index; when SA is used as an independent variable in the structural seismic fragility curve, When PGA is used as an independent variable,

[0089] Step 3: Use Copula function to calculate the vulnerability of the double column pier substructure system

[0090] The component correlation is calculated using the Gumb Copula function. The distribution function expression of the multivariate Gumbel Copula function is:

[0091]

[0092] Where: α is the relevant parameter, and α∈(0,1).

[0093] By introducing the Copula function and considering the correlation of the seismic demand of components, the vulnerability of multiple components to simultaneous damage can be expressed as:

[0094] P(X1X2···X k )=C(P1,P2,···,P k ), where 1<k≤n (6)

[0095] Where: P k is the vulnerability of a single component; C(P1,P2,···,P k ) is a multivariate Copula function that considers the correlation between multiple components.

[0096] Substituting the above formula into the vulnerability expressions of the series system and the parallel system, the vulnerability P of the series system can be obtained. fcl for

[0097]

[0098] Step 4: Calculate the post-earthquake functional loss function of the double-pillar pier bridge substructure based on the system vulnerability

[0099] The system vulnerability taking into account the correlation of components is calculated using the Copula function, and the functional loss of the bridge is calculated based on the exceedance probability of the vulnerability. The calculation formula is as follows.

[0100]

[0101] Where: j is the damage level of the bridge system; C s,j I is the maintenance cost of the structural system under the j damage level, which is related to the degree of damage to the structure; s Cost of reconstruction after total destruction; is the cost-loss ratio. j is the destruction probability of a bridge with damage state j under a certain PGA.

[0102] The destruction probability P of a bridge with damage state j under a certain PGA j The calculation formula is as follows:

[0103]

[0104] is the exceedance probability of each damage state under a certain PGA action.

[0105] Step 5: Calculate the seismic toughness index of the double-column pier substructure using the post-earthquake function loss function and function recovery function of the double-column pier bridge substructure

[0106] The repair time is calculated based on the damage probability of different damage states of the bridge. The calculation formula is:

[0107]

[0108] Where: T RET is the repair time of the bridge after it is damaged by earthquake; j is the repair time of the structural system under the j damage level.

[0109] The function-time function expression is:

[0110] Q(t)=1-L E *{H(tt 0E )-H[t-(t 0E +T RE )]}*f Rec (t,t 0E ,T RE ) (11)

[0111] Where: L E is the functional loss function; f Rec (t,t 0E ,T RE ) is the functional recovery function; H(x) is the Heaviside step function, and its expression is as follows.

[0112]

[0113] Based on various recovery functions, the following is the functional recovery function of the double-column pier bridge after the earthquake.

[0114] (1) Linear functional recovery function

[0115] The specific expression of the linear functional recovery function is:

[0116]

[0117] After the bridge is subjected to earthquake action, the structural system function-time function expression corresponding to the linear function recovery function is:

[0118]

[0119] The function-time function curve of the linear functional recovery function is as follows: Figure 1 As shown:

[0120] When considering the delayed repair time of the structure after an earthquake, the mathematical expression of the resilience index of the structural system will be as follows:

[0121]

[0122] Where: T 0E The time to start repairing; T LC To control the time, T LC =t 0E +T RE -t0.

[0123] The structural repair is carried out according to the mathematical model of the linear functional recovery function. The toughness index of the double-column pier bridge structure is:

[0124]

[0125] By calculating the definite integral, we can get:

[0126]

[0127] (2) Exponential function recovery function

[0128] The specific expression of the exponential function recovery function is:

[0129]

[0130] After the bridge is subjected to earthquake action, the structural system function-time function expression corresponding to the exponential function recovery function is:

[0131]

[0132] The function-time function curve of the exponential function recovery function is as follows: Figure 2 As shown:

[0133] The structural repair is carried out according to the mathematical model of the exponential functional recovery function. The toughness index of the double-column pier bridge structure is:

[0134]

[0135] By calculating the definite integral, we can get:

[0136]

[0137] (3) Trigonometric function recovery function

[0138] The specific expression of the trigonometric function recovery function is:

[0139]

[0140] Then the structural system function-time function expression corresponding to the trigonometric function recovery function of the bridge after earthquake action is:

[0141]

[0142] The function-time function curve of the trigonometric function recovery function is as follows: Figure 3 As shown:

[0143] The structural repair is carried out according to the mathematical model of trigonometric function recovery function, and the toughness index of the double-column pier bridge structure is:

[0144]

[0145] By calculating the definite integral, we can get:

[0146]

[0147] The embodiment of the present invention performs a systematic damage probability calculation and analysis on each component of the substructure of a double-column pier bridge based on a Copula function, and performs a seismic toughness assessment method for the substructure of a double-column pier bridge that takes into account the systematic damage probability and the delay time, making the seismic toughness assessment result clearer and more accurate. The seismic toughness index is calculated based on three different functional recovery functions, and the seismic toughness assessment method that is most suitable for the actual project can be selected by comparing the seismic toughness index results calculated using different functional recovery functions. According to the stress characteristics of the substructure of a double-column pier bridge, a damage index calculation method for the double-column pier column is proposed, making the damage probability and seismic toughness assessment results more reliable.

[0148] Application examples:

[0149] Model Introduction

[0150] The present invention takes a double-column pier bridge in a certain actual project as the research object. The bridge adopts a construction method of simple support first and then continuous support. The upper structure is a 3×30m prestressed concrete simple supported T-beam, 5 prefabricated T-beams are used for each hole, the net width of the bridge deck is 11.4m, the main beam height is 2.0m, and C50 concrete is used for prefabrication. The piers are double-column piers, the abutments are pile-column abutments, the pile foundations are single-column pile foundations, and the cross-section forms are all solid circular cross-sections with a centerline spacing of 7.2m. Among them, the diameter of the 1# pier is 1.5m, the diameter of the 0# abutment and the pile foundation of the 1# pier is 1.8m, the diameter of the 2# and 3# piers is 1.8m, and the diameter of the pile foundation is 2.0m. The longitudinal steel bars of the piers and pile foundations are HRB400 with a diameter of 28mm, which are arranged at equal intervals around, and the stirrups are HPB300 with a diameter of 10mm, which are arranged in a spiral manner with a spacing of 10cm. The thickness of the concrete protective layer of the piers and pile foundations is 4cm and 6cm respectively. The cap beam is 11.6m long and has a cross section of 2.2m×1.8m. The cross section of the tie beam is 1.1m×1.3m and the cross section of the ground tie beam is 1.3m×1.5m. The lower structure is made of C35 concrete. The bearings at the abutments and 3# piers use GJZF4350×450×101 PTFE slide rubber bearings, and the other piers use GJZ350×450×99 plate rubber bearings. The full bridge model is as follows: Figure 4 shown.

[0151] Superstructure simulation

[0152] When designing the superstructure, the vertical load is usually considered as the main consideration, but previous earthquake records show that the intensity of most vertical earthquakes is not high. In addition, the earthquake damage to the superstructure is mainly caused by the collision of adjacent span superstructures caused by displacement, the collision of the superstructure and the abutment, and the falling beam, while the damage to the superstructure itself is relatively rare. In view of the fact that the example selected in the embodiment of the present invention is a ductile seismic design, the pier will become the main component for absorbing seismic wave energy. Therefore, when studying the seismic action, it is generally believed that the superstructure is in the elastic stage and has not yet entered the plastic stage. Therefore, the embodiment of the present invention uses beam units to simulate the main beam, and the material is defined as a linear elastic material, and the transverse connection between the main beams is simulated by virtual beams. In addition, the bridge deck loads such as the second phase paving and anti-collision guardrails are applied to the beam units in the form of linear loads.

[0153] Support simulation

[0154] In the double-column pier bridge structure studied in the embodiment of the present invention, GJZF4350×450×101 bearings are installed on the 0# pier and the 3# pier respectively, while GJZ350×450×99 bearings are installed on the 1# pier and the 2# pier. The GJZ350×450×99 bearing here refers to a rectangular plate rubber bearing with a cross-section of 35cm×45cm and a bearing thickness of 9.9cm; while the GJZF4350×450×101 bearing refers to a rectangular polytetrafluoroethylene skateboard rubber bearing with a cross-section of 35cm×45cm and a bearing thickness of 10.1cm. When considering the damage situation, the horizontal force and deformation relationship of the plate rubber bearing is as follows: Figure 5 As shown in the figure, the restoring force model of the PTFE slide rubber bearing is as follows: Figure 6 shown.

[0155] Pier simulation

[0156] For bridges that adopt ductile seismic design, the piers are the most critical components in the bridge system, whether from the perspective of strength criteria or deformation criteria. As ductile components, plastic hinges will be generated at the pier top, pier body and tie beam connection parts of the double-column pier with tie beam, which will play an energy-absorbing role under the action of earthquake, thereby realizing the protection of capacity protection components. In order to study the nonlinear behavior of the pier after entering the plastic stage, the embodiment of the present invention uses nonlinear materials and fiber sections in the simulation of the pier. The steel bar adopts a double-broken line model, and the confined concrete and unconstrained concrete of the pier adopt the Mander constitutive model. Specifically, Figure 7 and Figure 8 shown.

[0157] After defining the inelastic material properties, the fiber section segmentation is performed on the pier sections with diameters of 1.5m and 1.8m. The confined concrete and unconfined concrete of the pier are divided into 20 parts along the x-axis and y-axis respectively. The fiber section segmentation is shown in the figure below. Fig. 9 shown.

[0158] Tie beam simulation

[0159] As a capacity protection component, the tie beam of the bridge pier will form a plastic hinge at the connection position with the pier column when an earthquake occurs, so as to dissipate the energy generated by the earthquake and reduce the damage to the bridge structure caused by the earthquake. However, this will also make it easier to cause damage near the connection position between the tie beam and the pier column. In order to study the degree of damage to the tie beam under the action of an earthquake, the embodiment of the present invention uses the Takeda three-fold line hysteresis characteristic to define the skeleton hinge to simulate the plastic hinge area of ​​the tie beam, and obtain the rotation angle of the plastic hinge area of ​​the tie beam through this method.

[0160] Earthquake input

[0161] Selection of ground motion parameters

[0162] At present, earthquake peak acceleration and spectral acceleration are the two most commonly used seismic intensity indicators in structural vulnerability analysis. The seismic peak acceleration is an easily obtained parameter in bridge seismic resistance, and is also a widely recognized and applied seismic intensity indicator. Domestic and foreign scholars have given it an important position in bridge structure vulnerability analysis. Therefore, the embodiment of the present invention selects the seismic peak acceleration as an indicator for judging the magnitude of seismic intensity.

[0163] Seismic wave selection method

[0164] In order to ensure the accuracy of the calculation results of the vulnerability analysis of the double-column pier bridge structure, the embodiment of the present invention selects the measured seismic wave as the input value of the structural earthquake corresponding analysis, and considers randomness and accuracy when selecting the seismic wave, and selects according to the conditions such as the seismic wave spectrum characteristics, peak acceleration, duration and the number of seismic waves. According to the bridge site conditions and the "Highway Bridge Seismic Design Code", the design response spectrum is drawn, and this is used as the target spectrum. 10 seismic motion records that meet the above conditions are selected from 100 natural waves in the PEER strong earthquake database of the Pacific Earthquake Engineering Research Center of the United States. According to the vulnerability analysis, the seismic motion intensity needs to be modulated to a state where more than 90% of the components are damaged. Therefore, the embodiment of the present invention uses the amplitude modulation method (IDA) to modulate each seismic wave, and modulates the peak acceleration PGA from 0.1g to 2.5g one by one, with an amplitude of 0.1g, to form 10 groups of 250 seismic waves, and then inputs the model to calculate the structural response along the longitudinal bridge direction and the transverse bridge direction, which is used for the damage probability calculation of the double-column pier bridge structure. The longitudinal bridge direction and transverse bridge direction in the embodiment of the present invention respectively represent the situation where an earthquake occurs along the longitudinal bridge direction and transverse bridge direction of a double-column pier bridge. The amplitude modulation formula is as follows:

[0165]

[0166] Where: A and a(t) are the peak acceleration and time-course acceleration function before amplitude modulation, respectively; A' and a'(t) are the peak acceleration and time-course acceleration function after amplitude modulation, respectively.

[0167] Ten earthquake waves that meet the spectrum characteristics, effective peak acceleration and duration were selected from the PEER strong earthquake database of the Pacific Earthquake Engineering Center of the United States. The acceleration response spectrum of the selected ground motion records is as follows: Fig.10 shown.

[0168] Determination of damage parameters of double-column pier bridge components

[0169] (1) Support

[0170] The bearings of the 0# and 3# bridge piers in the embodiment of the present invention are polytetrafluoroethylene rubber bearings, and the bearings of the 1# and 2# bridge piers are plate-type rubber bearings. The bearing uses displacement as the damage index, where the damage state parameters of the polytetrafluoroethylene rubber bearing refer to the research data of Li Lifeng et al., and the damage state parameters of the plate-type rubber bearing refer to the research data of Nielson et al. The specific damage state index parameters are shown in Table 1:

[0171] Table 1

[0172] Damage Status Plate rubber bearing / mm PTFE slide support / mm No damage 0<d≤29 0<d≤90 Minor injuries 29<d≤104 90<d≤150 Moderate damage 104<d≤136 150<d≤200 Serious injuries 136<d≤187 200<d≤300 Complete destruction 187<d 300<d

[0173] (2) Pier

[0174] The curvature of the pier bottom is obtained by moment-curvature analysis of the pier bottom section of a double-column pier bridge. According to the research of scholars such as Pan, Agrawal and Liu Hang, as well as the classification standards for earthquake damage levels of lifeline projects, four corresponding characteristic points on the moment-curvature curve of the pier bottom section are usually selected as the dividing points of the pier damage state. That is, the cracking point, the equivalent yield point, the maximum moment point and the limit point. The curvature damage index value of the bridge pier bottom section is shown in the figure.

[0175] The cracking point refers to the intersection of the moment-curvature relationship line and the ideal line within the elastic range. This point indicates that the protective layer concrete in the reinforced concrete has cracked. The equivalent yield point refers to the intersection of the two double-fold lines of the moment-curvature ideal line. This point is considered to be the turning point where the reinforced concrete section changes from linear to nonlinear. The maximum moment point refers to the point where the moment reaches its peak value on the moment-curvature curve. The limit point indicates the point with the largest curvature at the intersection of the moment-curvature ideal line and the relationship line. The classification of the damage states of the piers in the embodiment of the present invention is shown in Table 2.

[0176] Table 2

[0177] Damage Status Guidelines No damage <![CDATA[0<φ≤φ y ]]> Minor injuries <![CDATA[φ y <φ≤φ y ']]> Moderate damage <![CDATA[φ′ y <φ≤φ d ]]> Serious injuries <![CDATA[φ d <φ≤φ u ]]> Complete destruction <![CDATA[φ u <φ]]>

[0178] Note: φ is the curvature of the bottom section of the double-column pier bridge.

[0179] The substructure of the double-column pier bridge is a bent frame type, which is an over-static structure. When an earthquake occurs along the longitudinal direction of the bridge, the axial force at the bottom of the pier remains unchanged. The constant axial force value can be used to perform the moment-curvature analysis of the pier bottom section to obtain the unique cracking point, equivalent yield point, maximum moment point and limit point curvature that describe the damage state of the pier column. Then, when the earthquake occurs along the transverse direction of the bridge, the axial force at the bottom section of the pier will change with time. Therefore, the curvature of the above four characteristic points of the moment-curvature analysis of the pier bottom section cannot be used to describe the damage state of the double-column pier using a certain axial force value. By analyzing the axial forces of the piers calculated by the above 250 earthquake waves along the transverse direction of the bridge, it is found that the maximum axial force value at the bottom of the double-column pier is concentrated in a range, and a series of moment-curvature curves can be obtained by using the axial forces in this range to perform the moment-curvature analysis of the pier bottom. From these moment-curvature curves, it can be obtained that the curvatures of the cracking point, equivalent yield point, maximum moment point and limit point on this curve are similar to each other. Therefore, the embodiment of the present invention counts 250 groups of axial forces at the bottom of the pier and calculates their frequencies of occurrence. Then, within the interval where these axial forces occur, the axial force for moment-curvature analysis of the cross section is determined with a gradient of 500KN, and the moment-curvature analysis of the cross section at the bottom of the pier is performed using the obtained axial force. Finally, the cracking point, equivalent yield point, maximum moment point and limit point of each of these moment-curvature curves are multiplied by the corresponding frequency to obtain an index for evaluating the degree of damage to the pier column. The specific calculation formula is as follows.

[0180]

[0181] Where: K DX It is an index for evaluating the damage degree of a bridge pier; F j K is the frequency value of a certain axial force at the bottom of a bridge pier; j It is the curvature of the characteristic points on the moment-curvature curve of the pier bottom section corresponding to a certain axial force, including the cracking point, equivalent yield point, maximum moment point and limit point.

[0182] The parameters of different damage states of piers 1#, 2# and 3# calculated according to the above method are shown in Table 3.

[0183] Table 3

[0184]

[0185]

[0186] (3) Tie beam

[0187] The tie beam uses the rotation angle as the damage index. Combining the research of Nie Hongxin et al. and the structural design specifications, the damage parameters of the tie beam are selected as shown in Table 4.

[0188] Table 4

[0189] Damage Status Tie beam root angle / radian No damage 0<θ≤0.004 Minor injuries 0.004<θ≤0.008 Moderate damage 0.008<θ≤0.016 Serious injuries 0.016<θ≤0.020 Complete destruction 0.020<θ

[0190] Analysis of earthquake toughness parameters

[0191] Loss of functionality

[0192] The economic loss caused by the damage of the bridge structure under the action of an earthquake is called direct economic loss. The direct economic ratio refers to the ratio of the loss amount of the structure in an earthquake to the original cost of the project. In order to facilitate the rapid assessment of resilience, the embodiment of the present invention regards the economic loss of the bridge in an earthquake as the earthquake loss of the bridge function, and conducts the bridge resilience assessment work based on this.

[0193] The earthquake loss ratio is determined according to Table A.5 of the "Part 4 of Earthquake Site Work: Direct Disaster Loss Assessment" (GB / T 18208.4-2011). For highway bridge structures in life system engineering, the structural damage loss ratio is shown in Table 5.

[0194] Table 5

[0195] category Basically intact Minor damage Moderate damage Severe damage destruction scope 0～10 11～20 21～40 41～70 71～100 Median 5 16 31 56 86

[0196] According to the seismic design theory, it is considered that the bridge structure is in a basically intact state under the action of an earthquake and does not need to be repaired, and no economic loss will be incurred. The damage ratio of this state is considered to be 0; when the bridge structure is in a destroyed state, it does not need to be repaired and can be directly demolished and rebuilt. The damage ratio of this state is considered to be 100%. Therefore, the loss ratios of the basically intact, slightly damaged, moderately damaged, severely damaged and destroyed states described in the embodiments of the present invention are 0, 16%, 31%, 56% and 100% respectively.

[0197] The transcendental probability of different damage levels of the double-column pier bridge is calculated based on the binary Gumbel Copula function, and then the probability of occurrence of different damage levels of the bridge structure system considering the correlation of components is calculated using formula (9). The curve diagram is shown in Fig.12 shown.

[0198] according to Fig.12The data show that the damage probability curves of the slight damage and moderate damage states show a trend of increasing first and then decreasing. In the slight damage state, the maximum probability occurs in the range of 0.2g-0.4g in the transverse direction, while it is mainly concentrated in the range of 0.3g-0.7g in the longitudinal direction; for the moderate damage state, the maximum probability occurs in the range of 0.8g-1.1g in the transverse direction, while it is mainly concentrated in the range of 0.9g-2.0g in the longitudinal direction. The damage probability curve of the severe damage state shows a trend of increasing first and then decreasing in the transverse direction and the longitudinal direction of the 1# pier, while it increases all the time in the longitudinal direction of the 2# and 3# piers. The maximum probability of the severe damage state occurs in the range of 1.6g-1.9g in the transverse direction, while it is mainly concentrated in the longitudinal direction of more than 2.0g; the damage probability curve of the complete damage state shows a trend of increasing all the time. In addition, the maximum probability of the complete damage state is greater than 2.5g. Overall, when the earthquake action is weak, the main damage to the bridge is slight damage. As the earthquake intensity increases, the degree of damage gradually increases, and it may eventually reach a complete damage state.

[0199] Repair time

[0200] The repair time will vary depending on the degree of damage to the bridge caused by the earthquake. The present invention combines relevant literature to analyze the repair time of bridge structures in different damage states, and considering that the construction period of this bridge is 240 days, the repair time of the double-column pier bridge in different damage states is shown in Table 6.

[0201] Table 6

[0202]

[0203]

[0204] Formula (10) is used to calculate the repair time of the bridge structure under different ground motion intensities PGA. Fig.13 shown.

[0205] according to Fig.13 The data shows that when the local vibration intensity PGA is less than 0.3g, the repair time remains constant and extremely short, indicating that the bridge structure is not damaged and no repair is required at this time; when the local vibration intensity exceeds 1.8g, the growth rate of the repair time gradually slows down, indicating that the structure is close to complete destruction and the repair time is close to the reconstruction period, and then it needs to be demolished and rebuilt.

[0206] Effects of different earthquake motion intensities on the post-earthquake functional recovery of bridges

[0207] The post-earthquake functional recovery of a bridge is affected by many factors, such as delay time, repair time, and repair plan. The delay time is also affected by factors such as inspection time and material delivery. Its functional recovery is a very complex process. In this embodiment of the present invention, it is assumed that the ratio of the delay time to the repair time is A, and the post-repair functional value is taken as 1 for analysis.

[0208] From the previous text, we can know that the post-earthquake functional recovery process of bridges is affected by the seismic intensity PGA, repair time, delay time and the type of functional recovery function. Among them, the repair time and delay time are related to the degree of bridge damage. The higher the bridge damage level, the longer the required repair time and delay time. If A = 0.2, the post-earthquake functional recovery process of bridges can be described by a three-dimensional curve of seismic intensity PGA and time. The three-dimensional relationship between bridge functional recovery and seismic intensity PGA and repair time is shown in Figure 14-16 As shown. Figure 14-16 The data show that the opening of the curved surface reflects the characteristics of each recovery function under different types of functional recovery forms. The function Q of the three types of functional recovery functions in the longitudinal direction of the bridge is higher than that in the transverse direction of the bridge, indicating that when the earthquake occurs along the transverse direction of the bridge, the structural performance of the bridge is most seriously damaged and the post-earthquake reinforcement work is the most difficult. From the contour lines at the bottom of the three-dimensional image, it can be seen that the area enclosed by the exponential contour lines is the smallest, the area of ​​the trigonometric function type is second, and the area of ​​the linear type is the smallest, indicating that when the function of the bridge is restored to "1", the exponential type has the best recovery, the trigonometric function type has the second best recovery, and the linear type has the worst recovery.

[0209] Analysis on seismic toughness of substructure of double-pillar bridge

[0210] By conducting seismic resilience analysis considering the delay time, taking A = 0.2, substituting the functional losses of the double-column pier bridge in the longitudinal and transverse directions under different earthquake motion intensities into the corresponding resilience index formula, the resilience index values ​​of the double-column pier bridge structure under different earthquake motion intensities are obtained as follows: Fig.17 shown.

[0211] according to Fig.17 The data show that the seismic resilience indexes of bridges calculated by the three functional recovery functions are exponential recovery, trigonometric recovery and linear recovery from large to small. The seismic resilience indexes in the longitudinal direction of the bridge are all higher than those in the transverse direction of the bridge. When the peak seismic acceleration PGA in the figure is less than 0.5g, the seismic resilience index R0 is greater than 0.9, and the resilience of the bridge structure is at an excellent level; when PGA is between 0.5-1.5g, the seismic resilience index R0 is between 0.75-0.9, and the resilience of the bridge structure is at a good level; when PGA is between 1.5-2.0g, the seismic resilience index R0 is between 0.6-0.75, and the resilience of the bridge structure is at a medium level; when PGA is greater than 2.0g, the seismic resilience index R0 is less than 0.6, and the resilience of the bridge structure is at a poor level.

[0212] Embodiment 2:

[0213] The embodiment of the present invention further provides a device for evaluating the seismic toughness of a double-column pier bridge substructure, comprising:

[0214] The first calculation module is used to determine the damage index of a single component;

[0215] A second calculation module is used to determine the damage probability of a single component according to the component damage index;

[0216] The third calculation module is used to calculate the vulnerability of the double column pier substructure system using the Copula function according to the damage probability of a single component;

[0217] The fourth calculation module is used to calculate the post-earthquake functional loss function of the substructure of the double-column pier bridge according to the system vulnerability;

[0218] The fifth calculation module is used to calculate the seismic toughness index of the double-column pier substructure by using the post-earthquake function loss function and function recovery function of the double-column pier bridge substructure.

[0219] As an implementation of an embodiment of the present invention, the calculation formula of the index used by the first calculation module to evaluate the damage degree of the pier column is as follows:

[0220]

[0221] Among them, K DX It is an index for evaluating the damage degree of a bridge pier; F j K is the frequency value of a certain axial force at the bottom of a bridge pier; j It is the curvature of the characteristic point on the moment-curvature curve of the pier bottom section corresponding to a certain axial force.

[0222] As an implementation method of an embodiment of the present invention, the third calculation module uses the Gumb Copula function to calculate the component correlation, and the distribution function expression of the multivariate Gumbel Copula function is:

[0223]

[0224] Among them, α is the relevant parameter, and α∈(0,1),

[0225] By introducing the Copula function, the vulnerability of multiple components to simultaneous damage can be expressed as:

[0226] P(X1X2…X k )=C(P1,P2,…,P k )

[0227] Among them, P kis the vulnerability of a single component; C(P1,P2,···,P k ) is a multivariate Copula function that considers the correlation of multiple components;

[0228] Substituted into the vulnerability expressions of the series system and the parallel system, the vulnerability of the series system P fcl for:

[0229]

[0230] As an implementation method of an embodiment of the present invention, the fourth calculation module uses the Copula function to calculate the system vulnerability considering the correlation of components, and calculates the functional loss of the bridge according to the exceedance probability of the vulnerability, and the calculation formula is:

[0231]

[0232] Where j is the damage level of the bridge system; C s,j is the repair cost of the structural system under the jth damage level; s Cost of reconstruction after total destruction; is the cost-loss ratio; P j is the destruction probability of a bridge with damage state j under a certain PGA;

[0233] The destruction probability P of the bridge with damage state j under PGA j The calculation formula is:

[0234]

[0235] in, is the exceedance probability of each damage state under a certain PGA action.

[0236] As an implementation method of an embodiment of the present invention, the function recovery function of the double-column pier bridge after an earthquake includes: a linear function recovery function, an exponential function recovery function and a trigonometric function recovery function.

[0237] The embodiments described above are only descriptions of the preferred embodiments of the present invention and are not intended to limit the scope of the present invention. Without departing from the design spirit of the present invention, various modifications and improvements made to the technical solutions of the present invention by ordinary technicians in this field should all fall within the protection scope determined by the claims of the present invention.

Claims

1. A method for evaluating the seismic toughness of a double-column pier bridge substructure, characterized in that: include: Step 1: Determine the damage index of a single component; Step 2: Determine the damage probability of a single component through the component damage index; Step 3: Based on the damage probability of a single component, the Copula function is used to calculate the vulnerability of the double-column pier substructure system; Step 4: Calculate the post-earthquake functional loss function of the substructure of the double-column pier bridge according to the system vulnerability; Step 5: Use the post-earthquake function loss function and function recovery function of the double-column pier bridge substructure to calculate the seismic toughness index of the double-column pier substructure.

2. The method for evaluating the seismic toughness of the substructure of a double-column pier bridge according to claim 1, characterized in that: In step 1, the calculation formula for evaluating the damage degree of the pier column is as follows: Among them, K DX It is an index for evaluating the damage degree of a bridge pier; F j K is the frequency value of a certain axial force at the bottom of a bridge pier; j It is the curvature of the characteristic point on the moment-curvature curve of the pier bottom section corresponding to a certain axial force.

3. The method for evaluating the seismic toughness of the substructure of a double-column pier bridge according to claim 2, characterized in that: In step 3, the Gumbel Copula function is used to calculate the component correlation. The distribution function expression of the multivariate Gumbel Copula function is: Among them, α is the relevant parameter, and α∈(0,1), By introducing the Copula function, the vulnerability of multiple components to simultaneous damage is expressed as: P(X1X2…X k )=C(P1,P2,…,P k ) Among them, P k is the vulnerability of a single component; C(P1,P2,···,P k ) is a multivariate Copula function that considers the correlation of multiple components; Substituted into the vulnerability expressions of the series system and the parallel system, the vulnerability of the series system P fcl for:

4. The method for evaluating the seismic toughness of the substructure of a double-column pier bridge according to claim 3, characterized in that: In step 4, the system vulnerability considering the correlation of components is calculated using the Copula function, and the functional loss of the bridge is calculated according to the exceedance probability of the vulnerability. The calculation formula is: Where j is the damage level of the bridge system; C s,j is the repair cost of the structural system under the jth damage level; s Cost of reconstruction after total destruction; is the cost-loss ratio; P j is the destruction probability of a bridge with damage state j under a certain PGA; The destruction probability P of the bridge with damage state j under PGA j The calculation formula is: in, is the exceedance probability of each damage state under a certain PGA action.

5. The method for evaluating the seismic toughness of the substructure of a double-column pier bridge according to claim 4, characterized in that: The function recovery functions of double-column pier bridges after earthquake include linear function recovery function, exponential function recovery function and trigonometric function recovery function.

6. A device for evaluating the seismic toughness of the substructure of a double-column pier bridge, characterized in that: include: The first calculation module is used to determine the damage index of a single component; A second calculation module is used to determine the damage probability of a single component according to the component damage index; The third calculation module is used to calculate the vulnerability of the double column pier substructure system using the Copula function according to the damage probability of a single component; The fourth calculation module is used to calculate the post-earthquake functional loss function of the substructure of the double-column pier bridge according to the system vulnerability; The fifth calculation module is used to calculate the seismic toughness index of the double-column pier substructure by using the post-earthquake function loss function and function recovery function of the double-column pier bridge substructure.

7. The device for evaluating the seismic toughness of the substructure of a double-column pier bridge according to claim 6, characterized in that: The calculation formula of the index used by the first calculation module to evaluate the damage degree of the pier column is as follows: Among them, K DX It is an index for evaluating the damage degree of a bridge pier; F j K is the frequency value of a certain axial force at the bottom of a bridge pier; j It is the curvature of the characteristic point on the moment-curvature curve of the pier bottom section corresponding to a certain axial force.

8. The device for evaluating the seismic toughness of the substructure of a double-column pier bridge according to claim 7, characterized in that: The third calculation module uses the Gumb Copula function to calculate the component correlation. The distribution function expression of the multivariate Gumbel Copula function is: Among them, α is the relevant parameter, and α∈(0,1), By introducing the Copula function, the vulnerability of multiple components to simultaneous damage is expressed as: P(X1X2…X k )=C(P1,P2,…,P k ) Among them, P k is the vulnerability of a single component; C(P1,P2,···,P k ) is a multivariate Copula function that considers the correlation of multiple components; Substituted into the vulnerability expressions of the series system and the parallel system, the vulnerability of the series system P fcl for:

9. The device for evaluating the seismic toughness of the substructure of a double-column pier bridge according to claim 8, characterized in that: The fourth calculation module uses the Copula function to calculate the system vulnerability considering the correlation of components, and calculates the functional loss of the bridge according to the exceedance probability of the vulnerability. The calculation formula is: Where j is the damage level of the bridge system; C s,j is the repair cost of the structural system under the jth damage level; s Cost of reconstruction after total destruction; is the cost-loss ratio; P j is the destruction probability of a bridge with damage state j under a certain PGA; The destruction probability P of the bridge with damage state j under PGA j The calculation formula is: in, is the exceedance probability of each damage state under a certain PGA action.

10. The double-column pier bridge substructure seismic toughness assessment device according to claim 9, characterized in that: The function recovery functions of double-column pier bridges after earthquake include linear function recovery function, exponential function recovery function and trigonometric function recovery function.

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