CN112580138A - Urban bridge load limit determination method based on traffic data and reliability theory - Google Patents

Urban bridge load limit determination method based on traffic data and reliability theory Download PDF

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CN112580138A
CN112580138A CN202011516435.3A CN202011516435A CN112580138A CN 112580138 A CN112580138 A CN 112580138A CN 202011516435 A CN202011516435 A CN 202011516435A CN 112580138 A CN112580138 A CN 112580138A
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load
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冯德成
袁捷
陈适之
孙震
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Southeast University
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    • G06—COMPUTING; CALCULATING OR COUNTING
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    • G06F30/00—Computer-aided design [CAD]
    • G06F30/10—Geometric CAD
    • G06F30/13—Architectural design, e.g. computer-aided architectural design [CAAD] related to design of buildings, bridges, landscapes, production plants or roads
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    • G06F30/23—Design optimisation, verification or simulation using finite element methods [FEM] or finite difference methods [FDM]
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    • G06—COMPUTING; CALCULATING OR COUNTING
    • G06F—ELECTRIC DIGITAL DATA PROCESSING
    • G06F2119/00—Details relating to the type or aim of the analysis or the optimisation
    • G06F2119/02—Reliability analysis or reliability optimisation; Failure analysis, e.g. worst case scenario performance, failure mode and effects analysis [FMEA]
    • G—PHYSICS
    • G06—COMPUTING; CALCULATING OR COUNTING
    • G06F—ELECTRIC DIGITAL DATA PROCESSING
    • G06F2119/00—Details relating to the type or aim of the analysis or the optimisation
    • G06F2119/14—Force analysis or force optimisation, e.g. static or dynamic forces

Abstract

The invention discloses an urban bridge load limit determining method based on traffic data and a reliability theory, aiming at the current situation that the original bridge is increasingly overloaded by muck trucks and other freight heavy-duty vehicles, the dynamic weighing equipment is used for collecting the data of the passing vehicles, a random traffic model is randomly sampled and established based on a load limit value, an influence line is used for loading the random traffic model to obtain an extreme value sample of bridge control section response, and then the distribution of the extreme value of the bridge control section response is obtained through generalized extreme value distribution fitting. And determining a reliability index corresponding to the current load limiting value according to a reliability theory and a bridge limit state equation based on the dead load effect and the bridge bearing capacity of the design file, the finite element software calculation and the related detection test, and selecting a proper bridge load limiting value according to the reliability index. The invention provides scientific basis for making management measures of relevant departments and managing bridge safety, and provides a calculation method for solving the problem that the current part of bridge load limit value is unclear and inaccurate.

Description

Urban bridge load limit determination method based on traffic data and reliability theory
Technical Field
The invention relates to the fields of random traffic flow load models, bridge bearing capacity assessment and the like, and mainly relates to a bridge load limit value calculation method based on a reliability theory.
Background
China's in-service highway bridges have differences in design load, resistance attenuation conditions and the like, and the number of potential overweight vehicles is huge, so that the current overload determination standard cannot accurately provide reliable basis for the load limit value of the bridge, the treatment strength of the highway management department on overweight automobiles is increased, and the examination and approval work of overload transportation traffic licenses is also in a predicament. Although domestic scholars do a great deal of theoretical and experimental research work in the aspect of overload bridge load limiting value, a typical vehicle load model proposed in the last 90 th century is still adopted at present, a perfect bridge load limiting standard is not formed, an overload bridge load limiting value analysis model with engineering applicability is not provided, research in the aspect of a bridge load limiting mode is delayed, and formulation of national highway bridge load limiting specifications is restricted.
The overload of the vehicle can seriously harm the life and property safety, the effect of the vehicle load on the bridge structure can cause high attention, the cognition of the actual loading condition of the structure is urgent and has great significance, the load limit standard of the bridge is determined from the reliability, scientific basis can be provided for the formulation of management measures of relevant departments and the safe management and maintenance of the bridge, and the problem that the current load limit value of part of the bridge is not clear and accurate is solved.
Disclosure of Invention
The invention provides a method for calculating the reliability of a load limiting value of a bridge for heavy-duty vehicles to pass, provides an overload bridge load limiting value analysis model with engineering applicability, determines a load limiting standard of the bridge from the perspective of reliability, and provides a scientific basis for formulation of management measures of relevant departments and safe management and maintenance of the bridge.
In order to achieve the purpose, the invention adopts the following technical scheme:
a city bridge load limit determination method based on traffic data and a reliability theory comprises the following steps:
step 1: the method comprises the steps that bridge passing vehicle information is collected through dynamic weighing equipment, vehicle types, vehicle weights, vehicle speed distribution and vehicle head distance data on a passing line are collected, all vehicles are classified into a plurality of limited vehicle types 1, 2, … … and k according to the number of axles, and mean value standardization processing is conducted on the wheel base of each vehicle type;
step 2: fitting each axle weight of each vehicle type by using a probability density distribution function to obtain the probability density distribution condition of each axle weight of each vehicle type, and simultaneously determining the vehicle distance distribution of the lane;
and step 3: setting an initial load limit value WLRandomly sampling vehicles to form a random traffic flow load model, and comparing the load exceeding a load limit value WLExtracting the vehicle again;
and 4, step 4: determining a control section of a bridge to be load-limited and calculating a corresponding influence line, loading a random traffic flow model by using the influence line, for a multi-lane bridge, superposing the random traffic flow load of each lane on the control section in response, and selecting a daily bridge control section response extreme value to obtain a bridge control section response extreme value sample taking days as a unit;
and 5: carrying out generalized extremum distribution fitting on the extremum sample of the bridge control section response to obtain the bridge control section response extremum distribution Sd；
Step 6: calculating the dead load effect S of the control section based on the design file, the calculation of the bridge finite element model and the related detection test resultsSAnd a bearing capacity R;
and 7: according to the reliability theory and the bridge limit state equation Z ═ R-Sd-SSCalculating the current load limit value WLThe corresponding reliability index beta of the lower bridge;
and 8: comparing the reliability index beta obtained by analysis with the related standard terms, and if the reliability index beta does not meet the related standard terms, modifying the load limit value WLRepeating the steps (3) to (7) until the load limit value W meeting the requirement of the reliability index is metL。
As a further preferable scheme, the axle weight distribution of the vehicle model in the step 2 adopts mixed gaussian distribution, and the expression is as follows:
Figure BDA0002848102150000021
wherein
Figure BDA0002848102150000022
Is the axial weight Gaussian distribution function of the ith distribution of the j axisjiAnd σjiMean and variance of the Gaussian distribution, ajiThe axial weight x belongs to gj(x|μji,σji) The probability of the distribution;
the distance between the vehicles on the lanes adopts lognormal distribution or generalized extremum distribution, and the lognormal distribution is as follows:
Figure BDA0002848102150000023
wherein x is a random variable representing the vehicle distance, mu is a central parameter, and sigma is a shape parameter;
the generalized extremum distribution is:
Figure BDA0002848102150000031
wherein x is a random variable representing the vehicle distance, k is a uniform coefficient of a 3-class extremum distribution function, mu is a central parameter, and sigma is a shape parameter.
As a further preferable scheme, in step 3, randomly sampling is performed, the number n of traffic flows on the day is determined, and the sampling sequence is as follows: the 1 st vehicle type, the 1 st vehicle axle weight, the first vehicle distance, the 2 nd vehicle type, the 2 nd vehicle axle weight, the 2 nd vehicle distance … …, the nth vehicle type and the nth vehicle axle weight.
As a further preferred scheme, the influence line loading method in the step 4 is to store random traffic flow model information in a one-dimensional matrix { F }, namely the matrix { F } contains traffic flow vehicle-mounted information, wherein AWijRepresents the ith vehicle jth axle weight:
{F}＝[AW 11 0…0AW ij 0…0…]
the random traffic flow load model of one lane is a discrete concentrated load separated by one wheelbase or one wheelbase, nonzero values in a one-dimensional matrix represent axle weights, the number of 0 between two axle weights represents the distance between the axle weights, delta L is set as the distance between any two adjacent values, and the size of the delta L determines the calculation precision;
the bridge control interface influence line information is stored in a one-dimensional matrix { L }, namely the matrix { L } contains bridge bearing capacity information, and delta L is set to be the distance between any two adjacent values:
{L}＝[x0 x1 x2…xk…xm]
wherein xkShowing the effect of loading unit axial weight on the control section at a distance influence line initial position k deltal,
and multiplying any adjacent m +1 values of { F } with all m +1 values in { L }, and finishing one-time loading.
As a further preferred scheme, the step 5 generalized extreme distribution fitting may adopt Gumbel distribution of Gumbel distribution or Weibull distribution of Weibull distribution.
Advantageous effects
The invention provides a scientific basis for formulation of management measures of relevant departments and safe management and maintenance of bridges, and provides a calculation method based on traffic flow data and a reliability theory for solving the problems of unclear and inaccurate bridge load limitation caused by the increasingly serious condition of road and bridge vehicle overload, the change of load design standards of bridges, the non-uniform load design standards of established bridges and the like in China. The method can consider the axle load and the wheel base information of the vehicle, process and consider the change condition of the vehicle load in reality by using the mathematical model, fully consider the uncertainty characteristic of the vehicle load, and is more accurate compared with the load limit value determined by using a standard load loading method.
Drawings
FIG. 1 is a schematic flow diagram of the present invention;
FIG. 2 is a model 4-axis weight frequency distribution histogram and fitting distribution;
FIG. 3 is a vehicle spacing sample;
FIG. 4 is a frequency distribution histogram and fitting distribution of extreme values of vehicle load effect at a certain bridge load limit of 50 t.
Detailed Description
The invention is further described below with reference to the accompanying drawings.
The method for determining the load limit of the urban bridge based on traffic data and the reliability theory is explained by combining an existing concrete bridge of a certain city and obtaining traffic data of 102537 vehicles in 26 days by using a dynamic weighing system, wherein the bridge is a three-span variable cross-section box type concrete bridge, the total length is 150m, the span combination is 45+60+45m, the single width is 12m, the single width is double lanes, and the structural safety level is one level.
The implementation steps are as follows:
step 1, extracting data of passing vehicles recorded by a dynamic weighing system (WIM) in the city to obtain original traffic flow information, and summarizing and concluding information of axle weight, axle distance, speed and the like of each vehicle. All vehicles are divided into six types according to the number of axles, because 2-axle vehicles occupy the most and the axle distance is large in dispersion, two-axle vehicles are divided into a vehicle type 1 and a vehicle type 2, the vehicle types 3 to 6 are respectively three-axle to six-axle vehicles, the vehicle types of six axles and above occupy less, and the vehicle types of more than six axles are not considered. The same vehicle model has the same number of axles, the wheelbases are objectively different, the wheelbases are sampled too complicated and have little influence on the calculation result, the average value of the wheelbases of each vehicle model is subjected to standardized processing for reducing the processing amount, namely, the wheelbases of each vehicle model are counted, and the average value of the wheelbases is taken to replace all the wheelbases of the vehicle model. Taking model 4, a four-axle truck as an example, the first wheelbase after mean normalization is 2.01m, the average value representing the counted first wheelbase of the three-axle truck is 2.01m, and the wheelbase of 2.01m will represent the first wheelbase of all three-axle trucks.
Through the simplification of the mean value, the information of each vehicle type is shown in table 1, wherein AW represents the axle weight, the first number of the subscript represents the vehicle type number, and the second number represents the wheel base number.
TABLE 1 proportion of each vehicle type and model indication
Figure BDA0002848102150000051
Step 2, fitting the axle weight and the vehicle distance of each vehicle type by using a probability density distribution function, fitting the Gaussian mixture distribution characteristic shown by the collected vehicle axle weight information by using a Gaussian mixture distribution function, wherein the Gaussian mixture distribution expression is as follows:
Figure BDA0002848102150000052
wherein
Figure BDA0002848102150000061
Is the axial weight Gaussian distribution function of the ith distribution of the j axisjiAnd σjiMean and variance of the Gaussian distribution, ajiThe axial weight x belongs to gj(x|μji,σji) Probability of distribution.
Taking the vehicle type 4 as an example, the distribution parameters after the vehicle axle weight information is fitted are shown in the following table 2, and the probability distribution map is shown in fig. 2.
TABLE 2 vehicle axle weight Gaussian mixture distribution parameters
Figure BDA0002848102150000062
For the influence of the vehicle distance on the load effect, the distance between two vehicles is calculated according to the vehicle passing time and the speed, and the average value of the speeds is multiplied by the time difference of the two vehicles reaching the dynamic weighing to be used as the distance between the two vehicles, so as to obtain a vehicle distance sample, as shown in fig. 3. The generalized extreme value distribution fitting is carried out on the vehicle distance sample, and the vehicle distance distribution function in the embodiment is
y＝f(x)＝0.00509exp{-[1+0.00489(x-232.93)]-1.042}[1+0.00489(x-232.93)]-2.042
Two typical traffic flow running states, namely dense traffic flow and sparse traffic flow, are taken, the original traffic distance is corrected, the average value is respectively normalized to 10m and 100m, the average value standardization processing method is to scale the traffic distance so as to consider the adverse condition influence of the traffic distance, the traffic distance distribution conditions before and after scaling are similar, and the average value of the traffic distance is manually scaled to 10m and 100m to obtain a corrected traffic distance distribution model.
And 3, sampling the axle weight distribution model and the vehicle distance distribution model, determining 5000 vehicles per day in traffic flow quantity according to local vehicle data, and setting an initial bridge load limit value of 50 t. The sampling sequence is as follows: and (3) resampling the extracted vehicle axle weight when the extracted vehicle axle weight exceeds a load limit value until 5000 pieces of vehicle information are completely extracted.
And 4, establishing a bridge finite element analysis model by using the midas finite element analysis software, determining the control section of the bridge, calculating a corresponding influence line, and loading by using the influence line.
The influence lines are loaded on a matlab platform for programming, the bending moment of a section is controlled for example, and the bending moment influence lines are stored in a one-dimensional matrix { L } - [ x ] every 0.1m0 x1 x2…xk…x1600]In the middle, the bridge length is 160m, and the matrix elements are 1601. And storing a daily random traffic flow load model in a one-dimensional matrix every 0.1m by taking a day as a unit, taking 1601 adjacent elements from the 1 st element to form a traffic flow load matrix, multiplying the traffic flow load matrix vector by an influence line vector to obtain a primary load effect, taking 1601 adjacent elements from the 2 nd element to form a traffic flow load matrix, repeating the calculation until all vehicles on the day are finished, and taking the maximum value of the load effect to obtain the extreme value response of the day. And repeating 365 times of sampling calculation, multiplying by an impact coefficient specified by a specification to obtain a vehicle load effect extreme value sample of one year, and calculating a response of one year for calculating the bridge reliability of a corresponding load recurrence period.
And 5, solving a frequency distribution histogram of the bridge control section response extreme value sample by using matlab software, and simultaneously carrying out generalized extreme value distribution fitting, as shown in FIG. 4.
Step 6, combining the design file, the bridge finite element model and the related detection test result, calculating to obtain the cross-span midspan bending resistance bearing capacity 26630.7kN.m of the bridge, and the cross-span bending moment 16031.6kN.m of the bridge under the self weight, so that the bearable random traffic flow effect limit value is as follows: 26630.7-16031.6-10599.1 kn.m, reliability Z is 10599.1kn.m minus the probability that the random traffic effect value is greater than zero. And then calculating the corresponding reliability index of the bridge under the current load limit value of 50t to be 3.24.
And 7, referring to the reliability index specification of unified design for reliability of highway engineering (JTG 2120) 2020, modifying the load limiting value to 36t when the calculated reliability index is not less than the requirement in the table 3 and is not satisfied, repeating the steps, and determining that the adjusted load limiting value meets the requirement, namely determining that the load limiting value of the bridge is 36 t.
TABLE 3 reliability index beta of structural Member
Figure BDA0002848102150000081
The above description is only for the preferred embodiment of the present invention, but the scope of the present invention is not limited thereto, and any person skilled in the art should be considered to be within the technical scope of the present invention, and the technical solutions and the inventive concepts thereof according to the present invention should be equivalent or changed within the scope of the present invention.

Claims (5)

1. A city bridge load limit determination method based on traffic data and a reliability theory is characterized by comprising the following steps:
step 1: the method comprises the steps that bridge passing vehicle information is collected through dynamic weighing equipment, vehicle types, vehicle weights, vehicle speed distribution and vehicle head distance data on a passing line are collected, all vehicles are classified into a plurality of limited vehicle types 1, 2, … … and k according to the number of axles, and mean value standardization processing is conducted on the wheel base of each vehicle type;
step 2: fitting each axle weight of each vehicle type by using a probability density distribution function to obtain the probability density distribution condition of each axle weight of each vehicle type, and simultaneously determining the vehicle distance distribution of the lane;
and step 3: setting an initial load limit value WLRandomly sampling vehicles to form a random traffic flow load model, and comparing the load exceeding a load limit value WLExtracting the vehicle again;
and 4, step 4: determining a control section of a bridge to be load-limited and calculating a corresponding influence line, loading a random traffic flow model by using the influence line, for a multi-lane bridge, superposing the random traffic flow load of each lane on the control section in response, and selecting a daily bridge control section response extreme value to obtain a bridge control section response extreme value sample taking days as a unit;
and 5: carrying out generalized extremum distribution fitting on the extremum sample of the bridge control section response to obtain the bridge control section response extremum distribution Sd；
Step 6: calculating the dead load effect S of the control section based on the design file, the calculation of the bridge finite element model and the related detection test resultsSAnd a bearing capacity R;
and 7: according to the reliability theory and the bridge limit state equation Z ═ R-Sd-SSCalculating the current load limit value WLThe corresponding reliability index beta of the lower bridge;
and 8: comparing the reliability index beta obtained by analysis with the related standard terms, and if the reliability index beta does not meet the related standard terms, modifying the load limit value WLRepeating the steps 3 to 7 until the load limit value W meeting the requirement of the reliability index is metL。
2. The urban bridge load limiting determination method based on traffic data and reliability theory according to claim 1, characterized in that: step 2, vehicle model axle weight distribution adopts mixed Gaussian distribution, and the expression is as follows:
Figure FDA0002848102140000011
wherein
Figure FDA0002848102140000012
Is the axial weight Gaussian distribution function of the ith distribution of the j axisjiAnd σjiMean and variance of the Gaussian distribution, ajiThe axial weight x belongs to gj(x|μji,σji) The probability of the distribution;
the distance between the vehicles on the lanes adopts lognormal distribution or generalized extremum distribution, and the lognormal distribution is as follows:
Figure FDA0002848102140000021
wherein x is a random variable representing the vehicle distance, mu is a central parameter, and sigma is a shape parameter;
the generalized extremum distribution is:
Figure FDA0002848102140000022
wherein x is a random variable representing the vehicle distance, k is a uniform coefficient of a 3-class extremum distribution function, mu is a central parameter, and sigma is a shape parameter.
3. The urban bridge load limiting determination method based on traffic data and reliability theory according to claim 1, characterized in that: in the step 3, the random sampling firstly determines the traffic flow number n at the day, and the sampling sequence is as follows: the 1 st vehicle type, the 1 st vehicle axle weight, the first vehicle distance, the 2 nd vehicle type, the 2 nd vehicle axle weight, the 2 nd vehicle distance … …, the nth vehicle type and the nth vehicle axle weight.
4. The urban bridge load limiting determination method based on traffic data and reliability theory according to claim 1, characterized in that: the influence line loading method in the step 4 is to store random traffic flow model information in a one-dimensional matrix { F }, namely the matrix { F } contains traffic flow vehicle-mounted information, wherein AWijRepresents the ith vehicle jth axle weight:
{F}＝[AW11 0…0 AWij 0…0…]
the random traffic flow load model of one lane is a discrete concentrated load separated by one wheelbase or one wheelbase, nonzero values in a one-dimensional matrix represent axle weights, the number of 0 between two axle weights represents the distance between the axle weights, delta L is set as the distance between any two adjacent values, and the size of the delta L determines the calculation precision;
the bridge control interface influence line information is stored in a one-dimensional matrix { L }, namely the matrix { L } contains bridge bearing capacity information, and delta L is set to be the distance between any two adjacent values:
{L}＝[x0 x1 x2…xk…xm]
wherein xkShowing the effect of loading unit axial weight on the control section at a distance influence line initial position k deltal,
and multiplying any adjacent m +1 values of { F } with all m +1 values in { L }, and finishing one-time loading.
5. The urban bridge load limiting determination method based on traffic data and reliability theory according to claim 1, characterized in that: the generalized extreme distribution fitting in the step 5 can adopt Gumbel distribution of Gumbel distribution or Weibull distribution of Weibull distribution.
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