CN111008412A - Crack width-based reliability assessment method for in-service ballastless track structure - Google Patents
Crack width-based reliability assessment method for in-service ballastless track structure Download PDFInfo
- Publication number
- CN111008412A CN111008412A CN201911006887.4A CN201911006887A CN111008412A CN 111008412 A CN111008412 A CN 111008412A CN 201911006887 A CN201911006887 A CN 201911006887A CN 111008412 A CN111008412 A CN 111008412A
- Authority
- CN
- China
- Prior art keywords
- ballastless track
- track structure
- crack width
- service
- reliability
- Prior art date
- Legal status (The legal status is an assumption and is not a legal conclusion. Google has not performed a legal analysis and makes no representation as to the accuracy of the status listed.)
- Pending
Links
Images
Abstract
The invention discloses a crack width-based reliability assessment method for an in-service ballastless track structure, which comprises the following specific steps of: establishing a function G (X) w for evaluating the crack width of a ballastless track structurelim-w; counting probability distribution and statistical parameters of random variables in the function by adopting a mathematical statistical method, wherein the probability distribution and the statistical parameters of actual stress of the tensioned steel bars in the in-service ballastless track structure are obtained by analyzing monitoring data; calculating the failure probability P of the crack width of the ballastless track structuref＝P[G(X)<0]Converted into reliability index β ═ Φ‑1(1‑Pf) And comparing the reliable indexes of the service state of the ballastless track structure obtained by calculation and analysis with the design reliable indexes. The invention relates to a crack width-based reliability evaluation method for an in-service ballastless track structure,the reliability of the ballastless track structure can be accurately quantified in the probability sense based on scientific monitoring data.
Description
Technical Field
The invention belongs to the technical field of ballastless tracks, and particularly relates to a method for evaluating the reliability of an in-service ballastless track structure based on crack width.
Background
The ballastless track structure of the high-speed railway has the characteristics of good smoothness and less maintenance, and is widely applied in China. However, the ballastless track structure is exposed in a complex atmospheric environment for a long time and is influenced by factors of train load, environmental conditions and the like, the track structure inevitably generates damage accumulation and load capacity degradation, and once the track structure is damaged, the safe and stable running of the train is even influenced in a serious condition. Therefore, the method is particularly important for real-time and effective evaluation of the service state of the ballastless track of the high-speed railway.
The existing state evaluation method for the ballastless track structure is a method based on determinacy, the size of a detection value is compared with an evaluation standard value for evaluation, and the reliability level of the service state of the ballastless track structure cannot be quantitatively expressed. Considering that actually, the construction and operation processes of the ballastless track structure are subject to a plurality of uncertainties, the reliability method is adopted for evaluation, and the evaluation is more scientific and reasonable. The basic idea of the reliability assessment method is to take the response of a structural system under the combined action of the generalized resistance of the structural system and multiple factors as a random variable and perform calculation and analysis on the failure probability of a functional function of a certain limit state. Therefore, the method for evaluating the reliability of the service state of the ballastless track of the high-speed railway based on the field monitoring data is established, the service state evaluation of the ballastless track which is accurately quantified in the probability sense is realized, and the method has important engineering application value for formulating the maintenance and maintenance strategy of the ballastless track structure system of the high-speed railway and ensuring the safe operation of the high-speed railway in China.
Disclosure of Invention
Aiming at the defects or the improvement requirements of the prior art, the invention provides an in-service ballastless track structure reliability assessment method based on crack width, which comprises the steps of establishing a function for assessing the crack width of a ballastless track structure, arranging a plurality of monitoring points with sensors on the ballastless track structure, monitoring and acquiring the stress of each part of the ballastless track structure under load in real time, screening and eliminating abnormal monitoring data, counting the probability distribution and the statistical parameters of random variables in the function by adopting a mathematical statistical method, wherein the probability distribution and the statistical parameters of the actual stress of a tensioned steel bar in the in-service ballastless track structure are obtained by analyzing the monitoring data, calculating failure probability and reliable indexes based on a probability model of the function, analyzing more scientifically, truthfully and accurately according to the monitoring data, and accurately quantifying the reliability of the ballastless track in the probability sense, the method has important value for making maintenance strategies for the ballastless track structural system of the high-speed rail and ensuring the safe operation of the high-speed railway in China.
In order to achieve the purpose, the invention provides a crack width-based reliability assessment method for an in-service ballastless track structure, which comprises the following specific steps:
s1 function for establishing ballastless track structure crack width evaluation
G(X)＝wlim-w
Wherein, wlimIs the maximum crack width limit value and is,
for calculating the width of the crack
S2 deep analysis of probability model and statistical parameter of random variable in function based on monitoring data
Arranging a plurality of monitoring points provided with sensors at intervals on a ballastless track, analyzing general random variable parameters to determine the mean value, standard deviation and variation coefficient of the parameters, screening the monitored actual tension steel bar stress-strain data in the in-service ballastless track structure by using a data verification method, obtaining and converting the data into effective steel bar stress values, and analyzing the probability distribution type and statistical parameters of actual steel bar stress obedience;
s3 calculating crack width reliability index of ballastless track structure
Calculating failure probability P of ballastless track structurefWherein P isf＝P[G(X)<0]And obtaining the probability P according to the graphfA value of (d);
calculating a reliable index β of the ballastless track structure according to the failure probability, wherein β ═ phi-1(1-Pf)，Φ-1(. h) is the inverse of a standard normal distribution;
s4, comparing the reliable indexes of the service state of the ballastless track structure obtained through calculation and analysis with the design reliable indexes in the design specification to evaluate the service state of the ballastless track structure.
Further, in step S3, the concrete solving step includes:
s31 generating N groups of independent sample points (X) according to probability model of random variable in function1,X2,X3,···,Xn)(i＝0,1,2,···,n)；
S32, substituting the extracted N groups of sample points into the structural function, and calculating the function value of Z;
s33 for Z ═ g (X)1,X2,X3,···,Xn) The array of <0 is counted and is marked as Nf；
S34 uses formula Pf＝NfThe failure probability of the structure is obtained;
s35 using the formula β ═ Φ-1(Pf) And solving a reliability index, and evaluating the service state of the track structure.
Further, calculating the width of the crack of the reinforced concrete tension member of the ballastless track
Calculated according to the following formula:
wherein, αcrThe stress characteristic coefficient of the component is psi, the strain non-uniformity coefficient of the longitudinal tension steel bar between cracks is sigmasFor the reinforcement stress obtained by monitoring the data, EsIs the modulus of elasticity of the steel bar, csThe distance from the outer edge of the outermost longitudinal tension bar to the bottom edge of the tension zone, deqIs the equivalent diameter, rho, of the longitudinal reinforcement of the tension zoneteThe reinforcement ratio of the longitudinal tension steel bar is calculated according to the effective section area of the tension concrete.
Further, calculating the crack width of the reinforced concrete flexural member of the ballastless track
Can be calculated according to the following formula:
wherein, K1Is the influence coefficient of the surface shape of the steel bar, K2R is the ratio of the distance from the neutral axis to the edge of tension to the distance from the neutral axis to the center of gravity of the tendon under tension, σsFor the reinforcement stress obtained by monitoring the data, EsIs the modulus of elasticity of the steel bar, and d is the diameter of the tensioned steel bar; mu.szThe effective reinforcement ratio of the tensioned steel bar is obtained.
Further, the data verification method in step S1 includes chi-square verification or K-S verification.
Further, the sensors are all arranged longitudinally along the line in the axial direction.
Furthermore, sensors are arranged at the large end thorn, the friction plate and the abutment front and the abutment tail of the bridge abutment of the ballastless track, and sensors are arranged at the beam end and the span of the simply supported beam.
In general, compared with the prior art, the above technical solution contemplated by the present invention can achieve the following beneficial effects:
(1) the method for evaluating the reliability of the in-service ballastless track structure based on the crack width comprises the steps of arranging a plurality of monitoring points with sensors on the ballastless track structure, monitoring and obtaining the stress of each part of the ballastless track structure under load in real time, screening and removing abnormal monitoring data, screening the tensioned actual steel bar stress-strain data in the in-service ballastless track structure obtained by monitoring by using a data verification method, obtaining and converting the data into effective steel bar stress values, analyzing the probability distribution type and statistical parameters obeyed by the actual steel bar actual stress, obtaining the failure probability based on a probability model of a function, then quantitatively calculating and reliable indexes according to the failure probability, and obtaining more scientific, real and accurate analysis according to the monitoring data so as to accurately quantify the reliability of the ballastless track in the probability sense, the method has important value for making maintenance strategies for the ballastless track structural system of the high-speed rail and ensuring the safe operation of the high-speed railway in China.
(2) According to the in-service ballastless track structure reliability assessment method based on the crack width, formulas for calculating the crack width are respectively set for the reinforced concrete tension member and the flexural member of the ballastless track, so that the calculated crack width obtained according to the monitored stress data is more accurate and closer to reality, and the final ballastless track structure reliability assessment is more scientific.
(3) According to the in-service ballastless track structure reliability assessment method based on crack width, the sensors are axially and longitudinally arranged along a line, the large-end thorn, the friction plate and the abutment front and the abutment tail of the ballastless track are respectively provided with the sensors, and the beam end and the span of the simply supported beam are respectively provided with the sensors, so that the integrity and the scientificity of monitoring are ensured, and the authenticity and the accuracy of assessment data are ensured.
Drawings
Fig. 1 is a schematic distribution diagram of ballastless track detection points in an embodiment of the present invention;
FIG. 2 is a flow chart of reliability indicator calculation in an embodiment of the present invention;
FIG. 3 is a schematic diagram of crack width reliability changes at each detection point in 2015-2017 monitored and calculated in the embodiment of the invention.
In all the figures, the same reference numerals denote the same features, in particular: 101-a first sensor, 102-a second sensor, 103-a third sensor, 104-a fourth sensor, 105-a fifth sensor, 106-a sixth sensor, 107-a seventh sensor, 108-an eighth sensor, 109-a ninth sensor, 110-a tenth sensor, 111-an eleventh sensor, 112-a twelfth sensor, 113-a thirteenth sensor, 114-a fourteenth sensor, 115-a fifteenth sensor, 116-a sixteenth sensor; 2-big end thorn, 3-friction plate, 4-abutment, 5-first simple supported beam, 6-second simple supported beam, 7-third simple supported beam, 8-fourth simple supported beam, 9-fifth simple supported beam and 10-sixth simple supported beam.
Detailed Description
In order to make the objects, technical solutions and advantages of the present invention more apparent, the present invention is described in further detail below with reference to the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are merely illustrative of the invention and are not intended to limit the invention. In addition, the technical features involved in the embodiments of the present invention described below may be combined with each other as long as they do not conflict with each other.
A plurality of monitoring points are arranged on the ballastless track structure of the high-speed railway, and sensors are arranged on the monitoring points and used for monitoring the stress values of all parts of the ballastless track structure in real time, so that the reliability of the ballastless track structure of the high-speed railway at present is calculated and evaluated according to the stress values obtained by monitoring. Fig. 1 is a schematic distribution diagram of ballastless track detection points in an embodiment of the present invention. As shown in fig. 1, the monitoring points are arranged on the structure to be monitored at intervals, and a plurality of monitoring points are arranged at intervals; preferably, the sensors are all arranged longitudinally along the line. For example, in the reliability monitoring of the slab ballastless track base plate, monitoring points are all arranged on the outer rail side of the base plate, a sixteenth sensor 116, a fifteenth sensor 115, a fourteenth sensor 114 and a thirteenth sensor 113 are sequentially arranged in front of and at the tail of the large-end pin 2, the friction plate 3 and the abutment 4, a first sensor 101, a second sensor 102, a third sensor 103, a fourth sensor 104, a fifth sensor 105, a sixth sensor 106, a seventh sensor 107, an eighth sensor 108, a ninth sensor 109, a tenth sensor 110, an eleventh sensor 111 and a twelfth sensor 112 are sequentially arranged at the beam ends and spans of the first simple support beam 5, the second simple support beam 6, the third simple support beam 7, the fourth simple support beam 8, the fifth simple support beam 9 and the sixth simple support beam 10, the data of the base plate are reasonably monitored in real time through the arrangement of the sensors, and the reliability of the ballastless track structure is calculated according to the data.
The method for evaluating the reliability of the in-service ballastless track structure based on the crack width specifically comprises the following steps:
s1 building ballastless track structure crack width assessment function
The ballastless track reinforced concrete structure is allowed to crack in the using process, but the durability of the ballastless track reinforced concrete structure is ensured by controlling the crack width, and the reliability of the ballastless track structure is obtained by monitoring and evaluating the crack width.
S11, establishing a function for evaluating the reliability of the crack width of the ballastless track structure as follows:
G(X)＝wlim-w formula (1)
In the formula (I), the compound is shown in the specification,
for the maximum crack width limit value (mm), referring to the concrete structure design specification (GB50010-2010, 2015 edition), the crack width limit of the ordinary reinforced concrete is 0.2mm under the environmental condition that an aggressive medium exists, and when the thickness of the protective layer of the reinforced concrete exceeds 30mm, the crack width limit can be amplified by multiplying the ratio of the actual thickness of the protective layer to 30mm by 0.2 mm;
to calculate the crack width (mm), the crack was measured according to the railway track design rules (extreme state method) (Q/CR 9130-2018):
s12 obtaining and calculating the crack width
Preferably, the calculated crack width of the reinforced concrete tension member of the ballastless track
Calculated according to the following formula:
in the formula αcrFor the stress characteristic coefficient of the member, for the reinforced concrete tension member, the eccentricity is pulled by 2.4, and the axis is pulled by 2.7;
psi is the uneven coefficient of the longitudinal tension steel bar strain among cracks: in general, when 0.2 ≦ ψ ≦ 1.0 calculated from equation (3), and when 0.2 ≦ ψ ≦ 1.0 is calculated, when ψ is less than 0.2, ψ is taken to be 0.2, when ψ >1.0, ψ is taken to be 1.0, and ψ is taken to be 1.0 for a member directly receiving a repetitive load;
Esthe elastic modulus of the steel bar is a constant value and can be directly obtained;
csthe distance (mm) from the outer edge of the outermost longitudinal tension steel bar to the bottom edge of the tension area, csCan be obtained according to current record or measurement, and the value range is in 20 ~ 60: when c is going tosWhen the number is less than 20, take cs20; when c is going tosWhen > 65, take cs＝65；
ftkThe standard value of the concrete tensile strength is a constant value and can be directly obtained according to design specifications and standards;
ρtethe reinforcement ratio of the longitudinal tension steel bar is calculated according to the effective section area of the tension concrete; for the unbonded post-tensioning member, only taking the longitudinal tensioned steel bars to calculate the reinforcement ratio; in the calculation of the maximum crack width, ρ is generally calculated by equation (5)teNot less than 0.01, if rho is calculatedteWhen the value is less than 0.01, taking rhote＝0.01；
AteIs the effective tensile concrete cross-sectional area; a. thesThe area of the section of the longitudinal steel bar in the tension area; a. thepThe section area of the longitudinal prestressed tendon in the tension area can be measured or obtained according to the existing data;
deqthe equivalent diameter (mm) of the longitudinal steel bar in the tension area; diThe nominal diameter of the ith longitudinal steel bar in the tension area; n isiThe number of the ith longitudinal steel bars in the tension area is the number of the ith longitudinal steel bars in the tension area; v. ofiThe coefficient of the relative adhesion property of the ith longitudinal steel bar in the tension area is 0.7 of the plain steel bar and 1.0 of the ribbed steel bar for the non-prestressed steel bar.
σsThe stress of the steel bar is obtained by monitoring data, is the stress of the member under the coupling action of actually bearing various external loads (integral temperature action, concrete shrinkage and creep action, temperature gradient action, beam body deflection action and the like), and is a comprehensive random variable when reliability analysis is carried out, and the stress sigma of the longitudinally-tensioned steel bar is a longitudinal tensile stress sigmas。
Preferably, the calculated crack width of the reinforced concrete flexural member of the ballastless track
Can be calculated according to the following formula:
in the formula: k1Calculating crack width K for the surface shape influence coefficient of the steel bar1Ribbed bar K ═ 1.01＝0.72；
K2Influence coefficient for load characteristicα is coefficient, 0.5 for diagonal reinforcing bar, 0.3 for ribbed reinforcing bar, M1Bending moment under variable action; m2Bending moment under permanent action; m is bending moment under the action of all calculated loads;
r is the ratio of the distance from the neutral axis to the tension edge to the distance from the neutral axis to the center of gravity of the tension steel bar, and for the beam and the plate, r can be respectively 1.1 and 1.2;
Esis the modulus of elasticity of the steel bar; d is the diameter of the tensioned steel bar; mu.szEffective reinforcement ratio, n, for the tensioned reinforcement1、n2、n3The number of the tension steel bars is β1、β2、β3For single bars β to account for the modulus of the bundled bars11.0, two bundles β20.85, three in one β3＝0.70；
As1The sectional area of a single steel bar; a. thec1The area of the tensioned concrete that interacts with the tensioned rebar is taken as the area of the concrete that is heavier than the center of gravity of the tensioned rebar.
σsThe stress of the steel bar is obtained by monitoring data, is the stress of the member under the coupling action of actually bearing various external loads (integral temperature action, concrete shrinkage and creep action, temperature gradient action, beam body deflection action and the like), is a comprehensive random variable when carrying out reliability analysis, and is obtained according to sigma obtained by monitoringsThereby obtaining the calculated crack width
S2 deep analysis of probability model and statistical parameter of random variable in function based on monitoring data
The parameters involved in the function are many and are classified into constant parameters and random variable parameters. The structural resistance is a maximum crack width limit value and is a constant value rather than a random variable, so that statistical analysis is mainly performed on random variable parameters in a crack width calculation formula, and the parameters in crack width calculation include, for example, some quantities with extremely small variability, common random variable parameters such as the elastic modulus of a steel bar, the thickness of a concrete protective layer, the diameter of the steel bar and the like, and also include action effect parameters obtained through monitoring. The small amount of variability is treated as a constant, and the following treatment is carried out on the common random variable parameters such as the elastic modulus of the steel bar, the thickness of the concrete protective layer, the diameter of the steel bar and the like and the action effect parameters:
s21 analysis to determine average value, standard deviation and variation coefficient of general random variable parameters
The probability types and statistical parameters of the general random variable parameters are determined by analyzing test values or measured values, and the calculation formulas of the mean value, the standard deviation and the coefficient of variation are shown in formulas (9) to (11).
In the formula (I), the compound is shown in the specification,
is the sample mean, n is the sample volume, xiFor the ith sample value, σ1Is the standard deviation of the sample, CvIs the sample coefficient of variation.
S22 Effect parameter
The actual stress distribution of the steel bars in the service state of the ballastless track can be determined by analyzing the monitoring data, and the actual stress of the steel bars is taken as a comprehensive effect parameter when the reliability is evaluated. Screening effective monitoring data, and analyzing the probability distribution types possibly obeyed by actual steel bar stress by using hypothesis testing methods such as chi-square test, K-S test and the like: normal distribution, lognormal, extreme I, II and III, weibull, chi distribution, exponential, uniform distribution.
S23 then plots the probability distribution based on the type of probability distribution obeyed by the actual bar stress and the data determined from the general random variable parametric analysis in S21 and the actual bar stress data after screening.
S3 calculating crack width reliability index of ballastless track structure
According to the established function and parameter analysis, the crack width reliability level of the ballastless track structure in service can be quantized into a probability mathematical expression, and the reliability index is calculated.
Pf＝P[G(X)＝fy-σs≤0]Formula (12)
β＝Φ-1(1-Pf) Formula (13)
In the formula, β is a reliable index of ballastless track structure, phi-1(. is an inverse function of a standard normal distribution, PfThe failure probability of the ballastless track structure is shown. f. ofy-σs＝wlim-w, wherein fy＝wlim-w+σs
As shown in fig. 2. The concrete solving steps are as follows:
s31 generating N groups of independent sample points (X) according to probability model of random variable in function1,X2,X3,···,Xn)(i＝0,1,2,···,n)；
S32, substituting the extracted N groups of sample points into the structural function, and calculating the function value of Z;
s33 for Z ═ g (X)1,X2,X3,···,Xn) The array of <0 is counted and is marked as Nf；
S34 uses formula Pf＝NfThe failure probability of the structure is obtained;
s35 using the formula β ═ Φ-1(Pf) And solving a reliability index, and evaluating the service state of the track structure.
S4 evaluating service state of ballastless track structure
When reliability of the service state of the existing ballastless track structure is evaluated, the reliability index of the normal use limit state of the railway track member in the railway track design specification (limit state method) (Q/CR9130-2018) is preferably 0-2.5. And comparing the reliable indexes of the service state of the ballastless track structure obtained by calculation and analysis with the design reliable indexes to evaluate the service state of the ballastless track structure.
The reliability evaluation process of the in-service ballastless track structure based on the crack width will be described in detail below by taking the limit state of normal use of the crack width of the CRTSII type slab ballastless track bed plate as an example. The specific treatment process comprises the following steps:
firstly, monitoring points are arranged on a ballastless track of a CRTSII type slab ballastless track small-radius curve section, and base plate steel bar stress at 16 measuring points is monitored for a long time and is respectively arranged at the beam end of a 6-hole simply supported beam in front of an abutment, in the span, in front of the abutment, at the tail of the abutment, on a friction plate and at a large-end thorn. In the same section, the measuring points are all arranged on the outer rail side of the base plate, and the sensors are all longitudinally arranged along the line in the axial direction.
And establishing a function. As the CRTS II type slab ballastless track base plate on the bridge is of a longitudinally-connected structure and is a tension member, the maximum crack width of the base plate is calculated according to a tension member formula, and the function for establishing the crack width reliability evaluation of the base plate is shown as the formula (7):
in the formula, wlimThe maximum crack width limit (mm) is 0.23mm, since the base plate protective layer has a thickness of 35 mm. The remaining parameters are defined above.
Then, a random variable parameter is determined
For general random variable parameters, the effective reinforcement ratio is constant, and the statistical characteristics of other random variables are listed in table 1.
TABLE 1 basic random variable statistical characteristics
For the effect parameters: the actual stress distribution of the steel bars in the service state of the ballastless track can be determined by analyzing the monitoring data, and the actual stress of the steel bars is taken as a comprehensive effect parameter when the reliability is evaluated. And screening the small-radius curve section monitoring work point data of the Jingfu GaoFeijiejin village grand bridge, and selecting the measuring point monitoring data which is not abnormal for statistical analysis. And (3) performing hypothesis test on the monitoring data by adopting a K-S test method, wherein the stress of the steel bars of the base plate of the ballastless track structure in service obeys Gamma distribution, and the statistical parameters are shown in Table 2.
Table 22015-addition 2017-year base plate steel bar stress monitoring data statistical parameter
And (3) calculating a reliable index of the crack width of the base plate, selecting five measuring points for reliability analysis according to the monitoring data of 2017 in 2015-.
Ballastless track structure service state assessment
(1) When the line is opened and operated in the period of 2015 for 6 months, the reliability of the crack width of the ballastless track at each measuring point position of the monitored work point is obviously greater than 0-2.5 ((corresponding failure probability P) of the reliability index of a design target specified in the design Specification (extreme condition method) of railway track (Q/CR9130-2018)f＝0～6.210×10-3) And the track structure state is good at the initial operation stage.
(2) The bed plate crack width reliability showed a small reduction from 2015 to 2017: the average reduction rate in 2016 is 10.77% compared with that in 2015, the average reduction rate in 2017 is 5.49% compared with that in 2016, and the specific development trend is not obvious. The service state of the base plate is good after the line is opened and operated for 2 years in 2015 and 6 months, and the operation requirement is met.
It will be understood by those skilled in the art that the foregoing is only a preferred embodiment of the present invention, and is not intended to limit the invention, and that any modification, equivalent replacement, or improvement made within the spirit and principle of the present invention should be included in the scope of the present invention.
Claims (7)
1. A crack width-based reliability assessment method for an in-service ballastless track structure is characterized by comprising the following specific steps:
s1 function for establishing ballastless track structure crack width evaluation
G(X)＝wlim-w
Wherein, wlimIs the maximum crack width limit, and w is the calculated crack width
S2, based on the probability model and statistical parameters of random variables in the monitoring data deep analysis function, arranging a plurality of monitoring points with sensors at intervals on the ballastless track, analyzing the parameters of general random variables to determine the mean value, standard deviation and variation coefficient of the parameters, screening the strain data of the tensioned steel bars in the in-service ballastless track structure obtained by monitoring by using a data verification method, converting the strain data into the stress values of the steel bars, and analyzing the probability distribution type and statistical parameters of the actual stress obedience of the steel bars;
s3 calculating crack width reliability index of ballastless track structure
Calculating failure probability P of ballastless track structurefWherein P isf＝P[G(X)<0]And obtaining the probability P according to the graphfA value of (d);
calculating a reliable index β of the ballastless track structure according to the failure probability, wherein β ═ phi-1(1-Pf)，Φ-1(. h) is the inverse of a standard normal distribution;
s4, comparing the reliable indexes of the service state of the ballastless track structure obtained through calculation and analysis with the design reliable indexes in the design specification to evaluate the service state of the ballastless track structure.
2. The method for evaluating the reliability of the ballastless track structure in service based on the crack width according to claim 1, wherein in the step S3, the concrete solving step includes:
s31 generating N groups of independent sample points (X) according to probability model of random variable in function1,X2,X3,···,Xn)(i＝0,1,2,···,n)；
S32, substituting the extracted N groups of sample points into the structural function, and calculating the function value of Z;
s33 for Z ═ g (X)1,X2,X3,···,Xn) The array of <0 is counted and is marked as Nf；
S34 uses formula Pf＝NfThe failure probability of the structure is obtained;
s35 using the formula β ═ Φ-1(Pf) And solving a reliability index, and evaluating the service state of the track structure.
3. The in-service ballastless track structure reliability evaluation method based on crack width according to claim 1, wherein the calculated crack width w of the ballastless track reinforced concrete tension member is calculated according to the following formula:
wherein, αcrThe stress characteristic coefficient of the component is psi, the strain non-uniformity coefficient of the longitudinal tension steel bar between cracks is sigmasFor the reinforcement stress obtained by monitoring the data, EsIs the modulus of elasticity of the steel bar, csThe distance from the outer edge of the outermost longitudinal tension bar to the bottom edge of the tension zone, deqIs the equivalent diameter, rho, of the longitudinal reinforcement of the tension zoneteThe reinforcement ratio of the longitudinal tension steel bar is calculated according to the effective section area of the tension concrete.
4. The method for evaluating the structural reliability of the ballastless track in service based on the crack width according to claim 1, wherein the calculated crack width w of the reinforced concrete flexural member of the ballastless track can be calculated according to the following formula:
wherein, K1Is the influence coefficient of the surface shape of the steel bar, K2R is the ratio of the distance from the neutral axis to the edge of tension to the distance from the neutral axis to the center of gravity of the tendon under tension, σsFor the reinforcement stress obtained by monitoring the data, EsIs the modulus of elasticity of the steel bar, and d is the diameter of the tensioned steel bar; mu.szThe effective reinforcement ratio of the tensioned steel bar is obtained.
5. The in-service ballastless track structure reliability assessment method based on crack width as claimed in claim 1, wherein the data verification method in step S1 comprises chi-square test or K-S test.
6. The method for evaluating the structural reliability of the ballastless track in service based on the crack width as claimed in claim 1, wherein the sensors are all arranged longitudinally along the line in the axial direction.
7. The in-service ballastless track structure reliability assessment method based on crack width according to claim 1, characterized in that sensors are arranged at the front and the tail of the large end thorn (2), the friction plate (3) and the abutment (4) of the ballastless track, and sensors are arranged at the beam end and the span of the simply supported beam.
Priority Applications (1)
| Application Number | Priority Date | Filing Date | Title |
|---|---|---|---|
| CN201911006887.4A CN111008412A (en) | 2019-10-22 | 2019-10-22 | Crack width-based reliability assessment method for in-service ballastless track structure |
Applications Claiming Priority (1)
| Application Number | Priority Date | Filing Date | Title |
|---|---|---|---|
| CN201911006887.4A CN111008412A (en) | 2019-10-22 | 2019-10-22 | Crack width-based reliability assessment method for in-service ballastless track structure |
Publications (1)
| Publication Number | Publication Date |
|---|---|
| CN111008412A true CN111008412A (en) | 2020-04-14 |
Family
ID=70110947
Family Applications (1)
| Application Number | Title | Priority Date | Filing Date |
|---|---|---|---|
| CN201911006887.4A Pending CN111008412A (en) | 2019-10-22 | 2019-10-22 | Crack width-based reliability assessment method for in-service ballastless track structure |
Country Status (1)
| Country | Link |
|---|---|
| CN (1) | CN111008412A (en) |
Cited By (2)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN112528539A (en) * | 2020-12-07 | 2021-03-19 | 黄河水利委员会黄河水利科学研究院 | Method for determining safety control operation water level of emergency water gate |
| CN113688469A (en) * | 2020-05-19 | 2021-11-23 | 中国石油天然气股份有限公司 | Method and device for evaluating reliability of transportation pipeline, computer equipment and storage medium |
Citations (5)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN102966008A (en) * | 2011-08-31 | 2013-03-13 | 中国铁道科学研究院铁道建筑研究所 | Ballastless track system |
| CN105064153A (en) * | 2015-07-21 | 2015-11-18 | 中南大学 | Method for treating cracks at seam positions of CRTS II ballastless track plates |
| CN106570286A (en) * | 2016-11-09 | 2017-04-19 | 中南大学 | Bridge-ballastless track structure extreme temperature prediction method and system |
| CN106845014A (en) * | 2017-02-22 | 2017-06-13 | 中南大学 | A kind of computational methods of track plates thermal cracking width |
| CN109033618A (en) * | 2018-07-24 | 2018-12-18 | 中南大学 | The appraisal procedure that non-fragment orbit typical case hurt influences bullet train safety in operation |
-
2019
- 2019-10-22 CN CN201911006887.4A patent/CN111008412A/en active Pending
Patent Citations (5)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN102966008A (en) * | 2011-08-31 | 2013-03-13 | 中国铁道科学研究院铁道建筑研究所 | Ballastless track system |
| CN105064153A (en) * | 2015-07-21 | 2015-11-18 | 中南大学 | Method for treating cracks at seam positions of CRTS II ballastless track plates |
| CN106570286A (en) * | 2016-11-09 | 2017-04-19 | 中南大学 | Bridge-ballastless track structure extreme temperature prediction method and system |
| CN106845014A (en) * | 2017-02-22 | 2017-06-13 | 中南大学 | A kind of computational methods of track plates thermal cracking width |
| CN109033618A (en) * | 2018-07-24 | 2018-12-18 | 中南大学 | The appraisal procedure that non-fragment orbit typical case hurt influences bullet train safety in operation |
Non-Patent Citations (1)
| Title |
|---|
| 张国虎: "基于可靠度的CRTSⅡ型无砟轨道轨道板耐久性研究", 《中国优秀硕士学位论文全文数据库》 * |
Cited By (3)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN113688469A (en) * | 2020-05-19 | 2021-11-23 | 中国石油天然气股份有限公司 | Method and device for evaluating reliability of transportation pipeline, computer equipment and storage medium |
| CN112528539A (en) * | 2020-12-07 | 2021-03-19 | 黄河水利委员会黄河水利科学研究院 | Method for determining safety control operation water level of emergency water gate |
| CN112528539B (en) * | 2020-12-07 | 2023-12-12 | 黄河水利委员会黄河水利科学研究院 | Method for determining safe control operation water level of disease risk sluice |
Similar Documents
| Publication | Publication Date | Title |
|---|---|---|
| Vilanova et al. | Experimental study of bond-slip of GFRP bars in concrete under sustained loads | |
| CN110376058B (en) | Method for monitoring strength of concrete structure attached to climbing formwork equipment in real time | |
| CN110502855B (en) | Method for identifying damage of uniform-section continuous beam with support reaction influence line curvature | |
| CN107908879B (en) | Method for evaluating fatigue performance of concrete beam bridge | |
| Vecchi et al. | Corrosion morphology of prestressing steel strands in naturally corroded PC beams | |
| Siriwardane et al. | Application of new damage indicator-based sequential law for remaining fatigue life estimation of railway bridges | |
| CN111008412A (en) | Crack width-based reliability assessment method for in-service ballastless track structure | |
| CN111460717B (en) | Influence line-based method for counting passing equivalent times of overloaded vehicle of simply supported beam bridge | |
| CN103246766B (en) | The actual moment of flexure projectional technique of girder of beam bridge and beam bridge Bearing Capacity Evaluation method | |
| CN115081863A (en) | Building material entrance intelligent acceptance analysis management platform based on digital twinning technology | |
| Elachachi et al. | A probabilistic multi-scale time dependent model for corroded structural suspension cables | |
| Braml et al. | Assessment of existing structures using probabilistic analysis methods in combination with nondestructive testing methods | |
| Moshtaghin et al. | Experimental characterization of longitudinal mechanical properties of clear timber: Random spatial variability and size effects | |
| Lochan et al. | Determination of tensile strength of GFRP bars using flexure tests | |
| CN112464345A (en) | Deformation-based seismic damage reinforced concrete column crack width calculation method | |
| Pestka et al. | Influence of wood moisture on strength and elastic modulus for pine and fir wood subjected to 4-point bending tests | |
| CN117057600A (en) | Online monitoring and analyzing method for concrete bridge structural cracks | |
| Jeyasehar et al. | Nondestructive evaluation of prestressed concrete beams using an artificial neural network (ANN) approach | |
| CN111310273A (en) | Full-bridge structure safety state monitoring method and system based on multi-source data | |
| CN108333335B (en) | Method for determining resistance reduction coefficient of concrete beam bridge | |
| CN116067592A (en) | Rapid diagnosis method for longitudinal bridge damage of prefabricated assembled girder bridge | |
| CN111008413A (en) | Method for evaluating bearing capacity of ballastless track structure of high-speed railway based on monitoring data | |
| CN110795798B (en) | Steel wire rope reliable life calculation method based on multiple samples | |
| Yu et al. | Comprehensive study on corrosion induced structural deterioration of steel bars in reinforced concrete beams | |
| CN114136769A (en) | Carbon fiber plate capable of strain detection based on image processing and use method |
Legal Events
| Date | Code | Title | Description |
|---|---|---|---|
| PB01 | Publication | ||
| PB01 | Publication | ||
| SE01 | Entry into force of request for substantive examination | ||
| SE01 | Entry into force of request for substantive examination | ||
| RJ01 | Rejection of invention patent application after publication |
Application publication date: 20200414 |
|
| RJ01 | Rejection of invention patent application after publication |