CN108416089B - Method for inverting structural parameters of rigid pavement of airport - Google Patents

Method for inverting structural parameters of rigid pavement of airport Download PDF

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CN108416089B
CN108416089B CN201810082626.XA CN201810082626A CN108416089B CN 108416089 B CN108416089 B CN 108416089B CN 201810082626 A CN201810082626 A CN 201810082626A CN 108416089 B CN108416089 B CN 108416089B
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deflection
deflection basin
data
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cement concrete
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凌建明
刘诗福
袁捷
杨戈
杜浩
刘海伦
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Shanghai Tongke Transportation Technology Co ltd
Tongji University
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Abstract

The invention relates to the field of structural performance evaluation of airport pavement, in particular to a method for inverting structural parameters of an airport rigid pavement. The invention provides a method for detecting airport cement concrete pavement structure parameters, which comprises the following steps: acquiring actually measured deflection basin data of each deflection basin, and screening the actually measured deflection basin data; acquiring representative deflection basin data; obtaining the comprehensive derivation index representing the deflection basinA c (ii) a Determining relative stiffness radiuslTaking the value of (A); obtaining foundation reaction modulusK(ii) a Obtaining the modulus of elasticity of a cement concrete slabE. The method provided by the invention is a scientific and reasonable rigid pavement structure parameter inversion method, fully utilizes the deflection information of each measuring point of the deflection basin, reduces the fitting error of the theoretical deflection basin and the actual measurement deflection basin, improves the robustness and reliability of the inversion result, and can solve various problems in the performance evaluation of the conventional airport cement concrete pavement structure.

Description

Method for inverting structural parameters of rigid pavement of airport
Technical Field
The invention relates to the field of structural performance evaluation of airport pavements, in particular to a method for inverting structural parameters of an airport rigid pavement, which can be widely applied to the structural performance evaluation of pavements such as airport cement concrete runways, taxiways, parking ramps and the like.
Background
Whether the airport is newly built or is in service, the structural performance evaluation of the flight area pavement of the airport is always one of the most important contents for the detection of the airport pavement. More than 90% of airports in China are cement concrete pavements, and a Falling Weight Deflectometer (FWD) is adopted to perform rigid pavement structure parameter inversion, so that the method is a key technology for pavement structure performance evaluation, structure reinforcement design and finite element parameter calibration. In the existing civil airport pavement evaluation management technical specification (MH/T5024-2009), the traditional deflection basin AREA index (AREA) method is recommended to be adopted for carrying out pavement structure parameter inversion. The method establishes a one-to-one corresponding relation with the relative rigidity radius by constructing a deflection basin area index, but emphasizes that a deflection value at a load center is used, and deflection information of other measuring points is not effectively utilized; and when the reaction modulus of the foundation is calculated, only the deflection value at the load center is matched, so that the fitting error of the theoretical deflection basin and the actually measured deflection basin is larger.
Therefore, the scientific and reasonable rigid pavement structure parameter inversion method fully utilizes the deflection information of each measuring point of the deflection basin, reduces the fitting error of the theoretical deflection basin and the actual measurement deflection basin, improves the robustness and reliability of the inversion result, and is a problem to be solved urgently in the performance evaluation of the airport cement concrete pavement structure at present.
Disclosure of Invention
In view of the above-mentioned shortcomings of the prior art, the present invention provides a method for detecting structural parameters of an airport cement concrete pavement, which is used to solve the problems in the prior art.
In order to achieve the above objects and other related objects, the present invention provides a method for detecting structural parameters of an airport cement concrete pavement, comprising:
1) acquiring actually measured deflection basin data (actually measured deflection basin data is actually measured deflection values, and one deflection basin corresponds to one group of deflection values) of each deflection basin, and screening the actually measured deflection basin data;
2) obtaining representative deflection basin data, wherein the representative deflection basin data is an average value of deflection basin data obtained by screening actually measured deflection basin data;
3) obtaining a representative deflection basin comprehensive derivation index AcThe specific calculation method is as follows:
Figure BDA0001561467960000011
wherein A iscHas the unit of m2；wiThe deflection value of a measuring point i is represented by m; c. CiIs a factor of the deflection value of a measuring point i, is the square of the distance of the measuring point from the load center and has the unit of m2(ii) a n is the number of measuring points;
4) determining the value of the relative rigidity radius according to the principle that the comprehensive derivative index representing the deflection basin is closest to the derivative index of the theoretical deflection basincThe calculation method of' is as follows:
Figure BDA0001561467960000021
wherein A iscUnit of' is m2；riThe distance between a measuring point i and the load center is m; c. Ci' is the square of the distance of the measuring point i from the center of the load (i.e. r)i 2) Unit is m2(ii) a a is the circular uniform load radius of equipment used when the actually measured deflection basin data of each deflection basin is obtained, and the unit is m;
5) obtaining the foundation reaction modulus K, wherein the specific calculation method is as follows:
Figure BDA0001561467960000022
wherein the content of the first and second substances,p＝140kN/(πa2)；
6) according to
Figure BDA0001561467960000023
Acquiring the elastic modulus E of the cement concrete slab;
wherein mu is the Poisson's ratio of the cement concrete slab; h is the thickness of the cement concrete in m.
In some embodiments of the present invention, measured Deflectometer (FWD) data for each Deflectometer is obtained by FWD.
In some embodiments of the invention, a is 0.15 m.
In some embodiments of the present invention, the screening of the measured deflection basin data specifically includes removing invalid measured deflection basin data, where the invalid measured deflection basin data generally refers to data that does not conform to an actual deflection rule, for example, those deflection basins that have a large distance from a load center but have a larger measured deflection value.
In some embodiments of the invention, the screened deflection basin is given the same weight and a weighted average calculates representative deflection basin data for that region. Considering that the deflection basins of the same region have the same importance, when the representative deflection basin is obtained, the weighted average calculates the representative deflection basin of the region.
In some embodiments of the invention, ciIs the square of the distance of the measuring point i from the center of the load.
In some embodiments of the invention, the iteration interval of the relative stiffness radii is 0-2m, and the step size is 0.01m ± 0.005 m.
The method provided by the invention is a scientific and reasonable rigid pavement structure parameter inversion method, fully utilizes the deflection information of each measuring point of the deflection basin, reduces the fitting error of the theoretical deflection basin and the actual measurement deflection basin, improves the robustness and reliability of the inversion result, and can solve various problems in the performance evaluation of the conventional airport cement concrete pavement structure. The inversion method has higher fitting degree with measured values, the reliability is improved by 42 percent compared with the traditional deflection basin area index method, and the system has stronger robustness.
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FIG. 1 shows the relationship between the deflection basin comprehensive derivative index and the relative stiffness radius of the present invention.
Detailed Description
The embodiments of the present invention are described below with reference to specific embodiments, and other advantages and effects of the present invention will be easily understood by those skilled in the art from the disclosure of the present specification. The invention is capable of other and different embodiments and of being practiced or of being carried out in various ways, and its several details are capable of modification in various respects, all without departing from the spirit and scope of the present invention.
Example 1
50 groups of deflection test data are acquired on the spot by adopting a drop weight deflection vehicle on an air park of a 4C grade airport in a certain east China area, after the data are preprocessed, an effective data sample is 43 groups (detailed data is shown in a table 1), and representative deflection basins (average values of 43 deflection basin data) in the area are shown in a table 2.
TABLE 1
Figure BDA0001561467960000031
Figure BDA0001561467960000041
TABLE 2
Figure BDA0001561467960000042
By respectively adopting the inversion method provided by the invention and a traditional deflection basin area index method (forest is level, Yuanjie, Lingming, talking to Ming. rigid pavement deflection basin area index inversion improvement method [ J ]. Chinese highway bulletin, 2009,22(03):14-19.), the inversion method provided by the invention specifically comprises the following steps:
1) according toThe data in the table 2 are calculated to obtain the comprehensive derivative index A representing the deflection basinc(where n is 6), the specific calculation method is as follows:
Figure BDA0001561467960000043
wherein: w is aiThe deflection value (in m) of the measuring point i; c. CiIs the square of the distance of the measuring point i from the center of the load (unit is m)2) (ii) a n is the number of measuring points;
calculating to obtain a representative deflection basin comprehensive derivative index Ac＝0.66m2(AcHas the unit of m2)；
2) Determining the value of the relative rigidity radius according to the principle that the comprehensive derivative index representing the deflection basin is closest to the comprehensive derivative index of the theoretical deflection basin, wherein the calculation method of the comprehensive derivative index of the theoretical deflection basin comprises the following steps:
the theoretical deflection value is calculated as follows:
Figure BDA0001561467960000051
Figure BDA0001561467960000052
wherein: ω (r) is the deflection (in m) from the load center r (m); p is the load density (N/m)2) (ii) a a is the radius (m) of the circular uniformly distributed load; xi is an integral variable; k is the reaction modulus (N/m) of the subgrade under the slab3)；J0、J 10 order and 1 order Bessel functions respectively; l is the relative stiffness radius (m) of the slab and the foundation; e is the modulus of elasticity (unit: Pa) of the panel; mu is the Poisson's ratio of the cement concrete slab, h is the thickness (unit: m) of the cement concrete slab
Therefore, the theoretical deflection value for the measurement point i is calculated as follows:
Figure BDA0001561467960000053
Figure BDA0001561467960000054
in the formula: omega (r)i) For measuring point i from load center ri(m) a deflection (m); p is the load density (N/m)2) (ii) a a is the radius (m) of the circular uniformly distributed load; xi is an integral variable; k is the reaction modulus (N/m) of the subgrade under the slab3)；J0、J 10 order and 1 order Bessel functions respectively; l is the relative stiffness radius (m) of the slab and the foundation; e is the elastic modulus (Pa) of the panel; μ is the poisson's ratio of the plate; h is the thickness (m) of the plate.
Derived index A of theoretical deflection basinc' (unit is m)2) The calculation method of (2) is as follows:
Figure BDA0001561467960000055
wherein r isiTaking the distance from the measuring point i to the load center as shown in the table 2, wherein the unit is m; c. Ci' is the square of the distance of the measuring point i from the center of the load (i.e. r)i 2Unit is m2) And a is 0.15m (the common round uniform load radius of the FWD equipment).
The formula of the derivative index of the theoretical deflection basin is a function related to the relative stiffness radius l, the derivative index of the theoretical deflection basin is calculated by taking the value of the relative stiffness radius l in a certain range according to a certain step length (the step length refers to the increasing amplitude of each value, and specifically can be 0.01m +/-0.005 m, and the value range of the relative stiffness radius is 0-2m), the calculation result is shown in fig. 1, the relative stiffness radius l which is closest to the derivative index of the actually measured deflection basin is taken as a final value, and the obtained value of the relative stiffness radius l is shown in table 3.
3) Obtaining the foundation reaction modulus K, wherein the specific calculation method is as follows:
Figure BDA0001561467960000061
wherein:
Figure BDA0001561467960000062
the measured deflection value of the measuring point i,
Figure BDA0001561467960000063
to measure the theoretical deflection value of point i, let
Figure BDA0001561467960000064
Calculating to obtain the value of the reaction modulus K of the foundation;
Figure BDA0001561467960000065
wherein the content of the first and second substances,p＝140kN/(πa2)(pis the common load concentration of FWD devices), the calculation results are shown in table 3;
4) according to
Figure BDA0001561467960000066
And obtaining the elastic modulus E of the cement concrete slab, wherein mu is 0.15, and h is 0.34 m.
The inversion results are shown in table 3:
TABLE 3
Figure BDA0001561467960000067
Therefore, compared with the traditional deflection basin area index method, the inversion method provided by the invention has smaller relative error sum of squares and absolute error sum of squares, which shows that the inversion method provided by the invention has higher fitting degree with measured values.
Example 2
Assuming that the values of all parameters of the rigid pavement structure are as follows: the thickness of the cement concrete slab is 0.4m, the elastic modulus is 38GPa, and the Poisson ratio is 0.15; the foundation reaction modulus is 100MN/m3(ii) a A circular uniform load (140KN) of 0.3m diameter. Calculating theoretical curves of different measuring pointsThe formula for the calculation of the precipitation is shown in Table 4, referring to example 1.
TABLE 4
Figure BDA0001561467960000068
Errors in the FWD deflection test include systematic errors and random errors. The measurement accuracy of the current international mainstream FWD equipment is +/-2 um +/-2%, and the relation between the measured deflection value and the theoretical deflection value is as follows:
Figure BDA0001561467960000071
in the formula: w is amRepresents the measured deflection value, w, under the effect of FWD errortTheoretical value, r, representing deflection test1、r2、r3、r4Is a random number from 0 to 1. Random errors are added to the deflection values of each measuring point in the table 4, 100 groups of actually measured deflection basins are generated in a simulation mode (see the following table 5), and the results of two inversion methods under the action of the measurement errors are analyzed and analyzed in a statistical mode in the following table 6 (the inversion methods refer to the example 1).
TABLE 5
Figure BDA0001561467960000072
Figure BDA0001561467960000081
Figure BDA0001561467960000091
TABLE 6
Figure BDA0001561467960000092
Statistical analysis shows that under the action of measurement errors, the structural parameter result obtained by inversion of the method provided by the invention tends to be a true value, and the reliability of the method provided by the invention is improved by 42% compared with that of the traditional deflection basin area index method by combining all indexes, namely the method has stronger system robustness.
In conclusion, the present invention effectively overcomes various disadvantages of the prior art and has high industrial utilization value.
The foregoing embodiments are merely illustrative of the principles and utilities of the present invention and are not intended to limit the invention. Any person skilled in the art can modify or change the above-mentioned embodiments without departing from the spirit and scope of the present invention. Accordingly, it is intended that all equivalent modifications or changes which can be made by those skilled in the art without departing from the spirit and technical spirit of the present invention be covered by the claims of the present invention.

Claims (6)

1. A method for detecting airport cement concrete pavement structure parameters comprises the following steps:
1) acquiring actually measured deflection basin data of each deflection basin, and screening the actually measured deflection basin data;
2) obtaining representative deflection basin data, wherein the representative deflection basin data is an average value of deflection basin data obtained by screening actually measured deflection basin data;
3) obtaining a representative deflection basin comprehensive derivation index AcThe specific calculation method is as follows:
Figure FDA0003169302200000011
wherein A iscHas the unit of m2；wiThe deflection value of a measuring point i is represented by m; c. CiIs a factor of the deflection value of a measuring point i, is the square of the distance of the measuring point from the load center and has the unit of m2(ii) a n is the number of measuring points;
4) determining relative rigidity according to the principle that the comprehensive derivative index representing the deflection basin is closest to the derivative index of the theoretical deflection basinRadius l value, derived index A of theoretical deflection basincThe calculation method of' is as follows:
Figure FDA0003169302200000012
wherein A iscUnit of' is m2；riThe distance between a measuring point i and the load center is m; c. Ci' is the square of the distance from a measuring point i to the center of the load, and the unit is m2(ii) a a is the circular uniform load radius of equipment used when the actually measured deflection basin data of each deflection basin is obtained, and the unit is m; xi is an integral variable;
5) obtaining the foundation reaction modulus K, wherein the specific calculation method is as follows:
Figure FDA0003169302200000013
wherein p is 140 kN/(pi a)2)，J0、J10 order and 1 order Bessel functions respectively; xi is an integral variable;
Figure FDA0003169302200000014
actually measuring a deflection value for the measuring point i;
6) according to
Figure FDA0003169302200000015
Acquiring the elastic modulus E of the cement concrete slab;
wherein mu is the Poisson's ratio of the cement concrete slab; h is the thickness of the cement concrete in m.
2. The method of claim 1, wherein the measured deflection basin data for each deflection basin is obtained by a drop weight deflectometer.
3. The method for detecting airport cement concrete pavement structure parameters of claim 1, wherein a is 0.15 m.
4. The method of claim 1, wherein the screening of the measured deflection basin data is performed to remove invalid measured deflection basin data.
5. The method of claim 1, wherein the screened deflection basins are weighted equally, and the representative deflection basin data of the same area is calculated by weighted average.
6. The method of claim 1, wherein the iteration interval of the relative stiffness radius is 0-2m, and the step size is 0.01m ± 0.005 m.
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