CN114997010A - Nondestructive testing method for evaluating bridge pier rigidity - Google Patents

Nondestructive testing method for evaluating bridge pier rigidity Download PDF

Info

Publication number
CN114997010A
CN114997010A CN202210598719.4A CN202210598719A CN114997010A CN 114997010 A CN114997010 A CN 114997010A CN 202210598719 A CN202210598719 A CN 202210598719A CN 114997010 A CN114997010 A CN 114997010A
Authority
CN
China
Prior art keywords
pier
modal
design
stiffness
bridge pier
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.)
Granted
Application number
CN202210598719.4A
Other languages
Chinese (zh)
Other versions
CN114997010B (en
Inventor
亓兴军
丁晓岩
王珊珊
亓圣
曹三鹏
Current Assignee (The listed assignees may be inaccurate. Google has not performed a legal analysis and makes no representation or warranty as to the accuracy of the list.)
Shandong Jianzhu University
Shandong High Speed Group Co Ltd
Original Assignee
Shandong Jianzhu University
Shandong High Speed Group Co Ltd
Priority date (The priority date 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 date listed.)
Filing date
Publication date
Application filed by Shandong Jianzhu University, Shandong High Speed Group Co Ltd filed Critical Shandong Jianzhu University
Priority to CN202210598719.4A priority Critical patent/CN114997010B/en
Publication of CN114997010A publication Critical patent/CN114997010A/en
Application granted granted Critical
Publication of CN114997010B publication Critical patent/CN114997010B/en
Active legal-status Critical Current
Anticipated expiration legal-status Critical

Links

Images

Classifications

    • G—PHYSICS
    • G06—COMPUTING; CALCULATING OR COUNTING
    • G06F—ELECTRIC DIGITAL DATA PROCESSING
    • G06F30/00—Computer-aided design [CAD]
    • G06F30/20—Design optimisation, verification or simulation
    • G06F30/23—Design optimisation, verification or simulation using finite element methods [FEM] or finite difference methods [FDM]
    • G—PHYSICS
    • G06—COMPUTING; CALCULATING OR COUNTING
    • G06F—ELECTRIC DIGITAL DATA PROCESSING
    • 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
    • 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
    • Y—GENERAL TAGGING OF NEW TECHNOLOGICAL DEVELOPMENTS; GENERAL TAGGING OF CROSS-SECTIONAL TECHNOLOGIES SPANNING OVER SEVERAL SECTIONS OF THE IPC; TECHNICAL SUBJECTS COVERED BY FORMER USPC CROSS-REFERENCE ART COLLECTIONS [XRACs] AND DIGESTS
    • Y02—TECHNOLOGIES OR APPLICATIONS FOR MITIGATION OR ADAPTATION AGAINST CLIMATE CHANGE
    • Y02T—CLIMATE CHANGE MITIGATION TECHNOLOGIES RELATED TO TRANSPORTATION
    • Y02T90/00—Enabling technologies or technologies with a potential or indirect contribution to GHG emissions mitigation

Abstract

The invention discloses a nondestructive testing method for evaluating bridge pier rigidity. The method comprises the steps of arranging a plurality of acceleration sensors on a pier to be tested, testing the frequency, the vibration mode and other mode parameters of the pier column under the excitation of an environment, combining a finite element model, calculating the normalization coefficient of the actually measured vibration mode of the pier, identifying the modal compliance matrix of the structure, predicting the actual modal displacement of the pier under the action of a design horizontal load, determining the actual modal stiffness of the pier to be tested, and finally judging whether the stiffness of the pier meets the design requirement or not according to the ratio of the modal stiffness to the theoretical design stiffness. The method disclosed by the invention not only can be used for identifying and extracting the actual structural rigidity information of the pier stud from the pier modal test data, and rapidly and reliably detecting the actual rigidity of the pier, but also can be used for saving a large amount of manpower, financial resources and material resources in actual engineering application, and has the characteristics of convenience and quickness in detection process and accurate evaluation result.

Description

Nondestructive testing method for evaluating bridge pier rigidity
Technical Field
The invention relates to a nondestructive testing method for evaluating the horizontal rigidity of a pier, and belongs to the field of bridge safety detection evaluation.
Background
The rigidity of the pier is not only an important index for structural design and construction quality detection, but also an important parameter for evaluating the bearing capacity and the earthquake and disaster resistance of the pier. The bridge pier is influenced by adverse factors such as flowing water erosion, earthquake action, vehicle and ship impact and the like during service, damages of different degrees and different types are easily generated, the rigidity of the bridge pier is reduced, and the stability of the bridge structure is reduced. In addition, for the bridge pier, the damaged part is not easy to find in time through appearance inspection, and the evaluation of the actual rigidity by using static loading also has considerable difficulty. The state verification of the bridge pier can be based on modal testing, and the safety state of the bridge pier is qualitatively evaluated by using the natural vibration frequency and the vibration response amplitude index, however, the basic modal parameters cannot be directly connected with the rigidity for describing the use performance of the structure. Therefore, how to identify and extract the actual structural rigidity information of the pier column from the pier modal test data, rapidly and reliably detect the actual rigidity of the pier, and ensure the safe operation of the existing bridge is a problem to be solved urgently at home and abroad.
Disclosure of Invention
Aiming at the defects in the prior art, the invention provides the nondestructive testing method which is convenient and quick to operate and can evaluate the actual rigidity of the pier only under the excitation of the environment.
The invention is realized by the following technical scheme: a nondestructive testing method for evaluating bridge pier rigidity is characterized by comprising the following steps: the method comprises the following steps:
(1) selecting a pier to be detected as a detection evaluation object according to the actual service state of the pier;
(2) establishing a finite element model according to a drawing of a pier to be detected, calculating a theoretical vibration mode of the structure, and arranging measuring points according to a theoretical vibration mode possibly existing in the pier and the position of a key section of the pier;
(3) arranging acceleration sensors on each measuring point of the pier by using a bridge inspection vehicle or an overhead working vehicle, collecting horizontal acceleration time-course response data of the measuring points of the pier column under environmental excitation, and identifying and obtaining the actual measurement frequency and the vibration mode of the pier by using a modal parameter identification method;
(4) calculating the normalization coefficient of each order of the actually measured vibration mode of the bridge pier by using the actually measured frequency and the vibration mode of the bridge pier; the normalized coefficient calculation formula is as follows:
Figure BDA0003669119600000021
wherein: a is i Normalizing coefficient for mode shape
M is quality matrix of bridge pier
φ i Is the ith order actual measurement mode vibration type column vector of the bridge pier
φ i T Is phi i The transposed vector of (1);
(5) and normalizing the actually measured vibration mode by using the following formula, and calculating to obtain the normalized vibration mode of the structure:
Figure BDA0003669119600000022
wherein the content of the first and second substances,
Figure BDA0003669119600000023
for the ith order normalized mode column vector, phi i Is the ith order measured modal shape column vector of the pier, a i Is a vibration mode normalization coefficient;
(6) calculating to obtain an actually measured displacement flexibility matrix F of the pier by using the following formula d ：
Figure BDA0003669119600000024
Wherein the content of the first and second substances,
Figure BDA0003669119600000025
for the ith order normalized mode column vector,
Figure BDA0003669119600000026
is composed of
Figure BDA0003669119600000027
Transposed vector of (a) (. omega.) i Is the ith order modal frequency;
(7) calculating the design horizontal load f of the pier top by adopting the pier bottom design bending moment for controlling the reinforcement of the pier bottom section;
(8) and (3) predicting the modal displacement of the bridge pier under the action of the design horizontal load by using the actual measurement displacement flexibility matrix of the bridge pier obtained in the step (6) and the design horizontal load calculated in the step (7) through the following formula:
d＝F d f
wherein d is a column vector formed by modal displacement of each measuring point under the design horizontal load action of the bridge pier, F d F is a column vector formed by pier top design horizontal loads;
(9) calculating the modal stiffness of the key section of the bridge pier by using the predicted modal displacement of the bridge pier and the calculated design horizontal load of the top of the bridge pier through the following formula;
Figure BDA0003669119600000028
wherein, K e The modal stiffness of the bridge pier is shown, f is the design horizontal load of the bridge pier top, and delta is the modal displacement of the key section of the bridge pier under the effect of the design horizontal load;
(10) calculating the design displacement of the pier under the action of the pier top design horizontal load by adopting a pier finite element model, and calculating the theoretical design rigidity of the key section of the pier by combining the design displacement and the design horizontal load according to the following formula;
Figure BDA0003669119600000031
wherein, K s Designing the rigidity for the theory of the pier, wherein f is the designed horizontal load of the pier top, and d is the designed displacement of the key section of the pier under the effect of the designed horizontal load;
(11) the method comprises the following steps of determining the rigidity ratio of a key section of the bridge pier by utilizing the actual measurement modal rigidity of the bridge pier and theoretical design rigidity obtained by calculation of a finite element model through the following formula, wherein if the rigidity ratio is more than or equal to 1, the actual rigidity state of the bridge pier meets the design requirement, otherwise, the actual rigidity of the bridge pier does not meet the design requirement:
Figure BDA0003669119600000032
wherein ζ is the stiffness ratio, K e Is the actual measured modal stiffness, K, of the bridge pier s And the rigidity is theoretically designed for the bridge pier.
According to the method, the model test is carried out on the bridge pier, the displacement flexibility matrix of the actual bridge pier is tested and identified, the model displacement of the bridge pier under the effect of the design horizontal load is predicted, the model rigidity of the key section of the bridge pier is further determined, and then the comparison is carried out with the theoretical design rigidity calculated by the bridge pier finite element model, so that the purpose of evaluating the actual rigidity of the bridge pier is achieved.
Further, the modal parameter identification method is EFDD, polymax or SSI.
Further, the key section of the pier is a pier top section and/or a pier column size change section and/or a tie beam connecting section.
The invention has the beneficial effects that: according to the method, a plurality of acceleration sensors are distributed on the pier to be tested, the frequency, the vibration mode and other mode parameters of the pier column under the excitation of an environment are tested, a finite element model is combined, the normalization coefficient of the actually measured vibration mode of the pier is calculated, the displacement flexibility matrix of the structure is identified, the actual modal displacement of the pier under the action of a design horizontal load is predicted, the actual modal stiffness of the pier column to be tested is determined, and finally whether the stiffness of the pier meets the design requirement or not is judged according to the ratio of the modal stiffness to the theoretical design stiffness. The method disclosed by the invention not only can be used for identifying and extracting the actual structural rigidity information of the pier stud from the pier modal test data, and rapidly and reliably detecting the actual rigidity of the pier, but also can be used for saving a large amount of manpower, financial resources and material resources in actual engineering application, and has the characteristics of convenience and quickness in detection process and accurate evaluation result.
Drawings
FIG. 1 is a schematic flow diagram of the process of the present invention;
FIG. 2 is a diagram of the overall dimensions of the pier stud under test (unit: mm);
FIG. 3 is a schematic view (unit: mm) of an arrangement of acceleration sensors of a bridge pier in an embodiment;
FIG. 4a is a graph of the measured 1 mode shape of the pier stud in the mode test according to the embodiment;
FIG. 4b is a graph of the measured 2 mode shape of the pier stud in the mode test according to the embodiment;
FIG. 5 is a three-dimensional graph (unit: m/N) of the compliance matrix calculated by testing the pillars in the embodiment.
Detailed Description
The invention is further illustrated by the following non-limiting examples:
the conventional pier dynamic detection and evaluation technology generally qualitatively evaluates the safety state of a pier by using the natural vibration frequency and the vibration response amplitude index, and the basic modal parameters cannot be directly related to the rigidity describing the use performance of the structure, so that the accurate evaluation of the pier rigidity is difficult to realize. Therefore, the invention provides a nondestructive testing and evaluating method for bridge pier horizontal rigidity, which identifies and extracts actual structural rigidity information of a pier column from bridge pier modal test data, thereby realizing rapid detection and evaluation of the bridge pier rigidity. According to the method, firstly, according to the actual general situation of the existing bridge structure, a pier to be detected is selected, an acceleration sensor arrangement scheme is formulated, vibration acceleration time-course response data of the pier under environmental excitation is collected, basic modal parameters such as frequency, vibration mode and the like of the pier are identified through a modal identification method, then, a finite element model of the pier is combined, vibration mode normalization is carried out on the actually measured vibration mode, an actually measured displacement flexibility matrix of the pier is calculated, modal displacement of the pier column structure under the effect of design horizontal load is predicted, therefore, the actual modal stiffness of the pier is determined, and finally, the ratio of the actual modal stiffness to the theoretical design stiffness is utilized to judge whether the stiffness of the pier meets the design requirements.
The method combines a bridge pier modal testing technology under environmental excitation with a modal displacement compliance matrix identification technology, and calculates the actual modal stiffness of the key section of the bridge pier under the action of a design horizontal load. The method comprises the following specific steps:
(1) according to the actual general situation of the bridge structure, selecting a bridge pier to be detected, and widely collecting relevant data of the bridge pier, wherein the relevant data mainly comprise completion drawings, construction logs, maintenance data, maintenance reinforcement data and the like of the bridge pier.
(2) And establishing a finite element model according to relevant data of the pier to be measured, calculating a theoretical vibration mode of the structure, and reasonably arranging measuring points through a theoretical vibration mode possibly existing in the pier and the key section position of the pier.
(3) An acceleration sensor is arranged on each measuring point of a pier by using a bridge inspection vehicle or an overhead working vehicle, the horizontal acceleration time-course response data of the pier column measuring points under environmental excitation is collected, and the actually measured frequency and the vibration mode of the pier are obtained by identifying through a modal parameter identification method, wherein the modal parameter identification method can be an EFDD (extended edge detection), polymax, SSI (structural similarity) and other modal parameter identification methods.
(4) And calculating the normalization coefficient of each-order actually measured vibration mode of the bridge pier by using the actually measured frequency and vibration mode of the bridge pier.
The mode shape reflects the inherent characteristics of the structure and represents the mode displacement ratio of the structure under each order of mode. Certain order displacement vibration mode phi identified by structural modal analysis i Not necessarily exactly the normalized displacement mode shape, which corresponds to the normalized displacement mode shape
Figure BDA0003669119600000051
Has a proportionality coefficient a i As shown in formula (1):
Figure BDA0003669119600000052
substitute it into
Figure BDA0003669119600000053
The normalized coefficient a of the vibration mode can be obtained i ：
Figure BDA0003669119600000054
Wherein: a is i Normalizing coefficient for mode shape
M is quality matrix of bridge pier
φ i Is the ith order actual measurement mode vibration type column vector of the bridge pier
φ i T Is phi i Is transposed vector
(5) After the normalization coefficient of the actual measurement vibration mode of each order of the bridge pier is obtained by calculation through the calculation method in the step 4, the normalization vibration mode of the structure is obtained by calculation through a formula (3):
Figure BDA0003669119600000055
wherein:
Figure BDA0003669119600000056
normalized vibration pattern column vector of ith order for pier
φ i Is the ith order actual measurement mode vibration type column vector of the bridge pier
a i Normalizing coefficient for mode shape
(6) Calculating a displacement flexibility matrix of the bridge pier, and obtaining an actually measured displacement flexibility matrix F of the bridge pier by using a formula (4) d ：
Figure BDA0003669119600000061
Wherein the content of the first and second substances,
Figure BDA0003669119600000062
for the ith order normalized mode column vector,
Figure BDA0003669119600000063
is composed of
Figure BDA0003669119600000064
Transposed vector of (c), ω i Is the ith order modal frequency;
(7) calculating the design horizontal load of the pier top, adopting pier bottom design bending moment for controlling pier bottom section reinforcement and combining the design height of the pier column according to concrete structure design specifications, and calculating the pier top design horizontal load f by utilizing a formula (5):
Figure BDA0003669119600000065
wherein M is d The design bending moment of the pier bottom is provided, and h is the design height of the pier column;
(8) and (5) calculating the modal displacement of the pier under the action of the design horizontal load by utilizing the actual measurement displacement flexibility matrix of the pier obtained in the step (6) and the pier top design horizontal load calculated in the step (7) through a formula (6):
d＝F d f (6)
wherein d is a column vector formed by modal displacement of each measuring point under the design horizontal load action of the bridge pier, F d The method comprises the following steps of (1) obtaining an actual measurement displacement flexibility matrix of a pier, wherein f is a column vector consisting of pier top design horizontal loads;
(9) calculating the modal stiffness of the key section of the bridge pier by using the modal displacement of the bridge pier and the calculated design horizontal load through a formula (7):
Figure BDA0003669119600000066
wherein, K e The method comprises the steps of (1) obtaining actual-measured modal stiffness of a bridge pier, wherein f is a designed horizontal load of a bridge pier top, and delta is modal displacement of a key section of the bridge pier under the effect of the designed horizontal load;
(10) the design displacement of pier under the finite element model calculation design horizontal load effect of pier combines design displacement and design horizontal load, calculates the theoretical design rigidity of pier key cross section through equation (8):
Figure BDA0003669119600000067
wherein, K s Designing the rigidity for the theory of the pier, wherein f is the designed horizontal load of the pier top, and d is the designed displacement of the key section of the pier under the effect of the designed horizontal load;
(11) calculating the rigidity ratio of the key section of the bridge pier by using the actual measurement modal rigidity of the bridge pier and the theoretical design rigidity obtained by calculating the finite element model through a formula (9), wherein if the rigidity ratio is more than or equal to 1, the actual working state of the bridge pier meets the design requirement, otherwise, the actual rigidity of the bridge pier does not meet the design requirement:
Figure BDA0003669119600000071
wherein ζ is the stiffness ratio, K e Measured modal stiffness, K, of a pier s And the rigidity is theoretically designed for the bridge pier.
The present invention will be described in detail below using a laboratory pier model as an example.
In this example, the pier body and the bearing platform of the laboratory model pier column are made of C40 concrete, the height of the pier body is 2.3m, the cross-sectional dimension is 0.4 × 0.4m, the height of the bearing platform is 0.5m, and the cross-sectional dimension is 1.4 × 1.4 m. And respectively carrying out a pseudo-static test and an environment excitation modal test, comparing and analyzing modal stiffness measured by the modal test with structural stiffness measured by the pseudo-static test, proving the accuracy of the actual measurement modal stiffness, then calculating theoretical design stiffness of the pier top section based on a pier stud finite element model, finally calculating the stiffness ratio of the actual measurement modal stiffness to the theoretical design stiffness, and evaluating and judging the stiffness condition of the model pier stud.
(1) Collecting basic data of the model pier stud and knowing the general view of the pier stud.
(2) And (3) establishing a finite element model according to relevant data of the model pier stud, and determining the arrangement of the measuring points of the acceleration sensor, wherein the arrangement of the measuring points of the acceleration sensor is shown in an attached figure 3.
(3) An acceleration sensor is installed on a measuring point of a pier body, horizontal acceleration time-course response data of a pier column under environmental excitation is collected, model parameter identification methods such as EFDD, polymax and SSI are applied, the first two-step frequencies of the pier are identified to be 25.854HZ and 119.121HZ respectively, the first two-step vibration modes of the pier column are identified, and the actually measured vibration modes are shown in attached figures 4a and 4 b.
(4) And calculating the vibration mode normalization coefficient. And (4) substituting the frequency and the vibration mode identified in the step (3) into a formula (2) to calculate a vibration mode normalization coefficient. The first two orders of vibration mode normalization coefficients are respectively 1.05 multiplied by 10 -3 And 8.34X 10 -4 The magnitude of the value is related to the amplitude of the actually measured vibration mode, the environmental excitation strength and the like.
(5) And calculating the normalized vibration mode of the pier. Substituting the actually measured vibration mode in the step 3 and the vibration mode normalization coefficient calculated in the step 4 into a formula (3) to calculate the first two-order normalized vibration mode of the model pier stud.
(6) And identifying an actually measured displacement flexibility matrix of the model pier stud. Substituting the normalized vibration mode and the actually measured frequency into a formula (4) to calculate an actual displacement compliance matrix of the model pier stud, and drawing a compliance matrix three-dimensional graph shown in an attached drawing 5 in order to visually display the matrix, wherein the compliance unit is m/N.
(7) The pier bottom design bending moment for controlling the reinforcement of the pier bottom section is adopted, the design height of the pier column is combined, and the design horizontal load f of the pier top is calculated and obtained to be 28.37kN by using a formula (5).
(8) And calculating the modal displacement of the bridge pier under the design horizontal load effect. And (4) substituting the actual measurement displacement flexibility matrix of the pier obtained in the step (6) and the design horizontal load calculated in the step (7) into a formula (6) to calculate that the modal displacement of the pier top section is 3.16 mm.
(9) And calculating the actually measured modal stiffness of the model pier stud. And substituting the modal displacement of the model pier column and the design horizontal load of the pier into a formula (7) to calculate to obtain the modal stiffness of the pier column of 8.98 kN/mm.
(10) And calculating the design displacement and the theoretical design rigidity of the pier under the effect of the design horizontal load. Through a finite element model of a test pier stud, the design displacement of the pier top section under the action of the design horizontal load is calculated to be 3.47mm, and the design displacement and the design horizontal load are substituted into a formula (8) to calculate to obtain the theoretical design rigidity of the pier to be 8.17 kN/mm.
(11) And calculating the rigidity ratio of the key section of the pier. Substituting the actual measurement modal stiffness and the theoretical design stiffness of the pier top into the formula (9), wherein the stiffness ratio of the test pier column calculated by the formula (9) is 1.10 and is more than 1, and the actual stiffness state of the test pier column meets the design requirement.
In order to illustrate the reliability and accuracy of the method, the model pier stud is subjected to a pseudo-static test, the modal stiffness measured by the modal test is compared and analyzed with the initial tangential elastic stiffness of a load displacement curve measured by the pseudo-static test, and the test comparison is as follows:
(12) designing a pseudo-static force load test scheme of the model pier stud. The pseudo-static test adopts displacement loading control, and the specific working conditions are as follows:
pier stud pseudo-static test operating mode: pushing the pier top displacement to 4mm, and carrying out 3 times of cyclic loading;
(13) and predicting modal displacement of the pier stud. And (3) extracting load once every 1mm of loading displacement in the pier stud pseudo-static test, calculating the displacement of the model pier stud under the pseudo-static load action by using a formula (6) based on the actual displacement flexibility matrix of the model pier stud measured in the step (6), wherein the modal displacement and the pseudo-static displacement are in a ratio shown in table 1.
(14) And comparing the actually measured modal stiffness of the model pier stud with the initial tangent elastic stiffness of the pseudo-static test. The physical meaning of the tangent slope of the initial loading point on the load-displacement curve of the pseudo-static test is the initial tangent stiffness of the structure, the load-displacement curve measured by the modal test is a straight line with constant slope, the slope of the straight line is the modal stiffness of the pier stud, and the comparison result of the two is shown in table 2.
As can be seen from the table 2, the initial tangential stiffness value of the load-displacement curve of the pseudo-static test is very consistent with the modal stiffness value measured by the modal test, and the relative error is less than 1%, so that the accuracy of the actual modal stiffness measured by the pier column is fully proved.
Therefore, the following can be demonstrated through the above-mentioned inventive process and the results of the verification of the inventive contents: the method can identify and calculate the ratio of the actual structural rigidity of the pier column to the theoretical design rigidity based on the modal test of the pier, and quickly and reliably perform nondestructive test to evaluate the actual rigidity state of the pier.
Table 1 working condition 1 test pier column prediction modal displacement
Figure BDA0003669119600000091
TABLE 2 Modal stiffness vs. initial tangent stiffness
Figure BDA0003669119600000092
Other parts in this embodiment are the prior art, and are not described herein again.

Claims (3)

1. A nondestructive testing method for evaluating bridge pier rigidity is characterized by comprising the following steps: the method comprises the following steps:
(1) selecting a pier to be detected as a detection evaluation object according to the actual service state of the pier;
(2) establishing a finite element model according to a drawing of a pier to be detected, calculating a theoretical vibration mode of the structure, and arranging measuring points according to a theoretical vibration mode possibly existing in the pier and the position of a key section of the pier;
(3) arranging an acceleration sensor on each measuring point of the pier by using a bridge inspection vehicle or an overhead working vehicle, collecting horizontal acceleration time-course response data of the measuring points of the pier column under environmental excitation, and identifying and obtaining the actually measured frequency and the vibration mode of the pier by using a modal parameter identification method;
(4) calculating the normalization coefficient of each order of the actually measured vibration mode of the bridge pier by using the actually measured frequency and the vibration mode of the bridge pier; the normalized coefficient calculation formula is as follows:
Figure FDA0003669119590000011
wherein: a is i Normalizing coefficient for mode shape
M is quality matrix of bridge pier
φ i Is the ith order actual measurement mode vibration type column vector of the bridge pier
φ i T Is phi i The transposed vector of (1);
(5) and normalizing the actually measured vibration mode by using the following formula, and calculating to obtain the normalized vibration mode of the structure:
Figure FDA0003669119590000012
wherein the content of the first and second substances,
Figure FDA0003669119590000013
for the ith order normalized mode column vector, phi i Is the ith order measured modal shape column vector of the pier, a i Is a vibration mode normalization coefficient;
(6) calculating to obtain an actually measured displacement flexibility matrix F of the pier by using the following formula d ：
Figure FDA0003669119590000014
Wherein the content of the first and second substances,
Figure FDA0003669119590000015
for the ith order normalized mode column vector,
Figure FDA0003669119590000016
is composed of
Figure FDA0003669119590000017
Transposed vector of (a) (. omega.) i Is the ith order modal frequency;
(7) calculating the design horizontal load f of the pier top by adopting the pier bottom design bending moment for controlling the reinforcement of the pier bottom section;
(8) and (3) predicting the modal displacement of the bridge pier under the action of the design horizontal load by using the actual measurement displacement flexibility matrix of the bridge pier obtained in the step (6) and the design horizontal load calculated in the step (7) through the following formula:
d＝F d f
wherein d is a column vector formed by modal displacement of each measuring point under the design horizontal load action of the bridge pier, F d The method comprises the following steps of (1) obtaining an actual measurement displacement flexibility matrix of a pier, wherein f is a column vector consisting of pier top design horizontal loads;
(9) calculating the modal stiffness of the key section of the bridge pier by using the predicted modal displacement of the bridge pier and the calculated design horizontal load of the top of the bridge pier through the following formula;
Figure FDA0003669119590000021
wherein, K e The modal stiffness of the bridge pier is shown, f is the design horizontal load of the bridge pier top, and delta is the modal displacement of the key section of the bridge pier under the effect of the design horizontal load;
(10) calculating the design displacement of the pier under the action of the pier top design horizontal load by adopting a pier finite element model, and calculating the theoretical design rigidity of the key section of the pier by combining the design displacement and the design horizontal load according to the following formula;
Figure FDA0003669119590000022
wherein, K s Designing the rigidity for the theory of the pier, wherein f is the designed horizontal load of the pier top, and d is the designed displacement of the key section of the pier under the effect of the designed horizontal load;
(11) the method comprises the following steps of utilizing actual measurement modal stiffness of the bridge pier and theoretical design stiffness obtained by calculation of a finite element model, determining the stiffness ratio of a key section of the bridge pier through the following formula, wherein if the stiffness ratio is more than or equal to 1, the actual stiffness state of the bridge pier meets the design requirement, otherwise, the actual stiffness of the bridge pier does not meet the design requirement:
Figure FDA0003669119590000023
wherein ζ is the stiffness ratio, K e Measured modal stiffness, K, of a pier s And the rigidity is theoretically designed for the bridge pier.
2. The nondestructive testing method for evaluating the rigidity of a pier according to claim 1, wherein: the modal parameter identification method is EFDD or polymax or SSI.
3. The nondestructive testing method for evaluating the rigidity of a pier according to claim 1 or 2, wherein: the key section of the pier is a pier top section and/or a pier column dimension change section and/or a tie beam connection section.
CN202210598719.4A 2022-05-30 2022-05-30 Nondestructive testing method for evaluating rigidity of bridge pier Active CN114997010B (en)

Priority Applications (1)

Application Number Priority Date Filing Date Title
CN202210598719.4A CN114997010B (en) 2022-05-30 2022-05-30 Nondestructive testing method for evaluating rigidity of bridge pier

Applications Claiming Priority (1)

Application Number Priority Date Filing Date Title
CN202210598719.4A CN114997010B (en) 2022-05-30 2022-05-30 Nondestructive testing method for evaluating rigidity of bridge pier

Publications (2)

Publication Number Publication Date
CN114997010A true CN114997010A (en) 2022-09-02
CN114997010B CN114997010B (en) 2024-03-29

Family

ID=83029784

Family Applications (1)

Application Number Title Priority Date Filing Date
CN202210598719.4A Active CN114997010B (en) 2022-05-30 2022-05-30 Nondestructive testing method for evaluating rigidity of bridge pier

Country Status (1)

Country Link
CN (1) CN114997010B (en)

Citations (4)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN106354955A (en) * 2016-08-30 2017-01-25 南京航空航天大学 Sliding bearing rigidity recognition method based on mill vibration mode parameters
KR101938352B1 (en) * 2018-04-30 2019-01-14 김도빈 Calculation method and program for a stiffness corfficient of a bridge by using dynamic vibration experiment test data
CN110532657A (en) * 2019-08-21 2019-12-03 哈尔滨工业大学 Bridge pier structure state evaluating method based on transmission vehicle excitation and wavelet packet analysis
CN113310649A (en) * 2021-05-27 2021-08-27 山东建筑大学 Test method for predicting modal deflection of medium and small bridges

Patent Citations (4)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN106354955A (en) * 2016-08-30 2017-01-25 南京航空航天大学 Sliding bearing rigidity recognition method based on mill vibration mode parameters
KR101938352B1 (en) * 2018-04-30 2019-01-14 김도빈 Calculation method and program for a stiffness corfficient of a bridge by using dynamic vibration experiment test data
CN110532657A (en) * 2019-08-21 2019-12-03 哈尔滨工业大学 Bridge pier structure state evaluating method based on transmission vehicle excitation and wavelet packet analysis
CN113310649A (en) * 2021-05-27 2021-08-27 山东建筑大学 Test method for predicting modal deflection of medium and small bridges

Non-Patent Citations (1)

* Cited by examiner, † Cited by third party
Title
林贤坤;张令弥;郭勤涛;张宇峰;: "基于模态挠度法的预应力连续箱梁桥状态评估", 土木工程学报, no. 10, 15 October 2010 (2010-10-15) *

Also Published As

Publication number Publication date
CN114997010B (en) 2024-03-29

Similar Documents

Publication Publication Date Title
CN101221104B (en) Structure health monitoring method based on distributed strain dynamic test
Kim et al. Vibration-based damage monitoring in model plate-girder bridges under uncertain temperature conditions
CN111353252B (en) Bridge static load test method based on environmental excitation
CN103076394B (en) Safety evaluation method for ocean platform based on integration of vibration identification frequencies and vibration mode
Perera et al. Identification of damage in RC beams using indexes based on local modal stiffness
Bonopera et al. Compressive column load identification in steel space frames using second-order deflection-based methods
CN110926735A (en) Bridge structure rapid diagnosis method based on multidimensional dynamic parameters
Wu et al. Two-level damage detection strategy based on modal parameters from distributed dynamic macro-strain measurements
CN113310649A (en) Test method for predicting modal deflection of medium and small bridges
Brasiliano et al. Damage identification in continuous beams and frame structures using the residual error method in the movement equation
Fang et al. Vibration-based damage detection of a steel-concrete composite slab using non-model-based and model-based methods
CN113639941A (en) Method for testing bridge strain flexibility matrix
CN109781863A (en) Structure erosion two-stage detection method and its system based on fast vibration test
CN114997010A (en) Nondestructive testing method for evaluating bridge pier rigidity
CN115713020A (en) Rapid test and evaluation method for bearing rigidity of simply supported beam bridge based on local vibration mode
Li et al. Performance alarming for stay cables based on a frequency–deformation relationship model
Hansen Determination and assessment of fatigue stresses on concrete bridges
Phares et al. Evolution of a bridge damage-detection algorithm
CN113567263B (en) Method for testing normal working life of highway reinforced concrete bridge
CN113567242B (en) Method for detecting resistance of reinforced concrete or prestressed concrete beam
KR20130033171A (en) Acceleration-impedance based monitoring technique for prestressed concrete girder
Godart et al. Appraising structures affected by the alkali–aggregate reaction
Zhou et al. An experimental study of the feasibility of identifying the impact damages of reinforced concrete piers using a modal frequency method
Bonessio et al. A multi-mode approach for multi-directional damage detection in frame structures
Bertola et al. Predicting the usefulness of monitoring information for structural evaluations of bridges

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
GR01 Patent grant
GR01 Patent grant