Rapid early warning and estimation method for structural state of continuous rigid frame bridge based on long-term deflection change

Abstract

This invention discloses a rapid early warning and estimation method for the structural state of prestressed concrete continuous rigid frame bridges based on long-term deflection changes, belonging to the field of bridge structural health monitoring and assessment technology. This method involves setting up permanent observation points during the operation of the continuous rigid frame bridge to collect long-term deflection data and establish a deflection characteristic equation. Combined with the prestress-deflection and main beam stress-deflection regression relationships, it achieves dynamic calculation of the structure's prestress and stress state. Simultaneously, it sets early warning thresholds based on deflection development trends to provide rapid early warning of abnormal structural deformation and completes the serviceability limit state and ultimate limit state assessments according to current standards. This invention solves the problems of reliance on short-term data, delayed early warning, and inaccurate state estimation in traditional bridge assessments. It achieves long-term dynamic tracking and accurate prediction of structural state, providing a scientific basis for bridge maintenance decisions and is applicable to the health monitoring and performance assessment of continuous rigid frame bridges during the operation period.

Description

Technical Field

[0001] This invention relates to the field of bridge structural health monitoring and assessment technology, specifically to a rapid early warning and estimation method for the structural state of continuous rigid frame bridges based on long-term deflection changes. Background Technology

[0002] Continuous rigid frame bridges are widely used in highway and railway transportation engineering due to their large span, reasonable stress distribution, and excellent seismic performance. However, these bridges are dominated by dead loads, and during the operation period, they are prone to long-term downward deflection due to factors such as concrete creep, shrinkage, prestress loss, and environmental erosion. This can lead to stress redistribution in the main beam, deterioration of structural performance, and in severe cases, cracking, reduced load-bearing capacity, and other safety hazards.

[0003] Foreign studies have largely focused on deformation under short-term loads and long-term deflection values ​​at mid-span, without fully considering the nonlinear evolution characteristics of the long-term deflection curves of continuous rigid frame bridges. Relying on short-term monitoring data makes it difficult to reflect the long-term performance evolution of the structure, resulting in unpredictable assessment results. Early warning mechanisms lack specificity, often using fixed thresholds and failing to consider the differences in deflection development trends among individual bridges, leading to false or missed warnings. The correlation between structural state estimation and deflection changes is insufficient, and a systematic deflection-prestress-stress coupling relationship has not been established, resulting in low accuracy of assessment results. The assessment process is cumbersome, requiring specialized personnel to perform complex data processing, making rapid and automated assessment difficult and unsuitable for routine monitoring of in-service bridges.

[0004] Based on the analysis of a large amount of measured data on the long-term deflection profile of continuous rigid frame bridges, this invention obtains an evolution model of the long-term deflection of continuous rigid frame bridges and proposes a rapid early warning method based on long-term deflection changes. Combining the evolution model of the long-term deflection of continuous rigid frame bridges, and based on the evolution analysis of the structural state parameters of continuous rigid frame bridges with a large number of different design parameters and completed bridge stress states, the correlation between the prestress loss and stress changes of key sections of continuous rigid frame bridges and the long-term deflection curve is obtained. Summary of the Invention

[0005] To address the shortcomings of existing technologies, the present invention aims to provide a rapid early warning and estimation method for the structural state of continuous rigid frame bridges based on long-term deflection changes, thereby enabling dynamic tracking of long-term structural performance, rapid early warning of abnormal deformation, and accurate estimation of structural state, providing a scientific basis for bridge maintenance.

[0006] To achieve the above objectives, the present invention adopts the following technical solution:

[0007] A rapid early warning and estimation method for the structural state of a continuous rigid frame bridge based on long-term deflection changes includes the following steps:

[0008] 1. Observation point layout: Permanent observation points shall be laid out on the beams of the continuous rigid frame bridge during the operation period. The observation points shall generally be laid out as 4 points for the side spans and 8 points for the middle span. If the number of observation points is reduced due to historical reasons or site conditions, it shall be ensured that there is no less than one observation point in the middle area of ​​the side spans and that the observation points in the middle spans cover 4 points. When leveling is used, the leveling points shall be made of anti-corrosion and anti-aging leveling nails to ensure the long-term stability of the observation points. After the observation points are laid out, the first deflection measurement shall be carried out as the initial data, and the measurement time and the atmospheric temperature at the bridge site shall be recorded.

[0009] 2. Deflection data collection: At least 6 deflection measurements shall be conducted during the operation period, with an interval of no less than 1 year between each measurement. Each measurement should be conducted in the same season as much as possible, and the time period with stable ambient temperature (daily temperature difference ≤ 5℃) should be selected to reduce the impact of seasonal temperature difference and solar temperature difference. The leveling measurement should meet the requirements of second-order leveling measurement.

[0010] 3. Deflection data do not consider pier and abutment settlement. Linear interpolation is used to eliminate the influence of pier deformation and abutment settlement according to formula (1):

[0011] Equation (1)

[0012] In the formula: —Settlement correction for pier top and support points;

[0013] —The distance from pivot A to pivot B;

[0014] —The distance from the deflection measuring point to fulcrum A;

[0015] —Settlement at fulcrum A;

[0016] —Settlement at fulcrum B.

[0017] 4. Establishment of the flexural characteristic equation.

[0018] 1) Equation (2-1) is used to describe the long-term deflection of a continuous rigid frame bridge over time.

[0019] Equation (2-1);

[0020] In the formula, t—the time after the bridge is completed (after the completion of the second phase of construction), in years;

[0021] y—Deflection at time t after the bridge is completed, unit: mm;

[0022] t1—Time of the first measurement after bridge completion, in years; if the first measurement is carried out immediately after bridge completion, it is set to 0.

[0023] A—an undetermined constant;

[0024] —Time constant to be determined;

[0025] —Undetermined coefficients for the shape of the curve over time.

[0026] 2) Determination of equation parameters A, T0, and p

[0027] (1) Based on long-term deflection measurement data, calculate the average deflection at symmetrical locations of the main beam, such as the average deflection at symmetrical locations in the mid-span areas of the two side spans, at measuring points at 1 / 4 and 3 / 4 of the mid-span.

[0028] (2) Examine the mean deflection at the symmetrical position calculated in (1). For measuring points where the difference between the last measurement and the first measurement is greater than or equal to 5 mm, the equation parameters are determined in the following two cases:

[0029] When the number of measurements during the operation period is no less than 10, regression analysis is performed on the deflection data of each deflection measuring point of the main beam according to formula (2-1) to determine the equation parameters A, T0, and p of each measuring point. The regression analysis can use the least squares method, and the goodness of fit R² should not be lower than 0.95 to ensure the reliability of the equation. At the same time, the regression standard deviation is obtained and denoted as σ.

[0030] When the number of measurements during the operation period is less than 10, the undetermined time constant of each measuring point can be considered as such. Undetermined coefficients of the curve shape over time Similarly, regression is initially determined according to the system of equations (2-2). As the amount of measurement data increases in the later stages (greater than or equal to 10 times), the regression is further adjusted using the "..." method. The method determines the equation parameters A, T0, and p for each measuring point separately; the regression analysis can use the least squares method, and the goodness of fit R² should not be lower than 0.95 to ensure the reliability of the equation. At the same time, the regression standard deviation is obtained, denoted as σ.

[0031] Equation (2-2);

[0032] In the formula, , , ..., —The average deflection of the symmetrical measuring point when the difference between the average deflection of the last measurement and the average deflection of the first measurement is greater than or equal to 10 mm;

[0033] , , ..., —Undetermined constants for symmetrical measuring points when the difference between the mean deflection of the symmetrical measuring point in the last measurement and the first measurement is greater than or equal to 5 mm;

[0034] The remaining parameters are the same as in equation (2-1).

[0035] (3) Examine the mean deflection at the symmetrical position calculated in (1). For measuring points where the difference between the last measurement and the first measurement is less than 5 mm, the undetermined parameters T0 and p in the equation can be taken as T0 and p at the mid-span measuring point, and the undetermined constant A i Calculate according to formula (2-3):

[0036] Equation (2-3);

[0037] In the formula, A i —Undetermined constants for symmetrical measuring points when the difference between the mean deflection of the symmetrical measuring points in the last measurement and the first measurement is less than 5 mm;

[0038] —The undetermined constant of the mid-span determined by step “(2)”.

[0039] —The average of all measured deflection values ​​at the symmetrical measuring point;

[0040] —The average deflection measured at the mid-span of the middle span;

[0041] 5. Setting the long-term deflection early warning threshold for continuous rigid frame bridges.

[0042] Based on the mid-span deflection characteristic equation of the continuous rigid frame bridge established in step "4", the theoretical deflection value μ at time t during the operation period is predicted.

[0043] Considering measurement error, based on the Raida criterion, the threshold range is set to μ±3σ, where σ is the regression standard deviation of the deflection characteristic equation;

[0044] The long-term deflection value of the current continuous rigid frame bridge is measured by leveling or structural health monitoring system.

[0045] By comparing the current long-term deflection value with the set threshold range, if the threshold is exceeded, an early warning is triggered, and manual inspection is initiated in a timely manner to investigate the cause of the abnormality, thereby realizing early warning of the structural status of the continuous rigid frame bridge.

[0046] As monitoring data accumulates, repeat the steps. ~ The flexural characteristic equation and threshold range are updated to improve the accuracy of early warning.

[0047] 6. Prediction of prestress loss and stress change in box girders during operation.

[0048] When there is a warning in step "5", or when it is necessary to analyze the structural state of a continuous rigid frame bridge when it deflects to a certain extent, the prestress loss and stress change of the box girder can be calculated according to the following steps to provide support for the structural state assessment.

[0049] Based on the deflection regression equations for each symmetrical measuring point determined in step "4", and taking t1=0, calculate the predicted total deflection value at any time t. When the deflection measuring points are not arranged according to the "4-points of the side span and 8-points of the middle span", the modified Bessel interpolation method can be used for interpolation. Calculate the mean deflection value at the symmetrical positions of the 4-points of each side span of the continuous rigid frame bridge, denoted as... , , Calculate the average deflection at 1 / 8 and 7 / 8, 2 / 8 and 6 / 8, and 3 / 8 and 5 / 8 of the mid-span, and denote it as . , , The deflection value at the mid-span is recorded as follows: .

[0050] A model of a continuous rigid frame bridge was established using beam element finite element method to determine the completed bridge state. The average stress of the prestressed steel strands in the bottom slab of the mid-span, the top slab of the box girder, and the bottom slab of the side span was extracted when the bridge was completed. The stresses in the closure section of the side span, the root of the box girder, the 1 / 4 span section of the mid-span, and the top and bottom slabs of the closure section of the mid-span were also extracted.

[0051] Substitute the steps according to equation (3) "The deflection values ​​at each measuring point obtained at time t are used to predict the prestress loss of the continuous rigid frame bridge at time t."

[0052]

[0053] Equation (3);

[0054] In the formula: —The main beam at the time of bridge completion Average stress of prestressed steel strands;

[0055] —Main beam at time t during operation period Average stress of prestressed steel strands;

[0056] — =1,2,3 represent the bottom slab bundle of the mid-span, the top slab bundle of the box girder, and the bottom slab bundle of the side span, respectively.

[0057] — =1~7 represents the mean deflection at the symmetrical positions of the four points of each side span at time t during the operation period, the mean deflection at 1 / 8 and 7 / 8, 2 / 8 and 6 / 8, 3 / 8 and 5 / 8 of the middle span, and the deflection at the middle of the middle span, respectively. Unit: mm;

[0058] , —The span of the side span and the middle span of a continuous rigid frame bridge, in meters;

[0059] —Parameters to be determined =0~7, see Table 1:

[0060] Table 1 Prestress Loss-Deflection Equation Coefficients

[0061]

[0062] Substitute equation (4) into step " "The deflection values ​​at each measuring point obtained at time t are used to predict the stress changes at key sections of the box girder of the continuous rigid frame bridge at time t."

[0063]

[0064] Equation (4);

[0065] In the formula: —The main beam at the time of bridge completion Stress in each part;

[0066] —Main beam at time t during operation period Stress in each part;

[0067] — =1~8, representing the stresses in the side span closure section, the root of the box girder, the middle span 1 / 4 span, and the top and bottom plates of the middle span closure section, respectively;

[0068] — =1~7, representing the mean deflection at the symmetrical positions of the four points of each side span at time t during the operation period, the mean deflection at 1 / 8 and 7 / 8, 2 / 8 and 6 / 8, 3 / 8 and 5 / 8 of the middle span, and the deflection at the middle of the middle span, respectively. Unit: mm;

[0069] —Parameters to be determined =0~7, see Table 2;

[0070] Table 2 Stress-Deflection Regression Equations for Main Girder

[0071]

[0072] The coefficients in Tables 1 and 2 are obtained by regression analysis based on a large number of continuous rigid frame bridge samples with different design parameters and completed bridge stress states. The calculation model takes into account the influence of nonlinear creep of concrete, and the regression method adopts the response surface method. The regression results show that the stress and prestress loss of the key section of the continuous rigid frame bridge are affected by many factors, but are mainly related to the span of the structure, the completed bridge stress, and the long-term deflection curve. The span of the structure and the completed bridge stress reflect the influence of design and construction, and the long-term deflection curve comprehensively reflects the shrinkage and creep, prestress loss, and vehicle dead load effect in the later operation. Therefore, Equations (3) and (4) can be used to quickly estimate the prestress loss and stress of the structure.

[0073] 7. Structural performance evaluation. Based on the actual structural condition determined in step (6), the performance of the continuous rigid frame bridge is evaluated in accordance with the "Design Specifications for Highway Reinforced Concrete and Prestressed Concrete Bridges and Culverts" (JTG3362-2018).

[0074] In addition, the calculation logic of steps “3~7” can be written into a dedicated program (such as an Excel plugin or Python script). After inputting the observation data, it can automatically output the deflection prediction value, prestress loss, stress change, early warning results and evaluation report, so as to achieve rapid estimation of the structural state.

[0075] Compared with the prior art, the present invention has the following advantages:

[0076] (i) Based on a large amount of long-term measured data of deflection of in-service continuous rigid frame bridges, this invention constructs a long-term deflection characteristic equation that can reflect the true nonlinear evolution law of the structure. It can accurately predict the deflection development trend and, combined with dynamic thresholds, realize rapid and accurate early warning of abnormal structural deformation, overcoming the shortcomings of traditional methods that rely on short-term data and have high randomness in evaluation results.

[0077] (ii) Adopting a closed-loop approach of “measurement, regression, prediction, and verification”, abandoning traditional complex simulation modeling and multi-parameter analysis, and directly using measured data to drive structural state judgment, the accuracy and convenience of long-term deflection prediction and state assessment are greatly improved, which is more in line with engineering practice.

[0078] (iii) The warning threshold is dynamically updated and self-corrected as measured data increases, fully taking into account the individual differences in the deflection development of different bridges, solving the problem of false warnings and missed warnings that are easy to occur with traditional fixed thresholds, and significantly improving the reliability and pertinence of warnings.

[0079] (iv) Innovatively establish the coupling regression relationship between deflection, prestress loss and main beam stress, and comprehensively consider the influence of the full cross-section deflection distribution of the side span and middle span on the structural stress, rather than relying solely on the single-point deflection at the mid-span. The evaluation results are more in line with the actual stress state of the structure, and are more scientific and reliable.

[0080] (v) The overall process is standardized and modularized, and can be packaged into an automated program to achieve one-click calculation and automatic output. It does not require complicated operation by professional personnel and is suitable for routine monitoring and rapid assessment of large-scale in-service bridges, which can significantly improve maintenance efficiency and reduce assessment costs. It is directly compatible with existing deflection monitoring systems and conventional test data, with low application threshold and strong promotion. It can significantly improve the practical value of bridge health monitoring systems, provide scientific basis for maintenance decisions and selection of repair and reinforcement timing, and ensure the long-term operational safety of long-span continuous rigid frame bridges. Attached Figure Description

[0081] Figure 1 The measured deflection over the years for Bridge Example 1 in Embodiment 1 of the present invention;

[0082] Figure 2 Example 1 of the present invention is a bridge example to predict deflection;

[0083] Figure 3 This is the long-term deflection early warning threshold setting for Bridge Example 1 in Embodiment 1 of the present invention;

[0084] Figure 4 The measured deflection over the years for Bridge Example 2 in Embodiment 2 of the present invention;

[0085] Figure 5 Example 2 of the present invention is a bridge example for predicting deflection;

[0086] Figure 6 This is the setting of the long-term deflection early warning threshold for Bridge Example 2 in Embodiment 2 of the present invention;

[0087] Figure 7 This is a flowchart of the structural performance status evaluation method based on flexural deformation according to the present invention. Detailed Implementation

[0088] To make the technical means, inventive features, and objectives of this invention easier to understand, the technical solution of the invention will be further explained below with reference to two embodiments and specific implementation methods of the rapid early warning and estimation method for the structural state of continuous rigid frame bridges based on long-term deflection changes:

[0089] Example 1: A bridge located on a secondary highway has a total length of 756m, a total deck width of 12.5m, a carriageway width of 9m, and two lanes. The design load level is Highway-I. The superstructure is a 103m + 190m + 103m prestressed concrete continuous rigid frame. The box girder has a top width of 12m and a bottom width of 6.5m, and is a single-box, single-cell cross-section. The girder height at the root is 12m, and at mid-span it is 3.8m. The web thicknesses are 0.8m, 0.6m, and 0.5m respectively, and the bottom slab thickness varies from 0.32m in the middle according to a 1.6-degree parabola to 1.4m at the root. The bridge was completed and opened to traffic in 2012.

[0090] Set up observation points according to step 1.

[0091] In 2019, leveling points were set up for the bridge. The leveling points for the side spans were set up at the abutments, the 4-points of the side spans, and the top of the piers, while the leveling points for the middle spans were set up at the 8-points.

[0092] Follow steps 2 and 3 to measure deflection data and eliminate pier deformation and abutment settlement.

[0093] Six leveling measurements were conducted in 2019 (completed bridge, benchmark), 2020, 2021, 2022, 2023, and 2024. The long-term deflection changes of the bridge after eliminating pier deformation and abutment settlement according to step 3 are shown in Table 3. Figure 1 As shown.

[0094] Table 3. Measured Deflections of Bridge Example 1 Over the Years

[0095]

[0096] Following step 4, establish the flexural characteristic equation.

[0097] (1) Calculate the mean deflection at the symmetrical position, as shown in Table 4.

[0098] Table 4. Average measured deflection values ​​at symmetrical locations of Bridge Example 1 over the years.

[0099] (2) As shown in Table 4, as of the last measurement in 2024, the measuring points with a mean deflection of 5 mm or more at the symmetrical position are the middle of the side span and the eighth point of the middle span; the number of measurements is 6, which is less than 10. t1 = 2019 - 2012 = 7 years. The parameters of the deflection characteristic equation are determined by regression according to formula (2-2) in step 4. The regression results are shown in Table 5.

[0100] Table 5 Parameters of the Deflection Characteristic Equation for Bridge Example 1

[0101] (3) As shown in Table 4, up to the last measurement in 2024, the average deflection at the symmetrical positions was less than 5 mm at the measuring points in the 1 / 4 and 3 / 4 side spans; and the average deflection at the mid-span of the 1 / 4, 3 / 4, and middle spans was less than 5 mm. The values ​​are -2.37mm, 1.06mm, and -24.84mm respectively; the parameters T0 and p for the 1 / 4 and 3 / 4 side spans can be taken from the values ​​of the middle span, which are 8.092 and 1.393 respectively; the parameter A is calculated according to formula (2-3), which are -2.37 / -24.84×210.135=20.049 and 1.06 / -24.84×210.135=-8.967 respectively.

[0102] Based on the determination of the parameters in the above regression equation, the deflection values ​​of the bridge at different operating times can be predicted, such as... Figure 2 As shown.

[0103] Follow step 5 to set the long-term deflection early warning threshold.

[0104] Table 5 shows that the mid-span deflection characteristic equation for Bridge Example 1 is A=210.135, T0=8.904 years, p=1.393, and the regression standard deviation σ=1.56mm. The first measurement was in 2019, and the bridge was completed and opened to traffic in 2012, so t1=7 years. Substituting into equation (2-1), and setting the threshold range to μ±3σ according to step 5, as shown... Figure 3 As shown. From Figure 3 As can be seen from the data, when the operation period is 35 years, based on the first measurement in 2019, the predicted mid-span deflection is 95.3±4.68mm. When the measured value exceeds this range, an early warning should be issued and the bridge should be inspected on-site. If no abnormality is found during the inspection, the measured data should be updated and the parameters of the deflection characteristic equation should be updated according to step 4. If an abnormality is found during the inspection, measures should be taken in a timely manner to ensure the structural and vehicle traffic safety.

[0105] Following step 6, predict the prestress loss and stress change of the bridge.

[0106] Based on the deflection regression equations for each measuring point determined in step (4), take t1=0 and calculate the predicted total deflection value at any time t; calculate the mean deflection at the symmetrical positions of the four points of each side span of the continuous rigid frame bridge, denoted as , , Calculate the average deflection at 1 / 8 and 7 / 8, 2 / 8 and 6 / 8, and 3 / 8 and 5 / 8 of the mid-span, and denote it as . , , The deflection value at the mid-span is recorded as follows: The deflection values ​​for operation periods of 10 years, 20 years, and 50 years are shown in Table 6.

[0107] Table 6. Predicted deflection values ​​(mm) during the operation period of Bridge Example 1

[0108] Based on the above deflection data and combined with the bridge beam unit model, the prestress loss and stress change are calculated according to Equations (4) and (5), as shown in Tables 6 and 7.

[0109] Table 7 Prediction of Prestress Changes in Bridge Example 1

[0110]

[0111] As shown in Table 7, it is estimated that after 50 years of operation, the average stress of the prestressed steel strands in the mid-span bottom slab, box girder top slab, and side-span bottom slab will decrease by 18%, 53%, and 42%, respectively. Prestress loss is a key parameter for the structural state of continuous rigid frame bridges, and obtaining this parameter can provide support for further and more comprehensive analysis of the structural bearing capacity and service performance.

[0112] Table 8. Prediction of stress variation at key sections of Bridge Example 1

[0113] As shown in Table 8, it is expected that the dead load stress of the key sections of the main beam will change to varying degrees after 50 years of operation. The performance evaluation can be carried out based on the changes in dead load stress obtained in Table 7.

[0114] Follow step 7 to conduct a structural performance status assessment.

[0115] A model of a continuous rigid frame bridge was established using beam element finite element method to determine the completed bridge state. The stresses of the side span closure section, the root of the box girder, the 1 / 4 span section of the middle span, and the top and bottom plates of the middle span closure section were extracted respectively. The stress changes of each key section under dead load as determined in Table 7 were used to combine loads according to the "Design Specification for Highway Reinforced Concrete and Prestressed Concrete Bridges and Culverts" (JTG3362-2018) to evaluate the actual performance state of the structure determined in step (6): it was determined whether the tensile stress and compressive stress of each section of the main beam exceeded the specification limit and the risk of structural cracking was assessed.

[0116] The evaluation results of Bridge Example 1 are shown in Table 9.

[0117] Table 9. Stress Analysis of Bridge Example 1 under Normal Serviceability Limit State (Unit: MPa)

[0118] Note: Negative values ​​in the table indicate pressure.

[0119] As shown in Table 9, it is estimated that after 50 years of operation, the compressive stress in the bottom slab of the main girder side span closure section, the top slab at the pier top, the top slab at the L / 4 section of the middle span, and the bottom slab of the middle span closure section will decrease to some extent. Tensile stress will appear in the bottom slab of the side span closure section, which is 1.0 MPa, exceeding the standard limit of 1.10 MPa. The compressive stress in the top slab of the main girder side span closure section, the bottom slab at the pier top, the top slab at the L / 4 section of the middle span, and the top slab of the middle span closure section will increase to some extent, with the maximum being 18.2 MPa in the top slab of the middle span closure section, slightly exceeding the standard limit of 17.75 MPa, but still somewhat lower than the standard value of 35.5 MPa for the compressive strength of the bottom slab concrete.

[0120] Therefore, it can be seen that, based on the current flexural characteristics, the structural performance of the bridge will be significantly reduced after 50 years of operation, but it will still basically meet the requirements of current specifications.

[0121] Example 2: A bridge located on a secondary highway has a total length of 265.00m, a total deck width of 12.0m, a carriageway width of 11.0m, two lanes, and a vehicle load rating of 20 for cars and 100 for trailers. The superstructure is a 64m+115m+64m prestressed concrete continuous rigid frame. The box girder adopts a single-box, single-cell structure with straight webs. The top slab of the box girder is 12.0m wide, and the bottom slab is 6.0m wide. The beam height at both ends and the mid-span is 2.5m, the beam height at the pier top is 6.0m, and the beam height of the remaining main girders varies according to a quadratic parabola. The web thickness of the box girder is 40cm and 50cm, except for 70cm on the No. 0 block of the main girder; the bottom slab thickness gradually changes from 80cm at the root to 32cm at the mid-span according to a quadratic parabola. This bridge was completed in 2004.

[0122] Set up observation points according to step 1.

[0123] After the bridge was completed in 2004, permanent leveling observation points were set up. The leveling points for the side spans were set up at the abutments, 1 / 3 of the span, and the top of the piers, while the leveling points for the middle span were set up at 4 points.

[0124] Follow steps 2 and 3 to measure deflection data and eliminate pier deformation and abutment settlement.

[0125] Twelve deflection measurements were conducted in 2004 (completed bridge, reference year), 2007, 2008, 2009, 2010, 2011, 2012, 2013, 2014, 2015, 2016, and 2017. The long-term deflection changes of the bridge after eliminating pier deformation and abutment settlement according to step 3 are shown in Table 10. Figure 4 As shown.

[0126] Table 10. Measured Deflections of Bridge Example 2 Over the Years

[0127]

[0128] Following step 4, establish the flexural characteristic equation.

[0129] (1) Calculate the mean deflection at the symmetrical position, as shown in Table 11.

[0130] Table 11 Average measured deflection values ​​at symmetrical locations over the years for Bridge Example 2

[0131]

[0132] (2) As shown in Table 11, as of the last measurement in 2017, the mid-span quarter point has a mean deflection of 5 mm or more at the symmetrical position. The number of measurements was 12, which is greater than 10. t1 = 2004 - 2004 = 0 years. The parameters of the deflection characteristic equation were determined by regression according to formula (2-1) in step 4. The regression results are shown in Table 12.

[0133] Table 12 Parameters of the Deflection Characteristic Equation for Bridge Example 2

[0134] (3) As shown in Table 12, as of the last measurement in 2024, the average deflection at symmetrical positions was less than 5 mm at 1 / 3 of the side span; the average deflection at mid-span of 1 / 3 of the side span and the middle span was less than 5 mm. The values ​​are -1.27mm and -97.63mm respectively. The parameters T0 and p of the 1 / 3 side span can be taken from the values ​​of the middle span, which are 10.804 and 1.187 respectively; the parameter A is calculated according to formula (2-3) as -1.27 / -97.63×247.434=3.219.

[0135] Based on the determination of the parameters in the above regression equation, the deflection values ​​of the bridge at different operating times can be predicted, such as... Figure 5 As shown.

[0136] Follow step 5 to set the long-term deflection early warning threshold.

[0137] Table 12 shows that the mid-span deflection characteristic equation for Bridge Example 2 is A = 298.113 m, T0 = 10.804 years, p = 1.187, and the regression standard deviation σ = 1.620. Following step 5, the threshold range is set to μ ± 3σ. Figure 6 As shown. From Figure 6 As can be seen from the data, when the operating period is 35 years, the predicted mid-span deflection is 193.4 ± 4.86 mm. When the measured value exceeds this range, an early warning should be issued and the bridge should be inspected on-site. If no abnormality is found during the inspection, the measured data should be updated and the parameters of the deflection characteristic equation should be updated according to step 4. If an abnormality is found during the inspection, measures should be taken in a timely manner to ensure the structural and vehicle traffic safety.

[0138] Following step 6, predict the prestress loss and stress change of the bridge.

[0139] Based on the deflection regression equations for each measuring point determined in step (4), the predicted deflection value at any time t is calculated; and the deflection values ​​at the 4th point of the side span and the 8th point of the middle span are obtained by interpolation using the modified Bessel interpolation method. The mean deflection value at the symmetrical position of the 4th point of each side span of the continuous rigid frame bridge is calculated, and the mean deflection values ​​at 1 / 8 and 7 / 8, 2 / 8 and 6 / 8, 3 / 8 and 5 / 8 of the middle span are obtained. The deflection values ​​for operation periods of 10 years, 30 years and 50 years are shown in Table 13.

[0140] Table 13. Predicted deflection values ​​(mm) during the operation period of Bridge Example 2

[0141] Based on the above deflection data and combined with the bridge beam unit model, the prestress loss and stress change are calculated according to Equations (4) and (5), as shown in Tables 14 and 15.

[0142] Table 14 Prediction of Prestress Changes in Bridge Example 2

[0143]

[0144] As shown in Table 14, it is estimated that after 50 years of operation, the average stress of the prestressed steel strands in the mid-span bottom slab, box girder top slab, and side-span bottom slab will decrease by 82%, 43%, and 0.2%, respectively. Prestress loss is a key parameter for the structural state of continuous rigid frame bridges, and obtaining this parameter can provide support for further and more comprehensive analysis of the structural bearing capacity and service performance.

[0145] Table 15 Prediction of Stress Variation at Key Sections in Bridge Example 2

[0146] As shown in Table 15, it is expected that the dead load stress of the key sections of the main beam will change to varying degrees after 50 years of operation. The performance evaluation can be carried out based on the changes in dead load stress obtained in Table 14.

[0147] Follow step 7 to conduct a structural performance status assessment.

[0148] A model of a continuous rigid frame bridge was established using beam element finite element method to determine the completed bridge state. The stresses of the side span closure section, the root of the box girder, the 1 / 4 span section of the middle span, and the top and bottom plates of the middle span closure section were extracted respectively. The stress changes of each key section under dead load as determined in Table 14 were used to combine loads according to the "Design Specification for Highway Reinforced Concrete and Prestressed Concrete Bridges and Culverts" (JTG3362-2018) to evaluate the actual performance state of the structure determined in step (6): it was determined whether the tensile stress and compressive stress of each section of the main beam exceeded the specification limit and the risk of structural cracking was assessed.

[0149] The evaluation results for Bridge Example 2 are shown in Table 16.

[0150] Table 16 Stress Analysis of Bridge Example 2 under Normal Serviceability Limit State (Unit: MPa)

[0151] Note: Negative values ​​in the table indicate pressure.

[0152] As shown in Table 16, with the evolution of the bridge's deflection during operation, it is estimated that after 50 years of operation, the top slab at the cantilever root, the top slab at the mid-span 1 / 4 section, and the bottom slab of the mid-span closure section will experience significant tensile stresses, at 4.2, 4.9, and 3.6 MPa respectively, far exceeding the standard limit of 1.1 MPa and the standard value of tensile strength of 2.7 MPa. The compressive stress at the bottom slab at the cantilever root will increase significantly, reaching 28.81 MPa, far exceeding the standard limit of 16.2 MPa and approaching the standard value of compressive strength of 32.4 MPa. Therefore, if the bridge continues to develop in this trend, after 50 years of operation, the top slab at the cantilever root, the top slab at the mid-span 1 / 4 section, and the bottom slab of the mid-span closure section will face a significant risk of tensile cracking, while the bottom slab at the cantilever root will face a significant risk of compressive cracking.

[0153] Comparing Examples 1 and 2, the two bridges with different spans exhibit different degrees of deflection and varying degrees of stress changes. The deflection shapes along the longitudinal direction also differ, as do the prestress losses and stress variations in the main girder sections at different locations. After 50 years of operation, the deflection-to-span ratio of Bridge 1 is projected to reach 1 / 986, which is not considered severe among bridges of its type. Currently, after 14 years of operation, no serious defects (such as transverse cracks in the top and bottom slabs or diagonal cracks in the web) have been found in the box girder during maintenance and inspection. In Example 2, after 50 years of operation, the deflection-to-span ratio is projected to reach 1 / 540, indicating more severe deflection. The top slab at the cantilever root, the top slab at 1 / 4 of the mid-span section, and the bottom slab of the mid-span closure section pose a significant risk of tensile cracking, while the bottom slab at the cantilever root poses a significant risk of compressive cracking. During its operational period, this bridge developed defects such as transverse cracks in the top and bottom slabs and diagonal cracks in the web, which were reinforced in 2018.

[0154] It should be understood that the specific embodiments described above are merely illustrative or explanatory of the principles of the invention and do not constitute a limitation thereof. Therefore, any modifications, equivalent substitutions, improvements, etc., made without departing from the spirit and scope of the invention should be included within the protection scope of the invention. Furthermore, the appended claims are intended to cover all variations and modifications falling within the scope and boundaries of the appended claims, or equivalent forms of such scope and boundaries.

Claims

1. A rapid early warning and estimation method for the structural state of a prestressed concrete continuous rigid frame bridge based on long-term deflection changes, characterized in that, Includes the following steps: S1. Observation point layout: Permanent observation points are laid out on the main beam of the continuous rigid frame bridge during the operation period. The side spans are laid out with 4 points and the middle span with 8 points, ensuring that there is no less than 1 observation point in the middle of the side span and 4 points in the middle span. After the layout is completed, the initial deflection is measured and the initial data, measurement time and ambient temperature are recorded. S2. Deflection data collection: At least 6 deflection measurements will be conducted during the operation period, with a time interval of no less than 1 year between each measurement. Measurements will be taken during stable temperature periods with a daily temperature difference of ≤5℃. Second-order leveling will be used, and linear interpolation will be used to eliminate the influence of pier and abutment settlement. S3. Establish the deflection characteristic equation: Take the mean value of the deflection at the symmetrical position measurement point, and according to whether the number of measurements is ≥10, use independent regression or joint regression to fit the characteristic equation of the long-term deflection change over time, and obtain the equation parameters and regression standard deviation σ. S4. Dynamic warning threshold setting: Based on the mid-span deflection characteristic equation, the predicted deflection value μ at time t is predicted, and the warning interval is set to μ±3σ according to the Raida criterion; the measured deflection is compared with the threshold, and if it exceeds the threshold, a structural anomaly warning is triggered. S5. Prestress Loss and Stress Prediction: Based on the predicted deflection values ​​at each measuring point, substitute them into the preset deflection-prestress regression equation and deflection-stress regression equation to calculate the prestress loss of the key steel strands of the main beam and the stress change of the key section. S6. Structural Status Assessment: Based on the current highway bridge and culvert design specifications, and combined with the predicted stress, the serviceability limit state and ultimate limit state assessments are conducted, and the structural status assessment results are output.

2. The rapid early warning and estimation method for the structural state of a prestressed concrete continuous rigid frame bridge based on long-term deflection changes as described in claim 1, characterized in that, The flexural characteristic equation mentioned in step S3 includes: Equation (2-1); Equation (2-2); In the formula, t—the time after the bridge is completed (after the completion of the second phase of construction), in years; y—Deflection at time t after the bridge is completed, unit: mm; t1—Time of the first measurement after bridge completion, in years; if the first measurement is carried out immediately after bridge completion, it is set to 0. A—an undetermined constant; —Time constant to be determined; —Undetermined coefficients for the shape of the curve over time; , , ..., —The average deflection of the symmetrical measuring point when the difference between the average deflection of the last measurement and the average deflection of the first measurement is greater than or equal to 10 mm; , , ..., —Undetermined constants for symmetrical measuring points when the difference between the mean deflection of the symmetrical measuring point in the last measurement and the first measurement is greater than or equal to 5 mm; When the number of measurements is ≥10, regression analysis is performed on the deflection data of each deflection measuring point of the main beam according to Equation 2-1, and each measuring point is fitted independently; when the number of measurements is <10, regression is performed according to the equation system of Equation 2-2 to preliminarily determine, unify t0 and p, and jointly fit the A value of each measuring point; for measuring points with deflection changes of less than 5mm, t0 and p at the mid-span are used and A is calculated according to the average ratio.

3. The rapid early warning and estimation method for the structural state of a prestressed concrete continuous rigid frame bridge based on long-term deflection changes as described in claim 2, characterized in that: Undetermined constant A i The calculation is as follows, according to formula (2-3): Equation (2-3); In the formula, A i —Undetermined constants for symmetrical measuring points when the difference between the mean deflection of the symmetrical measuring points in the last measurement and the first measurement is less than 5 mm; —The undetermined constant of the mid-span determined by step "(2)". —The average of all measured deflection values ​​at the symmetrical measuring point; —The average deflection measured at the mid-span of the span.

4. The rapid early warning and estimation method for the structural state of a prestressed concrete continuous rigid frame bridge based on long-term deflection changes as described in claim 1, characterized in that, In step S2, the following correction formula is used to eliminate the settlement of the pier and abutment: Equation (1); In the formula: —Settlement correction for pier top and support points; —The distance from pivot A to pivot B; —The distance from the deflection measuring point to fulcrum A; —Settlement at fulcrum A; —Settlement at fulcrum B.

5. The rapid early warning and estimation method for the structural state of a prestressed concrete continuous rigid frame bridge based on long-term deflection changes as described in claim 1, characterized in that, The prestress loss calculation in step S5 uses the following formula: Equation (3); In the formula: —The main beam at the time of bridge completion Average stress of prestressed steel strands; —Main beam at time t during operation period Average stress of prestressed steel strands; — =1,2,3 represent the bottom slab bundle of the mid-span, the top slab bundle of the box girder, and the bottom slab bundle of the side span, respectively. — =1~7 represents the mean deflection at the symmetrical positions of the four points of each side span at time t during the operation period, the mean deflection at 1 / 8 and 7 / 8, 2 / 8 and 6 / 8, 3 / 8 and 5 / 8 of the middle span, and the deflection at the middle of the middle span, respectively. Unit: mm; , —The span of the side span and the middle span of a continuous rigid frame bridge, in meters; —Parameters to be determined =0~7, see Table 1; Table 1 Prestress Loss-Deflection Equation Coefficients 。 6. The rapid early warning and estimation method for the structural state of a prestressed concrete continuous rigid frame bridge based on long-term deflection changes as described in claim 1, characterized in that, The stress calculation of the key section in step S5 uses the following formula: Equation (4); In the formula: —The main beam at the time of bridge completion Stress in each part; —Main beam at time t during operation period Stress in each part; — =1~8, representing the stresses in the side span closure section, the root of the box girder, the middle span 1 / 4 span, and the top and bottom plates of the middle span closure section, respectively; — =1~7, representing the mean deflection at the symmetrical positions of the four points of each side span at time t during the operation period, the mean deflection at 1 / 8 and 7 / 8, 2 / 8 and 6 / 8, 3 / 8 and 5 / 8 of the middle span, and the deflection at the middle of the middle span, respectively. Unit: mm; —Parameters to be determined =0~7, see Table 2; Table 2 Stress-Deflection Regression Equations for Main Girder 。 7. The rapid early warning and estimation method for the structural state of a prestressed concrete continuous rigid frame bridge based on long-term deflection changes as described in claim 1, characterized in that, In step S4, the warning threshold is updated periodically as the measured data increases. Each time a new set of observation data is added, the equation parameters are refitted and the threshold range is corrected.

8. The rapid early warning and estimation method for the structural state of a prestressed concrete continuous rigid frame bridge based on long-term deflection changes as described in claim 1, characterized in that, The key sections in step S5 include: the side span closure section, the root of the box girder, the 1 / 4 span section of the middle span, and the top and bottom slabs of the middle span closure section; the key steel strands include: the bottom slab strand of the middle span, the top slab strand of the box girder, and the bottom slab strand of the side span.

9. The rapid early warning and estimation method for the structural state of a prestressed concrete continuous rigid frame bridge based on long-term deflection changes as described in claim 1, characterized in that, All calculation steps are encapsulated into an automated program, which automatically outputs the following after inputting deflection observation data: deflection prediction value, early warning judgment result, prestress loss, stress change and specification compliance assessment report.

10. A rapid early warning system for the structural state of a continuous rigid frame bridge based on long-term deflection changes, characterized in that, include: The observation module is used for the establishment of permanent deflection measurement points and standardized leveling data acquisition. The data preprocessing module is used for settlement correction, calculation of the mean value of symmetrical measuring points, and removal of temperature effects. The equation fitting module is used to construct long-term flexural characteristic equations and output parameters and regression standard deviations. The early warning module is used to dynamically calculate the μ±3σ threshold and determine if it exceeds the limit; The state calculation module is used for prestress loss and critical section stress prediction. The evaluation module is used to perform limit state evaluations according to current standards and output the results. The system is suitable for symmetrically arranged prestressed concrete continuous rigid frame bridges with spans of 50m to 250m, but not for asymmetrical, non-prestressed, or spanless rigid frame bridges.

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