Bridge non-uniformly degraded girder flexural rigidity updating method based on vehicle response

Abstract

The invention belongs to the technical field of structural safety detection, and discloses a method for updating flexural rigidity of a non-uniformly degraded girder of a bridge based on vehicle response, which comprises the following steps: (1) carrying out a rapid load test on the bridge; (2) constructing a stiffness function considering non-uniform degradation of the main beam; and (3) establishing a target function of displacement and strain shape combination and finishing model updating. According to the method, the rigidity distribution condition of the main beam is inversed by using a rigidity function and a model updating method based on the non-uniform degradation of the main beam of the bridge, the continuity and rationality of the rigidity of the main beam are ensured, and the rigidity of a large number of bridge units can be updated by using fewer parameters. The provided objective function meets the requirement of full-bridge non-uniform rigidity updating, the problem of distortion of an optimization result of a single objective function is solved, and a large amount of structural information can be provided for main beam rigidity inversion. Required response can be obtained through a rapid load test, and the defects that a bridge load test is high in cost and long in time are effectively overcome.

Description

Technical Field

[0001] The invention belongs to the technical field of structural safety detection, and relates to a method for updating the bending stiffness of a bridge non-uniformly degraded main beam based on vehicle-induced response. Background Art

[0002] As a key transportation hub, bridges play an important role in the transportation industry. Currently, there are more than one million bridges in China. After years of use, bridge girders usually crack and deflect excessively. As the main load-bearing member of a bridge, the main girder determines the state of the entire bridge. Therefore, it is necessary to timely and accurately assess the degree of deterioration and bearing capacity of bridge girders to prevent the deterioration of the disease from affecting traffic safety. Studies have shown that cracking is one of the main factors affecting the deflection and bearing capacity of the main girder. Unexpected loads, prestress loss, steel corrosion, etc. may all lead to cracking. The height of the crack directly affects the effective section moment of inertia of the beam. The crack extends along the height direction of the main girder, and the neutral axis of the cross section is increased, which weakens the overall stiffness of the cross section of the main girder. In addition, problems such as material degradation can also affect the stiffness of the bridge main girder. Therefore, it is very important to quickly and accurately determine the degree of stiffness loss and its impact on the bearing capacity.

[0003] The cracking of the main beam is a key factor affecting the deflection of the main beam. This cracking weakens the overall stiffness of the main beam cross section. Cracks usually appear on the bottom and side of the main beam. Among them, the transverse cracks on the bottom and the oblique cracks on the side have a serious impact on the overall performance of the structure and significantly affect its stiffness. The transverse cracks on the bottom are densely distributed in the middle of the span. Severe cracks may extend to the side and form vertical cracks, which greatly affect the bending bearing capacity. The oblique cracks in the side mainly appear at one-quarter of the span, which has a greater impact on the shear capacity and a smaller impact on the bending capacity. In general, when the main beam deteriorates overall under normal conditions, the impact of these cracks on the stiffness of the bridge is most serious in the middle of the span because the middle of the span is usually the location of the maximum bending moment. As the distance from the support decreases, the degree of cracking gradually decreases, and the impact on stiffness decreases. In addition, the interior of the main beam is often subjected to various types of prestressing and ordinary steel bars, which also affect the stiffness of the main beam. Due to these factors, the stiffness of the main beam shows an uneven change trend along the length of the main beam.

[0004] Stiffness loss has a great influence on bridge performance, and the determination of stiffness loss depends on the stiffness form or response form assumed in advance. The finite element method is one of the most widely used and reliable analysis methods in bearing capacity assessment. Therefore, assuming a stiffness form is a simpler and more suitable method for model analysis. Many scholars believe that the stiffness of the main beam of the bridge is uniform within a certain length range and can be divided into several parts, such as each span is divided into one or three sections (beam end, mid-span). However, this method assumes that the stiffness within each segment is uniform, which may lead to poor longitudinal continuity of the bridge stiffness. In particular, in stiffness reversal, the stiffness of two adjacent segments may be pathological, resulting in an unrealistically large gap between adjacent stiffness. This unrealistic stiffness value will lead to a misjudgment of the degree of deterioration of the main beam and have an adverse effect on the results of bearing capacity assessment. Scholars have also begun to consider the continuity of stiffness and the influence of defects on stiffness, and proposed stiffness function forms such as Gaussian function, Dirac function, polynomial function, etc. However, most forms of stiffness functions are inconvenient to use in practical engineering, and the polynomial function form of stiffness function may be a better choice to represent the overall degradation of concrete main beams.

[0005] The load-bearing capacity evaluation of bridges is usually carried out with the help of bridge finite element models. The model can be updated by finite element model updating technology. The load-bearing capacity evaluation mainly compares the static load effect with the structural resistance. Therefore, the data used for model updating mainly consists of static responses. Sanayei et al. (2012) conducted a car static load test on a continuous beam bridge and updated the finite element model of the bridge based on the obtained strain data. Bentz et al. (2017) updated the reinforced concrete bridge model using static load strain data obtained from heavy trucks. Lin et al. (2022) updated a suspension bridge model using deflection influence lines. Zhou et al. (2023) updated a box girder bridge model using data from mobile loading tests. Static load tests obtain less information or require more sensors, while moving load tests can obtain more information based on a small number of sensors and can invert more structural information during the model update process. Therefore, using the response caused by moving loads to update the finite element model of the bridge has significant advantages.

[0006] In summary, when evaluating the bearing capacity of a bridge, it is necessary to consider the uneven distribution of its stiffness in order to obtain a finite element model that is consistent with the actual degradation of the main beam. In order to quickly obtain sufficient measured response data to update the model, it is necessary to change the traditional static load test method to achieve the purpose of quickly, accurately and reasonably evaluating the bearing capacity of the bridge. To this end, studying a method for updating the bending stiffness of the unevenly degraded main beam of a bridge based on vehicle-induced response is of great significance for evaluating the bearing capacity status of the bridge. Summary of the invention

[0007] The purpose of the present invention is to provide a method for updating the bending stiffness of a bridge non-uniformly degraded main beam based on vehicle-induced response.

[0008] The technical solution of the present invention:

[0009] A method for updating the bending stiffness of a bridge beam with uneven degradation based on vehicle-induced response, the steps are as follows:

[0010] Step 1. Bridge rapid load test

[0011] The response data required for updating the bridge assessment model is obtained through the bridge rapid load test. The response data is composed of the structural vehicle-induced response generated by a test vehicle with more than two axles passing through the bridge.

[0012] The loading process meets the following criteria: 1) The bridge rapid load test should be carried out without interference from other vehicles; 2) The test vehicle crosses the bridge at a speed of 5-10 km / h; 3) The test vehicle drives across the bridge in a straight line. For multi-lane bridges, the test vehicle drives once on each lane;

[0013] The static response of the bridge is directly related to the stiffness of the bridge. The deflection and strain are used to update the stiffness of the bridge assessment model. The deflection measurement point is located at the mid-span; the strain measurement point is located at the mid-span and near the support position.

[0014] Step 2. Construction of main beam stiffness function

[0015] The actual condition of the bridge is evaluated by updating the bridge evaluation model. When the bridge evaluation model is updated, the stiffness change of each bridge unit is expressed as a stiffness coefficient, that is:

[0016]

[0017] Among them, B e is the updated stiffness of the bridge element, is the initial stiffness of the bridge element, α e is the stiffness coefficient of each unit;

[0018] Therefore, the direct update of stiffness is converted into the update of stiffness coefficient; considering the non-uniformity and continuity of main beam stiffness, the stiffness function is used to establish the constraints and connections between the stiffness of bridge units; the stiffness function is composed of multiple polynomial basis functions, and its form is as follows:

[0019]

[0020] Right now:

[0021]

[0022] Where N(x) is the stiffness basis function, is the position of the bridge unit to be updated, p is the basis function magnification factor, n is the number of basis functions, n e is the number of bridge units to be updated (n e >>n);

[0023] The basis function of the stiffness function is constructed using Legendre polynomials. The first three order polynomials are selected to construct the stiffness function. The first two basis functions reflect the overall change of bridge stiffness, and the third basis function reflects the uneven change of bridge stiffness. The first three order stiffness basis functions are as follows:

[0024]

[0025]

[0026] N 3 (x) = -x 2 +1(6)

[0027] Where: x is the position of the bridge unit;

[0028] At this point, the stiffness changes of each unit on the bridge main beam are converted into stiffness coefficients, and the stiffness coefficients are converted into linear combinations of basis functions. When the model is updated, the correction parameter is changed from stiffness B to the amplification coefficient p of each basis function, which realizes a more reasonable update of the bridge assessment model.

[0029] Step 3. Bridge Assessment Model Update

[0030] The objective function of updating the bridge assessment model is established by the deflection and strain data obtained in step 1, which reflects the difference between the performance of the bridge assessment model and the actual bridge performance; the objective function of the deflection f 1 As shown below:

[0031]

[0032] Among them, Δ e is the measured deflection, Δ a is the deflection at the corresponding position on the bridge assessment model, j is the number of deflectometers, and k is the number of sample points in the deflection time history;

[0033] Strain contains more local information, so the strain shape is used to construct the objective function and eliminate the local information; the objective function of strain f 2 As shown below:

[0034]

[0035] Where m is the number of strain gauges, S e is the measured strain vector, S a is the strain vector corresponding to the bridge evaluation model; the final objective function is the deflection objective function f 1 and the objective function of strain f 2 To combine, that is:

[0036] f=f 1 +f2 (9)

[0037] Where f is the objective function of the combination;

[0038] Finally, the optimization algorithm is used to update the basis function amplification coefficient in step 2 to minimize the objective function, thus completing the process of updating the bridge assessment model and obtaining a finite element model whose stiffness is more closely matched with the actual one for load-bearing capacity assessment.

[0039] Beneficial effects of the present invention:

[0040] 1. A method for updating the bending stiffness of unevenly degraded bridge beams is proposed. This method ensures the continuity and rationality of the beam stiffness and can update the stiffness of a large number of bridge elements using fewer parameters.

[0041] 2. A moving load test scheme for bridges is proposed to replace the static load test, which can obtain more information about the bridge stiffness using a small number of sensors and can reduce the test time and cost of interrupting traffic;

[0042] 3. An objective function combining deflection residual and strain shape is proposed for model update based on moving load. This objective function can better update the uneven stiffness degradation of the main beam, achieve more reasonable main beam stiffness update, and obtain more accurate bearing capacity evaluation results. BRIEF DESCRIPTION OF THE DRAWINGS

[0043] Figure 1 Flow chart of the implementation of the method adopted by the present invention;

[0044] Figure 2 A two-span continuous box girder bridge in an embodiment of the method of the present invention: (a) front view; (b) AA section; (c) BB section; (d) finite element model;

[0045] Figure 3 It is a schematic diagram of stiffness simulation in an embodiment of the method of the present invention;

[0046] Figure 4 Schematic diagram of stiffness basis function in an embodiment of the method of the present invention;

[0047] Figure 5 A stiffness update result diagram in an embodiment of the method of the present invention;

[0048] Figure 6 Graphs showing response results before and after updating in an embodiment of the method of the present invention: (a) deflection; (b) strain;

[0049] Figure 7 Graph showing longitudinal strain distribution in an embodiment of the method of the present invention. DETAILED DESCRIPTION

[0050] The specific implementation of the present invention is further described below in conjunction with the accompanying drawings and technical solutions.

[0051] Example:

[0052] In the example, a concrete box girder bridge with a span of 25+25m is simulated. Figure 2 As shown. This bridge is a uniform cross-section bridge with transverse diaphragms at the support positions. The bridge model is established using shell elements, and the change in bridge stiffness is simulated by changing the elastic modulus. Considering the redundancy of bridge stiffness, the overall stiffness of the bridge is increased by 10%. In order to simulate the deterioration of the bridge, the stiffness of the box girder is reduced, and the middle part of the main beam is subjected to a larger bending moment and is more prone to cracking. Therefore, the stiffness reduction is greater near the mid-span, and in the mid-span, the stiffness is reduced by a maximum of 30%. In addition, considering the uncertainty of the actual stiffness of the bridge, a random change of stiffness of no more than 10% is performed. Figure 3 The stiffness diagram along the longitudinal direction of the bridge is shown. A simulated rapid load test was conducted on the bridge model without considering the dynamic effect. The test vehicle was simulated as a 35t four-axle vehicle, and the vehicle drove straight across the bridge. According to the above scheme, the mid-span deflection, mid-span strain and strain near the bridge support were extracted, and these responses were used to update the initial model.

[0053] The objective function is constructed using the above method to update the stiffness of the bridge model. The stiffness basis function is as follows: Figure 4 In addition to the stiffness function scheme used for model updating, the traditional segmentation scheme is also used for updating for comparison. Each bridge span is divided into three stiffness segments, and the updated stiffness results are shown in Figure 5 The response before and after the update in the left span is as follows Figure 6 As shown. Regardless of the method used, the response is consistent because the objective function is constructed from the response and minimized. However, there is a significant difference in the updated stiffness. The stiffness updated by the proposed method is closer to the set stiffness. In contrast, the stiffness obtained using the stiffness segmentation scheme is similar to the average result within each segment. Therefore, there is a significant difference in the stiffness at the segment connections, which is inconsistent with actual expectations. The stiffness at these connections can be considered distorted.

[0054] The bearing capacity assessment is mainly to check whether the structural response meets the requirements under the specified load. Here, a uniformly distributed load is applied to the bridge to prove the effectiveness of the assessment. Table 1 shows the response of the bridge at different locations. In Table 1, the stiffness function update results and the segmented stiffness update results are compared with the actual values. It is obvious that the method proposed in this paper achieves better response matching during the model update process. The inter-segment strain error in the model obtained by the segmented scheme is large. The longitudinal strain distribution of the entire bridge is shown in Figure 7 As shown. Figure 7It can be seen that the model update by the piecewise stiffness method has obvious strain errors, and the strain discontinuity observed in some locations is obviously unreasonable and inconsistent with the actual situation. This difference undermines the credibility of such strain data for state assessment. Therefore, the method proposed in this paper guarantees the accuracy and credibility of the assessment results.

[0055] Table 1 Responses of different bridge locations

[0056]

Claims

1. A method for updating the bending stiffness of unevenly degraded main beams of bridges based on vehicle-induced response, characterized in that: Here are the steps: Step 1. Bridge rapid load test The response data required for updating the bridge assessment model is obtained through the bridge rapid load test. The response data is composed of the structural vehicle-induced response generated by a test vehicle with more than two axles passing through the bridge. The loading process meets the following criteria: 1) The bridge rapid load test should be carried out without interference from other vehicles; 2) The test vehicle crosses the bridge at a speed of 5-10 km / h; 3) The test vehicle drives across the bridge in a straight line. For multi-lane bridges, the test vehicle drives once on each lane; The static response of the bridge is directly related to the stiffness of the bridge. Deflection and strain are used to update the accuracy of the bridge assessment model. The deflection measurement point is located at the mid-span; the strain measurement point is located at the mid-span and near the support position. Step 2. Construction of main beam stiffness function The actual condition of the bridge is evaluated by updating the bridge evaluation model. When the bridge evaluation model is updated, the stiffness change of each bridge unit is expressed as a stiffness coefficient, that is: Among them, B e is the updated stiffness of the bridge element, is the initial stiffness of the bridge element, α e is the stiffness coefficient of each unit; Therefore, the direct update of stiffness is converted into the update of stiffness coefficient; considering the non-uniformity and continuity of main beam stiffness, the stiffness function is used to establish the constraints and connections between the stiffness of bridge units; the stiffness function is composed of multiple polynomial basis functions, and its form is as follows: Right now: Where N(x) is the stiffness basis function, is the position of the bridge unit to be updated, p is the magnification factor, n is the number of basis functions, and n e is the number of bridge units to be updated, n e >>n; The basis function of the stiffness function is constructed using Legendre polynomials. The first three order polynomials are selected to construct the stiffness function. The first two basis functions reflect the overall change of bridge stiffness, and the third basis function reflects the uneven change of bridge stiffness. The first three order stiffness basis functions are as follows: N3(x)=-x 2 +1 (6) Where x is the position of the bridge element; At this point, the stiffness changes of each bridge unit on the main beam are converted into stiffness coefficients, and the stiffness coefficients are converted into linear combinations of basis functions. When the bridge assessment model is updated, the correction parameter is changed from stiffness B to the amplification coefficient p of each basis function, so as to achieve a more reasonable update of the bridge assessment model. Step 3. Bridge Assessment Model Update The objective function of the bridge assessment model update is established by the deflection and strain data obtained in step 1, reflecting the difference between the performance of the bridge assessment model and the actual bridge performance; the objective function f1 of the deflection is as follows: Among them, Δ e is the measured deflection, Δ a is the deflection at the corresponding position on the bridge assessment model, j is the number of deflectometers, and k is the number of sample points in the deflection time history; Strain contains more local information, so the strain shape is used to construct the objective function and eliminate the local information; the objective function f2 of strain is as follows: Where m is the number of strain gauges, S e is the measured strain vector, S a is the corresponding strain vector on the bridge assessment model; the final objective function is a combination of the deflection objective function f1 and the strain objective function f2, namely: f=f1+f2 (9) Where f is the objective function of the combination; Finally, the optimization algorithm is used to update the basis function amplification coefficient in step 2 to minimize the objective function, thus completing the process of updating the bridge assessment model and obtaining a finite element model whose stiffness is more closely matched with the actual one for load-bearing capacity assessment.

Images