Keywords

1 Introduction

The traditional waveform steel web combined box girder whose concrete bottom plate is easy to be tensile cracked and other problems under the action of positive bending moment, which seriously affects the durability and service life of the bridge [1, 2]. Conventional corrugated steel web combined box girder in the positive moment under the action of the concrete bottom plate is prone to tensile cracking disease [3]. Domestic experts and scholars have improved the traditional corrugated web combination box girder by replacing the concrete bottom plate of the traditional corrugated web combination box girder with a steel plate. The advantages of the respective material properties of steel and concrete in steel–concrete combined girder bridges are fully utilized [4, 5]. As a result, a new type of steel–concrete combined structure is formed—steel bottom plate waveform web—concrete combined box girder.

The steel base plate corrugated web-concrete combined box girder has high load carrying capacity and seismic performance. In order to ensure its safe and long-lasting operation, durability analysis is needed [6, 7]. Zhang [8] and others proposed an analytical method that can accurately analyze the vertical bending mechanical properties of corrugated web steel box girders; Gan [9] established the elastic control differential equations of this type of box girder to study its damage mechanism; Chen [10] analyzed the changes in stress and stiffness of the box girder of the combined structure, which is positively significant for the promotion and development of this type of box girder structure in the future. However, none of the existing studies have deeply analyzed the durability performance of this type of combined box girder. As the bridge is exposed to the atmospheric environment for a long time, then the bridge tends to suffer from uniform corrosion, and its de-icing salt corrosion problem is the most serious. As a new type of combined structure newly proposed in recent years, corrosion on the corrugated web steel bottom plate combined box girder in the durability performance of the impact of the study has not. In view of this, it is of great significance to carry out the research on the effect of uniform corrosion on the durability of new steel-hybrid composite structure girder bridges in this paper. In view of this, this paper carries out static loading test on steel bottom plate corrugated web-concrete composite box girder, and analyzes the durability based on the time-varying reliability, which is a certain guidance for the design of this kind of structure.

2 Durability Index of Combined Box Girder

By establishing the durability limit state objective, the influence of corrosion on the durability of steel base plate waveform web-concrete combined box girder is analysed, so as to put forward the measures to improve the durability of combined box girder and ensure the normal use function of combined box girder. In this paper, the functional equation constructed by deflection and stress of the combined box girder is taken as the structural functional equation of the normal use limit state. Under the existing external and internal factors, the reliability equations of different times are established by combining the time-varying reliability with the changes of structural deflection and stress after corrosion, and referring to the Steel Structure Design Standard (GB 50017-2017) [11].

2.1 Structural Deflection Time-Varying Reliability Assessment Model

The structural functional equations for the normal service limit state can be constructed from the deflections:

$$ Z(t) = \left[ f \right]_{\max } - f $$
(1)

formula: \(\left[ f \right]_{\max }\) is the structural deflection limit value specified in the code.

Assumptions \(\left[ f \right]_{\max }\) and \(f\) all obey normal distribution, and the time-varying reliability index of the member is obtained from the primary second-order method of moments:

$$ \beta = \frac{{\overline{{[f]_{\max } }} - \overline{f} }}{{\sqrt {\delta_{{\left[ f \right]_{\max } }}^{2} + \delta_{f}^{2} } }} $$
(2)

Formula: \(\overline{{[f]_{\max } }}\) is \([f]_{\max }\) average value; \(\overline{f}\) is \(f\) average value; \(\delta_{{[f]_{\max } }}\) is \([f]_{\max }\) standard deviation; \(\delta_{f}\) is \(f\) standard deviation.

2.2 Structural Stress Time-Varying Reliability Assessment Modeling

Structural functional equations for normal service limit states can be constructed from the stresses:

$$ Z(t) = \left[ \sigma \right] - \sigma $$
(3)

Formula: \(\left[ \sigma \right]\) is the structural stress limit value specified in the code, \(\sigma\) is the value of stress obtained from the test.

Hypothesis \([\sigma ]\) and \(\sigma\) all of them obey normal distribution, and the time-varying reliability index of the member is obtained by the primary second-order method of moments:

$$ \beta = \frac{{\overline{\left[ \sigma \right]} - \overline{\sigma } }}{{\sqrt {\delta_{\left[ \sigma \right]}^{2} + \delta_{\sigma }^{2} } }} $$
(4)

Formula: \(\overline{[\sigma ]}\) is \([\sigma ]\) average value; \(\overline{\sigma }\) is \(\sigma\) average value; \(\delta_{\left[ \sigma \right]}\) is \([\sigma ]\) standard deviation; \(\delta_{\sigma }\) is \(\sigma\) standard deviation.

3 Uniform Corrosion on Steel Bottom Plate Wave Web Combined Box Girder Model Test Research

3.1 Test Overview

With a span of 30 m steel base plate waveform web-concrete combination box girder as a structural prototype, according to the similarity theory to do 1:9 scaled model.

The span of the box girder is L = 3.4 m, the height of the girder is 0.4 m, the width of the top plate is 1 m, the thickness is 0.05 m, the width of the bottom plate is 0.58 m, and there is a cross partition at the pivot point, L/4 and in the middle of the span, and the material of the girder is C50 concrete; the web plate is made of corrugated steel plate with a thickness of 3 mm, and the bottom plate is made of flat steel plate with a thickness of 5 mm, and the material of the girder is Q345 steel plate; and the web and the top plate adopt the buried type of shear connectors. The test beams are shown in Figs. 1 and 2.

Fig. 1
A schematic of a test beam. The total length of the test beam is 3400. It consists of actuators and distributed beams.

Elevation of the test beam (mm)

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Fig. 2
A photograph of a test beam loading device platform.

Test beam loading device

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The centralized symmetric loading was carried out on the test beams before and after corrosion respectively, and the test beams were preloaded before the test with two load levels of 4 and 8 kN. In this paper, the maximum load applied during the symmetric loading stage was 80 kN, and the test loading was divided into 8 levels of loading, with each level of loading in increments of 10 kN. After the loading readings were stabilized for 2 min, the corresponding actual load, deflection and stress–strain data were recorded. The loading process utilizes the structural laboratory to load the model test beams with reaction frames and jacks, and the loading process is controlled by pressure sensors, the corresponding strain data are recorded regularly by the static data acquisition system, and the vertical displacements are recorded by the percentile meter.

The model test beams were immersed in a chloride salt solution with a concentration of 6% for 517 days, and the corrosion conditions are shown in Figs. 3 and 4.

Fig. 3
A photograph of the uniform corrosion condition of the web.

Uniform corrosion of the web

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Fig. 4
A photograph of the uniform corrosion condition of the baseplate.

Uniform corrosion of the base plate

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3.2 Analysis of Static Test Results

Load-mid-span vertical displacement analysis

The values of load-vertical displacement in the span cross-section of the model test beam before and after corrosion are shown in Table 1, and the change rule of load-vertical displacement in the span cross-section of the model test beam before and after corrosion is shown in Fig. 5.

Table 1 Vertical displacement values in span before and after corrosion
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Fig. 5
A fitted-line graph depicts the mid-span deflection versus load before and after corrosion. Both curves have approximately similar trends. The after-corrosion curve has a slightly higher range that begins from (10, 0.5) and gradually rises to (80, 3.3).

Load-mid-span vertical deflection curve

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The mid-span deflection of the model test beam increases with increasing load during loading. The mid-span deflections before and after corrosion do not differ much when the load is small, and the difference between the mid-span deflections before and after corrosion is larger as the load keeps increasing. When the load is 10 kN, the mid-span displacement of the model beam after corrosion increases by 13.89% compared with that before corrosion. When the load increases to 80kN, the mid-span displacement of the model beam after corrosion increases by 20.52% compared with that before corrosion. It can be seen that uniform corrosion has a significant effect on the durability of steel base plate corrugated web-concrete combination box girders.

Positive stress analysis of steel base plate

The stress values of strain gauges numbered D6 in the steel base plate before and after corrosion of the model test beam for each load level are shown in Fig. 6.

Fig. 6
A fitted-line graph depicts the steel base plate stress versus load before and after corrosion. Both curves have approximately similar trends. The after-corrosion curve has a slightly higher range that begins at (10, 1) and gradually rises to (80, 33).

Load-stress curve

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The stress values before and after corrosion do not differ much when the load is small, and there is a significant difference in the stress value of the steel base plate with the increasing load; when comparing the 80kN load, it is found that the stress of the steel base plate after corrosion differs by 5.93% compared with the stress before corrosion. It can be seen that uniform corrosion has little effect on the stresses in the box girders of the combined structure.

4 Based on the Time-Varying Reliability of the Bridge Durability Analysis

According to the Unified Standard for Reliability Design of Highway Engineering Structures (JTG 2120–2020) [12], the load carrying capacity limit state target reliability index of highway bridges is 5.2. The time-varying reliability index at different t moments is calculated by Matlab software using the primary second-order method of moments, and is shown in Fig. 7.

Fig. 7
A fitted-line graph depicts the time-varying reliability indicators versus time. It includes three plots of deflection, stress, and specification. Deflection and stress have approximately similar ranges following a concave-down, decreasing pattern. The specification line is almost constant at 5.

Time-varying reliability index under deflection and stress

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As can be seen from Fig. 7, The time-varying reliability indexes calculated based on stress and deflection do not differ much. The time-varying reliability index based on deflection of the uncorroded test beam is 10.9, and the time-varying reliability based on stress is 10.4, with a difference of 4.8%; in the uniform corrosion state, the reliability index of the composite box girder shows a decreasing trend, and when the composite box girder serves in this environment for 89 years, the reliability index is less than 5.2 stipulated in the specification, and at this time, the structure will be invalidated.

5 Conclusion

  1. (1)

    With reference to the specification and existing literature, the functional equations constructed by deflection and stress of the combined box girder are taken as the structural functional equations of the limit state of normal use at different t moments.

  2. (2)

    The model test beam before and after corrosion was subjected to static loading test, and the test loading was divided into 8 levels of loading, with each level of loading in increments of 10kN, and the maximum load of loading was 80kN.

  3. (3)

    Under static loading, the deflection and stress were all roughly linear, and the mid-span deflection and stress before and after corrosion did not differ much when the load was small, and with the increase of load, the deflection and stress before and after corrosion had a significant difference.

  4. (4)

    In the uniform corrosion state, the reliability index of the combined box girder shows a decreasing trend, when the combined box girder serves in this environment for 89 years, its reliability index is less than the specification of 5.2, at this time the structure will fail.