Calculation and Analysis of Load Test Safety Control for Through Tied-Arch Bridge with Single Bearing Surface

Through tied-arch bridges with single bearing surface (SBS-TTABs) are unique and complex in terms of structural design and construction. For large-span arch bridges, the most effective way to identify the overall stress behaviors is to establish a reliable and reasonable finite-element model for theoretical calculation, and to verify the calculated results through field test [1-4]. The relevant studies have laid a solid basis for the research into the overall static behavior and dynamic response of SBS-TTABs.

For example, Fang et al. [5] conducted static and dynamic load tests on the completion state of Chaotianmen Yangtze River Bridge in Chongqing. Hui et al. [6] carried out a static load test on Caiyuanba Yangtze River Bridge, a highway-light rail bridge in Chongqing. Bu [7] examined the mechanical performance of long-span concrete filled steel tube (CFST) tied arch bridges. Yang and Shen [8] tested and analyzed the static and dynamic load performance of super long-span bridges with continuous steel truss and flexible arch.

Armendariz and Bowman [9] evaluated the load capacity of an arch bridge in Indiana, US through finite-element analysis and five static truck tests. Mohammadzadeh et al. [10] explored the impacts of ballast mats on the structural performance of masonry arch bridges through dynamic load tests. Chiozzi et al. [11] developed a MATLAB-based computational tool, named ArchNURBS, to evaluate the safety of arched masonry structures. Gara et al. [12] carried out impact load tests on a steel arch bridge in the construction phase. Focusing on various types of bridges, Lorenzoni, et al. [13] investigated how the extraction of modal parameters is affected by structural topology, extraction duration, load, and environmental effect. Using the LAN XI dynamic test system proposed by Kilikevicius et al. [14] analyzed the structural dynamic response of an old bridge, and acquired the main dynamic parameters of the bridge. Aras [15] performed modal tests on an overpass during the construction, and thus determined the transition of structural system.

This paper probes deep into a long-span SBS-TTAB in southeastern China. Based on the stress features and visual quality of the bridge, the safety performance of the bridge was investigated, including the deflection of control sections, the stress distribution law of concrete main beam, and the cable force of suspension rods under live load. Static and dynamic load tests were performed on the main bridge, and the test results were compared with the theoretical values. The mechanical properties of the bridge were reasonably computed, and evaluated in details. The results provide a good reference for load tests on completion state of similar bridges.

3.1 Control calculation of long-span rigid tied-arch bridge

For long-span tied arch bridges, the bridge design hinges on the determination of reasonable completion state. After years of service, the rigidity distribution between arch rib and the rigid main beam (tie bar) changes in rigid tied-arch bridges. Hence, the actual completion state might not be the same as the ideal completion state. Therefore, the actual line shape and internal force state of the test beam section should be identified first through load tests on completion state. The specific steps are as follows:

Step 1. Clarify the form and size of the main beam and arch rib, and determine the dead load.

Step 2. Collect relevant materials on design, construction and monitoring, construct an accurate finite-element model, optimize the bridge structure in the light of construction, and obtain the ideal line shape and internal force state of the completion state through repeated adjustment.

Step 3. Measure the cable force of suspension rods, back-calculate the cable length of the rods under no stress, fine-tune the line shape to approximate the actual completion state, and take the internal force state under dead load as the initial state of live load calculation.

3.2 Finite-element simulation

The finite-element simulation of Qin Bridge was carried out on midas. Specifically, the arch rib, i.e. the single concrete-filled steel tube, was simulated as beam elements; the suspension rods were simulated as truss elements; the main beam was simulated by the grillage method; the auxiliary structures, e.g. bridge deck pavements and sidewalks, were simulated under external load, including the initial cable force of the suspension rods. On this basis, the main bridge was meshed into 1,210 grids and 766 nodes. The calculation parameters of structural members and loads were obtained from the design documents. The finite-element model of the main bridge is presented as Figure 3 below.

According to the principle of matrix calculation, the undamped free vibration of the bridge structure can be described by the following differential equation:

$\left[ M \right]\left\{ {\ddot{\delta }} \right\}+\left[ K \right]\left\{ \delta  \right\}=\left\{ 0 \right\}$     (1)

Thus, the free vibration of the bridge can be expressed as the following characteristic equation:

$\left([K]-\omega^{2}[M]\right)\{A\}=\{0\}$     (2)

Through calculation, the undamped vertical fundamental frequency was obtained as 1.63Hz.

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Figure 3. Finite-element model

3.3 Load of control calculation

The design vehicle load of the bridge is Urban-A level. Thus, the theoretical load of our load tests was controlled under this level.

5.1 Results of deflection test and analysis

For the lack of space, this subsection mainly analyzes the measured deflections under the maximum positive bending moment on midspan section, arch crown section, and 1/4 arch rib section. Figures 8 and 9 compare the measured maximum vertical deflections on midspan section and arch crown section with theoretical values.

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Figure 8. Deflection distribution of midspan section

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Figure 9. Deflection distribution of arch crown section

Under bias load, the effect of bias load was prominent in the transverse direction of the midspan, as the maximum deflection was measured as 17.77mm. The maximum deflection on arch crown section was 11.01mm. The calibration coefficients of measuring points for midspan deflection were 0.60-0.88, while that of measuring points for arch crown deflection was 0.63.

Under balanced load, the maximum deflection measured in the transverse direction of the midspan was located at the centerline of the single-land road, and was synchronized in the upstream and the downstream. The maximum deflections in the upstream and the downstream were 7.36mm, and 7.64mm, respectively. The maximum deflection was 7.85mm at thec arch crown. The calibration coefficients of measuring points for midspan deflection were 0.74-0.89, while those of measuring points for arch crown deflection were 0.78.

Figure 10 compares the measured deflection of maximum positive bending moment on 1/4 arch rib section with theoretical value. Under bias load, the maximum deflection on 1/4 arch rib section was 12.21mm; under balanced load, the maximum deflection on 1/4 arch rib section was 8.02mm. The calibration coefficients under the two loads were 0.70 and 0.77, respectively.

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Figure 10. Deflection distribution of 1/4 arch rib section

It can be seen that the midspan section of the main span has obvious bias load effect. The measured and theoretical bias load coefficients were 1.64 and 1.85, respectively. In general, the main bridge has good bending resistance. The measured maximum deflection of the deck was below the designed control value L/600 (200.00mm), and the calibration coefficients were all smaller than 1. The results show that the finite-element model can reasonably reflect the overall static behavior of the bridge.

5.2 Results of strain test and analysis

This subsection focuses on the strain test results from sections A, B, E, and F (Tables 3 and 4). Under the bias load, the calibration coefficients of strain measuring points on section A were 0.53-0.86, while those on section B were 0.74. Under balanced load, the calibration coefficients of strain measuring points on section A were 0.48-0.88, while those on section B were 0.67. Under balanced load, the calibration coefficients of strain measuring points on section D were 0.43-0.71, while those on Section B were 0.64.

Under all working conditions, the strain calibration coefficients were smaller than 1, indicating that the strength of the main beam has a certain surplus. After unloading, the relative residual strains at measuring points were below 20%, as required in the Specification for Inspection and Evaluation of Load-bearing Capacity of Highway Bridges (JTG/T J21-2011) [16]. This means the elastic recovery ability of the main beam and arch rib sections meets the requirements.

Table 3. Strain assessment results under working conditions I and II

Note: 1. “-” means compressive strain, and “+” means tensile strain; 2. The bracketed figures are the test results under working condition II.

Table 4. Stress assessment results under working condition V

5.3 Results of cable force tests and analysis

Table 5 lists the results of cable force tests of suspension rod 10# under the working condition of maximum cable force increment.

As shown in Table 5, the measured cable forces agreed well with the theoretical values, with the negative maximum deviation being -9.24%. This means the live load propagates normally via the suspension rod to the arch rib. The accuracy of the finite-element model is further confirmed.

Table 5. The results of cable force tests under maximum cable force increment

Under the test loads, the deflection measured at each point of the main bridge was smaller than the theoretical value, and the calibration coefficients were basically between 0.60 and 0.88. The results show that the main bridge still has some surplus in rigidity. Under the test loads, the strain measured at each point of the main bridge was smaller than the theoretical value, and the calibration coefficients were basically between 0.48 and 0.88. This means the main bridge still has some surplus in strength. Under the test loads, the measured cable force at each point was smaller than the theoretical value, indicating that the suspension rods of the main bridge have some surplus in tensile strength. The above results of static and dynamic tests prove that the long-span SBS-TTAB has sufficient capacity to withstand Urban-A level vehicle load, under normal use conditions.

Under the test loads, the maximum relative residual deflection and the maximum relative residual strain at each measuring point were 12.98% and 11.76%, respectively. Both were below the 20% threshold specified in JTG/T J21-2011. It shows that the bridge span has excellent elastic recovery ability. The bias load coefficients on the midspan section were relatively large. The torsional rigidity of such a wide box beam, with two cable planes in the middle span, has a nonnegligible impact on bias load coefficient.

The vibration features of the span structure were stable, and the results of driving test agreed well with those of the bumping test. The vibrations induced by bumping attenuated quickly, reflecting the good attenuation performance of the main beam. The measured damping ratio of the bridge fell in the normal range. The impact coefficient measured on the midspan section was smaller than the theoretical value, indicating that the vehicle impact on the bridge structure is smaller than the theoretical design value. To sum up, the results of static and dynamic tests prove the stability and reliability of the target bridge.