Load Testing and Analysis of a Large Span Through Simply-Supported Steel Box Arch Bridge

Abstract

To evaluate the true load-bearing capacity and engineering reliability of a large span through a simply supported steel box arch bridge, a load test was conducted on the bridge. The example used in this test is the Jingchu Avenue Bridge located in Jingmen City, Hubei Province. Specifically, the static load test delineated six operational conditions, measuring parameters encompassing strain, hanger cable force, deflection, and potential cracks. The dynamic load test gauged the bridge’s dynamic response and various indicators, including pulse tests, vehicle tests, jump tests, and barrier-free vehicle tests. The findings indicated that the maximum measured strain values during the static load test surpassed the calculated values; nonetheless, the verification factors and relative residual strains adhered to the code requirements, and no cracks were detected. The dynamic load test unveiled that the measured frequency values exceeded the theoretical ones, the damping ratios were within the normal range, and the measured impact coefficients were lower than the values stipulated in the code, all of which were in conformance with the code requirements. The data obtained from this experiment can be utilized to refine the long-term maintenance plan for the bridge, especially as it holds considerable value for structural health monitoring and aging assessment.

1. Introduction

Transportation infrastructure serves as an essential prerequisite for urban development, with bridges, as a vital component of the transportation system, experiencing significant advancements alongside the rapid growth of the transportation industry. Simply supported steel box arch bridges constitute a substantial portion of current bridge construction projects. These bridges are characterized by their excellent stability, high bending and torsional stiffness, lighter self-weight compared to concrete arch bridges, and superior load-bearing capacity [1]. They also excel in aesthetic appeal, construction maintenance, and economic benefits [2].

In recent years, the number of simply supported steel box arch bridges being constructed has consistently increased, along with an expansion in their maximum spans and diversification in structural designs. This has provided extensive engineering experience for the construction of such bridges [3,4,5]. However, it has also resulted in increasingly complex stress conditions within the bridges. Therefore, accurately and effectively assessing the condition of existing bridges to determine their load-bearing capacity and reliability levels has become particularly crucial [6]. Conducting load testing research to evaluate the safe load-bearing capacity and operational quality of bridge structures is essential for ensuring their reliability and stability. It is also the most effective and direct method for understanding the actual working conditions of bridge structures under test loads [7]. The initial purpose of load testing was to demonstrate the safe usage of bridges [8]. The task of load testing typically is not to determine the load-bearing capacity of bridge structures but to prove the sufficient safety of their impact resistance [9]. Bridge load testing involves applying test loads equivalent to the design loads on the bridge structure, thereby inducing displacements and vibrations to measure stress, deflection, acceleration, and other parameters at specified locations. This directly assesses the structural characteristics of the bridge and provides fundamental evaluation indicators for its maintenance. Dynamic load testing is one of the key methods for calibrating reliable numerical models. It provides valuable information about structural properties such as frequency, mode shapes, and damping, which are crucial for verifying and optimizing the accuracy of the numerical model. The dynamic response data obtained through vibration testing can effectively assess and model the structural performance without the need for additional loading or interrupting the structure’s operation [10]. Static load testing is more sensitive to detecting local defects and deformations. In particular, measurements of strain and displacement can effectively reveal the elastic behavior of a bridge under static loads. This makes static testing particularly useful for identifying local damage or deformations that dynamic tests might not detect [11].

Currently, scholars and engineers have conducted extensive experimental and theoretical research on bridge load testing and achieved certain research results. Frýba et al. [12] determined and described the relationship between the natural frequencies of bridges and their damage through modal analysis and identification of bridge characteristics. Chen et al. [13] provided a detailed description of the roles and classifications of load testing for highway bridges and summarized the basic principles of bridge load testing. Deng et al. [14] established a finite element model updating method for continuous box girder bridges based on static load testing to evaluate bridge structural performance. Wang et al. [15] conducted static and dynamic load tests on a steel-concrete composite box girder bridge and analyzed and evaluated its performance and load-bearing capacity. Zhen et al. [16] analyzed the loading methods and measurement point layout through inspections of a three-span continuous beam bridge and evaluated the results of the load testing. Huseynov et al. [17] studied the transverse load distribution factors of bridge deck structures under different boundary conditions and conducted load testing analysis on a composite I-girder bridge. Jia et al. [18], using a simply supported composite beam bridge as the engineering background, investigated the actual load-bearing capacity of the reinforced bridge based on field load testing methods. Li et al. [19] conducted load testing analysis on the Xitang Bridge, indicating that the concrete-filled steel tubular arch bridge meets the requirements for normal use. Liao et al. [20], using specialized bridge finite element software, calculated the measurement values of the bridge structure under design standard loads and compared them with the load testing results of a rigid frame arch bridge, concluding that the load-bearing capacity did not meet normal use requirements. Fang et al. [21] conducted load testing on the Chongqing Chaotianmen Yangtze River Bridge, proving that the through-type continuous steel truss tied arch bridge possesses sufficient strength and stiffness. Currently, load testing for most bridge types, particularly beam bridges, has achieved a well-established status. However, the frequency of load tests on arch bridges remains scarce, and instances involving lower-deck simply-supported steel box tied-arch bridges are exceptionally rare. Given their distinctive load-bearing properties, it is imperative to thoroughly account for these characteristics and implement appropriate measures to guarantee the precision and safety of the load-testing process.

Conducting bridge load tests and safety assessments is pivotal in ensuring the safe operation of bridges; with the rapid progression of technology, bridge load testing techniques have continually advanced, integrating numerous new instruments and methodologies into the testing and evaluation processes. This has markedly improved the convenience, speed, and precision of the tests. For instance, Stathis C. S. et al. [22] utilized a Robotic Total Station to analyze the displacement characteristics of the Gorgopotamos Bridge in Greece under train loads, observing vertical deflections of up to 6 mm and identifying dominant frequencies within the range of 3.18–3.63 Hz. In another study, Moschas F. et al. [23] employed a redundant system comprising collocated geodetic sensors and an accelerometer to measure displacements of a 40-m-long footbridge under vertical synchronized jumps; they detected vertical, lateral, and longitudinal deflections and confirmed the consistency of results across various sensors and methodologies. Zhou et al. [24] proposed a model to eliminate camera jitter errors in visual deflection measurement systems, which are induced by irregular vibrations such as airflow and ground movement. Experimental verification demonstrated that this model significantly enhances measurement accuracy and possesses universal applicability. Lisztwan et al. [25] combined analytical modeling, numerical simulation, and full-scale load testing techniques to assess the behavior of a historical bowstring concrete bridge, effectively evaluating its current condition and load-bearing capacity. However, despite their excellent performance on medium- and small-span bridges, these load-testing techniques still encounter challenges when applied to large-span bridges. Issues such as increased errors, higher operational complexity, and substantial costs are prominent. Furthermore, the analysis and evaluation of bridge load test data are of utmost importance. In this context, Matos et al. [26] compared condition rating systems for bridges in Italy, Slovakia, and Portugal, emphasizing the methodological differences and the urgent need for standardization in bridge health assessments across European countries. Wang et al. [27] introduced a method that leverages influence line testing and load transition to assess bridge load-bearing capacity with accuracy and efficiency, validation through real-world bridge tests demonstrated that this method yields smaller errors compared to traditional load tests while also significantly reducing labor, materials, and time, this underscores its efficiency and practicality in bridge assessments. Wan et al. [28] examined the evolution of bridge structural health monitoring technologies, with a focus on the application of knowledge-driven and data-driven artificial intelligence methods; they also suggested future trends toward hybrid knowledge-data-driven approaches. Qing et al. [29] conducted field testing on the Ganjiang Bridge and updated its finite element model based on displacement assurance criteria (DAC) and frequency; this comprehensive assessment of the bridge’s mechanical performance established an accurate baseline model for future structural health monitoring endeavors. In the future, as artificial intelligence technology continues to advance, bridge load testing will see the integration of more cutting-edge technologies and algorithms. For example, applying domain relationship extraction models and technologies [30] to test data processing can not only more efficiently extract key information but also provide timely warnings for abnormal data, further promoting the intelligent and efficient development of bridge load testing.

Consequently, this paper presents an analysis of a load test conducted on a large span through a simply supported steel box tied-arch bridge. This experimental bridge is situated in Jingmen City, Hubei Province, and constitutes the bridge of Jingchu Avenue. The load testing of this bridge is distinguished by its multiple control sections, diverse loading conditions, and an extensive array of measurement points. During the static load test, various mechanical parameters were measured, encompassing strain, stress, hanger cable force, deflection, and horizontal displacement at the arch supports. The dynamic load test, on the other hand, assessed the bridge’s natural frequencies and dynamic responses under a range of excitations, including pulse tests, vehicle-induced vibrations, and braking-induced vibrations. The comprehensive load test of this bridge has yielded invaluable data that contributes to the advancement of bridge design theory and the refinement of construction techniques. Furthermore, it serves as a continuous repository of technical data, providing a scientific foundation and offering a valuable reference for similar bridge structures.

2. Project Overview

The bridge features a span configuration of 90 m + 24.24 m, with the width varying between 43 m and 47 m. The main bridge incorporates a 90 m span under-deck simply supported steel box arch, whereas the southern approach bridge utilizes 24.24 m prestressed concrete cast-in-place box girders. The arch axis of the primary arch traces a parabolic curve, ascending 17.44 m with a rise-to-span ratio of 1/5. Positioned at an 11° angle outside the main arch, the secondary arch exhibits a parabolic curve in its vertical plane projection, reaching a height of 21.8 m and maintaining a rise-to-span ratio of 1/4. Seventeen transverse tie rods, spaced 3m apart, are arranged between the main and secondary arches, with no transverse connections between the arch ribs. The bridge boasts 11 pairs of hangers, spaced 6 m apart longitudinally and anchored 35.8 m apart laterally. These hangers are constructed from 7 mm diameter galvanized parallel steel wires, and the main cables are tensioned at one end. An overview of the arch bridge’s layout is presented in Figure 1.

3. Experimental Content

The experimental content comprises static load testing, dynamic load testing, and pulse testing of the main bridge.

3.1. Static Load Test

Utilizing the principle of equivalent internal forces, the test load vehicle applies loads to the main bridge in accordance with the structure’s influence line. Key structural parameters, including strain, deflection, hanger cable forces, and crack propagation, are measured during this process.

3.2. Dynamic Load Test

The inherent vibration characteristics of the structure, such as mode shapes, critical damping ratios, and natural frequencies, are ascertained through pulse tests, vehicle running tests, and jumping vehicle tests. Furthermore, the dynamic response of the bridge span structure to operational vehicle loads is measured using a smooth driving test conducted when the bridge deck surface is in pristine condition.

4. Static Load Test

4.1. Theoretical Calculation of Static Load Test

Prior to conducting the static load test, a specialized finite element program for bridges, Midas Civil, was utilized for modeling and calculations. The internal force influence lines for each control section were determined, followed by static load computations. Subsequently, the results of these static calculations were compared with the actual load test results. The finite element calculation model is shown in Figure 2. The finite element model uses beam elements to simulate the main beam and main arch, with the material being Q345qD steel, an elastic modulus of 206 GPa, a Poisson’s ratio of 0.3, and a unit weight of 98.21 kN/m³. The suspenders are modeled using cable elements, with the material being steel wire rope, an elastic modulus of 195 GPa, a Poisson’s ratio of 0.3, and a unit weight of 78.5 kN/m³. The suspenders are connected to both the main arch and the main beam through elastic connections. The deck is modeled using shell elements. The entire bridge consists of 950 elements and 835 nodes. General supports are used to simulate the bearings, offering high flexibility, allowing adjustment of the bearing’s degrees of freedom based on actual conditions, and having wide applicability. However, in some complex cases, general support may not fully capture nonlinear effects, leading to deviations between the calculated results and actual conditions. Additionally, the model becomes more complex, potentially increasing computation time, and requires more accurate input data and reasonable constraint conditions. Inadequate input could lead to model deviations, affecting the reliability of the analysis results. The vehicle load corresponds to Class-A urban vehicles, with a pedestrian load of 4 kN/m². The bending moment envelope diagram is presented in Figure 3.

4.2. Static Load Test Conditions

The static load test was conducted in accordance with the relevant provisions of the Technical Code for the Inspection and Evaluation of Urban Bridges [31]. The number of loading vehicles and the arrangement of wheel positions for each test condition were determined based on the most unfavorable effect value generated by the live load in a specific condition, as calculated according to the following formula:

$$0.85\le \eta =S_{stat}/S_{(1+\mu )}\le 1.05$$

(1)

where: $\eta$—Static load test efficiency;

$S_{stat}$—Effect value under test load for a specific condition;

$S$—Most unfavorable calculated effect value for the test condition, based on the design standard live load without considering impact effects;

$(1+\mu )$—Dynamic coefficient used in the design calculation.

A total of 16 loading vehicles were used in the test, with each loading vehicle weighing 350 kN. The vehicle loading method is relatively simple and convenient to operate, and it is closer to actual working conditions, making it highly applicable. However, the load size may vary due to factors such as vehicle type, weight, and tire size, which could result in uneven load distribution and make it difficult to achieve precise load control. Additionally, differences between the field experimental conditions and theoretical assumptions may cause discrepancies between the test loading scheme and the loading schemes specified in the standards. The static load test is shown in Figure 4.

The test parameters of the static load test are analyzed.

(1) The Structural Calibration Factor is defined as the ratio of Measured Elastic Strain to Calculated Strain or Measured Elastic Displacement to Calculated Displacement. This metric serves as a comparison between the actual and theoretical states of the structure. Specifically, a Structural Calibration Factor of less than 1 signifies that the bridge’s actual condition surpasses its theoretical condition. Conversely, a factor greater than 1 implies that the bridge’s actual condition is inferior to its theoretical state, indicating a potential insufficiency in structural load-bearing capacity, as per the Specifications for Load Capacity Testing and Evaluation of Highway Bridges [32].

(2) Relative Residual Strain or Relative Residual Displacement:

$${S^{\prime }}_p={\displaystyle \frac{S_p}{S_t}}\times 100\%$$

(2)

where: ${S^{\prime }}_{\mathrm{p}}$ represents the relative residual strain, $S_{\mathrm{p}}$ represents the residual strain, and $S_{\mathrm{t}}$ represents the total strain.

A smaller value of ${S^{\prime }}_{\mathrm{p}}$ indicates that the structure is closer to an elastic working state. When the relative residual strain or relative residual displacement exceeds 20%, it indicates that the actual condition of the structure is unsafe compared to the ideal condition. In such cases, the load-bearing capacity should be directly judged as inadequate based on the test results, in accordance with the Specifications for Load Capacity Testing and Evaluation of Highway Bridges [32].

(3) Upward displacement is considered negative, and downward displacement is considered positive.

(4) Tension is considered positive, and compression is considered negative. Stress is measured in MPa, and strain is measured in με. When calculating the measured stress, the elastic modulus of the steel structure is taken as $E=2.06\times {10}^5$ Mpa.

(5) The influence of pier settlement has been deducted from the displacement measurements.

4.3. Strain Measurement Point Locations and Measurement Method

4.3.1. Static Load Test Measurement Point Layout and Load Design

The layout of the test sections is shown in Figure 5. Among them, the test object for the increment of hanger cable force is the D6 hanger at the mid-span. The strain measurement points for the arch ribs, tie rods, and main beam are shown in Figure 6.

This experiment uses the UCAM-60B static strain system to monitor and record the strain data of the bridge in real-time. After strain gauges and sensors are installed in regions of the bridge where the stress is complex, and strain variations are significant, strain calibration is a key step to ensure measurement accuracy. Calibration typically includes zero-point calibration and full-scale calibration. Zero-point calibration is performed without any strain input, with the goal of ensuring that the system’s output is zero or close to zero under zero strain conditions. Full-scale calibration involves using a standard or simulator with known full-scale strain to calibrate the system, ensuring that the system’s output is accurate at full range. In addition, to verify the system’s linearity, measurements may be taken at several different strain points to ensure a linear relationship between the system’s output and input. The image below (Figure 7) shows the field staff performing strain measurements.

4.3.2. Deflection Measurement Point Locations

The deflection measurement points are arranged at one-eighth intervals along the main beam, with the specific layout of these points shown in Figure 8. Total station prisms are positioned at the quarter points of the arch ring to observe the deformation of the arch ring under various loading conditions. These prisms are symmetrically arranged both upstream and downstream.

4.3.3. Loading Conditions and Wheel Position Arrangement

(1) Loading Conditions

Following the core principles established in the Specifications for Load Capacity Testing and Evaluation of Highway Bridges [32], we have determined the loading scenarios for the load test by thoroughly integrating the internal force envelope diagrams and influence lines derived from finite element analysis. This approach ensures a comprehensive and accurate reflection of the bridge’s actual stress state. In selecting load conditions, we adhered to the specifications and considered various typical load scenarios that the bridge might encounter during daily operation, including, but not limited to centered and eccentric loading. Centered loading represents a load symmetrically distributed along the centerline of the bridge deck, reflecting the bridge’s performance under uniform stress. Eccentric loading, conversely, simulates the load deviation from the centerline, which is essential for evaluating the bridge’s stability and safety under asymmetric stress.

In determining wheel positions, we relied on the internal force influence lines obtained from finite element analysis. These lines describe how the internal force at a specified section of the bridge changes in response to the position of a unit moving load, offering clear insight into the impact of load positioning on structural forces. By analyzing these influence lines, we can pinpoint the locations that most significantly affect the internal force at specific sections of the bridge. Based on these principles, the static load test loading conditions are summarized in

Table 1. Loading test conditions.

Condition	Test Item	Design Effect	Loading Effect	Loading Efficiency
1	A-A Section (Arch Rib L/2 Section) Maximum Positive Bending Moment Effect (Medium Load)	806.58	778.61	0.97
	A-A Section (Arch Rib L/2 Section) Maximum Deflection Effect (Medium Load)	−9.58	−9.01	0.94
	D6 Hanger Maximum Cable Force Increment (Medium Load)	351.85	310.12	0.88
	D-D Section (Tie Beam L/2 Section) Maximum Positive Bending Moment Effect (Medium Load)	2241.31	2141.13	0.96
	D-D Section (Tie Beam L/2 Section) Maximum Axial Force Effect (Medium Load)	2269.72	2061.14	0.91
	D-D Section (Tie Beam L/2 Section) Maximum Deflection Effect (Medium Load)	−15.20	−13.65	0.90
2	A-A Section (Arch Rib L/2 Section) Maximum Positive Bending Moment Effect (Eccentric Load)	897.41	827.99	0.92
	A-A Section (Arch Rib L/2 Section) Maximum Deflection Effect (Eccentric Load)	−10.83	−9.91	0.92
	D6 Hanger Maximum Cable Force Increment (Eccentric Load)	395.47	374.37	0.95
	D-D Section (Tie Beam L/2 Section) Maximum Positive Bending Moment Effect (Eccentric Load)	2502.73	2215.12	0.89
	D-D Section (Tie Beam L/2 Section) Maximum Axial Force Effect (Eccentric Load)	2557.25	2317.88	0.91
	D-D Section (Tie Beam L/2 Section) Maximum Deflection Effect (Eccentric Load)	−17.14	−15.07	0.88
3	B-B Section (Arch Rib L/4 Section) Maximum Positive Bending Moment Effect (Medium Load)	1242.50	1200.94	0.97
	B-B Section (Arch Rib L/4 Section) Maximum Deflection Effect (Medium Load)	−11.39	−10.27	0.90
	C-C Section (Tie Beam L/4 Section) Maximum Positive Bending Moment Effect (Medium Load)	3272.06	2953.29	0.90
4	B-B Section (Arch Rib L/4 Section) Maximum Positive Bending Moment Effect (Eccentric Load)	1388.99	1320.09	0.95
	B-B Section (Arch Rib L/4 Section) Maximum Deflection Effect (Eccentric Load)	−12.71	−10.87	0.86
	C-C Section (Tie Beam L/4 Section) Maximum Positive Bending Moment Effect (Eccentric Load)	3654.82	3136.33	0.86
5	C-C Section (Tie Beam L/4 Section) Maximum Axial Force Effect (Medium Load)	2412.40	2123.86	0.88
	C-C Section (Tie Beam L/4 Section) Maximum Deflection Effect (Medium Load)	−15.10	−14.41	0.95
6	C-C Section (Tie Beam L/4 Section) Maximum Axial Force Effect (Eccentric Load)	2723.41	2339.84	0.86
	C-C Section (Tie Beam L/4 Section) Maximum Deflection Effect (Eccentric Load)	−16.82	−16.23	0.96

.

Under the six analyzed working conditions, the static responses highlight the stress and deformation behavior of the structure under varying load distributions. For researchers working with similar steel box arch bridge structures, understanding these static responses is crucial. Under centered loading, the bridge exhibits a relatively symmetrical internal force distribution, representing uniform stress. This condition is important for assessing the overall stability of the bridge. Eccentric loading conditions, however, reveal the bridge’s response to asymmetric loads, particularly the stress concentrations that may occur in localized areas. Therefore, examining these static responses under different conditions provides valuable insights for the design and assessment of similar structures, particularly when analyzing real-world stress scenarios throughout the bridge’s service life.

(2) Wheel Position Arrangement

The bridge is a bidirectional structure with eight lanes. During the application of uniform loads, the test vehicles are evenly distributed across each lane in both the eastbound and westbound directions. For the application of eccentric loads, all vehicles are arranged in the eastbound lanes of the bridge. The arrangement of wheel positions for conditions 1–6 is illustrated in Figure 9.

4.4. Static Load Test Results Data Analysis

4.4.1. Strain Analysis

(1) Arch Rib 1/2 and 1/4 Sections

After analyzing the data across various operating conditions, it was observed that under the load of Condition 1, the maximum compressive strain occurred at the 1/2 and 1/4 cross-section positions of Arch Rib 1, which were lower than the calculated values. The verification factor satisfied the code requirements [33]. Furthermore, the maximum relative residual strain rate was below the code limit of 20%. The measured data are presented in

Table 2. Measured data of arch ribs under working condition 1.

Measurement Point Location		Measurement Point ID	Strain Test Result (με)	Calculated Value (με)	Residual Strain (με)	Residual Strain Rate (%)	Verification Factor
East Side Arch Ring (L/4)	Top Plate	B01	−11	−18	0	0.0	/
		B02	−21	−26	−1	4.7	0.81
	Web Plate	B03	−38	−39	−1	2.6	0.97
		B04	−42	−46	0	0.0	0.91
	Bottom Plate	B05	−38	−59	−1	2.6	0.64
		B06	−53	−66	0	0.0	0.80
West Side Arch Ring (L/4)	Top Plate	B07	−23	−26	0	0.0	0.88
		B08	−6	−18	−1	/	/
	Web Plate	B09	−44	−46	0	0.0	0.96
		B10	−33	−39	0	0.0	0.85
	Bottom Plate	B11	−57	−66	0	0.0	0.86
		B12	−58	−59	0	0.0	0.98
East Side Arch Ring (L/2)	Top Plate	C01	−45	−57	−1	2.2	0.79
		C02	−59	−70	0	0.0	0.84
	Web Plate	C03	−23	−32	0	0.0	0.72
		C04	−44	−45	0	0.0	0.98
	Bottom Plate	C05	−5	−7	−1	/	0.71
		C06	−14	−20	0	0.0	0.70
West Side Arch Ring (L/2)	Top Plate	C07	−55	−70	1	/	0.79
		C08	−43	−57	0	0.0	0.75
	Web Plate	C09	−40	−45	1	/	0.89
		C10	−30	−32	1	/	0.94
	Bottom Plate	C11	−19	−20	1	/	0.95
		C12	−2	−7	0	0.0	/

.

(2) Arch Foot

The measured data under operating conditions 3, 4, 5, and 6 show that, under Condition 3, the strain at the arch foot is the largest, but it is lower than the calculated value. The verification factor meets the requirements of the code [33]. The maximum relative residual strain rate is less than the code limit of 20%. The measured data can be found in

Table 3. Measured data of arch footings under working condition 3.

Measurement Point Location		Measurement Point ID	Strain Test Result (με)	Calculated Value (με)	Residual Strain (με)	Residual Strain Rate (%)	Verification Factor
East Side Arch Ring (Arch Foot)	Top Plate	A01	−52	−59	0	0.0	0.88
		A02	−30	−32	−2	6.6	0.94
	Web Plate	A03	−30	−47	0	0.0	0.64
		A04	−17	−27	0	0.0	0.63
	Bottom Plate	A05	−22	−35	−2	9.0	0.63
		A06	−13	−22	0	0.0	0.59
West Side Arch Ring (Arch Foot)	Top Plate	A07	−30	−32	−1	3.3	0.94
		A08	−51	−59	−2	3.9	0.86
	Web Plate	A09	−19	−27	−1	5.2	0.70
		A10	−33	−47	−1	3.0	0.70
	Bottom Plate	A11	−15	−22	0	0.0	0.68
		A12	−21	−35	0	0.0	0.60

.

(3) Tie Beam

Through the data analysis under various operating conditions, it was found that under Condition 1, the maximum tensile strain occurs at the L/2 cross-section of the tie beam, while under Condition 3, the maximum tensile strain occurs at the L/4 cross-section of the tie beam. The verification factors for all tensile strains are less than 1. After unloading, the maximum relative residual strain rate is less than the code limit of 20%, indicating that the structure is in an elastic working state. The measured data for the tie beam can be found in

Table 4. Measured data of tie beams under working condition 1.

Measurement Point Location		Measurement Point ID	Strain Test Result (με)	Calculated Value (με)	Residual Strain (με)	Residual Strain Rate (%)	Verification Factor
East Side Tie Beam (L/2)	Top Plate	E1	−5	2	0	0.0	/
		E2	−12	−1	0	0.0	/
	Bottom Plate	E3	51	72	−1	−2.0	0.71
		E4	49	70	0	0.0	0.70
West Side Tie Beam (L/2)	Top Plate	E5	−11	−1	1	−9.1	/
		E6	−8	2	0	0.0	/
	Bottom Plate	E7	46	70	−1	−2.2	0.66
		E8	51	72	−1	−2.0	0.71

and

Table 5. Measured data of tie beams under working conditions 3.

Measurement Point Location		Measurement Point ID	Strain Test Result (με)	Calculated Value (με)	Residual Strain (με)	Residual Strain Rate (%)	Verification Factor
East Side Tie Beam (L/4)	Top Plate	D01	−20	−24	0	0.0	0.83
		D02	−21	−29	0	0.0	0.72
	Bottom Plate	D03	67	94	0	0.0	0.71
		D04	66	91	1	1.5	0.73
West Side Tie Beam (L/4)	Top Plate	D05	−21	−29	1	/	0.72
		D06	−16	−24	1	/	0.67
	Bottom Plate	D07	62	91	0	0.0	0.68
		D08	64	94	0	0.0	0.68

.

Some measurement points exhibited compressive stresses that surpassed the calculated values. This can be attributed to the fact that, during the deformation of the main arch, a portion of the tensile force applied to the tie beams is shared by the main beam, resulting in a decrease in tensile stress. Consequently, when combined with compressive stress, this leads to compressive stress values that exceed the calculated ones.

(4) Main Beam

Under the load of Condition 1, the strain values observed at the top plate and U-rib measurement points of the main beam were relatively low. The tensile stresses at the bottom plate measurement points ranged from 15 με to 44 με, with an average strain value of 29 με, which is less than the calculated value of 35 με. The verification factor was 0.83. The measured strain verification factor met the code requirements [33], indicating that the structural strength is in accordance with the design specifications. Following unloading, the residual strain was minimal, with a maximum relative residual strain rate of 8.3%, which is well below the code limit of 20%. This suggests that the structure is operating within its elastic range.

4.4.2. Suspension Rod Tension Test

Under the load of Condition 1, the largest increase in tension was measured at the mid-span of the D6 suspension rod. The verification factors for the tension increase of the D6 suspension rods at the left and right arch ribs were 0.98 and 0.96, respectively, both of which are less than 1. The measured tension increase verification factors satisfied the code requirements [33], indicating that the structural strength meets the design specifications.

4.4.3. Deflection Analysis

Under the load of Condition 1, the maximum measured deflection was observed at the mid-span of the main arch ring, as illustrated in Figure 10. All measured values were smaller than the calculated values, with verification factors ranging from 0.70 to 0.75. The measured results demonstrate that the stiffness of the bridge structure meets the design requirements. After unloading, the measured residual deformation rates were all below 20%, in compliance with the code requirements.

Under the load of Condition 5, the maximum deflection was measured at the L/4 section of the main arch ring, as depicted in Figure 11. The verification factors for this deflection ranged from 0.63 to 0.68. The measured results suggest that the stiffness of the bridge structure is in accordance with the design requirements. Following unloading, the measured residual deformation rates were all less than 20%, satisfying the code requirements.

5. Dynamic Load Test

5.1. Test Content

5.1.1. Dynamic Load Test Loading Conditions

Through a series of tests, including pulsation tests, running vehicle tests, jump vehicle tests, and an obstruction-free driving test, the inherent vibration characteristics of the bridge structure are determined. The obstruction-free driving test specifically measures the dynamic response of the bridge deck structure under the load of operating vehicles when the deck surface is in good condition. Using relevant evaluation guidelines, the overall structural performance of the bridge is assessed to evaluate its actual operational condition and load-bearing capacity. The specific conditions for the dynamic load tests are presented in

Table 6. Dynamic load test conditions.

Condition No.	Test Content		Test Parameters
1	Pulsation Test		Frequency, Vibration Mode, Damping Ratio
2	Obstruction-Free Driving Test	10 km/h	Structural Dynamic Deflection, Impact Coefficient
3		20 km/h
4		30 km/h
5		40 km/h
6		50 km/h
7		60 km/h
8	20 km/h Jump Vehicle Test

.

5.1.2. Analysis of Test Parameters

(1) Frequency is typically determined through modal analysis to calculate the natural frequencies or resonant frequencies of the bridge structure. These frequencies represent the vibration characteristics of the bridge under specific conditions. The natural frequency of the bridge structure solely depends on its mass and stiffness, serving as a crucial indicator for changes in stiffness.

(2) Mode Shape: Mode shapes illustrate the vibration patterns and deformation modes of the bridge at different frequencies. The mode shape diagram obtained from modal analysis can predict how the bridge will vibrate when subjected to various excitation frequencies.

(3) Damping Ratio: The damping ratio represents the ratio between the damping coefficient and critical damping coefficient. It quantifies the normalized amount of damping in a structure and indicates how vibrations decay after excitation. The damping ratio determines how quickly energy dissipates during vibration, i.e., it governs the vibration decay rate.

(4) Amplitude: Amplitude generally refers to the maximum displacement experienced by a vibrating bridge from its resting position. Excessive amplitude may lead to fatigue damage in structural components, potentially causing resonance phenomena.

(5) Impact Coefficient: The impact coefficient describes the ratio between vibration amplitude and static force under an impact load condition. It characterizes the vibrational properties of bridges subjected to impact conditions, with higher values indicating poorer safety, seismic resistance, and stability.

5.2. Dynamic Load Test Measurement Point Layout

The schematic diagram illustrating the measurement points for the dynamic load test is presented in Figure 12. Figure 12a depicts the arrangement of measurement points for the modal test of the main bridge, while Figure 12b shows the layout of the measurement points specifically for the running vehicle test.

When sensors are placed on the bridge and instruments such as strain testing systems, dynamic strain gauges, and signal acquisition and analysis devices are used, the strain, acceleration, displacement, and other signals of the bridge under dynamic loading are collected. Data processing and analysis are performed using a computer to extract dynamic performance parameters, such as the bridge’s natural frequency, damping ratio, and amplitude, in order to assess the bridge’s safety and load-bearing capacity under dynamic loads. Figure 13 shows the installation of vibration sensors on the bridge arch ribs.

5.3. Dynamic Load Test Results and Analysis

5.3.1. Results and Analysis of the Bridge’s Natural Vibration Characteristics Test

The natural vibration characteristics of a bridge are typically assessed using three methods: impact excitation, ambient vibration excitation, and forced vibration excitation. In the impact excitation method, a specialized hammer or similar device is employed to apply an impulsive force to the bridge, inducing vibrations. Although this method can replicate the impact loads encountered in real-world engineering scenarios, the complexity of such loads may introduce significant errors in test results. The forced vibration excitation method is commonly utilized to simulate specific frequency and amplitude vibration environments for evaluating system performance under vibrational conditions. This approach enables precise control over both frequency and amplitude parameters and allows for repeated testing; however, it necessitates high-end equipment and incurs substantial costs. On the other hand, the ambient vibration excitation method utilizes naturally occurring environmental stimuli like wind flow, water currents, or ground motion to stimulate structural responses. This cost-effective and time-efficient technique is also referred to as pulse testing—which has been chosen as the preferred methodology for this experiment.

The pulse test involves the placement of highly sensitive sensors on the bridge to record its vibration over an extended period under environmental excitation, such as wind, water flow, or ground motion. Subsequently, the recorded vibration time history is processed and analyzed in both the time domain and frequency domain to determine the natural vibration characteristics of the bridge. The pulse test assumes that environmental excitation follows a stationary stochastic process. In the low- and mid-frequency range, ambient vibrations exhibit a relatively uniform excitation spectrum. When the frequency of environmental excitation matches or closely aligns with the bridge’s natural frequency, energy absorption occurs, leading to an increase in amplitude. Conversely, when there is a significant difference between environmental excitation frequency and the bridge’s natural frequency, a large phase difference arises, resulting in energy cancellation and, subsequently, smaller amplitudes, by analyzing amplitude and phase relationships of vibration response at different measurement points, mode shapes corresponding to various modal frequencies can be determined for the bridge. Averaging multiple time history curves enables the determination of natural frequencies for each mode exhibited by the bridge. It should be noted that ambient vibrations may introduce additional noise and interference, which can affect test result accuracy; hence, extra data processing, including the exclusion of abnormal data, is required.

Performing time-domain and frequency-domain analyses on the pulsation test signals revealed the measured first-order frequency of lateral vibration for the main bridge to be 1.425 Hz, compared to a finite element calculated frequency of 1.14 Hz. The measured first-order frequency of vertical vibration was 2.95 Hz, whereas the calculated frequency was 1.71 Hz. Additionally, the measured first-order torsional frequency stood at 3.60 Hz, higher than the calculated value of 1.948 Hz. For the approach bridge, the measured natural frequency of the first-order vertical bending mode was 6.375 Hz. These results indicate that the vertical overall stiffness of the bridge meets the design requirements. Refer to

Table 7. Test results of main bridge’s pulsation natural frequency.

Mode Description	Calculated Frequency (Hz)	Measured Frequency (Hz)	Damping Ratio (%)
Main Arch 1st Order Symmetrical Lateral Bending Mode	1.140	1.425	0.41
Main Beam 1st Order Antisymmetrical Vertical Bending Mode	1.710	2.95	0.63
Main Beam 1st Order Torsional Mode	1.948	3.60	0.77
Approach Bridge 1st Order Vertical Bending Mode	/	6.375	1.55

for detailed test results of the main bridge’s pulsation natural frequencies. The mode shape diagrams of the main arch and main beam simulated by Midas Civil are shown in Figure 14.

5.3.2. Forced Vibration Test Results and Analysis

Under obstacle-free conditions on the bridge deck, two loading vehicles were driven along the centerline of the bridge lanes at various speeds ranging from 10 km/h to 60 km/h. This was performed to measure the dynamic response and impact coefficient of the bridge structure under the load of operating vehicles. Figure 15 shows photos of the dynamic load test with the rolling car test and the jumping car test.

(1)

Amplitude

During the running vehicle test, the maximum vertical amplitude of the main bridge was recorded at 1.157 mm. This occurred at the L/4 measurement point of the main arch when the vehicle speed was 60 km/h. In the jump vehicle test, the maximum vertical amplitude was 0.649 mm, observed at the L/4 measurement point of the main beam. For the approach bridge, the maximum vertical amplitude was 0.079 mm, recorded at a vehicle speed of 40 km/h during the running vehicle test. From the amplitude data, both the main bridge and the approach bridge show relatively small amplitudes during the rolling car and jumping car tests. It can be preliminarily concluded that the bridge’s safety under dynamic loading is controllable. The following figure (Figure 16) shows the vertical measurement points of the main beam during the 20 km/h jumping car test time history curve.

(2)

Impact Coefficient

According to the General Specification for Highway Bridges and Culverts Design [34], the value of the impact coefficient is as follows:

$$\begin{array}{c}\mathrm{When} f<1.5 \mathrm{Hz},\mu =0.05.\\ \mathrm{When} 1.5 \mathrm{Hz}<f<14 \mathrm{Hz},\mu =0.1767\ln (f)-0.0157.\\ \mathrm{When} f>14 \mathrm{Hz},\mu =0.45\end{array}$$

where f is the measured fundamental frequency of the structure, and μ is the impact coefficient.

The impact coefficients for each test condition were determined from the forced vibration time history curve, as presented in

Table 8. Bridge impact coefficient during running test.

Condition	Impact Coefficient		Maximum Value
	1st Measurement	2st Measurement
10 km/h Running Vehicle Test	0.01	0.02	0.03
20 km/h Running Vehicle Test	0.01	0.02
30 km/h Running Vehicle Test	0.03	0.02
40 km/h Running Vehicle Test	0.02	0.03
50 km/h Running Vehicle Test	0.03	0.03
60 km/h Running Vehicle Test	0.03	0.03

. The theoretically calculated impact coefficient for the superstructure of the bridge is 0.08. Upon examining the table, it is evident that the impact coefficients under both running and jump vehicle excitations are lower than the theoretical value. This indicates that the dynamic response of the structure under moving loads is relatively close to the theoretical predictions, and the bridge deck is smooth and meets the safety and usability requirements.

6. Conclusions

6.1. Results

(1) Under the static load test, the strain structural safety factor of the test span ranged from 0.13 to 1.00, and the deflection safety factor ranged from 0.63 to 0.81. Both factors were less than 1, indicating that the structure’s strength and stiffness met the design requirements. After unloading, the relative residual strain and relative residual displacement at each measurement point were both less than 20%, suggesting that the structure was in an elastic working state. During the test, no cracking of the steel structure or welds was observed in the key sections of the bridge. Subsequent inspection after the test confirmed that there were no cracks in the entire bridge.

(2) The measured first-order frequency of the main bridge’s lateral vibration was 1.425 Hz, compared to the finite element calculation frequency of 1.14 Hz. Similarly, the measured first-order vertical vibration frequency was 2.95 Hz, while the calculated frequency was 1.71 Hz. The measured first-order torsional frequency was 3.60 Hz, with a calculated value of 1.948 Hz. In all cases, the measured values were higher than the theoretical calculations. The measured first-order vertical bending frequency of the approach bridge was 6.375 Hz. These results indicate that the vertical overall stiffness of the bridge satisfies the design requirements. The damping ratios of the test spans fell within the normal range and the measured impact coefficients were all lower than the values prescribed by the code and were in compliance with the specifications.

(3) This load test not only furnishes a scientific foundation and safety guarantee for the sub-carrying through-truss cable-stayed arch bridge but also offers valuable data and experience to a broader range of similar bridge engineering domains. The test outcomes verify the performance of the arch bridge under actual load circumstances, providing a reference for subsequent structural optimization designs.

6.2. Discussion

Revised sentence: Conducting load testing on the bridge can provide an accurate reflection of its condition at the time of testing. To ensure the safety of the bridge during subsequent periods of use, it is recommended to regularly inspect the bridge in accordance with the Technical Standards for Urban Bridge Maintenance [35]. This will enable timely detection and resolution of any defects. Additionally, implementing long-term health monitoring for the bridge structure is particularly advantageous for its operation and maintenance. A concise yet comprehensive discussion on this topic follows:

(1) Bridge structural health monitoring, as opposed to traditional manual monitoring, possesses all-weather and full-time domain capabilities, facilitating the accurate, real-time, and prompt accomplishment of bridge monitoring. Carrying out long-term bridge structural health monitoring enables the timely detection of abnormal changes and potential issues in the structure, enhancing bridge safety. It also facilitates the prompt identification of deterioration, damage, or fatigue phenomena in bridge structures, which can be addressed through timely repairs and reinforcements, thereby extending the bridge’s service life. Moreover, through data analysis and the establishment of predictive models, decisions regarding bridge maintenance can be optimized, leading to cost reduction.

(2) The accuracy of bridge structural health monitoring data is influenced by various factors, including sensor performance and installation location, the data processing system, and temperature fluctuations. Among these factors, the impact of temperature on bridge structural health monitoring should not be underestimated. A strong positive correlation exists between temperature and strain in the bridge structure. Therefore, it is crucial to thoroughly consider the effects of temperature and employ precise compensation methods to minimize or eliminate its influence on measurement results during long-term monitoring.

(3) The field of bridge structural health monitoring is continuously advancing, with current research focusing on the integration of technologies such as the Internet of Things (IoT) and machine learning. However, further development is still required in this area. Future advancements include the utilization of more efficient and precise sensors, as well as the integration of multiple sensor types for multi-modal monitoring to provide comprehensive solutions for monitoring complex structures. Moreover, there is a need to develop more intelligent algorithms capable of processing large volumes of monitoring data in a precise and sophisticated manner. By combining machine learning with predictive models, real-time data can be used to dynamically assess the structure’s condition and predict its remaining service life and maintenance requirements. The incorporation of these emerging technologies will significantly enhance the efficiency, intelligence, and accuracy of bridge structural health monitoring systems while greatly improving the safety and longevity of engineering structures.

(4) In order to improve the predictive accuracy of finite element models, model updating techniques have become an effective approach. By incorporating experimental data into the calibration of model parameters, the accuracy of the numerical model can be significantly enhanced. Especially in modal analysis, optimizing the distribution of mass and stiffness in the model allows the numerical predictions of natural frequencies, mode shapes, and other modal parameters to better align with actual experimental results, thereby providing more reliable data support for structural health monitoring. Future research could further explore how to incorporate more measured data, consider more complex nonlinear effects, develop model updating programs, and improve the computational efficiency of algorithms in order to further enhance the accuracy and practicality of model updating.