Abstract

Three pretensioned adjacent concrete box beam bridges were studied with a structural health monitoring (SHM) paradigm based on strain measurements and finite element static analyses. An accurate model for one bridge and an approximate model for the other two were created using ansys software. The analyses were used to calculate the strains generated by six concentrated loads that mimic the presence of a truck. Pristine and damage scenarios were implemented, and the associated numerical strains were compared to the experimental strains measured with proprietary wireless sensors during a truck test. As the results from the approximate models deviated significantly from the field response of the bridge, the accurate model applied to one bridge was extended to the other two. The comparison between numerical and experimental results revealed the presence of noncritical anomalies related to strain distribution across adjacent beams. Such issues were confirmed with the examination of the historical strains streamed for several months to a repository, using simple data processing strategies. The intellectual contribution of the work resides in the combination of finite element analysis and SHM applied to three existing bridges with very similar structural characteristics. This combination revealed the presence of noncritical issues impossible to be diagnosed with conventional inspection.

1 Introduction

National Bridge Inventory (NBI) statistics [1] indicate that there are nearly 620,000 highway bridges in the United States, 7.6% of which are rated poor [2]. Timely interventions are critical to prioritize maintenance and minimizing the cost-to-benefit ratio of maintenance (e.g., postings, traffic disruption). However, several factors (budget, personnel, traffic-related logistics, etc.) make it impossible to assess and intervene on all bridges with the desired frequency. According to Gibson et al. [3], in the United States, 11 State DOTs (Departments of Transportation) use methodological frameworks that leverage NBI data on the physical condition of bridges to quantify the criticality of each asset and identify bridges whose intervention should be prioritized [3].

Episodes such as the failure of structural components or bridges [4] that have passed routine nondestructive inspection based, for example, on visual testing, ultrasounds, or eddy current testing [5,6] warrant complementary strategies based on structural health monitoring (SHM), in which sensors bonded/bolted/embedded to the structure of interest stream data to a central repository, and smart processing can automatically flag critical issues as they unfold [7]. Despite the replacement of periodic inspection of engineering structures into SHM systems has been discussed for many years [8], the industrial take-up of SHM technology has been slow, with very few widely deployed applications [8].

The most common bridge health monitoring applications use strain gages, accelerometers, and displacement sensors [9], Tiltmeters [10,11], pressure sensors, and acoustic emission [12,13] can be used as well. SHM approaches can be data driven [1430] or physics based [3147]. The former relies on the extraction of damage-sensitive features to be coupled to unsupervised or supervised learning algorithms. These methods require field baseline data (unsupervised approaches) or field data inclusive of damaged configurations (supervised learning). Data-driven methods do not require a physics model of the structure [1424]. Azimi and Pekcan [14] explored the application of convolutional neural networks for damage detection in large-scale systems. Liu et al. [15] utilized neural networks and multisensor feature fusion to classify sensor data. Shang et al. [16] developed a deep convolutional denoising autoencoder network to extract damage features from field measurements of undamaged structures in the presence of noise and uncertainties. Bao et al. [17] proposed a two-step procedure utilizing a deep neural network to identify anomalies resulting from structural damage. Xu et al. [18] employed a restricted Boltzmann machine to identify cracks in steel box girders of bridges. Abdeljaber et al. [19] examined the use of a 1D convolutional neural network for data fusion and damage-sensitive feature extraction from raw acceleration signals to detect and locate damage in large-scale structures. Ghahremani et al. [20] investigated damage detection using convolutional neural networks and recorded acceleration signals. Alamdari et al. [21] employed a modified k-means clustering algorithm to identify potential structural damage in jack arches of the Sydney Harbour Bridge. Although data-driven SHM methods have been applied to bridges, they encounter certain challenges. Unsupervised learning algorithms require an ample amount of data encompassing all possible baseline configurations, while supervised methods necessitate data from damaged configurations, which may not always be feasible or realistic in practical situations [22,23]. The interested reader is referred to Ref. [24] for a comprehensive review of data-driven methods.

In another group of data-driven methods, the long-term monitoring data were analyzed under temperature variations to detect potential anomalies. Kromanis and Kripakaran [25] provided a framework to capture the relationship between temperature gradients in a structure and the subsequent thermal responses. They used four different supervised learning algorithms. In addition, principal component analysis was applied to data for dimension reduction. The predicted responses of the bridges due to temperature change showed good alignment with the measured responses. Zhu et al. [26] combined mode decomposition, data reduction, and blind separation to uncover the effects of temperature on the response of a truss given bridge. Gu et al. [27] employed a two-step damage detection technique using artificial neural networks to mitigate the impact of temperature on natural frequencies. Ni et al. [28] applied a support vector machine to model the temperature effects on modal frequencies of a cable-stayed bridge, Ting Kau Bridge located in Hong Kong. Jin et al. [29] conducted research to separate temperature-induced variations in natural frequencies of a highway bridge, the Meriden Bridge located in Connecticut. Kostic and Gul [30] modeled a footbridge using finite element analysis and simulated 2000 cases with different temperatures and damages. They integrated a sensor-clustering-based time-series analysis with an artificial neural network to study the influence of the temperature.

Physics-based methods, on the other hand, rely instead on accurate modeling, typically done via commercial FE codes. Worldwide examples include but are not limited to the modeling and monitoring of Aizhai Suspension Bridge [31], Nanjing Yangtze River Bridge [32], Xiabaishi Bridge [33], the cable suspension Tsing Ma Bridge [34], and a precast concrete bridge in the Dominican Republic [35]. Some physics-based methods may be supported by the use of the truck load test. For example, Kaloop et al. [36] collected static and dynamic data from the Dorim-Goh Bridge in Korea using ambient trucks and information in time and frequency domains. Another example is the work of Hedegaard et al. [37] who created a linear elastic finite element model of the concrete posttensioned box girder I-35W St. Anthony Falls Bridge and validated it using truck load tests. Schlune et al. [38] developed a FE model for the new Svinesund Bridge, a single-arch bridge, to assess its health using static and dynamic measurements. Ghahremani et al. [39] employed an evolutionary optimization algorithm to update numerical FE models of truss and frame structures. Yang et al. [40] employed 3D terrestrial laser scanning to measure the static response and update the FE model. Zanjani Zadeh and Patniak [41] developed a 3D FE model of a composite steel stringer-supported reinforced concrete deck highway bridge, updating the model properties with measured data from moving truck load tests. Cheng et al. [42] established an FE model for a 131 m large transmission tower to facilitate SHM, manually adjusting and updating the model to achieve a realistic representation of the measured experimental dynamic characteristics. Giagopoulos et al. [43] proposed a framework for identifying fatigue damage by combining operational experimental measurements with a high-fidelity FE model. Schommer et al. [44] investigated SHM on a prestressed concrete beam using an FE model and analyzing static and dynamic responses, including the influence of temperature on the recorded data. Gatti [45] compared the structural responses obtained from static and dynamic load tests with predictions from an FE model to monitor a prestressed reinforced concrete bridge constructed in the late 1960s. Further research on physics-based methods can be found in Refs. [46,47].

In the study presented in this article, three prestressed concrete box beam bridges were modeled using ansys 2020 r2 software. The digital replica of one bridge and an approximate model of the other two were created to evaluate strengths and limitations of the simplification. The results of the numerical static analysis applied to each bridge were compared against the experimental values recorded with an array of proprietary wireless sensors during a truck test. Based on this comparison, an enhanced finite element model (EFEM) relative to the approximate models was also generated. It is disclosed here that the authors did not install the sensors and did not perform the experiment. Access to the field data was provided by the research sponsor (see the Acknowledgment). In addition, a SHM paradigm to identify structural anomalies from the long-term data was developed. The paradigm included some simple, but effective, statistics applied to the individual sensors, and the outlier analysis (OA) applied to the sensors as a whole. OA is an unsupervised algorithm able to determine whether a new datum is inconsistent. In this study, the Mahalanobis squared distance (MSD) scalar Dζ is calculated as follows [4853]:
(1)
where {xζ} is the potential outlier vector, {x¯} is the mean vector of the baseline, [K] is the covariance matrix of the baseline, and T is the transpose symbol.

The novelty and the merit of this article is in the systematic study of three nearly identical bridges using a holistic SHM approach that includes accurate finite element modeling, real long-term data, and controlled truck loading test. Such holistic study allows to identify the strength and limitations of high- and low-fidelity finite element modeling. The low-fidelity models are much less expensive in terms of computation cost. Therefore, in case an approximate (low fidelity) model provides accurate results, it is more favorable to use them rather than complicated high-fidelity models. On the other hand, high-fidelity models can be more reliable in terms of predicting the structural responses of interest. In addition, this study demonstrates the advantages of relatively simple signal processing that can be used for long-term monitoring without using complex setups such as digital image correlation [54] and artificial intelligence [55]. Finally, the study helped to find some unexpected but not critical behavior in two bridges. This article expands the work of Ghahremani et al. [56] where the finite element analysis of one of the bridges presented here was discussed. Besides the inclusion of two more bridges, the present article includes the effect of the damage on the static response of the three structures and expands the SHM paradigm for long-term monitoring. The outline of the analysis and investigations conducted in this work are summarized in the flowchart shown in Fig. 1. It is noted here that the SHM system, the location and the types of sensors, and the protocol used to perform the controlled truck test were not decided by the authors as they were executed before the beginning of the research. Having said that, static loading is overall preferred over dynamic loading due to ease implementation and execution. Dynamic analysis requires the installation of accelerometers or other sensing methods that requires proper excitation. Additionally, dynamic data may be more prone to ambient noise and may not be susceptible to localized damage or certain types of structural anomalies. The use of a detailed finite element model in support of a monitoring system for any given bridge is a valuable instrument to manage the given asset. The proof that the model can accurately predict the response of the bridge to certain controlled loads allows engineers to simulate countless damage scenarios that bridge owners can use to gage the severity of damage observed in other bridges of similar structural characteristics.

Fig. 1
Flowchart of the analyses conducted in this study
Fig. 1
Flowchart of the analyses conducted in this study
Close modal

This paper is organized as follows. Section 2 describes the three bridges. Section 3 introduces the monitoring system installed by the owner of the proprietary sensors and the protocol of the controlled truck test. The details of the finite element models are presented in Sec. 4. The results of the truck tests, including the comparison with the numerical calculations, are presented in Sec. 5. The analysis of the historical data is detailed in Sec. 6. Finally, this article ends with some concluding remarks.

2 The Bridges

Figure 2 shows the photos of the bridges, which are in the State of Pennsylvania. The box beams are connected to a cast-in-place concrete deck via steel rebars acting as shear keys on top of the beams. Besides, the box beams are connected in the transverse direction using shear keys that are filled with grout, also known as conventional grouted connections. The first bridge (Fig. 2(a)), hereinafter referred to as the Somerset Bridge, consists of two 25.2 m (82.68 ft) long spans, made of eight concrete box beams. The beams can expand at the abutments and are fixed at the middle pier. There is no connection between the girders of the first and second spans. However, since the deck is a cast-in-place slab connected to all the girders by shear keys, the loads applied to one span can be partially transferred to the adjacent span through the deck. The reinforcement consists of 54 grade 250, 3/8-in. diameter, seven-wire strands. The design concrete deck is 140 mm (5.5 in.) thick.

Fig. 2
Photos of the three bridges considered in this study: (a) upstream view of the BMS 55-3014-0050-0509 bridge, for convenience referred here as the Somerset Bridge, (b) Cooks Mill Bridge (BMS ID 05-3001-0080-0000), and (c) single span ID 29-2004-0040-0000 bridge over little Tonoloway Creek in Fulton County
Fig. 2
Photos of the three bridges considered in this study: (a) upstream view of the BMS 55-3014-0050-0509 bridge, for convenience referred here as the Somerset Bridge, (b) Cooks Mill Bridge (BMS ID 05-3001-0080-0000), and (c) single span ID 29-2004-0040-0000 bridge over little Tonoloway Creek in Fulton County
Close modal

The second bridge (Fig. 2(b)) is the Cooks Mill Bridge in Bedford County. It carries traffic over the Wills Creek River in the Londonderry Township. This three-span pretensioned concrete adjacent box beam bridge was built in 1961 for a total length of 59.4 m (195 ft).

The last structure (Fig. 2(c)) is a single span bridge, hereinafter referred to as the Tonoloway Bridge in Fulton County, built in 1987. It also consists of eight pretensioned adjacent concrete box beams supported by reinforced abutments for a total length of 27 m (87 ft) and curb-to-curb width of 9.2 m (30.2 ft).

The cross section of each bridge is shown in Fig. 3.

Fig. 3
Cross section of the (a) Somerset Bridge, (b) Cooks Mill Bridge, and (c) of the Tonolaway Creek Bridge. Units expressed in inches following the shop drawings provided to the authors. The location of some sensors and the north (N) and the south (S) of the bridges are identified for convenience.
Fig. 3
Cross section of the (a) Somerset Bridge, (b) Cooks Mill Bridge, and (c) of the Tonolaway Creek Bridge. Units expressed in inches following the shop drawings provided to the authors. The location of some sensors and the north (N) and the south (S) of the bridges are identified for convenience.
Close modal

3 Structural Health Monitoring System and Truck Tests

A company not involved with the study presented in this article installed the proprietary SHM system and performed the controlled load truck test on the bridges. The Somerset Bridge was instrumented with 30 bolted type wireless strain gages. The gages have the following specifications: sampling rate: 8 s, which can change to 20 ms if the strain value exceeds certain thresholds, transmission interval: 6 min, resolution: 3.6 microstrain, and range: ±4000 microstrain. Each gage embeds a thermocouple. Both spans were instrumented with one sensor bolted to the bottom of each box beam, as shown in Fig. 4(a). Four gages, namely, S01, S10, S21, and S30, were bolted to the outer face of the side girders. Figure 4(a) also shows the presence of ten more sensors, but they were not considered in the study presented here.

Fig. 4
Schematics of the location of the strain sensors at the (a) Somerset Bridge, (b) Cooks Mill Bridge, and (c) of the Tonolaway Creek Bridge. The box beams have a skew angle of 30 deg.
Fig. 4
Schematics of the location of the strain sensors at the (a) Somerset Bridge, (b) Cooks Mill Bridge, and (c) of the Tonolaway Creek Bridge. The box beams have a skew angle of 30 deg.
Close modal

The bridge was tested with a truck. The steer axle was 18,400 lb, and the drive tandem axles were 40,060 lb. The truck crossed the bridge slowly at a known lateral distance from the north parapet. The distances were 0.305 m (1 ft) through 5.8 m (19 ft) at 0.61 m (2 ft) steps. Two crossings per distance were completed.

The Cooks Mill Bridge was instrumented with ten bolted type strain gages at the bottom of the midspan of each beam and on the outside web of the fascia beams (Fig. 4(b)). The sensors bolted to both bridges were not temperature compensated. The tests were conducted with the same truck using the same protocol adopted for the Somerset Bridge.

Finally, the Tonoloway Bridge was instrumented with ten adhesive type strain gages at the locations schematized in Fig. 4(c). The test was conducted using a 57,120 lb truck: steer axle: 16,940 lb; drive “tandem” axles: 40,180 lb. Three types of tests were completed. In the first group of tests, the truck traveled over the bridge at a known lateral distance from the south parapet. In the second group, the truck stayed stationary at the middle of the span for about 30–50 s. In the third group of tests, the truck traveled close to 80 kmh (50 mph) over the bridge.

4 Modeling: Setup and Simulated Damage

The finite element replica of the Somerset Bridge was created (Fig. 5). Three-dimensional 20 node solid body elements were used for the parapets, the beams, and the deck. REINF264 elements were used to analyze the strands, rebars, and stirrups that were considered line bodies. The model consisted of 83,891 elements. The material properties are summarized in Table 1 and are representative of the properties selected for the other two bridges as well.

Fig. 5
Somerset Bridge. Snapshots from the high-fidelity finite element model: (a) overall look and (b) cross section
Fig. 5
Somerset Bridge. Snapshots from the high-fidelity finite element model: (a) overall look and (b) cross section
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Table 1

Properties of the concrete and steel components used in the finite element models

ConcreteBeams5000 psi
Deck4000 psi
Parapets3500 psi
SteelStirrupsGrade 40 steel
Rebars (deck)Grade 60 steel
Strands (for prestressing)Grade 250 steel
ConcreteBeams5000 psi
Deck4000 psi
Parapets3500 psi
SteelStirrupsGrade 40 steel
Rebars (deck)Grade 60 steel
Strands (for prestressing)Grade 250 steel

For the other two structures, a low-fidelity model (LFM) was created. The box beams and the parapets were “line bodies” and analyzed using “beam elements.” The rebars inside the slabs were replaced by a 0.75 in. steel plate. An EFEM was also built by considering the box beams and the parapets as “solid bodies” to be analyzed using “solid elements.” The LFM of the Tonoloway Bridge included 178,774 nodes, whereas the modified models included 314,522 nodes and 3128 structural components, most of which were the rebars and the strands of the concrete box beams. The EFEM of the Cooks Mill Bridge had 7300 structural components and major parts of them are the rebars and strands. For illustrative purposes, the LFM Cooks Mill Bridge is shown in Fig. 6.

Fig. 6
Cooks Mill Bridge. Snapshots of the low-fidelity model: (a) before meshing and (b) after meshing
Fig. 6
Cooks Mill Bridge. Snapshots of the low-fidelity model: (a) before meshing and (b) after meshing
Close modal

For each bridge, a static analysis was conducted by applying a six point-load on the deck (Fig. 7). Pristine conditions were simulated by considering the shop drawings provided to the authors by the Pennsylvania Department of Transportation. Then, the six damage scenarios summarized in Tables 24 were implemented individually and subjected to the same load conditions. Scenarios 5 and 6 represented loss of composite behavior by changing the contact type of the girders from “Bounded” to “No Separation.” In ansys software, the “Bounded” contact type between two objects means that the objects are perfectly bounded to each other, and they cannot slide or be separated. “No Separation” contact type between two components means that the objects can slide along the contact surface, but they cannot be separated.

Fig. 7
Details of the configuration and dimension of the test truck: (a) side view and (b) top view
Fig. 7
Details of the configuration and dimension of the test truck: (a) side view and (b) top view
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Table 2

Damage scenarios simulated in the study presented in this paper: Somerset Bridge

Damage scenarioDescription
1The cross-sectional area of all strands in concrete beams was reduced by 20%
2The modulus of elasticity of beam’ concrete was reduced by 10%
3The modulus of elasticity of concrete for G4 (S5), G7 (S8), and G11 (S24) was reduced by 50%
4A few cracks in G3, G4, G8, G13, and G14 were modeled. The crack width is 0.2 in. and its depth is 2 in
5The contact type of the G4, G5, and G12 with the deck was changed from “Bounded” to “No Separation” (loss of composite behavior). In ansys software, “Bounded” contact type between two objects means that the objects are perfectly bounded to each other, and they cannot slide or be separated. “No Separation” contact type between two components means that the objects can slide along the contact surface, but they cannot be separated
6The contact type of the G4, G5, and G12 with the deck was changed from “Bounded” to “No Separation” (loss of composite behavior). Also, the contact of the mentioned beams with adjacent shear keys was changed to “No Separation.”
Damage scenarioDescription
1The cross-sectional area of all strands in concrete beams was reduced by 20%
2The modulus of elasticity of beam’ concrete was reduced by 10%
3The modulus of elasticity of concrete for G4 (S5), G7 (S8), and G11 (S24) was reduced by 50%
4A few cracks in G3, G4, G8, G13, and G14 were modeled. The crack width is 0.2 in. and its depth is 2 in
5The contact type of the G4, G5, and G12 with the deck was changed from “Bounded” to “No Separation” (loss of composite behavior). In ansys software, “Bounded” contact type between two objects means that the objects are perfectly bounded to each other, and they cannot slide or be separated. “No Separation” contact type between two components means that the objects can slide along the contact surface, but they cannot be separated
6The contact type of the G4, G5, and G12 with the deck was changed from “Bounded” to “No Separation” (loss of composite behavior). Also, the contact of the mentioned beams with adjacent shear keys was changed to “No Separation.”
Table 3

Damage scenarios simulated in the study presented in this paper: Cooks Mill Bridge

Damage scenarioDescription
110% reduction of the modulus of elasticity of the boxes’ concrete, while the stiffness of the deck and parapets was left unchanged
2Severe localized stiffness loss: 40% lower modulus of elasticity of one box
3Steel corrosion was simulated under damage scenario by reducing the cross-sectional area of all the strands by 20%
4Localized cracks in G2 and G5 were modeled under damage scenario 4. The crack width and depth were 0.2 in. and 2 in., respectively Three cracks were introduced at the bottom surface of some concrete beams
5Damage scenario 5 consisted of modifying the contact type of girders G4 and G6 with the deck. Such contact was changed from “Bounded” to “No Separation,” which means loss of composite behavior
6Damage scenario 5 with modified adjacent shear keys connections, which were changed to “No Separation.”
Damage scenarioDescription
110% reduction of the modulus of elasticity of the boxes’ concrete, while the stiffness of the deck and parapets was left unchanged
2Severe localized stiffness loss: 40% lower modulus of elasticity of one box
3Steel corrosion was simulated under damage scenario by reducing the cross-sectional area of all the strands by 20%
4Localized cracks in G2 and G5 were modeled under damage scenario 4. The crack width and depth were 0.2 in. and 2 in., respectively Three cracks were introduced at the bottom surface of some concrete beams
5Damage scenario 5 consisted of modifying the contact type of girders G4 and G6 with the deck. Such contact was changed from “Bounded” to “No Separation,” which means loss of composite behavior
6Damage scenario 5 with modified adjacent shear keys connections, which were changed to “No Separation.”
Table 4

Damage scenarios simulated in the study presented in this paper: Tonoloway Bridge

Damage scenarioDescription
1The modulus of elasticity of beams’ concrete was reduced by 10%
2The modulus of elasticity of concrete for G3 (S4) and G6 (S7) was reduced by 50%
3The cross-sectional area of all strands in concrete beams was reduced by 20%
4Cracks in G2 and G5 were modeled. The crack width is 0.2 in. and its depth is 2 in
5The contact type of the G4 and G5 with the deck was changed from “Bounded” to “No Separation” (loss of composite behavior)
6The contact type of the G4 and G5 with the deck was changed from “Bounded” to “No Separation” (loss of composite behavior). Also, the contact of the mentioned beams with adjacent shear keys was changed to “No Separation.”
Damage scenarioDescription
1The modulus of elasticity of beams’ concrete was reduced by 10%
2The modulus of elasticity of concrete for G3 (S4) and G6 (S7) was reduced by 50%
3The cross-sectional area of all strands in concrete beams was reduced by 20%
4Cracks in G2 and G5 were modeled. The crack width is 0.2 in. and its depth is 2 in
5The contact type of the G4 and G5 with the deck was changed from “Bounded” to “No Separation” (loss of composite behavior)
6The contact type of the G4 and G5 with the deck was changed from “Bounded” to “No Separation” (loss of composite behavior). Also, the contact of the mentioned beams with adjacent shear keys was changed to “No Separation.”

5 Truck Test Results

The sensors data, hereinafter referred to as raw strain, were downloaded from a password-protected repository. Then, the value of the raw data was subtracted from their 15-min moving average in order to obtain the so-called true strain. The true strain targets the detection of transient events and filters out long-term factors such as thermal effect and drift. The term true strain shall not be considered the actual strain on the bridge as prestress level and the reference temperature at the time of installation are not known to the authors.

For illustrative purposes, Fig. 8 shows the raw (Fig. 8(a)) and the corresponding true strains (Fig. 8(b)) associated with sensor S06 during the test of the Cooks Mill Bridge. The number of spikes (twenty) is consistent with the number of truck crossings. The earlier peaks are likely linked to the arrival of the crew onsite and test preparation. Figure 8(a) shows that the baseline strain, i.e., the measurement without the truck, changed about 25 µε due to temperature rise. Such variation is almost larger than the strain induced by the truck itself. Figure 8(b) demonstrates that the 15-min average removes the thermal-related bias, and the increase in strain due to the truck can be easily quantified. As expected, the values of these peaks are not constant because the truck crossed the bridge at different lateral distances from the parapets, i.e., at different distances from the strain gages. As gage six was closer to the south part of the bridge, the highest strains occurred around the second half of the test. Similar outcomes were seen for the other sensors and the other bridges.

Fig. 8
Truck load test of the Cooks Mill Bridge: (a) raw strains and (b) corresponding true strains measured by gage 06
Fig. 8
Truck load test of the Cooks Mill Bridge: (a) raw strains and (b) corresponding true strains measured by gage 06
Close modal

Figure 9 compares the experimental maximum strains recorded by each sensor at a given crossing to the numerical strains calculated under pristine and damage scenario 1. The case of the Somerset Bridge with the truck 1.52 m (5 ft) away from the north parapet and at the middle of span 1 (Fig. 9(a)) and span 2 (Fig. 9(b)) is presented. The static calculations are consistent with the fact that the wheels are closest to gages S04 and S25 and farthest from S09 and S29. The excellent agreement between the numerical and the experimental values is evident with the exception of S05, S06, and S25. The discordant response of these three gages is explained with Fig. 10, which shows the results under damage scenario 6 that simulated the absence of shear keys at the locations shown in Fig. 11 and the loss of composite behavior of the shown girders. The lack of proper load transfer across adjacent boxes causes uneven distribution of the strains. Figures 9 and 10 demonstrate the quality of the high-fidelity model developed in this study, and the importance of accurate modeling for the explanation of issues revealed with the use of the sensing system.

Fig. 9
Somerset Bridge. Predicted and numerical (under pristine and damage scenario 1) strains when the truck was 1.52 m (5 ft) away from the north parapet. “Sensor(Exp.1)” and “Sensor(Exp.2)” are experimental, whereas “Pristine” and “Damage Scenario 1” are numerical results: (a) truck is at the middle of the first span, and (b) truck is at the middle of the second span
Fig. 9
Somerset Bridge. Predicted and numerical (under pristine and damage scenario 1) strains when the truck was 1.52 m (5 ft) away from the north parapet. “Sensor(Exp.1)” and “Sensor(Exp.2)” are experimental, whereas “Pristine” and “Damage Scenario 1” are numerical results: (a) truck is at the middle of the first span, and (b) truck is at the middle of the second span
Close modal
Fig. 10
Somerset Bridge. Predicted and numerical (under pristine and damage scenario 6) strains when the truck was 1.52 m (5 ft) away from the north parapet. “Sensor(Exp.1)” and “Sensor(Exp.2)” are experimental, whereas “Pristine” and “Damage Scenario 6” are numerical results: (a) truck is at the middle of the first span and (b) truck is at the middle of the second span
Fig. 10
Somerset Bridge. Predicted and numerical (under pristine and damage scenario 6) strains when the truck was 1.52 m (5 ft) away from the north parapet. “Sensor(Exp.1)” and “Sensor(Exp.2)” are experimental, whereas “Pristine” and “Damage Scenario 6” are numerical results: (a) truck is at the middle of the first span and (b) truck is at the middle of the second span
Close modal
Fig. 11
The shear keys at the Somerset Bridge that their contacts with the adjacent beams were changed to “No Separation”
Fig. 11
The shear keys at the Somerset Bridge that their contacts with the adjacent beams were changed to “No Separation”
Close modal

The interpretation of Fig. 10 is corroborated with Fig. 12, which shows the experimental and the calculated strains induced by the truck 4.57 m (15 ft) away from the north parapet.

Fig. 12
Somerset Bridge. Predicted and numerical (under pristine and damage scenario 6) strains when the truck was 4.57 m (15 ft) away from the north parapet. “Sensor(Exp.3)” and “Sensor(Exp.4)” are experimental, whereas “Pristine” and “Damage Scenario 6” are numerical results: (a) truck is at the middle of the first span and (b) truck is at the middle of the second span
Fig. 12
Somerset Bridge. Predicted and numerical (under pristine and damage scenario 6) strains when the truck was 4.57 m (15 ft) away from the north parapet. “Sensor(Exp.3)” and “Sensor(Exp.4)” are experimental, whereas “Pristine” and “Damage Scenario 6” are numerical results: (a) truck is at the middle of the first span and (b) truck is at the middle of the second span
Close modal

Similar analyses were conducted for the other two bridges. The results relative to the Cooks Mill Bridge when the truck was 1.52 m (5 ft) away from the north parapet are presented in Fig. 13(a), which shows the results of the LFM and the EFEM. Clearly, the LFM did not capture the response of the strain gages located far away from the point of application of the forces. Beam elements are 1D elements, while solid elements are 3D elements with more nodes and degrees-of-freedom. Owing to the poor accuracy of the LFM, the EFEM was used to calculate the stresses under damaged conditions as shown in Fig. 13(b). Figure 13(b) presents the results relative to damage scenario 6, where girders G4 and G6 lost composite behavior and their contact with adjacent beams using shear keys was changed to “No Separation” as shown in Fig. 14. Figure 13(b) shows that the strains were not distributed uniformly. As the contacts of G4 and G6 with the deck and the adjacent shear keys were changed, the stress at those girders is underestimated. Also, the model overestimates the strain for the other beams because the other beams compensate the defect of G4 and G6 due to the load redistribution. Finally, Fig. 13(c) shows the result of the same damage scenario but for a different truck distance from the parapet. The application of the LFM to the Tonolaway Bridge yielded the same considerations in terms of accuracy, and its outcome is not presented here.

Fig. 13
Cooks Mill Bridge analysis. Comparison of the experimental and numerical data. (a) Use of low-fidelity finite element models with the truck 1.52 m (5 ft) away from the north parapet. (b) Same load scenario as in (a) but using EFEM. (c) Same as (b) but the truck at truck 4.57 m (15 ft) away from the north parapet. “Sensor(Exp.1),” “Sensor(Exp.2),” “Sensor(Exp.3),” and “Sensor(Exp.4)” are experimental, whereas “Pristine” and “Damage Scenario 6” are numerical results.
Fig. 13
Cooks Mill Bridge analysis. Comparison of the experimental and numerical data. (a) Use of low-fidelity finite element models with the truck 1.52 m (5 ft) away from the north parapet. (b) Same load scenario as in (a) but using EFEM. (c) Same as (b) but the truck at truck 4.57 m (15 ft) away from the north parapet. “Sensor(Exp.1),” “Sensor(Exp.2),” “Sensor(Exp.3),” and “Sensor(Exp.4)” are experimental, whereas “Pristine” and “Damage Scenario 6” are numerical results.
Close modal
Fig. 14
The shear keys that their contacts with the adjacent beams were changed to “No Separation”
Fig. 14
The shear keys that their contacts with the adjacent beams were changed to “No Separation”
Close modal

The static analyses conducted for all three bridges led to the following additional considerations. The linearity of the models was such that the 10% reduction of the concrete stiffness led to about 10% increase in the overall strains. Under damage scenario 2, the beams adjacent to girders G3 and G6 bear some effects, whereas the beams far away from the damage experience lesser strain increase. The reduction of the strands cross section did not lead to a significant change in strain. Because prestress was not included in any of the models, it is believed that the reason behind the results is that the concrete and strand bear the force caused by the truck together. As the cross-sectional area of concrete is more than the cross-sectional area of strands, the stress is mainly transferred to the concrete. Some manual calculations were done for the Somerset Bridge considering 20% reduction in strands’ cross section. The calculations verify the obtained results from the ansys model. Finally, the models predict that the presence of localized cracks at the bottom of some concrete beams causes such small variations undetectable with the installed sensors.

6 Long-Term Monitoring

6.1 Raw Strain Data.

The historical data downloaded from the password-protected repository of each bridge were analyzed in order to formulate a general SHM paradigm. For representative purposes, Fig. 15 shows the raw strain and the corresponding 15-min average of the gages labeled as S05 in Fig. 4. The ±4σ interval is overlapped. As the SHM systems were installed months apart, the monitoring windows were different. The history of the Somerset Bridge (Fig. 15(a)) and the Cooks Mill Bridge (Fig. 15(b)) show the seasonal trend with peak-to-peak values of about 400 µɛ, which is one order of magnitude larger than the strain increase experienced during the truck test. This difference can be attributed to the absence of temperature compensation in the sensors. As such, the recorded values encompass both thermally induced strains in the concrete and additional effects caused by the sensors themselves. The spike seen in Fig. 15(a) was likely due to an electromagnetic interference as it was observed across all the sensors. Not shown in Fig. 15, the strains from the sensors bolted to the outer walls exhibited wider ranges because they were more exposed to solar radiations. The extreme strains recorded in January 2019 (Figs. 15(a) and 15(b)) were caused by exceptionally cold ambient temperatures. Figure 15(c) presents the results relative to the Tonolaway Bridge. A few isolated spikes occurred throughout the monitored period, likely caused by electromagnetic interference because the associated strains were 1–2 order of magnitude higher than what was recorded during the truck tests and were seen also in the other gages. Some of those spikes seem to have shifted the value of the raw strain permanently. Owing to the vertical scale of the plot, the daily trends associated with the temperature cannot be seen. In addition, the sensor S05 drifted significantly for several months, and a similar behavior was seen in other gages. It was concluded that these adhesive type gages drifted because concrete moisture degraded the bondline. Owing to this behavior, the long-term analysis of the Tonolaway Bridge was dismissed in this study and is not considered further.

Fig. 15
Raw strain and corresponding 15-min average recorded by sensor 05 mounted on the (a) Somerset Bridge, (b) Cooks Mill Bridge, and (c) Tonolaway Bridge
Fig. 15
Raw strain and corresponding 15-min average recorded by sensor 05 mounted on the (a) Somerset Bridge, (b) Cooks Mill Bridge, and (c) Tonolaway Bridge
Close modal

6.2 Raw Strain–Temperature Analysis.

The raw strain and the corresponding temperature measured by S05 bolted to the Cooks Mill Bridge are shown in Fig. 16. The linear regression and the ±4σ interval are overlapped. The few scattered dots around 10 °C (50 °F) are likely due to maintenance activities of the sensing systems. This hypothesis was not discussed with the owner of the sensors and is based on observations from the other sensors.

Fig. 16
Cooks Mill Bridge. Raw strain versus raw temperature measured by gage 05.
Fig. 16
Cooks Mill Bridge. Raw strain versus raw temperature measured by gage 05.
Close modal

The slope of the regression and the residual R2 computed for every sensor of the Cooks Mill Bridge are plotted in Fig. 17. It is reminded here that S01 and S10 were bolted to the north and south exterior box, respectively. Most values were around 0.96–0.99 because the sensors were not temperature compensated. Nonetheless, the slopes can be used to identify uneven responsiveness of each box to thermal load. Despite S01 and S10 are exposed to different solar illumination, their slope is nearly identical. However, the slopes associated with gages S02 and S09 that are symmetrically opposite with respect to the bridge centerline vary by about 12%. In addition, the beams with gages S03 and S08 expand much less than their adjacent beams. In numbers, the slope of gage S07 is 25% higher than the slope of gage S08. Sensors S04 through sensors S17 have nearly the same values.

Fig. 17
Cooks Mill Bridge. Slope of linear regression of the strain versus temperature graphs (the values are expressed in µɛ/°F) and residual R2 of the linear interpolation strain versus temperature. S01–S10 are bolted to the first span, and S21–S30 are bolted to the second span.
Fig. 17
Cooks Mill Bridge. Slope of linear regression of the strain versus temperature graphs (the values are expressed in µɛ/°F) and residual R2 of the linear interpolation strain versus temperature. S01–S10 are bolted to the first span, and S21–S30 are bolted to the second span.
Close modal

Similar considerations can be extrapolated from Fig. 18, which refers to the Somerset Bridge. Some boxes did not expand as much as the adjacent one, and this aligns with the truck load test results discussed in the previous section. For example, the gradient (−7.66 µɛ/°F) of gage S03 is 27% higher than the adjacent member S02 (−6.05 µɛ/°F) and 13% higher than the adjacent beam S04 (−6.8 µɛ/°F). These numbers reveal uneven expansion/contraction. Similar considerations can be extrapolated for sensors S22–S24. Overall, Span 1 and Span 2 have different gradients. For example, the slope of S23 (−5.16 µɛ/°F) is 30% smaller than its counterpart S03 (−7.66 µɛ/°F). These responses are in part aligned with what discussed about the truck test, and a numerical study that takes into account the effect of thermal load is warranted. Finally, it is interesting to note that the strain gradients estimated across the Cooks Mill Bridge are close to those in the Somerset Bridge. This empirical evidence may be used to generalize some structural responses of bridges having similar design.

Fig. 18
Somerset Bridge. Slope of linear regression of the strain versus temperature graphs (the values are expressed in µɛ/°F) and residual R2 of the linear interpolation strain versus temperature. S01–S10 are bolted to the first span, and S21–S30 are bolted to the second span.
Fig. 18
Somerset Bridge. Slope of linear regression of the strain versus temperature graphs (the values are expressed in µɛ/°F) and residual R2 of the linear interpolation strain versus temperature. S01–S10 are bolted to the first span, and S21–S30 are bolted to the second span.
Close modal

6.3 Live Load Analysis.

Figure 19 shows the true strain for sensors S05 bolted to the Cooks Mill Bridge. Values above 20 µɛ can be considered equivalent to the crossing of a 26,517 kg (58,460 lb) truck. When combined with the model, plots like Fig. 19 can identify unexpected transient events, but cannot reveal sensors drift or creep. Still, these graphs have the advantages of not being biased by any kind of offset. The use of threshold, like the one overlapped in the figure, may help setting an upper limit to flag an alert. The large negative true strains are likely due to the vibrations caused by a heavy truck crossing at high speed. As a matter of fact, it was shown that the same algorithm applied to the case of a slow-crossing truck does not cause significant negative strains. It is emphasized here that negative strains do not imply that the beam was under compression because the reference temperature and the prestress level of the box beams at the time of installation were not known.

Fig. 19
Cooks Mill Bridge. True strain calculated as the difference between the raw strain and the moving averaged strain.
Fig. 19
Cooks Mill Bridge. True strain calculated as the difference between the raw strain and the moving averaged strain.
Close modal

From Fig. 19, the number of occurrences at a given strain value bin was extracted and plotted in Fig. 20. For convenience, the value of the largest strain increase recorded by the same gage during the truck testing is overlapped. This graph shows few events above +100 µɛ. These episodes may likely be ignored especially when recorded by the whole array of sensors as they might be caused by electromagnetic interference. In this figure, negative and positive values correspond to transient strains below and above the 15-min average raw strains, respectively.

Fig. 20
Cooks Mill Bridge. Histogram chart relative to the true cleaned strain of gage S05.
Fig. 20
Cooks Mill Bridge. Histogram chart relative to the true cleaned strain of gage S05.
Close modal

Figure 21 presents the quantitative value of the ±4σ interval overlapped to the true strain dada as shown in Fig. 19. The results relative to the sensors bolted to the Somerset Bridge (Figs. 21(a) and 21(b)) and the Cooks Mill Bridge (Fig. 21(c)) are presented, and they may serve as additional indicators of the loading resistance capacity of the individual girders and the ability to transfer loadings evenly across adjacent girders. The data relative to the first span of the Somerset Bridge show that sensors S05 and S06 bore the largest strain. This is consistent with the fact that most traffic is likely to occur close to the centerline of the bridge in the absence of incoming vehicles from the opposite direction. Interestingly, the same response was not seen for the second span of the bridge for which the width of the ±4σ interval associated with sensor S24 (equal to 29 µɛ) is double the value of the adjacent sensors. As there is a road intersection close to the east abutment, it is hypothesized that the traffic is slower when traveling above span 2.

Fig. 21
Values of the ±4 standard deviation range of the true clean strain calculated for (a) and (b) the Somerset Bridge and (c) the Cooks Mill Bridge
Fig. 21
Values of the ±4 standard deviation range of the true clean strain calculated for (a) and (b) the Somerset Bridge and (c) the Cooks Mill Bridge
Close modal

The OA applied to sensors S01–S10 and to sensors S21–S30 of the Somerset Bridge is presented in Figs. 22(a) and 22(b), respectively. The measurements collected in May 2018 constituted the baseline. A few outliers are visible in June 2018, and February, March, and April of year 2019. As expected, the electromagnetic interference discussed in previous figures stands out clearly in Fig. 22. The same OA was applied to the ten strain gages on the Cooks Mills Bridge. The result is shown in Fig. 23. The largest MSD is visible on November 16, 2020, caused by the same event observed in Fig. 19. Specifically, a high true strain was seen in S03, S04, S08, and S09, likely due to maintenance of the hardware. As a matter of fact, these four sensors were not streaming data for a few months when they became active again on that day.

Fig. 22
Mahalanobis squared distance applied to the live strains from gages (a) 1–10 and (b) 21–30
Fig. 22
Mahalanobis squared distance applied to the live strains from gages (a) 1–10 and (b) 21–30
Close modal
Fig. 23
Mahalanobis squared distance applied to the live strains from all ten strain gages on the Cooks Mill Bridge
Fig. 23
Mahalanobis squared distance applied to the live strains from all ten strain gages on the Cooks Mill Bridge
Close modal

7 Conclusions

This article presented the numerical formulation and the empirical application of a SHM strategy for three concrete box bridges instrumented with strain gages bolted or adhesively bonded to the bottom of each box beam. The strain measurements relative to a truck load test and the measurements collected during several months were downloaded from a password-protected repository and processed. The interpretation of the experimental data was supported with a high-fidelity and a low-fidelity finite element model. The comparison of the numerical results to the field data revealed the limits of line-element beam-element modeling (approximate or low-fidelity model) that were originally developed for two of the three bridges considered in this study. Due to such limitations, enhanced versions of the approximate models were used for further analysis. This study did not reveal the onset of the growth of critical damage. The analysis of the truck test on the Somerset Bridge revealed some uneven distribution of the load. The use of the 15-min moving average may cause false positives when two consecutive samples of the raw data are collected 30 min apart or more and, at the same time, the thermal effect changed the baseline strain significantly. As such, the true strains computed from such samples should be discarded. Furthermore, the results show that the finite element models along with the data-driven methodologies have the potential to identify damages and anomalies in the three box girder bridges with relative accuracy. In the future, the availability of accurate modeling of a given bridge instrumented with an adequate SHM system may help owners at gaging the severity and quantifying the structural significance of any damage observed during the periodic inspections. The assessment may be extended to any other bridge with very similar geometric and structural characteristics.

Acknowledgment

This research was supported by the Pennsylvania Department of Transportation (PennDOT) under contract number 4400018535, Work Order-003 titled “Data Management, Mining, and Inference for Bridge Monitoring.” We are grateful to PennDOT for having provided the shop drawings, and granting access to the data repository and shared the truck load test reports written by the owners of the wireless sensors installed on the bridges. The third author performed this research while working under the supervision of the first author.

Conflict of Interest

There are no conflicts of interest.

Data Availability Statement

Data provided by a third party listed in Acknowledgment.

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