Abstract
The traditional BWIM (bridge weigh-in-motion) system measures the deformation of the bridge by means of sensors and uses these measurements to estimate the characteristics of passing traffic by means of dedicated algorithms. However, the application of the BWIM system is subordinated to the type of superstructure, composition, geometry, materials, and shape of the bridge, the location of the strain sensors used in the system, and the need to calibrate the measured strain curve and of a precise model of the structure at hand. In order to be free from these constraints, this paper proposes a simpler BWIM system using the bridge bearings as a weighing scale to measure the reaction forces at the supports resulting from the passing traffic. To that goal, the piezocomposite element known for its durability and responsiveness to external loading is embedded appropriately in the bridge bearing to achieve the piezo-bearing. This paper presents the BWIM system constituted by the so-called piezo-bearing, the results of a series of tests conducted to verify the responsiveness of the system to external dynamic excitation, and a numerical example to validate the feasibility of the proposed BWIM system. The numerical example shows that the identification of the characteristics of the vehicle crossing the bridge can be realized based simply upon the theory of mechanics using the time histories of the measured reaction forces instead of the deformation of the bridge.
1. Introduction
Traffic load is known to be the major cause of pavement degradation. Traffic is characterized by very different types of vehicles varying in magnitude, number of axles, and axle grouping. Truck weight regulations were enacted because heavier loads accelerate the accumulation of damage in pavement and increase the costs spent to maintain the pavement in good condition [1, 2]. It is thus necessary to have clear insight into the traffic by acquiring proper traffic data that will help drawing adequate maintenance and control strategies. Knowing the actual traffic loads in terms of weight, configuration, and number is critical in assessing the pavement lifetime and its integrity.
As part of the road network, monitoring traffic on bridge structures is an attractive approach since it can reduce uncertainties in the traffic load assessment and provide data enabling to optimize bridge maintenance strategies. Based on the weigh-in-motion (WIM), Moses [3] was the first who introduced the concept of BWIM to weigh the vehicles and their axles while traveling at full highway speed using the bridge itself as weigh-platform [4, 5].
The traditional BWIM (bridge weigh-in-motion) system measures the deformation of the bridge by means of sensors and uses these measurements to estimate the characteristics of passing traffic by means of dedicated algorithms [6]. The sensing hardware of a typical BWIM system includes strain sensors, axle-detecting sensors, data acquisition system, and computer. The strain sensors installed on the bridge soffit are generally electrical-resistant strain gauges arranged in a Wheatstone bridge configuration to amplify the very low measured strain [7]. Although current BWIM systems develop accuracy levels enabling to select vehicles to be weighed using static scales, Richardson et al. [6] reported that BWIM systems using such electrical-resistant strain gauges could not achieve sufficient accuracy for enforcement of overloaded vehicles. Besides, axle-detecting sensors were originally road surface sensors, but considering the lack of durability of the system caused by damage under heavy traffic, additional strain sensors are now installed on the bridge soffit to detect axle peaks [7].
The sensor layout depends on several factors including the function and sensitivity-to-strain variations of the sensors, the type of bridge, and the expected strain levels. The sensors are usually installed at the midspan of the bridge, which is characterized by the most pronounced responses, to measure the bending strain generated by the vehicle loads. Moreover, the sensitivity of strain responses to axle loads is specific to the bridge type and sensor layout [2]. Lydon et al. [7] also stressed this dependency on the bridge type involving not only the structural type and materials of the bridge but also its alignment. It is noteworthy that BWIM systems have not been applied to prestressed concrete bridges and skewed bridges despite their considerable presence in the bridge stock of most countries.
Concurrently with the hardware, huge efforts are being devoted to the development of BWIM algorithms. At the beginning, most of the algorithms were based on the Moses [3] algorithm which took root on the fact that the measured change in strain is related to the bending moment where the relation involves the dimensions and material properties of the bridge. In such algorithms, the identification is approached as an optimization problem minimizing the error between the measured response and the response computed using the vehicle parameters. Later, moving force identification (MFI) was introduced successfully to account for the presence of multiple vehicles on the bridge. MFI methods intended to obtain the time history of the wheel loads passing through the bridge but failed to achieve real-time identification due to expensive computational efforts [2].
From this review, it appears that, despite its high degree of maturity, the BWIM system has still drawbacks like the dependence on the type of superstructure, composition, geometry, materials, and shape of the bridge, the location of the strain gauges used in the system, and the need to calibrate the measured strain curve and of a precise model of the structure at hand [2, 6–9].
Considering that the bearing is a natural component of the bridge, a simpler and easy-to-implement BWIM system in terms of both hardware and software would use the bearing as a weighing scale to measure the reaction forces at the supports resulting from the passing traffic. This BWIM system would ease the identification of the wheel loads crossing the bridge based simply upon the theory of mechanics using the time histories of the measured reaction forces instead of the deformation of the bridge. To that goal, the authors proposed to use piezoceramics instead of the conventional sensors owing to their responsiveness and sensitivity to dynamic loads. However, piezoceramics exhibit brittleness and poor performance that make them impracticable for sensing in civil structures characterized by large loads and impacts. Therefore, a dedicated piezocomposite electricity-generating element (PCGE) was designed to develop a new BWIM system embedded in the bridge bearing to realize simple and cost-effective traffic monitoring [8, 10].
This paper presents the BWIM system constituted by the so-called piezo-bearing, the results of a series of tests conducted to grasp the responsiveness of the system under external dynamic excitation, and a numerical example to show the effectiveness of the proposed system.
2. Piezo-Bearing with d33-Mode PCGE
2.1. PCGE for On-Bridge Traffic Monitoring
The piezoelectric effect is the ability of certain materials to generate an electric charge in response to applied mechanical force. Among these materials, lead zirconate titanate (PZT) crystals can generate measurable piezoelectricity when their original dimension is deformed by about 0.1%. Used extensively for energy harvesting, PZT is an electroceramic material that is extremely fragile to shocks or impacts [11]. Considering the environment in which the piezoelectric element will be employed, large pressure will be acting constantly on the element together with regular impacts applied by the rolling wheels. This implies that the piezoelectric element to be developed should be resistant to pressure and impact while exhibiting sufficient sensitivity to produce voltage large enough for the monitoring purpose.
A fair solution to meet these requirements is provided by multilayered piezocomposites (Figure 1) due to their higher electromechanical coupling coefficients and higher piezoelectric voltage constants compared to conventional dense materials. Moreover, the material parameters of the piezocomposite can be accommodated by adjusting appropriately the ceramic-to-polymer volume fractions in the different layers to satisfy the specific performance for the purposed application [12, 13]. Accordingly, multilayered d33-mode piezocomposite electricity-generating element (PCGE) was considered since the pressure and wheel loads applied on the bridge bearing act only in the vertical direction.
The PCGE is fabricated according to the layup design by stacking several layers of selected materials over the bottom layer made of glass/epoxy fabric. The so-composed ceramic wafer is connected using two electrodes made of copper attached at its top and bottom (Figure 1). Curing is then performed as follows in an autoclave: the temperature is first increased gradually during 1 hour from room temperature to 177°C, that is then maintained for 2 hours before cooling to the room temperature. At the end of this process, the PCGE develops thermal residual stresses throughout its thickness because the different layers have different coefficients of thermal expansion. The designed d33-mode PCGE shown in Figure 2 presents six layers combining the piezoceramic material, glass/epoxy composite, and carbon/epoxy composite [8, 10].
2.2. Composition of the Piezo-Bearing
The widely used pot bearing is selected for the implementation of the BWIM system. As shown in Figure 3, the pot bearing is simply an elastomeric pad tightly confined in a steel cylinder. The load is transferred downward via a piston attached on the upper bearing plate to the elastomeric pad, which is the load-carrying medium with multidirectional rotational capacity. Note that this configuration allows the generation of a uniform compression inside the bearing when subjected to external loading. The PCGE with a size of 76 × 76 mm2 is installed between the pot plate and the elastomeric disc. Previous tests showed that this arrangement led the PCGE to produce higher voltage output due to the difference between the deformation of the elastomer and steel plate [14–16].
2.3. Performance Tests of the Piezo-Bearing
The durability and responsiveness to load of the proposed piezo-bearing were evaluated experimentally. First, the cyclic loading test was performed using the apparatus shown in Figure 4 to verify whether the d33-mode PCGE inserted in the pot bearing would last as long as the bearing itself. Note that, in the fatigue test, the PCGE was not inserted in the pot bearing and was protected only by a thin rubber pad, which made the PCGE exposed to harsher conditions that it would actually be. The PCGE was hit more than two million times, and the results showed that the PCGE kept its integrity under the low stress level. This indicated that the selected PCGE would fulfill reliably its measuring role with durability comparable to that of the bearing [17].
Dynamic tests were also performed on the piezo-bearing to verify the responsiveness and relationship between the load applied on the bearing and the corresponding output voltage of the PCGE inserted in the bearing. The tested bearing corresponds to the smallest commercially available pot bearing with a load-bearing capacity of 500 kN. Loading was applied using the 500 kN universal testing machine (UTM) of the KOCED Laboratory Facility at Keimyung University, Korea.
To provide various load cases and simulate as possible the load configurations of the bearing in a real bridge, permanent load was basically applied as the weight of the superstructure and live harmonic loading was additionally applied with different frequencies to simulate the vehicles running at different speeds on the superstructure. Considering the limitations of the UTM, the permanent load was set to 100 kN and 200 kN, and live loads with amplitudes of 30 kN, 60 kN, 90 kN, 120 kN, and 150 kN were applied at frequencies of 0.5 Hz, 1.0 Hz, and 3.0 Hz, which correspond to vehicles spaced by about 10 m running, respectively, at 18 km/, 36 km/h, and 108 km/h. Each load case was repeated three times to secure consistency of the measurements. A data acquisition system (NI cDAQ-9178) connected to a voltmeter (NI-9225) and load cell (SM-500L CAS, NI-9237) measured the output voltage and applied loads during the tests [18].
The results of the dynamic tests shown in Figure 5 for loading frequencies of 0.5 Hz, 1.0 Hz, and 3.0 Hz together with their regression lines confirm that the PCGE maintains a linear relationship between the applied load and its output voltage regardless of the permanent load sustained by the bearing. This indicates that the output voltage produced by the PCGE can sufficiently become an indicator of the vehicular load crossing the bridge.
It is also observed that the slope of the linear relations varies according to the speed of the vehicle. The problem is that it was practically impossible to perform the test at other frequencies due to the limitations in the testing equipment and the large loads required to simulate the permanent load and traffic load. Accordingly, as a first attempt and despite the poor number of experimental data, a fitting curve was computed using these 3 frequency cases to provide a relationship between the ratio of the load-to-output voltage data (slope of voltage-load lines) and the loading frequency under the assumption that the slopes of the lines relating the output voltage to the load in Figure 5 depend only on the frequency of the excitation (speed of the vehicle).
Considering the linear nature of the response of the PCGE to the applied load, it seems reasonable to apply a least-squares fit for the relation between this slope and the frequency. The equation for the linear model for the 3 points relating the exciting frequency (0.5, 1.0, and 3.0 Hz) and the slopes of the data in Figure 5 is as follows and plotted in Figure 6:where = axle load of the vehicle (kN); = output voltage measured by the bearing (V); and = exciting frequency (Hz).
Equation (1) of the least-square fitting line in Figure 6 can be rewritten as follows by expressing the frequency using the speed of the vehicle () and the span length of the bridge () and matching the units:where = span length of the bridge (m) and = speed of the vehicle passing through the bridge (km/h).
Equation (2) provides a means of determining the axle load () of the vehicle using the output voltage () of the PCGE when the speed of the vehicle is known.
3. On-Bridge Traffic Monitoring Using the Proposed BWIM System with Piezo-Bearing
To demonstrate the applicability of the proposed BWIM system, a numerical example is presented. The considered bridge is a single-span bridge with a length of 40 m and width of 10.98 m, of which slab is made of concrete and supported by 4 steel girders. The bridge supports 3 one-way traffic lanes, and the 3-dimensional model shown in Figure 7 is used for the application. It is assumed that each girder is supported at its ends by the proposed BWIM bearing, of which positions are indicated by the node numbers in Figure 7.
The considered vehicular load is the DB-24 truck load of the Korea Highway Bridge Design Code. It is a three-axle truck with the characteristics shown in Figure 8. For the numerical example, the distance between the middle and rear axles is set to 4200 mm. Moving load analysis is conducted for the truck running at speeds of 20 km/h and 80 km/h on Lane 2. It is assumed that the linear model of the piezo-bearing expressed in equation (2) is applicable. This means that the axle load can be identified once the span length of the bridge and the speed of the passing vehicle are known.
From a mechanics perspective, the time history of the load measured by the bearing will show a peak whenever one axle of the vehicle passes over the bearing. In Figures 9 and 10 presenting the time histories of the loads measured by the bearings, respectively, at the entrance (joint 336) and exit (joint 344) of the vehicle, the peaks corresponding to the access or exit of each axle of the DB-24 truck running at a speed of 20 km/h can be clearly distinguished in the graph provided by the bearing closest to the lane on which the vehicle travels.
For clarity, Figure 11 plots concurrently the time histories of joints 336 (entrance) and 344 (exit). In the time histories, the peaks indicated by 1, 2, and 3 correspond, respectively, to the access or exit of the front, middle, and rear axles of the 3-axle truck on the bridge. Applying the first-in/first-out (FIFO) principle, peak 1 occurs at 0.19 s (entrance side) and 7.2 s (exit side) in Figure 11. These occurrence times of peak 1 at the entrance and exit show that it took 7.01 s (=7.2 − 0.19) for the truck to cross the bridge (40 m), which gives a speed of 20.542 km/h. The same calculation for peaks 2 and 3 gives speeds of 20.574 km/h and 20.484 km/h, respectively. Compared to the running speed of 20 km/h considered in the analysis, the speed obtained using this peak-to-peak time lapse appears to estimate accurately the actual speed of the vehicle. Accordingly, the assumption that equation (2) is applicable for identifying the axle load once the speed of the vehicle is known appears to be reasonable.
Figures 12 and 13 present the same time histories for the DB-24 truck running at a speed of 80 km/h. Here also, the entrance and exit of each axle of the load-train can be clearly identified in the time history of the load measured by the bearing closest to the lane crossed by the vehicle (joint 336 at the entrance side and joint 344 at the exit side).
As done for the previous case, Figure 14 plots concurrently the time histories of joints 336 (entrance) and 344 (exit). In the time histories, the peaks indicated by 1, 2, and 3 correspond, respectively, to the access or exit of the front, middle, and rear axles of the 3-axle truck on the bridge. The occurrence times of peak 1 at the entrance and exit show that it took 1.67 s (= 1.81 − 0.14) for the truck to cross the bridge (40 m), which gives a speed of 86.227 km/h. The same calculation for peaks 2 and 3 gives speeds of 86.227 km/h and 85.207 km/h, respectively. Compared to the running speed of 80 km/h considered in the analysis, the speed obtained using this peak-to-peak time gap appears to approximate the actual speed of the vehicle with an error below 7.8%, which is lower than the error of 10% commonly allowed for traffic speedometers. In this case also, the assumption that equation (2) is applicable for identifying the axle load once the speed of the vehicle is known appears to be reasonable.
Tables 1 and 2 arrange the values of the loads measured by the piezo-bearings corresponding to the peaks together with their occurrence time in Figures 9–14. Considering the equilibrium of forces, the vehicle load applied on the bridge is distributed to the underlying bearings. Accordingly, the sum of the values measured by the piezo-bearings at the entrance or exit of the bridge and picked at the time at which the peaks are identified shall be added together to provide the actual cumulated load of the axles accessing or exiting the bridge. These sums () are also listed in the last column of Tables 1 and 2.
In Tables 1 and 2, the cases where all the axles are loaded on the bridge are at peak 3 at the entrance side and peak 1 at the exit side. The three axles of the truck are loaded on the bridge but are not located above the bearings at the same time. This means that the loads measured by the bearings are only indicative of the axle loads and do not give the values of the axle loads themselves. The positions of the loads at peaks 1, 2, and 3 at the exit side are shown in Figure 15.
(a)
(b)
(c)
Considering that the loads measured by the bearings correspond in fact to the support reactions oriented in the opposite direction, these measured loads can be used to calculate the axle loads by the influence caused by a series of concentrated loads using the influence lines (ILs) for the support reaction shown in Figure 16.
Once the speed of the vehicle is known, the time lapse between the peaks at the entrance side or exit side provides the distance between the axles. Based on the location of the loads for each peak at the exit side in Figure 15, the influence for the support reaction () at the exit side in Figure 16 can be used to calculate successively the loads of the rear, middle, and front axles as expressed in the following equations:where = identified value of the rear axle load of the truck and = sum of loads measured by joints 342, 343, 344, and 345 at occurrence of peak 3 at the exit side.where = identified value of the rear axle load of the truck; = sum of loads measured by joints 342, 343, 344, and 345 at occurrence of peak 2 at the exit side; = value of the rear axle load of the truck provided by equation (3); and = distance between middle and rear axles of the truck.where = identified value of the front axle load of the truck; = sum of loads measured by joints 342, 343, 344, and 345 at occurrence of peak 1 at the exit side; = value of the middle axle load of the truck provided by equation (4); = distance between front and middle axles of the truck; = value of the rear axle load of the truck provided by equation (3); and = distance between middle and rear axles of the truck.
Figure 17 shows the flowchart for the identification of the axle loads using the loads measured by the bearings.
Note that, in Figure 17, the identification of the number of peaks will give information on the type of vehicle passing on the bridge based on the standardized vehicle classification system. The vehicle classification system categorizes the vehicles into 13 classes from motorcycles, passenger cars, and buses to multiple-axle trucks according to the number of axles and the distance between consecutive axles.
Using the flowchart in Figure 17, Table 3 arranges the identified axle loads of the DB-24 truck running at 20 km/h and 80 km/h with the errors. For the calculation of the error, the estimated values are compared with the actual values of the DB-24 truck model (Figure 8) of the Korea Highway Bridge Design Code with the front axle load of 48 kN, middle axle load of 192 kN, and rear axle load of 192 kN, which gives a total load of 432 kN, and the distance between the axles is .
As mentioned above, the speed obtained using the peak-to-peak time gap approximates the actual speed of the vehicle with an error below 7.36% on the average, which is lower than the error of 10% commonly allowed for traffic speedometers. Recalling that the linear model in equation (2) relating the output voltage to the load was established using data measured at excitation frequencies of 0.5 Hz, 1.0 Hz, and 3.0 Hz (vehicles running, respectively, at 18 km/, 36 km/h, and 108 km/h), the linear model obtained by the least-squares method is sufficiently applicable considering that the speed limits in Korea are 60 km/h in urban areas, 80 km/h in highways, and 100 km/h and 110 km/h in expressways.
The error in the estimation of the distance between the axles appears to increase with the speed of the vehicle but remains below 7.92% for the considered cases. However, this error had poor effect on the estimation of the axle loads, of which error remained below 5.42%. The final total load of the truck could be estimated with an error below 2.43%. Since all the trucks are characterized by their number of axles, axle distance, and axle loads, the type of truck can thus be identified, and eventual overload can be captured.
Based upon the simplest theory of mechanics, the proposed BWIM system with built-in PCGE offers thus all the functions required for the conventional BWIM that are capturing and recording axle weights and distances and gross weights and velocities of vehicles regardless of the type, material, composition, and shape of the bridge.
4. Conclusions
This paper presented a new BWIM system overcoming the drawbacks of former systems. The proposed BWIM system appears in the form of a piezo-bearing in which the PCGE is embedded. To that goal, a PCGE was designed and fabricated to offer all the advantages of piezoceramics while being free from their material brittleness. A series of performance tests including fatigue test and dynamic test showed that the PCGE can be used to sustain the large load involved in the traffic monitoring in civil structures. Moving load analysis was performed on a full three-dimensional model of a bridge using a typical truck load to verify the applicability of the proposed BWIM system for the on-bridge traffic monitoring. The following conclusions can be drawn from the results of the moving load analysis:(1)A linear model for converting the measured output voltage of the PCGE into loading was proposed considering its linear nature. Further experiments shall be implemented to verify the adequacy of the model for a wider range of exciting frequencies.(2)The time histories of the loads measured by the piezo-bearings were used to distinguish the entrance or exit of the axle loads on the bridge. The passage of each axle load could be identified by the occurrence of peaks in the time histories. Based on the standardized vehicle classification system, the identification of the number of peaks can give information on the type of vehicle passing on the bridge and, in turn, allowed the estimation of the speed of the vehicle and distances between the axles.(3)An algorithm based on the concept of influence line for support reaction was established to calculate each axle load of the vehicle using the identified load peaks.(4)The simulated data could estimate the speed of the vehicle passing the bridge as well as the axle weights and distances and gross weights of the vehicle with good accuracy regardless of the type, material, composition, and shape of the bridge purely based on the theory of structural mechanics.
Data Availability
The data used to support the findings of this study are available from the corresponding author upon request.
Conflicts of Interest
The authors declare that they have no conflicts of interest.
Acknowledgments
The authors are thankful for funds provided by Korea Institute of Civil Engineering and Building Technology (KICT), Republic of Korea (Project No. 2018-0255). This work was also supported by the Energy Efficiency & Resources Core Technology Program of the Korea Institute of Energy Technology Evaluation and Planning (KETEP) and granted financial resource from the Ministry of Trade, Industry & Energy, Republic of Korea (No. 20142020103979).