Structural Health Monitoring of a Brazilian Concrete Bridge for Estimating Specific Dynamic Responses
Abstract
:1. Introduction
2. Case Study
2.1. Brazilian Concrete Bridge
2.2. Vehicle Loadings
2.3. Structural Health Monitoring (SHM)
2.4. Definition of the Equivalent Beam
3. VBI System
3.1. Modified Suspended Rigid BEAM Model
3.1.1. Bridge Response
3.1.2. Vehicle Response
3.2. Sprung Mass Model
3.3. Additional Effects for VBI
3.3.1. Vehicle Vertical Accelerations
3.3.2. Pavement Irregularities
- (1)
- The contribution of the IM factors due to irregularities could be low. When considering three imperfections, in [70], it was shown as the total 2D irregularities are about ±4.0 mm. In [11], a more accurate analysis by considering 3D pavement irregularities was carried out, estimating an amplitude of about ±5.0 mm. In [38,39], it was shown that the irregularities affect the vertical bridge displacements little; in fact, the response obtained accounting for the irregularities is very similar to the analytical solutions without irregularities. However, for larger amplitude (e.g., > ±15.0 mm), the irregularity effects should not be neglected, as shown in [12]. In [34], road surface irregularities in the lateral directions can quite amplify the IM factor;
- (2)
- Most codes do not explicitly account for the irregularities; therefore, they are not considered in design practice for bridges. Codes provide equations and methods for new bridges where the pavement is considered of a very good quality and under standard maintenance (i.e., class A [72]). The irregularities are considered in, e.g., Spanish code [28] and European code [54] using a factor between 0.50 and 1.0, and in the literature [30], where is proposed a factor between 0.70 and 6.0. However, in [28,54], the irregularity contribution on the IM factors is very small, e.g., for the studied bridge, it is 0.42%.
3.4. IM Factor
4. Analyses and Results
4.1. Calibration and Some Structural Responses
4.2. Other Structural Responses
4.3. IM Factors
5. Conclusions
- The real test measurements of the Brazilian bridge for 8 months consisted of three phases: registration and elaboration of accelerations from T1 and T2 sensors and visualisation of collected data by using a 4G mobile phone each ~2.0 min to a predefined cloud [66]. Data were filtered and corrected to eliminate noise interferences for obtaining reliable responses. The two-axle 2C vehicle with v = 16.0 m/s was used for dynamic test. The monitoring provided a maximum acceleration and displacement of the bridge of about 8.0 m/s2 and 0.60 cm, respectively;
- The FEM and modified analytical models were carried out to simulate the bridge and the vehicle response. These models accounted for the geometrical and mechanical characteristics of the system. From these models, not only the bridge displacements were obtained but also the vehicle accelerations; for this, proposed equations provided more conservative vertical accelerations with values up to about three times the standard value of 0.315 m/s2. With respect to the registered value of 6.0 mm, other models provide a difference of about 1.0% (FEM), 20% (sprung model) and 5% (suspended model), indicating that the FEM and modified suspended models well estimate the bridge response;
- From the codes and literature, several IM factors were calculated for the studied bridge. The results show that a monitored IM factor (IM = 0.403) is 2.5 greater than IM from codes (i.e., 2.5 × 0.16). Moreover, the results show that a unique way to estimate IMs does not exist; therefore, more accurate research should be developed, and “in-situ” studies for bridges are necessary.
Author Contributions
Funding
Institutional Review Board Statement
Informed Consent Statement
Data Availability Statement
Acknowledgments
Conflicts of Interest
References
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Parameter | Value |
---|---|
Longitudinal length, L | 41.90 m |
Transversal length, D | 17.70 m |
Pile length | 15.0 m |
Pavement weight | 24.0 kN/m3 a |
Wheel-guard weight | 7.85 kN/m3 b |
Bridge mass, mb | 8500.95 kN |
Bridge frequency, fb | 2.421 Hz c |
Bridge damping ratio | 5.0% [49] |
Horizontal stiffness of one elastomeric pad | 24,000.0 kN/m d |
Concrete elastic modulus, E | 50.0 GPa d |
Concrete transversal modulus, G | 23.0 GPa |
Parameter | Value |
---|---|
Vehicle mass, mv | 15,000.0 kg a |
Front suspended mass, mv,1 | 772.0 kg a |
Rear suspended mass, mv,2 | 1066.0 kg a |
Length d11 | 0.50 m [56] |
Length d | 4.50 m [56] |
Length d22 | 2.0 m [56] |
Front suspended frequency, fv,1 | 3.71 Hz b |
Rear suspended frequency, fv,2 | 6.86 Hz b |
Front suspended stiffness, k1 | 580.0 kN/m [35] |
Rear suspended stiffness, k2 | 1180.0 kN/m [35] |
Vehicle frequency, fv | 2.41 Hz c |
Mass moment of inertia, Jc | ~25,000.0 kg m2 |
Equivalent Parameter | Value |
---|---|
Concrete elastic modulus × inertia, (EI)eq | 1.94 × (50.0 GPa × 0.7255 m4) = 70.37 GN m2 a |
Mass, mb,eq | 6714.34 kg/m b |
Longitudinal length, Leq | 42.0 m c |
Frequency, fb,eq | 2.40 Hz c |
Reference | Specification for IM Factors |
---|---|
Codes and manuals | |
American (AASHTO) [47] | It amplifies static live load stresses. It is estimated by L. IM < 0.30–0.33 a |
American (AREA) [5] | It is estimated by L and D |
Brazilian (NBR) [49] | It amplifies static vertical moving loads. It is estimated by L. IM < 0.35 b |
English (BS5400) [48] | It amplifies static bending moments and shears. It is estimated by L. IM < 1.0 |
Italian (NTC) [50] | It amplifies static stresses and displacements. It is estimated by L. IM < 1.0 |
Portuguese (RSA) [51] | It amplifies static loads and transversal forces. It is estimated by L. IM < 1.0 |
Spanish (IAPF) [55] | It amplifies static forces. It is estimated by L, v, fb |
European (Eurocode) [54] | It amplifies static forces and moments. It is estimated by L, v, fb |
Canadian (CSA) [41] | It amplifies static live loads. It is estimated by fb and the number of axles. IM < 0.40 |
Published studies | |
Deng and Cai (2010) [30] | It is estimated by L and pavement irregularities. IM < 0.33 a |
Rodrigues et al. (2013) [56] | It is estimated by L, v, fb |
Carneiro et al. (2021) [16] | It is estimated by L, v, fb |
This study | It was defined by “in-situ” experimental tests, FEM and analytic VBI models |
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Zacchei, E.; Lyra, P.H.C.; Lage, G.E.; Antonine, E.; Soares, A.B., Jr.; Caruso, N.C.; de Assis, C.S. Structural Health Monitoring of a Brazilian Concrete Bridge for Estimating Specific Dynamic Responses. Buildings 2022, 12, 785. https://doi.org/10.3390/buildings12060785
Zacchei E, Lyra PHC, Lage GE, Antonine E, Soares AB Jr., Caruso NC, de Assis CS. Structural Health Monitoring of a Brazilian Concrete Bridge for Estimating Specific Dynamic Responses. Buildings. 2022; 12(6):785. https://doi.org/10.3390/buildings12060785
Chicago/Turabian StyleZacchei, Enrico, Pedro H. C. Lyra, Gabriel E. Lage, Epaminondas Antonine, Airton B. Soares, Jr., Natalia C. Caruso, and Cassia S. de Assis. 2022. "Structural Health Monitoring of a Brazilian Concrete Bridge for Estimating Specific Dynamic Responses" Buildings 12, no. 6: 785. https://doi.org/10.3390/buildings12060785
APA StyleZacchei, E., Lyra, P. H. C., Lage, G. E., Antonine, E., Soares, A. B., Jr., Caruso, N. C., & de Assis, C. S. (2022). Structural Health Monitoring of a Brazilian Concrete Bridge for Estimating Specific Dynamic Responses. Buildings, 12(6), 785. https://doi.org/10.3390/buildings12060785