# A Most-Unfavorable-Condition Method for Bridge-Damage Detection and Analysis Using PSP-InSAR

^{*}

## Abstract

**:**

_{3}and D

_{4}of Suzhou Bridge, and it was deduced that the main girder between piers D

_{3}and D

_{4}may have been damaged in July 2017. As a validation, taking the differential deformation value between piers D

_{3}and D

_{4}as an input, the maximum tensile stress, and the maximum compressive stress were calculated as 2.1 MPa and 8.4 MPa, respectively, through a finite element model. The tensile stress exceeded the design value of the concrete, further confirming the damage of the girder between piers D

_{3}and D

_{4}. Moreover, all results are consistent with the Suzhou Bridge damage information shown in existing records, which verify the accuracy and reliability of the proposed method.

## 1. Introduction

## 2. Materials and Methods

#### 2.1. Study Area and Materials Description

_{4}and D

_{5}. This makes it impossible to directly obtain the deformation data of pier positions.

#### 2.2. Method

#### 2.2.1. Three-Dimensional Deformation Model Construction

#### 2.2.2. The Most-Unfavorable-Condition Method

- 1.
- The most-unfavorable working-condition I:

- 2.
- The most-unfavorable working condition II:

_{1}) as a reference, the relative deformation values of PS points on other piers can be calculated. A new time-series working-conditions expression is:

_{1}to D

_{N}, pick out the maximum differential deformation values as:

#### 2.3. Test Design

## 3. Results

#### 3.1. 3D Deformation Model Construction

#### 3.1.1. Model Construction Method Comparison and Analysis

^{2}is the coefficient of determination. The lower the Max_Err and SSE values, the better the interpolation. The higher the R

^{2}value, the better the interpolation [22].

^{2}, which are smaller than the fitting results from quadratic polynomial surface fitting and thin-plate spline interpolation. The fitting coefficient of Green’s function-based interpolation is 0.98182, which is much closer to 1 than the other two methods. It proves that the fitting effect of the interpolation method based on Green’s function is the best.

#### 3.1.2. Three-Dimensional Deformation Model Construction

_{4}). Then, the time-series deformation values of PS points on the other four piers can be obtained from the time-series 3D deformation model. The time-series deformation surfaces of the five piers are shown in Figure 12.

_{4}was −14.5 mm/y.

#### 3.2. The Most-Unfavorable Working-Condition Analysis

- Condition I:

_{1}to D

_{5}are −48.9 mm, −45.7 mm, −51.5 mm, −76.2 mm, and −51.2 mm, respectively. Then, according to Equations (10) and (11), the maximum deformation rate values based on condition 91 are from condition 89. The maximum deformation rate values of all five piers are 4.05 mm/issue, 3.15 mm/issue, 2.25 mm/issue, 2.65 mm/issue and 2.5 mm/issue, respectively. Thus, under Equation (12), a new time-series working condition of PS points on piers can be built from conditions 89 to 91, as shown in Equation (16). The corresponding period is from 1 July to 2 August and it indicates that the Suzhou Bridge may have been damaged during this period.

- 2.
- Condition II:

_{3}are also listed in Equation (16). Then, the differential deformation of adjacent piers was calculated. According to Equation (14), in working condition 90, the maximum value of D

_{4}–D

_{3}was 25.73 mm, as shown below in Equation (17). The corresponding time of working condition 90 is 17 July 2017.

_{1}. It can be clearly seen from the figure that the maximum relative deformation occurs between piers D

_{3}and D

_{4}, as shown in Figure 14. The results indicate that the damage occured between piers D

_{3}and D

_{4}in July 2017. The damage results from this proposed method are consistent with the recorded damage information. Besides this, it can also be seen that the cause of the damage to Suzhou Bridge is the unusual differential deformation between piers D

_{3}and D

_{4}.

#### 3.3. Damage Detection Using Finite Element Model

_{1}to D

_{5}. The positions of piers are shown by black arrows in Figure 15. The maximum tensile stress is 2.1 MPa, and the maximum compressive stress is 8.4 MPa. In the finite element calculation results, the tensile stress of the fourth girder between piers D

_{3}and D

_{4}exceeds the design value of the concrete (the tensile stress design value of the D-ramp concrete of Suzhou Bridge is 1.8 MPa). In the results of the most-unfavorable-condition method, the main girder, caused by unusual differential deformation between pier D

_{4}and D

_{3}, produces a large tensile force in the middle. The results of the two methods are consistent.

## 4. Conclusions

_{3}and D

_{4}, and the occurrence time was 17 July 2017.

_{3}and D

_{4}), the proposed most-unfavorable-condition method for bridge-damage detection and analysis is verified accurately and reliably.

_{4}and D

_{5}. Although no damage has been found so far, the girder between piers D

_{4}and D

_{5}should be classified as a potential damage area and should be closely monitored.

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Conflicts of Interest

## References

- Lanari, R.; Reale, D.; Bonano, M.; Verde, S.; Muhammad, Y.; Fornaro, G.; Casu, F.; Manunta, M. Comment on “Pre-Collapse Space Geodetic Observations of Critical Infrastructure: The Morandi Bridge, Genoa, Italy” by Milillo et al. (2019). Remote Sens.
**2020**, 12, 4011. [Google Scholar] [CrossRef] - Milillo, P.; Giardina, G.; Perissin, D.; Milillo, G.; Coletta, A.; Terranova, C. Pre-Collapse Space Geodetic Observations of Critical Infrastructure: The Morandi Bridge, Genoa, Italy. Remote Sens.
**2019**, 11, 1403. [Google Scholar] [CrossRef] [Green Version] - Weissgerber, F.; Colin-Koeniguer, E.; Nicolas, J.-M.; Trouvé, N. 3D Monitoring of Buildings Using TerraSAR-X InSAR, DInSAR and PolSAR Capacities. Remote Sens.
**2017**, 9, 1010. [Google Scholar] [CrossRef] [Green Version] - The State-of-the-Practice of Modern Structural Health Monitoring for Bridges: A Comprehensive Review. Available online: http://www.mtri.org/bridgecondition/doc/State-of-PracticeSHMforBridges(July2010).pdf (accessed on 3 February 2021).
- Omar, T.; Nehdi, M.L. Remote sensing of concrete bridges decks using unmanned aerial vehicle infrared thermography. Automat. Constr.
**2017**, 83, 360–371. [Google Scholar] [CrossRef] - Liu, X.; Wang, P.; Lu, Z.; Gao, K.; Wang, H.; Jiao, C.; Zhang, X. Using terrestrial laser scanning (TLS), Ground-based microwave interferometry, and permanent scatterer interferometry synthetic aperture radar (PS-InSAR). Remote Sens.
**2019**, 11, 580. [Google Scholar] [CrossRef] [Green Version] - Alani, A.M.; Aboutalebi, M.; Kilic, G. Applications of ground penetrating radar (GPR) in bridge deck monitoring and assessment. J. Appl. Geophys.
**2013**, 97, 45–54. [Google Scholar] [CrossRef] - Meng, X.; Dodson, A.H.; Roberts, G.W. Detecting bridge dynamics with GPS and triaxial accelerometers. Eng. Struct.
**2007**, 29, 3178–3184. [Google Scholar] [CrossRef] - Zhang, B.C.; Ding, X.L.; Werner, C.L.; Tan, K.; Zhang, B.; Jiang, M.; Zhao, J.W.; Xu, Y.L. Dynamic Displacement Monitoring of Long-Span Bridges with a Microwave Radar Interferometer. ISPRS J. Photogramm. Remote Sens.
**2018**, 138, 252–264. [Google Scholar] [CrossRef] - Lee, J.; Lee, K.C.; Lee, S.; Lee, Y.J.; Sim, S.H. Long-term displacement measurement of bridges using a LiDAR system. Struct. Control Health Monit.
**2019**, 26, 2428. [Google Scholar] [CrossRef] - Sousa, J.J.; Bastos, L. Multi-temporal SAR interferometry reveals acceleration of bridge sinking before collapse. Nat. Hazards Earth Syst. Sci. Discuss.
**2013**, 13, 659–667. [Google Scholar] [CrossRef] - Sousa, J.J.; Hlavacova, I.; Bakon, M.; Lazecky, M.; Patricio, G.; Guimaraes, P.; Ruiz, A.M.; Bastos, L.; Sousa, A.; Bento, R. Potential of Multi-Temporal InSAR Techniques for Bridges and Dams Monitoring. Procedia Technol.
**2014**, 16, 834–841. [Google Scholar] [CrossRef] [Green Version] - Costantini, M.; Falco, S.; Malvarosa, F.; Minati, F. A new method for identification and analysis of persistent scatterers in series of SAR images. In Proceedings of the IEEE International Geoscience and Remote Sensing Symposium (IGARSS), Boston, MA, USA, 7–11 July 2008; Volume 2, pp. 449–452. [Google Scholar]
- Costantini, M.; Falco, S.; Malvarosa, F.; Minati, F.; Trillo, F.; Vecchioli, F. Persistent Scatterer Pair Interferometry: Approach and Application to COSMO-SkyMed SAR Data. IEEE J. Sel. Top. Appl. Earth Obs. Remote Sens.
**2014**, 7, 2869–2879. [Google Scholar] [CrossRef] - Kireeva, V.I.; Volokhov, E.M.; Lebedev, M.O. Assessment of differential subsidence harmful effects on large bridge structures during the underground space development. E3S Web Conf.
**2021**, 266, 03003. [Google Scholar] [CrossRef] - Abdelrahman, A.; Tawfik, M.; El-Saify, A. Investigation on the performance of bridge approach slab. MATEC Web Conf.
**2018**, 162, 04014. [Google Scholar] [CrossRef] [Green Version] - Gao, S.; Zhang, C. Construction of Fairing Surface with Polynomial Interpolation. J. Comput.-Aided Des. Comput. Graph.
**2008**, 6, 759–764. (In Chinese) [Google Scholar] - Cheng, Y.; Sun, H.Y. Thin Plate Spline Interpolation and Modeling of Height Anomaly of Large Area. Sci. Surv. Mapp.
**2008**, 4, 42–44. [Google Scholar] - Wessel, P. A general-purpose Green’s function-based interpolator. Comput. Geosci.
**2009**, 35, 1247–1254. [Google Scholar] [CrossRef] - Sandwell, D.T. Biharmonic Spline Interpolation of GEO-3 and SEASAT Altimeter Data. Geophys. Res. Lett.
**1987**, 14, 139–142. [Google Scholar] [CrossRef] [Green Version] - Solovyev, S.A. Application of the low-rank approximation technique in the Gauss elimination method for sparse linear systems. A.a.trofimuk Institute of Petroleum Geology & Geophysics. Numer. Methods Program.
**2014**, 7, 441–460. [Google Scholar] - Xiang, L.; Ding, Y.; Wei, Z.; Zhang, H.; Li, Z. Research on the Detection Method of Tunnel Surface Flatness Based on Point Cloud Data. Symmetry
**2021**, 13, 2239. [Google Scholar] [CrossRef] - Cai, Y.; Zhang, K.; Ye, Z.; Liu, C.; Lu, K.; Wang, L. Influence of Temperature on the Natural Vibration Characteristics of Simply Supported Reinforced Concrete Beam. Sensors
**2021**, 21, 4242. [Google Scholar] [CrossRef] [PubMed] - Cai, Z.; Wang, Z.; Lin, K.; Sun, Y.; Zhuo, W. Seismic Behavior of a Bridge with New Composite Tall Piers under Near-Fault Ground Motion Conditions. Appl. Sci.
**2020**, 10, 7377. [Google Scholar] [CrossRef]

**Figure 13.**Uneven deformation values of each pier column under the most-unfavorable working conditions.

Item | Value |
---|---|

Satellite | COSMO-SkyMed |

Imaging mode | Stripmap |

Ground resolution | 3 m × 3 m |

Incident angle | ~20.07° |

Polarization mode | HH |

Amount of data | 96 |

Time span | Sep. 2011~Nov. 2017 |

Dimension | $\mathbf{Green}\mathbf{Function}{\mathit{\phi}}_{\mathit{m}}\left(\mathit{Q}\right)$ |
---|---|

1 | ${\left|Q\right|}^{3}$ |

2 | ${\left|Q\right|}^{2}\left(\mathrm{ln}\left|Q\right|-1\right)$ |

3 | $\left|Q\right|$ |

4 | $\mathrm{ln}\left|Q\right|$ |

5 | ${\left|Q\right|}^{-1}$ |

6 | ${\left|Q\right|}^{-2}$ |

m | ${\left|Q\right|}^{4-m}$ |

Fitting Method | Max_Err/mm | SSE/mm^{2} | R^{2} |
---|---|---|---|

Quadratic polynomial surface interpolation | 11.296 | 4.237 | 0.0177 |

Thin plate splines interpolation | 6.3394 | 1.655 | 0.6163 |

Green’s function-based interpolation | 0.33 | 0.185 | 0.9182 |

No. | D1 | D2 | D3 | D4 | D5 | No. | D1 | D2 | D3 | D4 | D5 |
---|---|---|---|---|---|---|---|---|---|---|---|

1 | 0 | 0 | 0 | 0 | 0 | 49 | −21.2 | −14.3 | −13 | −26 | −9.3 |

2 | −1.3 | 0.1 | 2.68 | 1.28 | 1.3 | 50 | −18.0 | −14.5 | −12.9 | −24.5 | −9 |

3 | −2.1 | −1.3 | 1.88 | 1.88 | 0.8 | 51 | −23.0 | −14.1 | −13 | −25 | −10.2 |

4 | −1 | −1.5 | 2.18 | 1.48 | 1 | 52 | −22.8 | −16.7 | −13.5 | −26 | −10.9 |

5 | −3.24 | −1.9 | −1.65 | 0.98 | 0.7 | 53 | −23.9 | −16.3 | −15.2 | −27.1 | −8.8 |

6 | −2.98 | −2.3 | 2.62 | 2.58 | −1.1 | 54 | −23.0 | −16.1 | −14.3 | −28.1 | −8.8 |

7 | −4.56 | −1.9 | 1.12 | 2.78 | 0.7 | 55 | −22.7 | −14.7 | −19.2 | −29.5 | 0.6 |

8 | −4.8 | −4.6 | 1.42 | 2.78 | 1.2 | 56 | −19.0 | −14.7 | −16.8 | −27.5 | −10.7 |

9 | −5.0 | −4.6 | 2.32 | 1.98 | 1.5 | 57 | −27.5 | −16.5 | −21.5 | −28.3 | −9.7 |

10 | −4.4 | −2.4 | 1.52 | 1.68 | 1.2 | 58 | −24.8 | −15.2 | −18.8 | −28.4 | −10.5 |

11 | −3.9 | −2.2 | 4.22 | 3.37 | 3.1 | 59 | −25.0 | −16.2 | −19.2 | −32.8 | −13.3 |

12 | −7.2 | −2.5 | 1.32 | −1.63 | −0.9 | 60 | −27.4 | −19.1 | −22.9 | −35.8 | −13.1 |

13 | −7.2 | −2.9 | −2.98 | −4.43 | −8.5 | 61 | −26.1 | −18.6 | −23.6 | −33 | −13.2 |

14 | −0.8 | −2 | 2.67 | 1.67 | 6.9 | 62 | −20.0 | −21 | −27.5 | −37.6 | −13.5 |

15 | 5.7 | −3.2 | 9.61 | 11.07 | 9.7 | 63 | −28.5 | −22.3 | −26.9 | −37.2 | −13.4 |

16 | 1.1 | 2.5 | 2 | 2.27 | 7.2 | 64 | −28.8 | −21.1 | −25.8 | −35.8 | −12.2 |

17 | −3.7 | 3.6 | 1.6 | 3.37 | 7.4 | 65 | −29.7 | −20.1 | −29.5 | −36.7 | −14.9 |

18 | −7.3 | −5.1 | −2.1 | −5.83 | 4.9 | 66 | −30.9 | −23 | −27.5 | −38.5 | −13.8 |

19 | 1.5 | 0.9 | 2.9 | −4.43 | 6 | 67 | −28.2 | −20.9 | −27.7 | −37 | −14.7 |

20 | −7.1 | −4.6 | 0.2 | −10.1 | 4.8 | 68 | −29.0 | −23.3 | −27.4 | −39 | −14.8 |

21 | −5.9 | 0.6 | 2.1 | −14.1 | 3.1 | 69 | −29.9 | −21.1 | −28.2 | −39.5 | −14.8 |

22 | −6.0 | 2.6 | 3.1 | −16.5 | 4.6 | 70 | −28.7 | −19.6 | −26.3 | −39.2 | −16 |

23 | −8.2 | 3.1 | 2.2 | −16.1 | 3.6 | 71 | −30.6 | −19.7 | −28.5 | −42 | −16.3 |

24 | −6.3 | 0 | 2.2 | −16.3 | 3.7 | 72 | −32.1 | −21.3 | −29 | −46 | −17.9 |

24 | −5.4 | 3.8 | 3.3 | −13.7 | 4.7 | 73 | −32.5 | −19.2 | −28.2 | −46.3 | −19.5 |

26 | −8.3 | 4.1 | 2.5 | −17 | 4.6 | 74 | −26.0 | −20.2 | −27.5 | −46.6 | −22.4 |

27 | −2.3 | 3.7 | −7.2 | −15.6 | 3.8 | 75 | −32.0 | −19.4 | −29.6 | −49.5 | −24.1 |

28 | −13.2 | −6.7 | −7.8 | −17.5 | 7.4 | 76 | −28.0 | −17.8 | −27.9 | −50.69 | −23.7 |

29 | −14.0 | −6.2 | −8.4 | −20.9 | −1.9 | 77 | −26.0 | −21.8 | −32.2 | −55.1 | −24.2 |

30 | −12.1 | −6.2 | −6.5 | −18.4 | 4 | 78 | −28.0 | −21.3 | −35.5 | −53.7 | −24.6 |

31 | −10.8 | −4.7 | −7.6 | −17.6 | 4.1 | 79 | −25.0 | −22.8 | −36.1 | −48.7 | −24.9 |

32 | −11.8 | −9.3 | −9.9 | −20.6 | 2.7 | 80 | −26.0 | −33.6 | −44.1 | −57.1 | −35 |

33 | −13.0 | −8.2 | −8.6 | −19.5 | 3.2 | 81 | −25.9 | −33 | −43.8 | −56.7 | −36.6 |

34 | −13.5 | −10.3 | −10.4 | −19.9 | 2.3 | 82 | −26.1 | −33.9 | −42.8 | −60.1 | −37 |

35 | −13.3 | −11.9 | −8.7 | −22 | 3.3 | 83 | −35.7 | −34.3 | −41.9 | −60.4 | −37.7 |

36 | −13.5 | −11.5 | −8.2 | −20.5 | 2.8 | 84 | −35.2 | −35.1 | −42.7 | −61.7 | −37.8 |

37 | −10.9 | −11.9 | −7.6 | −16.7 | 2.7 | 85 | −36.5 | −33.9 | −44.1 | −62.9 | −38.9 |

38 | −12.7 | −9.5 | −7.5 | −19.8 | −5.4 | 86 | −36.8 | −33.8 | −43.6 | −63.8 | −39.3 |

39 | −18.0 | −15.1 | −12 | −22.3 | −6.8 | 87 | −38.0 | −34.5 | −44.8 | −68.7 | −45.5 |

40 | −13.9 | −9.6 | −9.5 | −23.8 | −5.5 | 88 | −43.0 | −39.2 | −47.2 | −71 | −47.1 |

41 | −22.6 | −17.5 | −14.7 | −22.9 | −6.3 | 89 | −40.8 | −39.4 | −47 | −70.9 | −46.2 |

42 | −21.1 | −13.7 | −10.9 | −21.4 | −5.9 | 90 | −45.7 | −43.5 | −49.8 | −75.53 | −50.3 |

43 | −20.7 | −15.1 | −12.5 | −23.4 | −6.4 | 91 | −48.9 | −45.7 | −51.5 | −76.2 | −51.2 |

44 | −21.1 | −13.9 | −9.5 | −22.9 | −5.3 | 92 | −44.6 | −40.6 | −48.5 | −70.2 | −47.6 |

45 | −18.7 | −9.5 | −8.3 | −23.5 | −3.4 | 93 | −41.4 | −36.5 | −44.3 | −67.9 | −44.6 |

46 | −19.7 | −8.6 | −4.8 | −20.1 | −3.1 | 94 | −38.1 | −32.8 | −42.2 | −65.3 | −42 |

47 | −20.4 | −12.4 | −11.3 | −23.3 | −7.8 | 95 | −35.7 | −30.7 | −41.6 | −66.4 | −41.9 |

48 | −21.0 | −14.9 | −13.1 | −23.2 | −9 | 96 | −35.3 | −31.6 | −40.8 | −66.4 | −40.2 |

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## Share and Cite

**MDPI and ACS Style**

Wang, R.; Zhang, J.; Liu, X.
A Most-Unfavorable-Condition Method for Bridge-Damage Detection and Analysis Using PSP-InSAR. *Remote Sens.* **2022**, *14*, 137.
https://doi.org/10.3390/rs14010137

**AMA Style**

Wang R, Zhang J, Liu X.
A Most-Unfavorable-Condition Method for Bridge-Damage Detection and Analysis Using PSP-InSAR. *Remote Sensing*. 2022; 14(1):137.
https://doi.org/10.3390/rs14010137

**Chicago/Turabian Style**

Wang, Runjie, Jiameng Zhang, and Xianglei Liu.
2022. "A Most-Unfavorable-Condition Method for Bridge-Damage Detection and Analysis Using PSP-InSAR" *Remote Sensing* 14, no. 1: 137.
https://doi.org/10.3390/rs14010137