SpringerLink
Log in

Structural safety evaluation using proof loads based on Bayesian inference

  • Original Paper
  • Published:
Journal of Civil Structural Health Monitoring Aims and scope Submit manuscript

Abstract

Structural safety evaluation is a critical issue in the realm of civil engineering. It involves factors such as uncertainties, external loads, and structural damage after long-term service. Presently, real-time safety evaluation of structural resistance remains challenging for real-world structures. This study proposes a resistance updating model for reinforced concrete beams based on Bayesian inference. The measured static loads of six experimental beams were taken as the proof loads for assessing real-time safety, and a stiffness degradation coefficient (SDC) was developed to embody resistance reduction. The SDC was continuously updated based on the deflection monitoring data of the beams under the proof loads. Specifically, the beam resistances were defined as the random distributions, and their initial distributions were calculated according to the material properties of the beams. Then, the corresponding SDCs of each proof load were estimated. Based on the initial resistance distributions and the real-time SDCs, the iterative updating of the resistance distributions was carried out using Bayesian inference. Subsequently, the future reliability indices of these beams were inferred using the JC method, which utilized the updated resistance distributions and the assumed future load distributions. Finally, a reliability index evolution model was established to evaluate the safety of the experimental beams. The analysis results showed that the proposed method can effectively estimate the resistance to provide an upper limit of future loading. The proposed method is sensitive to the proposed SDC but insensitive to the initial distributions of the resistance.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Subscribe and save

Springer+ Basic
EUR 32.99 /Month
  • Get 10 units per month
  • Download Article/Chapter or Ebook
  • 1 Unit = 1 Article or 1 Chapter
  • Cancel anytime
Subscribe now

Buy Now

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6
Fig. 7
Fig. 8
Fig. 9
Fig. 10
Fig. 11
Fig. 12
Fig. 13
Fig. 14
Fig. 15

Similar content being viewed by others

References

  1. Ma YF, Zhang JR, Wang L, Liu YM (2013) Probabilistic prediction with Bayesian updating for strength degradation of RC bridge beams. Struct Saf 44:102–109. https://doi.org/10.1016/j.strusafe.2013.07.006

    Article  Google Scholar 

  2. GB 50010-2010 (2010) Code for design of concrete structures. China Architecture & Building Press, Bei**g (in Chinese)

    Google Scholar 

  3. Monavari B, Chan THT, Nguyen A, Thambiratnam DP (2018) Structural deterioration detection using enhanced autoregressive residuals. Int J Struct Stab Dyn 18(12):1850160. https://doi.org/10.1142/S0219455418501602

    Article  Google Scholar 

  4. Al-Osta MA, Al-Sakkaf HA, Sharif AM, Ahmad S, Baluch MH (2018) Finite element modeling of corroded RC beams using cohesive surface bonding approach. Comput Concr 22(2):167–182. https://doi.org/10.12989/cac.2018.22.2.167

    Article  Google Scholar 

  5. Li HN, Cheng H, Wang DS (2018) Time-variant seismic performance of offshore RC bridge columns with uncertainty. Int J Struct Stab Dyn 18(12):1850149. https://doi.org/10.1142/S0219455418501493

    Article  Google Scholar 

  6. Dias-da-Costa D, Cervenka V, Graca-e-Costa R (2018) Model uncertainty in discrete and smeared crack prediction in RC beams under flexural loads. Eng Fract Mech 199:532–543. https://doi.org/10.1016/j.engfracmech.2018.06.006

    Article  Google Scholar 

  7. Sharma H, Hurlebaus S, Gardoni P (2012) Performance-based response evaluation of reinforced concrete columns subject to vehicle impact. Int J Impact Eng 43:52–62. https://doi.org/10.1016/j.ijimpeng.2011.11.007

    Article  Google Scholar 

  8. Allaix DL, Carbone VI, Mancini G (2015) Modelling uncertainties for the load bearing capacity of corroded simply supported RC beams. Struct Concr 16(3):333–341. https://doi.org/10.1002/suco.201500016

    Article  Google Scholar 

  9. Lu H, Zhang YM (2011) Reliability-based robust design for structural system with multiple failure modes. Mech Based Des Struct Mach 39(4):420–440. https://doi.org/10.1080/15397734.2011.560541

    Article  Google Scholar 

  10. Park C, Kim NH, Haftka RH (2015) The effect of ignoring dependence between failure modes on evaluating system reliability. Struct Multidiscip Optim 52(2):251–268. https://doi.org/10.1007/s00158-015-1239-7

    Article  Google Scholar 

  11. Hall WB (1988) Reliability of service-proven structures. J Struct Eng 114:608–624. https://doi.org/10.1061/(ASCE)0733-9445(1988)114:3(608)

    Article  Google Scholar 

  12. Faber MH, Val DV, Stewart MG (2000) Proof load testing for bridge assessment and upgrading. Eng Struct 22(12):1677–1689. https://doi.org/10.1016/S0141-0296(99)00111-X

    Article  Google Scholar 

  13. Stewart MG, Val DV (1999) Role of load history in reliability-based decision analysis of aging bridges. J Struct Eng 125(7):776–783. https://doi.org/10.1061/(ASCE)0733-9445(1999)125:7(776)

    Article  Google Scholar 

  14. Stewart MG (2001) Effect of construction and service loads on reliability of existing RC buildings. J Struct Eng 127(10):1232–1235. https://doi.org/10.1061/(ASCE)0733-9445(2001)127:10(1232)

    Article  Google Scholar 

  15. Brüske H, Thöns S (2019) Value of pre-construction proof loading information for structural design. Wind Energy 22(12):1716–1732. https://doi.org/10.1002/we.2398

    Article  Google Scholar 

  16. Adey B, Hajdin R, Bruhwiler E (2003) Risk-based approach to the determination of optimal interventions for bridges affected by multiple hazards. Eng Struct 25(7):903–912. https://doi.org/10.1016/S0141-0296(03)00024-5

    Article  Google Scholar 

  17. Li QW, Wang C (2015) Updating the assessment of resistance and reliability of existing aging bridges with prior service loads. J Struct Eng 141(12):4015072. https://doi.org/10.1061/(ASCE)ST.1943-541X.0001331

    Article  Google Scholar 

  18. Wang C, Li QW (2016) Simplified method for time-dependent reliability analysis of aging bridges subjected to nonstationary loads. Int J Reliab Qual Saf Eng 23(1):1650003. https://doi.org/10.1142/S0218539316500030

    Article  Google Scholar 

  19. Malerba PG, Sgambi L, Ielmini D, Gotti G (2017) Influence of corrosive phenomena on bearing capacity of RC and PC beams. Adv Concr Constr 5(2):117–143. https://doi.org/10.12989/acc.2017.5.2.117

    Article  Google Scholar 

  20. Meda A, Mostosi S, Rinaldi Z, Riva P (2014) Experimental evaluation of the corrosion influence on the cyclic behaviour of RC columns. Eng Struct 76:112–123. https://doi.org/10.1016/j.engstruct.2014.06.043

    Article  Google Scholar 

  21. Ma YF, Wang GD, Su XC, Wang L, Zhang JR (2018) Experimental and modelling of the flexural performance degradation of corroded RC beams under fatigue load. Constr Build Mater 191:994–1003. https://doi.org/10.1016/j.conbuildmat.2018.10.031

    Article  Google Scholar 

  22. Sheng J, Yin SP, Wang F, Yang Y (2017) Experimental study on the fatigue behaviour of RC beams strengthened with TRC after sustained load corrosion. Constr Build Mater 131:713–720. https://doi.org/10.1016/j.conbuildmat.2016.11.030

    Article  Google Scholar 

  23. Wang C, Li QW, Zou AM, Zhang L (2015) A realistic resistance deterioration model for time-dependent reliability analysis of aging bridges. J Zhejiang Univ-Sci A 16(7):513–524. https://doi.org/10.1631/jzus.A1500018

    Article  Google Scholar 

  24. Enright MP, Frangopol DM (1999) Condition prediction of deteriorating concrete bridges using Bayesian updating. J Struct Eng 125(10):1118–1125. https://doi.org/10.1061/(ASCE)0733-9445(1999)125:10(1118)

    Article  Google Scholar 

  25. Enright MP, Frangopol DM (1998) Service-life prediction of deteriorating concrete bridges. J Struct Eng 124(3):309–317. https://doi.org/10.1061/(ASCE)0733-9445(1998)124:3(309)

    Article  Google Scholar 

  26. Enright MP, Frangopol DM (1998) Probabilistic analysis of resistance degradation of reinforced concrete bridge beams under corrosion. Eng Struct 20(11):960–971. https://doi.org/10.1016/S0141-0296(97)00190-9

    Article  Google Scholar 

  27. Enright MP, Frangopol DM (1999) Reliability-based condition assessment of deteriorating concrete bridges considering load redistribution. Struct Saf 21(2):159–195. https://doi.org/10.1016/S0167-4730(99)00015-6

    Article  Google Scholar 

  28. Enright MP, Frangopol DM (1999) Maintenance planning for deteriorating concrete bridges. J Struct Eng 125(12):1407–1414. https://doi.org/10.1061/(ASCE)0733-9445(1999)125:12(1407)

    Article  Google Scholar 

  29. Mori Y, Ellingwood BR (1993) Reliability-based service-life assessment of aging concrete structures. J Struct Eng 119(5):1600–1621. https://doi.org/10.1061/(ASCE)0733-9445(1993)119:5(1600)

    Article  Google Scholar 

  30. Ellingwood BR, Mori Y (1993) Probabilistic methods for condition assessment and life prediction of concrete structures in nuclear-power-plants. Nucl Eng Des 142(2–3):155–166. https://doi.org/10.1016/0029-5493(93)90199-J

    Article  Google Scholar 

  31. Model Code (2001) Joint Committee of Structural Safety, JCSS; 2001. http://www.jcss.ethz.ch

  32. Rageh A, Linzell DG, Azam SE (2018) Automated, strain-based, output-only bridge damage detection. J Civ Struct Heal Monit 8(5):833–846. https://doi.org/10.1007/s13349-018-0311-6

    Article  Google Scholar 

  33. Seo J, Hu JW, Lee J (2016) Summary review of structural health monitoring applications for highway bridges. J Perform Constr Facil 30(4):04015072. https://doi.org/10.1061/(ASCE)CF.1943-5509.0000824

    Article  Google Scholar 

  34. Kalogiratou Z, Simos TE (2003) Newton-cotes formulae for long-time integration. J Comput Appl Math 158(1):75–82. https://doi.org/10.1016/S0377-0427(03)00479-5

    Article  MathSciNet  MATH  Google Scholar 

  35. Krauth W (1998) Introduction to Monte Carlo algorithms. Adv Comput Simul 501:1–35. https://doi.org/10.1007/BFb0105457

    Article  MATH  Google Scholar 

Download references

Acknowledgements

This research was funded by the National Natural Science Foundation of China (Grant Nos. 51578158 and 52178276) and also by the Qishan Scholar Program of Fuzhou University (Grant No. XRC-1688).

Author information

Authors and Affiliations

  1. School of Civil Engineering, Fuzhou University, Fuzhou, 350108, Fujian, People’s Republic of China

    Jia-li Tan & Sheng-en Fang

  2. National & Local Joint Engineering Research Center for Seismic and Disaster Informatization of Civil Engineering, Fuzhou University, Fuzhou, 350108, People’s Republic of China

    Sheng-en Fang

Authors
  1. Jia-li Tan
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Sheng-en Fang
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Sheng-en Fang.

Additional information

Publisher's Note

Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Tan, Jl., Fang, Se. Structural safety evaluation using proof loads based on Bayesian inference. J Civil Struct Health Monit 12, 15–27 (2022). https://doi.org/10.1007/s13349-021-00523-7

Download citation

  • Received:

  • Revised:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s13349-021-00523-7

Keywords

Search

Navigation