Probabilistic modelling of a steel truss structure taking into account the corrosion degradation of the rod elements

Introduction. Long-term operation of steel trusses in aggressive environments is accompanied by corrosion-induced degradation of the rod elements, which leads to reduced load-bearing capacity and an increased probability of failure. Deterministic approaches to service-life assessment often produce overly conservative predictions and do not account for the stochastic nature of damage evolution. The aim of this study is to develop and verify a probabilistic methodology for assessing the condition and residual service life of a steel truss structure while accounting for spatially heterogeneous corrosion.

Materials and methods. A finite element model of a typical truss was implemented in ANSYS Mechanical (SHELL181 elements), with segmentation of profile walls to simulate local degradation. The corrosion process was represented by discrete damage states within a Markov framework; transitions between states were modeled using probabilistic laws and the Monte Carlo method. The algorithm was implemented as a specialized Python script integrated into the ANSYS computational workflow, with stepwise geometry updates, mesh regeneration, and recalculation of the stress-strain state.

Results. For a 70-year time horizon, the following values were obtained: a safety factor of 2.8, a failure probability below 10–4, and a residual service life exceeding 25 years. It is shown that accounting for the probabilistic nature of state transitions and the spatial variability of corrosion significantly affects stress distribution and reliability estimates compared with simplified deterministic schemes.

Conclusions. The proposed methodology provides a quantitatively substantiated forecast of degradation and can be applied to planning monitoring programs, repair scheduling, and safety assurance measures for steel truss systems.

1. Perel’muter A.V. Selected problems of reliability and safety of building structures. Moscow, ASV, 2007; 255. EDN QNMXBJ. (rus.).

2. Tamrazyan A.G., Matseevich T.A., Savin S.Yu. Assessment of the technical condition of load-bearing structures of buildings based on accident risk forecasting. Building and Reconstruction. 2024; 6(116):82-91. DOI: 10.33979/2073-7416-2024-116-6-82-91. EDN EQZYKS. (rus.).

3. Dormidontova T.V., Solkaryan N.G. Optimization of structural reliability. Ways to Improve Road Quality. 2015; 87-92. EDN TWPPXZ. (rus.).

4. Merkulov S.I. Development of the theory of structural safety of facilities under corrosion impacts. Bulletin of Belgorod State Technological University named after V.G. Shukhov. 2014; 3:44-46. EDN SGFDVL. (rus.).

5. Morozov V.I., Antsygin O.I., Savchenko A.P. Calculating and modeling the operation of structures with corrosion damages. Bulletin of Civil Engineers. 2009; 1(18):25-30. EDN JXOKEJ. (rus.).

6. Ovchinnikov I.I., Ovchinnikov I.G. Nonlinear mechanics of structures interacting with aggressive environments and physical fields : monograph. Ufa, Izd-vo UGNTU, 2024; 290. (rus.).

7. Stewart M.G., Al-Harthy A. Pitting corrosion and structural reliability of corroding RC structures: Experimental data and probabilistic analysis. Reliability Engineering & System Safety. 2008; 93(3):373-382. DOI: 10.1016/j.ress.2006.12.013

8. Chernin L., Val D.V. Prediction of corrosion-induced cover cracking in reinforced concrete structures. Construction and Building Materials. 2011; 25(4):1854-1869. DOI: 10.1016/j.conbuildmat.2010.11.074

9. Tamrazyan A.G., Matseevich T.A. Reliability optimization of structures taking into account uncertainties in design. Actual problems of the construction industry and education – 2022 : collection of reports of the Third National Scientific Conference. 2023; 50-54. EDN UPVVFT. (rus.).

10. Melchers R.E., Beck A.T. Structural Reliability Analysis and Prediction. 3rd ed. Wiley, 2017; 472. DOI: 10.1002/9781119266105

11. Val D.V., Chernin L., Stewart M.G. Experimental and numerical investigation of corrosion-induced cover cracking in reinforced concrete structures. Journal of Structural Engineering. 2009; 135(4):376-385. DOI: 10.1061/(asce)0733-9445(2009)135:4(376)

12. Biondini F., Vergani M. Deteriorating beam finite element for nonlinear analysis of concrete structures under corrosion. Structure and Infrastructure Engineering. 2015; 11(4):519-532. DOI: 10.1080/15732479.2014.951863

13. Vu K.A.T., Stewart M.G. Structural reliability of concrete bridges including improved chloride-induced corrosion models. Structural Safety. 2000; 22(4):313-333. DOI: 10.1016/s0167-4730(00)00018-7

14. Biondini F., Camnasio E., Palermo A. Lifetime seismic performance of concrete bridges exposed to corrosion. Structure and Infrastructure Engineering. 2014; 10(7):880-900. DOI: 10.1080/15732479.2012.761248

15. Soloveva A.A., Solovev S.A. A research into the development of models of random variables as part of the structural reliability analysis performed in the absence of some statistical information. Vestnik MGSU [Monthly Journal on Construction and Architecture]. 2021; 16(5):587-607. DOI: 10.22227/1997-0935.2021.5.587-607. EDN VJCFGH. (rus.).

16. Kumar R., Gardoni P., Sanchez‐Silva M. Effect of cumulative seismic damage and corrosion on the life-cycle cost of reinforced concrete bridges. Earthquake Engineering & Structural Dynamics. 2009; 38(7):887-905. DOI: 10.1002/eqe.873

17. Frangopol D.M., Kim S. Service life, reliability and maintenance of civil structures. Service Life Estimation and Extension of Civil Engineering Structures. 2011; 145-178. DOI: 10.1533/9780857090928.2.145

18. Kim S., Frangopol D.M. Inspection and monitoring planning for RC structures based on minimization of expected damage detection delay. Probabilistic Engineering Mechanics. 2011; 26(2):308-320. DOI: 10.1016/j.probengmech.2010.08.009. EDN OELPXH.

19. Darmawan M.S., Stewart M.G. Spatial time-dependent reliability analysis of corroding pretensioned prestressed concrete bridge girders. Structural Safety. 2007; 29(1):16-31. DOI: 10.1016/j.strusafe.2005.11.002

20. Mori Y., Ellingwood B.R. Reliability-based service-life assessment of aging concrete structures. Journal of Structural Engineering. 1993; 119(5):1600-1621. DOI: 10.1061/(asce)0733-9445(1993)119:5(1600)

21. Davydov A.N. Markov chain as a mathematical model of building structure working under load. Urban Construction and Architecture. 2017; 7(1):(26):4-8. DOI: 10.17673/Vestnik.2017.01.1. EDN YRDUAZ. (rus.).

22. Rodriguez J., Ortega L.M., Casal J. Load carrying capacity of concrete structures with corroded reinforcement. Construction and Building Materials. 1997; 11(4):239-248. DOI: 10.1016/s0950-0618(97)00043-3

23. Tuutti K. Corrosion of Steel in Concrete. Stockholm, Swedish Cement and Concrete Research Institute, 1982; 469.

24. Val D.V., Stewart M.G. Life-cycle cost analysis of reinforced concrete structures in marine environments. Structural Safety. 2003; 25(4):343-362. DOI: 10.1016/s0167-4730(03)00014-6

25. O’Connor A.J., Kenshel O. Experimental evaluation of the scale of fluctuation for spatial variability modeling of chloride-induced reinforced concrete corrosion. Journal of Bridge Engineering. 2013; 18(1):3-14. DOI: 10.1061/(asce)be.1943-5592.0000370

26. Straub D. Stochastic modeling of deterioration processes through dynamic Bayesian networks. Journal of Engineering Mechanics. 2009; 135(10):1089-1099. DOI: 10.1061/(asce)em.1943-7889.0000024

27. Kwon K., Frangopol D.M. Bridge fatigue reliability assessment using probability density functions of equivalent stress range based on field monitoring data. International Journal of Fatigue. 2010; 32(8):1221-1232. DOI: 10.1016/j.ijfatigue.2010.01.002

28. Matseevich T.A., Dankov S.A. Probabilistic Approach of State Transition Elements of Truss Structures at Corrosion. E3S Web of Conferences. 2024; 535:01003. DOI: 10.1051/e3sconf/202453501003

29. Matseevich T.A., Andreev I. F The finite element model of chloride diffusion in pre-stressed corroded reinforcement bars of reinforced concrete structures. Vestnik MGSU [Monthly Journal on Construction and Architecture]. 2022; 17(11):1462-1470. DOI: 10.22227/1997-0935.2022.11.1462-1470. EDN VXJBVQ. (rus.).