Probabilistic criterion for assessing the robustness of reinforced concrete frames during fracture localization

Introduction. The problem of ensuring mechanical safety of buildings and structures under emergency impacts of force and environmental character is associated with the need to assess their robustness. The property of robustness of objects is manifested after the onset of an emergency situation and is closely related to the process of assessing the stability of a structural system to progressive collapse. Currently, there are proposals for robustness assessment in conceptual form and in the form of general analytical expressions that require adaptation to a specific structural system. This paper proposes a methodology and an example of the probabilistic indices of robustness calculation.

Materials and methods. The probabilistic index is calculated on the basis of the classical reliability theory with modification of the formula for the reliability index, which includes the values of random values of bending moments perceived by the section and moments caused by external load. The index is calculated for a failure pattern that does not involve the formation of a cable-stayed mechanism, i.e. the progressive failure is localized by the formation of several plastic hinges, taking into account the operation of the concrete in the limit state. A statistical test method is used to model random variables, considering experimental data on load variation and mechanical characteristics of materials.

Results. An example of two scenarios of accidental impacts on the monolithic frame of a multistory building, preventively designed with consideration of the possibility to taking accidental impacts, is considered. The scattering of ultimate bending moments is simulated, the reliability characteristics of elements, the probabilities of failure-free operation of the system with account of localization of progressive failure are calculated, the probabilistic survivability index for each emergency situation is calculated.

Conclusions. The methodology of quantitative assessment of survivability on the basis of probabilistic index, which includes the possibility of failure-free operation of a part of structural elements of the system and failure of individual elements in the zone of localization of emergency impact, is proposed. The operability of the proposed methodology on specific examples is shown, which will allow to estimate the robustness of both designed and reconstructed structural systems.

1. Tamrazyan A.G. Conceptual approaches to robustness assessment of building structures, buildings and facilities. Reinforced Concrete Structures. 2023; 3(3):62-74. DOI: 10.22227/2949-1622.2023.3.62-74. EDN IKRNWX. (rus.).

2. Kolchunov V.I., Iliushchenko T.A., Fedorova N.V., Savin S.Y., Tur V.V., Lizahub A.Al. Structural robustness : an analytical review. Building and Reconstruction. 2024; 3(113):31-71. DOI: 10.33979/2073-7416-2024-113-3-31-71. EDN FHLGWH. (rus.).

3. Tamrazyan A.G. Survivability as the degree of operability of structures in case of damage. Industrial and Civil Engineering. 2023; 7:22-28. DOI: 10.33622/0869-3019.2023.07.22-28. EDN DTAOGR. (rus.).

4. Kolchunov V.I., Savin S.Yu. Survivability criteria for reinforced concrete frame at loss of stability. Magazine of Civil Engineering. 2018; 4(80):73-80. DOI: 10.18720/MCE.80.7. EDN XYLDTF.

5. Lan X., Li Z., Fu F., Qian K. Robustness of steel braced frame to resist disproportionate collapse caused by corner column removal. Journal of Building Engineering. 2023; 69:106226. DOI: 10.1016/J.JOBE.2023.106226

6. Kolchunov V.I., Fedorova N.V., Savin S.Yu., Amelina M.A. Probabilistic model of reinforced concrete frame failure in case of loss of stability. Industrial and Civil Engineering. 2024; 10:4-11. DOI: 10.33622/0869-7019.2024.10.04-11. EDN KYFSCZ. (rus.).

7. Qu T., Zeng B., Zhou Z., Huang L., Chang D. Dynamic and uncertainty-based assessment of the progressive collapse probability of prestressed concrete frame structures with infill walls. Structures. 2024; 61:106105. DOI: 10.1016/J.ISTRUC.2024.106105

8. Ding L., Chen J., Caspeele R. Determination of dynamic collapse limit states using the energy-based method for multi-story RC frames subjected to column removal scenarios. Engineering Structures. 2024; 311:118170. DOI: 10.1016/J.ENGSTRUCT.2024.118170

9. Adam J.M., Parisi F., Sagaseta J., Lu X. Research and practice on progressive collapse and robustness of building structures in the 21st century. Engineering Structures. 2018; 173:122-149. DOI: 10.1016/j.engstruct.2018.06.082

10. Wang S., Cheng X., Li Y., Yang X., Zhang H., Guo R. et al. Assessing progressive collapse regions of reinforced concrete frame structures using Graph Convolutional Networks. Engineering Structures. 2025; 322:119076. DOI: 10.1016/J.ENGSTRUCT.2024.119076

11. Husain M., Yu J., Osman B.H., Ji J. Progressive collapse resistance of post-tensioned concrete beam-column assemblies under a middle column removal scenario. Journal of Building Engineering. 2021; 34:101945. DOI: 10.1016/j.jobe.2020.101945

12. Kasimov R.G., Skvortsova E.O. Progressive destruction and protection of stone buildings. Traditions and innovations in construction and architecture. Construction : collection of articles. 2019; 809-816. EDN JWROEE. (rus.).

13. Bessonov S.N., Solodov N.V. Survivability of spatial lattice structures made of “Kislovodsk” type pipes when calculating for progressive (avalanche) collapse. Science-intensive technologies and innovations (XXV scientific readings) : collection of reports of the International scientific and practical conference. 2023; 76-80. EDN PPBABI. (rus.).

14. Qian K., Weng Yu.H., Fu F., Deng X.F. Numerical evaluation of the reliability of using single-story substructures to study progressive collapse behaviour of multi-story RC frames. Journal of Building Engineering. 2021; 33:101636. DOI: 10.1016/j.jobe.2020.101636. EDN KMLTXW.

15. Praxedes C., Yuan X.-X. Robustness-oriented optimal design for reinforced concrete frames considering the large uncertainty of progressive collapse threats. Structural Safety. 2022; 94:102139. DOI: 10.1016/j.strusafe.2021.102139

16. Tamrazyan A.G., Tyagur D.V. On the influence of corrosion damage on the structural characteristics of bending reinforced concrete elements when determining survivability. Safety of the construction stock of Russia. Problems and solutions : proceedings of the International Academic Readings. 2023; 156-162. EDN UTPYXZ. (rus.).

17. Kabancev O.V., Mitrovic B. For the selection of characteristics of limit states of monolithic reinforced concrete systems for the mode of progressive drop. Proceedings of Higher Educational Institutions. Textile Industry Technology. 2018; 6(378):234-241. EDN TTXZYZ. (rus.).

18. Alekseytsev A.V., Antonov M.D. Resistance to progressive collapse of monolithic frames of buildings at localized damage of nodes from push-through. Vestnik MGSU [Monthly Journal on Construction and Architecture]. 2024; 19(9):1454-1468. DOI: 10.22227/1997-0935.2024.9.1454-1468. EDN KBUTDH. (rus.).

19. Serpik I.N., Kurchenko N.S., Alekseytsev A.V., Lagutina A.A. Analysis of the dynamic behavior of plane frames at emergency actions considering geometrical, material and structural nonlinearities. Industrial and Civil Engineering. 2012; 10:49-51. EDN PFGIFZ. (rus.).

20. Terekhov I.A., Trekin N.N., Kodysh E.N., Shmakov S.D. Ensuring the mechanical safety of reinforced concrete bearing structures at all stages of the life cycle. International Construction Congress. Science. Innovations. Objectives. Construction : collection of abstracts of reports. 2023; 48-50. DOI: 10.37538/2949-219Х-2023-48-50. EDN GGBZDR. (rus.).

21. Trekin N.N., Kodysh E.N., Terekhov I.A., Shmakov S.D. Classification of structures of industrial enterprises according to the possibility of protection from progressive collapse. Engineering and Construction Bulletin of the Caspian Region. 2024; 1(47):15-20. DOI: 10.52684/2312-3702-2024-47-1-15-20. EDN WPLTSL. (rus.).