Studies of the influence of the number of storeys of reinforced concrete frames on the degradation of natural frequencies and character of earthquake damage

Introduction. The objectives of this work are to study the influence of degradation of the frequency parameters of reinforced concrete buildings under the action of seismic loading and to evaluate the nature of destruction depending on the number of storeys of the building itself, using numerical experiments in the LS-DYNA software package. To obtain natural frequencies and forms at certain times in a problem solved by an explicit integration scheme, solutions are sought using an implicit scheme.

Materials and methods. Five structures of different storeys are considered. The design schemes of the buildings use direct reinforcement of load-bearing elements. The Continuous Surface Cap Model (CSCM) is used to model the concrete. This material allows the accumulation of damage to be taken into account. The ideal elastic-plastic Prandtl model is used to model reinforcement. The reinforcement was modelled with rods and was directly immersed in concrete. To implement this, the Euler-Lagrange equation was used. The calculation was carried out on a rigid base, taking into account physical, geometric and structural non-linearities. The seismic impact was specified in the form of 2-component accelerograms normalized to 8 points on the MSK-64 scale.

Results. Various results of the study were obtained. Curves of change and degradation of natural frequencies for frames of different number of storeys are obtained. Damage accumulation curves for the entire framework were also obtained.

Conclusions. The analysis of the obtained results shows that during an earthquake with an intensity of 8 points, there is a significant (up to 30 %) reduction of frequencies of natural oscillations of the considered frames. The greatest amount of damage occurs at the stage of active phase of seismic impact. With the increase in the number of storeys, the intensity of degradation of natural frequencies increases, the rate of accumulation and the amount of damage increase.

1. Tosti F., Ferrante C. Using ground penetrating radar methods to investigate reinforced concrete structures. Surveys in Geophysics. 2020; 41(3):485-530. DOI: 10.1007/s10712-019-09565-5

2. Esfandiari A., Rahai A., Sanayei M., Bakhtiari-Nejad F. Model updating of a concrete beam with extensive distributed damage using experimental frequency response function. Journal of Bridge Engineering. 2016; 21(4). DOI: 10.1061/(asce)be.1943-5592.0000855

3. Mkrtychev O.V., Dzhinchvelashvili G.A., Busalova M.S. Calculation of a multi-storey monolithic concrete building on the earthquake in nonlinear dynamic formulation. Procedia Engineering. 2015 ; 111:545549. DOI: 10.1016/j.proeng.2015.07.039

4. Andreev M.I., Bulushev S.V., Dudareva M. Verification of the eccentrically compressed reinforced concrete column calculation model based on the results of a full-scale experimental study. MATEC Web of Conferences. 2018; 251:04013. DOI: 10.1051/matecconf/201825104013

5. Mkrtychev O.V., Busalova M.S., Dorozhinskiy V.B. Verification of the spar model of a reinforced concrete beam. MATEC Web of Conferences. 2017; 117:00124. DOI: 10.1051/matecconf/201711700124

6. Syed Z.I., Hejah E.S., Mohamed O.A. Modelling of dapped-end beams under dynamic loading. International Journal of Mechanical Engineering and Robotics Research. 2017; 242-247. DOI: 10.18178/ijmerr.6.3.242-247

7. Lee J., Zi G., Lee I., Jeong Y., Kim K., Kim W. Numerical simulation on concrete median barrier for reducing concrete fragment under harsh impact loading of a 25-ton truck. Journal of Engineering Materials and Technology. 2017; 139(2). DOI: 10.1115/1.4035766

8. Novozhilov Y.V., Dmitriev A.N., Mikhaluk D.S. Precise calibration of the continuous surface cap model for concrete simulation. Buildings. 2022; 12(5):636. DOI: 10.3390/buildings12050636

9. Gertsik S.M., Novozhilov Yu.V., Mikhaluk D.S. Numerical simulation of the dynamics of a reinforced concrete slab under an air shock wave. Computational Continuum Mechanics. 2020; 13(3):298-310. DOI: 10.7242/1999-6691/2020.13.3.24. EDN OPARMR. (rus.).

10. Chen H. An introduction to *CONSTRAINED_BEAM_IN_SOLID. FEA Information Engineering Journal. 2017; Q1(6):14-18.

11. Jiang H., Zhao J. Calibration of the continuous surface cap model for concrete. Finite Elements in Analysis and Design. 2015; 97:1-19. DOI: 10.1016/j.finel.2014.12.002

12. Sharath R., Arumugam D., Dhanasekaran B., Subash T.R. Numerical modeling of concrete response to high strain rate loadings. 11th European LS-DYNA Conference. 2017.

13. Pachocki L., Wilde K. Numerical simulation of the influence of the selected factors on the performance of a concrete road barrier H2/W5/B. MATEC Web of Conferences. 2018; 231:01014. DOI: 10.1051/matecconf/201823101014

14. Bulushev S.V., Dudareva M.S. Nonlinear models of reinforced concrete beam elements with the actual reinforcement. IOP Conference Series: Materials Science and Engineering. 2020; 753(3):032040. DOI: 10.1088/1757-899X/753/3/032040

15. Xu S., Wu P., Liu Z., Wu C. Calibration of CSCM model for numerical modeling of UHPCFTWST columns against monotonic lateral loading. Engineering Structures. 2021; 240:112396. DOI: 10.1016/j.engstruct.2021.112396

16. Yin X., Li Q., Xu X., Chen B., Guo K., Xu S. Investigation of continuous surface cap model (CSCM) for numerical simulation of strain-hardening fibre-reinforced cementitious composites against low-velocity impacts. Composite Structures. 2023; 304:116424. DOI: 10.1016/j.compstruct.2022.116424

17. Mkrtychev O.V., Sidorov D.S., Bulushev S.V. Comparative analysis of results from experimental and numerical studies on concrete strength. MATEC Web of Conferences. 2017; 117:00123. DOI: 10.1051/matecconf/201711700123

18. Durnovceva S.A. The synthesis method of seismic vibrations corresponding to a given family of response spectra. Bulletin of St. Petersburg University. Applied Mathematics. Computer science. Management processes. 2013; 2:112-120. (rus.).

19. Bulushev S.V. Comparison of the calculation results of structures for specified accelerograms by nonlinear static and nonlinear dynamic methods. Structural Mechanics of Engineering Constructions and Buildings. 2018; 14(5):369-378. DOI: 10.22363/1815-5235-2018-14-5-369-378. EDN YQJUZN. (rus.).

20. Rouabhi A., Urozhaev A.V. Research of non-stationary dynamic processes using wavelet analysis. Construction: Science and Education. 2012; 4:2. (rus.).