Deformation of concrete under volumetric stress state

Introduction. The relevance of the development of analytical models describing nonlinear deformation of concrete under conditions of complex stress state is due to their importance both in theoretical and applied aspects. The key factors that should be taken into account when creating such models are the heterogeneity of concrete material properties, its structural change under loading, the occurrence of cracks, as well as phenomena associated with non-equilibrium processes occurring in concrete over a long period of time. The main objective of the study is to create an analytical model of the deformation diagram of concrete that allows an accurate description of the nonlinear behaviour of concrete under uniaxial, biaxial and triaxial loading conditions. This model should be versatile and easy to use. It is important that the model allows analysis and reflects as accurately as possible the results obtained from experiments with concrete of different strength classes.

Materials and methods. In the process of forming a model that shows the behaviour of concrete considering uniaxial stress state, it was decided to include a fourth order polynomial function in the work. Which is because it is suitable to perform an approximation that has a relationship between stresses and relative strains. After obtaining the model of concrete deformation under uniaxial stress, it was involved in the process of forming the constitutive relations for the volumetric stress state as a basis.

Results. An analytical nonlinear formula was formed to determine and show the existence of the dependence between stress and relative deformations of concrete under uniaxial loading conditions. To visualize this dependence, a continuous polynomial function is used, which describes the behaviour of concrete at any degree of deformation. It also contains a descending section of the diagram, which shows, in particular, the ultimate deformations. The given analytical dependence can be used as a basic component in establishing the characteristics and properties of concrete within the framework of the formulation of determining relations as a descriptive method to indicate the deformations of concrete under volumetric stress state.

Conclusions. The analytical relationship can be used in the form of key characteristics that define and describe the properties of concrete within the engagement of fundamental equations representing the behaviour of concrete under volumetric stress state. This method is quite accurate and will be an excellent solution when carrying out the design of reinforced concrete structures in the field of engineering.

1. Zhou W., Feng P., Lin H. Constitutive relations of coral aggregate concrete under uniaxial and triaxial compression. Construction and Building Materials. 2020; 251:118957. DOI: 10.1016/J.CONBUILDMAT.2020.118957

2. Tu H., Zhou H., Lu J., Gao Y., Shi L. Elastoplastic coupling analysis of high-strength concrete based on tests and the Mohr-Coulomb criterion. Construction and Building Materials. 2020; 255:119375. DOI: 10.1016/J.CONBUILDMAT.2020.119375

3. Zhao L., Zhang L., Mao J., Liu Z. An elastoplastic damage model of concrete under cyclic loading and its numerical implementation. Engineering Fracture Mechanics. 2022; 273:108714. DOI: 10.1016/J.ENGFRACMECH.2022.108714

4. Lu D., Su C., Zhou X., Wang G., Du X. A cohesion-friction combined hardening plastic model of concrete with the nonorthogonal flow rule: Theory and numerical implementation. Construction and Building Materials. 2022; 325:126586. DOI: 10.1016/J.CONBUILDMAT.2022.126586

5. Wang G., Lu D., Zhou X., Wu Y., Du X., Xiao Y. A stress-path-independent damage variable for concrete under multiaxial stress conditions. International Journal of Solids and Structures. 2020; 206:59-74. DOI: 10.1016/J.IJSOLSTR.2020.09.012

6. Lu D.X., Nguyen N.H.T., Bui H.H. A cohesive viscoelastic-elastoplastic-damage model for DEM and its applications to predict the rate- and time-dependent behaviour of asphalt concretes. International Journal of Plasticity. 2022; 157:103391. DOI: 10.1016/J.IJPLAS.2022.103391

7. Korsun V.I., Karpenko S.N., Makarenko S.Yu., Nedoresov A.V. Modern strength criteria for concrete under triaxial stress states. Building and Reconstruction. 2021; 5(97):16-30. DOI: 10.33979/2073-7416-2021-97-5-16-30. EDN HYNCLS. (rus.).

8. Panfilov D.A., Pischulev A.A., Gimadetdinov K.I. Review of diagrams of concrete deformation under compression in national and foreign concrete codes. Industrial and Civil Engineering. 2014; 3:80-84. EDN RYGLKB. (rus.).

9. Rimshin V.I., Krishan A.L., Mukhametzyanov A.I. Constructing a deformation diagram of uniaxially compressed concrete. Vestnik MGSU [Proceedings of Moscow State University of Civil Engineering]. 2015; 6:23-31. EDN TYCWVB. (rus.).

10. Murashkin V.G. About application of con-crete deformation models in reconstruction. Expert: Theory and Practice. 2022; 4(19):41-44. DOI: 10.51608/26867818_2022_4_41. EDN YODXVE. (rus.).

11. Treschev A.A., Zakharova I.A., Sudakova I.A. Selection of diagrams for deformation of composite materials and more. Expert: Theory and Practice. 2022; 2(17):81-90. DOI: 10.51608/26867818_2022_2_81. EDN DJPYVA. (rus.).

12. Berg O.L. Physical foundations of the theory of strength of concrete and reinforced concrete. Moscow, Stroyizdat, 1962; 96. (rus.).

13. Gvozdev A.A. On the redistribution of forces in statically indeterminate reinforced concrete conventional and prestressed structures. Moscow, Gosstroyizdat, 1955; 127. (rus.).

14. Kholmyanskiy M.M., Kogan Ye.A. On the stre-ngth and crack resistance of standardized concrete under non-uniform tension with control of deformations and forces. Limit states of concrete and reinforced concrete structures : materials of conferences and meetings on hydraulic engineering. 1982; 202-205. (rus.).

15. Bondarenko V.M. Some issues of nonlinear theory of reinforced concrete. Khar’kov, 1968; 324. (rus.).

16. Karpenko N.I., Yarmakovskiy V.N., Karpenko S.N., Kadiev D.Z. On the construction of the diagram of calculation method of rod structures under the action of low negative temperatures. News of Higher Educational Institutions. Construction. 2018; 6(714):5-17. EDN AJBMUG. (rus.).

17. Eryshev V.A., Toshin D.S. Concrete deformation diagram under repeated few loads. News of Higher Educational Institutions. Construction. 2005; 10(562):109-114. EDN PFAKVN. (rus.).

18. Bezgodov I.M., Levchenko P.Yu. To the question about the method of obtaining concrete deformation complete diagrams. Concrete Technologies. 2013; 10(87):34-36. EDN SYTIYL. (rus.).

19. Radaikin O. Comparative analysis of various diagrams of concrete deformation according to the criterion of energy consumption for deformation and destruction. Bulletin of BSTU named after V.G. Shukhov. 2019; 10:29-39. DOI: 10.34031/article_5db33945315bb4. 76965991. EDN MPQNBL. (rus.).

20. Selyaev V.P., Selyaev P.V., Alimov M.F., Sorokin E.V. Analytical description of concrete deformation diagrams for the calculation of plastic surfaces from nonlinearly deformable material. Building and Reconstruction. 2018; 3(77):22-30. EDN OVHMHN. (rus.).

21. Tamrazyan A.G., Chernik V.I. Stress-strain model for concrete confined by a discrete FRP-jackets. Industrial and Civil Engineering. 2020; 8:43-53. DOI: 10.33622/0869-7019.2020.08.43-53. EDN JSBMLZ. (rus.).

22. Adishchev V.V., Berezina E.V., Yershova N.V. Experimental testing of the method for transforming reference diagrams of concrete deformation under bending. News of Higher Educational Institutions. Construction. 2011; 8-9(632-633):118-124. EDN OZNFUR. (rus.).

23. Murashkin V., Murashkin G. Application of concrete deformation model for calculation of bearing capacity of reinforced concrete structures. MATEC Web of Conferences. 2018; 196:04008. DOI: 10.1051/matecconf/201819604008

24. Geniyev G.A., Kissyuk V.N., Tyupin G.A. Theory of Plasticity of Concrete and Reinforced Concrete. Moscow, Stroyizdat, 1974; 316. (rus.).

25. Karpenko N.I., Eryshev V.A., Rimshin V.I. The Limiting Values of Moments And Deformations Ratio in Strength Calculations Using Specified Material Diagrams. IOP Conference Series: Materials Science and Engineering. 2018; 463:032024. DOI: 10.1088/1757-899X/463/3/032024

26. Gvozdev A.A. Strength of concrete under biaxial stress state. Concrete and Reinforced Concrete. 1974; 7:10-11. (rus.).