Main Article Content

Petr Arleninov
Sergey Krylov


The study provides experimental and theoretical investigations of stress relaxation in concrete under preset constant deformation of specimens and proposes an approach to the mathematical determination of stress relaxation in concrete. In addition to mathematical modeling, parallel long-term tests were performed on concrete specimens of the same class under four different regimes: determination of concrete creep in compression (concrete prism specimens in spring installations) according to GOST 24544; determination of concrete relaxation in compression (concrete prism specimens in special installations, determination of concrete creep in bending (concrete specimens-beams in rack-type installations working in bending and loaded with gravity load) according to GOST 24544; determination of concrete relaxation in bending (concrete specimen beams, with applied initial deformation in the middle of the span Determination of stress drop was performed using electronic dynamometers built between the specimen and the point of load application. A new concept, "relaxation measure Rm", was proposed. This value is similar in meaning to the creep measure and characterizes the degree of stress reduction in time due to relaxation when loaded with a unit relative strain. The introduction of relaxation measure allows to simplify the relaxation equation and significantly simplifies its solution. According to the results of calculation by the proposed computational algorithms for determining the relaxation measure in comparison with the experimental data, a satisfactory convergence of the results is obtained Qualitative conclusions about the applicability of the methodology of SP 63.13330 for reducing the modulus of elasticity of concrete in creep and relaxation.


Download data is not yet available.

Article Details

How to Cite
Arleninov, P., & Krylov, S. (2024). MATHEMATICAL MODELING OF RELAXATION PROCESS IN CONCRETE. International Journal for Computational Civil and Structural Engineering, 20(2), 25-33.


Yonghui Huang, Jiyang Fu, Ronghui Wang, Rui Rao, Niujing Ma // Experimental study on creep behaviour of high-strength concrete filled steel tubular (HSCFST) columns. Case Studies in Construction Materials. Volume 20, July 2024, e02690. DOI:

Cole Shurbert-Hetzel, Dana Daneshvar, Agathe Robisson, Behrouz Shafei // Data-enabled comparison of six prediction models for concrete shrinkage and creep. Case Studies in Construction Materials. Volume 19, December 2023, e02406. DOI:

Francisco Dias, Luis Fernando, Paullo Muñoz, Deane Roehl // A numerical model for basic creep of concrete with aging and damage on beams. Applied Mathematical Modelling. Volume 121, September 2023, Pages 185-203. DOI:

Bazant, Z.P. // Stability of Elastic, Anelastic, and Disintegrating Structures, and Finite Strain Effects: an Overview. Comprehensive Structural Integrity, 2023, pp. V2-680-V2-710. DOI:

Bazant Z. P., Yunping Xi // Continuous retardation spectrum for solidification theory of concrete creep. Proceedings of Engineering Mechanics - ASCE, 121(2), 1995, pp 281-288. DOI:

Chiorino M.A., Carreira J. Factors Affecting Creep and Shrinkage of Hardened Concrete and Guide for Modelling. The Indian Concrete Journal, 2012.

Kolchunov, V.I., Kolchunov, V.I. // Deformation Models of Reinforced Concrete under Special Effects. Industrial and Civil Engineering. - 2018. - № 8. - С. 54-60. - EDN UWOAEP.

Travush V.I., Shakhramanyan Y.A., Kolotovichev A.M. // "Lakhta Centre": automated monitoring of deformations of load-bearing structures and foundations. Academia. Architecture and Construction. - 2018. - № 4. - С. 94-108. DOI 10.22337/2077-9038-2018-4-94-108. DOI:

Travush V.I., Arleninov P.D., Desyatkin M.A., Ivashchenko A.N., Kaprielov, S.S., Konin D.V., Krylov A.S., Krylov S.B., Chilin I.A. Sheinfeld A.V. // Bearing capacity of steel-reinforced concrete walls with sheet reinforcement for static loads. International Journal for Computational Civil and Structural Engineering, (2023)19(4), 166-181. DOI:

Chepurnenko A.S., Litvinov, S.V., Yazyev S.B. // Determination of Rheological Parameters of Concrete by Nonlinear Optimisation Methods. International Journal for Computational Civil and Structural Engineering, (2023)19(4), 147-154. DOI:

Rimshin V.I., Krishan A.L., Mukhametzyanov. A.I. // Construction of deformation diagram of uniaxial compressed concrete. Vest. MSCU № 6 2015. - С. 23-31. DOI:

Sanzharovsky R.S., Musabaev T.T. Elastoplastic deformation of reinforced concrete shells and slabs with cracks // Izv. of Higher Education Institutions. Ser. Structural and Architectural Engineering. 1996.- №5. P.Z-11.

Kaprielov S.S., Karpenko N.I., Sheinfeld A.V., Kuznetsov E.N. // About regulation of elasticity and creep modulus of high-strength concrete with modifier MB-50S. Concrete and Reinforced Concrete. - 2003. - № 6. - С. 8-12.

Kaprielov S.S., Karpenko N.I., Sheinfeld A.V., Kuznetsov E.N. // Influence of organomineral modifier MB-50S on structure and deformability of cement stone and high-strength concrete. Concrete and Reinforced Concrete. - 2003. - № 3. - С. 2-7.

Nesvetaev G.V., Kuzmenko T.G. // About correlation of tensile strength limits of cement concrete in bending and compression. Engineering bulletin of Don. - 2023. - № 8(104). - С. 304-316.

Bondarev B.A., Chernousov N.N., Chernousov R.N., Sturova V.A. // Investigation of strength properties of steel-fibreslag concrete under axial tension and compression with account of its age. Construction Materials. - 2017. - № 5. - С. 20-25.

Aleksandrovskiy S.V. // Creep and Shrinkage of Concrete and Reinforced Concrete Structures -M.: Stroyizdat, 1976. - 349 с.

Arutyunyan N.Kh. // Creep of aging materials. Creep of concrete. Mechanics in the USSR for 50 Years, vol.Z. MTT. -M.: Nauka, 1972. С.155-202.

Galustov K.Z. // Nonlinear Theory of Concrete Creep and Calculation of Reinforced Concrete Structures - Moscow: Izd. fiz. mat. litt., 2006. - С. 94-110.

Bondarenko V.M., Bondarenko S.V. // Engineering methods of nonlinear theory of reinforced concrete. -M.: Stroyizdat, 1982. - С. 100-106.

Recommendations on taking into account creep and shrinkage of concrete in the calculation of concrete and reinforced concrete structures. -M.: NIIZHB. 1988. - С. 5-15.

Tamrazyan A.G., Yesayan. S.G. // Mechanics of concrete creep - M.: MSCU, 2012. - 490 с.

Arleninov, P.D.; Krylov, S.B.; Kalmakova, P.S.; Donov, A.V. Experimental studies of concrete relaxation process in different modes. Vestnik SIC Stroitelstroy. 2023. № 1 (36). С. 86-98. DOI:

Similar Articles

You may also start an advanced similarity search for this article.