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The durability of concrete is a critical operational parameter that directly determines the service life of concrete structures. Achieving a concrete mixture with specified rheological and strength properties is a vital technological stage, as the quality of the initial material governs the load-bearing capacity of the final reinforced concrete elements. In the technological process, the transformation of concrete mixture components into a liquid non-Newtonian system with distinct rheological characteristics, followed by solidification into a structured composition, depends significantly on the variability of physico-mechanical, thermophysical, and structural-mechanical properties of both individual components and the overall mixture.
Developing comprehensive mathematical models that describe the entire technological cycle—from production to placement—poses a multifactorial challenge aimed at ensuring the design durability of construction structures. Particular emphasis is placed on modeling heat and mass transfer processes within heterogeneous concrete systems, as these non-stationary external influences critically affect the operational characteristics of the final material. Transport and hardening parameters heavily influence structural transformations within the cement stone, ultimately impacting strength and deformation properties. Effective resolution of this problem necessitates modern numerical modeling techniques that incorporate the rheological behavior of concrete mixtures and hydration kinetics.
The proposed mathematical and algorithmic framework underpins efforts to minimize concrete structure degradation by simulating rheological parameters during transportation and placement. A principal achievement is the creation of heat and mass transfer analysis algorithms that integrate predictive models with real-time monitoring data, laying a methodological foundation for future technological process control systems. The solutions further include optimization of logistical parameters under varying temperature and humidity conditions and the establishment of criteria to assess the structural homogeneity of concrete mixtures.
Developing comprehensive mathematical models that describe the entire technological cycle—from production to placement—poses a multifactorial challenge aimed at ensuring the design durability of construction structures. Particular emphasis is placed on modeling heat and mass transfer processes within heterogeneous concrete systems, as these non-stationary external influences critically affect the operational characteristics of the final material. Transport and hardening parameters heavily influence structural transformations within the cement stone, ultimately impacting strength and deformation properties. Effective resolution of this problem necessitates modern numerical modeling techniques that incorporate the rheological behavior of concrete mixtures and hydration kinetics.
The proposed mathematical and algorithmic framework underpins efforts to minimize concrete structure degradation by simulating rheological parameters during transportation and placement. A principal achievement is the creation of heat and mass transfer analysis algorithms that integrate predictive models with real-time monitoring data, laying a methodological foundation for future technological process control systems. The solutions further include optimization of logistical parameters under varying temperature and humidity conditions and the establishment of criteria to assess the structural homogeneity of concrete mixtures.
1. Vernigorova V.N., Sadenko S.M. On the Non-Stationary Nature of Physico-Chemical Processes in Concrete Mixture. Stroitel'nye Materialy. 2017. 1-2. P. 86 – 89. DOI: 10.31659/0585-430X-2017-745-1-2-86-89
2. Javid A.A.S., Ghoddousi P., Aghajani S., Naseri H., Pour S.H. Investigating the Effects of Mixing Time and Mixing Speed on Rheological Properties, Workability, and Mechanical Properties of Self-Consolidating Concretes. International Journal of Civil Engineering. 2020. 19. P. 339 – 355. DOI: 10.1007/s40999-020-00562-z
3. Ferraz D.F., Martho Ariane C.R., Burns E.G., Romano R., Rafael G.P. Effect of Mixing Procedure on the Rheological Properties and Hydration Kinetics of Portland Cement Paste. Rheology and Processing of Construction Materials. Springer. 2020. 23. P. 311 – 319. DOI: 10.1007/978-3-030-22566-7_36
4. De La Rosa A., Ruiz G., Masih V.W., Zanon R. Innovative high-technology concrete mix design method integrating rheological properties and Fracture Mechanics. Construction and Building Materials. 2025. 485. 139538. DOI: 10.1016/j.conbuildmat.2024.139538
5. Scrivener K.L., Juilland P., Monteiro P.J.M. Advances in understanding hydration of Portland cement. Cement and Concrete Research. 2015. 78 (A). P. 38 – 56. DOI: 10.1016/j.cemconres.2015.05.025
6. Juilland P., Gallucci E., Flatt R., Scrivener K. Dissolution theory to the induction period in alite hydration. Cement and Concrete Research. 2010. 40 (6). P. 831 – 844. DOI: 10.1016/j.cemconres.2010.01.012
7. Hu Q., Aboustait M., Kim T., Bullard J.W., Scherer G., Hanan J.C., Rose V., Winslow C., Houchin M., Ley M.T., Winarski R., Gelb J. Direct measurements of 3d structure, chemistry and mass density the induction period of C3S hydration. Cement and Concrete Research. 2016. 89. P. 14 – 26. DOI: 10.1016/j.cemconres.2016.07.008
8. Dikonda R.K., Mbonimpa M., Tikou B. Specific Mixing Energy of Cemented Paste Backfill, Part II: Influence on the Rheological and Mechanical Properties and Practical Applications. Minerals. 2021. 11. 1159. DOI: 10.3390/min11111159
9. Cazacliu B., Roquet N. Concrete mixing kinetics by means of power measurement. Cement and Concrete Research. 2009. 39 (3). P. 182 – 194. DOI: 10.1016/j.cemconres.2008.12.005
10. Brykov A.S. Hydration of Portland cement. St. Petersburg: SPbSTI(TU), 2008. 300 p.
11. Bullard J.W., Jennings H.M., Livingston R.A., Nonat A., Scherer G.W., Schweitzer J.S., Scrivener K.L., Thomas J.J. Mechanisms of cement hydration. Cement and Concrete Research. 2011. 41 (12). P. 1208 – 1223. DOI: 10.1016/j.cemconres.2010.09.011
12. Scrivener K., Ouzia A., Juilland P., Mohamed A.K. Advances in understanding cement hydration mechanism. Cement and Concrete Research. 2019. 124. 105823. DOI: 10.1016/j.cemconres.2019.105823
13. Shirzad K., Viney C. Revisiting time-dependent growth and nucleation rates in the Johnson–Mehl–Avrami–Kolmogorov equation. Royal Society Open Science. 2025. 12 (5). 241696. DOI: 10.1098/rsos.241696
14. Stromme K.O. On the application of the Avrami-Erofeev equation in non-isothermal reaction kinetics. Thermochimica Acta. 1986. 97. P. 363 – 368. DOI: 10.1016/0040-6031(86)87040-X
15. Shirzad K., Viney C. Revisiting time-dependent growth and nucleation rates in the Johnson–Mehl–Avrami–Kolmogorov equation. Royal Society Open Science. 2025. 12 (5). 241696. DOI: 10.1098/rsos.241696
16. Maekawa K., Ishida T., Kishi T. Multi-scale modeling of concrete performance: integrated material and structural mechanics. International Journal of Engineering and Technology (UAE). 2003. 1 (2). P. 91 – 126.
17. Thomas J., Biernacki J., Bullard J., Bishnoi S. Modeling and Simulation of Cement Hydration Kinetics and Microstructure Development. Cement and Concrete Research. 2011. 41 (12). P. 1257 – 1278. DOI: 10.1016/j.cemconres.2010.10.004
18. Jennings H., Johnson S. Simulation of Microstructure Development During the Hydration of a Cement Compound. Journal of the American Ceramic Society. 2005. 69 (11). P. 790 – 795. DOI: 10.1111/j.1151-2916.1986.tb07361.x
19. Le N.L.B., Stroeven M., Sluys L.J., He H., Guo Z. A novel numerical multi-component model for simulating hydration of cement. Computer Methods in Materials Science. 2013. 78. P. 12 – 21. DOI: 10.1016/j.commatsci.2013.05.021
20. Breugel K.V. Numerical simulation of hydration and microstructural development in hardening cement-based materials (I) theory. Cement and Concrete Research. 1995. 25 (2). P. 319 – 331. DOI: 10.1016/0008-8846(95)00017-8
21. Tian Y., Jin X., Jin N. Thermal cracking analysis of concrete with cement hydration model and equivalent age method. Computers and Concrete. 2013. 11 (4). P. 271 – 289. DOI: 10.12989/CAC.2013.11.4.271
22. Bishnoi S., Scrivener K.L. µic: A new platform for modelling the hydration of cements. Cement and Concrete Research. 2009. 39 (4). P. 266 – 274. DOI: 10.1016/j.cemconres.2008.12.002
23. Shashank B., Karen L. Sc. µic: A new platform for modelling the hydration of cements. Cement and Concrete Research. 2009. 39 (4). P. 266 – 274. DOI: 10.1016/j.cemconres.2008.12.002
24. Pang X., Meyer C. Modeling cement hydration by connecting a nucleation and growth mechanism with a diffusion mechanism. Part II: Portland cement paste hydration. Science and Engineering of Composite Materials. 2015. 22 (2). P. 175 – 186. DOI: 10.1515/secm-2013-0259
25. Thomas J.J., Biernacki J.J., Bullard J.W., Bishnoi S., Dolado J.S., Scherer G.W., Luttge A. Modeling and simulation of cement hydration kinetics and microstructure development. Cement and Concrete Research. 2011. 41 (12). P. 1257 – 1278. DOI: 10.1016/j.cemconres.2010.10.004
26. Teichmann A., Strahm B., Garrecht H., Blandini L. Effects of a two-stage mixing process on the characteristics of concrete: Part I - Hardened concrete characteristics. Results in Materials. 2024. 23. 100604. DOI: 10.1016/j.rinma.2024.100604
27. Zakharov B.A. Analysis of Technological Features of Centrifugal Separation of Fine Mineral Particles. Gornyy Informatsionno-Analiticheskiy Byulleten. 2009. 15 (12). P. 430 – 435.]
28. Wallevik J., Wallevik O. Analysis of shear rate inside a concrete truck mixer. Cement and Concrete Research. 2017. 95. P. 9 – 17. DOI: 10.1016/j.cemconres.2017.02.007
29. Emeljanova I., Anishchenko A., Dobrohodova O. Means to Enhance Operating Efficiency of the Concrete Mixer Trucks with the Purpose of Highly-Homogeneous Concrete Mix Preparation. International Journal of Engineering and Technology (UAE). 2018. 7 (3.2.) P. 102 – 106. DOI: 10.14419/ijet.v7i3.2.14383
30. Kaliganov A., Konovalov V., Chupshev A., Teryushkov V. Modelling the effect of continuous mixer operating parameters on mixture quality. E3S Web of Conferences. 2020. 164. 08009. DOI: 10.1051/e3sconf/202016408009
31. Hao E., Zhang Y., Li Z., Wang Z., Li J., Liu J. Research on the mechanism of pore structure on water transportation in cement-based materials. PLoS One. 2025. 20 (7). e0327659. DOI: 10.1371/journal.pone.0327659
32. Golovchenko I.V. Selection of Rational Methods for Preparation, Delivery and Placing of Concrete Mix in Conditions of High Ambient Temperatures. Vestnik Nauki i Obrazovaniya Severo-Zapada Rossii. 2016. 2 (4). P. 1 – 5.
33. Payr F., Schmid V. Optimizing Deliveries of Ready-Mixed Concrete. 2nd International Symposium on Logistics and Industrial Informatics, LINDI. 2009. P. 1 – 6. DOI: 10.1109/LINDI.2009.5258569
34. Liu L., Zhang Y., Wang K., Zhang J., Zhang H. Effect of time-dependence on the concrete transportation process. Powder Technology. 2024. 437. 119535. DOI: 10.1016/j.powtec.2024.119535
35. Fedosov S., Bakanov M. Evolution of Mathematical Models of Non-stationary Heat (Mass) Conductivity Processes in Bodies of Canonical Form. Theoretical Foundations of Chemical Engineering. 2025. 58 (6). P. 1359 – 1369. DOI: 10.1134/S0040579525600470
36. Fedosov S.V., Lapidus A.A., Narmaniya B.E., Ayzatullin M.M. Cauchy problem for modeling of unsteady mass transfer processes in an unbounded plate by the integral Laplace transform method. Construction Materials and Products. 2024. 7 (5). P. 4. DOI: 10.58224/2618-7183-2024-7-5-4
37. Pommersheim J.M., Clifton J.R. Mathematical modeling of tricalcium silicate hydration. II. Hydration sub-models and the effect of model parameters. Cement and Concrete Research. 1982. 12 (6). P. 765 – 772. DOI: 10.1016/0008-8846(82)90049-6
2. Javid A.A.S., Ghoddousi P., Aghajani S., Naseri H., Pour S.H. Investigating the Effects of Mixing Time and Mixing Speed on Rheological Properties, Workability, and Mechanical Properties of Self-Consolidating Concretes. International Journal of Civil Engineering. 2020. 19. P. 339 – 355. DOI: 10.1007/s40999-020-00562-z
3. Ferraz D.F., Martho Ariane C.R., Burns E.G., Romano R., Rafael G.P. Effect of Mixing Procedure on the Rheological Properties and Hydration Kinetics of Portland Cement Paste. Rheology and Processing of Construction Materials. Springer. 2020. 23. P. 311 – 319. DOI: 10.1007/978-3-030-22566-7_36
4. De La Rosa A., Ruiz G., Masih V.W., Zanon R. Innovative high-technology concrete mix design method integrating rheological properties and Fracture Mechanics. Construction and Building Materials. 2025. 485. 139538. DOI: 10.1016/j.conbuildmat.2024.139538
5. Scrivener K.L., Juilland P., Monteiro P.J.M. Advances in understanding hydration of Portland cement. Cement and Concrete Research. 2015. 78 (A). P. 38 – 56. DOI: 10.1016/j.cemconres.2015.05.025
6. Juilland P., Gallucci E., Flatt R., Scrivener K. Dissolution theory to the induction period in alite hydration. Cement and Concrete Research. 2010. 40 (6). P. 831 – 844. DOI: 10.1016/j.cemconres.2010.01.012
7. Hu Q., Aboustait M., Kim T., Bullard J.W., Scherer G., Hanan J.C., Rose V., Winslow C., Houchin M., Ley M.T., Winarski R., Gelb J. Direct measurements of 3d structure, chemistry and mass density the induction period of C3S hydration. Cement and Concrete Research. 2016. 89. P. 14 – 26. DOI: 10.1016/j.cemconres.2016.07.008
8. Dikonda R.K., Mbonimpa M., Tikou B. Specific Mixing Energy of Cemented Paste Backfill, Part II: Influence on the Rheological and Mechanical Properties and Practical Applications. Minerals. 2021. 11. 1159. DOI: 10.3390/min11111159
9. Cazacliu B., Roquet N. Concrete mixing kinetics by means of power measurement. Cement and Concrete Research. 2009. 39 (3). P. 182 – 194. DOI: 10.1016/j.cemconres.2008.12.005
10. Brykov A.S. Hydration of Portland cement. St. Petersburg: SPbSTI(TU), 2008. 300 p.
11. Bullard J.W., Jennings H.M., Livingston R.A., Nonat A., Scherer G.W., Schweitzer J.S., Scrivener K.L., Thomas J.J. Mechanisms of cement hydration. Cement and Concrete Research. 2011. 41 (12). P. 1208 – 1223. DOI: 10.1016/j.cemconres.2010.09.011
12. Scrivener K., Ouzia A., Juilland P., Mohamed A.K. Advances in understanding cement hydration mechanism. Cement and Concrete Research. 2019. 124. 105823. DOI: 10.1016/j.cemconres.2019.105823
13. Shirzad K., Viney C. Revisiting time-dependent growth and nucleation rates in the Johnson–Mehl–Avrami–Kolmogorov equation. Royal Society Open Science. 2025. 12 (5). 241696. DOI: 10.1098/rsos.241696
14. Stromme K.O. On the application of the Avrami-Erofeev equation in non-isothermal reaction kinetics. Thermochimica Acta. 1986. 97. P. 363 – 368. DOI: 10.1016/0040-6031(86)87040-X
15. Shirzad K., Viney C. Revisiting time-dependent growth and nucleation rates in the Johnson–Mehl–Avrami–Kolmogorov equation. Royal Society Open Science. 2025. 12 (5). 241696. DOI: 10.1098/rsos.241696
16. Maekawa K., Ishida T., Kishi T. Multi-scale modeling of concrete performance: integrated material and structural mechanics. International Journal of Engineering and Technology (UAE). 2003. 1 (2). P. 91 – 126.
17. Thomas J., Biernacki J., Bullard J., Bishnoi S. Modeling and Simulation of Cement Hydration Kinetics and Microstructure Development. Cement and Concrete Research. 2011. 41 (12). P. 1257 – 1278. DOI: 10.1016/j.cemconres.2010.10.004
18. Jennings H., Johnson S. Simulation of Microstructure Development During the Hydration of a Cement Compound. Journal of the American Ceramic Society. 2005. 69 (11). P. 790 – 795. DOI: 10.1111/j.1151-2916.1986.tb07361.x
19. Le N.L.B., Stroeven M., Sluys L.J., He H., Guo Z. A novel numerical multi-component model for simulating hydration of cement. Computer Methods in Materials Science. 2013. 78. P. 12 – 21. DOI: 10.1016/j.commatsci.2013.05.021
20. Breugel K.V. Numerical simulation of hydration and microstructural development in hardening cement-based materials (I) theory. Cement and Concrete Research. 1995. 25 (2). P. 319 – 331. DOI: 10.1016/0008-8846(95)00017-8
21. Tian Y., Jin X., Jin N. Thermal cracking analysis of concrete with cement hydration model and equivalent age method. Computers and Concrete. 2013. 11 (4). P. 271 – 289. DOI: 10.12989/CAC.2013.11.4.271
22. Bishnoi S., Scrivener K.L. µic: A new platform for modelling the hydration of cements. Cement and Concrete Research. 2009. 39 (4). P. 266 – 274. DOI: 10.1016/j.cemconres.2008.12.002
23. Shashank B., Karen L. Sc. µic: A new platform for modelling the hydration of cements. Cement and Concrete Research. 2009. 39 (4). P. 266 – 274. DOI: 10.1016/j.cemconres.2008.12.002
24. Pang X., Meyer C. Modeling cement hydration by connecting a nucleation and growth mechanism with a diffusion mechanism. Part II: Portland cement paste hydration. Science and Engineering of Composite Materials. 2015. 22 (2). P. 175 – 186. DOI: 10.1515/secm-2013-0259
25. Thomas J.J., Biernacki J.J., Bullard J.W., Bishnoi S., Dolado J.S., Scherer G.W., Luttge A. Modeling and simulation of cement hydration kinetics and microstructure development. Cement and Concrete Research. 2011. 41 (12). P. 1257 – 1278. DOI: 10.1016/j.cemconres.2010.10.004
26. Teichmann A., Strahm B., Garrecht H., Blandini L. Effects of a two-stage mixing process on the characteristics of concrete: Part I - Hardened concrete characteristics. Results in Materials. 2024. 23. 100604. DOI: 10.1016/j.rinma.2024.100604
27. Zakharov B.A. Analysis of Technological Features of Centrifugal Separation of Fine Mineral Particles. Gornyy Informatsionno-Analiticheskiy Byulleten. 2009. 15 (12). P. 430 – 435.]
28. Wallevik J., Wallevik O. Analysis of shear rate inside a concrete truck mixer. Cement and Concrete Research. 2017. 95. P. 9 – 17. DOI: 10.1016/j.cemconres.2017.02.007
29. Emeljanova I., Anishchenko A., Dobrohodova O. Means to Enhance Operating Efficiency of the Concrete Mixer Trucks with the Purpose of Highly-Homogeneous Concrete Mix Preparation. International Journal of Engineering and Technology (UAE). 2018. 7 (3.2.) P. 102 – 106. DOI: 10.14419/ijet.v7i3.2.14383
30. Kaliganov A., Konovalov V., Chupshev A., Teryushkov V. Modelling the effect of continuous mixer operating parameters on mixture quality. E3S Web of Conferences. 2020. 164. 08009. DOI: 10.1051/e3sconf/202016408009
31. Hao E., Zhang Y., Li Z., Wang Z., Li J., Liu J. Research on the mechanism of pore structure on water transportation in cement-based materials. PLoS One. 2025. 20 (7). e0327659. DOI: 10.1371/journal.pone.0327659
32. Golovchenko I.V. Selection of Rational Methods for Preparation, Delivery and Placing of Concrete Mix in Conditions of High Ambient Temperatures. Vestnik Nauki i Obrazovaniya Severo-Zapada Rossii. 2016. 2 (4). P. 1 – 5.
33. Payr F., Schmid V. Optimizing Deliveries of Ready-Mixed Concrete. 2nd International Symposium on Logistics and Industrial Informatics, LINDI. 2009. P. 1 – 6. DOI: 10.1109/LINDI.2009.5258569
34. Liu L., Zhang Y., Wang K., Zhang J., Zhang H. Effect of time-dependence on the concrete transportation process. Powder Technology. 2024. 437. 119535. DOI: 10.1016/j.powtec.2024.119535
35. Fedosov S., Bakanov M. Evolution of Mathematical Models of Non-stationary Heat (Mass) Conductivity Processes in Bodies of Canonical Form. Theoretical Foundations of Chemical Engineering. 2025. 58 (6). P. 1359 – 1369. DOI: 10.1134/S0040579525600470
36. Fedosov S.V., Lapidus A.A., Narmaniya B.E., Ayzatullin M.M. Cauchy problem for modeling of unsteady mass transfer processes in an unbounded plate by the integral Laplace transform method. Construction Materials and Products. 2024. 7 (5). P. 4. DOI: 10.58224/2618-7183-2024-7-5-4
37. Pommersheim J.M., Clifton J.R. Mathematical modeling of tricalcium silicate hydration. II. Hydration sub-models and the effect of model parameters. Cement and Concrete Research. 1982. 12 (6). P. 765 – 772. DOI: 10.1016/0008-8846(82)90049-6
Fedosov S.V., Bakanov M.O., Aleksandrova O.V. Heat and mass transfer in concrete mixtures during transpor-taion along the route «Manufacturer of liquid-phase solution – consumer of solid-phase concrete». Construction Materials and Products. 2025. 8 (6). 6. https://doi.org/10.58224/2618-7183-2025-8-6-6