Nonlinear Calculation of the Reinforced Concrete Road Pavement Slabs of Highways on the Elastic Basis by the Zhemochkin Method

A rectangular reinforced concrete slab is considered taking into account its physical nonlinearity on a linearly elastic homogeneous base under the action of a vertical external load. The anisotropy and heterogeneity of the slab are due to the properties of reinforced concrete, as well as the formation of cracks from the action of an arbitrary load during operation. The nonlinear problem was solved by the Zhemochkin method using the iterative algorithm of the Ilyushin elastic solution method. The Ritz method (determining the deflections of a slab with a pinched normal) and the Boussinesq solution (determining the displacements of points on the surface of an elastic half-space) were used to determine the coefficients of the resolving equations of the Zhemochkin method. At the first iteration, the slab was calculated as linearly elastic, 

orthotropic, and homogeneous; at subsequent iterations, it was calculated as linearly elastic, anisotropic, and inhomogeneous at each Zhemochkin site. The deflections of the middle surface of the slab from a unit force were determined as a series according to the first five particular Clebsch solutions. Experimental and numerical researches have been carried out. The latter – with the help of the MATHEMATICA computer program. The results obtained showed that the proposed calculation method allows one to accurately describe the distribution of settlements and reactive stresses under the slab. Verification of the methodology for static nonlinear calculation of a rectangular reinforced concrete slab, taking into account its physical nonlinearity, was carried out by comparing the results of calculations of maximum settlement and average pressures under the slab, obtained using the proposed methodology, and the results obtained using the layer-by-layer summation method and modern software systems Lira and PLAXIS 3D.

1. . Semenyuk S. D., Kumashov R. V. (2020) Experimental Research of the Displacements of the Reinforced Concrete Slabs of Highways Pavement and Assessment of the Accuracy of the Calculation Method. Problemy Sovremennogo Betona i Zhelezobetona: Sb. Nauch. Tr. [Problems of Modern Concrete and Reinforced Concrete: Collection of Scientific Papers]. Minsk, Iss. 12, 185–208 (in Russian).

2. Solomin V. I., Shmatkov S. B. (1986) Calculation Methods and Optimal Design of Reinforced Concrete Foundation Structures. Moscow, Stroyizdat Publ. 206 (in Russian).

3. Gvozdev A. A. (1949) Calculation of the Bearing Capacity of Structures by the Method of Limit Equilibrium. Moscow, Stroyizdat Publ. 280 (in Russian).

4. Rzhanitsyn A. R. (1991) Structural Mechanics. Moscow, Vysshaya Shkola Publ. 439 (in Russian).

5. Rzhanitsyn A. R. (1983) Limit Equilibrium of Plates and Shells. Moscow, Nauka Publ., Main Office of Physical and Mathematical Literature. 288 (in Russian).

6. Klepikov S. N. (1970) Interaction of Structures with the Base. Kiev, State Committee for Construction of the USSR, Scientific Research Institute of Building Constructions (NIISK). 329 (in Russian).

7. Semenyuk S. D. (2003) Reinforced Concrete Spatial Foundations of Residential and Civil Buildings on an Unevenly Deformed Base. Mogilev, Belarusian-Russian University. 269 (in Russian).

8. Makovkin G. A., Likhacheva S. Yu. (2012) Application of FEM to Solving Problems of Solid Mechanics. Part 1. Novgorod, Nizhny Novgorod State University of Architecture and Civil Engineering (NNGASU). 71 (in Russian).

9. Lebedev A. V. (2012) Numerical Methods for Calculating Building Structures. Saint-Petersburg, Saint Petersburg University of Architecture and Civil Engineering (SPbGASU). 55 (in Russian).

10. Ilyin V. P., Karpov V. V., Maslennikov A. M. (1990) Numerical Methods for Solving Structural Mechanics Problems. Minsk, Vysheyshaya Shkola Publ. 346 (in Russian).

11. Zhemochkin B. N., Sinitsyn A. P. (1962) Practical Methods for Calculating Foundation Beams and Slabs on an Elastic Foundation. Moscow, Gosstroyizdat Publ. 240 (in Russian).

12. Piskunov N. S. (1985) Differential and Integral Calculus for Higher Technical Educational Institutions. Vol. 1. 13th еd. Moscow, Nauka Publ., Main Office of Physical and Mathematical Literature. 432 (in Russian).

13. Bosakov, S. V. (2002) Static Calculations of Slabs on an Elastic Foundation. Minsk, Belarusian National Technical University. 128 (in Russian).

14. SP [Construction Regulations] 5.03.01–2020. Concrete and Reinforced Concrete Structures. Minsk, Publishing House of Ministry of Architecture and Construction, 2020. 178 (in Russian).

15. Timoshenko S. P., Voynovsky-Kriger S. (1963) Plates and Shells. Moscow, Fizmat Publ. 536 (in Russian).

16. Boussinesq J. (1885) Applications des Patentiels a L’etude de L’equilibre et du Movement des Solides Elastiques. Paris, Gauthiers-Villars. 721 (in French).

17. Semenyuk S. D., Kumashov R. V. (2018) Reinforced Concrete Coating Plates of Highways on an Elastic Half-Space. International Journal for Computation Civil and Structural Engineering, 14 (2), 149–157. https://doi.org/10.22337/2587-9618-2018-14-2-149-157.

18. Kumashov R. V. (2018) Methodology and Results of Field Tests of a Reinforced Concrete Slab for Road Pavement 2PP30.18-30. Materialy, Oborudovanie i Resursosberegayushchie Tekhnologii: Materialy Mezhdunar. Nauch.-Tekhn. Konf. [Materials, Equipment and Resource-Saving Technologies: Proceedings of Scientific and Technical Conference]. Mogilev, Belarusian-Russian University, 298–299 (in Russian).

19. TKP [Technical Code of Common Practice] 45-5.01-67–2007 (02250). Slab Foundations. Design Rules. Minsk, Publishing House of Ministry of Architecture and Construction, 2018. 94 (in Russian