Сalculation of settlement of an extended slab foundation of finite stiffness based on computer modelling data

The paper presents a database for estimation the magnitude of the settlement of an extended slab foundation of finite stiffness in the initial phase of projecting. The offered solution uses only interpolation methods without involving powerful computing devices. The computer program FEA, which formalises the finite element method, was used to obtain the result. The maximum horizontal and vertical dimensions of the computational schemes were . The computational scheme consisted of 57 500 finite elements in the form of right isosceles triangles conjugated at 29 106 nodes. The width of the stiffness matrix of the linear equation system was 466. This made it possible to eliminate the influence of trivial boundary conditions on the results. 560 computational operations were performed. It corresponded to the number of possible combinations of numerical values of the variables calculated parameters adopted in computer modelling of process of the slab foundation settlement. As an upshot of the computations, the authors made a table of coefficients of approximating expressions for the curves constructed from the results of the calculated dependences of slab foundation settlement on the variable design parameters. The article provides a calculation of settlements of two extended slab foundations of different widths, using a constructed database and interpolation methods. The control calculation in the FEA showed the difference between the values of the control settlements and the values obtained using the proposed tables and the linear interpolation method for 13.45 and 22.08 %. Summing up the results, the offered database can be used for preliminary (estimation) calculations of extended slab foundations settlements.

1. Matvienko, J. O., Dyba, V. P., & Matvienko, M. P. (2020). Formula of the design resistance of soil for plate foundations. Construction and Geotechnics, 12(3), pp. 37-45. (In English). DOI 10.15593/2224-9826/2021.3.04.

2. Bartolomey, L. A., Bogomolova, O. A., Geidt, V. D., & Geidt, A. V. (2022). Computer simulation of rigid plate settlement on a homogeneous weight base. Construction and Geotechnics, 13(2), pp. 5-17. (In Russian). DOI 10.15593/2224-9826/2022.2.01.

3. Bartolomey, L. A., Bogomolova, O. A., Geidt, V. D., & Geidt, A. V. (2022). Computer simulation of the stamp sediment on a homogeneous base taking into account the rigidity of the foundation structure. Mekhanika gruntov v geotekhnike i fundamentostroenii : Materialy nauchno-tekhnicheskoy konferentsii, Novocherkassk, September, 28–30. Novocherkassk, OOO "Lik" Publ., pp. 144-138. (In Russian).

4. Skvortsov, K. D., & Osokin, A. I. (2020). Optimization of the formula of the design resistance of soil. Bulletin of civil engineers, (5(82)), pp. 117-122. (In Russian). DOI 10.23968/1999-5571-2020-17-5-117-122.

5. Bogomolov, A. N., Bogomolova, O. A., Vaingolts, A. I., & Yermakov, O. V. (2014). The comparison of the results of calculation of the bearing capacity of two-layer basis of deep strip foundations in different ways. Vestnik Permskogo gosudarstvennogo tekhnicheskogo universiteta. Stroitel'stvo i arkhitektura, (2), 106-116. (In Russian).

6. Van Baars, S. (2017). Numerical check of the Meyerhof bearing capacity equation for shallow foundations. Innovative Infrastructure Solutions, 3(1), pp. 1-13. (In English). DOI 10.1007/s41062-017-0116-1.

7. Pilyagin, A. V. (1998). Opredelenie raschetnogo soprotivleniya osnovaniy pri razlichnykh skhemakh zagruzheniya. Soil Mechanics and Foundation Engineering, (4-5), pp. 28-31. (In Russian).

8. Pilyagin, A. V. (2004). K voprosu opredeleniya raschetnogo soprotivleniya osnovaniy pri razlichnykh skhemakh zagruzheniya. Izvestiya Kazanskoy gosudarstvennoy arkhitekturno-stroitel'noy akademii, (1(2)), pp. 43-44. (In Russian).

9. Prandtl, L. (1920). About the hardness of plastic bodies [Über die Härte plastischer Körper]. News from the Royal society of scientists in Göttingen. Maths and physics class [Nachrichten von der Königl. Gesellschaft der Wissenschaflien zu Göttingen. Mathematisch-physikalische Klasse], (1), pp. 74-85. (In German).

10. Reissner, H. J. (1924). The Earth pressure problem [Zum Erddruckproblem]. Proceedings of the 1st International Congress for Applied Mechanics. Biezeno, C. B., & Burgers, J. M. (eds.). Delft, the Netherlands, pp. 295-311. (In German).

11. Gol'dshteyn, M. N., Kushner, S. G., & Shevchenko, M. I. (1977). Raschety osadok i prochnosti osnovaniy zdaniy i sooruzheniy. Kyiv, Budivel'nik Publ., 208 p. (In Russian).

12. Van Baars, S. (2016). Failure mechanisms and corresponding shape factors of shallow foundations. 4th Int. Conf. on New Developments in Soil Mechanics and Geotechnical Engineering, Nicosia, 2016. Nicosia, North Cyprus, Publ. Near East University, pp. 551-558. (In English).

13. Van Baars, S. (2016). The influence of superposition and eccentric loading on the bearing capacity of shallow foundations. Journal of Computations and Materials in Civil Engineering, 1(3), pp. 121-131. (In English).

14. Vesić, A. S. (1973). Analysis of ultimate loads of shallow foundations. Journal of the soil mechanics and foundations division, 99, pp. 45-71. (In English).

15. Vesić, A. S. (1975). Bearing capacity of shallow foundations. Foundation Engineering Handbook. H. F. Winterkorn, H. Y. Fan (eds.). New York, Cincinatti, Atlanta, Dallas, San Francisco, London, Toronto, Melbourne, Publ. Van Nostrand Reinhold Company, pp. 121-147. (In English).

16. Zhu, M., & Michalowski, R. L. (2005). Shape factors for limit loads on square and rectangular footings. Journal of geotechnical and geoenvironmental engineering, (131), pp. 223-231. DOI 10.1061/(ASCE)1090-0241(2005)131:2(223). (In English).

17. Bogomolov, A. N., Ushakov, A. N., Bogomolova, O. A., & Shiyan, S. I. (2010). Predlozhenija o podhode k raschetu osnovanij sooruzhenij. Jubilejnaja konferencija, posvjashhennaja 80-letiju kafedry mehaniki gruntov, osnovanij i fundamentov, 110-letiju so dnja rozhdenija N. A. Cytovicha, 100-letiju so dnja rozhdenija S. S. Vjalova, Moscow, September, 30 – October, 01. Moscow, Moscow State University of Civil Engineering Publ., pp. 147-151. (In Russian).

18. Bartolomey, L. A., Bogomolova, O. A., Geidt, V. D., & Geidt, A. V. (2023). Numerical determination of the value of the calculated resistance of the base under the stamp of final stiffness, taking into account the rigidity over the foundation structure. Construction and Geotechnics, 14(2), pp. 92-104. (In Russian). DOI 10.15593/2224-9826/2023.2.07.

19. Bogomolov, A. N., Bogomolova, O. A., Redin, A. V., & Ushakov, A. N. Svidetel'stvo o gosudarstvennoj registracii programmy dlja JeVM № 2015617889 Rossijskaja Federacija. FEA. Applied: 25.05.2015. Published: 23.07.201. (In Russian).

20. Zienkiewicz, O. C. (1971). The finite element method in engineering science. London, Publ. McGraw-Hill, 531 р. (In English).

21. Shmel'ter, Ja., Dacko, M., Dobrochinskij, S., & Vechorek, M. (1986). Metod konechnyh jelementov v statike sooruzhenij. Moscow, Stroyizdat Publ., 220 p. (In Russian).

22. Bartolomey, L. A., Bogomolova, O. A., Geidt, V. D., & Geidt, A. V. (2023). Assignment of the dimensions of the calculation schemes in computer simulation of the stress state of the plate foundation base based on the finite element method. Vestnik Volgogradskogo gosudarstvennogo arkhitekturno-stroitel'nogo universiteta. Seriya: Stroitel'stvo i arkhitektura, (2(91)), pp. 5-17. (In Russian).

23. Florin, V. A. (1959). Obshchie zavisimosti i napryazhennoe sostoyanie osnovaniy sooruzheniy, Vol. 1. Leningrad, Gosstroyizdat Publ., 357 p. (In Russian).

24. Bogomolov, A. N., Kalinovskiy, S. A., Bogomolova, O. A., & Prokopenko, A. V. (2013). Coefficient of lateral earth pressure as one of values that determine bearing capacity of entire base of strip foundation. Vestnik Volgogradskogo gosudarstvennogo arkhitekturno-stroitel'nogo universiteta. Seriya: Stroitel'stvo i arkhitektura, (31-2(50)), pp. 251-257. (In Russian).

25. Bogomolov, A. N., Vikhareva, O. A., & Shiyan, S. I. (2007). On the issue of minimal coefficient values of lateral earth pressure. Vestnik Volgogradskogo gosudarstvennogo arkhitekturno-stroitel'nogo universiteta. Seriya: Stroitel'stvo i arkhitektura, (7(26)), pp. 6-10. (In Russian).

26. Lyashenko, P. A., & Denisenko, V. V. (2019). Metod opredeleniya koeffitsienta bokovogo davleniya gruntov. Aktual'nye problemy stroitel'nogo i dorozhnogo kompleksov : Materialy mezhdunarodnoy nauchno-tekhnicheskoy konferentsii, posvyashchennoy 50-letiyu Instituta stroitel'stva i arkhitektury PGTU, Yoshkar-Ola, May, 15. Yoshkar-Ola : Volga state university of technology, pp. 85-90. (In Russian).

27. Rekomendatsii po metodam opredeleniya koeffitsientov bokovogo davleniya i poperechnogo rasshireniya glinistykh gruntov. Gersevanov Research Institute of Bases and Underground Structures (NIIOSP). Moscow, NIIOSP Publ., 30p. (In Russian).

28. Nuzhdin, L. V., Korobova, O. A., & Nuzhdin, M. L. (2014). Prakticheskiy metod rascheta osadok fundamentov s uchetom deformatsionnoy anizotropii gruntov osnovaniya. Vestnik Permskogo natsional'nogo issledovatel'skogo politekhnicheskogo universiteta. Stroitel'stvo i arkhitektura, (4), pp. 245-263. (In Russian).