Analytical and Numerical Methods for Determining the Stressed State of a Soil Massif in Solving a Plane Problem

In the conditions of modern realities, when foreign software settlement systems may be completely inaccessible, there is a need for domestic modern products. It is worth noting the importance of improving the quality of educational and scientific material in matters of numerical methods in relation to engineering and construction specialties. There are a number of fundamental works that outline the basic mathematical principles and implementation of calculations of the stressed deformable state of the soil in various cases. Often, information in the literature may contain typographical errors or be incompletely disclosed, so it is especially important to present the material in detail and with examples to ensure repeatability of the results by readers. In the article describes in detail the method of numerical calculation of the elastic problem of the soil medium using the finite element method. The chosen method makes it possible to take into account the interaction of various physical characteristics of materials. Particular attention is paid to the procedural part, namely the generation of local stiffness matrices and right-hand side vectors, and the peculiarities of their calculation. As a result, a comparison is made of the values of normal and shear stresses based on the results of numerical simulation and rigorous analytical expressions. To compare the results, a ready-made closed source Plaxis software package was chosen, which does not allow to copy it, but allows, according to the selected criteria, to determine the accuracy of the solver created by the FEM author. Verification of the calculation results in Mathcad, obtained by the author, is confirmed by the convergence of the nature of stress isofields, which were also obtained in the Plaxis calculation complex. In the conclusions, the author identified shortcomings and proposed ways to solve them.

V.M. POLUNIN, Candidate of Sciences (Engineering) (This email address is being protected from spambots. You need JavaScript enabled to view it.)

St. Petersburg State University of Architecture and Civil Engineering (4, 2nd Krasnoarmeyskaya Street, St. Petersburg, 190005, Russian Federation)

1. Фадеев А.Б. Метод конечных элементов в геомеханике. М.: Недра, 1987. 359 с.
1. Fadeev A.B. Metod konechnyh elementov v geomekhanike. [Finite element method in geomechanics]. Moscow: Nedra. 1987. 359 p.
2. Klaus-Jürgen Bathe Edward L. Wilson. Numerical methods in finite element analysis. Prentice-Hall. 1976. 800 p.
3. Парамонов В.Н. Метод конечных элементов при решении нелинейных задач геотехники. СПб.: ГК «Геореконструкция», 2012. 263 с.
3. Paramonov V.N. Metod konechnyh elementov pri reshenii nelinejnyh zadach geotekhniki. [Finite element method for solving non-linear geotechnical problems]. Saint Petersburg: Georekonstrukciya. 2012. 263 p.
4. He Z., Su B., Yu-long L. Seepage analysis based on weak galerkin finite element method. Yantu Gongcheng Xuebao. Chinese Journal of Geotechnical Engineering. 2022.
5. Галлагер Р. Метод конечных элементов. Основы. М.: Мир, 1984. 428 с.
5. Gallager R. Metod konechnyh elementov. Osnovy. [Finite Element Method. Basics]. Moscow: Mir. 1984. 428 p.
6. Нестеров И.В., Мерзлякова А.Д. Особенности формирования адаптивных сеток МКЭ для решения задач геотехники // Механика композитных материалов и конструкций, сложных и гетерогенных сред: Сборник трудов 11-й Всероссийской научной конференции. М., 2021. С. 356–361.
6. Nesterov I.V., Merzlyakova A.D. Features of the formation of adaptive FEM grids for solving geotechnical problems. Mekhanika kompozitnyh materialov i konstrukcij, slozhnyh i geterogennyh sred. Sbornik trudov 11th Vserossijskoj nauchnoj konferencii. Moscow. 2021, pp. 356–361. (In Russian).
7. Bin W. Phil V., Hicks M., Zhen C. Development of an implicit material point method for geotechnical applications. Computers and Geotechnics. 2016, pp. 159–167.
8. Сахно И.Г. Численное моделирование геомеханических процессов с учетом их нелинейности // Проблемы горного давления. Донецкий национальный технический университет. 2012. № 1. С. 57–67.
8. Sahno I.G. Numerical modeling of geomechanical processes taking into account their nonlinearity. Problemy gornogo davleniya. Doneckij nacional’nyj tekhnicheskij universitet. 2012. No. 1, pp. 57–67. (In Russian).
9. Loseva E., Osokin A., Mironov D., Dyakonov I. Specific features of the construction and quality control of pile foundations in engineering and geological conditions of saint Petersburg. Architecture and Engineering. 2020. № 5 (2), pp. 38–45.
10. Loseva E., Lozovsky I., Zhostkov R., Syasko V. Wavelet analysis for evaluating the length of precast spliced piles using low strain integrity testing. Applied Sciences. 2022. No. 12 (21). DOI: https://doi.org/10.3390/app122110901
11. Schanz T. Aktuelle Entwicklungen bei Standsicherheits- und Verformungsberechnungen in der Geotechnik. Empfehlungen des Arbeitskreises 1.6 «Numerik in der Geotechnik», Abschnitt 4. Geotechnik. 2006. No. 1, pp. 13–28.
12. Lade Р.V. Overview and evalution of constitutive models, Soil Constitutive Models: Evaluation, Selection, and Calibration. Ed. J.A. Yamamuro, V.N. Kaliakin. American Society of Civil Engineers. 2005. Vol. 128, pp. 69–98.
13. Полунин В.М., Лобов И.К., Гурский А.В. Численное моделирование процесса высокочастотного виброизвлечения шпунтовых свай в условиях водо-насыщенных пылевато-песчаных и пылевато-глинистых грунтов // Вестник гражданских инженеров. 2021. № 2 (85). С. 94–101.
13. Polunin V.M., Lobov I.K., Gurskij A.V. Numerical modeling of the process of high-frequency vibroextraction of sheet piles in conditions of water-saturated dusty-sandy and dusty-argillaceous soils. Vestnik grazhdanskih inzhenerov. 2021. No. 2 (85), pp. 94–101. (In Russian).
14. Мангушев Р.А., Пеньков Д.В. Сравнение результатов численных расчетов с использованием современных моделей грунта (hardening soil, hardening soil small и generalized hardening soil) с результатами мониторинга // Вестник гражданских инженеров. 2021. № 2 (85). С. 85–93.
14. Mangushev R.A., Pen’kov D.V. Comparison of the results of numerical calculations using modern soil models (hardening soil, hardening soil small and generalized hardening soil) with monitoring results. Vestnik grazhdanskih inzhenerov. 2021. No. 2 (85), pp. 85–93. (In Russian).
15. Скворцов К.Д., Мангушев Р.А. Учет влияния деформаций шпунтовых ограждений котлованов на дополнительные осадки зданий окружающей застройки // Вестник гражданских инженеров. 2022. № 5 (94). С. 61–68.
15. Skvorcov K.D., Mangushev R.A. Accounting for the influence of deformations of sheet pilings of foundation pits on additional settlements of environmental buildings. Vestnik grazhdanskih inzhenerov. 2022. No. 5 (94), pp. 61–68. (In Russian).
16. Шутова О.А., Пономарев А.Б. Численное моделирование вибрационного воздействия автотранспорта на фундаменты зданий // Вестник Пермского национального исследовательского политехнического университета. Строительство и архитектура. 2018. Т. 9. № 1. С. 93–102.
16. Shutova O.A., Ponomarev A.B. Numerical modeling of the vibration impact of vehicles on the foundations of buildings. Vestnik Permskogo nacional’nogo issledovatel’skogo politekhnicheskogo universiteta. Stroitel’stvo i arhitektura. 2018. Vol. 9. No. 1, pp. 93–102. (In Russian).
17. Сливец К.В., Колмогорова С.С., Коваленко И.А. Параметры мерзлых грунтов при численном моделировании теплофизических задач // Известия Петербургского университета путей сообщения. 2022. Т. 19. № 2. С. 359–366.
17. Slivec K.V., Kolmogorova S.S., Kovalenko I.A. Parameters of frozen soils in the numerical simulation of thermophysical problems. Izvestiya Peterburgskogo universiteta putej soobshcheniya. 2022. Vol. 19. No. 2, pp. 359–366. (In Russian).
18. Chandrakant S. Desai Musharraf Z. Advanced Geotechnical Engineering. Taylor & Francis Group. 2014. 599 p.
19. Larry J. Segerlind. Applied finite element analysis. Department of Agricultural Engineering. 1976. 393 p.