Contact tensions under the sole of rigid deep laying foundations and ground anchors

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Authors:


V. G. Shapoval, orcid.org/0000-0003-2993-1311, Dnipro University of Technology, Dnipro, Ukraine; Zaporizhzhia branch of State enterprise “State Research Institute of Building Constructions”, Zaporizhzhia, Ukraine, e-mail: This email address is being protected from spambots. You need JavaScript enabled to view it.

H.P.Ivanova*, orcid.org/0000-0003-4219-7916, Dnipro University of Technology, Dnipro, Ukraine, e-mail This email address is being protected from spambots. You need JavaScript enabled to view it.

S.N.Hapieiev, orcid.org/0000-0003-0203-7424, Dnipro University of Technology, Dnipro, Ukraine, e-mail This email address is being protected from spambots. You need JavaScript enabled to view it.

V.V.Yanko, orcid.org/0000-0003-1025-3047, Dnipro University of Technology, Dnipro, Ukraine, e-mail This email address is being protected from spambots. You need JavaScript enabled to view it.

S.O.Barsukova, orcid.org/0000-0003-0821-1091, Dnipro University of Technology, Dnipro, Ukraine, e-mail This email address is being protected from spambots. You need JavaScript enabled to view it.

* Corresponding author e-mail: This email address is being protected from spambots. You need JavaScript enabled to view it.


повний текст / full article



Naukovyi Visnyk Natsionalnoho Hirnychoho Universytetu. 2023, (2): 058 - 063

https://doi.org/10.33271/nvngu/2023-2/058



Abstract:



Purpose.
To solve the problem of the allocation of contact vertical normal tensions along the sole of a rigid round stamp, located in an elastic isotropic half-space at a certain depth h 0. To compare the obtained solution with the well-known classical result for h = 0, to check the obtained results for adequacy.


Methodology.
Based on the analysis of the decision on the stress-strain state of the base, inside which there is a vertical arbitrary load distributed over the area of the circle, the necessary formulas are obtained to solve the problem. An algorithm for constructing an approximate solution has been developed, the essence of which is to use a combination of the boundary element method and the iteration process by S.N.Klepikov. For a number of depths, approximate solutions of the considered problem are obtained.


Findings.
The proposed algorithm for the approximate solution of the problem of indenting a round rigid stamp into the upper boundary of an elastic isotropic half-space has good agreement with the exact solution and can be used to solve contact problems. The outlines of the contact stress diagrams depend on the depth at which they are determined – the greater the depth, the flatter the outlines of the diagrams are, while starting from a certain depth, the diagrams of contact stresses practically coincide. The greater the depth is at which the stamp is located, the more force must be applied to obtain equal displacements of the stamp.


Originality.
The obtained research results significantly expand the possibilities of solving various problems of soil mechanics and foundation engineering, make it possible to obtain absolutely new results. In particular, a clear dependence of the contact stresses along the sole of a rigid round stamp on the depth at which it is located was identified. In addition, the presented data allow us to designate an absolutely new direction in the calculation of the foundations of ground anchors, namely, the calculation of their deformations.


Practical value.
For engineering practice, it is important that the greater the value of Poisson’s ratio of the base is, the greater the contact stresses are, other things being equal.



Keywords:
deep laying foundations, contact tensions, hard stamp, ground anchor, base sinking, isotropic half-space

References.


1. International Building Code 2021 (IBC 2021) – UpCodes (n.d.). Retrieved from https://up.codes/viewer/illinois/ibc-2021.

2. Soil Anchors: Overview, History, Components, Applications (n.d.). Retrieved from https://www.embibe.com/exams/soil-anchors/.

3. Geotechnical Engineering Handbook (n.d.). Retrieved from https://ftp.idu.ac.id/wpcontent/uploads/ebook/tdg/TERRAMECHANICS%20AND%20MOBILITY/Geotechnical%20Engineering%20Handbook,%20Volumes%201%20-%203%20(%20PDFDrive%20).pdf.

4. Zaletov, S. (2013). Mathematical modeling of the process of the deformation of an isotropic half-space under the action of distributed load at elastic fixing of the boundary. Proceedings of 6 th International Conference of Young Scientists CSE-2013, 2013, 132-133. Retrieved from http://www.wikicfp.com/cfp/servlet/event.showcfp?eventid=32586&copyownerid=4050.

5. Oliveira, M. F. F., Dumont, N. A., & Selvadurai, A. P. S. (2012). Boundary element formulation of axisymmetric problems for an elastic half-space. Engineering Analysis with Boundary Elements, 36(10), 1478-1492.

6. Kachanov, M. L., Shafiro, B., & Tsukrov, I. (n.d.). Handbook of Elasticity Solutions Softcover reprint of hardcover by. Retrieved from https://link.springer.com/book/10.1007/978-94-017-0169-3.

7. Shapoval, A. V., Morklyanik, B. V., Andreev, V. S., Shapoval, V. G., & Kabrel, V. I. (2011). Stress-strain state of the soil half-space, inside which an axisymmetric distributed load is applied. Dnepropetrovsk: Porogi. Retrieved from http://ir.nmu.org.ua/handle/123456789/2912.

8. Korn, G. A., & Korn, T. M. (Eds.). Mathematical Handbook for Scientists and Engineers: Definitions, Theorems, and Formulas for Reference and Review (Dover Civil and Mechanical Engineering) (n.d.). Retrieved from https://www.amazon.com/Mathematical-Handbook-Scientists-Engineers-Definitions/dp/0486411478.

9. Watson, G. N. A treatise on the Theory of Bessel functions. Cambridge: the University Press. Retrieved from https://www.cambridge.org/nl/academic/subjects/mathematics/real-and-complex-analysis/treatise-theory-bessel-functions-2nd-edition-1?format=PB&isbn=9780521483919.

10. Shapoval, V. G., Shapoval, A. V., Morklyanik, B. V., & Andreev, V. S. (2016). Variational methods of boundary elements and splines in contact problems: monograph. Lviv: Ministerstvo obrazovaniya i nauki Ukrainyi, Natsionalnyi Gornyi Universytet.

 

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ISSN (print) 2071-2227,
ISSN (online) 2223-2362.
Journal was registered by Ministry of Justice of Ukraine.
Registration number КВ No.17742-6592PR dated April 27, 2011.

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