Mathematic and computer modeling of cohesion effect forces on spatial deformation processes of soil massif

2020;
: pp. 196–205
https://doi.org/10.23939/mmc2020.01.196
Received: February 20, 2020
Revised: May 18, 2020
Accepted: May 20, 2020
1
The National University of Ostroh Academy
2
The National University of Water and Environmental Engineering
3
The National University of Water and Environmental Engineering

The article presents the modeling and solving of the deformation processes problem of the soil massif under the forces of cohesion effect.  Spatial deformation processes of soil massif are described by the components of displacements, by normal and tangential stresses, and by strains.  Also, the corresponding boundary value problem includes the mass and heat transfer equations in a soil massif.  The functions of cohesion forces in the soil are considered that have linear, quadratic and logarithmic dependence.  The results of the studies are presented in the form of graphs of displacement surfaces as well as in percentage ratios of the corresponding functions.  Numerical experiments have shown that on average the forces of linear dependence have the greatest influence on the displacement while the logarithmic dependence provides the least effect.

  1. Sergienko I. V., Skopetskii V. V., Deineka V. S.  Mathematical Simulation and Investigation of Processes in Inhomogeneous Media.  Naukova Dumka, Kiev (1991), (in Ukarainian).
  2. Hetnarski R. B.  Encyclopedia of thermal stresses.  Springer  Reference, Dordrecht (2014).
  3. Vlasyuka A. P., Zhukovskaya N. A.  Mathematical Simulation of the Stressed-Strained State of the Foundation of Earth Dams with an Open Surface Under the Influence of Heat and Mass Transfer in the Two-Dimensional Case.  Journal of Engineering Physics and Thermophysics. 88 (2), 329–341 (2015).
  4. Vlasyuk A. P., Zhukovska N. A., Zhukovskyy V. V., Klos-Witkowska A., Pazdriy I., Iatsykovska U.  Mathematical modelling of three-dimensional problem of soil mass stressed-strained state considering mass and heat transfer:  2017 9th IEEE International Conference on Intelligent Data Acquisition and Advanced Computing Systems: Technology and Applications (IDAACS). Vol. 1, 265–269 (2017).
  5. Vlasyuk A. P., Borowik B., Zhukovska N. A., Zhukovskyy V. V., Karpinskyi V.  Computer modelling of heat and mass transfer effect on the three-dimensional stressed-strained state of soil massif.  18th International Multidisciplinary Scientific Geoconference SGEM 2018. Vol. 18, No. 1.2, 153–160 (2018).
  6. Vlasyuk A., Zhukovska N., Zhukovskyy V., Hesham R.  Mathematical Modelling of Spatial Deformation Process of Soil Massif with Free Surface.  Advances in intelligent systems and computing IV.  Vol. 1080, 107–120 (2020).
  7. Kuzlo M. T.  Investigation of the effect of the concentration of saline solutions on clutch forces in clay soils.  Hydrotechnical construction. 5, 51–53 (2013).
  8. Kuzlo M. T., Moshynskyi V. S., Martyniuk P. M.  Mathematical modelling of soil Massif's deformations under its drainage.  International Journal of Apllied Mathematics. 31 (6), 751–762 (2019).
  9. Remez N., Osipova T., Kraychuk O., Kraychuk S.  Simulation of the solid waste landfill settlement taking into account underlying soil.  Eastern-European Journal of Enterprise Technologies. 3 (10), 12–17 (2016).
  10. Kaliukh I., Trofymchuk O., Lebid O.  Numerical Solution of Two-Point Static Problems for Distributed Extended Systems by Means of the Nelder–Mead Method.  Cybernetics and Systems Analysis. 55 (4), 616–624 (2019).
  11. Vodka O.  Computation tool for assessing the probability characteristics of the stress state of the pipeline part defected by pitting corrosion.  Advances in Engineering Software. 90, 159–168 (2015).
  12. Dyyak I. I., Rubino B., Savula Y. H., Styahar A. O.  Numerical analysis of heterogeneous mathematical model of elastic body with thin inclusion by combined BEM and FEM.  Mathematical Modeling and Computing. 6 (2), 239–250 (2019).
  13. Dassios I., O'Keeffe G., Jivkov A. P.  A mathematical model for elasticity using calculus on discrete manifolds.  Mathematical Methods in the Applied Sciences. 41 (18), 9057–9070 (2018).
  14. Safonyk A., Martynov S., Kunytskyi S., Pinchuk O.  Mathematical modelling of regeneration the filtering media bed of granular filters.  Advances in Modelling and Analysis. 73 (2), 72–78 (2018).
  15. Karnaukhov V. G.  On A. D. Kovalenko's Research Works on the Thermomechanics of Coupled Fields in Materials and Structural Members and Its Further Development. International Applied Mechanics. 41 (9), 967–975 (2005).
  16. Samarskii A. A.  The theory of difference schemes.  Vol. 240 of Pure and applied mathematics.  Marcel Dekker, New York (2001).
  17. Vlasyuk A. P., Kuzlo M. T.  Experimental investigations of some of the parameters of filtration of salt solutions in sandy soils.  Melioration and Water Handling Facilities: Interdepartmental Thematic Scientific Collection. 43–46 (2000), (in Ukrainian).
Mathematical Modeling and Computing, Vol. 7, No. 1, pp. 196–205 (2020)