Mathematical Modelling of Spatial Deformation Process of Soil Massif with Free Surface

  • Anatoliy Vlasyuk
  • Nataliia ZhukovskaEmail author
  • Viktor Zhukovskyy
  • Rajab Hesham
Conference paper
Part of the Advances in Intelligent Systems and Computing book series (AISC, volume 1080)


The study of deformation processes of soil massifs with free surface under mass and heat transfer is important in the design, construction and operation of buildings. The article presents a mathematical model of the deformation state problem of the soil massif under mass and heat transfer and the present free surface in the three-dimensional case. The basic equations, boundary conditions and conditions of congruence for displacements, strains, stresses, and also additional functions are given. For computer modelling of the set boundary value problem, a software package for the capabilities of the Microsoft Visual Studio 2017 framework for Windows Desktop in the C# programming language was created. It is shown that the presence of a free surface that breaks the area of the investigated soil in the area of water-saturated soil and the area of the soil in its natural state changes the distributions of the displacements of the soil mass in these areas.


Mathematical model Soil massif Stress-strain state Mass and heat transfer Free surface 


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© Springer Nature Switzerland AG 2020

Authors and Affiliations

  • Anatoliy Vlasyuk
    • 1
  • Nataliia Zhukovska
    • 2
    Email author
  • Viktor Zhukovskyy
    • 2
  • Rajab Hesham
    • 2
  1. 1.National University of Ostroh AcademyOstrohUkraine
  2. 2.The National University of Water and Environmental EngineeringRivneUkraine

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