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

Conference paper
Part of the Advances in Intelligent Systems and Computing book series (AISC, volume 1080)

## Abstract

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.

## Keywords

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

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## 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