Development of a mathematical model of dynamic soil deformation taking into account the variable coefficient of volumetric viscosity

¹ National Technical University of Ukraine “Igor Sikorsky Kyiv Polytechnic Institute”, 37 Beresteiskyi Ave., 03056 Kyiv, Ukraine
² Taurida National V.I. Vernadsky University, 33 Dzhona Makkeina St., 01042 Kyiv, Ukraine
³ Institute of Hydromechanics of the National Academy of Sciences of Ukraine, 8/4 Marii Kapnist St., 03057 Kyiv, Ukraine
⁴ Institute of Telecommunications and Global Information Space, 25 Chokolivskyi Ave., 03186 Kyiv, Ukraine
⁵ Ukrainian State University of Science and Technologies, 4 Nauky Ave., 49600 Dnipro, Ukraine

^* Corresponding author: h.haiko@kpi.ua

Abstract

Determining soil deformations under the influence of dynamic loads of different nature, including during military actions, is an important scientific and practical problem. At the same time, when solving problems of determining the stress-strain state of soils under the action of short-term dynamic loads, little attention has been paid to the multicomponent composition and viscous properties. The aim of the research is to develop a mathematical model of soil deformation taking into account the variable coefficient of volumetric viscosity both during loading and unloading. The methods of mathematical modeling and numerical integration are used in the research. The possibility of using the proposed model to determine the deformation of soils under explosive and shock loads is shown, which helps control the properties of soils for the protection of shallow underground structures. The results of a comparison of the obtained analytical data with the experimental data are presented.