Multiple parametric mathematical model of the process of consolidation of inhomogeneous soils

Sh. Altynbekov

Matematičeskoe modelirovanie, Tome 30 (2018) no. 10, pp. 44-66.

Résumé

The basic equations of consolidation of saline soils are compiled for three cases: the phases are incompressible, the effect of the initial pressure gradient is not very significant, the phases are compressible; the influence of the initial pressure gradient is significant. A new nonlinear relationship is established between the sum of the principal stresses and the porosity coefficient, which simultaneously describes three types of inhomogeneity. A function is proposed that characterizes the change in the age of the soil skeleton as a function of spatial coordinates. Properties of the creep parameters included in this dependence are described. It is proved that the property of an inhomogeneous old soil can be described by functions of spatial coordinates. On the basis of this dependence, and based on existing and developed models, a multi-parameter mathematical model of the process of consolidation of soils is constructed, containing previously existing ones. The questions of existence, uniqueness and correctness for the boundary value problem are investigated. The methods of its solution are justified. The possibility of applying the methods of iteration, total approximation and sweep has been proved. The approximation error, stability and convergence of a locally one-dimensional scheme (VOC) are investigated. An estimate of the solution of the problem is given using the sweep formula.

Détail

Keywords: soil mechanics, mathematical model, boundary-value problems.
Mots-clés : consolidation

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