Modelling the dynamic poroelastic state of saturated-unsaturated soil considering non-local interactions
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Vsevolod Bohaienko [1] ; Tetiana Blagoveshchenskaya [1]
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[1] Glushkov Institute of Cybernetics
Glushkov Institute of Cybernetics
Ucrania
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- Localización: SeMA Journal: Boletín de la Sociedad Española de Matemática Aplicada, ISSN-e 2254-3902, ISSN 2254-3902, Vol 83, Nº. 1, 2026, págs. 45-64
- Idioma: inglés
- DOI: 10.1007/s40324-024-00369-1
- Texto completo no disponible (Saber más ...)
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Resumen
Deformations in soil with the change of moisture content, especially during the transition between moisture-saturated and unsaturated states, have a feedback on moisture transport processes. The significance of such an interaction should be studied while performing long-term forecast of soil state. Together with another important factor-the features of soil that are peculiar for porous media of fractal structure-this motivates the development of the tools for simultaneous simulation of moisture transport and deformation of soil, in particular, using the means of fractional-order calculus. In this context, we propose a new space-fractional model of poroelasticity and a finite-difference technique for obtaining numerical solutions of corresponding initial-boundary value problems. To increase the speed of calculations, a multi-threading parallel processing scheme is used. The convergence of the scheme is confirmed experimentally by solving a constructed problem with a given exact solution. Further modelling of an applied problem-the irrigation process-demonstrates an insignificant influence of poroelasticity on the total duration of irrigation simulated for 1 year. However, the accumulation of changes in simulated soil porosity, the duration of irrigation, and inter-irrigation intervals confirms the need to take poroelasticity into account in long-term forecast. Taking non-local interactions into account led to the 8% change in the total duration of irrigation for the order of fractional derivatives equal to 0.9 compared to the case of an integer-order model.
