Modelling the dynamic poroelastic state of saturated–unsaturated soil considering non-local interactions

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.