Abstract
A wide range of phenomena in natural or engineered systems emerge from strongly coupled hydraulic, chemical and mechanical processes involving a mix of clearly discrete and quasi-continuous mechanisms. Non-local formulations of these processes, e.g. based on Peridynamics, offer significant advantages compared to classical local formulations. Existing Peridynamics models for water flow and chemical transport are applicable only to saturated systems and use loosely coupling schemes, such as explicit time stepping approaches. This work advances the non-local approach by developing a bond-based formulation for coupled water flow and chemical transport in partially saturated porous media. An implicit solution is proposed for coupling the PD formulation of chemical transport with water flow formulation. Firstly, the proposed formulation is verified against results from finite element/finite difference transient solutions for 1-D and 2-D coupled problems. The agreement between results demonstrates the accuracy of the proposed methodology. Secondly, a series of case studies are presented to illustrate the model’s capability to capture discontinuities and heterogeneities, including stationary cracks, propagating cracks, and randomly distributed permeable and impermeable inclusions. The results show that the multi-physics Peridynamics-based formulations and computational model (Pyramid) provide clear advantages to classical local formulations for analyses of reactive transport in partially saturated porous media with physically realistic microstructures.
Highlights
Modelling approaches based on classic formulations of transport phenomena in porous material utilise the basic physics of fluid flow and chemical transport where the fluid and chemical fluxes are proportional to the gradient of a potential which are applied alongside the constitu tive equations, describing the material’s properties
This paper presents the development of a PD formulation for coupled water flow and chemical transport in discontinuous and/or heteroge neous unsaturated porous media
A series of case studies are presented of transient water flow and chemical transport in fractured and heterogeneous unsaturated porous media, by which the effects of fractures and randomly distributed permeable and impermeable regions are investigated by the new capabilities of the proposed model
Summary
Modelling approaches based on classic formulations of transport phenomena in porous material utilise the basic physics of fluid flow and chemical transport where the fluid and chemical fluxes are proportional to the gradient of a potential which are applied alongside the constitu tive equations, describing the material’s properties. PD formulations of coupled multiphysics problems have been developed which are based on sequential numerical ap proaches to solve the coupled problem (Agwai, 2011; Madenci and Oterkus, 2014; Oterkus et al, 2014, 2017; Ouchi et al, 2015) In these models the processes are sequentially addressed within a time step which can fail to satisfy convergence in the solutions. To the authors’ knowledge, there is no PD formulation which can describe an implicit coupled water flow and chemical transport in partially saturated porous media Such coupled hydro-chemical formu lation is an essential step to develop PD-based fully coupled hydrochemical–mechanical models for studying the chemo-mechanical problems such as erosion assisted degradation of materials or hydraulic-chemo-mechanical behaviour of fractured systems where coupling effects are inherently combined with modelling challenges associated with discontinuity and heterogeneity of the system. A series of case studies are presented of transient water flow and chemical transport in fractured and heterogeneous unsaturated porous media, by which the effects of fractures and randomly distributed permeable and impermeable regions are investigated by the new capabilities of the proposed model
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