On the theory of consolidation with double porosity—III A finite element formulation

We employ a finite element method to consider the numerical solution of Aifantis' equations of double porosity.1–5 The physical and mathematical foundations of the theory of double porosity were considered in two previous papers, 6,7 where analytical solutions of the relevant equations are also given. For practical purposes and for the completeness of the presentation, we re‐derive the basic equations without resorting to the more rigorous scheme of multiporosity theory.1–6 Instead, we follow the more familiar approach of Biot8,9 which we now extend from the case of single porosity to the case of double porosity. Then a general finite element formulation of the relevant eqations is thoroughly discussed and explicitly described for the two‐dimensional case where four‐node rectangular non‐conforming isoparametric elements are employed. Three numerical examples are presented in detail to illustrate the method and assess the differences between single and double porosity models in consolidation.