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A dual-continuum model can offer a practical approach to understandingfirst-order behaviours of poromechanically coupled multiscale systems. To closethe governing equations, constitutive equations with models to calculateeffective constitutive coefficients are required. Several coefficient modelshave been proposed within the literature. However, a holistic overview of thedifferent modelling concepts is still missing. To address this we first compareand contrast the dominant models existing within the literature. In terms ofthe constitutive relations themselves, early relations were indirectlypostulated that implicitly neglected the effect of the mechanical interactionarising between continuum pressures. Further, recent users of completeconstitutive systems that include inter-continuum pressure coupling haveexplicitly neglected these couplings as a means of providing direct relationsbetween composite and constituent properties, and to simplify coefficientmodels. Within the framework of micromechanics, we show heuristically thatthese explicit decouplings are in fact coincident with bounds on the effectiveparameters themselves. Depending on the formulation, these bounds correspond toend-member states of isostress or isostrain. We show the impacts of usingconstitutive coefficient models, decoupling assumptions and parameter bounds onporomechanical behaviours using analytical solutions for a 2D model problem.Based on the findings herein, we offer recommendations for how and when to usedifferent coefficient modelling concepts.

Foundations and their practical implications for the constitutive coefficients of poromechanical dual-continuum models