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

## TL;DR

This paper reviews and compares various models for constitutive coefficients in dual-continuum poromechanical systems, highlighting the effects of assumptions and bounds on system behavior and providing practical recommendations.

## Contribution

It provides a comprehensive comparison of existing coefficient models, analyzes the implications of decoupling assumptions, and offers guidance on their appropriate application.

## Key findings

- Explicit decouplings align with bounds on effective parameters.
- Decoupling assumptions relate to end-member states like isostress or isostrain.
- Using bounds and assumptions significantly impacts poromechanical behavior.

## Abstract

A dual-continuum model can offer a practical approach to understanding first-order behaviours of poromechanically coupled multiscale systems. To close the governing equations, constitutive equations with models to calculate effective constitutive coefficients are required. Several coefficient models have been proposed within the literature. However, a holistic overview of the different modelling concepts is still missing. To address this we first compare and contrast the dominant models existing within the literature. In terms of the constitutive relations themselves, early relations were indirectly postulated that implicitly neglected the effect of the mechanical interaction arising between continuum pressures. Further, recent users of complete constitutive systems that include inter-continuum pressure coupling have explicitly neglected these couplings as a means of providing direct relations between composite and constituent properties, and to simplify coefficient models. Within the framework of micromechanics, we show heuristically that these explicit decouplings are in fact coincident with bounds on the effective parameters themselves. Depending on the formulation, these bounds correspond to end-member states of isostress or isostrain. We show the impacts of using constitutive coefficient models, decoupling assumptions and parameter bounds on poromechanical behaviours using analytical solutions for a 2D model problem. Based on the findings herein, we offer recommendations for how and when to use different coefficient modelling concepts.