Discussion

Comment on “Averaging theory for description of environmental problems: What have we learned?” by William G. Gray, Cass T. Miller, and Bernhard A. Schrefler

Over the last few years, several researchers working on the development of “biogeochemical” or “ecosystem-scale” models of soil carbon dynamics have reported struggling with a number of difficult challenges. At the same time, work in this area has focused exclusively on microbial activity described at a macro-ecological level, and has entirely bypassed the abundant literature produced in the last two decades on the study of soil processes at the microscale. Juxtaposition of these different observations suggests that a radical shift of perspective is in order. In this general context, the present article carries out an in-depth analysis of several of the key limitations of current ecosystem-scale models and recommends a number of steps to shift the perspective to one that is argued to have a better chance of success in the relatively short time we have to address several pressing soil-related environmental problems. These steps, in particular, require the development of large-spatial-scale models of soil carbon dynamics to be far more interdisciplinary than it has been till now, and to adopt a “bottom-up” approach, building on what the research at the microscale reveals about soil processes. Nevertheless, because it may assist in upscaling efforts, it is argued that some room should be preserved for work to continue on the search for empirical models applicable at large spatial scales.

The linearized version of a recently formulated Variational Macroscopic Theory of biphasic isotropic Porous Media (VMTPM) is employed to derive a general stress partitioning law for media undergoing flow conditions under prevented fluid seepage and negligible inertia effects, typically met in biphasic specimens subjected to jacketed tests.

The principle of virtual work, relevant to the specialization of VMTPM to such characteristic flow conditions, naturally yields a stress partitioning law, between solid and fluid phase of a saturated medium, that exactly matches with the celebrated Terzaghi’s principle. It is also shown that the stress tensor of the solid phase work-associated with the strain measure of the VMTPM naturally corresponds to the Terzaghi’s effective stress. Accordingly, under undrained conditions, Terzaghi’s law is proved to be a completely general stress partitioning law for a saturated biphasic medium irrespective of its constitutive and/or microstructural features as well as of the compressibility of its constituent phases.

Since the developments reported are obtained ruling out thermodynamic constraints and any assumption on the internal microstructure and on the compressibility of the phases, the results obtained indicate that Terzaghi’s law could more generally apply to a broader class of biphasic media and be not restricted within the context of geomechanics.