Stress Partitioning in Two-Phase Media: Experiments and Remarks on Terzaghi’s Principle

  • Roberto SerpieriEmail author
  • Francesco Travascio
Part of the Advanced Structured Materials book series (STRUCTMAT, volume 67)


Stress partitioning in multiphase porous media is a fundamental problem of solid mechanics, yet not completely understood: no unanimous agreement has been reached on the formulation of a stress partitioning law encompassing all observed experimental evidences in two-phase media, and on the range of applicability of such a law. This chapter has two main objectives. The first one is to show the capability of the variational poroelastic theory developed in Chaps.  2 and  3 (VMTPM) to systematically and consistently describe stress partitioning in compression tests characterized by different loading and drainage conditions, and for three classes of materials: linear media, media with solid phase having no-tension response, and cohesionless granular media. The second objective is to perform a theoretical-experimental analysis on the range of applicability of the notions of effective stress and effective stress principles, in light of the general medium-independent stress partitioning law derived in Chap.  2 which predicts that the external stress, the fluid pressure and the stress tensor work associated with the macroscopic strain of the solid phase are always partitioned according to a relation formally compliant with Terzaghi’s law, irrespective of the microstructural and constitutive features of a given medium. Herein, the description of boundary conditions with unilateral contact is examined making use of a simple and straightforward extension of the standard formulation of contact in single-continuum problems, employing a set-valued law and a gap function. Next, the modalities of stress partitioning characteristic of Undrained Flow (UF) conditions, corresponding to absence of fluid seepage, are examined in further detail, identifying the possibility to characteristically define in a physically meaningful way, expressly at UF conditions, a stress tensor field of the whole mixture, as a quantity closely related to the concept of total stress tensor field. The systematic study carried out in this chapter allows showing that compliance with the classical statement of Terzaghi’s effective stress principle can be rationally derived as the peculiar behavior of the specialization of VMTPM recovered for cohesionless granular media, without making use of artificial incompressibility constraints. Moreover, it is shown that the experimental observations on saturated sandstones, generally considered as proof of deviations from Terzaghi’s law, are ordinarily predicted by VMTPM. In addition, a rational deduction of the phenomenon of compression-induced liquefaction in cohesionless mixtures is reported: such effect is found to be a natural implication of VMTPM when unilateral contact conditions are considered for the solid above a critical porosity. Finally, a characterization of the phenomenon of crack closure in fractured media is inferred in terms of macroscopic strain and stress paths. Altogether these results exemplify the capability of VTMPM to describe and predict a large class of linear and nonlinear mechanical behaviors observed in two-phase saturated materials. As a conclusion of this study, a generalized statement of Terzaghi’s principle for multiphase problems is proposed.


Volumetric Strain Unilateral Contact Open Contact Sandstone Specimen External Traction 
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Authors and Affiliations

  1. 1.Dipartimento di IngegneriaUniversità degli Studi del SannioBeneventoItaly
  2. 2.University of MiamiBiomechanics Research LaboratoryCoral GablesUSA

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