Work and energy equations and the principle of generalized effective stress for unsaturated soils

The effective stress principle has been efficiently applied to saturated soils in the soil mechanics and geotechnical engineering practice; however, its applicability to unsaturated soils is still under debate. The appropriate selection of stress state variables is essential for the construction of constitutive models for unsaturated soils. Owing to the complexity of unsaturated soils, it is difficult to determine the deformation and strength behaviors of unsaturated soils uniquely with the previous single-effective-stress variable theory and two-effective-stress-variable theory in all the situations. In this paper, based on the porous media theory, the specific expression of work is proposed, and the effective stress of unsaturated soils conjugated with the displacement of the soil skeleton is further derived. In the derived work and energy balance equations, the energy dissipation in unsaturated soils is taken into account. According to the derived work and energy balance equations, all of the three generalized stresses and the conjugated strains have effects on the deformation of unsaturated soils. For considering these effects, a principle of generalized effective stress to describe the behaviors of unsaturated soils is proposed. The proposed principle of generalized effective stress may reduce to the previous effective stress theory of single-stress variable or the two-stress variables under certain conditions. This principle provides a helpful reference for the development of constitutive models for unsaturated soils.

[1]  Alexander M. Puzrin,et al.  A thermomechanical framework for constitutive models for rate-independent dissipative materials , 2000 .

[2]  John Burland,et al.  Limitations to the Use of Effective Stresses in Partly Saturated Soils , 1962 .

[3]  Guy T. Houlsby,et al.  The work input to an unsaturated granular material , 1997 .

[4]  R. de Boer,et al.  Theory of Porous Media , 2020, Encyclopedia of Continuum Mechanics.

[5]  Lyesse Laloui,et al.  Thermodynamically based mixture models of saturated and unsaturated soils , 1999 .

[6]  X. Li,et al.  Thermodynamics-based constitutive framework for unsaturated soils. 2: A basic triaxial model , 2007 .

[7]  Scott W. Sloan,et al.  A density‐dependent elastoplastic hydro‐mechanical model for unsaturated compacted soils , 2007 .

[8]  Nasser Khalili,et al.  Effective Stress in Unsaturated Soils: Review with New Evidence , 2004 .

[9]  Simon J. Wheeler,et al.  Coupling of hydraulic hysteresis and stress–strain behaviour in unsaturated soils , 2003 .

[10]  Lyesse Laloui,et al.  Effective stress concept in unsaturated soils: Clarification and validation of a unified framework , 2008 .

[11]  R de Boer,et al.  Theory of Porous Media: Highlights in Historical Development and Current State , 2000 .

[12]  X. S. Li,et al.  Thermodynamics-based constitutive framework for unsaturated soils. 1: Theory , 2007 .

[13]  Mandar M. Dewoolkar,et al.  Formulation of capillary hysteresis with internal state variables , 2006 .

[14]  R. M. Bowen,et al.  Incompressible porous media models by use of the theory of mixtures , 1980 .

[15]  G. Houlsby.  The work input to a granular material , 1979 .

[16]  Bernhard A. Schrefler,et al.  Mechanics and thermodynamics of saturated/unsaturated porous materials and quantitative solutions* , 2002 .

[17]  G. E. Blight,et al.  Effective Stress Evaluation for Unsaturated Soils , 1967 .

[18]  Cristina Jommi,et al.  Remarks on the constitutive modelling of unsaturated soils , 2000 .

[19]  William G. Gray,et al.  Mechanics and thermodynamics of multiphase flow in porous media including interphase boundaries , 1990 .

[20]  William G. Gray,et al.  Analysis of the solid phase stress tensor in multiphase porous media , 2007 .

[21]  A. Gens,et al.  A constitutive model for unsaturated soils: thermomechanical and computational aspects , 2004 .

[22]  A. Bishop,et al.  Some Aspects of Effective Stress in Saturated and Partly Saturated Soils , 1963 .

[23]  D. Fredlund,et al.  STRESS STATE VARIABLES FOR UNSATURATED SOILS , 1977 .

[24]  P. R. Day,et al.  Pore Pressure and Suction in Soils , 1962 .

[25]  Bernhard A. Schrefler,et al.  FINITE ELEMENT SIMULATION OF THE SUBSIDENCE OF A GAS RESERVOIR UNDERGOING A WATERDRIVE. , 1982 .

[26]  Ronaldo I. Borja,et al.  Cam-Clay plasticity. Part V: A mathematical framework for three-phase deformation and strain localization analyses of partially saturated porous media , 2004 .

[27]  William G. Gray,et al.  Unsaturated Flow Theory Including Interfacial Phenomena , 1991 .

[28]  Jean Vaunat,et al.  An elasto-plastic hydro-mechanical model for unsaturated soils , 2000 .

[29]  A. Bishop,et al.  Experimental study of partly saturated soil in the triaxial apparatus , 1961 .

[30]  D. Fredlund,et al.  Limitations of the Axis Translation Technique , 1980 .

[31]  Li Xiang,et al.  An Elastoplastic Hydro-mechanical Model for Unsaturated Soils , 2007, International Conference on Computational Science.

[32]  A. Cemal Eringen,et al.  A continuum theory of swelling porous elastic soils , 1994 .

[33]  Alessandro Tarantino,et al.  Experimental Evidence and Theoretical Approaches in Unsaturated Soils , 2000 .

[34]  William G. Gray,et al.  Thermodynamic basis of capillary pressure in porous media , 1993 .

[35]  Laurence D. Wesley,et al.  Principle of Effective Stress , 2009 .

[36]  E. L. Matyas,et al.  Volume Change Characteristics of Partially Saturated Soils , 1968 .

[37]  Lyesse Laloui,et al.  Solid–liquid–air coupling in multiphase porous media , 2003 .

[38]  A. Hansen.  Reexamining some basic definitions of modern mixture theory , 1989 .

[39]  Christoph Wehrli,et al.  The Derivation of Constitutive Relations from the Free Energy and the Dissipation Function , 1987 .

[40]  William G. Gray,et al.  The solid phase stress tensor in porous media mechanics and the Hill–Mandel condition , 2009 .