Abstract
Based on the balance equations for mass, linear momentum, energy in porous media theory and some hypotheses in unsaturated soil mechanics, an expression of the total deformation work W is derived, and with the help of the specific expression of the work, the effective stress conjugated with the displacement of the soil skeleton is suggested by the authors, which has the similar form as the expressions proposed by Wheeler (2003) and some other researchers according to their experience and intuition, but the effective stress presented in this paper is derived on the basis of porous media theory and its assumptions, whose premise and hypothesis are clear. It is also pointed out that due to the complexity of the physical mechanism and various influencing factors, it is impossible in unsaturated soil mechanics to determine the deformation of solid skeleton by the effective stress only, like in the saturated soil mechanics. Besides, by using the expression of the deformation work and the free energy A α for each phase, the applicability of the Phase Separation Principle proposed by Passman (1984) in unsaturated soil is discussed, and it is considered that the principle should not strictly apply to unsaturated soil mechanics.
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Aitchison G D, Donald I B. Some preliminary studies of unsaturated soils. In: Proc. 2nd Austr.-N. Zealand Conf Soil Mech. Found Eng. Wellington: Techinical Publications for the New Zealand Institution of Engineering, 1956. 192–199
Bishop A W. The principle of effective stress. Teknisk Ukeblad, 1959, 106: 859–863
Bishop A W, Blight G E. Some aspects of effective stress in saturated and partly saturated soils. Geotechnique, 1963, 13(3): 177–197
Blight G E. A study of effective stress for volume change. In: Moisture Equilibrium and Moisture Changes in Soils Beneath Covered Areas. Sydney: Butterworths, 1965. 259–269
Fredlund D G, Morgenstern N R. Stress state variables for unsaturated soils. J Geotech Eng, ASCE, 1977, 103(GT5): 447–466
Wheeler S J, Sharma R J, Buisson M S R. Coupling of hydraulic hysteresis and stress-strain behavior in unsaturated soils. Geotechnique, 2003, 53(1): 41–54
Dean E T, Houlsby G T. Editorial. Geotechnique, 2005, 55(5): 415–417
Li X K. The effective stress principle in unsaturated soil. J Dalian Univ Technol (in Chinese), 1997, 37(4): 381–385
Xie D Y. Consideration of some fundamental viewpoints in studying effective stress of unsaturated soils (in Chinese). Chinese J Geotech Eng (in Chinese), 2006, 28(2): 170–173
Houlsby G T. The work input to a granular material. Geotechnique, 1979, 29(3): 354–358
Houlsby G T. The work input to an unsaturated granular material. Geotechnique, 1997, 47(1): 193–196
Passman S T. A theory of multiphase mixtures. In: Trusdell C, ed. Rational Thermodynamics. New York: Springer-Verlag, 1984. 286–325
Reint de Boer. Highlights in the historical development of the porous media theory: Toward a consistent macroscopic theory. Appl Mech Rev, 1996, 49(4): 201–262
de Boer R. Theory of Porous Media. Berlin: Springer-Verlag, 2000. 345–353
Hansen A C. Reexamining some basic definitions of modern mixture theory. Int J Eng Sci, 1989, 27(12): 1531–1544
Trusdell C, Toupin R. The classical field theory. In: Flugge’s Handbush de Physik, vol. III/1. Berlin: Springer-Verlag, 1960. 226–793
Houlsby G T, Puzrin A M. A thermomechanical framework for constitutive models for rate-independent dissipative materials. Int J Plasticity, 2000, 16: 1017–1047
Collins I F. The concept of stored plastic work for frozen elastic energy in soil mechanics. Geotechnique, 2005, 5: 373–382
Collins I F, Kelly P A. A thermomechanical analysis of a family of soil models. Geotechnique, 2002, 7: 507–518
Wei C, Muraleetharan K K. A continuum theory of porous media saturated by multiphase immiscible fluids: I. Linear poroelasticity. Int J Eng Sci, 2002, 40: 1807–1833
Bishop A W. The principle of effective stress. Teknisk Ukeblad, 1959,106 (39): 113–143
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Supported by the National Natural Science Foundation of China (Grant No. 50778013) and Beijing Natural Science Foundation (Grant No. 8082020)
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Zhao, C., Zhang, X. Derivation of the work expression and discussion on the effective principle and the phase separation theorem in unsaturated soil. Sci. China Ser. E-Technol. Sci. 51, 1530–1541 (2008). https://doi.org/10.1007/s11431-008-0107-8
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DOI: https://doi.org/10.1007/s11431-008-0107-8