CONSOLIDATION THEORY OF UNSATURATED SOIL BASED ON THE THEORY OF MIXTURE(Ⅰ)

Abstract

Abstract: Unsaturated soil is a three-phase media and is composed of soil grain, water and gas. In this paper, the consolidation problem of unsaturated soil is investigated based on the theory of mixture. A theoretical formula of effective stress on anisotropic porous media and unsaturated soil is derived. The principle of effective stress and the principle of Curie symmetry are taken as two fundamental constitutive principles of unsaturated soil. A mathematical model of consolidation of unsaturated soil is proposed, which consists of 25 partial differenfial equations with 25 unknowns. With the help of increament linearizing method, the model is reduced to 5 governing equations with 5 unknowns, i.e., the three displacement components of solid phase, the pore water pressure and the pore gas pressure. 7 material parameters are involved in the model and all of them can he measured using soil tests. It is convenient to use the model to engineering practice. The well known Biot’s theory is a special case of the model.

Key words: unsaturated soil, consolidation, theory of mixture, effective stress, the principle of Curie symmetry

Chen Zhehg-han;Xie Ding-yi;Liu Zu-dian. CONSOLIDATION THEORY OF UNSATURATED SOIL BASED ON THE THEORY OF MIXTURE(Ⅰ). Applied Mathematics and Mechanics (English Edition), 1993, 14(2): 137-150.

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References

[1] Jiang Peng-nian,On the engineering properties of unsaturated soils,Chinese Journal ofGeotechnical Engineering,11,6(1989).(in Chinese)
[2] Bao Cheng-gang,Stress-strain relation and strength properties of unsaturated soil,Chinese Journal of Geotechnical Engineering,7,1(1986).(in Chinese)
[3] Barden,L.,Consolidation of campacted and unsaturated clays,Geotechnique,15,3(1965),267-285.
[4] Predlund,D.G.and J.U.Hafan,One-dimensional consolidation theory:Unsaturatedsoils,Canadian Geotechnical Journal,16,3(1979),521-531.
[5] Fredlund,D.G.,Consoliation of unsaturated porous media,Proc.of the NATO Advanced Study Institute on Mechanics of Fluids in Porous Media,Newark,Delaware,U.S.A.(1982),525-578.
[6] Fredlund D.G.,Soil mechanics principle that embrances unsaturated soils,Proc.of 11th ICSMEF,San Francisco,USA(1985),313-321.
[7] Thigpen,L.and Berryman,J.G.,Mechanics of porous elastic materials containing multiphase fluids,Int.J.Engng.Sci,25,1(1985),1203-1214.
[8] Vardoulakis,I.and D.E.Beskos,Dynamic behavior of nearly saturated porous media,Mechanics of Materials,5(1986),87-108.
[9] Boer,R.and W.Ehler.,On the problem of fluid-and gas-filled elasto-plastic solids.Int.J.Solids.Structures,22,11(1986),1231-1242.
[10] Bowen R.M.,Theory of Mixture,in Continuum Physics,Series,edited by A.C.Eringen,New York.Academic Press(1976).
[11] Bowen,R.M.,Incompressible porous media models by use of the theory of mixture,Int.J.Engng.Sci,18(1980),1129-1148.
[12] Bowen R.M.,Compressible porous media models by use of the theory of mixture,Int.J.Engng.Sci,20,6(1982),697-735.
[13] Bedfore,A.and D.S.Drumheller,Theories of immiscible and structured mixtures.Int.J.Engng.Sci.,21,8(1983),863-960.
[14] Passsman,S.L.,J.W.Nunziato and E.K.,Walsh,A theory of multiphase mixtures,Rational Thermodynamics,Ed.by C.Truesdell,Springer-Verlag,New York(1984),286325.
[15] Chen Zheng-han and Xie Ding-yi,Two important problems on current research of theory of mixture,4th National Conference of Modern Mathematics and Mechanics,Lanzhou,China(1991).(in Chinese)
[16] Degroot,S.R.and P.Mazur,Non-Equilibrium Thermodynamics,Wiley(Interscience),New York(1962).
[17] Skempton,A.W.,Effective Stress in Solids,Concrete and Rock,Pore Pressure andSuction in Soils,Butterworths,London(1960),4-16.
[18] Biot,M.A.and D.G.Willis,The elastic coefficients of the theory of consolidation,J.Appl.Mech.,24(1957),594-601.
[19] Nur,A.and J.D.Byerlee,An exact effective stress law for elastic deformation of rock with fluids,J.Geophys.Res.,76(1971),6414-6419.
[20] Carroll,M.M.,Mechanical response of fluid-saturated porous materials,Proc.15th IUTAM,North-Holland,New York(1980),251-262.
[21] Mctigue,D.F.,R.K.Wilson and J.W.Nunziato,An effective stress principle for partially saturated media,Mechanics of Granular materials,Ed.by J.T.Jenkins and M.Satake,Elsevier(1983),195-210.
[22] Li Xi and Guo Shang-ping,A thoery on seepage process by use of theory of mixture,Scientia Sinica,Series A,1,3(1988),265-274.
[23] Chen Zheng-han,Consolidation theory of unsaturated soil based on the theory of mixture:Mathematics model,test investigation,boundary value problems,Dissertaion of Ph.D.,Shanxi Mechanical College,Xi’an,China(1991).(in Chinese).
[24] Chen Zheng-han,Xie Ding-yi and Liu Zu-dian,A consolidation theory of unsaturated soil,Symposium on New Methods in Geomechanics,Shanghai,China(1989).(in Chinese)
[25] Guo Zhong-heng,Non-Linear Elastic Theory,Science Press(1980).(in Chinese)
[26] Huang Ke-zhi,et al.,Tensor Analysis,Qinghua University Press(1985).(in Chinese)