Modeling cementitious materials as multiphase porous media: theoretical framework and applications

In this paper a general model for the analysis of concrete as multiphase porous material, based on the so-called Hybrid Mixture Theory, is presented. The development of the model equations, taking into account both bulk phases and interfaces of the multiphase system is described, starting from the microscopic scale. An exploration of the second law of thermodynamics is also presented: it allows defining several quantities used in the model, like capillary pressure, disjoining pressure or effective stress, and to obtain some thermodynamic restrictions imposed on the evolution equations describing the material deterioration. Then, two specific forms of the general model adapted to the case of concrete at early ages and beyond and to the case of concrete structures under fire are shown. Some numerical simulations aimed to prove the validity of the approach adopted also are presented and discussed.

[1]  J. Auriault.  Dynamic Behavior of Porous Media , 1991 .

[2]  J. Mazars.  APPLICATION DE LA MECANIQUE DE L'ENDOMMAGEMENT AU COMPORTEMENT NON LINEAIRE ET A LA RUPTURE DU BETON DE STRUCTURE , 1984 .

[3]  Geppino Pucci,et al.  A frontal solver tuned for fully coupled non‐linear hygro‐thermo‐mechanical problems , 2003 .

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

[5]  Zdeněk P. Bažant,et al.  Thermodynamic functions for ageing viscoelasticity : Integral form without internal variables , 1999 .

[6]  Yunping Xi,et al.  Continuous Retardation Spectrum for Solidification Theory of Concrete Creep , 1995 .

[7]  Miguel Cervera,et al.  THERMO-CHEMO-MECHANICAL MODEL FOR CONCRETE. II: DAMAGE AND CREEP , 1999 .

[8]  J. Z. Zhu,et al.  The finite element method , 1977 .

[9]  Bernhard A. Schrefler,et al.  Modelling of hygro-thermal behaviour of concrete at high temperature with thermo-chemical and mechanical material degradation , 2003 .

[10]  Zdenek P. Bazant,et al.  MICROPRESTRESS-SOLIDIFICATION THEORY FOR CONCRETE CREEP. II: ALGORITHM AND VERIFICATION , 1997 .

[11]  B. Schrefler,et al.  The Finite Element Method in the Static and Dynamic Deformation and Consolidation of Porous Media , 1998 .

[12]  William G. Gray,et al.  General conservation equations for multi-phase systems: 1. Averaging procedure , 1979 .

[13]  William G. Gray,et al.  General conservation equations for multi-phase systems: 2. Mass, momenta, energy, and entropy equations , 1979 .

[14]  J. Auriault.  Nonsaturated deformable porous media: Quasistatics , 1987 .

[15]  J. Chaboche.  Continuum Damage Mechanics: Part I—General Concepts , 1988 .

[16]  Per Freiesleben Hansen,et al.  Influence of temperature on autogenous deformation and relative humidity change in hardening cement paste , 1999 .

[17]  Zdenek P. Bazant,et al.  Solidification Theory for Concrete Creep. II: Verification and Application , 1989 .

[18]  Z. Bažant.  FRACTURE MECHANICS OF CONCRETE STRUCTURES , 1992 .

[19]  Zdeněk P. Bažant,et al.  Viscoelasticity with Aging Caused by Solidification of Nonaging Constituent , 1993 .

[20]  H. Brenner,et al.  Transport processes in porous media , 1986 .

[21]  Olivier Coussy,et al.  Modeling of Thermochemomechanical Couplings of Concrete at Early Ages , 1995 .

[22]  Sven Thelandersson,et al.  Modeling of Combined Thermal and Mechanical Action in Concrete , 1987 .

[23]  Bernhard A. Schrefler,et al.  A parallel algorithm for thermo-hydro-mechanical analysis of deforming porous media , 1996 .

[24]  Surendra P. Shah,et al.  Fracture mechanics of concrete , 1995 .

[25]  Reint de Boer,et al.  Highlights in the Historical Development of the Porous Media Theory: Toward a Consistent Macroscopic Theory , 1996 .

[26]  Bernhard A. Schrefler,et al.  Modelling of hygro‐thermal behaviour and damage of concrete at temperature above the critical point of water , 2002 .

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

[28]  James R. Lawson,et al.  Effects of elevated temperature exposure on heating characteristics, spalling, and residual properties of high performance concrete , 2001 .

[29]  Franz-Josef Ulm,et al.  Microprestress-Solidification Theory for Concrete Creep. I: Aging and Drying Effects , 1997 .

[30]  Bernhard A. Schrefler,et al.  Hygro‐thermo‐chemo‐mechanical modelling of concrete at early ages and beyond. Part I: hydration and hygro‐thermal phenomena , 2006 .

[31]  Olivier Coussy,et al.  Strength growth as chemo-plastic hardening in early age concrete , 1996 .

[32]  K. Hutter,et al.  On the thermodynamics of a mixture of isotropic materials with constraints , 1995 .

[33]  Gabriel A. Khoury,et al.  Strain components of nuclear-reactor-type concretes during first heat cycle , 1995 .

[34]  Bernhard A. Schrefler,et al.  Numerical analysis of hygro-thermal behaviour and damage of concrete at high temperature , 1999 .

[35]  H. Schöpf.  C. Truesdell, Rational Thermodynamics, New York, McGraw-Hill Book Company, 1969, XII. 208 S , 1978 .

[36]  William G. Gray,et al.  Thermodynamic approach to effective stress in partially saturated porous media , 2001 .

[37]  R. Taylor.  The Finite Element Method, the Basis , 2000 .

[38]  D. Evelyne.  Thèse de doctorat d'Etat , 1988 .

[39]  Bernard Schrefler,et al.  Modelling creep and shrinkage of concrete by means of effective stresses , 2007 .

[40]  Zdeněk P. Bažant,et al.  Mathematical modeling of creep and shrinkage of concrete , 1988 .

[41]  Zdenek P. Bazant,et al.  Solidification theory for concrete creep. I: formulation , 1989 .

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

[43]  Bernhard A. Schrefler,et al.  Hygro‐thermo‐chemo‐mechanical modelling of concrete at early ages and beyond. Part II: shrinkage and creep of concrete , 2006 .

[44]  Bernhard A. Schrefler,et al.  Concrete at high temperature with application to tunnel fire , 2002 .

[45]  William G. Gray,et al.  General conservation equations for multi-phase systems: 3. Constitutive theory for porous media flow. , 1980 .

[46]  Bernhard A. Schrefler,et al.  Modelling of deformations of high strength concrete at elevated temperatures , 2004 .