Modelling of hygro-thermal behaviour of concrete at high temperature with thermo-chemical and mechanical material degradation

Abstract A mathematical model for analysis of hygro-thermal behaviour of concrete as a multi-phase porous material at high temperatures, accounting for material deterioration, is presented. Full development of the model equations, starting from the macroscopic balances of mass, energy and linear momentum of single constituents is presented. Constitutive relationships for concrete at high temperature, including those concerning material damage, are discussed. The classical isotropic non-local damage theory is modified to take into account the mechanical- and the thermo-chemical concrete damage at high temperature. The final form of the governing equations, their discretised FE form, and their numerical solution are presented. The results of two numerical examples, concerning fire performance of 1-D and 2-D HPC structures, are discussed.

[1]  Franz-Josef Ulm,et al.  THE "CHUNNEL" FIRE. II: ANALYSIS OF CONCRETE DAMAGE , 1999 .

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

[3]  Bernhard A. Schrefler,et al.  Simulation of damage-permeability coupling in hygro-thermo mechanical analysis of concrete at high temperature , 2002 .

[4]  G. L. England,et al.  Moisture flow in concrete under steady state non-uniform temperature states: experimental observations and theoretical modelling , 1995 .

[5]  N. V. Churaev Liquid and Vapour Flows in Porous Bodies: Surface Phenomena , 2000 .

[6]  S. J. Gregg,et al.  Adsorption Surface Area and Porosity , 1967 .

[7]  Long T. Phan,et al.  International Workshop on Fire Performance of High-Strength Concrete, NIST, Gaithersburg, MD, February 13-14, 1997, Proceedings | NIST , 1997 .

[8]  J. Chaboche Continuum Damage Mechanics: Part II—Damage Growth, Crack Initiation, and Crack Growth , 1988 .

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

[10]  Z. Bažant,et al.  The chunnel fire. I: Chemoplastic softening in rapidly heated concrete , 1999 .

[11]  Bernhard A. Schrefler,et al.  The effective stress principle: Incremental or finite form? , 1996 .

[12]  Z. Bažant,et al.  Concrete at High Temperatures: Material Properties and Mathematical Models , 1996 .

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

[14]  Supplement to An Adaptive Finite Element Method for Two-Phase Stefan Problems in Two Space Dimensions. Part I: Stability and Error Estimates , 1991 .

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

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

[17]  Adrian E. Scheidegger,et al.  The physics of flow through porous media , 1957 .

[18]  Gilles Pijaudier-Cabot,et al.  Coupled diffusion-damage modelling and the implications on failure due to strain localisation , 1998 .

[19]  B. Schrefler,et al.  Modelling of heated concrete , 2002 .

[20]  Zdenek P. Bazant,et al.  Pore Pressure and Drying of Concrete at High Temperature , 1978 .

[21]  Pierre-Alain Gremaud,et al.  On a numerical approach to Stefan-like problems , 1991 .

[22]  Zdeněk P. Bažant,et al.  Pore Pressure in Heated Concrete Walls: Theoretical Prediction , 1979 .

[23]  Hans Muhlhaus,et al.  Continuum models for materials with microstructure , 1995 .

[24]  Marco Picasso,et al.  An adaptive finite element algorithm for a two-dimensional stationary Stefan-like problem , 1995 .

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

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

[27]  Abid Abu-Tair,et al.  The extraction of pore fluid from concrete using a heavy liquid extraction method , 2002 .

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

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

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

[31]  Modelling heat and moisture transfer in deformable porous building materials , 1996 .

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

[33]  Bernhard A. Schrefler,et al.  Thermo‐hydro‐mechanical analysis of partially saturated porous materials , 1996 .

[34]  Z. P. Bažant,et al.  Nonlinear water diffusion in nonsaturated concrete , 1972 .

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

[36]  Ricardo H. Nochetto,et al.  AN ADAPTIVE FINITE ELEMENT METHOD FOR TWO-PHASE STEFAN PROBLEMS IN TWO SPACE DIMENSIONS. PART I: STABILITY AND ERROR ESTIMATES , 1991 .

[37]  David Jon Furbish,et al.  Fluid Physics in Geology: An Introduction to Fluid Motions on Earth's Surface and within Its Crust , 1996 .

[38]  William G. Gray,et al.  Macroscale equilibrium conditions for two-phase flow in porous media , 2000 .