Monte Carlo Simulations of Mesoscale Fracture of Concrete with Random Aggregates and Pores: a Size Effect Study

Abstract Size effect in concrete under tension is studied by Monte Carlo simulations of mesoscale finite element models containing random inclusions (aggregates and pores) with prescribed volume fractions, shapes and size distributions (called meso-structure controls). For a given size and a set of controls, a number of realisations with different spatial distribution of inclusions are simulated to produce statistical data for macroscopic load/stress–strain curves. The complex meso-crack initiation and propagation is captured by pre-inserted cohesive interface elements. The effects of specimen size and meso-structure controls on macroscopic strength and toughness are analysed, and empirical size-effect laws for their dependences are proposed by data regression. It is also shown that the mesoscale porosity affects both strength and toughness and should not be ignored in size effect studies of concrete.

[1]  Hong-ping Zhu,et al.  Tensile fracture simulation of random heterogeneous asphalt mixture with cohesive crack model , 2012 .

[2]  M. V. Vliet.  Size effect in Tensile Fracture of Concrete and Rock , 2000 .

[3]  Hau-Kit Man,et al.  Size effect on strength and fracture energy for numerical concrete with realistic aggregate shapes , 2008 .

[4]  Alberto Carpinteri,et al.  Size effects on nominal tensile strength of concrete structures: multifractality of material ligaments and dimensional transition from order to disorder , 1995 .

[5]  Z. Bažant,et al.  Scaling of quasibrittle fracture: asymptotic analysis , 1997 .

[6]  W. Weibull.  A Statistical Distribution Function of Wide Applicability , 1951 .

[7]  Qiang Yu.  Size Effect in Fracture of Concrete Specimens and Structures: New Problems and Progress , 2004 .

[8]  Z. Bažant.  Size Effect in Blunt Fracture: Concrete, Rock, Metal , 1984 .

[9]  D. Jeulin,et al.  Determination of the size of the representative volume element for random composites: statistical and numerical approach , 2003 .

[10]  Andrey P. Jivkov,et al.  Monte Carlo simulations of mesoscale fracture modelling of concrete with random aggregates and pores , 2015 .

[11]  Harm Askes,et al.  Representative volume: Existence and size determination , 2007 .

[12]  Antonio Aguado,et al.  Meso-structural study of concrete fracture using interface elements. II: compression, biaxial and Brazilian test , 2008 .

[13]  Antonio Aguado,et al.  Meso-structural study of concrete fracture using interface elements. I: numerical model and tensile behavior , 2008 .

[14]  J. Mier,et al.  Experimental investigation of size effect in concrete and sandstone under uniaxial tension , 2000 .

[15]  Harm Askes,et al.  Quantification of stochastically stable representative volumes for random heterogeneous materials , 2006 .

[16]  Ignacio Carol,et al.  3D meso-structural analysis of concrete specimens under uniaxial tension , 2006 .

[17]  I. Gitman.  Representative volumes and multi-scale modelling of quasi-brittle materials , 2006 .

[18]  Ch. Zhang,et al.  Two-dimensional X-ray CT image based meso-scale fracture modelling of concrete , 2015 .

[19]  A. Carpinteri.  Decrease of apparent tensile and bending strength with specimen size: two different explanations based on fracture mechanics , 1989 .

[20]  M. Elices,et al.  GENERALIZED SIZE EFFECT EQUATION FOR QUASIBRITTLE MATERIALS , 1997 .

[21]  Bhushan Lal Karihaloo,et al.  Deterministic Size Effect in The Strength of Cracked Concrete Structures , 2006 .

[22]  Silvio Valente,et al.  Size effects in the mixed mode crack propagation: Softening and snap-back analysis , 1990 .

[23]  Peter Grassl,et al.  Meso-scale modelling of the size effect on the fracture process zone of concrete , 2011, 1107.2311.

[24]  Andrey P. Jivkov,et al.  Pore space and brittle damage evolution in concrete , 2013 .

[25]  Alberto Carpinteri,et al.  Multifractal scaling law for the nominal strength variation of concrete structures , 1993 .

[26]  Peter Grassl,et al.  Random Lattice-Particle Simulation of Statistical Size Effect in Quasi-Brittle Structures Failing at Crack Initiation , 2009 .

[27]  Stefano Zapperi,et al.  Statistical models of fracture , 2006, cond-mat/0609650.

[28]  Hau-Kit Man,et al.  Influence of particle density on 3D size effects in the fracture of (numerical) concrete , 2008 .

[29]  P. Wriggers,et al.  Mesoscale models for concrete: homogenisation and damage behaviour , 2006 .

[30]  Zhenguo Tu,et al.  Mesoscale modelling of concrete for static and dynamic response analysis -Part 1: model development and implementation , 2011 .

[31]  M.R.A. van Vliet,et al.  Influence of microstructure of concrete on size/scale effects in tensile fracture , 2003 .

[32]  Yunping Xi,et al.  Statistical Size Effect in Quasi-Brittle Structures: I. Is Weibull Theory Applicable? , 1991 .

[33]  Xiangting Su,et al.  Monte Carlo simulation of complex cohesive fracture in random heterogeneous quasi-brittle materials , 2009 .

[34]  Z. Bažant,et al.  Fracture and Size Effect in Concrete and Other Quasibrittle Materials , 1997 .

[35]  Z. M. Wang,et al.  Mesoscopic study of concrete I: generation of random aggregate structure and finite element mesh , 1999 .

[36]  T. C. Powers,et al.  Structure and Physical Properties of Hardened Portland Cement Paste , 1958 .

[37]  Xiaozhi Hu,et al.  Size effect on specific fracture energy of concrete , 2007 .