Spherical harmonic-based random fields for aggregates used in concrete

Abstract Two non-Gaussian random field models are developed for characterizing the geometry of star-like inclusions in two-phase or multi-phase materials. For illustration, the models are calibrated to the geometrical features of a population of 128 similar ASTM C57 aggregates used in concrete. The first model is a sum of spherical harmonic functions with random non-Gaussian coefficients. The second model is a nonlinear memoryless mapping of a sum of spherical harmonic functions with Gaussian coefficients. The two random field models are used to develop Monte Carlo algorithms for generating virtual aggregates. By construction, the virtual aggregates capture essential statistics of the target population of aggregates. The performance of the proposed models is assessed by quantitative and qualitative metrics.

[1]  David W. Fowler,et al.  Some properties of irregular 3-D particles , 2006 .

[2]  E. Garboczi.  Three-dimensional mathematical analysis of particle shape using X-ray tomography and spherical harmonics: Application to aggregates used in concrete , 2002 .

[3]  David W. Luerkins.  Theory and Application of Morphological Analysis: Fine Particles and Surfaces , 1991 .

[4]  Edward J. Garboczi,et al.  A Hard Core/Soft Shell Microstructural Model for Studying Percolation and Transport in Three-Dimensional Composite Media | NIST , 1999 .

[5]  Nelson L. Max,et al.  Spherical harmonic molecular surfaces , 1988, IEEE Computer Graphics and Applications.

[6]  L. S. Leung.  Design of fluidized Gas—Solids flow in standpipes , 1977 .

[7]  J. Finney,et al.  Representation of the size and shape of a single particle , 1975 .

[8]  Jeffrey W. Bullard,et al.  VIRTUAL TESTING OF CEMENT AND CONCRETE: USA 2004 , 2004 .

[9]  System response to partially known input , 2004 .

[10]  E. Garboczi,et al.  Intrinsic viscosity and the electrical polarizability of arbitrarily shaped objects. , 2001, Physical review. E, Statistical, nonlinear, and soft matter physics.

[11]  P. R. Fisk,et al.  Distributions in Statistics: Continuous Multivariate Distributions , 1971 .

[12]  Anthony Roberts.  Statistical reconstruction of three-dimensional porous media from two-dimensional images , 1997 .

[13]  G. Stachowiak,et al.  Simulation of three-dimensional abrasive particles , 2005 .

[14]  Graham J. L. Kemp,et al.  Fast computation, rotation, and comparison of low resolution spherical harmonic molecular surfaces , 1999, J. Comput. Chem..

[15]  Paul Bratley,et al.  A guide to simulation , 1983 .

[16]  T. A. A. Broadbent,et al.  Survey of Applicable Mathematics , 1970, Mathematical Gazette.

[17]  S. Torquato,et al.  Random Heterogeneous Materials: Microstructure and Macroscopic Properties , 2005 .

[18]  E. Garboczi,et al.  Using LADAR to characterize the 3-D shape of aggregates: Preliminary results , 2006 .

[19]  Dallas N. Little,et al.  Computations of particle surface characteristics using optical and X-ray CT images , 2005 .

[20]  Jan D. Miller,et al.  3D characterization and analysis of particle shape using X-ray microtomography (XMT) , 2005 .

[21]  E. Hobson.  The Theory of Spherical and Ellipsoidal Harmonics , 1955 .

[22]  A. Olson,et al.  Approximation and characterization of molecular surfaces , 1993, Biopolymers.

[23]  Mircea Grigoriu,et al.  Random field models for two-phase microstructures , 2003 .

[24]  Garboczi,et al.  Intrinsic conductivity of objects having arbitrary shape and conductivity. , 1996, Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics.

[25]  Jeffrey W. Bullard,et al.  Shape analysis of a reference cement , 2004 .

[26]  Mircea Grigoriu,et al.  Applied non-Gaussian processes : examples, theory, simulation, linear random vibration, and MATLAB solutions , 1995 .

[27]  Snyder,et al.  Geometrical percolation threshold of overlapping ellipsoids. , 1995, Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics.

[28]  E. Garboczi,et al.  Intrinsic Viscosity and the Polarizability of Particles Having a Wide Range of Shapes , 2007 .