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International Journal for Multiscale Computational Engineering
IF: 1.016 5-Year IF: 1.194 SJR: 0.452 SNIP: 0.68 CiteScore™: 1.18

ISSN Print: 1543-1649
ISSN Online: 1940-4352

International Journal for Multiscale Computational Engineering

DOI: 10.1615/IntJMultCompEng.2012001697
pages 177-184

MULTI-SCALE MODELLING OF SNOW MICROSTRUCTURE

Anna Carbone
Applied Science and Technology Department, Politecnico di Torino,Torino, Italy; ETH Zurich, Switzerland
B. M. Chiaia
Department of Structural and Geotechnical Engineering, Politecnico di Torino, Corso Duca degli Abruzzi 24, I-10129 Torino, Italy
B. Frigo
Department of Structural and Geotechnical Engineering, Politecnico di Torino, Corso Duca degli Abruzzi 24, I-10129 Torino, Italy
C. Turk
Applied Science and Technology Department, Politecnico di Torino, Corso Duca degli Abruzzi 24, I-10129 Torino, Italy

ABSTRACT

A three-dimensional multiscale spatial model of snow with evolving microstructure is presented. Many engineering and environmental problems require a comprehensive understanding of snow behavior which arises as a consequence of phenomena spanning a wide spectrum of spatial length scales. Snow is classically described as a granular heterogeneous medium consisting of air and three water phases: ice, vapor, and liquid. The ice phase consists of grains arranged on a matrix according to a random load-bearing skeleton. The challenge is to achieve a detailed description of the mechanical and morphological characteristics of different snow microstructures that may have the same global density. Snow density can be determined by in situ measurements with quite good accuracy, and by means of the box-counting method, the fractal dimension of snow samples characterized by grains with different diameters could be determined. It was suggested that the fractal dimension can be adopted as a relevant parameter for quantifying snow morphology, in terms of the distribution of voids, and density over a wide range of spatial scales. In this work this concept is further developed. Snow density is simulated by means of a lacunar fractal, namely, a generalized Menger sponge. Then, a fully threedimensional invasive stochastic fractal model is adopted. This model performs a three-dimensional mapping of the snow density to a three-dimensional fractional Brownian field. In particular, snow samples with evolving microstructure are quantified as a continuous function of the fractal dimension.


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