Clone granular soils with mixed particle morphological characteristics by integrating spherical harmonics with Gaussian
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RESEARCH PAPER
Clone granular soils with mixed particle morphological characteristics by integrating spherical harmonics with Gaussian mixture model, expectation–maximization, and Dirichlet process Quan Sun1 • Junxing Zheng1 Received: 7 November 2019 / Accepted: 2 April 2020 Springer-Verlag GmbH Germany, part of Springer Nature 2020
Abstract Computers have been taught to clone granular soil particles for discrete element method simulations to alleviate difficulties of using three-dimensional imaging techniques for scanning a large number of particles. In this process, computers analyze a few scanned particles to extract morphological characteristics of the target soil, which are used to clone as many particles as necessary. However, many natural granular soils contain a wide range of particle shapes mixing more than one type of morphological characteristics, causing difficulties in cloning. This research aims to address this challenge by integrating spherical harmonics with Gaussian mixture model, expectation–maximization, and Dirichlet process. Spherical harmonics coefficients are used to characterize morphological information of the granular soil. Gaussian mixture model is used to fit a function to the mixed morphological characteristics. The expectation–maximization and Dirichlet process are used to estimate the fitting parameters in Gaussian mixture model. Then, Gaussian mixture model is used to generate new spherical harmonics coefficients and then generate new particles. The effectiveness and accuracy of the proposed methodology are verified using a Griffin sand. Although this approach is developed for granular soils, the proposed technique can also be used to clone other particulate materials. Keywords Discrete element method Gaussian mixture model Granular particle generation Particle shape characterization Spherical harmonics X-ray computed tomography
1 Introduction Particle shape profoundly affects the engineering behavior of granular soils. For example, experimental studies have shown that sands consisting of angular and elongated particles exhibit larger values of index void ratios, internal friction, dilatancy, constant volume friction angle, compressibility, and small-strain modulus than sands with rounded and spherical particles [2, 3, 7, 9, 10, 16, 18–20, 25, 27, 35, 42, 44, 52, 60–62, 68]. Therefore, realistic particle geometries have been increasingly used in
& Junxing Zheng [email protected] Quan Sun [email protected] 1
Department of Civil, Construction and Environmental Engineering, Iowa State University, Ames, IA 50011, USA
analytical and numerical methodologies for explaining the observed macro-mechanical behavior of granular soils. For example, realistic particles were increasingly used in the discrete element method (DEM) to more precisely simulate the realistic mechanical behavior of granular soils [59, 63, 66]. The realistic particles can be scanned by various threedimensional (3D) imaging techniques, such as X-ray compute
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