טכניון מכון טכנולוגי לישראל
הטכניון מכון טכנולוגי לישראל - בית הספר ללימודי מוסמכים  
M.Sc Thesis
M.Sc StudentLarom Yuval
SubjectDiscrete Geometric Modeling of Granular Soils, based on
Statistical Percolative Principles
DepartmentDepartment of Civil and Environmental Engineering
Supervisors Professor Avi Ostfeld
Dr. Shmulik Pinkert
Full Thesis textFull thesis text - English Version


Abstract

Soil is a non-homogeneous material composed of numerous grains with unique and amorphous morphology. The mechanical behavior of the soil can be modeled either by using continuum methods or by discrete methods, which express the mechanical behavior as a product of internal interactions between different soil grains. Ordinary discrete methods have been attributed Euclidean spherical shapes to the soil particles.  This thesis suggests a new geometric numerical modeling approach for discrete representation of a more realistic pore-scale morphology using an amorphous non-Euclidean geometry of soil grains' shape.

In the suggested model, the soil skeleton is described upon a numerical grid, in which each particle is composed of numerous numerical elements. The Soil-skeleton composition process follows a statistically-based consistent algorithm while implementing ideas derived from fractal and percolation theories.

The model enables the generation of random non-repetitive soil-skeleton morphology that keeps the same macro-scale geotechnical properties. The statistical values are governed by a set of functions that ensure (1) rational grain shapes (2) rational geometry for the grains attachment zones, (3) boundary conditions, and (4) the numerical stability of the whole process. The input parameters for these functions and their relation to some geotechnical properties are well defined. The model succeeds to show that the macro-scale (geotechnical) properties are not affected by the random generation process due to the utilized systematic statistical scheme. 

The algorithm is applied in a 2D domain. However, the dissertation presents a general formulation and algebraic expressions that could be further used in a 3D implementation. The results of the model are analyzed at the macro-scale level, whereby the grading curve is examined, and at the micro-scale level, where the grain shape is investigated (roundness, angularity, and roughness). The stability and the convergence of the method are verified for different input parameters. Measurement and interpretation at the granular scale are correlated with a variety of geotechnical properties. In addition, first steps of inverse analysis are presented that relates between the model parameters and the grading parameters so that a soil sample with desirable characteristics can be simulated.

The model should be further expanded to 3D domain and could be used for investigation of further issues related to a non-homogeneous distribution of various materials (liquids or solids) in the porous medium.