Presentation on theme: "Microstructure Analysis of Geomaterials: Directional Distribution Eyad Masad Department of Civil Engineering Texas A&M University International Workshop."— Presentation transcript:
Microstructure Analysis of Geomaterials: Directional Distribution Eyad Masad Department of Civil Engineering Texas A&M University International Workshop in Geomaterials September 25-27 Prague, Czech Republic
Soil Structure vs. Soil Fabric Mitchell (1993): Soil structure: combination of fabric (arrangement of particles) and interparticle bonding.
Applications Model microstructure parameters (anisotropy and heterogeneity). Model verification. Computer simulation of fluid flow, deformation at the microstructure level.
Anisotropy vs. Homogeneity A B Define G as a material property: Heterogeneity: Anisotropy : G (A1) G(A2) A1 A2 G (A) G(B)
Anisotropy vs. Homogeneity A B A1 A2 Assumptions: Aggregate material is isotropic Binder material in isotropic
Measurements Representative Elemental Volume l (min) l (max) n
Anisotropy within the RVE M ij : microstructure tensor E(l): probability density function l i denotes the unit normal of an elementary solid angle d . represents the whole surface of a sphere representing the RVE, and d = sin d d for three dimensions, and d = d for two dimensions.
Mathematical Formulation of Directional Distribution Kanatani (1984, 1985)
Second Order Approximation of Directional Distribution 2 nd order directional distribution function of aggregate orientation: n(l): number of features oriented in the l-direction n a : average number of features Microstructure orientation tensor:
Parameters of Microstructure Distribution Tensor Tensor components: Second invariant of orientation tensor:
Microstructure Distribution Tensor Uniform Distribution =1.0, Transverse Anisotropic Random Distribution =0.0, Isotropic
Microstructure Quantities n+n+ n-n- Contact normal x1x1 x2x2 n+n+ n-n- Branch vector x1x1 x2x2 A B A, B : particle center n+n+ n-n- x x2x2 particle orientation
Correlation Function A B C I = 1 (solids), I = 0 (voids) M, N = number of points i, j = distance between two points p p+h
Correlation Function i, j estimate of particle size S(i.j) n n2n2 slope = -s/4 estimate of pore size Two-point correlation function: specific surface area particle size pore size
Normalized Correlation Function Normalize with respect to the solids ratio Use the spherical harmonic series with tensor notation
Quantifying parameters of directional distribution Average angle of inclination from the horizontal: Vector magnitude: q V.M. = 0 %>>>> random distribution q V.M. = 100% >>>> perfectly oriented distribution
Applications Ottawa Sand Glass Beads Silica Sand Quantifying the microstructure Low Angularity Smooth High Angularity Low Elongation Rounded High Elongation
Simulation of Soil Microstructure Measure 3-D DirectionalACF Generate a 3-D Gaussian noise Filtering thresholding Compare ACF of the model with the actual ACF Control ACF Control the average porosity