Download presentation

Presentation is loading. Please wait.

Published byDayana Cougill Modified over 3 years ago

1
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

2
Soil Structure vs. Soil Fabric Mitchell (1993): Soil structure: combination of fabric (arrangement of particles) and interparticle bonding.

3
Applications Model microstructure parameters (anisotropy and heterogeneity). Model verification. Computer simulation of fluid flow, deformation at the microstructure level.

4
Anisotropy vs. Homogeneity A B Define G as a material property: Heterogeneity: Anisotropy : G (A1) G(A2) A1 A2 G (A) G(B)

5
Anisotropy vs. Homogeneity A B A1 A2 Assumptions: Aggregate material is isotropic Binder material in isotropic

6
Measurements Representative Elemental Volume l (min) l (max) n

7
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.

8
Mathematical Formulation of Directional Distribution Kanatani (1984, 1985)

9
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:

10
Parameters of Microstructure Distribution Tensor Tensor components: Second invariant of orientation tensor:

11
Microstructure Distribution Tensor Uniform Distribution =1.0, Transverse Anisotropic Random Distribution =0.0, Isotropic

12
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

13
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

14
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

15
Normalized Correlation Function Normalize with respect to the solids ratio Use the spherical harmonic series with tensor notation

16
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

17
Applications Ottawa Sand Glass Beads Silica Sand Quantifying the microstructure Low Angularity Smooth High Angularity Low Elongation Rounded High Elongation

18
Sample Preparation

20
Localized Directional Distribution Function v directional porosity function

21
Directional porosity

23
Autocorrelation function Validation of the directional autocorrelation expression

24
Autocorrelation Function

25
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

26
Measured vs. Simulated ACF

27
Equations of Fluid Flow (two dimensional analysis) r Numerical solution of Navier-Stokes equation and the equation of continuity

28
Boundary Conditions p 1 p 2 h

29
Pressure difference maintained at inlet and outlet Periodic Boundary Conditions u(x=0) = u(x=h) v(x=0) = v(x=h) u(y=0) = u(y=h) v(y=0) = v(y=h) No slip: u s = 0, v s = 0

30
Limitations Specific surface area

31
Flow Fields

32
increase in porosity Ottawa sand

33
Flow Fields silica sandOttawa sandglass beads

34
Asphalt Mixes To quantify aggregates distribution 0 < < 1 (= 0.5 for asphalt mixes)

35
Aggregate Orientation in Asphalt Concrete Aggregate orientation exhibits transverse anisotropy (axisymmetry) with respect to the horizontal direction.

36
Moving Window Technique to Measure Heterogeneity

37
Length Scale: Autocorrelation Function r = (i 2 +j 2 ) 0.5 Two-point ACF is given as: Isotropic: S is independent on direction of i and j. Weak Homogeneity: S is not dependent on location (x,y)

38
Length Scale: 3-D Autocorrelation Function

39
Three-Dimensional Orientation of Aggregates

40
Aggregate Orientation

41
Damage Experiment 2 Replicates

42
Effect of Deformation on Void Content

43
Change in Void Measurements: Deformed Specimens

44
Damage Evolution Top Region Middle Region Bottom Region Strain: 0%Strain: 1%Strain: 2%Strain: 4% Strain: 8%

45
Extended Drucker-Prager Yield Surface Hardening/softening Shear, and stress path

46
Model Parameters – cohesion and adhesion

47
Model Parameters – friction parameter

48
Model Parameters – damage parameter

49
Model Parameters – aggregate distribution

51
Experiments and Results “Compression” Gravel mixes

52
Compression Test Simulation Granite mixes

53
Compression Test Simulation Limestone mixes

54
Extension Test Simulation GravelGraniteLimestone

55
Lateral Strain Simulation GravelGraniteLimestone

56
Granite Limestone Gravel

58
Finite Element Simulation for Pavement Section Isotropic Anisotropic

59
Effect of Anisotropy on Permanent Deformation a) Isotropic layer ( =0) b) Anisotropic layer ( =30 percent)

60
Granite Limestone Gravel

Similar presentations

OK

Information Geometry and Model Reduction Sorin Mitran 1 1 Department of Mathematics, University of North Carolina, Chapel Hill, NC, USA Reconstruction.

Information Geometry and Model Reduction Sorin Mitran 1 1 Department of Mathematics, University of North Carolina, Chapel Hill, NC, USA Reconstruction.

© 2018 SlidePlayer.com Inc.

All rights reserved.

To ensure the functioning of the site, we use **cookies**. We share information about your activities on the site with our partners and Google partners: social networks and companies engaged in advertising and web analytics. For more information, see the Privacy Policy and Google Privacy & Terms.
Your consent to our cookies if you continue to use this website.

Ads by Google

Ppt on trial and error dvd Ppt on polytene chromosomes of drosophila Ppt on current account convertibility Ppt on airbags in cars Free download ppt on green revolution Ppt on nickel cadmium battery Ppt on network theory of immigration Ppt on fuel from plastic waste pdf Ppt on game theory poker Ppt on central limit theorem in statistics