Final presentation (2)

Structure-Property Linkage of Packed Soil Particles

ME-8883

TEAM MEMBER: Mahdi Roozbahani, Jie(Jessie) Cao

Dec 8, 2014

CONTENTS

Motivation and Objective

Method of Approach Packed Soil Particles Samples

Numerical Hydraulic Conductivity Analysis

2-Point Statistics Analysis

Dimensionality Reduction

Regression Analysis

Summary and Conclusions

MOTIVATION AND OBJECTIVE Hydraulic conductivity is a key parameter in soil mechanics. Experimental tests are cost expensive and difficult to conduct. Available empirical solutions have restricted applications. Numerical simulations are very computational expensive.

Develop a fast,rigorous approach to quantify hydraulic conductivity of packed soil particles based on thorough microstructural information.

Objective

METHOD OF APPROACH

Packed Soil Particles Subsamples FVM Analysis

2-Point StatisticsPCA & Regression Analysis

PACKED SOIL PARTICLES SAMPLES Gravitational Sphere Packing Simulation

Geometrical simulation method Pack spherical particles Drop-roll concept

GSP Animation

PACKED SOIL PARTICLES SAMPLES

Mono-sized Subsample Binary-sized Subsample

Multi-sized Subsample Real Subsample

NUMERICAL HYDRAULIC CONDUCTIVITY ANALYSIS

Finite Volume Method for incompressible single-phase flow

(assumptions)

Pre

ssu

re G

rad

ien

t

(basic model)

(Darcy’s law)

constant pressure gradient

NUMERICAL HYDRAULIC CONDUCTIVITY ANALYSIS

Hydraulic Conductivity Results of 703 Subsamples

2-POINT STATISTICS ANALYSIS Visualization 2-Point Statistics in 2D

Void phase – central slice (Mono-sized sample)

Visualization 2-Point Statistics in 2D

Particle phase – central slice (Mono-sized Sample)

2-POINT STATISTICS ANALYSIS

Visualization 2-Point Statistics

Void Phase (Mono-sized sample)

2-POINT STATISTICS ANALYSIS

Visualization 2-point Statistics

Particle Phase (Mono-sized Sample)

2-POINT STATISTICS ANALYSIS

Singular Value Decomposition (SVD) Principal Component Analysis (PCA)

DIMENSIONALITY REDUCTION

Cumulative Eigenvalue Explanation

Visualization in the first two principal components

DIMENSIONALITY REDUCTION

First Principal Component

Sec

ond

Prin

cipa

l Com

pone

nt

Visualization in the first two principal components

DIMENSIONALITY REDUCTION

First Principal Component

Sec

ond

Prin

cipa

l Com

pone

nt

What happens to Binary-sized sample?

DIMENSIONALITY REDUCTION

Visualization in the first three principal components

DIMENSIONALITY REDUCTION

First Trial - 2D Regression

REGRESSION ANALYSIS

Hyd

rau

lic C

on

du

cti

vit

y (

m/s

)

PC1

PC2

f(x,y) = p00 + p10*x + p01*yCoefficients (with 95% confidence bounds): p00 = 0.2371 (0.2345, 0.2397) p10 = 0.0008264 (0.0007775, 0.0008753) p01 = -0.000629 (-0.001082, -0.0001759)

Goodness of fit:SSE: 0.8705 R-square: 0.6476 Adjusted R-square: 0.6466 RMSE: 0.03526

Multi-polynomial regression analysis

REGRESSION ANALYSIS

Multi-polynomial regression analysis

REGRESSION ANALYSIS

n: number of dimensions d: polynomial degreeyhat: predicted value of hydraulic conductivity

y: numerically calculated value of hydraulic conductivity

Leave-one-out cross validation

REGRESSION ANALYSIS

SUMMARY AND CONCLUSIONS A data-driven approach is applied to establish the structure-hydraulic-

conductivity relationships in packed soil particles.

Four packed soil particles samples are examined (mono-sized, binary-sized and multi-sized samples generated by GSP, as well as a real sand samples) by randomly sampling 703 subsamples.

Hydraulic conductivity is estimated based on numerical approach (FVM).

2-Point spatial correlations are employed to define the microstructures mathematically.

PCA is used to obtain a reduced-order representations for microstructures.

Desired structure-property correlation is mined using regression method combining leave-one-out cross validation analysis.

REFERENCES• Roozbahani, M. M., Graham‐Brady, L., & Frost, J. D. (2014). Mechanical trapping

of fine particles in a medium of mono‐sized randomly packed spheres. International Journal for Numerical and Analytical Methods in Geomechanics.

• Çeçen, A., Fast, T., Kumbur, E. C., & Kalidindi, S. R. (2014). A data-driven approach to establishing microstructure–property relationships in porous transport layers of polymer electrolyte fuel cells. Journal of Power Sources, 245, 144-153.

• Mönkeberg, F., & Hiptmair, R. (2012). Finite volume methods for fluid flow in porous media.

• Aarnes, J. E., Gimse, T., & Lie, K. A. (2007). An introduction to the numerics of flow in porous media using Matlab. In Geometric Modelling, Numerical Simulation, and Optimization (pp. 265-306). Springer Berlin Heidelberg.

• Santamarina, J. C., Klein, A., & Fam, M. A. (2001). Soils and Waves: Particulate Materials Behavior, Characterization and Process Monitoring.

• Lu, Y. (2010). Reconstruction, characterization, modeling and visualization of inherent and induced digital sand microstructures.

Thank you!

ME-8883

TEAM MEMBER: Mahdi Roozbahani, Jie(Jessie) Cao

Dec 8, 2014