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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