Mobilization and Deposition of Variably Charged Soil Colloids in Saturated Porous Media
Quantifying soil complexity using network models of soil porous structure
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Transcript of Quantifying soil complexity using network models of soil porous structure
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Quantifying soil complexity using network models
of soil porous structureMarko Samec (1), Antonio Santiago (2), Juan Pablo Cardenas (2),
Rosa Maria Benito (2), Ana Maria Tarquis (3), Sacha Jon Mooney (4), Dean Korošak (1,5)
(1) Faculty of Civil Engineering, University of Maribor, Maribor, Slovenia ([email protected]) (2) Grupo de Sistemas Complejos, Departamento de Física, Universidad Politécnica de Madrid, 28040 Madrid, Spain
(3) Departamento de Matemática Aplicada, Universidad Politécnica de Madrid, 28040 Madrid, Spain (4) Environmental Sciences Section,University of Nottingham, Nottingham, UK
(5) Institute of Physiology, Faculty of Medicine, University of Maribor, Maribor, Slovenia
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SEE INTO
DESCRIB
E
QUANTIF
Y
porous matter
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SEE INTO
DESCRIBE
QUANTIFY
3D X-ray CT
porous matter
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SEE INTO
DESCRIBE
QUANTIFY
complex network theory
porous matter
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SEE INTO
DESCRIB
E
QUANTIF
Y
complexity hsingle parameter
porous matter
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how can one see into the porous structure of material
X-RAY COMPUTED TOMOGRAPHY
?
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X-ray COMPUTED TOMOGRAPHY
part of x-rays absorbed
higher density of the matter,
more X-rays are absorbed
the ones that manage to pass, create image
pore space
measuring cell
solid space
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X-ray COMPUTED TOMOGRAPHY concept
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X-ray COMPUTED TOMOGRAPHY image analysis
tomography image
crop and scale
contrast
threshold algorithm
binary image
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X-ray COMPUTED TOMOGRAPHY image analysis
sample average pore size
[mm2]
perimeter
[mm]
porosity
[%]
circularity
cement 0 h 0,000946 0,130280 4,70 0,69937
cement 2 h 0,000945 0,123051 2,70 0,72173
cement 24 h 0,000923 0,127010 4,11 0,70707
clay 0 h 0,003331 0,223884 0,83 0,68927
clay 2 h 0,004022 0,247481 1,00 0,68024
clay 24 h 0,003497 0,233920 1,01 0,66495
SC 0 days 0,004285 0,241832 2,56 0,66450
SC 14 days 0,002455 0,191862 2,89 0,68797
SC 28 days 0,003884 0,252968 2,78 0,67895
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how can one describethe porous structure of material
COMPLEX NETWORK THEORY
?
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BEGININGS
Seven Bridges of Königsberg, Euler (1735)
sociogram, Moreno (1993)
p53 gene network , Volgestein et al. (2000)
medicine, biology, computer science, particle
physics, economics, sociology, ecology,
epidemology, neuroscience,...
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node or vertex
link or edge
direction
weight
node degree
degree distribution
BASICS
1 1 0 0 1 0
1 0 1 0 1 0
0 1 0 1 0 0
0 0 1 0 1 1
1 1 0 1 0 0
0 0 0 1 0 0
𝑘𝑖 = 𝑎𝑖𝑗𝑗
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BASICS
Erdos-Renyi network (random linking)
scale-free networks (preferential linking)degree distribution
00
number of links k
degr
ee d
istr
ibuti
on P
(k)
many nodes with only a few links
a few hubs with large number of links
𝑃(𝑘)~𝑘−𝛾
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X-ray COMPUTED TOMOGRAPHY image analysisCL
AY
φ = 0,9 %
CEM
ENT
φ = 1,8 %
φ = 4,2 %
STAB
ILIZ
ED C
LAY
φ = 2,4 %
φ = 4,2 %
Cumulative size distributions,
determined from X-CT images of different porosity
φ. All samples show scale-free behaviour of size distribution (solid line)
with the exponent α=1,8-2.
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NETWORK MODELS for description of porous structure of building materials
threshold network model (SN)
preferential attachement model (EN)
the network heterogeneity can be adjusted by changing the parameters b and m
𝑠𝑖𝑠𝑗𝑑𝑖𝑗𝑚 > 𝜀
𝜋𝑖𝑗~𝑘𝑖 𝜎ሺ𝑖,𝑗ሻ 𝜎ሺ𝑖,𝑗ሻ= 𝑠𝑗𝑏𝑑𝑖𝑗𝑚
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can one quantifydifferent porous structure of material
COMPLEXITY
?
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COMPLEXITY
correlation matrices
to further explore the effect of the network
parameter m on node correlations we
calculated the complexity h of the pore network
based on node-node link correlations
a) m≪1
b) m=1
c) m>>1
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COMPLEXITY
α 1,4 1,5 1,6
h 2,85231 3,06864 3,48277
to further explore the effect of the network
parameter m on node correlations we
calculated the complexity h of the pore network
based on node-node link correlations
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by combining X-ray CT and complex network models
we can quantify
complexityof porous structure with single parameter
CONCLUSIONS
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Quantifying soil complexity using network models
of soil porous structureMarko Samec (1), Antonio Santiago (2), Juan Pablo Cardenas (2),
Rosa Maria Benito (2), Ana Maria Tarquis (3), Sacha Jon Mooney (4), Dean Korošak (1,5)
(1) Faculty of Civil Engineering, University of Maribor, Maribor, Slovenia ([email protected]) (2) Grupo de Sistemas Complejos, Departamento de Física, Universidad Politécnica de Madrid, 28040 Madrid, Spain
(3) Departamento de Matemática Aplicada, Universidad Politécnica de Madrid, 28040 Madrid, Spain (4) Environmental Sciences Section,University of Nottingham, Nottingham, UK
(5) Institute of Physiology, Faculty of Medicine, University of Maribor, Maribor, Slovenia