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Figure 1:
Grain size distribution curves of analyzed samples.
Figure 2:
Setup for measurement.
Figure 3:
Permeameter fixture.
Figure 4:
General concept of a pore-network model.
Figure 5:
Analogous model of the resistor network.
Figure 6:
Rendered view of reconstructed a) sample 1, b) sample 2, and c) sample 3.
Figure 7:
Exemplary slice, volumes of interest and binarized image of a) sample 1, b) sample 2, and c) sample 3.
Figure 8:
Results of measurements in permeameter and best-fitting theoretical curves: a) sample 1, b) sample 2, and c) sample 3, and d) reference run without the sample attached. The vertical axis is scaled logarithmically for better fitting evaluation.
Figure 9:
Comparison of measured and simulated grain size distribution curves from different sizes of VOI for a) sample 1, b) sample 2, and c) sample 3.
Figure 10:
Relative differences between hydraulic conductivity calculated with data from simulated sifting and those from granulometric analysis.
Figure 11:
Tracks of random walkers after 1250 time steps in sample 3. Only 10% of all workers are shown for clarity.
Figure 12:
Pore network extracted from a) sample 1, b) sample 2, and c) sample 3 with a zoomed fragment of the network.
Figure 13:
Streamlines of flow calculated using LBM: a) sample 1, b) sample 2, and c) sample 3.
Figures 14:
Calculated and measured hydraulic conductivities for a) sample 1, b) sample 2, and c) sample 3.
Results of simulations using the lattice-Boltzmann method.
Sample no.
Sample name
VOI size
Porosity derived from image data
Permeability
Hydraulic conductivity at 10°C
[vx]
φimg [−]
k [μm2]
K [m/s]
1
Fine sand
4003
0.365
23.489
1.758E-4
6003
0.364
17.567
1.317E-4
2
Fine sand with lignite
4003
0.511
20.923
1.565E-4
6003
0.511
23.193
1.736E-4
3
Medium sand
4003
0.309
16.778
1.259E-4
6003
0.317
15.396
1.151E-4
Results of measurements with the described small-scale permeameter setup.
Sample no.
Sample name
Mean conductivity derived from the best-fit curve
Conductivity of the apparatus
Hydraulic conductivity in the measurement temperature
Hydraulic conductivity at 10°C
Kequiv [m/s]
Kap [m/s]
Kex [m/s]
Kcorr [m/s]
1
Fine sand
2.663E-5
4.927E-3
2.678E-5
1.951E-5
2
Fine sand with lignite
4.457E-6
4.461E-6
3.250E-6
3
Medium sand
6.183E-5
6.262E-5
4.562E-5
Results of simulations using the pore-network modeling approach.
Sample no.
Sample name
VOI size
Porosity derived from image data
Permeability
Hydraulic conductivity at 10°C
[vx]
φimg [−]
k [μm2]
K [m/s]
1
Fine sand
4003
0.365
23.666
1.786E-4
6003
0.364
23.587
1.780E-4
8003
0.363
24.061
1.816E-4
2
Fine sand with lignite
4003
0.511
28.433
2.145E-4
6003
0.511
27.969
2.110E-4
8003
0.506
27.338
2.063E-4
3
Medium sand
4003
0.309
17.311
1.306E-4
6003
0.317
20.301
1.532E-4
8003
0.317
22.087
1.667E-4
Measured properties of the samples.
Sample no.
Sample name
Soil type according to PN-EN ISO 14688-2:2018
Bulk density
Specific density
Porosity in loose state
Hydraulic conductivity in falling-head test at 10°C
Uniformity coefficient U=d60/d10
GSD curve slope coefficient C=d302/(d60·d10)
[−]
ρ [g/cm3]
ρs [g/cm3]
φ [−]
K [m/s]
U [−]
C [−]
1
Fine sand
FSa
1.549
2.634
0.412
1.702E-5
1.840
1.054
2
Fine sand with lignite
FSa
1.238
2.644
0.532
3.189E-6
2.532
1.027
3
Medium sand
MSa
1.652
2.654
0.377
4.067E-5
3.147
1.003
Results of estimation using the Kozeny–Carman equation.