Evolution of Hydraulic Conductivity of Unsaturated Compacted Na-Bentonite under Confined Condition—Including the Microstructure Effects
Abstract
:1. Introduction
2. Theory and Methodology
2.1. Pore Evolution of Compacted Bentonite
2.1.1. Specific Surface Area
2.1.2. Evolution of Pore System
2.1.3. Tortuosity
2.2. Model for Unsaturated Hydraulic Conductivity
3. Results and Discussion
3.1. Experimental Data and Parameters of Model
3.2. Saturated Hydraulic Conductivity
3.3. Unsaturated Hydraulic Conductivity
4. Summary and Conclusions
Author Contributions
Funding
Institutional Review Board Statement
Informed Consent Statement
Data Availability Statement
Acknowledgments
Conflicts of Interest
Abbreviations
k | Hydraulic permeability (m/s) |
kr | Relative hydraulic conductivity |
Proposed relative hydraulic conductivity of compacted bentonite | |
ksat | The saturated hydraulic conductivity (m/s) |
kunsat | The unsaturated hydraulic conductivity (m/s) |
Se | The effective saturation |
θ | The actual volumetric water content |
θr | The residual volumetric water content |
θs | The saturated volumetric water content |
α | The constant parameter in Mualem [54] |
μ | A dimensionless number in Burdine [31] |
Ψ | Suction of soil/bentonite(MPa) |
Ψd | The air entry value (MPa) |
λ | A fitting factor related to pore-size distribution |
Cs | Shape factor |
τ | Tortuosity |
γw | Unit weight of water (N/m3) |
η | Viscosity of water (Pa∙s) |
SA | Specific surface area (m2/kg) |
Φ | Porosity |
ρd | Dry density of soil (kg/m3) |
Atot | Total specific surface area (m2/kg) |
n | The number of TOT layers of per particle |
N | Total number of TOT layers of bentonite sample |
Aext | External specific surface area of bentonite (m2/g) |
As | The surface area of a single TOT layer |
msi | Mass of one particle (kg) |
msmectite | Mass of smectite (kg) |
ms | Mass of solid (kg) |
b C | A constant related to water adsorption rate A correction term |
ω | Water content (kg/kg) |
ρw | Density of water (kg/m3) |
mw | The mass of water (kg) |
Vt | Total volume of soil sample (m3) |
Vw | Volume of total water in soil (m3) |
Dry density of smectite (kg/m3) | |
dTOT | Thickness of TOT layer (9.5 Å) |
dt | Basal spacing (Å) |
hw | Total interlayer water thickness of soil |
Vimw | Micro pore volume/volume of interlayer water |
Ve | Macro pore volume/effect pore volume |
Vs | Volume of solid (m3) |
diw | Interlayer water thickness between two TOT layers |
Φmacro | Macro porosity (Effective porosity) |
Φmicro | Micro porosity (Interlayer porosity) |
ρs | Density of the solid (kg/m3) |
ρi | Density of the non-smectite minerals or impurities (kg/m3) |
Gs | Specific gravity of clay |
Xsm | The mass fraction of smectite in the bentonite |
Le | Effective path length of flow |
L | Sample length |
ref | The reference case in which measurements are available |
β | A fitting factor between Φ and Ψ in Pham et al. [92] |
σ | Coefficient related to porosity and size of pore |
Xhs | Mole fraction of hydrated smectite |
Msm | Molar mass of dry smectite (Kg/mol) |
ζc | The number of moles of waters in the interlayer adsorption or desorption reaction |
υil | The molar volume of the interlayer water (m3/mol) |
a, m | Curve-fitting parameters by van Genuchten [24] |
nmax, nmin | The maximum and minimum number of TOT layers of bentonite particle respectively |
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Water Layers | Basal Spacing (Å) | |||||
---|---|---|---|---|---|---|
[69] | [70] | [49] | [66] | |||
0 | 9.5 | 10 | 9.5 | 9.5 | 9.2–10.1 | 10 |
1 | 12.4 | 12.5 | 12.3 | 12.4 | 12.2–12.7 | 12.6 |
2 | 15.4 | 15.5 | 15.0 | 15.6 | 15.2–15.7 | 15.6 |
3 | 18.4 | 18.5 | 18.5 | 18.9 | 18.4–19 | 18.6 |
4 | 21.6 * | \ | \ | 21.8 * | 21.4–22 * | 21.6 |
Water Layers | Water Content (g/g, %) | ||||
---|---|---|---|---|---|
[71,72] | [70] | [66] | [49] | ||
0 | <7 | <8.6 | <11.1 | <10.8 | <8.8 |
1 | 7–20 | 8.6–16.8 | 11.1–19.2 | 10.8–23.3 | 8.8–19.7 |
2 | 10–20 | 16.8–28.4 | 19.2–32.4 | 23.3–35.4 | 19.7–30.3 |
3 | 20–35 | >28.4 | 32.4–69.4 | >35.4 | >30.3 |
4 | \ | \ | >69.4 | \ | \ |
Mineral | GMZ | MX80 |
---|---|---|
Montmorillonite (%) | 75.4 1 | 79 1 |
Particle < 2 μm (%) | 60 1 | 60 1 |
Specific surface area (m2/g) | 570 1 | 756 4 |
Gs | 2.66 1 | 2.82 2 |
CEC (meq/100 g) | 77.3 1 | 82.3 1 |
WL (%) | 313 1 | 519 1 |
WP (%) | 38 1 | 35 1 |
IP | 275 1 | 484 1 |
Molar mass (g/mol O10(OH)2)) | \ | 378.79 3 |
1—[15,17]. 2—[93]. 3—[94]. 4—[49]. |
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Chen, T.; Du, M.; Yao, Q. Evolution of Hydraulic Conductivity of Unsaturated Compacted Na-Bentonite under Confined Condition—Including the Microstructure Effects. Materials 2022, 15, 219. https://doi.org/10.3390/ma15010219
Chen T, Du M, Yao Q. Evolution of Hydraulic Conductivity of Unsaturated Compacted Na-Bentonite under Confined Condition—Including the Microstructure Effects. Materials. 2022; 15(1):219. https://doi.org/10.3390/ma15010219
Chicago/Turabian StyleChen, Tian, Mao Du, and Qiangling Yao. 2022. "Evolution of Hydraulic Conductivity of Unsaturated Compacted Na-Bentonite under Confined Condition—Including the Microstructure Effects" Materials 15, no. 1: 219. https://doi.org/10.3390/ma15010219
APA StyleChen, T., Du, M., & Yao, Q. (2022). Evolution of Hydraulic Conductivity of Unsaturated Compacted Na-Bentonite under Confined Condition—Including the Microstructure Effects. Materials, 15(1), 219. https://doi.org/10.3390/ma15010219