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MI-ECku: A novel methodology for estimating unsaturated hydraulic conductivity of porous media

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Abstract

Numerous applications of hydraulic conductivity of porous media (e.g., soils, clay liners, rocks, concrete, ceramic filters, etc.) in their unsaturated state are well established in the field of geotechnical and agriculture engineering. In recent years, researchers have developed laboratory techniques by resorting to thermal flux sensors, electrical impedance spectroscopy, geotechnical centrifuge, and tensiometers, for determining the unsaturated hydraulic conductivity, ku, of the porous media. However, these methodologies and techniques are susceptible to yield ‘uncertain’, if not ‘erroneous’, results mainly: (i) due to the difficulties associated with maintaining uniform saturation of the specimen and (ii) intricacies in maintaining a pressure gradient along the porous media (having nanometric pore size) to facilitate flow at a constant suction. To overcome these limitations, a novel methodology, MI-ECku (read as, my-easy ku), that employs, (i) ‘modified Kozeny-Carmen relationship’ and the pore-size distribution characteristics (obtained from mercury intrusion porosimetry, MIP) and (ii) the electrical conductivity (obtained from impedance spectroscopy) of the porous media, has been proposed for determining ku. The robustness and ease of utilization of MI-ECku have been demonstrated by employing the standard porous media, SPM, which contains a rigid pore structure and inert mineralogy. It has been noticed that ku of the SPM determined by MI-ECku is in good agreement with those predicted by van Genuchten-Mualem model and hence it can be employed for estimating ku of various porous media such as compacted soils and rocks.

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Abbreviations

η :

Porosity

η MIP :

Porosity obtained from the mercury intrusion porosimetry results

S r :

Degree of saturation

K :

Intrinsic permeability

k :

Hydraulic conductivity

k r , k s and k u :

Relative, saturated and unsaturated hydraulic conductivity, respectively

µ :

Dynamic viscosity

d, d m and d avg :

Diameter, mode diameter and average diameter, respectively

Z :

Electrical Impedance

EC, EC s, and EC dry :

Electrical conductivity, saturated and dry state electrical conductivity, respectively

P :

Pressure

T :

Surface tension of mercury (= 0.48 N/m)

α :

Contact angle between mercury and SPM

c v :

Cumulative volume of the pores

v w and ww :

Volume and weight of water, respectively

c :

Pore shape coefficient

G :

Pore geometry

V :

Total volume of the SPM

θ, θ s and θ r :

Volumetric moisture content, saturated and residual moisture content

w :

Gravimetric water content

m:

Van Genuchten fitting parameter

k*:

Dielectric constant

RIC:

Relative increase in electrical conductivity

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Acknowledgements

Authors would like to acknowledge the help and support rendered by Dr. Kannan Iyer, Dr. Bruna Lima Lopes and Dr. Siju K Swamy during the course of this study.

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Authors and Affiliations

  1. Department of Civil Engineering, National Institute of Technology Trichy, Tiruchirappalli, Tamil Nadu, 620015, India

    Jeevan Joseph

  2. Department of Civil Engineering, Indian Institute of Technology Bombay, Powai, Mumbai, 400076, India

    Shetty Rakshith & D. N. Singh

  3. School of Earth Sciences and Engineering, Nanjing University, Nanjing, 210023, China

    C. S. Tang

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  1. Jeevan Joseph
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Correspondence to D. N. Singh.

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Joseph, J., Rakshith, S., Singh, D.N. et al. MI-ECku: A novel methodology for estimating unsaturated hydraulic conductivity of porous media. Acta Geotech. 17, 3855–3865 (2022). https://doi.org/10.1007/s11440-022-01500-0

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