Technical Papers
Jun 5, 2023

Scale Effect on the Apparent Anisotropic Hydraulic Conductivity of Geomaterials

Publication: ASCE-ASME Journal of Risk and Uncertainty in Engineering Systems, Part A: Civil Engineering
Volume 9, Issue 3

Abstract

Properties of geomaterials often exhibit stratification and anisotropy due to various influencing factors such as weathering and sedimentation. However, the measurement of anisotropy is a difficult task since anisotropy not only depends on the direction but also varies with scale. In the current study, hydraulic conductivity is considered a typical geomaterial property and simulated by random field theory. A novel method based on two-dimensional and three-dimensional analytical expressions is proposed to estimate the apparent hydraulic conductivity (k) in different directions and determine the corresponding anisotropic ratios. A series of simulation tests on specimens with various dimensions from one strong anisotropy site are also performed via the finite element method. The analytical solutions of the proposed method are verified by numerical results. Results indicate that the anisotropic ratio shows a substantial sensitivity to the sample scale. A decrease in sample scale can result in the reduction of the anisotropic ratio; as a result, k gradually approaches to a point level’s value, and the effect of anisotropy decreases. This work not only sheds light on the gap between the laboratory results and the field’s inherent properties but also provides guidelines on upscaling small-scale (e.g., laboratory scale) results to field-scale applications.

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Data Availability Statement

All data, models, or code that support the findings of this study are available from the corresponding author upon reasonable request.

Acknowledgments

This research is supported by the National Natural Science Foundation of China (Grant No. 52079099), and the International Joint Research Platform Seed Fund Program of Wuhan University (Grant No. WHUZZJJ202207). Guan Chen would like to thank the financial support of the Sino-German (CSC-DAAD) Postdoc Scholarship Program.

References

Adams, A. L., T. J. Nordquist, J. T. Germaine, and P. B. Flemings. 2016. “Permeability anisotropy and resistivity anisotropy of mechanically compressed mudrocks.” Can. Geotech. J. 53 (9): 1474–1482. https://doi.org/10.1139/cgj-2015-0596.
Ai, Z. Y., L. J. Wang, and B. Li. 2015. “Analysis of axisymmetric thermo-elastic problem in multilayered material with anisotropic thermal diffusivity.” Comput. Geotech. 65 (Apr): 80–86. https://doi.org/10.1016/j.compgeo.2014.11.012.
Ashour, H. A. 1988. “A compressive strength criterion for anisotropic rock materials.” Can. Geotech. J. 25 (2): 233–237. https://doi.org/10.1139/t88-027.
ASTM. 2016. Standard test methods for measurement of hydraulic conductivity of saturated porous materials using a flexible wall permeameter. ASTM D5084-16a. West Conshohocken, PA: ASTM.
Backeberg, N. R., F. Iacoviello, M. Rittner, T. M. Mitchell, A. P. Jones, R. Day, J. Wheeler, P. R. Shearing, P. Vermeesch, and A. Striolo. 2017. “Quantifying the anisotropy and tortuosity of permeable pathways in clay-rich mudstones using models based on X-ray tomography.” Sci. Rep. 7 (1): 14838. https://doi.org/10.1038/s41598-017-14810-1.
Beer, M., Y. Zhang, S. T. Quek, and K. K. Phoon. 2013. “Reliability analysis with scarce information: Comparing alternative approaches in a geotechnical engineering context.” Struct. Saf. 41 (Mar): 1–10. https://doi.org/10.1016/j.strusafe.2012.10.003.
Bourret, J., N. Tessier-Doyen, R. Guinebretiere, E. Joussein, and D. S. Smith. 2015. “Anisotropy of thermal conductivity and elastic properties of extruded clay-based materials: Evolution with thermal treatment.” Appl. Clay Sci. 116–117 (Nov): 150–157. https://doi.org/10.1016/j.clay.2015.08.006.
Buttle, J. M., and D. A. House. 1997. “Spatial variability of saturated hydraulic conductivity in shallow macroporous soils in a forested basin.” J. Hydrol. 203 (1): 127–142. https://doi.org/10.1016/S0022-1694(97)00095-4.
Casagrande, L., and S. Poulos. 1969. “On the effectiveness of sand drains.” Can. Geotech. J. 6 (3): 287–326. https://doi.org/10.1139/t69-030.
Chan, H. T., and T. C. Kenney. 1973. “Laboratory investigation of permeability ratio of new liskeard varved soil.” Can. Geotech. J. 10 (3): 453–472. https://doi.org/10.1139/t73-038.
Cheung, Y. K., P. K. K. Lee, and K. H. Xie. 1991. “Some remarks on two and three dimensional consolidation analysis of sand-drained ground.” Comput. Geotech. 12 (1): 73–87. https://doi.org/10.1016/0266-352X(91)90012-5.
Choo, J., Y. J. Kim, J. H. Lee, T. S. Yun, J. Lee, and Y. S. Kim. 2012. “Stress-induced evolution of anisotropic thermal conductivity of dry granular materials.” Acta Geotech. 8 (1): 91–106. https://doi.org/10.1007/s11440-012-0174-7.
Clavaud, J. B., A. Maineult, M. Zamora, P. Rasolofosaon, and C. Schlitter. 2008. “Permeability anisotropy and its relations with porous medium structure.” J. Geophys. Res. Solid Earth 113 (B1): B01202. https://doi.org/10.1029/2007JB005004.
Dai, S., J. Kim, Y. Xu, W. Waite, J. Jang, J. Yoneda, and P. Kumar. 2018. “Permeability anisotropy and relative permeability in sediments from the National Gas Hydrate Program Expedition 02, offshore India.” Mar. Pet. Geol. 108 (Oct): 705–713. https://doi.org/10.1016/j.marpetgeo.2018.08.016.
Dewhurst, D. N., K. M. Brown, M. B. Clennell, and G. K. Westbrook. 1996. “A comparison of the fabric and permeability anisotropy of consolidated and sheared silty clay.” Eng. Geol. 42 (4): 253–267. https://doi.org/10.1016/0013-7952(95)00089-5.
El-Ramly, H. 2001. “Probabilistic analyses of landslide hazards and risks: Bridging theory and practice.” Ph.D. thesis, Dept. of Civil and Environmental Engineering, Univ. of Alberta, Edmonton.
Fenton, G. A., and D. V. Griffiths. 2008. Vol. 461 of Risk assessment in geotechnical engineering. New York: Wiley.
Ghysels, G., S. Benoit, H. Awol, E. P. Jensen, A. D. Tolche, C. Anibas, and M. Huysmans. 2018. “Characterization of meter-scale spatial variability of riverbed hydraulic conductivity in a lowland river (Aa River, Belgium).” J. Hydrol. 559 (Apr): 1013–1027. https://doi.org/10.1016/j.jhydrol.2018.03.002.
Guilleminot, J., C. Soize, and R. G. Ghanem. 2012. “Stochastic representation for anisotropic permeability tensor random fields.” Int. J. Numer. Anal. Methods Geomech. 36 (13): 1592–1608. https://doi.org/10.1002/nag.1081.
Hicher, P. Y., and C. S. Chang. 2006. “Anisotropic nonlinear elastic model for particulate materials.” J. Geotech. Geoenviron. Eng. 132 (8): 1052–1061. https://doi.org/10.1061/(ASCE)1090-0241(2006)132:8(1052).
Huang, X., J. Guo, K. Li, Z. Z. Wang, and W. Wang. 2023. “Predicting the thermal conductivity of unsaturated soils considering wetting behavior: A meso-scale study.” Int. J. Heat Mass Transfer 204 (May): 123853. https://doi.org/10.1016/j.ijheatmasstransfer.2023.123853.
Johnston, I. W., G. A. Narsilio, and S. Colls. 2011. “Emerging geothermal energy technologies.” KSCE J. Civ. Eng. 15 (4): 643–653. https://doi.org/10.1007/s12205-011-0005-7.
Jorand, R., C. Vogt, G. Marquart, and C. Clauser. 2013. “Effective thermal conductivity of heterogeneous rocks from laboratory experiments and numerical modeling: Thermal conductivity of rocks.” J. Geophys. Res. Solid Earth 118 (10): 5225–5235. https://doi.org/10.1002/jgrb.50373.
Journel, A. G., and C. H. J. Huijbregts. 1978. Mining geostatistics. London: Academic Press.
Khajevand, R. 2018. “Geotechnical investigations for landslide hazard and risk analysis, a case study: The landslide in Kojour Region, North of Iran.” Innovative Infrastruct. Solutions 3 (1): 54. https://doi.org/10.1007/s41062-018-0160-5.
Li, A. J., R. S. Merifield, and A. V. Lyamin. 2010. “Three-dimensional stability charts for slopes based on limit analysis methods.” Can. Geotech. J. 47 (12): 1316–1334. https://doi.org/10.1139/T10-030.
Li, D. Q., X. H. Qi, K. K. Phoon, L. M. Zhang, and C. B. Zhou. 2014. “Effect of spatially variable shear strength parameters with linearly increasing mean trend on reliability of infinite slopes.” Struct. Saf. 49 (Jul): 45–55. https://doi.org/10.1016/j.strusafe.2013.08.005.
Li, K. Q., D. Q. Li, and Y. Liu. 2020. “Meso-scale investigations on the effective thermal conductivity of multi-phase materials using the finite element method.” Int. J. Heat Mass Transfer 151 (Apr): 119383. https://doi.org/10.1016/j.ijheatmasstransfer.2020.119383.
Li, K. Q., Y. Liu, and Q. Kang. 2022a. “Estimating the thermal conductivity of soils using six machine learning algorithms.” Int. Commun. Heat Mass Transfer 136 (Jul): 106139. https://doi.org/10.1016/j.icheatmasstransfer.2022.106139.
Li, K. Q., Y. Liu, and Z. Y. Yin. 2023. “An improved 3D microstructure reconstruction approach for porous media.” Acta Mater. 242 (Jan): 118472. https://doi.org/10.1016/j.actamat.2022.118472.
Li, K. Q., Z. Miao, D. Q. Li, and Y. Liu. 2022b. “Effect of mesoscale internal structure on effective thermal conductivity of anisotropic geomaterials.” Acta Geotech. 17 (8): 3553–3566. https://doi.org/10.1007/s11440-022-01458-z.
Li, Y. L. E. 2012. “Finite element analysis of heavily laminated and heterogenous soils.” Undergraduate thesis, Dept. of Civil Engineering, National Univ. of Singapore.
Liu, Y., F. H. Lee, S. T. Quek, and M. Beer. 2014. “Modified linear estimation method for generating multi-dimensional multi-variate Gaussian field in modelling material properties.” Probab. Eng. Mech. 38 (Oct): 42–53. https://doi.org/10.1016/j.probengmech.2014.09.001.
Liu, Y., K. Q. Li, D. Q. Li, X. S. Tang, and S. X. Gu. 2022. “Coupled thermal–hydraulic modeling of artificial ground freezing with uncertainties in pipe inclination and thermal conductivity.” Acta Geotech. 17 (1): 257–274. https://doi.org/10.1007/s11440-021-01221-w.
Liu, Y., S. T. Quek, and F. H. Lee. 2016. “Translation random field with marginal beta distribution in modeling material properties.” Struct. Saf. 61 (Jul): 57–66. https://doi.org/10.1016/j.strusafe.2016.04.001.
Liu, Y., W. Zhang, L. Zhang, Z. Zhu, J. Hu, and H. Wei. 2018. “Probabilistic stability analyses of undrained slopes by 3D random fields and finite element methods.” Geosci. Front. 9 (6): 1657–1664. https://doi.org/10.1016/j.gsf.2017.09.003.
Lu, Y., W. M. Ye, Q. Wang, Y. Zhu, Y. G. Chen, and B. Chen. 2020. “Investigation on anisotropic thermal conductivity of compacted GMZ bentonite.” Bull. Eng. Geol. Environ. 79 (3): 1153–1162. https://doi.org/10.1007/s10064-019-01636-6.
Mitchell, J. K., and K. Soga. 2005. Fundamentals of soil behavior. 3rd ed. Hoboken, NJ: Wiley.
Niandou, H., J. F. Shao, J. P. Henry, and D. Fourmaintraux. 1997. “Laboratory investigation of the mechanical behaviour of Tournemire shale.” Int. J. Rock Mech. Min. Sci. 34 (1): 3–16. https://doi.org/10.1016/S1365-1609(97)80029-9.
Phoon, K. K., and F. H. Kulhawy. 1999. “Characterization of geotechnical variability.” Can. Geotech. J. 36 (4): 612–624. https://doi.org/10.1139/t99-038.
Popov, Y., G. Beardsmore, C. Clauser, and S. Roy. 2016. “ISRM suggested methods for determining thermal properties of rocks from laboratory tests at atmospheric pressure.” Rock Mech. Rock Eng. 49 (10): 4179–4207. https://doi.org/10.1007/s00603-016-1070-5.
Potts, D. M., and L. Zdravkovic. 1999. Finite element analysis in geotechnical engineering: Theory. London: Thomas Telford.
Šafanda, J. 1995. “Effect of thermal conductivity anisotropy of rocks on the subsurface temperature field.” Geophys. J. Int. 120 (2): 323–330. https://doi.org/10.1111/j.1365-246X.1995.tb01821.x.
Scholes, O. N., S. A. Clayton, A. F. A. Hoadley, and C. Tiu. 2007. “Permeability anisotropy due to consolidation of compressible porous media.” Transp. Porous Media 68 (3): 365–387. https://doi.org/10.1007/s11242-006-9048-5.
Shao, J. F., H. Zhou, and K. T. Chau. 2005. “Coupling between anisotropic damage and permeability variation in brittle rocks.” Int. J. Numer. Anal. Methods Geomech. 29 (12): 1231–1247. https://doi.org/10.1002/nag.457.
Shipton, Z., J. Evans, K. R. Robeson, C. B. Forster, and S. Sh. 2002. “Structural heterogeneity and permeability in faulted eolian sandstone: Implications for subsurface modeling of faults.” AAPG Bull. 86 (5): 863–883.
Siddiquee, M. S. A., M. S. Islam, F. Tatsuoka, and M. K. Islam. 2017. “An anisotropic model for granular material based on experiments.” Geotech. Geol. Eng. 36 (3): 1447–1462. https://doi.org/10.1007/s10706-017-0400-z.
Talukdar, P., and A. Dey. 2019. “Hydraulic failures of earthen dams and embankments.” Innovative Infrastruct. Solutions 4 (1): 42. https://doi.org/10.1007/s41062-019-0229-9.
Wang, C. D., and C. S. Tzeng. 2009. “Displacements and stresses due to nonuniform circular loadings in an inhomogeneous cross-anisotropic material.” Mech. Res. Commun. 36 (8): 921–932. https://doi.org/10.1016/j.mechrescom.2009.08.001.
Yin, Z. Y., M. Hattab, and P. Y. Hicher. 2011. “Multiscale modeling of a sensitive marine clay.” Int. J. Numer. Anal. Methods Geomech. 35 (15): 1682–1702. https://doi.org/10.1002/nag.977.
Zhang, N., S. L. Shen, H. N. Wu, J. C. Chai, Y. S. Xu, and Z. Y. Yin. 2015. “Evaluation of effect of basal geotextile reinforcement under embankment loading on soft marine deposits.” Geotext. Geomembr. 43 (6): 506–514. https://doi.org/10.1016/j.geotexmem.2015.05.005.
Zhang, Q., Z. Y. Wang, Z. Y. Yin, and Y. F. Jin. 2022. “A novel stabilized NS-FEM formulation for anisotropic double porosity media.” Comput. Methods Appl. Mech. Eng. 401 (Part B): 115666. https://doi.org/10.1016/j.cma.2022.115666.
Zhang, Z., X. Liu, Y. Zhang, M. Zhou, and J. Chen. 2020. “Time interval of multiple crossings of the Wiener process and a fixed threshold in engineering.” Mech. Syst. Signal Process. 135 (Jan): 106389. https://doi.org/10.1016/j.ymssp.2019.106389.

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Go to ASCE-ASME Journal of Risk and Uncertainty in Engineering Systems, Part A: Civil Engineering
ASCE-ASME Journal of Risk and Uncertainty in Engineering Systems, Part A: Civil Engineering
Volume 9Issue 3September 2023

History

Received: Feb 12, 2023
Accepted: Apr 4, 2023
Published online: Jun 5, 2023
Published in print: Sep 1, 2023
Discussion open until: Nov 5, 2023

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Postgraduate Researcher, State Key Laboratory of Water Resources Engineering and Management, Institute of Engineering Risk and Disaster Prevention, Wuhan Univ., 299 Bayi Rd., Wuhan 430072, China; Postdoc Fellow, Dept. of Civil and Environmental Engineering, The Hong Kong Polytechnic Univ., Hung Hom, Kowloon, Hong Kong 999077, China. Email: [email protected]
Postgraduate Researcher, Institute for Risk and Reliability, Leibniz Univ. Hannover, Hannover 30167, Germany (corresponding author). ORCID: https://orcid.org/0000-0002-3709-1247. Email: [email protected]
Professor, State Key Laboratory of Water Resources Engineering and Management, Institute of Engineering Risk and Disaster Prevention, Wuhan Univ., 299 Bayi Rd., Wuhan 430072, China. ORCID: https://orcid.org/0000-0003-1006-7842. Email: [email protected]
Zhen-Yu Yin [email protected]
Professor, Dept. of Civil and Environmental Engineering, The Hong Kong Polytechnic Univ., Hung Hom, Kowloon, Hong Kong 999077, China. Email: [email protected]

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