Incorporating Global Distribution with Site-Specific Data for Probabilistic Analysis of Soil–Water Characteristic Curve of Bentonite
Publication: Journal of Hazardous, Toxic, and Radioactive Waste
Volume 25, Issue 3
Abstract
Probabilistic analysis of the soil–water characteristic curve (SWCC) is essential for the application of reliability-based design (RBD) in unsaturated geotechnical engineering projects. Conventional frequentist analysis requires a large number of data points to minimize statistical uncertainty. However, obtaining large regional/site-specific datasets of SWCC of bentonite is practically difficult owing to time and cost constraints. A common approach in the literature is to supplement the limited site-specific data with prior knowledge using a Bayesian approach. However, almost all the works are limited to non-clayey soils and utilize non-informative uniform priors for SWCC parameters. Therefore, this technical note proposes the incorporation of global SWCC distribution with site-specific data for probabilistic analysis of SWCC of bentonite. Twelve SWCCs of bentonite are experimentally measured in this study and a copula-based global/generic distribution for SWCC of bentonite from the literature is utilized. It is shown that incorporating global distribution as an informative prior can significantly reduce the uncertainty in the posterior distribution of SWCC parameters as compared with popularly utilized uniform priors. Finally, to demonstrate the practical significance of the proposed approach towards unsaturated RBD, a stochastic seepage analysis is conducted. It is found that the popularly used uniform priors for SWCC parameters might significantly overestimate the failure probability.
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Acknowledgments
The authors thank the anonymous reviewers for providing extensive and critical comments to an earlier version of this manuscript.
References
ASTM. 2008. Standard test methods for determination of the soil water characteristic curve for desorption using a hanging column, pressure extractor, chilled mirror hygrometer, and/or centrifuge. ASTM D6836. West Conshohocken, PA: ASTM.
Carsel, R. F., and R. S. Parrish. 1988. “Developing joint probability distributions of soil water retention characteristics.” Water Resour. Res. 24 (5): 755–769. https://doi.org/10.1029/WR024i005p00755.
Ching, J., and K.-K. Phoon. 2019. “Constructing site-specific multivariate probability distribution model using bayesian machine learning.” J. Eng. Mech. 145 (1): 04018126. https://doi.org/10.1061/(ASCE)EM.1943-7889.0001537.
Chiu, C., W. Yan, and K.-V. Yuen. 2012. “Reliability analysis of soil–water characteristics curve and its application to slope stability analysis.” Eng. Geol. 135 (4): 83–91. https://doi.org/10.1016/j.enggeo.2012.03.004.
Gardner, W. 1958. “Some steady-state solutions of the unsaturated moisture flow equation with application to evaporation from a water table.” Soil Sci. 85 (4): 228–232. https://doi.org/10.1097/00010694-195804000-00006.
Gelman, A., J. B. Carlin, H. S. Stern, D. B. Dunson, A. Vehtari, and D. B. Rubin. 2013. Bayesian data analysis. Boca Raton, FL: Chapman and Hall/CRC.
Li, D.-Q., L. Wang, Z.-J. Cao, and X.-H. Qi. 2019. “Reliability analysis of unsaturated slope stability considering SWCC model selection and parameter uncertainties.” Eng. Geol. 260 (7): 105207. https://doi.org/10.1016/j.enggeo.2019.105207.
Likos, W. J., and J. Yao. 2014. “Effects of constraints on van Genuchten parameters for modeling soil–water characteristic curves.” J. Geotech. Geoenviron. Eng. 140 (12): 06014013. https://doi.org/10.1061/(ASCE)GT.1943-5606.0001168.
Mualem, Y. 1976. “A new model for predicting the hydraulic conductivity of unsaturated porous media.” Water Resour. Res. 12 (3): 513–522. https://doi.org/10.1029/WR012i003p00513.
Nelsen, R. B. 2007. An introduction to copulas. Berlin: Springer Science & Business Media.
Phoon, K.-K. 2018. “Probabilistic site characterization.” ASCE-ASME J. Risk Uncertainty Eng. Syst. Part A: Civ. Eng. 4 (4): 02018002. https://doi.org/10.1061/AJRUA6.0000992.
Phoon, K.-K., A. Santoso, and S.-T. Quek. 2010. “Probabilistic analysis of soil–water characteristic curves.” J. Geotech. Geoenviron. Eng. 136 (3): 445–455. https://doi.org/10.1061/(ASCE)GT.1943-5606.0000222.
Prakash, A., B. Hazra, and S. Sekharan. 2020a. “Probabilistic analysis of soil–water characteristic curve of bentonite: Multivariate copula approach.” Int. J. Geomech. 20 (2): 04019150. https://doi.org/10.1061/(ASCE)GM.1943-5622.0001554.
Prakash, A., B. Hazra, and S. Sreedeep. 2018a. “Probabilistic analysis of unsaturated fly ash slope.” J. Hazard. Toxic Radioact. Waste 23 (1): 06018002. https://doi.org/10.1061/(ASCE)HZ.2153-5515.0000428.
Prakash, A., B. Hazra, and S. Sreedeep. 2018b. “Uncertainty quantification in water retention characteristic curve of fly ash using copulas.” J. Test. Eval. 47 (4): 3080–3102.
Prakash, A., B. Hazra, and S. Sreedeep. 2020b. “Probabilistic analysis of soil–water characteristic curve using limited data.” Appl. Math. Modell. 89 (2): 752–770.
Prakash, A., B. Hazra, and S. Sreedeep. 2020c. Uncertainties in water retention curve of bentonite. In Advances in computer methods and geomechanics, edited by A. Prashant, A. Sachan, and C. Desai, 13–24. Singapore: Springer.
Rutqvist, J., and C.-F. Tsang. 2004. A fully coupled three-dimensional THM analysis of the FEBEX in situ test with the ROCMAS code: prediction of THM behavior in a bentonite barrier. In Vol. 2 Elsevier geo-engineering book series, 143–148. Amsterdam, Netherlands: Elsevier.
Sharma, A., B. Hazra, and S. Sekharan. 2021. “Stochastic seepage and slope stability analysis using vine-copula based multivariate random field approach: Consideration to non-gaussian spatial and cross-dependence structure of hydraulic parameters.” Comput. Geotech. 130 (2): 103918. https://doi.org/10.1016/j.compgeo.2020.103918.
Sharma, A., B. Hazra, G. Spagnoli, and S. Sekharan. 2020. “Probabilistic estimation of specific surface area and cation exchange capacity: A global multivariate distribution.” Can. Geotech. J. (in press).
Simunek, J., M. T. Van Genuchten, and M. Sejna. 2005. The HYDRUS-1D software package for simulating the one-dimensional movement of water, heat, and multiple solutes in variably-saturated media. University of California-Riverside Research Reports, 3, 1–240.
Stormont, J. C., and C. E. Anderson. 1999. “Capillary barrier effect from underlying coarser soil layer.” J. Geotech. Geoenviron. Eng. 125 (8): 641–648. https://doi.org/10.1061/(ASCE)1090-0241(1999)125:8(641).
Tariq, A. U. R., and D. S. Durnford. 1993. “Soil volumetric shrinkage measurements: A simple method.” Soil Sci. 155 (5): 325–330. https://doi.org/10.1097/00010694-199305000-00003.
Tripathy, S., M. Y. M. Tadza, and H. R. Thomas. 2014. “Soil–water characteristic curves of clays.” Can Geotech. J. 51 (8): 869–883. https://doi.org/10.1139/cgj-2013-0089.
Tripathy, S., H. R. Thomas, and R. Bag. 2015. “Geoenvironmental application of bentonites in underground disposal of nuclear waste: Characterization and laboratory tests.” J. Hazard. Toxic Radioact. Waste 21 (1): D4015002.
van Genuchten, M. T. 1980. “A closed-form equation for predicting the hydraulic conductivity of unsaturated soils 1.” Soil Sci. Soc. Am. J. 44 (5): 892–898. https://doi.org/10.2136/sssaj1980.03615995004400050002x.
Wang, L., Z.-J. Cao, D.-Q. Li, K.-K. Phoon, and S.-K. Au. 2018. “Determination of site-specific soil–water characteristic curve from a limited number of test data–A Bayesian perspective.” Geosci. Front. 9 (6): 1665–1677. https://doi.org/10.1016/j.gsf.2017.10.014.
Wang, L., L. Tang, Z. Wang, H. Liu, and W. Zhang. 2020. “Probabilistic characterization of the soil–water retention curve and hydraulic conductivity and its application to slope reliability analysis.” Comput. Geotech. 121 (4): 103460. https://doi.org/10.1016/j.compgeo.2020.103460.
Yan, W., C. Chiu, and K.-V. Yuen. 2017. “Prediction and modeling of permeability function and its application to the evaluation of breakthrough suction of a two-layer capillary barrier.” Can. Geotech. J. 54 (6): 778–788. https://doi.org/10.1139/cgj-2016-0339.
Yeh, T.-C. J. 1989. “One-dimensional steady state infiltration in heterogeneous soils.” Water Resour. Res. 25 (10): 2149–2158. https://doi.org/10.1029/WR025i010p02149.
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Journal of Hazardous, Toxic, and Radioactive Waste
Volume 25 • Issue 3 • July 2021
Copyright
© 2021 American Society of Civil Engineers.
History
Received: Jul 30, 2020
Accepted: Mar 29, 2021
Published online: May 12, 2021
Published in print: Jul 1, 2021
Discussion open until: Oct 12, 2021
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