Probabilistic Design Framework for Granular Filters
Publication: Journal of Geotechnical and Geoenvironmental Engineering
Volume 147, Issue 11
Abstract
A granular filter is required to satisfy two requirements of retention and hydraulic conductivity. The current design approaches are based on the representative grain sizes for retention and hydraulic conductivity requirements. The importance of consideration of the grain-size distribution (GSD) in satisfying the filter requirements is highlighted in this paper. An assessment criterion is presented for retention and hydraulic conductivity requirements based on GSD. A probabilistic assessment criterion is developed for retention requirements considering the grain size and constriction size as random variables. For hydraulic conductivity requirements, a probabilistic assessment criterion is defined by considering hydraulic conductivity’s variability and a semianalytical model for saturated hydraulic conductivity. The limit states for developed criteria are established based on published experimental data. The proposed approach is demonstrated with examples, and it is illustrated that the filter bandwidth is governed by the convexity of the soil GSD.
Get full access to this article
View all available purchase options and get full access to this article.
Data Availability Statement
All data, models, and code generated or used during the study appear in the published article.
Acknowledgments
The work described in this paper is financially supported by Prime Minister’s Fellowship Scheme for Doctoral Research, a public–private partnership between the Science and Engineering Research Board, Department of Science and Technology, Government of India, and the Confederation of Indian Industry with industry partner Maccaferri Environmental Solutions Pvt. Ltd. The authors wish to thank the editor, associate editor, and reviewers for their careful reading of the manuscript and many insightful comments and suggestions.
References
Aberg, B. 1992. “Void ratio of noncohesive soils and similar materials.” J. Geotech. Eng. 118 (9): 1315–1334. https://doi.org/10.1061/(ASCE)0733-9410(1992)118:9(1315).
Chapuis, R. P. 2012. “Predicting the saturated hydraulic conductivity of soils: A review.” Bull. Eng. Geol. Environ. 71 (3): 401–434. https://doi.org/10.1007/s10064-012-0418-7.
Deb, S. K., and M. K. Shukla. 2012. “Variability of hydraulic conductivity due to multiple factors.” Am. J. Environ. Sci. 8 (5): 489–502. https://doi.org/10.3844/ajessp.2012.489.502.
Duncan, J. M. 2000. “Factors of safety and reliability in geotechnical engineering.” J. Geotech. Geoenviron. Eng. 126 (4): 307–316. https://doi.org/10.1061/(ASCE)1090-0241(2000)126:4(307).
Feng, S., P. J. Vardanega, E. Ibraim, I. Widyatmoko, and C. Ojum. 2019. “Permeability assessment of some granular mixtures.” Géotechnique 69 (7): 646–654. https://doi.org/10.1680/jgeot.17.T.039.
Foster, M., and R. Fell. 2001. “Assessing embankment dam filters that do not satisfy design criteria.” J. Geotech. Geoenviron. Eng. 127 (5): 398–407. https://doi.org/10.1061/(ASCE)1090-0241(2001)127:5(398).
Fry, J. J. 2016. “Lessons on internal erosion in embankment dams from failures and physical models.” In Proc., 8th Int. Conf. on Scour and Erosion (ICSE8), 41–58. Boca Raton, FL: CRC Press.
Giroud, J. P. 2010. “Development of criteria for geotextile and granular filters.” In Vol. 1 of Proc., 9th Int. Conf. on Geosynthetics, edited by E. M. Palmeira, D. M. Vidal, A. S. J. F. Sayao, and M. Ehrlich, 45–64. Jupiter, FL: International Geosynthetics Society.
Hazen, A. 2013. “Some physical properties of sands and gravels, with special reference to their use in filtration.” In Vol. 2 of State sanitation: A review of the work of the Massachusetts State Board of Health, 232–248. Cambridge, MA: Harvard University Press.
Humes, C. 1996. “Scattering of the composition of soils: An aspect for the stability of granular filters.” In Proc. Geofilters Conf., edited by J. Lafleur and A. L. Rollin, 21–34. Montreal: Bitech Publications.
ICOLD (International Commission on Large Dams). 1994. Embankment dams—Filters and drains. Bulletin. No. 95. Paris: ICOLD.
Indraratna, B., V. T. Nguyen, and C. Rujikiatkamjorn. 2012. “Hydraulic conductivity of saturated granular soils determined using a constriction-based technique.” Can. Geotech. J. 49 (5): 607–613. https://doi.org/10.1139/t2012-016.
Indraratna, B., A. K. Raut, and H. Khabbaz. 2007. “Constriction-based retention criterion for granular filter design.” J. Geotech. Geoenviron. Eng. 133 (3): 266–276. https://doi.org/10.1061/(ASCE)1090-0241(2007)133:3(266).
Indraratna, B., and F. Vafai. 1997. “Analytical model for particle migration within base soil-filter system.” J. Geotech. Geoenviron. Eng. 123 (2): 100–109. https://doi.org/10.1061/(ASCE)1090-0241(1997)123:2(100).
Indraratna, B., F. Vafai, and E. Dilema. 1996. “An experimental study of the filtration of a lateritic clay slurry by sand filters.” Proc. Inst. Civ. Eng. Geotech. Eng. 119 (2): 75–83. https://doi.org/10.1680/igeng.1996.28167.
Kalore, S. A., G. L. Sivakumar Babu, and R. Mahajan. 2021. “Approach to estimate hydraulic conductivity function from soil–water retention curve for noncohesive soils.” J. Mater. Civ. Eng. 33 (10): 04021289. https://doi.org/10.1061/(ASCE)MT.1943-5533.0003917.
Kenney, T. C., and D. Lau. 1985. “Internal stability of granular filters.” Can. Geotech. J. 22 (2): 215–225. https://doi.org/10.1139/t85-029.
Lafleur, J. 1984. “Filter testing of broadly graded cohesionless soils.” Can. Geotech. J. 21 (4): 634–643. https://doi.org/10.1139/t84-070.
Lafleur, J., J. Mlynarek, and A. L. Rollin. 1989. “Filtration of broadly graded cohesionless soils.” J. Geotech. Eng. 115 (12): 1747–1768. https://doi.org/10.1061/(ASCE)0733-9410(1989)115:12(1747).
Moraci, N., M. C. Mandaglio, and D. Ielo. 2012. “A new theore6tical method to evaluate the internal stability of granular soils.” Can. Geotech. J. 49 (1): 45–58. https://doi.org/10.1139/t11-083.
Nguyen, V. T., C. Rujikiatkamjorn, and B. Indraratna. 2013. “Analytical solutions for filtration process based on constriction size concept.” J. Geotech. Geoenviron. Eng. 139 (7): 1049–1061. https://doi.org/10.1061/(ASCE)GT.1943-5606.0000848.
NRCS (Natural Resources Conservation Service). 1994. Soil engineering. National engineering handbook. Washington, DC: US Dept. of Agriculture.
NRCS (Natural Resources Conservation Service). 2017. Soil engineering. National engineering handbook. Washington, DC: US Dept. of Agriculture.
Phoon, K. K. 2008. Reliability-based design in geotechnical engineering: Computations and applications. New York: Taylor & Francis.
Richards, K., and K. Reddy. 2007. “Critical appraisal of piping phenomena in earth dams.” Bull. Eng. Geol. Environ. 66 (4): 381–402. https://doi.org/10.1007/s10064-007-0095-0.
Schuler, U. 1996. “Scattering of the composition of soils: An aspect for the stability of granular filters.” In Proc., Geofilters ′96, edited by J. Lafleur and A. L. Rolin, 21–34. Montréal: Bitech Publications.
Sherard, J., and L. Dunnigan. 1989. “Critical filters for impervious soils.” J. Geotech. Eng. Div. 115 (7): 927–947. https://doi.org/10.1061/(ASCE)0733-9410(1989)115:7(927).
Sherard, J., L. Dunnigan, and J. Talbot. 1984. “Basic properties of sand and gravel filters.” J. Geotech. Eng. 110 (6): 684–700. https://doi.org/10.1061/(ASCE)0733-9410(1984)110:6(684).
Silveira, A. 1965. “An analysis of the problem of washing through in protective filters.” In Proc., Soil Mechanical and Foundations Engineering Conf., 551–555. Toronto: University of Toronto Press.
Silveira, A., T. de Lorena Peixoto, and J. Nogueira. 1975. “On void size distribution of granular materials.” In Proc., 5th Pan-American Conf. Soil Mechanics and Foundations Engineering, 161–176. Buenos Aires, Argentina: Argentine Society of Soil Mechanics and Foundations Engineering.
Srivastava, A., and G. L. Sivakumar Babu. 2011. “Analytical solutions for protective filters based on soil-retention and permeability criteria with respect to the phenomenon of soil boiling.” Can. Geotech. J. 48 (6): 956–969. https://doi.org/10.1139/t11-014.
Talukdar, P., and A. Dey. 2019. “Hydraulic failures of earthen dams and embankments.” Innovative Infrastruct. Solutions 4 (1): 1–20. https://doi.org/10.1007/s41062-019-0229-9.
Terzaghi, K. 1922. “Failure of dam foundations by piping and means for preventing it.” [In German.] Die Wasserkraft Zeitschrift fur die gesamte Wasserwirtschaft 17 (24): 445–449.
Wang, Y., and Y. Dallo. 2014. “On estimation of the constriction size distribution curve for cohesionless soils.” Eur. J. Environ. Civ. Eng. 18 (6): 683–698. https://doi.org/10.1080/19648189.2014.909335.
Information & Authors
Information
Published In
Copyright
© 2021 American Society of Civil Engineers.
History
Received: Apr 6, 2020
Accepted: Jul 15, 2021
Published online: Sep 13, 2021
Published in print: Nov 1, 2021
Discussion open until: Feb 13, 2022
Authors
Metrics & Citations
Metrics
Citations
Download citation
If you have the appropriate software installed, you can download article citation data to the citation manager of your choice. Simply select your manager software from the list below and click Download.
Cited by
- Hucheng Yang, Shengrui Su, Peng Li, Jianxun Chen, Investigation of the Microstructure Characteristics and Deformation Mechanisms of the Carbonaceous Slate under Hydromechanical Coupling, Geofluids, 10.1155/2023/5490136, 2023, (1-16), (2023).
- Shubham Kalore, G. L. Sivakumar Babu, Recent developments in design criteria for granular and geotextile filters, E3S Web of Conferences, 10.1051/e3sconf/202336802015, 368, (02015), (2023).
- Shubham A. Kalore, G.L. Sivakumar Babu, Improved design criteria for nonwoven geotextile filters with internally stable and unstable soils, Geotextiles and Geomembranes, 10.1016/j.geotexmem.2022.07.004, 50, 6, (1120-1134), (2022).
- Shubham A. Kalore, G.L. Sivakumar Babu, Hydraulic conductivity requirement of granular and geotextile filter for internally stable soils, Geotextiles and Geomembranes, 10.1016/j.geotexmem.2022.02.003, 50, 3, (510-520), (2022).