Optimum Design of Unsaturated Finite Clayey Slopes Using Second-Order Reliability Method
Publication: International Journal of Geomechanics
Volume 23, Issue 2
Abstract
This paper discusses the second-order reliability-based design optimization (SORBDO) of unsaturated finite slopes. An efficient search algorithm is proposed to locate the most probable slip surfaces using the Morgenstern–Price method of slices. The variability of fitting parameters of the soil water characteristic curve (SWCC) and shear strength parameters have been taken into account for evaluating the reliability of unsaturated finite slopes. Six unsaturated shear strength (USS) models are considered for the analysis of unsaturated soils. The most conservative model for the optimum design of finite slopes is recommended. Moreover, the results indicate that the mean and standard deviation of the fitting parameters of SWCC have a significant effect on the critical centers, critical slip surfaces, and reliability index of the unsaturated finite slopes. The results demonstrate a significant change in the critical centers associated with critical slip surfaces due to the change in the mean and coefficient of variation of the fitting parameters of SWCC. Statistical analysis of the experimental data shows that a positive correlation exists between fitting parameters of SWCC related to air entry value (af) and residual water content (mf). Negative correlations are found between the fitting parameters of SWCC related to air entry value (af) and slope (nf). Similarly, the SWCC fitting parameters related to residual water content (mf) and slope (nf) have negative correlations for clayey soils. It is observed that the correlated value of the reliability index is overestimated with reference to the uncorrelated value for clayey soil slopes. The proposed design charts are beneficial for engineers and practitioners for the sustainable design of unsaturated finite slopes. Overall, the developed rigorous SORBDO framework offers a more rational approach for assessing critical failure surfaces and critical centers, considering the interdependency of random variables.
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References
Al-Karni, A. A., and M. A. Al-Shamrani. 2000. “Study of the effect of soil anisotropy on slope stability using method of slices.” Comput. Geotech. 26 (2): 83-103. https://doi.org/10.1016/S0266-352X(99)00046-4.
Babu, G. L. S., and D. S. N. Murthy. 2005. “Reliability analysis of unsaturated soil slopes.” J. Geotech. Geoenviron. Eng. 131 (11): 1423–1428. https://doi.org/10.1061/(ASCE)1090-0241(2005)131:11(1423).
Bao, C., B. Gong, and L. Zhan. 1998. “Properties of unsaturated soils and slope stability of expansive soils.” In Vol. 1 of Proc., 2nd Int. Conf. on Unsaturated Soils, 71–98. Beijing: International Academic Publishers.
Basha, B. M., and G. L. S. Babu. 2010. “Optimum design for external seismic stability of geosynthetic reinforced soil walls: Reliability based approach.” J. Geotech. Geoenviron. Eng. 136 (6): 797–812. https://doi.org/10.1061/(ASCE)GT.1943-5606.0000289.
Basha, B. M., and G. L. S. Babu. 2012. “Target reliability-based optimisation for internal seismic stability of reinforced soil structures.” Géotechnique 62 (1): 55–68. https://doi.org/10.1680/geot.8.P.076.
Basha, B. M., A. S. S. Raghuram, and K. R. Reddy. 2018. “Reliability analysis of transport of nanoscale iron particles in saturated porous media.” J. Geotech. Geoenviron. Eng. 144 (12): 04018090. https://doi.org/10.1061/(ASCE)GT.1943-5606.0001979.
Chiu, C. F., W. M. Yan, and K. V. Yuen. 2012. “Reliability analysis of soil–water characteristics curve and its application to slope stability analysis.” Eng. Geol. 135–136: 83–91. https://doi.org/10.1016/j.enggeo.2012.03.004.
Cho, S. E. 2009. “Probabilistic stability analyses of slopes using the ANN-based response surface.” Comput. Geotech. 36 (5): 787–797. https://doi.org/10.1016/j.compgeo.2009.01.003.
Dadashzadeh, N., H. S. B. Duzgun, and S. Gheibi. 2015. “A second-order reliability analysis of rock slope stability in Amasya, Turkey.” In Proc., 13th Int. Congress of Rock Mechanics. Montreal: International Society for Rock Mechanics and Rock Engineering.
Duncan, J. M. 1996. “State of the art: Limit equilibrium and finite-element analysis of slopes.” J. Geotech. Eng. 122 (7): 577–596. https://doi.org/10.1061/(ASCE)0733-9410(1996)122:7(577).
Fredlund, D. G., and J. Krahn. 1977. “Comparison of slope stability methods of analysis.” Can. Geotech. J. 14 (3): 429–439. https://doi.org/10.1139/t77-045.
Fredlund, D. G., N. R. Morgenstern, and R. A. Widger. 1978. “The shear strength of unsaturated soils.” Can. Geotech. J. 15 (3): 313–321. https://doi.org/10.1139/t78-029.
Fredlund, D. G., and H. Rahardjo. 1993. Soil mechanics for unsaturated soils. New York: Wiley.
Fredlund, D. G., H. Rahardjo, and J. K. M. Gan. 1987. “Nonlinearity of strength envelope for unsaturated soils.” In Vol. 1 of Proc., 6th Int. Conf. on Expansive Soils, 49–54. New Delhi, India: International Society for Soil Mechanics and Foundation Engineering.
Fredlund, D. G., and A. Xing. 1994. “Equations for the soil–water characteristic curve.” Can. Geotech. J. 31 (4): 521–532. https://doi.org/10.1139/t94-061.
Fredlund, D. G., A. Xing, M. D. Fredlund, and S. L. Barbour. 1996. “The relationship of the unsaturated soil shear strength to the soil–water characteristic curve.” Can. Geotech. J. 33 (3): 440–448. https://doi.org/10.1139/t96-065.
Garven, E. A., and S. K. Vanapalli. 2006. “Evaluation of empirical procedures for predicting the shear strength of unsaturated soils.” In 4th Int. Conf. on Unsaturated Soils, Geotechnical Special Publication 147, edited by G. A. Miller, C. E. Zapata, S. L. Houston, and D. G. Fredlund, 2570–2581. Reston, VA: ASCE.
Gavin, K., and J. F. Xue. 2009. “Use of a genetic algorithm to perform reliability analysis of unsaturated soil slopes.” Géotechnique 59 (6): 545–549. https://doi.org/10.1680/geot.8.T.004.
Gavin, K., and J. F. Xue. 2010. “Design charts for the stability analysis of unsaturated soil slopes.” Geotech. Geol. Eng. 28 (1): 79–90. https://doi.org/10.1007/s10706-009-9282-z.
Geo-slope International. 2016. Slope/W, slope stability analysis. Calgary, AB, Canada: Geo-slope International.
Godt, J. W., R. L. Baum, and N. Lu. 2009. “Landsliding in partially saturated materials.” Geophys. Res. Lett. 36 (2): L02403. https://doi.org/10.1029/2008GL035996.
Guan, G. S., H. Rahardjo, and L. E. Choon. 2010. “Shear strength equations for unsaturated soil under drying and wetting.” J. Geotech. Geoenviron. Eng. 136 (4): 594–606. https://doi.org/10.1061/(ASCE)GT.1943-5606.0000261.
Hasofer, A. M., and N. C. Lind. 1974. “A extract and invariant first order reliability format.” J. Eng. Mech. 100 (1): 111–121.
Johari, A., A. H. Nejad, and A. A. Javadi. 2016. “Analytical reliability analysis of soil–water characteristic curve.” In Vol. 9 of E3S Web of Conf. – E-UNSAT 2016. Les Ulis, France: EDP Sciences.
Khalili, N., and M. H. Khabbaz. 1998. “A unique relationship for χ for the determination of the shear strength of unsaturated soils.” Géotechnique 48 (5): 681–687. https://doi.org/10.1680/geot.1998.48.5.681.
Lamborn, M. J. 1986. “A micromechanical approach to modeling partly saturated soils.” M.Sc. thesis, Dept. of Civil and Environmental Engineering, Texas A&M Univ.
Leong, E. C., and H. Rahardjo. 1997. “Review of soil–water characteristic curve equations.” J. Geotech. Geoenviron. Eng. 123 (12): 1106–1117. https://doi.org/10.1061/(ASCE)1090-0241(1997)123:12(1106).
Low, B. K. 2014. “FORM, SORM, and spatial modeling in geotechnical engineering.” Struct. Saf. 49: 56–64. https://doi.org/10.1016/j.strusafe.2013.08.008.
Lu, N., and W. J. Likos. 2004. Unsaturated soil mechanics. New York: Wiley.
Morgenstern, N. R., and V. E. Price. 1965. “The analysis of the stability of general slip surfaces.” Géotechnique 15 (1): 79–93. https://doi.org/10.1680/geot.1965.15.1.79.
Öberg, A. L., and G. Sällfors. 1997. “Determination of shear strength parameters of unsaturated silts and sands based on the water retention curve.” Geotech. Test. J. 20 (1): 40–48. https://doi.org/10.1520/GTJ11419J.
Phoon, K. K., and F. H. Kulhawy. 1999. “Evaluation of geotechnical property variability.” Can. Geotech. J. 36 (4): 625–639. https://doi.org/10.1139/t99-039.
Prakash, A., B. Hazra, A. Deka, and S. Sreedeep. 2017. “Probabilistic analysis of water retention characteristic curve of fly ash.” Int. J. Geomech. 17 (12): 04017111. https://doi.org/10.1061/(ASCE)GM.1943-5622.0001024.
Prakash, A., B. Hazra, and S. Sreedeep. 2020. “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.
Rackwitz, R., and B. Fiessler. 1978. “Structural reliability under combined random load sequences.” Comput. Struct. 9 (5): 489–494. https://doi.org/10.1016/0045-7949(78)90046-9.
Raghuram, A. S. S., and B. M. Basha. 2021. “Second-order reliability-based design of unsaturated infinite soil slopes.” Int. J. Geomech. 21 (4): 04021024. https://doi.org/10.1061/(ASCE)GM.1943-5622.0001954.
Raghuram, A. S. S., B. M. Basha, and K. V. N. S. Raviteja. 2021. “Variability characterization of SWCC for clay and silt and its application to infinite slope reliability.” J. Mater. Civ. Eng. 33 (8): 04021180. https://doi.org/10.1061/(ASCE)MT.1943-5533.0003809.
Sahis, M. K., G. Bhattacharya, and R. Chowdhury. 2014. “Reliability analysis of rainfall induced slope instability of unsaturated soil slopes.” In Unsaturated soils: Research & applications, edited by N. Khalili, A. Russell, and A. Khoshghalb, 1287–1293. London: Taylor and Francis.
Siacara, A. T., G. F. Napa-García, A. T. Beck, and M. M. Futai. 2020. “Reliability analysis of earth dams using direct coupling.” J. Rock Mech. Geotech. Eng. 12 (2): 366–380. https://doi.org/doi.org/10.1016/j.jrmge.2019.07.012.
Sundararajan, C. R. 1995. Probabilistic structural mechanics handbook: Theory and industrial applications. 1st ed. New York: Springer.
SVSlope. 2016. Slope stability analysis and user’s manual. Saskatoon, Canada: SoilVision System.
USACE. 1999. Risk-based analysis in geotechnical engineering for support of planning studies, engineering and design. Rep. No. 20314-1000. Washington, DC: Dept. of Army, USACE.
Vahedifard, F., D. Leshchinsky, K. Mortezaei, and N. Lu. 2016. “Effective stress-based limit-equilibrium analysis for homogeneous unsaturated slopes.” Int. J. Geomech. 16 (6): D4016003. https://doi.org/10.1061/(ASCE)GM.1943-5622.0000554.
Vanapalli, S. K. 1994. “Simple test procedures and their interpretation in evaluating the shear strength of unsaturated soils.” Ph.D. thesis, Dept. of Civil Engineering, Univ. of Saskatchewan.
Vanapalli, S. K., D. G. Fredlund, D. E. Pufahl, and A. W. Clifton. 1996. “Model for the prediction of shear strength with respect to soil suction.” Can. Geotech. J. 33 (3): 379–392. https://doi.org/10.1139/t96-060.
Vilar, O. M. 2006. “A simplified procedure to estimate the shear strength envelope of unsaturated soils.” Can. Geotech. J. 43 (10): 1088–1095. https://doi.org/10.1139/t06-055.
Zapata, C. E., W. N. Houston, S. L. Houston, and K. D. Walsh. 2000. “Soil–water characteristic curve variability.” In Geo-Denver 2000: Advances in Unsaturated Geotechnics, Geotechnical Special Publication 99, edited by C. D. Shackelford, S. L. Houston, and N.-Y. Chang, 84–124. Reston, VA: ASCE.
Zhai, Q., and H. Rahardjo. 2013. “Quantification of uncertainties in soil–water characteristic curve associated with fitting parameters.” Eng. Geol. 163 (Aug): 144–152. https://doi.org/10.1016/j.enggeo.2013.05.014.
Zhai, Q., H. Rahardjo, A. Satyanaga, G. L. Dai, and Y. J. Du. 2020. “Effect of the uncertainty in soil–water characteristic curve on the estimated shear strength of unsaturated soil.” J. Zhejiang Univ. Sci. A. 21 (4): 317–330. https://doi.org/10.1631/jzus.A1900589.
Zhang, L. L., D. G. Fredlund, M. D. Fredlund, and G. W. Wilson. 2014. “Modeling the unsaturated soil zone in slope stability analysis.” Can. Geotech. J. 51 (12): 1384–1398. https://doi.org/10.1139/cgj-2013-0394.
Zhang, L. L., J. Li, X. Li, J. Zhang, and H. Zhu. 2016. Rainfall-induced soil slope failure. Boca Raton, FL: Taylor & Francis.
Zhu, D. Y., C. F. Lee, Q. H. Qian, and G. R. Chen. 2005. “A concise algorithm for computing the factor of safety using the Morgenstern–Price method.” Can. Geotech. J. 42 (1): 272–278. https://doi.org/ 10.1139/t04-072.
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Published In
International Journal of Geomechanics
Volume 23 • Issue 2 • February 2023
Copyright
© 2022 American Society of Civil Engineers.
History
Received: Mar 15, 2022
Accepted: Jul 15, 2022
Published online: Nov 18, 2022
Published in print: Feb 1, 2023
Discussion open until: Apr 18, 2023
ASCE Technical Topics:
- Clays
- Engineering fundamentals
- Geomechanics
- Geotechnical engineering
- Material mechanics
- Material properties
- Materials engineering
- Mathematics
- Parameters (statistics)
- Shear strength
- Slopes
- Soil analysis
- Soil mechanics
- Soil properties
- Soil strength
- Soil water
- Soils (by type)
- Statistics
- Strength of materials
- Unsaturated soils
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