A PARAMETRIC STUDY OF SLOPE STABILITY ANALYSIS IN COHESIVE SOILS USING A PROBABILISTIC METHOD
Abstract
The probabilistic analysis of slope stability, accounting for the heterogeneity of the soil medium, was attempted in this study using an advanced approach called the Random Finite Element Method (RFEM). The method was used to investigate the effects of two statistical parameters, namely the coefficient of variation (CoV) and the isotropic spatial correlation length (θ = θx= θy) of different soil parameters on the probability of failure (Pf) of a cohesive soil slope. The statistical effects of cohesion (C), angle of internal friction (Φ), modulus of elasticity (E), and unit weight (ɣ) of the 5V:6H soil slope were examined. The investigated values of θ were 1, 5, 10, 20, 30, and 50 m. The considered CoV values of cohesion (CoVC) were 0, 0.1, 0.2, 0.3, 0.4, 0.5, and 0.7 and the CoV values of Φ (CoVΦ) were 0, 0.05, 0.10, 0.15, 0.20, and 0.30. It is highlighted that the correlation length was directly proportional to the Pf for all the implemented parameters. Moreover, the results show that higher values of CoV of all the parameters corresponded to higher Pfs. Notably, changes in the CoVC and CoVΦ had a more significant impact on failure probability compared to variations in the modulus of elasticity or unit weight. For the cases with high correlation length and large CoVC, a measured failure probability of about 45% was noted. In terms of uncertainty of Φ, the slope with large CoVΦ experienced the Pf varying from 20% to 40% at the larger values of θ. Finally, the study brought attention to the significance of considering the spatial variability of soil properties for conservative evaluation of the stability of soil slopes.
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References
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Baecher, G. B., & Christian, J. T. (2003). Reliability and statistics in geotechnical engineering. J. Wiley.
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Carter, M., & Bentley, S. P. (2016). Soil Properties and their Correlations. John Wiley & Sons.
Chai, J., & Carter, J. P. (2011). Deformation Analysis in Soft Ground Improvement. Springer Science & Business Media.
Chok, Y. H., Jaksa, M., Griffths, D. V., Fenton, G. A., & Kaggwa, W. S. (2015). Probabilistic analysis of a spatially variable c′-φ′ slope. Australian Geomechanics Journal, 50, 17–27.
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El-Ramly, H., Morgenstern, N. R., & Cruden, D. M. (2002). Probabilistic slope stability analysis for practice. Canadian Geotechnical Journal, 39(3), 665–683. https://doi.org/10.1139/t02-034
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Fenton, G. A., & Griffiths, D. V. (2008). Risk Assessment in Geotechnical Engineering. John Wiley & Sons, Inc. https://doi.org/10.1002/9780470284704
Fenton, G. A., & Vanmarcke, E. H. (1990). Simulation of Random Fields via Local Average Subdivision. Journal of Engineering Mechanics, 116(8), 1733–1749. https://doi.org/10.1061/(ASCE)0733-9399(1990)116:8(1733)
Griffiths, D., & Fenton, G. A. (1993). Seepage beneath water retaining structures founded on spatially random soil. In Geotechnique (Vol. 43, Issue 4, pp. 577–587). https://doi.org/10.1680/geot.1993.43.4.577
Griffiths, D., & Fenton, G. A. (2004). Probabilistic slope stability analysis by finite elements. In Journal of geotechnical and geoenvironmental engineering (Vol. 130, Issue 5, pp. 507–518). https://doi.org/10.1061/(ASCE)1090-0241(2004)130:5(507)
Griffiths, D., Fenton, G. A., & Manoharan, N. (2002). Bearing capacity of rough rigid strip footing on cohesive soil: Probabilistic study. In Journal of Geotechnical and Geoenvironmental Engineering (Vol. 128, Issue 9, pp. 743–755). https://doi.org/10.1061/(ASCE)1090-0241(2002)128:9(743)
Griffiths, D., Huang, J., & Fenton, G. A. (2009). Influence of spatial variability on slope reliability using 2-D random fields. In Journal of geotechnical and geoenvironmental engineering (Vol. 135, Issue 10, pp. 1367–1378). https://doi.org/10.1061/(ASCE)GT.1943-5606.0000099
Griffiths, D., Paice, G., & Fenton, G. A. (1994). Finite element modeling of seepage beneath a sheet pile wall in spatially random soil. Geomechanics Research Center, Colorado School of Mines.
Griffiths, D. V., Fenton, G. A., & Denavit, M. D. (2007). Traditional and Advanced Probabilistic Slope Stability Analysis. Probabilistic Applications in Geotechnical Engineering, 1–10. https://doi.org/10.1061/40914(233)19
Griffiths, D. V., & Lane, P. A. (1999). Slope stability analysis by finite elements. Géotechnique, 49(3), 387–403. https://doi.org/10.1680/geot.1999.49.3.387
Gunaratne, M. (Ed.). (2014). The foundation engineering handbook (2. ed). CRC Press.
Huang, J., Zhu, H., Griffiths, D., & A, F. (2015, January 1). Effect of spatial variability on failure mechanism location in random undrained slopes.
Jimenez, R., & Sitar, N. (2009). The importance of distribution types on finite element analyses of foundation settlement. Computers and Geotechnics, 36(3), 474–483. https://doi.org/10.1016/j.compgeo.2008.05.003
Krabbenhoft, K., Lyamin, A., & Krabbenhoft, J. (2015). Optum computational engineering (OptumG2). Computer Software.
Liu, Y., Zhang, W., Zhang, L., Zhu, Z., Hu, J., & Wei, H. (2018). Probabilistic stability analyses of undrained slopes by 3D random fields and finite element methods. Geoscience Frontiers, 9(6), 1657–1664. https://doi.org/10.1016/j.gsf.2017.09.003
Malkawi, A. I. H., Hassan, W. F., & Abdulla, F. A. (2000). Uncertainty and reliability analysis applied to slope stability. Structural Safety, 22(2), 161–187. https://doi.org/10.1016/S0167-4730(00)00006-0
Nguyen, H. B. K., Rahman, M. M., & Karim, M. R. (2023). Effect of soil anisotropy and variability on the stability of undrained soil slope. Frontiers in Built Environment, 9, 1117858. https://doi.org/10.3389/fbuil.2023.1117858
Paice, G., Griffiths, D. V., & Fenton, G. (1994). Influence of Spatially Random Soil Stiffness on Foundation Settlements. Vertical and Horizontal Deformations of Foundations and Embankments. https://www.semanticscholar.org/paper/Influence-of-Spatially-Random-Soil-Stiffness-on-Paice-Griffiths/4d0246706ba73d736e0c095ec34bb3bcd56df483
Phoon, K.-K., & Kulhawy, F. H. (1999). Characterization of geotechnical variability. 36.
Pramanik, R., Baidya, D. K., & Dhang, N. (2017). Reliability analysis for settlement calculation of surface strip footing under different soil conditions using fuzzy sets theory. Proceedings of Geotechnics for Natural and Engineered Sustainable Technologies (GeoNEst): Indian Geotechnical Conference (IGC-2017). Guwahati.
Rao, V. V. S., & Sivakumar Babu, G. L. (Eds.). (2016). Forensic Geotechnical Engineering. Springer India. https://doi.org/10.1007/978-81-322-2377-1
Reeves, G. M., Sims, I., & Cripps, J. C. (2006). Clay Materials Used in Construction. Geological Society of London.
Sheykhloo, P. A. (2015). Risk assessment and spatial variability in geotechnical stability problems. https://www.semanticscholar.org/paper/Risk-assessment-and-spatial-variability-in-problems-Sheykhloo/8fb934e52142ce92121dc1d5e9e42f9209693820
Smith, I. M., & Griffiths, D. V. (1998). Programming the finite element method (3rd ed). John Wiley & Sons.
Smith, I. M., & Griffiths, D. V. (2004). Programming the finite element method (4th ed). Wiley.
Szynakiewicz, T., Griffiths, D., & Fenton, G. (2002). A probabilistic investigation of c′, φ′ slope stability. Proceedings of the 6th International Congress on Numerical Methods in Engineering and Scientific Applications, CIMENICS’02, Pub. Sociedad Venezolana de Métodos Numéricos En Ingeniería, 25–36.
Zhu, D., Griffiths, D., & Fenton, G. (2019). Probabilistic stability analyses of layered excavated slopes. In Geotechnique Letters (Vol. 9, Issue 3, pp. 161–164). https://doi.org/10.1680/jgele.18.00252
Zhu, D., Griffiths, D., Huang, J., & Fenton, G. (2017). Probabilistic stability analyses of undrained slopes with linearly increasing mean strength. In Géotechnique (Vol. 67, Issue 8, pp. 733–746). https://doi.org/10.1680/jgeot.16.P.223
Allahverdizadeh, P., Griffiths, D. v., & Fenton, G. a. (2015a). Influence of highly anisotropic properties on probabilistic slope stability. In Geotechnical Engineering for Infrastructure and Development (Vols. 1–7, pp. 1555–1559). ICE Publishing. https://doi.org/10.1680/ecsmge.60678.vol4.228
Allahverdizadeh, P., Griffiths, D. V., & Fenton, G. A. (2015b). The Random Finite Element Method (RFEM) in Probabilistic Slope Stability Analysis with Consideration of Spatial Variability of Soil Properties. IFCEE 2015, 1946–1955. https://doi.org/10.1061/9780784479087.178
Alonso, E. E. (1976). Risk analysis of slopes and its application to slopes in Canadian sensitive clays. Géotechnique, 26(3), 453–472. https://doi.org/10.1680/geot.1976.26.3.453
Baecher, G. B., & Christian, J. T. (2003). Reliability and statistics in geotechnical engineering. J. Wiley.
Bowles, J. E. (1996). Foundation analysis and design (5th ed). McGraw-Hill.
Carter, M., & Bentley, S. P. (2016). Soil Properties and their Correlations. John Wiley & Sons.
Chai, J., & Carter, J. P. (2011). Deformation Analysis in Soft Ground Improvement. Springer Science & Business Media.
Chok, Y. H., Jaksa, M., Griffths, D. V., Fenton, G. A., & Kaggwa, W. S. (2015). Probabilistic analysis of a spatially variable c′-φ′ slope. Australian Geomechanics Journal, 50, 17–27.
Das, B. M. (2011). Geotechnical Engineering Handbook. J. Ross Publishing.
Duncan, J. M. (2000). Factors of Safety and Reliability in Geotechnical Engineering. Journal of Geotechnical and Geoenvironmental Engineering, 126(4), 307–316. https://doi.org/10.1061/(ASCE)1090-0241(2000)126:4(307)
Duncan, J. M., Wright, S. G., & Brandon, T. L. (2014). Soil strength and slope stability (Second edition). John Wiley & Sons Inc.
El-Ramly, H., Morgenstern, N. R., & Cruden, D. M. (2002). Probabilistic slope stability analysis for practice. Canadian Geotechnical Journal, 39(3), 665–683. https://doi.org/10.1139/t02-034
Fenton, G. A., & Griffiths, D. (1996). Statistics of free surface flow through stochastic earth dam. In Journal of geotechnical engineering (Vol. 122, Issue 6, pp. 427–436). https://doi.org/10.1061/(ASCE)0733-9410(1996)122:6(427)
Fenton, G. A., & Griffiths, D. (2002). Probabilistic foundation settlement on spatially random soil. In Journal of Geotechnical and Geoenvironmental Engineering (Vol. 128, Issue 5, pp. 381–390). https://doi.org/10.1061/(ASCE)1090-0241(2002)128:5(381)
Fenton, G. A., & Griffiths, D. (2003). Bearing-capacity prediction of spatially random c φ soils. In Canadian geotechnical journal (Vol. 40, Issue 1, pp. 54–65). https://doi.org/10.1139/t02-086
Fenton, G. A., Griffiths, D., & Ojomo, O. O. (2011). Consequence factors in the ultimate limit state design of shallow foundations. In Canadian geotechnical journal (Vol. 48, Issue 2, pp. 265–279). https://doi.org/10.1139/T10-053
Fenton, G. A., & Griffiths, D. V. (2008). Risk Assessment in Geotechnical Engineering. John Wiley & Sons, Inc. https://doi.org/10.1002/9780470284704
Fenton, G. A., & Vanmarcke, E. H. (1990). Simulation of Random Fields via Local Average Subdivision. Journal of Engineering Mechanics, 116(8), 1733–1749. https://doi.org/10.1061/(ASCE)0733-9399(1990)116:8(1733)
Griffiths, D., & Fenton, G. A. (1993). Seepage beneath water retaining structures founded on spatially random soil. In Geotechnique (Vol. 43, Issue 4, pp. 577–587). https://doi.org/10.1680/geot.1993.43.4.577
Griffiths, D., & Fenton, G. A. (2004). Probabilistic slope stability analysis by finite elements. In Journal of geotechnical and geoenvironmental engineering (Vol. 130, Issue 5, pp. 507–518). https://doi.org/10.1061/(ASCE)1090-0241(2004)130:5(507)
Griffiths, D., Fenton, G. A., & Manoharan, N. (2002). Bearing capacity of rough rigid strip footing on cohesive soil: Probabilistic study. In Journal of Geotechnical and Geoenvironmental Engineering (Vol. 128, Issue 9, pp. 743–755). https://doi.org/10.1061/(ASCE)1090-0241(2002)128:9(743)
Griffiths, D., Huang, J., & Fenton, G. A. (2009). Influence of spatial variability on slope reliability using 2-D random fields. In Journal of geotechnical and geoenvironmental engineering (Vol. 135, Issue 10, pp. 1367–1378). https://doi.org/10.1061/(ASCE)GT.1943-5606.0000099
Griffiths, D., Paice, G., & Fenton, G. A. (1994). Finite element modeling of seepage beneath a sheet pile wall in spatially random soil. Geomechanics Research Center, Colorado School of Mines.
Griffiths, D. V., Fenton, G. A., & Denavit, M. D. (2007). Traditional and Advanced Probabilistic Slope Stability Analysis. Probabilistic Applications in Geotechnical Engineering, 1–10. https://doi.org/10.1061/40914(233)19
Griffiths, D. V., & Lane, P. A. (1999). Slope stability analysis by finite elements. Géotechnique, 49(3), 387–403. https://doi.org/10.1680/geot.1999.49.3.387
Gunaratne, M. (Ed.). (2014). The foundation engineering handbook (2. ed). CRC Press.
Huang, J., Zhu, H., Griffiths, D., & A, F. (2015, January 1). Effect of spatial variability on failure mechanism location in random undrained slopes.
Jimenez, R., & Sitar, N. (2009). The importance of distribution types on finite element analyses of foundation settlement. Computers and Geotechnics, 36(3), 474–483. https://doi.org/10.1016/j.compgeo.2008.05.003
Krabbenhoft, K., Lyamin, A., & Krabbenhoft, J. (2015). Optum computational engineering (OptumG2). Computer Software.
Liu, Y., Zhang, W., Zhang, L., Zhu, Z., Hu, J., & Wei, H. (2018). Probabilistic stability analyses of undrained slopes by 3D random fields and finite element methods. Geoscience Frontiers, 9(6), 1657–1664. https://doi.org/10.1016/j.gsf.2017.09.003
Malkawi, A. I. H., Hassan, W. F., & Abdulla, F. A. (2000). Uncertainty and reliability analysis applied to slope stability. Structural Safety, 22(2), 161–187. https://doi.org/10.1016/S0167-4730(00)00006-0
Nguyen, H. B. K., Rahman, M. M., & Karim, M. R. (2023). Effect of soil anisotropy and variability on the stability of undrained soil slope. Frontiers in Built Environment, 9, 1117858. https://doi.org/10.3389/fbuil.2023.1117858
Paice, G., Griffiths, D. V., & Fenton, G. (1994). Influence of Spatially Random Soil Stiffness on Foundation Settlements. Vertical and Horizontal Deformations of Foundations and Embankments. https://www.semanticscholar.org/paper/Influence-of-Spatially-Random-Soil-Stiffness-on-Paice-Griffiths/4d0246706ba73d736e0c095ec34bb3bcd56df483
Phoon, K.-K., & Kulhawy, F. H. (1999). Characterization of geotechnical variability. 36.
Pramanik, R., Baidya, D. K., & Dhang, N. (2017). Reliability analysis for settlement calculation of surface strip footing under different soil conditions using fuzzy sets theory. Proceedings of Geotechnics for Natural and Engineered Sustainable Technologies (GeoNEst): Indian Geotechnical Conference (IGC-2017). Guwahati.
Rao, V. V. S., & Sivakumar Babu, G. L. (Eds.). (2016). Forensic Geotechnical Engineering. Springer India. https://doi.org/10.1007/978-81-322-2377-1
Reeves, G. M., Sims, I., & Cripps, J. C. (2006). Clay Materials Used in Construction. Geological Society of London.
Sheykhloo, P. A. (2015). Risk assessment and spatial variability in geotechnical stability problems. https://www.semanticscholar.org/paper/Risk-assessment-and-spatial-variability-in-problems-Sheykhloo/8fb934e52142ce92121dc1d5e9e42f9209693820
Smith, I. M., & Griffiths, D. V. (1998). Programming the finite element method (3rd ed). John Wiley & Sons.
Smith, I. M., & Griffiths, D. V. (2004). Programming the finite element method (4th ed). Wiley.
Szynakiewicz, T., Griffiths, D., & Fenton, G. (2002). A probabilistic investigation of c′, φ′ slope stability. Proceedings of the 6th International Congress on Numerical Methods in Engineering and Scientific Applications, CIMENICS’02, Pub. Sociedad Venezolana de Métodos Numéricos En Ingeniería, 25–36.
Zhu, D., Griffiths, D., & Fenton, G. (2019). Probabilistic stability analyses of layered excavated slopes. In Geotechnique Letters (Vol. 9, Issue 3, pp. 161–164). https://doi.org/10.1680/jgele.18.00252
Zhu, D., Griffiths, D., Huang, J., & Fenton, G. (2017). Probabilistic stability analyses of undrained slopes with linearly increasing mean strength. In Géotechnique (Vol. 67, Issue 8, pp. 733–746). https://doi.org/10.1680/jgeot.16.P.223
Published
2024-10-08
How to Cite
HAJI, A. J., & HUSSAIN, M. S. (2024). A PARAMETRIC STUDY OF SLOPE STABILITY ANALYSIS IN COHESIVE SOILS USING A PROBABILISTIC METHOD. Journal of Duhok University, 27(1), 16-29. Retrieved from https://journal.uod.ac/index.php/uodjournal/article/view/3363
Section
Pure and Engineering Sciences
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