Random Finite-Element Analysis of Slope Considering Strength Anisotropy and Spatial Variability of Soil
Abstract
Soil is a complex material that exhibits both spatial variability and anisotropy. For simplicity, the traditional approach for analyzing slope stability often assumes that soil is homogeneous or isotropic, which can lead to an overestimation of slope stability and reliability. To address this issue, a novel approach is proposed in this study that uses an anisotropic yield criterion based on the random finite-element method to evaluate the influence of strength anisotropy on slope stability, while accounting for the influence of spatial variability on reliability. The proposed approach is applied to a typical case of slope reliability analysis. It is shown that the results of the proposed approach are consistent with those of previous studies and OPTUM G2 outcomes. The assessment involves determining the safety factors for both homogeneous and anisotropic conditions, while also taking into account the probability of failure in the presence of spatial variability. It is found that strength anisotropy significantly affects slope stability and reliability, as the factor of safety decreases from 1.255 to 1.037 and the probability of failure increases from 3.5% to 52.1% when considering strength anisotropy (, ). In addition, a sensitivity analysis is performed to investigate the influence of slope geometric parameters, strength anisotropic parameters, and spatial variability parameters on slope stability and reliability.
Get full access to this article
View all available purchase options and get full access to this article.
Data Availability Statement
Data will be made available upon reasonable request to the corresponding author.
Acknowledgments
The authors appreciate the financial support from the National Natural Science Foundation of China (Grant No. 42077236), the Sichuan Province Science and Technology Support Program (Grant Nos. 2022NSFSC0407 and 2021YFH0037).
References
Abbo, A. J., and S. W. Sloan. 1995. “A smooth hyperbolic approximation to the Mohr-Coulomb yield criterion.” Comput. Struct. 54 (3): 427–441. https://doi.org/10.1016/0045-7949(94)00339-5.
Aghajani, H. F., H. Salehzadeh, and H. Shahnazari. 2015. “Stability analysis of sandy slope considering anisotropy effect in friction angle.” Sadhana-Acad. Proc. Eng. Sci. 40 (6): 1955–1974. https://doi.org/10.1007/s12046-015-0414-2.
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.
Arai, K., and M. Nakagawa. 1986. “Influence of strength anisotropy on the search for critical noncircular slip surface.” Soils Found. 26 (3): 129–136. https://doi.org/10.3208/sandf1972.26.3_129.
Au, S. K., and J. L. Beck. 2003. “Important sampling in high dimensions.” Struct. Saf. 25 (2): 139–163. https://doi.org/10.1016/S0167-4730(02)00047-4.
Bjerrum, L., and O. Eide. 1956. “Stability of strutted excavations in clay.” Géotechnique 6 (1): 32–47. https://doi.org/10.1680/geot.1956.6.1.32.
Booker, J. R., and E. H. Davis. 1972. “A general treatment of plastic anisotropy under conditions of plane strain.” J. Mech. Phys. Solids 20 (4): 239–250. https://doi.org/10.1016/0022-5096(72)90003-8.
Burgess, J., G. A. Fenton, and D. V. Griffiths. 2019. “Probabilistic seismic slope stability analysis and design.” Can. Geotech. J. 56 (12): 1979–1998. https://doi.org/10.1139/cgj-2017-0544.
Casagrande, A., and N. Carillo. 1944. “Shear failure of anisotropic soils.” Proc. Boston Soc. Civ. Eng. 31 (4): 74–87.
Chen, W. F. 1975. Limit analysis and soil plasticity. Amsterdam, Netherlands: Elsevier.
Cho, S. E. 2007. “Effects of spatial variability of soil properties on slope stability.” Eng. Geol. 92 (3–4): 97–109. https://doi.org/10.1016/j.enggeo.2007.03.006.
Cho, S. E. 2010. “Probabilistic assessment of slope stability that considers the spatial variability of soil properties.” J. Geotech. Geoenviron. Eng. 136 (7): 975–984. https://doi.org/10.1061/(ASCE)GT.1943-5606.0000309.
Christian, J. T., C. C. Ladd, and G. B. Baecher. 1994. “Reliability applied to slope stability analysis.” J. Geotech. Eng. 120 (12): 2180–2207. https://doi.org/10.1061/(ASCE)0733-9410(1994)120:12(2180).
El-Kadi, A. I., and S. A. Williams. 2000. “Generating two-dimensional fields of autocorrelated, normally distributed parameters by the matrix decomposition technique.” Ground Water 38 (4): 530–532. https://doi.org/10.1111/j.1745-6584.2000.tb00245.x.
Fenton, G. A., and D. V. Griffiths. 2008. Risk assessment in geotechnical engineering. New York: Wiley.
Griffiths, D. V., and G. A. Fenton. 2004. “Probabilistic slope stability analysis by finite elements.” J. Geotech. Geoenviron. Eng. 130 (5): 507–518. https://doi.org/10.1061/(ASCE)1090-0241(2004)130:5(507).
Griffiths, D. V., J. Huang, and G. A. Fenton. 2009. “Influence of spatial variability on slope reliability using 2-D random fields.” J. Geotech. Geoenviron. Eng. 135 (10): 1367–1378. https://doi.org/10.1061/(ASCE)GT.1943-5606.0000099.
Griffiths, D. V., and P. A. Lane. 1999. “Slope stability analysis by finite elements.” Géotechnique 49 (3): 387–403. https://doi.org/10.1680/geot.1999.49.3.387.
Hansen, J. B., and R. E. Gibson. 1949. “Undrained shear strengths of anisotropically consolidated clays.” Géotechnique 1 (3): 189–200. https://doi.org/10.1680/geot.1949.1.3.189.
He, Y., H. Hazarika, N. Yasufuku, Z. Han, and Y. Li. 2015a. “Three-dimensional limit analysis of seismic displacement of slope reinforced with piles.” Soil Dyn. Earthquake Eng. 77 (Aug): 446–452. https://doi.org/10.1016/j.soildyn.2015.06.015.
He, Y., H. Hazarika, N. Yasufuku, J. Teng, Z. Jiang, and Z. Han. 2015b. “Estimation of lateral force acting on piles to stabilize landslides.” Nat. Hazards 79 (3): 1981–2003. https://doi.org/10.1007/s11069-015-1942-0.
He, Y., Y. Liu, H. Hazarika, and R. Yuan. 2019a. “Stability analysis of seismic slopes with tensile strength cut-off.” Comput. Geotech. 112 (Sep): 245–256. https://doi.org/10.1016/j.compgeo.2019.04.029.
He, Y., Y. Liu, Y. Zhang, and R. Yuan. 2019b. “Stability assessment of three-dimensional slopes with cracks.” Eng. Geol. 252 (26): 136–144. https://doi.org/10.1016/j.enggeo.2019.03.001.
He, Y., X. Y. Wang, R. Yuan, K. W. Liu, and P. Z. Zhuang. 2019c. “On the computational precision of finite element algorithms in slope stability problems.” Math. Probl. Eng. 2019 (Oct): 1–15. https://doi.org/10.1155/2019/9391657.
He, Y., J. Yu, R. Yuan, W. Wang, and N. Nikitas. 2022. “Stability and failure mechanisms in three-dimensional cracked slope: Static and dynamic analysis.” Comput. Geotech. 144 (Feb): 104626. https://doi.org/10.1016/j.compgeo.2021.104626.
Ji, J., H. J. Liao, and B. K. Low. 2012. “Modeling 2-D spatial variation in slope reliability analysis using interpolated autocorrelations.” Comput. Geotech. 40 (Sep): 135–146. https://doi.org/10.1016/j.compgeo.2011.11.002.
Jiang, S. H., D. Q. Li, Z. J. Cao, C. B. Zhou, and K. K. Phoon. 2015. “Efficient system reliability analysis of slope stability in spatially variable soils using Monte Carlo simulation.” J. Geotech. Geoenviron. Eng. 141 (2): 04014096. https://doi.org/10.1061/(ASCE)GT.1943-5606.0001227.
Jiang, S. H., D. Q. Li, L. M. Zhang, and C. B. Zhou. 2014. “Slope reliability analysis considering spatially variable shear strength parameters using a non-intrusive stochastic finite element method.” Eng. Geol. 168 (Aug): 120–128. https://doi.org/10.1016/j.enggeo.2013.11.006.
Koutsoftas, D. C., and C. C. Ladd. 1985. “Design strengths for an offshore clay.” J. Geotech. Eng. 111 (3): 337–355. https://doi.org/10.1061/(ASCE)0733-9410(1985)111:3(337).
Lade, P. V. 1981. Vol. 740 of Torsion shear apparatus for soil testing, 145–163. West Conshohocken, PA: ASTM.
Li, D., Y. Chen, W. Lu, and C. Zhou. 2011. “Stochastic response surface method for reliability analysis of rock slopes involving correlated non-normal variables.” Comput. Geotech. 38 (1): 58–68. https://doi.org/10.1016/j.compgeo.2010.10.006.
Li, D. Q., S. H. Jiang, Z. J. Cao, W. Zhou, C. B. Zhou, and L. M. Zhang. 2015. “A multiple response-surface method for slope reliability analysis considering spatial variability of soil properties.” Eng. Geol. 187 (Aug): 60–72. https://doi.org/10.1016/j.enggeo.2014.12.003.
Lo, K. Y. 1965. “Stability of slopes in anisotropic soils.” J. Soil Mech. Found. Div. 91 (4): 85–106. https://doi.org/10.1061/JSFEAQ.0000778.
Low, B. K., and W. H. Tang. 1997. “Probabilistic slope analysis using Janbu’s generalized procedure of slices.” Comput. Geotech. 21 (2): 121–142. https://doi.org/10.1016/S0266-352X(97)00019-0.
Low, B. K., and W. H. Tang. 2007. “Efficient spreadsheet algorithm for first-order reliability method.” J. Eng. Mech. 133 (12): 1378–1387. https://doi.org/10.1061/(ASCE)0733-9399(2007)133:12(1378).
Shogaki, T., and N. Kumagai. 2008. “A slope stability analysis considering undrained strength anisotropy of natural clay deposits.” Soils Found. 48 (6): 805–819. https://doi.org/10.3208/sandf.48.805.
Sloan, S. W. 2013. “Geotechnical stability analysis.” Géotechnique 63 (7): 531–571. https://doi.org/10.1680/geot.12.RL.001.
Smith, I. M., D. V. Griffiths, and L. Margetts. 2015. Programming the finite element method. 5th ed. New York: Wiley.
Su, S. F., and H. J. Liao. 1999. “Effect of strength anisotropy on undrained slope stability in clay.” Géotechnique 49 (2): 215–230. https://doi.org/10.1680/geot.1999.49.2.215.
Vanmarcke, E. H. 1977. “Probabilistic modeling of soil profiles.” J. Geotech. Eng. Div. 103 (11): 1227–1246. https://doi.org/10.1061/AJGEB6.0000517.
Yuan, R., H. S. Yu, N. Hu, and Y. He. 2018. “Non-coaxial soil model with an anisotropic yield criterion and its application to the analysis of strip footing problems.” Comput. Geotech. 99 (7): 80–92. https://doi.org/10.1016/j.compgeo.2018.02.022.
Yuan, R., H. S. Yu, D. S. Yang, and N. Hu. 2019. “On a fabric evolution law incorporating the effects of -value.” Comput. Geotech. 105 (Feb): 142–154. https://doi.org/10.1016/j.compgeo.2018.09.019.
Zhou, H. Z., J. B. Zhang, X. X. Yu, Q. C. Hu, G. Zheng, H. J. Xu, Y. P. Shi, Y. He, and S. C. Yang. 2024. “Stochastic bearing capacity and failure mechanism of footings placed adjacent to slopes considering the anisotropic spatial variability of the clay undrained strength.” Int. J. Geomech. 24 (4). https://doi.org/10.1061/IJGNAI.GMENG-9136.
Information & Authors
Information
Published In
Natural Hazards Review
Volume 25 • Issue 2 • May 2024
Copyright
© 2024 American Society of Civil Engineers.
History
Received: Aug 10, 2023
Accepted: Dec 20, 2023
Published online: Mar 8, 2024
Published in print: May 1, 2024
Discussion open until: Aug 8, 2024
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.