Model Updating of Slope Stability Analysis Using 3D Conditional Random Fields
Publication: ASCE-ASME Journal of Risk and Uncertainty in Engineering Systems, Part A: Civil Engineering
Volume 7, Issue 3
Abstract
In situ soil properties exhibit spatial variability, which is often described using a three-dimensional (3D) random field. With site investigations, soil properties at some specific locations are available. The corresponding data can be incorporated by a conditional random field to update the uncertainty parameters so that a more realistic or refined model can be achieved. Two algorithms, the Kriging and patching algorithms, are introduced for generating a 3D conditional random field. The conditional random field is linked with finite-element modeling, within the framework of Monte Carlo, to evaluate the performance of these two approaches in slope stability analyses. Sparsely distributed borehole data and cone penetration test (CPT) data are considered. The results indicate that for cases with limited sampled data, the patching algorithm gains an advantage over the Kriging algorithm in terms of prediction accuracy and uncertainty reduction. Data near the sliding surfaces of a slope remarkably affect the stability; thus, with sufficient ground information near the sliding surfaces, a conditional random field can provide better guidance for slope design.
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Data Availability Statement
All data, models, or code that support the findings of this study are available from the corresponding author upon reasonable request.
Acknowledgments
This research is supported by the National Natural Science foundation of China (Grant No. 52079099).
References
Cho, E. 2012. “Probabilistic analysis of seepage that considers the spatial variability of permeability for an embankment on soil foundation.” Eng. Geol. 133–134 (Apr): 30–39. https://doi.org/10.1016/j.enggeo.2012.02.013.
Cressie, N. 1990. “The origins of Kriging.” Math. Geol. 22 (3): 239–252. https://doi.org/10.1007/BF00889887.
Fenton, G. A., and D. V. Griffiths. 2008. Risk assessment in geotechnical engineering. New York: Wiley.
Fenton, G. A., and E. H. Vanmarcke. 1990. “Simulation of random fields via local average subdivision.” J. Eng. Mech. 116 (8): 1733–1749. https://doi.org/10.1061/(ASCE)0733-9399(1990)116:8(1733).
Ghedjati, S., M. Lamara, and Y. Houmadi. 2020. “Finite difference probabilistic slope stability analysis based on collocation-based stochastic response surface method (CSRSM).” Innov. Infrastruct. Solutions 5 (3): 73. https://doi.org/10.1007/s41062-020-00322-x.
Griffiths, D. V., and G. A. Fenton. 2001. “Bearing capacity of spatially random soil: The undrained clay Prandtl problem revisited.” Géotechnique 51 (4): 351–359. https://doi.org/10.1680/geot.2001.51.4.351.
Griffiths, D. V., and G. A. Fenton. 2007. Probabilistic method in geotechnical engineering. Berlin: Springer.
Henderson, C. R. 1975. “Best linear unbiased estimation and prediction under a selection model.” Biometrics 31 (2): 423–447. https://doi.org/10.2307/2529430.
Hicks, A., J. D. Nuttall, and J. Chen. 2014. “Influence of heterogeneity on 3D slope reliability and failure consequence.” Comput. Geotech. 61 (Sep): 198–208. https://doi.org/10.1016/j.compgeo.2014.05.004.
Hicks, M. A., and W. A. Spencer. 2010. “Influence of heterogeneity on the reliability and failure of a long 3D slope.” Comput. Geotech. 37 (7–8): 948–955. https://doi.org/10.1016/j.compgeo.2010.08.001.
Huang, L., Y. M. Cheng, Y. F. Leung, and L. Li. 2019. “Influence of rotated anisotropy on slope reliability evaluation using conditional random field.” Comput. Geotech. 115 (Nov): 103133. https://doi.org/10.1016/j.compgeo.2019.103133.
Huang, L., Y. Zhang, M. K. Lo, and Y. M. Cheng. 2020. “Comparative study of conditional methods in slope reliability evaluation.” Comput. Geotech. 127 (Nov): 103762. https://doi.org/10.1016/j.compgeo.2020.103762.
Johari, A., and H. Fooladi. 2020. “Comparative study of stochastic slope stability analysis based on conditional and unconditional random field.” Comput. Geotech. 125 (Sep): 103707. https://doi.org/10.1016/j.compgeo.2020.103707.
Kim, J. M., and N. Sitar. 2013. “Reliability approach to slope stability analysis with spatially correlated soil properties.” Soils Found. 53 (1): 1–10. https://doi.org/10.1016/j.sandf.2012.12.001.
Li, 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 (Mar): 60–72. https://doi.org/10.1016/j.enggeo.2014.12.003.
Li, Y., M. A. Hicks, and P. J. Vardon. 2017. “Cost-effective design of long spatially variable soil slopes using conditional simulation.” In Geo-Risk 2017: Reliability-Based Design and Code Developments, Geotechnical Special Publication 283, edited by J. Huang, G. A. Fenton, L. Zhang, and D. V. Griffiths, 394–402. Reston, VA: ASCE. https://doi.org/10.1061/9780784480700.
Li, Y. J., M. A. Hicks, and P. J. Vardon. 2016. “Uncertainty reduction and sampling efficiency in slope designs using 3D conditional random fields.” Comput. Geotech. 79 (Oct): 159–172. https://doi.org/10.1016/j.compgeo.2016.05.027.
Liu, L. L., Y. M. Cheng, and S. H. Zhang. 2017. “Conditional random field reliability analysis of a cohesion-frictional slope.” Comput. Geotech. 82 (Feb): 173–186. https://doi.org/10.1016/j.compgeo.2016.10.014.
Liu, Y., F. H. Lee, S. T. Quek, and M. Beer. 2014. “Modified linear estimation method for generating multi-dimensional multivariate Gaussian field in modelling material properties.” Probab. Eng. Mech. 38 (Oct): 42–53. https://doi.org/10.1016/j.probengmech.2014.09.001.
Liu, Y., S. T. Quek, and F. H. Lee. 2016. “Translation random field with marginal beta distribution in modelling material properties.” Struct. Saf. 61 (Jul): 57–66. https://doi.org/10.1016/j.strusafe.2016.04.001.
Liu, Y., W. G. Zhang, L. Zhang, Z. R. Zhu, J. Hu, and H. Wei. 2018. “Probabilistic stability analyses of undrained slopes by 3D random fields and finite element methods.” Geosci. Front. 9 (6): 1657–1664. https://doi.org/10.1016/j.gsf.2017.09.003.
Lloret-Cabot, M., G. A. Fenton, and M. A. Hicks. 2014. “On the estimation of scale of fluctuation in geostatistics.” Assess. Manage. Risk Eng. Syst. Geohazards 8 (2): 129–140. https://doi.org/10.1080/17499518.2013.871189.
Lloret-Cabot, M., M. A. Hicks, and A. P. van Den Eijnden. 2012. “Investigation of the reduction in uncertainty due to soil variability when conditioning a random field using Kriging.” Geotech. Lett. 2 (3): 123–127. https://doi.org/10.1680/geolett.12.00022.
Mohseni, S., M. Payan, and R. J. Chenari. 2018. “Soil–structure interaction analysis in natural heterogeneous deposits using random field theory.” Innov. Infrastruct. Solutions 3 (1): 62. https://doi.org/10.1007/s41062-018-0168-x.
Namikawa, T. 2016. “Conditional probabilistic analysis of cement-treated soil column strength.” Int. J. Geomech. 16 (1): 04015021. https://doi.org/10.1061/(ASCE)GM.1943-5622.0000481.
Ou-Yang, J. Y., M. Hu, D. Q. Li, and Y. Liu. 2020. “Conditional slope stability analysis considering spatial variability of soils and site investigation information.” In Proc., 7th Asian-Pacific Symp. on Structural Reliability and Its Applications (APSSRA2020), 278–282. Tokyo: Asian-Pacific Symposium on Structural Reliability and Its Applications.
Ou-Yang, J. Y., D. Q. Li, X. S. Tang, and Y. Liu. 2021. “A patching algorithm for conditional random fields in modelling material properties.” Comput. Methods Appl. Mech. Eng. 377 (Apr): 113719. https://doi.org/10.1016/j.cma.2021.113719.
Pan, Y. T., Y. Liu, A. Tyagi, F. H. Lee, and D. Q. Li. 2021. “Model-independent strength-reduction factor for effect of spatial variability on tunnel with improved soil surrounds.” Géotechnique 71 (5): 1–17. https://doi.org/10.1680/jgeot.19.P.056.
Phoon, K. K., and F. H. Kulhawy. 1999. “Characterization of geotechnical variability.” Can. Geotech. J. 36 (4): 612–624. https://doi.org/10.1139/t99-038.
Ren, W. X., and H. B. Chen. 2010. “Finite element model updating in structural dynamics by using the response surface method.” Eng. Struct. 32 (8): 2455–2465. https://doi.org/10.1016/j.engstruct.2010.04.019.
Robertson, P. K. 2009. “Interpretation of cone penetration tests—A unified approach.” Can. Geotech. J. 46 (11): 1337–1355. https://doi.org/10.1139/T09-065.
Shinozuka, M., and G. Deodatis. 1988. “Response variability of stochastic finite element systems.” J. Eng. Mech. 114 (3): 499–519. https://doi.org/10.1061/(ASCE)0733-9399(1988)114:3(499).
Shinozuka, M., and G. Deodatis. 1996. “Simulation of multi-dimensional Gaussian stochastic fields by spectral representation.” Appl. Mech. Rev. 49 (1): 29–53. https://doi.org/10.1115/1.3101883.
van den Eijnden, A. P., and M. A. Hicks. 2011. “Conditional simulation for characterizing the spatial variability of sand state.” In Proc., 2nd Int. Symp. on Computational Geomechanics, 288–296. Delft, Netherlands: Delft Univ. of Technology.
Vanmarcke, E. H. 1983. Random fields: Analysis and synthesis. Cambridge, MA: MIT Press.
Wang, Y., Z. J. Cao, and D. Q. Li. 2016. “Bayesian perspective on geotechnical variability and site characterization.” Eng. Geol. 203 (Mar): 117–125. https://doi.org/10.1016/j.enggeo.2015.08.017.
Yamazaki, F., M. Shinozuka, and G. Dasgupta. 1988. “Neumann expansion for stochastic finite element analysis.” J. Eng. Mech. 114 (8): 1335–1354. https://doi.org/10.1061/(ASCE)0733-9399(1988)114:8(1335).
Yi, J. T., L. Y. Huang, D. Q. Li, and Y. Liu. 2020. “A large-deformation random finite-element study: Failure mechanism and bearing capacity of spudcan in a spatially varying clayey seabed.” Géotechnique 70 (5): 392–405. https://doi.org/10.1680/jgeot.18.P.171.
Yücemen, M. S., and A. S. Al-Homoud. 1990. “Probabilistic three-dimensional stability analysis of slopes.” Struct. Saf. 9 (1): 1–20. https://doi.org/10.1016/0167-4730(90)90017-J.
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Published In
ASCE-ASME Journal of Risk and Uncertainty in Engineering Systems, Part A: Civil Engineering
Volume 7 • Issue 3 • September 2021
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© 2021 American Society of Civil Engineers.
History
Received: Jan 14, 2021
Accepted: Mar 29, 2021
Published online: Jul 7, 2021
Published in print: Sep 1, 2021
Discussion open until: Dec 7, 2021
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