An Investigation of Cross-Sectional Spatial Variation with Random Finite Element Method Slope Stability Analysis
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ORIGINAL PAPER
An Investigation of Cross-Sectional Spatial Variation with Random Finite Element Method Slope Stability Analysis Ashley P. Dyson . Ali Tolooiyan
Received: 28 October 2019 / Accepted: 28 June 2020 Ó Springer Nature Switzerland AG 2020
Abstract The selection of two-dimensional crosssections for plane-strain slope stability analysis often requires a range of assumptions such that the most appropriate cross-section is considered. When faced with complex strata, surface topologies and porewater pressure distributions, the selection of an appropriate cross-section is non-trivial. Circumstances are further complicated when considering spatially variable soils and heterogeneous strength parameters. In this study, the effects of spatially variable geotechnical parameters are examined for a range of two-dimensional random finite element method (RFEM) simulations of an open-pit mine. A distinct set of random field instances are provided to each cross-section to isolate the impact of geometry and strata variation when coupled with spatially variable soil characterisations. Particular attention is given to the regions providing the greatest impact on factors of safety and representative slip surfaces for each slope geometry, evaluating the need for full three-dimensional RFEM simulation. Further
A. P. Dyson Geotechnical and Hydrogeological Engineering Research Group (GHERG), Federation University Australia, Churchill, VIC 3842, Australia e-mail: [email protected] A. Tolooiyan (&) School of Engineering, University of Tasmania, Hobart, TAS 7001, Australia e-mail: [email protected]; [email protected]
statistical analyses are conducted to establish which random field slope stability cross-sections are significantly different from the underlying cross-section population, thereby identifying the best cross-section to represent the overall slope geometry. Keywords Random field Slope stability analysis Random finite element method Cross-section Spatial variability List of symbols Bold symbols indicate vector notation c Cohesion Ck Total similarity matrix of the cluster k d Normal standard deviate for a desired confidence level with Monte Carlo simulation E Elastic modulus F Force G(x) Standard normal random field k Permeability K Random field cluster m Number of random variables in Monte Carlo simulation Mi ith random field matrix realisation s Standard deviation t ð xÞ Deterministic term of soil variability model wð xÞ Fluctuation term for soil variability model Xi Sequence of independent lognormal random variables c Unit weight
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Geotech Geol Eng
e h h1 h2 hx hy l m nð x Þ qð s Þ r1 r3 s sx sy / w
Relative percentage error in estimating Pf with Monte Carlo simulation Scale of fluctuation Major principal scale of fluctuation Minor principal scale of fluctuation Scale of fluctuation parallel to the x axis Scale of fluctuation parallel to the y axis Mean value of a geotechnical parameter Poisson’s ratio Soil variability model, consisting
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