Stochastic seismic slope stability assessment using polynomial chaos expansions combined with relevance vector machine

Abstract This paper presents probabilistic assessment of seismically-induced slope displacements considering uncertainties of seismic ground motions and soil properties. A stochastic ground motion model representing both the temporal and spectral non-stationarity of earthquake shakings and a three-dimensional rotational failure mechanism are integrated to assess Newmark-type slope displacements. A new probabilistic approach that incorporates machine learning in metamodeling technique is proposed, by combining relevance vector machine with polynomial chaos expansions (RVM-PCE). Compared with other PCE methods, the proposed RVM-PCE is shown to be more effective in estimating failure probabilities. The sensitivity and relative influence of each random input parameter to the slope displacements are discussed. Finally, the fragility curves for slope displacements are established for site-specific soil conditions and earthquake hazard levels. The results indicate that the slope displacement is more sensitive to the intensities and strong shaking durations of seismic ground motions than the frequency contents, and a critical Arias intensity that leads to the maximum annual failure probabilities can be identified by the proposed approach.

[1]  R. Ghanem,et al.  Stochastic Finite Elements: A Spectral Approach , 1990 .

[2]  A. Soubra,et al.  Kriging-Based Reliability Analysis of Strip Footings Resting on Spatially Varying Soils , 2018, Journal of Geotechnical and Geoenvironmental Engineering.

[3]  K. Campbell.  Campbell-Bozorgnia NGA Ground Motion Relations for the Geometric Mean Horizontal Component of Peak and Spectral Ground Motion Parameters , 2007 .

[4]  Athanassios Ganas,et al.  Predictive model of Arias intensity and Newmark displacement for regional scale evaluation of earthquake-induced landslide hazard in Greece , 2014 .

[5]  Yu-Chun Chien,et al.  A general model for predicting the earthquake-induced displacements of shallow and deep slope failures , 2016 .

[6]  B. Leshchinsky.  Nested Newmark model to calculate the post-earthquake profile of slopes , 2018 .

[7]  Qiujing Pan,et al.  An efficient reliability method combining adaptive Support Vector Machine and Monte Carlo Simulation , 2017 .

[8]  Jun Xu,et al.  A cubature collocation based sparse polynomial chaos expansion for efficient structural reliability analysis , 2018, Structural Safety.

[9]  Bruno Sudret,et al.  Global sensitivity analysis using polynomial chaos expansions , 2008, Reliab. Eng. Syst. Saf..

[10]  M. Lo,et al.  Probabilistic Analyses of Slopes and Footings with Spatially Variable Soils Considering Cross-Correlation and Conditioned Random Field , 2017 .

[11]  L. Peyras,et al.  Reliability analysis of embankment dam sliding stability using the sparse polynomial chaos expansion , 2018, Engineering Structures.

[12]  A. Kiureghian,et al.  A PROBABILISTIC METHODOLOGY FOR ASSESSING SEISMIC SLOPE DISPLACEMENTS , 2002 .

[13]  Armen Der Kiureghian,et al.  A stochastic ground motion model with separable temporal and spectral nonstationarities , 2008 .

[14]  Changbing Qin,et al.  Kinematic analysis of seismic slope stability with a discretisation technique and pseudo-dynamic approach: a new perspective , 2017, Géotechnique.

[15]  Sanaz Rezaeian,et al.  Stochastic Modeling and Simulation of Ground Motions for Performance-Based Earthquake Engineering , 2010 .

[16]  Anthony T. C. Goh,et al.  Multivariate adaptive regression splines for analysis of geotechnical engineering systems , 2013 .

[17]  C. Lee,et al.  Empirical estimation of the Newmark displacement from the Arias intensity and critical acceleration , 2011 .

[18]  Randall W. Jibson,et al.  Analysis of the seismic origin of landslides: Examples from the New Madrid seismic zone , 1993 .

[19]  E. Harp,et al.  A method for producing digital probabilistic seismic landslide hazard maps , 2000 .

[20]  Liang Li,et al.  Reliability back analysis of shear strength parameters of landslide with three-dimensional upper bound limit analysis theory , 2016, Landslides.

[21]  Jin Man Kim,et al.  Probabilistic evaluation of seismically induced permanent deformation of slopes , 2013 .

[22]  Gang Wang,et al.  A one-step Newmark displacement model for probabilistic seismic slope displacement hazard analysis , 2016 .

[23]  R. Jibson,et al.  Maps Showing Seismic Landslide Hazards in Anchorage, Alaska , 2009 .

[24]  B. Sudret,et al.  An adaptive algorithm to build up sparse polynomial chaos expansions for stochastic finite element analysis , 2010 .

[25]  Y. F. Leung,et al.  Reliability assessment of slopes considering sampling influence and spatial variability by sobol' sensitivity index , 2018 .

[26]  Randall W. Jibson,et al.  Methods for assessing the stability of slopes during earthquakes—A retrospective , 2011 .

[27]  Robert V. Whitman,et al.  Earthquake Induced Displacements of Sliding Blocks , 1986 .

[28]  Radoslaw L. Michalowski,et al.  Stability Charts for 3D Failures of Steep Slopes Subjected to Seismic Excitation , 2011 .

[29]  F. Huang,et al.  Limit Analysis for the Face Stability of a Shallow-Shield Tunnel Based on a Variational Approach to the Blow-Out Failure Mode , 2018, International Journal of Geomechanics.

[30]  Manchao He,et al.  Monitoring prediction of a rockslide in an open-pit mine and numerical analysis using a material instability criterion , 2018, Bulletin of Engineering Geology and the Environment.

[31]  K Keefer David,et al.  Predicting earthquake-induced landslides, with emphasis on arid and semi-arid environments , 1989 .

[32]  D. Dias,et al.  Three-Dimensional Stability of a Slope Subjected to Seepage Forces , 2017 .

[33]  K. Campbell,et al.  NGA Ground Motion Model for the Geometric Mean Horizontal Component of PGA, PGV, PGD and 5% Damped Linear Elastic Response Spectra for Periods Ranging from 0.01 to 10 s , 2008 .

[34]  J. K. Howard,et al.  Probabilistic Use of Arias Intensity in Geotechnical Earthquake Engineering , 2008 .

[35]  Radoslaw L. Michalowski,et al.  Three-Dimensional Stability of Slopes and Excavations , 2009 .

[36]  Edwin L. Harp,et al.  Map showing slope stability during earthquakes in San Mateo County, California , 1985 .

[37]  George Eastman House,et al.  Sparse Bayesian Learning and the Relevan e Ve tor Ma hine , 2001 .

[38]  Dian-Qing Li,et al.  Stochastic response surface method for reliability analysis of rock slopes involving correlated non-normal variables , 2011 .

[39]  N. Newmark.  Effects of Earthquakes on Dams and Embankments , 1965 .

[40]  Q. Pan,et al.  Three dimensional seismic and static stability of rock slopes , 2015 .

[41]  Radoslaw L. Michalowski,et al.  Three-dimensional displacement analysis of slopes subjected to seismic loads , 2013 .

[42]  Wei-Xin Ren,et al.  An efficient metamodeling approach for uncertainty quantification of complex systems with arbitrary parameter probability distributions , 2017 .

[43]  Qiujing Pan,et al.  A sequential sparse polynomial chaos expansion using Bayesian regression for geotechnical reliability estimations , 2020, International Journal for Numerical and Analytical Methods in Geomechanics.

[44]  Yi He,et al.  Three-dimensional limit analysis of seismic displacement of slope reinforced with piles , 2015 .

[45]  D. Dias,et al.  Probabilistic Analysis of Pressurized Tunnels against Face Stability Using Collocation-Based Stochastic Response Surface Method , 2011 .