Kriging based reliability and sensitivity analysis – Application to the stability of an earth dam

Abstract This article presents a Kriging-based probabilistic analysis of an earth dam. The dam failure probability with respect to the sliding stability is investigated by considering the influence of various factors: the filter drain length, the full reservoir water level location and the correlation between the input parameters. A procedure which combines the Kriging surrogate model with the Monte Carlo Simulation (MCS), the Global Sensitivity Analysis (GSA) and the First Order Reliability Method (FORM) is proposed. It aims at benefiting from the computational efficiency of a Kriging surrogate model to provide as much as possible results such as the failure probability, the sensitivity index of each input parameter and the design point. Having more useful results in a probabilistic analysis can help engineers to make more rational decisions. The proposed procedure is compared with the direct MCS, GSA and FORM, and shows a good accuracy and efficiency. In addition, two commonly used slope stability analysis methods (strength reduction method (SRM) and limit equilibrium method (LEM)) are compared in a probabilistic framework. The comparison shows that the two methods can lead to similar estimates of the failure probability for most cases, except when the pore water pressure is important for the determination of the critical slip surface. This kind of results can help engineers to judge when LEM is accurate enough and when SRM is required for a probabilistic analysis.

[1]  Stefano Marelli,et al.  Rare Event Estimation Using Polynomial-Chaos Kriging , 2017 .

[2]  A. M. Hasofer,et al.  Exact and Invariant Second-Moment Code Format , 1974 .

[3]  S. Marelli,et al.  An active-learning algorithm that combines sparse polynomial chaos expansions and bootstrap for structural reliability analysis , 2017, Structural Safety.

[4]  Qiujing Pan,et al.  Probabilistic evaluation of tunnel face stability in spatially random soils using sparse polynomial chaos expansion with global sensitivity analysis , 2017 .

[5]  Sung-Eun Cho,et al.  Effects of spatial variability of soil properties on slope stability , 2007 .

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

[7]  Dirk P. Kroese,et al.  Simulation and the Monte Carlo method , 1981, Wiley series in probability and mathematical statistics.

[8]  R. Rackwitz,et al.  Structural reliability under combined random load sequences , 1978 .

[9]  Thomas J. Santner,et al.  The Design and Analysis of Computer Experiments , 2003, Springer Series in Statistics.

[10]  Colin J F P Jones,et al.  Evaluating the effects of the magnitude and amplification of pseudo-static acceleration on reinforced soil slopes and walls using the limit equilibrium Horizontal Slices Method , 2008 .

[11]  L. Peyras,et al.  A comparative study of different reliability methods for high dimensional stochastic problems related to earth dam stability analyses , 2019, Engineering Structures.

[12]  Jon C. Helton,et al.  Extension of Latin hypercube samples with correlated variables , 2008, Reliab. Eng. Syst. Saf..

[13]  C. F. Lee,et al.  A concise algorithm for computing the factor of safety using the Morgenstern-Price method , 2005 .

[14]  Hongping Zhu,et al.  Assessing small failure probabilities by AK–SS: An active learning method combining Kriging and Subset Simulation , 2016 .

[15]  Nicolas Gayton,et al.  AK-MCS: An active learning reliability method combining Kriging and Monte Carlo Simulation , 2011 .

[16]  Rafael Baker,et al.  Stability charts for pseudo-static slope stability analysis , 2006 .

[17]  Yu Wang,et al.  Quantifying the cross-correlation between effective cohesion and friction angle of soil from limited site-specific data , 2016 .

[18]  Y. M. Cheng,et al.  Two-dimensional slope stability analysis by limit equilibrium and strength reduction methods , 2007 .

[19]  Peter Lumb,et al.  Safety factors and the probability distribution of soil strength , 1970 .

[20]  Abdul-Hamid Soubra,et al.  Probabilistic Analysis of Circular Tunnels in Homogeneous Soil Using Response Surface Methodology , 2009 .

[21]  D. Dias,et al.  Probabilistic stability analysis of an embankment dam considering soil spatial variability , 2019, Computers and Geotechnics.

[22]  Timothy D. Stark,et al.  Unsaturated and Transient Seepage Analysis of San Luis Dam , 2017 .

[23]  J. Bray,et al.  Pseudostatic Coefficient for Use in Simplified Seismic Slope Stability Evaluation , 2009 .

[24]  Jun Ma,et al.  Identification of representative slip surfaces for reliability analysis of soil slopes based on shear strength reduction , 2017 .

[25]  D. Krige.  A statistical approach to some basic mine valuation problems on the Witwatersrand, by D.G. Krige, published in the Journal, December 1951 : introduction by the author , 1951 .

[26]  W. Tang,et al.  Efficient Spreadsheet Algorithm for First-Order Reliability Method , 2007 .

[27]  Richard J. Bathurst,et al.  Influence of cross correlation between soil parameters on probability of failure of simple cohesive and c-ϕ slopes , 2016 .

[28]  D. Dias,et al.  Probabilistic analysis of ultimate seismic bearing capacity of strip foundations , 2018, Journal of Rock Mechanics and Geotechnical Engineering.

[29]  Claudio Carvajal,et al.  Probabilistic stability analysis of an earth dam by Stochastic Finite Element Method based on field data , 2018, Computers and Geotechnics.

[30]  Paola Annoni,et al.  Estimation of global sensitivity indices for models with dependent variables , 2012, Comput. Phys. Commun..

[31]  N. Morgenstern,et al.  The analysis of the stability of general slip surfaces , 1965 .

[32]  Carl E. Rasmussen,et al.  Gaussian processes for machine learning , 2005, Adaptive computation and machine learning.

[33]  João Cardoso,et al.  Review and application of Artificial Neural Networks models in reliability analysis of steel structures , 2015 .

[34]  Bertrand Iooss,et al.  Title: Open TURNS: An industrial software for uncertainty quantification in simulation , 2015, 1501.05242.

[35]  Daniel Dias,et al.  Reliability analysis of shallow tunnels using the response surface methodology , 2017 .

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

[37]  Andrew C. Heath,et al.  Simple genetic algorithm search for critical non-circular failure surface in slope stability analysis , 2005 .

[38]  D. Dias,et al.  Reliability analysis of a mechanically stabilized earth wall using the surface response methodology optimized by a genetic algorithm , 2018 .

[39]  Abdul-Hamid Soubra,et al.  Probabilistic analysis of an offshore monopile foundation taking into account the soil spatial variability , 2019, Computers and Geotechnics.

[40]  Stefano Marelli,et al.  UQLab: a framework for uncertainty quantification in MATLAB , 2014 .

[41]  D. Dias,et al.  Probabilistic analysis of piled earth platform under concrete floor slab , 2017 .

[42]  Y. Cheng,et al.  Soil nailed slope by strength reduction and limit equilibrium methods , 2010 .

[43]  Yung-ming Cheng,et al.  STABILITY ANALYSIS OF SLOPE WITH WATER FLOW BY STRENGTH REDUCTION METHOD , 2010 .

[44]  Dian-Qing Li,et al.  Slope reliability analysis considering spatially variable shear strength parameters using a non-intrusive stochastic finite element method , 2014 .

[45]  D. V. Griffiths,et al.  Probabilistic Settlement Analysis by Stochastic and Random Finite-Element Methods , 2009 .

[46]  James R. Martin,et al.  Model selection in geological and geotechnical engineering in the face of uncertainty - Does a complex model always outperform a simple model? , 2018, Engineering Geology.

[47]  Xin Li,et al.  A Kriging-based hybrid optimization algorithm for slope reliability analysis , 2012 .

[48]  K. Phoon,et al.  Characterization of Geotechnical Variability , 1999 .

[49]  Zeyu Wang,et al.  ESC: an efficient error-based stopping criterion for kriging-based reliability analysis methods , 2018, Structural and Multidisciplinary Optimization.