Contents lists available at ScienceDirect Engineering Geology journal homepage: www.elsevier.com/locate/enggeo Probabilistic analysis and design of stabilizing piles in slope considering stratigraphic uncertainty Wenping Gong a, ⁎ , Huiming Tang a , Hui Wang b , Xiangrong Wang b , C. Hsein Juang c, ⁎ a Faculty of Engineering, China University of Geosciences, Wuhan, Hubei 430074, China b Department of Civil and Environmental Engineering and Engineering Mechanics, The University of Dayton, Dayton, OH 45469-0243, USA c Department and Civil Engineering and Graduate Institute of Applied Geology, National Central University, Taoyuan City 32001, Taiwan ARTICLE INFO Keywords: Slope Stabilizing Piles Factor of Safety Stratigraphic uncertainty Probability of failure Optimization-based design ABSTRACT The uncertainty involved in the interpreted geological model may be categorized as the stratigraphic uncertainty and the properties uncertainty. Note that although the inﬂuence of the properties uncertainty on the behavior or performance of the geotechnical system and the geotechnical design has been extensively reported in the lit- erature, the studies that address the stratigraphic uncertainty are limited. This paper presents a study regarding the inﬂuence of the stratigraphic uncertainty on the behavior of the geotechnical system and the geotechnical design. In which, the uncertainty in the stratigraphic conﬁguration is characterized using the stochastic Markov random ﬁeld-based approach with a large number of potential stratigraphic realizations. With these stratigraphic realizations as inputs, the inﬂuence of the stratigraphic uncertainty on the behavior of the geotechnical system is evaluated in a probabilistic manner; then, the design of the geotechnical system is formulated as a bi-objective optimization-based problem that considers the design safety and the cost simultaneously. To demonstrate the eﬀectiveness of the proposed probabilistic analysis and design approach, the problem of designing stabilizing piles in a slope consisting of multiple strata is studied. The parametric study is further conducted to analyze how the probabilistic analysis results are inﬂuenced by the pile parameters and how the probabilistic design results are inﬂuenced by the additional boreholes. 1. Introduction In that geomaterials are natural materials, rather than manu- factured ones, the behavior of a geotechnical system, a system that is either embedded in or founded on the geomaterials, can be greatly inﬂuenced by the site conﬁguration and thus the design of the geo- technical system is usually site-speciﬁc. Due to the inadequate knowl- edge of the deposit histories and tectonic activities, the geological model at a site, a model that characterizes the geological and geo- technical information, may not be known prior to the site investigation. Thus, the site investigation plays a vital role in geological and geo- technical practices. Among the various site investigation techniques, borehole exploration is the most commonly used approach to obtain the subsurface geological model. Due to the limited budget and the tight project schedule, however, only a limited number of boreholes can be aﬀorded in a given project. As a result, the geological and geotechnical information can only be known at sparse borehole locations, whereas, at other locations such information is not available and has to be in- terpreted based on those at borehole locations. The incomplete knowledge of the formation of the geological bodies, together with the insuﬃcient number of boreholes, can lead to the uncertainty in the interpreted geological model. It should be noted that the issues of the characterization of the uncertainty of the interpreted geological model and the inﬂuence of such uncertainty on the geotechnical design are long standing challenges to the geologists and engineers. The uncertainty of the interpreted geological model arises mainly from the following two sources, interpretation of the stratigraphic conﬁguration and that of the properties of each lithological formation or stratum (Wang et al., 2016). To cope with the uncertainty involved in the determination of the stratigraphic structures at borehole loca- tions, probabilistic approaches including Bayesian method (Cao and Wang, 2013), clustering method (Liao and Mayne, 2007), wavelet transform modulus maxima method (Ching et al., 2015) and machine learning-based methods (Wang et al., 2018a) have been developed. On the basis of the stratigraphic structures obtained at borehole locations, the stratigraphic conﬁguration at the site may be interpreted from the spatial interpolation of the boundaries between adjacent strata (Patel and McMechan, 2003; Li et al., 2015; Chen et al., 2018); and, the https://doi.org/10.1016/j.enggeo.2019.105162 Received 7 November 2018; Received in revised form 27 February 2019; Accepted 22 May 2019 ⁎ Corresponding authors. E-mail addresses: wenpinggong@cug.edu.cn (W. Gong), hsein@clemson.edu (C.H. Juang). Engineering Geology 259 (2019) 105162 Available online 24 May 2019 0013-7952/ © 2019 Elsevier B.V. All rights reserved. T