Reliability-Based Stability Analysis of a Baltic Cliff by the Combined Response Surface Method
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ORIGINAL PAPER
Reliability-Based Stability Analysis of a Baltic Cliff by the Combined Response Surface Method Karol Winkelmann Jarosław Go´rski
. Lesław Zabuski
. Jarosław Przewło´cki
.
Received: 19 June 2019 / Accepted: 21 May 2020 The Author(s) 2020
Abstract The study presents a probabilistic stability analysis of a Baltic cliff in Jastrze˛bia Go´ra, Poland. Progressive slope erosion is a threat to adjacent buildings, so safety assessment of the slope is essential. The cliff shows a compound, multi-layered geological structure, which makes the analysis of its reliability a complex multivariate problem. A simple, straightforward computational procedure was proposed, incorporating the Response Surface Method (RSM) linked with the standard Monte Carlo (MC) simulation method and the Point Estimate Method (PEM). PEM samples make it possible to analyse the sensitivity of the cliff’s stability to variation in subsoil parameters and to reduce the number of random variables of the problem. The proposed methods were tested in two cases: a high failure probability (undrained state) and a moderate failure probability (drained case). The so-called combined Response Surface Method (CRSM) proposed here may be K. Winkelmann (&) J. Go´rski Faculty of Civil and Environmental Engineering, Gdan´sk University of Technology, Narutowicza 11/12, 80-233 Gdan´sk, Poland e-mail: [email protected] L. Zabuski Institute of Hydro-Engineering, Polish Academy of Sciences, Kos´cierska 7, 80-328 Gdan´sk, Poland J. Przewło´cki Faculty of Architecture, Gdan´sk University of Technology, Narutowicza 11/12, 80-233 Gdan´sk, Poland
successfully applied in geotechnical computations characterized by dispersion and uncertainty of soil data as well as a relatively high damage probability. Keywords Probabilistic sensitivity Reliability Cliff stability Monte Carlo method Response Surface Method Point Estimate Method
1 Introduction Since the interest in reliability-based slope stability analysis began over 50 years ago, different methods have been proposed to assess slope reliability, including the correction factor methods, First-Order SecondMoment (FOSM), Second-Order Second-Moment (SOSM), First-Order Reliability Method (FORM), Second-Order Reliability Method (SORM) and Monte Carlo (MC) method (Wu and Kraft 1970; Cornell 1971; Alonso 1976; Tang et al. 1976; Vanmarcke 1977; Low et al. 1997; Chowdhury and Grivas 1982; Chowdhury et al. 1987; Tobutt 1982; Christian et al. 1994; El-Ramly et al. 2002; Babu and Mukesh 2004). A milestone in probabilistic analysis of slopes was the application of the Finite Element Method (FEM) in geotechnical problems. Various FEM-based probabilistic methods have been proposed. Developments in both hardware and software have made the MC simulation dominant. The FEM-based MC application
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Geotech Geol Eng
is usually called the Random Finite Element Method (RFEM), which fully incorporate spatial correlation and averaging (Griffiths and Fenton 2004). This method
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