Issue 50

G. Belokas, Frattura ed Integrità Strutturale, 50 (2019) 354-369; DOI: 10.3221/IGF-ESIS.50.30 354 Focused on the research activities of the Greek Society of Experimental Mechanics of Materials Probabilistic geotechnical engineering analysis based on first order reliability method Georgios Belokas University of West Attica, Greece gbelokas@uniwa.gr, https://orcid.org/0000-0003-2674-7877 A BSTRACT . Limit equilibrium engineering analysis needs the incorporation of probabilistic approaches for the determination of soil strength statistical measures for deterministic and probabilistic analyses. For the commonly used Mohr–Coulomb strength model, the uncertainty and the characteristic values of cohesion ( c ) and angle of shearing resistance ( φ ) determination is not straight- forward. This paper applies the first order reliability method ( FORM ) to estimate these values from the direct shear and the typical triaxial tests. The method is verified with test data. Furthermore, the FORM is applied to the planar failure limit equilibrium problem to determine the statistical measures of the safety margin ( SM ) and safety factor ( SF ). It is observed that the critical slip surface for the best estimate of the mean ( SM m , SF m ), for a 5% probability of exceedance ( SM p=5% , SF p=5% ) and for the characteristic value ( SM k , SF k ) do not coincide. It is interesting that the maximum probability of having a SM <0 or SF <1 does not correspond to the minimum best estimate of the SM or SF . FORM can be a very useful tool for complete probabilistic analyses. Further- more, probabilistic approaches applied to soil properties estimation can set a framework for the selection of their characteristic values for deterministic analyses. K EYWORDS . Soil strength; Geotechnical engineering; Probabilistic approaches; Reliability; Characteristic values. Citation: Belokas, G., Probabilistic geotech- nical engineering analysis based on first order reliability method, Frattura ed Integrità Strut- turale, 50 (2019) 354-369. Received: 16.02.2019 Accepted: 22.05.2019 Published: 01.10.2019 Copyright: © 2019 This is an open access article under the terms of the CC-BY 4.0, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited. I NTRODUCTION he limit equilibrium analysis for the design of geotechnical works requires the application of reliability theory principles for: a) the determination of soil properties in deterministic analyses and b) the uncertainty estimation of the safety margin ( SM ) or safety factor ( SF ) in probabilistic analyses. Modern codes of practice (e.g. Eurocode 7 – EC7) provide the alternative of both types of analysis, which may include one of the following methods: a) Monte Carlo, b) Point Estimate, and c) First Order Reliability. The application of First Order Reliability Method ( FORM ) for geo- technical engineering limit states analyses (e.g. [1,2]), a method for the estimation of error propagation, has been commonly T