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Reliability analysis of empirical predictive models for earthquake-induced sliding
displacements of slopes
Analyse de fiabilité des modèles empiriques de prédiction des déplacements sismiques de pentes
Fotopoulou S., Pitilakis K.
Department of Civil Engineering, Aristotle University, Thessaloniki, Greece
ABSTRACT: The goal of this study is twofold: (i) to identify the influence of the earthquake characteristics on the magnitude of the
residual co-seismic slope displacements of a typical slope using different predictive analytical models and (ii) to compare the results
of the analytical models with an exact fully dynamic non-linear analysis. In particular, three analytical models were used to predict the
permanent slope displacements: the classical Newmark rigid block model, the decoupled Rathje and Antonakos model and the
coupled Bray and Travasarou sliding block model. In addition, 2 dimensional fully non-linear numerical analyses were performed
using the code FLAC for idealized sand and clayey step-like slopes considering different real acceleration time histories as input
motion. All three models predict displacements that are generally in good agreement with the numerical results for the sand slope
case. On the contrary, for the clay more flexible slope the correlation is not so good. However it is shown that the some crucial
parameters, like the frequency content of the input motion, are not always appropriately captured in all analytical models.
RÉSUMÉ : L'objectif de cette étude est (i) d'identifier l'influence des caractéristiques du tremblement de terre sur l'ampleur des
déplacements co-sismiques résiduels d’une pente, en utilisant différents modèles analytiques et (ii) de comparer les déplacments
analytiques avec une analyse numérique plus élaborée. En particulier, trois modèles différents étaient utilisés pour estimer les
déplacements permanents : le modèle de base de bloc rigide de Newmark, le modèle découplé de Rathje et Antonakos et le modèle
couplé de Bray et Travasarou. L’analyse numérique a été effectuée sur la même pente avec le code FLAC et pour les mêmes
matériaux de sol (sable et argile). Dans le cas de pente sableuse les déplacements calculés par les trois modèles analytiques sont
généralement en relativement bon accord avec les résultats numériques. La comparaison est moins bonne pour la pente argileuse.
Néanmoins il a été démontré que tous les modèles analytiques ne tiennent pas en compte proprement quelques paramètres importants
comme la fréquence du mouvement fort des sols.
KEYWORDS: co-seismic slope displacements, Newmark-type displacement models, non-linear dynamic numerical analysis.
1 INTRODUCTION
It is common practice in geotechnical earthquake engineering to
assess the expected seismic performance of slopes and earth
structures by estimating the potential for seismically induced
permanent displacements using one of the available
displacement-based analytical procedures. Considering that
(total and/or differential) displacements ultimately govern the
serviceability level of a slope after an earthquake, the use of
such approaches is strongly recommended. Typically, two
different approaches of increased complexity are proposed to
assess permanent ground displacements in case of seismically
triggered slides: Newmark-type displacement methods and
advanced stress- strain dynamic methods.
The sliding-block analog proposed by Newmark (1965) still
provides the conceptual basis on which all other displacement-
based methods have been developed aiming to yield more
accurate estimates of slope displacement. This has been
accomplished by proposing more efficient ground motion
intensity measures (e.g. Saygili and Rathje, 2008), improving
the modeling of dynamic resistance of the slope characterized
by its yield coefficient (e.g. Bray, 2007) and by analyzing the
dynamic slope response more rigorously (e.g. Bray and
Travasarou, 2007; Rathje and Antonakos, 2011). In terms of
their assumptions to analyze the dynamic slope response,
displacement based methods can be classified into three main
types: rigid block, decoupled and coupled. A short description
of the different types of Newmark-type displacement methods
as well as recommendations for the selection of the most
appropriate ones is given in Jibson (2011).
Advanced stress-deformation analyses based on continuum
(finite element, FE, finite difference, FDM) or discontinuum
formulations usually incorporating complicated constitutive
models, are becoming recently more and more attractive, as
they can provide approximate solutions to problems which
otherwise cannot be solved by conventional methods e.g. the
complex geometry including topographic and basin effects,
material anisotropy and non-linear behavior under seismic
loading, in situ stresses, pore water pressure built-up,
progressive failure of slopes due to strain localization. Several
investigators have implemented continuum FE or FD codes to
evaluate the residual ground displacements of slopes using
elastoplastic constitutive models (e.g. Chugh and Stark, 2006;
Lenti and Martino, 2012 etc.).
In this paper we study the accuracy of three different
Newmark-type based models i.e. the conventional analytical
Newmark (1965) rigid block approach, the Rathje and
Antonakos (2011) decoupled model and Bray and Travasarou
(2007) coupled model, classically used to estimate the expected
co-seismic slope displacements, with a more refined numerical
approach, considering different earthquake input motions scaled
to different PGA values and compliance of the sliding surface.
For the purpose of this comparative study we selected a typical
configuration of a 30
o
inclined sand and clayey slope.
