1799
General report for TC 205
Safety and serviceability in geotechnical design: a reliability-based perspective
Rapport général du TC 205
Sécurité et maintenance en conception géotechnique : une perspective fiabiliste –
Salgado R.
School of Civil Engineering, Purdue University – West Lafayette, United States
ABSTRACT: A transition has been underway in geotechnical engineering from design based on analyses that treat problems as if
every pertinent variable were deterministic only to recognize at the end that uncertainties exist by using a factor of safety to design
based on probability concepts. In probabilistic design, key problem variables are treated, at least implicitly, as random variables, and
probabilities of undesired outcomes (defined through the concept of limit states) are kept below certain maximum acceptable values.
The ways to perform these analyses are many, depending on choices as to, for example, which variables to treat as random and which
method of analysis (e.g., the limit equilibrium method, the finite element method) to use to solve the underlying boundary-value
problem. Different approaches have been followed in North American and Europe, the two regions where use of probabilistic, limit
states-based design is more common. Many unresolved issues remain. This paper highlights some of these issues in the context of
papers submitted on the topic to the 18th ICSMGE.
RÉSUMÉ: Une transition s’est déroulée en géotechnique depuis une conception basée sur des analyses qui traitent les problèmes
comme si chaque variable pertinente était déterministe vers la prise en compte des incertitudes par l’utilisation de facteurs de sécurité
dans le cadre d’une conception basée sur des concepts probabilistes. Dans ce cadre probabiliste, les variables clés du problème sont
traitées, au moins implicitement, comme des variables aléatoires et les probabilités des résultats attendus (définis par le concept d’état
limite) sont maintenues en-dessous certaines valeurs maximales acceptables. Il y a de nombreux moyens de réaliser ces analyses,
selon le choix, par exemple, des variables à traiter comme aléatoires et des méthodes d’analyse utilisée pour régler le problème aux
limites considéré (e.g., la méthode des équilibres limites ou les éléments finis). Différentes approches ont été suivies en Amérique du
Nord et en Europe, les deux régions où l’utilisation des méthodes probabilistes aux états-limites sont les plus répandues. De
nombreuses questions restent posées. Cet article met en évidence ces questions dans le contexte des articles soumis au 18
ème
CIMSG
sur ce thème.
KEYWORDS: stability, serviceability, geotechnical design, Eurocode 7, load factors, resistance factors, partial factors, characteristic
and design values.
1 BACKGROUND
Development of the Eurocode started a large-scale effort to
address geotechnical engineering problems in a more systematic
manner from the point of view of the uncertainties present in
these problems. One major theme of this effort has been to
allocate uncertainties more precisely, e.g., between loads and
resistances or, in the case of the Eurocode, between loads and
the quantities that enable calculation of soil resistances. Another
important theme has been to transition away from
ad hoc
measures of safety to probabilities of failure, with failure
defined rather specifically. This emphasis on probability of
failure has started an important debate concerning what
probabilities of failure are acceptable given project importance
and consequences of failure.
In Europe, the path followed was to account for uncertainties
by dividing shear strengths or, more generally, soil properties
controlling the specific resistance being calculated by material
factors typically greater than one. Actions (defined in the code
as loads or applied displacements) would be increased by
factors also greater than one. This general approach is usually
referred to as a partial factors approach. In North America, a
different philosophy developed. In the still-evolving North
American practice, an approach called Load and Resistance
Factor Design (LRFD) is used. The main difference with respect
to European practice is that design is based on the following
inequality:
n
i
(RF)R (LF )Q
where R
n
is the nominal resistance, RF is the corresponding
resistance factor, Q
i,n
are nominal loads (with dead load, live
load, etc., identified each by a different value of i), and LF
i
are
the corresponding load factors.
Both the Eurocode and its North American counterparts are
based on the concept of Limit-States Design (LSD). Limit states
exist on the boundary between acceptable and unacceptable
states. They offer a solid conceptual basis for the definition of
failure, which then becomes the achievement of an undesirable
state as defined by the limit states. The probability of failure
then becomes nothing more than the probability of achievement
of an undesirable state. Figure 1 shows a hypothetical design
problem involving two variables, resistance and load, both of
which are random variables. The line in the figure separates
acceptable pairings of Q and R (Q < R) from those that would
lead to failure. The line is the locus of limit states, and states
above the line are failure states.
The advantage of use of inequality (1) over the European
approach is that the resistance factor reflects all of the
uncertainties involved in calculating resistance, including
uncertainties in both soil property determination and the
analysis used to calculate the resistance. This advantage is likely
more of a conceptual nature, for it is possible to account for
analysis uncertainty also in the European approach, but that
must be done through the material factors dividing the strength
parameters, which cease to be then pure factors on material
properties.
i,n
(1)
