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Technical Committee 205 /
Comité technique 205
resistance from clients and colleagues when attempting to
incorporate into their design uncertainty that others may wish to
ignore. It can be argued that codes containing partial factors or
load and resistance factors determined carefully and
scientifically would be of assistance in minimizing this
problem.
Limit states design codes have not been and could not be
based primarily on reliability analysis and research, largely
because the research was not available. Many challenges
remain, chiefly among them a proper assessment of soil
variability both for code design and for specific projects.
Although it is a stated goal of modern limit states codes to use
acceptable probability of failure as a design reference and a
basis to develop values of materials or resistance factors, the
present reality is that codes have been largely developed based
on calibrations, as noted by Länsivaara and Poutanen (2013),
and code development committee deliberations. As results of
better, more specific research become available, code designers
may be able to take advantage of these results to modify values
and recommendations in future editions of design codes.
Although this paper focuses on safety and serviceability as
addressed by codes and design calculations, not every risk can
be quantified; some are best avoided. For example, blunders can
be avoided by having layers of checks on procedures and
calculations put in place. Other risks may be avoided by taking
a broad view of the project, looking for things that can go
wrong and adapting designs and construction procedures based
on this assessment. Robert (2013) discusses this type of project-
management approach to risk management.
The next sections examine specific aspects of the design of
slopes, foundations and retaining structures using modern limit
states codes.
4 STABILITY OF SLOPES
4.1
General Remarks
Stability limit states, also known as ultimate limit states, are
associated with dangerous outcomes. In mechanics terms, they
would often be associated with collapse. A loss of slope
stability would be associated with large slope movements after
driving actions overcame available resistance. This is the
primary design check for slopes, although more contained slope
movement that would not be analyzed in the same manner are
also sometimes critical.
Loads are, for the most widely used slope stability analysis
methods, expressed through driving moments. The driving
moment due to dead loads (self-weight of a potential sliding
mass or permanent external loads acting on the boundary of the
sliding mass) may be denoted by M
d,DL
. The driving moment
due to live loads (nonpermanent loads on the crest of the slope,
such as vehicular loads) may be denoted by M
d,LL
. Resistances
are expressed through a resisting moment M
r
. In terms of
driving and resisting moments, inequality (1) becomes:
rn
DL d,DL
LL d,LL
n
(RF)M LF M LF M
n
(5)
Studies on probabilistic stability analysis of slopes and
embankments started in the early 1970s and have continued
(e.g., Cornell 1971, Tang et al. 1976, Christian et al. 1992). In
early slope reliability analysis studies, the first-order second-
moment method was popular for the assessment of probability
of slope failure. More recent studies have made use of the first-
order reliability method (FORM) and Monte Carlo simulations
(MCSs) to assess the probability of slope failure (Christian et al.
1994, Tobutt 1982).
In probabilistic slope stability analysis, it is essential to
consider the spatial variability of the soil in the slope. This is
the most significant shortcoming of original studies on this
topic. If a soil slope is assumed to remain homogenous when
soil properties are varied (say, using Monte Carlo simulations)
in an analytical study, the reality that these properties in fact
vary with some degree of independence across the slope is
completely ignored, and probabilities of failure calculated in
this manner will not be accurate. Salgado and Kim (2013) have
used an advanced FORM method, coupled with random field
modeling of the slope, to develop resistance factors for use in
slope stability as a function of soil spatial variability. Although
the results have been consolidated in terms of resistance factors,
it would be possible to develop partial material factors from
their reliability analyses. The fact that model uncertainty in
slope stability analysis is small to negligible (Kim et al. 1999,
Kim et al. 1992, Yu et al. 1998) makes it relatively easy to
obtain Eurocode-like material factors from reliability analyses
such as those performed by Salgado and Kim (2013).
As pointed out by Länsivaara and Poutanen (2013), use of
(5) or another inequality like it requires the slope stability
software to provide the values of moments from permanent,
temporary and other loads separately. Although not yet
common, this will not be an impediment for long (STABL WV,
for example, is a slope stability software that already provides
this level of information detail).
A key decision in performing reliability-based design or
developing resistance or material factors is what the acceptable
probability of failure
p
f
is. Christian (2004) characterized risk as
a function of number of fatalities, referring to various efforts by
regulators and others. Most slopes would be well designed with
p
f
= 10
-3
, but lower values of
p
f
might be needed for structures
whose failure would lead to large economic or human loss.
4.2
Papers
Länsivaara and Poutanen (2013) review the prescriptions of the
Eurocode (EN-1997) regarding slope stability. The Eurocode
prescribes three different ways of checking stability: design
approaches DA1, DA2 or DA3.
According to these authors, DA1 with combination 2 and
DA3 are most commonly used for slope stability analysis. There
are also three different reliability classes (RC1, RC2 and RC3),
which allow the accounting for consequences of attainment of a
limit state, into which a slope would be fit before analyses are
done. Another way allowed by the code to account for
consequences of attainment of a limit state is to increase
material factors for cases with more consequential failures.
As seen earlier, material strength is divided by a material
factor, and this is supposed to account for uncertainties in shear
strength and any analysis uncertainty. The material factor for
effective stress analyses for soils modeled as Mohr-Coulomb
materials is 1.25; for a total stress analysis of a slope with soil
modeled as a Tresca material, it is 1.4. Self-weight is left
unfactored but live (temporary) loads (actions) on the slope are
factored by 1.3. Länsivaara and Potanen (2013) suggest that
there is an "overestimation of safety" implied in typical factors
of safety used in total stress analysis of the stability of clay
slopes. Salgado and Kim (2013) also observed this possibility in
the results of reliability analysis of slopes modeled using
random fields.
Lechwicsz and Wrzesiński (2013) report on field-scale
staged construction of an embankment on top of an organic soil
deposit, the last stage built up until failure occurred. The shear
strength of the soil profile on which the embankment was built
was characterized using results of the vane shear test corrected
according to the Swedish Geotechnical Institute method
(Larsson et al. 1984) with correction factors determined based
on triaxial compression (TC), triaxial extension (TE) and direct
simple shear (DSS) testing of the materials in the laboratory.
The shear strength data determined in this manner allowed
estimation of the probability distributions of the undrained shear
strength. Their analysis of the results of these field experiments
focused on testing the Eurocode 7 DA1, DA2 and DA3 design
approaches.
