1802
Proceedings of the 18
th
International Conference on Soil Mechanics and Geotechnical Engineering, Paris 2013
The embankment was constructed in three stages on organic
subsoil from 1983 to 1987. The structure was then brought to
failure by increasing the height of the fill (Wolski et al. 1988,
1989). The organic soil at the site, present as two separate layers
(a 3.1-m-thick amorphous peat layer and a 4.7-m-thick
calcareous-organic soil layer) is underlain by a sand layer. The
water table is located near the ground surface, but the sand layer
was subjected to artesian conditions, with the piezometric level
as much as 1.5 meters above the ground surface. Effective
stresses
in situ
were in the single digits (in units of kPa). The
OCR of the organic soils was estimated to decrease from 5 near
the surface to 2 at depth. The undrained shear strength was
determined both before and after construction of the
embankment. After consolidation, the strength was observed to
increase below the embankment, with larger increases near the
center. Interestingly, there seems to have been a slight
reduction, on average, of the coefficients of variation of the
shear strength from the values before embankment construction
(all except one greater than 0.11 and as high as 0.19) after the
embankment was constructed and consolidation completed;
originally, these values were as low as 0.03, with several
observations below 0.1. Consolidation may have evened out
some spatial variability initially present.
The stability analysis performed for the third stage and the
failure test assumed the organic subsoil to be divided into three
different shear zones: A – below the embankment crest, B –
below the embankment slope and C – to the side of the
embankment. In these analyses, which relied on the Bishop
Simplified Method, various approaches to account for
uncertainty in shear strength were considered: direct use of
mean values, use of characteristic values determined as the
mean less 0.5 or one times the standard deviation, and
application or not of a partial factor
m
= 1.25 to the mean and
characteristic values of shear strength. This value is not the 1.4
prescribed by the Eurocode for Tresca materials, but the authors
did not elaborate.
Based on comparisons between these different analyses and
the results of the test embankment, the authors recommended
use of design approach DA1 with combination 1 and use of
characteristic values of undrained shear strength defined as a
conservative mean (mean less a fraction of the standard
deviation) for slope stability analysis under similar conditions.
Design Approaches DA1 with combination 2 and DA3 were
deemed excessively conservative.
One of the most challenging aspects of probabilistic stability
analyses of slopes is that the spatial nature of the variability of
slopes must be taken into account in order to produce
reasonable results, as noted earlier. Lechwicsz and Wrzesiński
(2013) attempt to assess, using judgment, the degree of
conservativeness of different approaches to determination of
characteristic strengths and partial factors to use in design, but
that appears to be a difficult task to complete until more
rigorous analyses that fully consider spatial variability of the
slope are properly done and scrutinized. The test to failure of
the embankment slope that they describe is precisely the type of
field result needed to combine with the rigorous reliability
analyses done today to validate theoretical work. More
information on spatial variability, which is difficult to assess,
particularly in the horizontal direction, is certainly needed in
field tests of this type.
5 FOUNDATIONS
5.1
General Remarks
Foundation engineering problems are interaction problems: a
foundation element (e.g., a footing or a pile) or a collection of
foundation elements interact with the soil around them through
the interface between the elements and the soil. The presence of
this interface can be exploited in probabilistic analyses of
foundation limit states: the variability, spatial in nature, of soil
properties result in contact stresses at this interface that are a
function of the response of the entire soil mass. It is customary
to observe (directly measure or deduce from instrumentation
using load cells and strain gauges) the values of these boundary
loads on foundation elements, and the variability of these
stresses can be used, combined with specific methods of
analysis, to perform reliability analyses. This approach, as
already discussed, is not viable for slope stability analysis.
Basu and Salgado (2012), for example, performed such an
analysis for drilled shafts in sand. They placed the analyses of
Loukidis and Salgado (2008) and Lee and Salgado (1999) on a
probabilistic basis and used Monte Carlo simulations to
determine the resistance factors corresponding to probability of
failure equal to 10
-3
and 10
-4
. Rigorous reliability analysis
combined with realistic and appropriate soil models, with a
rigorous method of analysis of a particular boundary-value
problem, and with careful accounting of variability of every
random variable entering the calculation produces excellent and
transparent results. The body of work of this type is still limited,
but it is likely to produce results that will be useful to code
designers.
Differently from slopes, which are most often checked for
stability, deflection-based limit states, whether potentially
leading to ultimate or serviceability limit states, are more
frequent for foundations than a classical foundation plunge limit
state. In more complex structures, such as piled rafts, analyses
are more involved, often requiring numerical solutions, which
makes a reliability analysis more challenging and makes it more
difficult to consider spatial variability indirectly.
One of the hardest decisions for engineers to make in the
context of reliability-based design is on the acceptable
probability of failure. In every geotechnical design problem, the
answer can be different. For example, in connection with pile
foundations used in traditional solutions (not in a piled raft), a
possible way to think of probability of failure
p
f
would be to
pose a question such as "how often would an engineer be
willing to deal with cracking of the superstructure (an indicator
of a possible ULS) to keep initial foundations cost low?" A
possible answer would be that no more often than would be the
case if one pile in ten thousand settled too much, which could
then lead to an acceptable probability of failure of 10
-4
.
5.2
Papers
Loehr et al (2013) discussed work that they have done for the
Missouri Department of Transportation attempting to develop
state-specific resistance factors for Missouri. The guidance
offered by AASHTO on which resistance factors to use is very
general, prompting this type of effort by individual states in the
United States.
The work of Loehr et al (2013) aimed to develop
prescriptions for drilled shaft design that would not be overly
constraining. The authors worked with epistemic probabilities,
which they however do not provide details on. One of the main
advantages of LRFD, in these authors' view, is that LRFD
enables placing a value on the marginal boring, CPT log or
laboratory test, which in turn allows advocacy for a more
complete site characterization. The authors illustrate this point
with an example of drilled shaft design with site
characterization done with different levels of detail. This
potential use of LRFD, of facilitating the economic evaluation
of site characterization and other decisions affecting design, has
also been remarked on by other authors (e.g., Foye and Salgado
2005, Foye et al. 2011a and b).
Katzenbach et al. (2013) review a relatively new soil
improvement method that resembles a piled raft. In this method,
(usually unreinforced) concrete columns are installed beneath a
raft (mat). The mat and columns do not actually touch, being
separated by a layer of stone or gravel (Figure 2). The concrete
columns, in effect piles, have diameter ranging from 0.25 to
0.80m.
