1800
Proceedings of the 18
th
International Conference on Soil Mechanics and Geotechnical Engineering, Paris 2013
Another important difference between Eurocode-related
efforts and development of North American LRFD is in the
process. The Eurocode started with an exclusive focus on
buildings (Simpson and Driscoll 1998) but then developed into
a code with broad application in geotechnical design. In North
America, particularly in the United States, the effort targeted
transportation infrastructure, leaving state DOTs and individual
researchers with the task of developing load and resistance
factors that made sense and could be used in a practical manner.
This has in a way been an incentive for performing research in
the subject.
Figure 1– Design problem with load and resistance being ramdom
variables (after Salgado and Kim 2013).
The topic of safety and serviceability in geotechnical
engineering, which involves design methods and approaches for
a variety of geotechnical problems based on analyses that
account for probabilities and variability in pertinent variables, is
complex and should evolve over the years with the development
of better methods of analyses and a greater understanding of
variability in geotechnical problems. The following sections
summarize current knowledge and challenges, together with the
contributions of papers submitted to the XVIII ICSMGE.
2 RELIABILITY ANALYSIS
Research on limit-states design (LSD) in its various forms
has ranged from simple calibrations of material factors (in the
Eurocode framework) or resistance factors (in the LRFD
framework) so that results would match those obtained using
traditional methods with accepted values of factors of safety to
reliability analysis performed with various levels of
sophistication. The tools to perform sophisticated reliability
analysis have evolved considerable in the last 20 years, and
most advances that will be useful to code designers in the future
are likely to result from this type of analysis.
Figure 1 shows a cloud of points representing pairings of
load Q and resistance R around the mean point (
R
,
Q
) of these
two variables. Each of these points is a simultaneous realization
of random variables R and Q. Since Q and R are more likely to
be close to their respective mean, there is a heavier
concentration of points near (
R
,
Q
); however, if the load and
resistance in a hypothetical problem deviate from their means
by sufficiently large amounts, Q may end up exceeding R,
which would, by definition, constitute failure. This cloud of
points may be obtained using Monte Carlo simulations if the
probability distributions of Q and R are known. The probability
of failure can be estimated from the ratio of the number
n
of
points above the limit state line shown in the figure to the total
number
N
of points. Mathematically:
lim
f
N
n
p
N
(2)
where
N
must be large enough for
p
f
to converge.
Also shown in Figure 1 are dispersion ellipses. A dispersion
ellipse represents the locus of the resistance-load pairings with
the same level of deviation from the mean. Note that there is
one dispersion ellipse that is tangent to the failure line at a point
known as the most likely "failure point" FP, also known as the
"design point". From the point of view of development of
material factors or resistance factors, if the probability of failure
calculated for the simulations of Figure 1 is the value that
should be targeted in design, the relationship between the design
point FP and the mean point MP yields directly the factors that
would be used in design. This is easiest to show for LRFD, in
which case the factors RF and LF shown in inequality (1) would
follow from:
LS
LS
R
Q
R RF
and LF
Q
(3)
where R
LS
and Q
LS
are the resistance and load at the design
point FP; and
R
and
Q
are the means of resistance and load.
For different reasons, code designers may set load factors
LF
i
*
that must apply to a range of design settings. If a resistance
factor is developed using reliability analysis (calculated from an
equation like (3)), this resistance factor is consistent with the
load factor calculated using the same equation. If it is to be used
with a different load factor specified in a code, it must be
adjusted. If we refer to the adjusted resistance factor as RF
*
, it
may be computed by requiring that inequality (1) apply equally
whether RF
*
and LF
i
*
or RF and LF
i
are used:
*
i
i,n
*
i
i,n
(LF )Q
RF RF
(LF)Q
(4)
3 CODE DESIGN
The main goal of modern LSD-based codes is to prevent the
occurrence of limit states or, more precisely, to guide or
prescribe designs so as to keep the probability of such
occurrence acceptably small. The concepts presented in Figure
1 apply equally to ultimate (ULS) and serviceability (SLS) limit
states.
One of the key points in connection with LRFD and with
partial factor design if model (analysis) uncertainty is included
in the factors is that factors are specific to a given analysis. It is
not possible to use resistance factors in an
ad hoc
manner or the
purpose of LRFD or partial factor design is lost. This is a
significant culture change for geotechnical engineers, for factors
of safety have traditionally been used with considerable
flexibility. This significant difference between practice as it is
evolving at present and the practice of years back has important
implications. It becomes difficult, for example, to use a method
of analysis or design for which factors have not been developed.
There are also ethical and professional conduct implications, as
touched upon by Redaelli (2013), who points out that ethics
should constrain engineers from selecting factors of safety
based on financial motivations. In geotechnical engineering,
Redaelli (2013) argues, the high level of uncertainty invites a
reliance on judgment, which in turn enables geotechnical
engineers willing to deliberately distort design outcomes for
their own interests or for the interest of their direct employer to
easily do so. Redaelli (2013) believes that honest and
scrupulous engineers in a consulting company may meet with
