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Towards reliability-based design for geotechnical engineering
K. K. Phoon
National University of Singapore, Singapore
ABSTRACT: This paper presents an overview of the evolution in structural and geotechnical design
practice over the past half a decade or so in relation to how uncertainties are dealt with. For the general
reader who is encountering reliability-based design (RBD) for the first time, this would provide a
valuable historical perspective of our present status and important outstanding issues that remain to beresolved. The key elements of RBD are briefly discussed and the availability of statistics to provide
empirical support for the development of simplified RBD equations is highlighted. Several important
implementation issues are presented with reference to an EPRI study for reliability-based design of
transmission line structure foundations. Reliability-based design, simplified or otherwise, provides a
more consistent means of managing uncertainties, but it is by no means a perfect solution. Engineering
judgment still is indispensable in many aspects of geotechnical engineering reliability analysis merely
removes the need for guesswork on how uncertainties affect performance and is comparable to the use of
elasto-plastic theory to remove the guesswork on how loads induce stresses and deformations.
INTRODUCTION
The basis for making a geotechnical design decision is not as well studied nor subjected to the same
degree of formal scrutiny as structural design. Goble (1999) noted in an NCHRP Synthesis Report on
Geotechnical Related Development and Implementation of Load and Resistance Factor Design (LRFD)
Methods that the "education of geotechnical engineers strongly emphasizes the evaluation of soil and rock
properties" and "the design process does not receive the emphasis that it does in structural engineering
education". In fact, the first time the topic "Codes and Standards" was selected for formal discussion in a
major ISSMGE conference was in 1989 (Ovesen 1989). Examination of current practice shows that
procedures for selecting nominal soil strengths are not well-defined or followed uniformly. Some
engineers use the mean value, while others use the most conservative of the measured strengths (Whitman,
1984). Different calculation methods are preferred in different localities or even by different engineers in
the same locality (Goble 1999). The manner in which the factor of safety is incorporated in the design
equation also is highly varied (Kulhawy 1984, 1996). Green & Becker (2001) made similar observationsin a National Report on Limit State Design in Geotechnical Engineering in Canada. Golder (1966) noted
quite aptly in a discussion of the second Terzaghi Lecture by Arthur Casagrande that: "We do not know
how we make a decision."
Ironically, this view is rarely acknowledged publicly in the geotechnical engineering profession. The
predominant view ranges from "If it is not broke, why fix it" (Green & Becker 2001) to a general feeling
that conventional practice is perfectly adequate to do optimal design (Committee on Reliability Methods
1995, Kulhawy 1996). Although existing practice has undoubtedly served the profession well for many
years, this paper argues that genuine improvements are possible if our practice were to be complemented
by reliability-based design (RBD) methodologies. No one is advocating total abandonment of existing
practice for something entirely new. In fact, the reverse is probably closer to the truth - many aspects of
current design practice would still appear in new RBD codes, albeit in a modified form (Kulhawy &
Phoon 1996). It is also important to highlight that geotechnical design would be subjected to increasing
codification as a result of code harmonization across material types and national boundaries. It is also
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clear that regulatory pressure eventually would bring geotechnical design within an umbrella framework
predominantly established by structural engineers. In the United States, this process is already well
underway for highway bridge design. In reference to AASHTO LRFD Specifications (AASHTO 2002),
Withiam (2003) noted that the leverage to drive implementation was the intention to sunset (i.e. no
longer publish) the long-standing AASHTO Standard Specifications that have provided nationalrequirements for highway bridge superstructure and substructure design since the 1930s. The difficulty
of maintaining status quo was highlighted about 10 years ago in the National Research Council Report on
Reliability Methods for Risk Mitigation in Geotechnical Engineering (Committee on Reliability Methods
1995).
A fundamental change in mindset, similar to what has taken place in the structural community since
the 1970s, is needed for the profession to take the next step. It is accurate to say that this change has not
taken place in the geotechnical community in North America (Goble 1999, DiMaggio et al. 1999, Green
& Becker 2001), although significant initiatives have been launched by major agencies in recent years
such as OHBDC3 (Ministry of Transportation Ontario 1992), CAN/CSA-S472-92 (CSA 1992a), API RP
2A-LRFD (API 1993), EPRI (Phoon et al. 1995), NBCC (National Research Council of Canada 1995),
AASHTO LRFD Bridge Code (AASHTO 2002), and CHBDC (CSA 2000).Currently, the geotechnical community is mainly preoccupied with the transition from working or
allowable stress design (WSD/ASD) to Load and Resistance Factor Design (LRFD). The term "LRFD" is
used in a loose way to encompass methods that require all limit states to be checked using a specific
multiple-factor format involving load and resistance factors. This term is used most widely in the United
States and is equivalent to "Limit State Design (LSD)" in Canada. Both LRFD and LSD are
philosophically akin to the partial factors approach commonly used in Europe, although a different
multiple-factor format involving factored soil parameters is used. The emphasis in LRFD or its
equivalent in Canada and Europe is primarily on the re-distribution of the original global factor safety in
WSD into separate load and resistance factors (or soil parameter partial factors). The absence of strong
analytical calibration and verification in Eurocode 7 (CEN/TC250 1994) and OHBDC3 (Ministry of
Transportation Ontario 1992) is noted by DiMaggio et al. (1999) in an FHWA Report on "Geotechnical
Engineering Practices in Canada and Europe". Paikowsky & Stenersen (2000) also noted a similar lackof data supporting current AASHTO LRFD specifications.
There are strong practical reasons to consider geotechnical LRFD as a simplified reliability-based
design procedure, rather than an exercise in rearranging the original global factor of safety. This calls for
a willingness to accept the fundamental philosophy that: (a) absolute reliability is an unattainable goal in
the presence of uncertainty and (b) probability theory can provide a formal framework for developing
design criteria that would ensure that the probability of "failure" (used herein to refer to exceeding of any
prescribed limit state) is acceptably small. In other words, geotechnical LRFD should be derived as the
logical end-product of a philosophical shift in mindset to probabilistic design in the first instance and a
simplification of rigorous reliability-based design into a familiar look and feel design format in the
second. The need to draw a clear distinction between accepting reliability analysis as a necessary
theoretical basis for geotechnical design and downstream calibration of simplified multiple-factor designformats, with emphasis on the former, was emphasized by Phoon et al. (2003a).
The former provides a consistent method for propagation of uncertainties and a unifying framework
for risk assessment across disciplines (structural and geotechnical design) and national boundaries. Other
competing frameworks have been suggested (e.g., -method by Simpson et al. 1981, worst attainablevalue method by Bolton 1989, Taylor series method by Duncan 2000) but none has the theoretical breadth
and power to handle complex real-world problems that may require nonlinear 3-D finite element or other
numerical approaches for solution. In the development of Eurocode 7, much attention has been focused
on the geotechnical aspects of code harmonisation (Frank 2002, Ovesen 2002, Orr 2002). This clearly
takes precedence over safety aspects, but the time is perhaps ripe to decide if a theoretical platform is
necessary to rationalise risk assessment. If the platform is not reliability analysis, then what alternative is
available?
The need to derive simplified reliability-based design (RBD) equations perhaps is of practical
importance to maintain continuity with past practice, but it is not necessary and increasingly fraught with
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difficulties when sufficiently complex problems are posed. The limitations faced by simplified RBD have
no bearing on the generality of reliability theory. This is analogous to arguing that limitations in closed-
form elastic solutions are related to elasto-plastic theory. The use of finite element software on relatively
inexpensive and powerful PCs (with gigahertz processors, gigabyte of memory, and hundreds of
gigabytes - verging on terabyte - of disk) permit real world problems to be simulated on an unprecedentedrealistic setting almost routinely. Phoon et al. (2003a) presented some examples to clarify that limitations
of the implementation (say LRFD) do not carry over to the underlying reliability framework. Attention
should be focused on the more basic issue pertaining to the relevance of reliability theory in geotechnical
design.
This paper presents an overview of the evolution in structural and geotechnical design practice over
the past half a decade or so in relation to how uncertainties are dealt with. For the general reader who is
encountering reliability-based design for the first time, this would provide a valuable historical
perspective of our present status and important outstanding issues that remain to be resolved. The key
elements of RBD are briefly discussed and the availability of statistics to provide empirical support for
the development of simplified RBD equations is highlighted. Several important implementation issues
are presented with reference to an EPRI study for reliability-based design of transmission line structurefoundations (Phoon et al. 1995). Numerous examples of RBD calibration are given elsewhere (Phoon &
Kulhawy 2002a, b; Phoon et al. 2003c; Phoon & Kulhawy 2004)
HISTORICAL OVERVIEW
Structural LRFD
The classical structural reliability theory became widely known through a few influential publications
such as Freudenthal (1947) and Pugsley (1955). The fundamental philosophy is that absolute reliability is
an unattainable goal in the presence of uncertainty. Probability theory can provide a formal framework
for developing design criteria that would ensure that the probability of "failure" (used herein to refer toexceeding of any prescribed limit state) is acceptably small. While the philosophy is elegant, the theory is
mathematically intractable and numerically cumbersome. Cornell (1969) probably was the first to
introduce the concept of a reliability index for simplified probabilistic design. Only second-moment
information (mean and covariance) on uncertain parameters was needed and the computation was made
simple by adopting the Gaussian model for random variables. However, the idea still was rather radical
and could have been ignored if not for Lind (1971), who demonstrated that Cornell's reliability index
could be used to derive load and resistance factors formally. The ability to repackage probabilistic design
into a simplified multiple-factor design format with the same look and feel as existing design formats,
while retaining theoretical rigor, is an important development from a practical point of view. To the
authors' knowledge, LRFD was first implemented for steel building structures by Ravindra & Galambos
(1978) using the theoretical basis established by Cornell (1969) and Lind (1971).In the meantime, serious theoretical difficulties were encountered with Cornell's index, with the most
severe being the problem of invariance. Cornell's index was found to vary when certain simple limit
states were reformulated in a mechanically equivalent way. Although second-moment reliability-based
structural design was becoming widely accepted in the early seventies, the goal of developing simplified
design criteria firmly founded on a rigorous reliability basis remained elusive. This unsatisfactory
condition was resolved eventually by Hasofer & Lind (1974), when they proved mathematically that the
nearest distance of the limit state function from the origin of a standard Gaussian space is an invariant
measure of reliability. This major theoretical breakthrough enforces invariance while retaining the
practical second-moment simplification of Cornell's index. The last piece of significant addition to the
theoretical repertoire for solving time-invariant reliability problems was the algorithm of Rackwitz &
Fiessler (1978), which provided a practical and computationally efficient recipe for computing this
reliability index with no restriction on the number of random variables. The reliability method proposed
by Hasofer & Lind (1974) and its subsequent generalizations to handle non-Gaussian and correlated
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random variables commonly is called the First-Order Reliability Method (FORM). Ellingwood et al.
(1980) were probably the first to apply FORM in a comprehensive way for simplified probabilistic design.
Their study primarily presented load factors for buildings that were calibrated rationally using FORM and
available statistical data.
The above review may not do justice to the voluminous research conducted in structural reliabilityover the past forty or so years. However, it does provide an overview of the historical development of
structural LRFD and the accompanying key theoretical advances supporting this development. In the
aftermath of recent natural hazards (e.g., Northridge and Kobe earthquakes), the structural engineering
profession currently is focusing on performance-based design aimed at meeting client-specific
performance goals, in addition to complying with local building codes (Wen 2000, Buckle 2002). An
example of a performance criteria matrix proposed by the California Department of Transportation
(Caltrans) is shown in Table 1. Efficient techniques for solving time-dependent nonlinear system
reliability problems are needed for such problems. Clearly, theoretical developments in structural
reliability and applications to probabilistic design are still being pursued actively in the structural
community.
Geotechnical LRFD
The development of geotechnical LRFD has taken a different track. One of the first efforts to rationalize
foundation design can be attributed to Hansen (1965), who recommended separate checks for ultimate
and serviceability limit states. In contrast, existing WSD often uses the global factor of safety for indirect
control of serviceability. Hansen (1965) also recommended the use of partial factors for loads and soil
parameters. These partial factors of safety were determined subjectively based on two guidelines: (a) a
larger partial factor should be assigned to a more uncertain quantity, and (b) the partial coefficients should
result in approximately the same design dimensions as that obtained from traditional practice. Ovesen
(1989) highlighted the direct application of a partial factor to the source of uncertainty (soil parameter) as
a notable improvement. The partial factors of safety suggested in 1965 were adopted in the Danish Code
of Practice for Foundation Engineering (DGI 1978, 1985) with minor modifications. More recentimplementations include the Canadian Foundation Engineering Manual, CFEM, third edition (Canadian
Geotechnical Society 1992), Geoguide 1, second edition (Geotechnical Engineering Office 1993), and
Eurocode 7 (CEN/ TC250 1994).
Table 1. Caltrans performance criteria matrix (adapted from Buckle 2002)
Bridge Type 1
(Ordinary bridges)
Bridge Type 2
(Important bridges)
Function evaluation earthquake
(Frequent earthquake about 200-year
event)
PL1
DL2
PL1
DL1
Safety evaluation earthquake(Rare earthquake about 1000 to 2000-
year event)
PL2DL3
PL1DL2
where:
PL1 - Performance Level 1, characterized by immediate and full access to normal traffic almost
immediately after the earthquake
PL2 - Performance Level 2, characterized by limited access possible in days, full access within months
DL1 - Damage Level 1, characterized by minimal damage with essentially elastic performance
DL2 - Damage Level 2, characterized by repairable damage which may executed with minimum loss of
functionality
DL3 - Damage Level 3, characterized by significant damage which may result in closure but not
collapse
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In North America, the factored resistance approach is the preferred design format. LRFD procedures
for bridge superstructures and substructures were introduced in Canada in 1979 as part of the first edition
of the Ontario Highway Bridge Design Code, OHBDC1 (Ministry of Transportation Ontario 1979, Green
1991). Green (1991) further noted that these procedures were "basically a simple rearrangement of factor
of safety design provisions". The design of deep foundations for power generating stations (OntarioHydro 1985) broadly followed the second edition, OHBDC2 (Ministry of Transportation Ontario 1983,
Klym & Lee 1989). OHBDC is currently in its third edition (OHBDC3), but the foundation resistance
factors are not based on reliability calibrations (Green & Becker 2001). In contrast, OHBDC for
superstructures was calibrated using reliability theory in its second edition (Grouni & Nowak 1984). The
target reliability indices selected were 3.5 for ultimate limit state and 1.0 for serviceability limit state
(Nowak & Lind 1979).
For fixed offshore platforms, the Canadian standard for foundations, CAN/CSA-S472-92 (CSA
1992a), contains no specification of resistance factors for foundation design, although reliability-based
LRFD is available for structural design (Been et al. 1993). Been et al. (1993) further noted that resistance
factors were calibrated to the global factor of safety in an earlier 1989 draft commentary (CSA 1989) but
were dropped in the 1992 version (CSA 1992b).The main geotechnical design manual in Canada is the Canadian Foundation Engineering Manual,
CFEM (Canadian Geotechnical Society 1992). As noted previously, the 1992 version (third edition) is
based on the partial factors of safety approach, although the fourth edition currently under preparation is
expected to be revised to be consistent with the factored resistance format (Green & Becker 2001). The
partial factors of safety in the third edition were calibrated so that they result, on average, in overall
factors of safety that are in agreement with existing practice (Meyerhof 1984). To the authors
knowledge, CFEM is the only design guide that indirectly recognizes the difficulty of using a single
partial factor for each soil parameter to cover the wide range of design equations in which the same soil
parameter can appear. Resistance modification factors and performance factors were recommended to
ensure more reasonable agreement with existing practice. However, this procedure is not entirely
successful, as noted by Baike (1985) and Valsangkar & Schriver (1991). The conflict between the need
for simplicity or using small numbers of partial factors of safety, and the need to produce designscomparable with existing practice, does not appear to lend itself readily to simple solutions.
The development of LRFD for foundations in the 1995 National Building Code of Canada (NBCC)
followed a semi-analytical approach (Becker 1996b). Becker (1996b) opined that a full reliability-based
LRFD is difficult to apply because of a lack of statistical data and it is time-consuming and expensive.
Therefore, the resistance factors for foundation design were calibrated to fit WSD and to be consistent
with a lumped parameter lognormal reliability formula. A target reliability index of 3.5 was used in
NBCC for foundation design. As a reference, the NBCC for structural design was calibrated using a
target of 3.5 for ductile behavior with normal consequence of failure and a target of 4.0 if either theconsequence of failure is severe or the failure mode is brittle (Becker 1996b).
In the United States, the resistance factors for design of foundations in the AASHTO LRFD Bridge
Code (AASHTO 2002) were derived from NCHRP Report 343 (Barker et al. 1991). The main rationaleis to remove the inconsistency between load factor design for superstructures and allowable stress design
for foundations, which has resulted in duplication of design efforts because two sets of loads must be
evaluated (Rojiani et al. 1991). The resistance factors appear to be determined using a mixture of
judgment, calibration with WSD, and reliability analysis. Reliability analysis seems to be used in a
limited way (Rojiani et al. 1991, Yoon & O'Neill 1997). The risk levels implied by an extensive range of
existing calculation procedures (e.g., rational methods, semi-empirical methods, in-situ methods) formed
the basis for the target reliability indices. Paikowsky & Stenersen (2000) further noted that the current
AASHTO specifications were developed using insufficient data, hence they utilized mostly back-
calculated factors. Most interestingly, the target reliability index for bridge superstructures is 3.5 (Grubb
1997), which is much higher than the target reliability indices quoted in NCHRP Report 343 (2.0 to 2.5,
2.5 to 3.5, and 3.5 for driven piles, drilled shafts and spread footings, respectively). Project NCHRP 24-
17 was initiated to provide: (a) recommended revisions to the driven pile and drilled shaft portions of
section 10 of AASHTO Specifications and (b) detailed procedure for calibrating deep foundation
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resistance factors. The present recommendation is to design for a target reliability of 2.33 if there are five
or less piles in a group and 3.00 otherwise (Paikowsky 2002).
For API RP 2A-LRFD (API 1993), foundations are treated as one of the structural elements in the
RBD calibration process (Moses & Larrabee 1988). A lumped resistance parameter with a bias of 1.0 and
a coefficient of variation (COV) of 20% was assumed for pile capacity. The foundation resistance factorwas adjusted to achieve an average reliability index of 2.2 for pile axial capacity. A lumped resistance
model also was assumed for transmission line structure foundations in the ASCE Manual & Report 74
(Task Committee on Structural Loadings 1991) to preserve a common reliability calibration scheme for
structural and foundation components. Resistance factors for a range of lumped resistance COVs (20 to
50%) and target probabilities of failure (0.25% to 1%) were presented. The range of probability of failure
corresponds to reliability indices between 2.3 and 2.8. Geotechnical considerations were marginalized
because API RP 2A-LRFD and ASCE Manual & Report 74 were focused on structural design. The first
attempt to develop simplified RBD specifically for transmission line structure foundations with primary
emphasis on geotechnical considerations was described in EPRI Report TR-105000 (Phoon et al. 1995).
A number of geotechnical aspects in this study are of general applicability and will be discussed in detail
later.
RELIABILITY CALIBRATION
Basic theory
The principal difference between RBD and the traditional or partial factors of safety design approaches
lies in the application of reliability theory, which allows uncertainties to be quantified and manipulated
consistently in a manner that is free from self-contradiction. A simple application of reliability theory is
shown in Figure 1 to define some of the key terms used in RBD. Uncertain design quantities, such as the
load (F) and the capacity (Q), are modeled as random variables, while design risk is quantified by the
probability of failure (pf). The basic reliability problem is to evaluate pf from some pertinent statistics ofF and Q, which typically include the mean (mF or mQ) and the standard deviation (sF or sQ), and possibly
the probability density function.
A simple closed-form solution for pf is available if both Q and F are normally distributed. For this
condition, the safety margin (M = Q - F) also is normally distributed with the following mean (mM) and
standard deviation (sM):
FQM mmm = (1a)2F
2Q
2M sss += (1b)
Once the probability distribution of M is known, the probability of failure (pf) can be evaluated as:
pf = Prob(Q < F) = Prob(Q - F < 0) = Prob(M < 0) =
M
M
s
m(2)
in which Prob() = probability of an event and () = standard normal cumulative function. Numericalvalues for () can be obtained easily using the function NORMSDIST(-) in MS Excel. The
probability of failure is usually very small for civil infrastructures. A more convenient measure of design
risk is the reliability index (), which is defined as:
= --1(pf) =2F
2Q
FQ
ss
mm
+
(3)
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Figure 1. Reliability assessment for capacity (Q) > load (F)
in which -1() = inverse standard normal cumulative function. The function -1 () also can be obtainedeasily from MS Excel using NORMSINV(). The reliability indices for most geotechnical componentsand systems lie between 1 and 5, corresponding to probabilities of failure ranging from about 0.16 to 3 10
-7, as shown in Figure 2. It is tempting to compare with the traditional factor of safety because both
parameters lie in the same range. However, their relationship is actually non-unique, as shown below:
( ) 2F2QFSFS
COVCOVm
1m
+
= (4)
in which mFS = mQ/mF = mean factor of safety and COVQ = sQ/mQ = coefficient of variation (COV) of
capacity, COVF = sF/mF = COV of load. Different reliability indices can be obtained for the same mean
factor of safety, depending on COVs of Q and F. In this sense, can be considered as an extension andmore complete version of FS that attempts to incorporate both deterministic and statistical information on
Q and F.
The problem of calculating pf for the general case in which Q is modeled as a nonlinear function of
several non-normal random variables is more difficult than the simple case shown in Figure 1. A
commonly used numerical technique that provides good approximate solutions for engineering
applications is the First-Order Reliability Method (FORM). This technique can be easily implemented
using MS Excel. Details are given by Low & Phoon (2002).
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1E-07
1E-06
1E-05
1E-04
1E-03
1E-02
1E-01
1E+00
0 1 2 3 4 5
Reliability index
Probability
offailur
High
Poor
Hazardous
Above average
Good
Below average
Unsatisfactory
310-7
0.023
0.16 0.07
610-3
310-5
10-3
Figure 2. Relationship between reliability index () and probability of failure (pf) (adapted from TableUS Army Corps of Engineers 1997, Table B-1)
Load and resistance factors
The basic objective of RBD is to ensure that the probability of failure of a component does not exceed an
acceptable threshold level. Based on this objective, an economical design would be one in which the
probability of failure does not depart significantly from the threshold. For the design problem shown inFigure 1, the RBD objective can be formally stated as follows:
pf = Prob(Q < F) pT (5)
in which pT = acceptable target probability of failure. Hence, the only basic difference between RBD and
existing practice is that one controls the probability of failure, rather than the factor of safety. In non-
mathematical terms, this is equivalent to controlling the fraction of unacceptable solutions in a weighted
parametric study, where the weights refer to the likelihood of a set of input parameters being correct.
Reliability-based design, as exemplified by Equation 5, allows the engineer to make a conscious choice
on an acceptable level of design risk and then proceed to a set of design dimensions that are consistent
with that choice. In contrast to the traditional or partial factors of safety approach, logical consistency
between the computed design risk and the uncertainties inherent in the design process is assured by
probabilistic analysis, such as FORM.
A log-normal probability model is commonly used in place of the simple normal probability model
because most physical quantities are non-negative (e.g., Paikowsky 2002). The analytical solution is
available but the following well-known approximation is typically used for reliability calibration (e.g.,
Ravindra & Galambos 1978, Becker 1996a):
( )2Q
2F
FSe
COVCOV
mlog
+= (6)
To derive the LRFD format, the denominator in Equation 6 must be linearized as follows (Lind 1971):
( )QF2
Q
2
F COVCOV75.0COVCOV ++ (7)
Using Equations 6 and 7, the following simple LRFD format can be obtained:
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Qn = Fn (8)
in which Qn, Fn = nominal capacity and load, and , = resistance and load factors given by:
( )Qn
QCOV75.0exp
Q
m = (9a)
( )Fn
F COV75.0expF
m+= (9b)
It can be seen that reliability-calibrated resistance and load factors include the target risk level () and theunderlying parametric uncertainties (COVQ and COVF) rationally into the design process.
Reservations have been expressed about the increase in the complexity of the design calculations
resulting from the use of reliability theory. Complicated reliability calculations are undesirable because:
(a) statistical information is not sufficiently well-defined to warrant sophisticated treatment, (b) there is a
greater risk of making computational errors, (c) a study in soil behavior prediction is reduced to a mere
mathematical exercise, and (d) attention will be diverted from the proper characterization of the ground
mass and appreciation of the physical, chemical, and mechanical processes taking place in it (Beal, 1979;
Semple, 1981; Simpson, et al., 1981; Boden, 1981). These reservations are not without merits. Excessive
preoccupation with maintaining simplicity would, however, ultimately be a disservice to the geotechnical
engineering profession. Historical hindsight has shown clearly that the judicious use of rational methods,
as initiated by Terzaghi in 1943, was the primary cause of most of the significant advances in soil
mechanics following World War II. The cost to pay for rationality is that design calculations could
become more complicated. However, this cost is more than offset by the benefits associated with the use
of rational methods. For example, the improvement in soil behavior prediction allows less conservatism
to be applied in the design. The use of reliability methods is the next logical step toward greater
rationality in design, and their potential benefits should not be discarded heedlessly because of the
reluctance to advance beyond the current level of complexity in design.
GEOTECHNICAL UNCERTAINTIES
Parametric uncertainty
The evaluation of soil and rock properties is one of the key design aspects that distinguishes geotechnical
from structural engineering. None of the current geotechnical LRFD implementations consider this
important issue explicitly. The purpose of this section is to highlight two important observations: (a)
geotechnical variability is a complex attribute that needs careful evaluation, and (b) extensive statistical
data are available for use as first-order estimates in RBD calibration and application. Extensivecalibration studies by Phoon et al. (1995) indicated that foundation resistance factors in the RBD
equations can be calibrated for broad categories of data quality (e.g., COV of undrained shear strength =
10-30%, 30-50%, 50-70%) without compromising on the uniformity of reliability achieved. Hence, it is
not true that there are insufficient statistical data to warrant realistic reliability calculations.
There are three primary sources of geotechnical uncertainties: (a) inherent variabilities, (b)
measurement uncertainties, and (c) transformation uncertainties. The first results primarily from the
natural geologic processes that produced and continually modify the soil mass in-situ. The second is
caused by equipment, procedural and/or operator, and random testing effects. Equipment effects result
from inaccuracies in the measuring devices and variations in equipment geometries and systems
employed for routine testing. Procedural and/or operator effects originate from the limitations in existing
test standards and how they are followed. In general, tests that are highly operator-dependent and have
complicated test procedures will have greater variability than those with simple procedures and littleoperator dependency, as described in detail elsewhere (Kulhawy & Trautmann 1996). Random testing
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error refers to the remaining scatter in the test results that is not assignable to specific testing parameters
and is not caused by inherent soil variability. The third component of uncertainty is introduced when
field or laboratory measurements are transformed into design soil properties using empirical or other
correlation models (e.g., correlating the standard penetration test N value with the undrained shear
strength). Obviously, the relative contribution of these components to the overall uncertainty in thedesign soil property depends on the site conditions, degree of equipment and procedural control, and
quality of the correlation model. Therefore, soil property statistics that are determined from total
variability analyses only can be applied to the specific set of circumstances (site conditions, measurement
techniques, correlation models) for which the design soil properties were derived. Useful guidelines on
typical coefficients of variation of many common soil properties are summarized in Tables 2 to 5. Others
are reported by Jones et al. (2002).
Model uncertainty
A similar effort is underway to quantify uncertainties associated with geotechnical calculation models.
Although many geotechnical calculation models are simple, reasonable predictions of fairly complexsoil-structure interaction behavior still can be achieved through empirical calibrations. Because of our
geotechnical heritage that is steeped in such empiricisms, model uncertainties can be significant. Even a
simple estimate of the average model bias is crucial for reliability-based design. If the model is
conservative, it is obvious that the probabilities of failure calculated subsequently will be biased, because
those design situations that belong to the safe domain could be assigned incorrectly to the failure domain,
as a result of the built-in conservatism.
Robust model statistics can only be evaluated using: (a) realistically large-scale prototype tests, (b) a
sufficiently large and representative database, and (c) reasonably high quality testing where extraneous
uncertainties are well-controlled. With the possible exception of foundations, insufficient test data are
available to perform robust statistical assessment of the model error in many geotechnical calculation
models. The development of a fully rigorous reliability-based design code that can handle the entire
range of geotechnical design problems is currently impeded by the scarcity of these important statistics.Sidi (1986) was among the first to report model statistics that were established firmly using a large load
test database assembled by Olson & Dennis (1982). The focus of the study was on friction piles in clay
subjected to axial loading. Briaud & Tucker (1988) conducted a similar study using a 98-pile load test
database obtained from the Mississippi State Highway Department. Recent literature includes estimation
of model statistics for the calibration of deep foundation resistance factors for AASHTO [American
Association of State Highway and Transportation Officials] (Paikowsky 2002). A substantial part of the
study pertains to the evaluation of driven pile axial capacity using dynamic methods. None of these
studies addresses the applicability of model statistics beyond the conditions implied in the database. This
question mirrors the same concern expressed previously on the possible site-specific nature of soil
variabilities.
Phoon & Kulhawy (2003) presents a critical evaluation of model factors using an extensive databasecollected as part of an EPRI (Electric Power Research Institute) research program on transmission line
structure foundations (Chen & Kulhawy 1994). This study considers only free-head rigid drilled shafts,
using the databases summarized in Table 6. Three common models for lateral soil resistance, by Reese,
Hansen, and Broms, are used to compute the theoretical lateral capacity under undrained and drained
loading modes. Details are given elsewhere (Chen & Kulhawy 1994). Also, there are several methods to
interpret lateral capacity from load tests: displacement limit, rotation limit, lateral or moment limit, and
hyperbolic capacity (Hirany & Kulhawy 1988). All theoretical models are based on failure mechanisms
requiring full mobilization of soil strength. Therefore, the hyperbolic capacity is probably closest to this
ultimate state assumed in the analyses. A plausible and common method of correcting for model error is
to assume the following multiplicative model (e.g., Ang & Tang 1984, Sidi 1986):
Hh = M Hu (10)
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Table 2. Approximate guidelines for inherent soil variability (Source: Phoon and Kulhawy 1999a).
Test type Propertya
Soil type Mean COV(%)
Lab strength su(UC) Clay 10-400 kN/m2 20-55
su(UU) Clay 10-350 kN/m2 10-30su(CIUC) Clay 150-700 kN/m
2 20-40
' Clay & sand 20-40o 5-15
CPT qT Clay 0.5-2.5 MN/m2 < 20
qc Clay 0.5-2.0 MN/m2 20-40
Sand 0.5-30.0 MN/m2 20-60
VST su(VST) Clay 5-400 kN/m2 10-40
SPT N Clay & sand 10-70 blows/ft 25-50
DMT A reading Clay 100-450 kN/m2 10-35
Sand 60-1300 kN/m2 20-50
B reading Clay 500-880 kN/m2 10-35
Sand 350-2400 kN/m2 20-50
ID Sand 1-8 20-60
KD Sand 2-30 20-60
ED Sand 10-50 MN/m2 15-65
PMT pL Clay 400-2800 kN/m2 10-35
Sand 1600-3500 kN/m2 20-50
EPMT Sand 5-15 MN/m2
15-65
Lab index wn Clay & silt 13-100 % 8-30
wL Clay & silt 30-90 % 6-30
wP Clay & silt 15-25 % 6-30
PI Clay & silt 10-40 % b
LI Clay & silt 10 % b
, d Clay & silt 13-20 kN/m3 < 10
Dr Sand 30-70 % 10-40c
50-70d
a - su = undrained shear strength; UC = unconfined compression test; UU = unconsolidated-undrained
triaxial compression test; CIUC = consolidated isotropic undrained triaxial compression test; ' =effective stress friction angle; qT = corrected cone tip resistance; qc = cone tip resistance; VST = vaneshear test; N = standard penetration test blow count; A & B readings, ID, KD, & ED = dilatometer A & B
readings, material index, horizontal stress index, & modulus; pL & EPMT = pressuremeter limit stress &
modulus; wn = natural water content; wL = liquid limit; wP = plastic limit; PI = plasticity index; LI =
liquidity index; & d = total & dry unit weights; Dr= relative densityb - COV = (3-12%) / mean
c - total variability for direct method of determination
d - total variability for indirect determination using SPT values
in which Hh = measured hyperbolic capacity, Hu = computed lateral capacity, and M = model factor,
typically assumed to be a log-normal random variable. The empirical distributions of M for model-scale
laboratory tests and full-scale field tests are summarized in Figure 3.
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Table 3. Summary of total measurement error of some laboratory tests (Phoon & Kulhawy 1999a)
No. No. Tests / Property Value Property
data Group (unitsb) COV (%)
Propertya
Soil type groups Range Mean Range Mean Range Mean
su(TC) Clay, silt 11 - 13 7-407 125 8-38 19
su(DS) Clay, silt 2 13-17 15 108-130 119 19-20 20
su(LV) Clay 15 - - 4-123 29 5-37 13
(TC) Clay, silt 4 9-13 10 2-27o
19.1o 7-56 24
(DS)Clay, silt 5 9-13 11 24-40
o33.3
o 3-29 13
Sand 2 26 26 30-35o
32.7o 13-14 14
tan (TC) Sand, silt 6 - - - - 2-22 8
tan (DS) Clay 2 - - - - 6-22 14
wn Fine-grained 3 82-88 85 16-21 18 6-12 8
wL Fine-grained 26 41-89 64 17-113 36 3-11 7
wP Fine-grained 26 41-89 62 12-35 21 7-18 10
PI Fine-grained 10 41-89 61 4-44 23 5-51 24
Fine-grained 3 82-88 85 16-17 17.0 1-2 1
a - su = undrained shear strength; = effective stress friction angle; TC = triaxial compression test;UC = unconfined compression test; DS = direct shear test; LV = laboratory vane shear test; wn = natural water
content; wL = liquid limit; wP = plastic limit; PI = plasticity index; = total unit weightb - units of su = kN/m
2; units of wn, wL, wP, and PI = %; units of = kN/m
3
The model-scale load tests were conducted in uniform kaolinite clay and filter sand deposits prepared
under controlled laboratory conditions. Hence, uncertainties arising from evaluation of soil parameters
are minimal. In addition, construction variabilities and measurement errors associated with load tests also
are minimal. Therefore, model uncertainties computed from laboratory tests should be an accurate
indicator of errors arising from the use of simplified calculation models. The main concern is whether the
model factors are applicable beyond the uniform profile and specific soil type used in the laboratory.
Model factors from field tests are expected to be more general because they are computed from load tests
conducted in more diverse site environments. However, it is reasonable to query if the statistics of such
model factors are lumped statistics, in the sense that extraneous sources of uncertainties (e.g.,
construction variabilities, measurement errors incurred during load test, uncertainties in soil parameter
evaluation) are inextricably included in the computation.
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Table 4. Summary of measurement error of common in-situ tests (Kulhawy & Trautmann 1996)
Coefficient of variation, COV (%)
Test Equipment Procedure Random Totala
Rangeb
Standard penetration test (SPT) 5c - 75d 5c - 75d 12 - 15 14c - 100d 15 - 45
Mechanical cone penetration test
(MCPT)
5 10e -15f 10e -15f 15e -22f 15 - 25
Electric cone penetration test
(ECPT)
3 5 5e
-10f
7e
- 12f
5 - 15
Vane shear test (VST) 5 8 10 14 10 - 20
Dilatometer test (DMT) 5 5 8 11 5 - 15
Pressuremeter test, pre-bored (PMT) 5 12 10 16 10 - 20g
Self-boring pressuremeter test
(SBPMT)
8 15 8 19 15 - 25g
a - COV(Total) = [COV(Equipment)2
+ COV(Procedure)2
+ COV(Random)2]
0.5
b - Because of limited data and judgment involved in estimating COVs, ranges represent probable magnitudes of
field test measurement error
c, d - Best to worst case scenarios, respectively, for SPT
e, f - Tip and side resistances, respectively, for CPT
g - It is likely that results may differ for po, pf, and pL, but the data are insufficient to clarify this issue
A comparison between laboratory and field data such as that shown in Figure 3 is illuminating.
Laboratory and field results are plotted as white and grey histograms in the first row of each cell,
respectively. Visual inspection and simple statistics [mean, standard deviation (S.D.), coefficient of
variation (COV)] show that the histograms are similar. The p-values from the Mann-Whitney test
formally show that the null hypothesis of equal medians cannot be rejected at 5% significance level, with
the exception of the drained factor for the Hansen model. Therefore, it is reasonable to argue that the
results presented in Figure 3 have wider applicability beyond the conditions implied by the underlying
databases, and the model uncertainties are mainly caused by errors intrinsic to the respective simplified
calculation models. A more robust estimate of the empirical distribution is obtained by combining the
laboratory and field data, as shown in the second row of each cell in Figure 3. For rigid drilled shafts
subjected to lateral-moment loading, the COV of the model factor appears to fall within a narrow range of
25 to 40%. Another detailed example on cantilever walls in sand is discussed by Phoon et al. (2003d).
PRACTICAL IMPLEMENTATION ISSUES
Conceptual basis for EPRI study
Although existing geotechnical LRFD codes look the same as their structural counterparts, they are
incompatible with structural RBD on closer inspection because one or more of the following key elements
are missing (Kulhawy & Phoon 2002):
a. The primary objective in structural RBD is to achieve a minimum target reliability index across aspecified domain of interest (e.g., foundation geometries and types, loading modes, soil conditions,
etc.). Structural RBD requires deliberate and explicit choices to be made on the target reliability
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Table 5. Approximate guidelines for design soil property variability (Phoon & Kulhawy 1999b)
Design Point Spatial avg. Correlation
propertya
Testb Soil type COV (%) COV
c(%) equation
su(UC) Direct (lab) Clay 20-55 10-40 -su(UU) Direct (lab) Clay 10-35 7-25 -
su(CIUC) Direct (lab) Clay 20-45 10-30 -
su(field) VST Clay 15-50 15-50 14
su(UU) qT Clay 30-40e
30-35e 18
su(CIUC) qT Clay 35-50e
35-40e 18
su(UU) N Clay 40-60 40-55 23
sud KD Clay 30-55 30-55 29
su(field) PI Clay 30-55e - 32
Direct (lab) Clay, sand 7-20 6-20 -)TC( qT Sand 10-15
e10
e 38
cv PI Clay 15-20e
15-20e 43
Ko Direct (SBPMT) Clay 20-45 15-45 -
Ko Direct (SBPMT) Sand 25-55 20-55 -
Ko KD Clay 35-50e
35-50e 49
Ko N Clay 40-75e - 54
EPMT Direct (PMT) Sand 20-70 15-70 -
ED
Direct (DMT) Sand 15-70 10-70 -
EPMT N Clay 85-95 85-95 61
ED N Silt 40-60 35-55 64
a - su = undrained shear strength; UU = unconsolidated-undrained triaxial compression test;
UC = unconfined compression test; CIUC = consolidated isotropic undrained triaxial compression
test; su(field) = corrected su from vane shear test; = effective stress friction angle; TC = triaxialcompression; cv = constant volume ; Ko = in-situ horizontal stress coefficient; EPMT =pressuremeter modulus; ED = dilatometer modulus
b - VST = vane shear test; qT = corrected cone tip resistance; N = standard penetration test blow count;
KD = dilatometer horizontal stress index; PI = plasticity index
c - averaging over 5 meters
d - mixture of su from UU, UC, and VSTe - COV is a function of the mean; refer to COV equations in Phoon & Kulhawy (1999b) for details
Table 6. Databases on laterally-loaded rigid drilled shafts (Phoon & Kulhawy 2003)
Description No. tests D/B e/D
Undrained loading:
Model-scale lab tests 47 3.0 8.0 0.03 4.0
Full-scale field tests 27 2.3 10.5 0.03 6.8
Drained loading:
Model-scale lab tests 55 2.6 9.0 0.06 5.0
Full-scale field tests 22 2.5 7.0 0 5.4
Note: D = depth; B = diameter; e = load eccentricity
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Model Undrained Drained
Undrained:
Reese (1958)
Drained:Reese et al. (1974)
0.4 1.2 2.0 2.8 3.6
Hh/Hu(Reese)
0
5
10
15
20
Freq
uency
Mean =S.D. =COV =
n =
p =
1.430.370.2647
0.315
Lab
1.400.470.3327
Field
0.4 1.2 2.0 2.8 3.6
Hh/Hu(Reese)
0
5
10
15
20
Freq
uency
Mean =S.D. =COV =
n =
p =
1.190.570.4855
0.433
Lab
1.190.360.3022
Field
0.4 1.2 2.0 2.8 3.6
Hh/Hu(Reese)
0
5
10
15
20
Frequency
Mean =S.D. =COV =
n =
1.420.410.2974
0.4 1.2 2.0 2.8 3.6
Hh/Hu(Reese)
0
5
10
15
20
Frequency
Mean =S.D. =COV =
n =
1.190.510.4377
Hansen (1961)
0.4 1.2 2.0 2.8 3.6
Hh/Hu(Hansen)
0
5
10
15
20
Frequency
Mean =S.D. =COV =
n =p =
1.950.550.28470.296
Lab
1.850.570.3127
Field
0.4 1.2 2.0 2.8 3.6
Hh/Hu(Hansen)
0
5
10
15
20
Frequency
Mean =S.D. =COV =
n =p =
1.050.330.31550.002
Lab
0.830.250.3022
Field
0.4 1.2 2.0 2.8 3.6
Hh/Hu(Hansen)
0
5
10
15
20
Fre
quency
Mean =S.D. =COV =
n =
1.920.560.2974
0.4 1.2 2.0 2.8 3.6
Hh/Hu(Hansen)
0
5
10
15
20
Frequ
ency
Mean =S.D. =COV =
n =
0.980.320.33
77
Undrained:
Broms (1964a)
Drained:
Broms (1964b)
0.4 1.2 2.0 2.8 3.6
Hh/Hu(Broms)
0
5
10
15
20
Frequency
Mean =S.D. =COV =
n =p =
2.280.800.35470.875
Lab
2.290.950.4127
Field
0.4 1.2 2.0 2.8 3.6
Hh/Hu(simplified Broms)
0
5
10
15
20
Frequency
Mean =S.D. =COV =
n =p =
1.310.530.40550.844
Lab
1.270.410.3222
Field
0.4 1.2 2.0 2.8 3.6
Hh/Hu(Broms)
0
5
10
15
20
Frequency
Mean =S.D. =COV =
n =
2.280.850.3774
0.4 1.2 2.0 2.8 3.6
Hh/Hu(simplified Broms)
0
5
10
15
20
Frequency
Mean =S.D. =COV =
n =
1.300.500.3877
Figure 3. Model factors for rigid drilled shafts under undrained and drained lateral-moment loading
modes (Phoon & Kulhawy 2003)
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index, scope of calibration domains, and representative designs populating each domain. This is
philosophically different from the objective of achieving designs comparable to working stress
design.
b. The secondary objective in structural RBD is to increase uniformity of reliability across the domain
of interest, which is rarely emphasized and verified in geotechnical LRFD. In fact, the typical use ofa single resistance factor for each loading mode is not adequate for this task, as elaborated in item 6
below.
c. Soil variability is the most significant source of uncertainty, but it is not quantified in a robust way (if
at all) and incorporated explicitly in the code calibration process.
d. Probabilistic load models compatible with the relevant structural codes are not spelled out clearly. It
is unclear if the original structural load models have been used for code calibration. Load
combinations are not amenable to simplified lognormal reliability analysis (in contrast to the more
general first-order reliability method or FORM highlighted in item 5) unless they are approximated as
some lumped load parameters.
e. Rigorous reliability analysis using FORM is not used as the main tool to integrate loads, basic soil
parameters, and calculation models in a realistic and self-consistent way, both physically andprobabilistically. The commonly adopted approach of simplifying geotechnical capacity as a single
lognormal random variable has limitations (Phoon et al. 2003b).
f. No guidelines on selection of nominal or characteristic soil parameters are usually given. It is also
unclear how resistance factors will be affected by the site conditions, measurement techniques, and
correlation models used to derive the relevant design parameters.
There are no technical and/or practical difficulties in addressing these incompatibilities directly. The
basic solution is to follow a more general calibration procedure as outlined below.
Achieving uniform reliability
In EPRI Report TR-105000, uniform reliability is realized by partitioning the design domains and using a
Multiple Resistance Factor Design (MRFD) format. The design of drilled shafts (bored piles) for upliftunder undrained loading will be used as an example. Two simple design formats were selected for
reliability calibration:
LRFD: F50uQun (11)MRFD: F50suQsun + tuQtun + wW (12)
in which F50 = 50-year return period load, Qun = nominal uplift capacity, Qsun = nominal side resistance,
Qtun = nominal tip resistance, W = weight of foundation, and u, su, tu and w = resistance factors.Figure 4a show the reliability levels implicit in existing ULS designs. Note that the existing WSD format
is essentially the same as the LRFD format (Equation 11), because the reciprocal of the traditional factor
of safety (FS) is equal to the resistance factor (u). Therefore, the variation in the reliability index () or
probability of failure (pf) at a fixed FS is indicative that the LRFD format will produce fairly pooruniformity in reliability when it is applied over the entire design domain. In EPRI Report TR-105000, the
uniformity in reliability was improved by using the following general calibration procedure:
a. Perform a parametric study on the variation of the reliability level with respect to each deterministic
and statistical parameter in the design problem. Examples of deterministic parameters that control the
design of drilled shafts include the diameter (B) and depth to diameter (D/B) ratio. Examples of
statistical parameters include the mean and coefficient of variation (COV) of the undrained shear
strength (su).
b. Partition the parameter space into several smaller domains. An example of a simple parameter space
is shown in Figure 5. The reason for partitioning is to achieve greater uniformity in reliability over
the full range of deterministic and statistical parameters. For those parameters identified in Step (a)
as having a significant influence on the reliability level, the size of the partition clearly should be
smaller. In addition, partitioning ideally should conform to existing geotechnical conventions.
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(a) (b)
Figure 4. Drilled shafts in undrained uplift: (a) reliability levels implicit in existing ultimate limit state
design and (b) performance of ultimate limit state RBD formats
c. Select a set of representative points from each domain. Note that each point in the parameter space
denotes a specific set of parameter values (Figure 5). Ideally, the set of representative points should
capture the full range of variation in the reliability level over the whole domain.
d. Determine an acceptable foundation design for each point and evaluate the reliability levels in the
designs. Foundation design is performed using the set of parameter values associated with each
point, along with a simplified RBD format and a set of trial resistance factors. The reliability of the
resulting foundation design then is evaluated using the FORM algorithm.
e. Quantify the deviations of the reliability levels from a pre-selected target reliability index, T. The
following simple objective function can be used:
n
1=i
2Tiwtusu )-(=),,(H (13)
in which H() = objective function to be minimized, n = number of points in the calibration domain,and i = reliability index for the ith point in the domain.
f. Adjust the resistance factors and repeat Steps (d) and (e) until the objective function is minimized.
The set of resistance factors that minimizes the objective function (H) is the most desirable because
the degree of uniformity in the reliability levels of all the designs in the domain is maximized. The
following measure can be used to quantify the degree of uniformity that has been achieved:
n
H= (11)
g. Repeat Steps (c) to (f) for the other domains.
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Figure 5. Partitioning of parameter space for calibration of resistance factors.
Table 7. Undrained uplift resistance/deformation factors for drilled shafts (Source: Phoon et al. 1995, pp.
6-7 & 17).
LRFD
(ULS)
MRFD
(ULS)
LRFD
(SLS)Mean su
(kN/m2)
COV su(%)
u su tu w u25 - 50 10 30 0.44 0.44 0.28 0.50 0.65
Medium clay 30 50 0.43 0.41 0.31 0.52 0.63
50 70 0.42 0.38 0.33 0.53 0.62
50 - 100 10 30 0.43 0.40 0.35 0.56 0.64
Stiff clay 30 50 0.41 0.36 0.37 0.59 0.61
50 70 0.39 0.32 0.40 0.62 0.58
100 - 200 10 30 0.40 0.35 0.42 0.66 0.61
Very stiff clay 30 50 0.37 0.31 0.48 0.68 0.57
50 70 0.34 0.26 0.51 0.72 0.52
Note: Target = 3.2 for ultimate limit state (ULS) and 2.6 for serviceability limit state (SLS)
The results of the RBD calibration exercise for drilled shafts in undrained uplift loading are shown in
Table 7. Exact comparison with other LRFD resistance factors is difficult, but AASHTO recommends u= 0.55 for uplift capacity of drilled shaft (-method) in clay (NCHRP Report 343, Table 4.10.6-3) whileOHBDC/CHBDC and NBCC recommends u = 0.3 for tension capacity of deep foundations evaluatedusing static analysis (Green & Becker 2001). Note that the target reliability indices are 2.5 to 3.5 for
AASHTO (probably closer to 2.5 as reported by Rojiani et al. 1991) and 3.5 for OHBDC/CHBDC/NBCC.
The EPRI resistance factors vary from 0.34 to 0.44 depending on the quality of data, as shown in Table 7.
They lie between AASHTO and OHBDC/CHBDC/NBCC factors, but are closer to the latter than the
former, partially because the target reliability index is 3.2. More importantly, a single resistance factor
cannot be expected to maintain uniform reliability over a wide and diverse range of design scenarios asshown in Figure 4a. The EPRI study shows that the use of a simple 3x3 partitioning on the mean and
COV of undrained shear strength is sufficient to produce designs with distinctively more uniform
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reliability (compare Figures 4a and 4b). The partitioning on the mean undrained shear strength also was
selected to conform to existing geotechnical conventions, as noted previously.
The EPRI study further recommended use of the Multiple Resistance Factor Design (MRFD) format
for achieving a more consistent target reliability (Equation 12). The MRFD format is a natural
generalization of the LRFD format that involves the application of one resistance factor to eachcomponent of the capacity rather than the overall capacity. MRFD is more physically meaningful for
foundation design because the variability of each component can be significantly different. In addition, it
achieves greater uniformity in reliability as shown in Figure 4b.
CONCLUSIONS
New reliability-based design (RBD) methodologies that are already adopted widely by the structural
community are not accepted readily in the geotechnical community, partially because of the questionable
robustness of the statistics used for code calibration and unfamiliarity with probabilistic concepts.
However, maintaining status quo is increasingly untenable because of gathering momentum in code
harmonization and broadening divergence between geotechnical and structural design. Becausegeotechnical design is only one component of harmonised codes, it is anticipated that structural reliability
methods will eventually prevail in geotechnical design.
There is a need to draw a clear distinction between accepting reliability analysis as a necessary
theoretical basis for geotechnical design and downstream calibration of simplified multiple-factor design
formats, with emphasis on the former. Simplified reliability-based design (RBD) equations in the form of
LRFD/MRFD are probably required for routine design at present, but their limitations have no bearing on
the generality of reliability theory. This paper argues that there is sufficient statistical support for the
development of these simplified RBD formats. Reliability-based design, simplified or otherwise,
provides a more consistent means of managing uncertainties, but it is by no means a perfect solution.
Engineering judgment still is indispensable in many aspects of geotechnical engineering reliability
analysis merely removes the need for guesswork on how uncertainties affect performance and is
comparable to the use of elasto-plastic theory to remove the guesswork on how loads induce stresses anddeformations. Lacasse et al. (2004) observed that:
Engineering depends on judgment, the exercise of which depends on knowledge derived from theoretical
concepts, experiment, measurements, observations, and past experience. These building blocks have to
be recognized, assembled, and evaluated collectively before judgment can be rendered.
Historical hindsight has shown clearly that the judicious use of rational methods, as initiated by
Terzaghi in 1943, was the primary cause of most of the significant advances in soil mechanics following
World War II. The cost to pay for rationality is that design calculations could become more complicated.
However, this cost is more than offset by benefits such as reduction in conservatism because of improved
understanding and hence increased confidence in the design. The use of reliability methods is the nextlogical step toward greater rationality in design, and their potential benefits should not be discarded
heedlessly because of the reluctance to advance beyond the current level of complexity in design.
ACKNOWLEDGMENTS
Financial support from the Site Investigation Committee, Korean Geotechnical Society; Hyundai
Engineering & Construction Co., Ltd.; and Daelim Industry Co., Ltd are gratefully acknowledged. The
author is also grateful to Dr Gil Lim Yoon for his kind invitation to deliver this special lecture and
making all the arrangements for this visit.
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Baike, L. D. 1985. Total and partial factors of safety in geotechnical engineering. Can. Geotech. J., 22(4):
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Barker, R M, Duncan, J. M., Rojiani, K. B., Ooi, P. S. K., Tan, C. K. & Kim, S. G. 1991. Manuals for
design of bridge foundations, NCHRP Report 343, Transportation Research Board, Washington.
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