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byGordon A. Fenton
Dalhousie University, Halifax, Canada
Load and Resistance Factor Geotechnical Design Code Development in Canada
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Overview
1. Past: Where we’ve been
• allowable stress design
• partial (strength) vs. total resistance
factors
2. Present: Where we are
• current implementation in NBCC and
CHBDC
3. Future: Where we are going
• incorporating site/model understanding
• allowing for failure consequence
• how to get the factors?
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Past: Where we’ve been
• geotechnical design based on working
(allowable) stress prior to 1979
• 1979 and 1983 bridge foundation design codes
adopt partial factor format from Danish practice
• partial factor format did not lead to design
consistency with allowable stress approach, so
not readily accepted by geotechnical engineers.
• total resistance factor format adopted in the
bridge foundation design code in 1991
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WSD TO LRFD
DEVELOPMENT OF A GEOTECHNICAL DESIGN CODE
� Working (or Allowable) Stress Design (WSD) was the
basis of geotechnical design until 1979,
� Geotechnical design codes have since been migrating
towards a Load and Resistance Factor Design (LRFD)
approach embedded in a Limit States Design (LSD)
framework,
ˆ ˆs iR F L≥ ∑
ˆ ˆgu u i ui ui
i
R I Lϕ η γΨ ≥ ∑
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WORKING STRESS DESIGN
� Factors of safety (Fs ) based on experience and
observed performance
� All uncertainty lumped into a single factor
� Many years of empirical experience (extensive
database)
� Simple, deterministic
� Does not lend itself to the estimation of failure
probability
� thus difficult to get a sense for probability of
failure
� Fs is not quantitatively meaningful
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LOAD AND RESISTANCE FACTOR DESIGN
RATIONALE
�account for load and resistance uncertainties separately
� introduce reliability-based design benefitsinto geotechnical designs, e.g. increased construction economies for low failure consequence (low risk) problems, increased investigation effort, etc.
�harmonize with structural codes
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Load and Resistance Factor Design
• replaces single factor-of-safety with a set of partial safety factors(load and resistance factors) acting on individual components of resistance and load (Taylor, 1948, Freudenthal, 1951, 1956, Hansen, 1953, 1956)
Load and resistance factorsare derived to account for;
• variability in load and material properties
• variability in construction
• model error(approximations in design relationships)
• failure consequences
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Load and Resistance Factor Design
• load factors, γi > 1, account for variability in loads
• resistance factor, ϕ < 1, accounts for variability in soil properties, variability in construction, and model error
• consequence factor, Ψ , accounts for failure consequences
ˆ ˆ (LRFD)i iR Lϕ γΨ ≥∑
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Load and Resistance Factor Design
Two commonresistance factor implementations:
1) total resistance factor: a single resistancefactor applied to the final computed soilresistance (as shown in previous slide)
2) partial resistance factors: multiple resistancefactors applied to components of soilstrength separately, e.g. to tan(φ’ ), c’ ,etc. Also known as factored strength.
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Partial Resistance Factor Approach
• only explicitly considers uncertainties associated with material strength parameters(e.g. not with model error)
• often implemented with myriad partial factorsin order to account for all sources of material uncertainty – sense of real behaviour often lost
• may not capture true mechanism of failurewhen failure mechanism sensitive to changes in material strengths
• non-linearity issues: resistance based on partial resistance factors is not the same as total factored resistance based on unfactored material parameters
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Total Resistance Factor Approach
• resistance computed as with the WSD approach – better representation of actual failure mechanism
• resistance is factored onceat the end
• very similar to traditional Fs approach, except specifically applied to the resistance
• allows for a smoother transitionfrom WSD to LRFD
• allows engineers to work with “real” numbersuntil the last step where the result is factored.
• consistent with structural codes, where each material has its own single resistance factor – soil is an engineering material
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Comparison of LRFD Codes
• The following table lists the load and resistance factors used in a variety of geotechnical design codesfrom around the world.
• Where the code suggests a range of values (dependent, for example, on investigation intensity), only the range is presented.
• To assess the relative conservatismof the various codes, the required area of a spread footing designed against bearing failure (ULS) using , , c´ = 100, φ´ = 30° is computed in the rightmost column. The codes are ranked from the most conservative (top) to theleast conservative (bottom).
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ˆ 3700DL = ˆ 1000LL =
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Values of Load and Resistance Factors
Code Dead Load
Live Load
tan(φ’ ) c’ Bearing Sliding Area
CFEM – 1992 1.25 1.5 0.8 0.5-0.65 5.22
NCHRP 343 – 1991 1.3 2.17 0.35-0.6 0.8-0.9 4.88
NCHRP12-55 - 2004 1.25 1.75 0.45 0.8 4.70
Denmark – 1965 1.0 1.5 0.8 0.57 4.47
AASHTO – 2007 1.25 1.75 0.45-0.55 0.8-0.9 4.23
B. Hansen – 1956 1.0 1.5 0.83 0.59 4.15
AS 5100 – 2004 1.2 1.8 0.35-0.65 0.35-0.65 4.14
CHBDC – 2006 1.2 1.7 0.5 0.8 4.07
AS 4678 – 2002 1.25 1.5 0.75-0.95 0.5-0.9 3.89
Eurocode7 Model 1 1.0 1.3 0.8 0.8 3.06
Eurocode7 Model 2 1.35 1.5 0.71 0.91 3.04
ANSI A58 – 1980 1.2-1.4 1.6 0.67-0.83 2.84
(shallow foundations)
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Present: Where we are
1. National Building Code of Canada (2010)
specifies Limit States Design, but resistance
factors do not appear in the code – they
appear in the User’s Guide. Importance
factors applied to (site specific) snow, wind,
and seismic loads.
2. Canadian Highway Bridge Design Code
(2006) specifies both Limit States Design and
the required resistance factors. Importance
factors applied to snow, wind, and seismic
loads.
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National Building Code of Canada User’s Guide
2010
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Canadian Highway Bridge Design Code 2006
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Reliability-Based Design Goals:
• Account for uncertaintyrationally and consistently
• Make use of PDFs of loads and resistances(at least mean and variance)
• Quantify probability of failure
• Achieve societally acceptable levels of riskfor our engineered systems (where risk = failure consequence times failure probability)
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Future: Where we’re going
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RELIABILITY-BASED CODE OBJECTIVES
“You pay for a site investigation whether you have one or
not” (Institution of Civil Engineers, Inadequate Site
Investigation, 1991)
There is a desire in the Canadian geotechnical community
to:
� provide a means to adjust design/construction economies based
on level of site understanding
� take site investigation/modeling intensity into account in the design
process
� provide rationale for increased investigation/modeling effort
� provide a means to adjust geotechnical system reliability based
on potential failure consequences
� higher reliability for more important structures/systems regardless of
loading type
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RATIONALE FOR RELIABILITY-BASED
FOUNDATION DESIGN
Reliability-based design concepts
� allow quantification of reliability,
� allow designs to target a specified reliability level,
� reward better site investigation by permitting a higher
factor to be used in design, thus permitting a more
economical design while ensuring acceptable reliability,
� lead to harmonization with other structural codes by
establishing a common conceptual framework to address
reliability issues.
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CONCEPTUAL OVERVIEW FOR RELIABILITY-
BASED DESIGN
� the probability and consequence of failure are considered in
determining resistance and consequence factors
� reliability-based resistance factors are applied to the resistance,
� at both ultimate and serviceability limit states
� and, eventually, under both static and seismic loading conditions
� cost-effective resistance and consequence factors depend on
� the degree of understanding of the site conditions and accuracy of the design
model (resistance factors)
� the consequence of not providing adequate geotechnical resistance to imposed
loads (consequence factor)
� the overall goal is to save money, for specified tolerable risk and
required performance, by considering the trade-off between initial
design and construction costs and long-term costs, including cost of
failure.
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FLOATING RESISTANCE FACTOR TABLE
(CONCEPTUAL)
HIGH Consequence
1.0 0.8 0.6
1.2 1.0DEFAULT VALUE
0.8
1.4 1.2 1.0
LOW Consequence
LOW Uncertainty HIGH Uncertainty
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RELIABILITY-BASED DESIGN CODE DEVELOPMENT
Basic idea is to split traditional into
1. Load factors – from load section of code,
2. Resistance factors, : capture “resistance” uncertainty� Depend on level of site and prediction model understanding
� Propose three degrees of site understanding: high, typical, and low
� Consider SLS and ULS resistance factors separately (different target maximum acceptable failure probability)
3. Consequence factor, : captures system importance (failure consequence)� Propose three consequence levels: high, typical, and low
� High: β = 3.7 (pf
= 1/10,000) at ULS, β = 3.1 (pf
= 1/1000) at SLS
� Typical: β = 3.5 (pf
= 1/5,000) at ULS, β = 2.9 (pf
= 1/500) at SLS
� Low: β = 3.1 (pf
= 1/1,000) at ULS, β = 2.3 (pf
= 1/100) at SLS
and gu gsϕ ϕ
Ψ
sF
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LOAD AND RESISTANCE FACTOR DESIGN
� Ultimate Limit State (ULS)
Factored ultimate geotechnical resistance ≥ effect of factored ULS loads
where
= consequence factor,
= ultimate geotechnical resistance factor,
= ultimate characteristic geotechnical resistance,
= i’th ULS load factor,
= i’th load effect for a given ULS.
ˆ ˆgu u ui ui
i
R Lϕ γΨ ≥∑
Ψ
guϕˆ
uR
uiγˆ
uiL23
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LOAD AND RESISTANCE FACTOR DESIGN
� Serviceability Limit State (SLS)
Factored serviceability geotechnical resistance ≥ effect of factored SLS loads
where
= consequence factor,
= serviceability geotechnical resistance factor,
= serviceability characteristic geotechnical resistance,
= i’th SLS load factor, and
= i’th load effect for a given SLS.
ˆ ˆgs s si si
i
R Lϕ γΨ ≥∑
Ψgsϕ
ˆsR
siγˆ
siL
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DEGREE OF SITE AND PREDICTION MODEL
UNDERSTANDING
Site and prediction model understanding includes;
� understanding of the ground and the geotechnical
properties throughout the site,
� the type and degree of confidence about the
numerical prediction models to be used to estimate
serviceability and ultimate geotechnical resistances,
and
� observational (monitoring) methods for
confirmation.
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DEGREE OF SITE AND PREDICTION MODEL
UNDERSTANDING
Motivation:
� Differentiating between levels of site understanding
allows for design economies – the greater the level of
understanding, the lower the risk of failure and the
greater the economy of the final design should be.
� Allows the designer to show “proof” (thus justifying
higher design phase costs) that increased understanding
(e.g. increased site investigation) leads to construction
savings and lower total project costs.
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DEGREE OF SITE AND PREDICTION MODEL
UNDERSTANDING
Three levels of site understanding are proposed in the next CHBDC:
� High understanding: Extensive project-specific investigation procedures and/or knowledge is combined with prediction models of demonstrated (or proven) quality to achieve a high level of confidence with performance predictions.
� Typical understanding: Usual project-specific investigation procedures and/or knowledge is combined with conventional prediction models to achieve a typical level of confidence with performance predictions.
� Low understanding: Understanding of the ground properties and behaviour are based on limited representative information (e.g. previous experience, extrapolation from nearby and/or similar sites, etc.) combined with conventional prediction models to achieve a lower level of confidence with the performance predictions.
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ULS GEOTECHNICAL RESISTANCE FACTORS
(STATIC LOADING)
Limit State Degree of UnderstandingLow Typical High
Shallow FoundationsBearing resistance 0.45 0.5 0.6Passive resistance 0.4 0.5 0.6Horizontal resistance (sliding) 0.75 0.8 0.85
Ground AnchorsStatic analysis – tension 0.3 0.4 0.5
Static test – tension 0.55 0.6 0.65
Deep Foundations – PilesStatic analysis
Compression 0.35 0.4 0.5Tension 0.35 0.4 0.45
Static testCompression 0.5 0.6 0.7Tension 0.3 0.4 0.5
Dynamic analysis – compression 0.3 0.4 0.5
Dynamic test – compression (field measurement and analysis)
0.4 0.5 0.6
Horizontal passive resistance 0.4 0.5 0.6
guϕ
(for illustration only – factors are not finalized) 28
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SLS GEOTECHNICAL RESISTANCE FACTORS
(STATIC LOADING)
Limit StateDegree of UnderstandingLow Medium High
Shallow FoundationsSettlement 0.7 0.9 1.0
EmbankmentsSettlement 0.7 0.8 0.9Lateral displacements 0.6 0.7 0.8
Deep Foundations – PilesSettlement 0.8 0.9 1.0Lateral displacements 0.7 0.8 0.9
Retaining SystemsSettlement 0.35 0.4 0.45Horizontal Deformation 0.4 0.45 0.5
AnchorsDisplacement 0.5 0.6 0.7
gsϕ
(for illustration only – factors are not finalized)
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CONSEQUENCE FACTOR
Motivation:
� Different structures will have different consequences of failure.
For example, the failure of an expressway bridge has far higher
consequences (life threat, economic, etc.) than does the failure
of a low volume rural bridge.
� The target maximum acceptable failure probability of a
structure with high failure consequence should be significantly
lower than that for a structure with low failure consequence.
� Rational assessment on the basis of failure probability and
consequence of failure will allow for more realistic allocation of
infrastructure budgets.
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CONSEQUENCE FACTOR
Geotechnical systems can be assigned consequence levels
associated with exceeding various limit states;
�High consequence – structure is designed to be essential
to post-disaster recovery (e.g. hospital or bridge lifeline),
and/or has large societal and/or economic impacts,
�Typical consequence – structure is designed for typical
failure consequences, e.g. the usual office building, bridge,
etc. This is the default consequence level.
�Low consequence – failure of the structure poses little
threat to human safety, e.g. storage utilities, very low
traffic volume bridges, temporary structures.
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CONSEQUENCE FACTOR TABLE
Consequence
Level
Reliability Index, β(SLS in parentheses)
ExampleConsequence Factor, Ψ
High 3.7 (3.1)Lifelines, Emergency
0.9
Typical 3.5 (2.8)Highway bridges
1.0
Low 3.1 (2.3)Secondary bridges
1.1
(for illustration only – factors are not finalized)
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SUMMARY OF PHILOSOPHICAL CHANGES
� introduced three levels of site understanding – high,
typical (default), and low – through the resistance factor
� resistance factors vary with site understanding – higher for better
understanding
� this approach allows for greater economies in the tradeoff between
design/investigation effort and overall construction costs
� introduced three levels of failure consequence – high,
typical (default), and low – through the consequence
factor
� consequence factor, which modifies the factored resistance, varies
with consequence level – lower for higher consequences
� this also allows for greater economies in the tradeoff between
target reliability and construction costs
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The Random Finite Element Method involves a combination of
Random Field Theory (e.g. Fenton and Vanmarcke 1990)
with the
Finite Element Method (e.g. Smith and Griffiths 2004)
The method takes into account the mean, standard deviation
and spatial correlation length of the input ground
parameters as well as for random loading.
The method takes full account of the statistical nature of local
averaging of ground properties over the finite elements.
The method is applied in a Monte-Carlo framework.
Determination of Resistance Factors
Level III: Fully Probabilistic Analysis
The Random Finite Element Method (RFEM)
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RFEM
The Random Finite Element Method (RFEM) offers many advantages over
conventional probabilistic analysis tool—especially for nonlinear analyses.
-reduced model error: no a priori judgment relating to the shape or
location of the failure surface. The FE analysis “seeks out” the critical
mechanism.
-a “worst case” spatial correlation has been clearly identified for most
geotechnical problems which leads to the highest probability of
failure. We don’t need to know the correlation length.
-allows for the investigation of the affect of site understanding on
design
and code development.
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Degree of Site Understanding
Shallow Foundation Bearing Capacity
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Shallow Foundation Bearing Capacity
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RESISTANCE FACTORS FOR BEARING CAPACITY
Resistance factors can be estimated theoretically;
o for various failure consequence levels (e.g. low, pm=
0.01, or high, pm = 0.0001)
o for various levels of site understanding.
Note the worst case correlation length.
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Earth Pressure Analysis
Active Pressure
Consider a frictional soil where we map tanφ’ onto the mesh (c’=0)
Typical realizations of the Monte-Carlo simulations.
Light zones are low strength and dark zones are high strength 39
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H
Single soil sample at a depth of H/2 and H/2 away from the wall
2
H
2H
Now sample the soil and predict force
on the wall using traditional methods.
Design the factored wall resistance
against sliding to be ˆgu u s aR F Pϕ =
Earth Pressure Analysis
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Estimated probability that the actual active force on wall exceeds the
factored design resistance for a) friction angle and unit weight
independent, and b) friction angle and unit weight strongly
correlated
Earth Pressure Analysis
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Shallow Foundation Settlement
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Shallow Foundation Settlement
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Shallow Foundation Settlement
Various sampling schemes to predict foundation settlement
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Shallow Foundation Settlement
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Deep Foundations
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Deep Foundations
Failure probability as a function of
1. site understanding, r
2. residual variability, cv
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Deep Foundation Resistance Factors
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D = averaging domain under the footing
Q = sampling region
H = depth to bedrock
Parameters Values Considered
Coefficient of variation,
Vc
0.1, 0.2, 0.3, 0.5
Correlation length, θ (m) 0.1, 1.0, 2.0, 3.0, 6.0, 10.0, 50.0
Sampling distance, r (m) 0.0, 4.5, 9.0
Resistance factor, ϕgu 0.4, 0.5, 0.65
Consequence factor, ψu
0.80, 0.85, 0.90, 0.95, 1.00,
1.05, 1.10, 1.15, 1.20
September 21, 2009
Fig. 1 Sampling layout Table 1 Parameters considered
Soil cohesion, c, is assumed to be lognormally distributed
with mean µc=100 kN/m2 , friction angle with mean µc =20o
Consequence Factors for Bearing Capacity
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Target pf
0.93 1.13
September 21, 2009
Fig. 2 Failure probability plot Fig. 3 Failure probability-consequence factor plot
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Consequence Factors for Bearing Capacity
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φgu=0.5
Fig. 5 High failure consequence plot
ψu=0.95
Fig. 6 Low failure consequence plot
ψu=1.15
Fig. 4 Resistance factor plot
September 21, 200951
Consequence Factors for Bearing Capacity
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September 21, 2009
Source Consequence Level
Low Medium High
Recommended 1.15 1.0 0.90
AASHTO (2007) 1.25 1.0 0.91
AS 5100.3 (2004) - 1.0 0.83
Eurocode I (Gulvanessian et al., 2002) 1.11 1.0 0.91
NBCC (2005, snow and wind loads) 1.25 1.0 0.87
NBCC (2005, earthquake loads) 1.25 1.0 0.77
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Consequence Factors for Bearing Capacity
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How to Use Theoretical Results
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SUMMARY
o Geotechnical design codes are migrating towards LRFD/LSD to
allow;
• harmonization with structural codes
• quantification of reliability
o Soil and rock are typically site specific and highly (spatially)
variable. The development of LRFD in geotechnical engineering is a
significant challenge.
o Reliability-based design codes are currently largely developed
through calibration with WSD.
o Design codes should allow for varying degrees of site understanding
and take failure consequence into account.
o Sophisticated probabilistic tools exist to assess risk and develop
required resistance and consequence factors (e.g. RFEM).
o Much work is still required, but efforts are ongoing world-wide.