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ENCE 4610ENCE 4610Foundation Foundation

Analysis and Analysis and DesignDesign

Lecture 21LRFD Methods

AASHTO LRFD Method and Factors

Solving the “Factor of Ignorance” via Probability

• LRFD is an attempt to define that “factor of ignorance” based on probabilistic considerations

• Principal Source: Design and Construction of Driven Pile Foundations, based on AASHTO LRFD Bridge Design Specifications, 7th Edition, 2014, with 2015 Interim.

“It should be remembered, however, that these are not true factors of safety, but include a "factor of ignorance." The author suggests that when the ultimate resistance of any pile has been determined, in fixing the factor of safety...the most unfavorable conditions possible in the supporting strata should be judged (the range of conditions possible being narrowed with better knowledge of the subsurface conditions and of the possibility of disturbance from extraneous sources) and a proportion of the factor of safety -- a "factor of ignorance" -- then allowed in respect to these possible conditions, the manner of determining the ultimate load, and the type of loading to be borne. The remaining proportion of the factor of safety -- or true margin of safety --should be approximately constant for all classes of loading and foundation conditions involving the same value of loss in case of failure; and the overall factor of safety...will then be equal to the product of the true factor of safety with the "factor of ignorance." (David Victor Isaacs, 1931)

From ASD to LRFDFrom ASD to LRFD• Limitations of ASD

– Does not adequately account for variability of loads and resistances. The FS is applied only to resistance. Loads are considered to be without variation (i.e., deterministic).

– Does not embody a reasonable measure of strength, which is a more fundamental measure of resistance than is allowable stress.

– Selection of a FS is subjective, and does not provide a measure of reliability in terms of probability of failure.

• History– Until early 1970’s all civil

engineering design was done using ASD

– Transition for superstructures was complete by mid-1990’s

– Transition to LRFD for substructures began around this time and has continued to the present

Advantages of Challenges of LRFDAdvantages of Challenges of LRFD• Advantages

– Accounts separately for variability in load and resistance prediction

– Achieves more consistent levels of safety in structure and substructure design

– Does not require knowledge of probability or reliability theory

• Challenges– Implementation requires a

change for engineers accustomed to ASD

– Resistance factors vary with design methods and are not constant

– Rigorous calibration of load and resistance factors to meet individual situations requires availability of statistical data and probabilistic design algorithms

LRFD Design ApproachLRFD Design Approach

(usually) 1 ,11

≤∑=

φγ

φγ

i

n

m

iii RQ

Distribution of Load and ResistanceDistribution of Load and Resistance

Empirical Rates of Failure for Civil Empirical Rates of Failure for Civil Works FacilitiesWorks Facilities

Loading for Substructure Loading for Substructure DesignDesign

AASHTO Load Designations

LRFD Equation as Used in LRFD Equation as Used in AASHTO SpecificationsAASHTO Specifications

Limit States and LoadsLimit States and Loads• Strength Limit States

o Involve the total or partial collapse of the structure

o Include bearing capacity failure, sliding and overall instability

• Service Limit Stateso Affect the function of the

structure under regular service conditions

o Include excessive settlement, excessive lateral deflections, and structural deterioration of the foundation or excessive vibration

• For a structure to be sound, Resistance >Effect of the Loads

• Definition of Limit Stateo A condition beyond which a

structural component, such as a foundation or other bridge component, ceases to fulfill the function for which it was designed

Limit States, Limit States, AASHTO AASHTO

SpecificationSpecification

AASHTO Strength and AASHTO Strength and Service Load FactorsService Load Factors

Combination of Loads

Example of Load Factoring

and Combination

Determination of Resistance FactorsDetermination of Resistance Factors• Calibration of

Resistance Factors– Engineering judgment– Fitting to ASD– Reliability theory– A combination of approaches

• Selection of Resistance Factors

– Variability of the soil and rock properties

– Reliability of the equations used for predicting resistance

– Quality of the construction workmanship

– Extent of soil exploration– Consequence(s) of a failure

Resistance Factors

Resistance Factors

LRFD Driven Pile Example

• Given– Loose SM sand, water table 60’

from surface– 14” square concrete pile– Dead Axial Load DD = 150 kips– Live Axial Load LL = 100 kips

• Find– Pile length that will develop

sufficiently large resistance load to meet LRFD requirements

– Settlement at Service I load– Consider Strength I-V cases and

Service I case

LRFD Driven Pile Example

• Resistance Factors– φ= 0.35 (beta method)– Factored Resistance =

362.5/0.35 = 1036 kips• By trial and error, using

TAMWAVE the pile length comes to 130’

LRFD Driven Pile Example

• Service I Load = 250 kips

• Required Resistance = 250/0.35 = 714 kips

• Based on load test, pile head deflection is approximately 1.1”(can be sharpened with linear interpolation)

QuestionsQuestions

Solving the “Factor of Ignorance” via ProbabilityAASHTO Load DesignationsLRFD Equation as Used in AASHTO SpecificationsCombination of LoadsExample of Load Factoring and CombinationResistance FactorsResistance FactorsLRFD Driven Pile ExampleLRFD Driven Pile ExampleLRFD Driven Pile Example