Reliability-based design of Reliability-based design of pile foundationspile foundations

Presented byPresented byDesh Raj SonyokDesh Raj Sonyok

Sittampalam SathiskumarSittampalam Sathiskumar

Department of Civil and Geological EngineeringDepartment of Civil and Geological EngineeringNew Mexico State UniversityNew Mexico State University

12/08/200512/08/2005

Design MethodologiesDesign Methodologies Working or Allowable Stress DesignWorking or Allowable Stress Design (WSD or ASD) (WSD or ASD)

Limit States DesignLimit States Design Ultimate Limit State (Ultimate Limit State (ULSULS): ):

Factored resistance ≥ Factored load effectFactored resistance ≥ Factored load effect

Serviceability Limit State (Serviceability Limit State (SLSSLS):): Deformation ≤ Tolerable deformation to remain serviceableDeformation ≤ Tolerable deformation to remain serviceable

Load and Resistance Factor DesignLoad and Resistance Factor Design (LRFD) (LRFD)

where where RR = resistance and = resistance and QQ = mean load = mean load

FS

Q

FS

RQQ ultnall ==≤

)( QRPPf <=

Eq. (1)Eq. (1)

Eq. (2)Eq. (2)

Reliability Analysis (Reliability Analysis (Kulhawy, 2002)

any design methodology that is firmly founded on a rigorous reliability basis any design methodology that any design methodology that incorporates the principles of incorporates the principles of reliability analysis, either explicitly or reliability analysis, either explicitly or otherwise, is classified as reliability otherwise, is classified as reliability based designbased design..

Geotechnical VariablesGeotechnical Variables

Inherent variabilitiesInherent variabilitiesMeasurement uncertaintiesMeasurement uncertaintiesTransformation uncertaintiesTransformation uncertainties

Uncertainty in soil property estimates Uncertainty in soil property estimates (Kulhawy and Phoon, 2002)(Kulhawy and Phoon, 2002)

Assessment of Reliability:Assessment of Reliability: Normal Random VariableNormal Random Variable

First Order Reliability Method First Order Reliability Method (FORM).(FORM).

Evaluates the probability of failure Evaluates the probability of failure numericallynumerically

Gives good approximate solutions for Gives good approximate solutions for most cases. (Madsen et al., 1986) most cases. (Madsen et al., 1986)

adopted by many authors for calibrating adopted by many authors for calibrating reliability-based design equations reliability-based design equations

Target Probability of Failure, PTarget Probability of Failure, PTT

Prob(Q<F) should be less than or equal to pProb(Q<F) should be less than or equal to pTT

Finding pFinding pTT::

(1) Cost-benefit analysis. (1) Cost-benefit analysis. not practical --- evaluating failure costsnot practical --- evaluating failure costs

(2) Failure rates estimated from actual case (2) Failure rates estimated from actual case histories.histories. No formal system exists for the registration No formal system exists for the registration of failures. (Leonards, 1982)of failures. (Leonards, 1982) (3) A method by Ellingwood, et al. (1980).(3) A method by Ellingwood, et al. (1980).

Applicability of FORM: A case studyApplicability of FORM: A case study Foundation plan for study platforms (W.h.Tang and R.B.Gilbert, 1993)Foundation plan for study platforms (W.h.Tang and R.B.Gilbert, 1993)

Pile yield probabilities Pile yield probabilities (W.h.Tang and R.B.Gilbert, 1993)(W.h.Tang and R.B.Gilbert, 1993)

System collapse probabilities System collapse probabilities (W.h.Tang and R.B.Gilbert ,1993)(W.h.Tang and R.B.Gilbert ,1993)

LRFD MethodLRFD Method

The reliability of any given pile is described by its The reliability of any given pile is described by its probability of failure probability of failure ppf f which is defined as the which is defined as the probability that the resistance is smaller than the probability that the resistance is smaller than the load effect. load effect.

ppf f = = PP( resistance < load effect)( resistance < load effect)

Performance function for substructures:Performance function for substructures:

where Rn = calculated (nominal) resistance; ∅= resistance factor; Qi = nominal load effect; γi = load factor; and η = factor to account for effects of ductility, redundancy, and operational importance

∑≥ iin QR γηφ Eq. (3)Eq. (3)

LRFD Method (contd.)LRFD Method (contd.)Reliability index β associated with the linear performance function can be calculated using the mean value first-order, second moment method (MVFOSM)

where QD and QL = nominal values of dead and live loads, respectively; λR, λQD, and λQL = bias factors for resistance, dead load, and live load, respectively; COVR, COVQD, and COVQL = coefficients of variation for resistance, dead load, and live load, respectively; and FS = factor of safety in the traditional allowable stress design (ASD).

Eq. (4)Eq. (4)

LRFD Method (contd.)LRFD Method (contd.)

The bias factors:The bias factors:

n

mR R

R=λ

where Rm = measured value of resistance. In this study, Rm is taken to be the measured Davisson capacity, whereas Rn is taken to be the predicted capacity by any given prediction method

Eq. (5)Eq. (5)

An isolated single pileAn isolated single pile A pile groupA pile group A pile system connected by A pile system connected by

superstructuresuperstructure

Scales of Pile Foundations

Scales of Pile Foundations

Reliability of Single PilesReliability of Single Piles

Being studied extensively during the past Being studied extensively during the past two decades (Zhang et al. 2001). two decades (Zhang et al. 2001).

forms the basis for the evaluating the forms the basis for the evaluating the reliability of pile groups. (Tang et al. 1990)reliability of pile groups. (Tang et al. 1990)

results of major studiesresults of major studies (Table 1)(Table 1) The overall range of The overall range of ββss obtained by different obtained by different

researchers ranges from researchers ranges from 1.7 to 3.11.7 to 3.1

Reliability statistics of single pileReliability statistics of single pile

Reliability of Driven Pile GroupReliability of Driven Pile Group

Driven piles are Driven piles are most often used in groups and connected to superstructures.

Group effects - the pile-soil cap interaction induced by overlapping of stresses in soil and changes in the density of the soil around the piles due to pile penetration.

System effects - the interaction between groups of piles and the superstructure they support.

Group effects and system effects - may alter significantly the reliability of the foundation.

Pile Group and System EfficiencyPile Group and System Efficiency Pile group efficiency (Pile group efficiency (ξ) : :

- - the ratio of the ultimate capacity of a pile group to the sum of the capacities of individual piles, - a function of pile spacing and group size.

Pile system efficiency (Pile system efficiency (χχ) :) :- the ratio of the load required to bring all the piles in a pile system to - the ratio of the load required to bring all the piles in a pile system to their ultimate computed capacity and the load required to bring most their ultimate computed capacity and the load required to bring most heavily loaded pile to the same state (Bea, 1983). heavily loaded pile to the same state (Bea, 1983).

Pile Group ReliabilityPile Group Reliability

where where λλXX and and λλξξ = bias factors of= bias factors of χχ and and ξξ respectively respectively

COVCOV22RGRG = coefficient of variation of pile group.= coefficient of variation of pile group.

λλXX is the ratio of the true and nominal system factor is the ratio of the true and nominal system factor

λλξξ is the ratio of measured and nominal group is the ratio of measured and nominal group

efficiency factorsefficiency factors

Eq. (6)Eq. (6)

Target Reliability Index Target Reliability Index Contd…Contd…

Zhang et al. (2001): Zhang et al. (2001): ββGG = 2.0 – 4.1 = 2.0 – 4.1 (associated with (associated with

ASD if no system effect)ASD if no system effect)

ββTGTG = 3.0 – 3.5 = 3.0 – 3.5 (may sufficient (may sufficient

for driven pile groups).for driven pile groups).

Barker et al. (1991) and Withiam et al. (1997):Barker et al. (1991) and Withiam et al. (1997):

ββTSTS = 2.0 – 2.5 = 2.0 – 2.5 (for single pile)(for single pile)

Once Once ββTGTG is selected corresponding is selected corresponding ββTSTS for single for single

pile design to achieve the target reliability of the pile design to achieve the target reliability of the pile group can be calculated. pile group can be calculated.

Based on the above literature review, it Based on the above literature review, it seems reasonable to establish the target seems reasonable to establish the target reliability between reliability between 2.02.0 and and 3.0 3.0 for pile groupsfor pile groups and as high as and as high as 3.03.0 to to 3.53.5 for single piles for single piles which is similar to suggested range of which is similar to suggested range of NCHRP (2004) NCHRP (2004)

Target Reliability IndexTarget Reliability Index

Calculated Calculated ββTSTS to Achieve System to Achieve System

Reliability Index of 3.0Reliability Index of 3.0

Note: Dynamic methodNote: Dynamic method

Uncertainties in loading conditions and capacity of the piles influence the reliability of pile foundations.

Reliability-based LRFD is the only methodology that can ensure self-consistency from both physical and probabilistic requirements and is compatible with the theoretical basis underlying structural design

Based on the literature review, it seems reasonable to establish the target reliability between 2.0 and 3.0 for pile groups and as high as 3.0 to 3.5 for single piles.

ConclusionConclusion

Values of the target reliability index βTS for single piles required to achieve a specified target reliability index βTG for pile groups can be calculated for several pile capacity prediction methods.

Both group effects and system effects can result in added reliability of a pile system over that of single piles.

There is a need of further research in the reliability based design for the full range of geotechnical design in order to achieve a rational and practical design solution .

Conclusion Conclusion contd…contd…

Thank you Thank you for for

your attentionyour attention

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