LRFD Application in Driven Piles (Recent Development in Pavement & Geotech at LTRC)

Transcription

1 LRFD Application in Driven Piles (Recent Development in Pavement & Geotech at LTRC) 2007 Louisiana Transportation Engineering Conference February 12, 2007 Sungmin Sean Yoon, Ph. D., P.E. and Murad Abu-Farsakh, Ph. D., P.E. 1

2 Outline Problem statement Different design methods Statistical concept Methods used in LADOTD for driven piles LRFD calibration Conclusion 2

3 Problem Statement and Research Objectives Working Stress Design (WSD), Allowable Stress Design (ASD) vs. LRFD Bridge super structures vs. Foundation Federal Highway Administration and ASSHTO set a transition date of October 1, 2007 Resistance Factor (Φ) reflecting Louisiana soil and DOTD design process 3

4 Calibration of the Design Code for Bridge Substructure Identify the load and resistance parameters for bridge substructure Formulate the limit state functions Develop the reliability analysis procedure and calculate reliability indices Select the target reliability index Determine the load and resistance factors for bridge substructure (including earth pressure related loads) 4

5 Stress Design Methodologies vs. LRFD Working Stress Design (WSD) also called Allowable Stress Design (ASD) Q Q all R where, Q=design load; Q all =allowable design load; R n =resistance of the structure, and Q ult =ultimate resistance of the structure n FS Q ult FS 5

6 Stress Design Methodologies vs. LRFD Limit State Design (LSD) Ultimate Limit Stress (ULS) Factored resistance Factored load effects Service Limit Stress (SLS) Deformation Tolerable deformation to remain serviceable 6

7 Stress Design Methodologies vs. LRFD Load and Resistance Factor Design (LRFD) R r Q r Q rq n D D L L i i where, Φ=resistance factor, R n =ultimate resistance; r D =load factor for dead load; r L =load factor for live load; r i =corresponding load factor, and Q i =summation of load 7

8 Working Stress Design (WSD) vs. LRFD 8

9 Random Variation Load and resistance parameters are random variables Reliability index is a measure of structural performance Practical procedure for calculation of the reliability indices Target reliability index Load and resistance factors that result in design that is close to the target reliability index 9

10 Statistical Concept Mean (μ) and Mode Variance (σ 2 ) and Standard Deviation (σ) ( x 2 i x) n 1 Coefficient of Variation (COV) COV 2 Probability Density Function (PDF) 10

11 Limit State Function Limit State Function can be defined as g = R Q 11

12 Reliability Index, g R Q 2 2 g R Q 12

13 Reliability Based FS Capacity = R Load effect = Q FS design load design capacity 13

14 Relationship between and P f P f

15 First Order Second Moment (FOSM) 1 Load and Resistance Factor Design (LRFD) R r Q r Q rq n D D L L i i where, Φ=resistance factor, R n =ultimate resistance; r D =load factor for dead load; r L =load factor for live load; r i =corresponding load factor, and Q i =summation of load 15

16 First Order Second Moment (FOSM) 2 Rn rdq D rlq L rq (1) i i (2) Combining eq (1) and (2) using R n AASHTO (1994) 16

17 Methods used in LADOTD (Ultimate Capacity for Driven Piles) Static method α method - General adhesion for cohesive soil (Tomlison 1979) Nordlund method CPT method Schmertmann, LCPC, de Ruiter and Beringen Dynamic Analysis GRL WEAP Dynamic Measurement CAPWAP Measured Ultimate Pile Capacity Davisson, Butler-Hoy 17

18 Settlement (in) Davisson (Interpretation of Pile Load Tests) Static Load Test Results Load (Tons) Q ult = QL/AE x = D/120 (in)

19 Settlement (in) Butler-Hoy (Interpretation of Pile Load Tests) Static Load Test Results Load (Tons) Q ult Slope = 0.05 in./ton 19

20 Cone Penetration Test (CPT) Method Penetration Rate: 2 cm/sec Sleeve friction, fs Tip resistance, qc 20

21 Ultimate Pile Capacity from CPT Q ult = Q tip + Q shaft f Shaft friction Capacity, Q shaft = f i. A si End-bearing Capacity, Q tip = q t. A t q t 21

22 Depth Schmertmann method (CPT) Cone resistance q c where, q t : unit bearing capacity of pile f: unit skin friction c: reduction factor (0.2 ~ 1.25 for clayey soil) f s : sleeve friction D e? q t = q c1 q c1 + q c2 8D 2 'x' Envelope of minimum q c values c a q b c2 b yd 22

23 Depth LCPC method (CPT) D Pile a=1.5 D 0.7q ca q ca 1.3q ca q t = k b q eq (tip) k b = 0.6 clay-silt sand-gravel q c a a f q eq (side)/ k k s = 30 to 150 s f max q eq 23

24 de Ruiter and Beringen (CPT) In clay S u (tip) = q c (tip) / N k N k = 15 to 20 q t = N c.s u (tip) N c = 9 f =.Su(side) = 1 for NC clay = 0.5 for OC clay In sand q t similar to Schmertmann method f min f q q s c c ( side ) / ( side ) / 1. 2 TSF (sleeve friction) ( compression ) ( tension) 24

25 Implementation into a Computer Program Louisiana Pile Design by Cone Penetration Test 25

26 Probability (%) Probability density function Probability (%) Probability density function Histograms De Ruiter & Beringen method LCPC method R n / R m R n / R m Schmertmann method - method R n / R m R n / R m 26

27 Resistance factor, Resistance Factors, (Davisson) LCPC method Schmertmann method - ststic method Ratio of dead load to live load (Q D /Q L ) 27

28 Resistance factor, Resistance Factors, (Butler-Hoy) LCPC method Schmertmann method - ststic method Ratio of dead load to live load (Q D /Q L ) 28

29 Resistance Factors, T=2.5 Load Test Interpretation Method Pile Capacity Prediction Method Span Length 30 ft 90 ft α-method Davisson LCPC Schmertmann De Ruiter α-method Butler-Hoy LCPC Schmertmann De Ruiter

30 Conclusions Tentative resistance factors ( ) for Louisiana soil were evaluated for different driven pile design methods (Research is on going). Values of resistance factor depend on the pile load test interpretation and design methods. LRFD in deep foundation can improve its reliability due to more balanced design. There is a strong need for more statistical data to get more rational resistance factor. 30

31 LRFD Implementation in Louisiana Dr. Ching Tsai Wednesday 10:00-11:45 a.m. Session 83: Geotechnical Services Meeting Room 3 31

32 Acknowledgement The project is financially supported by the Louisiana Transportation Research Center and Louisiana Department of Transportation and Development (LA DOTD). LTRC Project No. 07-2GT. 32

33 References Paikowsky, S.G TRB presentation. Bea, Robert G presentation Nowak, Andrzej S TRB presentation. Mayne, Paul W. < NCHRP report 507: Load and Resistance Factor Design (LRFD) for Deep Foundation. 33

34 THANK YOU! Sungmin Sean Yoon LTRC 34