LRFD Calibration of Axially-Loaded Concrete Piles Driven into Louisiana Soils

Transcription

1 LRFD Calibration of Axially-Loaded Concrete Piles Driven into Louisiana Soils Louisiana Transportation Conference February 10, 2009 Sungmin Sean Yoon, Ph. D., P.E. (Presenter) Murad Abu-Farsakh, Ph. D., P.E. Ching Tsai, Ph.D., P.E. Zhongjie Zhang, Ph.D., P.E. Louisiana DOTD and LTRC 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) versus 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 Stress Design Methodologies vs. LRFD Working Stress Design (WSD) also called Allowable Stress Design (ASD), since early 1800s. Q R n Qall = = FS where, Q=design load; Q all = allowable design load; and R n = ultimate resistance of the structure 4

5 Stress Design Methodologies vs. LRFD Limit State Design (LSD), 1950s Ultimate Limit Stress (ULS) Factored resistance Factored load effects Service Limit Stress (SLS) Deformation Tolerable deformation to remain serviceable 5

6 Stress Design Methodologies vs. LRFD Load and Resistance Factor Design (LRFD) φr r Q + r Q = rq n D D L L i i where, Φ=resistance factor, R n =ultimate resistance; γ D =load factor for dead load; γ L =load factor for live load; γ i =corresponding load factor, and Q i =summation of load 6

7 Reliability Based FS 7

8 Working Stress Design (WSD) vs. LRFD 8

9 Limit State Function Limit State Function can be defined as g = R Q 9

10 Reliability Index, β f(g) = probability density of g g µ R µ Q β = = σ σ + σ 2 2 g R Q βσ g β: reliability index P f = shaded area 0 ln R ln Q = g g 10

11 Relationship between β and P f P f β

12 Reliability Index, β β1 β2 β Distance Overlapped area Probability of failure Design φ Pile Size β1 Short β2 Large 12

13 Reliability Index, β β1 β2 β Distance Overlapped area Probability of failure Design φ Pile Size β1 Short Large β2 Large Small 13

14 Reliability Index, β β1 β2 β Distance Overlapped area Probability of failure β1 Short Large High β2 Large Small Low Design φ Pile Size 14

15 Reliability Index, β β1 β2 β Distance Overlapped area Probability of failure Design φ β1 Short Large High Large β2 Large Small Low Small Pile Size 15

16 Reliability Index, β β1 β2 β Distance Overlapped area Probability of failure Design φ Pile Size β1 Short Large High Large Small β2 Large Small Low Small Big 16

17 How to Treat Uncertainty 1 2 Graph Variability Overlapped area Probability of failure Calculated φ Pile Size

18 How to Treat Uncertainty 1 2 Graph Variability Overlapped area Probability of failure Calculated φ Pile Size 1 Low 2 High 18

19 How to Treat Uncertainty 1 2 Graph Variability Overlapped area Probability of failure Calculated φ Pile Size 1 Low Small 2 High Large 19

20 How to Treat Uncertainty 1 2 Graph Variability Overlapped area Probability of failure 1 Low Small Low 2 High Large High Calculated φ Pile Size 20

21 How to Treat Uncertainty 1 2 Graph Variability Overlapped area Probability of failure Calculated φ 1 Low Small Low Large 2 High Large High Small Pile Size 21

22 How to Treat Uncertainty 1 2 Graph Variability Overlapped area Probability of failure Calculated φ Pile Size 1 Low Small Low Large Small 2 High Large High Small Big 22

23 Benefits of LRFD Improved reliability More rational and rigorous treatment of uncertainties in design Improved design and construction process (sub and super structures) 23

24 First Order Second Moment (FOSM) Load and Resistance Factor Design (LRFD) φr r Q + r Q = rq n D D L L i i (1) where, Φ=resistance factor, R n =ultimate resistance; γ D =load factor for dead load; γ L =load factor for live load; γ i =corresponding load factor, and Q i =summation of load 24

25 First Order Second Moment (FOSM) β = ln λ R FS λ DL Q Q ln DL DL Q Q LL LL λ 2 2 [( 1+ COV )( 1+ COV + COV )] 2 R LL 1+ COV DL 2 R + COV 1+ COV LL 2 DL 2 R + COV 2 LL (2) Combining eq (1) and (2) using R n φ = λ QD Q Q D L Q D λ R γ D + γ Q L + λ QL exp β T L 2 1+ COVQD + COV 1+ COV [( 1+ COV )( 1+ COV + COV )] ( ) ln R λ QD, λ QL = dead and live load bias factors AASHTO LRFD specification (1994) λ R = resistance bias factors = R m /R p λ QD =1.08, λ QL =1.15, r D =1.25, r L =1.75, COV QD =0.13, COV QL = R 2 QL QD QL 25

26 Statistical Methods for LRFD Calibration First Order Second Moment (FOSM) method: Linearization of limit state function by expanding Taylor series expansion First Order Reliability Method (FORM): Transformation of variables into the standardized and uncorrelated normal variables using the Hosofer-Lind Transformation Monte Carlo Simulation Method: Extrapolate CDF for each random variable using random number generator 26

27 Pile Load Test Database (Ultimate Capacity for Driven Piles) Square PPC Pile Size (mm) Friction Pile Type End- Bearing Predominant Soil Type Cohesive Cohesionless Limit of Informa -tion Total

28 Methods used in LADOTD (Ultimate Capacity for Driven Piles) Static method α - method - for cohesive soil (Tomlison 1979) Nordlund method for sand inter-layers CPT method Schmertmann, LCPC, De Ruiter and Beringen Dynamic Measurement CAPWAP Measured Ultimate Pile Capacity Butler-Hoy Method Davisson Method 28

29 Davisson (Interpretation of Pile Load Tests) Static Load Test Results 0.15+D/ Load (Tons) Q ult 0.50 L/AE 1 Settlement (in)

30 Pile Capacity from Soil Borings (Static Method) Shaft Friction Capacity Cohesive soils clays (α-method, Tomlinson) Q s L = 0 f C d dz where f = clay adhesion = α S u Non-cohesive soils sands and silts (Nordlund method) Q s L = K δ 0 C f P D sin( δ).c End Bearing Capacity Cohesive soils clays (α-method, Tomlinson) Q b = A. S. N d dz where A b = cross sectional area, N c = 9 Non-cohesive soils sands and silts (Nordlund method) Q = A.q. α. N b b b u c q 30

31 Ultimate Pile Capacity Q ult = Q tip + Q shaft f Shaft friction Capacity, Q shaft = Σf i. A si End-bearing Capacity, Q tip = q t. A t q t 31

32 Cone Penetration Test (CPT/PCPT) Penetration Rate = 2 cm/s Base area = 10 cm 2 Sleeve area = 150 cm 2 Cone angle = 60 o U 3 f s U 1 U 2 q c 32

33 Cone Penetrometer Versus Pile Due to similarity between the cone and pile, the cone can be considered as a simple mini pile. Q ult f s f s can be correlated to f, q c can be correlated to q t. f q c q t 33

34 Typical PCPT Test Results Tip Resistance (MPa) Sleeve Friction (MPa) Rf (%) Pore Pressure (MPa) u 2 u Tip Depth (m) U 3 f s Base U 1 U 2 q c R f = f q s c % 16 34

35 Schmertmann method (CPT) Cone resistance q c where, q t : unit bearing capacity of pile f: unit skin friction α c : reduction factor (0.2 ~ 1.25 for clayey soil) f s : sleeve friction Depth D e? q t = q c1 q c1 + q c2 2 8D 'x' Envelope of minimum q c values c a q b c2 b yd 35

36 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 Depth a a q c qeq (side)/ f = < k k s = 30 to 150 s f max q eq 36

37 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 = β.su(side) β = 1 for NC clay = 0.5 for OC clay In sand q t similar to Schmertmann method f = min fs (sleeve friction) qc ( side ) / 300 ( compression ) qc ( side ) / 400 ( tension) 1. 2 TSF 37

38 Implementation into a Computer Program Louisiana Pile Design by Cone Penetration Test 38

39 Predicted vs. Measured Ultimate Pile Resistances Predicted pile capacity, R P (tons) R Fit = 0.96 * R m R 2 = 0.87 Predicted pile capacity, R P (tons) R Fit = 1.12 * R m R 2 = Measured pile capacity, R m (tons) Measured pile capacity, R m (tons) (a) Static analysis method (b) Schmertmann method 39

40 Predicted vs. Measured Ultimate Pile Resistances Predicted pile capacity, R P (tons) R Fit = 1.07 * R m R 2 = 0.81 Predicted pile capacity, R P (tons) R Fit = 0.91 * R m R 2 = Measured pile capacity, R m (tons) Measured pile capacity, R m (tons) (c) LCPC method (d) De Ruiter& Beringen method 40

41 Predicted vs. Measured Ultimate Pile Resistances Predicted pile capacity, R P (tons) R Fit = 0.32 * R m R 2 = 0.69 Predicted pile capacity, R P (tons) R Fit = 0.92 * R m R 2 = Measured pile capacity, R m (tons) Measured pile capacity, R m (tons) (e) CAPWAP-EOD (f) CAPWAP-14 days BOR 41

42 Evaluation of Different Prediction Methods Pile Resistance Prediction Method No. of cases Arithmetic calculations R m /R p R p /R m Best fit calculations Mean σ COV Mean R fit /R m R 2 Static method Schmertmann method LCPC method De Ruiter& Beringen method CAPWAP-EOD CAPWAP-14 days BOR

43 Distribution of Bias (Static Analysis) Static Method Static Method Probability (%) Log-Normal Distribution Normal Distribution Standard Normal Variable, z Bias, X measured bias value predicted normal dist. predicted lognormal dist. from normal stat. R m / R P 43

44 Distribution of Bias (Schmertmann Method) Schmertmann Method Schmertmann Method Probability (%) Normal Distribution Log-Normal Distribution Standard Normal Variable, z Bias, X measured bias value predicted normal dist. predicted lognormal dist. from normal stat. R m / R P 44

45 Distribution of Bias (LCPC method) LCPC Method LCPC Method Probability (%) Log-Normal Distribution Normal Distribution Standard Normal Variable, z Bias, X measured bias value predicted normal dist. predicted lognormal dist. from normal stat. R m / R P 45

46 Distribution of Bias (De Ruiter& Beringen Method) De Ruiter Method De Ruiter& Beringen Method Probability (%) Log-Normal Distribution Normal Distribution Standard Normal Variable, z Bias, X measured bias value predicted normal dist. predicted lognormal dist. from normal stat. R P / R m 46

47 CAPWAP - Dynamic Analyses CAPWAP (EOD) Method 25 CAPWAP (BOR) Method Probability (%) Log-Normal Distribution Normal Distribution Probability (%) Log-Normal Distribution Normal Distribution R m / R P EOD R m / R P 14 days BOR 47

48 Resistance Factors, φ (Static analysis) 1.5 φ (Static Analysis) β T 48

49 Resistance Factors, φ (Direct CPT Methods) 1.5 φ (Direct CPT Methods) Schmertmann LCPC DeRuiter&Beringen β T 49

50 Resistance Factors, φ (CAPWAP-BOR) 1.5 φ (CPT CAPWAP-BOR Analysis) β T 50

51 Resistance Factors, φ (β T =2.33) using FOSM Design Method Resistance Factor, φ Proposed for soft soil AASHTO Efficiency Factor (φ/λ) Proposed for soft soil Static Method α-tomlinson method and Nordlund method Direct CPT Method Dynamic measurement Schmertmann LCPC/LCP 0.56 NA 0.52 De Ruiter and Beringen 0.68 NA 0.55 CAPWAP (EOD) 1.31 NA 0.36 CAPWAP (14 days BOR)

52 Comparison of Resistance Factors, φ (β T =2.33) using FOSM, FORM and M-C Design Method Resistance Factor, φ FOSM FORM M-C Static Method α-tomlinson method and Nordlund method Direct CPT Method Dynamic measurement Schmertmann LCPC/LCP De Ruiter and Beringen CAPWAP (EOD) N/A CAPWAP (14 days BOR)

53 Conclusions Preliminary resistance factors (φ) for Louisiana soil were evaluated for different driven pile design methods Statistical analyses comparing the predicted and measured pile resistances were conducted to evaluate the performance of the different pile design methods. LRFD in deep foundation can improve its reliability due to more balanced design. More statistical data is needed for more rational resistance factor. 53

54 Issues Load sharing and overall redundancy Reduced φ to reflect increased β Site variability Based on the filed and laboratory testing Resistance factor and number of static load test needed Scour 54

55 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. 55

56 THANK YOU! Sungmin Sean Yoon LADOTD 56