LRFD Calibration and Implementation of Strength and Serviceability Limit States Review of Research and Lessons Learned

Transcription

1 Safety Concepts and Calibration of Partial Factors in European and North American Codes of Practice LRFD Calibration and Implementation of Strength and Serviceability Limit States Review of Research and Lessons Learned Workshop 30/11 01/12/2011 Delft University of Technology, Delft, The Netherlands Samuel G. Paikowsky Geotechnical Engineering Research Laboratory Dept. of Civil and Environmental Engineering University of Massachusetts Lowell, USA November 30, 2011 Geosciences Testing & Research, Inc. (GTR) North Chelmsford, Massachusetts USA

2 Table of Contents 1 DESIGN PRACTICE Codes in the USA Limit State Design 2 DESIGN METHODOLOGIES Review Working Stress Design Uncertainties Structural and Geotechnical Designs 3 LOAD AND RESISTANCE FACTOR DESIGN (LRFD) Principles Target Reliability Probability of Failure LRFD For Deep Foundations 4 LRFD Deep Foundation Design Report - NCHRP 507 Dynamic Analyses of Piles Framework Databases Static Analysis of Driven Piles Dynamic Analysis of Driven Piles Static Analysis of Drilled Foundations

3 Table of Contents 5 LRFD Shallow Foundations Design Report - NCHRP 651 Databases Uncertainty of Vertical Centric Loading Source of Uncertainty Investigation of Nγ Development of Resistance Factors Eccentric and/or inclined Loading Resistance Factors for Controlled and Naturally Deposited Soils Shallow Foundations on Rock 6 LRFD Serviceability Limit State Design Report NCHRP Example Case History

4 1 DESIGN PRACTICE

5 1 DESIGN PRACTICE Codes Code Any systematic collection of regulations and rules of procedure or conduct. Importance Standardization Recognition of methods and procedures

6 1 DESIGN PRACTICE Codes in the USA Every state in the USA has a building code which is part of the state s laws. In addition, the Department of Transportation (a.k.a. Highway Department) of the state has its own specifications. A united code (IBC International Building Code) was developed in 2000 by uniting several previous codes (UBC Uniform Building Code and SBC Standard Building Code). Forty-four states (88%) adopted the IBC as their building code.

7 1 DESIGN PRACTICE Codes in the USA The construction of most bridges (all highway bridges) is funded primarily by the Federal Government via FHWA. These structures are obliged to be designed by the AASHTO specifications - (American Association of State Highway Transportation Officials). The AASHTO specifications are traditionally observed on all federally aided projects and generally viewed as a national code of US Highway practice, hence influencing the construction of all the foundations of highway bridges throughout the USA

8 1 DESIGN PRACTICE Codes in the USA The AASHTO Specifications, as well as most advanced codes worldwide, moved to RBD Reliability Based Design. The LRFD Load and Resistance Factor Design format of RBD is used by the AASHTO specifications since The major developments relevant to foundation design will be presented some had been implemented.

9 1 DESIGN PRACTICE Limit State Design (LSD) was initiated in the 1950 s for a more economical design. A design of a structure needs to ensure that while being economically viable it will suit the intended purpose during its working life. LS Limit State Condition beyond which the structure or a component fail to fulfill in some way the intended purpose for which it was designed. ULS Ultimate Limit State deals with strength (maximum loading capacity) of the structure / element. (aka Strength Limit State) SLS Serviceability Limit State deals with the functionality and service requirements of a structure to ensure adequate performance under expected conditions. e.g. - Relevance to Foundations: By and large axial loading of piles is controlled by ULS and lateral loading by SLS.

10 1 DESIGN PRACTICE Limit State Requirements Satisfying Limit States: Ultimate Limit State (ULS) Factored resistance Factored load effects Serviceability Limit State (SLS) Factored Deformation Tolerable deformation to remain serviceable

11 2 DESIGN METHODOLOGIES

12 2 DESIGN METHODOLOGIES Review Working Stress Design STATE OF STRESS DESIGN Working stress design (WSD) also called the Allowable Stress Design (ASD) method, has been used in Civil Engineering since the early 1800s. Q Q all = R n / FS = Q ult / FS Q = Design load (F) Q all = Allowable load (F) R n = Q ult = Nominal Resistance = Ultimate geotechnical foundation force resistance FS = Factor of safety The factor of safety is commonly defined as the ratio of the resistance of the structure (R n ) to the load effects (Q) acting on the structure.

13 2 DESIGN METHODOLOGIES Review - Working Stress Design ADVANTAGES Simple Vast Experience Serves as a Reference LIMITATIONS Lumps all uncertainty into a factor of safety Does not provide a direct evaluation of whether a method is conservative or unconservative

14 2 DESIGN METHODOLOGIES Review - Working Stress Design Factor Of Safety On Ultimate Axial Geotechnical Capacity Based On Specified Construction Control (AASHTO 1997 Standard Specifications) X - Construction Control Increasing Construction Control Specified on Plans Subsurface Exploration X X X X X Static Calculation X X X X X Dynamic Formula X Wave Equation X X X X CAPWAP Analysis X X Static Load Test X X Factor of Safety (FS) * 1.90 * Any combination that includes a static load test Design Capacities Specified on Plans so FS can be Adjusted if Construction Control is Altered

15 2 DESIGN METHODOLOGIES Review - Working Stress Design Comments 1. On the face of it logical and progressive but on what basis are the specifications founded? Is the control method F.S. suitable for the design method? 2. Rewards the use of quality control through dynamic measurements during driving and/or static load-testing. 3. Very Generic Does not provide any details regarding the methods. e.g.: What kind of subsurface investigation? What kind of static analysis? Dynamic Measurements - When? (EOD, Restrike?) On what kind of piles? Driving conditions? What about field interpretation? Can be examined and/or explained only against actual data.

16 2 DESIGN METHODOLOGIES Review - Working Stress Design SIMPLE EXAMPLE Assume a load of 200 tons and Pile Capacity Q ult = 100 tons (accurately predicted by all methods, i.e.bias = 1.0) Capacity Evaluation Method F.S. Load per Pile (tons) # of Piles Savings Static Analysis WEAP % CAPWAP % Static L.T %

17 2 DESIGN METHODOLOGIES Review - Working Stress Design Evaluation of Parameters Static Analysis of Driven Piles In Clay No. of cases and Mean of Prediction (msd. Over calculated using data ± 2 SD) (1/0.8 = 1.25) Actual Mean FS for driven piles in clay α Methods = 0.82 x 3.5 = 2.87 λ Method = 0.72 x 3.5 = 2.52 For Comparison FS for the Dynamic Methods CAPWAP - BOR 162 Mean = 1.16 Actual FS BOR = 1.16 x 2.25 = 2.61

18 2 DESIGN METHODOLOGIES Review - Working Stress Design Revisit Simple WSD Example Assume a load of 200 tons and Pile Capacity Q ult = 100 tons (Specifying now a concrete pile in clay and using the bias known for the methods) Capacity Evaluation Method F.S. (Load) Load per Pile - ton (w/o bias) # of Piles (w/o bias) Savings (w/o bias) Static Analysis α API Clay 3.50 on 123t 35.3 (28.6) 5.7 (7) - WEAP EOD CAPWAP BOR Static L.T on 60t 2.25 on 86t 2.00 on100t 22.0 (36.4) 38.4 (44.4) 9.1 (5.5) 5.2 (4.5) (values in original example ignoring the bias) +60% (-21%) -9% (-36%) -30% (-43%)

19 2 DESIGN METHODOLOGIES Review - Working Stress Design INTERMEDIATED CONCLUSION 1. The examination of factors of safety on the basis of their absolute values is misleading and do not represent the economical value of a specific method. 2. The same holds for any other design method e.g resistance factors for LRFD as will be shown. 3. Only the use of an actual database provides the bias of a design method and hence allows for a rational development of safety margins regardless of the design methodology.

20 Uncertainties - Structural Design Simplified Example of Beam Design and Sources of Uncertainty loading A = B = ql 2 A l B q shear Sources of Uncertainty 1. Loading 2. Dimensions 3. Material Properties y max y 4 5 ql 5 σ = = 384 EI 24 E max 2 l h moment ql M max = 8 deflection (Assuming homogenous crosssection, horizontal symmetry line and beam height, h.) 2 Most Noticeable: 1. No uncertainty in the model under given loading conditions the uncertainty in the material properties (i.e. yield) dictates the uncertainty in strength or uncertainty in Modulus E will dictate the uncertainty in the deflection 2. Largest uncertainty in the loading, source, magnitude, distribution (in case of bridges)

21 Uncertainties - Geotechnical Design Components of Foundations Design and Sources of Uncertainty Soil sampling and testing for engineering material parameters Analysis Model Method of Approach LOAD Use the load uncertainty from the structures (until better research is done) Assumed Failure Pattern under Foundations Uncertainty in the assumptions made in the model development leaves unknown analysis versus actual performance RESISTANCE Establish the uncertainty of the complete foundation capacity analysis by comparing a design procedure to measured failure. Loading Uncertainty due to site, material and testing variability and estimation of parameters Code of practice FOUNDATION DESIGN Traditional design although developed over many years and used as a benchmark has undocumented unknown uncertainty Uncertainty in loads created by and applied to the bridge, e.g. Dead Load e.g. weight of the bridge Live Load e.g. traffic and its effects (e.g. breaking) Wind & wind on traffic Extreme Events e.g. earthquake, ship collision

22 2 DESIGN METHODOLOGIES Uncertainties - Geotechnical Design Significant uncertainties exist in: (1) The process of defining geomaterial properties. (2) The calculation model. Defining uncertainty in the soil properties alone is therefore not sufficient in most cases to determine the uncertainty of the designed element/structure. The relationship between loads and displacements requires a separate model having its own uncertainty.

23 3 LOAD AND RESISTANCE FACTOR DESIGN (LRFD)

24 3 LRFD DESIGN LRFD for Foundations Principles The design of a foundation depends upon predicted loads and the capacity to resist them. Both loads and resistance (capacity) have various sources and levels of uncertainty that historically have been compensated for by experience and subjective judgment. These uncertainties can be quantified using probability-based design, or safety check expressions, aimed at achieving designs with consistent levels of reliability. The intent of the Load and Resistance Factor Design (LRFD) method is to separate uncertainties in loading from uncertainties in resistance and to assure a prescribed margin of safety.

25 3 LRFD DESIGN Probability Density Functions for Load and Resistance Q FS = R/Q Q n Load Effect (Q) Q, R Mean Load/Resistance. f R (R), f Q (Q) R n R Resistance (R) Q n, R n Nominal Load/Resistance consistent levels of reliability R, Q An illustration of probability density functions for load effect and resistance

26 Relationship Between Reliability Index and Target Reliability Reliability Index β 3 LRFD DESIGN Target Reliability Probability of Failure Probability of Failure p f E -4 Reliability is expressed using the reliability index, β, which is the number of standard deviations of the derived PDF of the limit state function g, (g = R Q) E E E E -5 An Illustration of a Combined Probability Density Function (g(r,q)) Representing the Margin of Safety and the Reliability Index, β (σg = Standard Deviation of g).

27 3 LRFD DESIGN LRFD FOR DEEP FOUNDATIONS For the strength limit state: R r = Factored resistance (F or F/A); φ = Resistance factor (dimensionless); R n = Nominal (Ultimate) resistance (F or F/A); η = Factors to account for ductility (η D ), redundancy (η R ), γ i 1994, 1 st. AASHTO LRFD Bridge Design Specs for Foundations R r = φr η η γ Q n i i and operational importance (η I ) Structural (dimensionless) = Load factor (dimensionless); Q i = Force effect, stress or stress resultant (F or F/A);

28 4 LRFD Deep Foundations Design

29 4 LRFD Deep Foundations Design Research Project NCHRP An extensive development of resistance factors for the AASHTO specifications of Deep Foundations was undertaken under NCHRP project and presented in NCHRP Report 507. These factors were developed based on large databases examining the deep foundations capacity prediction methods during design and construction. Google Search: NCHRP 507 will bring you to the pdf

30 4 LRFD Deep Foundations Design Research Team Massachusetts Group Samuel G. Paikowsky, PI Kirk Stenersen Kevin O'Malley Les Chernauskas Maryland Group Gregory Baecher Bilal Ayyub David Schelling Florida Group Michael McVay Ching Kuo Bjorn Birgisson Thai Nguyen Consultants James Withiam Michael O'Neill 30

31 4 LRFD Deep Foundations DESIGN Framework For The Development Of The Resistance Factors In NCHRP 507 R r φ Q Q n γ = Rn iqi REQUIRED INFORMATION Distribution of Load - Type, Mean, SD Distribution of Resistance Type, Mean, SD Probability of Failure Load Effect (Q) POSSIBLE SOURCES f R (R ), f Q (Q ) R n R Resistance (R) Distribution of Load Measurements on and Analyses of Structures e.g. Vehicles on a Bridge Distribution of Resistance Databases, Related Correlations - e.g. Soil Parameters, Judgment R, Q Probability of Failure Observations, Judgment, Probabilistic Theory

32 4 LRFD Deep Foundations DESIGN Framework For Calibration Required And Sources of Information Required Information Sources of Information Load Combination AASHTO Strength I DL & LL Load Factors γ D = 1.25 γ L = 1.75 Type Lognormal Distribution of Load Mean λ QD = 1.05 λ QL = 1.15 COV COV QD = 0.1 COV QL = 0.2 Nature of Resistance Geotechnical Axial resistance Distribution of Resistance Database Analysis Probability of Failure Review Available Literature/Develop

33 4 LRFD Deep Foundations DESIGN Databases Main Analyses: Driven Piles Static Analyses piles Drilled Shafts Static Analyses shafts Driven Piles Dynamic Analyses cases on 210 piles Peripheral Analyses: Static Load Test Interpretation DP piles Static Load Test Interpretation DS - 44 shafts Influence of Loading Rate - 75 piles Dynamic Measurements both EOD cases on 228 piles & BOR (without Static Load Test) WEAP (GRL Database) - 99 piles Case Method (Florida Study): EOD - 40 piles BOR - 37 piles

34 4 LRFD Deep Foundations DESIGN Calculated Resistance Factors Target Reliability (probability of exceedance = Probability of failure) Efficiency Factor Calibration Methods 34

35 4 LRFD Deep Foundations DESIGN Redundant vs. Non Redundant NCHRP 507 Recommendations β = 3.00 P f = 0.1% β = 2.33 P f = 1.0% Non - Redundant Logically Non - Redundant Redundant 35

36 4 LRFD Deep Foundations DESIGN Development of Resistance Factors NCHRP 507 Used two Calibration Methods: 1. FOSM First Order Second Moment The first version of the AASHTO specifications utilized First-Order, Second-Moment (FOSM) principles, assuming lognormal distribution for the resistance and bias factors, closed form relations were established (Barker et al., 1991). 2. FORM First Order Reliability Method FORM provides a means for calculating resistance and load factors φ and γ against a target reliability level β using an iterative process. 3. Comments All current calibrations are using MC simulations Always practical to compare to FOSM (Mostly on the conservative side for foundations Strength LS by about 10%) 36

37 4 LRFD Deep Foundations DESIGN Design Method Efficiency Resistance Factor Over Bias- φ/λ v 2.5 Resistance Factor (φ) FOSM λ QL = 1.15 λ QD = 1.05 COV QL = 0.2 COV QD =0.1 QD/QL = 2.5 β = 2.33 γ D = 1.25, γ L = 1.75 COV = COV = Bias (λ) Figure 15. Calculated resistance factors as a function of the bias and COV for the chosen load distributions and DD/LL ratio of Efficiency (φ/λ) FOSM λ QL = 1.15 λ QD = 1.05 COV QL = 0.2 COV QD = 0.1 Q D /Q L = 2.5 β = 2.33 γ D = 1.25 γ L = COV R Figure 16. Illustration of the efficiency factor as a measure of the effectiveness of a design method when using resistance factors. 37 Efficiency-Resistance factor.grf

38 4 LRFD Deep Foundations DESIGN Calculated and Recommended Resistance Factors Static Analyses Driven Piles Dynamic Analyses Driven Piles Static Analyses drilled shafts

39 4 LRFD Deep Foundations DESIGN DATABSE - Initial Relevant Analyses I Interpretation of Static Capacity Establish a Unique Failure Criterion as a Reference Static Capacity for the Calibrations of the static and dynamic analyses. Analysis of 196 Driven Pile Load Tests to failure Approach using 5 interpretation methods II Influence of Load Test Procedure Examining two detailed case histories of the Newbury Test Site. Examining the UML/Ukraine Database of 75 cases comparing slow maintained and static-cyclic load test results.

40 4 LRFD Deep Foundations DESIGN Static Analyses of driven Piles Summary of Methods Method Side resistance Tip resistance α-tomlinson (Tomlinson, 1980/1995) α-api (Reese et al., 1998) β in cohesive (AASHTO, 1996/2000) λ (US Army Corps of Engineers, 1992) β in cohesionless (Bowles, 1996) Nordlund and Thurman (Hannigan et al., 1995) Meyerhof SPT (Meyerhof, 1976/1981) SPT 97(Lai and Graham, 1995) FHWA CPT (McVay and Townsend, 1989) q q s = αs u q s = βσ q s = λ(σ +2S u ) s = Kδ CF DATABSE - Analyses q p = 9 S u Parameters required S u ; D b (bearing embedment) S u OCR βσ D r sin( δ + ϖ ) σ ' cosϖ q s = k N q p = α t N q σ q p = 0.4D/BN S u φ N Constraints +Bearing layer must be stiff cohesive + Number of soil layers 2 Only for cohesive soils + For cohesionless soils + SPT data q s = function(n) q p = fn(n) N SPTdata q s = function(f s ) q p = fn(q c ) q c, f s CPT data Specific Correlations were provided for soil parameters Interpretations 40

41 4 LRFD Deep Foundations DESIGN DATABSE - Analyses The performance of driven piles static analysis methods log-normal distribution Histogram & Frequency Distributions for 52 Cases of All Pile Types (Concrete, Pipe, H) in Clay Using α - API Method Number of Pile-Cases m lnx = σ lnx = m x = normal distribution σ x = Relative Frequency Ratio of Static Load Test Results over the Pile Capacity Prediction using the α-api method 41

42 4 LRFD Deep Foundations DESIGN DATABSE - Analyses The performance of driven piles static analysis methods 22 Histogram & Frequency Distributions for 146 Cases of All Pile Types (Concrete, Pipe, H) in Mixed Soils Using α - API/Nordlund/Thurman Design Methods Number of Pile-Cases σ x = normal distribution log-normal distribution m lnx = σ lnx = Relative Frequency 4 m x = Ratio of Static Load Test Results over the Pile Capacity Prediction using the α-api/nordlund/thurman design method 0 42

43 4 LRFD Deep Foundations DESIGN DATABSE - Analyses The performance of driven piles static analysis methods Histogram & Frequency Distributions for 80 Cases of Concrete Piles in Mixed Soils Using α - API/Nordlund/Thurman Design Methods Number of Pile-Cases log-normal distribution m lnx = σ lnx = normal distribution m x = σ x = Relative Frequency Ratio of Static Load Test Results over the Pile Capacity Prediction using the α-api/nordlund/thurman design method 0 43

44 Table 25. Recommended resistance factors for driven piles static analyses Pile Type Soil Type Design Method Redundant Resistance Factor φ φ/λ Nonredundant Redundant Nonredundant Concrete Pile. Pipe Pile Mixed SPT97 mob Clay α-api λ-method Sand β-method SPT97 mob FHWA CPT Mixed β-method/thurman αtomlinson/nordlund/thurman Sand Nordlund Clay α-tomlinson Mixed α-api/nordlund/thurman Sand Meyerhof Sand SPT97 mob, Nordlund SPT 97 mob Mixed α-api/nordlund/thurman Sand β-method Clay α-api Sand Meyerhof αtomlinson/nordlund/thurman Mixed β-method/thurman α-tomlinson Clay λ-method Mixed SPT 97 mob SPT 97 mob Sand Nordlund Meyerhof α-api H Piles Clay α-tomlinson λ-method α-api/nordlund/thurman Mixed αtomlinson/nordlund/thurman Sand β-method Mixed β-method/thurman Notes: 3/19/02 7/11/02 7/15/02 Non-Redundant = Four or less piles under one pile cap (β = 3.0 p f = 0.1%) Redundant = Five piles or more under one pile cap ( β = 2.33 p f = 1.0%) λ = bias = Mean K SX = measured/predicted φ/λ = efficiency factor, evaluating the relative economic performance of each method (the higher the better) φ/λ values relate to the exact calculated φ and λ and not to the assigned φ values in the table NCHRP 507 Recommended Resistance Factors Driven Piles Static Analyses

45 5 PERFORMANCE OF THE DYNAMIC METHODS Histogram & Frequency Distributions for all (377) CAPWAP pilecases in PD/LT2000 Number of Pile-Cases log-normal distribution m lnx = σ lnx = m x = normal distribution σ x = Relative Frequency > 3 Ratio of Static Load Test Results over the Pile Capacity Prediction using the CAPWAP method

46 5 PERFORMANCE OF THE DYNAMIC METHODS Histogram & Frequency Distributions for all BOR (162) CAPWAP pilecases in PD/LT2000 Number of Pile-Cases log-normal distribution m lnx = σ lnx = m x = normal distribution σ x = Relative Frequency > 3 Ratio of Static Load Test Results over the Pile Capacity Prediction using the CAPWAP method 0

47 5 PERFORMANCE OF THE DYNAMIC METHODS Histogram & Frequency Distributions for all EOD (128) Energy Approach pile-cases in PD/LT2000 Number of Pile-Cases log-normal distribution m lnx = σ lnx = m x = Relative Frequency normal distribution 10 σ x = Ratio of Static Load Test Results over the Pile Capacity Prediction using the Energy Approach method 0

48 4 LRFD DESIGN Recommended resistance factors Driven Piles Dynamic Analyses Dynamic Measurements Table 27. Recommended resistance factors for driven piles dynamic analyses Method Case Signal Matching (CAPWAP) Resistance factor, φ φ/ λ Redundant Non-Redundant Redundant Non-Redundant EOD EOD, AR<350, Bl. Ct.<16BP10cm BOR Energy EOD Approach BOR Dynamic ENR General Equations Gates General FHWA modified General WEAP EOD Notes: β = Reliability Index p f = Probability of Failure COV = Coefficient of Variation EOD = End of Driving BOR = Beginning of Restrike Bl. Ct. = Blow Count AR = Area Ratio ENR = Engineering News Record Equation BP10cm = Blows per 10cm Non-Redundant= Four or less piles under one pile cap (β = 3.0 p f = 0.1%) Redundant = Five piles or more under one pile cap.( β = 2.33 p f = 1.0%) λ = bias = Mean K SX = measured/predicted φ/ λ = efficiency factor, evaluating the relative economic performance of each method (the higher the better) φ/λ values relate to the exact calculated φ and λ and not to the assigned φ values in the table.

49 4 LRFD DESIGN Recommended resistance factors Drilled Shafts Static Analyses Shaft Resistance Total Resistance Table 29. Recommended resistance factors for drilled shafts Soil Type Design Method Construction Method Resistance Factors φ Non- Redundant Redundant φ/λ Non- Redundant Redundant R&W Sand All FHWA Clay FHWA All Slurry & Dry FHWA Sand Casing Clay Slurry & Dry R&W Casing Rock C&K All IGM All All FHWA All Skin Soils R&W Resistance Rock C&K All IGM Notes: 3/26/02 7/11/02 7/15/02 Non-Redundant = Four or less piles under one pile cap (β = 3.0 p f = 0.1%) Redundant = Five piles or more under one pile cap.( β = 2.33 p f = 1.0%) λ = bias = Mean K SX = measured/predicted φ/λ = efficiency factor, evaluating the relative economic performance of each method (the higher the better) φ/λ values relate to the exact calculated φ and λ and not to the assigned φ values in the table.

50 4 LRFD DESIGN Recommended resistance factors Static Load Test Table 30. Recommended resistance factors for static load tests Resistance Factor - φ No. of Load Tests Site Variability Per Site Low Medium High

51 4 LRFD DESIGN Recommended Number of Pile Tests During Production Table 28. Recommended number of dynamic tests to be conducted during production Site Var. Low Medium High No. of Method EA CAPWAP EA CAPWAP EA CAPWAP Piles Time EOD BOR EOD BOR EOD BOR > EA = Energy Approach Analysis CAPWAP = Signal Matching Analysis EOD = End of Driving BOR = Beginning of Restrike Minimum one test under each substructure

52 Site Variability Assessment - Example SPT Blow Counts (N & N') vs. Elevation (4 Borings) Ground Surface 0 Fill: n=12 m x (N) = 9, s x (N) = 7.1, COV = 79% m x (N') = 10, s x (N') = 8.1, COV = 81% High Variability Area A (4 borings) -5 Organic Silt: (n=10) m x (N) = 2, s x (N) = 2.1, COV = 129% m x (N') = 2, s x (N') = 2.1, COV = 128% High Variability Layer No. n m x σ x COV Variability El. (m) Glacio-Deltaic (Upper): n=61 m x (N) = 26, s x (N) = 8.2, COV = 32% m x (N') = 18, s x (N') = 5.0, COV = 28% Low/Medium Variability N N' N Avg % % % High High Low-Med N' Avg % Low -25 n Number of Values Glacio-Deltaic (Lower): n=16 m x (N) = 37, σ x (N) = 9.6, COV = 26% m x (N') = 19, σ x (N') = 4.8, COV = 25% Low/Medium Variability -40 SPT N or N' Area A Using SPT 4 Borings

53 Time Dependent Pile Capacity Guideline for scheduling static load tests and restrikes. For piles embedded completely in clay: For static testing purpose: t 75 = 1540 x r 2 For dynamic testing purpose: t 75 = 85 x r 2 For piles embedded in alternating soil conditions (granular and cohesive): For dynamic testing purpose: t 75 = 39 x r 2 Where: t 75% = time to reach 75% of maximum capacity in hours r = pile radius (or equivalent) in feet.

54 Using The Simple Example With NCHRP 507 Resistance Factors Assume a load of 200 tons with the relevant load factors and Pile Capacity Q ult = 100 tons (Specifying now a redundant concrete pile in clay and using the bias known for the methods) Capacity Evaluation Method φ (Load) Load per Pile (tons) # of Piles Savings Static Analysis α API Clay t 61.5 (28.6) 3.3 (7) - EA EOD t 50.6 (36.4) 3.9 (5.5) +18% (-21%) CAPWAP BOR t 55.9 (44.4) 3.6 (4.5) +9% (-36%) Medium Var site 1 Static L.T (4) -12% (-43%) 54

55 5 LRFD Shallow Foundations Design

56 5 LRFD Shallow Foundations DESIGN Research Team Samuel G. Paikowsky and Mary C. Canniff - GTR and UML Kerstin Lesny and Aloys Kisse - UDE Shailendra Amatya, and Robert Muganga - UML

57 5 LRFD Shallow Foundations DESIGN NCHRP Research 24-31: LRFD Design Specifications for Shallow Foundations Develop and Calibrate Procedures and Modify AASHTO s Section 10 (Foundations) Specifications for the Strength Limit State Design of Bridge Shallow Foundations. NCHRP Report 651 LRFD DESIGN AND CONSTRUCTION OF SHALLOW FOUNDATIONS FOR HIGHWAY STRUCTURES Google NCHRP

58 5 LRFD Shallow Foundations DESIGN UML-GTR ShalFound07 Database 549 cases built in ACCESS platform, 415 cases are suitable for ULS. UML-GTR RockFound07 Capacity Database 122 Cases of load tests to failure including 61 rock sockets, 33 shallow foundations on rock surface, 28 shallow foundations below surface ShalFound07 Divided into vertical centric and eccentric, and inclined cases RockFound07 DATABASES All vertical centric, shallow and drilled shafts 58

59 5 LRFD Shallow Foundations DESIGN Foundation type Plate load tests B 1m Small footings 1 < B 3m Large footings 3 < B 6m Rafts & Mats B > 6m Predominant Soil Type Country Total Sand Gravel Cohesive Mix Others Germany Others Total Note: Mixed are cases with alternating layers of sand or gravel and clay or silt Others are cases with either unknown soil types or with other granular materials like loamy Scoria 1m 3.3ft Large foundations are often not loaded to ULS failure (SLS controls) 59

60 5 LRFD Shallow Foundations DESIGN Bias of Estimated BC - Vertical Centric Loading Granular Soil Controlled Conditions Number of observations Controlled soil conditions n = 159 mean = 1.64 COV = lognormal distribution normal distribution Bias, λ = q u,meas / q u,calc Frequency Interpreted bearing capacity, qu,meas using Minimum Slope criterion (Vesic, 1963) (ksf) Calcualted bearing capacity, q u,calc (Vesic, 1975 and modified AASHTO) (ksf) Figure 62. (a) Histogram and probability density functions of the bias and (b) relationship between measured and calculated bearing capacity for vertical centrically loaded shallow foundations on controlled soil conditions Controlled soil conditions Data (n = 159) Data best fit line No bias line 60

61 5 LRFD Shallow Foundations DESIGN 1000 Source of Uncertainty Investigation of N γ q u / (0.5 γ B s γ ) N γ from load tests; n = 125 N γ (Vesic, 1973) N γ = exp(0.39φ f ) (R 2 = 0.666) friction angle, φ f (deg) Comparison of bearing capacity factor calculated based on test results; N γ = q u / (0.5γ B s γ ) from 125 tests carried out in controlled soil conditions (tests by Perau, 1995) and N γ proposed by Vesic (1973) in the range of soil friction angle of 42 and 46 61

62 5 LRFD Shallow Foundations DESIGN Source of Uncertainty Investigation of N γ λ N γ = [q u / (0.5 γ B s γ )] / NγVesic load test data; n = 125 λ Ν γ = exp(0.205φ f 8.655) (R 2 = 0.351) Friction Angle, φ f (deg) Figure 93. The ratio (λ Nγ ) between the back-calculated B.C. factor N γ based on experimental data to that proposed by Vesić versus soil friction angle. 62

63 5 LRFD Shallow Foundations DESIGN Uncertainty in B.C. compared to the Uncertainty of N γ Bias λ Data BC bias (n = 131) Bearing Capacity (BC) bias, λ Nγ bias, λνγ Friction Angle, φ f (deg) Figure 94. The ratio between measured and calculated bearing capacity (bias λ) compared to the bias in the B.C. factor N γ (λ Nγ ) versus the soil s friction angle for footings under vertical-centric loadings. 63

64 5 LRFD Shallow Foundations DESIGN Mean bias, λbc (n = 172) ±1 s.d. (x) no. of cases in each interval λ BC = exp(0.0372φ f ) (R 2 =0.200) Uncertainty in B.C. Bias λ (2) (4) (2) (3) (12) 95% confidence interval (30) (90) (2) 1.0 (3) (4) (4) (14) 0.5 (2) Friction angle φ f (deg) Figure 103. Bearing resistance bias vs. average soil friction angle (taken φ f ±0.5 ) including 95% confidence interval for all cases under vertical-centric loading. 64

65 5 LRFD Shallow Foundations DESIGN % confidence interval for λ Uncertainty in B.C. and Resistance Factors Bias λ (2) (4) (3) Resistance factor based on database (x) no. of cases in each interval Recommended f for Controlled soil conditions Recommended f for Natural soil conditions (2) (3) (4) (12) (2) (4) (14) (30) (90) (2) Resistance factor, φ n = Friction angle φ f (deg) Figure 104. Recommended resistance factors for soil friction angles (taken φ f ±0.5 ) between 30 and 46, with comparisons to 95% confidence interval and resistance factors obtained for the cases in the database; the bubble size represents the number of data cases in each subset. 65

66 5 LRFD Shallow Foundations DESIGN Final Resistance Factors Controlled Conditions Table 66 Recommended resistance factors for shallow foundations on granular soils placed under controlled conditions Soil friction angle φ f Vertical-centric or -eccentric Loading conditions Inclined-centric Inclined-eccentric Positive Negative Notes: 1) φ f determined by laboratory testing 2) compacted controlled fill or improved ground are assumed to extend below the base of the footing to a distance to at least two (2.0) times the width of the foundation (B). If the fill is less than 2B thick, but overlays a material equal or better in strength than the fill itself, then the recommendation stands. If not, then the strength of the weaker material within a distance of 2B below the footing; prevails. 3) The resistance factors were evaluated for a target reliability β T =

67 5 LRFD Shallow Foundations DESIGN Intermediate Conclusions and Summary It was found that for the footings of larger sizes (B>3m (9.9ft)), the load tests were not carried out to the failure load Biases for the tests in Natural Soil Condition and Controlled Soil Conditions were analyzed separately For the footing sizes in similar ranges (0.1m < B 1.0m), the scatter of bias was larger for footings on/in natural soil conditions The majority of the relevant data refers to small size foundations (B 3.3ft (1.0m)) on controlled compacted material. Many of the highway shallow foundations on soils are built on compacted materials and hence, the statistical data of the uncertainty can be used for that purpose There appears to be a trend of increase in bias with the footing size within the range of footing sizes available for testing (which seems to conform with the observation made by Vesic (1969)) 67

68 5 LRFD Shallow Foundations DESIGN ULS of Inclined Loading x 2 F 1 M 2 D M 1 F 2 M 3 F 3 b 2 x 3 b 3 x 1 g γ, φ f (a) Loading convention F 1 F 1 F F 1 1,const. δ = const. F 3 arctan e = const M 2 increasing δ F 3 (b) Radial load path (c) Step-like load path Figure 64. Loading convention and load paths used during tests. 68

69 5 LRFD Shallow Foundations DESIGN Bias of BC for Vertical-Eccentric Loading (using B ) Number of observations Vertical-eccentric loading n = 43 mean = 1.83 COV = lognormal distribution normal distribution Frequency Interpreted bearing capacity, qu,meas using Minimum Slope criterion (Vesic, 1963) (ksf) Vertical-eccentric loading Data (n = 43) Data best fit line No bias line Bias, λ = q u,meas / q u,calc Calcualted bearing capacity, q u,calc (Vesic, 1975 and modified AASHTO) (ksf) Figure 66. (a) Histogram and probability density functions of the bias and (b) relationship between measured and calculated bearing capacity for all cases of vertical eccentrically loaded shallow foundations

70 5 LRFD Shallow Foundations DESIGN Bias of BC for Inclined-Centric Loading Number of observations Inclined-centric loading n = 39 mean = 1.43 COV = lognormal distribution normal distribution Frequency Interpreted bearing capacity, qu,meas using Minimum Slope criterion (Vesic, 1963) (ksf) Inclined-centric loading Data (n = 39) Data best fit line No bias line Bias, λ = q u,meas / q u,calc Calcualted bearing capacity, q u,calc (Vesic, 1975 and modified AASHTO) (ksf) Figure 67. (a) Histogram and probability density functions of the bias and (b) relationship between measured and calculated bearing capacity for all cases of inclined centric loaded shallow foundations

71 5 LRFD Shallow Foundations DESIGN Loading Directions for Inclined-Eccentric Loadings F 1 e 3 b 3 b 3 3 F 1 F 3 F 3 F F M 2 1 F Moment acting in direction opposite to the lateral loading negative eccentricity e + M F Moment acting in the same direction as the lateral loading positive eccentricity (a) along footing width b 3 b F 1 e 2 b 2 Moment acting in direction opposite to the lateral loading negative e eccentricity - b 2 2 F 1 F 2 F 2 Moment acting in the same direction as the lateral loading positive eccentricity b 2 b 2 F 1 F 1 M 3 M 3 (b) along footing length + F 2 F Figure 69. Loading directions for the case of inclined-eccentric loadings: (a) along footing width and (b) along footing length 71

72 5 LRFD Shallow Foundations DESIGN Bias of BC for Inclined-Eccentric Loading Number of observations Inclined-eccentric loading n = 29 mean = 2.43 COV = lognormal distribution normal distribution Bias, λ = q u,meas / q u,calc Frequency Interpreted bearing capacity, qu,meas using Minimum Slope criterion (Vesic, 1963) (ksf) Inclined-eccentric loading Data (n = 29) Data best fit line No bias line Calcualted bearing capacity, q u,calc (Vesic, 1975 and modified AASHTO) (ksf) Figure 68. (a) Histogram and probability density functions of the bias and (b) relationship between measured and calculated bearing capacity for all cases of inclined eccentrically loaded shallow foundations. 72

73 5 LRFD Shallow Foundations DESIGN Bias of BC Cases with Inclined-Eccentric Loading Number of observations Inclined-eccentric loading Negative eccentricity n = 7 mean = 3.43 COV = lognormal distribution normal distribution Bias, λ = q u,meas / q u,calc Frequency Interpreted bearing capacity, qu,meas using Minimum Slope criterion (Vesic, 1963) (ksf) Calcualted bearing capacity, q u,calc (Vesic, 1975 and modified AASHTO) (ksf) Figure 71. (a) Histogram and probability density functions of the bias and (b) relationship between measured and calculated bearing capacity for all cases of inclined eccentrically loaded shallow foundations under negative eccentricity Inclined-eccentric loading Negative eccentricity Data (n = 7) Data best fit line No bias line 73

74 5 LRFD Shallow Foundations DESIGN Final Resistance Factors Controlled Conditions Table 66 Recommended resistance factors for shallow foundations on granular soils placed under controlled conditions Soil friction angle φ f Vertical-centric or -eccentric Loading conditions Inclined-centric Inclined-eccentric Positive Negative Notes: 1) φ f determined by laboratory testing 2) compacted controlled fill or improved ground are assumed to extend below the base of the footing to a distance to at least two (2.0) times the width of the foundation (B). If the fill is less than 2B thick, but overlays a material equal or better in strength than the fill itself, then the recommendation stands. If not, then the strength of the weaker material within a distance of 2B below the footing; prevails. 3) The resistance factors were evaluated for a target reliability β T =

75 5 LRFD Shallow Foundations DESIGN Final Resistance Factors Natural Conditions Table 67 Recommended resistance factors for shallow foundations on natural deposited granular soil conditions Loading conditions Soil friction angle φ f Vertical-centric or -eccentric Inclined-centric Inclined-eccentric Positive Negative Notes: 1) φ f determined from Standard Penetration Test results 2) granular material is assumed to extend below the base of the footing at least two (2.0) times the width of the foundation. 3) The resistance factors were evaluated for a target reliability β T =

76 5 LRFD Shallow Foundations DESIGN DATABASE UML/GTR RockFound 07 Comprised of 122 foundation case histories of load tests in/on rock and IGM s. The database has 61 footings cases (28 cases D>0, 33 cases D=0) and 61 rock socket cases for which the base behavior (load and displacement) under loading was monitored. 89 of the 122 cases were used for the uncertainty determination of the settlement of foundations on rock. 76

77 5 LRFD Shallow Foundations DESIGN Goodman (1989) - B.C. of Foundations on Rock Interpreted Foundation Capacity q L2 (ksf) q L2 = 2.16 (q ult ) (n = 119; R 2 = 0.897) q L2 = q ult 58 Footings cases 61 Rock Socket cases Goodman (1989) Bearing Capacity q ult (ksf) Figure 78. Relationship between Goodman s (1989) calculated bearing capacity (q ult ) and the interpreted bearing capacity (q L2 ). 77

78 5 LRFD Shallow Foundations DESIGN Goodman (1989) - B.C. of Foundations on Rock Rock-sockets and Footing cases Goodman (1989) mean = 1.35 COV = Foundation cases on Fractured Rocks Goodman (1989) mean = 1.24 COV = N u m b er of observ ations lognormal distribution normal distribution Frequ ency Number of observations lognormal distribution normal distribution Frequency Bias, λ = q u,meas / q u,calc Figure 79. Distribution of the ratio of the interpreted bearing capacity (q L2 ) to the bearing capacity (q ult ) calculated using Goodman s (1989) method for the rock sockets and footings in database UML-GTR RockFound Bias, λ = q u,meas / q u,calc Figure 80. Distribution of the ratio of the interpreted bearing capacity (q L2 ) to the bearing capacity (q ult ) calculated using Goodman s (1989) method for foundations on fractured rock in database UML-GTR RockFound

79 5 LRFD Shallow Foundations DESIGN Table 70 Recommended resistance factors for foundations in/on rock based on β T = 3.0 (p f = 0.135%) Method of Analysis Equation Application φ Efficiency Factor φ/λ (%) Carter and Kulhawy (1988) Goodman (1989) ult For fractured rocks: ( ) q = q m + s For non-fractured rocks: u qult qu N φ ( 1) = + ( Nφ 1) N φ 1 s qult = qu Nφ 1 Nφ 1 B All RMR RMR < RMR < RMR < All Measured φ f Measured s Measured s and φ f

80 6 LRFD Serviceability Limit State NCHRP AASHTO LRFD Specifications for Serviceability in the Design of Bridge Foundations Final report in NCHRP never Published Can be obtained

81 6 LRFD Serviceability Limit State RESEARCH TEAM Samuel G. Paikowsky, Mary Canniff, GTR, Inc. Ayhan Garbuz, Yu Fu, Roiy Guy Geotechnical Eng. Research Lab., University of Massachusetts Lowell Zeidan Ashraf, Guy Levi, Wisam Mualem and Sam Frydman, Technion Israel Institute of Technology, Structural Engineering and Construction Management area of the Civil Engineering Department Japan Team: Yusuke Honjo, Gifu University, Ikumasa Yoshida, Shuichi Suzuki, Hyoudou Junichi, TEPSCO, Tokyo, Masahiro Shirato, PWRI, Japan Susan Faraji, Faraji Consulting, Inc., Winchester, MA

82 6 LRFD Serviceability Limit State Objectives Develop procedures for serviceability design of bridge foundations, calibrate them and write specifications Practically, develop new methodology to calibrate serviceability in LRFD and write new specifications. Main Challenges Establish serviceability criteria for bridges under normal operation. Compilation of large high quality databases for axial and lateral single and group deep foundation displacements, as well as shallow foundations and bridge substructures. Establish uncertainty of displacement prediction methods. Develop methodology for establishing LRFD parameters for serviceability.

83 6 LRFD Serviceability Limit State Developed Serviceability Criteria Criteria Bridge Type Limit State Limitations Comments Angular distortion Simple l 50ft subjected to limit vertical Support /l < 1/200 displacements exc. rigid frame structures Angular distortion Continuous /l < 1/250 l 50ft steel exc. integral abutment bridges assuming pinned connection at the abutment Abutment differential vert. displacement for bridge lifetime Steel Concrete VA < 3in VA < 3in l 50ft steel I/l 20in 3 l 100ft Pier differential vert. displacement for bridge Steel VP < 2in l 50ft lifetime Concrete VP < 2in Abutment differential vert. Steel VA < 2in l 50ft displacement following bridge completion Concrete VA < 2in Moulton, 1986, Table 7; Current study Table 4.14 Moulton, 1986, p.58; Current study Table 4.14 Moulton, 1986, Table 7; Current study Table 4.14 Pier differential displacement Steel VP < 1.25in following bridge completion Concrete VP < 1.50in Horiz. displacements All Substructures h < 1.5in Controlling criteria AASHTO Moulton 1986, h < 2.0in Horiz. displacements combined with vert. displacements All Substructures h < 1.0in Controlling criteria AASHTO Moulton 1986, h < 1.5in

84 6 LRFD Serviceability Limit State Databases and Their Analyses Performance of DP Compression, Tension, and Lateral / Pile Type/Soil Type Performance of DF Compression, Tension, and Lateral / Construction Type/Soil Type Performance of Pile Groups Vertical / Lateral / Soil Type Performance of Shallow Foundations Prototype / Full Scale / Soil Type Performance of Full Scale Structures Piers / Abutments

85 6 LRFD Serviceability Limit State Methods of Analysis for Lateral Displacement of a Deep Foundation Equilibrium Method Broms (1964a, 1964b) p-y Curves Method (BEF, Winkler, 1887, McClleland and Focht, 1958, Matlock, 1970, Reese 1977,1984, 1985). COM624P (Wang and Reese, 1993) LPILE 5.0 (Reese et al. 2004) Strain Wedge Method (Norris, 1986) SWM 6.0 (Ashour and Norris, 2000) Normalized Relations Lateral Load vs. Normalized Disp. (current research)

86 6 LRFD Serviceability Limit State Laterally Loaded Single Piles Summarized by Method of Analysis COM624P Analysis λ COV H-Piles Pipe Piles (φ 18") Pipe Piles (φ 24") PPC All Pipe Piles SWM Analysis λ COV H-Piles Pipe Piles (φ 18") Pipe Piles (φ 24") PPC All Pipe Piles All Piles 1.40 All Piles DS in Soil λ, COV 0.80 λ, COV Pile Top Deflection (inch) Pile Top Deflection (inch)

87 6 LRFD Serviceability Limit State Lateral Displacement of Single Piles vs. Resistance Factor φ (25) (24) (19) (12) (12) (25) Resistance Factor φ (26) (23) (18) (12) (11) Resistance Factor φ (23) (18) (12) (11) H-Piles COM624P (no. of cases) Broms (no. of cases) SWM (no. of cases) Normalized (no. of cases) H-Piles Broms (no. of cases) Fit 1: Broms Y = X , R 2 = Fit 2: Log Y = ln(X) , R 2 = Lateral Displacement (inch) Lateral Displacement (inch)

88 6 LRFD Serviceability Limit State Example of Resistance factors for SLS Recommended Resistance Factors for SLS of Deep Foundations Pile Type H Method p-y curves COM624P / LPile SWM Normalized Range of Settlement (inch) Resistance Factor φ 0.00 < < < < < < < <

89 6 LRFD Serviceability Limit State Shallow Foundations Bias & COV vs. Settlement λ, COV 3.0 λ, COV AASHTO Bias (λ) COV D'Appolonia Bias (λ) COV Foundation Settlement (inch) Foundation Settlement (inch) Bias (λ) Relates to the mean of the ratio of measured over calculated loads for a given displacement

90 6 LRFD Serviceability Limit State Shallow Foundations Settlement vs. Resistance Factor φ (85) (51) (36) (18) (18) (17) 0.8 D'Appolonia (no. of cases) Recommended φ Y = 0.25*X -0.85, φ 0.7 (74) Resistance Factor φ (14) (13) (7) (6) Resistance Factor φ (52) (40) (22) (22) (21) (19) 0.2 AASHTO (No. of cases) Recommended φ Data Ranges 0.2 (18) (14) (11) Settlement (inch) Settlement (inch)

91 6 LRFD Serviceability Limit State Resistance Factors for Shallow Foundations SLS For reliability index β = 1.28 (p f = 10%), and load factors taken as unity Bias of LL = 1.15, COV QL = 0.2 Bias of DL = 1.05, COV QD = 0.1 Method AASHTO Range of Settlement (inch) Resistance Factor φ Efficiency Factor φ/λ 0.00 < < <

92

93 CASE HISTORY LRFD BRIDGE DESIGN USING AASHTO 2006 SPECIFICATIONS

94 Existing and Replacement Sakonnet River Bridges

95 Replacement Bridge Foundation Layout W. Abut H-PILES PIPE PILES P1 P2 P3 P4 P5 P6 H-PILES P7 P8 P9 SPREAD FOOTING E. Abut. Test Test Site Site SOIL PROFILE

96 HP 14x117 (112 ft/34m) Test Pile Vibrated to 92 ft (28m) Driven w/ ICE 1070 diesel hammer (3 22 kip-ft) (1 30 kn-m) 1, 7, & 14 days HP 14x117 El 4 to ft, 1 to 33 m

97 Current Specifications Resistance Factors for Driven Piles (Static Analysis) (AASHTO 2008 Interim 2006,, Table ) continued Nominal Resistance of Single Pile in Axial Compression Static Analysis Methods, ϕ stat Condition/Resistance Determination Method Skin Friction and End Bearing Clay&Mixed Soils α-method (Tomlinson, 1987; Skempton, 1951) β-method (Esrig & Kirby, 1979; Skempton, 1951) λ-method (Vijayvergiya & Focht, 1972; Skempton, 1951) Skin Friction and End Bearing: Sand Nordlund/Thurman Method (Hannigan et al., 2005) SPT-method (Meyerhof) CPT-method (Schmertmann) End bearing in rock (Canadian Geotech. Society, 1985) Resistance Factor Block Failure, ϕ b1 Clay 0.60 Uplift Resistance of Single Piles, ϕ up Nordlund Method α-method β-method λ-method SPT-method CPT-method Load test Group Uplift Resistance, ϕ ug Sand and clay 0.50 Horizontal Geotechnical Resistance of Single Pile or Pile Group All soils and rock 1.0 } Where is the end bearing? Where are the pile/soil types? Where is β method?