INTRODUCTION TO STATIC ANALYSIS PDPI 2013
What is Pile Capacity? When we load a pile until IT Fails what is IT
Strength Considerations Two Failure Modes 1. Pile structural failure controlled by allowable driving stresses 2. Soil failure controlled by factor of safety (ASD) resistance factors (LRFD) In addition, driveability is evaluated by wave equation
STATIC ANALYSIS METHODS Foundation designer must know design loads and performance requirements. Many static analysis methods are available. - methods in manual are relatively simple - methods provide reasonable agreement with full scale tests - other more sophisticated methods could be used Designer should fully know the basis for, limitations of, and applicability of a chosen method.
BASICS OF STATIC ANALYSIS Static capacity is the sum of the soil/rock resistances along the pile shaft and at the pile toe. Static analyses are performed to determine ultimate pile capacity and the pile group response to applied loads. The ultimate capacity of a pile and pile group is the smaller of the soil rock medium to support the pile loads or the structural capacity of the piles.
ASD for Driven Piles /Drilled Shafts: Axial Loading Traditional allowable stress design: F des < Q all Q ult FS In plain English: the design load may not exceed the allowable load, taken as the ultimate capacity divided by a factor of safety
LRFD: Load and Resistance Factor Design where: The following inequality must be satisfied i Q i R = sum of nominal side resistance & base resistance Q = applied axial force γ = load factors > 1.0 φ = resistance factors < 1.0 i R i
ULTIMATE CAPACITY, ASD Qu = (Design Load x FS) + other Other could be the resistance provided by scourable soil Other could be the resistance provided by Liquefiable soil Other is soil resistance at the time of driving not present later during the design life of the pile
ULTIMATE CAPACITY, LRFD Qu =(Σγ i Q i )/φ i + other Q i = various load components γ i = load factors φ = resistance factors ASD, LRFD, regardless-a target capacity for contractor is shown on plans
LRFD
Professor's Driven Pile Institute, Utah State University Structural Engineer Geotechnical Engineer Estimates, magnitude and direction of loads: Estimates soil resistance and calculates size, length and quantity of piles to resist the given loads. Any SCOUR?? Any SET UP The factored resistance must be greater than the factored applied loads!
TWO STATIC ANALYSIS ARE OFTEN REQUIRED 1. Design stage soil profile with sourable and/or unsuitable soils removed establish a pile tip elevation to accommodate the appropriate load (LRFD, ASD) 2. Construction stage soil profile, establish the soil resistance provided by soil profile at time of pile installation. This is the target resistance and includes scourable and unsuitable soils. This value should be shown on the plans.
Professor's Driven Pile Institute, Utah State University TWO STATIC ANALYSIS REQUIRED Bridge Pier 1. Calculate the required pile length to accommodate the factored load. Ignore resistance provided by scourable material. Estimated Maximum Scour Depth Contractor s Target 2. Given the required length now include the resistance of scourable soils when estimating soil resistance at time of Driving. (show on plans)
LOAD TRANSFER The ultimate pile capacity is typically expressed as the sum of the shaft and toe resistances: Q u = R s + R t This may also be expressed in terms of unit resistances: Q u = f s A s + q t A t The above equations assume that the ultimate shaft and toe resistances are simultaneously developed.
LOAD TRANSFER Q u Axial Load vs Depth Soil Resistance vs Depth R s = 0 R s R t R t Uniform R t R s 9-9 R t R s Triangular
DESIGN SOIL STRENGTH PARAMETERS Most of the static analysis methods in cohesionless soils use the soil friction angle determined from laboratory tests or SPT N values. In coarse granular deposits, the soil friction angle should be chosen conservatively. What does this mean??
DESIGN SOIL STRENGTH PARAMETERS In soft, rounded gravel deposits, use a maximum soil friction angle,, of 32 for shaft resistance calculations. In hard, angular gravel deposits, use a maximum friction angle of 36 for shaft resistance calculations.
DESIGN SOIL STRENGTH PARAMETERS In cohesive soils, accurate assessments of the soil shear strength and consolidation properties are needed for static analysis. The sensitivity of cohesive soils should be known during the design stage so that informed assessments of pile driveability and soil setup can be made.
DESIGN SOIL STRENGTH PARAMETERS For a cost effective design with any static analysis method, the foundation designer must consider time dependent soil strength changes. Ignore set up --- uneconomical Ignore relaxation --- unsafe
Static Analysis - Single Piles Methods for estimating axial static resistance of soils
Soil Mechanics Review Angle of friction Undrained shear strength Unconfined Compression Strength
Cohesionless Soils, Drained Strength Normal Force, N Friction Force, F F 1 2 F = N μ μ = coefficient of friction between material 1 and material 2 Tan ( ) = F/N Soil on Soil, we use Soil on Pile, we use δ N F = N TAN ( ) phi = angle such that TAN ( ) is coefficient of friction between materials 1 and 2
Cohesive Soils, Undrained Strength F c = zero F = Friction resistance (stress) N = Normal force (stress) N C is independent of overburden pressures (i.e. N) c = cohesion, stickiness, soil / soil a = adhesion, stickiness, soil / pile
Unconfined Compression σ 1 Strength σ 3 zero C C = cohesion = ½ q u σ 3 Maximum σ 1 = unconfined compression strength, q u
STATIC CAPACITY OF PILES IN COHESIONLESS SOILS
9-19 METHODS OF STATIC ANALYSIS FOR PILES IN COHESIONLESS SOILS Method Approach Design Parameters Meyerhof Method Brown Method Nordlund Method. FHWA Empirical Experience Empirical Semiempirical Part Theory Part Experience Results of SPT tests. N Results of SPT tests based of N 60 values. Charts provided by Nordlund. Estimate of soil friction angle is needed. Advantages Disadvantages Remarks Widespread use of SPT test and input data availability. Simple method to use. Widespread use of SPT test and input data availability. Simple method to use. Allows for increased shaft resistance of tapered piles and includes effects of pile-soil friction coefficient for different pile materials. Non reproducibility of N values. Not as reliable as the other methods presented in this chapter. N 60 values not always available. No limiting value on unit shaft resistance is recommended by Nordlund. Soil friction angle often estimated from SPT data. Due to non reproducibility of N values and simplifying assumptions, use should be limited to preliminary estimating purposes. Simple method based on correlations with 71 static load test results. Details provided in Section 9.7.1.1b. Good approach to design that is widely used. Method is based on field observations. Details provided in Section 9.7.1.1c.
METHODS OF STATIC ANALYSIS FOR PILES IN COHESIONLESS SOILS Method Approach Design Parameters Effective Stress Method. Methods based on Cone Penetration Test (CPT) data. Semiempirical Empirical Soil classification and estimated friction angle for β and N t selection. Results of CPT tests. Advantages Disadvantages Remarks β value considers pile-soil friction coefficient for different pile materials. Soil resistance related to effective overburden pressure. Testing analogy between CPT and pile. Reliable correlations and reproducible test data. Results effected by range in β values and in particular by range in N t chosen. Limitations on pushing cone into dense strata. Good approach for design. Details provided in Section 9.7.1.3. Good approach for design. Details provided in Section 9.7.1.7. 9-19
Nordlund Data Base Pile Types Timber, H-piles, Closed-end Pipe, Monotube, Raymond Step-Taper Pile Sizes Pile widths of 250 500 mm (10-20 in) Pile Loads Ultimate pile capacities of 350-2700 kn (40-300 tons) 9-25 Nordlund Method tends to overpredict capacity of piles greater than 600 mm (24 in)
Nordlund Method Considers: 1. The friction angle of the soil. 2. The friction angle of the sliding surface. 3. The taper of the pile. 4. The effective unit weight of the soil. 5. The pile length. 6. The minimum pile perimeter. 9-25 7. The volume of soil displaced.
9-27 Q u = d=d d=0 K C F p d sin( + ) cos C d d + t N q A t p t
Nordlund Method For a pile of uniform cross section ( =0) and embedded length D, driven in soil layers of the same effective unit weight and friction angle, the Nordlund equation becomes: Q u = (K δ C F p d sinδ C d D)+ (α t N q A t p ) t 9-26 R S R T
Nordlund Shaft Resistance R s = K δ C F p d sin δ C d D K = coefficient of lateral earth pressure Figures 9.11-9.14 C F = correction factor for K when Figure 9.15 p d = effective overburden pressure at center of layer = friction angle between pile and soil Figure 9.10 C d = pile perimeter D = embedded pile length
Nordlund Toe Resistance Lesser of R T = T N q p T A T R T = q L A T T = dimensionless factor Figure 9.16a N q = bearing capacity factor Figure 9.16b A T = pile toe area p T = effective overburden pressure at pile toe 150 kpa q L = limiting unit toe resistance Figure 9.17
Nordlund Method Procedure Steps 1 through 6 are for computing shaft resistance and steps 7 through 9 are for computing the pile toe resistance (cookbook) STEP 1 Delineate the soil profile into layers and determine the angle for each layer a. Construct p o diagram using procedure described in Section 9.4. b. Correct SPT field N values for overburden pressure using Figure 4.4 from Chapter 4 and obtain corrected SPT N' values. Delineate soil profile into layers based on corrected SPT N' values. c. Determine angle for each layer from laboratory tests or in-situ data. 9-28 d. In the absence of laboratory or in-situ test data, determine the average corrected SPT N' value, N', for each soil layer and estimate angle from Table 4-5 in Chapter 4.
Nordlund Method Procedure STEP 10 Compute the ultimate capacity, Q u. Q u = R s + R t STEP 11 Compute the allowable design load, Q a. Q a = Q u / Factor of Safety (ASD) 9-31
STATIC CAPACITY OF PILES IN COHESIVE SOILS
9-42 METHODS OF STATIC ANALYSIS FOR PILES IN COHESIVE SOILS Method Approach Method of Obtaining Design Parameters Advantages Disadvantages Remarks α-method (Tomlinson Method). FHWA Empirical, total stress analysis. Undrained shear strength estimate of soil is needed. Adhesion calculated from Figures 9.18 and 9.19. Simple calculation from laboratory undrained shear strength values to adhesion. Wide scatter in adhesion versus undrained shear strengths in literature. Widely used method described in Section 9.7.1.2a. Effective Stress Method. Semi- Empirical, based on effective stress at failure. β and N t values are selected from Table 9-6 based on drained soil strength estimates. Ranges in β and N t values for most cohesive soils are relatively small. Range in N t values for hard cohesive soils such as glacial tills can be large. Good design approach theoretically better than undrained analysis. Details in Section 9.7.1.3. Methods based on Cone Penetration Test data. Empirical. Results of CPT tests. Testing analogy between CPT and pile. Reproducible test data. Cone can be difficult to advance in very hard cohesive soils such as glacial tills. Good approach for design. Details in Section 9.7.1.7.
Tomlinson or α-method Unit Shaft Resistance, f s : f s = c a = αc u Where: c a = adhesion (Figure 9.18) α = empirical adhesion factor (Figure 9.19) 9-41
Tomlinson or α-method Shaft Resistance, R s : R s = f s A s Where: A s = pile surface area in layer (pile perimeter x length)
Tomlinson or α-method (US) Figure 9.18 Concrete, Timber, Corrugated Steel Piles Smooth Steel Piles D = distance from ground surface to bottom of clay layer or pile toe, whichever is less b = Pile Diameter
Tomlinson or α-method Unit Toe Resistance, q t : q t = c u N c Where: c u = undrained shear strength of the soil at pile toe N c = dimensionless bearing capacity factor (9 for deep foundations)
Tomlinson or α-method Toe Resistance, R t : R t = q t A t The toe resistance in cohesive soils is sometimes ignored since the movement required to mobilize the toe resistance is several times greater than the movement required to mobilize the shaft resistance.
Tomlinson or α-method R u = R S + R T and Q a = R U / FS
DRIVEN COMPUTER PROGRAM DRIVEN uses the FHWA recommended Nordlund (cohesionless) and α-methods (cohesive). Can be used to calculate the static capacity of open and closed end pipe piles, H-piles, circular or square solid concrete piles, timber piles, and Monotube piles. Analyses can be performed in SI or US units. Available at: www.fhwa.dot.gov/bridge/geosoft.htm 9-56
The Pile Design is not complete until the pile has been driven that s when we can estimate the capacity (E.O.D)
STATIC ANALYSIS SINGLE PILES LATERAL CAPACITY METHODS Reference Manual Chapter 9.7.3 9-82
Lateral Capacity of Single Piles Potential sources of lateral loads include vehicle acceleration & braking, wind loads, wave loading, debris loading, ice forces, vessel impact, lateral earth pressures, slope movements, and seismic events. These loads can be of the same magnitude as axial compression loads.
Lateral Capacity of Single Piles Soil, pile, and load parameters significantly affect lateral capacity. Soil Parameters Soil type & strength Horizontal subgrade reaction Pile Parameters Pile properties Pile head condition Method of installation Group action Lateral Load Parameters Static or Dynamic Eccentricity
Lateral Capacity of Single Piles Design Methods Lateral load tests Analytical methods Broms method, 9-86, (long pile, short pile) Reese s COM624P method LPILE program FB-PIER 9-85
Short pile soil fails Long pile pile fails
Figure 9.36 Soil Resistance to a Lateral Pile Load (adapted from Smith, 1989) 9-83
NIM
9-101 Figure 9.44 LPILE Pile-Soil Model
NIM
We have n equations and (n+4) unknowns BOUNDARY CONDITIONS (long pile) @ Pile Bottom Moment = 0 Shear = 0 @ Pile Top??
Figure 9.45 Typical p-y Curves for Ductile and Brittle Soil (after Coduto, 1994) 9-102
Integrate Differentiate Figure 9.36 Graphical Presentation of LPILE Results (Reese, et al. 2000) 9-92
LET S EAT!!