INTRODUCTION TO STATIC ANALYSIS

INTRODUCTION TO STATIC ANALYSIS
PDPI 2011

Design Considerations
Insertion of piles generally alters soil character, and intense stresses are set up near piles Complex soil-pile interaction Therefore, it is necessary to use practical semi-empirical design methods

Solution Requires Thorough Information & Understanding of:
Foundation loads Subsurface conditions & soil/rock properties Current practices in pile design & construction

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

Vol. One Pile Manual Chapter 9 STATIC ANALYSIS DRIVEN PILES
● Introduction ● Single pile design issues ● Group design issues ● Special design considerations ● Additional design and construction considerations

STATIC ANALYSIS METHODS
Static analysis methods and computer solutions are used to: ● Calculate pile length for loads ● Determine number of piles ● Determine most cost effective pile type ● Calculate foundation settlement ● Calculate performance under uplift and lateral loads

Static analysis methods and computer solutions are an integral part of the design process. Static analysis methods are necessary to determine the most cost effective pile type. For a given pile type: - calculate capacity - determine pile length Bid Quantity - determine number of piles

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.

BASICS OF STATIC ANALYSIS
Static analysis calculations of deformation response to lateral loads and pile group settlement are compared to the performance criteria established for the structure. Static analyses are performed using geotechnical evaluation of soil properties from laboratory test, standard penetration test results, or in-situ test data. On many projects, multiple static analyses are required.

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.

Qu = (Design Load x FS) + “other”
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 =(Σfi Qi)/φ Qi = various load components fi = load factors φ = resistance factor ASD, LRFD, regardless-a “target” capacity is shown on plans

TWO STATIC ANALYSIS ARE OFTEN REQUIRED
First analysis with scourable soil removed, this will give us required pile length for the required capacity. Second analysis with scourable soil in place and with pile length from first analysis, this will give us our ultimate static resistance at time of driving Liquefaction ?

complete until the pile
The Pile Design is not complete until the pile has been driven

TWO STATIC ANALYSIS REQUIRED
This is the profile that the Contractor sees 9 - 4

TWO STATIC ANALYSIS REQUIRED
This is the profile that Contractor sees 9 - 4

COHESIONLESS SOILS s b 3 – 5.5b 3 – 5b b = pile diameter
s = settlement and densification 9 - 7

COHESIVE SOILS H b 3b H = heave
high pore water pressure increase and decrease in effective stress, time effects 3b 9 - 7

LOAD TRANSFER The ultimate pile capacity is typically expressed as the sum of the shaft and toe resistances: Qu = Rs + Rt This may also be expressed in terms of unit resistances: Qu = fs As + qt At The above equations assume that the ultimate shaft and toe resistances are simultaneously developed.

Soil Resistance vs Depth
LOAD TRANSFER Qu Axial Load vs Depth Soil Resistance vs Depth Rs = 0 Rs Rt Rt Uniform Rt Rs Triangular 9 - 9 Rt Rs

STUDENT EXERCISE #1 Figure 9.7 on page 12 shows the effect of water table location on effective stresses. Low water table results in higher effective stresses, higher shear strength, and therefore higher driving resistances

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 ??

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.

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.

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

FACTOR OF SAFETY SELECTION
Historically, the range in factor of safety has depended upon the reliability of a particular static analysis method with consideration of : ● Level of confidence in the input parameters ● Variability of soil and rock ● Method of static analysis ● Effects of, and consistency of proposed pile installation method ● Level of construction monitoring

Construction Control Method
FACTORS OF SAFETY, ASD The factor of safety used in a static analysis should be based on the construction control method specified. Construction Control Method Factor of Safety Static load test with wave equation analysis 2.00 Dynamic testing with wave equation analysis 2.25 Indicator piles with wave equation analysis 2.50 Wave equation analysis 2.75 Gates dynamic formula 3.50 9 - 14

EXAMPLE SOIL PROFILE

EXAMPLE SOIL PROFILE Ultimate Capacity: Qu = Rs1 + Rs2 + Rs3 +Rt
Design Load: Qa = (Rs3 + Rt) / FS Soil Resistance to Driving: SRD = Rs1 + Rs2 + Rs3 +Rt (with no soil strength changes) SRD = Rs1 + Rs2 / 2 + Rs3 +Rt (with clay soil strength change)

LRFD for Driven Piles /Drilled Shafts: Axial Loading
Traditional allowable stress design: (1) In plain English: the design load may not exceed the allowable load, taken as the ultimate capacity divided by a factor of safety In this approach the designer addresses the risk of adverse performance (collapse, excessive deformations, etc.) through a single parameter, the factor of safety. Factors that impact the actual performance, including variations in loads and material strengths, quality of construction, and the possibility of unforeseen subsurface conditions, are lumped into a single factor of safety. This approach has many shortcomings, the most significant of which is that it does not provide a consistent and rational framework for incorporating the individual sources of engineering risk into the design.

LRFD: Load and Resistance Factor Design
The following inequality must be satisfied (2) In plain English: the summation of factored force effects must not exceed the summation of factored resistances The global factor of safety approach has been replaced by the concept of limit state design. The essential idea is that a design should start by identifying all potential failure modes or limit states. These could be strength limits, such as ultimate bearing capacity, or serviceability limits, such as allowable settlements. A check is conducted on each limit state and it must be shown that its occurrence is sufficiently improbable. The format of limit state design equations involves the application of partial factors to increase the loads and decrease the resistances. This approach represents a fundamental improvement over the single factor of safety approach because the partial factors are applied directly to the uncertain quantities (loads and resistances).

(2) gi = load factor; a multiplier applied to force effects
where: gi = load factor; a multiplier applied to force effects Qi = force effect on the foundation resulting from loads applied to the structure and corresponding to a specific limit state (may be axial, lateral, or moment) ji = resistance factor for resistance component i Ri = nominal value of resistance component i

Ideally, resistance factors are established through probabilistic reliability analyses of load test results, calibrated to a target probability of failure (e.g., 1 in 1,000) In practice, development of resistance factors for deep foundations is a work in progress and is based in part on probabilistic analyses but with adjustments to match designs based on historic practice (ASD) and judgment In this approach the designer addresses the risk of adverse performance (collapse, excessive deformations, etc.) through a single parameter, the factor of safety. Factors that impact the actual performance, including variations in loads and material strengths, quality of construction, and the possibility of unforeseen subsurface conditions, are lumped into a single factor of safety. This approach has many shortcomings, the most significant of which is that it does not provide a consistent and rational framework for incorporating the individual sources of engineering risk into the design.

Extreme Event Limit States
Equation 2 is to be satisfied for all potential failure modes or limit states Strength Limit States ultimate axial resistance Service Limit States limits deformations to tolerable values Extreme Event Limit States e.g., earthquake, scour, impact

Static Analysis - Single Piles
Methods for estimating axial static resistance of soils

Soil Mechanics Review Angle of friction Undrained shear strength
Unconfined Compression Strength

STATIC CAPACITY OF PILES IN COHESIONLESS SOILS

Cohesionless Soils, Drained Strength
Normal Force, N F = N μ Friction Force, F μ = coefficient of friction between material 1 and material 2 1 2 F N  Tan () = F/N F = N TAN () Soil on Soil, we use  Soil on Pile, we use δ  phi = angle such that TAN () is coefficient of friction between materials 1 and 2

METHODS OF STATIC ANALYSIS FOR PILES IN COHESIONLESS SOILS
Approach Design Parameters Advantages Disadvantages Remarks Meyerhof Method Empirical Results of SPT tests. Widespread use of SPT test and input data availability. Simple method to use. Non reproducibility of N values. Not as reliable as the other methods presented in this chapter. Due to non reproducibility of N values and simplifying assumptions, use should be limited to preliminary estimating purposes. Brown Method Results of SPT tests based of N60 values. N60 values not always available. Simple method based on correlations with 71 static load test results. Details provided in Section b. Nordlund Method. Semi‑ empirical Charts provided by Nordlund. Estimate of soil friction angle is needed. Allows for increased shaft resistance of tapered piles and includes effects of pile-soil friction coefficient for different pile materials. No limiting value on unit shaft resistance is recommended by Nordlund. Soil friction angle often estimated from SPT data. Good approach to design that is widely used. Method is based on field observations. Details provided in Section c. Experience N Part Theory Part Experience FHWA 9-19

METHODS OF STATIC ANALYSIS FOR PILES IN COHESIONLESS SOILS
Approach Design Parameters Advantages Disadvantages Remarks Effective Stress Method. Semi-empirical Soil classification and estimated friction angle for β and Nt selection. β value considers pile-soil friction coefficient for different pile materials. Soil resistance related to effective overburden pressure. Results effected by range in β values and in particular by range in Nt chosen. Good approach for design. Details provided in Section Methods based on Cone Penetration Test (CPT) data. Empirical Results of CPT tests. Testing analogy between CPT and pile. Reliable correlations and reproducible test data. Limitations on pushing cone into dense strata. Good approach for design. Details provided in Section 9-19

Nordlund Data Base Pile Types Pile Sizes Pile Loads
Timber, H-piles, Closed-end Pipe, Monotube, Raymond Step-Taper Pile Types Pile Sizes Pile Loads Pile widths of 250 – 500 mm ( in) Ultimate pile capacities of kN ( tons) Nordlund Method tends to overpredict capacity of piles greater than 600 mm (24 in) 9-25

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. 7. The volume of soil displaced. 9-25

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: RS RT 9-26

Nordlund Shaft Resistance
K = coefficient of lateral earth pressure CF = correction factor for K when  ≠  pd = effective overburden pressure at center of layer = friction angle between pile and soil Cd = pile perimeter D = embedded pile length Figures Figure 9.15 Figure 9.10

Nordlund Toe Resistance
RT = T N’q pT AT Lesser of RT = qL AT T = dimensionless factor N’q = bearing capacity factor AT = pile toe area pT = effective overburden pressure at pile toe ≤ 150 kPa qL = limiting unit toe resistance Figure 9.16a Figure 9.16b Figure 9.17

FS based on construction control method as in Table 9-1
Nordlund Method Ru = RS + RT and Qa = RU / FS, ASD FS based on construction control method as in Table 9-1

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 Construct po diagram using procedure described in Section 9.4. 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. Determine  angle for each layer from laboratory tests or in-situ data. 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. 9-28

STEP 2 Determine , the friction angle between the pile and soil based on the displaced soil volume, V, and the soil friction angle, . Compute volume of soil displaced per unit length of pile, V. Enter Figure 9.10 with V and determine / ratio for pile type. Calculate  from / ratio. 9-28

Relationship Between Soil Displacement, V, and /
0.25 0.75 / = 0.70 a – closed-end pipe and non-tapered Monotube piles b – timber piles c – pre-cast concrete piles d – Raymond Step-Taper piles e – Raymond uniform piles f – H-piles g – tapered portion of Monotube piles

/ = 0.65 a – closed-end pipe and non-tapered Monotube piles b – timber piles c – pre-cast concrete piles d – Raymond Step-Taper piles e – Raymond uniform piles f – H-piles g – tapered portion of Monotube piles

STEP 3 Determine the coefficient of lateral earth pressure K for each soil friction angle, . Determine K for each  angle based on displaced volume V, and pile taper angle, ω, using appropriate procedure in steps 3b, 3c, 3d, or 3e. If displaced volume is , 0.093, or m3/m and the friction angle is 25, 30, 35, or 40, use Figures 9.11 to 9.14. If displaced volume is given but  angle is not. Linear interpolation is required to determine K for  angle. 9-28

K versus ω  = 25◦ Figure 9.11 9-33

K versus ω  = 30◦ Figure 9.12 9-34

STEP 3 Determine the coefficient of lateral earth pressure K for each soil friction angle, . If displaced volume is not given but  angle is given, log linear interpolation is required to determine K for displaced volume V. If neither the displaced volume or  angle are given, first use linear interpolation to determine K for  angle and then use log linear interpolation to determine K for the displaced volume, V. See Table 9-4 for K as function of  angle and displaced volume V 9-29

Table 9-4(a) Design Table for Evaluating K for Piles when ω = 0˚ and
V = to m3/m (0.10 to 1.00 ft3/ft) N Displaced Volume -V, m3/m, (ft3/ft) 0.0093 (0.10) 0.0186 (0.20) 0.0279 (0.30) 0.0372 (0.40) 0.0465 (0.50) 0.0558 (0.60) 0.0651 (0.70) 0.0744 (0.80) 0.0837 (0.90) 0.0930 (1.00) 25 0.70 0.75 0.77 0.79 0.80 0.82 0.83 0.84 0.85 26 0.73 0.78 0.86 0.87 0.88 0.89 0.90 0.91 27 0.76 0.92 0.94 0.95 0.96 0.97 28 0.93 0.98 0.99 1.01 1.02 1.03 29 1.05 1.06 1.08 1.09 30 1.10 1.12 1.14 1.15 31 1.13 1.16 1.19 1.21 1.24 1.25 1.27 32 1.17 1.22 1.26 1.30 1.32 1.35 1.37 1.39 33 1.40 1.44 1.46 1.49 1.51 34 1.42 1.47 1.55 1.58 1.61 1.63 35 1.33 1.57 1.62 1.66 1.69 1.72 1.75 36 1.48 1.71 1.78 1.84 1.89 1.93 1.97 2.00 37 1.79 1.90 1.99 2.05 2.11 2.16 2.21 2.25 38 2.09 2.19 2.27 2.34 2.40 2.45 2.50 39 1.59 1.94 2.14 2.29 2.49 2.57 2.64 2.70 2.75 40 1.70 2.32 2.48 2.61 2.71 2.80 2.87 2.94 3.0

STEP 4 Determine the correction factor CF to be applied to K if  ≠ . Use Figure 9.15 to determine the correction factor for each K. Enter figure with  angle and / ratio to determine CF. 9-29

Correction Factor for K when   
Figure 9.15

STEP 5 Compute the average effective overburden pressure at the midpoint of each soil layer. STEP 6 Compute the shaft resistance in each soil layer. Sum the shaft from each layer to obtain the ultimate shaft resistance, RS. 9-30

STEP 7 Determine the αt coefficient and the bearing capacity factor, N'q, from the  angle near the pile toe. a. Enter Figure 9.16(a) with  angle near pile toe to determine αt coefficient based on pile length to diameter ratio. Enter Figure 9.16(b) with  angle near pile toe to determine, N'q. c. If  angle is estimated from SPT data, compute the average corrected SPT N' value over the zone from the pile toe to 3 diameters below the pile toe. Use this average corrected SPT N' value to estimate  angle near pile toe from Table 4-5. 9-30

STEP 8 Compute the effective overburden pressure at the pile toe. NOTE: The limiting value of pt is 150 kPa STEP 9 Compute the ultimate toe resistance, Rt. Use lesser of: RT = T N’q pT AT Figure 9-16a and 9-16b RT = qL AT Figure 9-17 9-30

αt Coefficient versus 
 (degrees) Figure 9.16a

Figure 9.16 Chart for Estimating αt Coefficient and Bearing Capacity Factor N'q (Chart modified from Bowles, 1977) Figure 9.16b

Limiting Unit Toe Resistance – (US)
Figure 9.17

STEP 10 Compute the ultimate capacity, Qu. Qu = Rs + Rt STEP 11 Compute the allowable design load, Qa. Qa = Qu / Factor of Safety (ASD) 9-31

STATIC CAPACITY OF PILES IN COHESIVE SOILS

Cohesive Soils, Undrained Strength
F N c  = zero F = Friction resistance ; N = Normal force (stress) C is independent of overburden pressures c = cohesion, stickiness, soil / soil a = adhesion, stickiness, soil / pile

Unconfined Compression Strength
σ1 σ3 zero C C = cohesion = ½ qu σ3 Maximum σ1 = unconfined compression strength, qu

METHODS OF STATIC ANALYSIS FOR PILES IN COHESIVE SOILS
Approach Method of Obtaining Design Parameters Advantages Disadvantages Remarks α-Method (Tomlinson Method). 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 a. Effective Stress Method. Semi-Empirical, based on effective stress at failure. β and Nt values are selected from Table 9-6 based on drained soil strength estimates. Ranges in β and Nt values for most cohesive soils are relatively small. Range in Nt values for hard cohesive soils such as glacial tills can be large. Good design approach theoretically better than undrained analysis. Details in Section 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 FHWA 9-42

Tomlinson or α-Method Unit Shaft Resistance, fs: fs = ca = αcu Where:
ca = adhesion (Figure 9.18) α = empirical adhesion factor (Figure 9.19) 9-41

Tomlinson or α-Method Shaft Resistance, Rs: Rs = fs As Where:
As = 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 b = Pile Diameter D = distance from ground surface to bottom of clay layer or pile toe, whichever is less

Tomlinson or α-Method Sand or Sandy Gravels D Stiff Clay b

D = distance into stiff clay layer b = Pile Diameter Figure 9.19a 9-47

Tomlinson or α-Method Soft Clay D Stiff Clay b

D = distance into stiff clay layer b = Pile Diameter Figure 9.19b 9-47

Tomlinson or α-Method D Stiff Clay b

D = distance into stiff clay layer 9-47 b = Pile Diameter Figure 9.19c

HIGHLY OVERCONSOLIDATED CLAYS
In highly overconsolidated clays, the undrained shear strength may exceed the upper limits of Figures 9.18 and 9.19. In these cases, the adhesion factor should be calculated according to API procedures based on the ratio of the undrained shear strength of the soil, cu, divided by the effective overburden pressure, po’. The ratio of cu / po’ is . For  ≤ 1.0, α = 0.5 -0.5 For  > 1.0, α = 0.5 -0.25 9-44

Tomlinson or α-Method Unit Toe Resistance, qt: qt = cu Nc Where:
cu = undrained shear strength of the soil at pile toe Nc = dimensionless bearing capacity factor (9 for deep foundations)

Tomlinson or α-Method Toe Resistance, Rt: Rt = qt At
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 Ru = RS + RT and Qa = RU / FS, ASD

STUDENT EXERCISE #2 Use the α-Method described in Section a and the Nordlund Method described in Section c to calculate the ultimate pile capacity and the allowable design load for a inch O.D. closed end pipe pile driven into the soil profile described below. The trial pile length for the calculation is 63 feet below the bottom of pile cap excavation which extends 3 feet below grade. The pipe pile has a pile-soil surface area of 3.38 ft2/ft and a pile toe area of 0.89 ft2. Use Figure 9.18 to calculate the shaft resistance in the clay layer. The pile volume is 0.89 ft3/ft. The effective overburden at 56 feet, the midpoint of the pile shaft in the sand layer is 3.73 ksf, and the effective overburden pressure at the pile toe is 4.31 ksf. Remember, the soil strengths provided are unconfined compression test results (cu = qu / 2).

Soil Profile 3 ft Silty Clay = 127 lbs / ft3 qu = 5.46 ksf
Set-up Factor = 1.75 Dense, Silty F-M Sand = 120 lbs / ft3  = 35˚ Set-up Factor = 1.0 3 ft

Solution We will compare this solution with the DRIVEN output (ie steps 1-9) STEP 10 Qu = Rs + Rt = = 1875 kN

Calculate the Shaft Resistance in the Clay Layer Using α-Method
STEP 1 Delineate the soil profile and determine the pile adhesion from Figure 9.18. Layer 1: qu = 5.46 ksf so cu = D/b = Therefore ca from Figure 9.18 = 2.73 ksf 43 ft / in = 40.5 1.47 ksf

ca = 1.47 ksf cu = 2.73 ksf Concrete, Timber, Corrugated Steel Piles Smooth Steel Piles b = Pile Diameter D = distance from ground surface to bottom of clay layer or pile toe, whichever is less 9-45 Figure 9.18

Calculate the Shaft Resistance in the Clay Layer Using α-Method
STEP 2 Compute the unit shaft resistance, fs, for each soil layer. STEP 3 Compute the shaft resistance in the clay layer. Layer 1: Rs1 = ( fs1 )( As )( D1) = fs = ca = 1.47 ksf Rs1 = (1.47 ksf)(3.38 ft2/ft)(43 ft) = kips

Calculate the Shaft Resistance in the Sand Layer Using the Nordlund Method
STEP 1 The po diagram, soil layer determination, and the soil friction angle, N, for each soil layer were presented in the problem introduction. STEP 2 Determine *. a. Compute volume of soil displaced per unit length of pile, V. V = 0.89 ft3/ft (per problem description) b. Determine */N from Figure 9.10. V = 0.89 ft3/ft 6 */N = or * = N

/ = 0.62 a – closed-end pipe and non-tapered Monotube piles b – timber piles c – pre-cast concrete piles d – Raymond Step-Taper piles e – Raymond uniform piles f – H-piles g – tapered portion of Monotube piles

STEP 1 The po diagram, soil layer determination, and the soil friction angle, , for each soil layer were presented in the problem introduction. STEP 2 Determine *. a. Compute volume of soil displaced per unit length of pile, V. V = 0.89 ft3/ft (per problem description) b. Determine */N from Figure 9.10. V = 0.89 ft3/ft 6 */N = or * = N = 0.62 0.62 0.62 (35˚) = 21.7˚

STEP 3 Determine K* for each soil layer based on displaced volume, V, and pile taper angle, . Layer 2: For  = 35˚, V = 0.89 ft3/ft and  = 0˚ From Figure 9.13: K = for V = 0.10 ft3/ft K = for V = 1.00 ft3/ft Using log linear interpolation K = for V = 0.89 ft3/ft STEP 4 Determine correction factor, CF, to be applied to K when  ≠ . (Figure 9.15.) Layer 2:  = 35˚ and / = CF = 0.62

Correction Factor for K when   
CF = 0.78  = 35˚ Figure 9.15

STEP 3 Determine K* for each soil layer based on displaced volume, V, and pile taper angle, . Layer 2: For  = 35˚, V = 0.89 ft3/ft and  = 0˚ From Figure 9.13: K = for V = 0.10 ft3/ft K = for V = 1.00 ft3/ft Using log linear interpolation K = for V = 0.89 ft3/ft STEP 4 Determine correction factor, CF, to be applied to K when  ≠ . Layer 2:  = 35˚ and / = CF = 0.62 0.78

STEP 5 Compute effective overburden pressure at midpoint of each soil layer, pd. From problem description, pd for layer 2 is 3.73 ksf. STEP 6 Compute the shaft resistance for each soil layer. Rs2 = K CF pd sin  Cd D = = kips (1.72) (0.78) (3.73 ksf) (sin 21.7˚) (3.38 ft2/ft) (20 ft)

Compute the Ultimate Shaft Resistance, Rs
Rs = Rs1 + Rs2 Rs = 213.6 kips kips 338.7 kips

Compute the Ultimate Toe Resistance, Rt
STEP 7 Determine αt coefficient and bearing capacity factor N'q from  angle of 35˚ at pile toe and Figures (a) and 9.16(b) At pile toe depth D/b = From Figure 9.16(a) αt = From Figure 9.16(b) N'q = 66 ft / in. = 62

αt Coefficient versus 
0.67 t  = 35˚  (degrees) Figure 9.16a

Figure 9.16 Chart for Estimating αt Coefficient and Bearing Capacity Factor N'q (Chart modified from Bowles, 1977) 65 Figure 9.16b

STEP 7 Determine αt coefficient and bearing capacity factor N'q from  angle of 35˚ at pile toe and Figures (a) and 9.16(b) At pile toe depth D/b = 62 From Figure 9.16(a) αt = 0.67 From Figure 9.16(b) N'q = 65 STEP 8 Compute effective overburden pressure at pile toe. pt = 4.31 ksf. However, maximum of 3.0 ksf governs.

STEP 9 Compute the ultimate toe resistance, Rt. a. Rt =αt N'q At pt b. Rt = qL At (qL determined from Figure 9.17) c. Use lesser value of Rt from Step 9a and 9b. Therefore, Rt = = (0.67)(65)(0.89 ft2)(3.0 ksf) = kips

Limiting Unit Toe Resistance
105 Figure 9.17

STEP 9 Compute the ultimate toe resistance, Rt. a. Rt =αt N'q At pt b. Rt = qL At (qL determined from Figure 9.17) c. Use lesser value of Rt from Step 9a and 9b. Therefore, Rt = = (0.67)(65)(0.89 ft2)(3.0 ksf) = kips = (105 ksf)(0.89 ft2) = 93.5 kips 93.5 kips

Compute the Ultimate Pile Capacity, Qu
STEP 10 Qu = Rs + Rt = kips = kips

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: 9-56

User inputs soil profile identifying soil statigraphy, soil type (cohesionless or cohesive), soil unit weight, soil strength parameters ( or cu) and percentage strength loss during driving. Program analysis options include: Soft compressible soils Scourable soils Pile plugging 9-56

DRIVEN calculates the pile capacity at the time of driving using user input soil strength losses (Driving), the capacity after time dependent strength changes have occurred (Restrike), and the capacity after extreme events (Ultimate). % Driving Strength Loss = 1 – [1 / setup factor] DRIVEN generates a partial soil input file for the GRLWEAP wave equation program. 9-61

PILES DRIVEN TO ROCK The capacity of piles driven to rock should be based on driving observations, local experience, and load test results. RQD values from NX size rock cores can provide a qualitative assessment of rock mass quality. What is RQD? RQD Rock Mass Quality 90 – 100 Excellent 75 – 90 Good 50 – 75 Fair 25 – 50 Poor 0 - 25 Very Poor 9-64

PILES DRIVEN TO ROCK Except for piles driven to soft rock, the structural capacity of the pile will be lower than the geotechnical capacity of the rock to support a toe bearing pile. (Fair to excellent quality rock). The structural capacity of the pile (Chapter 10) then governs the pile capacity. 9-64

METHODS BASED ON CPT DATA
Elsami and Fellenius (9-66) Nottingham and Schmertmann (9-68) Laboratoire des Ponts et Chaussees (LPC) (9-75)

UPLIFT CAPACITY OF SINGLE PILES
Increasingly important design consideration Sources of uplift loads include seismic events, vessel impact, debris loading and cofferdam dewatering. The design uplift load may be taken as 1/3 the ultimate shaft resistance from a static analysis.

UPLIFT CAPACITY OF SINGLE PILES
The design uplift load may be taken as 1/2 the ultimate tension load test failure load defined in Section of Chapter 19. A reduction in the design uplift load may be necessary under cyclic or sustained loading conditions. Clays – peak strength to a residual strength Sands – particle degradation or reorientation

Any Questions

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. Review that objective was achieved.

Historically, prescription values were used for lateral capacity of vertical piles, or battered (inclined) piles were added. Modern design methods are readily available which allow load-deflection behavior to be rationally evaluated. Review that objective was achieved.

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 Review that objective was achieved.

Design Methods Lateral load tests Analytical methods Broms’ method, 9-86, (long pile, short pile) Reese’s COM624P method LPILE program FB-PIER Review that objective was achieved. 9-85

Review that objective was achieved.
Figure Soil Resistance to a Lateral Pile Load (adapted from Smith, 1989) 9-83

Figure 9.44 LPILE Pile-Soil Model
Review that objective was achieved. Figure LPILE Pile-Soil Model 9-101

We have n equations and (n+4) unknowns
BOUNDARY CONDITIONS (long pile) @ Pile Bottom Moment = 0 Shear = 0 @ Pile Top ??

Review that objective was achieved.
Figure Typical p-y Curves for Ductile and Brittle Soil (after Coduto, 1994) 9-102

Integrate Differentiate
Review that objective was achieved. Figure Graphical Presentation of LPILE Results (Reese, et al. 2000) 9-92

LET’S EAT !!

Let’s Demo DRIVEN !

INTRODUCTION TO STATIC ANALYSIS

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INTRODUCTION TO STATIC ANALYSIS

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