INTRODUCTION TO STATIC ANALYSIS

1
INTRODUCTION TO STATIC ANALYSIS
PDPI 2011
2
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
3
Solution Requires Thorough Information
Understanding of

1. Foundation loads
2. Subsurface conditions soil/rock properties
3. Current practices in pile design construction

4
Strength ConsiderationsTwo 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

5
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
6
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

7
STATIC ANALYSIS METHODS
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
8
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.
9
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.
10
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.
11
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.
12
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

13
ULTIMATE CAPACITY, LRFD

• Qu (Sfi Qi)/f
• Qi various load components
• fi load factors
• f resistance factor
• ASD, LRFD, regardless-a target capacity is
  shown on plans

14
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 ?
15
The Pile Design is not complete until the pile
has been driven
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TWO STATIC ANALYSIS REQUIRED
This is the profile that the Contractor sees
9 - 4
17
TWO STATIC ANALYSIS REQUIRED
This is the profile that Contractor sees
9 - 4
18
COHESIONLESS SOILS
densification
9 - 7
19
COHESIVE SOILS
H
H heave
high pore water pressure increase and decrease in
effective stress, time effects
b
3b
9 - 7
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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.
21
LOADTRANSFER
Qu
Axial Load vs Depth
Soil Resistance vs Depth
Rs 0
Rs
Rt
Rt
Uniform
Rt
Rs
Triangular
9 - 9
Rs
Rt
22
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
23
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 ??
24
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.
25
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.
26
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
27
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
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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
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EXAMPLE SOIL PROFILE
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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)
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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

32
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

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(2)

• 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

34

• 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

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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

37
Static Analysis- Single Piles

• Methods for estimating axial static
• resistance of soils

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Soil Mechanics Review

• Angle of friction
• Undrained shear strength
• Unconfined Compression Strength

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STATIC CAPACITY OF PILES IN COHESIONLESS
SOILS
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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
Tan (?) F/N
F N TAN (?)
Soil on Soil, we use ? Soil on Pile, we use d
? phi angle such that TAN (?) is coefficient of
friction between materials 1 and 2
41
METHODS OF STATIC ANALYSIS FOR PILES IN COHESIONLESS SOILS METHODS OF STATIC ANALYSIS FOR PILES IN COHESIONLESS SOILS METHODS OF STATIC ANALYSIS FOR PILES IN COHESIONLESS SOILS METHODS OF STATIC ANALYSIS FOR PILES IN COHESIONLESS SOILS METHODS OF STATIC ANALYSIS FOR PILES IN COHESIONLESS SOILS METHODS OF STATIC ANALYSIS FOR PILES IN COHESIONLESS SOILS
Method 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 Empirical Results of SPT tests based of N60 values. Widespread use of SPT test and input data availability. Simple method to use. N60 values not always available. Simple method based on correlations with 71 static load test results. Details provided in Section 9.7.1.1b.
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 9.7.1.1c.
Experience
N
Part Theory Part Experience
FHWA
9-19
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METHODS OF STATIC ANALYSIS FOR PILES IN COHESIONLESS SOILS METHODS OF STATIC ANALYSIS FOR PILES IN COHESIONLESS SOILS METHODS OF STATIC ANALYSIS FOR PILES IN COHESIONLESS SOILS METHODS OF STATIC ANALYSIS FOR PILES IN COHESIONLESS SOILS METHODS OF STATIC ANALYSIS FOR PILES IN COHESIONLESS SOILS METHODS OF STATIC ANALYSIS FOR PILES IN COHESIONLESS SOILS
Method Approach Design Parameters Advantages Disadvantages Remarks
Effective Stress Method. Semi-empirical Soil classification and estimated friction angle for ß and Nt selection. ß value considers pile-soil friction coefficient for different pile materials. Soil resistance related to effective overburden pressure. Results effected by range in ß values and in particular by range in Nt chosen. Good approach for design. Details provided in Section 9.7.1.3.
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 9.7.1.7.
9-19
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Nordlund Data Base
Timber, H-piles, Closed-end Pipe, Monotube,
Raymond Step-Taper
Pile Types Pile Sizes Pile Loads
Pile widths of 250 500 mm (10 - 20 in)
Ultimate pile capacities of 350 -2700 kN (40 -300
tons)
Nordlund Method tends to overpredict capacity of
piles greater than 600 mm (24 in)
9-25
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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
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9-27
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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
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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 9.11 - 9.14
Figure 9.15
Figure 9.10
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Nordlund Toe Resistance
RT ?T Nq pT AT
Lesser of
RT qL AT

• ?T dimensionless factor
• Nq 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
49
Nordlund Method
Ru RS RT
and
Qa RU / FS, ASD
FS based on construction control method as in
Table 9-1
50
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

1. Construct po diagram using procedure described in
   Section 9.4.
2. 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.
3. Determine ? angle for each layer from laboratory
   tests or in-situ data.
4. 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
51
Nordlund Method Procedure
STEP 2 Determine ?, the friction angle between
the pile and soil based on the displaced soil
volume, V, and the soil friction angle, ?.

1. Compute volume of soil displaced per unit length
   of pile, V.
2. Enter Figure 9.10 with V and determine ?/? ratio
   for pile type.
3. Calculate ? from ?/? ratio.

9-28
52
Relationship Between Soil Displacement, V, and ?/?
V 0.11
0.25
0.75
?/? 0.70
e Raymond uniform piles f H-piles g tapered
portion of Monotube piles
a closed-end pipe and non-tapered Monotube
piles b timber piles c pre-cast concrete
piles d Raymond Step-Taper piles
53
Relationship Between Soil Displacement, V, and ?/?
V 1.0
?/? 0.65
e Raymond uniform piles f H-piles g tapered
portion of Monotube piles
a closed-end pipe and non-tapered Monotube
piles b timber piles c pre-cast concrete
piles d Raymond Step-Taper piles
54
Nordlund Method Procedure
STEP 3 Determine the coefficient of lateral
earth pressure K? for each soil friction
angle, ?.

1. Determine K? for each ? angle based on displaced
   volume V, and pile taper angle, ?, using
   appropriate procedure in steps 3b, 3c, 3d, or 3e.
2. If displaced volume is 0.0093, 0.093, or 0.930
   m3/m and the friction angle is 25, 30, 35, or 40,
   use Figures 9.11 to 9.14.
3. If displaced volume is given but ? angle is not.
   Linear interpolation is required to determine K?
   for ? angle.

9-28
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K? versus ?
? 25?
Figure 9.11
9-33
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K? versus ?
? 30?
Figure 9.12
9-34
57
Nordlund Method Procedure
STEP 3 Determine the coefficient of lateral
earth pressure K? for each soil friction
angle, ?.

1. If displaced volume is not given but ? angle is
   given, log linear interpolation is required to
   determine K? for displaced volume V.
2. 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
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Table 9-4(a) Design Table for Evaluating K? for Piles when ? 0 and V 0.0093 to 0.0930 m3/m (0.10 to 1.00 ft3/ft) Table 9-4(a) Design Table for Evaluating K? for Piles when ? 0 and V 0.0093 to 0.0930 m3/m (0.10 to 1.00 ft3/ft) Table 9-4(a) Design Table for Evaluating K? for Piles when ? 0 and V 0.0093 to 0.0930 m3/m (0.10 to 1.00 ft3/ft) Table 9-4(a) Design Table for Evaluating K? for Piles when ? 0 and V 0.0093 to 0.0930 m3/m (0.10 to 1.00 ft3/ft) Table 9-4(a) Design Table for Evaluating K? for Piles when ? 0 and V 0.0093 to 0.0930 m3/m (0.10 to 1.00 ft3/ft) Table 9-4(a) Design Table for Evaluating K? for Piles when ? 0 and V 0.0093 to 0.0930 m3/m (0.10 to 1.00 ft3/ft) Table 9-4(a) Design Table for Evaluating K? for Piles when ? 0 and V 0.0093 to 0.0930 m3/m (0.10 to 1.00 ft3/ft) Table 9-4(a) Design Table for Evaluating K? for Piles when ? 0 and V 0.0093 to 0.0930 m3/m (0.10 to 1.00 ft3/ft) Table 9-4(a) Design Table for Evaluating K? for Piles when ? 0 and V 0.0093 to 0.0930 m3/m (0.10 to 1.00 ft3/ft) Table 9-4(a) Design Table for Evaluating K? for Piles when ? 0 and V 0.0093 to 0.0930 m3/m (0.10 to 1.00 ft3/ft) Table 9-4(a) Design Table for Evaluating K? for Piles when ? 0 and V 0.0093 to 0.0930 m3/m (0.10 to 1.00 ft3/ft)
N Displaced Volume -V, m3/m, (ft3/ft) Displaced Volume -V, m3/m, (ft3/ft) Displaced Volume -V, m3/m, (ft3/ft) Displaced Volume -V, m3/m, (ft3/ft) Displaced Volume -V, m3/m, (ft3/ft) Displaced Volume -V, m3/m, (ft3/ft) Displaced Volume -V, m3/m, (ft3/ft) Displaced Volume -V, m3/m, (ft3/ft) Displaced Volume -V, m3/m, (ft3/ft) 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 0.84 0.85
26 0.73 0.78 0.82 0.84 0.86 0.87 0.88 0.89 0.90 0.91
27 0.76 0.82 0.86 0.89 0.91 0.92 0.94 0.95 0.96 0.97
28 0.79 0.86 0.90 0.93 0.96 0.98 0.99 1.01 1.02 1.03
29 0.82 0.90 0.95 0.98 1.01 1.03 1.05 1.06 1.08 1.09
30 0.85 0.94 0.99 1.03 1.06 1.08 1.10 1.12 1.14 1.15
31 0.91 1.02 1.08 1.13 1.16 1.19 1.21 1.24 1.25 1.27
32 0.97 1.10 1.17 1.22 1.26 1.30 1.32 1.35 1.37 1.39
33 1.03 1.17 1.26 1.32 1.37 1.40 1.44 1.46 1.49 1.51
34 1.09 1.25 1.35 1.42 1.47 1.51 1.55 1.58 1.61 1.63
35 1.15 1.33 1.44 1.51 1.57 1.62 1.66 1.69 1.72 1.75
36 1.26 1.48 1.61 1.71 1.78 1.84 1.89 1.93 1.97 2.00
37 1.37 1.63 1.79 1.90 1.99 2.05 2.11 2.16 2.21 2.25
38 1.48 1.79 1.97 2.09 2.19 2.27 2.34 2.40 2.45 2.50
39 1.59 1.94 2.14 2.29 2.40 2.49 2.57 2.64 2.70 2.75
40 1.70 2.09 2.32 2.48 2.61 2.71 2.80 2.87 2.94 3.0
59
Nordlund Method Procedure
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
60
Correction Factor for K? when ? ? ?
Figure 9.15
61
Nordlund Method Procedure
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
62
Nordlund Method Procedure
STEP 7 Determine the at 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 at 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
63
Nordlund Method Procedure
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.
RT ?T Nq pT AT
Use lesser of
Figure 9-16a and 9-16b
RT qL AT
Figure 9-17
9-30
64
at Coefficient versus ?
?t
? (degrees)
Figure 9.16a
65
Figure 9.16b
66
Limiting Unit Toe Resistance (US)
Figure 9.17
67
Nordlund Method Procedure
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
68
STATIC CAPACITY OF PILES IN COHESIVE SOILS
69
Cohesive Soils, Undrained Strength
F Friction resistance N Normal force
(stress)
C is independent of overburden pressures
c cohesion, stickiness, soil / soil a
adhesion, stickiness, soil / pile
70
Unconfined Compression Strength
s1
s3
zero
C
C cohesion ½ qu
Maximum s1 unconfined compression strength, qu
s3
71
METHODS OF STATIC ANALYSIS FOR PILES IN COHESIVE SOILS METHODS OF STATIC ANALYSIS FOR PILES IN COHESIVE SOILS METHODS OF STATIC ANALYSIS FOR PILES IN COHESIVE SOILS METHODS OF STATIC ANALYSIS FOR PILES IN COHESIVE SOILS METHODS OF STATIC ANALYSIS FOR PILES IN COHESIVE SOILS METHODS OF STATIC ANALYSIS FOR PILES IN COHESIVE SOILS
Method Approach Method of Obtaining Design Parameters Advantages Disadvantages Remarks
a-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 9.7.1.2a.
Effective Stress Method. Semi-Empirical, based on effective stress at failure. ß and Nt values are selected from Table 9-6 based on drained soil strength estimates. Ranges in ß 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 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.
FHWA
9-42
72
Tomlinson or a-Method
Unit Shaft Resistance, fs
fs ca acu
Where ca adhesion (Figure 9.18) a
empirical adhesion factor (Figure 9.19)
9-41
73
Tomlinson or a-Method
Shaft Resistance, Rs
Rs fs As
Where As pile surface area in layer
(pile perimeter x length)
74
Tomlinson or a-Method (US)
Figure 9.18
75
Tomlinson or a-Method
Sand or Sandy Gravels
D
Stiff Clay
b
76
Tomlinson or a-Method (US)
D distance into stiff clay layer
Figure 9.19a
b Pile Diameter
9-47
77
Tomlinson or a-Method
Soft Clay
D
Stiff Clay
b
78
Tomlinson or a-Method (US)
D distance into stiff clay layer
Figure 9.19b
b Pile Diameter
9-47
79
Tomlinson or a-Method
D
Stiff Clay
b
80
Tomlinson or a-Method (US)
D distance into stiff clay layer
b Pile Diameter
Figure 9.19c
9-47
81
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, a 0.5 ?-0.5
For ? gt 1.0, a 0.5 ?-0.25
9-44
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Tomlinson or a-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)
83
Tomlinson or a-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.
84
Tomlinson or a-Method
Ru RS RT
and
Qa RU / FS, ASD
85
STUDENT EXERCISE 2
Use the a-Method described in Section 9.7.1.2a
and the Nordlund Method described in Section
9.7.1.1c to calculate the ultimate pile capacity
and the allowable design load for a 12.75 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).
86
Soil Profile
87
Solution

• We will compare this solution with the DRIVEN
  output (ie steps 1-9)

STEP 10 Qu Rs Rt
1465 410 1875 kN
88
Calculate the Shaft Resistance in the Clay Layer
Using a-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 / 12.75 in 40.5
1.47 ksf
89
ca 1.47 ksf
cu 2.73 ksf
9-45
Figure 9.18
90
Calculate the Shaft Resistance in the Clay Layer
Using a-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)
213.6 kips
91
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
92
Relationship Between Soil Displacement, V, and ?/?
V 0.89
?/? 0.62
e Raymond uniform piles f H-piles g tapered
portion of Monotube piles
a closed-end pipe and non-tapered Monotube
piles b timber piles c pre-cast concrete
piles d Raymond Step-Taper piles
93
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, ?, 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
94
Calculate the Shaft Resistance in the Sand Layer
Using the Nordlund Method
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? 1.15 for V 0.10 ft3/ft
K? 1.75 for V 1.00
ft3/ft Using log linear interpolation K?
1.72 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
95
Correction Factor for K? when ? ? ?
CF 0.78
? 35
Figure 9.15
96
Calculate the Shaft Resistance in the Sand Layer
Using the Nordlund Method
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? 1.15 for V 0.10 ft3/ft
K? 1.75 for V 1.00
ft3/ft Using log linear interpolation K?
1.72 for V 0.89 ft3/ft
STEP 4 Determine correction factor, CF, to be
applied to K? when ? ? ?. Layer 2 ? 35
and ?/? CF
0.78
0.62
97
Calculate the Shaft Resistance in the Sand Layer
Using the Nordlund Method
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
125.1 kips
(1.72) (0.78) (3.73 ksf) (sin 21.7) (3.38
ft2/ft) (20 ft)
98
Compute the Ultimate Shaft Resistance, Rs
Rs Rs1 Rs2 Rs Rs
213.6 kips 125.1 kips
338.7 kips
99
Compute the Ultimate Toe Resistance, Rt
STEP 7 Determine at coefficient and bearing
capacity factor N'q from ? angle of 35 at
pile toe and Figures 9.16(a) and
9.16(b) At pile toe depth
D/b From Figure 9.16(a) at
From Figure 9.16(b) N'q
66 ft / 12.75 in. 62
100
at Coefficient versus ?
0.67
?t
? 35
? (degrees)
Figure 9.16a
101
65
Figure 9.16b
102
Compute the Ultimate Toe Resistance, Rt
STEP 7 Determine at coefficient and bearing
capacity factor N'q from ? angle of 35 at
pile toe and Figures 9.16(a) and
9.16(b) At pile toe depth D/b
62 From Figure 9.16(a) at
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.
103
Compute the Ultimate Toe Resistance, Rt
STEP 9 Compute the ultimate toe resistance,
Rt. a. Rt at 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) 116.3 kips
104
Limiting Unit Toe Resistance
105
Figure 9.17
105
Compute the Ultimate Toe Resistance, Rt
STEP 9 Compute the ultimate toe resistance,
Rt. a. Rt at 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) 116.3 kips
(105 ksf)(0.89 ft2) 93.5 kips
93.5 kips
106
Compute the Ultimate Pile Capacity, Qu
STEP 10 Qu Rs Rt
338.7 93.5 kips 432.2 kips
107
DRIVEN COMPUTER PROGRAM
DRIVEN uses the FHWA recommended Nordlund
(cohesionless) and a-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
108
DRIVEN COMPUTER PROGRAM
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
109
DRIVEN COMPUTER PROGRAM
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
110
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
111
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
112
METHODS BASED ON CPT DATA
Elsami and Fellenius
(9-66)
Nottingham and Schmertmann
(9-68)
Laboratoire des Ponts et Chaussees (LPC)
(9-75)
113
UPLIFT CAPACITY OF SINGLE PILES
Increasingly important design consideration Source
s 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.
114
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 19.8.3 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
115
Any Questions
116
STATIC ANALYSIS SINGLE PILESLATERAL CAPACITY
METHODS

• Reference Manual Chapter 9.7.3

9-82
117
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.

118
Lateral Capacity of Single Piles

• 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.

119
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

120
Lateral Capacity of Single Piles

• Design Methods
• Lateral load tests
• Analytical methods
• Broms method, 9-86, (long pile, short pile)
• Reeses COM624P method
• LPILE program
• FB-PIER

9-85
121
Figure 9.36 Soil Resistance to a Lateral Pile
Load (adapted from Smith, 1989)
9-83
122
NIM
123
Figure 9.44 LPILE Pile-Soil Model
9-101
124
NIM
125
NIM
126
We have n equations and (n4) unknowns
BOUNDARY CONDITIONS (long pile)
_at_ Pile Bottom
Moment 0
Shear 0
_at_ Pile Top
??
127
Figure 9.45 Typical p-y Curves for Ductile and
Brittle Soil (after Coduto, 1994)
9-102
128
Figure 9.45 Typical p-y Curves for Ductile and
Brittle Soil (after Coduto, 1994)
9-102
129
Integrate
Differentiate
Figure 9.36 Graphical Presentation of LPILE
Results (Reese, et al. 2000)
9-92
130
LETS EAT !!
131
Lets Demo DRIVEN !