6.8 Downdrag (Negative Skin Friction)
6.9.3 Design Criteria for Axially Loaded Piles
According to AASHTO LRFD Specification, the ultimate geotechnical resistance of piles subjected to axial loading can be expressed by
(6.39) where and are resistance factors (Table 6.11),qpis the ultimate unit point resistance,qs
is the ultimate unit skin friction, andApandAsare cross-sectional area and embedded surface area of pile, respectively.
On the other hand, according to AASHTO LRFD Specification, the ultimate structural resistance of piles subjected to axial loading can be expressed by
(6.40) wherePnis the ultimate structural resistance of the pile,Pris the factored structural resistance of the pile, and is the resistance factors (Table 6.14).
Example 6.6
Figure 6.25 shows a bridge pier supported by a steel pile (HP 360×108) group that has to be designed to carry a dead load of 5000 kN and a live load of 4000 kN. The CPT results for the site are also illustrated inFigure 6.25in an idealized form. Use the LRFD method to estimate the number of piles needed in the group assuming that the driving conditions are severe.
Step 1: Geotechnical resistance. For end bearing, Equation (6.21) For Z=10m,R1=1.0,R2=1.0
qp=(1.0)(1.0)(16,000+16,000)/2=16000 kPa Qp=16,000(0.346)(0.371)=2,053 kN
For skin-friction
Page 275
FIGURE 6.25
Illustration forExample 6.6.
SoCu=(α'/α)fs
Cucan be determined from Table 6.2andTable 6.4using trial and error. It is recorded in the column 4 of Table 6.12.
Referring to Table 6.12for determination of segmental frictional contributions.
Total Qside=583.6 kN TABLE 6.11
Resistance Factors for Geotechnical Resistance of Piles—ASD-Based Calibration (Safety Factor of 2.75)
Method/Soil/Condition Resistance Factor
Ultimate bearing resistance of single piles Skin friction: clay
α-Method 0.70
β-Method 0.50
λ-Method 0.55
End bearing: clay and rock
Clay 0.70
Rock 0.50
Skin friction and end bearing:
sand
SPT method 0.45
CPT method 0.55
Skin friction and end bearing: all soils
Load test 0.80a
Pile driving analyzer 0.70
Block failure Clay 0.65
Uplift resistance of single piles α-Method 0.60
λ-Method 0.45
SPT method 0.35
CPT method 0.45
Load test 0.80
Group uplift resistance Sand 0.55
Clay 0.55
aASD safety factor of 2.0.
Source:From Federal Highway Administration, 1997,Load and Resistance Factor Design (LRFD) for Highway Bridge Substructures,Washington, DC. With permission.
Page 276 TABLE 6.12
Illustration of Computations forExample 6.6
Depth (m) α' Steel (Table 6.4) fs(kPa) Cu(kPa) fpile(kPa) Fsegmental(kPN)
0 0
1.73 2 30 75 60 114
3.46 1.25 30 39.87 37.5 185
4 1.14 30 35.73 34.2 42.6
5.19 0.9 20 17.47 18 68.3
6.92 0.82 20 15.81 16.4 65.5
8.65 0.8 20 15.40 16 61.7
10 0.75 20 14.38 15 46
583.6 kN
Step 2: Structural resistance
Step 3: Compute applied loads
Pu=1.25(5000)+1.75(4000) P=5,000+4,000
=13,250 kN =9,000kN
Step 4: Determine the number of piles required.
Geotechnical criterion
LRFD ASD
=13,250/1,449 =9,000(2.75)/2,636
=9.1=10 piles =9.4=10 piles
Structural criterion
=13,250/1,021.7 =9000(2.75)/2919
=13 piles =8.47=9 piles
Then the number of piles required is 13.
Example 6.7
ForExample 6.3, the factored axial resistance can be obtained from Equation (6.39) as follows:
FromTable 6.13, for CPT results
Weight of structural components=700 kN Weight of vehicular traffic=200 kN
The LHS of Equation (6.37) can be used to compute the factored load as
Page 277 TABLE 6.13
Resistance Factors for Geotechnical Resistance of Piles (Reliability-Based Calibration)
Values by Method of Axial Pile Capacity Estimation
A A
Pile Length (m) βT Type I Type II β Type I Type II CPT SPT
10 2.0 0.78 0.92 0.79 0.53 0.65 0.59 0.48
30 2.0 0.84 0.96 0.79 0.55 0.71 0.62 0.51
10 2.5 0.65 0.69 0.68 0.41 0.56 0.48 0.36
30 2.5 0.71 0.73 0.68 0.44 0.62 0.51 0.38
0.78 0.74 0.56 0.55 0.43
0.70 0.50 0.55 0.55 0.45
Source:From Federal Highway Administration, 1997,Load and Resistance Factor Design (LRFD) for Highway Bridge Substructures,Washington, DC. With permission.
TABLE 6.14
Resistance Factors for Structural Design of Axially Loaded Piles
Pile Type Resistance Factor
Steel
Severe driving conditions 0.35
Good driving conditions 0.45
Prestressed concrete 0.45
Concrete-filled pipe
Steel pipe 0.35
Concrete 0.55
Timber 0.55
Source:From Federal Highway Administration, 1998,Load and Resistance Factor Design (LRFD) for Highway Bridge Substructures,Washington, DC. With permission.
∑γiQi=1.25(700)+1.75(200)=1225 kN
It is seen that Equation (6.37) is satisfied for the geotechnical strength.
As for the structural strength,Table 6.14provides the structural resistance factor for a concrete pile with a steel casing as 0.35.
Assuming that the compressive strength of concrete is 20 MPa Factored resistance=20,000(0.35)=7000 kPa
Factored load=(ẳ)B(0.4)2(7000)=879 kN<1225 kN
Since Equation (6.37) is not satisfied from a structural perspective, the diameter of the pile has to be increased to about 0.5 m, which would improve the geotechnical strength further.
In the case of piles driven into rock, the static capacity can be estimated in a manner similar to that followed for soils. According to Kulhawy and Goodman (1980), the ultimate point
bearing capacity of a pile driven in rock would be given by
Page 278
FIGURE 6.26
Wedge bearing capacity factors for foundations on rock. (From Tomlinson, M.J., 1994,Pile Design and Construction Practices,4th ed., E & FN Spon, London. With permission.)
TABLE 6.15
Permissible Stresses during Pile Driving
Pile Type Stress Level
Steel 0.90Fy(compression)
0.90Fy(tension) Concrete
0.70Fy of steel reinforcement (tension) Prestressed concrete (normal
environments)
andfpemust be in MPa; the resulting max stress is also in MPa
(severe corrosive environments) fpe(tension)
Timber 3σall(compression)
3σall(tension)
Source: From AASHTO, 1996, Standard Specificationsfor Highway Bridges, 16th ed., American Association of State Highway and Transportation Officials, Washington, DC. With permission.
(6.41) where cis the cohesion,B is the base width,Dis the depth of the pile base below the rock surface, γis the effective density of the rock mass,Nc, Nq,andNγare bearing capacity factors
a circular pile, andFγ=0.8 for a square pile and 0.7 for a circular pile.
Page 279 TABLE 6.16
Properties of Rock Mass Related to the Unconfined Strength and the Rock Quality Designation (RQD) Value
RQD Cohesion
0–10 0.1qu 30°
70–100 0.1qu 30–60°
Source: From Tomlinson, M.J., 1994, Pile Design and Construction Practices, 4th ed., E & FN Spon, London.
With permission.
TABLE 6.17
Friction Angle of Intact Rock
Classification Type Friction Angle
Low friction Schists (high mica content) 20–27 Shale
Marl
Medium friction Sandstone 27–34
Siltstone Chalk Gneiss
Low friction Basalt 34–40
Granite
Source: From Tomlinson, M.J., 1994, Pile Design and Construction Practices, 4th ed., E & FN Spon, London.
With permission.