LRFD Steel Girder SuperStructure Design Example
Pile Foundation Design Example Design Step P
Table of Contents
Design Step P.1  Define Subsurface Conditions and Any Geometric Constraints
Design Step P.2  Determine Applicable Loads and Load Combinations
Design Step P.3  Factor Loads for Each Combination
Design Step P.4  Verify Need for a Pile Foundation
Design Step P.5  Select Suitable Pile Type and Size
Design Step P.6  Determine Nominal Axial Structural Resistance for Selected Pile Type / Size
Design Step P.7  Determine Nominal Axial Geotechnical esistance for Selected Pile Type / Size
Design Step P.8  Determine Factored Axial Structural Resistance for Single Pile
Design Step P.9  Determine Factored Axial Geotechnical Resistance for Single Pile
Design Step P.10  Check Drivability of Pile
Design Step P.11  Do Preliminary Pile Layout Based on Factored Loads and Overturning Moments
Design Step P.12  Evaluate Pile Head Fixity
Design Step P.13  Perform Pile Soil Interaction Analysis
Design Step P.14  Check Geotechnical Axial Capacity
Design Step P.15  Check Structural Axial Capacity in lower portion of pile)
Design Step P.16  Check Structural Axial Capacity in Combined Bending and Axial Load (upper portion of pile)
Design Step P.17  Check Structural Shear Capacity
Design Step P.18  Check Maximum Horizontal and Vertical Deflection of Pile Group at Beam Seats Using Service Load Case
Design Step P.19  Additional Miscellaneous Design Issues
References
Design Step P.1  Define Subsurface Conditions and Any Geometric Constraints
This task involves determining the location and extent of soil and rock materials beneath the proposed abutment and determining engineering design properties for each of those materials. It also includes identification of any specific subsurface conditions that may impact the performance of the structure. The design of the foundation system needs to address any identified issues.
A subsurface investigation was conducted at the site. Two test borings were drilled at each substructure unit. Soils were sampled at 3 foot intervals using a split spoon sampler in accordance with ASTM D1586. Rock was continuously sampled with an N series core barrel in accordance with ASTM D2113.
For Abutment 1, one boring was drilled at each side of the abutment. These borings are illustrated graphically in Section A1 below.
Refer to Design Step 1 for introductory information about this design example. Additional information is presented about the design assumptions, methodology, and criteria for the entire bridge, including the Pile Foundation Design.
The following units are defined for use in this design example:
Figure P1 Section A1  Subsurface Conditions at Abutment 1
Evaluation of Section A1 indicates that subsurface conditions are relatively uniform beneath the proposed abutment consisting of essentially 2 materials.
Loose silty sand was encountered in the top 35 feet of each boring. This material is nonplastic and contains about 15% fine material. Below a depth of about 5' the soil is saturated.
Rock was encountered at about elevation 70 in both borings. The rock consists of a hard gray sandstone. Fractures are tight with no infilling and occur at a spacing of 13'; primarily along bedding planes which are horizontal. Slight weathering was observed in the upper 1' foot of the rock but the remainder of the rock is unweathered.
Special Geotechnical Considerations:
The loose fine sandy soils could be subject to liquefaction under seismic loading. Liquefaction is a function of the anticipated maximum earthquake magnitude and the soil properties. If liquefaction is a problem, the soils can not be relied upon to provide lateral support to deep foundation systems. For this example it is assumed that the potential for liquefaction has been evaluated and has been found to be negligible. (Note: Seed and Idriss (NCEER970022) provides more up to date material for evaluation of liquefaction)
C10.5.4, SAppendix A10
The weight of the approach embankment will cause compression of the loose soil horizon. The granular material should compress essentially elastically with little or no long term consolidation. However, since the full height abutment will likely be placed prior to completion of the approach embankment in the vicinity of the abutment, soil compression beneath the abutment must be accounted for in foundation design. For shallow foundations, this compression will result in settlement and rotation of the footing. For deep foundations this compression could result in negative skin friction (downdrag) loads on the foundation elements; particularly in the back row of piles.
S10.7.1.4, C10.7.1.4
Development of Parameters for Design:
Layer 1  Soil
Depth:
Assuming a bottom of footing elevation of 101 FT and a top of rock elevation of 70 FT as described above:
Unit Weight ( Υ ):
Consider relevant published data when selecting design parameters. For unit weights of insitu soil materials, a good reference is NAVFAC DM7.122. Based on this reference, general and local experience, and the above description of the soil horizon as loose silty sand, the unit weights were selected as follows:
C10.4.1
Dry unit weight:
Wet unit weight:
Unit weight of water:
Effective unit weight:
Angle of internal friction ( φ ):
The angle of internal friction can be estimated based on correlation to Standard Penetration Test (SPT) N values. The raw SPT Nvalues determined in the test borings must be corrected for overburden pressure as follows:
SEquation 10.7.2.3.34
where:
Corrected SPT blow count (Blows/FT)
Note: The formula above is generally considered valid for values of σ' > 0.25 TSF (Bowles 1977):
SPT blow count (Blows/FT):
Vertical effective stress at bottom of sample (TSF):
where:
Thickness of soil layer i above point being considered (FT):
Effective unit weight of soil layer i (PCF):
Number of soil layer under consideration:
This formula is implemented for each of the borings below. Wet unit weight is used for the soil above the water table and effective unit weight is used for the soil below the water table.
Depth to Top of Sample (FT)

Depth to Bottom of Sample (FT)

U_{eff i} (PCF)

s_{n}' (TSF)

N Blows/Ft (BPF)

N_{corr} Blows/Ft (BPF)


Boring A11


0

1.5

110

0.0825

5

9

3

4.5

110

0.2475

5

7

6

7.5

47.6

0.3189

4

6

9

10.5

47.6

0.3903

3

4

12

13.5

47.6

0.4617

5

6

15

16.5

47.6

0.5331

6

7

18

19.5

47.6

0.6045

3

4

21

22.5

47.6

0.6759

3

3

24

25.5

47.6

0.7473

6

7

27

28.5

47.6

0.8187

9

10

30

31.5

47.6

0.8901

12

12

33

34.5

47.6

0.9615

14

14

Boring A12


0

1.5

110

0.0825

2

4

3

4.5

110

0.2475

3

4

6

7.5

47.6

0.3189

5

7

9

10.5

47.6

0.3903

6

8

12

13.5

47.6

0.4617

8

10

15

16.5

47.6

0.5331

4

5

18

19.5

47.6

0.6045

6

7

21

22.5

47.6

0.6759

9

10

24

25.5

47.6

0.7473

10

11

27

28.5

47.6

0.8187

10

11

30

31.5

47.6

0.8901

11

11

33

34.5

47.6

0.9615

13

13

Table P1 Calculation of Corrected SPT Blow Count
Find average values for zone between bottom of footing and top of rock. This means ignoring the first two values of each boring.
The correlation published in FHWAHI96033 Page 417 (after Bowles, 1977) is used to determine the angle of internal friction. This correlation is reproduced below.
Description

Very Loose

Loose

Medium

Dense

Very Dense


N_{corr} =

04

410

1030

3050

>50

j_{f} =

2530^{o}

2732^{o}

3035^{o}

3540^{o}

3843^{o}

a =

0.5

0.5

0.25

0.15

0

b =

27.5

27.5

30

33

40.5

Table P2 Correlation
This correlation can be expressed numerically as:
where:
a and b are as listed in Table P2.
Thus
^{o} say ^{o}
Modulus of elasticity (E):
Estimating E_{0} from description
STable 10.6.2.2.3b1
Loose Fine Sand E_{0}= 80  120 TSF
Estimating E_{0} from N_{corr}
Note, in Table 10.6.2.2.3b1 N_{1} is equivalent to N_{corr}
Clean fine to medium sands and slightly silty sands
STable 10.6.2.2.3b1
Based on above, use:
Poisons Ratio ( ν ):
Estimating ν from description
STable 10.6.2.2.3b1
Loose Fine Sand:
Shear Modulus (G):
From Elastic Theory:
Coefficient of variation of subgrade reaction (k):
As per FHWAHI96033, Table 913:
This is used for lateral analysis of deep foundation elements
Submerged Loose Sand
Layer 2  Rock:
Depth:
Rock is encountered at elevation 70 and extends a minimum of 25 FT beyond this point.
Unit Weight ( Υ ):
Determined from unconfined compression tests on samples of intact rock core as listed below:
Boring No.

Depth (FT)

U (PCF)


A11

72.5

152

A11

75.1

154

A12

71.9

145

A12

76.3

153

P11

81.2

161

P12

71.8

142

A21

76.3

145

A22

73.7

151

Average U

150.375

Table P3 Unit Weight
Unconfined Compressive Strength (q):
Determined from unconfined compression tests on samples of intact rock core as listed below:
Boring No.

Depth (FT)

q_{u} (PSI)


A11

72.5

12930

A11

75.1

10450

A12

71.9

6450

A12

76.3

12980

P11

81.2

14060

P12

71.8

6700

A21

76.3

13420

A22

73.7

14890

Average q_{u}

11485

Table P4 Unconfined Compressive Strength
Modulus of elasticity (E):
STable 10.6.2.2.3d2
This is to be used for prediction of deep foundation response
For sandstone, Average:
Poisons Ratio ( ν ):
STable 10.6.2.2.3d1
This is to be used for prediction of pile tip response
For sandstone, Average:
Shear Modulus (G):
From elastic theory
Rock Mass Quality:
Rock mass quality is used to correct the intact rock strength and intact modulus values for the effects of existing discontinuities in the rock mass. This is done through empirical correlations using parameters determined during core drilling.
Data from the test borings is summarized below:
Depth (FT)

Run Length (FT)

Recovery (%)

RQD (%)


Boring A11


35

5

100

80

40

5

96

94

45

5

100

96

50

5

98

92

55

5

98

90

Boring A12


35

5

98

90

40

5

100

80

45

5

100

96

50

5

96

90

55

5

98

96

Averages

98.4

90.4

Table P5 Rock Mass Quality
Design Step P.2  Determine Applicable Loads and Load Combinations
Loads and load combinations are determined elsewhere in the design process. The critical load cases for evaluation of foundation design are summarized below:
The load combination that produces the maximum vertical load on the foundation system. This will typically be a Strength I and a Service I load case with the maximum load factors applied.
The load combination that produces the maximum overturning on the foundation which will tend to lift a spread footing off the bearing stratum or place deep foundation elements in tension.
The load combination that produces the maximum lateral load. If several combinations produce the same horizontal load, select the one with the minimum vertical load as this will be critical for evaluation of spread footing sliding or response of battered deep foundations. In some cases, particularly deep foundations employing all vertical elements, the highest lateral load and associated highest vertical load should also be evaluated as this case may produce higher foundation element stress and deflections due to combined axial load and bending in the foundation elements.
Design Step P.3  Factor Loads for Each Combination
It is extremely important to understand where the loads are being applied with respect to foundation design. In this case the loads were developed based on an assumed 10' 3" wide by 46' 10 1/2" long footing that is offset behind the bearings a distance of 1' 9". The loads are provided at the horizontal centroid of the assumed footing and at the bottom of that footing. A diagram showing the location and direction of the applied loads is provided below.
Figure P2 Application of Loads
LIMIT STATE  AXIAL FORCE P_{vert} (K)  LONG MOMENT M_{long} (KFT)  TRANS MOMENT M_{trans} (KFT)  LATERAL LOAD (IN LONG. DIR.) P_{long} (K)  LATERAL LOAD (IN TRANS. DIR.) P_{trans} (K)  

Maximum Vertical Load  STRI MAX/FIN  2253  7693  0  855  0 
SERI MAX/FIN  1791  4774  162  571  10  
Maximum Overturning  STRI MIN/FIN  1860  7291  0  855  0 
SERI MIN/FIN  1791  4709  162  568  10  
Maximum Lateral Load  STRIII MAX/FIN  1815  6374  508  787  37 
SERI MAX/FIN  1791  4774  162  571  10 
Table P6 Summary of Factored Loads
It should be noted that the calculations performed in Design Step P are based on preliminary pile foundation design forces. In an actual design, the geotechnical engineer would need to revisit the pile foundation design calculations and update the results based on the final design bottom of booting forces given at the end of Design Step 7.7.
Design Step P.4  Verify Need for a Pile Foundation
Evaluate a spread footing design:
Check vertical capacity:
Presumptive Bearing Capacity for loose sand with silt (SM)
Presumptive bearing capacity
STable 10.6.2.3.11
Presumptive bearing capacity is a service limit state, thus compare against maximum service load.
S10.5.2
From Design Step P.3, the Maximum service load is
The Required area:
The length of the footing is controlled by the length of the abutment step required to support the steel beams and the approach roadway. This is determined from previous geometry calculations.
Maximum possible length of footing
Preliminary minimum required width
Excessive loss of contact:
This is a strength limit state thus use strength loads for the case of maximum overturning which is STR I Min.
S10.5.3
Determine the maximum eccentricity e_{B} in the direction parallel to the width of the footing (B)
From the loads obtained in Design Step P.3,
To prevent excessive loss of contact e_{B} must be less than B/4.
S10.6.3.1.5
Width of the footing:
In order to resolve the bearing pressure and eccentricity issue, the footing will have to be widened and the centroid shifted toward the toe. This can be accomplished by adding width to the toe of the footing. Note that the issue could also be resolved by adding width to the heel of the footing, which would increase the weight of soil that resists overturning. This would require recalculation of the loads and was not pursued here.
In order to satisfy bearing pressure and eccentricity concerns, the footing width is increased incrementally until the following two criteria are met:
Based on Strength Loads
> Based on Service Loads
Where B' is the effective footing width under eccentric load
SEquation 10.6.3.1.51
For the Strength Load case:
Footing width B (FT)

Distance from heel to Centroid of footing (FT)

Distance from heel to centroid of load (FT)

e_{B} (FT)

B/4 (FT)


10.25

5.13

9.05

3.92

2.56

11.00

5.50

9.05

3.55

2.75

12.00

6.00

9.05

3.05

3.00

13.00

6.50

9.05

2.55

3.25

14.00

7.00

9.05

2.05

3.50

15.00

7.50

9.05

1.55

3.75

16.00

8.00

9.05

1.05

4.00

17.00

8.50

9.05

0.55

4.25

Table P7 Excessive Loss of Contact  Strength
For the Strength Load Case, the condition was satisfed first when the width of the footing B = 13.00 FT
For the Service Load Case
From the loads obtained from Design Step P.3,
Footing width B (FT)

Distance from heel to Centroid of footing (FT)

Distance from heel to centroid of load (FT)

e_{B} (FT)

B' (FT)


10.25

5.13

7.80

2.67

4.91

11.00

5.50

7.80

2.30

6.41

12.00

6.00

7.80

1.80

8.41

13.00

6.50

7.80

1.30

10.41

14.00

7.00

7.80

0.80

12.41

15.00

7.50

7.80

0.30

14.41

16.00

8.00

7.80

0.21

16.41

Table P8 Presumptive Bearing Pressure  Service
For the Service Load Case, the condition was satisfed first when the width of the footing B = 15.00 FT
The first width to satisfy both conditions is 15.00 FT. Which would require the toe of the footing to be extended:
This increase may not be possible because it may interfere with roadway drainage, roadside utilities, or the shoulder pavement structure. However, assume this is not the case and investigate potential settlement of such a footing.
Settlement is a service limit state check.
For the granular subsoils, settlement should be esentially elastic thus Settlement (S_{0}) is computed from:
SEquation 10.6.2.2.3b1
Assume the footing is fully loaded, thus q_{0} is the presumptive bearing capacity and effective loaded area is as calculated above
Average bearing pressure on loaded area:
Effective are of footing:
Length of footing
Width of the footing
Therfore, the Effective Area is
Modulus of elasticity of soil, from Design Step P.1:
Poisson's ratio of soil, from Design Step P.1:
Shape factor for rigid footing:
From Table 10.6.2.2.3b2 for rigid footing:
L'/B'  b_{z} 

3  1.15 
5  1.24 
STable 10.6.2.2.3b2
Table P9 Rigid Footing
By interpolation, at
Note: This computation assumes an infinite depth of the compressible layer. Other computation methods that allow for the rigid base (NAVFAC DM7.1211) indicate the difference between assuming an infinite compressible layer and a rigid base at a depth equal to 3 times the footing width (H/B = 3) below the footing can be estimated by computing the ratio between appropriate influence factors (I) as follows:
As per NAVFAC DM7.1212, and DM7.1213:
I for rigid circular area over infinite halfspace:
I for rigid circular area over stiff base at H/B of 3:
The influence value determined above is for a Poisson's ratio of 0.33. A Poisson's ration of 0.25 is used for the soil. This difference is small for the purposes of estimating elastic settlement.
Ratio of I values:
Since I is directly proportional to settlement, this ratio can be multiplied by S_{0} to arrive at a more realistic prediction of settlement of this footing.
This settlement will occur as load is applied to the footing and may involve some rotation of the footing due to eccentricities of the applied load. Since most of the loads will be applied after construction of the abutment (backfill, superstructure, deck) this will result in unacceptable displacement.
The structural engineer has determined that the structure can accommodate up to 1.5" of horizontal displacement and up to 0.5" vertical displacement. Given the magnitude of the predicted displacements, it is unlikely this requirement can be met. Thus, a deep foundation system or some form of ground improvement is required.
Note that the above calculation did not account for the weight of the approach embankment fill and the effect that this will have on the elastic settlement. Consideration of this would increase the settlement making the decision to abandon a spread footing foundation even more decisive.
Design Step P.5  Select Suitable Pile Type and Size
It will be assumed that for the purposes of this example, ground improvement methods such as vibroflotation, vibro replacement, dynamic deep compaction, and others have been ruled out as impractical or too costly. It is further assumed that drilled shaft foundations have been shown to be more costly than driven pile foundations under the existing subsurface conditions (granular, water bearing strata). Thus a driven pile foundation will be designed.
Of the available driven pile types, a steel Hpile end bearing on rock is selected for this application for the following reasons.
It is a low displacement pile which will minimize friction in the overlying soils.
It can be driven to high capacities on and into the top weathered portion of the rock.
It is relatively stiff in bending thus lateral deflections will be less than for comparably sized concrete or timber piles.
Soils have not been shown to be corrosive thus steel loss is not an issue.
To determine the optimum pile size for this application, consideration is given to the following:
1) Pile diameter:
HPiles range in size from 8 to 14 inch width. Since pile spacing is controlled by the greater of 30 inches or 2.5 times the pile diameter (D); pile sizes 12 inches and under will result in the same minimum spacing of 30 inches. Thus for preliminary analysis assume a 12 inch HPile.
2) Absolute Minimum Spacing:
Per referenced article, spacing is to be no less than:
S10.7.1.5
Where the pile diameter:
3) Minimum pile spacing to reduce group effects:
As per FHWAHI96033, Section 9.8.1.1:
Axial group effects for end bearing piles on hard rock are likely to be negligible thus axial group capacity is not a consideration. However, note that the FHWA driven pile manual recommends a minimum cc spacing of 3D or 1 meter in granular soils to optimize group capacity and minimize installation problems. The designer's experience has shown 3D to be a more practical limit that will help avoid problems during construction.
Lateral group effects are controlled by pile spacing in the direction of loading and perpendicular to the direction of loading.
From Reese and Wang, 1991, Figure 5.3 (personal communication):
For spacing perpendicular to the direction of loading 3D results in no significant group impacts.
As per FHWAHI96033, Section 9.8.4 & NACVFAC DM7.2241:
For spacing in the direction of loading, various model studies indicate that group efficiency is very low at 3D spacing, moderate at about 5D spacing and near 100% for spacings over about 8D. Thus it is desirable to maintain at least 5D spacing in the direction of the load and preferable to maintain 8D spacing.
Maximum pile spacing
Spacing the piles more than 10 feet cc results in higher bending moments in the pile cap between each pile and negative bending moments over the top of each pile that may result in additional steel reinforcing or thicker pile caps. Thus it is desirable to keep the pile spacing less than 10 feet cc.
4) Edge clearance
Referenced section indicates minimum cover:
S10.7.1.5
Thus for a 12 inch pile, minimum distance from edge of footing to center of pile:
5) Maximum pile cap dimensions
The length of the pile cap in the direction perpendicular to the centerline (L) is limited to the width of the abutment. Thus:
From Design Step P.4:
The width of the pile cap in the direction parallel to the centerline of the bridge (B) can generally be made wider as required. Initial loadings were developed assuming a width of 10.25 FT thus use this dimension as a starting point.
Determine the maximum and minimum number of piles that can be placed beneath the cap (See sketch below for definition of variables)
Figure P3 Plan View of Pile Cap
In B direction:
is defined as: Width of the pile cap  2 times the edge distance
Max number of spaces at 5D spacing (N_{B})
Minimum number of spaces at 10' each (N_{B})
Since the number of spaces has to be an integer
Which results in two rows of piles in the B direction.
In L direction:
is defined as: Width of the pile cap  2 times the edge distance
Max number of spaces at 3D spacing (N_{L})
Minimum number of spaces at 10' each (N_{L})
Since the number of spaces has to be an integer
to 14
Which results in 6 to 15 rows of piles in the L direction.
Determine maximum axial load acting on piles
Using factored loads and diagram below, determine reactions on the front and back pile rows:
Figure P4 Section View of Pile Cap
Summing the forces in the zdirection and the moments about point B:
For STR I max, from Table P.6:
For STR I min, from Table P.6:
Max axial load on front row of piles:
Since the front row can have 6  15 piles,
Max anticipated factored pile load can range between:
and
Assuming the following:
Axial pile resistance is controlled by structural resistance
SEquation 6.9.2.11 and SEquation 6.9.4.11
Structural resistance
NOTE: λ in equation 6.9.4.11 is assumed to be zero (because unbraced length is zero) resulting in the simplified equation shown above.
S6.5.4.2
NOTE: Grade 36 steel is assumed at this stage even though most Hpile sections are available in higher grades at little or no cost differential. The need for using a higher strength steel will be investigated in future design steps
Compute required pile area to resist the anticipated maximum factored pile load. The required steel area can range between:
and
For preliminary layout and design, select: HP 12x53
Properties of HP 12x53:
Note: Plastic section modulus is used to evaluate nominal moment capacity
Design Step P.6  Determine Nominal Axial Structural Resistance for Selected Pile Type / Size
Ultimate axial compressive resistance is determined in accordance with either equation 6.9.4.11 or 6.9.4.12. The selection of equation is based on the computation of l in equation 6.9.4.13 which accounts for buckling of unbraced sections. Since the pile will be fully embedded in soil, the unbraced length is zero and therefore l is zero. Based on this this, use equation 6.9.4.11 to calculate the nominal compressive resistance.
S6.9.4.1
SEquation
6.9.4.11
where:
Therefore:
Design Step P.7  Determine Nominal Axial Geotechnical Resistance for Selected Pile Type / Size
Geotechnical axial resistance for a pile end bearing on rock is determined by the CGS method outlined in 10.7.3.5
Nominal unit bearing resistance of pile point, q_{p}
SEquation 10.7.3.51
for which:
SEquation 10.7.3.52
where:
Average compressive strength of rock core:
From Design Step P.1:
Spacing of discontinuities:
Based on high observed RQD in Design Step P.1 and description of rock:
Width of discontinuities:
Joints are tight as per discussion in Design Step P.1:
Pile width:
HP 12x53 used:
Depth of embedment of pile socketed into rock:
Pile is end bearing on rock:
Diameter of socket:
Assumed but does not matter since H_{s} = 0:
so:
and:
Thus:
Nominal geotechnical resistance (Q_{p}):
SEquation 10.7.3.23
where:
Nominal unit bearing resistance as defined above:
Area of the pile tip:
Area determined assuming a plug develops between flanges of the HPile. This will be the case if the pile is driven into the upper weathered portion of the rock.
Therefore:
Design Step P.8  Determine Factored Axial Structural Resistance for Single Pile
Factored Structural Resistance (Pr):
SEquation 6.9.2.1
where:
Resistance factor for Hpile in compression, no damage anticipated:
S6.5.4.2
Nominal resistance as computed in Design Step P.6:
Therefore:
Design Step P.9  Determine Factored Axial Geotechnical Resistance for Single Pile
Factored Geotechnical Resistance (Q_{R}):
SEquation 10.7.3.22
Note: remainder of equation not included since piles are point bearing and skin friction is zero.
where:
Resistance factor, end bearing on rock (CGS method):
STable 10.5.52
Factor to account for method controlling pile installation:
For this porject, stress wave measurements will be specified on 2% of the piles (a minimum of one per substructure unit) and the capacity will be verified by CAPWAP analysis. Thus:
STable 10.5.52
and therefore:
Nominal resistance as computed in Design Step P.7:
Therefore:
Note: This is greater than the structural capacity, thus structural capacity controls.
Design Step P.10  Check Drivability of Pile
Pile drivability is checked using the computer program WEAP. The analysis proceeds by selecting a suitable sized hammer. Determining the maximum pile stress and driving resistance (BPF) at several levels of ultimate capacity and plotting a bearing graph relating these variables. The bearing graph is then entered at the driving resistance to be specified for the job (in this case absolute refusal of 20 BPI or 240 BPF will be used) and the ultimate capacity and driving stress correlating to that driving resistance is read.
If the ultimate capacity is not sufficient, a bigger hammer is specified and the analysis is repeated.
If the driving stress exceeds the permitted driving stress for the pile, a smaller hammer is specified and the analysis is repeated.
Drivability of Piles If a suitable hammer can not be found that allows driving the piile to the required ultimate capacity without exceeding the permissible driving stress, modification to the recommended pile type are necessary. These may include:

Develop input parameters for WEAP
Driving lengths of piles
The finished pile will likely be 3233 feet long which includes a 1 foot projection into the pile cap and up to 1' of penetration of the pile tip into the weathered rock. Therefore assume that 35' long piles will be ordered to allow for some variation in subsurface conditions and minimize pile wasted during cut off.
Distribution and magnitude of side friction
This pile will be primarily end bearing but some skin friction in the overlying sand will develop during driving. This skin friction can be quickly computed using the FHWA computer program DRIVEN 1.0. The soil profile determined in Step P.1 is input and an HP12x53 pile selected. The pile top is set at 4 foot depth to account for that portion of soil that will be excavated for pile cap construction. No driving strength loss is assumed since the HPile is a low displacement pile and excess pore pressure should dissipate rapidly in the loose sand. Summary output from the program is provided below.
Figure P5 DRIVEN 1.0 Output
Figure P6 Bearing Capacity
From this analysis, the side friction during driving will vary in a triangular distribution, and will be about:
The distribution will start 4 feet below the top of the pile which is:
below the top of the pile.
The desired factored resistance was determined in Design Step P.8 and is controlled by structural resistance of the pile. This value is:
The ultimate resistance that must be achieved during wave equation analysis will be this value divided by the appropriate resistance factor for wave equation analysis + the estimated side friction.
NOTE: Side friction is added here because downdrag is expected to reduce or reverse the skin friction in the final condition. Therefore, sufficient point capacity must be developed during driving to adequately resist all applied loads plus the downdrag.
STable 10.5.52
From Design Step P.9:
Thus:
and
At this Ultimate point resistance the percent side friction is:
and the resistance required by wave equation analysis is:
Soil parameters (use Case damping factors):
Damping Factors Case damping factors are used here because of experience with similar jobs. In general, Smith damping factors are preferred. In this case, the Smith damping factors would likely give very similar results to what is computed using the selected Case damping factors. 
The parameters for loose sand and hard sandstone were estimated based on local experience with similar soils.
Loose Sand
Skin Damping:
Skin Quake:
Toe Damping:
Toe Quake:
Use skin damping and skin quake for pile shaft.
Hard Sandstone
Skin Damping:
Skin Quake:
Toe Damping:
Toe Quake:
Use toe damping and toe quake for pile toe.
Hammer Selection:
As a rule of thumb, start out with a rated energy of 2000 ftlbs times the steel area of the pile.
Area: from Design Step P.5
Rated Energy:
Select open ended diesel common to area
DELMAG 1232 (ID=37) rated at:
Helmet weight:
Hammer Cushion Properties:
Area:
Elastic Modulus:
Thickness:
COR:
Hammer Efficiency:
Permissible Driving Stress:
Driving Stress,
S10.7.1.16
Note that the equation above was modified to yield stress rather than load.
where:
Resistance factor for driving:
S6.5.4
Steel yield stress, from Design Step P.5:
Summary of Wave Equations Analysis:
Figure P7 Wave Equation Analysis
at refusal the pile has an ultimate capacity of
at refusal the driving stress in the pile is
Check:
The ultimate capacity exceeds that required
> OK
The permissible driving stress exceeds the actual value
>
This condition is not satisfied  no good.
Try reducing hammer energy
DELMAG D 12 (ID=3) rated at
Hammer Cushion Properties same as before
Summary of Wave Equations Analysis:
Figure P8 Wave Equation Analysis
at refusal the pile has an ultimate capacity of
at refusal the driving stress in the pile is
Check:
The ultimate capacity exceeds that required
>
This condition is not satisfied  no good
The permissible driving stress exceeds the actual value
>
This condition is not satisfied  no good.
A decision must be made at this point:
Is pile drivable to minimum of Ultimate Geotechnical Axial Resistance or Ultimate Structural Resistance without pile damage?
Based on above analysis, no hammer can possibly drive this pile to the required capacity without exceeding the permissible driving stress.
There are 2 approaches to resolving this problem
1) Reduce the factored resistance of the pile to a value that can be achieved without over stressing the pile.
Based on the above bearing graph and allowing for some tolerance in the driving stress (requiring the contractor to select a driving system that produces exactly 32.4 KSI in the pile is unreasonable) a reasonable driven capacity is estimated. Using a minimum driving stress of 29 KSI (0.8 Fy) the penetration resistance is about 100 BPF and the ultimate capacity would be:
This value includes skin friction during driving which was set in the program to be 9% of the ultimate resistance. Therefore, point resistance at this driving stress would be:
and:
2) Increase the yield strength of the pile without increasing the previously computed factored resistance
Using grade 50 steel
Driving Stress:
S10.7.1.16
(Equation modified to yield stress instead of load)
where:
Resistance factor for driving:
S6.5.4
Steel yield stress:
<
Since option 2 involves little or no additional cost and option 1 will result in significant increase in cost due to required additional piles, select option 2
In this case The Delmag 1232 produced acceptable driving results.
It can be seen from the results of the wave equation analysis that the driving stress times the pile area is about equal to the mobilized pile capacity. Thus, if the factored structural resistance determined in step P.8 is used as the final design pile resistance, then the ultimate required dynamic capacity determined above is valid and the driving stress associated with this capacity can be estimated by:
Driving Stress
where:
Ultimate required capacity as previously determined by wave equation analysis:
Pile area, from Design Step 9.5:
Driving Stress
Thus, so long as the contractor selects a hammer that will produce a driving stress between about 37 and 45 KSI at refusal, an acceptable driven capacity should be achieved during construction.
Using a minimum driving stress of
As defined previously
Again, side friction is subtracted from the ultimate capacity since it will be present during driving but will not be present in the final condition. Resistance is based on the point resistance achieved during driving the pile to refusal.
and the minimum driven resistance is
Recompute structural resistance based on higher yield steel, as in Design Step P.6
SEquation 6.9.4.11
where
Nominal compressive resistance:
The factored axial structural resistance, as in Design Step P.8 is:
SEquation 6.9.2.11
Driven capacity controls
Thus final axial resistance of driven pile:
Design Step P.11  Do Preliminary Pile Layout Based on Factored Loads and Overturning Moments
The purpose of this step is to produce a suitable pile layout beneath the pile cap that results in predicted factored axial loads in any of the piles that are less than the final factored resistance for the selected piles. A brief evaluation of lateral resistance is also included but lateral resistance is more fully investigated in step P.13
The minimum number of piles to support the maximum factored vertical load is:
where:
The maximum factored vertical load on the abutment, from Design Step P.3, Load Case STR I max:
The final controlling factored resistance for the selected pile type, from Design Step P.10:
Piles
Additional piles will be required to resist the over turning moment.
From Design Step P.5, the maximum load that needed to be supported by each row of piles was calculated.
The required number of piles in the front row is determined as above.
Piles
Additional load in the corner pile will come from the lateral moment but this is small, so start with 7 piles in the front row.
Piles
This results in a pile spacing of:
cc spacing of piles:
where:
The length of footing available for piles, from Design Step P.5:
cc spacing of piles:
Set cc spacing of piles = 7' 4"
This is approaching the maximum pile spacing identified in Step 5 thus set the back row of piles to the same spacing. This will result in the back row of piles being under utilized for axial loads. However, the additional piles are expected to be necessary to help handle lateral loads and to resist downdrag loads that will be applied to the back row only. Further, a load case in which the longitudinal loads such as temperature and braking loads are reversed will increase the loads on the back row.
Thus, the final preliminary layout is diagramed below
Figure P9 Plan View of Pile Cap
The spreadsheet below is used to calculate individual pile loads using the following formula:
where:
Vertical load and moments applied at the centroid of the pile group:
Distance from centroid of pile group to pile in the x and y directions:
Moment of inertia of the pile group about the y and x axis respectively:
Calculation of Individual Pile Loads on an Eccentrically Loaded Footing:
Input Applied Loads:
At x = 0, y = 0
The coordinate system for the following calculations is provided in Figure P.10:
Figure P10 Coordinate System
Table P10 is used to calculate the vertical load and moments, and the moment of inertia of the pile group.
Input Pile Location

Calculated Values



Pile Number

x

y

x'

y'

x' ^{2}

y' ^{2}

Pile load

1

3.875

22

3.875

22

15.01563

484

19.1221

2

3.875

22

3.875

22

15.01563

484

302.735

3

3.875

14.6667

3.875

14.6667

15.01563

215.111

19.1221

4

3.875

14.6667

3.875

14.6667

15.01563

215.111

302.735

5

3.875

7.33333

3.875

7.33333

15.01563

53.7778

19.1221

6

3.875

7.33333

3.875

7.33333

15.01563

53.7778

302.735

7

3.875

0

3.875

0

15.01563

0

19.1221

8

3.875

0

3.875

0

15.01563

0

302.735

9

3.875

7.33333

3.875

7.333333

15.01563

53.7778

19.1221

10

3.875

7.33333

3.875

7.333333

15.01563

53.7778

302.735

11

3.875

14.6667

3.875

14.66667

15.01563

215.111

19.1221

12

3.875

14.6667

3.875

14.66667

15.01563

215.111

302.735

13

3.875

22

3.875

22

15.01563

484

19.1221

14

3.875

22

3.875

22

15.01563

484

302.735
