U.S. Department of Transportation 

Federal Highway Administration

Publication No. FHWA-NHI-16-064

FHWA GEC 012

September 2016

NHI Courses No. 132021 and 132022

Design and Construction of

Driven Pile Foundations –

Comprehensive Design Examples

Developed following:

AASHTO LRFD Bridge Design 

Specifications, 7th Edition, 2014, 

with 2015 Interim.

 and AASHTO LRFD Bridge 

Construction Specifications, 3rd

Edition, 2010, with ‘11, ‘12, ’13, ‘14, 

and ‘15 Interims.
NOTICE

The contents of this report reflect the views of the authors, who are responsible for the facts 

and accuracy of the data presented herein. The contents do not necessarily reflect policy of 

the Department of Transportation. This report does not constitute a standard, specification, or 

regulation. The United States Government does not endorse products or manufacturers. Trade 

or manufacturers′ names appear herein only to illustrate methods and procedures, and are 

considered essential to the objective of this document.
Technical Report Documentation Page

1. REPORT NO.

FHWA-NHI-16-064

2. GOVERNMENT ACCESSION NO. 3. RECIPIENT'S CATALOG NO.

4. TITLE AND SUBTITLE

Geotechnical Engineering Circular No. 12 

Design and Construction of Driven Pile Foundations

- Comprehensive Design Examples

5. REPORT DATE

September 2016

6. PERFORMING ORGANIZATION CODE

7. AUTHOR(S)

Patrick J. Hannigan, PE, Frank Rausche, PhD, PE, 

Garland E. Likins, PE, Brent R. Robinson, PE, and 

Matthew L. Becker, EI.

8. PERFORMING ORGANIZATION 

REPORT NO.

9. PERFORMING ORGANIZATION NAME AND ADDRESS

Ryan R. Berg & Associates, Inc.

2190 Leyland Alcove

Woodbury, MN 55125

10. WORK UNIT NO.

11. CONTRACT OR GRANT NO.

DTFH61-11-D-00049

12. SPONSORING AGENCY NAME AND ADDRESS

National Highway Institute

U.S. Department of Transportation

Federal Highway Administration, Washington, DC 20590

13. TYPE OF REPORT & PERIOD 

COVERED

Final Report

14. SPONSORING AGENCY CODE

15. SUPPLEMENTARY NOTES

FHWA COTR: Heather Shelsta

FHWA Technical Working Group: Naser Abu-Hejleh, PhD, PE; Scott Anderson, PhD, 

PE; and Silas Nichols, PE

16. ABSTRACT

This document presents comprehensive design examples for driven pile foundations on

highway structures. The worked design examples supplement the material presented in 

FHWA-NHI-16-009 and FHWA-NHI-16-010, the primary FHWA guidance documents on 

driven pile foundations. The worked LRFD design examples address strength, service 

and extreme limit state considerations for a two span bridge structure in highly variable 

subsurface conditions. Pile foundation design examples in cohesionless, cohesive, and 

layered soil profiles are presented as well as pile design on hard rock. The worked 

examples follow the step by step design and construction process outlined in Chapter 2 

of FHWA-NHI-16-009.

17. KEY WORDS

Driven pile foundations, foundation economics, site 

characterization, geomaterial properties, axial compression 

resistance, axial tension resistance, lateral resistance, pile 

groups, nominal resistance determination tests, 

construction monitoring and quality assurance.

18. DISTRIBUTION STATEMENT

No restrictions.

19. SECURITY CLASSIF.

Unclassified

20. SECURITY CLASSIF.

Unclassified

21. NO. OF PAGES

265

22. PRICE
CONVERSION FACTORS

Approximate Conversions to SI Units Approximate Conversions from SI Units

When You Know Multiply By To Find When You Know Multiply By To Find

(a) Length

inch (in.) 25.4 millimeter (mm) millimeter (mm) 0.039 inch (in.)

foot (ft) 0.305 meter (m) meter (m) 3.28 foot (ft)

yard (yd) 0.914 meter (m) meter (m) 1.09 yard (yd)

mile (mi) 1.61 kilometer (km) kilometer (km) 0.621 mile (mi)

(b) Area

square inches (in2) 645.2 square millimeters (mm2) square millimeters (mm2) 0.0016 square inches (in2)

square feet (ft2) 0.093 square meters (m2) square meters (m2) 10.764 square feet (ft2)

Acres (ac) 0.405 hectares (ha) hectares (ha) 2.47 Acres (ac)

square miles (mi2) 2.59 square kilometers (km2) square kilometers (km2) 0.386 square miles (mi2)

square inches (in2) 645.2 square millimeters (mm2) square millimeters (mm2) 0.0016 square inches (in2)

(c) Volume

fluid ounces (oz) 29.57 milliliters (mL) milliliters (mL) 0.034 fluid ounces (oz)

Gallons (gal) 3.785 liters (L) liters (L) 0.264 Gallons (gal)

cubic feet (ft3) 0.028 cubic meters (m3) cubic meters (m3) 35.32 cubic feet (ft3)

cubic yards (yd3) 0.765 cubic meters (m3) cubic meters (m3) 1.308 cubic yards (yd3)

(d) Mass

ounces (oz) 28.35 grams (g) grams (g) 0.035 ounces

pounds (lb) 0.454 kilograms (kg) kilograms (kg) 2.205 pounds

short tons (2000 lb) (T) 0.907 megagrams (tonne) (Mg) megagrams (tonne) (Mg) 1.102 short tons (2000 lb)

(e) Force

pound (lb) 4.448 Newton (N) Newton (N) 0.2248 pound (lb)

(f) Pressure, Stress, Modulus of Elasticity

pounds per square foot (psf) 47.88 Pascals (Pa) Pascals (Pa) 0.021 pounds per square foot (psf)

pounds per square inch (psi) 6.895 kiloPascals (kPa) kiloPascals (kPa) 0.145 pounds per square inch (psi)

(g) Density

pounds per cubic foot (pcf) 16.019 kilograms per cubic meter 

(kgm3)

kilograms per cubic meter 

(kgm3) 0.0624 pounds per cubic feet (pcf)

(h) Temperature

Fahrenheit temperature (oF) 5/9(oF- 32) Celsius temperature (oC) Celsius temperature (oC) 9/5(oC)+ 32 Fahrenheit temperature (oF)

Notes: 

1) The primary metric (SI) units used in civil engineering are meter (m), kilogram (kg), second (s), Newton (N), and Pascal (Pa=N/m2

).

2) In a "soft" conversion, an English measurement is mathematically converted to its exact metric equivalent.

3) In a "hard" conversion, a new rounded metric number is created that is convenient to work with and remember.
PREFACE

The purpose of this manual is to provide updated, state-of-the-practice information 

for the design and construction of driven pile foundations in accordance with the 

Load and Resistance Factor Design (LRFD) platform. Engineers and contractors 

have been designing and installing pile foundations for many years. During the past 

three decades, the industry has experienced several major improvements including 

newer and more accurate methods of predicting and measuring geotechnical 

resistance, vast improvements in design software, highly specialized and 

sophisticated equipment for pile driving, and improved methods of construction 

control. Previous editions of the FHWA Design and Construction of Driven Pile 

Foundations manual were published 1985, 1996, and 2006 and chronical the many 

changes in design and construction practice over the past 30 years. This two 

volume edition, GEC-12, serves as the FHWA reference document for highway 

projects involving driven pile foundations.

Volume I, FHWA-NHI-16-009, covers the foundation selection process, site 

characterization, geotechnical design parameters and reporting, selection of pile 

type, geotechnical aspects of limit state design, and structural aspects of limits state 

design. Volume II, FHWA-NHI-16-010, addresses static load tests, dynamic testing 

and signal matching, rapid load testing, wave equation analysis, dynamic formulas, 

contract documents, pile driving equipment, pile accessories, driving criteria, and 

construction monitoring. Comprehensive design examples are presented in 

publication FHWA-NHI-16-064. 

Throughout this manual, numerous references will be made to the names of 

software or technology that are proprietary to a specific manufacturer or vendor. 

Please note that the FHWA does not endorse or approve commercially available 

products, and is very sensitive to the perceptions of endorsement or preferred 

approval of commercially available products used in transportation applications. Our 

goal with this development is to provide recommended technical guidance for the 

safe design and construction of driven pile foundations that reflects the current state 

of practice and provides information on advances and innovations in the industry. 

To accomplish this, it is necessary to illustrate methods and procedures for design 

and construction of driven pile foundations. Where proprietary products are 

described in text or figures, it is only for this purpose.

 
The primary audience for this document is: agency and consulting engineers 

specialized in geotechnical and structural design of highway structures; engineering 

geologists and consulting engineers providing technical reviews, or who are 

engaged in the design, procurement, and construction of driven pile foundations 

This document is also intended for management, specification and contracting 

specialists, as well as for construction engineers interested in design and contracting 

aspects of driven pile systems.

This document draws material from the three earlier FHWA publications in this field; 

FHWA-DP-66-1 by Vanikar (1985), FHWA HI 97-013 and FHWA HI 97-014 by 

Hannigan et al. (1998), and FHWA NHI-05-042 and FHWA NHI-05-043 by Hannigan 

et al. (2006). Photographs without specific acknowledgement in this two volume 

document are from these previous editions, their associated training courses, or 

from the consulting practice of GRL Engineers, Inc.

The following individuals were part of the Ryan R. Berg & Associates internal peer 

review team and are acknowledged for their technical advice and contributions to 

this version of the document:

Mr. Jerry DiMaggio - Applied Research Associates, Inc.

Mr. Van E. Komurka – Wagner Komurka Geotechnical Group, Inc.

Mr. Billy Camp – S&ME, Inc.

Dr. Brian Anderson – Auburn University
TABLE OF CONTENTS

LIST OF TABLES............................................................................................. vi

LIST OF FIGURES ........................................................................................ xiv

D COMPREHENSIVE DESIGN EXAMPLES..............................................1

D.1 Block 1: Establish Global Project Performance Requirements .....8

D.2 Block 2: Determine Structure (Bridge) Geometry, 

Substructure Locations and Elevations.........................................9

D.3 Block 3: Define General Site Geotechnical Conditions, 

Scour, and Seismicity ...................................................................9

D.4 Block 4: Perform Preliminary Structure Modeling. Determine 

Preliminary Substructure Loads and Tolerable Deformations.....10

D.5 Block 5: Develop and Execute Subsurface Exploration and 

Laboratory Testing Program for Feasible Foundation 

Systems......................................................................................10

D.6 Block 6: Evaluate Information and Determine Candidate 

Foundation Systems ...................................................................20

D.7 Block 7: Determine if a Deep Foundation is Required ................20

D.8 Block 8: Select Candidate Driven Pile Types and Sections ........20

D.9 Block 9: North Abutment – Calculate Nominal and Factored 

Structural Resistances for all Candidate Piles ............................21

D.10 Block 10: North Abutment – Calculate Nominal and Factored 

Geotechnical Resistances in Axial Compression and Tension 

Versus Depth for all Candidate Piles; Perform Preliminary 

Pile Drivability Analyses..............................................................22

D.10.1 Geotechnical Resistance in Axial Compression..............26

D.10.2 Geotechnical Resistance in Axial Tension......................34

D.10.3 Preliminary Pile Drivability Assessment..........................37

D.11 Block 11: North Abutment – Estimate Preliminary Number of 

Piles, Preliminary Pile Group Size, and Resolve Individual 

Pile Loads for All Limit States .....................................................46

D.12 Block 12: North Abutment – Estimate Pile Penetration Depth 

for Maximum Axial Compression Loads; Check Group 

Efficiency in Axial Compression..................................................49

i
D.13 Block 13: North Abutment – Establish Minimum Pile 

Penetration Depth for Axial Tension Loads; If Conditions 

Warrant, Modify Design and Return to Block 10 ........................ 51

D.14 Block 14: North Abutment – Establish Minimum Pile 

Penetration Depth for Lateral Loads. Determine p-y Models, 

Required Geomaterial Parameters, and Perform Lateral 

Load Analysis; If Conditions Warrant, Modify Design and 

Return to Block 10...................................................................... 56

D.15 Block 15: North Abutment – Establish Pile Penetration 

Depths that Satisfy Tolerable Deformations; Estimate Group 

Settlement over the Minimum and Maximum Range of Pile 

Penetration Depths From Blocks 12 through 14 and Identify 

All Pile Toe Elevations Which Result in Intolerable 

Deformations; If Conditions Warrant, Modify Design and 

Return to Block 10...................................................................... 62

D.16 Block 16: North Abutment – Check pile drivability to 

maximum pile penetration depth requirements established in 

Blocks 12 through 15 ................................................................. 76

D.17 Block 17: North Abutment – Determine the Neutral Plane 

Location and Resulting Drag Force; Check Structural 

Strength Limit State for Pile Penetration Depth From 

Block 16 ..................................................................................... 77

D.18 Decision Block 18: Does Estimated Total Settlement and 

Differential Settlement Between Adjacent Substructure 

Locations Satisfy Requirements and Angular Distortion Limits? 83

D.19 Block 19: North Abutment – Evaluate Economics of 

Candidate Piles, Preliminary Group Configurations, and 

Other Factors ............................................................................. 83

D.20 Decision 20: Is the Preliminary Design of All Substructure 

Foundations Complete? ............................................................. 92

D.21 Block 9: Pier 2 – Calculate Nominal and Factored Structural 

Resistances for all Candidate Piles............................................ 93

D.22 Block 10: Pier 2 – Calculate Nominal and Factored 

Geotechnical Resistances in Axial Compression and Tension 

versus Depth for all Candidate Piles; Perform Preliminary 

Pile Drivability Analyses ............................................................. 94

D.22.1 Geotechnical Resistance in Axial Compression............. 99

D.22.1.1 Geotechnical Resistance in Axial 

Compression at the Design Flood................ 101

ii
D.22.1.2 Geotechnical Resistance in Axial 

Compression at the Check Flood .................108

D.22.2 Geotechnical Resistance in Axial Tension....................114

D.22.2.1 Geotechnical Resistance in Axial Tension 

at the Design Flood.......................................114

D.22.2.2 Geotechnical Resistance in Axial Tension 

at the Check Flood........................................119

D.22.3 Preliminary Pile Drivability Assessment........................123

D.23 Block 11: Pier 2 – Estimate Preliminary Number of Piles, 

Preliminary Pile Group Size, and Resolve Individual Pile 

Loads for All Limit States ..........................................................129

D.24 Block 12: Pier 2 – Estimate Pile Penetration Depth for 

Maximum Axial Compression Loads. Check Group Efficiency 

in Axial Compression ................................................................134

D.25 Block 13: Pier 2 – Establish Minimum Pile Penetration Depth 

for Axial Tension Loads. If Conditions Warrant, Modify 

Design and Return to Block 10 .................................................136

D.26 Block 14: Pier 2 – Establish Minimum Pile Penetration Depth 

for Lateral Loads. Determine p-y Models, Required 

Geomaterial Parameters, and Perform Lateral Load Analysis. 

If Conditions Warrant, Modify Design and Return to Block 10 ..136

D.27 Block 15: Pier 2 – Establish Pile Penetration Depths that 

Satisfy Tolerable Deformations. Estimate Group Settlement 

over the Minimum and Maximum Range of Pile Penetration 

Depths From Blocks 12 to 14 and Identify All Pile Toe 

Elevations Which Result in Intolerable Deformations. If 

Conditions Warrant, Modify Design and Return to Block 10 .....147

D.28 Block 16: Pier 2 – Check pile drivability to maximum pile 

penetration depth requirements established in Blocks 12 

through 15.................................................................................161

D.29 Block 17: Pier 2 – Determine the Neutral Plane Location and 

Resulting Drag Force. Check Structural Strength Limit State 

for Pile Penetration Depth From Block 16.................................162

D.30 Decision 18: Does Estimated Total Settlement and Differential 

Settlement Between Adjacent Substructure Locations Satisfy 

Requirements and Angular Distortion Limits?...........................166

D.31 Block 19: Pier 2 – Evaluate Economics of Candidate Piles, 

Preliminary Group Configurations, and Other Factors ..............167

D.32 Decision 20: Is the Preliminary Design of All Substructure 

Foundations Complete?............................................................172

iii
D.33 Block 9: South Abutment – For all Candidate Piles, Calculate 

Nominal and Factored Structural Resistances ......................... 173

D.34 Block 10: South Abutment – For All Candidate Piles, 

Calculate Nominal and Factored Geotechnical Resistances 

in Axial Compression and Tension versus Depth. Perform 

Preliminary Pile Drivability Analyses ........................................ 174

D.34.1 Geotechnical Resistance in Axial Compression........... 177

D.34.2 Geotechnical Resistance in Axial Tension (uplift) ........ 187

D.34.3 Preliminary Pile Drivability Assessment ....................... 191

D.35 Block 11: South Abutment – Estimate Preliminary Number of 

Piles, Preliminary Pile Group Size, and Resolve Individual 

Pile Loads for All Limit States................................................... 199

D.36 Block 12: South Abutment – Estimate Pile Penetration Depth 

for Maximum Axial Compression Loads. Check Group 

Efficiency in Axial Compression ............................................... 202

D.37 Block 13: South Abutment – Establish Minimum Pile 

Penetration Depth for Axial Tension Loads. If Conditions 

Warrant, Modify Design and Return to Block 10 ...................... 203

D.38 Block 14: South Abutment – Establish Minimum Pile 

Penetration Depth for Lateral Loads. Determine p-y Models, 

Required Geomaterial Parameters, and Perform Lateral 

Load Analysis. If Conditions Warrant, Modify Design and 

Return to Block 10.................................................................... 209

D.39 Block 15: South Abutment – Establish Pile Penetration 

Depths that Satisfy Tolerable Deformations. Estimate Group 

Settlement over the Minimum and Maximum Range of Pile 

Penetration Depths From Blocks 12 to 14 and Identify All Pile 

Toe Elevations Which Result in Intolerable Deformations. If 

Conditions Warrant, Modify Design and Return to Block 10 .... 215

D.40 Block 16: South Abutment – Check pile drivability to 

maximum pile penetration depth requirements established in 

Blocks 12 through 15 ............................................................... 237

D.41 Block 17: South Abutment – Determine the Neutral Plane 

Location and Resulting Drag Force. Check Structural 

Strength Limit State for Pile Penetration Depth From 

Block 16 ................................................................................... 238

D.42 Decision 18: Does Estimated Total Settlement and Differential 

Settlement Between Adjacent Substructure Locations Satisfy 

Requirements and Angular Distortion Limits? .......................... 242

iv
D.43 Block 19: South Abutment – Evaluate Economics of 

Candidate Piles, Preliminary Group Configurations, and 

Other Factors............................................................................243

D.44 Decision 20: Is the Preliminary Design of All Substructure 

Foundations Complete?............................................................248

D.45 Block 21: Refine Structural Modeling and Determine Loads 

at Foundation Top and Lateral Earth Pressure Loads on 

Abutments.................................................................................248

D.46 Decision 22: Did Loads Significantly Change, and Require 

Reevaluation of the Foundation Design?..................................249

D.47 Block 23: For Dynamic Elastic Analyses, Reevaluate 

Foundation Stiff nesses Using Unfactored Loads in Structural 

Model to get New Foundation Loads ........................................249

D.48 Decision 24: Did Loads Significantly Change, and Require 

Reevaluation of the Foundation Design?..................................249

D.49 Decision 25: Does the Design Meet All Limit State 

Requirements? .........................................................................249

D.50 Block 26: Design Pile Caps and Abutments..............................250

D.51 Block 27: Finalize Plans and Specifications Including Pile 

Quantities, Minimum Pile Penetration Requirements from 

Blocks 13 through 15, and Required Nominal Resistances ......250

D.51.1 Required Nominal Resistance at the North Abutment ..251

D.51.2 Required Nominal Resistance at Pier 2 ........................252

D.51.3 Required Nominal Resistance at the South Abutment..253

D.52 Block 28: Perform Evaluation of Contractor’s Proposed 

Equipment.................................................................................254

D.52.1 Wave Equation for the North Abutment ........................256

D.52.2 Wave Equation for Pier 2..............................................259

D.52.3 Wave Equation for the South Abutment........................262

D.53 Block 29: Set Preliminary Driving Criteria, Drive Test Pile(s) 

and Assess Constructability......................................................265

D.54 Block 30: Adjust Driving Criteria or Design ...............................265

D.55 Block 31: Drive Production Piles with Construction 

Monitoring, Resolve any Pile Installation Problems ..................265

D.56 Block 32: Perform Post-Construction Evaluation and 

Refinement For Future Designs................................................265

v
LIST OF TABLES

Table D-1 General Bridge Geometry Summary .......................................... 9

Table D-2 Nominal Structural Resistances in Axial Compression, 

Flexure and Shear.................................................................... 21

Table D-3 Factored Structural Resistance in Axial Compression, 

Flexure and Shear.................................................................... 22

Table D-4 Correction of Field SPT N Value for Energy and Vertical 

Effective Stress at the North Abutment using S-1 .................... 24

Table D-5 Effective Stress Friction Angle Correlations at the North 

Abutment.................................................................................. 25

Table D-6 Nominal Shaft, Nominal Toe and Nominal Geotechnical 

Resistance for HP 12x74 at the North Abutment...................... 28

Table D-7 Summary of Pile Hammers Used in Drivability Analyses ......... 39

Table D-8 Dynamic Soil Properties for North Abutment Soil Profile.......... 40

Table D-9 Summary of Nominal Driving Resistance Versus Pile 

Penetration Depth for HP 12x74 at the North Abutment .......... 42

Table D-10 Summary of Preliminary Drivability Results at North 

Abutment.................................................................................. 45

Table D-11 Limit State Loads on North Abutment ...................................... 47

Table D-12 Potential Pile Group Configurations ......................................... 47

Table D-13 Limit State Loads and Row Reactions for Group 

Configuration 1......................................................................... 49

Table D-14 Factored Load Per Pile for Alternative Pile Group 

Configurations.......................................................................... 49

Table D-15 Estimated Pile Penetration Depth Requirements for the 

Factored Geotechnical Resistance in Axial Compression at 

the Strength I Limit State.......................................................... 50

Table D-16 Estimated Minimum Pile Penetration Depth for Maximum 

Factored Geotechnical Resistance in Axial Tension at the 

Strength I Limit State................................................................ 52

Table D-17 Geometry of Soil Block Layers for Nominal Group Tension 

Resistance Computation with Pile Toe at 27 Feet.................... 53

Table D-18 Calculation of Soil Volume and Soil Block Weight for 

Nominal Group Tension Resistance......................................... 54

vi
Table D-19 Established Minimum Required Pile Penetration Depth for 

Factored Geotechnical Resistance in Axial Tension at 

North Abutment.........................................................................55

Table D-20 LPILE Summary Output at Pile Head for Front Row, 

pm=0.90.....................................................................................57

Table D-21 LPILE Summary Output at Pile Head for Second Row, 

pm=0.625...................................................................................57

Table D-22 Established Minimum Pile Penetration Depth Required for 

Lateral Loading at the North Abutment .....................................61

Table D-23 Estimated Pile Group Settlement Using Meyerhof (1976) 

Method For All Pile Group Configurations.................................64

Table D-24 Vertical Effective Stress Increase from Embankment 

Surcharge .................................................................................67

Table D-25 Calculation of Settlement by Janbu Tangent Modulus for 

Equivalent Footing at Elevation 270 feet ..................................70

Table D-26 Estimated Pile Group Settlement Using Janbu Tangent 

Modulus with Neutral Plane Method For All Pile Group 

Configurations...........................................................................71

Table D-27 Pile Penetration Depth Required to Locate Neutral Plane 

at Elev. 270.0 feet.....................................................................72

Table D-28 Established Minimum Pile Penetration Depths to Satisfy 

Tolerable Deformations at the North Abutment.........................73

Table D-29 Elastic Compression Calculation ..............................................75

Table D-30 Calculation of Load in Pile, Factored Load and Comparison 

to Nominal Structural Resistance..............................................81

Table D-31 Ratio of Factored Load to Nominal Structural Resistance in 

Axial Compression, φφφφ(min), at the Pile Toe...........................82

Table D-32 Ratio of Factored Load to Nominal Structural Resistance in 

Axial Compression, φφφφ(min), at the Neutral Plane ...................82

Table D-33 Does Candidate Pile Section Meet Structural Resistance 

Requirement Considering Drag Force Associated with 

Minimum Pile Penetration Depth? ............................................83

Table D-34 Established Minimum Pile Penetration Depth at the North 

Abutment ..................................................................................84

Table D-35 Estimated Minimum Penetration Depth for Factored 

Geotechnical Resistance at Strength I Limit State....................84

Table D-36 Estimated Cost Per Linear Foot for 5 Candidate Pile 

Sections....................................................................................85

Table D-37 Cost per Pile at Established Minimum Penetration Depth 

for Piles Meeting Structural Requirements................................86

vii
Table D-38 Pile Group Cost at Established Minimum Penetration 

Depth for Piles Meeting Structural Requirements .................... 86

Table D-39 Factored Geotechnical Resistance, Rr, at Estimated 

Minimum Pile Penetration Depth.............................................. 87

Table D-40 Estimated Total Pile Cap Thickness......................................... 87

Table D-41 Estimated Volume of Reinforced Concrete in Pile Cap............ 88

Table D-42 Estimated Cost of Reinforced Concrete Pile Cap..................... 88

Table D-43 Estimated Foundation Cost Including Piles and Pile Cap at 

North Abutment........................................................................ 89

Table D-44 Comparison of Pile Over/Underrun Costs for Three Lowest 

Cost Alternatives at the North Abutment .................................. 90

Table D-45 Comparison of Pile Group Over/Underrun Costs for Three 

Lowest Cost Alternatives at the North Abutment...................... 91

Table D-46 Nominal Structural Resistance in Axial Compression, 

Flexure and Shear.................................................................... 93

Table D-47 Factored Structural Resistance in Axial Compression, 

Flexure and Shear.................................................................... 94

Table D-48 Correction of Field SPT N Value for Energy and Vertical 

Effective Stress at Pier 2 using Boring S-2 .............................. 96

Table D-49 Soil Layer Effective Stress Friction Angle Correlations at 

Pier 2........................................................................................ 97

Table D-50 Undrained Shear Strength, su, for Soil Layer 3 at Pier 2 .......... 98

Table D-51 Nominal Shaft, Nominal Toe and Nominal Geotechnical 

Resistance for HP 12x74 at Pier 2 (pre-scour)....................... 100

Table D-52 Nominal Shaft, Nominal Toe and Nominal Geotechnical 

Resistance for HP 12x74 at Pier 2 (design flood)................... 103

Table D-53 Nominal Shaft, Nominal Toe and Nominal Geotechnical 

Resistance for HP 12x74 at Pier 2 (check flood).................... 109

Table D-54 Summary of Pile Hammers Used in Drivability Analyses ....... 124

Table D-55 Dynamic Soil Properties for Pier 2 Soil Profile ....................... 125

Table D-56 Summary of Nominal Driving Resistance Versus Pile 

Penetration Depth for HP 12x74 at Pier 2 .............................. 127

Table D-57 Summary of Preliminary Drivability Results at Pier 2 ............. 129

Table D-58 Limit State Loads on Pier 2 .................................................... 130

Table D-59 Potential Pile Group Configurations ....................................... 130

Table D-60 Calculation of Individual Pile Load ......................................... 133

Table D-61 Factored Axial Compression Load Per Pile for Alternative 

Pile Group Configurations ...................................................... 134

Table D-62 Factored Lateral Load Per Pile for Alternative Pile Group 

Configurations........................................................................ 134

viii
Table D-63 Estimated Pile Penetration Depths for the Factored 

Geotechnical Resistance in Axial Compression at the 

Strength V Limit State.............................................................135

Table D-64 Estimated Pile Penetration Depths for the Factored 

Geotechnical Resistance in Axial Compression at the 

Extreme Event II Limit State ...................................................135

Table D-65 LPILE Summary Output at Pile Head for Front Row, 

pm=0.90...................................................................................137

Table D-66 LPILE Summary Output at Pile Head for Second Row, 

pm=0.625.................................................................................138

Table D-67 LPILE Summary Output at Pile Head for Third and Fourth 

Row, pm=0.50 .........................................................................138

Table D-68 LPILE Summary Output at Pile Head for Front Row, 

pm=1.0.....................................................................................141

Table D-69 LPILE Summary Output at Pile Head for Second Row, 

pm=0.85...................................................................................141

Table D-70 LPILE Summary Output at Pile Head for Third and Fourth 

and Fifth Rows, pm=0.70.........................................................142

Table D-71 Minimum Pile Penetration Depth Required for Strength V 

Lateral Loads at Pier 2............................................................145

Table D-72 Minimum Pile Penetration Depth Required for Extreme 

Event II Lateral Loads at Pier 2...............................................146

Table D-73 Established Minimum Pile Penetration Depth Required for 

Lateral Loading at Pier 2.........................................................146

Table D-74 Soil Properties Determined from One Dimensional 

Consolidation Test ..................................................................147

Table D-75 Settlement Estimate for Hough Method With Equivalent 

Footing Located at Elev. 235.0 feet ........................................151

Table D-76 Summary of Pile Group Settlement Estimation Using 

Hough (1959) Method For All Pile Group Configurations at 

Pier 2 ......................................................................................152

Table D-77 Settlement Estimation for Neutral Plane Method with the 

Neutral Plane at EL 235.0 feet................................................155

Table D-78 Estimated Pile Group Settlement Using Janbu Tangent 

Modulus with Neutral Plane Method For All Pile Group 

Configurations.........................................................................156

Table D-79 Summary of Pile Penetration Depth Required to Locate 

Neutral Plane at Depth Determined From Settlement 

Estimation...............................................................................157

ix
Table D-80 Established Minimum Pile Penetration Depths to Satisfy 

Tolerable Deformations at Pier 2............................................ 158

Table D-81 Elastic Compression Calculation............................................ 160

Table D-82 Ratio of Factored Load to Nominal Structural Resistance in 

Axial Compression, φφφφ(min), at the Pile Toe ........................ 165

Table D-83 Ratio of Factored Load to Nominal Structural Resistance in 

Axial Compression, φφφφ(min), at the Neutral Plane................. 165

Table D-84 Does Candidate Pile Section Meet Structural Resistance 

Requirement Considering Drag Force Associated with 

Minimum Pile Penetration Depth?.......................................... 165

Table D-85 Summary of Foundation Total Settlement, Differential 

Settlement, and Angular Distortion......................................... 167

Table D-86 Established Minimum Pile Penetration Depth at Pier 2.......... 168

Table D-87 Estimated Minimum Penetration Depth for Factored 

Geotechnical Resistance at Strength V Limit State................ 168

Table D-88 Cost per Pile at Established Minimum Penetration Depth 

for Piles Meeting Structural Requirements............................. 169

Table D-89 Pile Group Cost at Established Minimum Penetration 

Depth for Piles Meeting Structural Requirements .................. 170

Table D-90 Estimated Total Pile Cap Thickness....................................... 171

Table D-91 Estimated Volume of Reinforced Concrete in Pile Cap.......... 171

Table D-92 Estimated Cost of Reinforced Concrete Pile Cap................... 171

Table D-93 Estimated Foundation Cost Including Piles and Pile Cap at 

Pier 2...................................................................................... 172

Table D-94 Nominal Structural Resistances in Axial Compression, 

Flexure and Shear.................................................................. 173

Table D-95 Factored Structural Resistance in Axial Compression, 

Flexure and Shear.................................................................. 174

Table D-96 Undrained Shear Strength, su, for Soil Layer 1 at the South 

Abutment................................................................................ 176

Table D-97 Undrained Shear Strength, su, for Soil Layer 2 at the South 

Abutment................................................................................ 176

Table D-98 Undrained Shear Strength, su, for Soil Layer 3 at the South 

Abutment................................................................................ 177

Table D-99 Laboratory Determined Properties of Limestone Bedrock...... 177

Table D-100 Nominal Shaft, Nominal Toe and Nominal Geotechnical 

Resistance for HP 12x74 at the South Abutment................... 179

Table D-101 Summary of Pile Hammers Used in Drivability Analyses ....... 192

Table D-102 Dynamic Soil Properties for South Abutment Soil Profile ....... 193

x
Table D-103 Nominal Shaft, Nominal Toe and Nominal Driving 

Resistance for HP 12x74 .......................................................196

Table D-104 Summary of Preliminary Drivability Results at South 

Abutment ................................................................................199

Table D-105 Limit State Loads on South Abutment ....................................199

Table D-106 Potential Pile Group Configurations........................................200

Table D-107 Factored Loads and Row Reactions.......................................201

Table D-108 Factored Load Per Pile for Alternative Pile Group 

Configurations.........................................................................202

Table D-109 Estimated Pile Penetration Depths for the Factored 

Geotechnical Resistance in Axial Compression at the 

Strength I Limit State ..............................................................203

Table D-110 Estimated Minimum Pile Penetration Depth Required for 

Factored Geotechnical Resistance in Axial Tension at the 

Strength I Limit State ..............................................................204

Table D-111 Established Minimum Pile Penetration Depth Required for 

Factored Geotechnical Resistance in Axial Tension at 

South Abutment......................................................................209

Table D-112 LPILE Summary Output at Pile Head for Front Row, 

pm=0.90...................................................................................211

Table D-113 LPILE Summary Output at Pile Head for Second Row, 

pm=0.625.................................................................................211

Table D-114 Established Minimum Required Pile Penetration Depth for 

Lateral Loading at the South Abutment ..................................215

Table D-115 Vertical Effective Stress Increase from Embankment 

Surcharge ...............................................................................219

Table D-116 Soil Properties Determined from One Dimensional 

Consolidation Test ..................................................................220

Table D-117 Calculation of Settlement using Equivalent Footing and 

Conventional Primary Consolidation Equations......................224

Table D-118 Summary of Pile Group Settlement Estimates Based on 

Equivalent Footing Depth and Conventionally Settlement 

Computations..........................................................................224

Table D-119 Settlement Estimate for Neutral Plane Method with the 

Neutral Plane at EL 270.0 feet................................................230

Table D-120 Summary of Pile Group Settlement Estimates Based on 

Janbu Tangent Modulus with Neutral Plane Method For All 

Group Configurations..............................................................231

Table D-121 Established Minimum Required Pile Penetration Depths to 

Satisfy Tolerable Deformations at the South Abutment ..........233

xi
Table D-122 Elastic Compression Calculation............................................ 235

Table D-123 Ratio of Factored Load to Nominal Structural Resistance in 

Axial Compression, φφφφ(min), at the Neutral Plane................. 241

Table D-124 Does Candidate Pile Section Meet Structural Resistance 

Requirements Considering Drag Force at Minimum Pile 

Penetration Depth? ................................................................ 242

Table D-125 Summary of Foundation Total Settlement, Differential 

Settlement, and Angular Distortion for HP 12x74 Pile 

Section ................................................................................... 243

Table D-126 Established Minimum Pile Penetration Depth at the South 

Abutment................................................................................ 244

Table D-127 Estimated Minimum Penetration Depth for Factored 

Geotechnical Resistance at Strength I Limit State ................. 245

Table D-128 Cost per Pile at Established Minimum Penetration Depth 

for Piles Meeting Structural Requirements............................. 246

Table D-129 Pile Group Cost at Established Minimum Penetration 

Depth for Piles Meeting Structural Requirements .................. 246

Table D-130 Estimated Total Pile Cap Thickness....................................... 247

Table D-131 Estimated Volume of Reinforced Concrete in Pile Cap.......... 247

Table D-132 Estimated Cost of Reinforced Concrete Pile Cap................... 247

Table D-133 Estimated Foundation Cost Including Piles and Pile Cap at 

South Abutment ..................................................................... 248

Table D-134 Estimated Total Foundation Cost at All Substructures 

Locations on the Southbound Bridge ..................................... 250

Table D-135 Final Design Foundation Summary and Associated 

Penetration Depths for the Southbound Bridge...................... 251

xii
xiii
LIST OF FIGURES

Figure D-1 Design process flow chart. ......................................................... 2

Figure D-1 Design process flow chart (continued). ...................................... 3

Figure D-1 Design process flow chart (continued). ...................................... 4

Figure D-1 Design process flow chart (continued). ...................................... 5

Figure D-1 Design process flow chart (continued). ...................................... 6

Figure D-1 Design process flow chart (continued). ...................................... 7

Figure D-2 Boring Log S-1, Page 1 of 3..................................................... 11

Figure D-2 Boring Log S-1, Page 2 of 3..................................................... 12

Figure D-2 Boring Log S-1, Page 3 of 3..................................................... 13

Figure D-3 Boring Log S-2, Page 1 of 2..................................................... 14

Figure D-3 Boring Log S-2, Page 2 of 2..................................................... 15

Figure D-4 Boring Log S-3, Page 1 of 3..................................................... 16

Figure D-4 Boring Log S-3, Page 2 of 3..................................................... 17

Figure D-4 Boring Log S-3, Page 3 of 3..................................................... 18

Figure D-5 Site Profile View....................................................................... 19

Figure D-6 Effective stress diagram for North Abutment using Boring 

S-1. .......................................................................................... 23

Figure D-7 Design profile at the North Abutment. ...................................... 26

Figure D-8 Geotechnical resistance in axial compression versus pile 

penetration depth for HP 12x74 candidate pile section at 

North Abutment........................................................................ 29

Figure D-9 Nominal geotechnical resistance in axial compression versus 

pile penetration depth for all candidate pile sections at the 

North Abutment........................................................................ 30

Figure D-10 Design chart of nominal and factored geotechnical resistance 

in axial compression versus pile penetration depth for HP 

12x74 at the North Abutment. .................................................. 31

Figure D-11 Factored geotechnical resistance, Rr, in axial compression 

based on field determination by static load test and dynamic 

testing 2% of the piles, φφφφφφφφ=0.80. ......................................... 32

Figure D-12 Factored geotechnical resistance, Rr, in axial compression 

based on field determination by dynamic testing 2% of the 

piles, φφφφφφφφ=0.65...................................................................... 32

xiv
Figure D-13 Factored geotechnical resistance, Rr, in axial compression 

based on field determination by wave equation analysis, 

φφφφφφφφ=0.50................................................................................33

Figure D-14 Factored geotechnical resistance, Rr, in axial compression 

based on determination using Nordlund Method static 

analysis, φφφφφφφφφφ=0.45.................................................................33

Figure D-15 Nominal shaft resistance versus penetration depth for all 

candidate pile sections at the North Abutment..........................34

Figure D-16 Design chart of nominal and factored geotechnical resistance 

in axial tension for HP 12x74 at the North Abutment. ...............35

Figure D-17 Factored geotechnical resistance, Rr, in axial tension based 

on field determination by static load test, φdyn=0.60..................36

Figure D-18 Factored geotechnical resistance, Rr, in axial tension based 

on field determination by dynamic testing with signal 

matching, φdyn=0.50..................................................................36

Figure D-19 Factored geotechnical resistance, Rr, in axial tension based 

on determination using Nordlund Method static analysis, 

φstat=0.35. .................................................................................37

Figure D-20 Nominal driving resistance for HP 12x74 at the North 

Abutment. .................................................................................41

Figure D-21 Comparison of nominal driving resistance and nominal 

geotechnical resistance in axial compression for HP 12x74 at 

the North Abutment...................................................................41

Figure D-22 Preliminary drivability results at the North Abutment. ...............44

Figure D-23 Hammer size comparison to drive the HP 12x74 pile section...46

Figure D-24 Group Configuration 1 pile cap plan view. ................................48

Figure D-25 Elevation view of cap free body diagram. .................................48

Figure D-26 Nominal tension resistance of pile group based on soil block 

weight. ......................................................................................53

Figure D-27 Factored load versus deflection in longitudinal direction for 

HP 12x74 at North Abutment....................................................58

Figure D-28 Front row bending moment versus depth in longitudinal 

direction. ...................................................................................59

Figure D-29 Bending moment versus deflection in longitudinal direction 

for HP 12x74 at North Abutment...............................................59

Figure D-30 Vertical effective stress increase due to strip load....................65

Figure D-31 Vertical effective stress increase due to embankment 

surcharge..................................................................................65

Figure D-32 Neutral plane at 50% toe mobilization for HP 12x74 at the 

North Abutment.........................................................................72

xv
Figure D-33 Neutral plane at 100% toe mobilization for HP 12x74 at the 

North Abutment........................................................................ 78

Figure D-34 Pile cost versus penetration depth. .......................................... 86

Figure D-35 Change in cost per pile from over/ underrun. ........................... 90

Figure D-36 Change in total cost of foundation from overrun/ underrun. ..... 91

Figure D-37 Effective stress diagram for Pier 2 using Boring S-2................ 95

Figure D-38 Undrained shear strength, su, versus depth for Soil Layer 3 at 

Pier 2........................................................................................ 97

Figure D-39 Design soil profile at Pier 2....................................................... 98

Figure D-40 Nominal geotechnical resistance in axial compression versus 

pile penetration depth for HP 12x74 at Pier 2 (pre scour). ..... 101

Figure D-41 Nominal geotechnical resistance in axial compression versus 

pile penetration depth for HP 12x74 at Pier 2 (design flood).. 102

Figure D-42 Nominal geotechnical resistance in axial compression versus 

penetration depth for all candidate pile sections at Pier 2 

(design flood). ........................................................................ 104

Figure D-43 Design chart of nominal and factored geotechnical resistance 

in axial compression versus pile penetration depth for HP 

12x74 at the Pier 2 (design flood). ......................................... 105

Figure D-44 Factored geotechnical resistance, Rr, in axial compression 

based on field determination by static load test and dynamic 

testing 2% of the piles, φdyn=0.80........................................... 106

Figure D-45 Factored geotechnical resistance, Rr, in axial compression 

based on field determination by dynamic testing 2% of the 

piles, φdyn=0.65. ..................................................................... 106

Figure D-46 Factored geotechnical resistance, Rr, in axial compression 

based on field determination by wave equation analysis, 

φdyn=0.50................................................................................ 107

Figure D-47 Factored geotechnical resistance, Rr, in axial compression 

based on determination using Nordlund Method static 

analysis, φstat=0.45................................................................. 107

Figure D-48 Nominal geotechnical resistance in axial compression versus 

pile penetration depth for HP 12x74 at Pier 2 (check flood). .. 110

Figure D-49 Nominal geotechnical resistance in axial compression versus 

penetration depth for all candidate pile sections at Pier 2 

(check flood)........................................................................... 110

Figure D-50 Design chart of nominal and factored geotechnical resistance 

in axial compression versus pile penetration depth for HP 

12x74 at the Pier 2 (check flood)............................................ 111

xvi
Figure D-51 Factored geotechnical resistance, Rr, in axial compression 

based on field determination by static load test and dynamic 

testing 2% of the piles, φdyn=0.80............................................112

Figure D-52 Factored geotechnical resistance, Rr, in axial compression 

based on field determination by dynamic testing 2% of the 

piles, φdyn=0.65. ......................................................................113

Figure D-53 Factored geotechnical resistance, Rr, in axial compression 

based on field determination by wave equation analysis, 

φdyn=0.5. .................................................................................113

Figure D-54 Factored geotechnical resistance, Rr, in axial compression 

based on determination using static analysis, φstat=0.45 or 

φstat=0.35. ...............................................................................114

Figure D-55 Nominal shaft resistance versus pile penetration depth for all 

candidate pile sections at Pier 2 (design flood).......................116

Figure D-56 Design chart of nominal and factored geotechnical resistance 

in axial tension versus pile penetration depth for HP 12x74 at 

the Pier 2 (design flood)..........................................................116

Figure D-57 Factored geotechnical resistance, Rr, in axial tension based 

on field determination by static load test, φdyn=0.60 (design 

flood).......................................................................................117

Figure D-58 Factored geotechnical resistance, Rr, in axial tension based 

on field determination by dynamic testing with signal 

matching, φdyn=0.50 (design flood). ........................................118

Figure D-59 Factored geotechnical resistance, Rr, in axial tension based 

on determination using static analysis, φstat=0.35 or φstat=0.25 

(design flood)..........................................................................118

Figure D-60 Nominal shaft resistance versus pile penetration depth for all 

candidate pile sections at Pier 2 during Extreme Event 

(check flood). ..........................................................................120

Figure D-61 Design chart of nominal and factored geotechnical resistance 

in axial tension versus depth for HP 12x74 at the Pier 2 

during Extreme Event (check flood)........................................120

Figure D-62 Factored geotechnical resistance, Rr, in axial tension based 

on field determination by static load test, φdyn=0.60................121

Figure D-63 Factored geotechnical resistance, Rr, in axial tension based 

on field determination by dynamic testing with signal 

matching, φdyn=0.50................................................................122

Figure D-64 Factored geotechnical resistance, Rr, in axial tension based 

on determination using static analysis, φstat=0.35 or 

φstat=0.25. ...............................................................................122

xvii
Figure D-65 Nominal driving resistance for HP 12x74 at Pier 2................. 126

Figure D-66 Comparison of nominal driving resistance and nominal 

geotechnical resistance in axial compression for HP 12x74 at 

Pier 2...................................................................................... 126

Figure D-67 Preliminary drivability results at Pier 2. .................................. 128

Figure D-68 Group Configuration 6 pile cap plan view............................... 131

Figure D-69 Factored load versus deflection in longitudinal direction for 

HP 12x74 at Pier 2................................................................. 139

Figure D-70 Front row bending moment versus depth in longitudinal 

direction. ................................................................................ 140

Figure D-71 Bending moment versus deflection in longitudinal direction 

for HP 12x74 at Pier 2............................................................ 140

Figure D-72 Factored load versus deflection in transverse direction for HP 

12x74 at Pier 2....................................................................... 143

Figure D-73 Front row bending moment versus depth in transverse 

direction. ................................................................................ 143

Figure D-74 Bending moment versus deflection in transverse direction for 

HP 12x74 at Pier 2................................................................. 144

Figure D-75 Equivalent footing and stress distribution toe bearing piles in 

hard clay or sand considering Group Configuration 6 

dimensions at Pier 2............................................................... 148

Figure D-76 Hough (1959) method chart to determine bearing capacity 

index from SPT (N1) at Pier 2................................................. 149

Figure D-77 Neutral plane at 40 feet below the pile cap and resulting 

stress distribution for Group Configuration 6.......................... 153

Figure D-78 Neutral plane location considering 50% toe mobilization for 

HP 12x74 at Pier 2................................................................. 157

Figure D-79 Neutral plane location considering 100 percent toe 

mobilization for HP 12x74 at Pier 2....................................... 163

Figure D-80 Pile cost versus penetration depth. ........................................ 169

Figure D-81 Effective stress diagram for the South Abutment using Boring 

S-3. ........................................................................................ 175

Figure D-82 Undrained shear strength, su, versus depth at the South 

Abutment................................................................................ 176

Figure D-83 Design soil profile at the South Abutment. ............................. 178

Figure D-84 Bearing capacity factors for foundations on rock.................... 181

Figure D-85 Nominal geotechnical resistance in axial compression versus 

pile penetration depth for HP 12x74 at the South Abutment. . 183

xviii
Figure D-86 Nominal geotechnical resistance in axial compression versus 

pile penetration depth for all candidate pile sections at South 

Abutment. ...............................................................................183

Figure D-87 Design chart of nominal and factored geotechnical resistance 

in axial compression versus pile penetration depth for HP 

12x74 at the South Abutment. ................................................184

Figure D-88 Factored geotechnical resistance, Rr, in axial compression 

based on field determination by static load test and dynamic 

testing 2% of the piles,φφφφφφφφ=0.80. .........................................185

Figure D-89 Factored geotechnical resistance, Rr, in axial compression 

based on field determination by dynamic testing 2% of the 

piles, φφφφφφφφ=0.65.....................................................................186

Figure D-90 Factored geotechnical resistance, Rr, in axial compression 

based on field determination by wave equation analysis, 

φφφφφφφφ=0.50..............................................................................186

Figure D-91 Factored geotechnical resistance, Rr, in axial compression 

based on determination using alpha method static analysis, 

φφφφφφφφφφ=0.35..............................................................................187

Figure D-92 Nominal shaft resistance versus penetration depth for all 

candidate pile sections at the South Abutment.......................188

Figure D-93 Design chart of nominal and factored geotechnical resistance 

in axial tension versus pile penetration depth for HP 12x74 at 

the South Abutment. ...............................................................189

Figure D-94 Factored geotechnical resistance, Rr, in axial tension based 

on field determination by static load test, φdyn=0.60................189

Figure D-95 Factored geotechnical resistance, Rr, in axial tension based 

on field determination by dynamic testing with signal 

matching, φdyn=0.50................................................................190

Figure D-96 Factored geotechnical resistance, Rr, in axial tension based 

on determination using alpha method static analysis, 

φstat=0.25. ...............................................................................190

Figure D-97 Nominal driving resistance for HP 12x74 at the South 

Abutment. ...............................................................................194

Figure D-98 Comparison of nominal driving resistance and nominal 

geotechnical resistance in axial compression for HP 12x74 at 

the South Abutment. ...............................................................195

Figure D-99 Preliminary drivability results for five candidate H-pile 

sections at the South Abutment..............................................198

Figure D-100 Group Configuration 3 pile cap plan view. ..............................200

Figure D-101 Elevation view of cap free body diagram. ...............................201

xix
Figure D-102 Tension resistance of pile group in cohesive soil. .................. 206

Figure D-103 Factored load versus deflection for HP 12x74 at South 

Abutment................................................................................ 212

Figure D-104 Front row bending moment versus depth............................... 213

Figure D-105 Bending moment versus deflection for HP 12x74 at South 

Abutment................................................................................ 213

Figure D-106 Vertical effective stress increase due to strip load. ................ 216

Figure D-107 Profile of vertical stress increase due to embankment 

surcharge. .............................................................................. 217

Figure D-108 Equivalent footing at 35 feet below the pile cap with 

respective stress distribution for conventional settlement 

analysis. ................................................................................. 221

Figure D-109 Neutral plane at 35 feet below the pile cap and resulting 

stress distribution. .................................................................. 225

Figure D-110 Neutral plane location considering 50% toe mobilization for 

HP 12x74 at the South Abutment........................................... 232

Figure D-111 Neutral plane location considering 100 percent toe 

mobilization for HP 12x74 at the South Abutment.................. 239

Figure D-112 Pile cost versus penetration depth. ........................................ 245

Figure D-113 Contractor’s ICE I-36 V2 hammer submittal form................... 255

Figure D-114 Preliminary drivability with Contractor’s hammer at the North 

Abutment................................................................................ 256

Figure D-115 Compression and tension stress versus blow count. ............. 257

Figure D-116 Nominal resistance and stroke versus blow count. ................ 257

Figure D-117 Inspectors Chart for ICE I-36 V2 at the North Abutment. ....... 258

Figure D-118 Drivability with Contractor’s hammer at Pier 2........................ 259

Figure D-119 Compression and tension stress versus blow count. ............. 260

Figure D-120 Nominal resistance and stroke versus blow count. ................ 260

Figure D-121 Inspectors Chart for ICE I-36 V2 at Pier 2.............................. 261

Figure D-122 Drivability with Contractor’s hammer at the South Abutment. 262

Figure D-123 Compression and tension stress versus blow count. ............. 263

Figure D-124 Nominal resistance and stroke versus blow count. ................ 263

Figure D-125 Inspectors Chart for ICE I-36 V2 at the South Abutment........ 264

xx
xxi
LIST OF SYMBOLS

AA - Pile cross sectional area.

AAdd - Angular distortion.

AApp - Pile toe area.

AAss - Pile shaft surface area.

BB - Width of pile group.

bb - Pile width or diameter, Width/ Height of square.

bbff - Flange width of pile section.

bpm - Blow per minute.

CC - Wave speed of pile material.

CC′ - Dimensionless bearing capacity index, determined from average 

corrected SPT N value, for layer with consideration of SPT hammer type.

CCaa - Pile adhesion.

CCcc - Compression index.

CCdd - Pile perimeter at depth d.

CCFF - Correction factor for Kδ when δ ≠ φ.

CCnn - Correction factor for SPT N value.

CCrr - Recompression index.

CCss - Swell index.

′ - Effective cohesion.

DD - Pile embedded length; Pile width for WEAP quake calculation.

DDBB - Pile embedded length into bearing stratum.

DDnn - Depth from reference to neutral plane.

ww - Web depth of pile section.

EE - Elastic modulus of pile material.

EEmm - Rock Mass Modulus.

EEnn - Rated hammer energy.

ER - SPT Hammer efficiency as determined by energy measurements in 

accordance with ASTM D4633.

EEss - Elastic modulus of soil.

eeoo - Initial soil layer void ratio.

FFyy - Yield stress of steel.

gg - Acceleration due to gravity.

HH - Soil layer thickness.

xxii
HHoo - Initial soil layer thickness.

h - Ram stroke.

hii - Thickness of soil strata.

hww - Height of water (pressure head) for calculation of pore water pressure.

kkcc - Modulus of subgrade reaction for cyclic lateral loading.

L - Total pile length.

NNtt - Toe bearing capacity coefficient. 

MMn - Nominal flexural resistance (structural).

MMpp - Plastic moment about the weak axis.

MMr - Factored flexural resistance (structural).

MMrrrr - Factored flexural resistance about x-axis.

MMrr - Factored flexural resistance about y-axis.

MMuu - Factored moment load (structural).

MMuu - Factored moment about x-axis.

MMuu - Factored moment about y-axis.

mmnn - Dimensionless modulus number.

mmnn - Dimensionless recompression modulus number.

NNcc - Dimensionless bearing capacity factor.

NNqq - Dimensionless bearing capacity factor.

NN60 - SPT N value corrected for 60% energy transfer.

(NN1)60 - SPT N value corrected for energy and overburden stress.

NNγ - Bearing capacity factor.

 - Number of piles in pile group.

PPmm - P-multiplier for p-y curve.

PPnn - Nominal structural resistance in axial compression.

PPrr - Factored structural resistance in axial compression.

PPuu - Factored axial load (structural).

PPuu - Maximum single pile axial load.

ppaa - Atmospheric pressure.

ppff - Design foundation pressure.

QQ - Factored Axial Load; Unfactored Axial Load.

QQdd - Dead or sustained load on a pile.

QQmm - Maximum axial compressive force in the pile.

qq - Surcharge.

qquu - Unconfined compressive strength.

RRnn - Nominal resistance.

RRnn - Nominal driving resistance.

RRnnnn - Nominal resistance of pile group.

RRpp - Nominal toe resistance.

xxiii
RRrr - Factored resistance.

RRrrrrrr rr - Resistance loss from relaxation.

RRrr - Factored resistance of the pile group.

RRss - Nominal shaft resistance.

RRss - Resistance loss from scour.

RRuu - Nominal uplift resistance of the pile group.

S - Settlement.

SSdd - Differential settlement of the foundation.

SScc - Settlement from primary consolidation.

SSh - Horizontal abutment movement.

uu - Undrained shear strength.

- Pipe pile wall thickness.

cc - Thickness of pile cap (8.9).

ff - Flange thickness of pile section (8.2) (8.5).

ss - Thickness of compressible soil beneath neutral plane.

ww - Web thickness of pile section.

VVnn - Nominal shear resistance (structural).

VVrr - Factored shear resistance (structural).

VVuu - Factored shear load (structural).

W - Ram weight.

WWcc - Estimated weight of pile cap.

WW - Effective weight of the pile/soil block including pile cap weight.

WWss - Estimated weight of soil above pile cap.

w - Moisture content.

xx - Distance along x-axis from the center of the column to each pile 

center.

YYoo - Pile head deflection.

- Distance along y-axis from the center of the column to each pile center.

ZZ - Length of pile group .

Δ - Elastic deformation of pile.

ΔΔεε - Change of strain.

Δσ - Change of stress.

εε - Strain.

εε50 - Strain at one half the maximum principal stress.

ƞ - Pile group efficiency.

γ - Total unit weight of soil.

γ' - Buoyant unit weight of soil.

γdd - Dead Load Factor.

γff - Unit weight of embankment fill.

xxiv
γii - Unit weight of soil strata for calculation of in-situ stress.

γ - Load factor for force effect due to live loads.

γpp - Load factor for force effect due to permanent loads.

γγww - Unit weight of water.

σ - Normal stress (pressure) on plane of failure, stress.

σ′ - Effective normal stress (pressure) on plane of failure (σ – u).

σσ′dd - Vertical effective stress at the center of depth increment d.

σσdd - Driving stress.

σσ′oo - Effective stress prior to stress increase.

σσpp - Preconsolidation pressure or stress.

σσrr - Reference stress for settlement with Janbu Tangent Modulus.

σσ′vv - Vertical effective stress.

σσ′vv - Vertical effective stress at the sample depth.

σσ′1 - Effective stress after stress increase.

φφ - Resistance factor, statistically based multiplier on nominal resistance.

φφ′ - Effective Stress Friction Angle.

φφcc - Resistance factor (pile structural resistance in compression).

φφddaa - Resistance factor (pile structural resistance during driving).

φφdd - Resistance factor (based on the construction control method).

φφff - Resistance factor (pile structural resistance in flexure).

φφss - Resistance factor (based on the static analysis method).

φφuu - Resistance factor for group uplift (based on the uplift analysis method).

φφuu - Resistance factor (based on the uplift analysis method).

φφvv - Resistance factor (pile structural resistance in shear).

xxv
LIST OF ACRONYMNS

AASHTO - American Association of State Highway and Transportation Officials

ASTM - American Society for Testing and Materials

BOR - Beginning of Restrike

CED - Closed End Diesel hammer

CEP - Closed End Pipe

CFA - Continuous Flight Auger

DA - Design Angular Distortion

DD - Downdrag

DF - Drag Force

DLT - Dynamic Load Test

EOD - End of Drive

ER - SPT hammer efficiency as determined by energy measurements

FHWA - Federal Highway Administration

I.D. - Inner diameter

NHI - National Highway Institute

O.D. - Outer Diameter

OEP - Open Ended Pipe

SA - Static Analysis

SPT - Standard Penetration Test

SLT - Static Load Test

WE - Wave Equation

WEAP - Wave Equation Analysis Program

xxvi
xxvii

APPENDIX D

COMPREHENSIVE DESIGN EXAMPLES

This appendix presents comprehensive design examples for a driven pile foundation 

project. The worked design examples supplement the material presented in 

publications FHWA-NHI-16-009 and FHWA-NHI-16-010, the primary FHWA 

guidance documents on driven pile foundations. The worked LRFD design 

examples address strength, service, and extreme limit state considerations for a 

bridge structure in highly variable subsurface conditions. Worked design examples 

in cohesionless, cohesive, and layered soil profiles are presented as well as pile 

design on hard rock. All limit states considerations are addressed as applicable in 

the worked design examples.

The bridge dimensions and superstructure loads were provided by a transportation 

agency, while the bridge structure is supported at two abutments and a pier. The 

soil profile for the worked design examples was developed to illustrate use of the 

manual’s design methods and procedures in a variety of subsurface conditions. 

Each substructure location presents a different subsurface condition. A 

cohesionless soil profile is presented at the North Abutment. At the pier, worked 

examples in a layered subsurface profile are presented. At the South Abutment, 

worked examples for a cohesive soil profile underlain by a hard bedrock are 

presented. Strength, service, and extreme limit states are addressed at each 

substructure location as appropriate. An economic evaluation of candidate pile 

types is also included at each substructure location. 

The worked design examples follow the step by step design and construction 

process outlined in Chapter 2 of FHWA-NHI-16-009. The design process flow chart 

introduced in Chapter 2 is followed in the worked design examples and is presented 

herein as Figure D-1.

1
Figure D-1 Design process flow chart.

2
Figure D-1 Design process flow chart (continued).

3
Figure D-1 Design process flow chart (continued).

4
Figure D-1 Design process flow chart (continued).

5
Figure D-1 Design process flow chart (continued).

6
Figure D-1 Design process flow chart (continued).

7
D.1 Block 1: Establish Global Project Performance Requirements

The general structure requirements have been determined and are summarized 

below.

1. The project will consist of new twin river bridges, one for northbound traffic 

and one for southbound traffic. Both bridges will be designed for three travel 

lanes.

2. The project will be constructed at one time.

3. The general structure layout and approximate substructure locations are 

known but approach grades have yet to be established.

4. The foundation engineer has visited the site. During normal flow, the river is 

approximately 80 feet wide and 5 feet deep at the proposed bridge location. 

The north side of the river has a bank approximately 20 feet high consisting of 

silty sand. The ground surface on the south side of the river has a slightly 

more gradual slope with surficial soils consisting of silty clay. The new 

bridges will be approximately 200 feet long with a higher approach 

embankment required on the south side.5. Based on other bridge 

structures similar to those contemplated for this project, limit state axial 

compression loads are anticipated to be on the order of 2000 to 2500 kips at 

the abutments and 2500 to 3500 kips at the pier.

Based on safety, drainage, and rideability considerations, a maximum total 

settlement at any substructure location of 1.5 inches and maximum 

differential settlement between substructure locations of 1 inch are desired. 

In addition, the lateral deformation is limited to 1 inch.

6. The new bridge structure is not subject to vessel or vehicle impact loading or 

seismic activity. However, substantial scour is a design consideration.

7. Lateral squeeze may or may not be a design consideration depending upon 

the subsurface conditions encountered.

8. No modifications appear warranted in the preliminary design such as 

adjustments in substructure locations or span lengths.

8
9. No site or surrounding environmental considerations (low headroom, utility 

conflicts, aggressive soil environments, limitations on noise, vibrations, etc.) 

need to be considered in the design.

10. There are no special factors influencing bridge span length.

D.2 Block 2: Determine Structure (Bridge) Geometry, Substructure Locations 

and Elevations

The general bridge geometry, probable substructure locations, and the top of 

foundation elevations have been established. This information is presented in Table 

D-1.

Table D-1 General Bridge Geometry Summary

Substructure Substructure Station

Top of Foundation 

Elevation

(feet)

North Abutment 1223 + 26 + 312.0

Pier 2 1224 + 26 + 280.0

South Abutment 1225 + 26 + 307.0

D.3 Block 3: Define General Site Geotechnical Conditions, Scour, and 

Seismicity

Available foundation plans and structure performance have been collected from 

other projects in the vicinity. The project is located in an area known for variable 

subsurface conditions. Post construction issues of unsatisfactory structure 

performance have not been reported in the vicinity. The hydraulic engineer has 

been consulted to determine probable scour depths that may impact the foundation 

selection. Seismicity is not a design consideration.

9
D.4 Block 4: Perform Preliminary Structure Modeling. Determine Preliminary 

Substructure Loads and Tolerable Deformations

Preliminary structural analysis and modeling of the proposed bridge structure has 

been performed at this time. The preliminary strength, service and extreme events 

limit state loads and performance requirements at the foundation top have also been 

established. The tolerable vertical and lateral deformations previously stated in 

Block 1 have been confirmed by the bridge office as performance requirements.

D.5 Block 5: Develop and Execute Subsurface Exploration and Laboratory 

Testing Program for Feasible Foundation Systems

Prior to this stage, only the general bridge geometry, preliminary superstructure limit 

state loads and general site geotechnical conditions were known. The substructure 

locations now have been determined. A subsurface exploration and laboratory 

testing program has been implemented with a single boring performed at each 

substructure location. The soil boring logs for the southbound bridge are presented 

in Figures D-2 through D-4.

At each respective sample depth, the boring logs indicate the SPT N value in 

cohesionless soil layers, or the undisturbed Shelby tube sampling interval in 

cohesive layers. The results from subsequent unconfined compression tests and 

other index tests performed on the undisturbed samples are also provided on the 

boring logs at the respective sample depth. The results of the subsurface 

exploration and laboratory testing program are used to prepare a subsurface profile; 

define soil and rock parameters including strength, compressibility, parameter 

variation, liquefaction susceptibility, and seismic earth pressure parameters; define 

subsurface water conditions, as well as identify critical cross sections for design. 

The results of the subsurface exploration program and laboratory test results have 

been used to generate a generalized soil profile which is presented in Figure D-5. 

This generalized soil profile is an invaluable resource as the foundation selection 

process proceeds. A design profile for each substructure location will be developed 

from the information gathered in this block and used in later blocks.

10
Figure D-2 Boring Log S-1, Page 1 of 3.

11
Figure D-2 Boring Log S-1, Page 2 of 3.

12
Figure D-2 Boring Log S-1, Page 3 of 3.

13
Figure D-3 Boring Log S-2, Page 1 of 2.

14
Figure D-3 Boring Log S-2, Page 2 of 2.

15
Figure D-4 Boring Log S-3, Page 1 of 3.

16
Figure D-4 Boring Log S-3, Page 2 of 3.

17
Figure D-4 Boring Log S-3, Page 3 of 3.

18
Figure D-5 Site Profile View.

19
D.6 Block 6: Evaluate Information and Determine Candidate Foundation 

Systems

The question to be answered is what candidate foundation systems are appropriate 

for consideration based on the site conditions. This question will be answered 

based primarily on the strength and compressibility of the geomaterials, the 

proposed loading conditions, the project deformation limits, the project schedule, 

and the foundation cost. The hydraulic analysis indicates the potential for 

substantial scour at the center pier. The selection of the appropriate foundation 

system including cost considerations is discussed in greater detail in Chapter 3.

D.7 Block 7: Determine if a Deep Foundation is Required

Based on the strength and compressibility of the near surface geomaterials, scour 

concerns, as well as the required construction timeline, it is decided that a deep 

foundation system is required for structure support. Driven piles and other deep 

foundation systems must now be evaluated. Through this process, some foundation 

systems become less viable as constructability and cost considerations are refined. 

In the final analysis, the design, construction, and testing costs associated with 

addressing the variable subsurface conditions at this site are prohibitive for all of the 

drilled deep foundation solutions. Accordingly, driven piles are selected for the 

structure support; and drilled shaft, micropile, CFA pile, and other drilled deep 

foundation systems are eliminated.

D.8 Block 8: Select Candidate Driven Pile Types and Sections 

Driven pile foundation systems consisting of steel H-piles, closed-end steel pipe 

piles, and prestressed concrete piles are initially considered technically and 

economically feasible. However, due to pile drivability concerns presented by the 

extremely dense gravel layer at Pier 2, closed-end steel pipe piles and prestressed 

concrete piles are eliminated from further consideration. In this geographic region, 

steel H-piles are commonly used. Local contractors are familiar with H-pile 

installation and splicing, and H-piles are readily available from a local manufacturing 

facility. For these reasons, in addition to the ease with which H-piles can 

accommodate length variations associated with site variability, H-piles are viewed as 

the primary candidate pile type. Several H-pile sections are viable, and those 

sections will be advanced as candidate driven pile foundation systems.

20
Foundation loads are now closer to being finalized as are the tolerable deformation 

limits for the structure. At this stage in the design process, detailed analyses are 

required at each substructure location. Therefore, Block 9 through Block 19 will be 

repeated for each of the three substructure locations: North Abutment, Pier 2, and 

South Abutment. The design process will be presented for these blocks at a given 

substructure location before repeating the same steps at the next substructure 

location.

D.9 Block 9: North Abutment – Calculate Nominal and Factored Structural 

Resistances for all Candidate Piles

The nominal structural resistance is now evaluated for five candidate H-pile sections. 

The H-pile sections selected for evaluation include a HP 10x42, a HP 12x53, a HP 

12x74, a HP 14x89, and a HP 14x117. A detailed step by step example for 

calculation of the nominal structural resistance was previously presented in Section 

8.5.3 for an HP 14x117 H-pile section. Therefore, this process is not repeated for 

the five candidate pile sections. Table D-2 presents the calculated nominal 

structural resistances in axial compression, flexure, and shear for the five candidate 

sections. An unbraced length of 1 foot was assumed in these calculations.

Table D-2 Nominal Structural Resistances in Axial Compression, Flexure and 

Shear 

H-pile Section HP 

10x42

HP 

12x53

HP 

12x74

HP 

14x89

HP 

14x117

Pn, Nominal Resistance in Axial 

Compression (kips) 618 767 1088 1303 1718

Mny, Nominal Resistance in 

Weak Axis Flexure (kip-ft) 82 114 118 257 380

Mnx, Nominal Resistance in 

Strong Axis Flexure (kip-ft) 176 295 433 592 807

Vn, Nominal Resistance in 

Shear (kips) 118 149 214 246 331

It is anticipated that the piles at the North Abutment will be driven into the dense 

gravel with sand deposit, or possibly to the underlying bedrock. The dense gravel 

with sand deposit contains occasional cobbles. In these conditions, pile shoes are 

recommended for use with the H-piles to reduce the risk of damage. Therefore, the 

applicable structural resistance factors, φφcc, are 0.5 for axial compression resistance 

and 0.7 for combined axial compression and flexural resistance. A resistance factor 

21
of φφvv =1.0 is used for shear, and a resistance factor of φφff=1.0 is applicable for 

flexure only. Table D-3 summarizes the calculated factored structural resistances in

axial compression, combined axial compression and flexure, flexure, and shear.

Table D-3 Factored Structural Resistance in Axial Compression, Flexure and 

Shear

H-pile Section HP 

10x42

HP 

12x53

HP 

12x74

HP 

14x89

HP 

14x117

Pr, Factored Resistance in 

Axial Compression,

φφcc = 0.5 (kips)

309 383 544 652 859

Pr, Factored Resistance in 

Axial Compression and Flexure,

φφcc = 0.7 (kips)

433 537 762 912 1203

Mry, Factored Resistance in 

Weak Axis Flexure,

φφff=1.0 (kip-ft)

82 114 118 257 380

Mrx, Factored Resistance in 

Strong Axis Flexure,

φφff=1.0 (kip-ft)

176 295 433 592 807

Vr, Factored Resistance in 

Shear

φφvv =1.0 (kips)

118 149 214 246 331

D.10Block 10: North Abutment – Calculate Nominal and Factored Geotechnical 

Resistances in Axial Compression and Tension Versus Depth for all 

Candidate Piles; Perform Preliminary Pile Drivability Analyses

The engineering properties of the subsurface materials at the North Abutment were 

determined in Block 5. The results of the boring program and laboratory tests are 

now used to develop a design profile for each substructure location. Engineering 

judgement was used in developing the design profile to delineate the subsurface

conditions into layers with similar properties. An effective stress diagram, depicted 

in Figure D-6, was also constructed in association with the design profile. This 

diagram includes the total stress, porewater pressure, and effective stress versus 

depth. Figure D-6 also presents the basic soil profile for quick reference to the 

relevant soil layers. The effective stress diagram was computed using Equations

5-7 through 5-9 from Chapter 5. These equations are repeated below. For Figure 

D-6, the total stress, porewater pressure, and effective stress were calculated at 1 

foot increments using a spreadsheet.

22
σσvv = ∑ (γγiihii) nn

ii [Eq. 5-7]

uu = γγwwhww [Eq. 5-8]

σσ′vv = ∑ (γγiihii) − γγwwhww nn

ii [Eq. 5-9]

Figure D-6 Effective stress diagram for North Abutment using Boring S-1.

To continue development of an idealized design profile, field SPT N values were 

corrected for hammer energy transfer and vertical effective stress. The field SPT N 

values were first corrected for energy transfer using Equation 5-1. These results are 

presented in Table D-4 Typical correlations for SPT hammer type and energy 

transfer are provided in Section 5.1.1 (e.g., typical energy transfer of 80% for 

automatic hammer). The SPT hammer on the drill rig used for this project’s 

subsurface exploration program was calibrated in accordance with ASTM D4633. 

Results of this calibration indicated an average energy transfer of 75%. Therefore, 

the ER value in Equation 5-1 is equal to 75.

NN60 = NN �

EEEE

60� [Eq. 5-1]

The SPT N value was corrected for vertical effective stress as presented in Equation 

5-2, using the Peck et al. (1974) correction factor, CCnn. The depth value for this 

calculation was taken from the middle depth of the SPT sampling event after the 6 

23
inch seating interval (e.g., the SPT N value recorded from 0.5-1.5 feet was corrected 

using the vertical effective stress at a depth of 1 foot).

(NN1)60 = CCnnNN60 [Eq. 5-2]

CCnn = 0.77 log � 20

σσ′vvvv

� [Eq. 5-3]

Table D-4 Correction of Field SPT N Value for Energy and Vertical Effective 

Stress at the North Abutment using S-1

Soil Layer Depth (ft) σ'vo (ksf) Field N value N60 Cn (N1)60

1 1 0.105 4 5 1.99 10

1 6 0.630 4 5 1.39 7

1 11 1.155 6 8 1.19 9

1 16 1.618 6 8 1.07 8

1 21 1.831 8 10 1.03 10

2 26 2.058 13 16 0.99 16

2 31 2.306 15 19 0.95 18

2 36 2.554 11 14 0.92 13

2 41 2.802 15 19 0.89 17

2 46 3.050 18 23 0.86 19

3 51 3.363 40 50 0.83 41

3 56 3.676 39 49 0.80 39

3 61 3.989 41 51 0.77 40

3 66 4.302 43 54 0.75 40

3 71 4.615 41 51 0.72 37

3 76 4.928 44 55 0.70 39

3 81 5.241 45 56 0.68 38

3 86 5.554 48 60 0.66 40

3 91 5.867 46 58 0.64 37

3 96 6.180 47 59 0.62 37

After correcting the SPT N values for energy transfer and vertical effective stress, an 

average corrected N value was determined for each respective layer. The N value 

from the first SPT sample in Layer 1 was not included in this procedure since the 

bottom of the footing at the North Abutment is below this sample depth.

24
Table D-5 presents the average (N1)60 value for each layer at the North Abutment, 

the coefficient of variation, COV, within the layer, and the effective stress friction 

angle, φ', chosen for the layer. The coefficient of variation for each layer was less 

than 25% indicating low variability within each of the identified layers. Therefore, 

separating the soil profile into additional layers was not performed, as it would have 

been with the existence of higher variability soil.

The (N1)60 values were used to estimate the effective stress friction angle of each 

soil layer in accordance with Table 5-5. Layer 3 consists of hard angular gravel with 

sand. Therefore, as discussed in Section 5.5.1 of Chapter 5, the design friction 

angle in this layer was limited to 36 degrees for estimating the shaft resistance while 

a friction angle of 40 degrees was used to estimate the toe resistance.

Table D-5 Effective Stress Friction Angle Correlations at the North Abutment

Soil Layer Average (N1)60 COV φ' shaft 

(degrees)

φ' toe 

(degrees) 

1 9 14.4% 33 33

2 17 13.5% 36 36

3 39 3.7% 36 40

The design profile for the North Abutment is presented in Figure D-7, with the bottom 

of footing elevation 5 feet below ground surface elevation. Some soil properties in 

the design soil profile such as the elastic moduli, Es, and the initial cyclic modulus of 

subgrade reaction, kc, have been selected based on published correlations in the 

absence of laboratory and field testing. For this particular soil profile, the elastic 

moduli were determined from the SPT correlation in Table 5-11 and the initial cyclic 

moduli of subgrade reaction were selected based on representative values shown in 

Table 7-22. The figure format used to summarize the design profile is used at all 

substructure locations and therefore includes design value placeholders for cohesive 

soil parameters, the undrained shear strength, su, and 50% strain factor, ε50. 

However, cohesive soils are not present at the North Abutment.

25
Figure D-7 Design profile at the North Abutment.

D.10.1 Geotechnical Resistance in Axial Compression

The nominal geotechnical resistance in axial compression is now determined for the 

selected candidate H-pile sections. The nominal geotechnical resistance can be 

calculated by hand or with computer software using an appropriate analysis method 

for cohesionless soils and the pile type. Chapter 7 describes appropriate methods 

for this purpose as well as computer programs available at the time of this manual’s 

publication.

For this abutment, the DrivenPiles computer program was used to calculate the 

nominal resistance, shaft resistance, and toe resistance each as a function of depth 

for each of the five candidate H-piles. This software program was selected since it 

uses the FHWA recommended Nordlund method. This method is appropriate for

calculating the nominal geotechnical resistance of H-piles in cohesionless soils such 

as those encountered in Boring S-1. The DrivenPiles program code also allows the 

analyst to select a different friction angle for shaft and toe resistance calculations in 

any layer. This option was utilized for the gravel with sand and occasional cobbles 

comprising Layer 3.

A summary of the shaft, toe, and nominal geotechnical resistance determined by the 

Nordlund static analysis method is presented for one of the candidate pile sections 

26
in Table D-6. These results are also presented graphically in Figure D-8. The depth 

indicated in both Table D-6 and Figure D-8 is referenced from the bottom of footing, 

which is 5 feet below the original ground surface elevation. The nominal shaft, 

nominal toe, and nominal geotechnical resistances were calculated for all of the 

candidate pile sections in a similar manner. The nominal geotechnical resistances in 

axial compression versus pile penetration depth are presented in Figure D-9 for all 

candidate pile types.

Once the nominal geotechnical resistance in axial compression versus pile 

penetration depth has been calculated, the factored geotechnical resistance in axial 

compression versus pile penetration depth can be determined. The factored 

geotechnical resistance depends on the resistance determination method selected

for the design.

If pile installation will be controlled by driving to a depth determined by static analysis 

method, then the factored geotechnical resistance in axial compression as a function 

of pile penetration depth can be determined by multiplying the calculated nominal 

resistance at a given depth by the resistance factor associated with the static 

analysis method, φφss . AASHTO (2014) resistance factors for static analysis 

methods are presented in Table 7-1 of this manual. 

If the nominal resistance will be confirmed by a field determination method, the 

factored geotechnical resistance in axial compression as a function of pile 

penetration depth can be determined by multiplying the calculated nominal 

geotechnical resistance at a given depth by the resistance factor associated with the 

field determination method, φφdd . AASHTO (2014) resistance factors for field 

resistance determination methods are presented in Table 7-2.

27
Table D-6 Nominal Shaft, Nominal Toe and Nominal Geotechnical Resistance for 

HP 12x74 at the North Abutment

Depth

(feet)

Nominal 

Shaft 

Resistance 

(kips)

Nominal 

Toe 

Resistance 

(kips)

Nominal

Geotechnical 

Resistance 

(kips)

Depth

(feet)

Nominal 

Shaft 

Resistance 

(kips)

Nominal 

Toe 

Resistance 

(kips)

Nominal

Geotechnical

Resistance 

(kips)

0.01 0.0 16.4 16.4 37 151.0 155.4 306.4

1 1.1 19.7 20.7 38 157.9 155.4 313.3

2 2.3 23.0 25.3 39 165.0 155.4 320.4

3 3.7 26.2 30.0 40 172.1 155.4 327.5

4 5.3 29.5 34.9 41 179.4 155.4 334.8

5 7.2 32.8 40.0 42 186.8 155.4 342.2

6 9.2 36.1 45.2 43 194.3 155.4 349.7

7 11.4 39.4 50.7 44 202.0 155.4 357.4

8 13.7 42.6 56.4 44.99 209.7 155.4 365.1

9 16.3 45.9 62.2 45.01 209.8 398.8 608.6

9.99 19.1 49.2 68.2 46 217.6 406.4 624.0

10.01 19.1 49.2 68.3 47 225.7 414.1 639.8

11 22.0 50.5 72.5 48 233.9 421.8 655.7

12 25.0 51.3 76.2 49 242.2 428.1 670.3

13 28.0 51.3 79.3 50 250.7 428.1 678.8

14 31.2 51.3 82.4 51 259.4 428.1 687.5

15 34.4 51.3 85.6 52 268.2 428.1 696.3

16 37.7 51.3 88.9 53 277.2 428.1 705.3

17 41.0 51.3 92.3 54 286.3 428.1 714.4

18 44.5 51.3 95.7 55 295.5 428.1 723.6

19 48.0 51.3 99.2 56 304.9 428.1 733.0

19.99 51.5 51.3 102.8 57 314.5 428.1 742.6

20.01 51.6 110.2 161.8 58 324.2 428.1 752.3

21 56.5 112.8 169.3 59 334.1 428.1 762.2

22 61.5 115.5 176.9 60 344.1 428.1 772.2

23 66.6 118.1 184.7 61 354.2 428.1 782.3

24 71.9 120.8 192.7 62 364.6 428.1 792.7

25 77.2 123.5 200.7 63 375.0 428.1 803.1

26 82.7 126.2 208.9 64 385.7 428.1 813.7

27 88.3 128.8 217.2 65 396.4 428.1 824.5

28 94.0 131.5 225.6 66 407.3 428.1 835.4

29 99.9 134.2 234.1 67 418.4 428.1 846.5

30 105.9 136.9 242.7 68 429.6 428.1 857.7

31 111.9 139.5 251.5 69 441.0 428.1 869.1

32 118.2 142.2 260.4 70 452.5 428.1 880.6

33 124.5 144.9 269.4 71 464.2 428.1 892.3

34 130.9 147.6 278.5 72 476.0 428.1 904.1

35 137.5 150.2 287.7 73 488.0 428.1 916.1

36 144.2 152.9 297.1 74 500.1 428.1 928.2

28
Table D-6 Nominal Shaft, Nominal Toe and Nominal Geotechnical Resistance for 

HP 12x74 at the North Abutment (continued)

Depth

(feet)

Nominal 

Shaft 

Resistance 

(kips)

Nominal 

Toe 

Resistance 

(kips)

Nominal

Geotechnical 

Resistance 

(kips)

Depth

(feet)

Nominal 

Shaft 

Resistance 

(kips)

Nominal 

Toe 

Resistance 

(kips)

Nominal

Geotechnical 

Resistance 

(kips)

75 512.4 428.1 940.5 84 629.8 428.1 1057.8

76 524.9 428.1 953.0 85 643.5 428.1 1071.6

77 537.4 428.1 965.5 86 657.48 428.1 1085.58

78 550.2 428.1 978.3 87 671.57 428.1 1099.67

79 563.05 428.1 991.15 88 685.82 428.1 1113.92

80 576.09 428.1 1,004.19 89 700.21 428.10 1,128.31

81 589.28 428.1 1,017.38 90 714.76 428.10 1,142.86

82 602.6 428.1 1030.7 91 729.46 428.10 1,157.56

83 616.1 428.1 1044.2 91.99 744.16 428.10 1,172.26

Figure D-8 Geotechnical resistance in axial compression versus pile penetration 

depth for HP 12x74 candidate pile section at North Abutment.

29
Figure D-9 Nominal geotechnical resistance in axial compression versus pile 

penetration depth for all candidate pile sections at the North Abutment.

Figure D-10 presents a design chart of the nominal resistance, Rn, and the factored 

geotechnical resistance, Rr, in axial compression versus pile penetration depth for 

the HP 12x74 H-pile section at the North Abutment. The design chart includes the 

nominal geotechnical resistance as well as a number of factored geotechnical 

resistances. The factored geotechnical resistances are presented for a selection of 

resistance determination methods. The factored geotechnical resistance versus 

penetration depth is plotted for resistance determination by a static load test with 

dynamic testing of 2% of the piles (φφdd =0.80), by dynamic testing of at least two 

piles per site condition, but no less than 2% of the production piles, with signal 

matching (φφdd =0.65), and by wave equation analysis (φφdd =0.50). The factored 

geotechnical resistance is also plotted for resistance determination by the Nordlund 

static analysis method (φφss =0.45). For a single pile section (HP 12x74), this figure 

illustrates the effects the various resistance determination methods have on the pile 

length required for a given factored resistance, the factored resistance available 

from a given pile section, and the potential impact of these factors on the number of 

piles needed to resist axial compression loads.

30
Figure D-10 Design chart of nominal and factored geotechnical resistance in axial 

compression versus pile penetration depth for HP 12x74 at the North Abutment.

The factored geotechnical resistance in axial compression for all candidate pile 

sections is presented in Figures D-11 through D-14 based on the same resistance 

determination methods. For all the candidate pile sections, these figures illustrate 

the effects the various resistance determination methods have on the pile length 

required for a given factored resistance, the factored resistance available from a 

given pile section, and the potential impact of these factors on the number of piles 

needed to resist axial compression loads.

31
Figure D-11 Factored geotechnical resistance, Rr, in axial compression based on 

field determination by static load test and dynamic testing 2% of the piles, φφdd =0.80.

Figure D-12 Factored geotechnical resistance, Rr, in axial compression based on 

field determination by dynamic testing 2% of the piles, φφdd =0.65.

32
Figure D-13 Factored geotechnical resistance, Rr, in axial compression based on 

field determination by wave equation analysis, φφdd =0.50.

Figure D-14 Factored geotechnical resistance, Rr, in axial compression based on 

determination using Nordlund Method static analysis, φφss =0.45.

33
D.10.2 Geotechnical Resistance in Axial Tension

In a similar manner, the nominal and factored geotechnical resistances in axial 

tension (uplift) were calculated using the Nordlund method and with the DrivenPiles 

computer program. Figure D-15 presents the nominal shaft resistance versus 

penetration depth for all the candidate pile sections. As outlined in Section 7.2.3.2.1 

of Chapter 7, the factored resistance in axial tension is the shaft resistance 

multiplied by the resistance factor, φup, for the resistance determination method. 

Figure D-15 Nominal shaft resistance versus penetration depth for all candidate pile 

sections at the North Abutment.

Figure D-16 presents a design chart of the nominal shaft resistance, Rs, and the 

factored geotechnical resistance, Rr, in axial tension versus pile penetration depth for 

the HP 12x74 H-pile section at the North Abutment. A resistance factor of 0.60 is 

used when the tension resistance is determined by a static load test, 0.50 when 

determined by a dynamic test with signal matching, and 0.35 when determined by 

the Nordlund static analysis method. For a single pile section (HP 12x74), this figure 

illustrates the effects the various resistance determination methods have on the pile 

length required for a given factored resistance, the factored resistance available 

from a given pile section, and the potential impact of these factors on the number of 

piles needed to resist axial tension loads.

34
Figure D-16 Design chart of nominal and factored geotechnical resistance in axial 

tension for HP 12x74 at the North Abutment.

Figures D-17 to D-19 present the factored geotechnical resistance in axial tension 

versus penetration depth based on the field determination method for each of the 

candidate pile sections. For all the candidate pile sections, these figures illustrate 

the effects the various resistance determination methods have on the pile length 

required for a given factored resistance, the factored resistance available from a 

given pile section, and the potential impact of these factors on the number of piles 

needed to resist axial tension loads.

A review of the soil profile at the North Abutment indicates no unsuitable soil layers 

are present that should be ignored for load support. Abutment scour and 

liquefaction due to a seismic event are also not considerations. 

35
Figure D-17 Factored geotechnical resistance, Rr, in axial tension based on field 

determination by static load test, φdyn=0.60.

Figure D-18 Factored geotechnical resistance, Rr, in axial tension based on field 

determination by dynamic testing with signal matching, φdyn=0.50.

36
Figure D-19 Factored geotechnical resistance, Rr, in axial tension based on 

determination using Nordlund Method static analysis, φstat=0.35.

D.10.3 Preliminary Pile Drivability Assessment

A preliminary assessment of pile drivability is now performed. A check of pile 

drivability at this time is essential to assess the constructability of candidate pile 

types and/or sections and to eliminate sections with insufficient drivability. Section 

12.4 provides a detailed discussion of wave equation drivability analyses and their 

applications.

A candidate pile section must be capable of being driven to the penetration depth 

necessary to achieve the nominal geotechnical resistance in axial compression and 

tension, and to a penetration depth necessary to satisfy lateral load demands as well 

as axial and lateral deformation requirements. A suitably sized pile hammer must be 

capable of driving the pile to this penetration depth and nominal resistance at a 

reasonable blow count without exceeding material stress limits. As detailed in 

Chapter 12, the blow count should be between 30 and 120 blows per foot at the 

nominal resistance. If the pile cannot be driven within these requirements, a larger 

pile hammer, a pile section with greater impedance, or pile installation aids such as 

predrilling or jetting may be required to satisfy or improve drivability. 

37
Driving stresses during pile installation should remain below the driving stress limits 

associated with the pile type and material strength. For the candidate steel H-piles, 

compression driving stress limits are given by Equation 8-33. As per ASTM A-572 

requirements, new steel H-piles are rolled with a minimum yield stress of 50 ksi. 

The driving stress limit, σdd , for candidate pile sections is then calculated as follows:

σdd = φφdd �0.9 FFyy� [Eq. 8-33]

Where: φdd = resistance factor, 1.0 for steel piles.

FFyy = yield stress, 50 ksi.

Therefore, the driving stress limit, σdd , is 45 ksi.

σσdd = (1.0)�0.9 (50 kk kk)� = 45 kk kk

Drivability analyses were performed for all five candidate pile sections. Since the 

specific pile hammer is often unknown at this point in the design, a reasonably sized, 

commonly available single acting diesel hammer was chosen for each of the 

candidate pile sections. As noted in Section 15.19, a hammer having a ram weight 

of 1 to 2% of the larger of the required nominal resistance or required nominal 

driving resistance often provides a reasonable initial estimate of a trial hammer size 

for wave equation analysis.

Table D-7 summarizes the factored structural resistance in axial compression, Pr, 

and the corresponding minimum and maximum nominal driving resistance 

associated with full section utilization and field determination methods ranging from 

a static load test with dynamic testing (φdyn=0.80) to the FHWA modified Gates 

dynamic formula (φdyn=0.40). Given that utilization of the full structural resistance is 

uncommon for piles driven in soil, a reasonable initial estimate of the trial hammer 

size for a wave equation drivability analysis is 1 to 1.5% of the minimum Rndr. 

Driving stresses could exceed specified limits by choosing a hammer with a ram 

weight significantly larger than 2% of the minimum Rndr. For each pile hammer, the 

wave equation default values were used for the helmet weight, hammer cushion 

materials, and the hammer cushion material properties.

38
Table D-7 Summary of Pile Hammers Used in Drivability Analyses

Pile 

Section

Pile 

Cross 

Sectional 

Area 

(in2)

Factored 

Structural 

Resistance, 

Pr

(kips)

Minimum 

Rndr

φdyn=0.80

(kips)

Maximum

Rndr

φdyn=0.40

(kips)

Ram 

Weight 

1% of 

Min Rndr

(%)

Trial 

Diesel 

Hammer 

Model

Ram 

Weight 

(kips)

Rated 

Energy 

(ft-kips)

HP 10x42 12.4 309 386 773 3.86 D25-52 5.51 62.0

HP 12x53 15.5 383 478 958 4.78 D30-52 6.62 74.4

HP 12x74 21.8 544 680 1360 6.80 D36-52 7.94 89.3

HP 14x89 26.1 652 815 1630 8.15 D46-52 10.14 114.1

HP 14x117 34.4 860 1075 2150 10.07 D50-52 11.03 124.0

For the soil resistance model, the output from DrivenPiles was converted to unit 

shaft resistance and unit toe resistance values and then input into the wave equation 

program. Similar soil resistances are thereby calculated versus depth by both the 

static analysis and wave equation analysis programs.

The dynamic soil properties for each soil layer were chosen in accordance with wave 

equation program recommendations. Selection of soil quake and damping 

parameters is discussed in Section 12.6.7. For the North Abutment profile, some 

soil setup is expected in the upper silty fine sand layer and the underlying layer of 

medium dense sand with little silt. Therefore soil setup factors of 1.2 were selected 

for these two layers. No setup was expected in the dense gravel with sand of Layer 

3. Soil setup is discussed in Section 7.2.4.2 and a summary of typical soil setup 

factors is provided in Table 7-16. A summary of the dynamic soil properties chosen 

for the drivability analyses are summarized in Table D-8.

In soils that exhibit setup, the long term nominal resistance may be higher than the 

nominal driving resistance. Therefore, a gain/loss factor of 0.833 was used to 

estimate the nominal driving resistance versus depth in the drivability analyses. This

gain/loss factor was determined from the inverse of the highest soil setup factor 

within the soil model (e.g., 1 divided by 1.2 equals 0.833). A gain/loss factor of 1 

would be used if it was desired to model the nominal resistance instead of the 

nominal driving resistance and not consider the soil strength loss during driving and 

any subsequent soil setup. Refer to Chapter 12 for more detailed discussion on the 

selection of dynamic soil properties and soil setup factors.

39
Table D-8 Dynamic Soil Properties for North Abutment Soil Profile

Soil 

Layer

Pile 

Section

Shaft 

Quake

(in)

Toe 

Quake

(in)

Shaft 

Damping

(s/ft)

Toe 

Damping

(s/ft)

Soil SetUp Factor

1 HP 10 x 42 0.10 0.17 0.10 0.15 1.2

1 HP 12 x 53 0.10 0.20 0.10 0.15 1.2

1 HP 12 x 74 0.10 0.20 0.10 0.15 1.2

1 HP 14 x 89 0.10 0.23 0.10 0.15 1.2

1 HP 14 x 117 0.10 0.23 0.10 0.15 1.2

2 HP 10 x 42 0.10 0.17 0.05 0.15 1.2

2 HP 12 x 53 0.10 0.20 0.05 0.15 1.2

2 HP 12 x 74 0.10 0.20 0.05 0.15 1.2

2 HP 14 x 89 0.10 0.23 0.05 0.15 1.2

2 HP 14 x 117 0.10 0.23 0.05 0.15 1.2

3 HP 10 x 42 0.10 0.08 0.05 0.15 1.0

3 HP 12 x 53 0.10 0.10 0.05 0.15 1.0

3 HP 12 x 74 0.10 0.10 0.05 0.15 1.0

3 HP 14 x 89 0.10 0.12 0.05 0.15 1.0

3 HP 14 x 117 0.10 0.12 0.05 0.15 1.0

The DrivenPiles program calculates the nominal driving resistance which models the 

soil strength lost during driving as well as the geotechnical nominal resistance once 

setup occurs. Figure D-20 presents the nominal shaft, toe, and driving resistance 

versus pile penetration depth for the HP 12x74 H-pile section at the North Abutment. 

These nominal driving resistances are presented numerically in Table D-9. To 

quantify the expected soil setup at a given pile penetration depth, the values from 

Table D-9 can be compared against the nominal resistance previously presented in 

Table D-6. Figure D-21 illustrates the difference between the expected nominal 

driving resistance and the geotechnical nominal resistance after setup for the HP 

12x74 candidate pile section. For example, at a depth of 45 feet, the expected setup 

from shaft resistance is 35 kips.

40
Figure D-20 Nominal driving resistance for HP 12x74 at the North Abutment.

Figure D-21 Comparison of nominal driving resistance and nominal geotechnical 

resistance in axial compression for HP 12x74 at the North Abutment.

41
Table D-9 Summary of Nominal Driving Resistance Versus Pile Penetration 

Depth for HP 12x74 at the North Abutment

Depth

(feet)

Nominal 

Shaft 

Resistance 

(kips)

Nominal 

Toe 

Resistance 

(kips)

Nominal

Driving 

Resistance 

(kips)

Depth

(feet)

Nominal 

Shaft 

Resistance 

(kips)

Nominal 

Toe 

Resistance 

(kips)

Nominal 

Driving 

Resistance 

(kips)

0.01 0.01 16.43 16.44 37 125.82 155.41 281.23

1 0.87 19.68 20.55 38 131.59 155.41 287

2 1.91 22.96 24.87 39 137.46 155.41 292.87

3 3.1 26.24 29.34 40 143.43 155.41 298.84

4 4.45 29.52 33.97 41 149.5 155.41 304.91

5 5.96 32.8 38.76 42 155.67 155.41 311.08

6 7.63 36.08 43.71 43 161.94 155.41 317.35

7 9.46 39.36 48.82 44 168.31 155.41 323.72

8 11.45 42.64 54.09 44.99 174.71 155.41 330.12

9 13.59 45.92 59.52 45.01 174.86 398.77 573.63

9.99 15.88 49.17 65.04 46 182.68 406.4 589.07

10.01 15.92 49.21 65.14 47 190.73 414.1 604.83

11 18.32 50.53 68.85 48 198.93 421.8 620.73

12 20.8 51.26 72.06 49 207.28 428.1 635.38

13 23.35 51.26 74.6 50 215.78 428.1 643.88

14 25.96 51.26 77.21 51 224.44 428.1 652.53

15 28.63 51.26 79.89 52 233.24 428.1 661.34

16 31.37 51.26 82.63 53 242.2 428.1 670.3

17 34.18 51.26 85.43 54 251.31 428.1 679.4

18 37.05 51.26 88.3 55 260.56 428.1 688.66

19 39.98 51.26 91.24 56 269.97 428.1 698.07

19.99 42.95 51.26 94.2 57 279.53 428.1 707.63

20.01 43.02 110.15 153.17 58 289.25 428.1 717.34

21 47.05 112.8 159.85 59 299.11 428.1 727.21

22 51.23 115.47 166.7 60 309.12 428.1 737.22

23 55.5 118.14 173.64 61 319.29 428.1 747.39

24 59.87 120.81 180.69 62 329.6 428.1 757.7

25 64.35 123.48 187.83 63 340.07 428.1 768.17

26 68.92 126.15 195.07 64 350.69 428.1 778.79

27 73.6 128.83 202.43 65 361.46 428.1 789.56

28 78.37 131.51 209.88 66 372.38 428.1 800.48

29 83.24 134.19 217.43 67 383.45 428.1 811.55

30 88.21 136.86 225.08 68 394.67 428.1 822.77

31 93.29 139.54 232.83 69 406.05 428.1 834.15

32 98.46 142.21 240.67 70 417.57 428.1 845.67

33 103.73 144.88 248.61 71 429.25 428.1 857.35

34 109.1 147.55 256.66 72 441.08 428.1 869.17

35 114.57 150.22 264.79 73 453.06 428.1 881.15

36 120.15 152.89 273.03 74 465.18 428.1 893.28

42
Table D-9 Summary of Nominal Driving Resistance Versus Pile Penetration 

Depth for HP 12x74 at the North Abutment (continued)

Depth

(feet)

Nominal 

Shaft 

Resistance 

(kips)

Nominal 

Toe 

Resistance 

(kips)

Nominal 

Driving 

Resistance 

(kips)

Depth

(feet)

Nominal 

Shaft 

Resistance 

(kips)

Nominal 

Toe 

Resistance 

(kips)

Nominal 

Driving 

Resistance 

(kips)

75 477.47 428.1 905.56 84 594.79 428.1 1022.89

76 489.9 428.1 917.99 85 608.58 428.1 1036.68

77 502.48 428.1 930.58 86 622.52 428.1 1050.62

78 515.21 428.1 943.31 87 636.62 428.1 1064.72

79 528.1 428.1 956.2 88 650.86 428.1 1078.96

80 541.13 428.1 969.23 89 665.26 428.1 1093.36

81 554.32 428.1 982.42 90 679.81 428.1 1107.9

82 567.66 428.1 995.76 91 694.5 428.1 1122.6

83 581.15 428.1 1009.25 91.99 709.2 428.1 1137.3

Graphical outputs of the preliminary drivability analyses are shown in Figure D-22. 

The nominal driving resistance, the blow count or pile penetration resistance, and 

the compression driving stress are presented versus pile penetration depth for each 

of the five candidate pile sections. As previously noted, the recommended blow 

count limit is 120 blows per foot (10 blows per inch), and the recommended driving 

stress limit is 45 ksi. A circular reference marker is indicated on the blow count 

versus penetration depth plot highlighting the depth where the blow count first 

exceeds 120 blows per foot. This marker is also shown at the same depth on the 

nominal driving resistance versus depth plot indicating the nominal driving resistance 

achieved when practical refusal driving conditions are encountered with the selected 

hammer in the modeled driving conditions. Similarly, the marker is shown at the 

same depth on the compression driving stress versus depth plot indicating the 

compression driving stress when practical refusal driving conditions are 

encountered.

In Figure D-22, the drivability results for the HP 12x53 section stand out from the 

other pile sections. The drivability results for the HP 12x53 H-pile section driven with 

a D30-52 driving system operated at the maximum fuel setting illustrate that refusal 

driving conditions of 120 blows per foot are encountered near a pile penetration 

depth of 52 feet. Compression driving stresses for the HP 12x53 with this hammer 

exceed the 45 ksi compression stress limit at a pile penetration depth of 46 feet, and 

reach a maximum of 45.9 ksi at a depth of 49 feet.

43
Figure D-22 Preliminary drivability results at the North Abutment.

The D30-52 hammer was also modeled at a reduced fuel setting, fuel setting 3. 

However, while the driving stresses can now be maintained within limits, refusal 

driving conditions are now encountered 4 feet shallower at a pile penetration depth 

of 48 feet. These results indicate the HP 12x53 pile section cannot be driven 

beyond 48 feet without exceeding either blow count or driving stress limits. 

For the remaining candidate pile sections and selected pile hammers, the maximum 

pile penetration depth before achieving 120 blows per foot ranges between 57 and 

64 feet. Driving stresses for some of the other candidate pile sections were close to 

the driving stress limit, but in all cases, the blow count limit and not the driving stress 

limit determined maximum drivability. A summary of the preliminary drivability 

results is presented in Table D-10. Once the estimated and/or minimum pile toe 

elevations are determined in Block 12 through Block 15 of the design process, the 

drivability results in Figure D-22 and Table D-10 should be reviewed to confirm that 

the candidate pile section can be driven to the estimated or required pile penetration 

depth, at reasonable blow counts, and within driving stress limits.

44
Table D-10 Summary of Preliminary Drivability Results at North Abutment

Pile

Section

Pile

Hammer

Fuel

Setting

Pile 

Penetration 

Depth at 

Practical 

Refusal 

Limit

(feet)

Nominal 

Driving 

Resistance 

at Practical 

Refusal 

Limit

(kips)

Anticipated 

Nominal 

Resistance 

at Depth of 

Practical 

Refusal

(kips)

Penetration 

Depth 

Exceeding 

Compression 

Driving 

Stress Limit 

(feet)

Maximum 

Compression 

Driving 

Stress

(ksi)

HP 10x42 D25-52 4 61 489 512 > 61 43.7

HP 12x53 D30-52 4 52 605 634 46 45.9

HP 12x53 D30-52 3 48 571 600 > 48 44.5

HP 12x74 D36-52 4 61 746 780 > 61 40.1

HP 14x89 D46-52 4 57 941 985 > 57 44.5

HP 14x117 D50-52 4 64 1121 1172 > 64 41.4

As noted previously, a hammer having a ram weight of 1 to 2% of the required 

nominal driving resistance often provides a reasonable initial estimate of hammer 

size. However, if a candidate pile type does not satisfy drivability requirements with 

this initially selected hammer and driving stress levels are within limits, other 

hammers should be evaluated before eliminating the candidate pile type. For 

example, a D30-52 hammer was initially selected for the HP 12x74 H-pile. This 

driving system has a ram weight of 6.6 kips or 0.97% of the required nominal 

resistance, so it is slightly below the recommended trial hammer size. The blow 

count limit of 120 blows per foot with the D30-52 was reached at a nominal 

resistance of 680 kips and a pile penetration depth of 55 feet. However, 

compression driving stresses were 38.5 ksi or less, indicating a larger hammer could

be considered.

Drivability analyses were then performed for both a D36-52 and a D46-52 pile 

hammer. Figure D-23 presents the drivability results for all three of these driving 

systems. Note that the analyses indicate that the D36-52 can drive the candidate

pile section to a nominal driving resistance of 756 kips at a pile penetration depth of 

62 feet before reaching the blow count limit. The maximum predicted compression 

driving stress of 40 ksi are also within driving stress limits. Similarly, the D46-52 can 

drive the same candidate pile section to a nominal driving resistance of 867 kips at a 

pile penetration depth of 72 feet before reaching the blow count limit. The maximum 

predicted compression driving stress of 44 ksi with the D46-52 is also within driving 

stress limits. Hence, it would have been erroneous to eliminate the HP 12x74 pile 

section solely based on the D30-52 drivability results. The drivability results from the 

two other hammers clearly indicate the candidate section can be driven to 

significantly higher nominal driving resistances and to greater pile penetration depths 

before reaching drivability limits.

45
Figure D-23 Hammer size comparison to drive the HP 12x74 pile section.

At this time, the factored axial compression and tension resistances versus depth 

have been calculated and preliminary drivability assessments have been performed 

for all candidate pile sections. The factored geotechnical resistances have been 

evaluated for the resistance determination methods under consideration. Maximum 

achievable penetration depths have also been assessed with drivability analyses.

It is unreasonable to carry all possible combinations of candidate sections, 

resistance determination methods, and possible group configurations forward in the 

design process. Hence, experience, engineering judgement, and agency practice

should be combined when selecting candidate pile types and sections, resistance 

determination methods, and potential group configurations. Otherwise, the number 

of possible design permutations will become unreasonable.

D.11Block 11: North Abutment – Estimate Preliminary Number of Piles, 

Preliminary Pile Group Size, and Resolve Individual Pile Loads for All 

Limit States

The structural engineer has provided the anticipated loads for the controlling limit 

states at the North Abutment. These limit state loads are presented in Table D-11. 

The Strength I limit state loads are used to evaluate geotechnical resistance in axial 

46
compression and tension, as well as for lateral loading. Service I limit state loads 

were also provided by the structural engineer without live loads. The Service I 

without live load (LL) includes only unfactored permanent loads such as the 

superstructure and wearing surface, pile cap and stem, utilities, and vertical earth 

pressure among others. The Service I without live load should be used for 

evaluating vertical deformation. There are no loads in the transverse direction at this 

abutment.

Table D-11 Limit State Loads on North Abutment

Limit State Q

(kips)

Vuy

(kips)

Muy

(k-ft)

Strength I 2505 846 6625

Service I 1838 566 4600

Service I, without live load 1540 562 4162

Based on past experience, the agency generally utilizes 2 rows of piles at abutments

with a minimum center to center pile spacing of at least 3 pile diameters. Three 

potential pile group configurations are therefore being considered: 2 rows of 9 piles, 

2 rows of 11 piles, and 2 rows of 13 piles. These group configurations are identified 

as Group Configuration 1, 2, and 3, respectively in Table D-12. Because of site

constraints, the pile cap length is limited to 43 feet. Furthermore, the distance from 

the center of any exterior pile to the pile cap edge must be at least 1.25 feet in both 

the transverse (x) and longitudinal (y) direction.

Table D-12 Potential Pile Group Configurations

Group 

Configuration

Piles 

per 

Row

Total 

Number 

of Piles

Sbx*

(feet)

Total Footing 

Length

(feet)

Sby*

(feet)

Total Footing 

Width

(feet)

1 9 18 5.0 42.5 4.0 6.5

2 11 22 4.0 42.5 4.0 6.5

3 13 26 3.0 38.5 4.0 6.5

* Sbx and Sby are illustrated in Figure D-24.

The following calculation is for the Group Configuration 1 and all applicable loads.

For this configuration, 9 piles per row are used in two separate rows. Thus the 

transverse pile spacing, Sbx, is 5’-0” and the total footing length is 42’-6”. The 

longitudinal pile spacing, Sby, is 4’-0”. Figure D-24 shows the layout for the Group 

Configuration 1 pile cap.

47
Figure D-24 Group Configuration 1 pile cap plan view.

For the established limit state loads and the trial pile group configuration depicted in 

Figure D-24, reactions for both the front and the back rows of piles were determined. 

Compression loads are taken as positive. The maximum factored load applied to 

each pile was subsequently calculated by dividing the reactions by the number of 

piles. Figure D-25 shows the free body diagram for determining the reactions and 

the resulting factored load per pile for both the front and the back row.

Figure D-25 Elevation view of cap free body diagram.

48
Table D-13 summarizes the limit state loads and the corresponding front and back 

row reactions. Strength I loads, Service I loads and the Service I loads without live 

load (LL) are provided.

Table D-13 Limit State Loads and Row Reactions for Group Configuration 1

Limit State Q

(kips)

Muy

(k-ft)

Rfront

(kips)

Rback

(kips)

Strength I 2505 6625 2908 -406

Service I 1838 4600 2069 -231

Service I, without LL 1540 4162 1811 -271

Table D-14 presents the maximum factored load per pile based upon the number of 

piles in the group configuration. For Group Configuration 1, the Strength I limit state 

front-row reaction of 2908 kips divided by 9 piles yields a maximum factored load per 

pile of 323 kips. Table D-14 summarizes the factored load per pile for other limit 

states and group configurations.

Table D-14 Factored Load Per Pile for Alternative Pile Group Configurations

Group 

Configuration

Strength I,

Q

(compression)

(kips)

Strength I,

Q

(tension)

(kips)

Strength I,

Vuy

(kips)

Service I,

without LL

Q

(kips)

1 323 -46 47 201

2 265 -37 39 165

3 224 -31 33 139

D.12Block 12: North Abutment – Estimate Pile Penetration Depth for Maximum 

Axial Compression Loads; Check Group Efficiency in Axial Compression

The estimated minimum pile penetration depth necessary to obtain a factored 

geotechnical resistance that is equal or greater than the maximum factored load per 

pile is now determined. Note that the factored geotechnical resistance in axial 

compression and the resulting pile penetration depth is dependent upon the 

resistance determination method. Therefore, the influence of the field resistance 

determination method on the design needs to be evaluated at this point in the design 

process and some resistance determination methods may be eliminated from further 

design consideration.

49
The pile penetration depth necessary for the maximum factored geotechnical 

resistance of 323 kips on a given candidate pile section can be evaluated from 

Figure D-11 to Figure D-14 for the various resistance determination methods. For a 

factored geotechnical resistance of 323 kips in axial compression, it is estimated that 

pile length variation due to changes in the resistance determination method will be 

relatively minor. For this factored resistance, piles will also likely be driven into the 

gravel layer with cobbles encountered 45 feet below footing grade which increases 

the potential for pile damage. Therefore, it is decided that dynamic testing 2% of the 

production piles will be used for the resistance determination method.

Figure D-12 illustrated the factored geotechnical resistance versus penetration depth 

for the 5 candidate pile sections based on determination testing by dynamic testing 

2% of the piles. From the static analysis results presented in this plot, the estimated 

penetration depth for the maximum factored geotechnical resistance of 323 kips in 

axial compression ranges from 43 feet for the HP 14x117 H-pile section to 59 feet 

for the HP 10x42 H-pile section. Similarly, the estimated pile penetration depths for 

all candidate pile sections and all group configurations were determined and are 

summarized in Table D-15.

Table D-15 Estimated Pile Penetration Depth Requirements for the Factored 

Geotechnical Resistance in Axial Compression at the Strength I Limit State

Group 

Configuration

Factored

Load per 

Pile

(kips)

HP 

10x42 

(feet)

HP 

12x53 

(feet)

HP 

12x74 

(feet)

HP 

14x89 

(feet)

HP 

14x117 

(feet)

1 323 59 45 45 45 43

2 265 46 45 45 38 35

3 224 45 45 43 32 30

Next, the group efficiency in axial compression is evaluated. Per Section 7.2.2.1,

the nominal geotechnical resistance of a pile group in cohesionless soil, can be 

taken as the sum of the individual pile nominal geotechnical resistances. In a similar 

manner, the factored geotechnical resistance of the pile group in cohesionless soil is

taken as the sum of the individual pile factored geotechnical resistances. This is 

recommended so long as 1) the bearing layer is not underlain by weak soil layers, 2) 

the piles are not installed at a pile spacing of less than 3 times the pile diameter, and 

3) no special installation procedures are anticipated such as jetting or predrilling. 

Since all these conditions are met at the North Abutment, the nominal and factored 

group resistances are satisfactory.

50
D.13Block 13: North Abutment – Establish Minimum Pile Penetration Depth for 

Axial Tension Loads; If Conditions Warrant, Modify Design and Return to 

Block 10

The factored geotechnical resistance in axial tension must also be evaluated as the 

back row of piles will be loaded in tension (Table D-13). In this case, the minimum 

required factored geotechnical resistance in axial tension is established using the 

Strength I limit state and is determined following the procedure outlined in Section 

7.2.3.2. The analysis presented in this appendix slightly differs from the procedure 

outlined in Chapter 7 in that only a single row of piles is providing the tension 

resistance rather than the entire pile group. Two analyses are performed; one that 

considers the factored shaft resistances from individual piles, and one that considers 

the weight of a soil block acting with the piles. The lesser tension resistance 

determined from either method controls the design.

As noted in Table D-13, the Strength I limit state tension load on the back row of 

piles for the Group Configuration 1 is 406 kips. Therefore, the minimum factored 

geotechnical resistance in axial tension required from an individual pile is this 

factored load divided by the 9 piles in the rear row or 46 kips. In a similar manner, 

the minimum factored geotechnical resistance required from an individual pile in 

axial tension is 37 kips for Group Configuration 2, and 33 kips for Group 

Configuration 3.

As noted earlier, dynamic testing with signal matching will be used as the resistance 

determination method in the field. Therefore, the AASHTO resistance factor, φφup, is 

0.50 (Table 7-2 of Chapter 7). Figure D-18 provides plots of the factored 

geotechnical resistance in axial tension versus depth for all of the candidate pile 

types based on this resistance determination method. For each candidate section, 

this figure should be entered on the x-axis at the required factored axial tension 

resistance to determine the corresponding pile penetration depth. 

Following this procedure, the estimated pile penetration depth to achieve the 

factored geotechnical resistance in axial tension for each candidate pile section and 

group configuration is summarized in Table D-16.

51
Table D-16 Estimated Minimum Pile Penetration Depth for Maximum Factored 

Geotechnical Resistance in Axial Tension at the Strength I Limit State

Group 

Configuration

Required

Factored

Resistance

in Axial 

Tension 

(kips)

HP 

10x42

(feet)

HP 

12x53 

(feet)

HP 

12x74

(feet)

HP 

14x89

(feet)

HP 

14x117

(feet)

1 46 36 31 28 24 23

2 37 31 27 25 23 20

3 33 29 25 23 20 19

Next, the tension resistance of the pile row when considered as a soil block is 

calculated. For Group Configuration 1, the required factored tension resistance of 

the back row remains 406 kips (Table D-13) and the resistance is derived from the 

weight of soil as a block. The weight of soil needed in the block, WBB BB, to resist the 

tension load is determined with Equation 7-39 where WBB BB is substituted for RRuu .

RRrr = φφRRnn = φφuu RRuu Eq. [7-39]

Where:

RRrr = factored uplift resistance (kips).

φφug = resistance factor for group uplift per Table 7-1, 0.50.

RRuu = nominal uplift resistance of the pile group (kips).

and

RRuu = WBB BB

Solving for the minimum WBB BB:

WBB BB = rr

φφuuuu

Eq. [7-39 modified]

WBB BB = (406 )

(0.50)

WBB BB = 812 kkkk

The length of the pile group will change depending upon the group configuration. 

For Group Configurations 1 and 2, the pile group length is 41 feet from exterior pile 

52
edge to exterior pile edge assuming a 12 inch pile width/diameter. For Group 

Configuration 3, the pile group length is 37 feet using the same pile dimension. The 

effect of a smaller pile size on the pile group length is negligible (e.g. for HP 10x42 

section, the pile group length is 40.83 feet).

The soil profile consists of three layers each with different total and effective unit 

weights. Therefore, the weight contribution from each soil layer was used to 

calculate the soil block weight at a given pile toe elevation. The following calculation

is performed for Group Configuration 1 and 2 with a pile group length of 41 feet and 

an embedded pile length of 27 feet. Table D-17 presents a summary of the effective 

soil unit weight and geometry for each layer comprising the soil block. Figure D-26

provides a visual representation of the soil volume used to determine the soil block 

weight.

Table D-17 Geometry of Soil Block Layers for Nominal Group Tension Resistance 

Computation with Pile Toe at 27 Feet

Soil 

Block 

Layer

γ' 

(pcf)

Layer 

Thickness 

(feet)

Depth to 

Bottom 

(feet)

Zbottom

(feet)

Ztop

(feet)

Bbottom

(feet)

Btop

(feet)

1 105.0 10.0 10.0 49.5 54.5 9.5 14.5

2 42.6 10.0 20.0 44.5 49.5 4.5 49.5

3 49.6 20.0 27.0 41.0 44.5 1.0 4.5

Figure D-26 Nominal tension resistance of pile group based on soil block weight.

53
To determine the volume of soil for each layer, the geometry presented in Table 

D-17 was used to calculate the volume of each layer’s inverted obelisk using 

Equation D-1. The volume of each block layer was then multiplied by the respective 

soil unit weight to determine the soil block weight. All three block layers were then 

summed to calculate the total weight of the block. An example calculation is shown 

for Layer 1 of the soil block. Completed calculations are summarized in Table D-18.

Determine the volume of soil in Block Layer 1

V = h

6 �ZZbb BBtt + ZZtt BBbb + 2 ∗ �ZZtt BBtt + ZZbb BBbb �� Eq. D-1

V = (10 ff )

6 �(49.5 ff ) ∗ (14.5 ff ) + (54.5 ff ) ∗ (9.5 ff ) + 2

∗ �(54.5 ff ) ∗ (14.5 ff ) + (49.5 ff ) ∗ (9.5 ff )��

VBB BB LL 1 = 6260.8 ff 3

Calculate the effective soil weight in Block Layer 1

WBB BB LL 1 = VBB BB LL 1 ∗ γ′

WBB BB LL 1 = (6260.8 ff 3) ∗ (105 pp ) ( 1

1000 )

WBB BB LL 1 = 657.4 kkkk

Table D-18 Calculation of Soil Volume and Soil Block Weight for Nominal Group 

Tension Resistance

Block 

Layer

Depth to 

Bottom

(feet)

Volume of 

Soil 

(ft3)

γ' 

(pcf)

Weight of 

Soil 

(lbs)

Weight of 

Soil 

(kips)

1 10 6,260.8 105.0 657,387.5 657.4

2 20 3,310.8 42.6 141,041.5 141.0

3 27 830.1 49.6 41,172.1 41.2

839.6

The required soil block weight of 812 kips is achieved at approximately 27 feet of 

pile penetration. Hence any pile penetration depth of 27 feet or greater would satisfy 

the required nominal group tension resistance. For Group Configuration 3 with a pile 

group length of 37 feet, the minimum pile penetration depth to achieve a soil block 

weight in excess of the required nominal tension resistance of 812 kips is 28 feet.

54
The required minimum pile penetration depth to satisfy the nominal geotechnical 

resistance in axial tension is the greater depth of the above calculated individual or 

group resistances.

The minimum pile penetration depth necessary for the HP 12x74 section in Group 

Configuration 1 is determined as follows:

DDii ii ii = minimum penetration depth based on sum of individual pile 

resistance, 28 feet (Table D-16).

DDbb = minimum penetration depth based on weight of soil block, 27 

feet.

Therefore, the minimum pile penetration depth needed to satisfy the nominal 

geotechnical resistance in axial tension, DDmm −tt , is 28 feet.

In a similar manner, this check was performed for all candidate pile sections and all 

group configurations. The resulting minimum pile penetration depth necessary to 

achieve the nominal geotechnical resistance requirements for each candidate pile 

section within the specified group configuration is summarized in Table D-19. 

Table D-19 Established Minimum Required Pile Penetration Depth for Factored

Geotechnical Resistance in Axial Tension at North Abutment

Group 

Configuration

HP 10x42

(feet)

HP 12x53 

(feet)

HP 12x74

(feet)

HP 14x89

(feet)

HP 14x117

(feet)

1 36 31 28 27* 27*

2 31 27* 27* 27* 27*

3 29 28* 28* 28* 28*

* Indicates axial tension resistance governed by soil block weight.

55
D.14Block 14: North Abutment – Establish Minimum Pile Penetration Depth for 

Lateral Loads. Determine p-y Models, Required Geomaterial Parameters, 

and Perform Lateral Load Analysis; If Conditions Warrant, Modify Design 

and Return to Block 10

Next, lateral analyses are performed to establish the required minimum pile 

penetration depth for lateral loading and to evaluate pile deflection and structural 

resistance for the applied limit state loads. A minimum required pile penetration 

depth was established to satisfy the nominal geotechnical resistance requirements in 

axial tension in Block 13. A deeper minimum required pile penetration depth for 

lateral loading can result based on the combination of factored lateral loads and

structural resistances, or deflection limits. Excessive deflections and moments 

develop at relatively short pile lengths, where a depth to fixity is not achieved. 

Furthermore, the structural resistance of pile sections must be evaluated based 

upon the axial, lateral and moment loads. Factored structural resistances were

presented in Table D-3. A lateral deformation limit of 1 inch was established as a 

global performance requirement in Block 1 and confirmed In Block 4 as the design 

progressed.

The soil profile at the North Abutment was presented in Figure D-7. For lateral load 

analyses, appropriate p-y models must be selected for each soil layer. The input 

parameters necessary for lateral load analysis using the LPILE computer program

are included in the North Abutment soil profile in Figure D-7.

As discussed in Section 7.3.7.6, p-multipliers are applied to the p-y curves to model 

pile group behavior. The p-multipliers depend on the center to center pile spacing 

within the pile group. For all group configurations at the North Abutment, the pile 

spacing in the longitudinal direction is 4 feet. Therefore, per Section 7.3.7.6 and 

AASHTO (2014) design specifications, interpolation was used to determine 

p-multipliers for a pile spacing of 4b. In this case, the front row p-multiplier is 0.90, 

while the second row is 0.625.

Cyclic loading was analyzed for both rows using LPILE’s Load Type 2 option, which 

uses Shear and Slope to model a fixed head condition. Using the limit state loads at 

this abutment, lateral analyses in the longitudinal (y-direction) were performed about 

the pile section’s strong axis. Figure D-24 shows the pile orientation within the trial 

pile cap design.

The following calculation is presented for the HP 12x74 H-pile section using a range 

of factored axial and lateral loads and the Group Configuration 1. Tables D-20 and 

D-21 provide LPILE output summaries at the pile head for both rows considering a 

56
pile penetration depth for lateral loading of 45 feet. The pile head is assumed to 

terminate at the ground surface (i.e., no stickup).

Table D-20 LPILE Summary Output at Pile Head for Front Row, pm=0.90

Load 

Case

Load 

Type 

No.

Pile-Head 

Condition 1 

V (kips)

Pile-Head 

Condition 2 

S (rad)

Axial 

Load

(kips)

Pile-Head 

Deflection

(inches)

Maximum 

Moment in 

Pile 

(kip-ft)

Maximum 

Shear in 

Pile

(kips)

Pile-Head 

Rotation

(radians)

1 2 0 0 323 0.000 0.0 0 0

2 2 20 0 323 0.249 -95.5 20 0

3 2 30 0 323 0.396 -148.4 30 0

4 2 40 0 323 0.553 -203.1 40 0

5 2 45 0 323 0.640 -232.2 45 0

6 2 47 0 323 0.677 -244.3 47 0

7 2 50 0 323 0.736 -262.7 50 0

8 2 55 0 323 0.841 -294.5 55 0

9 2 60 0 323 0.953 -327.3 60 0

Table D-21 LPILE Summary Output at Pile Head for Second Row, pm=0.625

Load 

Case

Load 

Type 

No.

Pile-Head 

Condition 1 

V (kips)

Pile-Head 

Condition 2 

S (rad)

Axial 

Load

(kips)

Pile-Head 

Deflection

(inches)

Maximum 

Moment in 

Pile 

(kip-ft)

Maximum 

Shear in 

Pile

(kips)

Pile-Head 

Rotation

(radians)

1 2 0 0 323 0.000 0.0 0 0

2 2 20 0 323 0.320 -104.7 20 0

3 2 30 0 323 0.508 -162.3 30 0

4 2 40 0 323 0.727 -225.1 40 0

5 2 45 0 323 0.857 -259.3 45 0

6 2 47 0 323 0.910 -273.2 47 0

7 2 50 0 323 0.998 -294.7 50 0

8 2 55 0 323 1.151 -331.4 55 0

9 2 60 0 323 1.315 -369.3 60 0

The pile group deflection can be estimated from the above LPILE’s deflection results 

for the front and second rows. The factored load versus pile head deflection for 

each row is plotted in Figure D-27 along with the group average. The average 

lateral load per pile for a given group deflection is shown. A step by step discussion 

of this procedure is provided in Section 7.3.7.6. 

The rigid cap method assumes piles move together, and therefore experience the 

same shear and lateral load. Accordingly, at the resulting factored lateral load per 

pile, Vy, of 47 kips (Table D-14), the estimated lateral group deflection at the pile 

head is determined as 0.80 inches. This lateral deflection is less than the 1 inch 

tolerance based upon project design requirements.

57
Figure D-27 Factored load versus deflection in longitudinal direction for HP 12x74 

at North Abutment.

In addition to the lateral deflection limit, stresses from the resulting bending moment 

and shear must be evaluated to check that the pile section does not fail structurally. 

Using the LPILE tabular results, Figure D-28 plots the front row bending moment 

versus depth for the front row deflection of 0.8 inches.

Figure D-29 plots the maximum bending moment versus pile head deflection for both 

the front and back rows, however only the maximum bending moment for the front 

row is used as a “worst case” evaluation of the structural resistance in combined 

axial compression and flexure. As illustrated in Figure D-29, at the estimated pile 

head deflection of 0.80 inches, the maximum bending moment, Muy, is 280 kip-ft. 

58
Figure D-28 Front row bending moment versus depth in longitudinal direction.

Figure D-29 Bending moment versus deflection in longitudinal direction for HP 

12x74 at North Abutment.

59
Equation 8-58 must be satisfied for the factored axial compression load and moment 

in the pile. Using results of the lateral analysis, the factored structural resistance 

was evaluated at the pile head using the factored axial compression load and 

maximum bending moment (determined using factored loads). The factored 

structural resistances were determined and are summarized in Table D-3.

Equation 8-58 must be satisfied for the pile section to be acceptable.

PPuu = factored axial load, 323 kips (TableD-14).

PPrr = factored axial resistance, 762 kips (Table D-3).

Muu = factored moment about x-axis, 0 kip-ft (Block 11).

Mrrrr = factored flexural resistance about x-axis, 118 kip-ft (Table D-3).

Muu = factored moment about y-axis, 280 kip-ft (Figure D-29).

Mrr = factored flexural resistance about y-axis, 433 kip-ft (Table D-3).

Puu

Prr

+ 8.0

9.0 � Muuuu

Mrr

+

Muuuu

Mrr

� ≤ 1.0 [Eq. 8-58]

323 kips

762 kips + 8.09.0 � 0118

+ 280

433� ≤ 1.0

0.998 ≤ 1.0

The maximum shear from factored lateral loading was then compared to the factored 

shear resistance from Table D-3. Based on the factored loads, the factored shear 

resistance is acceptable.

VVrr = factored shear resistance, 214 kips (HP 12x74, Table D-3).

VVuu = factored shear load, 47 kips.

VVuu < VVrr

47 kkkk < 214 kkkk

The lateral analysis was also performed for each candidate pile section and the 

deflection and factored structural resistance was subsequently evaluated 

considering the factored loads for the group configurations shown in Table D-14. 

Pile head deflection must be limited to 1 inch, and based upon the applied loads and 

pile section, the factored structural resistance of the pile must also satisfy the 

60
structural resistance interaction equation presented as Equation 8-58. Pile sections 

satisfying both criteria were deemed acceptable. Furthermore, as presented in 

Table D-22, a minimum pile penetration depth was established based on the lateral 

load analyses. The minimum penetration depth is identified as “- - -“ for candidate 

pile sections not meeting the lateral deformation or structural resistance 

requirements.

Several of the larger pile sections provided sufficient stiffness to resist the applied 

loads, while smaller, less stiff sections did not (they failed the structural resistance 

check in Equation 8-58). Factored axial compression loads, in combination with

moments caused by factored lateral loads, resulted in some sections’ factored 

structural resistance being exceeded. As a direct result of this analysis, the 

HP10x42 pile section is unsuitable and eliminated as a candidate pile section for 

final design. However for the remainder of this example problem, this pile section 

will still be carried forward for illustrative purposes. Likewise, the HP 12x53 pile 

section is unsuitable and eliminated as a candidate pile section for Group 

Configurations 1 and 2.

Table D-22 Established Minimum Pile Penetration Depth Required for Lateral 

Loading at the North Abutment 

Group 

Configuration

HP 10x42

(feet)

HP 12x53 

(feet)

HP 12x74

(feet)

HP 14x89

(feet)

HP 14x117

(feet)

1 - - - - - - 25 10 10

2 - - - - - - 10 10 10

3 - - - 20 10 10 10

61
D.15Block 15: North Abutment – Establish Pile Penetration Depths that Satisfy 

Tolerable Deformations; Estimate Group Settlement over the Minimum 

and Maximum Range of Pile Penetration Depths From Blocks 12 through

14 and Identify All Pile Toe Elevations Which Result in Intolerable 

Deformations; If Conditions Warrant, Modify Design and Return to Block 

10

For the cohesionless soils at the North Abutment, pile group settlement was 

estimated using two methods, the Meyerhof (1976) Method and the Janbu tangent 

modulus method. Ideally, the settlement method chosen by the designer is one that 

has shown good correlation with observed results. The pile group settlement at the 

North Abutment was first calculated using the Meyerhof method. The Meyerhof 

approach is a traditional settlement estimation method for pile groups in 

cohesionless soils and one that is contained in the AASHTO (2014) design 

specifications. However, the soil conditions across the bridge substructure locations 

are quite variable and a settlement method that could be used at all substructure 

locations was also desired. Therefore, group settlement was also computed with the 

Janbu tangent modulus approach using an equivalent footing placed at the neutral 

plane.

The Meyerhof (1976) approach as presented in Section 7.3.5.2.1 was used to 

estimate group settlement. The settlement calculations were performed using only 

unfactored permanent loads. Therefore the loads from the Service I limit state

without live load were used to estimate settlement (load factor of 1.0 on permanent 

loads). The average contact stress for the trial pile group was calculated using the 

vertical load, Q, and pile group area Z x B. The length of the pile group in Group 

Configurations 1 and 2 is 41 feet. Therefore, the following calculation is only 

suitable for these two group configurations. Both the group length, Z, and width, B, 

were calculated from exterior pile edge to exterior pile edge.

Calculate the average contact stress, pf, from the trial pile group.

BB = pile group width in longitudinal direction, 5 feet.

ZZ = pile group length in transverse direction, 41 feet.

QQ = unfactored permanent load, 1540 kips.

ppff = QQ

BB∗ZZ

ppff = 1540

(5 ff )∗(41 ff ) = 7.512 kk

62
ppff = 7.512 kk

The group embedment influence factor, IIff, is determined based upon the pile group 

width and estimated pile depth using Equation 7-52.

DDBB = pile embedded length into bearing stratum. In this calculation, 5 

feet into dense gravel with sand (embedded length D = 50 feet).

DD′ = effective depth, 2/3* DDBB= 3.33 feet.

IIff = 1 − DD′

8BB ≥ 0.5 [Eq. 7-52]

IIff = 1 − 3.33 ff

8∗(5 ff ) ≥ 0.5

IIff = 0.92 ≥ 0.5

IIff = 0.92

The total settlement is conservatively estimated using Equation 7-50.

NN1(60) = average corrected SPT N value within a depth B below pile toe, 

59 bpf.

SS = 4 ppff IIff√BB

NN1(60)

[Eq. 7-50]

SS = 4∗(7.512 )∗(0.92)∗�5 ff

(59 bb )

SS = 1.04 hee

The above analysis was performed for additional pile penetration depths and for the 

pile group dimensions of all three group configurations. Table D-23 summarizes the 

analysis results for the Meyerhof (1976) estimated group settlement. The estimated 

group settlement depends upon the NN1(60) value of the soil into which the pile group 

is embedded. In particular, at the contact of the medium dense sand and dense 

gravel with sand layers, this effect is magnified. This is a limitation of the Meyerhof 

settlement method, in which soil layers below a depth of B, the pile group width,

63
below the pile toe are effectively disregarded. The Engineer should consider this 

when assessing the minimum pile penetration depth for settlement considerations. 

Table D-23 Estimated Pile Group Settlement Using Meyerhof (1976) Method For 

All Pile Group Configurations.

Pile Toe 

Elevation

(feet)

Pile 

Penetration 

Depth

(feet)

DB

(feet)

NN1(60) for 

Bearing 

Stratum

(bpf)

Estimated 

Settlement

Group 

Configuration

1 & 2

(inches)

Estimated 

Settlement

Group 

Configuration

3

(inches)

270.0 40.0 20.0 17 2.63 2.92

267.5 42.5 22.5 38 1.11 1.22

264.5 45.5 0.5 59 1.13 1.25

260.0 50.0 5.0 59 1.04 1.16

255.0 55.0 10.0 59 0.95 1.05

Note: DDBB = embedded pile length into bearing stratum.

The Meyerhof (1976) approach does not include or consider the increase in vertical 

effective stress from embankment loading. Depending on the embankment 

construction and pile installation timeline, consideration of the stress increase from 

embankment construction on pile group settlement estimates may or may not be 

appropriate. Embankment loading effects were included in the second settlement 

computation method performed using the neutral plane method and Janbu tangent 

modulus. For simplification, the vertical effective stress increase is determined by 

treating the embankment surcharge as a strip load. Figure D-30 demonstrates this 

concept and defines symbols, while the change in vertical effective stress with depth 

is determined using Equations D-2 through D-4.

∆σσvv = qq

Π [β + sin(β) ∗ cos(β + 2δ)] Eq. D-2

Where:

β = −1 � +bb

zz � − −1( −bbzz ) Eq. D-3

and

δ = −1( −bb

zz ) Eq. D-4

64
Figure D-30 Vertical effective stress increase due to strip load.

The 10 foot high embankment, with a soil unit weight 120 pcf, results in a surcharge 

stress at the embankment base of 1.2 ksf, and is assumed to extend 100 feet behind 

the abutment. Fill directly above the footing is already included in design as a 

permanent vertical load, EV, and therefore the embankment surcharge is assumed 

to act as a strip load beginning at the footing edge. The change in vertical effective 

stress from the embankment surcharge, Δσ’v(e), is determined under the footing 

centerline as depicted in Figure D-31. 

Figure D-31 Vertical effective stress increase due to embankment surcharge.

65
An example calculation is shown for a depth below footing, z, of 2.5 feet. Complete 

calculations were performed using a spreadsheet and are summarized in Table 

D-24. The bottom of the North Abutment footing is at Elevation 310 feet and 

therefore although the value of z in the following series of analyses may vary based 

upon the equivalent footing or neutral plane location. Elevation is used to provide a 

better comparison of effective stress change with depth.

Determine geometry of profile.

x = 3.25 ff + 100 ff

2 = 53.25 ff

b = 100 ff

2 = 50 ff

Determine angle β.

β = −1 � +bb

zz � − −1( −bbzz ) [Eq. D-3]

β = −1 �

53.25 ff +50 ff

2.1 ff � − −1 �

53.25 ff −50 ff

2.1 ff �

β = 0.63

Determine angle δ.

δ = −1( −bb

zz ) [Eq. D-4]

δ = −1 �

53.25 ff −50 ff

2.5 ff �

δ = 0.92

Calculate the change in vertical effective stress due to embankment surcharge.

qq = stress per unit length, 1.2 ksf.

∆σσ′vv( ) = qq

Π [β + sin(β) ∗ cos(β + 2δ)] [Eq. D-2]

∆σσ′vv( ) = 1.2

Π [0.63 + sin(0.63) ∗ cos(0.63 + 2 ∗ (0.92))]

∆σσ′vv( ) = 0.07 kk

66
Table D-24 Vertical Effective Stress Increase from Embankment Surcharge

Elevation

(feet)

Soil 

Layer

z

(feet) δ β Δσ’v(e)(ksf)

309.99 1 0.01 1.57 0.00 0.00

307.5 1 2.5 0.92 0.63 0.07

302.5 1 7.5 0.41 1.09 0.30

297.5 1 12.5 0.25 1.20 0.41

292.5 1 17.5 0.18 1.22 0.46

287.5 2 22.5 0.14 1.21 0.49

282.5 2 27.5 0.12 1.19 0.51

277.5 2 32.5 0.10 1.17 0.52

272.5 2 37.5 0.09 1.14 0.52

267.5 2 42.5 0.08 1.10 0.53

262.5 3 47.5 0.07 1.07 0.53

257.5 3 52.5 0.06 1.04 0.53

252.5 3 57.5 0.06 1.01 0.53

247.5 3 62.5 0.05 0.97 0.52

242.5 3 67.5 0.05 0.94 0.52

237.5 3 72.5 0.04 0.91 0.51

232.5 3 77.5 0.04 0.88 0.51

227.5 3 82.5 0.04 0.86 0.50

222.5 3 87.5 0.04 0.83 0.49

219.0 3 91.0 0.04 0.81 0.49

Note, the designer should determine if the construction schedule can accommodate 

the required time for embankment induced settlements to occur before the start of 

pile driving and superstructure construction. This example calculation assumes 

construction cannot be delayed, and therefore, the stress increase from 

embankment construction and foundations loads are applied concurrently.

Pile group settlement was calculated using the neutral plane method and Janbu 

tangent modulus as discussed in Section 7.3.5.6. An equivalent footing, with plan 

dimensions equal to those of the pile group, was evaluated at increasing pile 

penetration depths, and the resulting pile group settlement computed using the 

Janbu tangent modulus. This procedure allowed the shallowest depth of an 

equivalent footing to be determined that met vertical deformation requirements. The 

required minimum pile penetration depth was then determined by the pile toe 

elevation that would place the neutral plane at this same equivalent footing depth

where vertical deformation requirements were satisfied.

67
The following example calculation is performed for an equivalent footing located at 

Elevation 270 feet corresponding to a pile penetration depth of 60 feet. The length 

of the pile group in Group Configurations 1 and 2 is 41 feet from exterior pile edge to 

exterior pile edge. Since Group Configuration 3 has different pile group plan 

dimensions, this example is suitable for only Configurations 1 and 2. Similar to the 

vertical effective stress increase calculations from embankment loading, the soil 

profile was again divided into 5 foot thick layers. The elevation shown in Table D-25

references the midpoint of each respective 5 foot thick soil layer, while z is the depth 

below the equivalent footing to the midpoint of each respective 5-foot-thick soil layer. 

Tabulated values for this analysis are recorded in Table D-25.

Considering only the unfactored permanent load acting on the superstructure, Q, 

calculate the change in vertical effective stress below the equivalent footing, ΔΔσσ′vv(ss), 

at Elev. 267.5 feet.

Q = unfactored permanent load, 1540 kips (Service I, no LL, Table D-11).

B = pile group width, 5 feet.

Z = pile group length, 41 feet (Group Configurations 1 and 2 only).

z = depth below equivalent footing, 2.5 feet (Elev.267.5 feet).

ΔΔσσ′vv(ss) = QQ

(BB+zz)∗(ZZ+zz) [Eq. 7-55]

ΔΔσσ′vv(ss) = (1540 )

((5 ff )+(2.5 ff ))∗((41ff )+(2.5 ff ))

ΔΔσσ′vv(ss) = 4.72 kk

Including the change in effective stress from the embankment and superstructure, 

calculate the new effective stress below the equivalent footing at Elev. 267.5 feet.

σσ′vvo = initial vertical effective stress at depth z below the equivalent 

footing, 3.15 ksf.

∆σσ′vv( ) = change in effective stress at depth z below the equivalent 

footing from embankment loading, 0.53 ksf (Table D-24).

ΔΔσσ′vv(ss) = change in effective stress at depth z below the equivalent 

footing from superstructure loading, 4.72 ksf.

σσ′1( +ssss) = σσ′vv + ΔΔσσ′vv(ss) + ∆σσ′vv( )

68
σσ′1( +ssss) = (3.15 kk ) + (0.53 kk ) + (4.72 kk )

σσ′1( +ssss) = 8.40 kk f

Determine the stress increase by comparing σσ′vo and σσ′1(ss+e).

SS SS II = σσ′

1(ss+e) − σσ′

vo

σσ′vo

∗ 100% Eq. D-5

SS SS II = (8.40 )−(3.15 )

(3.15 ) ∗ 100%

SS SS II = 167%

The stress increase is greater than or equal to 10%. Deformation for this depth 

increment should be estimated and included in the sum of all depth increments in 

which the stress increase is not less than 10%. A rock layer, which is considered 

incompressible, is located at Elev. 218 feet at this abutment, and thus it is assumed 

that no settlement or compression occurs below this depth.

For the dense coarse grained soil at Elev. 267.5 feet, z = 2.5 (stress exponent of 

j = 1.0), determine the strain in the layer from the increase in vertical effective stress, 

ΔΔ , with Equation 7-61.

EEss = elastic modulus of soil, 1416 ksf (Figure D-7).

σσ′vo = initial vertical effective stress at depth z below the equivalent 

footing, 3.15 ksf.

σσ′1(ss+e) = new vertical effective stress below the equivalent footing, 8.40 

ksf.

ΔΔ = 1

EEss

�σσ′1(ss+e) − σσ′vv � [Eq. 7-61]

ΔΔ = 1

(1416 kk )

[(8.40 kk ) − (3.15 kk )]

ΔΔ = 0.0037

69
Calculate the layer compression denoted, S, with the initial height of the layer, HHoo.

SS = ΔΔ ∗ HHoo

SS = 0.0037 ∗ 5 ff ∗ �

12 hee

1 ffffff �

SS = 0.22 hee

Table D-25 Calculation of Settlement by Janbu Tangent Modulus for Equivalent 

Footing at Elevation 270 feet

Elev. 

(feet)

z 

(feet)

Ho

(feet)

Es

(ksf)

σ'vo 

(ksf)

B

(feet)

Z

(feet)

Δσ'v(ss)

(ksf)

Δσ’v(e)

(ksf)

σ'1(ss+e)

(ksf)

Stress 

Increase

(%)

Δε S

(in)

267.5 2.5 5 1416 3.15 7.5 43.5 4.72 0.53 8.40 167 0.0037 0.22

262.5 7.5 5 1416 3.46 12.5 48.5 2.54 0.53 6.52 89 0.0022 0.13

257.5 12.5 5 1416 3.77 17.5 53.5 1.64 0.53 5.94 58 0.0015 0.09

252.5 17.5 5 1416 4.08 22.5 58.5 1.17 0.53 5.78 42 0.0012 0.07

247.5 22.5 5 1416 4.40 27.5 63.5 0.88 0.52 5.80 32 0.0010 0.06

242.5 27.5 5 1416 4.71 32.5 68.5 0.69 0.52 5.92 26 0.0009 0.05

237.5 32.5 5 1416 5.02 37.5 73.5 0.56 0.51 6.09 21 0.0008 0.05

232.5 37.5 5 1416 5.33 42.5 78.5 0.46 0.51 6.30 18 0.0007 0.04

227.5 42.5 5 1416 5.65 47.5 83.5 0.39 0.50 6.53 16 0.0006 0.04

222.5 47.5 5 1416 5.96 52.5 88.5 0.33 0.49 6.78 14 0.0006 0.03

219.0 51.0 2 1416 6.27 56.0 92.0 0.30 0.49 7.06 13 0.0006 0.01

Total: 0.80

In a similar manner, the above analysis was performed for additional equivalent 

footing locations for all three trial group configurations. Table D-26 summarizes the 

results for the neutral plane method and Janbu tangent modulus estimated 

settlement. As established by global project performance requirements, vertical 

deformation (including settlement and elastic pile compression) should be limited to 

1.5 inches at each substructure location. Therefore, Table D-26 indicates that this 

requires that the equivalent footing be located at Elevation 270 feet, a minimum of 

40 feet below the bottom of pile cap (Elev. 310).

It is assumed that the equivalent footing acts at the same location as the neutral 

plane. Accordingly, an analysis was performed to determine the pile toe elevation 

70
necessary to locate the neutral plane at Elev. 270.0, thereby establishing the 

minimum required pile penetration depth to satisfy tolerable deformations.

Table D-26 Estimated Pile Group Settlement Using Janbu Tangent Modulus with 

Neutral Plane Method For All Pile Group Configurations.

Equivalent 

Footing 

Elevation

(feet)

Equivalent 

Footing

Depth

(feet)

Estimated 

Settlement

Group 

Configurations 

1 and 2

(inches)

Estimated 

Settlement

Group 

Configuration

3

(inches)

285.0 25 2.30 2.46

280.0 30 1.98 2.12

275.0 35 1.54 1.65

270.0 40 0.80 0.85

265.0 45 0.76 0.81

The location of the neutral plane and the magnitude of drag force are evaluated 

following the procedure outlined in Section 7.3.6, using unfactored permanent loads 

and nominal geotechnical resistance. Because load factors for the Service limit 

state are 1.0, applicable loads at this limit state may be considered unfactored. The

Service I, without LL limit state loads are therefore used for evaluation for the neutral 

plane. This example again utilizes the load for Group Configuration 1 (Q= 201 kips, 

Table D-14. Figure D-32 presents a graphical interpretation of the neutral plane for 

the HP12x74 pile driven to a penetration depth of 60 feet.

First, the sustained load plus the cumulative shaft resistance versus depth is plotted. 

Next, the mobilized toe resistance minus the cumulative shaft resistance versus pile 

penetration depth is plotted. The exact percentage of toe mobilization is unknown at 

this stage of design, therefore multiple toe mobilization curves should be evaluated 

to determine the neutral plane location. The 0% toe mobilization curve is the most 

conservative location to evaluate pile settlement since it locates the neutral plane at 

the highest elevation. The 100% toe mobilization curve should be used to check the 

pile section’s structural strength since it results in the greatest axial force in the pile. 

The structural strength check is performed in Block 17.

At the North Abutment, it is expected that piles will be supported partially by toe 

resistance. Therefore the 0% toe mobilization curve presents an unreasonable 

baseline to evaluate settlement in this case. With some toe resistance likely 

mobilized, the 50 percent toe mobilization curve is used to evaluate settlement.

71
Figure D-32 Neutral plane at 50% toe mobilization for HP 12x74 

at the North Abutment.

This analysis procedure was also performed for the remaining candidate pile 

sections and trial group configurations to determine the pile penetration depth 

required for the neutral plane to be located below a depth of 40 feet (Elev. 270.0 

feet). Table D-27 summarizes the analysis results. The load per pile for each group 

configuration was previously presented in Table D-14.

Table D-27 Pile Penetration Depth Required to Locate Neutral Plane 

at Elev. 270.0 feet

Group 

Configuration

Load per 

Pile

Q

(kips)

HP 

10x42

(feet)

HP 

12x53 

(feet)

HP 

12x74

(feet)

HP 

14x89

(feet)

HP 

14x117

(feet)

1 201 69 60 60 54 53

2 165 64 55 55 50 50

3 139 60 52 52 48 48

72
A comparison of the required pile penetration depth for both settlement estimation 

methods yielded dissimilar results. To limit total settlement and elastic compression 

to less than 1.5 inches, the Meyerhof Method requires a pile penetration depth of 

42.5 feet (Elev. 267.5 feet) for a HP 12x74 in Group Configuration 1. The Janbu 

tangent modulus approach requires a 17 foot deeper pile to satisfy the same 

settlement constraints with the same pile and group configuration. Table D-23

presents the minimum pile penetration depth based on group settlement estimation 

using the Meyerhof (1976) approach. Table D-27 presents the minimum pile 

penetration depth based on group settlement estimation using the Janbu Tangent 

modulus Method with the equivalent footing located at the neutral plane. Based on 

placing the neutral plane at or below EL 270, all candidate pile sections and group 

configurations require the piles to be driven into Soil Layer 3 (dense gravel with 

sand). After considering both settlement estimates, the results of the neutral plane 

and Janbu tangent modulus method were used to establish the minimum pile 

penetration depth for tolerable deformations.

A review of the soil profile at the North Abutment in Figure D-7 indicates no 

compressible soil layers below Soil Layer 3. Therefore, no effort is necessary to 

identify a maximum pile penetration depth to prevent punching through a dense 

layer into an unsuitable soil layer, or to causing a stress increase on a lower 

compressible layer causing excessive settlement. Table D-28 presents the 

established minimum pile penetration depths to satisfy tolerable deformations at the 

North Abutment using the Janbu tangent modulus approach.

Table D-28 Established Minimum Pile Penetration Depths to Satisfy Tolerable

Deformations at the North Abutment

Group 

Configuration

HP 10x42

(feet)

HP 12x53 

(feet)

HP 12x74

(feet)

HP 14x89

(feet)

HP 14x117

(feet)

1 69 60 60 54 53

2 64 55 55 50 50

3 60 52 52 48 48

Elastic shortening of the pile should be considered along with settlement. For elastic 

compression, the load per pile from the Service I, without LL limit state is applied at 

the pile head. As shown in Table D-14, this load is 201 kips.

Note that the drag force from negative shaft resistance increases the axial 

compression force in the pile. Negative shaft resistance above the neutral plane 

acts to increase axial compression force in the pile, whereas below the neutral 

73
plane, positive shaft resistance reduces the axial compression force in the pile. This 

effect must be accounted for in the elastic compression calculation. Accordingly, the 

unfactored axial load used to compute elastic compression, Q, changes for each pile 

segment length, increasing equal to the unfactored permanent load plus the shaft 

resistance down to the neutral plane. In this example, at and below the neutral 

plane location of 54 feet, the unfactored axial load is equal to the resistance 

distribution from 100% toe mobilization. A review of Figure D-29 indicates that the 

maximum drag force magnitude results from 100% toe mobilization.

Equation 7-48 is used to illustrate this example for the first 12 inch increment of the 

HP 12x74 pile section. The average shaft resistance and average load for each 

respective depth interval is used to estimate the elastic compression. For each 12 

inch segment, the elastic modulus remains constant, and was evaluated as 29,000 

ksi. The pile cross sectional area likewise remains constant as 21.8 in2

. Remaining 

calculations were performed using a spreadsheet; Table D-29 summarizes the 

elastic compression with depth. 

Determine the unfactored axial load in segment.

QQdd = unfactored permanent load, 201 kips.

RRss

− = average (negative) shaft resistance, 0.5 kips.

QQ = QQdd + RRss

− = 201 kkkk + 0.5 kkkk

Q = 201.5 kkkk

Calculate elastic compression of segment with unfactored axial load from combined 

unfactored permanent load and negative shaft resistance.

LL = segment length, 12 inches.

AA = cross sectional area of pile material, 21.8 in2.

EE = elastic modulus of pile, 29,000 ksi.

∆= QQ

AA [Eq. 7-48]

∆= (201.5 )∗(12 ii h )

(21.8 2)∗(29,000 kk kk)

∆= 0.00383 hee

74
Table D-29 Elastic Compression Calculation

Depth 

Below 

Pile Head

(feet)

Average 

Shaft 

Resistance 

(kips)

Average 

Unfactored 

Axial Load 

(kips)

Segment 

Compression, 

∆

(inches)

0 0.0 201.0 0.00000

0-1 0.5 201.5 0.00383

1-2 1.7 202.7 0.00385

2-3 3.0 204.0 0.00387

3-4 4.5 205.5 0.00390

4-5 6.3 207.3 0.00393

5-6 8.2 209.2 0.00397

6-7 10.3 211.3 0.00401

7-8 12.5 213.5 0.00405

8-9 15.0 216.0 0.00410

9-10 17.7 218.7 0.00415

10-11 20.5 221.5 0.00421

11-12 23.5 224.5 0.00426

12-13 26.5 227.5 0.00432

13-14 29.6 230.6 0.00438

14-15 32.8 233.8 0.00444

15-16 36.0 237.0 0.00450

16-17 39.3 240.3 0.00456

17-18 42.7 243.7 0.00463

18-19 46.2 247.2 0.00469

19-20 49.8 250.8 0.00476

20-21 54.0 255.0 0.00484

21-22 59.0 260.0 0.00493

22-23 64.0 265.0 0.00503

23-24 69.2 270.2 0.00513

24-25 74.5 275.5 0.00523

25-26 80.0 281.0 0.00533

26-27 85.5 286.5 0.00544

27-28 91.2 292.2 0.00555

28-29 97.0 298.0 0.00566

29-30 102.9 303.9 0.00577

30-31 108.9 309.9 0.00588

31-32 115.0 316.0 0.00600

32-33 121.3 322.3 0.00612

33-34 127.7 328.7 0.00624

34-35 134.2 335.2 0.00636

35-36 140.8 341.8 0.00649

36-37 147.6 348.6 0.00662

37-38 154.4 355.4 0.00675

38-39 161.4 362.4 0.00688

75
Table D-29 Elastic Compression Calculation (continued)

Depth 

Below 

Pile Head

(feet)

Average 

Shaft 

Resistance 

(kips)

Average 

Unfactored 

Axial Load 

(kips)

Segment 

Compression, 

∆

(inches)

39-40 168.5 369.5 0.00701

40-41 175.8 376.8 0.00715

41-42 183.1 384.1 0.00729

42-43 190.6 391.6 0.00743

43-44 198.2 399.2 0.00758

44-45 205.9 406.9 0.00772

45-46 213.7 414.7 0.00787

46-47 221.7 422.7 0.00802

47-48 229.8 430.8 0.00818

48-49 238.1 439.1 0.00833

49-50 246.5 447.5 0.00849

50-51 255.1 456.1 0.00866

51-52 263.8 464.8 0.00882

52-53 272.7 473.7 0.00899

53-54 281.7 482.7 0.00916

54-55 290.9 482.0 0.00915

55-56 300.2 472.0 0.00896

56-57 309.7 462.5 0.00878

57-58 319.3 452.8 0.00860

58-59 329.1 443.1 0.00841

59-60 339.1 433.1 0.00822

Total 0.37

For the pile head load of 201 kips (Group Configuration 1 loads), estimated elastic 

compression of the HP 12x74 pile section driven to 60 feet is 0.37 inches (pile toe at 

Elev. 250 feet). Combined with 0.80 inches of deformation from settlement (Table 

D-28), it is estimated that total vertical deformation at the North Abutment is 1.17

inches.

D.16Block 16: North Abutment – Check pile drivability to maximum pile 

penetration depth requirements established in Blocks 12 through 15

Preliminary pile drivability analyses were performed for the 5 candidate pile sections 

in Block 10. Plots of nominal driving resistance, blow count, and compression stress 

versus depth were presented in Figure D-22. This figure should now be reviewed 

considering the established or estimated minimum pile penetration depths. A 

candidate pile section must be capable of being driven to the penetration depth 

76
necessary to achieve the nominal geotechnical resistance in axial compression and 

tension, and to a penetration depth necessary to satisfy lateral load demands as well 

as axial and lateral deformation requirements. Estimated or minimum pile 

penetration depths were previously established in Blocks 12, 13, 14, and 15 and 

summarized in Tables D-15, D-19, D-22 and D-28.

Although a minimum pile penetration depth is not typically established for nominal 

geotechnical resistance in axial compression, the pile should also be capable of 

being driven reasonably close to the estimated pile penetration depth where the 

nominal resistance is expected to develop. If the pile cannot be driven to the 

required depth within driving stress limits and at reasonable blow counts, a larger 

pile hammer, a pile section with greater impedance, or pile installation aids such as 

predrilling or jetting may be required to satisfy or improve drivability. Alternatively, 

substructure design modifications should be considered.

For the candidate HP 12x74 H-pile section in the Group Configuration 1, the pile 

penetration depth for axial compression loading was estimated at 45 feet (Table 

D-15), the minimum penetration depth for axial tension loading was 28 feet (Table 

D-19), and the minimum penetration depth for lateral loading was 25 feet (Table 

D-22). The minimum pile penetration depth for group settlement was 60 feet (Table 

D-28) based on embankment and foundation loads occurring simultaneously. 

Accordingly, this candidate pile section must have sufficient drivability to the 

maximum of these depths (i.e., 60 feet). 

A review of Figure D-22 indicates that the HP 12x74 pile section can be driven to 61

feet with a D36-52 hammer before encountering practical refusal. The preliminary 

drivability evaluation (with soil and hammer model assumptions described in Block 

10), estimated that the blow count will not exceed 120 blows per foot or 10 blows per 

inch before this pile penetration depth. Compression driving stresses are estimated 

to remain below driving stress limits. Drivability results for a D46-52 pile hammer 

were also presented in Figure D-22 and indicated greater pile penetration depths 

were possible. Therefore, it is concluded that the HP 12x74 pile section can be 

driven to the 60 foot penetration depth.

D.17Block 17: North Abutment – Determine the Neutral Plane Location and 

Resulting Drag Force; Check Structural Strength Limit State for Pile 

Penetration Depth From Block 16

Previously in Block 15, the neutral plane was evaluated as part of the settlement 

calculations. The neutral plane and resulting drag force are now evaluated to check 

77
the structural strength limit state for candidate pile sections. Section 7.3.6 provides 

guidance for evaluating the neutral plane location and the magnitude of the drag 

force. The Service I, without live load limit state was used for the applied pile head 

load. This example again utilizes the load for Group Configuration 1 (Q = 201 kips,

Table D-14).

At 100 percent toe mobilization, the neutral plane is at its lowest potential location, 

and thus the highest drag force magnitude results. Accordingly, this is the toe 

mobilization curve that should be used to check the pile section’s structural strength. 

Figure D-33 presents a graphical interpretation of the neutral plane for the HP12x74 

pile section driven to the estimated pile penetration depth of 60 feet. In this case the 

neutral plane is located 54 feet below the pile head with a resulting maximum axial 

compression force in the pile of 486 kips.

Figure D-33 Neutral plane at 100% toe mobilization for HP 12x74 

at the North Abutment.

The resulting unfactored drag force, DF, is the difference between the maximum 

unfactored axial compression force in the pile, QQmm , minus the unfactored

permanent load (Q). In this case, the drag force is evaluated for 100 percent toe 

mobilization. 

DD = QQmm − QQ

DD = (486 kkkk ) − (201 kkkk ) = 285 kkkk

78
Following this calculation, the factored structural load was determined using

Equation 7-70. As discussed in Section 7.3.6, a load factor of 1.25 is applied to the 

permanent load while a load factor of 1.1 is applied to the drag force. Because the 

pile is driven into dense gravel with cobbles, the pile toe may be subject to damage 

during driving, and therefore as recommended by the AASHTO (2104) code, a 

structural resistance factor for axial compression φφcc of 0.50 would be applied to the 

nominal structural resistance of 1088 kips (Table D-2). Accordingly, the factored 

structural resistance, Pr, for the HP 12x74 pile section is 544 kips.

1.25 (QQ) + γpp(DD ) < PPrr [Eq. 7-70[

1.25 (201 kkkk ) + 1.1(285 kkkk ) = 565 kkkk

565 kkkk > 544 kkkk

In this case, the factored structural resistance is less than the factored loads, and 

therefore the pile section would be considered unacceptable. This evaluation of the 

structural resistance does not however consider the location of the neutral plane. In 

this case, the neutral plane is 6 feet above the pile toe for 100% toe mobilization, 

and this location on the pile may not be damaged.

The AASHTO (2014) design specifications do not specifically address drag force 

considerations relative to the pile structural resistance. For example, the factored 

structural resistance of an H-pile is the nominal structural resistance multiplied by 

the resistance factor for axial compression, φc. This resistance factor is 0.70 for 

combined axial and flexural resistance of undamaged piles, 0.60 for the axial 

resistance of piles in compression under good driving conditions, and 0.50 for the 

axial resistance of piles in compression subject to damage due to severe driving 

conditions. While not equivocally stated, it follows that if the neutral plane is located 

below the point of fixity and above the depth where H-piles are subject to potential 

damage during driving, then the sum of the sustained load plus drag force at the 

neutral plane is limited to 0.70 of the nominal structural resistance.

Hence for piles at the North Abutment, if the neutral plane is located at a depth 

where the pile section is likely to be straight and undamaged, a structural resistance 

factor for axial compression, φφcc, of 0.70 could be applied to the nominal structural 

resistance, Pn, of 1088 kips (Table D-2). Accordingly, the factored structural 

resistance, Pr, for the HP 12x74 pile section is 762 kips. Equation 7-68 is used to 

evaluate the structural resistance.

79
1.25 (QQ) + γpp(DD ) < PPrr [Eq. 7-70[

1.25 (201 kkkk ) + 1.1(285 kkkk ) = 565 kkkk

565 kkkk < 762 kkkk

In this case, the factored structural resistance is larger than the factored load, and 

therefore the pile section is acceptable.

It may be beneficial to review the ratio of factored load to nominal structural 

resistance or, PPuu / PPnn. The following evaluation serves to back calculate the 

minimum required structural resistance factor, φφcc(min), for the section to be 

acceptable considering the factored load.

φφcc(min) = PPuu

PPnn

φφcc(min) = (565 )

(1088 )

φφcc(min) = 0.52

To further evaluate the drag force on the HP 12x74 pile section, the ratio of factored 

load to nominal structural resistance or, PPuu / PPnn was performed at 1 foot increments 

over the portion of the pile. Table D-30 presents a calculation of unfactored load in 

the pile for 50 percent toe mobilization, the drag force, and the factored load at 1 foot 

increments over the lower 20 feet. The final column shows the ratio of factored load 

to nominal structural resistance, PPuu / PPnn. This comparison provides the Engineer with 

the minimum structural resistance factor required for the pile section to be 

acceptable. For example, at the pile toe (Elev. 248 feet), the pile section would be 

acceptable based on a structural resistance factor for axial compression, φφcc, of 0.50.

80
Table D-30 Calculation of Load in Pile, Factored Load and Comparison to Nominal 

Structural Resistance

Elevation

(feet)

Depth 

on Pile

(feet)

Nominal 

Shaft 

Resistance

(kips)

Q + Σ

Rs

(kips)

Unfactored 

Load in 

Pile

(kips)

Drag 

Force

DF

(kips)

Factored 

Load

PPuu

(kips)

PPuu/ PPnn

φφcc(min)

268.0 40 172 373 373 172 441 0.40

267.0 41 179 380 380 179 449 0.41

266.0 42 187 388 388 187 457 0.42

265.0 43 194 395 395 194 465 0.43

264.0 44 202 403 403 202 473 0.44

263.0 45 210 411 411 210 482 0.44

262.0 46 218 419 419 218 491 0.45

261.0 47 226 427 427 226 499 0.46

260.0 48 234 435 435 234 509 0.47

259.0 49 242 443 443 242 518 0.48

258.0 50 251 452 452 251 527 0.48

257.0 51 259 460 460 259 537 0.49

256.0 52 268 469 469 268 546 0.50

255.0 53 277 478 478 277 556 0.51

254.0 54 286 487 487 286 565 0.52

253.0 55 296 497 477 276 554 0.51

252.0 56 305 506 467 266 544 0.50

251.0 57 314 515 458 257 534 0.49

250.0 58 324 525 448 247 523 0.48

249.0 59 334 535 438 237 512 0.47

248.0 60 344 545 428 227 501 0.46

*Neutral plane located at Depth 54 feet (EL 254.0 feet) for 50 percent toe mobilization.

An analysis of the drag force was performed for each candidate pile section. The 

pile penetration depth utilized for the drag force structural resistance check was the 

required minimum penetration depth presented in Table D-28. Table D-31 presents 

the ratio of the factored load to nominal structural resistance, at the pile toe, for the 

all the candidate piles and group configurations. For H-piles which may be subject 

to damage during driving and require pile toe protection (i.e., as for piles driven to 

bedrock or through dense gravel, cobbles, etc.), the structural resistance factor in 

axial compression, φφcc, is 0.50. Considering 50 percent toe mobilization, only the HP 

12x74 and HP 14x117 pile section are acceptable for all group configurations.

81
Table D-31 Ratio of Factored Load to Nominal Structural Resistance in Axial 

Compression, φφcc(min), at the Pile Toe

Group 

Configuration

HP 10x42

φφcc(min)

HP 12x53

φφcc(min)

HP 12x74

φφcc(min)

HP 14x89

φφcc(min)

HP 14x117

φφcc(min)

1 0.55 0.63 0.46 0.50 0.41

2 0.54 0.63 0.46 0.43 0.35

3 0.54 0.55 0.43 0.38 0.32

The ratio of the factored load to nominal structural resistance was also evaluated at 

the neutral plane. In this case however, if the neutral plane was located at a depth 

where the pile section was assumed to be straight and undamaged, a higher 

resistance factor, φφcc, of up to 0.70 was applied. Table D-32 presents the ratio of the 

factored load to nominal structural resistance at the neutral plane, along with the 

respective neutral plane depth. For example, on the HP 12x74 pile section in Group 

Configuration 1, the minimum required structural resistance in axial compression 

φφcc(min) is 0.52, at a neutral plane depth of 54 feet. This location is 6 feet above the 

pile toe, and is assumed undamaged, therefore the higher resistance factor of 0.70

is applied. Accordingly, the pile section is considered acceptable. 

Conversely, for the HP 10x42 pile section in Group Configuration 1, the minimum 

required structural resistance in axial compression φφcc(min) is 0.74, at a neutral plane 

depth of 54 feet. This location is 15 feet above the pile toe (69 feet, Table D-32), 

and is also assumed undamaged. After applying the higher resistance factor of 

0.70, the pile section is considered unacceptable (and was also structurally 

unacceptable based upon the load at the pile toe, Table D-32).

Table D-32 Ratio of Factored Load to Nominal Structural Resistance in Axial 

Compression, φφcc(min), at the Neutral Plane

Group 

Configuration

HP 10x42

φφcc(min)/ 

NP depth 

(feet)

HP 12x53

φφcc(min)/ 

NP depth 

(feet)

HP 12x74

φφcc(min)/ 

NP depth 

(feet)

HP 14x89

φφcc(min)/ 

NP depth 

(feet)

HP 14x117

φφcc(min)/ 

NP depth 

(feet)

1 0.74 / 54 0.68 / 55 0.52 / 54 0.50 / 54 0.41 / 53

2 0.67 / 54 0.63 / 55 0.47 / 53 0.43 / 50 0.35 / 50

3 0.62 / 54 0.55 / 55 0.43 / 52 0.38 / 48 0.32 / 48

82
Based on results of the drag force analysis, a candidate pile section may be 

eliminated from consideration if the factored loads are higher than the factored 

structural resistance. As recorded in Table D-33, the larger candidate pile sections 

remained acceptable considering drag force.

Table D-33 Does Candidate Pile Section Meet Structural Resistance Requirement

Considering Drag Force Associated with Minimum Pile Penetration Depth?

Group 

Configuration HP 10x42 HP 12x53 HP 12x74 HP 14x89 HP 14x117

1 No No Yes Yes Yes

2 No No Yes Yes Yes

3 No No Yes Yes Yes

D.18Decision Block 18: Does Estimated Total Settlement and Differential 

Settlement Between Adjacent Substructure Locations Satisfy 

Requirements and Angular Distortion Limits?

This design step cannot yet be completed. The total settlement at the North 

Abutment has been estimated and it is within the established deformation limits. 

However, the foundation design and settlement estimates for the adjacent pier have 

yet to be performed. Therefore, differential settlement and angular distortion cannot 

be assessed at this time. This step will be revisited once design computations at the 

pier are performed. 

D.19Block 19: North Abutment – Evaluate Economics of Candidate Piles, 

Preliminary Group Configurations, and Other Factors

Until now, the design process has served to compare strength and service limits for 

several candidate pile types within trial group configurations. Some candidate pile 

types have not met all of the strength, service, or drivability requirements. It is useful 

to quickly review the suitable and unsuitable pile types and group configurations and 

then assess the cost of the viable foundation solutions.

Table D-34 summarizes the established minimum pile penetration depth based on 

analysis results from Blocks 12 through 15. For all candidate pile sections and 

group configurations at the North Abutment, the established minimum pile 

penetration depth was based on meeting tolerable vertical deformations. 

83
Several candidate sections did not meet structural resistance requirements for axial 

loading, lateral loading or both. The candidate pile sections and/or group 

configurations not meeting design requirements are identified with an asterisk in 

Table D-34. For all three group configurations, the HP 10x42 and HP 12x52 pile 

sections did not meet all structural resistance requirements. These candidate pile 

sections and group configuration will therefore be eliminated for the final design.

Table D-34 Established Minimum Pile Penetration Depth at the North Abutment

Group 

Configuration

HP 10x42

(feet)

HP 12x53 

(feet)

HP 12x74

(feet)

HP 14x89

(feet)

HP 14x117

(feet)

1 69* 60* 60 54 53

2 64* 55* 55 50 50

3 60* 52* 52 48 48

*Did not meet structural resistance requirement.

Table D-35 presents the estimated minimum penetration depth for each candidate 

section to meet the factored geotechnical resistance requirements at the Strength I 

limit state. The larger pile sections require less pile penetration depth than the 

smaller pile sections to provide the same geotechnical resistance. In addition, the 

factored load per pile decreases from Group Configuration 1 to Group Configuration 

3. However, from the analyses in Blocks 13 through 15, the established minimum 

penetration depth to preclude unacceptable vertical deformation requires all piles to 

be driven deeper than the depth needed solely for their factored geotechnical 

resistance. The minimum penetration depth requirement results in the additional 

geotechnical resistance gained by further pile embedment to be essentially wasted

and therefore uneconomical.

Table D-35 Estimated Minimum Penetration Depth for Factored Geotechnical 

Resistance at Strength I Limit State

Group 

Configuration

HP 10x42

(feet)

HP 12x53

(feet)

HP 12x74

(feet)

HP 14x89

(feet)

HP 14x117

(feet)

1 59* 45* 45** 45** 43**

2 46* 45* 45** 38** 35**

3 45* 45* 43** 32** 30**

*Did not meet structural resistance requirement.

**Must be driven deeper to meet deformation requirements (Table D-28).

84
The unit cost per foot of pile installed should be estimated. Past pricing information 

is generally the best guide. However due to fluctuations in the market price of 

material and other factors, pile costs are subject to change. Section 6.14 provides 

recent piling cost information from several state agency databases. In the 

calculation below, the cost of steel of $0.90 per pound is used as a baseline to 

determine pile cost. Equation D-5 shows the cost per linear foot calculation in which 

the cost is determined for the HP12x74 pile section. Table D-36 presents the cost 

per linear foot for each of the 5 candidate pile sections and shows reasonable 

agreement with the installed cost per foot of pile provided in Section 6.14.

Determine price per linear foot for HP12x74 pile section.

$ = cost per pound of steel, $0.90/lb.

ww = weight per linear foot of pile section, 74 lbs/ft.

Cost = $ ∗ ff Eq. D-6

Cost = �

$0.90� ∗ �74

ff �

Cost = $66.60

ff

Table D-36 Estimated Cost Per Linear Foot for 5 Candidate Pile Sections

HP 10x42

($ / ft)

HP 12x53

($ / ft)

HP 12x74

($ / ft)

HP 14x89

($ / ft)

HP 14x117

($ / ft)

37.80 47.70 66.60 80.10 105.30

The pile cost versus pile penetration depth is plotted for each of the 5 candidate pile 

sections in Figure D-34. In this calculation, the cost per linear foot is multiplied by 

the pile length, and due to the price difference per foot, the cost difference between 

pile sections becomes more pronounced with depth. Table D-37 shows the price 

per pile at the established minimum pile penetration depth. For example, for the HP 

12x 74 pile section in Group Configuration 1, the individual cost is determined by 

multiplying the cost per foot by the penetration depth. At its minimum pile 

penetration depth of 60 feet, the cost per pile is $3,996. There will be additional pile 

length embedded in the cap. However that length is currently undetermined, and for 

pile cost estimation and decision purposes, it can be considered negligible. Table 

D-38 shows the pile group cost reflecting the cost per pile and number of piles in the 

group.

85
Figure D-34 Pile cost versus penetration depth.

Table D-37 Cost per Pile at Established Minimum Penetration Depth for Piles 

Meeting Structural Requirements

Group 

Configuration HP 12x74 HP 14x89 HP 14x117

1 $3,996 $4,325 $5,438

2 3,663 4,005 5,130

3 3,463 3,845 4,925

Table D-38 Pile Group Cost at Established Minimum Penetration Depth for Piles 

Meeting Structural Requirements

Group 

Configuration HP 12x74 HP 14x89 HP 14x117

1 $71,928 $77,857 $97,880

2 80,586 88,110 112,860

3 90,043 99,965 128,045

Based upon this comparison, the HP 14x117 pile section proves to be least 

economical followed by the HP 14x89 section. Conversely, the HP 12x74 pile 

86
section in Group Configuration 1 appears to be the most economical. The cost of 

the pile cap must also be considered before selecting the lowest cost. 

The cost of the pile cap is estimated and factored into the total foundation cost. 

Section 8.9 outlines a procedure to estimate the total pile cap thickness. Equation 8-

80 is used along with the factored geotechnical resistance, per pile, to estimate this 

value. Table D-39 summarizes the factored geotechnical resistance for each pile 

section based upon the estimated minimum pile toe elevation.

Table D-39 Factored Geotechnical Resistance, Rr, at Estimated Minimum Pile 

Penetration Depth

Group 

Configuration

HP 12x74

(kips)

HP 14x89 

(kips)

HP 14x117

(kips)

1 323 323 323

2 265 265 265

3 224 224 224

A sample calculation for determining the cap thickness is shown below for the HP 

12x74 H-pile in Group Configuration 1. Table D-40 summarizes the estimated cap 

thickness for each pile section and pile group permutation calculated using this 

procedure.

Estimate the total pile cap thickness for a HP12x74 H-pile in Group Configuration 1.

PPuu = maximum single pile factored axial load, Q =323 kips (Table D-14).

tcc = PPuuuu

12

+ 30 [Eq. 8-80]

tcc = (323 )

12

+ 30

tcc = 57 hee

Table D-40 Estimated Total Pile Cap Thickness

Group 

Configuration

HP 12x74

(inches)

HP 14x89

(inches)

HP 14x117

(inches)

1 57 57 57

2 52 52 52

3 49 49 49

87
Next, the volume of reinforce concrete required to construct the pile cap is 

determined from the estimated total pile cap thickness. The total pile cap width and 

length values were previously provided in Table D-12. The resulting volume of 

reinforced concrete in the pile cap for each pile section and pile group permutation is 

presented in Table D-41. Note that pile cap volume is shown in cubic yards (CY).

Table D-41 Estimated Volume of Reinforced Concrete in Pile Cap

Group 

Configuration

HP 12x74

(CY)

HP 14x89

(CY)

HP 14x117

(CY)

1 48.5 48.5 48.5

2 44.4 44.4 44.4

3 37.6 37.6 37.6

To estimate the pile cap cost, past pricing information is generally the best guide. 

However, similar to estimating the pile cost, due to fluctuations in the market price of 

material and other factors, pile cap costs are subject to change. The cost of the 

reinforced concrete pile cap, furnished and constructed, is estimated to be $500 /CY. 

Using this estimated value, the volumes presented in Table D-41 were used to 

estimate the cost of the various reinforced concrete pile caps. The pile cap cost for 

each candidate section and group configuration permutation is shown in Table D-42.

Table D-42 Estimated Cost of Reinforced Concrete Pile Cap 

Group 

Configuration HP 12x74 HP 14x89 HP 14x117

1 $24,264 $24,264 $24,264

2 22,204 22,204 22,204

3 18,794 18,794 18,795

By adding the cost of the pile cap and piles for each permutation, the estimated total 

foundation cost is determined as presented in Table D-43. Considering both the pile 

and the pile cap costs, the HP 12x74 in Group Configuration 1 is the most

economical option.

With field resistance determination tests yet to be performed, only geotechnical 

correlations have been considered to estimate nominal resistance vs. depth 

relationships. Dynamic testing results may require additional (or less) pile 

embedment to satisfy resistance requirements. The potential for such variations 

between estimated and installed lengths becomes more-pronounced with friction

88
Table D-43 Estimated Foundation Cost Including Piles and Pile Cap

at North Abutment

Group 

Configuration HP 12x74 HP 14x89 HP 14x117

1 $96,192 $102,121 $122,145 

2 102,790 110,314 135,064 

3 108,838 118,759 146,839 

piles than with end-bearing piles. To provide insight into how such potential length 

variations might affect costs, an additional comparison of pile cost versus depth from 

the estimated depth was completed for the final three candidate pile sections.

In this comparison, Table D-44 shows the cost per pile and cost per pile group for 

the three lowest cost permutations of group configuration and candidate sections

from Table D-43 (i.e., the HP 12x74, the HP 14x89 section, and the HP14x117

section all in Group Configuration 1). Group Configuration 1 contains 18 piles. 

Although the pile sections have different established minimum penetration depth 

requirements, the depth provided in Table D-44 will be used as a baseline to 

evaluate the cost risk associated with pile overrun or underrun (“over/underrun”) that 

may result from field determination testing. At the North Abutment, the established 

minimum pile penetration depth is greater than the estimated pile penetration depth 

for factored geotechnical resistance in axial compression, therefore underrun is 

provided for demonstration purposes only.

If the estimated soil resistance is underpredicted and the 14x89 pile section in Group 

Configuration 1 is determined to have sufficient factored resistance upon field 

determination testing at 49 feet (underrun of 5 feet), the cost per pile would be 

reduced by $481 and thus a reduction of $8,651 relative to the original $102,121

estimate for the total foundation cost would result. A graphical representation of this 

effect is presented in Figure D-35 (Underrun is shown for demonstration purposes 

only at the North Abutment as the established minimum pile penetration depth is 60

feet for this pile section). Conversely, if for example, the HP 12x74 section must be 

driven 15 feet deeper (overrun of 15 feet) to achieve sufficient factored resistance;

an additional cost of $999 per pile would result. Based upon the number of piles and 

estimated pile cap cost, this would increase the total foundation cost by $17,982

from the original estimate of $96,192.

If it is assumed that the same pile over/underrun length will result for the pile 

sections after field determination testing, a cost comparison can be made for a range 

89
of over/underrun lengths for the final candidate pile sections and group 

configurations. This comparison can compare the sensitivity of foundation cost to 

over/underrun lengths among candidate pile sections, and therefore may aid 

selection among the sections.

Table D-44 Comparison of Pile Over/Underrun Costs for Three Lowest Cost 

Alternatives at the North Abutment

Over/ 

Underun

(feet)

HP 12x74

Change in 

Cost per 

Pile

HP 12x74

Change in 

Cost of 

Foundation

HP 14x89

Change in 

Cost per 

Pile

HP 14x89

Change in 

Cost of 

Foundation

HP 14x117

Change in 

Cost per 

Pile

HP 14x117

Change in 

Cost of 

Foundation

-5 ($400) $(7,193) $(481) $(8,651) $(616) $(11,081)

0 - - - - - -

5 333 5,994.00 401 7,209 $513 9,234

10 666 11,98 801 14,418 1,026 18,468

15 99 17,98 1,202 21,627 1,539 27,702

Figure D-35 Change in cost per pile from over/ underrun.

Table D-45 compares the overall foundation cost change associated with 

over/underrun lengths for the final thee candidate pile sections and pile group 

configuration permutations; graphical results of this interpretation are presented in 

Figure D-36 The change of foundation cost is again presented along with the 

relative difference based upon the same assumed pile over/underrun for the pile 

90
sections. The difference in foundation cost is referenced from the HP12x74 pile 

section in Group Configuration 1. For example if 15 feet of overrun occurs for each 

permutation, the resulting cost difference between the HP 12x74 section in Group 

Configuration 1 and the HP 12x74 section in Group Configuration 1 is $17,982

minus $21,627 or -$3,645.

Table D-45 Comparison of Pile Group Over/Underrun Costs for Three Lowest Cost 

Alternatives at the North Abutment

Over/ 

Underun

(feet)

HP 12x53

Change in 

Cost of 

Foundation

HP 14x89

Change in 

Cost of 

Foundation

Difference in

Cost of 

Foundation

HP 14x117

Change in 

Cost of 

Foundation

Difference in 

Cost of 

Foundation

-5 $(7,193) $(8,651) $1,458 $(11,081) $3,888 

0 - - - - -

5 5,994 7,209 (1,215) 9,234 (3,240)

10 11,988 14,418 (2,430) 18,468 (6,480)

15 17,982 21,627 (3,645) 27,702 (9,720)

Figure D-36 Change in total cost of foundation from overrun/ underrun.

In the absence of a test pile program, a definitive cost comparison cannot be made; 

however, the above described cost analysis can assist to reduce the number of 

options and estimate the relative risk of cost overruns or savings associated with a 

91
given candidate pile section and group configuration. At this juncture, a preliminary 

design of the Pier 2 and the South Abutment should be performed before making a 

final decision on pile type and size. This offers flexibility for the pile group design at 

other locations if the agency practice is to use the same pile sections at all 

foundation locations. If, for example, larger loads are required at Pier 2 or the South 

Abutment, the use of a larger pile section may be reason to further eliminate one or 

more of the candidate pile sections or group configurations. 

D.20Decision 20: Is the Preliminary Design of All Substructure Foundations 

Complete?

No. The preliminary foundation design has been completed for only the North 

Abutment. The preliminary design needs to be completed for the Pier and for the 

South Abutment. Return to Block 9 and begin the preliminary design for the next 

substructure location.

92
D.21Block 9: Pier 2 – Calculate Nominal and Factored Structural Resistances 

for all Candidate Piles

The nominal structural resistance is now re-evaluated for the five candidate H-pile 

sections at Pier 2. The H-pile sections selected for evaluation again include a HP 

10x42, a HP 12x53, a HP 12x74, a HP 14x89 and a HP 14x117. A detailed step by 

step example for calculation of the nominal structural resistance was previously 

presented in Section 8.5.3 for an HP 14x117 H-pile section. Therefore, this process 

is not repeated for the five candidate pile sections.

Due to channel degradation and local scour, the hydraulic engineer estimated scour 

depth is up to 5 feet below the bottom of pile cap for the design flood. The nominal 

structural resistance in axial compression must therefore account for a longer 

unbraced length. At the Strength limit state, the design flood event scour results in 

an unbraced length of 5 feet. Furthermore, for the check flood at the Extreme Event 

Limit State, the hydraulic engineer estimated scour potential up to 7 feet below the 

bottom of the pile cap. In this case, 7 feet of unbraced length is factored into the 

nominal structural resistance calculation. Table D-46 presents the nominal structural 

resistances in axial compression, flexure, and shear for the five candidate pile 

sections.

Table D-46 Nominal Structural Resistance in Axial Compression, 

Flexure and Shear 

H-pile Section HP 

10x42

HP 

12x53

HP 

12x74

HP 

14x89

HP

14x117

Pn, Nominal Resistance in Axial 

Compression (kips) 

(Strength V)

581 734 1043 1266 1670

Pn, Nominal Resistance in Axial 

Compression (kips) 

(Extreme Event II)

546 702 999 1229 1624

Mny, Nominal Resistance in Weak 

Axis Flexure (kip-ft) 82 114 118 257 380

Mnx, Nominal Resistance in Strong 

Axis Flexure (kip-ft) 176 295 433 592 807

Vn, Nominal Resistance in Shear 

(kips) 118 149 214 246 331

It is anticipated that the piles at Pier 2 will be driven into the dense gravel with sand 

deposit, or possibly to the underlying bedrock. The dense gravel with sand deposit 

contains occasional boulders. In these conditions, pile shoes are recommended for

93
use with the H-piles to reduce the risk of damage. Therefore, the applicable 

structural resistance factors, φφcc, are 0.5 for axial compression resistance and 0.7 for 

combined axial compression and flexural resistance. A resistance factor of φφvv =1.0 

is used for shear, and a resistance factor of φφff=1.0 is applicable for flexure only. 

Table D-47 summarizes the calculated factored structural resistances in axial 

compression, combined axial and flexure, flexure, and shear.

Table D-47 Factored Structural Resistance in Axial Compression, Flexure and 

Shear

H-pile Section HP 

10x42

HP 

12x53

HP 

12x74

HP 

14x89

HP

14x117

Pr, Factored Resistance in Axial 

Compression,φφcc = 0.5 (kips)

(Strength V)

290 367 521 633 835

Pr, Factored Axial and Flexural 

Resistance, φφcc = 0.70 (kips)

(Strength V)

407 514 730 886 1169

Pn, Factored Resistance in Axial 

Compression,φφcc = 0.5 (kips) 

(Extreme Event II)

273 351 500 615 812

Pr, Factored Axial and Flexural 

Resistance, φφcc = 0.70 (kips)

(Extreme Event II)

382 491 699 861 1137

Mry, Factored Resistance in Weak 

Axis Flexure, φφff=1.0 (kip-ft) 82 114 118 257 380

Mrx, Factored Resistance in Strong 

Axis Flexure, φφff=1.0 (kip-ft) 176 295 433 592 807

Vr, Factored Resistance in Shear 

φφvv =1.0 (kips) 118 149 214 246 331

D.22Block 10: Pier 2 – Calculate Nominal and Factored Geotechnical 

Resistances in Axial Compression and Tension versus Depth for all 

Candidate Piles; Perform Preliminary Pile Drivability Analyses

The engineering properties for the soil conditions encountered at Pier 2 were 

determined in Block 5. The results of the boring program and laboratory tests are

now used to develop a design profile for Pier 2. Engineering judgement was used in 

developing the design profile to delineate the subsurface conditions into layers with 

similar properties. An effective stress diagram, depicted in Figure D-37, was also

made for this soil profile. This diagram includes the total stress, porewater pressure 

and effective stress versus depth. Figure D-37 also presents the basic soil profile for 

quick reference to the relevant soil layers. The effective stress diagram was 

94
computed using Equations 5-7 through 5-9 from Chapter 5. These equations are 

repeated below. For Figure D-37 the total stress, porewater pressure and effective 

stress were calculated at 1 foot increments using a spreadsheet.

σσvv = ∑ (γγiihii) nn

ii [Eq. 5-7]

uu = γγwwhww [Eq. 5-8]

σσ′vv = ∑ (γγiihii) − γγwwhww nn

ii [Eq. 5-9]

Figure D-37 Effective stress diagram for Pier 2 using Boring S-2.

To continue development of an idealized soil profile, field SPT N values were 

corrected for hammer energy transfer and vertical effective stress. The field SPT N 

values were first corrected for energy transfer using Equation 5-1. These results are 

presented in Table D-48. Typical correlations for SPT hammer type and energy 

transfer are provided in Section 5.1.1 (e.g., typical energy transfer of 80% for 

automatic hammer). The SPT hammer on the drill rig used for this project’s soil 

exploration program was calibrated in accordance with ASTM D4633. Results of 

this calibration indicated an average energy transfer of 75%. Therefore, the ER

value in Equation 5-1 is equal to 75.

NN60 = NN �

EEEE

60� [Eq. 5-1]

95
The SPT N value was then corrected for vertical effective stress as presented in 

Equation 5-2, using the Peck et al. (1974) correction factor, CCnn. The depth value for 

this calculation was taken from the middle depth of the SPT sampling event after the 

6 inch seating interval (e.g., the SPT N value recorded from 0.5-1.5 feet was 

corrected using the vertical effective stress at 1 foot).

(NN1)60 = CCnnNN60 [Eq. 5-2]

CCnn = 0.77 log � 20

σσ′vvvv

� [Eq. 5-3]

After correcting the SPT N values for energy transfer and vertical effective stress, an 

average corrected N value was determined for each respective cohesionless soil 

layer. The N value from the first SPT sample in Layer 1 was not included in this 

procedure for Layer 1 since the bottom of the footing at Pier 2 is below this sample 

depth. 

Table D-49 presents the average (N1)60 value for each cohesionless layer at Pier 2, 

the coefficient of variation, COV, within the layer, and the effective stress friction 

angle chosen for the layer. The coefficient of variation for each layer was less than 

25% indicating low variability within each of the identified layers. Higher variability 

would have necessitated separating the soil profile into additional soil layers. 

Table D-48 Correction of Field SPT N Value for Energy and Vertical Effective 

Stress at Pier 2 using Boring S-2

Soil Layer Depth (ft) σ'vo (ksf) Field N value N60 Cn (N1)60

1 1 0.033 3 4 2.00 8

1 6 0.101 7 9 2.00 18

2 8 0.166 51 64 1.83 117

2 11 0.369 52 65 1.57 102

2 16 0.707 55 69 1.35 93

4 51 3.013 42 53 0.86 45

4 56 3.326 46 58 0.83 48

4 61 3.639 41 51 0.80 41

4 66 3.952 50 63 0.77 48

The (N1)60 values were used to estimate the effective stress friction angle of each 

soil layer in accordance with Table 5-5 of Chapter 5. These friction angle 

96
correlations are presented in Table D-49. Layer 2 consists of extremely dense 

gravel and Layer 4 consists of hard angular gravel with sand. Therefore, as 

discussed in Section 5.5.1, a design friction angle of 36 degrees was used for

estimating the shaft resistance in both of these layers while the friction angle noted 

in Table D-49 was used to estimate the toe resistance.

Table D-49 Soil Layer Effective Stress Friction Angle Correlations at Pier 2 

Soil Layer Average (N1)60 COV φ' shaft 

(degrees)

φ' toe 

(degrees) 

1 18 0.0% 32 32

2 104 9.6% 36 43

4 46 6.3% 36 38

Soil Layer 3 consists of very stiff silty clay. Unconfined compression strength tests 

were performed on each undisturbed cohesive soil sample. The undrained shear 

strength was then calculated by dividing the unconfined compression strength by 2.

Figure D-38 presents the undrained shear strength versus depth for Soil Layer 3. 

The undrained shear strength increases approximately linearly from 20 to 45 feet. 

Layer 3 was refined into 6 sublayer increments of 5 feet, each using the respective 

undrained shear strength value determined from laboratory testing. Table D-50

presents the shear strength values for Soil Layer 3 as well as sublayers a through f. 

Figure D-38 Undrained shear strength, su, versus depth for Soil Layer 3 at Pier 2.

97
Table D-50 Undrained Shear Strength, su, for Soil Layer 3 at Pier 2

Soil Layer Depth (ft) σ'vo (ksf) qu (tsf) su (ksf)

3a 21 1.045 3.10 3.10

3b 26 1.373 3.21 3.21

3c 31 1.701 3.25 3.25

3d 36 2.029 3.30 3.30

3e 41 2.357 3.34 3.34

3f 46 2.685 3.40 3.40

The design soil profile for Pier 2 is presented in Figure D-39, with the bottom of 

footing elevation noted 10 feet below ground surface. Some soil properties in the 

design soil profile such as the elastic moduli, Es, and the initial cyclic modulus of 

subgrade reaction, kc, have been selected based on published correlations in the 

absence of laboratory and field testing. For this particular soil profile, the elastic 

moduli were determined from the SPT correlation in Table 5-11 and the initial cyclic 

moduli of subgrade reaction were selected based on representative values shown in 

Table 7-22. The average cohesive soil strength for Layer 3 was used to select the 

50% strain factor, ε50, from Table 7-21. 

Figure D-39 Design soil profile at Pier 2.

98
D.22.1 Geotechnical Resistance in Axial Compression

The nominal geotechnical resistance in axial compression is now determined for the 

selected candidate H-pile sections. The nominal geotechnical resistance can be 

calculated by hand or with computer software using an appropriate analysis method 

based upon soil and pile type. Chapter 7 describes appropriate methods for this 

purpose as well as available computer programs.

For this example, the DrivenPiles computer program was used to calculate the 

nominal resistance, shaft resistance, and toe resistance as a function of depth for 

each of the five candidate H-piles. This software program was selected since it uses 

the FHWA recommended Nordlund method and alpha method to estimate the 

nominal geotechnical resistance of H-piles in cohesionless and cohesive soils, 

respectively. The DrivenPiles program also allows the analyst to select a different 

friction angle for shaft and toe resistance calculations in any layer. This option was 

utilized for the extremely dense gravel in Layer 2 and the gravel with sand 

comprising Layer 4. The computer program was also used to evaluate the nominal 

geotechnical resistance at Pier 2 during the design flood and at the check flood.

A summary of the nominal shaft, nominal toe, and nominal geotechnical resistance 

is presented for the HP 12x74 H-pile section in Table D-51. A graphical 

interpretation of the estimated resistance is presented in Figure D-40. The indicated 

pile penetration depth is referenced from the bottom of pile cap (Elev. 275.0 feet), 

which is 10 feet below the original ground surface (Elev. 285.0 feet).

99
Table D-51 Nominal Shaft, Nominal Toe and Nominal Geotechnical Resistance for 

HP 12x74 at Pier 2 (pre-scour)

Depth

(feet)

Nominal 

Shaft 

Resistance 

(kips)

Nominal 

Toe 

Resistance 

(kips)

Nominal 

Geotechnical 

Resistance 

(kips)

Depth

(feet)

Nominal 

Shaft 

Resistance 

(kips)

Nominal 

Toe 

Resistance 

(kips)

Nominal 

Geotechnical 

Resistance 

(kips)

0.01 0.0 106.5 106.5 29.99 109.9 30.5 140.4

1 1.1 123.0 124.2 30.01 110.1 30.8 140.9

2 2.4 139.7 142.1 31 115.1 30.8 145.9

3 3.9 156.4 160.2 32 120.2 30.8 151.0

4 5.5 173.1 178.5 33 125.3 30.8 156.1

4.99 7.2 189.6 196.8 34 130.4 30.8 161.2

5.01 7.3 189.9 197.2 34.99 135.5 30.8 166.3

6 9.2 206.4 215.6 35.01 135.6 31.4 166.9

7 11.3 223.1 234.4 36 140.6 31.4 172.0

8 13.5 239.8 253.3 37 145.7 31.4 177.1

9 16.0 256.5 272.4 38 150.8 31.4 182.2

9.99 18.5 273.0 291.5 39 155.9 31.4 187.3

10.01 18.6 28.6 47.2 39.99 161.0 31.4 192.3

11 22.4 28.6 51.0 40.01 161.1 251.3 412.4

12 26.3 28.6 54.9 41 168.5 256.4 424.9

13 30.4 28.6 59.0 42 176.2 261.5 437.7

14 34.6 28.6 63.2 43 184.0 266.6 450.6

14.99 38.9 28.6 67.5 44 191.9 271.7 463.7

15.01 39.0 29.6 68.6 45 200.0 275.4 475.4

16 43.1 29.6 72.8 46 208.3 275.4 483.6

17 47.4 29.6 77.0 47 216.7 275.4 492.0

18 51.8 29.6 81.4 48 225.2 275.4 500.6

19 56.4 29.6 86.0 49 234.0 275.4 509.3

19.99 61.0 29.6 90.6 50 242.8 275.4 518.2

20.01 61.1 30.0 91.1 51 251.8 275.4 527.2

21 65.5 30.0 95.5 52 261.0 275.4 536.3

22 70.1 30.0 100.1 53 270.3 275.4 545.6

23 74.8 30.0 104.8 54 279.8 275.4 555.1

24 79.7 30.0 109.7 55 289.4 275.4 564.7

24.99 84.7 30.0 114.6 56 299.1 275.4 574.5

25.01 84.7 30.5 115.2 57 309.0 275.4 584.4

26 89.5 30.5 119.9 58 319.1 275.4 594.5

27 94.4 30.5 124.9 59 329.3 275.4 604.7

28 99.5 30.5 129.9 59.99 339.6 275.4 614.9

29 104.7 30.5 135.1 60.01 339.7 1042.6 1382.3

100
Figure D-40 Nominal geotechnical resistance in axial compression versus pile 

penetration depth for HP 12x74 at Pier 2 (pre scour).

D.22.1.1 Geotechnical Resistance in Axial Compression at the Design Flood

The nominal geotechnical resistance in axial compression at the design flood must 

also be evaluated. In the design flood, 5 feet of channel degradation scour is 

anticipated. The channel degradation scour results in a change in vertical effective 

stress from the removal of 5 feet of channel materials. The channel degradation 

scour occurs above the bottom of the pile cap. Hence the channel degradation 

scour results in no loss of nominal resistance other than that caused by the 

reduction in overburden stress.

In addition to the channel degradation scour, 10 feet of local scour occurs during the 

design flood. This 10 feet of local scour occurring below the channel degradation 

scour results in the loss of frictional resistance on the upper 5 feet of the pile in the 

design flood event. Hence, these two scour mechanisms require a more rigorous 

analysis of the nominal resistance beyond simple subtraction of the shaft resistance 

within the scour prism. Therefore, the DrivenPiles program was used to calculate 

the shaft, toe and nominal resistance as a function of depth for each of the five 

candidate H-piles in the design flood. 

101
Figure D-41 presents plots of the nominal shaft resistance, Rs, the nominal toe 

resistance, Rp, and nominal resistance, Rn for the HP 12x74 pile section versus pile 

penetration depth. These results are also presented numerically in Table D-52. The 

depth indicated in both Figure D-41 and Table D-52 is referenced from the bottom of 

pile cap (EL 275 feet), which is 10 feet below the original ground surface elevation 

(EL 285 feet).

Figure D-41 Nominal geotechnical resistance in axial compression versus pile 

penetration depth for HP 12x74 at Pier 2 (design flood).

The nominal resistance versus depth at the design flood was calculated for all of the 

candidate pile sections in a similar manner. These results are presented in Figure 

D-42. 

102
Table D-52 Nominal Shaft, Nominal Toe and Nominal Geotechnical Resistance for 

HP 12x74 at Pier 2 (design flood)

Depth

(feet)

Nominal 

Shaft 

Resistance 

(kips)

Nominal 

Toe 

Resistance 

(kips)

Nominal 

Geotechnical 

Resistance 

(kips)

Depth

(feet)

Nominal 

Shaft 

Resistance 

(kips)

Nominal 

Toe 

Resistance 

(kips)

Nominal 

Geotechnical 

Resistance 

(kips)

0.01 0.0 0.0 0.0 29.99 100.8 30.8 131.7

1 0.0 0.0 0.0 30.01 105.9 30.8 136.7

2 0.0 0.0 0.0 31 111.0 30.8 141.8

3 0.0 0.0 0.0 32 116.1 30.8 146.9

4 0.0 0.0 0.0 33 121.2 30.8 152.0

4.99 0.0 149.7 149.7 34 126.3 30.8 157.1

5.01 1.5 166.2 167.8 34.99 126.4 31.4 157.7

6 3.3 182.9 186.1 35.01 131.4 31.4 162.8

7 5.1 199.6 204.7 36 136.5 31.4 167.9

8 7.2 216.2 223.4 37 141.6 31.4 173.0

9 9.3 232.8 242.1 38 146.7 31.4 178.1

9.99 9.4 28.6 38.0 39 151.8 31.4 183.1

10.01 13.2 28.6 41.8 39.99 151.9 238.0 389.9

11 17.1 28.6 45.7 40.01 158.9 243.1 402.0

12 21.2 28.6 49.8 41 166.2 248.2 414.4

13 25.4 28.6 54.0 42 173.6 253.3 426.9

14 29.7 28.6 58.3 43 181.1 258.4 439.6

14.99 29.8 29.6 59.4 44 188.9 263.5 452.4

15.01 33.9 29.6 63.5 45 196.7 268.6 465.4

16 38.2 29.6 67.8 46 204.7 273.8 478.5

17 42.6 29.6 72.2 47 212.9 275.4 488.2

18 47.2 29.6 76.8 48 221.2 275.4 496.6

19 51.8 29.6 81.4 49 229.7 275.4 505.0

19.99 51.9 30.0 81.9 50 238.3 275.4 513.6

20.01 56.3 30.0 86.3 51 247.0 275.4 522.4

21 60.9 30.0 90.9 52 256.0 275.4 531.3

22 65.6 30.0 95.6 53 265.0 275.4 540.4

23 70.5 30.0 100.5 54 274.3 275.4 549.6

24 75.4 30.0 105.4 55 283.6 275.4 559.0

24.99 75.5 30.5 106.0 56 293.1 275.4 568.5

25.01 80.3 30.5 110.7 57 302.8 275.4 578.2

26 85.2 30.5 115.7 58 312.6 275.4 588.0

27 90.3 30.5 120.7 59 322.5 275.4 597.9

28 95.5 30.5 125.9 59.99 322.7 922.6 1245.3

29 100.7 30.5 131.2 60.01 327.7 1042.6 1370.3

103
Figure D-42 Nominal geotechnical resistance in axial compression versus 

penetration depth for all candidate pile sections at Pier 2 (design flood).

Figure D-43 presents a design chart of the nominal and factored geotechnical 

resistance for the HP 12x74 pile section in axial compression during the design flood 

event. The design chart includes the nominal geotechnical resistance as well as the 

factored geotechnical resistance based on several resistance determination 

methods. The factored geotechnical resistance versus penetration depth is plotted 

for resistance determination by a static load test with dynamic testing of 2% of the 

piles (φφdd =0.80), by dynamic testing of at least two piles per site condition, but no 

less than 2% of the production piles, with signal matching (φφdd =0.65), and by wave 

equation analysis (φφdd =0.50). Also included is the factored geotechnical resistance 

based on the static analysis method used in this design example. For this, 

(φφss =0.45) was applied to the cohesionless soils as a result of using the Nordlund 

method while (φφss =0.35) applied to the cohesives soils as a result of using the 

alpha method. For a single pile section (HP 12x74), this figure illustrates the effects 

the various resistance determination methods have on the pile length required for a 

given factored resistance, the factored resistance available from a given pile section, 

and the potential impact of these factors on the number of piles needed to resist 

axial compression loads. 

104
Figure D-43 Design chart of nominal and factored geotechnical resistance in axial 

compression versus pile penetration depth for HP 12x74 at the Pier 2 (design flood).

The factored geotechnical resistance in axial compression for all candidate pile 

sections is presented in Figures D-44 through D-47 during the design flood event. 

The presented factored geotechnical resistances are based upon on the field 

determination method or static analysis method used. Accordingly, these figures 

can be used to assess the effects of the various determination methods on pile 

length, pile section selection, and the required number of piles to resist axial 

compression loads. 

105
Figure D-44 Factored geotechnical resistance, Rr, in axial compression based on 

field determination by static load test and dynamic testing 2% of the piles, φdyn=0.80.

Figure D-45 Factored geotechnical resistance, Rr, in axial compression based on 

field determination by dynamic testing 2% of the piles, φdyn=0.65.

106
Figure D-46 Factored geotechnical resistance, Rr, in axial compression based on 

field determination by wave equation analysis, φdyn=0.50.

Figure D-47 Factored geotechnical resistance, Rr, in axial compression based on 

determination using Nordlund Method static analysis, φstat=0.45.

107
D.22.1.2 Geotechnical Resistance in Axial Compression at the Check Flood

The nominal geotechnical resistance in axial compression at the Extreme Event 

check flood must also be evaluated. In the check flood, 5 feet of channel 

degradation scour is anticipated. The channel degradation scour results in a change 

in vertical effective stress from the removal of 5 feet of channel materials. The 

channel degradation scour occurs above the bottom of the pile cap. Hence the 

channel degradation scour results in no loss of nominal resistance other than that 

caused by the reduction in overburden stress.

In addition to the channel degradation scour, 12 feet of local scour occurs during the 

design flood. This 12 feet of local scour occurring below the channel degradation 

scour results in the loss of frictional resistance on the upper 7 feet of the pile in the 

Extreme Event check flood. Hence, these two scour mechanisms require a more 

rigorous analysis of the nominal resistance beyond simple subtraction of the shaft 

resistance within the scour prism. The DrivenPiles program was once again used to 

calculate the shaft, toe and nominal resistance as a function of depth for each of the 

five candidate H-piles in the check flood.

Table D-53 presents a summary of the estimated nominal geotechnical resistance 

considering scour at the check flood for the HP 12x74 pile section. These results are 

also presented graphically in Figure D-48. The depth indicated in both Table D-53

and Figure D-48 is referenced from the bottom of footing (EL 275 feet), which is 10 

feet below the original ground surface elevation (EL 285 feet). 

The nominal shaft, nominal toe, and nominal geotechnical resistance considering 

scour at the check flood were calculated for all of the candidate pile sections in a 

similar manner. These results are presented in Figure D-49.

108
Table D-53 Nominal Shaft, Nominal Toe and Nominal Geotechnical Resistance for 

HP 12x74 at Pier 2 (check flood)

Depth

(feet)

Nominal 

Shaft 

Resistance 

(kips)

Nominal 

Toe 

Resistance 

(kips)

Nominal 

Geotechnical 

Resistance 

(kips)

Depth

(feet)

Nominal 

Shaft 

Resistance 

(kips)

Nominal 

Toe 

Resistance 

(kips)

Nominal 

Geotechnical 

Resistance 

(kips)

0.01 0.0 0.0 0.0 29.99 97.5 30.5 127.9

1 0.0 0.0 0.0 30.01 97.6 30.8 128.4

2 0.0 0.0 0.0 31 102.6 30.8 133.5

3 0.0 0.0 0.0 32 107.7 30.8 138.6

4 0.0 0.0 0.0 33 112.8 30.8 143.7

5 0.0 0.0 0.0 34 118.0 30.8 148.8

6 0.0 0.0 0.0 34.99 123.0 30.8 153.8

6.99 0.0 0.0 0.0 35.01 123.1 31.4 154.5

7.01 0.0 183.1 183.1 36 128.2 31.4 159.5

8 1.9 199.6 201.4 37 133.3 31.4 164.6

9 3.9 216.2 220.2 38 138.4 31.4 169.7

9.99 6.1 232.8 238.8 39 143.5 31.4 174.8

10.01 6.1 28.6 34.7 39.99 148.5 31.4 179.9

11 9.9 28.6 38.5 40.01 148.6 238.0 386.6

12 13.9 28.6 42.5 41 155.7 243.1 398.7

13 18.0 28.6 46.6 42 162.9 248.2 411.1

14 22.2 28.6 50.8 43 170.3 253.3 423.6

14.99 26.5 28.6 55.1 44 177.9 258.4 436.3

15.01 26.6 29.6 56.2 45 185.6 263.5 449.1

16 30.7 29.6 60.3 46 193.5 268.6 462.1

17 35.0 29.6 64.6 47 201.5 273.8 475.2

18 39.4 29.6 69.0 48 209.6 275.4 485.0

19 43.9 29.6 73.5 49 217.9 275.4 493.3

19.99 48.5 29.6 78.1 50 226.4 275.4 501.8

20.01 48.6 30.0 78.6 51 235.0 275.4 510.4

21 53.0 30.0 83.0 52 243.8 275.4 519.1

22 57.6 30.0 87.6 53 252.7 275.4 528.1

23 62.4 30.0 92.4 54 261.8 275.4 537.1

24 67.2 30.0 97.2 55 271.0 275.4 546.4

24.99 72.2 30.0 102.2 56 280.4 275.4 555.7

25.01 72.3 30.5 102.7 57 289.9 275.4 565.2

26 77.0 30.5 107.5 58 299.6 275.4 574.9

27 82.0 30.5 112.4 59 309.4 275.4 584.7

28 87.0 30.5 117.5 59.99 319.3 275.4 594.6

29 92.2 30.5 122.7 60.01 319.4 1042.6 1362.0

109
Figure D-48 Nominal geotechnical resistance in axial compression versus pile 

penetration depth for HP 12x74 at Pier 2 (check flood).

Figure D-49 Nominal geotechnical resistance in axial compression versus 

penetration depth for all candidate pile sections at Pier 2 (check flood).

110
Figure D-50 presents a design chart of the nominal and factored geotechnical 

resistance in axial compression versus depth during the check flood for the HP 

12x74 candidate H-pile section. The design chart includes the nominal geotechnical 

resistance as well as the factored geotechnical resistance based on several 

resistance determination methods. The factored geotechnical resistance versus 

penetration depth is plotted for resistance determination by a static load test with 

dynamic testing of 2% of the piles (φφdd =0.80), by dynamic testing of at least two 

piles per site condition, but no less than 2% of the production piles, with signal 

matching (φφdd =0.65), and by wave equation analysis (φφdd =0.50). Also included is 

the factored geotechnical resistance based on the static analysis method used in 

this design example. For this, (φφss =0.45) was applied to the cohesionless soils as a 

result of using the Nordlund method while (φφss =0.35) was applied to the cohesive

soils as a result of using the alpha method. For a single pile section (HP 12x74), this 

figure illustrates the effects the various resistance determination methods have on 

the pile length required for a given factored resistance, the factored resistance 

available from a given pile section, and the potential impact of these factors on the 

number of piles needed to resist axial compression loads. 

Figure D-50 Design chart of nominal and factored geotechnical resistance in axial 

compression versus pile penetration depth for HP 12x74 at the Pier 2 (check flood).

111
The factored geotechnical resistance in axial compression at the check flood for all 

candidate pile sections is presented in Figures D-51 through D-54. The presented 

factored geotechnical resistances are based upon on the field determination method 

or static analysis method used. Accordingly, these figures will be used to assess the 

effects of the various determination methods on pile length, pile section selection, 

and the required number of piles to resist axial compression loads. 

Figure D-51 Factored geotechnical resistance, Rr, in axial compression based on 

field determination by static load test and dynamic testing 2% of the piles, φdyn=0.80.

112
Figure D-52 Factored geotechnical resistance, Rr, in axial compression based on 

field determination by dynamic testing 2% of the piles, φdyn=0.65.

Figure D-53 Factored geotechnical resistance, Rr, in axial compression based on 

field determination by wave equation analysis, φdyn=0.5.

113
Figure D-54 Factored geotechnical resistance, Rr, in axial compression based on 

determination using static analysis, φstat=0.45 or φstat=0.35.

D.22.2 Geotechnical Resistance in Axial Tension

The nominal and factored geotechnical resistances in axial tension (uplift) are now 

calculated. The calculations were performed using the DrivenPiles program which 

utilized the Nordlund method in cohesionless soil layers and the alpha method in 

cohesive soil layers. For geotechnical resistance in axial tension, only the shaft 

resistance is considered. Therefore, the shaft resistance results calculated for the 

geotechnical resistance in axial compression can be re-used for axial tension. 

These tabular outputs of the nominal shaft resistance versus depth were previously 

presented in Table D-52 for the design flood and Table D-53 for the check flood.

D.22.2.1 Geotechnical Resistance in Axial Tension at the Design Flood

The nominal geotechnical resistance in axial tension at the design flood must be 

evaluated. In the design flood, 5 feet of channel degradation scour is anticipated. 

The channel degradation scour results in a change in vertical effective stress from 

the removal of 5 feet of channel materials. The channel degradation scour occurs 

above the bottom of the pile cap. Hence the channel degradation scour results in no 

loss of nominal resistance other than that caused by the reduction in overburden 

stress.

114
In addition to the channel degradation scour, 10 feet of local scour occurs during the 

design flood. This 10 feet of local scour occurring below the channel degradation 

scour results in the loss of frictional resistance on the upper 5 feet of the pile in the 

design flood event. Hence, these two scour mechanisms require a more rigorous 

analysis of the nominal resistance beyond simple subtraction of the shaft resistance 

within the scour prism. 

The nominal geotechnical resistance in axial tension at the design flood (and 

associated factored geotechnical resistance based upon resistance determination 

method) will therefore be used to evaluate axial tension at the Strength limit state.

Figure D-55 presents plots of the nominal shaft resistance versus penetration depth 

for all the candidate pile sections during the design flood. As outlined in Section 

7.2.3.2.1, the factored uplift resistance for a single pile is the shaft resistance 

multiplied by the appropriate resistance determination resistance factor, φup. Figure 

D-56 presents a design chart of the nominal and factored geotechnical resistance in 

axial tension for the HP 12x74 H-pile section. A resistance factor of 0.60 is used 

when the uplift resistance is determined by a static load test and 0.50 is used when 

determined by a dynamic test with signal matching. If the axial tension resistance is 

evaluated using static analysis methods, a resistance factor of 0.35 is applied to the 

nominal shaft resistance determined by the Nordlund static analysis method in 

cohesionless soil layers, and a resistance factor of 0.25 is applied to the nominal 

shaft resistance determined by the alpha static analysis method in cohesive soil 

layers.

For a single pile section (HP 12x74), Figure D-56 illustrates the effects the various 

resistance determination methods have on the pile length required for a given 

factored resistance, the factored resistance available from a given pile section, and 

the potential impact of these factors on the number of piles needed to resist axial 

tension loads.

115
Figure D-55 Nominal shaft resistance versus pile penetration depth for all candidate 

pile sections at Pier 2 (design flood).

Figure D-56 Design chart of nominal and factored geotechnical resistance in axial 

tension versus pile penetration depth for HP 12x74 at the Pier 2 (design flood).

116
Figures D-57 to D-59 present the factored geotechnical resistance in axial tension 

versus penetration depth for all candidate pile sections at the design flood based on 

the resistance determination method. For all the candidate pile sections, these 

figures illustrate the effects the various resistance determination methods have on 

the pile length required for a given factored resistance, the factored resistance 

available from a given pile section, and the potential impact of these factors on the 

number of piles needed to resist axial tension loads.

Figure D-57 Factored geotechnical resistance, Rr, in axial tension based on field 

determination by static load test, φdyn=0.60 (design flood).

117
Figure D-58 Factored geotechnical resistance, Rr, in axial tension based on field 

determination by dynamic testing with signal matching, φdyn=0.50 (design flood).

Figure D-59 Factored geotechnical resistance, Rr, in axial tension based on 

determination using static analysis, φstat=0.35 or φstat=0.25 (design flood).

118
D.22.2.2 Geotechnical Resistance in Axial Tension at the Check Flood

The nominal geotechnical resistance in axial tension at the Extreme Event check 

flood must also be evaluated. In the check flood, 5 feet of channel degradation 

scour is anticipated. The channel degradation scour results in a change in vertical 

effective stress from the removal of 5 feet of channel materials. The channel 

degradation scour occurs above the bottom of the pile cap. Hence the channel 

degradation scour results in no loss of nominal resistance other than that caused by 

the reduction in overburden stress.

In addition to the channel degradation scour, 12 feet of local scour occurs during the 

check flood. This 12 feet of local scour occurring below the channel degradation 

scour results in the loss of frictional resistance on the upper 7 feet of the pile in the 

check flood Extreme Event. Hence, these two scour mechanisms require a more 

rigorous analysis of the nominal resistance beyond simple subtraction of the shaft 

resistance within the scour prism. 

The nominal geotechnical resistance in axial tension at the check flood (and 

associated factored geotechnical resistance based upon resistance determination 

method) will therefore be used to evaluate axial tension at the Extreme Event limit 

state.

Figure D-60 presents the nominal shaft resistance versus penetration depth for all 

the candidate pile sections. As outlined in Section 7.2.3.2.1 of Chapter 7, the 

factored uplift resistance for a single pile is the shaft resistance multiplied by the 

appropriate field determination resistance factor, φup. Figure D-61 presents a design 

chart of the nominal shaft resistance, Rs, and the factored geotechnical resistance, 

Rr, in axial tension versus pile penetration depth for the HP 12x74 H-pile section. A 

resistance factor of 0.60 is used when the uplift resistance is determined by a static 

load test, 0.50 when determined by a dynamic test with signal matching, 0.35 when 

determined by the Nordlund static analysis method and 0.25 when determined by 

the alpha static analysis method.

For a single pile section (HP 12x74), this figure illustrates the effects the various 

resistance determination methods have on the pile length required for a given 

factored resistance, the factored resistance available from a given pile section, and 

the potential impact of these factors on the number of piles needed to resist axial 

tension loads.

119
Figure D-60 Nominal shaft resistance versus pile penetration depth for all candidate 

pile sections at Pier 2 during Extreme Event (check flood).

Figure D-61 Design chart of nominal and factored geotechnical resistance in axial 

tension versus depth for HP 12x74 at the Pier 2 during Extreme Event (check flood).

120
Figures D-62 to D-64 present the factored geotechnical resistance in axial tension 

versus penetration depth based on the field determination method for each of the 

candidate pile sections. For all the candidate pile sections, these figures illustrate 

the effects the various resistance determination methods have on the pile length 

required for a given factored resistance, the factored resistance available from a 

given pile section, and the potential impact of these factors on the number of piles 

needed to resist axial tension loads.

Figure D-62 Factored geotechnical resistance, Rr, in axial tension based on field 

determination by static load test, φdyn=0.60.

121
Figure D-63 Factored geotechnical resistance, Rr, in axial tension based on field 

determination by dynamic testing with signal matching, φdyn=0.50.

Figure D-64 Factored geotechnical resistance, Rr, in axial tension based on 

determination using static analysis, φstat=0.35 or φstat=0.25.

122
D.22.3 Preliminary Pile Drivability Assessment

Preliminary assessments of pile drivability are now performed at this stage of the 

design. A drivability check at this time is essential to assess the constructability of 

candidate pile types and/or sections and to eliminate sections with insufficient 

drivability. Section 12.4 provides a detailed discussion of wave equation drivability 

analyses and their applications.

A candidate pile section must be capable of being driven to the penetration depth 

necessary to achieve the nominal geotechnical resistance in axial compression and 

tension, to a penetration depth necessary to satisfy lateral load demands, as well as 

a penetration depth necessary to satisfy deformation requirements. A suitably sized 

pile hammer must be capable of driving the pile to its established minimum 

penetration depth and to the nominal resistance at a reasonable blow count without 

exceeding material stress limits. As detailed in Chapter 12, the blow count should 

be between 30 and 120 blows per foot at the nominal resistance. If the pile cannot 

be driven within these requirements, a larger pile hammer, a pile section with greater 

impedance, or pile installation aids such as predrilling or jetting may be required to 

satisfy or improve drivability.

Driving stresses during pile installation should remain below the driving stress limits 

tied to pile type and material strength. For the candidate steel H-piles, compression 

driving stress limits are given by Equation 8-33. As per ASTM A-572 requirements, 

new steel H-piles are rolled with a minimum yield stress of 50 ksi. 

The driving stress limit, σdd , for candidate pile sections is then calculated as follows:

σdd = φφdd �0.9 FFyy� [Eq. 8-33]

Where: φdd = resistance factor, 1.0 for steel piles.

FFyy = yield stress, 50 ksi.

Therefore, the driving stress limit, σdd , is 45 ksi.

σσdd = (1.0)�0.9 (50 kk kk)� = 45 kk kk

Drivability analyses were performed for all five candidate pile sections. Since the 

specific pile hammer is often unknown at this point in the design, a reasonably sized, 

commonly available single acting diesel hammer was chosen for each of the 

candidate pile sections. As noted in Section 15.19, a hammer having a ram weight 

123
of 1 to 2% of the larger of the required nominal resistance or required nominal 

driving resistance often provides a reasonable initial estimate of hammer size for 

wave equation analysis. Table D-54 summarizes the factored structural resistance 

in axial compression, Pr, and corresponding minimum and maximum nominal driving 

resistance associated with full section utilization and the full range of field 

determination methods resistance factors (static load test and dynamic testing 

(φdyn=0.80), and FHWA modified Gates dynamic formula (φdyn=0.40)). Given that full 

utilization of the structural section is uncommon, a reasonable initial estimate of the 

hammer size for a wave equation drivability analysis is 1% of the minimum Rndr. 

Driving stress limits would likely be exceeded by choosing a significantly larger pile 

hammer. For each pile hammer, the wave equation default values were used for the 

helmet weight, hammer cushion materials, and the cushion material properties.

Table D-54 Summary of Pile Hammers Used in Drivability Analyses

Pile Section Pile 

Cross 

Sectional 

Area 

(in2)

Factored 

Structural 

Resistance, 

Pr

(kips)

Minimum 

Rndr

φdyn=0.80

(kips)

Maximum

Rndr

φdyn=0.40

(kips)

Ram 

Weight 

1% of Min 

Rndr

(%)

Diesel 

Model

Ram 

Weight 

(kips)

Rated 

Energy 

(ft-kips)

HP 10x42 12.4 309 386 773 3.86 D25-52 5.51 62.0

HP 12x53 15.5 383 478 958 4.78 D30-52 6.62 74.4

HP 12x74 21.8 544 680 1360 6.80 D36-52 7.94 89.3

HP 14x89 26.1 652 815 1630 8.15 D46-32 10.14 114.1

HP 14x117 34.4 860 1075 2150 10.07 D50-52 11.03 124.0

For the soil resistance model, the output from DrivenPiles was converted to unit 

shaft resistance and unit toe resistance values and then input into the wave equation 

program. Similar soil resistances are thereby calculated versus depth by both the 

static analysis and wave equation analysis programs.

The dynamic soil properties for each soil layer were chosen in accordance with wave 

equation program recommendations. Selection of soil quake and damping 

parameters is discussed in Section 12.6.7. Pile driving at Pier 2 will commence at 

the bottom of pile cap excavation of Elevation 270 feet. Therefore dynamic soil 

properties for Layer 1 are not required for the preliminary drivability analyses. For 

the Pier 2 soil profile, a setup up factor of 2.0 was selected for the very stiff silty clay 

comprising Layer 3, while no setup is expected in the extremely dense gravel of 

Layer 2 or the dense gravel with sand of Layer 4. Soil setup is discussed in Section 

7.2.4.2 and a summary of typical soil setup factors is provided in Table 7-16. The 

dynamic properties chosen are summarized in Table D-55.

124
Table D-55 Dynamic Soil Properties for Pier 2 Soil Profile

Soil 

Layer

Pile 

Section

Shaft 

Quake

(in)

Toe 

Quake

(in)

Shaft 

Damping

(s/ft)

Toe 

Damping

(s/ft)

Soil SetUp Factor

2 HP 10 x 42 0.10 0.08 0.05 0.15 1.0

2 HP 12 x 53 0.10 0.10 0.05 0.15 1.0

2 HP 12 x 74 0.10 0.10 0.05 0.15 1.0

2 HP 14 x 89 0.10 0.12 0.05 0.15 1.0

2 HP 14 x 117 0.10 0.12 0.05 0.15 1.0

3 HP 10 x 42 0.10 0.17 0.20 0.15 2.0

3 HP 12 x 53 0.10 0.20 0.20 0.15 2.0

3 HP 12 x 74 0.10 0.20 0.20 0.15 2.0

3 HP 14 x 89 0.10 0.23 0.20 0.15 2.0

3 HP 14 x 117 0.10 0.23 0.20 0.15 2.0

4 HP 10 x 42 0.10 0.08 0.05 0.15 1.0

4 HP 12 x 53 0.10 0.10 0.05 0.15 1.0

4 HP 12 x 74 0.10 0.10 0.05 0.15 1.0

4 HP 14 x 89 0.10 0.12 0.05 0.15 1.0

4 HP 14 x 117 0.10 0.12 0.05 0.15 1.0

In soils that exhibit setup, the nominal resistance will be higher than the nominal 

driving resistance. Therefore, a gain/loss factor of 0.5 was used to estimate the 

nominal driving resistance versus depth in the drivability analyses. This gain/loss 

factor was determined from the inverse of the highest soil setup factor within the soil 

model (e.g., 1 divided by 2.0 equals 0.5). A gain/loss factor of 1 would be used if it 

was desired to model the nominal resistance instead of the nominal driving 

resistance and not consider the soil strength loss during driving and any subsequent 

soil setup. Refer to Chapter 12 for more detailed discussion on the selection of 

dynamic soil properties and soil setup factors. 

The DrivenPiles program calculates the nominal driving resistance which models the 

soil strength lost during driving as well as the geotechnical nominal resistance once 

setup occurs. Figure D-65 presents the shaft resistance, toe resistance, and 

nominal driving resistance versus pile penetration depth for the HP 12x74 H-pile 

section at Pier 2. These nominal driving resistances are presented numerically in 

Table D-56. To quantify the expected soil setup at a given pile penetration depth, 

the values from Table D-56 can be compared against the nominal resistance 

previously presented in Table D-51. Figure D-66 illustrates the significant difference 

between the expected nominal driving resistance and the geotechnical nominal 

resistance after setup for the HP 12x74 candidate pile section.

125
Figure D-65 Nominal driving resistance for HP 12x74 at Pier 2.

Figure D-66 Comparison of nominal driving resistance and nominal geotechnical 

resistance in axial compression for HP 12x74 at Pier 2.

126
Table D-56 Summary of Nominal Driving Resistance Versus Pile Penetration 

Depth for HP 12x74 at Pier 2

Depth

(feet)

Nominal 

Shaft 

Resistance 

(kips)

Nominal 

Toe 

Resistance 

(kips)

Nominal 

Driving 

Resistance 

(kips)

Depth

(feet)

Nominal 

Shaft 

Resistance 

(kips)

Nominal 

Toe 

Resistance 

(kips)

Nominal 

Driving 

Resistance 

(kips)

0.01 0.0 106.5 106.5 29.99 64.3 30.5 94.7

1 1.1 123.0 124.2 30.01 64.3 30.8 95.1

2 2.4 139.7 142.1 31 66.8 30.8 97.7

3 3.9 156.4 160.2 32 69.4 30.8 100.2

4 5.5 173.1 178.5 33 71.9 30.8 102.8

4.99 7.2 189.6 196.8 34 74.5 30.8 105.3

5.01 7.3 189.9 197.2 34.99 77.0 30.8 107.8

6 9.2 206.4 215.6 35.01 77.1 31.4 108.4

7 11.3 223.1 234.4 36 79.6 31.4 111.0

8 13.5 239.8 253.3 37 82.1 31.4 113.5

9 16.0 256.5 272.4 38 84.7 31.4 116.1

9.99 18.5 273.0 291.5 39 87.2 31.4 118.6

10.01 18.6 28.6 47.2 39.99 89.8 31.4 121.1

11 20.5 28.6 49.1 40.01 89.9 251.3 341.2

12 22.5 28.6 51.1 41 97.3 256.4 353.7

13 24.5 28.6 53.1 42 104.9 261.5 366.4

14 26.6 28.6 55.2 43 112.7 266.6 379.4

14.99 28.8 28.6 57.4 44 120.7 271.7 392.4

15.01 28.8 29.6 58.4 45 128.8 275.4 404.2

16 30.9 29.6 60.5 46 137.1 275.4 412.4

17 33.0 29.6 62.6 47 145.5 275.4 420.8

18 35.2 29.6 64.8 48 154.0 275.4 429.4

19 37.5 29.6 67.1 49 162.7 275.4 438.1

19.99 39.8 29.6 69.4 50 171.6 275.4 446.9

20.01 39.8 30.0 69.8 51 180.6 275.4 455.9

21 42.0 30.0 72.0 52 189.7 275.4 465.1

22 44.3 30.0 74.3 53 199.1 275.4 474.4

23 46.7 30.0 76.7 54 208.5 275.4 483.9

24 49.1 30.0 79.1 55 218.1 275.4 493.5

24.99 51.6 30.0 81.6 56 227.9 275.4 503.2

25.01 51.7 30.5 82.1 57 237.8 275.4 513.2

26 54.0 30.5 84.5 58 247.9 275.4 523.2

27 56.5 30.5 86.9 59 258.1 275.4 533.4

28 59.0 30.5 89.5 59.99 268.4 275.4 543.7

29 61.6 30.5 92.1 60.01 268.5 1042.6 1311.1

Graphical outputs of the preliminary drivability analyses are shown in Figure D-67. 

The nominal driving resistance, the blow count or pile penetration resistance, and 

the compression driving stress are presented versus pile penetration depth for each 

127
of the five candidate pile sections. As previously noted, the recommended blow 

count limit is 120 blows per foot (10 blows per inch), and the recommended driving 

stress limit is 45 ksi. A circular reference marker is indicated on the blow count 

versus depth plot highlighting the depth where the blow count first exceeds 120 

blows per foot. This marker is also shown at the same depth on the nominal driving 

resistance versus depth plot indicating the nominal driving resistance achieved when 

practical refusal driving conditions are encountered with the selected hammer in the 

modeled driving conditions. Similarly, the marker is shown at the same depth on the 

compression driving stress versus depth plot indicating the compression driving 

stress when practical refusal driving conditions are encountered.

Figure D-67 Preliminary drivability results at Pier 2.

For all of the candidate pile sections and selected pile hammers, the blow count was 

60 blows per foot or less before encountering hard rock at a penetration depth of 60 

feet. Once bedrock was encountered, the blow count quickly transitioned to 120 

blows per foot. Compression driving stresses for all candidate pile sections were 

also less than the 45 ksi driving stress limit prior to reaching bedrock. 

If the final design requires piles be driven to hard bedrock, the driving criteria should 

be established to control compression stresses and prevent pile toe damage once 

hard rock is encountered (e.g., limit the number of blows at refusal driving 

128
conditions). A summary of the preliminary drivability results is presented in Table 

D-57. The anticipated nominal resistance in this table is the expected resistance 

after soil setup that can be mobilized by the driving system at 10 blows per inch. For 

piles terminated on hard rock, a higher geotechnical nominal resistance, up to the 

structural resistance of the pile is actually available. 

Once the estimated and/or minimum pile toe elevations are determined in Block 12 

through Block 15 of the design process, the drivability results in Figure D-67 and 

Table D-57 should be reviewed to confirm that the candidate pile section can be 

driven to the estimated or required pile penetration depth, at reasonable blow 

counts, and with driving stress limits.

Table D-57 Summary of Preliminary Drivability Results at Pier 2

Pile

Section

Pile

Hammer

Fuel

Setting

Pile 

Penetration 

Depth at 

Practical 

Refusal 

Limit

(feet)

Nominal 

Driving 

Resistance 

at Practical 

Refusal 

Limit

(kips)

Anticipated 

Nominal 

Resistance 

at Depth of 

Practical 

Refusal

(kips)

Penetration 

Depth 

Exceeding 

Compression 

Driving 

Stress Limit 

(feet)

Maximum 

Compression 

Driving 

Stress

(ksi)

HP 10x42 D25-52 4 60 440 500 60 46.4

HP 12x53 D30-52 4 60 540 610 60 44.9

HP 12x74 D36-52 4 60 700 770 60 42.6

HP 14x89 D46-52 4 60 870 950 60 43.2

HP 14x117 D50-52 4 60 1045 1125 60 41.8

D.23Block 11: Pier 2 – Estimate Preliminary Number of Piles, Preliminary Pile 

Group Size, and Resolve Individual Pile Loads for All Limit States

The structural engineer has provided the anticipated loads for the controlling limit 

states at Pier 2. These limit state loads are restated in Table D-58. The Strength V 

limit state loads are used to evaluate geotechnical resistance in axial compression 

and tension, as well as for lateral loading. Although loads at Service I limit state 

were provided by the structural engineer, live loads should be removed when 

evaluating vertical deformation. Moreover, the Service I without live load includes 

only unfactored permanent loads such as the superstructure and wearing surface, 

pile cap and stem, utilities and vertical earth pressure among others. The Extreme 

Event II limit state must also be evaluated at this substructure location to consider 

effects of the check flood and associated loads.

129
Table D-58 Limit State Loads on Pier 2

Limit State Q

(kips)

Vux

(kips)

Vuy

(kips)

Mux

(k-ft)

Muy

(k-ft)

Strength V 3456 18 109 -2981 3982

Service I 2682 15 100 -2749 2997

Service I, without LL 2172 0 0 0 0

Extreme Event II 3023 30 23 -797 1273

Pier construction will include a cofferdam and excavation of the existing 

geomaterials. The Agency practice for pier construction in a river is to use a 

substructure design with the smallest footprint. A minimum center to center pile 

spacing of 3 pile diameters is typical. Three potential pile group configurations for 

Pier 2 are under consideration. These are identified as Group Configurations 4, 5, 

and 6, respectively in Table D-59. Each group configuration has 5 rows of piles in 

the transverse direction. In the longitudinal direction, Group Configuration 4 has 3 

rows of piles while Group Configurations 5 and 6 have 4 rows of piles. Furthermore, 

the distance from the center of any exterior pile to the pile cap edge must be at least 

1.25 feet in both the transverse (x) and longitudinal (y) direction. 

Table D-59 Potential Pile Group Configurations

Group 

Configuration

Piles 

per 

Row 

Y dir

Piles 

per 

Row

X dir

Total 

Number 

of Piles

Sbx*

(feet)

Total Footing 

Length

(feet)

Sby*

(feet)

Total 

Footing 

Width

(feet)

4 3 5 15 3.0 14.5 3.0 8.5

5 4 5 20 3.0 14.5 3.0 11.5

6 4 5 20 5.0 22.5 4.0 14.5

* Sbx and Sby are illustrated in Figure D-68.

The following example calculation considers Group Configuration 6 and all 

applicable loads. For this alternative, 5 piles per row in the X direction and 4 piles 

per row in the Y direction are proposed. Thus the transverse pile spacing, Sbx, is 3’-

0” and the total footing length is 14’-6”. The longitudinal pile spacing, Sby, is 3’-0” 

and the total footing width is 11’-6”. Figure D-68 shows the layout for the Group 

Configuration 6 pile cap. 

130
Figure D-68 Group Configuration 6 pile cap plan view.

For the trial pile group configuration in Figure D-68, loads for each pile in the group 

were determined using the limit state loads presented in Table D-58. The lateral 

load per pile in each direction was calculated by dividing the factored horizontal load 

Vux or Vuy in Table D-58 by the number of piles, while the axial load per pile was 

calculated using Equation 8-79. For example, in Group Configuration 6, the lateral 

load per pile in the longitudinal direction is calculated by dividing 109 kips by 20 piles 

(i.e., 5.5 kips per pile). For the axial load per pile, an example calculation for the 

load applied to pile 5 at the Strength V limit state is presented below. Table D-60

shows the full calculation for all piles Group Configuration 6. The maximum 

individual pile load (on pile number 5) is 257 kips.

Puu = Puuuu+WWcc+WWss

nn + MMuuuuyy

∑ yy2 +

MMuuuu

∑ 2 [Eq. 8-79]

In this case, the factored limit state load, Q, replaces the factored axial load from 

superstructure/substructure acting upon pile cap, Puu , estimated weight of pile cap, 

WWcc and estimated weight of soil above pile cap, WWss as follows:

Q = Puu + WWcc + WWss

131
Calculate the individual pile axial load on pile number 5.

xx = distance along x-axis from the center of the column to each pile 

center, 10 feet.

= distance along y-axis from the center of the column to each pile 

center -6 feet.

∑ xx2 = sum of square distance along x-axis from the center of the column to 

each pile center, 1000 ft2.

∑ 2 = sum of square distance along y-axis from the center of the column to 

each pile center, 400 ft2

.

= total number of piles, 20 piles (Group Configuration 6, Table D-59).

Q = factored axial load at Strength V limit state, 3456 kips (Table D-58).

MMuu = factored moment about the x axis acting on the pile cap, -2,981 kip-ft. 

MMuu = factored moment about the y axis acting on the pile cap, 3,982 kip-ft.

Puu = Q

nn + MMuuuuyy

∑ yy2 +

MMuuuu

∑ 2 [Eq. 8-79]

Puu = (3,456 kips)

(20 pp ) + (−2,981 −ff )∗(−6 ff )

(400 ff 2 ) + (3,982 −ff )∗(10 ff )(1000 ff 2 )

Puu = 257 kkkk

132
Table D-60 Calculation of Individual Pile Load

Pile 

Number

x

(feet)

y

(feet)

x2

(ft2)

y2

(ft2)

Q

(kips)

MMuu

∑ 2

(kips)

MMuu xx

∑ xx2

(kips)

Puu

(kips)

1 -10.0 -6.0 100.0 36.0 172.8 44.7 -39.8 177.7

2 -5.0 -6.0 25.0 36.0 172.8 44.7 -19.9 197.6

3 0.0 -6.0 0.0 36.0 172.8 44.7 0.0 217.5

4 5.0 -6.0 25.0 36.0 172.8 44.7 19.9 237.4

5 10.0 -6.0 100.0 36.0 172.8 44.7 39.8 257.3

6 -10.0 -2.0 100.0 4.0 172.8 14.9 -39.8 147.9

7 -5.0 -2.0 25.0 4.0 172.8 14.9 -19.9 167.8

8 0.0 -2.0 0.0 4.0 172.8 14.9 0.0 187.7

9 5.0 -2.0 25.0 4.0 172.8 14.9 19.9 207.6

10 10.0 -2.0 100.0 4.0 172.8 14.9 39.8 227.5

11 -10.0 2.0 100.0 4.0 172.8 -14.9 -39.8 118.1

12 -5.0 2.0 25.0 4.0 172.8 -14.9 -19.9 138.0

13 0.0 2.0 0.0 4.0 172.8 -14.9 0.0 157.9

14 5.0 2.0 25.0 4.0 172.8 -14.9 19.9 177.8

15 10.0 2.0 100.0 4.0 172.8 -14.9 39.8 197.7

16 -10.0 6.0 100.0 36.0 172.8 -44.7 -39.8 88.3

17 -5.0 6.0 25.0 36.0 172.8 -44.7 -19.9 108.2

18 0.0 6.0 0.0 36.0 172.8 -44.7 0.0 128.1

19 5.0 6.0 25.0 36.0 172.8 -44.7 19.9 148.0

20 10.0 6.0 100.0 36.0 172.8 -44.7 39.8 167.9

Sum - - 1000.0 400.0 - - - 3456.0

The process outlined above was used to determine the individual pile lateral and 

axial load for the remaining limit state loads presented in Table D-58. The maximum 

individual pile axial load is carried forward in the analysis for each group 

configuration. Based upon the applied loads and group configurations selected, no 

pile is put into axial tension. Therefore, only axial compression and lateral loads are 

required for the foundation design at Pier 2. Table D-61 presents the maximum 

factored axial compression load per pile based upon the number of piles in each 

group configuration. Table D-62 presents the maximum factored lateral load per pile 

based upon the number of piles in each group configuration. 

133
Table D-61 Factored Axial Compression Load Per Pile for Alternative Pile Group 

Configurations

Group 

Configuration

Strength V,

Q

(kips)

Service I, without LL 

Q

(kips)

Extreme Event II 

Q

(kips)

4 418 145 256

5 299 109 188

6 257 109 176

Table D-62 Factored Lateral Load Per Pile for Alternative Pile Group 

Configurations

Group 

Configuration

Strength V, 

Vuy

(kips)

Strength V, 

Vux

(kips)

Extreme Event II 

Vuy

(kips)

Extreme Event II 

Vux

(kips)

4 8 2 2 2

5 6 1 2 2

6 6 1 2 2

D.24Block 12: Pier 2 – Estimate Pile Penetration Depth for Maximum Axial 

Compression Loads. Check Group Efficiency in Axial Compression

The estimated minimum pile penetration depth necessary to obtain the factored 

geotechnical resistance equal to the maximum factored load per pile should now be 

determined. Note that the factored geotechnical resistance in axial compression and 

the resulting pile penetration depth is dependent upon the resistance determination 

method. Therefore, the influence of the field resistance determination method on the 

design is evaluated at this point in the design process. Thus, some resistance 

determination methods may be eliminated from further design consideration.

At Pier 2, drivability and potential damage when driving through the extremely dense 

gravel deposit is a concern. In addition, piles will also likely be driven into the gravel 

layer with cobbles encountered 40 feet below footing grade. This layer also 

presents a concern for pile damage. Therefore, it is determined that the factored 

geotechnical resistance will be substantiated by dynamic testing 2% of the piles. 

Figure D-45 illustrates the factored geotechnical resistance versus penetration depth 

for the 5 candidate pile sections based on this resistance determination method. 

From this plot, the estimated penetration depth for a factored geotechnical 

resistance of 257 kips in axial compression for the Group Configuration 6 ranges 

from 40 feet for the HP 14x117 to 57 feet for the HP 10x42. Results of this 

comparison for each pile section and group configuration are listed in Table D-63.

134
Table D-63 Estimated Pile Penetration Depths for the Factored Geotechnical 

Resistance in Axial Compression at the Strength V Limit State

Group 

Configuration

Factored 

Load per 

Pile

(kips)

HP 

10x42 

(feet)

HP 

12x53 

(feet)

HP 

12x74 

(feet)

HP 

14x89 

(feet)

HP 

14x117 

(feet)

4 418 60 60 60 50 47

5 299 60 46 44 40 40

6 257 57 42 40 40 40

The Extreme Event II factored axial compression loads shown in Table D-61 were 

also used to estimate the pile penetration depth required to achieve the factored 

geotechnical resistance in axial compression. In this case, the nominal geotechnical 

resistance present in the check flood was used. Figure D-52 illustrates the factored 

geotechnical resistance versus penetration depth at the check flood for the 5 

candidate pile sections based on determination testing by dynamic testing 2% of the 

piles. From this plot, the estimated penetration depth for the maximum factored 

geotechnical resistance of 176 kips in axial compression associated with Group 

Configuration 6 is 40 feet for all candidate pile sections except for the HP 10x42 

section which requires approximately 57 feet. The 40 foot penetration depth is 

upper contact of the dense gravel layer. Results of this comparison for each pile 

section and group configuration are summarized in Table D-64. 

Table D-64 Estimated Pile Penetration Depths for the Factored Geotechnical 

Resistance in Axial Compression at the Extreme Event II Limit State

Group 

Configuration

Factored 

Load per 

Pile

(kips)

HP 

10x42 

(feet)

HP 

12x53 

(feet)

HP 

12x74 

(feet)

HP 

14x89 

(feet)

HP 

14x117 

(feet)

4 256 57 42 41 40 40

5 188 41 40 40 40 40

6 176 40 40 40 40 40

Based on the factored loads and estimated factored geotechnical resistances at Pier 

2, the estimated pile penetration depth considering Strength V loads require the 

deepest pile penetration depth. Therefore, the estimated pile penetration depths 

presented in Table D-63 will be carried forward in the design.

135
Although a mixed soil profile appears at Pier 2, the stratum providing the majority of 

nominal geotechnical resistance is cohesionless soil, and will therefore be used as 

the controlling stratum for group efficiency. Per Section 7.2.2.1, the nominal 

geotechnical resistance of a pile group in cohesionless soil can be taken as the sum 

of the individual pile nominal geotechnical resistances. In a similar manner, the 

factored geotechnical resistance of the pile group in cohesionless soil is taken as the 

sum of the individual pile factored geotechnical resistances. This is recommended 

so long as 1) the bearing layer is not underlain by weak soil layers, 2) the piles are 

not installed at a pile spacing of less than 3 times the pile diameter, and 3) no 

special installation procedures are anticipated such as jetting or predrilling. Since all 

these conditions are met at Pier 2, the factored group resistances are satisfactory. 

D.25Block 13: Pier 2 – Establish Minimum Pile Penetration Depth for Axial 

Tension Loads. If Conditions Warrant, Modify Design and Return to Block 

10

For the limit state loads identified in Table D-58 in combination with the group 

configurations at Pier 2 listed in Table D-59, no pile within any group configuration is 

loaded in tension. Therefore, the tension or uplift resistance is not evaluated, and 

there is no minimum pile penetration depth required for axial tension loads at Pier 2.

D.26Block 14: Pier 2 – Establish Minimum Pile Penetration Depth for Lateral 

Loads. Determine p-y Models, Required Geomaterial Parameters, and 

Perform Lateral Load Analysis. If Conditions Warrant, Modify Design and 

Return to Block 10

Next, lateral analyses are performed to establish the required minimum pile 

penetration depth for lateral loading and to evaluate pile deflection and structural 

resistance for the applied limit state loads. No minimum penetration depth was 

required to satisfy the nominal geotechnical resistance requirements in axial tension 

in Block 13. A minimum pile penetration depth may be required for lateral loading 

based on the combination of factored lateral loads and structural resistances, or 

deflection limits. Excessive deflections and moments develop at relatively short pile 

lengths, where a depth to fixity is not achieved. Furthermore, the structural 

resistance of pile sections must be evaluated based upon the axial, lateral and 

moment loads. Factored structural resistances were presented in Table D-47 while 

a lateral deformation limit of 1 inch was established as a global performance 

requirement in Block 1 and confirmed in Block 4 as the design progressed. 

136
As discussed in Section 7.3.7.6, p-multipliers are applied to the p-y curves to model 

pile group behavior. The p-multipliers depend on the center to center pile spacing 

within the pile group. For Group Configurations 6 at the Pier 2, the pile spacing in 

the longitudinal direction is 4 feet. Therefore, per Section 7.3.7.6 and AASHTO 

(2014) design specifications, interpolation was used to determine p-multipliers for a 

pile spacing of 4b. In this case, the front row p-multiplier is 0.90, the second row is 

0.625, and the third and fourth rows are 0.5. For the same group configuration, piles 

in the transverse direction are spaced at 5 feet. Therefore p-multipliers for a pile 

spacing of 5b were used. In this case, the front row p-multiplier is 1.0, the second 

row is 0.85 and the third and fourth rows are 0.7. 

Soil properties utilized for the lateral analysis are given in Figure D-39. Cyclic 

loading was performed for all rows using LPILE’s Load Type 2 option, which uses 

shear and slope to model a fixed head condition. Considering loading conditions at 

this pier, lateral analyses in the longitudinal (y-direction) were performed about the 

pile section’s strong axis. Figure D-68 shows the pile orientation within the trial pile 

cap design.

The following example is presented for the HP 12x74 pile section using a range of 

factored axial and lateral loads for Group Configuration 6. The Strength V limit state 

loads are applied in combination with the geotechnical resistance at the design 

flood, (i.e., 5 feet of scour below the pile head) Tables D-65 to D-67 provide LPILE 

output summaries for the longitudinal direction considering a pile penetration (from 

the bottom of pile cap) of 20 feet. Due to scour conditions, this is modeled as 15 

feet of embedded pile length with 5 feet of pile stickup. 

Table D-65 LPILE Summary Output at Pile Head for Front Row, pm=0.90

Load 

Case

Load 

Type 

No.

Pile-Head 

Condition 1 

V (kips)

Pile-Head 

Condition 2 

S (rad)

Axial 

Load

(kips)

Pile-Head 

Deflection

(inches)

Maximum 

Moment in 

Pile 

(kip-ft)

Maximum 

Shear in 

Pile

(kips)

Pile-Head 

Rotation

(radians)

1 2 0 0 257 0.000 0.0 0.0 0

2 2 1 0 257 0.011 -5.4 -1.3 0

3 2 2 0 257 0.023 -10.8 -2.4 0

4 2 3 0 257 0.035 -16.3 -3.3 0

5 2 4 0 257 0.048 -21.8 -4.1 0

6 2 5 0 257 0.060 -27.3 5.0 0

7 2 6 0 257 0.073 -32.8 6.0 0

8 2 7 0 257 0.086 -38.3 7.0 0

9 2 8 0 257 0.099 -43.8 8.0 0

10 2 9 0 257 0.112 -49.3 9.0 0

137
Table D-66 LPILE Summary Output at Pile Head for Second Row, pm=0.625

Load 

Case

Load 

Type 

No.

Pile-Head 

Condition 1 

V (kips)

Pile-Head 

Condition 2 

S (rad)

Axial 

Load

(kips)

Pile-Head 

Deflection

(inches)

Maximum 

Moment in 

Pile 

(kip-ft)

Maximum 

Shear in 

Pile

(kips)

Pile-Head 

Rotation

(radians)

1 2 0 0 257 0.000 0.0 0.0 0

2 2 1 0 257 0.012 -5.6 -1.2 0

3 2 2 0 257 0.026 -11.2 -2.2 0

4 2 3 0 257 0.040 -16.9 3.0 0

5 2 4 0 257 0.054 -22.7 4.0 0

6 2 5 0 257 0.069 -28.4 5.0 0

7 2 6 0 257 0.083 -34.2 6.0 0

8 2 7 0 257 0.098 -40.0 7.0 0

9 2 8 0 257 0.113 -45.7 8.0 0

10 2 9 0 257 0.128 -51.5 9.0 0

Table D-67 LPILE Summary Output at Pile Head for Third and Fourth Row, pm=0.50

Load 

Case

Load 

Type 

No.

Pile-Head 

Condition 1 

V (kips)

Pile-Head 

Condition 2 

S (rad)

Axial 

Load

(kips)

Pile-Head 

Deflection

(inches)

Maximum 

Moment in 

Pile 

(kip-ft)

Maximum 

Shear in 

Pile

(kips)

Pile-Head 

Rotation

(radians)

1 2 0 0 257 0.000 0.0 0.0 0

2 2 1 0 257 0.013 -5.7 -1.2 0

3 2 2 0 257 0.028 -11.5 -2.1 0

4 2 3 0 257 0.043 -17.4 3.0 0

5 2 4 0 257 0.059 -23.3 4.0 0

6 2 5 0 257 0.075 -29.2 5.0 0

7 2 6 0 257 0.091 -35.1 6.0 0

8 2 7 0 257 0.107 -41.1 7.0 0

9 2 8 0 257 0.124 -47.0 8.0 0

10 2 9 0 257 0.140 -52.9 9.0 0

From LPILE’s deflection results for individual rows, pile group deflection can be 

estimated. Factored load versus deflection for each row is plotted along with the 

average load for a given deflection as shown in Figure D-69. A discussion of this 

procedure is outlined in Section 7.3.7.6. 

The rigid cap method assumes piles move together, and therefore experience the 

same shear and lateral load. Accordingly, at the resulting factored lateral load per 

pile, Vuy, of 6 kips (Table D-62), the estimated lateral group deflection at the pile 

head is determined as 0.085 inches. This lateral deflection is less than the 1 inch 

tolerance based upon project specific requirements.

138
Figure D-69 Factored load versus deflection in longitudinal direction 

for HP 12x74 at Pier 2.

In addition to the lateral deflection limit, stresses from the resulting bending moment 

and shear must be evaluated to check that the pile section does not fail structurally. 

Using the LPILE tabular results, Figure D-70 plots the front row bending moment 

versus depth for a deflection of 0.085 inches.

Figure D-71 plots the maximum bending moment versus pile head deflection for all 

rows, however only the maximum bending moment for the front row is used as a 

“worst case” inspection of the structural resistance in combined axial compression 

and flexure. As illustrated in Figure D-71, at the estimated pile head deflection of 

0.085 inches, the maximum bending moment, Muy, is 38 kip-ft. 

139
Figure D-70 Front row bending moment versus depth in longitudinal direction.

Figure D-71 Bending moment versus deflection in longitudinal direction 

for HP 12x74 at Pier 2.

140
The lateral analysis was also performed for the transverse direction with the 

Strength V limit state loads and the geotechnical resistance at the design flood, (i.e., 

5 feet of scour below the pile head). Tables D-68 to D-70 provide LPILE output 

summaries for the transverse direction considering a pile penetration (from the 

bottom of footing) of 20 feet. Due to scour in the design flood, this is modeled as 15 

feet of embedded pile length with 5 feet of pile stickup.

Table D-68 LPILE Summary Output at Pile Head for Front Row, pm=1.0

Load 

Case

Load 

Type 

No.

Pile-Head 

Condition 1 

V (kips)

Pile-Head 

Condition 2 

S (rad)

Axial 

Load

(kips)

Pile-Head 

Deflection

(inches)

Maximum 

Moment in 

Pile 

(kip-ft)

Maximum 

Shear in 

Pile

(kips)

Pile-Head 

Rotation

(radians)

1 2 0.00 0 257 0.000 0.0 0.0 0

2 2 0.25 0 257 0.003 -1.3 -0.3 0

3 2 0.50 0 257 0.005 -2.6 -0.7 0

4 2 0.75 0 257 0.008 -4.0 -1.0 0

5 2 1.00 0 257 0.011 -5.3 -1.3 0

6 2 1.25 0 257 0.014 -6.7 -1.6 0

7 2 1.50 0 257 0.016 -8.0 -1.9 0

8 2 1.75 0 257 0.019 -9.3 -2.2 0

9 2 1.00 0 257 0.011 -5.3 -1.3 0

Table D-69 LPILE Summary Output at Pile Head for Second Row, pm=0.85

Load 

Case

Load 

Type 

No.

Pile-Head 

Condition 1 

V (kips)

Pile-Head 

Condition 2 

S (rad)

Axial 

Load

(kips)

Pile-Head 

Deflection

(inches)

Maximum 

Moment in 

Pile 

(kip-ft)

Maximum 

Shear in 

Pile

(kips)

Pile-Head 

Rotation

(radians)

1 2 0.00 0 0 0.000 0.0 0.0 0

2 2 0.25 0 0 0.003 -1.3 -0.3 0

3 2 0.50 0 0 0.006 -2.7 -0.7 0

4 2 0.75 0 0 0.008 -4.0 -1.0 0

5 2 1.00 0 0 0.011 -5.4 -1.3 0

6 2 1.25 0 0 0.014 -6.8 -1.6 0

7 2 1.50 0 0 0.017 -8.1 -1.8 0

8 2 1.75 0 0 0.020 -9.5 -2.1 0

9 2 1.00 0 0 0.011 -5.4 -1.3 0

141
Table D-70 LPILE Summary Output at Pile Head for Third and Fourth and Fifth 

Rows, pm=0.70

Load 

Case

Load 

Type 

No.

Pile-Head 

Condition 1 

V (kips)

Pile-Head 

Condition 2 

S (rad)

Axial 

Load

(kips)

Pile-Head 

Deflection

(inches)

Maximum 

Moment in 

Pile 

(kip-ft)

Maximum 

Shear in 

Pile

(kips)

Pile-Head 

Rotation

(radians)

1 2 0.00 0 0 0.000 0.0 0.0 0

2 2 0.25 0 0 0.003 -1.4 -0.3 0

3 2 0.50 0 0 0.006 -2.7 -0.7 0

4 2 0.75 0 0 0.009 -4.1 -1.0 0

5 2 1.00 0 0 0.012 -5.5 -1.3 0

6 2 1.25 0 0 0.015 -6.9 -1.5 0

7 2 1.50 0 0 0.018 -8.3 -1.8 0

8 2 1.75 0 0 0.022 -9.7 -2.0 0

9 2 1.00 0 0 0.012 -5.5 -1.3 0

From LPILE’s deflection results for individual rows, pile group deflection can be 

estimated. Factored load versus deflection for each row is plotted along with the 

average load for a given deflection as shown in Figure D-72. A discussion of this 

procedure is outlined in Section 7.3.7.6. 

The rigid cap method once again assumes piles move together, and therefore 

experience the same shear and lateral load. Accordingly, at the resulting factored 

lateral load per pile, Vuy, of 1 kip (Table D-62), the estimated lateral group deflection 

at the pile head is determined as 0.011 inches. This lateral deflection is less than 

the 1 inch tolerance based upon project specific requirements.

In addition to the lateral deflection limit, stresses from the resulting bending moment 

and shear must be evaluated to check that the pile section does not fail structurally. 

Using the LPILE tabular results, Figure D-73 plots the front row bending moment 

versus depth for deflection of 0.011 inches.

Figure D-74 plots the maximum bending moment versus pile head deflection for all 

rows, however only the maximum bending moment for the front row is used as a 

“worst case” inspection of the structural resistance in combined axial compression 

and flexure. As illustrated is Figure D-74, at the estimated pile head deflection of 

0.011 inches, the maximum bending moment, Muy, is 5.6 kip-ft. 

142
Figure D-72 Factored load versus deflection in transverse direction for HP 12x74 at 

Pier 2.

Figure D-73 Front row bending moment versus depth in transverse direction.

143
Figure D-74 Bending moment versus deflection in transverse direction

for HP 12x74 at Pier 2.

The interaction shown in Equation 8-58 must be satisfied for the factored axial 

compression load and moment in the pile. Using results of the lateral analysis, the 

factored structural resistance was evaluated at the pile head using the factored axial 

compression load and maximum bending moment (determined using factored 

loads). The factored structural resistances were determined as shown in Table 

D-47.

Equation 8-58 must be satisfied for the pile section to be acceptable.

PPuu = factored axial load, 257 kips (Table D-61).

PPrr = factored axial resistance, 730 kips (Table D-47).

Muu = factored moment about x-axis, 5.6 kip-ft (Figure D-74).

Mrrrr = factored flexural resistance about x-axis, 118 kip-ft (Table D-47).

Muu = factored moment about y-axis, 38 kip-ft (Figure D-71).

Mrr = factored flexural resistance about y-axis, 433 kip-ft (TableD-47).

Puu

Prr

+ 8.0

9.0 � Muuuu

Mrr

+

Muuuu

Mrr

� ≤ 1.0 [Eq. 8-58]

144
(257 )

(730 )

+ 8.0

9.0 � (5.6 −ff )(118 −ff ) + (38 −ff )(433 −ff )

� ≤ 1.0

0.47 ≤ 1.0

The maximum shear from factored lateral loading was then compared to the factored 

shear resistance from Table D-47. The maximum shear within the pile occurred at 

the pile head. Based on the factored loads, the factored shear resistance is 

acceptable.

VVrr = factored shear resistance, 214 kips (HP 12x74, Table D-47).

VVuu = factored shear load, 6 kips (Group Configuration 6, Table D-62).

VVuu < VVrr

6 kkkk < 214 kkkk

The lateral analysis was also performed for each alternative pile section, and 

subsequently the deflection and factored structural resistance was evaluated 

considering the factored loads for group configurations shown in Table D-62. Pile 

head deflection must be limited to 1 inch, and based upon the applied loads and pile 

section, the factored structural resistance of the pile must also satisfy the structural 

resistance interaction equation presented as Equation 8-58. Furthermore, the pile 

should be embedded such that fixity is established, and for this case, the second 

crossing of the moment versus depth curve with the y-axis (i.e., moment is 0 kip-ft) is 

assumed as fixity for this design example. A review of Figure D-70 shows this depth 

to be approximately 20 feet. Pile sections satisfying these criteria were deemed 

acceptable, and furthermore as presented in Table D-71, a minimum required pile 

penetration depth was established based on lateral loads at the Strength V limit 

state. The minimum penetration depth is identified as “- - -“ for candidate pile 

sections not meeting the lateral deformation or structural resistance requirements.

Table D-71 Minimum Pile Penetration Depth Required for Strength V Lateral Loads 

at Pier 2

Group 

Configuration

HP 10x42

(feet)

HP 12x53 

(feet)

HP 12x74

(feet)

HP 14x89

(feet)

HP 14x117

(feet)

4 - - - - - - 30 25 25

5 25 25 25 25 25

6 20 20 20 20 20

145
In a similar manner, the lateral analysis was repeated using the Extreme Event II 

limit state loads and the geotechnical resistance at the check flood. Although axial 

loads and lateral loads in the longitudinal direction decreased, further loss of 

geotechnical resistance from scour required an additional analysis. Table D-72

presents the minimum pile penetration depth required to satisfy lateral loading at the 

Extreme Event II limit state. As a result of reduced axial and lateral loads, the HP 

10x42 and HP 12x52 pile sections in Group Configuration 4 would be acceptable. 

For the remaining candidate pile sections and group configurations, no additional 

pile penetration was required beyond the previously identified pile penetration 

depths in Table D-71.

Table D-72 Minimum Pile Penetration Depth Required for Extreme Event II Lateral 

Loads at Pier 2

Group 

Configuration

HP 10x42

(feet)

HP 12x53 

(feet)

HP 12x74

(feet)

HP 14x89

(feet)

HP 14x117

(feet)

4 30 30 30 25 25

5 25 25 25 25 25

6 20 20 20 20 20

After evaluating lateral loads with the respective geotechnical resistance at the 

Strength and Extreme Event limit states, the established minimum pile penetration 

depth is taken as the worst case for each candidate section and group configuration. 

In this case, the more conservative depth for all candidate sections and group 

configurations is taken from the lateral loading evaluation at the Strength limit state. 

The established minimum pile penetration depth required for lateral loading is 

presented in Table D-73.

Table D-73 Established Minimum Pile Penetration Depth Required for Lateral 

Loading at Pier 2

Group 

Configuration

HP 10x42

(feet)

HP 12x53 

(feet)

HP 12x74

(feet)

HP 14x89

(feet)

HP 14x117

(feet)

4 - - - - - - 30 25 25

5 25 25 25 25 25

6 20 20 20 20 20

146
D.27Block 15: Pier 2 – Establish Pile Penetration Depths that Satisfy Tolerable 

Deformations. Estimate Group Settlement over the Minimum and 

Maximum Range of Pile Penetration Depths From Blocks 12 to 14 and 

Identify All Pile Toe Elevations Which Result in Intolerable Deformations. 

If Conditions Warrant, Modify Design and Return to Block 10

Pile group settlement at Pier 2 was estimated using two methods, the Hough (1959) 

method and the Janbu Tangent modulus method. Ideally, the settlement method 

chosen by the designer is one that has shown good correlation with observed 

results. In order to obtain the factored geotechnical resistance in axial compression, 

the piles must be driven into the dense gravel with sand layer (Soil Layer 4, Figure 

D-39). As this is a cohesionless soil, pile group settlement was first estimated using 

the Hough (1959) Method. The Hough approach is a traditional settlement 

estimation method for pile groups in cohesionless soils and one that is referenced in 

the AASHTO (2014) design specifications. However, the soil conditions across the 

bridge substructure locations are quite variable and a settlement method that could 

be used at all substructure locations was also desired. Therefore, group settlement 

was also computed with the Janbu Tangent modulus approach using an equivalent 

footing placed at the neutral plane.

Compressibility properties for the silty clay layer were determined from one 

dimensional consolidation tests which were performed on undisturbed samples 

collected near the middle of the clay layer. Table D-74 presents the void ratio, eo, 

overconsolidation ratio, OCR, compression index, Cc, and recompression index, Cr

for the silty clay layer. The OCR of the soil was used to calculate the 

preconsolidation stress, σ'p, at discrete depths.

Table D-74 Soil Properties Determined from One Dimensional Consolidation Test

Soil Layer eo OCR Cc Cr

3 0.80 2.01 0.30 0.03

The Hough (1959) method as presented in Section 7.3.5.2 was used to estimate 

group settlement. As mentioned, piles must be driven to the dense gravel layer (Soil 

Layer 4) to achieve the required factored geotechnical resistance in axial 

compression. The settlement calculations were performed using only unfactored 

permanent loads. Therefore, the loads from the Service I limit state without live load 

were used to estimate settlement (i.e., load factor of 1.0 on permanent loads). The 

average contact stress for the trial pile group was calculated using the vertical load, 

Q, and pile group area B x Z. The following calculation is performed for Group 

147
Configuration 6. Both the group width, B, and length, Z, were calculated from 

exterior pile edge to exterior pile edge.

An equivalent footing, with plan dimensions equal to those of the pile group, was 

evaluated at increasing pile penetration depths, and the resulting pile group 

settlement computed using the Hough (1959) method. The equivalent footing 

concept for piles driven to hard clay or sand through soft clay as presented in Figure 

7-46a of Chapter 7 was utilized this analysis.

The following calculation is performed for the equivalent footing located at the silty 

clay / dense gravel interface at Elevation 235.0 feet. This location is 40 feet below 

the bottom of pile cap at Elevation 275.0 feet. Figure D-75 illustrates the pile group 

and resulting stress distribution at the equivalent footing. It was also assumed that 

vertical deformation below the gravel and bedrock interface at Elevation 215.0 feet is 

negligible. For Group Configuration 6, the length of the pile group is 21 feet, while 

the width is 13 feet. These dimensions are taken from exterior pile edge to exterior 

pile edge. This example calculation is therefore only suitable for this configuration. 

The soil profile was divided into 5 foot thick layers to evaluate settlement. Tabulated 

values for this group settlement analysis are presented in Table D-75. The elevation 

shown in Table D-75 references the midpoint of each respective soil layer, while z is 

the depth below the equivalent footing to the midpoint of each respective soil layer.

Figure D-75 Equivalent footing and stress distribution toe bearing piles in hard clay 

or sand considering Group Configuration 6 dimensions at Pier 2.

148
For the Hough (1959) method, the bearing capacity index must first be determined 

using the corrected SPT (NN1) value, however a review of the design soil profile in 

Figure D-39 shows SPT (NN1)60 value as 46 for the dense gravel layer. To note, this 

value is corrected for both depth and energy. Figure D-76 presents the modified 

Hough (1959) method chart to determine the bearing capacity index from the 

respective soil layer’s (NN1) value. Because the graph will be entered with a 

corrected SPT (NN1)60 value, the x-axis scale consistent with the Safety hammer was 

used to enter the graph, while the soil type selected to determine the bearing 

capacity index was conservatively taken as the “clean, well graded fine to coarse 

sand.” Based on these two assumptions, the bearing capacity index, C’, was 

determined as 180.

Figure D-76 Hough (1959) method chart to determine bearing capacity index from 

SPT (N1) at Pier 2.

149
Considering only the unfactored permanent load, Q, calculate the vertical effective 

stress increase below the equivalent footing, ΔΔσσ′vv, at EL 235.0 feet.

Q = unfactored permanent load, 2182 kips (Service I, without LL, 

Table D-58).

BB = pile group width, 13 feet.

ZZ = pile group length, 21 feet (Group Configuration 6 only)

z = depth below equivalent footing, 2.5 feet (Elev. 232.5 feet)

 ΔΔσσ′vv = QQ

(BB+zz)+(ZZ+zz)) [Eq. 7-55]

 ΔΔσσ′vv = (2182 )

((13 ff )+(2.5 ff ))∗((21 ff )+(2.5 ff )))

 ΔΔσσ′vv = 5.96 kk

Determine the percent stress increase by comparing σσ′vo and σσ′1

σσ′vo = initial vertical effective stress at depth z below the equivalent footing, 

2.92 ksf.

σσ′1 = new vertical effective stress considering the unfactored permanent 

load, 2.92 ksf + 5.96ksf = 8.88 ksf.

PP SS SS II = σσ′

1 − σσ′vo

σσ′vo

∗ 100% [Eq. D-5]

PP SS SS II ee = (8.88 )−(2.92 )

(2.92 ) ∗ 100

PP SS SS II = 204%

The stress increase is greater than or equal to 10%. Deformation for this depth 

increment should be estimated and included in the sum of all depth increments in 

which the stress increase is not less than 10%. A rock layer, which is considered 

incompressible, is located at Elev. 215.0 feet at this substructure location, and thus it 

is assumed that no settlement or compression occurs below this depth.

150
For the dense gravel at Elev. 232.5 feet, z = 2.5 determine deformation in the layer 

from the increase in vertical effective stress, SS, with Equation 7-49.

HHoo = initial soil layer thickness, 5 feet.

CC′ = dimensionless bearing capacity index, 180 (Figure D-76).

σσ′vv = vertical effective stress at midpoint of layer prior to 

stress increase, 2.92 ksf.

ΔΔσσ′vv = vertical effective stress increase in the layer, 5.96 ksf.

SS = HHoo �

1

CC′ log σσ′vvvv+ ∆σσ′vvvv

σσ′vvvv

� [Eq. 7-49]

SS = (5 ff ) � 1

(180) log (2.92 )+(5.96 )

(2.92 ) � ∗ (

12 ii h

1 ff )

SS = 0.16 hee

Table D-75 Settlement Estimate for Hough Method With Equivalent Footing 

Located at Elev. 235.0 feet

EL 

(feet)

z 

(feet)

Ho 

(ksf)

σ'vo 

(ksf)

B

(feet)

Z

(feet)

Δσ'v(ss)

(ksf)

σ'1

(ksf)

Stress 

Incr. 

(%)

S

(in)

232.5 2.5 5 2.92 15.5 23.5 5.96 8.88 204 0.16

227.5 7.5 5 3.23 20.5 28.5 3.72 6.95 115 0.11

222.5 12.5 5 3.54 25.5 33.5 2.54 6.08 72 0.08

217.5 17.5 5 3.85 30.5 38.5 1.85 5.70 48 0.06

Total 0.41

The above analysis was performed for additional pile penetration depths considering 

pile group dimensions of all three group configurations. Table D-76 summarizes 

these analysis results for the Hough (1959) estimated settlement. For an equivalent 

footing at Elev. 240.0 feet, pile group settlement is magnified as 5 feet of silty clay 

remains below the equivalent footing, and thus consolidation settlement occurs. 

Conventional settlement equations as discussed in Section 7.3.5.6 were used to 

estimate settlement in this 5 feet thick layer in combination with the Hough (1959) 

method equations which were applied for the dense gravel. Elevation 235.0 feet is 

the upper contact of the dense gravel layer, and thus the comparatively smaller 

deformation below this depth is from elastic compression. A review of Table D-76

shows that for all group configurations, the vertical deformations reduce as the pile 

toe penetrates into the dense gravel layer at Elev. 235.0 feet. Therefore, the 

minimum pile penetration to design against intolerable deformations is 40 feet.

151
Table D-76 Summary of Pile Group Settlement Estimation Using Hough (1959) 

Method For All Pile Group Configurations at Pier 2

Equivalent 

Footing 

Elevation

(feet)

Pile Toe 

Elevation

(feet)

Pile 

Penetration

Depth

(feet)

Estimated 

Settlement

For Group 

Configuration 

4 

(inches)

Estimated 

Settlement

For Group 

Configuration 

5

(inches)

Estimated 

Settlement

For Group 

Configuration 

6

(inches)

240.0 240.0 35.0 4.77 3.96 2.33

235.0 235.0 40.0 0.63 0.56 0.41

230.0 230.0 45.0 0.52 0.46 0.33

Pile group settlement was also calculated using the neutral plane method and Janbu

tangent modulus as discussed in Section 7.3.5.6. An equivalent footing, with plan 

dimensions equal to those of the pile group, was evaluated at increasing pile 

penetration depths, and the resulting pile group settlement computed using the 

Janbu tangent modulus. This procedure allowed the shallowest depth of an 

equivalent footing to be determined that met vertical deformation requirements. The 

required minimum pile penetration depth was then determined based on the pile toe 

elevation that would place the neutral plane at this same equivalent footing depth 

where vertical deformation requirements were satisfied.

The following example calculation is performed for the neutral plane located 40 feet 

below the bottom of footing. Figure D-77 presents the pile group and resulting 

stress distribution at the equivalent footing. From Elev. 270.0 feet to 235.0 feet, 

strain calculations for cohesive soil (stress exponent of j=0) were applied for Soil 

Layer 3. Below Elev. 235.0 feet however, strain calculations for dense coarse 

grained soil (stress exponent of j=1) were applied for the Soil Layer 4. It was 

assumed that vertical deformation below the encountered bedrock at Elev. 215.0 

feet is negligible. For Group Configuration 6, the length of the pile group is 21 feet, 

while the width is 13 feet. This example calculation is therefore only suitable for this 

configuration. Dimensions are taken from exterior pile edge to exterior pile edge. 

The soil profile was again divided into 5 foot thick layers. Tabulated values for this 

analysis are recorded in Table D-77. The elevation shown in Table D-77 references 

the midpoint of each respective soil layer, while z is the depth below the equivalent 

footing to the midpoint of each respective soil layer.

152
Figure D-77 Neutral plane at 40 feet below the pile cap and resulting stress 

distribution for Group Configuration 6.

Considering only the unfactored permanent load, Q, calculate the vertical effective 

stress increase below the equivalent footing, ΔΔσσ′vv, at EL 232.5 feet.

Q = unfactored permanent load, 2182 kips (Service I, without LL, 

Table D-58).

BB = pile group width, 13 feet.

ZZ = pile group length, 21 feet (Group Configuration 6 only).

z = depth below equivalent footing, 2.5 feet (Elev. 232.5 feet).

 ΔΔσσ′vv(ss) = QQ

(BB+zz)+(ZZ+zz)) [Eq. 7-55]

 ΔΔσσ′vv(ss) = (2182 )

((13 ff )+(2.5 ff ))∗((21 ff )+(2.5 ff )))

 ΔΔσσ′vv(ss) = 5.96 kk

153
Determine the percent stress increase by comparing σσ′vo and σσ′1.

σσ′vo = initial vertical effective stress at depth z below the equivalent footing, 

2.92 ksf.

σσ′1 = new vertical effective stress considering the unfactored permanent 

load, 2.92 ksf + 5.96ksf = 8.88 ksf.

PP SS SS II = σσ′

1 − σσ′vo

σσ′vo

∗ 100% [Eq. D-5]

PP SS SS II = (8.88 )−(2.92 )

(2.92 ) ∗ 100

PP SS SS II = 205%

The stress increase is greater than or equal to 10%. Deformation for this depth 

increment should be estimated and included in the sum of all depth increments in 

which the stress increase is not less than 10%. A rock layer, which is considered 

incompressible, is located at Elev. 215 feet at this pier, and thus it is assumed that 

no settlement or compression occurs below this depth.

For the dense coarse grained soil at Elev. 232.5 feet, z = 2.5 (stress exponent of 

j = 1.0), determine the strain in the layer from the increase in vertical effective stress, 

εε, with Equation 7-61.

EEss = elastic modulus of soil, 1104 ksf (Figure D-39).

σσ′vo = initial vertical effective stress at depth z below the equivalent 

footing, 2.92 ksf.

σσ′1 = new vertical effective stress below the equivalent footing, 8.88 

ksf.

εε = 1

EEss

[σσ′1 − σσ′vv ] [Eq. 7-61]

εε = 1

(1104 kk )

[(8.88 kk ) − (2.92 kk )]

εε = 0.0054

154
Calculate the layer compression denoted, S, with the initial height of the layer, HHoo.

SS = εε ∗ HHoo

SS = 0.0054 ∗ 5 ff ∗ �

12 hee

1 ffffff �

SS = 0.32 hee

Table D-77 Settlement Estimation for Neutral Plane Method with

the Neutral Plane at EL 235.0 feet

EL 

(feet)

z 

(feet)

Ho 

(ksf)

σ'vo 

(ksf)

B

(feet)

Z

(feet)

Δσ'v(ss)

(ksf)

σ'1

(ksf)

Stress 

Incr. 

(%)

ε S

(in)

232.5 2.5 5 2.92 15.5 23.5 5.96 8.88 205 0.0054 0.32

227.5 7.5 5 3.23 20.5 28.5 3.72 6.95 115 0.0034 0.20

222.5 12.5 5 3.54 25.5 33.5 2.54 6.08 72 0.0023 0.14

217.5 17.5 5 3.85 30.5 38.5 1.85 5.70 48 0.0017 0.10

Total 0.76

Table D-78 summarizes the settlement analysis results estimated using the neutral 

plane method and Janbu Tangent modulus approach. Although not yet determined, 

it is preliminarily estimated that elastic pile compression may be on the order of 0.3 

inches, effectively limiting tolerable soil settlement to on the order of 1 inch. 

Therefore, to limit the total vertical deformation from elastic pile compression and 

settlement to less than 1.5 inches, the results in Table D-78 indicate that the neutral 

plane should be located 40 feet below the bottom of footing for Group Configuration 

6. In a similar manner, the neutral plane should be located 55 feet and 50 feet 

below the bottom of footing for Group Configuration 4 and 5, respectively.

155
Table D-78 Estimated Pile Group Settlement Using Janbu Tangent Modulus with 

Neutral Plane Method For All Pile Group Configurations

Neutral 

Plane 

Elevation

(feet)

Neutral 

Plane

Depth

(feet)

Estimated 

Settlement

GC 4 

(inches)

Estimated 

Settlement

GC 5

(inches)

Estimated 

Settlement

GC 6

(inches)

240.0 35 5.22 4.32 2.44

235.0 40 1.59 1.28 0.76

230.0 45 1.44 1.14 0.66

225.0 50 1.20 0.94 0.53

220.0 55 0.80 0.61 0.32

It is assumed that the equivalent footing acts at the same location as the neutral 

plane. Accordingly, an analysis was performed to determine the pile toe elevation 

necessary to locate the neutral plane at Elev. 235.0 (for piles in Group Configuration 

6), thereby establishing the minimum required pile penetration depth to satisfy 

tolerable deformations. 

The location of the neutral plane and the magnitude of drag force are evaluated 

following the procedure outlined in Section 7.3.6, using unfactored permanent loads 

and nominal geotechnical resistance. Because load factors for the Service limit 

state are 1.0, applicable loads at this limit state may be considered unfactored. The 

Service I, without LL limit state loads are therefore used for evaluation for the neutral 

plane. This example again utilizes the load for Group Configuration 6 (Q= 109 kips, 

Table D-61). Figure D-78 presents a graphical interpretation of the neutral plane for 

the HP 12x74 pile driven to 56 feet (pile toe at Elev. 219.0).

The unfactored permanent load and the cumulative shaft resistance are first plotted, 

followed by the mobilized toe resistance minus the cumulative shaft resistance (all 

vs. pile penetration depth). The exact percentage of toe mobilization is unknown at 

this stage of design, and therefore at least two of the toe mobilization curves should 

be evaluated to determine the neutral plane location. The 0% toe mobilization curve 

is the most conservative location to evaluate settlement (since it locates the neutral 

plane at the highest elevation), and the 100% toe mobilization curve should be used 

to check the pile section’s structural strength (since it results in the greatest axial 

force in the pile). The structural strength check is performed in Block 17.

At Pier 2, it is expected that piles will be supported partially by toe resistance when 

driven to the dense gravel layer. Therefore the 0% toe mobilization curve presents 

156
Figure D-78 Neutral plane location considering 50% toe mobilization

for HP 12x74 at Pier 2.

an unreasonable baseline to evaluate settlement in this case. Some toe resistance 

is likely mobilized, and to remain consistent with the other substructure locations, the 

50 % toe mobilization curve is again used to evaluate settlement.

Assuming 50 percent toe mobilization, the neutral plane is located 40 feet below the 

bottom footing with a resulting maximum load in the pile of 275 kips. For the 

remaining candidate pile sections and trial group configurations, the above analysis 

was also performed to determine the pile penetration depth required to locate the 

neutral plane at the depths indicated in Table D-78 for each respective pile group 

configuration. Table D-79 summarizes the results from these analyses. 

Table D-79 Summary of Pile Penetration Depth Required to Locate Neutral Plane 

at Depth Determined From Settlement Estimation

Group 

Configuration Load per 

Pile

Q

(kips)

HP 

10x42

(feet)

HP 

12x53 

(feet)

HP 

12x74

(feet)

HP 

14x89

(feet)

HP 

14x117

(feet)

4 145 60 60 60 60 60

5 109 60 60 60 58 60

6 109 60 58 56 52 49

157
To limit unacceptable settlement, it was decided that the method yielding the 

greatest settlement estimate would be used to establish the range of pile penetration 

depths to preclude unacceptable settlement. The neutral plane method illustrated 

above was therefore performed for additional equivalent footing depths until 

settlements within the project deformation criteria were estimated. Experience and 

judgement should be used to assess the required pile penetration depth with any 

settlement estimation approach.

A review of the soil profile at Pier 2 in Figure D-39 indicates no compressible soil 

layers below Soil Layer 4. Therefore, no effort is necessary to identify a maximum 

pile penetration depth to prevent punching though a dense layer into an unsuitable 

soil layer, or to apply a large stress increase on a lower compressible layer causing 

excessive settlement. Table D-80 presents the established minimum pile 

penetration depths to satisfy tolerable deformations at Pier 2.

Table D-80 Established Minimum Pile Penetration Depths to Satisfy Tolerable 

Deformations at Pier 2

Group 

Configuration

Load per 

Pile

Q

(kips)

HP 

10x42

(feet)

HP 

12x53 

(feet)

HP 

12x74

(feet)

HP 

14x89

(feet)

HP 

14x117

(feet)

4 145 60 60 60 60 60

5 109 60 60 60 58 60

6 109 60 58 56 52 49

Elastic shortening of the pile should be considered in the total pile deformation, 

noting that the drag force from negative shaft resistance adds to the axial 

compression force in the pile. Negative shaft resistance is determined from the 

previously discussed neutral plane calculation. For elastic compression, the load 

per pile from the Service I, without live load limit state (which is, in effect, and 

unfactored load) is applied at the pile head. As shown in Table D-61, this load is 

109 kips.

Note that the drag force from negative shaft resistance increases the axial 

compression force in the pile. Negative shaft resistance above the neutral plane 

acts to increase axial compression force in the pile, whereas below the neutral 

plane, positive shaft resistance reduces the axial compression force in the pile. This 

effect must be accounted for in the elastic compression calculation. Accordingly, the 

unfactored axial load used to compute elastic compression, Q, changes for each pile 

158
segment length, increasing equal to the unfactored permanent load plus the shaft 

resistance down to the neutral plane. In this example, the unfactored axial load is 

equal to the resistance distribution from 100% toe mobilization. The highest drag 

force magnitude results from this curve and represents the worst case.

Equation 7-48 is used to illustrate this example for the first 12 inch increment of the 

HP 12x74 pile section. The average shaft resistance and average load for each 

respective depth interval is used to estimate the elastic compression. For each 12 

inch segment, the elastic modulus remains constant, and was evaluated as 29,000 

ksi. The pile cross sectional area likewise remains constant as 21.8 in2. Remaining 

calculations were performed using a spreadsheet; Table D-81 summarizes the 

elastic compression with depth. 

Determine the unfactored axial load, Q, in segment.

QQdd = unfactored permanent load, 109.0 kips.

RRss

− = average (negative) shaft resistance, 1.1 kips.

Q = QQdd + RRss

− = 109.0 kkkk + 1.1 kkkk

Q = 110.1 kkkk

Calculate elastic compression of segment with unfactored axial load from combined 

unfactored permanent load and negative shaft resistance.

LL = segment length, 12 inches.

AA = cross sectional area of pile material, 21.8 in2.

EE = elastic modulus of pile, 29,000 ksi.

∆= QQ

AA [Eq. 7-48]

∆= (110.1 )∗(12 ii h )

(21.8 2)∗(29,000 kk kk)

∆= 0.00209 hee

159
Table D-81 Elastic Compression Calculation

Depth 

Below 

Pile Head

(feet)

Average 

Shaft 

Resistance 

(kips)

Average 

Unfactored 

Axial Load 

(kips)

∆

(inches)

0 0.0 109.0 0.00000

0-1 0.6 110.1 0.00209

1-2 1.8 110.8 0.00210

2-3 3.1 112.1 0.00213

3-4 4.7 113.7 0.00216

4-5 6.4 115.4 0.00219

5-6 8.2 117.2 0.00222

6-7 10.2 119.2 0.00226

7-8 12.4 121.4 0.00230

8-9 14.8 123.8 0.00235

9-10 17.3 126.3 0.00240

10-11 20.5 129.5 0.00246

11-12 24.4 133.4 0.00253

12-13 28.4 137.4 0.00261

13-14 32.5 141.5 0.00269

14-15 36.8 145.8 0.00277

15-16 41.1 150.1 0.00285

16-17 45.3 154.3 0.00293

17-18 49.6 158.6 0.00301

18-19 54.1 163.1 0.00310

19-20 58.7 167.7 0.00318

20-21 63.3 172.3 0.00327

21-22 67.8 176.8 0.00336

22-23 72.5 181.5 0.00344

23-24 77.3 186.3 0.00354

24-25 82.2 191.2 0.00363

25-26 87.1 196.1 0.00372

26-27 92.0 201.0 0.00381

27-28 97.0 206.0 0.00391

28-29 102.1 211.1 0.00401

29-30 107.4 216.4 0.00411

30-31 112.6 221.6 0.00421

31-32 117.7 226.7 0.00430

32-33 122.8 231.8 0.00440

33-34 127.9 236.9 0.00450

34-35 133.0 242.0 0.00459

35-36 138.1 247.1 0.00469

36-37 143.2 252.2 0.00479

37-38 148.3 257.3 0.00488

160
Table D-81 Elastic Compression Calculation (continued)

Depth 

Below 

Pile Head

(feet)

Average 

Shaft 

Resistance 

(kips)

Average 

Unfactored 

Axial Load 

(kips)

∆

(inches)

38-39 153.4 262.4 0.00498

39-40 158.5 267.5 0.00508

40-41 164.8 273.8 0.00520

41-42 172.3 281.3 0.00534

42-43 180.1 289.1 0.00549

43-44 187.9 296.9 0.00564

44-45 196.0 305.0 0.00579

45-46 204.2 313.2 0.00594

46-47 212.5 321.5 0.00610

47-48 221.0 330.0 0.00626

48-49 228.4 337.4 0.00640

49-50 227.1 336.1 0.00638

50-51 218.2 327.2 0.00621

51-52 209.1 318.1 0.00604

52-53 199.9 308.9 0.00586

53-54 190.5 299.5 0.00568

54-55 180.9 289.9 0.00550

55-56 171.2 280.2 0.00532

Total 0.23

For the pile head load of 109 kips (Group Configuration 1 loads), estimated elastic 

compression of the HP 12x74 pile section driven to 56 feet is 0.23 inches. 

Combined with 0.76 inches of deformation from settlement (Table D-78), it is 

estimated that total vertical deformation at Pier 2 is 0.99 inches.

D.28Block 16: Pier 2 – Check pile drivability to maximum pile penetration 

depth requirements established in Blocks 12 through 15

Preliminary pile drivability was previously evaluated for the 5 candidate pile sections 

in Block 10. The plots of nominal resistance, blow count and compression stress 

versus depth in Figure D-67 should now be reviewed considering the established 

minimum pile penetration depths. A candidate pile section must be capable of being 

driven to the penetration depth necessary to achieve the nominal geotechnical 

resistance in axial compression and tension, and to a penetration depth necessary 

to satisfy lateral load demands as well as axial and lateral deformation requirements. 

However, no minimum pile penetration depth is required to satisfy axial tension 

161
resistance. Minimum pile penetration depths have been previously established in 

Blocks 14 and 15 and are presented in Tables D-73 and D-80. 

Although a minimum pile penetration depth is not established for nominal 

geotechnical resistance in axial compression, the pile should also be capable of 

being driven close to this estimated pile penetration depth. If the pile cannot be 

driven to the required depth within driving stress limits and at reasonable blow 

counts, a larger pile hammer, a pile section with greater impedance, or pile 

installation aids such as predrilling or jetting may be required to satisfy or improve 

drivability. Alternatively, substructure design modifications should be considered.

For the HP 12x74 candidate pile section in Group Configuration 6 the pile 

penetration depth for axial compression loading was estimated at 41 feet (Table 

D-64). There is no minimum penetration depth for axial tension loading since there 

was no tension demand. The minimum penetration depth for lateral loading was 20 

feet (Table D-73). A minimum pile penetration depth of 56 feet is required to satisfy 

vertical deformation limits (Table D-80). Accordingly, candidate pile section must 

have sufficient drivability to the maximum of these depths, 56 feet. 

A review of Figure D-67 indicates that the HP 12x74 pile section can be driven to 

bedrock at approximately 60 feet, if required. In addition, from the preliminary 

drivability evaluation (with soil and hammer model assumptions described in Block 

10), it is estimated that the blow count will not exceed 120 blows per foot or 10 blows 

per inch before this penetration depth. Compression driving stresses are estimated 

to remain below driving-stress limits. Therefore, it is concluded that pile drivability to 

the estimated pile penetration depth is achievable.

D.29Block 17: Pier 2 – Determine the Neutral Plane Location and Resulting 

Drag Force. Check Structural Strength Limit State for Pile Penetration 

Depth From Block 16

Previously in Block 15, the neutral plane was evaluated as part of the settlement 

calculations. The neutral plane and resulting drag force are now evaluated to check 

the structural strength limit state for candidate pile sections. Section 7.3.6 of 

Chapter 7 provides a reference for evaluating the neutral plane location and the 

magnitude of the drag force. Load using the Service I, without live load limit state 

(which are, in effect, unfactored loads) are considered. This example again utilizes 

the load for Group Configuration 6 (Q= 109 kips, Table D-61). 

162
It is good practice that the drag force be evaluated for 100 percent toe mobilization. 

This results in the neutral plane at its lowest potential location, and thus the highest 

drag force magnitude. Accordingly, this is the toe mobilization curve that should be 

used to check the pile section’s structural resistance. Figure D-79 presents a 

graphical interpretation of the neutral plane location for the HP 12x74 pile section 

driven to the estimated pile penetration depth of 56 feet. In this case the neutral 

plane is located 49 feet below pile head with a resulting maximum axial compression

force in the pile of 342 kips.

Figure D-79 Neutral plane location considering 100 percent toe mobilization for 

HP 12x74 at Pier 2.

The resulting unfactored drag force, DF, is the difference between the maximum 

unfactored axial compression force in the pile, QQmm , minus the unfactored 

permanent load (Q). In this case, the drag force is evaluated for 100 percent toe 

mobilization. 

DD = QQmm − QQ

DD = (342 kkkk ) − (109 kkkk ) = 233 kkkk

Following this calculation, the structural resistance was checked with Equation 

7-70. As discussed in Section 7.3.6 of Chapter 7, a load factor of 1.25 is applied to 

163
the permanent load while a load factor of 1.1 is applied to the drag force. For Hpiles which may be subject to damage during driving and require pile toe protection 

(i.e., as for piles driven to bedrock or through dense gravel, cobbles, etc.), the 

structural resistance factor in axial compression, φφcc, is 0.5. This applied to the 

nominal structural resistance of 1043 kips (Table D-46). For this assumption, the 

factored structural resistance, Pr, for the HP 12x74 section is 521 kips.

PPuu = 1.25 (QQ) + γpp(DD ) < PPrr [Eq. 7-70]

PPuu = 1.25 (109 kkkk ) + 1.1(233 kkkk ) = 393 kkkk

393 kkkk < 521 kkkk 

In this case, the factored structural resistance is greater than the factored load, and 

therefore the pile section is acceptable. It may be beneficial to review the ratio of the 

factored load to the nominal structural resistance or, PPuu/ PPnn. The following evaluation 

serves to back calculate the minimum required structural resistance factor, φφcc(min), 

for the section to be acceptable considering the factored load.

φφcc(min) = PPuu

PPnn

φφcc(min) = (393 )

(1043 )

φφcc(min) = 0.38

The neutral plane and drag force analysis was also performed for each candidate

pile section considering 100 percent toe mobilization. Factored structural resistance 

was subsequently evaluated considering the factored loads for group configurations 

shown in Table D-61. The pile penetration depth utilized for the structural resistance 

check was the required minimum penetration depth presented in Table D-80. Table 

D-82 presents the ratio of the factored load to nominal structural resistance, at the 

pile toe, for the all the candidate piles and group configurations. For H-piles which 

may be subject to damage during driving and require pile toe protection (i.e., as for 

piles driven to bedrock or through dense gravel, cobbles, etc.), the structural 

resistance factor in axial compression, φφcc, is 0.5. A review of Table D-82 shows 

several unacceptable candidate sections and group configurations. The HP 10x42 

section is not acceptable in any group configuration, while the HP12x53 is not 

acceptable in Group Configuration 4 or 5. In a similar manner, the HP 12x74 section 

is not acceptable in Group Configuration 4.

164
Table D-82 Ratio of Factored Load to Nominal Structural Resistance in Axial 

Compression, φφcc(min), at the Pile Toe

Group 

Configuration

HP 10x42

φφcc(min)

HP 12x53

φφcc(min)

HP 12x74

φφcc(min)

HP 14x89

φφcc(min)

HP 14x117

φφcc(min)

4 0.74* 0.68* 0.51* 0.50* 0.39*

5 0.66* 0.62* 0.49* 0.46* 0.37*

6 0.66* 0.38 0.26 0.38 0.27

Note: * - pile toe on rock.

For each combination, the ratio of the factored load to nominal structural resistance 

was also independently evaluated at the neutral plane. Table D-83 presents the 

ratio of the factored load to nominal structural resistance at the neutral plane

Table D-83 Ratio of Factored Load to Nominal Structural Resistance in Axial 

Compression, φφcc(min), at the Neutral Plane

Group 

Configuration

HP 10x42

φφcc(min)

HP 12x53

φφcc(min)

HP 12x74

φφcc(min)

HP 14x89

φφcc(min)

HP 14x117

φφcc(min)

4 0.74* 0.68* 0.51* 0.50* 0.39*

5 0.66* 0.62* 0.49* 0.46* 0.35

6 0.66* 0.49 0.38 0.36 0.27

Note: * - neutral plane on rock.

Based on results of the drag force analysis, a candidate pile section may be 

eliminated from consideration if the factored loads are higher than the factored 

structural resistance. As noted in Table D-84, the larger candidate pile sections 

remained acceptable including drag force consideration.

Table D-84 Does Candidate Pile Section Meet Structural Resistance Requirement 

Considering Drag Force Associated with Minimum Pile Penetration Depth?

Group 

Configuration HP 10x42 HP 12x53 HP 12x74 HP 14x89 HP 14x117

1 No No No Yes Yes

2 No No Yes Yes Yes

3 No Yes Yes Yes Yes

165
D.30Decision 18: Does Estimated Total Settlement and Differential Settlement 

Between Adjacent Substructure Locations Satisfy Requirements and 

Angular Distortion Limits?

The North Abutment and Pier 2 have now been preliminarily designed and the 

estimated vertical deformations computed for both locations.

The vertical deformation limits and construction point concept detailed in Section 7.3 

of Chapter 7 was used to first calculate tolerable differential settlement based upon 

angular distortion. Using Equation D-1, the angular distortion between substructure 

supports is limited to 0.004 radians, and for a 100 ft span on a multispan bridge, this 

equates to 4.8 inches of tolerable differential settlement. 

Determine tolerable differential settlement, Sd, between substructure supports.

LLss = span length, 100 feet.

AA = angular distortion limit, 0.004 radians (Table 7-18).

SSdd = AA ∗ LLss Eq. D-7

SSdd = (0.004) ∗ (100 ff ) ∗ �

12 ii h

1 ff �

SSdd = 4.8 hee

Although this differential settlement is tolerable for angular distortion, project 

performance requirements limited the settlement at each substructure location to a 

maximum of 1.5 inches, the differential settlement between adjacent substructure 

locations limited to 1.0 inch, an a maximum angular distortion of 0.0008 radians. 

These requirements were established for rideability, drainage, and attached utility 

damage considerations. The estimated substructure performance is summarized in 

Table D-85.

166
Table D-85 Summary of Foundation Total Settlement, Differential Settlement, and 

Angular Distortion

Substructure 

Location

Settlement 

Method

Total 

Settlement

(inches)

Differential 

Settlement

(inches)

Span 

Length

(feet)

Angular 

Distortion

N. Abutment N. Plane 1.17

0.18 100 0.0002

Pier 2 N. Plane 0.99

The total settlement, differential settlement, and angular distortion for the two 

substructures designed so far are acceptable.

D.31Block 19: Pier 2 – Evaluate Economics of Candidate Piles, Preliminary 

Group Configurations, and Other Factors

Until now, the design process has served to compare strength and service limits for 

several candidate pile types within trial group configurations. Some candidate pile 

types have not met all of the strength, service, or drivability requirements. It is useful 

to quickly review the suitable and unsuitable pile types and group configurations and 

then assess the cost of the viable foundation solutions.

Table D-86 summarizes the established minimum pile penetration depth based on 

analysis results from Blocks 12 through 15. For the candidate pile sections and 

group configurations at Pier 2, the established minimum pile penetration depth was, 

in some cases, based on meeting tolerable vertical deformations, and in other 

cases, based on satisfying the geotechnical resistance demand. 

Several candidate sections did not meet structural resistance requirements for axial 

loading, lateral loading or both. The candidate pile sections and/or group 

configurations not meeting design requirements are identified with an asterisk in 

Table D-86. For all three group configurations, the HP 10x42 section did not meet 

all structural resistance requirements. In a similar manner, the HP 12x53 pile section 

is unacceptable in Group Configuration 4 or 5 and the HP 12x74 pile section is 

unacceptable in Group Configuration 4. These candidate pile sections and group 

configurations will therefore be eliminated for the final design.

167
Table D-86 Established Minimum Pile Penetration Depth at Pier 2

Group 

Configuration

HP 10x42

(feet)

HP 12x53 

(feet)

HP 12x74

(feet)

HP 14x89

(feet)

HP 14x117

(feet)

4 60* 60* 60* 60 60

5 60* 60* 60 60 60

6 60* 58 56 52 49

Note: * - Did not meet structural resistance requirement.

Table D-87 presents the estimated minimum penetration depth for each candidate 

section to meet the factored geotechnical resistance requirements at the Strength V 

limit state. The larger pile sections require less pile penetration depth than the 

smaller pile sections to provide the same geotechnical resistance. In addition, the 

factored load per pile decreases from Group Configuration 4 to Group Configuration 

6. However, from the analyses in Blocks 13 through 15, the established minimum 

penetration depth to preclude unacceptable vertical deformation requires all piles to 

be driven deeper than the depth needed for their factored geotechnical resistance. 

The minimum penetration depth requirement results in the additional geotechnical 

resistance gained by further pile embedment to be essentially wasted and therefore 

uneconomical.

Table D-87 Estimated Minimum Penetration Depth for Factored Geotechnical 

Resistance at Strength V Limit State

Group 

Configuration

HP 10x42

(feet)

HP 12x53

(feet)

HP 12x74

(feet)

HP 14x89

(feet)

HP 14x117

(feet)

4 60* 60* 60* 50 47**

5 60* 46* 44** 40** 40**

6 57* 42** 41** 40** 40**

Note: * - Did not meet structural resistance requirement.

Note: ** - Must be driven deeper to meet deformation requirements (Table D-80).

Reference should be made to Block 19 of the North Abutment for a discussion of 

individual pile cost. However Figure D-80 again presents the individual pile cost 

versus depth. 

168
Figure D-80 Pile cost versus penetration depth.

Table D-88 shows the price per pile at Pier 2 with consideration of the established 

minimum pile penetration depth. For example, for the HP 12x 74 pile section in 

Group Configuration 6, the individual cost is determined by multiplying the cost per 

foot by the penetration depth. At the minimum pile penetration depth of 56 feet, the 

cost per pile is $3,730. To note, there will be additional pile length embedded in the 

cap, however for pile cost estimation it can be considered negligible. Furthermore 

Table D-89 shows the pile group cost reflecting the cost per pile and number of piles 

in the group.

Table D-88 Cost per Pile at Established Minimum Penetration Depth for Piles 

Meeting Structural Requirements

Group 

Configuration HP 12x53 HP 12x74 HP 14x89 HP 14x117

4 - - $4,806 $6,156 

5 - $3,996 4,806 6,156 

6 $2,767 3,730 4,165 5,027 

169
Table D-89 Pile Group Cost at Established Minimum Penetration Depth for Piles 

Meeting Structural Requirements

Group 

Configuration

Number 

of Piles HP 12x53 HP 12x74 HP 14x89 HP 14x117

4 15 - - $72,090 $92,340 

5 20 - $79,920 96,120 123,120 

6 20 $55,332 74,600 83,304 100,548 

Based upon this comparison, the HP 14x117 pile section proves to be least 

economical. Conversely, based upon pile cost alone, the HP 12x53 pile section in 

Group Configuration 6 appears to be the most economical, followed by the HP 

14x89 in Group Configuration 4 and the HP 12x74 pile section in Group 

Configuration 6. Before selecting the lowest cost option solely considering the 

results in Table D-89, the cost of the pile cap should also be factored into the 

foundation cost, as discussed below.

Section 8.9 of Chapter 8 outlines a procedure to estimate the total pile cap 

thickness. Equation 8-77 is used to estimate this value along using the factored load 

per pile at the Strength limit state as previously presented in Table D-61. A sample 

calculation is shown for the HP 12x74 pile in Group Configuration 6, while tabulated 

results for each pile section and pile group permutation are presented in Table D-90.

Estimate the total pile cap thickness:

PPuu = maximum single pile factored axial load, Q =323 kips (Group 

Configuration 6, Table D-61).

tcc = PPuuuu

12

+ 30 [Eq. 8-80]

tcc = (257 )

12

+ 30

tcc = 51 hee

170
Table D-90 Estimated Total Pile Cap Thickness

Group 

Configuration

HP 12x53

(inches)

HP 12x74

(inches)

HP 14x89

(inches)

HP 14x117

(inches)

4 - - 65 65

5 - 55 55 55

6 51 51 51 51

Using the estimated total pile cap thickness, the volume of reinforce concrete 

required to construct the pile cap is determined. Total pile cap width and length 

values were previously provided in Table D-59. The resulting volume of reinforced 

concrete for each pile section and pile group permutation is presented in Table D-91 

Note that pile cap volume is shown in cubic yards (CY).

Table D-91 Estimated Volume of Reinforced Concrete in Pile Cap

Group 

Configuration

HP 12x53

(CY)

HP 12x74

(CY)

HP 14x89

(CY)

HP 14x117

(CY)

4 - - 24.7 24.7

5 - 28.2 28.2 28.2

6 51.8 51.8 51.8 51.8

To estimate the pile cap cost, past pricing information is generally the best guide; 

however, similar to estimating the pile cost, due to fluctuations in the market price of 

material and other factors, pile cap costs are subject to change. The cost of the 

reinforced concrete pile cap, furnished and constructed, is estimated to be $500 /CY. 

Using this estimated value, the volumes presented in Table D-91 were used to 

estimate the cost of the various reinforced concrete pile caps. The pile cap cost for 

each candidate section and group configuration permutation is shown in Table D-92.

Table D-92 Estimated Cost of Reinforced Concrete Pile Cap

Group 

Configuration HP 12x53 HP 12x74 HP 14x89 HP 14x117

4 - - $12,331 $12,331

5 - $14,110 14,110 14,110

6 $25,887 25,887 25,887 25,887

171
By adding the cost of the pile cap and piles for each permutation, the estimated total 

foundation cost is determined as presented in Table D-93. Additional construction 

costs should be accounted for such as excavations or required pile installation aides, 

however an exhaustive analysis is not presented in this design example. 

Considering both the pile and the pile cap costs, the HP 14x89 pile section in Group 

Configuration 4 is the more economical option. 

Table D-93 Estimated Foundation Cost Including Piles and Pile Cap 

at Pier 2

Group 

Configuration HP 12x53 HP 12x74 HP 14x89 HP 14x117

4 - - $84,421 $104,671 

5 - $94,030 110,230 137,230 

6 $81,219 100,479 109,191 126,435 

While the cost of pile over/underrun was evaluated at the North Abutment to account 

for inaccuracies in the assumed soil strength properties and estimated soil 

resistance, evaluation was not performed at Pier 2. Depending on the pile section 

and group configuration, piles must be driven to bedrock, or within 5 to 10 feet of 

bedrock, to satisfy tolerable deformations. These small variations, considering the 

total number of piles, reduce the risk of length over/underrun differences between 

the candidate sections. A further economic assessment is therefore not performed.

D.32Decision 20: Is the Preliminary Design of All Substructure Foundations 

Complete?

No. The preliminary foundation design has been completed for the North Abutment 

and the Pier. The preliminary design needs to be completed for the South 

Abutment. Return to Block 9 and begin the preliminary design for the next 

substructure location.

172
D.33Block 9: South Abutment – For all Candidate Piles, Calculate Nominal and 

Factored Structural Resistances

The nominal structural resistance is once again reviewed for the five candidate Hpile sections. The H-pile sections selected for evaluation at the South Abutment 

once again include a HP 10x42, a HP 12x53, a HP 12x74, a HP 14x89 and a HP 

14x117. The piles at the South Abutment have the same unsupported length as 

those at the North Abutment. Therefore, the nominal structural resistances at the 

South Abutment are unchanged from those determined previously at the North 

Abutment. A detailed step by step example for calculation of the nominal structural 

resistance was previously presented in Section 8.5.3 for an HP 14x117 H-pile 

section. Therefore, this process is not repeated for the five candidate pile sections. 

Table D-94 once again presents the calculated nominal structural resistances in 

axial compression, flexure, and shear for the five candidate sections. An unbraced 

length of 1 foot was assumed in these calculations.

Table D-94 Nominal Structural Resistances in Axial Compression, Flexure and 

Shear 

H-pile Section HP 

10x42

HP 

12x53

HP 

12x74

HP 

14x89

HP 

14x117

Pn, Nominal Resistance in Axial 

Compression (kips) 618 767 1088 1303 1718

Mny, Nominal Resistance in 

Weak Axis Flexure (kip-ft) 82 114 118 257 380

Mnx, Nominal Resistance in 

Strong Axis Flexure (kip-ft) 176 295 433 592 807

Vn, Nominal Resistance in 

Shear (kips) 118 149 214 246 331

At this time it has not been determined whether the piles at the South Abutment will 

be terminated in the very stiff clay or driven to bedrock. If driven to rock, pile shoes 

may be recommended to reduce the risk of damage. In this scenario, the applicable 

resistance factor, φφcc, would be 0.5 for resistance in axial compression. If terminated 

in the overlying clay where damage is unlikely to occur during driving, the applicable 

resistance factor, φφcc, would be 0.6 for resistance in axial compression. In any case, 

for combined resistance in axial compression and flexure (typically above fixity), the 

applicable resistance factor, φφcc, is 0.7. A resistance factor of φφvv =1.0 is used for 

shear, and a resistance factor of φφff=1.0 is applicable for flexure only. Table D-95

summarizes the calculated factored structural resistances in axial compression, 

combined axial compression and flexure, flexure, and shear.

173
Table D-95 Factored Structural Resistance in Axial Compression, Flexure and 

Shear

H-pile Section HP 

10x42

HP 

12x53

HP 

12x74

HP 

14x89

HP 

14x117

Pr, Factored Resistance in 

Axial Compression,

φφcc = 0.5 (kips)

309 383 544 652 859

Pr, Factored Resistance in 

Axial Compression and Flexure,

φφcc = 0.7 (kips)

433 537 762 912 1203

Mry, Factored Resistance in 

Weak Axis Flexure,

φφff=1.0 (kip-ft)

82 114 118 257 380

Mrx, Factored Resistance in 

Strong Axis Flexure,

φφff=1.0 (kip-ft)

176 295 433 592 807

Vr, Factored Resistance in 

Shear

φφvv =1.0 (kips)

118 149 214 246 331

D.34Block 10: South Abutment – For All Candidate Piles, Calculate Nominal 

and Factored Geotechnical Resistances in Axial Compression and 

Tension versus Depth. Perform Preliminary Pile Drivability Analyses

The engineering properties of the subsurface materials at the South Abutment were 

determined in Block 5. The results of the boring program and laboratory tests are 

now used to develop a design profile the South Abutment. Engineering judgement 

was used in developing the design profile to delineate the subsurface conditions into 

layers with similar properties. An effective stress diagram, depicted in Figure D-81, 

was then developed for this soil profile. This diagram includes the total stress, 

porewater pressure and effective stress versus depth. Figure D-81 also presents 

the basic soil profile for quick reference to the relevant soil layers. The effective 

stress diagram was computed using Equations 5-7 through 5-9 from Chapter 5. 

These equations are repeated below. For Figure D-81, the total stress, porewater 

pressure and effective stress were calculated at 1 foot increments using a 

spreadsheet.

σσvv = ∑ (γγiihii) nn

ii [Eq. 5-7]

uu = γγwwhww [Eq. 5-8]

σσ′vv = ∑ (γγiihii) − γγwwhww nn

ii [Eq. 5-9]

174
Figure D-81 Effective stress diagram for the South Abutment using Boring S-3.

As indicated by soil boring S-3 (Figures D-4), the soil conditions at the South 

Abutment consist of silty clay to a depth of 96 feet where bedrock is encountered. 

Unconfined compression strength tests were performed on each undisturbed 

cohesive soil sample. The undrained shear strength was then calculated by dividing 

the unconfined compression strength by 2.

Figure D-82 presents a plot of the undrained shear strength versus depth for the 

South Abutment soils. As illustrated, the undrained shear strength has distinct 

changes in undrained shear strength that can be used to identify three distinct soil 

layers and the layer boundaries. The undrained shear strength also increases 

approximately linearly with depth within each layer. 

Table D-96 summarizes the undrained shear strength values for Soil Layer 1 as well 

as sublayers a through e. Similarly, Table D-97 and Table D-98 present the 

undrained shear strength values for Soil Layer 2 and Soil Layer 3 respectively, as 

well as the individual sublayers.

175
Figure D-82 Undrained shear strength, su, versus depth at the South Abutment.

Table D-96 Undrained Shear Strength, su, for Soil Layer 1 at the South Abutment

Soil Layer Sample Depth (ft) σ'vo (ksf) qu (tsf) su (ksf)

1a 1 0.110 0.650 0.650

1b 6 0.488 0.660 0.660

1c 11 0.726 0.680 0.680

1d 16 0.964 0.700 0.700

1e 21 1.202 0.720 0.720

Table D-97 Undrained Shear Strength, su, for Soil Layer 2 at the South Abutment

Soil Layer Sample Depth (ft) σ'vo (ksf) qu (tsf) su (ksf)

2a 26 1.440 1.79 1.79

2b 31 1.748 1.83 1.83

2c 36 2.056 1.93 1.93

2d 41 2.364 2.00 2.00

176
Table D-98 Undrained Shear Strength, su, for Soil Layer 3 at the South Abutment

Soil Layer Sample Depth (ft) σ'vo (ksf) qu (tsf) su (ksf)

3a 46 2.672 3.11 3.11

3b 51 3.005 3.19 3.19

3c 56 3.338 3.30 3.30

3d 61 3.671 3.36 3.36

3e 66 4.004 3.39 3.39

3f 71 4.337 3.50 3.50

3g 76 4.670 3.55 3.55

3h 81 5.003 3.58 3.58

3i 86 5.336 3.60 3.60

3j 91 5.669 3.65 3.65

3k 96 6.002 3.70 3.70

The design soil profile for the South Abutment is presented in Figure D-83. The 

bottom of pile cap (Elev. 305 feet) is 5 feet below ground surface. Some soil 

properties in the design soil profile such as the initial cyclic modulus of subgrade 

reaction, kc, have been selected based on published correlations in the absence of 

laboratory testing. For this particular soil profile, the initial cyclic moduli of subgrade 

reaction was selected based on the values given in Table 7-22 which are delineated 

by soil shear strength. Similarly, the 50% strain factor, ε50, was estimated based 

upon the values given in Table 7-21 which vary by soil shear strength. If piles will be 

driven to bedrock, strength properties of the limestone bedrock are needed. These 

rock parameters obtained from laboratory tests on recovered rock core samples are 

summarized in Table D-99.

Table D-99 Laboratory Determined Properties of Limestone Bedrock

Effective 

Unit 

Weight

(kcf)

Undrained 

Shearing 

Resistance, uu

(ksf)

Friction 

Angle, φ

(degrees)

0.165 476 35.5

D.34.1 Geotechnical Resistance in Axial Compression

The nominal geotechnical resistance in axial compression is now calculated for the 

selected candidate H-pile sections. The nominal geotechnical resistance can be 

calculated by hand or with computer software using an appropriate analysis method 

177
Figure D-83 Design soil profile at the South Abutment.

based upon soil, rock, and pile type. Chapter 7 describes appropriate methods for 

this purpose as well as computer programs available at the time of this manual’s

publication.

For this abutment, the DrivenPiles computer program was used to calculate the 

nominal resistance, shaft resistance, and toe resistance each as a function of depth 

for each of the five candidate H-piles. For nominal geotechnical resistance 

calculations, each cohesive sample depth in Soil Layers 1, 2, and 3 was treated as 

an individual layer with respect to shear strength. This software program was 

selected since it uses the FHWA recommended alpha method to calculate the 

nominal geotechnical resistance of H-piles in cohesive soils. A summary of the 

shaft, toe, and nominal geotechnical resistance is presented for the HP 12x74 H-pile 

section in Table D-100. The depth shown is taken from the bottom of pile cap.

In the DrivenPiles program, the selection of the geomaterial is limited to either 

cohesionless or cohesive soil. Hence, the program cannot calculate the nominal toe 

resistance on rock and the only choice is either to model rock as a hard cohesive 

soil or a very dense cohesionless soil. The nominal toe resistance presented in 

Table D-100 at depth 91.25 feet was not calculated using the DrivenPiles program 

but rather calculated using the procedure for hard rock presented in Section 

7.2.1.4.2 of Chapter 7.

178
Table D-100 Nominal Shaft, Nominal Toe and Nominal Geotechnical Resistance for 

HP 12x74 at the South Abutment

Depth

(feet)

Nominal 

Shaft 

Resistance 

(kips)

Nominal 

Toe 

Resistance 

(kips)

Nominal 

Geotechnical 

Resistance 

(kips)

Depth

(feet)

Nominal 

Shaft 

Resistance 

(kips)

Nominal 

Toe 

Resistance 

(kips)

Nominal

Geotechnical 

Resistance 

(kips)

0.01 0.02 6.09 6.11 32 116.23 17.81 134.03

1 2.21 6.09 8.3 33 122.25 17.81 140.05

2 4.42 6.09 10.51 34 128.36 17.81 146.16

3 6.63 6.09 12.72 34.99 134.49 17.81 152.3

4 8.85 6.09 14.93 35.01 134.62 18.45 153.07

4.99 11.03 6.09 17.12 36 140.69 18.45 159.14

5.01 11.08 6.27 17.35 37 146.83 18.45 165.28

6 13.35 6.27 19.62 38 152.96 18.45 171.41

7 15.67 6.27 21.95 39 159.1 18.45 177.55

8 18.03 6.27 24.3 39.99 165.17 18.45 183.62

9 20.42 6.27 26.69 40.01 165.28 28.69 193.98

9.99 22.81 6.27 29.08 41 170.34 28.69 199.03

10.01 22.86 6.46 29.32 42 175.44 28.69 204.13

11 25.27 6.46 31.73 43 180.54 28.69 209.24

12 27.75 6.46 34.21 44 185.65 28.69 214.34

13 30.25 6.46 36.71 44.99 190.7 28.69 219.39

14 32.79 6.46 39.25 45.01 190.8 29.43 220.23

14.99 35.34 6.46 41.79 46 195.85 29.43 225.28

15.01 35.39 6.64 42.03 47 200.95 29.43 230.39

16 37.96 6.64 44.6 48 206.06 29.43 235.49

17 40.58 6.64 47.23 49 211.16 29.43 240.59

18 43.24 6.64 49.89 49.99 216.21 29.43 245.64

19 45.94 6.64 52.58 50.01 216.31 30.45 246.76

19.99 48.63 6.64 55.28 51 221.37 30.45 251.81

20.01 48.71 16.51 65.23 52 226.47 30.45 256.92

21 53.96 16.51 70.48 53 231.57 30.45 262.02

22 59.34 16.51 75.85 54 236.68 30.45 267.12

23 64.8 16.51 81.31 54.99 241.73 30.45 272.17

24 70.33 16.51 86.84 55.01 241.83 31 272.83

24.99 75.89 16.51 92.4 56.00 246.88 31 277.88

25.01 76 16.88 92.88 57 251.98 31 282.98

26 81.48 16.88 98.37 58 257.09 31 288.09

27 87.1 16.88 103.99 59 262.19 31 293.19

28 92.8 16.88 109.69 59.99 267.24 31 298.24

29 98.59 16.88 115.47 60.01 267.34 31.28 298.62

29.99 104.39 16.88 121.27 61 272.4 31.28 303.67

30.01 104.51 17.81 122.31 62 277.5 31.28 308.78

31 110.29 17.81 128.1 63 282.6 31.28 313.88

179
Table D-100 Nominal Shaft, Nominal Toe and Nominal Geotechnical Resistance for 

HP 12x74 at the South Abutment (Continued)

Depth

(feet)

Nominal 

Shaft 

Resistance 

(kips)

Nominal 

Toe 

Resistance 

(kips)

Nominal 

Geotechnical 

Resistance 

(kips)

Depth

(feet)

Nominal 

Shaft 

Resistance 

(kips)

Nominal 

Toe 

Resistance 

(kips)

Nominal 

Geotechnical 

Resistance 

(kips)

64 287.71 31.28 318.98 78 359.15 33.03 392.18

64.99 292.76 31.28 324.03 79 364.25 33.03 397.28

65.01 292.86 32.29 325.15 79.99 369.3 33.03 402.33

66 297.91 32.29 330.2 80.01 369.4 33.21 402.62

67 303.01 32.29 335.31 81 374.46 33.21 407.67

68 308.12 32.29 340.41 82 379.56 33.21 412.77

69 313.22 32.29 345.51 83 384.66 33.21 417.88

69.99 318.27 32.29 350.56 84 389.77 33.21 422.98

70.01 318.37 32.75 351.13 84.99 394.82 33.21 428.03

71 323.43 32.75 356.18 85.01 394.92 33.68 428.59

72 328.53 32.75 361.28 86 399.97 33.68 433.65

73 333.63 32.75 366.39 87 405.07 33.68 438.75

74 338.74 32.75 371.49 88 410.18 33.68 443.85

74.99 343.79 32.75 376.54 89 415.28 33.68 448.96

75.01 343.89 33.03 376.92 90 420.33 33.68 454.01

76 348.94 33.03 381.97 91 420.43 33.68 454.11

77 354.04 33.03 387.07 91.25 420.43 1527.00 1947.43

For piles driven to hard rock, the nominal toe resistance should be determined using 

Equation 7-34 as described in Section 7.2.1.4.2. The strength properties of the 

limestone bedrock were presented in Table D-99. The unit toe resistance, qp, of the 

hard rock can then be calculated using Equation 7-34.

qqpp = PPss uu NNcc + γ DD NNqq + PPtt γ (

bb NNγ

2 ) [Eq. 7-34]

This computation requires determination of the bearing capacity factors NNcc, NNqq, and 

NNγ from Figure D-84. Entering the figure with a friction angle of 35.5 degrees, the 

bearing capacity factors NNcc, NNqq, and NNγ , were determined to be 17, 14, and 24, 

respectively. Because piles will likely be seated on bedrock, the pile penetration into 

the rock surface is assumed as 0.25 feet.

180
Figure D-84 Bearing capacity factors for foundations on rock.

Equation 7-34 is now used to determine the unit resistance, qp, of the rock.

uu = undrained shearing resistance of the rock, 476 ksf.

γ = effective density of the rock mass, 0.165 kcf.

DD = pile penetration below the rock surface, assume 0.25 feet.

bb = pile width or diameter 1 foot (HP 12x74).

PPss = pile shape factor of 1.25 for square pile toe.

PPtt = pile base factor of 0.80 for a square pile toe.

NNcc = bearing capacity factor, 17 (Figure D-84).

NNqq = bearing capacity factor, 14 (Figure D-84).

NNγ = bearing capacity factor, 24 (Figure D-84).

qqpp = PPss uu NNcc + γ DD NNqq + PPtt γ (

bb NNγ

2 ) [Eq. 7-34]

qqpp = (1.25) ∗ (476 kk ) ∗ (17)

+ (0.165 kk ) ∗ (0.25 ff ) ∗ (14)

+ (0.80) ∗ (0.165 kk ) ∗ (

(1 ffffff ) ∗ (24)

2 )

qqpp = 10,117 kk

181
For the HP 12x74 pile section with toe area (area of steel, AAss) of 0.151 ft2

, the 

nominal toe resistance is then calculated as follows:

RRpp = qqpp ∗ AAss

RRpp = (10,117 kk ) ∗ (0.151 ff 2)

RRpp = 1,528 kkkk

The nominal shaft, nominal toe, and nominal geotechnical resistance are also 

presented graphically in Figure D-85. A review of Table D-94 indicates the nominal 

structural resistance for the HP 12x74 section is 1088 kips, which is less than the 

nominal toe resistance when driven to hard limestone bedrock. Therefore, the 

nominal structural resistance will control the design. The penetration depth indicated 

in both Table D-100 and Figure D-85 is referenced from the bottom of footing, which 

is 5 feet below the original ground surface elevation. The nominal shaft, nominal 

toe, and nominal geotechnical resistances were calculated for all of the candidate 

pile sections in a similar manner. The nominal geotechnical resistances in axial 

compression versus pile penetration depth for all candidate pile types are presented 

in Figure D-86.

Once the nominal geotechnical resistance in axial compression versus pile 

penetration depth has been calculated, the factored geotechnical resistance in axial 

compression versus pile penetration depth can be determined. The factored 

geotechnical resistance depends on the resistance determination method selected 

for the design.

If the nominal resistance will be confirmed by a field determination method, the 

factored geotechnical resistance in axial compression as a function of pile 

penetration depth can be determined by multiplying the calculated nominal 

geotechnical resistance at a given depth by the resistance factor associated with the 

field determination method, φφdd . AASHTO (2014) resistance factors for field 

resistance determination methods are presented in Table 7-2.

If pile installation will be controlled by driving to a depth determined by static analysis 

method, then the factored geotechnical resistance in axial compression as a function 

of pile penetration depth can be determined by multiplying the calculated nominal 

resistance at a given depth by the resistance factor associated with the static 

analysis method, φφss . AASHTO (2014) resistance factors for static analysis 

methods are presented in Table 7-1 of this manual. 

182
Figure D-85 Nominal geotechnical resistance in axial compression versus pile 

penetration depth for HP 12x74 at the South Abutment.

Figure D-86 Nominal geotechnical resistance in axial compression versus pile 

penetration depth for all candidate pile sections at South Abutment.

183
Figure D-87 presents a design chart of the nominal and factored geotechnical 

resistance in axial compression versus depth for the HP 12x74 candidate H-pile 

section. The design chart includes the nominal geotechnical resistance as well as 

factored geotechnical resistances based on several resistance determination 

methods. The factored geotechnical resistance versus penetration depth is plotted 

for resistance determination by a static load test with dynamic testing of 2% of the 

piles (φφdd =0.80), by dynamic testing of at least two piles per site condition, but no 

less than 2% of the production piles, with signal matching (φφdd =0.65), and by wave 

equation analysis (φφdd =0.50). Also included is the factored geotechnical resistance 

based on the static analysis method used at the abutment, the alpha method 

(φφss =0.35). An AASHTO resistance factor is not currently available for the static 

analysis method used for hard rock. Therefore, the field resistance determination 

method would control pile installation. 

For the HP 12x74 section, Figure D-87 illustrates the effects that the various 

resistance determination methods have on the pile length required for a given 

factored compression resistance, the range of factored resistances available from a 

given pile section, and the potential impact of these factors on the number of piles 

needed to resist axial compression loads.

Figure D-87 Design chart of nominal and factored geotechnical resistance in axial 

compression versus pile penetration depth for HP 12x74 at the South Abutment.

184
The factored geotechnical resistance in axial compression for all candidate pile 

sections is presented in Figures D-88 through D-91 based on the same resistance 

determination method. For all the candidate pile sections, these figures illustrate the 

effects the various resistance determination methods have on the pile length 

required for a given factored resistance, the factored resistance available from a 

given pile section, and the potential impact of these factors on the number of piles 

needed to resist axial compression loads.

Figure D-88 Factored geotechnical resistance, Rr, in axial compression based on 

field determination by static load test and dynamic testing 2% of the piles,φφdd =0.80.

185
Figure D-89 Factored geotechnical resistance, Rr, in axial compression based on 

field determination by dynamic testing 2% of the piles, φφdd =0.65.

Figure D-90 Factored geotechnical resistance, Rr, in axial compression based on 

field determination by wave equation analysis, φφdd =0.50.

186
Figure D-91 Factored geotechnical resistance, Rr, in axial compression based on 

determination using alpha method static analysis, φφss =0.35.

D.34.2 Geotechnical Resistance in Axial Tension (uplift)

In a similar manner, the nominal and factored geotechnical resistances in axial 

tension (uplift) were calculated using the alpha method and with the DrivenPiles 

computer program. Figure D-92 presents the nominal shaft resistance versus 

penetration depth for all the candidate pile sections. As outlined in Section 7.2.3.2.1, 

the factored resistance in axial tension is the shaft resistance multiplied by the 

resistance factor, φup, for the resistance determination method. 

Figure D-93 presents a design chart of the nominal and factored geotechnical 

resistance in axial tension versus pile penetration depth for HP 12x74 H-pile section. 

A resistance factor of 0.60 is used when the tension resistance is determined by a 

static load test, 0.50 when determined by a dynamic test with signal matching, and 

0.25 when determined by the alpha method static analysis. For a single pile section 

(HP 12x74), this figure illustrates the effects the various resistance determination 

methods have on the pile length required for a given factored resistance, the 

factored resistance available from a given pile section, and the potential impact of 

these factors on the number of piles needed to resist axial tension loads.

187
Figures D-94 to D-96 present the factored geotechnical resistance in axial tension 

versus penetration depth based on the field determination method for each of the 

candidate pile sections. For all the candidate pile sections, these figures illustrate 

the effects the various resistance determination methods have on the pile length 

required for a given factored resistance, the factored resistance available from a 

given pile section, and the potential impact of these factors on the number of piles 

needed to resist axial tension loads.

A review of the soil profile at the South Abutment indicates no unsuitable soil layers 

are present that should be ignored for load support. Abutment scour and 

liquefaction due to a seismic event are also not considerations. 

Figure D-92 Nominal shaft resistance versus penetration depth for all candidate pile 

sections at the South Abutment.

188
Figure D-93 Design chart of nominal and factored geotechnical resistance in axial 

tension versus pile penetration depth for HP 12x74 at the South Abutment.

Figure D-94 Factored geotechnical resistance, Rr, in axial tension based on field 

determination by static load test, φdyn=0.60.

189
Figure D-95 Factored geotechnical resistance, Rr, in axial tension based on field 

determination by dynamic testing with signal matching, φdyn=0.50.

Figure D-96 Factored geotechnical resistance, Rr, in axial tension based on 

determination using alpha method static analysis, φstat=0.25.

190
D.34.3 Preliminary Pile Drivability Assessment

Preliminary assessments of pile drivability are now performed at this stage of the 

design. A drivability check at this time is essential to assess the constructability of 

candidate pile types and/or sections and to eliminate sections with insufficient 

drivability. Section 12.4 provides a detailed discussion of wave equation drivability 

analyses and their applications. 

A candidate pile section must be capable of being driven to the nominal driving 

resistance. In this example, the nominal driving resistance is less than the nominal 

geotechnical resistance since soil set up will be incorporated into the design. In 

addition, a candidate pile section must be capable of being driven to the penetration 

depth necessary to achieve the nominal geotechnical resistance in axial tension, and 

to a penetration depth necessary to satisfy lateral load demands as well as axial and 

lateral deformation requirements. A suitably sized pile hammer must be capable of 

driving the pile to its established minimum penetration depth and to the nominal 

resistance at a reasonable blow count without exceeding material stress limits. As 

detailed in Chapter 12, the blow count should be between 30 and 120 blows per foot 

at the nominal resistance. If the pile cannot be driven within these requirements, a 

larger pile hammer, a pile section with greater impedance, or pile installation aids 

such as predrilling or jetting may be required to satisfy or improve drivability. 

Driving stresses during pile installation should remain below the driving stress limits 

tied to pile type and material strength. For the candidate steel H-piles, compression 

driving stress limits are given by Equation 8-33. As per ASTM A-572 requirements, 

new steel H-piles are rolled with a minimum yield stress of 50 ksi.

The driving stress limit, σdd , for candidate pile sections is then calculated as follows:

σdd = φφdd �0.9 FFyy� [Eq. 8-33]

Where: φdd = resistance factor, 1.0 for steel piles.

FFyy = yield stress, 50 ksi.

Therefore, the driving stress limit, σdd , is 45 ksi.

σσdd = (1.0)�0.9 (50 kk kk)� = 45 kk kk

Drivability analyses were performed for all five candidate pile sections. Since the 

specific pile hammer is often unknown at this point in the design, a reasonably sized, 

191
commonly available single acting diesel hammer was chosen for each of the 

candidate pile sections. As noted in Section 15.19, a hammer having a ram weight 

of 1 to 2% of the larger of the required nominal resistance or required nominal 

driving resistance often provides a reasonable initial estimate of hammer size for 

wave equation analysis.

Table D-101 summarizes the factored structural resistance in axial compression, Pr, 

and the corresponding minimum and maximum nominal driving resistance 

associated with full section utilization and field determination methods ranging from 

a static load test with dynamic testing (φdyn=0.80) to the FHWA modified Gates 

dynamic formula (φdyn=0.40). Given that utilization of the full structural resistance is 

uncommon for piles driven in soil, a reasonable initial estimate of the trial hammer 

size for a wave equation drivability analysis is 1 to 1.5% of the minimum Rndr. 

Driving stresses could exceed specified limits by choosing a hammer with a ram 

weight significantly larger than 2% of the minimum Rndr. For each pile hammer, the 

wave equation default values were used for the helmet weight, hammer cushion 

materials, and the hammer cushion material properties.

Table D-101 Summary of Pile Hammers Used in Drivability Analyses

Pile Section Pile 

Cross 

Sectional 

Area 

(in2)

Factored 

Structural 

Resistance, 

Pr

(kips)

Minimum 

Rndr

φdyn=0.80

(kips)

Maximum

Rndr

φdyn=0.40

(kips)

Ram 

Weight 

1% of Min 

Rndr

(%)

Diesel 

Model

Ram 

Weight 

(kips)

Rated 

Energy 

(ft-kips)

HP 10x42 12.4 309 386 773 3.86 D25-52 5.51 62.0

HP 12x53 15.5 383 478 958 4.78 D30-52 6.62 74.4

HP 12x74 21.8 544 680 1360 6.80 D36-52 7.94 89.3

HP 14x89 26.1 652 815 1630 8.15 D46-52 10.14 114.1

HP 14x117 34.4 860 1075 2150 10.07 D50-52 11.03 124.0

For the soil resistance model, the output from DrivenPiles was converted to unit 

shaft resistance and unit toe resistance values and then input into the wave equation 

program. Similar soil resistances are thereby calculated versus depth by both the 

static analysis and wave equation analysis programs. 

The dynamic soil properties for each soil layer were chosen in accordance with wave 

equation program recommendations. Selection of soil quake and damping 

parameters is discussed in Section 12.6.7. For the South Abutment profile, setup 

factors of 2.0 were selected for all of the silty clay layers. No setup was considered 

192
for the hard rock. Soil setup is discussed in Section 7.2.4.2 and a summary of 

typical soil setup factors is provided in Table 7-16. A summary of the dynamic soil 

properties chosen for the drivability analyses are summarized in Table D-102.

Table D-102 Dynamic Soil Properties for South Abutment Soil Profile

Soil 

Layer

Pile 

Section

Shaft 

Quake

(in)

Toe 

Quake

(in)

Shaft 

Damping

(s/ft)

Toe 

Damping

(s/ft)

Soil SetUp 

Factor

1 HP 10 x 42 0.10 0.17 0.20 0.15 2.0

1 HP 12 x 53 0.10 0.20 0.20 0.15 2.0

1 HP 12 x 74 0.10 0.20 0.20 0.15 2.0

1 HP 14 x 89 0.10 0.23 0.20 0.15 2.0

1 HP 14 x 117 0.10 0.23 0.20 0.15 2.0

2 HP 10 x 42 0.10 0.17 0.20 0.15 2.0

2 HP 12 x 53 0.10 0.20 0.20 0.15 2.0

2 HP 12 x 74 0.10 0.20 0.20 0.15 2.0

2 HP 14 x 89 0.10 0.23 0.20 0.15 2.0

2 HP 14 x 117 0.10 0.23 0.20 0.15 2.0

3 HP 10 x 42 0.10 0.17 0.20 0.15 2.0

3 HP 12 x 53 0.10 0.20 0.20 0.15 2.0

3 HP 12 x 74 0.10 0.20 0.20 0.15 2.0

3 HP 14 x 89 0.10 0.23 0.20 0.15 2.0

3 HP 14 x 117 0.10 0.23 0.20 0.15 2.0

4 HP 10 x 42 0.10 0.08 0.05 0.15 1.0

4 HP 12 x 53 0.10 0.10 0.05 0.15 1.0

4 HP 12 x 74 0.10 0.10 0.05 0.15 1.0

4 HP 14 x 89 0.10 0.12 0.05 0.15 1.0

4 HP 14 x 117 0.10 0.12 0.05 0.15 1.0

In soils that exhibit setup, the long term nominal resistance may be higher than the 

nominal driving resistance. Therefore, a gain/loss factor of 0.50 was used to 

estimate the nominal driving resistance versus depth in the drivability analyses. This 

gain/loss factor was determined from the inverse of the highest soil setup factor 

within the soil model (e.g., 1 divided by 2.0 equals 0.50). A gain/loss factor of 1 

would be used if it was desired to model the nominal resistance instead of the 

nominal driving resistance and not consider the soil strength loss during driving and 

any subsequent soil setup. Refer to Chapter 12 for more detailed discussion on the 

selection of dynamic soil properties and soil setup factors.

193
The DrivenPiles program calculates the nominal driving resistance which models the 

soil strength lost during driving as well as the geotechnical nominal resistance once 

setup occurs. Figure D-97 presents the nominal shaft, toe, and driving resistance 

versus pile penetration depth for the HP 12x74 H-pile section at the South Abutment. 

These results are also presented numerically in Table D-103. To quantify the 

expected soil setup at a given pile penetration depth, the values from Table D-103

can be compared against the nominal resistance previously presented in Table 

D-100. Figure D-98 illustrates the significant difference between the expected 

nominal driving resistance and the geotechnical nominal resistance after setup for 

the HP 12x74 candidate pile section. For example, at a depth of 45 feet, the 

expected setup from shaft resistance is 95 kips. Where significant soil setup is 

expected, a smaller pile driving hammer may be acceptable for pile installation since 

the nominal driving resistance will be significantly lower than the nominal 

geotechnical resistance.

Figure D-97 Nominal driving resistance for HP 12x74 at the South Abutment.

194
Figure D-98 Comparison of nominal driving resistance and nominal geotechnical 

resistance in axial compression for HP 12x74 at the South Abutment. 

195
Table D-103 Nominal Shaft, Nominal Toe and Nominal Driving Resistance 

for HP 12x74

Depth

(feet)

Nominal 

Shaft 

Resistance 

(kips)

Nominal 

Toe 

Resistance 

(kips)

Nominal 

Driving 

Resistance 

(kips)

Depth

(feet)

Nominal 

Shaft 

Resistance 

(kips)

Nominal 

Toe 

Resistance 

(kips)

Nominal 

Driving 

Resistance 

(kips)

0.01 0.01 6.09 6.1 32 58.11 17.81 75.92

1 1.1 6.09 7.19 33 61.12 17.81 78.93

2 2.2 6.09 8.3 34 64.18 17.81 81.99

3 3.3 6.09 9.41 34.99 67.25 17.81 85.05

4 4.4 6.09 10.51 35.01 67.31 18.45 85.76

4.99 5.52 6.09 11.61 36 70.35 18.45 88.8

5.01 5.54 6.27 11.81 37 73.41 18.45 91.87

6 6.67 6.27 12.95 38 76.48 18.45 94.93

7 7.84 6.27 14.11 39 79.55 18.45 98

8 9.01 6.27 15.29 39.99 82.59 18.45 101.04

9 10.21 6.27 16.48 40.01 82.64 28.69 111.34

9.99 11.4 6.27 17.68 41 85.17 28.69 113.86

10.01 11.43 6.46 17.89 42 87.72 28.69 116.41

11 12.64 6.46 19.1 43 90.27 28.69 118.96

12 13.87 6.46 20.33 44 92.82 28.69 121.52

13 15.13 6.46 21.59 44.99 95.35 28.69 124.04

14 16.4 6.46 22.85 45.01 95.4 29.43 124.83

14.99 17.67 6.46 24.13 46 97.93 29.43 127.36

15.01 17.69 6.64 24.34 47 100.48 29.43 129.91

16 18.98 6.64 25.62 48 103.03 29.43 132.46

17 20.29 6.64 26.93 49 105.58 29.43 135.01

18 21.62 6.64 28.26 49.99 108.11 29.43 137.54

19 22.97 6.64 29.61 50.01 108.16 30.45 138.6

19.99 24.32 6.64 30.96 51 110.68 30.45 141.13

20.01 24.36 16.51 40.87 52 113.23 30.45 143.68

21 26.98 16.51 43.5 53 115.79 30.45 146.23

22 29.67 16.51 46.18 54 118.34 30.45 148.78

23 32.4 16.51 48.91 54.99 120.86 30.45 151.31

24 35.16 16.51 51.68 55.01 120.91 31.00 151.91

24.99 37.94 16.51 54.46 56 123.44 31.00 154.44

25.01 38.0 16.88 54.88 57 125.99 31.00 156.99

26 40.74 16.88 57.63 58 128.54 31.00 159.54

27 43.55 16.88 60.44 59 131.1 31.00 162.1

28 46.4 16.88 63.29 59.99 133.62 31.00 164.62

29 49.29 16.88 66.18 60.01 133.67 31.28 164.95

29.99 52.19 16.88 69.08 61 136.2 31.28 167.48

30.01 52.25 17.81 70.06 62 138.75 31.28 170.03

31 55.15 17.81 72.95 63 141.3 31.28 172.58

196
Table D-103 Nominal Shaft, Nominal Toe and Nominal Driving Resistance 

for HP 12x74 (continued)

Depth

(feet)

Nominal 

Shaft 

Resistance 

(kips)

Nominal 

Toe 

Resistance 

(kips)

Nominal 

Driving 

Resistance 

(kips)

Depth

(feet)

Nominal 

Shaft 

Resistance 

(kips)

Nominal 

Toe 

Resistance 

(kips)

Nominal 

Driving 

Resistance 

(kips)

64 143.85 31.28 175.13 78 179.57 33.03 212.6

64.99 146.38 31.28 177.66 79 182.13 33.03 215.15

65.01 146.43 32.29 178.72 79.99 184.65 33.03 217.68

66 148.96 32.29 181.25 80.01 184.7 33.21 217.92

67 151.51 32.29 183.8 81 187.23 33.21 220.44

68 154.06 32.29 186.35 82 189.78 33.21 222.99

69 156.61 32.29 188.9 83 192.33 33.21 225.55

69.99 159.14 32.29 191.43 84 194.88 33.21 228.1

70.01 159.19 32.75 191.94 84.99 197.41 33.21 230.62

71 161.71 32.75 194.47 85.01 197.46 33.68 231.14

72 164.26 32.75 197.02 86 199.99 33.68 233.66

73 166.82 32.75 199.57 87 202.54 33.68 236.21

74 169.37 32.75 202.12 88 205.09 33.68 238.76

74.99 171.89 32.75 204.65 89 207.64 33.68 241.32

75.01 171.94 33.03 204.97 90 210.17 33.68 243.84

76 174.47 33.03 207.5 91 210.24 33.68 243.92

77 177.02 33.03 210.05 91.25 210.24 1527.00 1737.24

Graphical outputs of the preliminary drivability analyses are shown in Figure D-99. 

The nominal driving resistance, the blow count or pile penetration resistance, and 

the compression driving stress are presented versus pile penetration depth for each 

of the five candidate pile sections. As previously noted, the recommended blow 

count limit is 120 blows per foot (10 blows per inch), and the recommended driving 

stress limit is 45 ksi. A circular reference marker is indicated on the blow count 

versus depth plot highlighting the depth where the blow count first exceeds 120 

blows per foot. This marker is also shown at the same depth on the nominal driving 

resistance versus depth plot indicating the nominal driving resistance achieved when 

practical refusal driving conditions are encountered with the selected hammer in the 

modeled driving conditions. Similarly, the marker is shown at the same depth on the 

compression driving stress versus depth plot indicating the compression driving 

stress when practical refusal driving conditions are encountered.

In Figure D-99, preliminary drivability results illustrate all candidate pile sections can 

be driven to the hard rock layer without reaching the blow count limit of 120 blows 

per foot. Compression driving stresses are also well below the driving stress limit of 

45 ksi prior to reaching bedrock. 

197
Figure D-99 Preliminary drivability results for five candidate H-pile sections at the 

South Abutment.

For piles driven to hard rock, the driving criteria should be established to control 

compression stresses and prevent pile toe damage (e.g., limit the number of blows 

at refusal driving conditions). A summary of the preliminary drivability results is 

presented in Table D-104. The anticipated nominal resistance in this table is the 

expected resistance after soil setup that can be mobilized by the driving system at 

10 blows per inch. Since the piles terminate on hard rock, a higher geotechnical 

nominal resistance, up to the structural resistance of the pile, is actually available.

Once the estimated and/or minimum pile toe elevations are determined in Block 12 

through Block 15 of the design process, the drivability results should be reviewed to 

confirm that the candidate pile section can be driven to the required nominal driving

resistance, at the estimated or required pile penetration depth, at a reasonable blow 

count, and within driving stress limits. Upon determination of the estimated toe 

elevation, these plots should be reviewed to confirm that the pile can be driven to the

estimated toe elevation at reasonable blow counts and stresses.

198
Table D-104 Summary of Preliminary Drivability Results at South Abutment

Pile

Section

Pile

Hammer

Fuel

Setting

Pile 

Penetration 

Depth at

Practical 

Refusal 

Limit

(feet)

Nominal 

Driving 

Resistance 

at Practical 

Refusal 

Limit

(kips)

Anticipated 

Nominal 

Resistance 

at Depth of 

Practical 

Refusal

(kips)

Penetration 

Depth 

Exceeding 

Compression 

Driving 

Stress Limit 

(feet)

Maximum 

Compression 

Driving 

Stress

(ksi)

HP 10x42 D25-52 4 91.1 362 536 > 91.1 34.1

HP 12x53 D30-52 4 91.1 446 649 > 91.1 34.6

HP 12x74 D36-52 4 91.1 590 806 > 91.1 36.7

HP 14x89 D46-52 4 91.1 729 975 > 91.1 39.5

HP 14x117 D50-52 4 91.1 896 1143 > 91.1 39.2

D.35Block 11: South Abutment – Estimate Preliminary Number of Piles, 

Preliminary Pile Group Size, and Resolve Individual Pile Loads for All 

Limit States

The structural engineer has provided the anticipated loads for the controlling limit 

states at the South Abutment. These limit state loads are restated in Table D-105. 

The Strength I limit state loads are used to evaluate geotechnical resistance in axial 

compression and tension, as well as for lateral loading. Service I limit state loads 

were also provided by the structural engineer without live loads. The Service I 

without live load (LL) includes only unfactored permanent loads such as the 

superstructure and wearing surface, pile cap and stem, utilities, and vertical earth 

pressure among others. The Service I without live load should be used for 

evaluating vertical deformation. There are no loads in the transverse direction at this 

abutment. 

Table D-105 Limit State Loads on South Abutment

Limit State Q

(kips)

Vuy

(kips)

Muy

(k-ft)

Strength I -2815 946 6732

Service I -2082 629 3931

Service I, without live load -1783 546 3024

199
Based on past experience, the agency generally utilizes 2 rows of piles at abutments 

with a minimum center to center pile spacing of at least 3 pile diameters. Three 

potential pile group configurations are therefore being considered: 2 rows of 9 piles, 

2 rows of 11 piles, and 2 rows of 13 piles. These group configurations are identified 

as Group Configuration 1, 2, and 3, respectively in Table D-106. Because of site 

constraints, the pile cap length is limited to 43 feet. Furthermore, the distance from 

the center of any exterior pile to the pile cap edge must be at least 1.25 feet in both 

the transverse (x) and longitudinal (y) direction.

Table D-106 Potential Pile Group Configurations

Group 

Configuration

Piles 

per 

Row

Total 

Number 

of Piles

Sbx*

(feet)

Total Footing 

Length

(feet)

Sby*

(feet)

Total Footing 

Width

(feet)

1 9 18 5.0 42.5 4.0 6.5

2 11 22 4.0 42.5 4.0 6.5

3 13 26 3.0 38.5 4.0 6.5

Note: * - Sbx and Sby are illustrated in Figure D-100

The following calculation is for the Group Configuration 3 and all applicable loads. 

For this alternative, 13 piles per row are used in two separate rows, thus the 

transverse pile spacing, Sbx, is 5’-0” and the total footing length is 38’-6”. The 

longitudinal pile spacing, Sby, is 4’-0”. Figure D-100 shows the layout for the Group 

Configuration 3 pile cap. 

Figure D-100 Group Configuration 3 pile cap plan view.

200
For the established limit state loads and the trial pile group configuration in Figure 

D-100, reactions for both the front and the back rows of piles were determined. 

Compression loads are taken as positive. The maximum factored load applied to 

each pile was subsequently calculated by dividing the reactions by the number of 

piles. Figure D-101 shows the free body diagram for determining the factored load 

for both the front and the back row.

Figure D-101Elevation view of cap free body diagram.

Table D-107 summarizes the limit state loads and the front and back row reactions. 

Strength I loads, Service I loads and the Service I loads without live load (LL) are 

provided. The Service I load without live load is used for settlement calculations. 

Table D-107 Factored Loads and Row Reactions

Limit State Q

(kips)

Muy

(k-ft)

Rfront

(kips)

Rback

(kips)

Strength I -2815 6732 3091 -276

Service I -2082 3931 2037 46

Service I, without LL -1783 3024 1648 136

Table D-108 presents the maximum factored load per pile based upon the number of 

piles in each group configuration. For example, considering Group Configuration 3, 

the Service I, without live load, front-row reaction of 1648 kips is divided by 13 piles 

to yield a front-row factored load per pile equal to 127 kips. Table D-108 also 

provides the factored load per pile for other limit states and group configurations.

201
Table D-108 Factored Load Per Pile for Alternative Pile Group Configurations

Group 

Configuration

Strength I,

Q

(kips)

Strength I, 

Q (tension)

(kips)

Strength I, 

Vuy

(kips)

Service I, without LL 

Q

(kips)

1 344 -31 53 183

2 281 -25 43 150

3 238 -21 37 127

D.36Block 12: South Abutment – Estimate Pile Penetration Depth for Maximum 

Axial Compression Loads. Check Group Efficiency in Axial Compression

The estimated minimum pile penetration depth necessary to obtain a factored 

geotechnical resistance that is equal or greater than the maximum factored load per 

pile is now determined. Note that the factored geotechnical resistance in axial 

compression and the resulting pile penetration depth is dependent upon the 

resistance determination method. Therefore, the influence of the field resistance 

determination method on the design needs to be evaluated at this point in the design 

process and some resistance determination methods may be eliminated from further 

design consideration.

Since setup in the cohesive soils will be a significant component of the nominal 

resistance, it is determined that the nominal geotechnical resistance will be 

substantiated by dynamic testing 2% of the piles. Figure D-89 illustrates the nominal 

geotechnical resistance versus penetration depth for the 5 candidate pile sections 

based on this resistance determination method. From this plot, the estimated 

penetration depth for a factored geotechnical resistance of 238 kips in axial 

compression for the Group Configuration 3 ranges from 62 feet for the HP 14x117 

H-pile section to 91 feet for the HP 10x42 H-pile section. The estimated pile 

penetration depth needed for the factored load associated with each group 

configuration is provided for all candidate pile sections in Table D-109. 

202
Table D-109 Estimated Pile Penetration Depths for the Factored Geotechnical 

Resistance in Axial Compression at the Strength I Limit State

Group 

Configuration

Factored 

Load per 

Pile

(kips)

HP 

10x42 

(feet)

HP 

12x53 

(feet)

HP 

12x74 

(feet)

HP 

14x89 

(feet)

HP 

14x117 

(feet)

1 344 91 91 91 90 88

2 281 91 90 86 74 72

3 238 91 74 73 63 62

As described in Section 7.2.2.2, the nominal geotechnical resistance of a pile group 

in cohesive soil can be taken as the sum of the individual pile nominal geotechnical 

resistances. In a similar manner, the factored geotechnical resistance of the pile 

group in cohesive soil is taken as the sum of the individual pile factored geotechnical 

resistances. This is recommended so long as 1) the pile cap is in firm contact with 

the ground and 2) the piles are not installed at a pile spacing of less than 3 times the 

pile diameter or 3 feet. Since both conditions are met at the South Abutment, by 

inspection, the nominal and factored group resistances are satisfactory. 

As will be discussed later in Block 15, in order to satisfy tolerable deformations, the 

piles at the South Abutment will be driven to bedrock. Therefore, piles at the South 

Abutment are not subject to block failure as outlined in Section 7.2.2.3 of Chapter 7.

D.37Block 13: South Abutment – Establish Minimum Pile Penetration Depth 

for Axial Tension Loads. If Conditions Warrant, Modify Design and 

Return to Block 10

The factored geotechnical resistance in axial tension must also be evaluated as the 

back row of piles will be loaded in tension (Table D-107). In this case, the minimum 

required factored geotechnical resistance in axial tension is established using the 

Strength I limit state and is determined following the procedure outlined in Section 

7.2.3.2. The analysis presented in this appendix slightly differs from the procedure 

outlined in Chapter 7 in that only a single row of piles is providing the tension 

resistance rather than the entire pile group. Two analyses are performed; one that 

considers the factored shaft resistances from individual piles, and one that considers 

the weight of a soil block acting with the piles. The lesser tension resistance 

determined from either method controls the design.

203
As noted in Table D-107, the Strength I limit state tension load on the back row of 

piles for the Group Configuration 3 is 276 kips. Therefore, the minimum factored 

geotechnical resistance in axial tension required from an individual pile is this 

factored load divided by the 13 piles in the rear row or 21 kips. In a similar manner, 

the minimum factored geotechnical resistance required from an individual pile in 

axial tension is 31 kips for Group Configuration 1, and 25 kips for Group 

Configuration 2.

As noted earlier, dynamic testing with signal matching will be used as the resistance 

determination method in the field. Therefore, the AASHTO recommended 

resistance factor, φφup, is 0.5 (Table 7-2 of Chapter 7). Figure D-95 provides plots of 

the factored geotechnical resistance in axial tension versus depth for all of the 

candidate pile types based on this resistance determination method. For each 

candidate section, Figure D-95 should be entered on the x-axis at the required 

factored axial tension resistance to determine the corresponding pile penetration 

depth.

Following this procedure, the estimated pile penetration depth to achieve the 

factored geotechnical resistance in axial tension for each candidate pile section and 

group configuration is summarized in Table D-110.

Table D-110 Estimated Minimum Pile Penetration Depth Required for Factored 

Geotechnical Resistance in Axial Tension at the Strength I Limit State

Group 

Configuration

Required

Factored

Resistance

in Axial

Tension

(kips)

HP 

10x42

(feet)

HP 

12x53 

(feet)

HP 

12x74

(feet)

HP 

14x89

(feet)

HP 

14x117

(feet)

1 31 25 23 23 21 21

2 25 23 21 21 19 18

3 21 21 19 18 16 16

Next, the tension resistance of the pile row when considered as a soil block is 

calculated. For Group Configuration 3, the required factored tension resistance of 

the back row remains 276 kips (Table D-107) and the resistance is derived from the 

weight of soil as a block and an average of the soil shear strength. Equation 7-39 is 

used to determine the required nominal group resistance in axial tension.

204
RRrr = φφRRnn = φφuu RRuu [Eq. 7-39]

Where:

RRnn = nominal resistance (kips).

φφug = resistance factor for tension per Table 7-1, 0.50.

RRuu = nominal uplift resistance of the pile group (kips).

RRuu = rr

φφuuuu

Eq. [7-39 modified]

RRuu = (276 )

(0.5)

RRuu = 552 kkkk

The minimum required nominal uplift resistance is 552 kips.

Equation 7-41 is then used to determine the minimum embedded length required to 

satisfy the nominal group tension resistance for soil acting as a block. The length of 

the pile group will change depending upon the group configuration. For Group 

Configuration 1 and 2, the pile group length is 41 feet from exterior pile edge to 

exterior pile edge assuming a 12 inch pile width/diameter. For Group Configuration 

3, the pile group length is 37 feet using the same pile dimension. The effect of a 

smaller pile size on the pile group length is negligible (e.g. for HP 10x42 section, the 

pile group length is 40.83 feet). 

RRuu = 2 D (B + Z) uu + WW [Eq. 7-41]

D = embedded length of piles (feet).

B = width of pile group, assume 1 foot (1 row in tension).

Z = length of pile group, 37 feet (Group Configuration 3).

uu = weighted average of the undrained shear strength over the depth of 

pile embedment along the pile group perimeter (ksf) (Figure D-83).

WW = effective weight of the pile/soil block including pile cap weight (kips).

The calculation is performed for the HP 12x74 pile section in Group Configuration 3. 

The back row contains 13 piles, and the group length is 37 feet. Figure D-102

provides a visual representation of the soil volume used to determine tension 

resistance. The block of soil being evaluated is only as wide as, and lies between, 

the piles. Therefore it is not visible in the transverse elevation view in Figure D-102.

205
Figure D-102 Tension resistance of pile group in cohesive soil.

Several iterations were performed to incrementally increase the pile length and 

evaluate the nominal uplift resistance of the pile group. The minimum required 

embedded length of piles was determined to be 9 feet, and therefore, that 

calculation is presented below.

Calculate the weight of piles:

D = embedded length of piles, 9 feet.

W/ft = weight per linear foot of HP 12x74 pile section, 0.074 kip/ft.

WWpp = (Weight/ linear foot) ∗ DD ∗ NN PP PP

WWpp = �0.074

ff � ∗ (9 ff ) ∗ (13 pp )

WWpp = 8.66 kkkk

206
Calculate the weight of soil:

D = embedded length of piles, 9 feet.

B = width of pile group, assume 1 foot (1 row in tension).

Z = length of pile group, 37 feet (Group Configuration 3).

γγ′ss = effective unit weight of soil, 47.6 pcf (Figure D-83).

WWss = D ∗ BB ∗ Z ∗ γγ′ss

WWss = (9 ff ) ∗ (1 ff ) ∗ (37 ff ) ∗ (47.6 pp ) ∗ � 1

1000 �

WWss = 15.85 kkkk

Calculate weight of the pile cap, conservatively taken as the tributary are over piles 

in tension:

BBcc = width of pile cap, half of cap width 6.5 feet /2 = 3.25 ft 

(Table D-106).

ZZcc = length of pile group, 38.5 feet (Table D-106).

cc = thickness of pile cap, preliminary estimate, 4.2 feet.

γγcc cc = unit weight of reinforce concrete, 150 pcf.

WWcc = BBcc ∗ ZZcc ∗ cc ∗ γγcc cc

WWcc = (3.25 ff ) ∗ (38.5 ff ) ∗ (4.2 ff ) ∗ (150 pp ) ∗ � 1

1000 �

WWcc = 78.83 kips

Calculate the effective weight of the pile/soil block including pile cap weight:

WW = WWpp + WWss + WWcc

WW = (8.66 kkkk ) + (15.85 kkkk ) + (78.83 kkkk )

WW = 103.3 kkkk

207
Equation 7-41 is next used to calculate the group tension resistance for soil acting 

as a block. A weighted average shear strength value of 0.67 ksf was used for the 

first 10 feet below the footing in the silty clay soil layer (Figure D-83).

D = embedded length of piles, 9 feet.

B = width of pile group, assume 1 foot (1 row in tension).

Z = length of pile group, 37 feet (Group Configuration 3).

uu = weighted average undrained shear strength, 0.67 ksf (Figure D-83).

WW = effective weight of the block, 103.3 kips.

RRuu = 2 D (B + Z) uu + WW [Eq. 7-41]

RRuu (9 ff ) = 2 ∗ (9 ff ) ∗ �(1 ffffff ) + (37 ff )� ∗ (0.67 kk ) + (103.3 kkkk )

RRuu (9 ff ) = 561.6 kkkk

Therefore:

RRuu (9 ff ) > RRuu

561.6 kkkk > 552 kkkk

The required soil block weight is achieved at approximately 9 feet of pile penetration. 

Accordingly, any additional pile penetration would satisfy this requirement. For a pile 

group length of 41 feet (i.e., Group Configuration 1 and 2), the minimum pile 

penetration depth to achiegve a soil block weight in excess of the required 552 kips 

is also 9 feet. 

As noted earlier, two analyses are performed to determine the minimum pile 

penetration depth for nominal tension resistance. The first one considers the shaft 

resistances from individual piles, and the second one considers the weight of a soil 

block acting with the piles. The required minimum pile penetration depth to achieve 

geotechnical resistance in axial tension is the greater depth of the above calculated 

resistances. The estimated minimum penetration depth required for the factored 

geotechnical resistance in axial tension was summarized in Table D-110. For the 

HP 12x74 pile section in Group Configuration 3, the minimum pile penetration depth 

is 18 feet for the factored tension load of 21 kips.

DD(ii ii ii ) = minimum pile penetration depth based on sum of individual 

pile resistance = 18 feet (Table D-110).

208
DD(bb ) = minimum pile penetration depth based on weight of soil block 

= 9 feet. (calculated above).

DD(ii ii ii ) > DD(bb )

18 ff > 9 ff

Therefore, the minimum penetration depth DD(mm −tt ) is as follows:

DD(mm −tt ) = 18 ff

In a similar manner, this check was performed for all candidate pile sections and 

group configurations. The resulting established minimum required pile penetration 

depth to meet axial tension requirements for each candidate pile section within the 

specified group configuration is presented in Table D-111. 

Table D-111 Established Minimum Pile Penetration Depth Required for Factored 

Geotechnical Resistance in Axial Tension at South Abutment

Group 

Configuration

HP 10x42 

(feet)

HP 12x53 

(feet)

HP 12x74 

(feet)

HP 14x89 

(feet)

HP 14x117 

(feet)

1 25 23 23 21 21

2 23 21 21 19 18

3 21 19 18 16 16

D.38Block 14: South Abutment – Establish Minimum Pile Penetration Depth 

for Lateral Loads. Determine p-y Models, Required Geomaterial 

Parameters, and Perform Lateral Load Analysis. If Conditions Warrant, 

Modify Design and Return to Block 10

Next, lateral analyses are performed to establish the required minimum pile 

penetration depth for lateral loading and to evaluate pile deflection and structural 

resistance for the applied limit state loads. The minimum required pile penetration 

depth required to satisfy the nominal geotechnical resistance requirements in axial 

tension was determined to be 18 feet in Block 13. A deeper minimum required pile 

penetration depth for lateral loading can result based on the combination of factored 

lateral loads and structural resistances, or deflection limits. Excessive deflections 

and moments develop at relatively short pile lengths, where a depth to fixity is not 

209
achieved. Furthermore, the structural resistance of pile sections must be evaluated 

based upon the axial, lateral and moment loads. Factored structural resistances 

were presented in Table D-95 while a lateral deformation limit of 1 inch was 

established as a global performance requirement in Block 1 and confirmed In Block 

4 as the design progressed. 

The soil profile at the South Abutment was presented in Figure D-83. For lateral 

load analyses, appropriate p-y models must be selected for each soil layer. The 

input parameters necessary for lateral load analysis using the LPILE computer 

program are included in the South Abutment soil profile.

As discussed in Section 7.3.7.6, p-multipliers are applied to the p-y curves to model 

pile group behavior. The p-multipliers depend on the center to center pile spacing 

within the pile group. For all group configurations at the South Abutment, the pile 

spacing in the longitudinal direction is 4 feet. Therefore, per Section 7.3.7.6 and 

AASHTO (2014) design specifications, interpolation was used to determine 

p-multipliers for a pile spacing of 4b. In this case, the front row p-multiplier is 0.90, 

while the second row is 0.625.

Cyclic loading was performed for both rows using LPILE’s Load Type 2 option, which 

uses shear and slope to model a fixed head condition. Considering loading 

conditions at this abutment, lateral analyses in the longitudinal (y-direction) were 

performed about the pile section’s strong axis. Figure D-100 shows the pile 

orientation within the trial pile cap design.

The following example is presented for the HP 12x74 pile section using a range of 

factored axial and lateral loads for Group Configuration 3. Tables D-112 and D-113

provide LPILE output summaries for both rows at the pile head considering a pile 

penetration for lateral loading of 30 feet. The pile head is assumed to terminate at 

the ground surface (i.e. no stickup).

210
Table D-112 LPILE Summary Output at Pile Head for Front Row, pm=0.90

Load 

Case

Load 

Type 

No.

Pile-Head 

Condition 1 

V (kips)

Pile-Head 

Condition 2 

S (rad)

Axial 

Load

(kips)

Pile-Head 

Deflection

(inches)

Maximum 

Moment in 

Pile 

(kip-ft)

Maximum 

Shear in 

Pile

(kips)

Pile-Head 

Rotation

(radians)

1 2 0 0 238 0.000 0.0 0 0

2 2 15 0 238 0.116 -56.6 15 0

3 2 30 0 238 0.451 -141.7 30 0

4 2 35 0 238 0.611 -173.8 35 0

5 2 36 0 238 0.646 -180.4 36 0

6 2 37 0 238 0.682 -187.1 37 0

7 2 38 0 238 0.719 -193.9 38 0

8 2 40 0 238 0.796 -207.6 40 0

9 2 42 0 238 0.876 -221.5 42 0

10 2 50 0 238 1.344 -292.1 50 0

Table D-113 LPILE Summary Output at Pile Head for Second Row, pm=0.625

Load 

Case

Load 

Type 

No.

Pile-Head 

Condition 1 

V (kips)

Pile-Head 

Condition 2 

S (rad)

Axial 

Load

(kips)

Pile-Head 

Deflection

(inches)

Maximum 

Moment in 

Pile 

(kip-ft)

Maximum 

Shear in 

Pile

(kips)

Pile-Head 

Rotation

(radians)

1 2 0 0 238 0.000 0.0 0 0

2 2 15 0 238 0.196 -67.5 15 0

3 2 30 0 238 0.769 -169.8 30 0

4 2 35 0 238 1.060 -211.2 35 0

5 2 36 0 238 1.138 -221.2 36 0

6 2 37 0 238 1.223 -231.8 37 0

7 2 38 0 238 1.317 -242.9 38 0

8 2 40 0 238 1.531 -266.6 40 0

9 2 42 0 238 1.793 -292.7 42 0

The pile group deflection can be estimated from the above LPILE’s deflection results 

for the front and second rows. The factored load versus pile head deflection for 

each row is plotted in Figure D-103 along with the group average. The average 

lateral load per pile for a given group deflection is shown. A step by step discussion 

of this procedure is provided in Section 7.3.7.6.

The rigid cap method assumes piles move together, and therefore experience the 

same shear and lateral load. Accordingly, at the resulting factored lateral load per 

pile, Vuy, of 37 kips (Table D-108), the estimated lateral group deflection at the pile 

head is determined as 0.96 inches. This lateral deflection is less than the 1 inch 

tolerance based upon project specific requirements.

211
Figure D-103 Factored load versus deflection for HP 12x74 at South Abutment.

In addition to the lateral deflection limit, stresses from the resulting bending moment 

and shear must be evaluated to check that the pile section does not fail structurally. 

Using the LPILE tabular results, Figure D-104 plots the front row bending moment 

versus depth for a deflection of 0.96 inches.

Figure D-105 plots the maximum bending moment versus pile head deflection for 

both the front and back rows, however only the maximum bending moment for the 

front row is used as a “worst case” evaluation of the structural resistance in 

combined axial compression and flexure. As illustrated in Figure D-105 for the front 

row piles, at the estimated pile head deflection of 0.96 inches, the maximum bending 

moment, Muy, is 235 kip-ft. 

212
Figure D-104 Front row bending moment versus depth.

Figure D-105 Bending moment versus deflection for HP 12x74 at South Abutment.

213
The interaction shown in Equation 8-58 must be satisfied for the factored axial 

compression load and moment in the pile. Using results of the lateral analysis, the 

factored structural resistance was evaluated at the pile head using the factored axial 

compression load and maximum bending moment (determined using factored 

loads). The factored structural resistances were determined as shown in Table 

D-95.

Equation 8-58 must be satisfied for the pile section to be acceptable.

PPuu = factored axial load, 238 kips (Table D-108).

PPrr = factored axial resistance, 762 kips (Table D-95).

Muu = factored moment about x-axis, 0 kip-ft (Block 11).

Mrrrr = factored flexural resistance about x-axis, 118 kip-ft (Table D-95).

Muu = factored moment about y-axis, 235 kip-ft (Figure D-105).

Mrr = factored flexural resistance about y-axis, 433 kip-ft (Table D-95).

Puu

Prr

+ 8.0

9.0 � Muuuu

Mrr

+

Muuuu

Mrr

� ≤ 1.0 [Eq. 8-58]

238 kips

762 kips + 8.09.0 � 0118 kip−ft + 235 kip−ft433 kip−ft� ≤ 1.0

0.79 ≤ 1.0

The maximum shear from factored lateral loading was then compared to the factored 

shear resistance from Table D-95. Based on the factored loads, the factored shear 

resistance is acceptable.

VVrr = factored shear resistance, 214 kips (HP 12x74, Table D-95).

VVuu = factored shear load, 37 kips (Group Configuration 3, Table D-108).

VVuu < VVrr

37 kkkk < 214 kkkk

The lateral analysis was also performed for each alternative pile section. The 

deflection and factored structural resistance were evaluated considering the factored 

loads for group configurations shown in Table D-108. Pile head deflection must be 

limited to 1 inch, and based upon the applied loads and pile section, the factored 

structural resistance of the pile must also satisfy the structural resistance interaction 

214
equation presented as Equation 8-58. Pile sections satisfying both criteria were 

deemed acceptable, and furthermore as summarized in Table D-114, a minimum 

required pile penetration depth was established based on lateral load resistance 

considerations. The minimum penetration depth is identified as “- - -“ for candidate 

pile sections not meeting the lateral deformation or structural resistance 

requirements.

Several of the larger pile sections provided sufficient stiffness to resist the applied 

loads, while less stiff sections did not (they failed the structural resistance check in 

Equation 8-58). Factored axial compression loads, in combination with moments 

caused by factored lateral loads, resulted in some sections’ factored structural 

resistance being exceeded. Although the HP 12x53 pile section satisfied structural 

resistance requirements considering Group Configuration 3 factored loads, the pile 

section did not satisfy the 1 inch pile head deflection requirement for any pile 

penetration depth.

Table D-114 Established Minimum Required Pile Penetration Depth for Lateral 

Loading at the South Abutment 

Group 

Configuration

HP 10x42

(feet)

HP 12x53 

(feet)

HP 12x74

(feet)

HP 14x89

(feet)

HP 14x117

(feet)

1 - - - - - - - - - - - - 40

2 - - - - - - - - - 35 35

3 - - - - - - 35 35 35

D.39Block 15: South Abutment – Establish Pile Penetration Depths that Satisfy 

Tolerable Deformations. Estimate Group Settlement over the Minimum 

and Maximum Range of Pile Penetration Depths From Blocks 12 to 14 and 

Identify All Pile Toe Elevations Which Result in Intolerable Deformations. 

If Conditions Warrant, Modify Design and Return to Block 10

For the cohesive soils at the South Abutment, pile group settlement was estimated 

using two methods, classic consolidation theory in cohesive soils and the Janbu 

Tangent modulus method. Ideally, the settlement method chosen by the designer is 

one that has shown good correlation with observed results. The pile group 

settlement at the South Abutment was first calculated using classic consolidation 

theory with an equivalent footing per AASHTO (2014) design specifications. 

However, the soil conditions across the bridge substructure locations are quite 

variable and a settlement method that could be used at all substructure locations 

was also desired. Therefore, group settlement was also computed with the Janbu 

Tangent modulus approach using an equivalent footing placed at the neutral plane.

215
As established by global project performance requirements, vertical deformation 

(including both settlement and elastic compression) should be limited to 1.5 inches 

at each substructure location. 

The deformation analysis must consider all loads and resulting changes in vertical 

effective stress. Thus the analysis begins considering construction of the new 

embankment and the subsequent increase in vertical effective stresses below the 

abutment. For simplification, the vertical effective stress increase is determined by 

treating the embankment surcharge as a strip load. Figure D-106 demonstrates this 

concept and defines symbols, while the change in vertical effective stress with depth 

is determined using Equation D-2 through D-4.

∆σσvv = qq

Π [β + sin(β) ∗ cos(β + 2δ)] [Eq. D-2]

Where:

β = −1 � +bb

zz � − −1( −bbzz ) [Eq. D-3]

and

δ = −1( −bb

zz ) [Eq. D-4]

Figure D-106 Vertical effective stress increase due to strip load.

The 15 foot high embankment, with a soil unit weight 120 pcf, results in a surcharge 

stress at the embankment base of 1.8 ksf, and is assumed to extend 100 feet behind 

216
the abutment. Fill directly above the footing is already included in design as a 

permanent vertical load, EV, and therefore the embankment surcharge is assumed 

to act as a strip load beginning at the footing edge. The change in vertical effective 

stress from the embankment surcharge, Δσ’v(e), is determined under the footing 

centerline as depicted in Figure D-107. 

An example calculation is shown for a depth below footing, z, of 2.5 feet, while 

complete calculations were performed using a spreadsheet and are shown in Table 

D-115. The bottom of footing is at Elevation 305 feet. Therefore, although the value 

of z in the following series of analyses may vary based upon the equivalent footing 

or neutral plane location, the elevation is used to provide a comparison of effective 

stress change with depth.

Figure D-107 Profile of vertical stress increase due to embankment surcharge.

Determine geometry of profile.

x = 3.25 ff + 100 ff

2 = 53.25 ff

b = 100 ff

2 = 50 ff

Determine angle β.

β = −1 � +bb

zz � − −1( −bbzz ) [Eq. D-3]

217
β = −1 �

53.25 ff +50 ff

2.5 ff � − −1 �

53.25 ff −50 ff

2.5 ff �

β = 0.63

Determine angle δ.

δ = −1( −bb

zz ) [Eq. D-4]

δ = −1 �

53.25 ff −50 ff

2.5 ff �

δ = 0.92

Calculate the change in vertical effective stress due to embankment surcharge.

qq = stress per unit length, 1.8 ksf.

∆σσ′vv( ) = qq

Π [β + sin(β) ∗ cos(β + 2δ)] [Eq. D-2]

∆σσ′vv( ) = 1.8

Π [0.63 + sin(0.63) ∗ cos(0.63 + 2 ∗ (0.92))]

∆σσ′vv( ) = 0.10 kk

218
Table D-115 Vertical Effective Stress Increase from Embankment Surcharge

Elevation

(feet)

Soil 

Layer

z

(feet) δ β Δσ’v(e)(ksf)

304.99 1 0.01 1.57 0.00 0.00

302.5 1 2.5 0.92 0.63 0.10

297.5 1 7.5 0.41 1.09 0.46

292.5 1 12.5 0.25 1.20 0.61

287.5 1 17.5 0.18 1.22 0.69

282.5 2 22.5 0.14 1.21 0.73

277.5 2 27.5 0.12 1.19 0.76

272.5 2 32.5 0.10 1.17 0.78

267.5 2 37.5 0.09 1.14 0.79

262.5 3 42.5 0.08 1.10 0.79

257.5 3 47.5 0.07 1.07 0.79

252.5 3 52.5 0.06 1.04 0.79

247.5 3 57.5 0.06 1.01 0.79

242.5 3 62.5 0.05 0.97 0.78

237.5 3 67.5 0.05 0.94 0.78

232.5 3 72.5 0.04 0.91 0.77

227.5 3 77.5 0.04 0.88 0.76

222.5 3 82.5 0.04 0.86 0.75

217.5 3 87.5 0.04 0.83 0.74

214.5 3 90.5 0.04 0.82 0.73

The increase in vertical effective stress with depth is relatively sustained due to the 

long embankment length, and, as a result, settlement will be adversely affected. 

Therefore, the designer should determine if the construction schedule can 

accommodate the time required for embankment induced settlements to occur 

before the start of pile driving and superstructure construction. This example 

calculation assumes construction cannot be delayed, and therefore, the stress 

increase from embankment construction and foundations loads are applied 

concurrently.

Compressibility properties for the three silty clay layers were determined from one 

dimensional consolidation tests which were performed on undisturbed samples 

collected near the middle of each respective soil layer. Table D-116 presents the 

void ratio, eo, overconsolidation ratio, OCR, compression index, Cc, and 

recompression index, Cr for the three silty clay layers. The OCR of the various soil 

layers were used to calculate the preconsolidation stress, σ'p, at discrete depths.

219
Table D-116 Soil Properties Determined from One Dimensional Consolidation Test

Soil Layer eo OCR Cc Cr

1 0.94 1.68 0.34 0.03

2 0.80 2.01 0.30 0.03

3 0.54 1.71 0.20 0.02

The settlement at the South Abutment was first evaluated using an equivalent 

footing with stress distribution considering piles supported by shaft resistance in clay

as depicted by Figure D-108. A discussion of this approach is provided in Section 

7.3.5.3 of Chapter 7. Classic consolidation settlement equations were used to 

estimate pile group settlement. For this approach, an equivalent footing was placed 

at increasing pile penetration depths and resulting pile group settlements were 

estimated. Figure D-108 presents the equivalent footing concept with the 

appropriate stress distribution. The displayed group length dimension, Z, is 37 feet 

and is appropriate for only Group Configuration 3. The shallowest depth of an 

equivalent footing which satisfied vertical deformation requirements was thus 

determined. After calculating settlement, the location of the equivalent footing 

location was correlated to the required pile penetration depth. This depth was then 

used to establish the minimum required pile penetration depths to satisfy 

deformation requirements.

The following example calculation is performed for an equivalent footing located 35 

feet below the bottom of footing. From Elev. 270.0 feet to Elev. 214.0 feet, 

settlement calculations for cohesive soil were performed for the silty clay layers. 

The stress increase from the superstructure and embankment loads was less than 

the preconsolidation stress at each layer. Therefore, Equation 7-57 was used to 

estimate recompression settlement for overconsolidated soil. It was furthermore 

assumed that compression of the underlying limestone bedrock is negligible. 

The length of the pile group in Group Configuration 3 is 37 feet from exterior pile 

edge to exterior pile edge, and therefore this example is suitable for only this 

configuration. The same dimension for Group Configuration 1 and 2 is 41 feet. 

Similar to the stress increase calculations from embankment loading, the soil profile 

was again divided into 5 foot thick layers with the exception of the final layer which is 

1 foot thick. The elevation shown in Table D-117 references the midpoint of each 

respective soil layer, while z is the depth below the equivalent footing to the midpoint 

of each respective soil layer. Tabulated values for this analysis are recorded in 

Table D-117 with a total settlement estimated of 1.21 inches.

220
Figure D-108 Equivalent footing at 35 feet below the pile cap with respective stress 

distribution for conventional settlement analysis.

Considering only the unfactored permanent load, Q, calculate the vertical effective 

stress increase below the equivalent footing resulting from superstructure loads, 

ΔΔσσ′vv(ss), at Elev. 267.5 feet.

Q = unfactored permanent load, 1783 kips (Service I, without LL, Table 

D-105).

BB1 = pile group width at equivalent footing, 25 feet.

ZZ1 = pile group length at equivalent footing, 57 feet (Group Configuration 3 

only).

z = depth below equivalent footing, 2.5 feet (Elev. 267.5 feet).

ΔΔσσ′vv(ss) = QQ

(BB1+zz)+(ZZ1+zz)) [Eq. 7-55]

ΔΔσσ′vv(ss) = (1783 )

((25 ff )+(2.5 ff ))∗((57 ff )+(2.5 ff ))

ΔΔσσ′vv(ss) = 1.09 kk

221
Including the vertical effective stress increase from the embankment and 

superstructure, calculate the total vertical effective stress increase below the 

equivalent footing at Elev. 267.5 feet.

∆σσ′vv( ) = change in effective stress at depth z below the equivalent 

footing from embankment loading, 0.79 ksf (Table D-115).

ΔΔσσ′vv(ss) = change in effective stress at depth z below the equivalent 

footing from superstructure loading, 1.09 ksf.

ΔΔ ′vv( +ssss) = ∆σσ′vv( ) + ΔΔσσ′vv(ss)

ΔΔ ′vv( +ssss) = (0.79 kk ) + (1.09 kk )

ΔΔ ′vv( +ssss) = 1.88 kk

Determine the preconsolidation stress from the initial vertical effective stress and 

overconsolidation ratio at depth z below the equivalent footing (Elev. 267.5 feet).

σσ′vo = initial vertical effective stress at depth z below the equivalent 

footing, 2.24 ksf.

OCR = overconsolidation ratio, 2.01 (Soil Layer 2, Table D-116).

σσ′pp = σσ′vo ∗ OCR

σσ′pp = (2.24 ksf) ∗ (2.01)

σσ′pp = 4.50 kk

Evaluate the stress increase at depth z below the equivalent footing (Elev. 267.5 

feet) relative to the preconsolidation stress.

σσ′vo = initial vertical effective stress below equivalent footing, 2.70 ksf.

ΔΔ ′vv( +ssss)= change in effective stress below equivalent footing, 1.88 ksf.

σσ′pp = preconsolidation stress below equivalent footing, 4.50 ksf.

σσ′vo + ΔΔ ′vv( +ssss) ≤ σσ′pp

(2.24 kk ) + (1.88 kk ) ≤ (4.50 kk )

222
Determine the stress increase by comparing σσ′vo and σσ′1(ss+e).

SS SS II = σσ′

1(ss+e) − σσ′

vo

σσ′vo

∗ 100% [Eq. D-5]

SS SS II = (4.12 )−(2.24 )

(2.24 ) ∗ 100%

SS SS II = 84%

The stress increase is greater than or equal to 10%. Deformation for this depth 

increment should be estimated and included in the sum of all depth increments in 

which the stress increase is not less than 10%. 

Estimate consolidation settlement of layer for overconsolidated soil using Equation 

7-57 for (σ’vo + Δ’σ ≤ σ’p).

eeoo = initial soil layer void ratio, 0.80 (Soil Layer 2, Table D-116).

CCrr = recompression index, 0.03 (Soil Layer 2, Table D-116).

HHoo = initial height of soil layer, 5 feet.

σσ′vo = initial vertical effective stress at depth z below the equivalent 

footing, 2.24 ksf.

ΔΔ ′vv( +ssss)= change in vertical effective stress at depth z below the 

equivalent footing, 1.88 ksf.

SScc = CCrr

1+

HHoo log �

σσ′vvvv+ΔΔσσ′vv

σσ′vvvv

� [Eq. 7-57]

SScc = (0.03)

1+(0.80)

(5 ff ) ∗ �

(2.24 )+(1.88 )

(2.24 ) �

SScc = 0.0221 ff ∗ (

12 ii h

1 ff ) = 0.26 hee

223
Table D-117 Calculation of Settlement using Equivalent Footing and Conventional 

Primary Consolidation Equations

EL 

(feet)

z 

(feet)

Ho

(feet)

σ'vo 

(ksf)

OCR σ'p 

(ksf)

B

(feet)

Z

(feet)

Δσ'v(ss)

(ksf)

Δσ'v(e+ss)

(ksf)

Stress 

Incr. 

(%)

S

(in)

267.5 2.5 5 2.24 2.01 4.504812 27.5 59.5 1.09 1.88 84 0.26

262.5 7.5 5 2.54 1.71 4.3398945 32.5 64.5 0.85 1.64 65 0.17

257.5 12.5 5 2.87 1.71 4.902912 37.5 69.5 0.68 1.48 51 0.14

252.5 17.5 5 3.20 1.71 5.472342 42.5 74.5 0.56 1.35 42 0.12

247.5 22.5 5 3.53 1.71 6.041772 47.5 79.5 0.47 1.26 36 0.10

242.5 27.5 5 3.87 1.71 6.611202 52.5 84.5 0.40 1.18 31 0.09

237.5 32.5 5 4.20 1.71 7.180632 57.5 89.5 0.35 1.12 27 0.08

232.5 37.5 5 4.53 1.71 7.750062 62.5 94.5 0.30 1.07 24 0.07

227.5 42.5 5 4.87 1.71 8.319492 67.5 99.5 0.27 1.02 21 0.06

222.5 47.5 5 5.20 1.71 8.888922 72.5 104.5 0.24 0.98 19 0.06

217.5 52.5 5 5.53 1.71 9.458352 77.5 109.5 0.21 0.95 17 0.05

216.5 53.5 1 5.21 1.71 8.9038845 78.5 110.5 0.21 0.94 18 0.01

Total: 1.21

The above analysis was performed for additional equivalent footing locations 

considering dimensions of the three trial group configurations. Table D-118

summarizes the analysis results for pile group settlement using the equivalent 

footing with conventional primary consolidation. As established by global project 

performance requirements, total vertical deformation should be limited to 1.5 inches 

at each substructure location. To account for the additional deformation from elastic 

pile compression, the equivalent footing should be located 35 feet below the bottom 

of pile cap (i.e., located at Elev. 270.0 feet). Using the equivalent footing to pile 

penetration depth relationship displayed in Figure D-108, the respective pile 

penetration depth, D, is 53 feet ((3/2) *35 feet ≈ 53 feet) for an equivalent footing at a 

depth of 35 feet.

Table D-118 Summary of Pile Group Settlement Estimates Based on Equivalent 

Footing Depth and Conventionally Settlement Computations

Equivalent 

Footing 

Elevation

(feet)

Equivalent

Footing 

Depth

(feet)

Pile Toe 

Elevation

(feet)

Pile 

Toe 

Depth

(feet)

Estimated 

Settlement

Group 

Configuration 

1 and 2

(inches)

Estimated 

Settlement

Group 

Configuration 

3

(inches)

280.0 25 267.0 38 5.63 6.22

275.0 30 260.0 45 1.46 2.85

270.0 35 252.0 53 1.20 1.21

265.0 40 245.0 60 0.97 0.99

224
Pile group settlement was also evaluated using the neutral plane method and Janbu 

tangent modulus approach as outlined in Section 7.3.5 of Chapter 7. To compare 

settlement estimates using this approach with the conventional consolidation theory 

results presented in Table D-118, the neutral plane was placed at the same 

elevation as the equivalent footing location that resulted in the estimated settlement 

of 1.21 inches (i.e., the neutral plane was placed at 35 feet). Figure D-109 illustrates 

the neutral plane location and stress distribution used with this approach. To 

highlight the differences between these two methods, the equivalent footing at 35 

feet in Figure D-109 has plan dimension of 5 feet by 37 feet. However, the 

equivalent footing in Figure D-108 used with the conventional consolidation theory 

has an equivalent footing plan dimension of 25 feet by 57 feet. As a result of the 

greater contact stress, the neutral plane calculated settlements are significantly 

greater.

Figure D-109 Neutral plane at 35 feet below the pile cap and resulting stress 

distribution.

The following settlement calculation is performed for the neutral plane located 35 

feet below the bottom of footing. From Elev. 270.0 feet to 214.0 feet, strain 

calculations for cohesive soil (stress exponent of j=0) were applied for Soil Layers 1 

to 3. It was assumed that vertical deformation below the encountered bedrock at 

Elev. 214.0 feet is negligible. The length of the pile group in Group Configuration 3 

225
is 37 feet from exterior pile edge to exterior pile edge, and therefore this example is 

suitable for only this configuration. The same dimension for Group Configuration 1 

and 2 is 41 feet. Similar to the stress increase calculations from embankment 

loading, the soil profile was again divided into 5 foot thick layers with the exception 

of the final layer which is 1 foot thick. The elevation shown in Table D-119

references the midpoint of each respective soil layer, while z is the depth below the

equivalent footing to the midpoint of each respective soil layer. Tabulated values for 

this analysis are recorded in Table D-119.

Considering only the unfactored permanent load, Q, calculate the vertical effective 

stress increase below the equivalent footing resulting from superstructure loads, 

ΔΔσσ′vv(ss), at EL 267.5 feet.

Q = unfactored permanent load, 1783 kips (Service I, without LL, D-105).

BB = pile group width, 5 feet.

ZZ = pile group length, 37 feet (Group Configuration 3 only).

z = depth below equivalent footing, 2.5 feet (Elev. 267.5 feet).

 ΔΔσσ′vv(ss) = QQ

(BB+zz)+(ZZ+zz)) [Eq. 7-55]

 ΔΔσσ′vv(ss) = (1783 )

((5 ff )+(2.5 ff ))∗((37 ff )+(2.5 ff )))

 ΔΔσσ′vv(ss) = 6.02 kk

Including the vertical effective stress increase from the embankment and 

superstructure, calculate the total vertical effective stress increase below the 

equivalent footing at EL 267.5 feet.

∆σσ′vv( ) = change in effective stress at depth z below the equivalent 

footing from embankment loading, 0.79 ksf (Table D-115).

ΔΔσσ′vv(ss) = change in effective stress at depth z below the equivalent 

footing from superstructure loading, 6.02 ksf.

ΔΔ ′vv( +ssss) = ∆σσ′vv( ) + ΔΔσσ′vv(ss)

 ΔΔ ′vv( +ssss) = (0.79 kk ) + (6.02 kk )

ΔΔσσ′

( +ssss) = 6.81 kk

226
Determine the preconsolidation stress from the initial vertical effective stress and 

overconsolidation ratio at EL 267.5 feet.

σσ′vo = initial vertical effective stress at depth z below the equivalent 

footing, 2.24 ksf.

OCR = overconsolidation ratio, 2.01 (Soil Layer 2, Table D-116).

σσ′pp = σσ′vo ∗ OCR

σσ′pp = (2.24 ksf) ∗ (2.01)

σσ′pp = 4.50 kk

Evaluate the stress increase at depth at EL 267.5 feet relative to the 

preconsolidation stress.

σσ′vo = initial vertical effective stress at depth z below the equivalent 

footing, 2.24 ksf.

ΔΔ ′vv( +ssss)= change in effective stress at depth z below the equivalent 

footing, 6.81 ksf.

σσ′pp = preconsolidation stress at depth z below the equivalent footing, 

4.50 ksf.

σσ′vo + ΔΔ ′vv( +ssss) ≥ σσ′pp

(2.24 kk ) + (6.81 kk ) ≥ (4.50 kk )

Determine the percent stress increase by comparing σσ′vo and σσ′1(e+ss).

σσ′vo = initial vertical effective stress at depth z below the equivalent 

footing, 2.24 ksf.

σσ′1(e+ss) = new vertical effective stress considering both superstructure and 

embankment loads, 2.24 ksf + 6.81 ksf = 9.05 ksf.

PP SS SS II = σσ′

1(e+ss) − σσ′

vo

σσ′vo

∗ 100 [Eq. D-5]

PP SS SS II = (9.05)−(2.24)

2.24 ∗ 100

227
PP SS SS II ee = 304%

For cohesive soil at Elevation 272.5 feet, z = 2.5 (j = 0), the modulus number is 

determined by Equation 7-68.

eeoo = void ratio, 0.80 (Soil Layer 2, Table D-116).

CCcc = compression index, 0.30 (Soil Layer 2, Table D-116).

mmnn = 2.30 �

1+ 0

CCcc

� [Eq. 7-68]

mmnn = 2.30 �

1+(0.80)

(0.30) �

mmnn = 13.8

For cohesive soil at Elevation 272.5 feet, z = 2.5 (j = 0), the recompression modulus 

number is determined by Equation 7-69.

eeoo = initial soil layer void ratio, 0.80 (Soil Layer 2, Table D-116).

CCcc = recompression index, 0.03 (Soil Layer 2, Table D-116).

mmnn = 2.30 �

1+ 0

CCrr

� [Eq. 7-69]

mmnn = 2.30 �

1+(0.80)

(0.03) �

mmnn = 138

For overconsolidated cohesive soils (j = 0) in which the new vertical effective stress 

exceeds the preconsolidation stress, determine strain in layer with Equation 7-65.

σσ′pp = preconsolidation stress, 4.50 ksf.

σσ′vo = initial vertical effective stress at depth z below the equivalent 

footing, 2.24 ksf.

σσ′1(e+ss) = new vertical effective stress, 9.05 ksf.

mmnn = recompression modulus, 138.

mmnn = compression modulus, 13.8.

εε = 1

mmnn

ln ��

σσ′pp

σσ′vv0

�� + 1

mmnn

ln ��

σσ′1

σσ′pp

�� [Eq. 7-65]

228
εε = 1

(138)

ln ��

(4.50 )

(2.24 )

�� + 1

(13.8)

ln ��

(9.05 )

(4.50 )

��

εε = 0.0557

Calculate the layer compression denoted, S, with the initial height of the layer, HHoo.

SS = ΔΔ ∗ HHoo

SS = 0.0557 ∗ (5 ff ) �

12 hee

1 ffffff �

SS = 3.34 hee

For overconsolidated cohesive soils (j = 0) in which the new effective stress does not 

exceed the preconsolidation stress, such as at EL 252.5, determine strain in layer 

with Equation 7-66.

σσ′pp = preconsolidation pressure, 5.47 ksf (Table D-119).

σσ′vo = initial vertical effective stress at depth z below the equivalent 

footing, 3.20 ksf (Table D-119).

σσ′1(e+ss) = new vertical effective stress, 5.45 ksf (Table D-119).

mmnn = recompression modulus, 177.1 (Calculation not presented for 

Soil Layer 3).

εε = 1

mmnn

ln �� σσ′1

σσ′v0

�� [Eq. 7-66]

εε = 1

(177.1) ��

(5.35 )

(3.20 )

��

εε = 0.0030

Calculate the layer compression denoted, S, with the initial height of the layer, HHoo.

SS = εε ∗ HHoo

SS = 0.0030 ff ∗ (5 ff ) �

12 hee

1 ffffff �

SS = 0.18 hee

229
Table D-119 Settlement Estimate for Neutral Plane Method with

the Neutral Plane at EL 270.0 feet

EL 

(feet)

z 

(feet)

Ho 

(ksf)

σ'vo 

(ksf)

OCR σ'p

(ksf

B

(feet)

Z

(feet)

Δσ'ss

(ksf)

σ'1e+ss

(ksf)

Stress 

Incr. 

(%)

ε S

(in)

267.5 2.5 5 2.24 2.01 4.50 7.5 39.5 6.02 9.05 304 0.0556 3.34

262.5 7.5 5 2.54 1.71 4.34 12.5 44.5 3.21 6.53 157 0.0261 1.57

257.5 12.5 5 2.87 1.71 4.90 17.5 49.5 2.06 5.72 99 0.0117 0.70

252.5 17.5 5 3.20 1.71 5.47 22.5 54.5 1.45 5.45 70 0.0030 0.18

247.5 22.5 5 3.53 1.71 6.04 27.5 59.5 1.09 5.41 53 0.0024 0.14

242.5 27.5 5 3.87 1.71 6.61 32.5 64.5 0.85 5.50 42 0.0020 0.12

237.5 32.5 5 4.20 1.71 7.18 37.5 69.5 0.68 5.66 35 0.0017 0.10

232.5 37.5 5 4.53 1.71 7.75 42.5 74.5 0.56 5.86 29 0.0015 0.09

227.5 42.5 5 4.87 1.71 8.32 47.5 79.5 0.47 6.10 25 0.0013 0.08

222.5 47.5 5 5.20 1.71 8.89 52.5 84.5 0.40 6.35 22 0.0011 0.07

217.5 52.5 5 5.53 1.71 9.46 57.5 89.5 0.35 6.61 20 0.0010 0.06

214.5 53.5 1 5.21 1.71 8.90 58.5 90.5 0.34 6.27 20 0.0011 0.01

Total 6.46

For the same equivalent footing location of Elev. 270 feet, the above results of 6.46

inches of estimated settlement using the neutral plane approach is significantly 

larger than the 1.23 inches of settlement (Table D-118) based on consolidation 

theory. For this example calculation, it was decided that the settlement method 

yielding the greatest settlement magnitude would be used to establish the range of 

pile penetration depths that satisfy tolerable deformations. The neutral plane 

method illustrated above was performed for additional equivalent footing depths until 

tolerable settlements were estimated.

Table D-120 summarizes analysis results for pile group settlement estimated using 

the neutral plane method and Janbu Tangent modulus approach. Although not yet 

calculated, it is preliminarily estimated that elastic pile compression may be on the 

order of 0.5 inches, effectively limiting tolerable soil settlement to on the order of 1 

inch. Therefore, to limit the total vertical deformation including elastic pil 

compression and settlement to less than 1.5 inches, analysis results in Table D-120

indicate that the neutral plane should be located at Elev. 215.0 feet, 90 feet below 

the bottom of pile cap.

230
Table D-120 Summary of Pile Group Settlement Estimates Based on Janbu 

Tangent Modulus with Neutral Plane Method For All Group Configurations

Neutral 

Plane 

Elevation

(feet)

Neutral 

Plane

Depth

(feet)

Estimated 

Settlement

Group 

Configuration 

1 and 2

(inches)

Estimated 

Settlement

Group 

Configuration 

3

(inches)

235.0 70 1.85 2.13

230.0 75 1.50 1.77

225.0 80 1.23 1.41

220.0 85 1.07 1.25

215.0 90 0.28 0.35

It is assumed that the equivalent footing acts at the same location as the neutral 

plane. Accordingly, an analysis was then performed to determine the pile toe 

elevation necessary to locate the neutral plane at Elev. 215.0, thereby establishing 

the minimum required pile penetration depth to satisfy tolerable deformations.

The location of the neutral plane and the magnitude of drag force are evaluated 

following the procedure outlined in Section 7.3.6 of Chapter 7, using unfactored 

permanent loads and nominal geotechnical resistance. Because load factors for the 

Service limit state are 1.0, applicable loads at this limit state may be considered 

unfactored. The Service I, without LL limit state loads are therefore used for 

evaluation for the neutral plane. This example again utilizes the load for Group 

Configuration 3 (Q= 127 kips, Table D-108). Figure D-110 presents a graphical 

interpretation of the neutral plane for the HP 12x74 pile driven to 91 feet (seated on 

bedrock at Elev. 214.0). 

First, the sustained load plus the cumulative shaft resistance versus depth is plotted. 

Next, the mobilized toe resistance minus the cumulative shaft resistance versus pile 

penetration depth is plotted. The exact percentage of toe mobilization is unknown at 

this stage of design, and therefore multiple toe mobilization curves should be 

evaluated to determine the neutral plane location. The 0% toe mobilization curve is 

the most conservative location to evaluate pile settlement since it locates the neutral 

plane at the highest elevation. The 100% toe mobilization curve should be used to 

check the pile section’s structural strength since it results in the greatest axial force 

in the pile. The structural strength check is performed in Block 17.

231
At the South Abutment, it is expected that piles will be supported partially by toe 

resistance on bedrock, and therefore the 0% toe mobilization curve presents an 

unreasonable baseline to evaluate settlement in this case. Some toe resistance is

likely mobilized, and to remain consistent with the other substructure locations, the 

50 % toe mobilization curve is again used to evaluate settlement.

Figure D-110 Neutral plane location considering 50% toe mobilization for

HP 12x74 at the South Abutment.

Assuming 50 % toe mobilization, the neutral plane is located 90 feet below the 

bottom footing with a resulting maximum load in the pile of 549 kips. Since the pile 

toe is seated on bedrock at EL 214.0, vertical deformation will be limited to elastic 

shortening of the pile and elastic compression of the bedrock which is expected to 

be negligible. The minimum pile penetration required to satisfy tolerable 

deformations is therefore approximately 91 feet resulting in the piles being driven to 

bedrock to control vertical deformations.

This procedure was performed for the remaining candidate pile sections and trial 

group configurations. , the above analysis was also performed to determine the pile 

penetration depth required to locate the neutral plane below a depth of 90 feet (EL 

215.0 ft). The results of these analyses indicate that all the candidate pile sections 

and trial group configurations require the pile to be driven to bedrock (i.e., at an 

approximate depth of 91 feet.

232
As previously noted, a comparison of the required pile penetration depth determined 

from both settlement estimation methods yielded significantly different results. This 

is a direct result of the equivalent footing dimensions and stress distribution for each 

respective method. Previously, Table D-118 summarized the minimum pile 

penetration depth based on conventional settlement estimates for piles supported by 

shaft resistance in clay. Table D-121 presents the minimum pile penetration depth 

for all pile sections and group configurations based on settlement estimation using 

the neutral plane method with Janbu Tangent modulus. In the latter settlement 

approach, for all candidate pile sections and group configurations, the piles must be 

driven to bedrock at approximately 91 feet.

Experience should be used to establish a penetration depth with either settlement 

estimation approach. For this design example, the established minimum pile 

penetration depth to satisfy tolerable vertical deformations will be based solely on 

the settlement results using the neutral plane and Janbu tangent modulus. Table 

D-121 presents the established pile penetration depths to satisfy tolerable 

deformations at the South Abutment.

Table D-121 Established Minimum Required Pile Penetration Depths to Satisfy 

Tolerable Deformations at the South Abutment

Group Configuration All Candidate Pile Sections 

(feet)

1, 2 and 3 Bedrock (≈ 91)

Elastic shortening of the pile should be considered along with settlement. For elastic 

compression, the load per pile from the Service I, without live load limit state is 

applied at the pile head. As shown in Table D-108, this load is 127 kips.

Note that the drag force from negative shaft resistance increases the axial 

compression force in the pile. Negative shaft resistance above the neutral plane 

acts to increase axial compression force in the pile, whereas below the neutral 

plane, positive shaft resistance reduces the axial compression force in the pile. This 

effect must be accounted for in the elastic compression calculation. Accordingly, the 

unfactored axial load used to compute elastic compression, Q, changes for each pile 

segment length, increasing equal to the unfactored permanent load plus the shaft 

resistance down to the neutral plane. In this example, the unfactored axial load is 

equal to the resistance distribution from 100% toe mobilization. The highest drag 

force magnitude results from this curve and represents the worst case.

233
Equation 7-48 is used to illustrate this example for the first 12 inch increment of the 

HP 12x74 pile section. The average shaft resistance and average load for each 

respective depth interval is used to estimate the elastic compression. For each 12 

inch segment, the elastic modulus remains constant, and was evaluated as 29,000 

ksi. The pile cross sectional area likewise remains constant as 21.8 in2. Remaining 

calculations were performed using a spreadsheet; Table D-122 summarizes the 

elastic compression with depth. 

Determine the unfactored axial load, Q, in segment.

QQdd = unfactored permanent load, 127.0 kips.

RRss

− = average (negative) shaft resistance, 1.1 kips.

Q = QQdd + RRss

− = 127.0 kkkk + 1.1 kkkk

Q = 128.1 kkkk

Calculate elastic compression of segment with unfactored axial load from combined 

unfactored permanent load and negative shaft resistance.

LL = segment length, 12 inches.

AA = cross sectional area of pile material, 21.8 in2.

EE = elastic modulus of pile, 29,000 ksi.

∆= QQ

AA [Eq. 7-48]

∆= (128.1 )∗(12 ii h )

(21.8 2)∗(29,000 kk kk)

∆= 0.00243 hee

234
Table D-122 Elastic Compression Calculation

Depth 

Below 

Pile Head

(feet)

Average 

Shaft 

Resistance 

(kips)

Average 

Unfactored 

Axial Load 

(kips)

∆

(inches)

0 0.0 127.0 0.00000

0-1 1.1 128.1 0.00243

1-2 3.3 130.3 0.00247

2-3 5.5 132.5 0.00252

3-4 7.7 134.7 0.00256

4-5 10.0 137.0 0.00260

5-6 12.2 139.2 0.00264

6-7 14.5 141.5 0.00269

7-8 16.9 143.9 0.00273

8-9 19.2 146.2 0.00278

9-10 21.6 148.6 0.00282

10-11 24.1 151.1 0.00287

11-12 26.5 153.5 0.00291

12-13 29.0 156.0 0.00296

13-14 31.5 158.5 0.00301

14-15 34.1 161.1 0.00306

15-16 36.7 163.7 0.00311

16-17 39.3 166.3 0.00316

17-18 41.9 168.9 0.00321

18-19 44.6 171.6 0.00326

19-20 47.3 174.3 0.00331

20-21 51.3 178.3 0.00339

21-22 56.7 183.7 0.00349

22-23 62.1 189.1 0.00359

23-24 67.6 194.6 0.00369

24-25 73.2 200.2 0.00380

25-26 78.7 205.7 0.00391

26-27 84.3 211.3 0.00401

27-28 90.0 217.0 0.00412

28-29 95.7 222.7 0.00423

29-30 101.6 228.6 0.00434

30-31 107.4 234.4 0.00445

31-32 113.3 240.3 0.00456

32-33 119.2 246.2 0.00467

33-34 125.3 252.3 0.00479

34-35 131.5 258.5 0.00491

35-36 137.7 264.7 0.00502

36-37 143.8 270.8 0.00514

37-38 149.9 276.9 0.00526

235
Table D-122 Elastic Compression Calculation (continued)

Depth 

Below 

Pile Head

(feet)

Average 

Shaft 

Resistance 

(kips)

Average 

Unfactored 

Axial Load 

(kips)

∆

(inches)

38-39 156.0 283.0 0.00537

39-40 162.2 289.2 0.00549

40-41 167.8 294.8 0.00560

41-42 172.9 299.9 0.00569

42-43 178.0 305.0 0.00579

43-44 183.1 310.1 0.00589

44-45 188.2 315.2 0.00598

45-46 193.3 320.3 0.00608

46-47 198.4 325.4 0.00618

47-48 203.5 330.5 0.00627

48-49 208.6 335.6 0.00637

49-50 213.7 340.7 0.00647

50-51 218.8 345.8 0.00656

51-52 223.9 350.9 0.00666

52-53 229.0 356.0 0.00676

53-54 234.1 361.1 0.00685

54-55 239.3 366.3 0.00695

55-56 244.4 371.4 0.00705

56-57 249.4 376.4 0.00715

57-58 254.5 381.5 0.00724

58-59 259.6 386.6 0.00734

59-60 264.8 391.8 0.00744

60-61 269.9 396.9 0.00753

61-62 275.0 402.0 0.00763

62-63 280.1 407.1 0.00773

63-64 285.2 412.2 0.00782

64-65 290.3 417.3 0.00792

65-66 295.4 422.4 0.00802

66-67 300.5 427.5 0.00811

67-68 305.6 432.6 0.00821

68-69 310.7 437.7 0.00831

69-70 315.8 442.8 0.00840

70-71 320.9 447.9 0.00850

71-72 326.0 453.0 0.00860

72-73 331.1 458.1 0.00869

73-74 336.2 463.2 0.00879

74-75 341.3 468.3 0.00889

75-76 346.4 473.4 0.00899

236
Table D-122 Elastic Compression Calculation (continued)

Depth 

Below 

Pile Head

(feet)

Average 

Shaft 

Resistance 

(kips)

Average 

Unfactored 

Axial Load 

(kips)

∆

(inches)

76-77 351.5 478.5 0.009082

77-78 356.6 483.6 0.009179

78-79 361.7 488.7 0.009276

79-80 366.8 493.8 0.009373

80-81 371.9 498.9 0.009470

81-82 377.0 504.0 0.009567

82-83 382.1 509.1 0.009664

83-84 387.2 514.2 0.009760

84-85 392.3 519.3 0.009858

85-86 397.4 524.4 0.009955

86-87 402.5 529.5 0.010051

87-88 407.6 534.6 0.010148

88-89 412.7 539.7 0.010245

89-90 417.9 544.9 0.010342

90-91 423.0 550.0 0.010439

0.55

For the pile head load of 127 kips (Group Configuration 3 loads), estimated elastic 

compression of the HP 12x74 pile section driven to 91 feet is 0.55 inches. As the 

piles are driven to bedrock, it is assumed no settlement will occur, and therefore it is 

estimated that total vertical deformation at the South Abutment is 0.55 inches.

D.40Block 16: South Abutment – Check pile drivability to maximum pile 

penetration depth requirements established in Blocks 12 through 15

Preliminary pile drivability was previously evaluated for the 5 candidate pile sections 

in Block 10. The plots of nominal resistance, blow count and compression stress 

versus depth in Figure D-99 should now be reviewed considering the established 

minimum pile penetration depths. A candidate pile section must be capable of being 

driven to the penetration depth necessary to achieve the nominal geotechnical 

resistance in axial compression and tension, and to a penetration depth necessary 

to satisfy lateral load demands as well as axial and lateral deformation requirements. 

Minimum pile penetration depths have been previously established in Blocks 13, 14 

and 15 and are presented in Tables D-111, D-114 and D-126. 

237
Although a minimum pile penetration depth is not typically established for nominal 

geotechnical resistance in axial compression, the pile should also be capable of 

being driven reasonably close to the estimated pile penetration depth where the 

nominal resistance is expected to develop. If the pile cannot be driven to the 

required depth within driving stress limits and at reasonable blow counts, a larger 

pile hammer, a pile section with greater impedance, or pile installation aids such as 

predrilling or jetting may be required to satisfy or improve drivability. Alternatively, 

substructure design modifications should be considered.

For the candidate HP 12x74 pile section in Group Configuration 3, the pile 

penetration depth for axial compression loading was estimated at 73 feet (Table 

D-110), the minimum penetration depth for axial tension loading was 18 feet (Table 

D-111), the minimum penetration depth for lateral loading was 25 feet (Table D-114) 

and the estimated minimum penetration depth to satisfy vertical deformation limits

was 91 feet (Table D-126). Accordingly, candidate pile section must have sufficient 

drivability to the maximum of these depths, 91 feet, where driving is anticipated to 

terminate on bedrock.

A review of the preliminary drivability in Figure D-99 indicates that the HP 12x74 pile 

section can be driven to bedrock at approximately 91 feet. In addition, from the 

preliminary drivability evaluation (with soil and hammer model assumptions 

described in Block 10), it is estimated that the blow count will not exceed 120 blows 

per foot or 10 blows per inch before this penetration depth. Compression driving 

stresses are estimated to remain below driving-stress limits. Therefore, it is 

concluded that pile drivability to the estimated pile penetration depth is acceptable.

D.41Block 17: South Abutment – Determine the Neutral Plane Location and 

Resulting Drag Force. Check Structural Strength Limit State for Pile 

Penetration Depth From Block 16

Previously in Block 15, the neutral plane was evaluated as part of the settlement 

calculations. The neutral plane and resulting drag force are now evaluated to check 

the structural strength limit state for candidate pile sections. Section 7.3.6 provides 

guidance for evaluating the neutral plane location and the magnitude of the drag 

force. Load using the Service I, without LL limit state are considered for the applied 

pile head load. This example again utilizes the load for Group Configuration 3 (Q = 

127 kips, Table D-108).

At 100 percent toe mobilization, the neutral plane is at its lowest potential location, 

and thus the highest drag force magnitude results. Accordingly, this is the toe 

238
mobilization curve that should be used to check the pile section’s structural strength. 

Figure D-111 presents a graphical interpretation of the neutral plane for the 

HP12x74 pile section driven to the estimated pile penetration depth of 91 feet 

(seated on bedrock). In this case the neutral plane is located 91 feet below pile 

head with a resulting maximum axial compression force in the pile of 552 kips.

Figure D-111 Neutral plane location considering 100 percent toe mobilization for 

HP 12x74 at the South Abutment.

The resulting unfactored drag force, DF, is the difference between the maximum 

unfactored axial compression force in the pile, QQmm , minus the unfactored 

permanent load (Q). In this case, the drag force is evaluated for 100 percent toe 

mobilization. 

DD = QQmm − QQ

DD = (552 kkkk ) − (127 kkkk ) = 425 kkkk

Following this calculation, the structural resistance was evaluated with Equation 

7-70. As discussed in Section 7.3.6 of Chapter 7, a load factor of 1.25 is applied to 

the permanent load while a load factor of 1.1 is applied to the drag force. When 

driving through dense soil to rock, it may be generally appropriate to assume that the 

pile toe may be subject to damage during driving. Therefore, a structural resistance 

239
factor for axial compression, φφcc, of 0.5 is applied to the nominal structural resistance 

of 1088 kips (Table D-94). For this assumption, the factored structural resistance, 

Pr, for the HP 12x74 section is 544 kips.

PPuu = 1.25 (QQ) + γpp(DD ) < PPrr [Eq. 7-70]

PPuu = 1.25 (127 kkkk ) + 1.1(425 kkkk ) = 626 kkkk

626 kkkk > 544 kkkk 

In this case, the factored structural resistance is less than the factored loads, and 

therefore the pile section is unacceptable. 

It may be appropriate to reconsider the structural resistance factor used above 

based upon the driving conditions. The pile is driven through silty clay for 

approximately 91 feet, and the probability of damage in this zone is very low. In 

addition, a review of the boring logs (Figure D-2) indicates the transition from silty 

clay to bedrock is relatively abrupt, and there will be little difficulty seating the pile on 

bedrock. If an appropriately sized hammer (or appropriate energy setting) is 

selected, dynamic testing is performed to monitor and control driving stresses, and 

driving criteria is established such that the risk of pile toe damage is low, the use of a 

higher structural resistance factor may be warranted. Consideration could also be 

given to dynamically testing 100% of the piles as a further means of identifying and 

mitigating any damaged piles. AASHTO (2014) design specifications allow a 

structural resistance factor for axial compression of 0.6 for H-pile sections with good 

driving conditions where damage is unlikely.

Proceeding with the drag force analysis, if a structural resistance factor for axial 

compression, φφcc, of 0.6 is applied to the nominal structural resistance of 1088 kips 

(Table D-94), the factored structural resistance, Pr, for the HP 12x74 section is 652 

kips. Equation 7-68 is used to evaluate the structural resistance.

PPuu = 1.25 (QQ) + γpp(DD ) < PPrr [Eq. 7-70]

PPuu = 1.25 (127 kkkk ) + 1.1(425 kkkk ) = 626 kkkk

626 kkkk < 652 kkkk

In this case, the factored structural resistance is greater than the factored load, and 

therefore the pile section is acceptable. 

240
It may be beneficial to review the ratio of factored load to nominal structural 

resistance or, PPuu / PPnn. The following evaluation serves to back calculate the 

minimum required structural resistance factor, φφcc(min), for the section to be 

acceptable considering the factored load.

φφcc(min) = PPuu

PPnn

φφcc(min) = (626 )

(1088 )

φφcc(min) = 0.58

The neutral plane and drag force analysis was also performed for each candidate

pile section using 100 percent toe mobilization. Factored structural resistance was 

subsequently evaluated considering the factored loads for group configurations 

shown in Table D-108. The pile penetration depth utilized for the structural 

resistance check was the required minimum penetration depth presented in Table 

D-126 (91 feet for all piles and group configurations at the South Abutment). It was 

again assumed that the probability of pile damage is reduced using the means 

discussed above. Therefore, a structural resistance factor in axial compression, φφcc, 

of 0.6 was applied to the nominal structural resistance for each candidate pile 

section. Table D-123 presents the ratio of the factored load to nominal structural 

resistance, at the neutral plane (also the pile toe), for all the candidate piles and 

group configurations. 

Table D-123 Ratio of Factored Load to Nominal Structural Resistance in Axial 

Compression, φφcc(min), at the Neutral Plane

Group 

Configuration

HP 10x42

φφcc(min)

HP 12x53

φφcc(min)

HP 12x74

φφcc(min)

HP 14x89

φφcc(min)

HP 14x117

φφcc(min)

1 0.99** 0.90** 0.64** 0.59 0.46

2 0.93** 0.84** 0.60** 0.56 0.43

3 0.88** 0.81** 0.58 0.54 0.41

The neutral plane is located at the pile toe for all sections and group configurations.

Note: ** - Section not acceptable considering φφcc equal or greater than 0.60.

Based on results of the drag force analysis, a candidate pile section may be 

eliminated from consideration if the factored loads are higher than the factored 

structural resistance. Table D-124 summarizes results of the drag force analysis. 

241
The HP 12x74 pile section is acceptable in Group Configuration 3, while the HP 

14x89 and HP 14x117 pile sections are acceptable in all three group configurations.

Table D-124 Does Candidate Pile Section Meet Structural Resistance 

Requirements Considering Drag Force at Minimum Pile Penetration Depth?

Group 

Configuration HP 10x42 HP 12x53 HP 12x74 HP 14x89 HP 14x117

1 No No No Yes Yes

2 No No No Yes Yes

3 No No Yes Yes Yes

D.42Decision 18: Does Estimated Total Settlement and Differential Settlement 

Between Adjacent Substructure Locations Satisfy Requirements and 

Angular Distortion Limits?

All substructures have now been preliminarily designed and the estimated vertical 

deformations computed for each location.

The vertical deformation limits and construction point concept detailed in Section 7.3 

of Chapter 7 was used to first calculate tolerable differential settlement based upon 

angular distortion. Using Equation D-5, the angular distortion between substructure 

supports is limited to 0.004 radians, and for a 100 ft span on a multispan bridge, this 

equates to 4.8 inches of tolerable differential settlement. 

Determine tolerable differential settlement, Sd, between substructure supports.

LLss = span length, 100 feet.

AA = angular distortion limit, 0.004 radians (Table 7-18).

SSdd = AA ∗ LLss [Eq. D-7]

SSdd = (0.004) ∗ (100 ff ) ∗ �

12 ii h ss

1 ff �

SSdd = 4.8 hee

242
Although this differential settlement is tolerable for angular distortion, project 

performance requirements limited the settlement at each substructure location to a 

maximum of 1.5 inches, the differential settlement between adjacent substructure 

locations limited to 1.0 inch, and a maximum angular distortion of 0.0008 radians. 

These requirements were established for rideability, drainage, and attached utility 

damage considerations. The estimated substructure performance is summarized in 

Table D-125.

Table D-125 Summary of Foundation Total Settlement, Differential Settlement, and 

Angular Distortion for HP 12x74 Pile Section

Substructure 

Location

Settlement 

Method

Total 

Settlement

(inches)

Differential 

Settlement

(inches)

Span 

Length

(feet)

Angular 

Distortion

N. Abutment N. Plane 1.17

0.18 100 0.0002

Pier 2 N. Plane 0.99

0.44 100 0.0004

S. Abutment N. Plane 0.55

As illustrated in Table D-125, the total settlement, differential settlement, and angular 

distortion requirements are all satisfied.

D.43Block 19: South Abutment – Evaluate Economics of Candidate Piles, 

Preliminary Group Configurations, and Other Factors

The design process has served to compare strength and service limits for several 

candidate pile types within trial group configurations. Some candidate pile types 

have not met all of the strength, service, or drivability requirements. It is useful to 

quickly review the suitable and unsuitable pile types and group configurations and 

then assess the cost of the viable foundation solutions.

The number of initial candidate pile types has been reduced through evaluations of 

strength or drivability requirements while remaining candidate pile types are now 

subject to an economic analysis. Foundation cost and related economics are 

discussed in Section 3.4 of Chapter 3. Final selection of a pile type and group 

configuration is therefore based not only upon limit state requirements, but considers 

the associated cost. 

243
Table D-126 summarizes the established minimum pile penetration depth based on 

analysis results from Blocks 12 through 15. For all candidate pile sections and 

group configurations at the South Abutment, the established minimum pile 

penetration depth was based on meeting tolerable vertical deformations.

Several candidate sections did not meet structural resistance requirements for axial 

loading, lateral loading or both. The candidate pile sections and/or group 

configurations not meeting design requirements are identified with an asterisk in 

Table D-126. For all three group configurations, the HP 10x42 and HP 12x52 pile 

sections did not meet all structural resistance requirements. The HP 12x74 section 

was also structurally unacceptable for Group Configurations 1 and 2. These 

candidate pile sections and group configuration were eliminated for the final design.

Table D-126 Established Minimum Pile Penetration Depth at the South Abutment

Group 

Configuration

HP 10x42

(feet)

HP 12x53 

(feet)

HP 12x74

(feet)

HP 14x89

(feet)

HP 14x117

(feet)

1 91* 91* 91* 91* 91

2 91* 91* 91* 91 91

3 91* 91* 91 91 91

*Did not meet structural resistance requirement

Table D-127 presents the estimated minimum penetration depth for each candidate 

section to meet the factored geotechnical resistance requirements at the Strength I 

limit state. The larger pile sections require less pile penetration depth than the 

smaller pile sections to provide the same geotechnical resistance. In addition, the 

factored load per pile decreases from Group Configuration 1 to Group Configuration 

3. However, from the analyses in Blocks 13 through 15, the established minimum 

penetration depth to preclude unacceptable vertical deformation requires all piles to 

be driven deeper than the depth needed solely for their factored geotechnical 

resistance. The minimum penetration depth requirement results in the additional 

geotechnical resistance gained by further pile embedment to be essentially wasted 

and therefore uneconomical.

244
Table D-127 Estimated Minimum Penetration Depth for Factored Geotechnical

Resistance at Strength I Limit State

Group 

Configuration

HP 10x42

(feet)

HP 12x53

(feet)

HP 12x74

(feet)

HP 14x89

(feet)

HP 14x117

(feet)

1 91* 91* 91* 90* 88**

2 91* 90* 86* 74** 72**

3 91* 74* 73** 63** 62**

Note: * -Did not meet structural resistance requirement

Note: ** -Must be driven deeper to established minimum penetration depth (min. 91 

feet).

Reference should be made to Block 19 of the North Abutment for a more detailed 

discussion of individual pile cost. Figure D-112 again presents the estimated 

individual pile cost versus pile penetration depth.

Figure D-112 Pile cost versus penetration depth.

For the South Abutment, Table D-128 shows the price per pile when considering the 

established minimum pile penetration depth. For example, for the HP 12x74 pile

section in Group Configuration 3, the individual cost is determined by multiplying the 

cost per foot by the penetration depth. At the minimum pile penetration depth of 91 

feet, the cost per pile is $6,061. To note, there will be additional pile length 

embedded in the cap, however for pile cost estimation it can be considered 

negligible. Furthermore, Table D-129 shows the pile group cost reflecting the cost 

per pile and number of piles in the group.

245
Table D-128 Cost per Pile at Established Minimum Penetration Depth for Piles 

Meeting Structural Requirements

Group 

Configuration HP 12x74 HP 14x89 HP 14x117

1 - - $9,337

2 - $7,289 9,337

3 $6,061 7,289 9,337

Table D-129 Pile Group Cost at Established Minimum Penetration Depth for Piles 

Meeting Structural Requirements

Group 

Configuration

Required 

Number of

Piles

HP 12x74 HP 14x89 HP 14x117

1 18 - - $168,059

2 22 - $160,360 205,405 

3 26 $157,576 189,517 242,752

Based upon this comparison, the HP 14x117 pile section proves to be least 

economical. Based upon pile group cost, the HP 14x89 pile section in Group 

Configuration 1 appears to be the most economical followed by the HP 12x74 pile 

section in Group Configuration 3. However, before selecting the lowest cost option 

considering solely the results in Table D-129, the cost of the pile cap should also be 

estimated and factored into the foundation cost, as discussed below.

Section 8.9 of Chapter 8 outlines a procedure to estimate the total pile cap 

thickness. Equation 8-80 is used to estimate this value along using the factored load 

per pile at the Strength limit state as previously presented in Table D-108.

A sample calculation is shown for the HP 12x74 pile in Group Configuration 3. Table 

D-130 summarizes the estimated cap thickness for each pile section and pile group 

permutation calculated using this procedure.

Estimate the total pile cap thickness.

PPuu = maximum single pile factored axial load, Q =238 kips (Group 

Configuration 3, Table D-108).

tcc = PPuuuu

12

+ 30 [Eq. 8-80]

246
tcc = (238 )

12

+ 30

tcc = 50 hee

Table D-130 Estimated Total Pile Cap Thickness

Group 

Configuration

HP 12x74

(inches)

HP 14x89

(inches)

HP 14x117

(inches)

1 - - 59

2 - 53 53

3 50 50 50

Next, the volume of reinforce concrete required to construct the pile cap is 

determined from the estimated total pile cap thickness. The total pile cap width and 

length values were previously provided in Table D-106. The resulting volume of 

reinforced concrete for each pile section and pile group permutation is presented in 

Table D-131. Note that pile cap volume is shown in cubic yards (CY).

Table D-131 Estimated Volume of Reinforced Concrete in Pile Cap

Group 

Configuration

HP 12x74

(CY)

HP 14x89

(CY)

HP 14x117

(CY)

1 - - 50.0

2 - 45.5 45.5

3 38.5 38.5 38.5

To estimate the pile cap cost, past pricing information is generally the best guide; 

however, similar to estimating the pile cost, due to fluctuations in the market price of 

material and other factors, pile cap costs are subject to change. The cost of the

reinforced concrete pile cap, furnished and constructed, is estimated to be $500 /CY. 

Using this estimated value, the volumes presented in Table D-131 were used to 

estimate the cost of the various reinforced concrete pile caps. The pile cap cost for 

each candidate section and group configuration is shown in Table D-132.

Table D-132 Estimated Cost of Reinforced Concrete Pile Cap 

Group 

Configuration HP 12x74 HP 14x89 HP 14x117

1 - - $25,010

2 - $22,772 22,772

3 $19,245 19,245 19,245

247
By adding the cost of the pile cap and piles for each permutation, the estimated total 

foundation cost is determined as presented in Table D-133. Additional construction 

costs should be considered and included, if applicable, such as excavations support, 

dewatering, and utility relocation or other environmental impacts. However, an 

exhaustive analysis of the other considerations is not presented in this example. 

Considering both the pile and the pile cap costs, the HP 12x74 section in the Group 

Configuration 3 is the most economical solution at the South Abutment followed by 

the HP 14x89 section in Group Configuration 2. Contractor equipment 

considerations, potential economies from use of only one pile section across the 

project, and other factors should be weighed in deciding between the HP 12x74 and 

HP 14 x 89 section use at the three substructure locations.

Table D-133 Estimated Foundation Cost Including Piles and Pile Cap

at South Abutment

Group 

Configuration HP 12x74 HP 14x89 HP 14x117

1 - - $193,069

2 - $183,132 228,177

3 $176,821 208,762 261,997

While the cost of pile over/underrun at other substructure locations was evaluated to 

account for inaccuracies in the assumed soil strength properties and estimated soil 

resistance, this is not the case at the South Abutment. Piles must be driven to 

bedrock (approximately 91 feet) at the South Abutment to satisfy a tolerable 

deformation, which effectively eliminates risk of length over/overrun differences 

between any candidate pile sections and a further economic assessment is therefore 

not needed.

D.44Decision 20: Is the Preliminary Design of All Substructure Foundations 

Complete?

Yes, the preliminary foundation design has now been completed at all three 

substructure locations; North Abutment, Pier 2, and South Abutment.

D.45Block 21: Refine Structural Modeling and Determine Loads at Foundation 

Top and Lateral Earth Pressure Loads on Abutments

The structure and foundation response to the loading cases is now further refined 

based on the structural and geotechnical analyses completed in Block 9 through 

248
Block 17. The structural model is reanalyzed using the results from these 

preliminary substructure analyses to better define the structure loads at the 

foundation top, and lateral earth pressure loads on the abutments.

D.46Decision 22: Did Loads Significantly Change, and Require Reevaluation of 

the Foundation Design?

No. The refined structural modeling determined that the structural loads provided in 

Block 11 are suitable for the final design.

D.47Block 23: For Dynamic Elastic Analyses, Reevaluate Foundation Stiff 

nesses Using Unfactored Loads in Structural Model to get New 

Foundation Loads

Dynamic elastic analyses are not required since the structure is not subject to 

seismic events.

D.48Decision 24: Did Loads Significantly Change, and Require Reevaluation of 

the Foundation Design?

Since dynamic analyses are not required, re-evaluation of the foundation design is 

not necessary.

D.49Decision 25: Does the Design Meet All Limit State Requirements? 

All strength, service, and extreme limit state requirements have been satisfied by 

one or more candidate piles and associated group configurations as demonstrated in 

Blocks 9 through 18.

To complete the final design, a candidate pile section and associated pile group 

configuration must be selected at each substructure location. Table D-134

summarizes the total foundation cost for HP 12x74, HP 14x89 and HP 14x117 at 

each respective substructure location. If one pile section is used at all substructure 

locations for the bridge, the lowest cost foundation selection is the HP 12x74 at 

$367,043 followed by the HP 14x89 at $369,674. The most economical solution is 

to use HP 12x74 H-piles at both abutments and HP 14x89 H-piles at Pier 2. This 

solution has an estimated foundation cost of $357,434.

249
Table D-134 Estimated Total Foundation Cost at All Substructures Locations on the 

Southbound Bridge

Location

Most 

Economical

HP 12x74

Cost

Associated 

HP 12x74 

Group 

Configuration 

Most 

Economical

HP 14x89

Cost

Associated 

HP 14x89 

Group

Configuration 

Most 

Economical

HP 14x117

Cost

Associated 

HP 14x117 

Group 

Configuration 

North 

Abutment $96,192 1 $102,121 1 $122,145 1

Pier 2 94,030 5 84,421 4 104,671 4

South 

Abutment 176,821 3 183,132 2 193,069 1

Total 367,043 - 369,674 - 419,885 -

Although the results of the above economic assessment suggests the final design 

use different H-pile sections at different substructure locations, the $9,609 savings in 

the estimated foundation cost is likely insufficient to address potential increased 

costs from varying installation equipment or accessories as well as pile quantity 

discounts. Therefore, the final design will be based on the HP 12x74 section for the 

entire structure.

D.50Block 26: Design Pile Caps and Abutments

Preliminary design of pile caps is discussed in Section 8.9. Preliminary pile cap 

design was performed for this design example in Block 13. Final pile cap and 

abutment design is now performed by the structural engineer and is not detailed 

herein.

D.51Block 27: Finalize Plans and Specifications Including Pile Quantities, 

Minimum Pile Penetration Requirements from Blocks 13 through 15, and 

Required Nominal Resistances

Plans and specifications are finalized based upon the analyses and results from the 

previous design blocks. A summary of the final design is presented in Table D-135. 

At Pier 2, Group Configuration 6 was selected over Group Configuration 5 to reduce 

the risk of pile damage from driving piles through the dense gravel with cobbles to 

the bedrock. This decision increases the estimated final foundation cost from 

$367,043 to $373,492. This modest increase is justified by the replacement and 

redesign costs anticipated to accommodate a damaged pile.

250
Table D-135 Final Design Foundation Summary and Associated Penetration Depths 

for the Southbound Bridge

Location Group 

Configuration

Estimated 

Penetration 

Depth for 

Axial 

Compression 

(feet)

Minimum 

Penetration 

Depth for 

Axial 

Tension

(feet)

Minimum 

Penetration 

Depth for 

Lateral 

Deformation 

(feet)

Minimum 

Penetration 

Depth for 

Vertical 

Deformation

(feet)

Pile Section 

Drivability 

Limit

(feet)

North 

Abutment 1 45 28 25 60* 62

Pier 2 6 40 0 20 56* 60

South 

Abutment 3 73 18 35 91* 91

Note: * - Penetration depth controls the foundation design.

Plans and specifications are developed detailing the factored load, the nominal 

resistance determination method, the required nominal driving resistance, and 

associated estimated or minimum pile penetration depth estimates for strength or 

deformation requirements. As decided earlier in the design, dynamic testing with 

signal matching of at least 2% of the piles per location will be used for the resistance 

determination method in the field. 

D.51.1 Required Nominal Resistance at the North Abutment 

At the North Abutment, the required factored load per pile at the Strength I limit state

is 323 kips (Table D-14 of Block 10). Therefore the minimum required factored 

resistance in axial compression is 323 kips. Using the AASHTO resistance factor for 

nominal resistance determination by dynamic testing, φφdd = 0.65, the nominal 

resistance per pile is calculated with Equation 7-3.

RRrr = required factored resistance per pile, 323 kips (Table D-14).

φφdd = resistance factor (based on the static analysis method).

RRrr ≤ φφdd RRnn [Eq. 7-3]

Rearranging terms for RRnn:

RRnn ≥ rr

φφdd

[Eq. 7-3]

RRnn ≥ (323 )

(0.65)

RRnn ≥ 497 kkkk

251
The nominal resistance, RRnn, must therefore be greater than 497 kips per pile and this 

value is included on plan documents. As noted in Table D-6 and Figure D-9, for the 

HP 12x74 section in Group Configuration 1, the estimated depth to achieve this 

nominal resistance is 45 feet below the bottom of pile cap.

At the North Abutment, a limited amount of soil setup may also be considered in 

establishing the driving criteria. Figure D-21 illustrates the estimated soil setup at a 

depth of 45 feet is 35 kips. However, for tolerable deformations, a minimum pile 

penetration depth of 60 feet was specified. No additional setup occurs in the soils 

below 45 feet so the estimated setup at 60 feet is also 35 kips. Hence, production 

piles achieving a nominal driving resistance, RRnn , of 462 kips should attain the 

required nominal resistance of 497 kips during restrike. Based on the geomaterials, 

a restrike test interval of 1 day is specified. The required nominal driving resistance, 

RRnn , of 462 kips, the nominal resistance, RRnn, of 497 kips, the minimum penetration 

depth, and restrike interval are included on plan documents.

D.51.2 Required Nominal Resistance at Pier 2 

At Pier 2, the required factored load per pile at the Strength V limit state is 257 kips 

(Table D-61 of Block 10). Therefore the minimum required factored resistance in 

axial compression is 257 kips. Using the AASHTO recommended resistance factor 

φφdd =0.65, the nominal resistance per pile to be determined from field determination 

is calculated with Equation 7-3.

RRrr = required factored resistance per pile, 257 kips (Table D-61).

φφdd = resistance factor (based on the static analysis method).

RRrr ≤ φφdd RRnn [Eq. 7-3]

Rearranging terms for RRnn:

RRnn ≥ rr

φφdd

[Eq. 7-3]

RRnn ≥ (257 )

(0.65)

RRnn ≥ 395 kkkk

The nominal resistance, RRnn, must therefore be greater than 395 kips per pile (this 

value is included on plan documents). As noted in Table D-63 and Figure D-41, for 

252
the HP 12x74 section in Group Configuration 6, the minimum estimated depth to 

achieve this nominal resistance is 40 feet from the bottom of pile cap.

At Pier 2, more soil setup is anticipated due to the cohesive layer. Table D-52 and 

Table D-56 indicate the estimated soil setup at a depth of 40 feet is 71 kips. 

However, for tolerable deformations, a minimum pile penetration depth of 56 feet 

was specified. No additional setup occurs in the soils below 40 feet so the estimated 

setup at 60 feet is also 71 kips. Hence, production piles achieving a nominal driving 

resistance, RRnn , of 324 kips should attain the required nominal resistance of 395

kips during restrike. Based on the geomaterials and project size, a restrike test 

interval of 3 days is specified. The required nominal driving resistance, RRnn , of 324

kips, the nominal resistance, RRnn, of 395 kips, the minimum penetration depth, and the 

restrike interval are included on plan documents.

D.51.3 Required Nominal Resistance at the South Abutment

At the South Abutment, the required factored load per pile at the Strength I limit state

is 238 kips (Table D-108 of Block 10). Therefore the minimum required factored 

resistance in axial compression is 238 kips. Using the AASHTO recommended 

resistance factor φφdd =0.65, the nominal resistance per pile to be determined from 

field determination is calculated with Equation 7-3.

RRrr = required factored resistance per pile, 238 kips (Table D-108).

φφdd = resistance factor (based on the static analysis method).

RRrr ≤ φφdd RRnn [Eq. 7-3]

Rearranging terms for RRnn:

RRnn ≥ rr

φφdd

[Eq. 7-3]

RRnn ≥ (238 )

(0.65)

RRnn ≥ 366 kkkk

The nominal resistance, RRnn, must therefore be greater than 366 kips per pile (this 

value is included on plan documents). As noted in Table D-100 and Figure D-85, for 

the HP 12x74 section in Group Configuration 3, the minimum estimated depth to 

achieve this nominal resistance is 73 feet from the bottom of pile cap (Table D-109).

253
At the South Abutment, a significant amount of soil setup is anticipated. The 

nominal resistances in Table D-100 and Table D-103 indicate the estimated soil 

setup at a depth of 73 feet is 167 kips. However, for tolerable deformations, a 

minimum pile penetration depth of 91 feet was specified. This depth corresponds to 

the interface between the silty clay and bedrock layer. The estimated setup in the 

soil profile to 91 feet is 210 kips. Hence, production piles achieving a nominal 

driving resistance, RRnn , of 156 kips should attain the required nominal resistance of 

366 kips with time. In clay soils, restrikes are often performed 1 week after initial 

driving. However, to satisfy the tolerable deformation requirements the piles will be 

driven to hard rock, the piles will have more than sufficient nominal resistance 

without setup. Hence, waiting 1 week to conduct restrike tests is not realistic or 

needed. Based on the geomaterials and project size, a restrike test interval of 1 

days is specified. The required nominal driving resistance, RRnn , of 156 kips, the 

nominal resistance, RRnn, of 366 kips, the minimum penetration depth, and the restrike 

interval are included on plan documents. 

D.52Block 28: Perform Evaluation of Contractor’s Proposed Equipment

Project specifications require the Contractor to provide documentation for the pile 

driving hammer to be used. The drive system submittal form shown in Figure 15-50

of Chapter 15 is typically completed by the Contractor, and provided to the Engineer. 

A preconstruction wave equation is then performed considering the contractor’s 

specific hammer, selected pile section and respective soil model.

The Contractor has submitted an ICE I-36 V2 single acting diesel hammer for 

hammer approval. Figure D-113 presents a copy of the hammer submittal form.

254
Figure D-113 Contractor’s ICE I-36 V2 hammer submittal form.

255
D.52.1 Wave Equation for the North Abutment

At the North Abutment, the design stage drivability file was modified to evaluate the 

Contractor’s proposed driving system. The drivability results, presented in Figure 

D-114, show that the ICE I-36 V2 appears suitable to drive the HP 12x74 pile section 

to the required minimum penetration depth of approximately 60 feet, within specified 

blow count range of 30 to 120 blows per foot, and with driving stresses below the 

maximum driving stress limit of 45 ksi.

Figure D-114 Preliminary drivability with Contractor’s hammer at the North 

Abutment.

A wave equation bearing graph was also developed for the proposed driving system 

and HP 12x74 pile section at the required minimum pile penetration depth of 60 feet. 

The plot of compression stress and tension stress versus blow count is shown as 

Figure D-115. Driving stresses are less than the 45 ksi specification limit. Figure 

D-116 presents the bearing graph of the nominal resistance versus blow count, and 

the calculated hammer stroke versus blow count. In this, it is important to note that 

the required nominal driving resistance of 462 kips as well as the nominal resistance 

of 497 kips are well within the blow count range of 30 to 120 blows per foot.

256
Figure D-115 Compression and tension stress versus blow count.

Figure D-116 Nominal resistance and stroke versus blow count.

257
Figure D-117 provides a preliminary Inspectors Chart of hammer stroke versus blow 

count for the ICE I-36 V2 and a nominal driving resistance, RRnn , of 462 kips. This 

plot provide pile inspector with an additional tool to determine the necessary blow 

count at the observed hammer stroke. For example, the 462 kip nominal driving 

resistance is achieved at 62 blows per foot with a hammer stroke of 6 feet and at a 

blow count of 28 blows per foot at a hammer stroke of 11 feet. 

Figure D-117 Inspectors Chart for ICE I-36 V2 at the North Abutment.

258
D.52.2 Wave Equation for Pier 2

At the Pier 2, the design stage drivability file was again modified to evaluate the 

Contractor’s proposed driving system. The drivability results presented in Figure 

D-118 show that the ICE I-36 V2 appears suitable to drive the HP 12x74 pile section 

to the required minimum penetration depth of approximately 56 feet, within specified 

blow count range of 30 to 120 blows per foot, and with driving stresses below the 

maximum driving stress limit of 45 ksi. 

Figure D-118 Drivability with Contractor’s hammer at Pier 2.

A wave equation bearing graph was also developed for the proposed driving system 

and HP 12x74 pile section at the required minimum pile penetration depth of 56 feet. 

The plot of compression stress and tension stress versus blow count is shown as 

Figure D-119. Driving stresses are less than the 45 ksi specification limit. Figure 

D-120 presents the bearing graph of the nominal resistance versus blow count, and 

the calculated hammer stroke versus blow count. In this, it is important to note that 

the required nominal driving resistance of 324 kips as well as the nominal resistance 

of 395 kips are within slightly less than acceptable blow count range of 30 blows per 

foot. However, the analysis was performed using the maximum fuel setting. If it is 

desired to have the blow count above 30 blows per foot at the nominal driving 

resistance, a reduced fuel setting could be used. Also, the nominal driving 

259
Figure D-119 Compression and tension stress versus blow count.

Figure D-120 Nominal resistance and stroke versus blow count.

260
resistance is expected to be on the order of 500 kips at the minimum pile penetration 

depth where the blow count is above 30 blows per foot.

Figure D-121 provides a preliminary Inspectors Chart of hammer stroke versus blow 

count for the ICE I-36 V2 and a nominal driving resistance, RRnn , of 324 kips. This

plot provide pile inspector with an additional tool to determine the necessary blow 

count at the observed hammer stroke. For example, the 324 kip nominal driving 

resistance is achieved at 37 blows per foot with a hammer stroke of 5 feet and at a 

blow count of 20 blows per foot at a hammer stroke of 9 feet. 

Figure D-121 Inspectors Chart for ICE I-36 V2 at Pier 2.

261
D.52.3 Wave Equation for the South Abutment

At the South Abutment, the design stage drivability file was revisited and modified to 

evaluate the Contractor’s proposed driving system. The drivability results, presented 

in Figure D-122 show that the ICE I-36 V2 appears suitable to drive the HP 12x74 

pile section to the required minimum penetration depth of approximately 91 feet, 

within specified blow count range of 30 to 120 blows per foot, and with driving 

stresses below the maximum driving stress limit of 45 ksi. 

Figure D-122 Drivability with Contractor’s hammer at the South Abutment.

A wave equation bearing graph was also developed for the proposed driving system 

and HP 12x74 pile section at the required minimum pile penetration depth of 91 feet. 

The plot of compression stress and tension stress versus blow count is shown as 

Figure D-123. Driving stresses are less than the 45 ksi specification limit. Figure 

D-124 presents the bearing graph of the nominal resistance versus blow count, and 

the calculated hammer stroke versus blow count. In this, it is important to note that 

the required nominal driving resistance of 156 kips as well as the nominal resistance 

of 366 kips are below the recommended blow count range of 30 to 120 blows per 

foot. However, the analysis was performed using the maximum fuel setting. If it is 

desired to have the blow count above 30 blows per foot at the nominal driving 

resistance, a reduced fuel setting could be used. It should also be noted that the 

262
Figure D-123 Compression and tension stress versus blow count.

Figure D-124 Nominal resistance and stroke versus blow count.

263
nominal driving resistance will quickly transition from approximately 240 to 250 kips 

above rock to well in excess of 900 kips on rock. Hence, hammer operation at a 

reduced fuel setting is preferred to better control driving stresses.

Figure D-125 is a preliminary Inspectors Chart for the IC I-36 V2. For the nominal 

driving resistance, RRnn , of 156 kips, Figure D-125 plots the stroke and respective 

blow count determined from the wave equation analysis. This chart provides the 

inspector with an additional tool to compare the relative stroke and penetration 

resistance for a hammer varies in performance. For example, 156 kips of nominal 

resistance is achieved at 8 blows/ft with a hammer stroke of 6 feet and also at 11

blows/ft with a hammer stroke of 4 feet.

Figure D-125 Inspectors Chart for ICE I-36 V2 at the South Abutment.

264
D.53Block 29: Set Preliminary Driving Criteria, Drive Test Pile(s) and Assess 

Constructability

The required nominal driving resistance at each substructure location was 

determined in Block 27. These nominal driving resistances consider the selected 

resistance determination method as well as changes in the long term geotechnical 

resistance due to soil setup, scour, or construction activities. The wave equation 

analyses performed for each substructure location in Block 28 will be used to set the 

preliminary driving criteria. 

Two test piles are driven at production pile locations for each substructure. Dynamic 

monitoring is performed on these two piles during initial driving and again during 

restrike after an appropriate waiting period. Signal matching analysis is also 

performed on the initial driving and restrike dynamic test results to determine the 

magnitude of soil setup. The dynamic testing and signal matching results 

substantiate the constructability of the design..

D.54Block 30: Adjust Driving Criteria or Design

Refined wave equation analyses are now performed based on the dynamic test 

results. The refined wave equation analyses establish the production pile installation 

criteria at each substructure location. The required nominal driving resistance 

considers the magnitude of soil setup substantiated by the test pile monitoring during 

initial driving and restrike. The test pile results confirmed that design modifications 

are not required.

D.55Block 31: Drive Production Piles with Construction Monitoring, Resolve 

any Pile Installation Problems

Production piles are installed using the final driving criteria. Pile installation is 

documented in accordance with established quality control procedures.

D.56Block 32: Perform Post-Construction Evaluation and Refinement For 

Future Designs

After completion of the foundation construction, the design is reviewed and 

evaluated for its ability to satisfy the design requirements cost effectively.

265