Geotechnical Engineering Circular (GEC) No. 8
Design And Construction Of Continuous Flight Auger Piles
PDF Version (15 mb)
Table Of Contents
List Of Tables
- Table 5.01 Relationship between Undrained Shear Strength, Rigidity Index, and Bearing Capacity Factor for Cohesive Soils for FHWA 1999 Method
- Table 5.02 Soil Conditions Investigated for Drilled Displacement Piles
- Table 5.03 Efficiency (η) for Model Drilled Shafts Spaced 3 Diameters Center-to-Center in Various Group Configurations in Clayey Sand (Senna et al., 1993)
- Table 5.04 P-Multipliers (Pm) for Design of Laterally Loaded Pile Groups
- Table 6.01 Design Consideration for Foundation Selection of CFA and DD Piles
- Table 6.02 Pile Group Settlement Computation
- Table 7.01 General Guidelines for Auger Penetration Rate for CFA Piles
- Table A.01 Soil-Pile Friction Angle, Limiting Unit Side-Shear Resistance, and Limiting End-Bearing Values (API, 1993)
- Table A.02 Total Resistance - Results from Five Methods (McVay et al., 1994)
- Table A.03 Total Resistance - Results from Eight Different Methods (Zelada and Stephenson, 2000)
- Table A.04 Total Resistance - Results from Eight Methods (Zelada and Stephenson, 2000)
- Table A.05 Side-Shear Resistance - Results from Eight Methods (Zelada and Stephenson, 2000)
- Table A.06 End-Bearing Resistance - Results from Eight Methods (Zelada and Stephenson, 2000)
List Of Figures
- Figure 2.01 CFA Pile
- Figure 2.02 Schematic of CFA Pile Construction
- Figure 2.03 Schematic of Typical Drilled Shaft vs. CFA Foundation
- Figure 2.04 Group of CFA Piles with Form for Pile
- Figure 2.05 Effect of Over-Excavation using CFA Piles
- Figure 2.06 Displacement Pile
- Figure 2.07 Hole at Base of Auger for Concrete
- Figure 2.08 Grout Delivered to Pump
- Figure 2.09 Grout at Surface after Auger Withdrawal
- Figure 2.10 Finishing Pile and Reinforcement Placement
- Figure 2.11 Placement of a Single Full-Length
- Figure 2.12 Vibratory Drive Head Used to Install Rebar Cage
- Figure 3.01 Use of CFA Piles for Commercial Building Projects.
- Figure 3.02 Examples of Difficult Conditions for Augured Piles
- Figure 3.03 CFA Piles at Bridge Interchange
- Figure 3.04 Low Headroom CFA Pile Application
- Figure 3.05 Secant Pile Wall with CFA Pile Construction
- Figure 3.06 CFA Piles for Soundwall along Highway
- Figure 3.07 Pilecaps on CFA Piles For A Pile-Supported Embankment
- Figure 3.08 Drilled Displacement Piles Limit Spoil Removal
- Figure 3.09 CFA Pile Foundation for Soundwall
- Figure 3.10 Schematic Diagram of the Foundation on CFA Piles for the Krenek Road Bridge
- Figure 3.11 CFA Piles at the Krenek Road Bridge Site
- Figure 3.12 Comparison of Measured Settlements and Test Pile, Krenek Road Bridge Site.
- Figure 3.13 Secant CFA Pile Wall for a Light Rail System in Germany
- Figure 3.14 Schematic Plan View of a Secant Pile Wall
- Figure 3.15 Drilling CFA Piles through Guide for Secant Wall
- Figure 3.16 Diagram of Pile-Supported Embankment for Italian Railway Project
- Figure 4.01 Typical Crane-Mounted CFA
- Figure 4.02 Photo of Crane-Attached CFA System
- Figure 4.03 Low Headroom CFA Pile
- Figure 4.04 Low Headroom Rig with Segmental Augers
- Figure 4.05 Hydraulic Rig Drilling on M25 Motorway in England
- Figure 4.06 Soilmec Hydraulic CFA Rig with Kelley Extension
- Figure 4.07 Augers for Different Soil Conditions
- Figure 4.08 Auger for Use in Clay with Auger Cleaner Attachment
- Figure 4.09 Cutter Heads for Hard Material and Soil
- Figure 4.10 Hardened Cutting Head
- Figure 4.11 DeWaal Drilled Displacement Pile
- Figure 4.12 Omega Screw Pile
- Figure 4.13 Fundex Screw Pile
- Figure 4.14 Drilled Displacement Piles
- Figure 4.15 Additional Drilled Displacement Piles
- Figure 4.16 Double Rotary Cased CFA Piles
- Figure 4.17 Double Rotary Fixed Drive System
- Figure 4.18 Double Rotary System with Kelly-Bar Extension
- Figure 4.19 Typical Concrete/Grout Pumps
- Figure 4.20 In-Line Flowmeter
- Figure 4.21 Sensor for Concrete Pressure at Auger
- Figure 4.22 Completion of Pile Top Prior to Installation of Reinforcement
- Figure 4.23 Sand-Cement Grout Mixes
- Figure 4.24 Machine-Welded Reinforcement Cage on Project Site in Germany
- Figure 4.25 Use of Steel Pipe to Reinforce a CFA Pile for a Wall
- Figure 4.26 Installation of Reinforcement Cage into Battered CFA Pile
- Figure 5.01 Load-Displacement Relationships.
- Figure 5.02 Relationship for the α Factor with Su for Calculating the Unit Side-Shear for Cohesive Soils for the Coleman and Arcement (2002) Method.
- Figure 5.03 Unit Side-Shear Resistance as a Function of Cone Tip Resistance for Cohesive Soils - LPC Method
- Figure 5.04 Relationship for the β Factor for Calculating the Unit Side-Shear for Cohesionless Soils for the FHWA 1999 and Coleman and Arcement Methods.
- Figure 5.05 Unit Side-Shear as a Function of Cone Tip Resistance for Cohesionless Soils - LPC Method
- Figure 5.06 Unconfined Compressive Strength vs. Ultimate Unit Side-Shear for Drilled Shafts in Florida Limestone
- Figure 5.07 Correlation of Ultimate Unit Side-Shear Resistance for South Florida Limestone with SPT-N60 Value
- Figure 5.08 Side-Shear Development with Displacement for South Florida Limestone.
- Figure 5.09 Relative Load Capacity vs. Relative Displacement for CFA Sockets in Clay-Shale.
- Figure 5.10 Hyperbolic Model Parameter Qult as a Function of the Unconfined Compressive Strength (Qu) for CFA Sockets in Clay-Shale.
- Figure 5.11 Parameter ρ50/D as a Function of Unconfined Compressive Strength for CFA Sockets in Clay-Shale
- Figure 5.12 Ultimate Unit Side-Shear Resistance for Drilled Displacement Piles for Nesmith (2002) Method
- Figure 5.13 Ultimate Unit End-Bearing Resistance for Drilled Displacement Piles for Nesmith (2002) Method
- Figure 5.14 Overlapping Zones Of Influence in A Frictional Pile Group.
- Figure 5.15 Efficiency (Η) Vs. Center-To-Center Spacing (S), Normalized By Shaft Diameter (Bshaft), for Underreamed Model Drilled Shafts in Compression in Moist, Silty Sand.
- Figure 5.16 Relative Unit Side and Base Resistances for Model Single Shaft and Typical Shaft in a Nine-Shaft Group in Moist Alluvial Silty Sand.
- Figure 5.17 Block Type Failure Mode.
- Figure 5.18 Deeper Zone of Influence for End-Bearing Pile Group than for a Single Pile.
- Figure 5.19 Equivalent Footing Concept for Pile Groups.
- Figure 5.20 Pressure Distribution Below Equivalent Footing for Pile Group.
- Figure 5.21 Typical e vs. Log p Curve from Laboratory Consolidation Testing.
- Figure 5.22 p-y Soil Response of Laterally Loaded Pile Model
- Figure 5.23 Example Deflection and Moment Response of Laterally Loaded Pile Model
- Figure 5.24 Typical Stress-Strain Relationship Used for Steel Reinforcement
- Figure 5.25 Typical Stress-Strain Relationship Used for Concrete.
- Figure 5.26 Variation of Pile Stiffness (EI) with Bending Moment and Axial Load.
- Figure 5.27 The p-multiplier (Pm)
- Figure 5.28 Circular Column (Pile) with Compression Plus Bending
- Figure 5.29 Example Interaction Diagram for Combined Axial Load and Flexure
- Figure 5.30 Examples of Cases of Downdrag.
- Figure 5.31 Potential Geotechnical Limit States for Piles Experiencing Downdrag.
- Figure 5.32 Mechanics of Downdrag: Estimating the Depth to the Neutral Plane.
- Figure 5.33 Mechanics of Downdrag in a Pile Group.
- Figure 5.34 Soil Profile Su vs. Depth for Example Problem of CFA Pile in Cohesive Soil
- Figure 5.35 Soil Profile SPT-N vs. Depth for Example Problem of CFA Pile and DD Pile in Cohesionless Soil
- Figure 6.01 GULS and Short Term SLS for Axial Load on a Single CFA Pile
- Figure 6.02 Typical Conditions at the Project Site
- Figure 6.03 Idealized Soil Profile for Design
- Figure 6.04 Five-Pile Footing Layout
- Figure 6.05 Computed Lateral Load vs. Deflection
- Figure 6.06 Deflection and Bending Moments vs. Depth for Example Problem
- Figure 6.07 Maximum Bending Moments as a Function of Pile Top Deflection
- Figure 6.08 Bending Moment vs. Curvature for a 18-in. diameter Pile with 6 #7's
- Figure 6.09 Computed Axial Resistance vs. Depth
- Figure 7.01 Operator with Cab Mounted Display Used to Control Drilling
- Figure 7.02 Depth Encoder Mounted on Crane Boom
- Figure 7.03 In-line Flowmeter
- Figure 7.04 Pressure Sensors on Hydraulics to Monitor Rig Forces
- Figure 7.05 Display Panel for Observation by Inspector
- Figure 7.06 Example Data Sheet from Project
- Figure 7.07 Dipping Grout to Remove Contamination
- Figure 7.08 Cleaning the Top of a CFA Concrete Pile
- Figure 7.09 Placement of Reinforcing Cage with Plastic Spacers
- Figure 7.10 Cubes for Grout Testing
- Figure 7.11 Sonic Echo Testing Concept
- Figure 7.12 Sonic Echo Testing of Long Piles
- Figure 7.13 Downhole Sonic Logging Concept (SSL)
- Figure 7.14 Gamma-Gamma Testing Via Downhole Tube
- Figure 7.15 Static Load Test Setup on CFA Piles
- Figure 7.16 Proof Testing of Production Piles with Statnamic (RLT) Device
- Figure 7.17 Effect of Multiple Load Cycles on a CFA Pile
- Figure A.01 β Factor vs. Pile Length (Neely, 1991)
- Figure A.02 α vs. Undrained Shear Strength - Clayey Soils (Clemente et al., 2000)
- Figure A.03 β Factor vs. Depth - Zelada and Stephenson (2000) and FHWA 1999 Methods
- Figure A.04 Ultimate Unit End-Bearing Resistance vs. SPT-N Values - Zelada and Stephenson (2000) and Other Methods
- Figure A.05 Normalized Load-Settlement Relationship for Design of CFA Piles - Clay Soils of Texas Gulf Coast (O'Neill et al., 2002)
- Figure A.06 a vs. Average Undrained Shear Strength along Pile Length (Coyle and Castello, 1981)
- Figure A.07 Unit Side-Shear and End-Bearing Capacities - Cohesionless Soils (Coyle and Castello, 1981)
- Figure A.08 Relationship between SPT-N Values and f (Coyle and Castello, 1981)
- Figure A.09 Summary of Total Resistance - Results from Five Methods (McVay et al., 1994)
- Figure A.10 Summary of Total Resistance - Results from Eight Methods (Zelada and Stephenson, 2000)
- Figure A.11 Summary of Total Resistance - Results from Four Methods (Coleman and Arcement, 2002)
- Figure A.12 Total Capacity - Results from FHWA 1999 Method (Coleman and Arcement, 2002)
- Figure A.13 Total Capacity Results - Coleman and Arcement (2002) Method
- Figure A.14 Effective Lateral Earth Pressure near a CFA Pile during Construction (O'Neill et al., 2002)
- Figure A.15 Total Resistance - Results from Four Methods
- Figure A.16 Comparison of Study Results - Axial Capacity in Cohesive Soils
- Figure A.17 Comparison of Study Results - Axial Capacity in Cohesionless Soils
Technical Support Documentation Page
|1. Report No.
|2. Government Accession No.
|3. Recipient's Catalog No.
|4. Title and Subtitle
Geotechnical Engineering Circular No. 8
Design and Construction of Continuous Flight Auger (CFA) Piles
|5. Report Date
|6. Performing Organization Code|
Dan A. Brown, Ph.D., P.E., Steven D. Dapp, Ph.D., P.E., W. Robert Thompson, III, P.E., and Carlos A. Lazarte, Ph.D., P.E.
|8. Performing Organization Report No.
|9. Performing Organization Name and Address
10015 Old Columbia Road, Suite A-200
Columbia, MD 21046-1760
|10. Work Unit No. (TRAIS)
|11. Contract or Grant No.
|12. Sponsoring Agency Name and Address
Office of Technology Application
Office of Engineering/Bridge Division
Federal Highway Administration
U.S. Department of Transportation
400 Seventh Street, S.W.
Washington D.C., 20590
|13. Type of Report and Period Covered
|14. Sponsoring Agency Code|
|15. Supplementary Notes|
FHWA Technical Consultant: J.A. DiMaggio, P.E., S.C. Nichols, P.E.
This manual presents the state-of-the-practice for design and construction of continuous flight auger (CFA) piles, including those piles commonly referred to as augered cast-in-place (ACIP) piles, drilled displacement piles, and screw piles. CFA pile types, materials, and construction equipment and procedures are discussed. A performance-based approach is presented to allow contractors greater freedom to compete in providing the most cost-effective and reliable foundation system, and a rigorous construction monitoring and testing program to verify the performance. Quality control (QC)/quality assurance (QA) procedures are discussed, and general requirements for a performance specification are given.
Methods to estimate the static axial capacity of single piles are recommended based on a thorough evaluation and comparison of various methods used in the United States and Group effects for axial capacity and settlement, and lateral load capacities for single piles and pile groups are discussed. A generalized step-by-step method for selecting and designing CFA piles is presented, along with example calculations. An Allowable Stress Design (ASD) procedure is used.
|17. Key Words
Continuous flight auger piles, CFA, augered cast-in-place piles, ACIP, drilled displacement piles, screw piles, deep foundation, testing, automated monitoring, performance specification.
|18. Distribution Statement
|19. Security Classification (of this report)
|20. Security Classification (of this page)
|21. No. of Pages
English to Metric (SI) Conversion Factors
The primary metric (SI) units used in civil and structural engineering are:
- meter (m)
- kilogram (kg)
- second (s)
- Newton (N)
- Pascal (Pa)
The following are the conversion factors for units presented in this manual:
||From English Units
||To Metric (SI) Units
||For Aid to Quick Calculations
||1 lb(mass) = 0.5 kg
|1 lb(force) = 4.5 N
1 kip(force) = 4.5 kN
|1 plf = 14.5 N/m
1 klf = 14.5 kN/m
|Pressure, Stress, Modulus of Elasticity
|1 psf = 48 Pa
1 ksf = 48 kPa
1 psi = 6.9 kPa
1 ksi = 6.9 MPa
|1 in = 25 mm
1 ft = 0.3m
1 ft = 300 mm
|1 sq in = 650 mm2
1 sq ft = 0.09 m2
1 sq yd = 0.84 m2
|1 cu in = 16,400 mm3
1 cu ft = 0.03 m3
1 cu yd = 0.76 m3
A few points to remember:
- In a "soft" conversion, an English measurement is mathematically converted to its exact metric (SI) equivalent.
- In a "hard" conversion, a new rounded metric number is created that is convenient to work with and remember.
- Use only the meter and millimeter for length (avoid centimeter).
- The Pascal (Pa) is the unit for pressure and stress (Pa and N/m2).
- Structural calculations should be shown in MPa or kPa.
- A few basic comparisons worth remembering to help visualize metric dimensions are:
- One mm is about 1/25 inch, or slightly less than the thickness of a dime.
- One m is the length of a yardstick plus about 3 inches.
- One inch is just a fraction (1/64 inch) longer than 25 mm (1 inch = 25.4 mm).
- Four inches are about 1/16 inch longer than 100 mm (4 inches = 101.6 mm).
- One foot is about 3/16 inch longer than 300 mm (12 inches = 204.8 mm).
The authors express their appreciation to Mr. Jerry A. DiMaggio, P.E. of the Federal Highway Administration (FHWA), Office of Bridge Technology, Mr. Silas Nichols, P.E., of the FHWA Resource Center, and Mr. Chien-Tan Chang of the FHWA Office of Bridge Technology for providing valuable technical assistance, review, and project overview during this project. The authors thank the following individuals that served on the Technical Working Group for this project:
- Silas Nichols FHWA Resource Center
- Benjamin Rivers FHWA Resource Center
- Khalid Mohamed FHWA Eastern Federal Lands Highway Division
- Rich Barrows FHWA Western Federal Lands Highway Division
- James Brennan Kansas DOT
- Mark McClelland Texas DOT
The authors thank the following organizations and individuals for providing valuable information and reviewing this manual:
- International Association of Foundation Drilling (ADSC-IAFD) - Emerging Technologies Task Force
- Deep Foundations Institute (DFI) - Augered Cast-In-Place Pile Committee
In addition, the authors thank the following organizations and individuals for providing valuable information for the preparation of this document:
- Applied Foundation Testing, Green Cove Springs, Florida
- Bauer Maschinen GmbH, Schrobenhause, Germany
- Berkel and Company Contractors, Inc., Bonner Springs, Kansas
- British Research Establishment, U.K.
- Cementation Foundations Skanska, U.K.
- DGI-Menard, Inc., Bridgeville, Pennsylvania
- Franki Geotechnics B, Belgium
- Jean Lutz, S.A., France
- Morris-Shea Bridge Company, Inc., Irondale, Alabama
- Pile Dynamics, Inc., Cleveland, Ohio
- Societa Italiana Fondazioni (SIF), S.p.A, Italy
- Soilmec, S.p.A., Italy
- Soletanche Bachy, France
- STS Consultants, Vernon Hills, Illinois
- Trevi, S.p.A., Italy
- Prof. A. Mandolini, Second University of Naples, Naples, Italy
- Prof. W. Van Impe, Ghent University, Ghent, Belgium
- Prof. C. Vipulanandan, University of Houston, Houston, Texas
- Prof. Michael O'Neill (deceased), University of Houston, Houston, Texas
Finally, the authors thank Ms. Lynn Johnson, of Geosyntec Consultants, for word processing, editing, and assisting in the layout of the document.
The purpose of this document is to develop a state-of-the-practice manual for the design and construction of continuous flight auger (CFA) piles, including those piles commonly referred to as augered cast-in-place (ACIP) piles, drilled displacement (DD) piles, and screw piles. An Allowable Stress Design (ASD) procedure is presented in this document as resistance (strength reduction) factors have not yet been calibrated for CFA piles for a Load Resistance Factored Design (LRFD) approach. The intended audience for this document is engineers and construction specialists involved in the design, construction, and contracting of foundation elements for transportation structures.
CFA piles have been used in the U.S. commercial market but have not been used frequently for support of transportation structures in the United States. This underutilization of a viable technology is a result of perceived difficulties in quality control, and the difficulties associated with incorporating a rapidly developing (and often proprietary) technology into the traditional, prescriptive design-bid-build concept. Recent advances in automated monitoring and recording devices will alleviate concerns of quality control, as well as provide an essential tool for a performance-based contracting process.
This document provides descriptions of the basic mechanisms involving CFA piles, CFA pile types, applications for transportation projects, common materials, construction equipment, and procedures used in this technology. Recommendations are made for methods to estimate the static axial capacity of single piles. A thorough evaluation and comparison of various existing methods used in the United States and Europe is also presented. Group effects for axial capacity and settlement are discussed, as well as lateral load capacities for both single piles and pile groups. A generalized step-by-step method for the selection and design of CFA piles is presented. Quality control (QC)/quality assurance (QA) procedures are discussed, and a performance specification is provided. This generic specification may be adapted to specific project requirements.
A list of the references used in the development of this manual is presented. These references include the key publications on the design of augered pile foundations. Existing Federal Highway Administration (FWHA) and American Association of State Highway Officials (AASHTO) publications that include engineering principles related to the subject of CFA piles are also included in the references.
List Of Abbreviations
- American Association of State Highway and Transportation Officials
- American Concrete Institute
- Augered cast-in-place
- American Petroleum Institute
- American Society of Civil Engineers
- Allowable stress design
- American Society of Testing Materials
- Blows per foot
- Continuous flight auger
- Cross-hole sonic logging
- Drilled displacement
- Deep Foundations Institute
- Dynamic load test
- Department of Transportation
- Florida Department of Transportation
- Federal Highway Administration
- Geotechnical ultimate limit state
- Ground water table
- Sulphuric acid
- Intermediate geotechnical material
- Kips per cubic foot
- Kips per square inch
- Laboratorie Des Ponts et Chausses
- Load and Resistance Factor Design
- Sodium sulphate
- Sodium chloride
- National Geotechnical Experimentation Site
- National Highway Institute
- Pounds per cubic yard
- Hydrogen potential
- Parts per million
- pounds per square inch
- Polyvinyl chloride
- Quality Assurance/Quality Control
- Rapid load test
- Service load design
- Service limit state
- Standard penetration test
- Single-hole sonic logging
- Structural ultimate limit state
- Tons per square foot
- Total service load
- Texas Department of Transportation
- Viscosity-modifying admixtures
- Water-to-cement ratio
List Of Symbols
- Cross-sectional area of concrete inside spiral steel
- Average cross-sectional area for pile segment "i"
- Gross area
- Effective area
- Cross-sectional area of single pile
- Cross-sectional area of all piles in a group
- Cross-sectional area of pile group, not including overhanging cap area
- Cross-sectional area of reinforced steel
- Effective cross-sectional area in resisting shear
- Required area of transverse steel
- Shaft diameter
- Width of block
- Pile diameter
- Wave propagation velocity
- Compression index
- Recompression index
- Pile diameter
- Depth of concrete cover
- Diameter of longitudinal bars
- Distance normal to neutral axis of outer piles
- Pile diameter
- Depth of block
- Diameter of pile at the base
- Diameter of pile segment "i"
- Void ratio
- Initial void ratio
- Elastic modulus
- Initial tangent slope
- Young's Modulus of concrete or grout
- Average Young's Modulus of equivalent pier within compressible layer
- Average composite modulus for pile segment "i"
- Flexural rigidity of pile/beam
- Average Young's modulus of pile
- Undrained Young's modulus or secant modulus
- Soil average Young's modulus
- Young's Modulus of geomaterial between piles
- Side-Shear resistance
- Concrete compressive strength
- Ultimate compressive strength
- Ultimate Side-Shear resistance
- Ultimate unit Side-Shear resistance
- Average unit Side-Shear resistance
- Unit Side-Shear resistance of segment "i"
- Steel yield stress
- Axial force on pile
- Original thickness of layer
- Generic pile segment number
- Influence factor for group embedment
- Rigidity index
- Subgrade modulus
- K, Ks, K′
- Lateral earth pressure coefficient
- In-situ lateral earth pressure coefficient
- Active lateral earth pressure coefficient
- Passive lateral earth pressure coefficient
- Pile embedment length below top of grade
- Pile socket length
- Length of pile segment "i"
- Pile length
- M, Mt
- Overturning moment
- Nominal ultimate flexural resistance
- Number of pile segments
- SPT blow-count
- Average equivalent N value
- SPT-N value (bpf) corrected for 60% efficiency
- Average corrected SPT-N value
- CPT cone factor
- NC*, Nq
- Bearing capacity factor
- Value obtained from the Texas Cone Penetrometer
- Vertical effective consolidation stress
- Lateral soil reaction
- Preconsolidation pressure
- Foundation pressure
- Effective overburden or vertical pressure
- Compressive force
- Pa, Patm
- Standard atmospheric pressure
- Nominal ultimate axial resistance
- Lateral force
- Axial load
- Nominal ultimate axial resistance
- CPT tip resistance
- Average CPT tip resistance
- Ultimate unit end-bearing resistance
- Unconfined compressive strength
- Pile total resistance
- Average axial load at pile segment "i"
- Value of load of type "i"
- Ultimate total load
- Qt, Qult, Qmax
- Ultimate resistance
- Radius of rings formed along centroids of longitudinal bars
- Computed resistance at GULS
- Allowable static axial resistance
- RB, RBd
- End-bearing resistance
- Resistance of the block
- Side-shear resistance
- Total axial compressive resistance
- Ultimate resistance of pile group
- Ultimate resistance of "i" in pile group
- Pile spacing
- Pile slope
- Longitudinal spacing of reinforcement ties (spiral pitch)
- Total settlement of pile group
- Total settlement
- Safety factor
- Stiffness ratio
- Soil undrained shear strength
- Average undrained shear strength along pile length
- Su ave
- Average soil undrained shear strength
- Shear force
- Concrete shear strength
- Nominal shear resistance of concrete section
- Nominal shear resistance of transverse steel
- Load along pile length
- Pile displacement
- Correlation constant
- Correlation constant
- Coordinate along pile length
- Lateral deflection at a point with coordinate x
- Thickness of soil layer "i"
- Depth below watertable
- Length of block
- Depth from ground surface to middle of a soil layer or pile segment (in ft)
- Depth from ground surface to middle of a soil layer or pile segment (in m)
- Reduction factor
- Pile segment factor
- Reduction factor
- Soil unit weight
- γsoil, i
- Unit weight of soil layer "i"
- Water unit weight
- Soil-to-pile interface friction angle
- Elastic compression of pile
- Change in overburden pressure
- Strain at 50% of compressive strength in compression load tests
- Yield strain
- Pile efficiency
- Pile group efficiency
- Pile displacement
- Vertical effective stress
- Soil drained angle of internal friction
- Resistance factor
- Ratio of undrained shear strength and vertical effective stress in soil