Hướng dẫn thiết kế và thi công cọc khoan nhồi theo 22TCN272:05 và AASHTO LRFD

Hướng dẫn thiết kế và thi công cọc khoan nhồi theo 22TCN272:05 và AASHTO LRFD. Có nhiều thông tin quý giá mà người thiết kế và tính toán cần thiết như cách tính cốt thép chủ, đai xoắn đầu cọc,..theo Aashto LRFD

U.S Department of Transportation Federal Highway Administration Publication No FHWA-NHI-10-016 FHWA GEC 010 May 2010 NHI Course No 132014 Drilled Shafts: Construction Procedures and LRFD Design Methods Developed following: AASHTO LRFD Bridge Design Specifications, 4th Edition, 2007, with 2008 and 2009 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 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 manufacturer's names appear herein only because they are considered essential to the object of this document Technical Report Documentation Page Report No Government Accession No Recipient’s Catalog No FHWA NHI-10-016 Title and Subtitle Report Date DRILLED SHAFTS: CONSTRUCTION PROCEDURES AND LRFD DESIGN METHODS NHI COURSE NO 132014 GEOTECHNICAL ENGINEERING CIRCULAR NO 10 Author(s) May 2010 Performing Organization Code Performing Organization Report No Dan A Brown*, Ph.D, P.E., John P Turner**, Ph.D, P.E., and Raymond J Castelli, P.E Performing Organization Name and Address 10 Work Unit No (TRAIS) PB Americas, Inc One Penn Plaza, New York, NY 10119 11 Contract or Grant No * Dan Brown and Associates, PLLC., Sequatchie, TN 37374 University of Wyoming, Laramie, WY 82071 ** DTFH-61-D-00011/T-07-002 12 Sponsoring Agency Name and Address 13 Type of Report and Period Covered National Highway Institute U.S Department of Transportation Federal Highway Administration, Washington, D.C 20590 14 Sponsoring Agency Code 15 Supplementary Notes FHWA COTR – Louisa Ward/ Larry Jones FHWA Task Manager – Silas Nichols, P.E FHWA Technical Reviewers – J Maswoswe, Ph.D, P.E.; J DiMaggio, P.E and F I S Ibrahim, Ph.D., P.E See Acknowledgement for Additional Co-Authors, Contributors and Technical Reviewers This document is a major update and revision of the 1999 FHWA Drilled Shafts manual authored by Michael W O’Neill and Lymon C Reese, Publication No FHWA-IF-99-025 16 Abstract This manual is intended to provide a technical resource for engineers responsible for the selection and design of drilled shaft foundations for transportation structures It is used as the reference manual for use with the three-day National Highway Institute (NHI) training course No 132014 on the subject, as well as the 10th in the series of FHWA Geotechnical Engineering Circulars (GEC) This manual also represents a major revision and update of the FHWA publication on drilled shaft foundations co-authored by the late Michael O’Neal and late Lymon C Reese, published in 1988 and revised in 1999 This manual embraces both construction and design of drilled shafts, and addresses the following topics: applications of drilled shafts for transportation structure foundations; general requirements for subsurface investigations; construction means and methods; LRFD principles and overall design process; geotechnical design of drilled shafts for axial and lateral loading; extreme events including scour and earthquake; LRFD structure design; field loading tests; construction specifications; inspection and records; non-destructive integrity tests; remediation of deficient shafts; and cost estimation A comprehensive design example (Appendix A) is included to illustrate the step-by-step LRFD design process of drilled shafts as foundations for a highway bridge 17 Key Words 18 Distribution Statement Drilled Shafts, LRFD, Foundations, Site Characterization, Geomaterial Properties, Axial Capacity, Lateral Capacity, Seismic, Scour, Structural Design, Construction, Soil, Rock, Specifications, Inspection, Integrity Testing, Field Loading Test, Remediation 19 Security Classif (of this report) UNCLASSIFIED Form DOT F 1700.7(8-72) 20 Security Classif (of this page) No restrictions 21 No of Pages UNCLASSIFIED Reproduction of completed page authorized 970 22 Price CONVERSION FACTORS Approximate Conversions to SI Units When you know Multiply by To find Approximate Conversions from SI Units When you know Multiply by To find (a) Length inch foot yard mile 25.4 0.305 0.914 1.61 millimeter meter meter kilometer millimeter meter meter kilometer 0.039 3.28 1.09 0.621 inch foot yard mile 0.0016 10.764 2.47 0.386 square inches square feet acres square miles 0.034 0.264 35.32 1.308 fluid ounces gallons cubic feet cubic yards 0.035 2.205 1.102 ounces pounds short tons (2000 lb) 0.2248 pound 0.021 0.145 pounds per square foot pounds per square inch 0.0624 pounds per cubic feet (b) Area square inches square feet acres square miles 645.2 0.093 0.405 2.59 fluid ounces gallons cubic feet cubic yards 29.57 3.785 0.028 0.765 ounces pounds short tons (2000 lb) 28.35 0.454 0.907 pound 4.448 pounds per square foot pounds per square inch 47.88 6.895 pounds per cubic foot 16.019 Fahrenheit temperature(oF) 5/9(oF- 32) square millimeters square millimeters square meters square meters hectares hectares square kilometers square kilometers (c) Volume milliliters milliliters liters liters cubic meters cubic meters cubic meters cubic meters (d) Mass grams grams kilograms kilograms megagrams (tonne) megagrams (tonne) (e) Force Newton Newton (f) Pressure, Stress, Modulus of Elasticity Pascals Pascals kiloPascals kiloPascals (g) Density kilograms per cubic meter kilograms per cubic meter (h) Temperature 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 ACKNOWLEDGMENTS This reference manual is a major update and revision of the very successful Federal Highway Administration (FHWA) publication on drilled shaft foundations co-authored by the late Michael W O’Neal and late Lymon C Reese, published in 1988 and revised in 1999 Permission by the FHWA to include some original manuscripts and graphics from the previous versions is gratefully acknowledged This reference manual provides the technical contents for the NHI 132014 Course “Drilled Shafts” developed by Parsons Brinckerhoff (PB) team including Dan Brown, John Turner, Ray Castelli And C Jeremy Hung The Drilled Shafts course is also a major update and revision of the 2003 National Highway Institute (NHI) 132014 Course “Drilled Shafts” developed by PB and authored by late Michael W O’Neill, Dan Brown, & William Isenhower The authors would like to acknowledge the overwhelming support of Louisa Ward, NHI Program Manager, and Silas Nichols, FHWA Task Manger, and the reviews and contributions from Jerry DiMaggio of the Strategic Highway Research Program (SHRP2) at the National Academies Especially Mr DiMaggio’s guidance and input prior to his retirement from FHWA in 2008, and his continuing support afterward have been invaluable In addition, the authors thank the reviews and recommendations provided by the following individuals that served on the Technical Working Group for this project: • • • • • • • Silas Nichols, P.E Justice Maswoswe, Ph.D, P.E Firas I S Ibrahim, Ph.D, P.E Curtis Monk, P.E Naser Abu-Hejleh, Ph.D, P.E Peter Osborn, P.E Naresh C Samtani, Ph.D, P.E FHWA FHWA FHWA FHWA FHWA FHWA NCS Consultants, Inc Furthermore, the authors thank the following organizations and their technical committees and representatives for providing valuable information and review of the manual: • • • • International Association of Foundation Drilling (ADSC-IAFD) Deep Foundation Institute (DFI) The Deep Foundations Committee of the Geo-Institute of ASCE Transportation Research Board In addition, the authors are grateful for the generous contributions and reviews of John Bryson and Kwang Ro of PB, Anton Schindler of Auburn University, James Long of University of Illinois Mr K Gifford Goodhue, Jr., of KB International, reviewed an early draft of Chapter and offered many useful suggestions regarding the materials on use of drilling fluids in drilled shaft construction Mr Alan Macnab, Condon-Johnson & Associates, contributed the first draft of Section 22.5 on Contractor Cost Computations Professor Fred H Kulhawy, Cornell University, offered many useful suggestions and references on revisions to the beta-method for side resistance of drilled shafts in cohesionless soils presented in Chapter 13 and Appendix C Lastly, the Authors would also like to extend our gratitude to the supports provided by a number of professionals from Parsons Brinckerhoff and Dan Brown and Associates, PLLC., including Lauren Chu Amy Pavlakovich, Matthew Smith, Alejandra Morales, and Maria Roberts of PB for their assistance and overall word processing and compiling FHWA-NHI-10-016 Drilled Shafts Manual Acknowledgments May 2010 This page is intentional left blank TABLE OF CONTENTS LIST OF FIGURES xiii LIST OF TABLES xxiv CHAPTER - OVERVIEW - SELECTION AND USE OF DRILLED SHAFT FOUNDATIONS FOR TRANSPORTATION STRUCTURES .1-1 1.1 INTRODUCTION - PURPOSE AND ORGANIZATION OF MANUAL .1-1 1.2 TYPES OF DEEP FOUNDATIONS 1-3 1.3 DRILLED SHAFT FOUNDATIONS – DESCRIPTION AND HISTORY 1-3 1.4 SELECTION OF DRILLED SHAFTS 1-10 1.4.1 Applications 1-10 1.4.2 Advantages and Limitations .1-15 1.5 KEYS TO SUCCESSFUL USE OF DRILLED SHAFTS 1-15 1.6 SUMMARY .1-17 CHAPTER - SITE CHARACTERIZATION 2-1 2.1 INTRODUCTION .2-1 2.2 ROLE OF THE GEOTECHNICAL ENGINEER 2-1 2.3 SITE CHARACTERIZATION PROGRAM .2-3 2.3.1 Data Collection 2-3 2.3.2 Field Reconnaissance 2-4 2.3.3 Detailed Field Investigations 2-5 2.3.4 Information Required for Construction 2-22 2.4 GEOTECHNICAL REPORTS 2-24 2.4.1 Geotechnical Investigation Report .2-24 2.4.2 Geotechnical Design Report 2-24 2.4.3 Data Presentation 2-26 2.4.4 Differing Site Conditions .2-27 2.4.5 Geotechnical Baseline Report 2-29 2.4.6 SUMMARY 2-29 FHWA-NHI-10-016 Drilled Shafts Manual i Table of Contents May 2010 CHAPTER - GEOMATERIAL PROPERTIES 3-1 3.1 IN-SITU TESTING 3-1 3.1.1 Standard Penetration Test 3-1 3.1.2 Cone Penetration Test 3-5 3.2 SOIL PROPERTIES 3-7 3.2.1 Soil Index Properties and Classification 3-8 3.2.2 Shear Strength Properties .3-8 3.2.3 Deformation Properties 3-14 3.2.4 Soil Erodibility 3-16 3.2.5 In-Situ State of Stress 3-18 3.2.6 Unsaturated Soil Properties 3-19 3.3 PROPERTIES OF ROCK 3-21 3.3.1 Index Properties of Rock 3-21 3.3.2 Properties of Intact Rock 3-22 3.3.3 Strength of Rock Discontinuities 3-23 3.3.4 In-Situ Tests for Rock 3-23 3.3.5 Rock Mass Classification 3-26 3.3.6 Engineering Properties of Rock Mass 3-28 3.4 GEOMATERIALS REQUIRING SPECIAL CONSIDERATION 3-30 3.5 GEOMATERAL PROPERTIES AND LRFD .3-31 CHAPTER - GENERAL CONSTRUCTION METHODS 4-1 4.1 INTRODUCTION .4-1 4.2 DRY METHOD OF CONSTRUCTION .4-2 4.3 CASING METHOD OF CONSTRUCTION .4-6 4.4 WET METHOD OF CONSTRUCTION 4-12 4.5 BASE GROUTING 4-17 4.6 UNDERREAMS (BELLS) 4-20 4.7 BATTERED SHAFTS .4-22 4.8 SUMMARY .4-23 CHAPTER - TOOLS AND EQUIPMENT 5-1 5.1 INTRODUCTION 5-1 5.2 DRILLING MACHINES 5-1 5.2.1 Overview of Rotary Systems 5-2 FHWA-NHI-10-016 Drilled Shafts Manual ii Table of Contents May 2010 5.2.2 Mechanical vs Hydraulic Systems .5-3 5.2.3 Methods of Mounting Drilling Machine 5-3 5.2.4 Other Excavation Systems 5-9 5.2.5 Summary 5-13 5.3 TOOLS FOR EXCAVATION .5-13 5.3.1 Rotary Tools .5-13 5.3.2 Percussion and Other Tools 5-25 5.4 OTHER TECHNIQUES 5-29 5.4.1 Tools for Cleaning the Base of the Drilled Shaft Excavation 5-29 5.4.2 Grouting .5-30 5.4.3 Soil Mixing .5-30 5.4.4 Concrete Liner 5-31 5.5 SUMMARY 5-32 CHAPTER - CASING AND LINERS 6-1 6.1 TEMPORARY CASING 6-1 6.1.1 Types and Dimensions 6-1 6.1.2 Installation and Extraction of Temporary Casing 6-4 6.1.3 Possible Effects of Temporary Casing on Axial and Lateral Resistance 6-10 6.1.4 Removing Casing after Concrete Sets 6-12 6.2 PERMANENT CASING 6-14 6.2.1 Types and Dimensions .6-16 6.2.2 Installation of Permanent Casing .6-17 6.2.3 Effects of Permanent Casing on Axial and Lateral Resistance 6-17 6.2 SUMMARY 6-18 CHAPTER - DRILLING FLUIDS IN DRILLED SHAFT CONSTRUCTION 7-1 7.1 INTRODUCTION AND BACKGROUND .7-1 7.2 PRINCIPLES OF DRILLING FLUID PERFORMANCE FOR DRILLED SHAFTS 7-2 7.2.1 Mineral Slurries 7-2 7.2.2 Polymer Slurries 7-5 7.2.3 Blended Slurries 7-8 7.2.4 Example Applications and Limitations of Drilling Fluids in Drilled Shaft Construction .7-9 7.3 MATERIAL CHARACTERISTICS AND SLURRY MIX DESIGN 7-10 FHWA-NHI-10-016 Drilled Shafts Manual iii Table of Contents May 2010 7.3.1 Bentonite 7-10 7.3.1 Polymers 7-10 7.4 CONTROL OF DRILLING FLUID DURING CONSTRUCTION 7-15 7.4.1 Mixing and Handling of Mineral Slurry 7-15 7.4.2 Mixing and Handling of Polymer Slurry 7-17 7.4.3 Sampling and Testing .7-19 7.4.4 Specifications for Drilling Slurry .7-27 7.5 ADDITIONAL DESIGN AND CONSTRUCTION CONSIDERATIONS 7-29 7.5.1 Borehole Inspection Under Drilling Fluids 7-29 7.5.2 Influence of Slurry on Axial Resistance of Drilled Shafts 7-29 7.5.3 Bond with Reinforcing Steel 7-35 7.5.4 Summary of Major Handling Considerations 7-36 7.6 SELECTION OF DRILLING FLUIDS 7-38 7.7 EXAMPLES OF PROBLEMS AND SOLUTIONS WITH CONSTRUCTION UNDER DRILLING FLUIDS 7-39 7.6 SUMMARY 7-43 CHAPTER - REBAR CAGES 8-1 8.1 INTRODUCTION .8-1 8.2 PROPERTIES OF STEEL 8-1 8.3 LONGITUDINAL REINFORCING 8-3 8.4 TRANSVERSE REINFORCING 8-5 8.5 SPLICES 8-8 8.6 CONNECTION BETWEEN DRILLED SHAFT AND COLUMN 8-10 8.7 SIZING HOOPS 8-14 8.8 CENTERING DEVICES 8-15 8.9 STRENGTHENING THE CAGE TO RESIST LIFTING FORCES .8-16 8.10 ARRANGEMENTS FOR LIFTING CAGE 8-17 8.11 FABRICATION AND STORAGE 8-19 8.12 SUMMARY .8-21 CHAPTER - PLACEMENT AND DESIGN OF CONCRETE FOR DRILLED SHAFTS 9-1 9.1 INTRODUCTION .9-1 9.2 BASIC CHARACTERISTICS OF DRILLED SHAFT CONCRETE .9-1 9.3 PLACEMENT OF CONCRETE .9-2 FHWA-NHI-10-016 Drilled Shafts Manual iv Table of Contents May 2010 FHWA-NHI-10-016 Drilled Shafts Manual G-14 G – Standard CIDH Pile Anomaly Mitigation Plan May 2010 FHWA-NHI-10-016 Drilled Shafts Manual G-15 G – Standard CIDH Pile Anomaly Mitigation Plan May 2010 FHWA-NHI-10-016 Drilled Shafts Manual G-16 G – Standard CIDH Pile Anomaly Mitigation Plan May 2010 FHWA-NHI-10-016 Drilled Shafts Manual G-17 G – Standard CIDH Pile Anomaly Mitigation Plan May 2010 FHWA-NHI-10-016 Drilled Shafts Manual G-18 G – Standard CIDH Pile Anomaly Mitigation Plan May 2010 APPENDIX H ALTERNATIVE MODELS FOR ANALYSIS OF LATERAL LOADING This page is intentional left blank APPENDIX H ALTERNATIVE MODELS FOR ANALYSIS OF LATERAL LOADING INTRODUCTION This Appendix is provided to include an overview of several alternative models reported in the literature for analysis of lateral loading Alternative models include those based on elastic continuum, boundary element, and finite element models A brief overview of these models follows, with references for further investigation H.1 Elastic Continuum and Boundary Element Models The elastic continuum approach for laterally loaded deep foundations was developed by Poulos (1971), initially for analysis of a single pile under lateral and moment loading at the pile head The numerical solution is based on the boundary element method with the pile modeled as a thin elastic strip and the soil modeled as a homogeneous, isotropic elastic material This approach was used to approximate socketed piles by Poulos (1972) by considering two boundary conditions at the tip of the pile: (1) the pile is completely fixed against rotation and displacement at the tip (rock surface), and (2) the pile is free to rotate but fixed against translation (pinned) at the tip The fixed pile tip condition was intended to model a socketed deep foundation while the pinned tip was intended to model a pile bearing on, but not embedded into, rock While these tip conditions not adequately model the behavior of many rock socketed shafts, the analyses served to demonstrate some important aspects of socketed deep foundations For relatively stiff foundations, which applies to many drilled shafts, considerable reduction in displacement at the pile head can be achieved by socketing, especially if the effect of the socket is to approximate a "fixed" condition at the soil/rock interface The elastic continuum approach was further developed by Randolph (1981) through use of the finite element method Solutions presented by Randolph cover a wide range of conditions for flexible piles and the results are presented in the form of charts as well as convenient closed-form solutions for a limited range of parameters The solutions not adequately cover the full range of parameters applicable to drilled shafts used in practice Extension of this approach by Carter and Kulhawy (1992) to rigid shafts and shafts of intermediate flexibility, has led to analytical tools for drilled shafts in rock based on the continuum approach Sun (1994) applied elastic continuum theory to deep foundations using variational calculus to obtain the governing differential equations of the soil and pile system, based on the Vlasov model for a beam on elastic foundation This approach was extended to rock socketed shafts by Zhang et al (2000) The continuum models developed by Carter and Kulhawy and by Zhang et al are described below H.1.1 Carter and Kulhawy Model for an Elastic Shaft Embedded in an Elastic Rock Mass Carter and Kulhawy (1988, 1992) studied the behavior of flexible and rigid shafts socketed into rock and subjected to lateral loads and moments Solutions for the load-displacement relations were first generated using finite element analyses The finite element analyses followed the approach of Randolph (1981) for flexible piles under lateral loading Based on the FEM solutions, approximate closed-form equations HWA-NHI-10-016 Drilled Shafts Manual H-1 H –Lateral Loading Analysis May 2010 were developed to describe the response for a range of rock socket parameters typically encountered in practice The results provide a first-order approximation of horizontal groundline displacements and rotations and can incorporate an overlying soil layer The method is summarized as follows Initially, consider the case where the top of the shaft corresponds to the top of the rock layer (Figure H-1) The shaft is idealized as a cylindrical elastic inclusion with an effective Young’s modulus (Ee), Poisson’s ratio (υc), depth (D), and diameter (B), subjected to a known lateral force (H) and an overturning moment (M) For a reinforced concrete shaft having an actual flexural rigidity equal to (EI)c, the effective Young’s modulus is given by: Ee = (EI )c πB H-1 64 Figure H-1 Lateral Loading of a Rock-Socketed Shaft (Carter and Kulhawy 1992) It is assumed that the elastic shaft is embedded in a homogeneous, isotropic elastic rock mass, with properties Er and νr Effects of variations in the Poisson’s ratio of the rock mass (νr), are represented approximately by an equivalent shear modulus of the rock mass (G*), defined as: ⎛ 3ν ⎞ G ∗ = Gr ⎜1 + r ⎟ ⎠ ⎝ H-2 in which Gr = shear modulus of the elastic rock mass For an isotropic rock mass, the shear modulus is related to Er and νr by: Gr = Er 2(1 + ν r ) H-3 Based on a parametric study using finite element analysis, it was found that closed-form expressions could be obtained to provide reasonably accurate predictions of horizontal displacement (u) and rotation (θ) at the head of the shaft, for two limiting cases The two cases correspond to flexible shafts and rigid shafts The criterion for a flexible shaft is: FHWA-NHI-10-016 Drilled Shafts Manual H-2 H –Lateral Loading Analysis May 2010 D ⎛ Ee ⎞ ≥⎜ ⎟ B ⎝ G∗ ⎠ 2/7 H-4 For shafts satisfying Equation H-4, the response depends only on the modulus ratio (Ee/G*) and Poisson’s ratio of the rock mass (νr) and is effectively independent of (D/B) The following closed-form expressions, suggested by Randolph (1981), provide accurate approximations for the deformations of flexible shafts: ⎛ H ⎞⎛ E ⎞ u = 0.50⎜ ∗ ⎟⎜ e∗ ⎟ ⎝ G B ⎠⎝ G ⎠ −1 ⎛ H ⎞⎛ Ee ⎞ ∗ ⎟⎜ ∗ ⎟ ⎝ G B ⎠⎝ G ⎠ −3 θ = 1.08⎜ ⎛ M ⎞⎛ E ⎞ + 1.08⎜ ∗ ⎟⎜ e∗ ⎟ ⎝ G B ⎠⎝ G ⎠ −3 ⎛ M ⎞⎛ E ⎞ + 6.40⎜ ∗ ⎟⎜ e∗ ⎟ ⎝ G B ⎠⎝ G ⎠ −5 H-5 H-6 Carter and Kulhawy (1992) report that the accuracy of the above equations is verified for the following ranges of parameters: < Ee/Er < 106 and D/B > The criterion for a rigid shaft is: D ⎛E ⎞ ≤ 0.05⎜ e∗ ⎟ B ⎝G ⎠ H-7 And Ee G ∗ ≥ 100 H-8 (B 2D) When Equation H-7 and H-8 are satisfied, the displacements of the shaft will be independent of the modulus ratio (Ee/Er) and will depend only on the slenderness ratio (D/B) and Poisson's ratio of the rock mass (νr) The following closed-form expressions give reasonably accurate displacements for rigid shafts: ⎛ H ⎞⎛ D ⎞ u = 0.4⎜ ∗ ⎟⎜ ⎟ ⎝ G B ⎠⎝ B ⎠ −1 ⎛ H ⎞⎛ D ⎞ ⎟ ∗ ⎟⎜ ⎝ G B ⎠⎝ B ⎠ θ = 0.3⎜ −7 ⎛ M ⎞⎛ D ⎞ + 0.3⎜ ∗ ⎟⎜ ⎟ ⎝ G B ⎠⎝ B ⎠ −7 ⎛ M ⎞⎛ D ⎞ + 0.8⎜ ∗ ⎟⎜ ⎟ ⎝ G B ⎠⎝ B ⎠ −5 H-9 H-10 The accuracy of Equation H-9 and H-10 has been verified for the following ranges of parameters: < D/B < 10 and Ee/Er > Shafts can be described as having intermediate stiffness whenever the slenderness ratio is bounded approximately as follows: FHWA-NHI-10-016 Drilled Shafts Manual H-3 H –Lateral Loading Analysis May 2010 ⎛E ⎞ 0.05⎜ e∗ ⎟ ⎝G ⎠ D ⎛E ⎞ < < ⎜ e∗ ⎟ B ⎝G ⎠ H-11 For the intermediate case, Carter and Kulhawy suggest that the displacements be taken as 1.25 times the maximum of either: (1) The predicted displacement of a rigid shaft with the same slenderness ratio (D/B) as the actual shaft; or (2) the predicted displacement of a flexible shaft with the same modulus ratio (Ee/G*) as the actual shaft Values calculated in this way should, in most cases, be slightly larger than those given by the more rigorous finite element analysis for a shaft of intermediate stiffness Carter and Kulhawy next considered a layer of soil of thickness Ds overlying rock as shown in Figure H2 The analysis is approached by structural decomposition of the shaft and its loading, as shown in Figure H-2b It was assumed that the magnitude of applied lateral loading is sufficient to cause yielding within the soil from the ground surface to the top of the rock mass The portion of the shaft within the soil is then analyzed as a determinant beam subjected to known loading The displacement and rotation of point A relative to point O can be determined by established techniques of structural analysis The horizontal shear force (Ho) and bending moment (Mo) acting in the shaft at the rock surface level can be computed from statics, and the displacement and rotation at this level can be computed by the methods described previously The overall groundline displacements can then be calculated by superposition of the appropriate parts Figure H-2 Rock Socketed Shaft with Overlying Soil Layer (Carter and Kulhawy 1992) Determination of the limiting soil reactions is recommended for the two limiting cases of cohesive soil in undrained loading (φ = 0) and frictional soil (c = 0) in drained loading Ultimate resistance for shafts in cohesive soils is based on the method of Broms (1964a), in which the undrained soil resistance ranges from zero at the ground surface to a depth of 1.5B and has a constant value of 9su below this depth, where su = soil undrained shear strength For socketed shafts extending through a cohesionless soil layer, the following limiting pressure suggested by Broms (1964a) is assumed: pu = 3K pσ v′ FHWA-NHI-10-016 Drilled Shafts Manual H-12 H-4 H –Lateral Loading Analysis May 2010 Kp = + sin φ ′ − sin φ ′ H-13 in which σv' = vertical effective stress and φ' = effective stress friction angle of the soil For both cases (undrained and drained) solutions are given by Carter and Kulhawy (1992) for the displacement, rotation, shear, and moment at point O of Figure H-2 The contribution to groundline displacement and rotation from the loading transmitted to the rock mass (Ho and Mo) is determined based on Eqs H-5 and H-6 or Eqs H-9 and H-10 and added to the calculated displacement and rotation at the top of the socket to determine overall groundline response Application of the proposed theory is described by Carter and Kulhawy (1992) through back-analysis of a single case involving field loading of a pair of rock-socketed shafts The method has not been evaluated against a sufficient data base of field performance, and further research is needed to assess its reliability The analysis was developed primarily for application to electrical transmission line foundations in rock, although the concepts are not limited to foundations supporting a specific type of structure The approach is attractive for design purposes, because the closed-form equations can be executed by hand or on a spreadsheet Carter and Kulhawy (1992) state that the assumption of yield everywhere in the soil layer may represent an oversimplification, but that the resulting predictions of groundline displacements will overestimate the true displacements, giving a conservative approximation However, the assumption that the limit soil reaction is always fully mobilized may lead to erroneous results by overestimating the load carried by the soil and thus underestimating the load transmitted to the socket Furthermore, groundline displacements may be underestimated because actual soil resistance may be smaller than the limiting values assumed in the analysis H.1.2 Zhang, Ernst, and Einstein Nonlinear Model for an Elastic Shaft Embedded in an Elastic Rock Mass Zhang et al (2000) extended the continuum approach to predict the nonlinear lateral load-displacement response of rock socketed shafts The method considers subsurface profiles consisting of a soil layer overlying a rock layer The deformation modulus of the soil is assumed to vary linearly with depth, while the deformation modulus of the rock mass is assumed to vary linearly with depth and then to stay constant below the shaft tip Effects of soil and/or rock mass yielding on response of the shaft are considered by assuming that the soil and/or rock mass behaves linearly elastically at small strain levels and yields when the soil and/or rock mass reaction force p (force/length) exceeds the ultimate resistance pult (force/length) Analysis of the loaded shaft as an elastic continuum is accomplished using the method developed by Sun (1994) The numerical solution is by a finite difference scheme and incorporates the linear variation in soil modulus and linear variation in rock mass modulus above the base of the shaft Solutions obtained for purely elastic response are compared to those of Poulos (1971) and finite element solutions by Verruijt and Kooijman (1989) and Randolph (1981) Reasonable agreement with those published solutions is offered as verification of the theory, for elastic response The method is extended to nonlinear response by accounting for local yielding of the soil and rock mass The soil and rock mass are modeled as elastic-perfectly plastic materials, and the analysis consists of the following steps: FHWA-NHI-10-016 Drilled Shafts Manual H-5 H –Lateral Loading Analysis May 2010 For the applied lateral load H and moment M, the shaft is analyzed by assuming the soil and rock mass are elastic, and the lateral reaction force p of the soil and rock mass along the shaft is determined by solution of the governing differential equation and boundary conditions at the head of the shaft The computed lateral reaction force p is compared to the ultimate resistance pult If p > pult, the depth of yield zy in the soil and/or rock mass is determined The portion of the shaft in the unyielded soil and/or rock mass (zy < z < L) is considered to be a new shaft and analyzed by ignoring the effect of the soil and/or rock mass above the level z = zy The lateral load and moment at the new shaft head are given by: zy H o = H − ∫ pult dz H-14 M o = M + Hz y − ∫ pult (z y − z )dz H-15 zy Steps and are repeated and the iteration is continued until no further yielding of soil or rock mass occurs The final results are obtained by decomposition of the shaft into two parts which are analyzed separately, as illustrated previously in Figure H-2 The section of the shaft in the zone of yielded soil and/or rock mass is analyzed as a beam subjected to a distributed load of magnitude pult The length of shaft in the unyielded zone of soil and/or rock mass is analyzed as a shaft with the soil and/or rock mass behaving elastically Ultimate resistance developed in the overlying soil layer is evaluated for the two conditions of undrained loading (φ = 0) and fully-drained loading (c = 0) For fine-grained soils (clay), undrained loading conditions are assumed and the limit pressure is given by: pult = N p cu B Np = 3+ γ′ cu z+ H-16 J z≤9 2R H-17 in which cu = undrained shear strength, B = shaft diameter, γ' = average effective unit weight of soil above depth z, and J = a coefficient ranging from 0.25 to 0.5 For shafts in sand, a method attributed to Fleming et al (1992) is given as follows: pult = K p2 γ ′zB H-18 where Kp = Rankine coefficient of passive earth pressure defined by Equation H-11 Ultimate resistance of the rock mass is given by: pult = ( p L + τ max )B FHWA-NHI-10-016 Drilled Shafts Manual H-19 H-6 H –Lateral Loading Analysis May 2010 where τmax = maximum shearing resistance along the sides of the shaft and pL = normal limit resistance The limit normal stress pL is evaluated using the Hoek-Brown strength criterion with the strength parameters determined on the basis of correlations to Geological Strength Index (GSI) The resulting expression is: ⎛ γ ′z ⎞ pL = γ ′z + qu ⎜⎜ mb + s ⎟⎟ ⎝ qu ⎠ a H-20 According to Zhang et al (2000), a computer program was written to execute the above procedure Predictions using the proposed method are compared to results of field load tests reported by Frantzen and Stratten (1987) for shafts socketed into sandy shale and sandstone Computed pile head deflections show reasonable agreement with the load test results The method appears to have potential as a useful tool for foundations designers Availability of the computer program is unknown Programming the method using a finite difference scheme as described by Zhang et al (2000) is also possible H.2 Finite Element Soil Models Software now exists that will permit the nonlinear analysis of drilled shafts or groups of drilled shafts using the finite element method (FEM) with relative ease on a high-end PC or a workstation, for example ABAQUS (Hibbett et al., 1996) FEM analysis is justified when the soil or rock conditions, foundation geometry or loading of the group is unusual An example of a case in which a comprehensive FEM analysis might be conducted is for designing a group of drilled shafts that are to be socketed into sloping rock on a steep mountainside, in which it is necessary to use permanent tiebacks to secure the drilled shaft group to stable rock FHWA-NHI-10-016 Drilled Shafts Manual H-7 H –Lateral Loading Analysis May 2010 This page is intentional left blank ... .9-39 CHAPTER 10 - LRFD FOR DRILLED SHAFT DESIGN 10-1 10.1 INTRODUCTION TO LRFD 10-1 10.1.1 Development of Resistance Factors 10-3 10.2 AASHTO LIMIT STATES AND... 15.2.4 Discussion of the AASHTO Guide Specifications for LRFD Seismic Bridge Design 15-12 15.3 DESIGN FOR EFFECTS OF ICE AND COLLISIONS .15-13 15.3.1 LRFD Framework for Extreme... specific recommendations outlined in this manual Although the recommendations given in this publication represent generally recommended practice as of the time of this writing, it is not intended