Development of rational design methodology for spiral reinforcement in prestressed concrete piles in regions of high seismicity

Transcription

1 Retrospetive Theses and Dissertations 2007 Development o rational design methodology or spiral reinorement in prestressed onrete piles in regions o high seismiity Ann-Marie Fouad Fanous Iowa State University Follow this and additional works at: Part o the Civil Engineering Commons Reommended Citation Fanous, Ann-Marie Fouad, "Development o rational design methodology or spiral reinorement in prestressed onrete piles in regions o high seismiity" (2007). Retrospetive Theses and Dissertations This Thesis is brought to you or ree and open aess by Iowa State University Digital Repository. It has been aepted or inlusion in Retrospetive Theses and Dissertations by an authorized administrator o Iowa State University Digital Repository. For more inormation, please ontat digirep@iastate.edu.

2 Development o rational design methodology or spiral reinorement in prestressed onrete piles in regions o high seismiity by Ann-Marie Fouad Fanous A thesis submitted to the graduate aulty in partial ulillment o the requirements or the degree o MASTER OF SCIENCE Major: Civil Engineering (Strutural Engineering) Program o Study Committee: Sri Sritharan, Co-major Proessor Muhannad Suleiman, Co-major Proessor Lester Shmerr Iowa State University Ames, Iowa 2007

3 UMI Number: UMI Miroorm Copyright 2008 by ProQuest Inormation and Learning Company. All rights reserved. This miroorm edition is proteted against unauthorized opying under Title 17, United States Code. ProQuest Inormation and Learning Company 300 North Zeeb Road P.O. Box 1346 Ann Arbor, MI

4 ii TABLE OF CONTENTS LIST OF FIGURES... v LIST OF TABLES...viii CHAPTER 1. INTRODUCTION Historial Bakground Pile Types Preast Conrete Piles Seismi Design Approah Bridges Buildings Whars Sope o Researh Report Layout CHAPTER 2. LITERATURE REVIEW Introdution Current Seismi Design Pratie Curvature Demand Overview o Curvature Dutility Bakground o Curvature Dutility Analytial Work Song, Chai, and Hale, Banerjee, Stanton, and Hawkins, Field Investigation Koyamada, Miyamoto, and Tokimatsu, Lin, Tseng, Chiang, and Hung, Target Curvature Demand Coninement Reinorement Parameters Aeting Coninement Transverse Reinorement Requirements Uniorm Building Code (1997) International Building Code (2000), ASCE 7( 2005), and PCI (1993) New Zealand Code (2006) ATC-32 (1996) ACI Code (2005) Summary CHAPTER 3. DEVELOPMENT OF A RATIONALE APPROACH TO DESIGNING TRANSVERSE REINFORCEMENT FOR CONFINEMENT PURPOSES Objetive Development o a New Equation Existing Equations o Interest... 52

5 iii ACI-318 (2005) Equation New Zealand Standard (2006) Applied Tehnology Counil-32 (1996) PCI Reommended Pratie (1993) Proess o Development Modiiations to the Base Equation Preliminary Equation Moment-Curvature Analyses ANDRIANNA OpenSees Conined and Unonined Conrete Material Model Material Model or Prestressing Strands Moment-Curvature Idealization First Yield Moment Ultimate Moment Nominal Moment Analysis Variables Limits n External Axial Load Ratios New Limits on Axial Load Ratios Improvements to the Preliminary Equation Results o the Otagonal Setions Analyzed by the Modiied Equation Reommended Coninement Equation Veriiation or Otagonal Pile Setions Inluene o Conrete Strength on Curvature Dutility Capaity Veriiation or Square Pile Setions Integration o µ φ in the Coninement Equation CHAPTER 4. ANALYSIS OF PILES UNDER LATERAL LOADS TO ESTABLISH DISPLACEMENT LIMITS Introdution Objetive Overall Design Proess Soil-Pile Interation Analyses LPILE Solution Proess Features o LPILE Analyses and Results Sample Analysis Results CHAPTER 5. SUMMARY, CONCLUSIONS AND RECOMMENDATIONS Introdution Summary Conlusions Reommendations

6 iv REFERENCES APPENDIX A. DEFINITION OF AN ORDINARY BRIDGE A.1 Caltrans (2001) A.2 South Carolina DOT (2001) A.3 Washington State APPENDIX B. SPECIFICATIONS REGARDING STRUCTURES CAPABILITIES IN SPECIFIC SEISMIC RISK LEVELS B.1 ACI 318 Building Code (2005) B.2 ASCE 7 (2005) APPENDIX C SAMPLE OPENSEES INPUT C.1 Sample Input or a 16-Inh Otagonal Pile ACKNOWLEDGEMENTS

7 v LIST OF FIGURES Figure 1.1. Typial setion through a whar struture (Birdy and Dodd, 1999) Figure 2.1. Cross setions o prestressed onrete piles (PCI, 1999) Figure 2.2. Detail o a 12-inh preast, prestressed onrete square ross-setion used by Caltrans (2006) Figure 2.3. Detail o a 14-inh preast, prestressed onrete square ross-setion used by Caltrans (2006) Figure 2.4. Detail o a 24- preast, prestressed onrete square ross-setion used by POLA (2003) Figure 2.5. Potential loations o plasti hinges in piles Figure 2.6. Deleted shape and bending moment distribution o a laterally loaded ixed-head pile (a) First yield limit state (b) Seond yield limit state () Ultimate limit state (ater Song et al., 2004) Figure 2.7. Soil properties at the West Seattle site Figure 2.8. Soil properties at the Taoma site Figure 2.9. Soil properties at the San Franiso site Figure 2.7. Core onrete onined by transverse reinorement Figure 2.8. Spiral volumetri ratios or a 14-inh otagonal prestressed pile Figure 2.9. Spiral volumetri ratios or a 24-inh otagonal prestressed pile Figure 3.1. Spiral volumetri ratio o the equations o interest or a 14-inh square pile Figure 3.2. Spiral volumetri ratio o the equations o interest or a 16-inh otagonal pile Figure 3.3. Comparison o spiral volumetri reinorement requirement or a 16- inh otagonal pile with the preliminary equation Figure 3.4. Comparison o spiral volumetri reinorement requirement or a 24- inh otagonal pile with the preliminary equation Figure 3.5. Deinition o an otagonal pile setion in OpenSees Figure 3.6. Deinition o a square pile setion in OpenSees Figure 3.7. Monotoni envelope o Chang and Mander (1994) as shown by Waugh (2007) Figure 3.8. Input parameters required or an elasti-peretly-plasti uniaxial material objet in OpenSees (Mazzoni et al., 2004) Figure 3.9. Input parameters required or an elasti-peretly-plasti tension gap uniaxial material objet (Mazzoni et al., 2004) Figure Input parameters needed or an elasti-peretly-plasti ompression gap uniaxial material objet (Mazzoni et al., 2004) Figure Moment-urvature response omparing ANDRIANNA and OpenSees Figure Conrete and prestress steel strains versus moment or a 16-inh prestressed onrete otagonal pile setion Figure Moment-urvature response or a normal onrete setion and idealized response... 78

8 vi Figure 3.14a. Moment-urvature response o a 16-inh otagonal shaped prestressed onrete pile setion Figure 3.14b. Moment-urvature response o a 24-inh otagonal shaped prestressed onrete pile setion Figure 3.14a. Moment-urvature response o a 14-inh square shaped prestressed onrete pile setion Figure Details o dierent pile setions seleted or evaluation o the preliminary oninement equation with equal to 6000 psi and p values o 700 psi, 900 psi, 1100 psi, and 1200 psi Figure Details o dierent pile setions seleted or evaluation o the preliminary oninement equation with equal to 8000 psi and p values o 700 psi, 1000 psi, 1300 psi, and 1600 psi Figure Details o dierent pile setions seleted or evaluation o the preliminary oninement equation with equal to 10,000 psi and p values o 700 psi, 1200 psi, 1600 psi, and 2000 psi Figure Moment-urvature response showing the ase o φ r < φ sp or a 24-inh otagonal prestressed pile setion with axial load ratio o 0.3, o 8000 psi, and p o 1300 psi Figure Moment-urvature response showing the ase o φ r << φ sp or a 24-inh otagonal prestressed pile setion with axial load ratio o 0.6, o psi, and p o 1600 psi Figure Spiral volumetri ratio omparison or a 14-inh otagonal pile with the modiied ISU equation Figure Spiral volumetri ratio omparison or a 24-inh otagonal pile with the modiied ISU equation Figure Curvature dutility apaity o 16-inh and 24-inh prestressed pile setions with oninement reinorement as per Equation Figure Spiral volumetri ratio omparison or a 14-inh otagonal pile with the inalized ISU equation Figure Spiral volumetri ratio omparison or a 24-inh otagonal pile with the inalized ISU equation Figure Curvature dutility apaity o 16-inh and 24-inh prestressed pile setions with oninement reinorement as per Eq Figure Inluene o the onrete strength on the urvature dutility apaity or a 16-inh otagonal setion Figure Inluene o the onrete strength on the urvature dutility apaity or a 24-inh otagonal setion Figure Inluene o p on the urvature dutility apaity or a 16-inh otagonal setion Figure Inluene o p on the urvature dutility apaity or a 24-inh otagonal setion

9 vii Figure Moment-urvature relationship or a 14-inh square setion with o 6000 psi, p o 1200 psi, and a 0.2 axial load ratio Figure Curvature dutility apaity o 14-inh prestressed pile setion with oninement reinorement as per Eq Figure Relationship between the oninement reinorement o a 16-inh otagonal setion and the orresponding urvature dutility over axial load ratios ranging rom 0.2 to Figure Analysis results o prestressed pile setions that used the ISU equation with a urvature dutility demand o Figure Analysis results o prestressed pile setions that used the ISU equation with a urvature dutility demand o Figure 4.1. Proposed design proess integrating the expeted pile oundation displaement in the overall seismi design o the struture Figure 4.2. LPILE model o laterally loaded pile o soil response (a) Shemati proile o a pile embedded in soil, (b) Strutural idealization or the pile-soil interation, and () lateral spring ore-displaement relationship (Ensot, In. 2004) Figure 4.3. Subdivided pile model as used in LPILE or the inite dierene solution Figure 4.4. Complete moment versus urvature response rom OpenSees with the ondensed moment versus urvature relationship input in LPILE Figure 4.5. Boundary onditions input in LPILE Figure 4.6. Comparison o LPILE output against the moment versus urvature response used as the input in LPILE or Pile Figure 4.7 (a) Displaement, (b) Shear, and () Moment proiles o a 16-inh otagonal prestressed ixed-head pile in a very sti lay at a small and ultimate displaements

10 viii LIST OF TABLES Table 2.1. Pile details or piles embedded into the three West Coast sites Table 2.5. Depths o soil layers at the Konan junior high shool at Hokkaido, Japan Table 2.6. Summary o urvature demands estimated or piles in the ield during past earthquakes Table 2.7. Summary o urvature apaities reported or preast, prestressed onrete piles used in seismi regions Table 2.7. (ontinued) Table 3.1. A summary o the urvature dutility apaities obtained rom OpenSees or the otagonal setions using the modiied oninement equation (i.e., Eq. 3.26) Table 3.2. A summary o the urvature dutility apaities obtained rom OpenSees or the otagonal setions using the inalized oninement equation (i.e., Eq. 3.28) Table 3.3. A summary o urvature dutility apaities obtained rom OpenSees or the square setion using the inalized oninement equation (i.e., Eq. 3.42) Table 4.1. Parameters seleted or lay soil used in LPILE Table 4.2. Parameters seleted or sand used in LPILE Table 4.3. Ultimate urvature values o 16-inh otagonal prestressed piles using oninement reinorement based on the newly developed equation Table inh otagonal pile material properties analyzed in LPILE Table 4.6. Permissible displaement limits established or a 16-inh otagonal prestressed pile with a ixed-head ondition in dierent types Table 4.7. Permissible displaement limits established or a 16-inh otagonal prestressed pile with a pinned-head ondition in dierent soil types Table 4.8. Permissible displaement limits established or a 16-inh otagonal prestressed pile with a partially ixed-head ondition in dierent soil types

11 1 CHAPTER 1. INTRODUCTION 1.1 Historial Bakground Pile oundations date bak to 12,000 years ago when Neolithi inhabitants o Switzerland drove wooden poles into the sot bottom o lakes in order to build their homes on them (Prakash and Sharma, 1990). Timber piles supported Venie in the marshy delta and proteted early Italians rom the invaders o Eastern Europe, while allowing them to be lose to their soure o livelihood. Simply put, pile oundations make it possible to onstrut strutures in areas where the soil onditions are less than avorable or the design o shallow oundations (Prakash and Sharma, 1990). 1.2 Pile Types Piles, in general, are divided into two ategories: displaement or non-displaement piles, depending on the amount o soil displaed during installation. Non-displaement piles reer to the small eet in the state o stress in the pile s surrounding soil during the plaement o the pile, whereas displaement piles reer to the lateral movement o the soil surrounding the pile during the installation o the pile (Das, 2004). Examples o displaement piles inlude driven onrete and losed-ended steel pipe piles, while H-shaped steel piles are ommonly lassiied as non-displaement piles. Several dierent materials have been used in pile design pratie. These are timber piles, steel piles, and onrete piles. Until the late nineteenth and early twentieth enturies, timber piles were the only pile types used or deep oundations. This was due to their vertial load arrying apaity ombined with lightness, as well as their durability and ease

12 2 o utting and handling. Steel and onrete piles replaed timber piles or the mere at that these materials ould be abriated into units that were apable o sustaining ompressive, bending, and tensile stresses ar beyond the timber piles. Steel piles typially serve as nondisplaement piles and have been used or pile oundations due to the ease o abriation and handling, their ability to endure hard driving, and their low strength to weight ratio. The beneits o onrete piles inlude their ability to sustain high load-arrying apaity on land and oshore, as well as their durability within most soil and immersion onditions. The onrete piles ould also be ast in numerous strutural orms (Tomlinson, 1994). Conrete is readily available at a low ost, and it is more suitable in a orrosive environment. Conrete pile oundations may be lassiied into three major ategories: astin-plae onrete piles, omposite onrete piles, and preast onrete piles. With ast-inplae displaement piles, the onrete is plaed in a hole ormed in the ground by boring, jetting, or oring a hole, or by driving a shell or asing into the ground. A rebar age is lowered into the hole, shell, or asing and then illed with onrete. Some o the major advantages o ast-in-plae onrete piles are that they an support extremely large loads; they are designed or ultimate loads beause they are not subjeted to driving and liting stresses; and the predetermination o the pile s length is not ritial. Composite onrete piles an be omposed o either onrete-steel setions or onrete illed steel pipes. In the ase o onrete-steel setions, a standard steel member is

13 3 enased in onrete to protet the steel member in regions most vulnerable to deterioration. The signiiant advantages o the onrete-steel omposite piles are that they an be provided at onsiderable lengths at a relatively low ost; and they are well suited or marine strutures in whih the upper setion o the pile is subjeted to a orrosive environment. Some o the advantages o the onrete illed steel pipes are they are easy to ontrol during installation; they an be treated as non-displaement piles during an open-end installation; open-end pipe is best against obstrution; they have high load apaities (i.e., 200 tons); and they are easy to splie (Bowles, 1996). 1.3 Preast Conrete Piles Preast onrete piles are the third ategory o onrete piles. They are ast, ured and stored beore they are installed. The most ommon method o installation or preast piles is driving and thereore the piles must be designed to endure servie loads as well as handling and driving ores. Preast piles are urther subdivided into two main ategories: reinored preast onrete piles and preast, prestressed onrete piles (Prakash and Sharma, 1990). The reinored preast onrete piles onsist o an internal reinoring age o longitudinal bars and spiral or hoop reinorement. These piles are used primarily or moderately deep oundations in an aquati or marine environment. Some o the advantages o reinored preast piles are

14 4 they an be preabriated under ontrolled onditions to maintain good quality onstrution; they an be used or land strutures in areas where hard driving is neessary; and good orrosion resistane an be attained beause the ured onrete provides a high quality moisture barrier. In preast, prestressed onrete piles, prestressed tendons replae the typial longitudinal reinorement with spiral reinorement enasing the tendons. In addition to the advantages listed above or preast onrete piles, the preast, prestressed piles oer the ollowing beneits: there is less potential or raking during driving; there is urther redution to orrosion due to redued rak width resulting rom pre-ompression; and they an usually be made lighter, longer, and more durable due to the onrete being plaed under ontinuous ompression through prestressing. 1.4 Seismi Design Approah Preast, prestressed pile oundations are used to support bridges, buildings, and whar strutures. In the United States, high seismi regions suh as Caliornia, Washington, South Carolina, and Alaska adopt ertain standards or the design o oundations so that satisatory perormane o strutures an be ahieved when they are subjeted to earthquake motions. As desribed by Paulay and Priestley (1992) and Priestley et al. (1996), the seismi design philosophy adopted in these regions generally ollows the apaity design priniples. These priniples, as stated by Priestley et al. (1996), inlude:

15 5 under design-level earthquakes, the struture is allowed to respond inelastially through lexural yielding; loations o plasti hinges are pre-seleted and detailed areully to ensure that the struture an develop a dutile response; and suitable strength margins are provided to ensure that undesirable mehanisms o inelasti responses annot our. Thus, the seismi design philosophy promotes the notion that the oundation elements, inluding piles, should be inhibited rom experiening inelasti ations by oring the plasti hinging to our in the struture at or above the ground surae. An exeption is made when bridge olumns are extended into the ground as drilled shats, in whih ase in-ground plasti hinges are allowed to orm in the oundation shats under seismi loading. However, preventing inelasti ations to piles that support ootings is not always pratiable sine the moment gradient in the pile is inluened by loal variations in soil stiness along the pile length (Priestley et al. 1996). The extent o inelasti ation that an potentially our in piles during an atual earthquake is not well understood beause earthquake reonnaissane eorts typially do not investigate this issue unless evidene or pile ailure is seen at a partiular site. Preast, prestressed piles have been widely used in the design o oundations or bridges, buildings, and whar strutures in high seismi regions. The subsequent setions provide more speii details o the seismi design approah or the aorementioned strutures.

16 Bridges In the United States, the Seismi Design Criteria (SDC, 2006) published by the Caliornia Department o Transportation (Caltrans, 2006)), the South Carolina Department o Transportation Seismi Design Speiiations (SCDOT, 2001), and the Washington seismi design riteria (AASHTO, 2004) inlude speial provisions or seismi design. Outside o the US, three speiiations that are onsidered in seismi design provisions are the: 1) Speiiations or Highway Bridges published by the Japan Road Assoiation (JRA, 1996), 2) New Zealand Conrete Struture Standards (NZS, 2006), and 3) Canadian Highway Bridge Design Code (CAN/CSA, 1998). The seismi design o bridges is typially speiied or the design o ordinary bridges, as deined in Appendix A. Consistent with the apaity design philosophy, the oundation o bridges are required to be designed to resist the overstrength olumn apaity M o and the orresponding overstrength shear V o. The overstrength moment, M o, applies a 20% overstrength magniier to the plasti moment apaity o the pile to aount or the material strength variations between the pile and the adjaent members as well as the pile moment apaities that may be greater than the idealized plasti moment apaity. The overstrength shear is then ound based on the overstrength lexural moment. The type o soil surrounding the pile will greatly aet the design o the pile oundation. Foundations in ompetent soil an be analyzed and designed using a simple model that is based on assumptions onsistent with observed response o similar oundations during past earthquakes. Caltrans (2006) provides indiators that a soil is apable o produing ompetent oundation perormane whih inlude the ollowing: Standard penetration, upper layer (0-10 t [0-3 m]) N = 20 (Granular soils)

17 7 Standard penetration, lower layer (10-30 t [3-9 m]) N = 30 Undrained shear strength, s u > 1500 ps (72 KPa) (Granular soils) (Cohesive soils) Shear wave veloity, ν s > 600 t/s (180 m/s) Low potential or liqueation, lateral spreading, or sour where N = The unorreted blow ount rom the Standard Test Method or Penetration Test and Split- Barrel Sampling o Soil Pile oundations loated in marginal soils may ontain onsiderable lateral displaements beause the pile aps within the marginal soils may not govern the lateral stiness o the oundation. Marginal deines the range on soil that annot readily be lassiied as either ompetent or poor, where poor soil is traditionally haraterized as having a standard penetration, N<10. The ourse o ation or bridges in marginal soil will be determined on a projet-by-projet basis. I a soil is lassiied as marginal, the bridge engineer and oundation designer shall jointly selet the appropriate oundation type, determine the impat o the soil struture interation, and determine the analytial sophistiation required to reasonably apture the dynami response o the oundation as well as the overall dynami response o the bridge. Although the type o soil surrounding the pile will greatly aet the design o the pile oundation, it is onsistently noted that no inormation on the expeted level o lateral displaement o the pile oundation was provided in any o the seismi design riterion onsidered. Given the nature o the projet, several seismi design riteria were investigated to determine the given requirements or the minimum transverse reinorement or minimum dutility apaity. Chapter 2 reports several design equations used in the design o preast, prestressed piles and displays the vast disrepany between the equations being used.

18 8 Thorough researh o the seismi design riteria in regions with high seismi ativity indiated that no speii requirements or the minimum transverse reinorement or minimum dutility apaity o the piles were provided (i.e., SDC, 2006; SCDOT, 2001; JRA, 1996; and CAN/CSA, 1998). In Washington, however, detailing requirements or the spiral reinorement in the plasti hinge region or preast, prestressed piles are as ollows: For piles not greater than 24.0 inhes in diameter: spiral wire should be W3.9 or greater; spiral reinorement at the ends o piles having a pith o 3.0 inhes or approximately 16 turns; the top 6.0 inhes o pile having ive turns o additional spiral winding at 1.0 inh pith; and or the remainder o the pile, the strands should be enlosed with spiral reinorement with not more than 6.0 inh pith. For piles greater than 24.0 inhes in diameter: spiral wire should be W4.0 or greater; spiral reinorement at the ends o piles having a pith o 2.0 inhes or approximately 16 turns; the top 6.0 inhes o pile having ive turns o additional spiral winding at 1.5 inh pith; and or the remainder o the pile, the strands enlosed with spiral reinorement with not more than 4.0 inh pith.

19 Buildings In the United States, the ACI 318 Building Code (ACI, 2005) and the ASCE Minimum Design Loads or Buildings and Other Strutures (ASCE 7, 2005) inlude speial provisions or seismi design or buildings. Outside o the US, three high seismi regions are onsidered or the seismi design speiiations o buildings: 1) The National Building Code o Canada (2005); 2) The Building Standard Law in Japan (2004); and 3) New Zealand Conrete Struture Standards (NZS, 2006). The seismi design o buildings is typially speiied or buildings in high risk levels. A risk level is deined as the seismi perormane or the design ategory o a building. Speiiations regarding suh risk levels are provided in Appendix C. From the investigated odes, it is evident that the design or inelasti ations within the pile is not aounted or. In relation to this projet, partiular requirements o the transverse reinorement within a pile oundation o a building struture are provided by the ACI 318 Building Code (ACI, 2005), the ASCE Minimum Design Loads or Buildings and Other Strutures, (ASCE, 2005), and the New Zealand Conrete Struture Standards (NZS, 2006). Aording to the Notes on ACI Building Code Requirements or Strutural Conrete (PCA, 2005), when a pile is expeted to experiene tension ores rom an earthquake, a suitable load path is required to transer these tension ores rom the longitudinal reinorement o the olumn through the pile ap, to the reinorement o the pile oundation. With this knowledge, the ode alls or ontinuous reinorement, ully detailed, over the length resisting the tensile ores. Thus, the requirement o the transverse reinorement within a pile oundation o a building struture indiates that the:

20 10 1. transverse reinorement is essential at the top o the pile or at least ive times the member s ross-setional dimension, but not less than six eet below the bottom o the pile ap; and 2. or preast onrete driven piles, the length o the transverse reinorement shall be suiient to aount or potential variations in the elevation in pile tips. In the ASCE 7 (2005) design riteria are plaed on the plasti hinge regions or preast, prestressed piles in high seismi regions. These riteria are as ollows: 1. Length o dutile region: where the total pile length in the soil is 35 t or less, the dutile pile region shall be taken as the entire length o the pile. Where the pile length exeeds 35 t, the dutile pile region shall be taken as the greater o 35 t or the distane rom the underside o the pile ap to the point o zero urvature plus three times the least pile dimension. 2. Spiral spaing: in the dutile pile region, the enter to enter spaing o the spirals or hoop reinorement shall not exeed one-ith o the least pile dimension, six times the diameter o the longitudinal strand, or 8 in, whihever is smaller. 3. Spliing: spiral reinorement shall be splied by lapping one ull turn, by welding, or by the use o a mehanial onnetor. Where spiral reinorement is lap splied, the ends o the spiral shall terminate in a seismi hook in aordane with ACI 318, exept that the bend shall not be less than Volumetri ratio o transverse reinorement: a. where the transverse reinorement onsists o spirals or irular hoops, the required amount o the volumetri ratio o spiral transverse

21 11 reinorement in the dutile pile region is permitted to be obtained by providing an inner and an outer spiral. b. Where transverse reinorement onsists o retangular hoops and ross ties, the total ross-setional area o lateral transverse reinorement in the dutile region, the hoops and ross ties shall be equivalent to deormed bars not less than a number three in size. Retangular hoop ends shall terminate at a orner with seismi hooks.. Outside o the dutile pile region, the spiral or hoop reinorement with a volumetri ratio not less than one-hal o that required or transverse oninement reinorement shall be provided. Both the ACI ode (2005) and the ASCE 7 (2005) provide equations or the amount o transverse reinorement required in the dutile regions o the pile. Chapter 2 reports these design equations, along with several other design equations used in the design o preast, prestressed piles Whars Whar strutures serve as an aommodation to the import and export industry, and represent a large eonomi investment. However, when subjeted to earthquake damage, the assoiated eonomi loss will be very signiiant. Figure 1.1 portrays a normal setion through a typial whar struture and displays the three main omponents o it. 1. A rok dike onsisting o a quarry run rok plaed along the water s edge, whih serves to retain the baklands earth ill and also as an anhor to the whar piles.

22 12 Riprap protetion and onrete ratprooing is plaed on the surae o the quarry run material; 2. A onrete dek that extends the berthing ae into the deeper water; and 3. Vertial preast, prestressed onrete piles, whih are designed to support the dek loads and resist lateral seismi ores (Birdy and Dodd, 1999). Conrete Dek Bakland Fill Material Rok Dike Quarry Run Fill Riprap Protetion and Conrete Ratprooing Preast Prestressed Conrete Piles Figure 1.1. Typial setion through a whar struture (Birdy and Dodd, 1999) The pile oundations are driven into the ground-omposed o quarry run material, riprap protetion, and bakland ill material. The piles are driven diretly through the riprap material in order to avoid tilting o the pile oundations. In the proess o driving the preast, prestressed piles, high ompressive stresses generally develop at the pile head and the pile end, and thus these regions require spiral oninement with a very tight pith. The preast, prestressed pile oundations supporting the whar strutures ought to be designed as a dutile rame with plasti hinges orming in the piles under seismi ations. Adequate perormane o the pile oundations o a whar struture depend greatly on areul detailing o the pile-to-

23 13 superstruture onnetion as well as the P-delta eets, oninement reinorement, and axial load ratios. At the pile head, the prestressing strands may extend into the superstruture in order to urther provide ontinuity. Suiient development length must be supplied in order to avoid the strands pulling out o the superstruture beore the lexural apaity o the pile head is reahed, (Birdy and Dodd, 1999), although this length was not speiied. This spiral reinorement will also ontribute to onsiderable shear resistane. The details o the design o preast, prestressed pile oundation or a whar struture are omparable to the AASHTO LRFD Bridge Design Speiiations (see setion ) (Birdy and Dodd, 1999). Speii odes have been established by the Port o Los Angeles (POLA, 2004) and the Marine Oil Terminal Engineering and Maintenane Standards (MOTEMS, 2005) o Caliornia or the design o whar strutures. These odes, however, do not speiy requirements or the minimum amount o transverse reinorement or minimum dutility apaity o the piles. 1.5 Sope o Researh Setion 1.4 reviews the published seismi design riteria as well as urrent odes and standards and reveals that none o the investigated riterion aounts or the inelasti behavior o the pile oundation during a seismi event. For example, during a seismi event, the pile oundation may experiene moments that will indue raks along the length o the pile. These raks will result in a redution in the moment o inertia o the pile ross setion. In the urrent study, a methodology is developed that aounts or the variation o the moment o inertia o the pile as the deormation o the pile takes plae. The main objetive o this projet is to develop design equations to determine the minimum

24 14 transverse reinorement neessary to ahieve target dutility over a given range o axial loads in prestressed onrete piles used in high seismi regions. The researh will establish the minimum target dutility in a manner onsistent with the dutility requirements o urrent odes. The urrent seismi design philosophy emphasizes that inelasti ation in the oundation elements inluding piles should be inhibited by oring plasti hinging to our at the olumn base. However, preventing all inelasti ation in piles is not always pratiable sine the moment gradient in the pile is inluened by variations in soil stiness along the pile length. The extent o inelasti ation that ours in piles during an atual earthquake is not well understood. Given this unertainty, the projet will ous on the ollowing: 1. determine an appropriate urvature demand through a literature review; 2. establish an equation that will supply the minimum amount o transverse reinorement or a prestressed onrete pile, while providing the neessary urvature apaity beyond that established as the potential maximum urvature demand; 3. embed a urvature dutility ator within the developed equation in order to aid designers in providing an eonomially appropriate amount o transverse reinorement; 4. using the developed equation, determine permissible lateral displaements that the prestressed piles will be able to withstand in dierent soil onditions; and 5. ormulate reommendations suitable or the design o oninement reinorement or preast prestressed piles in seismi regions.

25 Report Layout The remainder o this report inludes a thorough desription o the proedures o this projet. The hapters to ollow inlude a detailed literature review inluding disussion on the expeted urvature demand, a omplete desription o the development o the proposed equation and the analysis done with the equation on speii piles, an extensive aount o the previously analyzed piles evaluated in ertain soil onditions, and the onlusions and reommendations upon the ompletion o the projet.

26 16 CHAPTER 2. LITERATURE REVIEW 2.1 Introdution Preast, prestressed piles have been widely used in the design o oundations in strutures built on dierent environmental onditions inluding those built on poor soil onditions and heavy marine environments. These strutures, as well as the preast, prestressed piles, are subjeted to variety o loads inluding lateral loads indued by wind, waves, and earthquakes. Given the ous o this report, this hapter is dediated to urrent seismi design pratie adopted or preast, prestressed onrete piles, the reported urvature demands and urvature apaities or these piles designed or seismi regions, and disussion on the design o transverse reinorement or preast, prestressed piles. 2.2 Current Seismi Design Pratie A variety o prestressed preast onrete piles are standardized by the preast industry. The ross setions o these piles may be square and solid, square and hollow, otagonal and solid, otagonal and hollow, irular and solid or irular and hollow; some examples are illustrated in Figure 2.1. Hollow Region Tie Continuous Strand Square Solid Square Hollow Otagonal Solid or Hollow Cirular Solid or Hollow Figure 2.1. Cross setions o prestressed onrete piles (PCI, 1999)

27 17 O the dierent ross setions, the preast, prestressed piles with solid square ross setions and solid otagonal ross setions are the most ommonly used types in design pratie in seismi regions (Arulmoli, 2006). This is due to the at that the square piles types are easier to ast, while the otagonal piles minimize the impat o spalling on the moment-urvature response o these piles. Given the typial length requirements, it is onvenient to ast the preast, prestressed piles in a horizontal position rather than in a vertial position. With the piles being ast horizontally, the square piles, in partiular, provide an ease to the asting proess. The most ommon sizes utilized in urrent seismi design pratie are 12-inh, 14-inh, and 16-inh square piles, and 16-inh and 24-inh otagonal piles. Figures 2.2, 2.3, and 2.4 provide typial details o the standard piles used or bridge oundations in seismi regions by the Caliornia Department o Transportation (Caltrans). T+ 3 " 8 Max Preast prestressed onrete P T = 100,000 LBS Min 4 strands, Min T " Min T = 1-0" "A" bars x 22-0" Min total 4 ** T = 1-0" **To be in plae when pile is ast Figure 2.2. Detail o a 12-inh preast, prestressed onrete square ross-setion used by Caltrans (2006)

28 " 8 Max 1" Chamer 1-2" Prestressing steel P = 136,000 LBS A s = 0.92 Square inhes Min "A" total bars x 23-0" 5 typial " Min 1-2" Figure 2.3. Detail o a 14-inh preast, prestressed onrete square ross-setion used by Caltrans (2006) PRESTRESS STRANDS 3"ø PVC JET TUBE SPIRAL 135 TYP SPIRAL SPLICE: TWO COMPLETE TURNS FOR W20 18" LAP FOR W11 6" MIN Figure 2.4. Detail o a 24- preast, prestressed onrete square ross-setion used by POLA (2003) In the design o preast, prestressed onrete piles, several reinorement types may be utilized and speiied in terms o reinorement ratios. Suh ratios inlude: the longitudinal mild steel reinorement ratio ( ρ ), longitudinal prestressed reinorement ratio l ( p ρ ), and volumetri ratio o the oninement reinorement ( ρ ). s The ratio o the mild steel reinorement and the ratio o the prestressed steel are deined as the total area o longitudinal reinorement with respet to the total area o the ross setion o the pile. The

29 19 volumetri ratio o the oninement reinorement is speiied by several dierent odes and is more thoroughly disussed in Setion 2.4. These ode-speiied ratios are largely empirial in nature and are not based on satisying a speii urvature demand, thus leading to signiiant dierenes in the reinorement requirements. Thereore, the ollowing setion is dediated to establishing a possible urvature demand or piles based on previous studies inluding ield investigations, site surveys, and analytial studies. 2.3 Curvature Demand Despite the advanements in seismi design over the past deades, strit limitations have been plaed on the use o preast, prestressed onrete piles in high seismi regions (Banerjee et al., 1987). For example, ATC 3-06 (1978) states that preast onrete piles shall not be used to resist lexure aused by earthquake motions unless it an be shown that they will be stressed to below the elasti limit under the maximum soil deormations that would our during an earthquake. This implies that the piles should not be subjeted to any inelasti ations. In ontrary, ACI 318 (2005) speiies requirements on the transverse reinorement in the oninement region o preast onrete piles. These requirements are stated in Chapter 1 o this report. These requirements were set primarily due to a lak o understanding o the urvature demands that the preast, prestressed piles would be subjeted to during moderate to large earthquakes (Banerjee et al., 1987). Investigating this lak o understanding is o paramount importane in this study beause it will establish the expeted urvature demand or the preast, prestressed piles used in seismi regions so that the appropriate oninement reinorement an be satisatorily quantiied or the plasti regions o these piles.

30 20 Two ritial urvatures o a pile are the maximum urvature demand and urvature apaity. The irst term reers to the maximum urvature that the pile setion may experiene when the oundation is subjeted to an earthquake input motion. This urvature value establishes the maximum urvature that the pile may ever experiene during its lietime. The urvature apaity, on the other hand, establishes the potential urvature that a pile setion an sustain without ompromising its ability to sustain the ombined axial and lexural ations. Under ideal irumstanes, upon the ourrene o an earthquake, whether a small, medium, or large event, the urvature that a pile undergoes along its length should be reorded. Suh ield data is o signiiant importane as the urvature that the pile must be able to resist in a major earthquake is not well understood. In the absene o suh ritial inormation on the maximum possible urvature demand or piles in seismi regions, the determination o oninement reinorement or the plasti hinge region in onrete piles beomes very hallenging. Thereore, through an extensive investigation o literature on reported urvature demands and urvature apaity o piles used in seismi regions, a tentative upper limit or the urvature demand is established in this hapter ater providing an overview o urvature dutility and how it relates to the urvature demand and urvature apaity o a pile. Although the urvature demands established rom subjeting piles to earthquake loading or investigation o piles subjeted to major earthquakes would be more useul, it is noted that suh data is seldom ound in the literature. Consequently, the apaity o piles ound in the literature is useul or establishing the maximum possible urvature demand in

31 21 reognition that widespread damage to piles and the orresponding urvature has not been reported ollowing major seismi events around the world Overview o Curvature Dutility The urvature demands on piles depend on the axial load, moment demand, material properties, pile ixity as well as the strength and stiness o the soil surrounding the top portion o the pile (Priestley et al and Song et al. 2004). In regions o the pile where the urvature demand is high, adequate setion dutility must be ensured through a satisatory pile design proedure. Curvature dutility o a pile may be used to deine its ability to undergo large amplitude yli lateral deormations by undergoing post-elasti strains in speii regions, without a signiiant redution in its lateral load arrying apaity (Joen and Park, 1990). These ritial regions, termed plasti hinges, are thereore detailed or experiening inelasti lexural ations (Paulay and Priestley, 1992). Figure 2.5 portrays the potential loations o the plasti hinges or piles with dierent head ixity onditions. Superstruture Pile Cap Plasti Hinge (a) Fixed Head Pile (b) Partially Fixed Head or Free Head Pile Figure 2.5. Potential loations o plasti hinges in piles

32 22 Depending on the boundary ondition o the pile head and the surrounding soil onditions, the urvature dutility demand in piles may dier signiiantly. For instane, deep oundations ontaining a boundary ondition o a ixed pile to pile-ap onnetion at the pile head may be subjeted to a urvature dutility demand under seismi loading. Thereore, it is o interest to investigate previous analytial work and ase studies in order to attempt to quantiy the urvature demand and/or urvature apaity needed or piles in dierent soil and boundary onditions. Several ase studies are reported in the subsequent setions to aid in the proess o quantiying the urvature demand and/or apaity. Setion 2.4 urther disusses the relevane o these values to the overall projet Bakground o Curvature Dutility Song et al. (2004) emphasized the neessity to gain a deeper understanding o the urvature demand utilizing an analytial model. In explaining this model, it was stated that deep oundations or buildings and bridges oten rely on the use o onrete piles that are restrained rom rotation at the pile head. With the lateral loads that the earthquakes indue, the ixity at the pile to pile-ap onnetion indues a large urvature demand in piles adjaent to the pile ap, ausing potential or ailure in the pile. When a large lateral load is applied to a pile oundation, a sequential yielding in the ritial regions o piles will develop until orming a ull plasti mehanism. A summary o the various limit states assoiated with this mehanism are provided below with illustrations in Figure 2.6: First yield limit state: haraterized by a bending moment demand at the pile to pileap onnetion reahing the irst yield moment o the pile setion, where it is

33 23 assumed that the plasti hinge irst orms at the pile head. The enter o rotation in this ase ours at the ground level. Seond yield limit state: a seond plasti hinge orms at a depth greater than the depth o the irst plasti hinge. O important note is the ontinued lateral displaement ater the ormation o the seond plasti hinge, whih is ailitated by inelasti rotations in both plasti hinges. Ultimate limit state: this limit state is deined by the irst lexural ailure o a hinge and is ditated by the limiting urvature in either o the plasti hinges. P y1 y2 y2 p V L p1 L m V y V u V u Ground Level L p2 Deleted Shape Bending Moment Proile θ p Deleted Shape Bending Moment Proile θ p θ p Inelasti Deletion Plasti Hinge M max M max M max (a) (b) () Figure 2.6. Deleted shape and bending moment distribution o a laterally loaded ixed-head pile (a) First yield limit state (b) Seond yield limit state () Ultimate limit state (ater Song et al., 2004) The analysis model developed by Song et al. (2004), with ous on CIDH piles, deines the lateral response o ixed-head piles using the limit states deined above. This model also predits the lateral stiness, lateral strength and the urvature dutility demand in the pile and relates the displaement dutility ator o the pile to the loal urvature dutility demand at the ritial pile setion or both ohesive and ohesionless soils. The urvature dutility

34 24 demand, whih is dierent or the two plasti hinges, depends on the displaement dutility imposed on the pile. By limiting the urvature dutility demand within the plasti hinge region, the severity o the loal damage an be ontrolled. The given analysis model an be summarized in the ollowing manner: The lateral response o ixed-head piles is represented by a linear elasti response, ollowed by irst yielding o the pile at the pile head and then by a ull plasti mehanism with seond plasti hinging at some depth below the pile head. The elasti response o the pile and its irst yield limit state are determined using a lassial solution o a lexural element supported by an elasti Winkler oundation. In this ase, the soil is replaed by a series o springs, whih provide a soil reation that is proportional to the lateral deletion (p-y urves). The ultimate lateral strength, or the maximum lateral load that the pile an resist without ailure, is determined using the lexural strength o the pile and an ultimate pressure distribution or the soil. The lateral strength o the pile an be determined by assuming that a suiiently large deletion has ourred so that an ultimate soil pressure that extends to the depth o the maximum bending moment is ully developed. This depth depends on the lexural strength o the pile and the ultimate soil pressure o the soil and deines the loation o the seond plasti hinge, whih in turn, inluenes the lateral strength and the dutility o the pile. The magnitude and distribution o the ultimate soil pressure ating on the pile depends on the ailure mehanism o the soil, the shape o the pile ross-setion, and the rition between the pile surae and the surrounding soil.

35 25 A kinemati relation between the global displaement dutility ator and loal urvature dutility demand is developed by assuming a onentrated plasti rotation at both plasti hinges. The kinemati relationship between displaement and urvature dutility demands is established through the dependeny o the urvature dutility demand upon the ratio o the irst yield lateral ore to ultimate lateral ore, the ratio o initial stiness to post irst yield stiness, the depth to the seond plasti hinge, and the plasti hinge length o the pile. The extension o the above approah to piles in a pile supported ooting will be relatively hallenging beause it is diiult to establish a relationship between the global displaement dutility ator and the loal urvature dutilities o dierent piles. As detailed in Chapter 4, this problem may be alleviated by deining dierent displaement limits or the piles and inorporating these displaements in the deinition o the global displaement dutility Analytial Work Song, Chai, and Hale, 2004 In order to examine the useulness o the model desribed in setion 2.3.2, two reinored onrete pile oundations with a ixed head embedded in two dierent soil types were examined by Song et al. These soils were sot lay and dense sand. The reinored onrete piles were 22 inhes (0.56 meters) in diameter and ontained an embedment length o 64.3 eet (19.6 meters). The reinorement o the pile was: (1) eight No. 22 longitudinal reinoring bars, resulting in a longitudinal steel ratio o 0.012; and (2) No. 16 transverse

36 26 spiral reinorement at a pith o 3.5 inhes, resulting in a onining steel ratio o with a onrete over o 3 inhes. The reinored onrete ixed-head pile oundation was initially assessed in sot lay ohesive soil. In ompleting the analysis o the numerial model, the urvature demand results in /inh or the CIDH pile. The same reinored onrete ixed-head pile oundation was next assessed in dense ohesionless sand at the irst yield limit state o the pile in order to observe the orrespondene between that limit state and the urvature dutility demand. In ompleting the numerial model, the urvature demand o /inh was estimated. These values o urvature demand provide a target urvature or onrete piles under the onditions that Song et al. hose or their examples Banerjee, Stanton, and Hawkins, 1987 Single piles embedded in representative soil proiles were subjeted to severe earthquake loading in order to analytially investigate the soil-pile interation. The objetive o the study was to ompute the bending behavior o single piles embedded in soil proiles taken rom three West Coast sites and assoiate the bending behavior o these piles under earthquake lateral loads. The ross-setional properties o the piles that were analyzed are detailed in Table 2.1.

37 27 Table 2.1. Pile details or piles embedded into the three West Coast sites Pile size (in.) Cross-setional area (in. 2 ) Moment o inertia (in. 4 ) Conentrated mass at the top (ton) , Note: γ = 150 p; E = 4750 ksi, ν = 0.15 The analysis proedure utilized an updated and reined inite element model that was used in a previously perormed study by Margason (1977). This proedure required modeling o the omplete pile-soil system using elasti and equivalent linear viso-elasti inite elements. The analysis was perormed in two steps: ree-ield analysis and interation analysis, both in the requeny domain using the method o omplex response. The ree-ield analysis determined ompatible base rok motions and deined the boundary ores or the seond step. The interation analysis involved the omplex harmoni equilibrium equations or the entire soil-pile system being solved iteratively at eah requeny o exitation. This iteration proess is neessary beause non-linear behavior o the soil was inluded. The non-linear soil behavior was represented in an equivalent linear method by a seant modulus that was hosen to satisy both the equilibrium and ompatibility. As mentioned above, the piles were embedded in soil proiles taken rom three West Coast sites: West Seattle, Taoma, and San Franiso. Figures 2.7, 2.8, and 2.9 provide the soil properties at the three sites.

38 28 Soil 0 Depth Soil Unit Low Strain Shear Wave Veloity, V s, p Alluviu Glaial Figure 2.7. Soil properties at the West Seattle site

39 29 Soil properties 0 depth Soil type Sandy Clay Clay Unit p V s, ps Sand Figure 2.8. Soil properties at the Taoma site

40 30 Soil properties 0 depth Soil Unit V s, ps p 1 Sand Clay Clay Sand Clay Cl Sand and Gravel Figure 2.9. Soil properties at the San Franiso site Through the two-step proess, the ollowing observations were made by the authors: the maximum indued urvature demands were signiiantly aeted by the harateristis o the surrounding soils; the indued urvatures were larger in soter soil and espeially severe at the interae between layers with signiiantly dierent modulus values;

41 31 the indued urvatures were redued as the pile size inreased; or a severe earthquake in relatively poor soil onditions, i.e. the West Seattle site and the Taoma site, the maximum indued pile urvatures ranged rom /inh to /inh; and or the San Franiso site, the maximum indued pile urvature was /inh Field Investigation A number o investigations were onduted on piles ater the ourrene o an earthquake to obtain inormation on the ause o pile ailures and to estimate the urvature demand imposed on piles in real earthquakes. Based on this inormation, the ollowing disussion aims to provide an upper bound values or the urvature demand that piles must be able to sustain in a major earthquake Koyamada, Miyamoto, and Tokimatsu, 2005 The Tokahi-Oki Earthquake, an earthquake with a magnitude o 8.0, ourred on September 26, It aused severe damage to the Konan junior high shool in Hokkaido Japan, a three-story reinored onrete rame building supported on high strength prestressed onrete pile oundations. In order to determine the main ators that aused the severe damage, a ield investigation was perormed, involving exavation o our perimeter piles. From this investigation, it was onluded that piles were damaged by ompression ailure with lexural raks at the pile heads. These ompression ailures indued dierential settlements o the superstruture, thereore leading to damage to the struture. Shear raks were ound in the walls o the shool building and were aused by the ollapse o the pile oundation. The pile oundations, omposed o high-strength prestressed onrete piles, were

42 eet long with a diameter o 15.7 inhes. Reinorement details o the piles were not provided. The piles were embedded into a non-uniorm layered soil, summarized in Table 2.5. Soil properties 0 depth Soil type Peat V s, ps 197 Clay Sandy Silt Gravel Mudstone Gravel Gravel Sandstone 1706 Table 2.5. Depths o soil layers at the Konan junior high shool at Hokkaido, Japan The ators ausing the damage o the pile oundation were also veriied by the researhers through analytial simulations. In this simulation model, a one-stik model with lumped mass idealized the superstruture whereas the pile oundation was modeled with

43 33 beam elements. The piles were onneted to the ree ield soil through non-linear lateral and shear interation springs. The non-linear behavior o piles was inorporated into the analysis by deining the relationships between the bending moment and the urvature, thus enabling evaluation o the degree o damage to piles. The kinemati bending moments and shear ores were omputed by subjeting the analysis model to the reorded ground motion, without the superstruture. The inertial bending moments and shear ores o the superstruture were obtained by subtrating the kinemati bending moments and shear ores rom the total bending moments and shear ores. It was ound that the bending moment demand in the piles at the pile head, whih inluded both the inertial and kinemati omponents, exeeded its ultimate moment apaity. This is onsistent with the soil proile where peat exists over approximately 20 eet along the pile length. Furthermore, the maximum urvature demand at the pile head due to the imposed seismi load was determined to be about /inh rom the analysis and was ound to be onsistent with the damage obtained rom the ield investigation Lin, Tseng, Chiang, and Hung, 2005 Earthquakes suh as the Niigata earthquake o 1964, the Kobe earthquake o 1995, and the Chi-Chi earthquake o 1999 aused lateral spreads, resulting in signiiant damage to the pile oundations o both bridges and buildings. Through exavation and ield surveys, it was dedued that liqueation may have aused the damage to the pile oundation, produing permanent ground displaement. A oundation model onsisting o Winkler springs was utilized to model the non-linear soil response interation, while the Bou-Wen hystereti model was used to stimulate the soil and pile material behavior.

44 34 Depending on the stiness o the liqueied soil, the length o the pile exposed to the liqueied soil, the axial load imposed on the pile, and the bending stiness o the pile, piles subjet to lateral spreading due to soil liqueation ould potentially experiene two distint ailure modes (Meyersohn, 1994): 1. lateral pile deletions indued by ground lateral spreading that may result in the pile reahing its bending apaity and hene develop a ull moment apaity; and 2. the ombined ation o lak o suiient lateral support due to the redued stiness o the liqueied soil and the lateral deletion imposed on the pile may result in pile bukling. Sine ground lateral spreads may be due to ombined and simultaneous ations o permanent ground displaements and axial loads, separate analyses ought to be perormed or studying the potential or bending and bukling ailure o piles. In this artile, the possible ailure modes o the ollowing three available pile oundations were studied in order to determine i the piles ailed by bending or bukling. Yahiyo Bridge, Japan During the 1964 Niigata earthquake, the abutments and piers o the Yahiyo Bridge were damaged. The oundations o these abutments and piers used reinored onrete piles, whih were 32.8 eet in length and 11.8 inhes in diameter. Reinorement details o the piles were not provided. The pile oundations were embedded into a 36 oot deep layered soil omposed o sandy silt, medium sand, and ine sand. Upon extration, the piles were observed to be severely damaged at a depth o 26.2 eet rom the top o the pile as well as ontaining horizontal raks aused by signiiant lexural ations. The maximum urvature

45 35 that the reinored onrete piles reahed was reported to be /inh, although authors did not disuss the proedure as to how this value was obtained. Four-Story Building in Mikagehoma, Japan The 1995 Kobe earthquake ritially damaged the prestressed high-strength onrete pile oundations that supported a our-story building in Mikagehoma, Japan. The piles were 75.5 eet long and had a diameter o 13.8 inhes. Reinorement details o the piles were not provided. Field investigations revealed signiiantly wide pile raks near the pile head, whih aused apparent tilting o the entire building. The maximum urvature that the prestressed high-strength onrete piles reahed was reported to be /inh. Again, no inormation was provided as to how this value was determined. Showa Bridge, Japan The Showa Bridge was ompletely destroyed during the 1964 Niigata earthquake. The 12-span bridge was 75.5 eet in length. The piers o the Showa Bridge were omposed o 0.07-inh thik driven steel pipe piles, whih were 269 eet long and 24 inhes in diameter. Reinorement details o the piles were again not provided. The soil onditions surrounding the pile oundations were omposed o liqueiable soil layer and a non-liqueied soil layer. The liqueiable soil layer slid horizontally 16.4 eet toward the enter o the river, suggesting that the pile ailures may have resulted rom pile bukling. The maximum urvature that the steel pipe pile reahed was estimated to be /inh, although how this value was obtained was not disussed.

46 Target Curvature Demand The literature summarized in the preeding setions indiated a target urvature dutility demand or piles in the range o /inh to /inh. Sine the number o researh artiles providing this inormation is limited, the urvature apaities reported or various pile setions were also examined. In regards to the urrent projet, these values are relevant beause they provide a quantiiable range or urvature apaities or piles used in seismi regions and that i this range is unaeptable widespread damage to the pile oundation would have been observed during past earthquakes. Summarized in Table 2.6 are various urvature demands disussed in the above setions, while Table 2.7 lists reported urvature apaities or dierent piles used in seismi regions. By omparing the two tables, it is observed that the apaities in Table 2.7 range rom /inh to /inh, and the maximum apaity o /inh is about 40 perent lower than the maximum demand o /inh that has reported to have aused pile damage. In the absene o a more reined data set, these upper values provide an indiation or the maximum urvature that should be onsidered or the investigation presented in this report.

47 Table 2.6. Summary o urvature demands estimated or piles in the ield during past earthquakes Doument Reerene Pile Type reinored Song, Chai, onrete Hale-2004 (CIDH) Analytial model or dutility assessment o ixed-head onrete piles Analytial model or dutility assessment o ixed-head onrete piles Damage o piles aused by lateral spreading-bak study o three ases Damage o piles aused by lateral spreading-bak study o three ases Damage o piles aused by lateral spreading-bak study o three ases Song, Chai, Hale-2004 Lin, Tseng, Chiang, Hung Lin, Tseng, Chiang, Hung Lin, Tseng, Chiang, Hung reinored onrete (CIDH) reinored onrete prestressed high strength onrete pile driven steel pile Pile Dimensions (in.) D = 22 D = 22 D = 11.8 L * = D = 13.8 L = 906 D = 24 thikness = 0.07 Type o Loading earthquake earthquake 1964 Niigata Earthquake 1995 Kobe Earthquake 1964 Niigata Earthquake Curvature Demand (in -1 ) Field inestigation and analysis study o damaged pile oundation during the 2003 Tokahi-Oki earthquake Koyamada, Miyamoto, Tokimatsu prestressed high strength onrete pile D = 15.7 L = Tokahi-oki Earthquake L * = length o pile

48 Table 2.7. Summary o urvature apaities reported or preast, prestressed onrete piles used in seismi regions Doument Reerene Pile Type Seismi design o prestressed Sheppard, square onrete piling 1980 piles Seismi design o prestressed Sheppard, square onrete piling 1981 piles Seismi design o prestressed onrete piling Seismi design o prestressed onrete piling Seismi design o prestressed onrete piling Sheppard, 1980 Sheppard, 1980 Sheppard, 1980 square piles square piles square piles Pile Dimensions (in.) 16x16 L = x18 L = Type o Loading axially until 600 kips, then monotonially to ailure axially until 600 kips, then monotonially to ailure axially until 200 kips by posttensioning, then monotonially to ailure prestressed to indue eet preompression o 700 kips, axially to 300 kips by posttensioning and ylially loaded prestressed to indue eet preompression o 700 kips, axially to 300 kips by posttensioning and ylially loaded Curvature Capaity (in -1 ) Seismi perormane o preast prestressed onrete piles Seismi perormane o preast prestressed onrete piles Banerjee, Stanton, Hawkins 1987 Banerjee, Stanton, Hawkins 1987 otogonal piles otogonal piles 14 yli lateral load tests 14 yli

49 39 Table 2.7. (ontinued) Doument Reerene Pile Type Pile Dimensions Type o Loading Seismi perormane o preast prestressed onrete piles Seismi perormane o preast prestressed onrete piles Seismi perormane o preast prestressed onrete piles Seismi perormane o preast prestressed onrete piles Seismi perormane o preast prestressed onrete piles Seismi perormane o preast prestressed onrete piles Seismi perormane o preast prestressed onrete piles Seismi perormane o preast prestressed onrete piles Banerjee, Stanton, Hawkins 1987 Banerjee, Stanton, Hawkins 1987 Banerjee, Stanton, Hawkins 1987 Banerjee, Stanton, Hawkins 1987 Banerjee, Stanton, Hawkins 1987 Banerjee, Stanton, Hawkins 1987 Banerjee, Stanton, Hawkins 1987 Banerjee, Stanton, Hawkins 1987 otogonal piles otogonal piles otogonal piles otogonal piles otogonal piles otogonal piles otogonal piles otogonal piles 14 yli 14 yli 14 yli 14 yli 14 yli 14 yli 14 yli 14 yli Curvature Capaity in

50 Coninement Reinorement In order to enhane strength and toughness o the onrete ore setion o a prestressed preast onrete pile, transverse onining reinorement is provided typially in the orm o spirals. At the pile ends, the spirals are losely spaed in order to prevent bursting and splitting stresses that would be aused by the release o prestress and during driving. In the potential plasti hinge regions, losely spaed spirals are also needed to ensure adequate urvature apaity o the pile ritial setions. In addition to inreasing both the lexural strength and shear strengths, the spiral reinorement also prevents premature bukling o the mild steel reinorement. The ollowing disussion provides a thorough explanation o the parameters neessary to determine the needed amount o the spiral reinorement to ensure adequate dutility apaity o preast, prestressed setions as well as urrent oninement reinorement requirements o several dierent design douments Parameters Aeting Coninement The transverse onining reinorement is typially quantiied as a volumetri ratio o the ore onrete setion and symbolized by ρ s an be deined as ollows: ρ s. Using the variables shown in Figure 2.7, ρ = s 4 A sp D s (Eq. 2.1) where A sp = the bar ross-setional area o spiral reinorement D = the diameter o the ore onrete measured between the enter o the spirals

51 41 s = longitudinal enter-to-enter spaing o transverse reinorement 1706 s A sp Figure 2.7. Core onrete onined by transverse reinorement Several dierent parameters inluene the required amount o oninement reinorement. These parameters an be identiied by examining the variables deining the urvature dutility apaity or ultimate ompression strain o the onined onrete. The urvature dutility o a ore onrete setion: φ φ u µ φ = (Eq. 2.2) y where µ φ = urvature dutility; φ u = ultimate urvature; and φ y = yield urvature. The ultimate urvature may be deined using the ultimate ompression strain as ε φ u = u u (Eq. 2.3) where ε u = the ultimate extreme iber ompression strain

52 42 u = the orresponding neutral-axis depth Aording to Mander et al. (1988), the ultimate ompression strain and the volumetri ratio o transverse reinorement are related by ε u = ρ s yh ε su (Eq. 2.4) = 2 l l (Eq. 2.5) where ρ s = the volumetri ratio o transverse reinorement; yh = the yield strength o the transverse reinorement; ε su = the ultimate reinorement strain apaity; =the ompressive strength o the onined onrete; = ompressive strength o unonined onrete; and l = eetive lateral onining stress = K e 2 yh A D s sp K e = oninement eetiveness oeiient Given that εu will also depend on the axial ore, P, that the setion will sustain at the ultimate limit state and the amount o longitudinal reinorement ratio, ρ l, it an be stated that the required value o ρs will be inluened by the ollowing parameters:, yh, ε su, P, and ρ l. Considering the other variables that are primarily used to express the key parameters in a non-dimensionalized orm, the variables that ρ s depends on are as ollows: A h = ross setional area o onined ore o reinored onrete setion, measured out-to-out o the transverse reinorement

53 43 A g = gross setion area o the onrete setion A st = total area o mild longitudinal steel reinorement d b = longitudinal reinorement bar diameter d sp = transverse reinorement bar diameter = ompressive strength o unonined onrete y = yield strength o longitudinal reinorement yh = yield strength o transverse reinorement p = ompressive stress in the onrete at the entroid o the ross setion due to prestress (ater losses) m = non-dimensional ratio equal to y /0.85 p t = ratio o non-prestressed longitudinal olumn reinorement, whih is equal to A st /A g P = external axial ore P e = external axial ore ρ l = longitudinal steel reinorement ratio Transverse Reinorement Requirements The transverse reinorement requirements speiied in several odes and standards were onsidered in this study. These inlude the Uniorm Building Code (UBC, 1997), International Building Code (IBC, 2000), the ASCE Minimum Design Loads or Buildings and other Strutures (ASCE 7, 2005), the PCI Reommended Pratie (PCI, 1993), the New Zealand Code o Pratie or Conrete Strutures (NZS, 2006), the Applied Tehnology

54 44 Counil (ATC, 1996), and the Amerian Conrete Institute (ACI, 2005). The subsequent setions disuss the requirements o transverse reinorement rom eah o the aorementioned odes and how they apply to preast, prestressed piles Uniorm Building Code (1997) Prior to the introdution o the International Building Code, the Uniorm Building Code was widely used in seismi regions. The 1997 edition o the Uniorm Building Code (UBC, 1997) established the requirements or spiral reinorement in prestressed onrete piles in Seismi Zones 3 and 4 as ollows: For piles 14 inhes and smaller, ρ s For piles 24 inhes and larger, ρ s International Building Code (2000), ASCE 7( 2005), and PCI (1993) The International Building Code (IBC, 2000) and the ASCE Minimum Design Loads or Buildings and other Strutures (ASCE 7, 2005) adopt some o the requirements o the PCI Reommended Pratie (PCI, 1993) and require the ollowing minimum volumetri ratio o transverse reinorement in the dutile region o preast, prestressed piles: ρ s = but not less than ρ s = A g 1.4P (Eq. 2.6) yh Ah Ag 1.4P (Eq. 2.7) yh Ag or 0.007

55 45 and not to exeed ρ s = The dierenes between the IBC and the PCI Reommended Pratie involve the maximum ρ s limit o and the external axial load, P. The maximum value o is only ound in the IBC, while P is deined dierently in the two odes as detailed below: The IBC deines P due to dead load, earthquake load, live load, roo load, snow load, and wind load, and is determined by either: P 1 2 = 1.2D + 1.0E + L + S (Eq. 2.8) or P = 0.9D + (1.0 E or 1.6W ) (Eq. 2.9) where D = dead load; E = earthquake load; L = live load; S = snow load; 1 = 1.0 or 0.5, depending on the type o live load; and 2 = 0.7 or 0.2, depending on the roo oniguration The PCI Reommended Pratie deines the axial load as a ombination o the external ompressive load on the pile and the axial load on the pile due to the eetive prestress. This ombination is represented by the ollowing equation: P = P + A (Eq. 2.10) e p g where P e = atored external axial load; and p = eetive prestress in onrete ater all losses

56 46 Thus, in order to obtain the most pratial value o P used in the volumetri ratio o the transverse reinorement, the ollowing ombination o the IBC deinition o P as well as the PCI Reommended Pratie deinition o P, should be utilized: P = 1.2D + 1.0E + 1 L + 2 S + p A g (Eq. 2.11) or P = 0.9D + (1.0E or 1.6W ) + (Eq. 2.12) p A g New Zealand Code (2006) There has been signiiant researh done regarding the volumetri ratio o the transverse reinorement in New Zealand (i.e., Joen and Park, 1990; Joen and Park, 1990; Priestley et al., 1981; and Park and Faloner, 1983), rom whih the PCI Reommended Pratie or the minimum transverse reinorement requirement was derived. The volumetri ratio o the transverse reinorement used in earlier New Zealand tests on prestressed onrete piles to study the oninement issues was based on the ollowing equations (Priestley et al., 1981): ρ s = but not less than ρ s = Ag P e (Eq. 2.13) Ah yh Ag P e (Eq. 2.14) yh Ag From the researh that was perormed by Priestley et al. (1981), the reommended transverse reinorement requirement or the 1982 New Zealand Design Code was

57 47 s ρ = + g e yh h g A P A A (Eq. 2.15) but not less than s ρ = + g e yh A P (Eq. 2.16) However, the New Zealand Code o Pratie or Conrete Strutures (NZS 3101, 1982) adopted the ollowing ormat o the aorementioned equations: s ρ = + g e yh h g A P A A φ (Eq. 2.17) but not less than s ρ = + g e yh A P φ (Eq. 2.18) where φ = the strength redution ator or whih values o 1.0 and 0.9 were reommended or researh and design purposes, respetively. Joen and Park (1990) noted that the P = P e + p A g replaed the term P e or prestressed onrete piles. In this reerene, the displaement dutility ator, y u = µ, was reported to be at least 8 when using the previously disussed spiral quantities in the potential plasti hinge regions. The 2006 New Zealand Code o Pratie or Conrete Strutures reommends the required volumetri ratio o spirals based on urther experimental testing and analysis (Watson et al., 1994). The resulting design equation in the urrent New Zealand Standard 3101 is the greater o either ) (1.3 = g yh h g t s A P A A m p φ ρ (Eq. 2.19)

58 48 or A st y 1 ρ s = 110d d sp yh b (Eq. 2.20) Equation 2.20 is related to the lateral restraint o the longitudinal bars against premature bukling, thus is not appliable to prestressed piles in whih the strands are not expeted to experiene any ompressive strains ATC-32 (1996) In the United States, in order to ensure adequate dutile perormane o bridge piers, the ollowing requirement is reommended by ATC-32 (ATC, 1996). ρ =.16 e ( 0.01) s 0 yh P A g ρ (Eq. 2.21) Aording to Priestley et al., (1992), or prestressed onrete piles, the above equation an be modiied by replaing P e with P, and thus: l ρ = ( 0.01) s 0 yh P A g ρ (Eq. 2.22) where P = P e + p A g. This doument urther states that the adequay o the spiral reinorement ought to be heked by omparing the displaement demand o the pile with l its apaity. In this proess, an appropriate equation or the ultimate ompression strain should be used ACI Code (2005) The ACI requires the minimum amount o the transverse reinorement in irular onrete setions in the ollowing orm.

59 49 ρ s A g = yh Ah (Eq. 2.23) but not less than ρ s = 0.12 yh (Eq. 2.24) Sine the introdution o the 1999 version o the ACI ode, the prestressed onrete piles in high seismi regions are required to satisy the above equations or the volumetri ratio o spirals in the plasti hinge regions. It is noted that Eq was derived onsidering only the eets o axial load and may not be appliable when the pile is subjeted to lexural and axial load eets Summary Figures 2.8 and 2.9 provide graphial omparison o the dierent design equations or the volumetri ratio o the transverse reinorement, in whih some o the requirements are omitted beause they are nearly idential to those plotted in these igures. Figure 2.8 portrays spiral requirements or a 14-inh otagonal pile with = 8000 psi, yh = 60 ksi, and a 2 inh onrete over, whereas Figure 2.9 shows spiral requirements or a 24-inh otagonal pile with = 8000 psi, yh = 60 ksi, and a 2 inh onrete over. From these two igures, the ollowing observations are made: The required ρs or prestressed piles dier signiiantly between design odes. At both low and high axial loads, this dierene is more than a ator o three. Exept or the ACI , the required ρs inreases with an inrease in the external ompressive axial load ratio.

60 50 The NZS requires the highest amount o oninement or high external axial loads, whereas ACI requires the highest amount o oninement or low external axial loads. The ACI requirement or both piles is signiiantly high at small axial loads and translates to #3 spiral reinorement at a spaing o less than 0.75 inhes. Suh a requirement is diiult to meet in pratie as it auses signiiant onstrution hallenges. The main objetive o the urrent study is to eliminate suh diiulties, yet provide rational and satisatory amounts o transverse reinorement in prestressed preast onrete piles ρs (Volumetri Ratio) ACI 318, 2005 NZS, 2006 PCI, ATC-32, 1996 UBC, P/ A g (Axial Load Ratio) Figure 2.8. Spiral volumetri ratios or a 14-inh otagonal prestressed pile

61 ρs (Volumetri Ratio) ACI 318, 2005 ATC-32, 1996 NZS, 2006 PCI, UBC, P/ A g (Axial Load Ratio) Figure 2.9. Spiral volumetri ratios or a 24-inh otagonal prestressed pile

62 52 CHAPTER 3. DEVELOPMENT OF A RATIONALE APPROACH TO DESIGNING TRANSVERSE REINFORCEMENT FOR CONFINEMENT PURPOSES 3.1 Objetive The preeding hapter inluded an overview o several equations that may be utilized or the design in transverse reinorement or prestressed onrete piles in areas o high seismi risk. The disussion onluded with a onern o the lak o onormity between the dierent design equations and onstrution hallenges assoiated with some o the reommended requirements. Furthermore, several o these equations did not oer a rationale approah to designing piles with the neessary amount o oninement. In most ases, the target urvature dutility or the onined prestressed setions is not speiied. Thereore, the objetive o this projet is to develop a design equation that determines the minimum transverse reinorement in order to ahieve a target dutility over a given range o axial loads in prestressed onrete piles used in high seismi regions. 3.2 Development o a New Equation Existing Equations o Interest To ommene the development o a new rationale equation or designing oninement reinorement in prestressed piles, our o the existing equations were areully

63 53 examined as the starting point. These equations are as ollows and the reasons or seleting these equations are disussed below. 1. ACI-318 (2005) A g ρ s = (Eq. 3.1) yh Ah yh 2. New Zealand Standard (2006) (1.3 p ) t m Ag P ρ s = (Eq. 3.2) Ah yh φ Ag 3. ATC-32 (1996) P e ρ s = ( 0.01) ρ l (Eq. 3.3) yh Ag 4. PCI Reommended Pratie (1993) A g 1.4P ρ s = (Eq. 3.4) yh Ah Ag ACI-318 (2005) Equation The equation or spiral reinorement ound in the ACI has been part o the ode sine Several tests and experienes show that a setion designed by this equation will ontain more than an adequate dutility and toughness (ACI, 2005). The amount o spiral reinorement that the ACI equation provides was developed to ensure the loadarrying apaity o onentrially loaded olumns suh that their apaity ater spalling o over will equal or slightly exeed the strength based on the unonined onrete strength and gross setional area. It is not until the onrete over spalls o that the eet o the

64 54 spiral reinorement in inreasing the load-arrying strength o the ore onrete will be reognized (ACI, 2005). Sine the ous is on onentrially loaded olumns, the transverse reinorement requirement or onrete setions subjeted to lexure and axial loads is not expeted to vary as a untion o the external axial load and this was witnessed in Figures 2.8 and 2.9. The signiiane o the ACI reommendation is the minimum bound portion o the equation. In the development o the new equation, whih is hereater reerred to as the ISU equation, this minimum bound should be ensured as this is a requirement or all onrete setions. When meeting this requirement, the applied axial load on the pile will be taken as zero. Aording to the ACI , the allowable spaing o the transverse steel is not to exeed the smallest o the ollowing: 1. d/4; 2. eight times the diameter o the smallest longitudinal bars; times the diameter o the hoop bars; and inhes New Zealand Standard (2006) Equation 3.2, based on the work o Watson et al. (1994), is o partiular interest as it is the only equation that onsiders the urvature dutility demand as a variable in the quantiiation o the amount o transverse reinorement. The non-simpliied version o this equation that inludes the urvature dutility demand is presented in Eq. 3.5, whereas the simpliied equation, given in Eq. 3.2 and provided below or onveniene, assumes a

65 55 urvature dutility o 20. The objetive in studying this equation is to determine how the urvature dutility ould potentially be inorporated into the oninement equation. ρ s ( φu / φ y 33pt m + 22) A = 111 A g h yh P φ A g (Eq. 3.5) ρ s (1.3 pt m) A = 2.4 A g h yh P φ A g (Eq. 3.2) The permitted enter-to-enter vertial spaing o transverse reinorement must be less than one-quarter o either the smallest lateral dimension or the diameter o the olumn or pier. This limitation is set to ensure adequate oninement o the ore onrete. The maximum vertial spaing o the transverse steel is kept relatively small beause the onrete is onined mainly by arhing between the spiral or hoops. Hene, i the vertial spaing is too large, a signiiant depth o unonined onrete will penetrate into the onrete ore between the spirals or hoops. This essentially redues the eetiveness o the onined onrete ore setion Applied Tehnology Counil-32 (1996) The ATC-32 equation ranks as the most inluential equation due to the transverse reinorement requirement with respet to the previously disussed ode equations. Figure 3.1 and Figure 3.2 portray the our design equations o interest. Figures 3.1 and 3.2, respetively, provide spiral requirements or a 14-inh square prestressed pile and a 16-inh otagonal prestressed pile with = 8000 psi, yh = 60 ksi, and a 2 inhes o over. In these igures, the ATC-32 equation provides the minimum amount o transverse reinorement in omparison to the other equations o interest. Furthermore, this equation is widely used in

66 56 seismi design o bridge olumns in the United States and targets a urvature dutility o 13 with the antiipation o having 50 perent more reserve apaity beyond the target value (ATC, 1996). The tolerable enter-to-enter spaing o the transverse steel is limited by the smallest o the ollowing: 1. one bar diameter; /3 times the maximum size o the oarse aggregate; or 3. one inh PCI Reommended Pratie (1993) The equation that is provided in the PCI Reommended Pratie ode requires relatively high amounts o transverse reinorement when ompared to the ATC-32 equation. This requirement is speiially neessary in highly dutile regions, and not over the entire length o the pile. The PCI reommended equation is o importane as this provides the urrent industry pratie or designing transverse reinorement or preast, prestressed piles in high seismi regions. The PCI equation is inluded in Figures 3.1 and 3.2 to give its relation to the other equations o interest.

67 ρs (Volumetri Ratio) ACI 318, 2005 ATC-32, 1996 PCI, 1993 NZS, P/ A g (Axial Load Ratio) Figure 3.1. Spiral volumetri ratio o the equations o interest or a 14-inh square pile ρs (Volumetri Ratio) ACI 318, 2005 ATC-32, 1996 PCI, 1993 NZS, P/ A g (Axial Load Ratio) Figure 3.2. Spiral volumetri ratio o the equations o interest or a 16-inh otagonal pile

68 Proess o Development The proess o development o a new equation began with the ATC-32 oninement equation as the basis, whih is reprodued below or onveniene. ρ s 0.16 P e yh A = l g ( ρ 0.01) (Eq. 3.6) Several modiiations to the above equation were investigated in order to better adapt this equation to prestressed onrete piles. These modiiations and the initially reommended equation are presented in the subsequent setions Modiiations to the Base Equation In examining the ATC-32 equation and assuming ρ l = ρ ρ, where ρρ is the ratio o prestressed reinorement, it beame apparent the 0.13( ρ 0.01) l term will introdue a negative value sine ρl values in onrete piles are typially less than Hene, it was deided that the ( ρ 0.01) l term should not be inluded in the oninement equation required or prestressed piles. As mentioned in Setion 3.2.1, the ACI equation was o interest beause o the minimum bound o the equation, provided here or onveniene. ρ s 0.12 yh (Eq. 3.7) An objetive in the development o the ISU equation was to embed the minimum bound o the ACI equation, so that when the applied axial load, P, is equal to zero, the resulting requirement or the transverse reinorement would be the minimum amount o transverse

69 59 reinorement required by ACI To ahieve this objetive, the onstant 0.5 in the ATC-32 equation was altered suh the new onstant times the ator 0.16 would yield Hene, or 0.16* x = 0.12 x = 0.75 Thereore, in addition to dropping the ( ρ 0.01) l term, the seond modiiation needed in the ATC-32 equation was to replae the onstant 0.5 with The axial load, P, was the next parameter that was studied in urther detail. The ATC-32 equation onsiders the axial load to be the applied axial load. In the ase o prestressed onrete setions, an additional ompressive load is introdued through pretensioning o the piles. Priestley et al., (1992), suggests that or prestressed onrete piles, the axial load term within the ATC-32 equation should be altered to P = P e + p A g, where P e and p and A g are the externally applied axial load, the prestressing ore and the rosssetional area o the pile setion, respetively. Investigation o the parameter P, urther disussed in a later setion in this hapter (i.e., Setion 3.4.1), revealed that the axial load parameter in the oninement equation should not inlude the p A g term, unlike Eqs and The inal modiiation to the ATC-32 equation began with an examination o the parameter A g. A modiiation to this parameter was neessary beause the transverse reinorement is to onine the ore area and not the gross area. Consequently, the inal modiiation to the ATC-32 equation was to replae the parameter A g with A h, to rationalize the oninement equation.

70 Preliminary Equation Taking the above modiiations into aount, Eq. 3.8 was established as a preliminary equation to determine the minimum transverse reinorement required or prestressed onrete piles subjeted to a range o axial loads in high seismi regions. ρ s = 0.16 yh P A h (Eq. 3.8) The requirement rom the above equation is plotted against the previously disussed equations o interest in Figures 3.3 and 3.4. These igures provide spiral reinorement requirements or a 16-inh and a 24-inh otagonal pile, with 2 inhes o over onrete. = 8000 psi, yh = 60 ksi, and ρs (Volumetri Ratio) ACI 318, 2005 ISU, Preliminary NZS, 2006 PCI, ATC-32, P/ A g (Axial Load Ratio) Figure 3.3. Comparison o spiral volumetri reinorement requirement or a 16-inh otagonal pile with the preliminary equation

71 ρs (Volumetri Ratio) ACI 318, 2005 ATC-32, 1996 ISU, Preliminary NZS, 2006 PCI, P/ A g (Axial Load Ratio) Figure 3.4. Comparison o spiral volumetri reinorement requirement or a 24-inh otagonal pile with the preliminary equation From Figures 3.3 and 3.4, it is observed that the preliminary equation and the PCI equation require similar amounts o oninement reinorement or the 16-inh otagonal pile. However, these requirements dier by a ator o 1.5 or the 24-inh otagonal pile. For both examples, the ATC-32 requirements are as muh as 43 perent lower than the requirements aording to Eq. 3.8 or the 16-inh otagonal setion and 34 perent lower than the requirements or the 24-inh otagonal setion. 3.3 Moment-Curvature Analyses To determine the urvature dutility apaity o a setion, it is neessary to perorm a moment-urvature analysis. There are several programs available to perorm suh an

72 62 analysis; however, only a ew o them are suitable or analyzing prestressed onrete setions. Two suh programs were seleted or perorming moment-urvature analyses in this projet: ANDRIANNA (Dowell, 2002) and OpenSees (Mazzoni et al., 2004). These programs are disussed in the subsequent setions, ollowed by disussion on idealization o the moment-urvature response o prestressed pile setions ANDRIANNA ANDRIANNA is intended to be used as a tool or eiiently analyzing reinored and prestressed onrete setions under monotoni loading (Dowell, 2002). As a userriendly program, the input proess or ANDRIANNA is airly straightorward. ANDRIANNA has the apabilities to analyze reinored onrete as well as prestressed onrete setions. The program is omposed o two FORTRAN modules: the GEOmetry pre-proessor and the MONOtoni analysis tool. The GEO module allows a detailed setion to be deined, while the MONO module perorms the monotoni moment-urvature analysis o the setion deined in the GEO module. The GEO module allows a user to deine a detailed setion with a minimal amount o input. It ontains the apabilities to deine setion holes, onined onrete regions as well as holes within the onined regions. Longitudinal reinorement an be lassiied as a straight pattern or a irular pattern, and prestressing strands an be presribed individually, with an appropriate initial stress or eah strand. The MONO module takes the setion desribed in the GEO module and perorms a moment-urvature analysis. In this proess, any external axial load is taken into aount, as well as deinitions o the key properties o materials that make up the setion. The material

73 63 behavior an be viewed graphially to ensure auray o the input data. The stress-strain urves o both the unonined and onined onrete ollow the model reommended by Mander et al. (1988), while the stress-strain urve o the prestressing strand is based on the Menegotto-Pinto model (1973). The eet o oninement may be deined as: 1. volumetri ratios o the transverse oninement reinorement in the two prinipal diretions; or 2. onining stress and ultimate ompressive strain apaity in the two prinipal diretions. A shortoming to the program is that the maximum number o ibers that an be used to disretize the setion is 30. Thereore this limitation led to the investigation o the program OpenSees or onduting the moment-urvature analyses o prestressed pile setions OpenSees OpenSees, an aronym or Open System or Earthquake Engineering Simulation, is a sotware ramework that allows users to simulate the seismi response o both strutural and geotehnial systems (Mazzoni et al., 2004). OpenSees aims to improve the modeling and omputational simulation through ommunity input, and is thus ontinually developing. The apabilities o this sotware inlude modeling and analyzing the non-linear response o systems. In OpenSees, moment-urvature analyses are perormed as an inremental analysis on a zero length setion, deined by two nodes, both loated at (0.0, 0.0). The zero-length setion is deined using a iber-based approah, whih is outlined below, together with the analysis approah or a prestressed pile setion.

74 64 Identiy a set o key points that will deine the setion o the pile Create the nodes or the model Create the models or materials represented in the setion and assign eah region o the setion with the orresponding material model (i.e., onined onrete, unonined onrete, prestress strands, et.) Deine the element type to be utilized Deine the external axial load and set the analysis parameters OpenSees allows setions to be deined by either irles or polygons, or a ombination o the two. The otagonal pile setions were thus deined in a ashion similar to that shown in Figure 3.5, while the square setions were deined as illustrated in Figure 3.6. Beause OpenSees was eventually used or perorming the moment-urvature analyses in this report beause o its superior apabilities, the ollowing setions in this hapter inlude a thorough disussion o the material models used or haraterizing the onined and unonined onrete, and the prestress strands.

75 65 Loation o prestressing strands Points deining the setion Figure 3.5. Deinition o an otagonal pile setion in OpenSees Loation o prestressing strands Points deining the setion Figure 3.6. Deinition o a square pile setion in OpenSees

76 Conined and Unonined Conrete Material Model The onrete material model that was utilized or the moment-urvature analyses in OpenSees was Conrete06 uniaxial material model. Implemented by Waugh (2007), this material model ollows the reommendations o Chang and Mander (1994) with simpliiation or unloading and reloading hystereti rules. The model takes eight input parameters to deine the monotoni envelope, shown in Figure 3.7. The input is provided in the ollowing orm: uniaxialmaterial Conrete06 $mattag $ $ε $E $t $εt $xp $xn $r where $mattag = unique material tag $ = peak ompression stress $ε = strain at peak ompression stress $E = initial elasti modulus o the onrete $t = peak tensile stress $εt = strain at peak tensile stress $xp = non-dimensional strain that determines where the straight line portion begins in tension $xn = non-dimensional strain that determines where the straight line portion beings in ompression $r = parameter that ontrols the desending branh

77 67 Figure 3.7. Monotoni envelope o Chang and Mander (1994) as shown by Waugh (2007) Unonined Conrete For unonined onrete with just a peak strength rom a ylinder test, the reommended values or the above parameters in US ustomary units are as ollows: 0 = unonined ylinder strength (psi) ε 0 = unonined onrete strain at peak ompressive strength ε 0 = (Eq. 3.9a) 3 E = *( ) 8 (psi) (Eq. 3.9b)

78 68 = 7.5* (psi) (Eq. 3.9) t 2 * ε t = E t (Eq. 3.9d) x p x n = 2 = 30 (reommended by Waugh) (reommended by Waugh) r = (Eq. 3.9e) Conined Conrete Coninement inreases the strength and the dutility o onrete. To aount or these eets, the peak strength and the strain at the peak strength must be inreased, while the value o r must be dereased. The onined onrete strength an be alulated based on the ollowing equation: = (1 + k * x ) (Eq. 3.10) 0 * 1 where = peak onrete strength o onined onrete 0 = unonined peak onrete strength k = A * B * x (Eq. 3.11a) x = (Eq. 3.11b) 2 0 where, 11 and 12 = maximum lateral oninement pressures in the two orthogonal diretions 4.989r ( r) e A = (Eq. 3.11)

79 69 B = 5 A ε r ( e ) ( 5k * ) = ε x 3 ( ) 8 E = * (Eq. 3.11d) (Eq. 3.11e) (Eq. 3.11) x n = 30 (reommended by Waugh) The ultimate strain apaity and the orresponding strength o the onrete are deined in Conrete06 using the reommendation o Mander et al. (1988). Aordingly, ε u 1.4* ρ * * ε = 2* ε + (Eq. 3.12) x yh su 0 E se = (Eq. 3.13) ε r = E E E se (Eq. 3.14) u = ε u * * r ε ε u r 1+ ε r (Eq. 3.15) The simplest way to determine u is to alulate the ultimate strain and stress rom Eq and Eq. 3.15, and then iterate on r using Eq This iteration requires the use o an equation solver or the ommand goal seek in EXCEL. It is possible to solve or r in a losed orm; however, the resulting equation is very ompliated and harder to use than

80 70 solving iteratively or r (Waugh, 2007). The values o r or this study ranged rom 1.3 to u = ε u n * ε ε u r ε ε u 1 + n + r 1 ε r 1 r (Eq. 3.16) n = E * ε (Eq. 3.17) Material Model or Prestressing Strands The prestressing strands in pile setions were modeled using two uniaxial material objets, whih represent the uniaxial stress-strain relationships. The speii ommands that were utilized or the moment-urvature analyses o the pile setions were the elastiperetly-plasti uniaxial material objet and elasti-peretly-plasti gap uniaxial material objet. The input o the elasti peretly-plasti uniaxial material model is in the ollowing orm: uniaxialmaterial ElastiPP $mattag $E $epsyp <$epsyn $eps0> where $mattag = unique material objet integer tag $E = tangent $epsyp = strain or deormation at whih material reahes plasti state in tension

81 71 $epsyn = strain at whih material reahes plasti state in ompression (optional, deault: tension value) $eps0 = initial strain (optional, deault: zero) Figure 3.8 provides a graphial view o the input parameters or the elasti peretly-plasti uniaxial material objet. Stress $E $epsn $eps0 $epsp Strain Figure 3.8. Input parameters required or an elasti-peretly-plasti uniaxial material objet in OpenSees (Mazzoni et al., 2004) The input o the elasti peretly-plasti gap uniaxial material model is in the ollowing orm: uniaxialmaterial ElastiPPGap $mattag $E $Fy $gap where $mattag = unique material objet integer tag $E = tangent stiness

82 72 $Fy = stress or ore at whih material reahes plasti state $gap = initial gap (strain or deormation) It should be noted that in order to reate a ompression-only gap element, NEGATIVE values need to be speiied or $Fy and $gap. Figure 3.9 provides a graphial view o the expeted material behavior and the input parameters needed or a tension gap, while Figure 3.10 provides the same inormation or a ompression gap. Appendix C ontains a sample input used or a moment-urvature analysis that was perormed in OpenSees. Stress $F y $E $gap Strain Figure 3.9. Input parameters required or an elasti-peretly-plasti tension gap uniaxial material objet (Mazzoni et al., 2004)

83 73 Stress $gap (negative value) $E Strain $F y (negative value) Figure Input parameters needed or an elasti-peretly-plasti ompression gap uniaxial material objet (Mazzoni et al., 2004) Analysis was onduted to veriy the results o the two programs. A 16-inh otagonal setion, with = 6000 psi, p = 700 psi, and an axial load ratio o 0.2 was analyzed using ANDRIANNA and OpenSees. The moment-urvature responses o both analyses are plotted in Figure 3.11.

84 ANDRIANNA 5000 Moment, kip-in OpenSees Curvature, in -1 Figure Moment-urvature response omparing ANDRIANNA and OpenSees With airly similar behavior onirming the auray o both programs, OpenSees was hosen or onduting the analyses in this projet or the ollowing reasons: it oers more ontrol related to the iber size; it ontains more support avenues, as it is a program that is onstantly being developed; and it oers a variety o material models that are advantageous or veriying the behavior o given materials Moment-Curvature Idealization A moment-urvature response may be better idealized using a bi-linear approximation (Priestley et al., 1996), although an elasti peretly-plasti approximation has been

85 75 suggested in some douments (i.e., Caltrans, 2004). This idealization is neessary to determine the yield and ultimate urvatures so that the urvature dutility apaity o a onrete setion an be deined. In order to idealize a moment-urvature response, some key moments and the orresponding urvatures must be identiied. These moments inlude the irst yield moment, the ultimate moment, and the nominal moment o the ross setion o a member. Deining these moments and orresponding urvatures onsistently is o paramount importane so that the eets o various parameters on urvature dutility apaity an be adequately studied. These key moments and urvatures an be easily identiied in reinored onrete setions, in whih the irst yield ondition is typially deined by the irst yielding o the mild steel reinorement. However, there are several hallenges involved in deining the idealized moment-urvature response o prestressed setions, espeially piles that are detailed with only prestressing steel and large over onrete. Due to the limited inormation on idealization o prestressed onrete piles in literature, several dierent options or idealizing moment-urvature responses o prestressed onrete piles were explored. The ollowing subsetions present details o the inalized idealization along with the hallenges that were assoiated with this proess First Yield Moment A bi-linear idealization should have an elasti portion, ollowed by a plasti portion. For prestressed onrete setions, the irst yield moment annot be related to the yielding o the longitudinal reinorement or two reasons: 1. the yielding o prestressing steels is not well deined (Naaman, 2004);

86 76 2. the non-linearity in a prestressed setion is typially initiated by the non-linear response o onrete as demonstrated in Figure Bending Moment, kip-in Prestressing Strand Strain Point o initial non-linear behavior Conrete Strain Strains, in./in. Figure Conrete and prestress steel strains versus moment or a 16-inh prestressed onrete otagonal pile setion Thereore, the irst yield moment or prestressed onrete piles is deined using a onrete strain o in/in, whih is the strain assoiated with the initial non-linear behavior o onrete, as illustrated in Figure The irst yield urvature, φ y, is thus equal to the urvature orresponding to a onrete strain value o in./in. or the irst yield moment Ultimate Moment Using the inormation ound in the literature, the ultimate moment was haraterized by one o the ollowing three onditions, whihever ours irst:

87 77 1. the ultimate moment is equal to 80 perent o the peak moment resistane o the setion; 2. the moment orresponding to the irst ourrene o a strain o 0.04 in./in. in a prestressing strand; 3. the moment assoiated with a strain in the extreme ompression iber o the ore onrete equal to the ultimate onrete strain o ε u, deined by Eq In all o the analyses perormed as part o this study, the ultimate moment was ontrolled by the third ondition Nominal Moment For normal reinored onrete setions, the nominal moment apaity is deined as the moment assoiated with the strain in the extreme onrete ompressive iber equal to a value o in./in. or the strain in the longitudinal reinorement equal to a value o in/in, whihever ours irst (Priestley et al., 1996). Using this inormation, the yield urvature is ound by extrapolating the elasti portion o the idealized urve (i.e., by a line extending rom the origin to the point deining the irst yield) to the nominal moment apaity, whih an be expressed as ollows: M φ y = φ y (Eq. 3.18) M n y where φ y = yield urvature M n = nominal moment apaity M y = irst yield moment φ y = irst yield urvature

88 78 Figure 3.13 portrays a moment-urvature relationship or a normal onrete setion and identiies the irst yield moment, irst yield urvature, nominal moment apaity, and yield urvature as deined by Eq M n Moment, kip-in M y Atual Idealized = 4000 ksi ρ l = 0.02 ρ s = φ φ y 0 y Curvature, in -1 Figure Moment-urvature response or a normal onrete setion and idealized response The moment-urvature responses o prestressed onrete pile setions have somewhat unique harateristis. An example o this response is shown in Figures 3.14a, 3.14b, and 3.14, in whih it is seen that a large dip in the moment value ollows the irst peak due to spalling o the over onrete that initiates as the extreme over onrete reahes a strain o φu approximately in./in. The prestressed onrete piles represented in Figures 3.14a, 3.14b, and 3.14 have the ollowing harateristis: axial load ratio o 0.2, o 6000 psi, and p o 1100 psi. Furthermore, it is noted that the pile setions typially have no mild steel reinorement and thus using a steel strain o is meaningless. With this in mind, deining the nominal moment apaity using a onrete strain o in./in. or a strain value

89 79 in extreme prestressing stand was investigated. However, neither o these deinitions provided satisatory idealized responses or the moment-urvature response o prestressed pile setions. Consequently, an alternative deinition was established or the idealized moment-urvature o these pile setions Maximum moment 2000 Ultimate moment Moment, kip-in First yield moment Minimum moment Curvature, in -1 Figure 3.14a. Moment-urvature response o a 16-inh otagonal shaped prestressed onrete pile setion

90 Maximum moment Bending Moment, kip-in First yield moment Minimum moment Ultimate moment Curvature, in -1 Figure 3.14b. Moment-urvature response o a 24-inh otagonal shaped prestressed onrete pile setion Maximum moment Bending Moment, kip-in First yield moment Minimum moment Ultimate moment Curvature, in -1 Figure 3.14a. Moment-urvature response o a 14-inh square shaped prestressed onrete pile setion

91 81 With the presene o the dip in the moment-urvature relationship (see Figure 3.14), the seond line in the bi-linear idealization o a prestressed pile setion needed to be deined in a manner that would provide an approximate balane o the areas between the atual and the idealized moment-urvature urves, beyond the irst yield point. O the dierent options onsidered, the average o the maximum moment and the minimum moment that ourred between the irst yield moment and the ultimate moment was ound to be reasonably onsistent and simple to deine the nominal moment apaity o prestressed onrete pile setions. Note that the minimum moment would typially our when the over onrete is ompletely rushed, whereas the maximum moment may orrelate with the ultimate moment apaity o the setion. In the remainder o this report, this nominal moment deinition is onsistently used or prestressed pile setions along with Eq to ind the yield urvature. In Figures 3.14a, 3.14b, and 3.14 the idealized response (as per the deinition presented above) is inluded, whih shows a satisatory orrelation between the atual and idealized responses Analysis Variables In the evaluation o the adequay o the oninement reinorement requirements or prestressed pile setions, varying the ollowing variables was onsidered important. p Setion dimensions and shapes Axial load ratio, deined by P e Ag (Eq. 3.19)

92 82 The values that were investigated were 6000 psi, 8000 psi, and psi, while the p were varied in the range rom 700 psi to 0.2. The dierent pile setions that were onsidered or this projet were the 16-inh otagonal pile setion, 24-inh otagonal pile setion, and 14-inh square pile setion. Figure 3.15, 3.16, and 3.17 summarize the dierent analysis ases hosen or evaluation o the preliminary transverse reinorement requirements presented in Eq The setions to ollow disuss in detail the variations used or the axial load ratios.

93 83 Figure Details o dierent pile setions seleted or evaluation o the preliminary oninement equation with equal to 6000 psi and p values o 700 psi, 900 psi, 1100 psi, and 1200 psi

94 84 Figure Details o dierent pile setions seleted or evaluation o the preliminary oninement equation with equal to 8000 psi and p values o 700 psi, 1000 psi, 1300 psi, and 1600 psi

95 85 Figure Details o dierent pile setions seleted or evaluation o the preliminary oninement equation with equal to 10,000 psi and p values o 700 psi, 1200 psi, 1600 psi, and 2000 psi

96 Limits n External Axial Load Ratios Aording to the PCI Design Handbook (2004), the allowable external axial load, N, whih a pile may be subjeted to is desribed in the ollowing orm: ( p ) A g N = 27 (Eq. 3.20) Through rearrangements o the variables in the above equation, the limitations on the axial load ratio were examined as ollows: N Ag p = (Eq. 3.21) The PCI Design Handbook speiies limits on the ompressive stress in the onrete at the entroid o the ross setion due to the prestressing ater losses, p, to a range between 700 psi and 0.2. Assuming = 10,000 psi to estimate the maximum possible axial load ratio, and inserting 700 psi or p into Eq gives: N A g ( 700) = Assuming = ( ( 0.07) ) = 0.28 = 10,000 psi to estimate the maximum possible axial load ratio, and inserting 0.2 times 10,000 psi or p into Eq gives N A g = ( 0.2( 10000) ) = ( ( 0.2) )

97 87 = 0.31 Aordingly, the resulting limit on the external axial load ratio or prestressed piles is 0.28 to Thereore, it appears that prestressed piles summarized in Figures 3.15, 3.16, and 3.17 should not be subjeted to an axial load ratio greater than about 0.3. However, this limitation on the axial load ratio was onsidered irrelevant or two reasons: 1. a rationale or enoring Eq ould not be ound; and 2. preast piles shown in Figures 3.15, 3.16, and 3.17 with axial load ratios larger than 0.28 to 0.31 are used in urrent pratie New Limits on Axial Load Ratios In this report, a new limit or the external axial load ratios is suggested or prestressed piles using two key urvature values: the urvature when rushing initiates in unonined onrete and spalling begins, φ sp, and the urvature orresponding to the raking moment, φ r. The moment at whih the rushing o the unonined onrete begins was deined using a onrete strain o in./in. The raking moment or a prestressed onrete setion is deined using the equation in the PCI Design Handbook (2004) as M r P Pe Sb = S b r M n A S b S b (Eq. 3.22) where S b = setion modulus with respet to the tension iber o the prestressed omposite setion; P = a ombination o the externally applied design load and the prestress ore ater losses;

98 88 A = e = ross-setional area; eentriity o design load or prestressing ore parallel to the axis measured rom the entroid o the setion; S b = r = setion modulus with respet to the bottom iber o the preast setion modulus o rupture o onrete; and M n = moment due to beam sel weight plus dead loads applied beore omposite ation. Several o the terms in the Eq an be eliminated when inding the raking moment o prestressed onrete pile setions. With the assumptions o onentrially applied axial load with the entroid o the pile setion and a uniormly distributed strand pattern, the eentriity term may be eliminated in Eq Furthermore, the moment assoiated with sel weight is also not required exept or the at that the sel weight o the pile may inrease the axial load, whih an be inluded in P. Thereore, the raking moment equation an be redued to M r P + A = Sb r (Eq. 3.23) Upon determination o urvatures at the raking moment and at the moment orresponding to the irst rushing o the over onrete, whih orresponds to a onrete strain o in/in, the dependeny o the moment-urvature response o pile setions on the order in whih these two events ourred was investigated. It beame apparent that i the urvature assoiated with the raking o onrete is less than the urvature assoiated with the spalling o onrete, the moment-urvature response was ound to be dependable with a small dip assoiated with spalling o the over onrete and a dierene o less than about 20

99 89 perent between the idealized moment and the atual resistane at any given urvature, as illustrated in Figure However, i φr is greater than φ sp, as in Figure 3.19, the moment drop due to spalling was signiiant and the dierene between the idealized moment and the atual resistane, at any given urvature, was as high as 80 perent. This behavior, inluened by large axial loads on the piles, was onsidered unaeptable or piles in seismi regions. Thereore, it was onluded that the axial load in prestressed piles should be limited suh that φr will not exeed φ sp ε = Idealized Response ε = ε u Moment, kip-in First rushing o over onrete ( ε = 0.004) ε = Craking 0 φ r φ sp Curvature, in -1 Figure Moment-urvature response showing the ase o otagonal prestressed pile setion with axial load ratio o 0.3, 1300 psi φ r < φ sp or a 24-inh o 8000 psi, and p o

100 ε = ε u Moment, kip-in ε = ε = Idealized Response Craking 4000 First rushing o over onrete ( ε = 0.004) φ r φ sp Curvature, in -1 Figure Moment-urvature response showing the ase o otagonal prestressed pile setion with axial load ratio o 0.6, 1600 psi φ r << φ sp or a 24-inh o psi, and p o 3.4 Improvements to the Preliminary Equation The suitability o the preliminary equation, provided below or onveniene, or quantiying the minimum oninement reinorement was examined by perorming momenturvature analyses on 16-inh and 24-inh otagonal piles, as well as 14-inh square pile setions and estimating their urvature dutility apaities as per Eq. 3.24: ρ s = 0.16 yh P A h (Eq. 3.24) φ φ u µ φ = (Eq. 3.25) y

101 91 The values o φ y and φ u were obtained using the moment-urvature idealization presented in Setion It was observed that the urvature dutility typially inreased as the applied axial load ratio inreased, resulting in a spread o the urvature dutility apaity in the range o 19 to 28 or the otagonal prestressed pile setions. The analysis o the square setion resulted in a urvature dutility range o 12 to 47. It was thus onluded that the dependeny o the preliminary oninement equation on the axial load ratio was too large. With this in mind, the onstant terms o the equation, speiially the 0.16 and the 0.75 were investigated in order to lessen the dependeny o the equation on the axial load ratio. Through a small set o setion analyses, it was determined that the two onstants needed to be replaed by 0.06 and 2.8, respetively. With this hange, the oninement equation an be expressed as ρ s = 0.06 yh 1.25P Ah (Eq. 3.26) In Eq. 3.26, i the axial load on the pile is zero, the minimum amount o transverse reinorement results in ρ s = yh (Eq. 3.27) Eq requires 40 perent greater than what the ACI ode requires as its minimum reinorement. Although this inrease in the minimum requirement o transverse reinorement is neessary to lessen the dependeny o the oninement equation on the axial load, it is noted that the resulting minimum oninement reinorement is generally less than that urrently used in pratie. Furthermore, it is important to realize that the 40 perent inrease in the minimum reinorement orresponds to a 63 perent redution on the equations dependeny on the axial load ratio. Suh a modiiation is expeted to help

102 92 quantiy the oninement reinorement with adequate onsideration to both the lexural ation and the external axial load. As disussed in Setion , the minimum reinorement requirement orresponding to zero axial load is redued to smaller values when the design alls or moderate or low dutility in the prestressed pile setions. Figures 3.20 and 3.21 show the spiral requirements, respetively, or a 14-inh and a 24-inh otagonal pile with = 8000 psi, yh = 60 ksi, and 2 inhes o over onrete. From these igures, it is observed that the modiied equation nearly onsistently requires less oninement reinorement than that stipulated by the preliminary equation. The exeption to this ours or piles with larger setions subjeted to small axial load ratios. Also observed in these igures is that the modiied equation shows less inrease in the oninement reinorement as the axial load inreases. Reall that in omparison to the ATC-32 requirements, the preliminary ISU equation diered as muh as 43 perent lower than the ATC-32 requirements or a 14-inh otagonal setion and 34 perent or a 24-inh otagonal setion. The dierene between the preliminary ISU equation and the ATC-32 equation is approximately 34 perent or the 24-inh otagonal setion, regardless o the axial load ratio. With the modiied ISU equation, the dierene inreases slightly to 37 perent or lower axial load ratios, but is signiiantly redued to 12 perent or higher axial load ratios. These dierenes should not be o a onern as they provide reinorement or dierent mean dutility values as detailed in Setion

103 ρs (Volumetri Ratio) ACI 318, 2005 ISU, Preliminary NZS, 2006 PCI, ATC-32, 1996 ISU, Modiied P/ A g (Axial Load Ratio) Figure Spiral volumetri ratio omparison or a 14-inh otagonal pile with the modiied ISU equation ρs (Volumetri Ratio) ACI 318, 2005 ATC-32, 1996 ISU, Preliminary NZS, PCI, 1993 ISU, Modiied P/ A g Figure Spiral volumetri ratio omparison or a 24-inh otagonal pile with the modiied ISU equation

104 Results o the Otagonal Setions Analyzed by the Modiied Equation The urvature dutility apaity o prestressed pile setions designed aording to Eq was examined or the ases summarized in Figure 3.22, ollowing the riteria established or the irst yield moment, the ultimate moment, and the nominal moment. The extended axial load ratio limitation was utilized throughout the analysis proess. A total o 150 moment-urvature analyses were ompleted on otagonal pile setions. The average dutility obtained rom the analyses was 19.2 with a standard deviation o 1.3. The results o these analyses are presented in tabular orm in Table 3.1 as well as in graphial orm in Figure 3.22.

105 95 Table 3.1. A summary o the urvature dutility apaities obtained rom OpenSees or the otagonal setions using the modiied oninement equation (i.e., Eq. 3.26) Axial Load Ratio inh otagonal pile with = 6000 psi p p x p x p x 16-inh otagonal pile with = 8000 psi p x p x p x p x 16-inh otagonal pile with = psi p x p x p x p x x 24-inh otagonal pile with = 6000 psi p p p p inh otagonal pile with = 8000 psi p p p x p x 24-inh otagonal pile with = psi p x p x p x p x x Not onsidered due to φ r > φ sp **Average = 19.2; Standard Deviation = ±1.3 µ φ

106 µφ (Curvature Dutility Capaity) Standard Deviation 19.2 Average 24" otagonal setion 16" otagonal setion P/ A g (Axial Load Ratio) Figure Curvature dutility apaity o 16-inh and 24-inh prestressed pile setions with oninement reinorement as per Equation 3.26 As seen in these summaries, the urvature dutility apaities o the pile analyzed was in the range o 16.1 to 22.8, with an average value o 19.2 and standard deviations o ±1.3. It is also observed that the 16-inh pile setions show dutility apaities rom 18.5 to 22.8 while the 24-inh pile setion has apaities in the range rom 16.1 to The main reason or the dependeny o the urvature dutility apaity on the seleted pile dimension was attributed to the dierene in the A g /A h value between pile setions. For example, the 24- inh otagonal pile setion has an A g /A h ratio o 1.51, whereas the 16-inh otagonal setion has an A g /A h ratio o The redution in A g /A h value eetively redued the oninement reinorement, resulting in a redution in the urvature dutility apaity. Upon realization o this issue, a inal modiiation was made to the oninement equation as detailed in the ollowing setion.

107 97 In Table 3.1, it is also observed that the initial prestressing has some inluene on the urvature dutility apaity o prestressed pile setions, partiularly at large axial load ratios. However, it was ound that these variations are largely due to inluene o p (the ompressive stress in the onrete at the entroid o the ross setion due to the prestressing ater losses) on the yield urvature ( φ y ) rather than on the ultimate urvature ( φ u ). An attempt to inlude p in the oninement equation led to unneessary onservative amounts o oninement reinorement or piles with lower axial load ratios. Thereore, it was deided not to inlude p in the oninement equation. 3.5 Reommended Coninement Equation It is identiied in the previous setion that the oninement equation should aount or the dierene in A g /A h value. This is beause the oninement reinorement is needed or the ore onrete while the axial load ratios are typially deined using the gross area o the pile setion. Using the 16-inh otagonal pile setion rom previously disussed setions as the basis, beause o its average dutility o approximately 20, it is suggested that Eq be modiied as ollows: ρ s = 1.25P 1. 87A yh Ah Ag 0 h (Eq. 3.28) where 1.87 (or 1 ) is the Ag /A h ratio or the 16-inh otagonal pile setion. Thereore, the 0.53 above equation an be simpliied to ρ s = 0.06 yh 1.25P A g (Eq. 3.29)

108 98 With this modiiation, the oninement equation will require the same amount o spiral reinorement or all pile setions subjeted to the same axial load ratio. Providing the same amount o transverse reinorement will lead to the same value or l, whih in turn ensures the same, and ε u or dierent pile setions. However, the ultimate urvature is ommonly deined as ollows: ε u φ u = (Eq. 3.30) u Sine the distane rom the neutral axis to the extreme ompression iber o eah setion is dierent, the resulting ultimate urvature or dierent pile setions will not be the same. As the pile setion dimension also inluenes the yield urvature, the resulting dutility apaity or the dierent pile setions are expeted to be omparable. The inalized oninement equation proposed or the design o prestressed piles is plotted in Figures 3.23 and 3.24 against the previously disussed equations o interest. Figure 3.23 plots the spiral requirements or a 14-inh otagonal pile with = 8000 psi, yh = 60 ksi, and 2 inhes o over onrete, while Figure 3.24 plots the spiral requirements or a 24-inh otagonal pile with = 8000 psi, yh = 60 ksi, and 2 inhes o over onrete.

109 ρs (Volumetri Ratio) ACI 318, 2005 NZS, 2006 PCI, ATC-32, 1996 ISU, Modiied P/ A g (Axial Load Ratio) Figure Spiral volumetri ratio omparison or a 14-inh otagonal pile with the inalized ISU equation ρs (Volumetri Ratio) ACI 318, 2005 PCI, 1993 NZS, 2006 ISU, Modiied 0.01 ATC-32, P/ A g (Axial Load Ratio) Figure Spiral volumetri ratio omparison or a 24-inh otagonal pile with the inalized ISU equation

110 Veriiation or Otagonal Pile Setions The validity o the oninement equation inalized in Eq was investigated using the various analysis options suggested or otagonal setions in Figures 3.15, 3.16, and 3.17 and the moment-urvature idealization established in Setion The extended axial load ratio limitation as desribed in Setion was utilized throughout the analysis proess. A total o 152 moment-urvature analyses were ompleted, whih resulted in an average dutility o 19.4 and standard deviations o ±1.1. The results o these analyses are presented in tabular orm in Table 3.2, as well as in graphial orm in Figure 3.25.

111 101 Table 3.2. A summary o the urvature dutility apaities obtained rom OpenSees or the otagonal setions using the inalized oninement equation (i.e., Eq. 3.28) Axial Load Ratio inh otagonal pile with = 6000 psi p p x p x p x 16-inh otagonal pile with = 8000 psi p x p x p x p x 16-inh otagonal pile with = psi p x p x p x p x x 24-inh otagonal pile with = 6000 psi p p p p inh otagonal pile with = 8000 psi p p p p x 24-inh otagonal pile with = psi p p x p x p x average x Not onsidered due to φ r > φ sp **Average µ φ = 19.4; Standard Deviation = ±1.1

112 µφ (Curvature Dutility Capaity) Standard Deviation 24" otagonal setion 19.4 Average 16" otagonal setion P/ A g (Axial Load Ratio) Figure Curvature dutility apaity o 16-inh and 24-inh prestressed pile setions with oninement reinorement as per Eq As seen in these summaries, the urvature dutility apaities o the pile analyzed is in the range o 16.6 to It was also observed that the 16-inh pile shows dutility apaities rom 18.5 to 22.8 while the 24-inh pile has apaities rom 16.6 to Although aounting or the dierene in the A g /A h ratio, Eq does not seem to improve the dierenes in the dutility apaity range or these two pile types. The impat on the urvature dutility apaity or the square pile setions are detailed in Setion Inluene o Conrete Strength on Curvature Dutility Capaity Upon investigating the inluene o the onrete strength on the urvature dutility apaity portrayed in Table 3.2, it beame apparent that the onrete strength had little to no eet on the urvature dutility apaity. Figures 3.26 and 3.27 plot the urvature dutility

113 103 apaities alulated or the 16-inh and 24-inh otagonal setions, respetively, against the ompressive strength o the unonined onrete. Notie that regardless o the axial load ratio, the urvature dutility apaities remain airly onstant. This result is not surprising onsidering the eets o the unonined ompressive strength o the onrete were aounted or in the ISU oninement equation. Figures 3.28 and 3.29 plot the urvature dutility apaities alulated or the 16-inh and 24-inh otagonal setions, respetively, against the ompressive stress in the onrete at the entroid o the ross setion due to prestress (ater losses). From these igures, it is observed that there is no apparent trend aused by the hange in p. 25 µ φ (Curvature Dutility Capaity) (psi) Trend Lines 0.2 Axial Load Ratio 0.25 Axial Load Ratio 0.3 Axial Load Ratio 0.35 Axial Load Ratio 0.4 Axial Load Ratio 0.45 Axial Load Ratio Figure Inluene o the onrete strength on the urvature dutility apaity or a 16-inh otagonal setion

114 µ φ (Curvature Dutility Capaity) (psi) Trend Lines 0.2 Axial Load Ratio 0.25 Axial Load Ratio 0.3 Axial Load Ratio 0.35 Axial Load Ratio 0.4 Axial Load Ratio 0.45 Axial Load Ratio 0.5 Axial Load Ratio Figure Inluene o the onrete strength on the urvature dutility apaity or a 24-inh otagonal setion 23 µφ (Curvature Dutility Capaity) p (psi) Trend Lines 0.2 Axial Load Ratio 0.25 Axial Load Ratio 0.3 Axial Load Ratio 0.35 Axial Load Ratio 0.4 Axial Load Ratio 0.45 Axial Load Ratio Figure Inluene o p on the urvature dutility apaity or a 16-inh otagonal setion

115 µ φ (Curvature Dutility Capaity) p (psi) Trend Lines 0.2 Axial Load Ratio 0.25 Axial Load Ratio 0.3 Axial Load Ratio 0.35 Axial Load Ratio 0.4 Axial Load Ratio 0.45 Axial Load Ratio Figure Inluene o p on the urvature dutility apaity or a 24-inh otagonal setion 3.7 Veriiation or Square Pile Setions The solid square is a widely used setion in the preast, prestressed industry. Chapter 2 provides details o various square setions being utilized in urrent pratie. With the preliminary oninement equation, the 14-inh square setion, produed a wide range o urvature dutility apaities in the range between 12 and 47 (Setion 3.4). With the modiied equation, the dutility range or the 14-inh square setion was ound to be large, reahing values as high as 28. With the inalized oninement equation, the urvature dutility apaities o this pile setion improved to a range rom 19.5 and However, several other onerns regarding the square prestressed pile setions emerged. From the moment-urvature response o dierent pile setions with, p, and axial load ratios as main variables, it was observed that the strength drop due to the spalling o over onrete

116 106 beame signiiant that the untionability o the pile beame a question o unertainty. Being a ommonly used pile type or bridges and buildings, the unertainty o the square setion is o utmost importane. With these onerns, the reommendations regarding the square setion are presented in Chapter 5. Further modiiations to the oninement equation were investigated using, p, and axial load ratios as variables, but an additional redution in the range o urvature dutility values or square prestressed pile setions was unable to be ahieved. This lak inability to redue the range o the urvature dutility values results rom the large area o onrete being spalled. The gross area o the square setion o interest is 196 in 2 and the orresponding ore is in 2. This redution in area upon the spalling o the unonined onrete dereases the setion by approximately 60 perent. With this redution in area, the moment-urvature response results in a large drop. Figure 3.26 provides an example o the moment-urvature relationship or an analyzed 14-inh square setion with an axial load ratio o only 0.2.

117 ε = Idealized Response Moment, kip-in Spalling ε = ε u 500 Craking Curvature, in -1 Figure Moment-urvature relationship or a 14-inh square setion with 6000 psi, p o 1200 psi, and a 0.2 axial load ratio o With the inormation in the preeding paragraphs, the ollowing limitation was plaed on the analysis o square setions: when the drop in the moment-urvature relationship exeeded 40 perent o the maximum moment, the analyses o a given square setion were ompleted. Figure 3.31 provides the urvature dutility apaity results o the analysis perormed on the 14-inh square setion while onining the setion with the ISU equation. Table 3.6 provides a tabular orm o the results, both taking the above limitation into aount. The average o the urvature dutility or the 14-inh square setion was 22.7 with standard deviations o ±2.5.

118 µ φ (Curvature Dutility Capaity) Standard Deviation 22.7 Average P/ A g (Axial Load Ratio) Figure Curvature dutility apaity o 14-inh prestressed pile setion with oninement reinorement as per Eq. 3.42

119 109 Table 3.3. A summary o urvature dutility apaities obtained rom OpenSees or the square setion using the inalized oninement equation (i.e., Eq. 3.42) inh square pile with = 6000 psi p x x x x x x x p x x x x x x x p x x x x x x x p x x x x x x x 14-inh square pile with = 8000 psi p x x x x x x x x p x x x x x x x x p x x x x x x x x p x x x x x x x x 14-inh square pile with = psi p x x x x x x x x p-1200 x x x x x x x x x p-1600 x x x x x x x x x p-2000 x x x x x x x x x x Not analyzed due to established limitiations; Average = 22.7 ; Standard Deviation = ±2.5 µ φ 3.8 Integration o µ φ in the Coninement Equation The inal parameter that was to be inluded in the ISU equation was the urvature dutility demand. From the observations made rom the inluene o the onrete strength and the axial load on the urvature dutility apaities, it beame evident that inluding the urvature dutility demand term in the orm o µ φ onstant within the ISU equation would be suiient and simple. In order to determine the plaement o this ratio, the oninement reinorement was plotted versus the urvature dutility apaity and the relationship was observed. In general, the relationship between the oninement reinorement and the urvature dutility apaity was linear. A sample o this plot is provided in Figure 3.32,

120 110 whih plots the oninement reinorement o a 16-inh otagonal setion versus its orresponding urvature dutility apaity. Thus, the ratio was inluded outside the parenthesis ontaining the axial load ratio µ φ (Curvature Dutility Capaity) ρ s (Volumetri Ratio) Figure Relationship between the oninement reinorement o a 16-inh otagonal setion and the orresponding urvature dutility over axial load ratios ranging rom 0.2 to 0.4 The onstant within the ratio was determined using the average value o the urvature dutility and the alulated standard deviation. Beause o the onerns regarding the square setion, only values orm the otagonal setions were utilized in determining the onstant. The average o the urvature dutility apaities o the otagonal setions was 19.4 with standard deviations o ±1.1. The onstant within the ratio was alulated by subtrating the standard deviation rom the average and rounding it to the nearest whole number. The

121 111 resulting value was 18. Hene, the urvature dutility demand term was inluded in the equation in the ollowing manner: ρ or s = µ + φ 1.25P 1. 87A yh 18 Ah Ag 0 h (Eq. 3.31a) ρ s = 0.06 yh µ + φ 1.25P A g (Eq. 3.31b) It is expeted that the ISU equation, as written above, will ensure a urvature dutility apaity o the value seleted or µ φ. To prove this at, Eq was analyzed or urvature dutility demand values o 6 and 12. Figure 3.27 plots the results rom this investigation when examined with a urvature dutility demand o 12 and Figure 3.28 graphs the results o the equation when examined with a urvature dutility demand o 6. Notie in eah igure that the urvature dutility demands o 6 and 12 are always attained.

122 µ φ (Curvature Dutility Capaity) " otagonal setion 24" otagonal setion P/ A g (Axial Load Ratio) Figure Analysis results o prestressed pile setions that used the ISU equation with a urvature dutility demand o µ φ (Curvature Dutility Capaity) " otagonal setion 24" otagonal setion P/ A g (Axial Load Ratio) Figure Analysis results o prestressed pile setions that used the ISU equation with a urvature dutility demand o 6

123 113 CHAPTER 4. ANALYSIS OF PILES UNDER LATERAL LOADS TO ESTABLISH DISPLACEMENT LIMITS 4.1 Introdution Chapter 3 provided results rom over 200 moment-urvature analyses perormed on otagonal and square pile setions that were onined with the reinorement reommended by the newly developed equation (Eq. 3.28). The ompressive strength o unonined onrete, the ompressive stress in the onrete gross setion due to prestress (ater losses), and the axial load ratio were the primary variables in these analyses. The seismi design approah, disussed in Setion 1.4 o this report, indiates that the urrent odes all or piles in pile-supported ootings to be designed with the intent that the piles will not experiene signiiant inelasti ations unless piles are extended above ground to diretly support the superstruture. With this in mind, the urvature apaities that were established in Chapter 3 through the moment-urvature analyses were used to perorm a set o lateral load analyses to determine the ombined inluene o the oninement and soil type on the lateral displaement limits o the pile, thereby aounting or inluene o soil types on preast, prestressed pile behavior. 4.2 Objetive The lateral load analyses aimed to establish permissible limits o lateral displaements or preast, prestressed piles in dierent soil onditions by utilizing the urvature apaities reported in Chapter 3. The permissible limit eventually deines the

124 114 displaement that a speii pile, in a given soil, an undergo prior to experiening ailure in aordane with the oninement requirement o Eq Through these analyses, it is intended to provide designers with a design proess that ensures design o oninement reinorement in piles onsistent with the assumptions made or the design o olumns and superstruture in aordane with the apaity design priniples. 4.3 Overall Design Proess In the urrent design pratie, there is a disonnet in that the expeted perormane o pile supported ootings is not integrated into the design o struture above the ground level, whih is expeted to undergo inelasti response under design-level earthquakes. Despite the assumption that piles should remain elasti during an earthquake response, piles in a pile-supported ooting an experiene some inelasti ations. Consequently, the struture above ground will not experiene the expeted level o inelasti response, thus aeting the energy dissipation ability o the struture. Thereore, it is important to integrate the expeted pile oundation displaement in the overall design o the superstruture. With this in mind, an overall seismi design proess that integrates the expeted oundation displaement is presented in Figure 4.1, whih involves the ollowing steps: 1. Deine pile properties: length, ross-setional dimensions, reinorement details, moment o inertia, setion area, modulus o elastiity, moment-urvature relationship that inludes the eet o oninement reinorement, and the external loading. 2. Deine soil proile and appropriate properties, taking into aount the variability o the average undrained shear strength, the strain at 50 perent o the ultimate shear stress o the soil, and the initial modulus o subgrade reation.

125 Deine the pile head onditions. 4. Deine the target displaement and the permissible displaement, where the target displaement reers to the desired displaement by the designer and the permissible displaement reers to the lateral displaement limit that the pile an sustain without ailure. This limit should be established aounting or the oninement reinorement, pile head boundary ondition, and the soil surrounding the pile. 5a. I the target and permissible displaements are the same, provide the ritial pile region with oninement as per Eq b. I the target and permissible displaements are dierent, provide the ritial pile region with oninement as per Eq. 3.31b. 6. Deine the dutility o the strutural system, inluding the eet o the target displaement o the pile supported ooting. 6. Complete the design o the struture above ground level, ensuring that the oundation displaement will never exeed the target displaement.

126 116 Deine Pile Properties Length Diameter Moment o Inertia Area Modulus o Elastiity M vs. EI External Loading Deine Soil Properties Considering Variability o Shear Strength Clay: Eetive Unit Weight Undrained Shear Strength 50% Strain, ε 50 Sand: Eetive Unit Weight Frition Angle Initial Modulus o Subgrade Reation, k Deine Pile Head Conditions: Fixed Pinned Partially Fixed Deine target and permissible No target = permissible Yes Determine Curvature Dutility Corresponding to target ρ s Determine Neessary Coninement µ φ 1.25P = P ρs = y A y g 0.53 Ag Determine µ system using target µ system u + = + y target target Complete the design o the struture above ground suh that oundation Figure 4.1. Proposed design proess integrating the expeted pile oundation displaement in the overall seismi design o the struture > target

127 Soil-Pile Interation Analyses The lateral load behavior o a pile oundation and its lateral displaement apaity are ditated by its strutural properties, pile head ixity, and the stiness and strength o the soil surrounding the upper portion o the pile and o the soil in the viinity o the pile ap (i the oundation inludes a pile ap). These variables determine the distribution o the soil reation along the pile length, inluening its resistane to lateral loads and the orresponding lateral deletion or a given lateral ore. To study the lateral load behavior o piles in dierent soil onditions and establish their permissible displaements, LPILE Plus Version 5.0 (Ensot, In. 2004) was utilized. The ollowing setion gives a general desription o the LPILE program. Subsequent setions provide a brie desription o the theory used in LPILE, general apabilities o LPILE, and onlude with the results rom the LPILE analysis pertaining to the urrent study. 4.5 LPILE LPILE is a ommerial program that inludes the apability to analyze a pile subjeted to lateral loading by treating it as a beam on an elasti oundation. The soil behavior in LPILE is modeled with nonlinear springs with presribed load-deletion urves, known as p-y urves, whih are internally generated by the omputer program based on soil type and key properties or ould be entered by the user. The p-y urves o various soil types in LPILE ollow published reommendations available in the literature and are disussed in detail later in this setion. The nonlinear behavior o a pile an be aommodated in LPILE by deining the moment-urvature response o the pile setions at appropriate plaes. For a given problem with appropriate boundary onditions, LPILE an analyze the response o a

128 118 pile under monotoni loading and produe deletion, shear, bending moment, and soil response along the pile length Solution Proess Figure 4.1 shematially shows a model or a laterally loaded pile inluding the p-y urves that represent the nonlinear behavior o the soil. P x P t M t y p p p p p y y y y x y (a) (b) () Figure 4.2. LPILE model o laterally loaded pile o soil response (a) Shemati proile o a pile embedded in soil, (b) Strutural idealization or the pile-soil interation, and () lateral spring ore-displaement relationship (Ensot, In. 2004) The standard beam-olumn equation an be used to determine the deormation o a pile subjeted to axial and lateral loads. This equation is expressed as d dx d y d y E + = p I p Px p W (Eq. 4.1) dx dx where P x = axial load on the pile (ore),

129 119 y = lateral deletion o the pile at point x along the length o the pile (length), p = W = soil resistane per unit length (ore/length), distributed load due to external loading along the length o the pile (ore/length); and E I = lexural rigidity o the pile p p (ore*length2 ). The soil resistane, p i, at any loation, i, along the pile depends on the state o the lateral displaement o the pile, y i, through the ollowing equation: p = E y (Eq. 4.2) i s i where E s = the soil modulus (ore/length 2 ) LPILE uses the inite dierene method to develop a solution o the dierential equation shown in Eq In the inite dierene method, the pile is divided into several segments with equal lengths that are reerred to as beam elements. Figure 4.2 shows an undeormed and deormed pile that is subdivided into segments. Eq. 4.1 an be expressed in the ollowing orm: y y Rm 1 + ym 1( 2Rm 1 2Rm + Qh ) + ym ( R m 1+ 4Rm + Rm+ 1 Qh + kmh )+ 2 4 ( 2R 2R + Qh ) + y R W 0 (Eq. 4.3) m 2 2 m+ 1 m m+ 1 m+ 2 m+ 1 mh = where R m = E m I m (lexural rigidity o pile at point m); and k m = E sm

130 120 y h h h h y m+2 y m+1 y m y m-1 y m-2 x Figure 4.3. Subdivided pile model as used in LPILE or the inite dierene solution The relations needed to alulate the slope, urvature, shear, and load are shown below. dy dx ym 1 ym+1 = (Eq. 4.4) 2h + 2 d y 2 dx 3 d y 3 dx 4 d y 4 dx ym 1 2 ym + ym+ 1 = (Eq. 4.5) 2 h ym 2 + 2ym 1 2 ym+ 1 + ym+ 2 = (Eq. 4.6) 3 2h ym 2 4ym 1 + 6ym 4ym+ 1 + ym+ 2 = (Eq. 4.7) 4 h To alulate the moment and shear within eah element, the lexural rigidity, E p I p, is needed. However in onrete piles, the lexural rigidity hanges aording to the state o deormation within eah element, thus induing a non-linear eet on the pile. LPILE has the apabilities

131 121 to aount or the non-linear behavior o eah element aording to a user-speiied momenturvature relationship. For the above equations, LPILE uses the ollowing steps to ind the solution or a presribed lateral load or displaement. A set o p-y urves are internally generated along the length o the pile or the seleted soil proile. A linear relation is established between the soil resistane, p, to the deletion, y, with the slope o the line representing the soil modulus at the given y. The soil modulus values are established rom eah o the p-y urves that were generated along the pile length. In order to omplete the omputation, LPILE uses the omputed values o the soil modulus and ontinues iterations on the deletion until the dierene in the alulated deletions is less than a speiied tolerane. One the deletions have been omputed, the derivatives o deletions equation an be utilized to ompute the rotation, bending moment, shear, and soil reation as presented in Eqs. 4.3, 4.4, 4.5, and Features o LPILE To aomplish the ompletion o a typial analysis required in the urrent study, the ollowing input are needed: seletion o the analysis type, identiiation o the pile properties, seletion o the loading type, seletion o the boundary onditions, and seletion o the soil surrounding the pile. In addition, a brie list o LPILE eatures relevant to the lateral analysis o piles and how these eatures were used in the urrent study are presented below. As previously noted, a user deined moment-urvature response an be deined or the pile setion, thereby enabling aurate representation o oninement eets in the analysis. This was ahieved by running moment-urvature analyses o the pile

132 122 setions using OpenSees (see Setion 3.3.2) and deining EI as M/φ, where M is the moment output and φ is the orresponding setion urvature. Five sets o boundary onditions are available to model the pile head. Depending on the boundary onditions, the pile-head loading may onsist o a lateral load, a bending moment, a speii lateral displaement, or a speii pile-head rotation. The boundary onditions o interest or this study were a pinned onnetion, a ixed onnetion, and a partially ixed onnetion. By keeping the moment value zero and inrementally hanging the displaement, a pinned onnetion at the pile head was established. By keeping the pile-head rotation zero and inrementally hanging the lateral displaement, a ixed onnetion at the pile head was established. To represent a partially ixed ondition, the slope values that were obtained at the pile top in the pinned ondition were divided by a ator o two to deine the partially ixed head ondition until reahing the yield limit state. For displaements ourring ater the yield limit state, there was no urther inrements to the slope value. Upon seleting the boundary ondition, ten dierent inremental displaement steps may be applied at the pile head or a single analytial run. This enables observation o the pile behavior when subjeted to a speii set o boundary onditions. I provided with basi soil properties, soil-resistane (i.e., p-y urves) urves an be internally generated by the program or 11 dierent types o soil: Sot Clay (Matlok, 1970), Sti Clay with Free Water (Reese, 1975), Sti Clay without Free Water (Reese, 1975), Sand (as reommended by Reese et al., 1974), Vuggy Limestone (Strong Rok), Silt (with ohesion and internal rition angle), API Sand (as reommended by API, 1997), Weak Rok (Reese, 1997), Liqueiable Sand (as

133 123 reommended by Rollins, 2003), and Sti Clay without ree water with speiied initial k. In addition, any user-speiied p-y urve may be utilized to represent the soil in LPILE. For the urrent study, the Sot Clay (Matlok, 1970) and the API Sand (as reommended by API, 1997) were used ater onsultation with Earth Mehanis, In., while varying the eetive unit weight, the average undrained shear strength, the 50 perent strain or the lay and varying eetive unit weight, the rition angle, and the initial modulus o subgrade reation or the sand. In varying the parameters used to deine the sot lay model by Matlok (1970), medium lay, sti lay, very sti lay, and hard lay an also be modeled rom the Matlok urves. In varying the parameters used to deine the API sand model (1997), loose sand, medium sand, dense sand, and very dense sand an modeled. Consultation with Earth Mehanis, In., provided the soil types and the orresponding parameter values that were established as the potential soil types. Table 4.1 gives the parameters s u, ε 50, k, and γ dry, o the lay models to be used in LPLIE, while Table 4.2 gives blow ount, φ, k (saturated), k (dry), and γ dry or the sand hosen or the LPILE analysis, where s u = average undrained shear strength, ε 50 = strain at 50% o the strength; k = initial modulus o subgrade reation, either saturated or dry; γ dry = eetive unit weight, φ = internal rition angle The soil onditions that are highlighted in these tables represent those analyzed in this study. These soil onditions were seleted with the intention that the range o displaement limits would be tighter in a stier lay or denser sand rather than sot lay or loose sand. Generally

134 124 in pratie, the Matlok Sot Clay Model is used or both the sot lay model and the sti lay model, but redues the value o ε 50 or the sti lay, as Reese Sti Clay Model is not as widely aepted (Arulmoli, 2007). Table 4.1. Parameters seleted or lay soil used in LPILE Soil Type / p-y Model s u ε 50 k γ dry sot lay (Matlok) ps KPa 0.02 NA medium lay (Matlok) ps KPa 0.01 NA lb/t 3 sti lay (Matlok) ps KPa 0.01 NA very sti lay (Matlok) ps KPa 0 NA hard lay (Matlok) ps KPa 0 NA 108 lb/t 3 Soil Type / p-y Model Table 4.2. Parameters seleted or sand used in LPILE Blowount per oot Frition Angle (φ ) k (Saturated) pi k (Dry) pi loose sand (API Sand) < lb/t 3 medium sand (API Sand) lb/t 3 dense sand (API Sand) lb/t 3 very dense sand (API Sand) > lb/t 3 γ dry 4.6 Analyses and Results To establish the permissible lateral displaement limits or preast, prestressed piles in dierent soil onditions using LPILE analyses, three dierent boundary onditions at the pile head were investigated: 1) ixed head; 2) pinned head; and 3) partially ixed head. The

135 125 L{ILE analyses were onduted or seleted 16-inh otagonal piles. Table 4.3 represents the ultimate urvatures that were established or the 16-inh otagonal prestressed pile setions with the newly developed equation. In this table, Pile 1 through Pile 7 represents the maximum and the minimum urvature apaities are identiied, with p,, and axial load ratios. Given that these piles represent the boundaries o the urvature apaities, only these 16-inh otagonal prestressed piles were analyzed in ive dierent soil onditions, identiied in Setion This was neessary to redue the number o LPILE analyses needed to establish the displaement limits. Displaement limits or other pile types are established and reported elsewhere (Fanous et al., 2007)

136 126 Table 4.3. Ultimate urvature values o 16-inh otagonal prestressed piles using oninement reinorement based on the newly developed equation Axial Load Ratio inh Otagonal Pile with = 6000 psi p (Pile 1) (Pile 7) p p p (Pile 4) 16-inh Otagonal Pile with = 8000 psi p (Pile 2) p p p (Pile 5) 16-inh Otagonal Pile with = psi p (Pile 3) p p (Pile 6) p Sample Analysis This setion provides a sample LPILE analysis o ixed-headed Pile 1 embedded in very sti lay. The properties o this pile are as ollows: = 6000 psi; p = 700 psi; P e / A g = 0.2; length = 30 eet; moment o inertia = 3952 in. 4 ; and modulus o elastiity = 4415 ksi.

137 127 The moment versus urvature response o this pile setion was obtained using OpenSees, whih omprised o 250 data points. This 250 data set was then ondensed to approximately 20 data points, whih were input in the orm o M vs. EI in LPILE. Figure 4.3 plots the omplete moment versus urvature response with that based on the ondensed number o data points. The omparison between the two urves ensures that the moment-urvature response o the pile was aurately represented in the LPILE analyses Moment, kip-in Complete M-φ response Condensed M-φ response Curvature, in -1 Figure 4.4. Complete moment versus urvature response rom OpenSees with the ondensed moment versus urvature relationship input in LPILE Upon entering the pile properties as well as the moment versus urvature relationship, the soil type was deined. The ollowing values were used to ompose the very sti lay: γ = lb/in 3 ; undrained ohesion, = lb/in 2 ; and

138 128 strain ator, ε 50 = The inal step in the analysis was to enter the boundary onditions. Being a ixed head pile, the pile head was maintained at zero slope, while the lateral displaement o the pile at this loation was progressively inreased. Figure 4.4 depits the boundary ondition input or this partiular ase, where ondition 1 represents the lateral displaement at the pile head, while ondition 2 represents the slope at the pile head. Figure 4.5. Boundary onditions input in LPILE One the boundary onditions are entered in LPILE, the exeution o the analysis ollowed. With the ompletion o running the analysis, LPILE provides an output along the length o the pile or eah target lateral displaement. The LPILE output along the pile length inludes: deletion (in.);