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37 Goals of PBSD The motivation behind PBSD is to provide bridge owners and designers with a better way to influence the performance of a bridge during an earthquake. The current provisions of the AASHTO guide specifications provide for only one level of performance, that of life safety at a single-hazard level. For a variety of reasons, including the importance of a bridge to post-event recovery, economic impacts resulting from closure, and the cost of repair or replacement after an earthquake, owners need more options for specifying bridge performance objectives at various seismic hazard levels and designers need guidance how to achieve these goals in a reliable way. Satisfying these two requirements is the purpose of PBSD. Full PBSD allows owners and designers to make informed decisions using metrics beyond engineering-based strains, rotations, and displacements. Such metrics would be based on impacts and risks to the public and stakeholders that include direct and indirect losses, cost of construction, cost of repair, and estimates of downtime. To achieve the goal of full PBSD, the designer must be able to characterize the 1. Seismic hazard at the site for a range of potential ground motions due to the tectonic setting, geology, and topography of the region; 2. Structural response of the bridge to this response; 3. Potential damage to the bridge due to these motions, which may be nonlinear and inelastic; and 4. Potential for loss in terms of time, agency resources, regional economy, or human injury. With the ability of the designer to move from earthquake ground shaking through structural response to loss, decisions can be made regarding the level of structural resistance that must be provided to achieve a potential loss limit state. As with nonseismic loading, it would be ideal to characterize the process from loading through to loss in a fully probabilistic manner. However, the state of the art and the state of the practice are not yet sufficiently advanced to address PBSD probabilistically, and thus deterministic methods were used in this project. Likewise, the state of the art for linking engineering design parameters (EDPs) to loss metrics such as construction and repair costs, downtime, and injuries, is immature and was not included in the methodology described to achieve PBSD. Nevertheless, the introduction of improved EDPs for a range of desired performance is a significant step forward toward implementation of PBSD. But full PBSD is out of reach at this time. While some owners and agencies may have advanced knowledge and techniques to apply probabilistic methods more completely than those used in this report, the research team recognizes that this document must be nationally applicable to all bridge types. It is a fact that the techniques for structural design and damage evaluation are not evenly advanced for all bridge, substructure, and foundation types. Certainly, reinforced concrete substructure C H A P T E R 3 Development of the AASHTO Guidelines for Performance-Based Seismic Design
38 Proposed AASHTO Guidelines for Performance-Based Seismic Bridge Design design and evaluation is the most complete methodology, the most widely used, and the type closest to full probabilistic design, as seen by the work Caltrans is now advancing in their latest seismic design criteria. However, a full probabilistic methodology is not universally ready for deployment in a nationwide fashion. Steps to Achieve PBSD The first step to implementing PBSD is to define the levels of performance desired and provide guidance to owners on when each level of performance would be appropriate. In the methodology proposed as follows, three performance levels are specified. ⢠Life Safety is the lowest level of performance, in which the potential for bridge collapse is minimized during an earthquake but perhaps requires replacement afterward. Since the life safety level has served as the basis for many of AASHTOâs legacy seismic provisions, the teamâs understanding of the relationship between performance and design parameters at this level is mature. ⢠Operational is an intermediate level of performance, in which the bridge is damaged but accessible by emergency vehicles and reparable with or without restrictions on traffic flow. This performance level presents the greatest challenge in terms of converting the performance objective into required design parameters. ⢠Fully Operational is the highest level of performance proposed herein, in which full use of the bridge is expected immediately following an earthquake. None of this should be taken to mean that an inspection to determine the condition of a bridge post-event will not be required to determine whether a bridge is adequate for emergency or other traffic. Keeping a structure essentially elastic by adding strength can provide this level of performance, as can other approaches such as use of seismic isolation. Adding strength alone may not provide protection for ground motions that are larger than the upper level motions. As a consequence, minimum detailing for ductility should be provided even in designs that are essentially elastic. The next step in PBSD is to link performance expec- tations to bridge operational category and earthquake ground motion level. Three operational categories are recommended and include Critical, Recovery, and Ordinary. These terms are intended to replace the operational categories in AASHTO LRFD Bridge Design Specifications, which uses Critical, Essential, and Other to describe, in decreasing order, the operational categories of bridges. In addition, two ground motion levels are proposed. These are a lower level motion and an upper level motion, with return periods of approximately 100 and 1000 years, respectively. These motions and their definitions are consistent with those recommended in the FHWAâs Retrofitting Manual for Highway Structures: Part 1âBridges (Buckle et al. 2006). Seismic design categories (SDC) are then used to link performance objectives to operational categories and ground motion by defining appropriate design requirements. Five SDCs are recommended, with A-D identical to A-D in the guide specifications and E a new category that has been added for essentially elastic design. A summary of the preceding key elements in PBSD is given in Table 12. These elements are then used to build a framework for PBSD as shown in the flowchart in Figure 20. This methodology comprises 12 major steps, which are further described in a subsequent section of the report. While the process mapped in Figure 20 is linear, iteration may be required at many of the steps shown. Such iteration may be local (within a particular step) or global (involving two or
Development of the AASHTO Guidelines for Performance-Based Seismic Design 39 Element No. Description Table No. Bridge Operational Categories 3 Critical Recovery Ordinary Table 13 Performance Levels and Associated Damage Descriptors and Engineering Design Parameters 3 PL1: Life Safety PL2: Operational PL3: Fully Operational Table 14, Table 15, and Table 16 Earthquake Ground Motion Levelsb 2 Lower Level (100 years) Upper Level (1000 years) Table 17 Seismic Hazard Levels 4 I, II, III, IV Table 18 Seismic Design Categories 5 A1, B1-2, C1-3, D1-3, and E1-2 Table 19, Table 20 a To the extent possible, methodology is compatible with AASHTO Guide Specifications for LRFD Seismic Bridge Design and the FHWAâs Seismic Retrofitting Manual for Highway Structures: Part 1â Bridges (Buckle et al. 2006). b Selection of 100 years and 1000 years for the return periods of the lower- and upper-level ground motion is discussed in Step 3 of Article 3.1 of the AASHTO guidelines. Table 12. Basic elements in performance-based design of bridgesa (Guidelines Table 3.0-1). more steps). In addition, iteration between the geotechnical and structural engineers will be required in many of these steps. It is intended that this methodology be as comprehensive as possible within the constraints of the current state of the art. Further, it is intended that the methodology be applicable to the same family of bridge types, configurations, geometries, and materials covered by the guide specifications. In addition, the framework of the methodology is applicable to bridges not covered by these specifications (such as suspension bridges) provided modifications are made to its implementation on a case-by-case basis. Since adoption is not mandatory, owners and designers will have the freedom to enhance or modify or simplify the process to suit local conditions and policies. Operational Categories The research team developed alternative terminology for the operational categories from that given by the AASHTO LRFD Bridge Design Specifications. The current wording in AASHTO LRFD uses Critical, Essential, and Other to describe in decreasing order the operational categories of bridges. These terms have caused confusion in the past, as the order of importance between Critical and Essential is difficult to determine. As an alternative, the team developed the terms Critical, Recovery, and Ordinary to replace them, as shown in Table 13. The Critical category is retained. Essential is replaced with Recovery, as the term is more descriptive of why the bridge is important to the regional transportation network after an earthquake. The fact that the bridge needs to play a role in the recovery of the region provides justification for a higher performance level. Other is replaced with Ordinary, to better describe the function of the bridge. This PBSD methodology uses two levels of ground motion to develop a bridge design. Each level of ground motion has an associated performance level (PL) coupled with an input seismic hazard and is thus âperformance based.â Each operational category is composed of two ground motion levels: a lower one with an average return period of 100 years and an upper one with an average return period of 1000 years. There are three basic performance levels: PL1 or
40 Proposed AASHTO Guidelines for Performance-Based Seismic Bridge Design Figure 20. Flowchart of basic steps in framework for PBSD of bridges (GM = ground motion) (Guidelines Figure 3.0-1).
Development of the AASHTO Guidelines for Performance-Based Seismic Design 41 Life Safety, PL2 or Operational, and PL3 or Fully Operational. Additionally, as seen in Table 14, the three operational categories have increasing performance for each motion level and each operational category. For example, the ordinary bridge category requires life safety performance (PL1) for the upper event. In contrast, a bridge in the critical category would require fully opera- tional performance (PL3) in both the lower level and upper level events. It is also important to realize that PBSD does not necessarily imply that a two-level earth- quake event methodology be used. A single-event methodology may be performance based as long as performance and damage are linked to the EDPs. A two-level seismic-event method- ology simply indicates that the owner or the authority having jurisdiction requires that the bridge performance for two different ground motion levels be considered in the design. Such a requirement is based on the notion that potential losses are best controlled with a two-level approach. Thus, many PBSD methodologies are two level, although multi-level design is not fundamentally a necessity for PBSD. Another facet of the methodology described in this report for the three operational categories is the use of 100 year and 1000 year motion levels. It is entirely plausible and reasonable that an owner or authority having jurisdiction could specify larger events for either of the two levels. The intent of this report is to provide a flexible framework that designers and owners can use to improve seismic performance, and other earthquake motion levels may be used based on the ownerâs preferences and needs, some of which may be based on cost, so long as basic life safety performance is met at the 1000 year level, as required by AASHTO LRFD. Performance Levels The performance level for each ground motion is determined based on bridge operational category. See Table 14. Category Description Critical Open to all traffic immediately following the upper and lower level Motions. Usable by emergency vehicles and for security/defense purposes after an earthquake larger than the upper level motion. Recovery As a minimum, open to emergency vehicles and for security/defense purposes immediately following the upper and lower level motions. Ordinary May be closed following the upper level motion, but no span is expected to collapse during this motion. As a minimum, open to emergency vehicles and for security/defense purposes immediately following the lower level motion. Table 13. Bridge operational categories (Guidelines Table 3.1-1). Ground Motion Bridge Operational Category Critical Essential Other Lower Level (100 years) PL3 Fully Operational PL3 Fully Operational PL3 See note below Upper Level (1,000 years) PL3 Fully Operational PL2 Operational PL1 Life Safety Note: If a bridge is located on a site where the hazard level is III or IV for the lower level ground motion and requiring Fully Operational performance (essentially elastic behavior as specified for PL3 in Table 16) would place an unreasonable burden on the design, owner may reduce the performance level to PL2. In this case, yield must be expected in the columns, and demand and capacity assessment requirements should be as in Table 21 for PL2 and not as in Step 10 of the AASHTO guidelines. Table 14. Assignment of performance level based on operational category (Guidelines Table 3.1-2).
42 Proposed AASHTO Guidelines for Performance-Based Seismic Bridge Design The research team adjusted the performance level for the lower level event, in order to better align with past practices and limit the burden on designers and owners as much as possible. The simplest approach was to set the performance level as PL3 Fully Operational for all bridges at the lower level event. This would allow for simplified elastic demand analyses and elastic demand to capacity ratio checks for this level of event, regardless of where a bridge is located. For certain locations within the United States, the hazard level, even at the reduced return period of the lower level event, may be such that achieving PL3 would be unduly burdensome in terms of construction cost. In these cases, a lower performance level is appropriate, with the trade-off that more rigorous demand analyses and capacity assessment methods are required. In that case, the designer may use the table provided for the upper level motions to determine the analysis and capacity methods to be used. Definitions of each performance level and expected damage states are given in Table 15. Damage levels have been taken from Hose and Seible (1999). Engineering Design Parameters A key component of the PBSD methodology is the development of the EDPs used to link performance to design decisions. A significant amount of effort has gone into the development of the parameters, as previously presented, and as repeated in Table 16. As discussed in this section, the EDPs include both strain and displacement limits. Performance Levels PL1: Life Safety PL2: Operational PL3: Fully Operational Significant damage is sustained during an earthquake and service is significantly disrupted, but the potential for collapse is minimized. The bridge may need to be replaced after a large earthquake. Damage sustained is minimal and access for emergency vehicles is available after inspection and clearance of debris. Bridge should be reparable with or without restrictions on traffic flow. No damage (or very minor damage that does not require immediate attention) is sustained and full service is available for all vehicles immediately after the earthquake. Significant damage includes permanent offsets and cracking. Exposed, buckled, and possibly some fractured reinforcing steel. Repair may be possible but will require invasive measures that may include column replacement. At a minimum, reinforcing bar segments are replaced or plastic hinge relocation techniques employed, if repair is attempted. Beams may be unseated from bearings, but no span is expected to collapse. Similarly, foundations are not damaged except in the event of large lateral flows due to liquefaction, in which case inelastic deformation in piles may be evident. Undesirable failure modes such as shear failure in reinforced concrete are avoided. Minimal damage includes minor inelastic response and narrow flexural cracking in concrete. Exposed reinforcing steel, but not visibly buckled. Damage requires repair using minimally invasive techniques that range from simple patching of cover concrete and epoxy injection to steel jackets. Permanent deformations are not apparent, and repairs can be made under nonemergency conditions with the possible exception of superstructure expansion joints, which may need removal and replacement. Very minor damage consists of minor cracking of concrete, possible incipient crushing or flaking of concrete cover. Table 15. Performance levels and associated damage descriptors (Guidelines Table 3.1-3).
Development of the AASHTO Guidelines for Performance-Based Seismic Design 43 Strain Limits The primary EDPs used to influence the performance of a bridge under seismic loadings are strain limits. These were chosen over other possible parameters, such as ductility ratios or drift ratios, because they appear to be more directly tied to key performance limits. Strains do require some effort on the part of the designer to calculate; however, these calculations predominantly involve manipulation of analysis results and do not require additional analyses. The under- standing of how strains are related to various damage states in reinforced concrete columns is relatively advanced. Engineering Design Parameters Performance Level PL1: Life Safety PL2: Operational PL3: FullyOperational Reinforcement tensile strain limit a,b (RC Column) '0.032 790 0.14 yhebar s buckling s s ce g f P E f A ε ε ε ε ε ε ε ε ε ε ε 0.8 bars buckling < 0.010 Concrete compressive strain limit (RC Column) 1.4 0.004 1.4 ' v yh su c ccf 0.004 1.4 ' uf f < 0.004 Steel tube tensile strain limit (RCFST) < 0.025 0.021 9100 v yh s c cc s y D t Concrete compressive strain limit (RCFST) NA NA NA Superstructure-to- abutment vertical offset No limit < 9â < 1â Superstructure-to- abutment horizontal offset No Limit < 6â < 1â Approach fill settlement limitc 1/50 < 1/100 < 1/250 Lateral flow/spread limit due to liquefaction Site Specific Evaluation Required < 12â < 6â Note: This table provides recommended strain limits for common bridge element types. The table is not intended to be exhaustive with respect to bridge element types. For element EDPs not included in the table, the designer in concurrence with the owner and peer review may develop project-specific EDP criteria. See Article 6.1, âStrain Limits,â of the AASHTO guidelines for further background on this table. NA = not applicable for RCFST. a bar bucklings is the tension strain in the reinforcing steel that will result in bar buckling in compression during the following cycle of seismic response. For definitions of the other variables in this table, refer to the Seismic Guide Specifications. b Deterministic values are based on the median predictor for PL1. The reduced value for PL2 is based on a 20% probability of initial bar buckling from the median predictor to create a higher standard of performance. c Approach fill settlement limits are defined in terms of vertical settlement versus horizontal distance of the approach slab (i.e., 1:50 is 0.5 feet settlement over a 25-foot approach slab length). For further discussion of approach fill settlement limits, see Article 6.3.3.1 of the AASHTO guidelines. s f Table 16. Performance levels and potential engineering design parameters (Guidelines Table 3.1-4).
44 Proposed AASHTO Guidelines for Performance-Based Seismic Bridge Design Table 3.1-4 (Table 16) of the proposed AASHTO guidelines details the strain limits for each performance level. The key values presented relate to the design of reinforced concrete columns, as these are the predominant construction type used in bridge design in high seismic areas. The strain limits shown for various performance levels in Table 16 should be considered ranges, with the deterministic values shown representing median values for the performance level under consideration. For example, when considering the fully operational concrete compressive strain limit, some structural members may exhibit crushing at values below or above this limit. Irrespective of the actual value, once cover concrete exhibits crushing, it should be repaired to ensure long-term serviceability. However, such repair does not impact the immediate operation of the structure. Life Safety Performance Level The tensile strain limit for reinforcing steel in reinforced concrete is a simplified version of the model presented in Goodnight et al. (2017b). The intent of this limit is to prevent bar fracture by limiting the tensile strain in the reinforcing steel to that of incipient bar buckling. The tensile strain limit will almost always control over the compressive strain limit. The concrete compressive strain limit is based upon the Mander model and includes a 1.4 factor to address known conservatism in the equation to define compressive strain capacity. Figure 21 illustrates various limit states for seismic design using a pushover curve for a reinforced concrete column. This differs slightly from the limit states used in the AASHTO Guide Specifications for LRFD Seismic Bridge Design, and these correspond to the tensile strain limits and the concrete compressive strain limits given in Table 16. The data in this appendix also correspond to the limits described in Appendix A posted with this report, which may be found by searching on NCHRP Research Report 949. The limits 0 to 4, shown in Figure 21, are described as follows: ⢠0 is the onset of spalling of the cover concrete, taken deterministically as an extreme fiber compressive strain of 0.004. Additionally, a column should not require any repair if the deformations remain below the spalling limits. Figure 21. Various limit states in a column undergoing elastoplastic deformation [Guidelines Figure 6.1.1-1].
Development of the AASHTO Guidelines for Performance-Based Seismic Design 45 ⢠1 is the first yield of the transverse steel. The location on the pushover curve of this limit state depends on transverse steel content, axial load, and curvature demand. ⢠2 is the incipient buckling of the longitudinal reinforcement, and this corresponds to the tensile strain limit given in Table 16. At this point of deformation, bar buckling is just begin- ning to occur, and generally this buckling is not readily visible to human eye, although it has been determined in the experimental work of Goodnight et al. (2017b) through the use of highly accurate optical instruments. Physically, this point corresponds to incipient buckling of longitudinal reinforcement after a previous deformation in the opposite direction that induced inelastic tensile strains in the same bars. See Figure 22. This point does not correspond to a limit state in the SGS. Determination of this point requires the use of a limiting tensile strain along with a specific tensile plastic hinge length that has been calibrated to the experi- mental data set that the researchers used. This tensile hinge length is used solely to establish Limit 2, as shown in Figure 21. Repair of a column whose maximum deformation is between spalling and incipient buckling should generally be restricted to epoxy injection of cracks and patching of damaged cover concrete. ⢠3 is the lower-bound compression strain limits as given by the well-established Mander confined concrete model as used in the SGS, and as also given in Table 16. The lower-bound compression limit state is that value given for PL2, which has a coefficient of 1.0 multiplying the strain limit. The physical basis for this strain limit is shown in Figure 23, where axial load is applied concentrically to a reinforced concrete column. The limit corresponds to crushing of the confined concrete of the core, and this limit is based on the assumption that the strain energy required to fracture the transverse steel equals the strain energy stored in the core when this failure occurs. The calculation of the limits is based on semi-empirical consideration of experimental data. The lower-bound compressive strain limit was used with the SGS to be conservative since a bar buckling prediction method did not exist at the time the SGS was developed. Columns that have been loaded above the incipient buckling limit but that have not reached the lower-bound compressive limit may be repaired with external jacketing. How- ever, consideration should be given to the possibility of damage to the transverse steel and Figure 22. Incipient buckling limit state (Guidelines Figure 6.1.1-2). Figure 23. Mander confined compression strain limit state.
46 Proposed AASHTO Guidelines for Performance-Based Seismic Bridge Design longitudinal steel. This damage state is not entirely definable by strain limits alone, and each column may need a case-by-case assessment of damage. ⢠4 is the upper-bound compressive strain limit, which is also based on the Mander model. This limit uses the same basic strain equation as Limit 3, except that a coefficient of 1.4 is applied to the limit. With both bar buckling and compressive concrete strains specified, as in this report, it is appropriate to increase the concrete compressive limit for PL1 by the 1.4 factor. Columns that have been deformed above the lower-bound compressive strain limits may require extensive reconstruction or replacement due to damage to both the transverse and longitudinal reinforcement. The pushover curve for a bridge column or pier is determined using the compressive plastic hinge length, which is the same as that used in the SGS, and by this method a complete pushover curve is developed. Then the tensile strain limit, along with the tensile plastic hinge length, is used to determine the displacement at which the tensile strain limit will be reached. The capacity of the bridge column or pier is then controlled by the limit that is reached first, incipient buckling (tensile strain limit) or confined-concrete crushing (compressive strain limit). Example pushover curves for two column diameters (48-in. and 60-in.), two axial loads (1,000 kips and 2,000 kips), two longitudinal steel ratios (1% and 2%), and three transverse steel ratios (0.3%, 0.5%, and 0.8%) are shown in Figures 24 and 25. Note that the 0.3% and 0.5% transverse steel ratios are the lower limits of transverse steel currently specified in the SGS for SDC B and C, respectively. In these figures, the SGS implicit equations for displacement capacity are shown super- imposed on the curves for reference. Also for reference, the limiting concrete compressive strain limit is the same as that in the SGS, and this corresponds to the limit for PL2 in this report. The tensile limit in the following plots are for PL1, and these limits are shown with a blue diamond. Thus, the curves provide a reference point for the new tensile limit for PL1 compared with the life safety limit state of the SGS. When compared with the SGS displacement capacities, it can be seen that for the higher axial loads, incipient bar buckling (tensile strain limit) generally controls over the compressive strains. For the lower axial loads, incipient bar buckling and the compressive crushing limits are generally closer to one another. If the higher crushing limits (1.4x factor) were used to generate a new PL1 set of pushover curves, then the new tensile strain limits would generally control for the lower axial loads. For RCFSTs, the steel tensile strain limit corresponds to the observed fracture strain of RCFST systems (Brown et al. 2015). Operation Performance Level The tensile strain limit for reinforcing steel in reinforced concrete is based upon the statistical data obtained from the Goodnight et al. (2017b) model, in which less than 10% of reinforcing bars are expected to buckle, which works out to be about 80% of the limit at the life safety performance level. The concrete compressive limit is based upon the Mander model. For RCFSTs, the steel tensile strain limit corresponds to a value that, if exceeded, results in tube buckling upon reversal (Brown et al. 2015). The limit is a function of diameter to thickness ratio of the tube. Fully Operational Performance Level The strains listed at this level are those approaching the limit where cover concrete crushing may occur, reinforcing bars have likely yielded, but residual crack widths are small (less than 1 mm) and do not require repair (or require very minor repair).
Development of the AASHTO Guidelines for Performance-Based Seismic Design 47 Translating Limit State Strains to Member Deformations The limiting strains defined for the EDPs will need to be interpreted in terms of member deformations. This assessment will depend on whether reinforced concrete (RC) bridge columns or RC pier walls are being considered. RC Bridge Columns (All Limit States) For reinforced concrete, if the plastic hinge method is used to establish a corresponding displacement limit, the appropriate tension or compression hinge lengths in Goodnight et al. (2017b) should be employed as follows. The tension hinge length is only used to translate a limit state curvature at a tensile strain limit to lateral deformations. The compression hinge length is used for everything else, including overall force versus deformation response and translation of curvatures at compressive limit states to lateral deformations. Lsp = αfyedbl Equivalent Strain Penetration Length α = 0.15 for ksi and α = 0.022 for MPa units 0.2 1 0.08k f f ue ye = â ï£ï£¬   ⤠Moment Gradient Coefficient Figure 24. Pushover curves for 48-in. diameter columns (Source: Goodnight et al. 2017a).
48 Proposed AASHTO Guidelines for Performance-Based Seismic Bridge Design Lpc = kLc + Lsp ⥠2Lsp Rectangular Compressive Hinge Length Lpt = Lpc + γD Rectangular Tension Hinge Length γ = 0.4 for bidirectional loading and γ = 0.33 for unidirectional loading Note that for simplicity, the 0.4 value in the tension hinge length for bidirectional loading is recommended, since it is rare to have unidirectional ductility demands. As the preceding equations indicate, the tension hinge length is simply the compressive hinge length plus 0.4x the diameter for circular sections. RC Pier Walls (All Limit States) The following expressions for the plastic hinge length for walls should be used if limit state displacement based upon the limit state strains is calculated (Paulay and Priestley 1992): 2 3 h he w= Effective Height Lp = k ⢠he + 0.1lw + LSP Plastic Hinge Length Figure 25. Pushover curves for 60-in. diameter columns (Source: Goodnight et al. 2017a).
Development of the AASHTO Guidelines for Performance-Based Seismic Design 49 0.2 1 0.08k f f u y = â ï£ï£¬   ⤠Factor for Plastic Hinge Length LSP = 0.15fye ⢠dbl Strain Penetration Length Approach Fill Rotation and Displacement Limits An EDP also needs to be developed to represent relative movement between the approach fill and the bridge abutment. Rather than defining limiting strains, this EDP is defined in terms of rotations and permanent displacements that occur between the abutment and the fill. The displacements can be either in the form of permanent settlement or horizontal displacement. The definition of approach fill settlement is shown in Figure 26, in which the settlement rotation limit is given as the vertical displacement of the approach divided by the approach length. Limits on vertical and lateral movement are identified in Table 16. The allowable displace- ments between the approach fill and an abutment were established by considering both rideability and foundation capacity requirements for the specified seismic performance level. Relative settlement between the approach fill and an abutment was identified as the primary consideration for rideability, while permanent horizontal movement of the approach fill and an abutment was identified as the primary consideration for meeting foundation capacity requirements. Although the settlement and lateral movement mechanisms represent a single composite response of the approach fill and the bridge abutment, the settlement and lateral movement evaluations are typically decoupled for convenience. The following subsections provide the basis for the displacement identified for the PL1, PL2, and PL3 performance limits. Settlement Limits The settlement limits for abutments are shown in terms of angular distortions. This angular distortion was defined by the relative settlement between the approach fill and the bridge abut- ment. Usually an approach slab with a length of 25 feet to 30 feet will provide the transition. Where no approach slab is used, the discussion of geometric offsets (Article 2.4.4 of the AASHTO guidelines) applies. L settlement Approach Fill Settlement = Figure 26. Definition of approach fill settlement.
50 Proposed AASHTO Guidelines for Performance-Based Seismic Bridge Design For a pile-supported abutment, the distortion results from the settlement of the fill and the underlying soil during or following seismic shaking. Normally, the pile-supported abutment would be assumed to undergo negligible settlement during the seismic event. For abutments supported on spread footings, the angular distortion would be caused by densification of material forming the approach fill, as well as any relative settlement of the abutment because of its imposed loads. Soil beneath the spreading footing below the approach fill and the footing would normally be assumed to be equal. Settlement is assumed to result from the densification that takes place in loose granular soils located above the groundwater or from liquefaction and subsequent dissipation of excess pore-water pressures located below the groundwater table. Various methods are available for estimating settlement of the soil. These include empirical relationships for liquefied soils devel- oped by Tokimatsu and Seed (1987) and by Ishihara and Yoshimine (1992), cone penetrometer test methods recommended by Zhang et al. (2004), or through laboratory testing methods. Amounts of settlement estimated by these methods depend on the density of the cohesion-less soils, the level of induced shear stress and strain during the seismic event, and the thickness of the liquefiable layers. For dry soils, approaches developed by Silver and Seed (1971), Youd (1972), and Pyke et al. (1975) have been used. Factors affecting the settlement of dry sand include relative density, shear stress or strain amplitude, and layer thickness. Most fills above the water table have been compacted as part of approach fill construction, and therefore the most signifi- cant concern occurs where abutment fills are supported on liquefiable soils. These settlements can be estimated using procedures noted above. The settlement limits for the PL1, PL2, and PL3 performance levels in Table 16 were developed using conclusions from NCHRP Web-Only Document 245: Bridge Superstructure Tolerance to Total and Differential Foundation Movements (Moon et al. 2017). These results are presented in terms of support movement, where the support settles relative to the adjacent piers or to the approach slab at the abutment. Tolerable movements for ride quality are rotations less than 1/250. Guidance is provided for both simple and continuous spans in NCHRP Web-Only Document 245. For the seismic case given in Table 16, the approach fill settles relative to the abutment; however, the same angular rotation applies. NCHRP Web-Only Document 245 defined the angular rotation limits consistent with require- ments in the current AASHTO LRFD Bridge Design Specifications. These limits are applicable for PL1, the life safety performance level in AASHTO. Under this level of differential movement, acceptable performance for gravity loading is assumed to occur. This recommendation means that for full operations (PL3) of the bridge following a seismic event, an angular rotation at the abutment of <1/250 could occur and still be within the guidance set in NCHRP Web-Only Document 245. In other words, as long as the angular rotation is less than this amount, full operations would be allowed, consistent with current AASHTO guidance. With this inter- pretation, angular rotations for the PL1 and PL2 performance limits would be higher, since these limits are for life safety and limited use. Allowable rotations of 1/50 and 1/100 were identified for PL1 and PL2, respectively, based on the assumption that any use of the bridge would be limited to emergency vehicles and speed would be controlled. For a typical 25-foot long approach slab, the relative movement between the approach fill and the abutment would be approximately 1 in., 3 in., and 6 in. for the PL3, PL2, and PL1, respectively, based on the perfor- mance limits identified in Table 16. The recommended angular rotation assumes that all settlement occurs within and below the approach fill and the deep foundations supporting the abutment do not settle during the seismic event. If the abutment is supported on spread footings, then the relative movement is between the base of the spread footing and the top of the approach fill. In either case, the geotechnical engineer would use current empirical, numerical, or test data to estimate the amount of relative movement.
Development of the AASHTO Guidelines for Performance-Based Seismic Design 51 If the interior bents for the bridge are also supported on spread footings, the allowable move- ment in terms of angular rotation of the footing relative to adjacent bents can be estimated using the methodology in NCHRP Web-Only Document 245. Lateral Displacement Limits Lateral displacement of the approach fill can occur with or without liquefaction. This move- ment occurs primarily during the seismic event because of inertial forces within the approach fill. Normally, it is assumed that the bridge abutment moves with the displacing fill, even when the abutment is supported on deep foundations. In this case, the passive earth pressure imposed by the moving soil pushes the abutment and supporting piles outward to the free face of the fill. Either of two methods can be used to estimate the lateral displacements of the approach fill: (1) simplified pseudo-static slope stability evaluations in combination with Newmark-type displacement methods or equations, or (2) numerical modeling with two-dimensional (2-D) or three-dimensional (3-D) computer programs such as FLAC and Plaxis. Restraint provided by piles penetrating through the approach fill, as well as reaction developed from diaphragm action of the deck, tends to limit displacements and can be included in the model of the approach fill and abutment, as described in NCHRP Report 472: Comprehensive Specification for the Seismic Design of Bridges (ATC/MCEER 2002) and Lateral Spreading Analysis of New and Existing Bridges (Shantz 2017). Most cases of bridge damage from lateral soil movement have occurred at locations where the approach fill is located on liquefiable soils. At these locations the liquefiable soil loses strength and under the reduced strength, the approach fill deforms laterally either under gravity stresses (flow failure) or inertial loading (lateral spreading). The abutment is assumed to move with the sliding approach fill, resulting in bending stresses within the piles supporting the abutment. Whether the amount of abutment movement that can be tolerated without damage to the piles or collapse is a very site-specific assessment that depends on the depth and thickness of the liquefiable layer in combination with the amount of lateral movement. A pile extending through the liquefiable layer is restrained from movement below the liquefiable layer and moves with the sliding mass above the liquefiable layer. Bending stresses within the pile will depend on the distance over which liquefaction occurs. Movement is typically assumed to be distributed over the thickness of the liquefiable layer plus one to two foundation diameters above and below the top and bottom of the liquefiable layer. If the zone of liquefaction is small and lateral movements are large, large curvatures will develop in the pile, which can be more problematic than if the liquefiable layer is thick. This mechanism is discussed in the example problems of NCHRP Report 472. The limits on lateral movement of the abutment listed in Table 16 for PL2 and PL3 are based on the fact that most piles can tolerate from several inches up to 12 in. of lateral movement, regardless of pile configuration and soil profile. Even when there is a thin liquefiable zone, concentration of a few inches of movement can be tolerated through redistribution of movement into adjacent nonliquefied zone. A limit of 6 in. is defined for the PL3 performance limit state, and doubling this is identified for the PL2 operational condition. In neither case will movements likely be discernible. However, for the PL1 life safety limit condition, site-specific analyses are required to define what amount of displacement could result in collapse of the bridge abutment from buckling of the foundation support system, since the amount of allowable movement will depend on a combination of the flexural stiffness of the piles, the thickness of the liquefied zone, and the level of seismic loading. This assessment needs to be considered on a case-by-case basis. The preceding discussions focus on abutments supported on deep foundations. Spread footings are not recommended above liquefiable soils because of the potential for large lateral movements from liquefaction, bearing failures from loss in soil strength, and post-earthquake
52 Proposed AASHTO Guidelines for Performance-Based Seismic Bridge Design settlement. If ground improvement is used to limit the development of liquefaction, then the potential for lateral movement can be evaluated using either simplified pseudo-static stability analysis method with Newmark-type displacement estimates or by numerical modeling. In some situations, the displacement of interior bents must also be considered if the zone of lateral spreading or flow extends beyond the abutment. Again, either the simplified pseudo-static stability analysis method with Newmark-type displacement estimates or numerical modeling can be used to assess this condition. Geometric Displacement Limits Limits on the allowable residual geometric offsets between the superstructure and abutment in the vertical and horizontal directions were established as part of the EDPs. For the Fully Operational (PL3) performance level, a maximum vertical offset of 1 in. was specified. Because this performance level requires the bridge to be available to normal traffic immediately follow- ing the seismic event, the vertical offset needs to be small enough to not impair the flow of traffic. Larger offsets may result in an impediment to high speed traffic, damage to vehicles, and a potential hazard to motorcycle traffic. The limit for horizontal offsets was set at 1 in., in order to prevent a snagging hazard from developing at the barrier. Larger horizontal offsets would mean a significant protrusion might develop at barrier transitions, which would be considered a safety hazard for normal traffic. At the Operational (PL2) performance level, the offset limits were increased to 9 in. vertical and 6 in. horizontal. These limits were developed based on the assumption that primarily emer- gency vehicle traffic would be using the bridge immediately following the event, but that some action might be required in order to allow normal traffic to use the bridge. The 9 in. dimension is based on a curb height, which emergency vehicles could easily mount albeit at a slow speed. A larger offset could be used but would require the vehicle slowing to nearly a stop. The horizontal limit of 6 in. was somewhat more arbitrary. Because these are residual displacement limits, for values much larger than 6 in., the dynamic displacements would probably have been large enough to induce significant second order effects (P-delta), such that the 6 in. limit is likely the practical maximum value that has any meaning. For the Life Safety (PL1) performance level, no residual offset limits are provided. Since no traffic is envisioned on the bridge after the event, no geometric limits are required. Demand Analysis and Capacity Assessment Requirements As the methodology was developed further, it became apparent that reliance on the seismic design categories as defined in the Seismic Guide Specifications would not be sufficient to adequately proscribe the types of demand analysis and capacity assessment needed. When the highest performance level is specified, the structure may remain entirely in the elastic range. However, if the hazard level is high, simplified demand analysis is likely insufficient to adequately define the demand, in particular if capacity design principles are elected not to apply (see the Capacity Design section). Another one of the goals of the research team was to preserve a minimal requirement for analysis for very low hazard levels, even for performance levels, which allows for extensive inelastic behavior at the upper level ground motion. In general, it is deemed desirable for the PBSD procedures to roughly converge to the current SGS for the Life Safety performance level in the lower seismic hazard zones. The solution adopted was to define directly both the minimum demand analysis requirements as well as the minimum capacity assessment method for each performance level and hazard level. Furthermore, bridges were classified into three different groups based on the regularity
Development of the AASHTO Guidelines for Performance-Based Seismic Design 53 of the structural system, structure type, amount of nonlinear behavior expected in the soils, and magnitude of the constructed value. These divisions are a step beyond what is currently addressed in the Seismic Guide Specifications, but the research team thought this was needed to ensure the appropriate level of analysis and assessment was applied for structures whose behavior may be complex. The guidelines rely on the methods of demand analysis and capacity assessment that have been implemented in the Seismic Guide Specifications and LRFD Bridge Design Specifications, as they have proved reliable and effective and will work equally well in the performance-based framework. In addition, the direct displacement-based design method has been introduced in an AASHTO document as an alternative approach to analysis and design. This method, which in a strictly analytical form has been referred to as the substitute structure method, directly accounts for the inelastic behavior of a structural system both in terms of a secant stiffness, as well as the damping associated with inelastic deformations. The method can be cumbersome when applied to multi-degree of freedom systems but avoids many of the inherent assumptions of elastic methods that lead to less accuracy in results. Seismic Hazard The designer is directed to determine the need for site-specific hazard and site-specific ground response analyses, in consultation with the owner. These site-specific analyses are typically more accurate than national hazard maps because they are based on studies of local site conditions. The decision to use site-specific analyses should primarily be based on (1) the operational category of the bridge (a higher category equates to a more rigorous analysis) and (2) properties of the soil profile at the bridge site. Both the upper and lower ground motion level shown in Table 17 should be considered in the study. For each return period in Table 17, a response spectrum is constructed using the appropriate references to the AASHTO Guide Specifications for national hazard maps and site coefficients. The seismic hazard level is then obtained using the spectral acceleration value (SD1), as shown in Table 18. Probability of Exceedance Approximate Return Period Lower Level Ground Motion 50% probability of exceedance in 75 years 100 years Upper Level Ground Motion 7% probability of exceedance in 75 years 1000 years Table 17. Ground motion levels (Guidelines Table 3.1-5). Hazard Level Value of SD1 = FVS1 I SD1 < 0.15 II 0.15 < SD1 < 0.30 III 0.30 < SD1 < 0.50 IV 0.50 < SD1 Table 18. Seismic hazard levels (Guidelines Table 3.1-6).
54 Proposed AASHTO Guidelines for Performance-Based Seismic Bridge Design Seismic Design Category The Seismic Design Category (SDC) is determined according to Table 19 based on (1) the required performance level, (2) the hazard level, and (3) the bridge attributes. The basic requirements for each SDC are given in Table 20 for the upper and lower ground motion levels. In addition, detailed requirements for the upper ground level motion are provided in Table 21 and are a function of the bridge attributes in addition to the performance and hazard levels. These attributes include the bridge geometry (regular or irregular), type (conventional or unconventional), the soil (linear or nonlinear), liquefaction potential, and the value of construction (low, moderate, or high). Geoseismic Hazards and Liquefaction Assessment In addition to normal site investigations necessary to determine the site class as described in previous sections, the designer is directed to assess the potential for geoseismic hazards and their associated impacts on bridge performance. Geoseismic hazards include ⢠Seismic-shaking-induced fill settlement and abutment displacements leading to excessive bridge movement or even collapse, access problems, or structural damage; ⢠Seismic-induced excess pore-water pressures and liquefaction of saturated sands, non- plastic silts, and gravels used for fills or serving as foundation soils that can contribute to slope and abutment instability and lead to loss of foundation-bearing capacity and lateral pile support; ⢠Down-drag forces on pile foundations due to seismic-induced ground settlement; ⢠Soil movement-induced lateral forces on foundations due to lateral spreading or ground lurching; and ⢠Progressive degradation in stiffness and strength characteristics of saturated cohesion-less soil and soft cohesive soils, resulting in changes in lateral support of deep foundations or loss in bearing capacity of spread footings. Table 19. Assignment of seismic design category based on performance and hazard levels and bridge attributes (Guidelines Table 3.1-7). Note: Sets of bridge attributes (i.e., Basic, Intermediate, and Complex) are described in Table 21 and further elaborated in Step 8 of the AASHTO guidelines. a If a bridge is located on a site where the Hazard Level is III or IV for the lower level ground motion and requiring fully operational performance (essentially elastic behavior as specified for PL3 in Table 16) would place an unreasonable burden on the design, owner may reduce the performance level to PL2. In this case, yield must be expected in the columns, and demand and capacity assessment requirements should be as in Table 21 for PL2 and not as in Step 10 of the AASHTO guidelines. b Design requirements selected by owner on a case-by-case basis. Hazard Level Ground Motion Level, Performance Level, and Bridge Attributes Lower Level Upper Level PL3 PL1 PL2 PL3 Basic, Intermediate, and Complex Basic and Intermediate Complex Complex Basic and Intermediate Basic and Intermediate Complex I E1 A1 C3 B2 C3 C3 b II E2 B1 D2 C2 D2 D3 b III a C1 b D2 b D3 b IV D1 b D2 b D3 b
Development of the AASHTO Guidelines for Performance-Based Seismic Design 55 Table 20. Basic requirements for each seismic design category (Guidelines Table 3.1-8). Ground Motion SDC Requirements Upper Level Ground Motion A1 No identification of ERS required No demand analysis No implicit capacity check No capacity design required, although connection strength should develop member strength Minimum detailing for support length, super-substructure connection forces, column transverse steel B1 Identification of ERS required Demand analysis required (equivalent static analysis) Implicit capacity check required (SGS Equation 4.8.1-1) (displacement, P â Î, support length) SDC B level of detailing B2 Identification of ERS required Demand analysis required (Equivalent Static Analysis) Capacity design should be considered for column shear SDC B level of detailing Liquefaction evaluation required C1 Identification of ERS required Demand analysis required (elastic dynamic analysis) Implicit capacity check required (SGS Equation 4.8.1-2) (displacement, P â Î, support length) Capacity design required including column shear requirement SDC C level of detailing Liquefaction evaluation required C2 Identification of ERS required Demand analysis required (elastic dynamic analysis) Capacity assessment required (nonlinear static procedure) (displacement, P â Î, support length) Capacity design required including column shear requirement SDC C level of detailing Liquefaction evaluation required C3 Identification of ERS required Demand analysis required (elastic dynamic analysis) Capacity assessment required (demand capacity ratio) (displacement, P â Î, support length) Capacity design required including column shear requirement Minimum detailing required despite essentially elastic behavior Liquefaction evaluation required Upper Level Ground Motion Lower Level Ground Motion D1 Identification of ERS required Demand analysis required (elastic dynamic analysis) Capacity assessment required (nonlinear static procedure) (displacement, P â Î, support length) Capacity design required including column shear requirement SDC D level of detailing Liquefaction evaluation required D2 Identification of ERS required Demand analysis required (elastic dynamic analysis) Capacity assessment required (Nonlinear Static Procedure) (displacement, P â Î, support length) Capacity design required including column shear requirement SDC D level of detailing Liquefaction evaluation required D3 Identification of ERS required Demand analysis required (elastic dynamic analysis) Capacity assessment required (demand capacity ratio) (displacement, P â Î, support length) Capacity design required including column shear requirement Minimum detailing required despite essentially elastic behavior Liquefaction evaluation required E1 Demand analysis required (simplified method) Capacity assessment required (demand capacity ratio) Liquefaction evaluation should be considered for certain conditions E2 Demand analysis required (equivalent static analysis) Capacity assessment required (demand capacity ratio) Liquefaction evaluation required Capacity design should be considered for column shear Capacity assessment required (demand capacity ratio) (displacement, P â Î, support length)
56 Proposed AASHTO Guidelines for Performance-Based Seismic Bridge Design Bridge Attributesa Performance Level Hazard Level SDC Demand Analysis b Capacity Assessmentc Basic ⢠Regular geometry ⢠Conventional type ⢠Linear soils ⢠Low-to-moderate value of construction Life Safety, PL1 I A1 None Connection Strength Check II B1 Equivalent Static Analysis Implicit Method B III C1 Elastic Dynamic Analysis Implicit Method C IV D1 Nonlinear Static Procedure Operational, PL2 I B2 Equivalent Static Analysis Demand Capacity Ratio Method II C2 Elastic Dynamic Analysis Nonlinear Static Procedure III-IV D2 Fully Operational, PL3 I C3 Elastic Dynamic Analysis Demand Capacity Ratio Method II-IV D3 Intermediate ⢠Irregular geometry ⢠Conventional type ⢠Nonlinear soils ⢠Liquefaction hazard ⢠Moderate-to-high value of construction Life Safety, PL1 I A1 None Connection Strength Check II B1 Elastic Dynamic Analysis Implicit Method B III C1 Elastic Dynamic Analysis Implicit Method C IV D1 Nonlinear Static Procedure Operational, PL2 I B2 Equivalent Static Analysis Demand Capacity Ratio Method II C2 Elastic Dynamic Analysis Nonlinear Static Procedure III-IV D2 Fully Operational, PL3 I C3 Elastic Dynamic Analysis Demand Capacity Ratio Method II-IV D3 Complex ⢠Irregular geometry ⢠Nonconventional type ⢠Nonlinear soils ⢠Liquefaction hazard ⢠High value of construction Life Safety, PL1 I C3 Elastic Dynamic Analysis Demand Capacity Ratio Method II D2 Nonlinear Static Procedure III-IV d Nonlinear Response History Nonlinear Response History Operational, PL2 I C3 Elastic Dynamic Analysis Demand Capacity Ratio Method II D2 Nonlinear Static Procedure III-IV d Nonlinear Response History Nonlinear Response History Fully Operational, PL3 I-IV d Linear Elastic Response History Demand Capacity Ratio Method a, b, c See Steps 9 and 10 of the AASHTO guidelines for definitions of terms and explanation of methods. d Design requirements selected by owner on a case-by-case basis. Table 21. Demand analysis and capacity assessment requirements for upper level ground motion (Guidelines Table 3.1-9). The designer is directed to Articles 6.2 and 6.8 of the AASHTO Guide Specifications for the geoseismic hazard evaluation and liquefaction assessment, respectively. Earthquake Resisting Systems It was found necessary to augment the list of earthquake resisting systems (ERS) currently identified in the Seismic Guide Specifications in order to account for the type of systems that may be employed to ensure the fully operational performance level. Type 0 was added to cover those systems where essentially all of the structure is restricted to the elastic range of behavior. Additionally, newly emerging systems such as those that utilize shape memory alloys are grouped into ERS Type 4. By creating these two new ERS types, the guidelines will be better able to ensure adequate requirements are specified, and unconservative results are avoided.
Development of the AASHTO Guidelines for Performance-Based Seismic Design 57 Capacity Design There is an underlying assumption in the displacement-based seismic design methodology utilized in the Seismic Guide Specifications that seismic loadings will control the design of the main elements of the ERS and that inelastic behavior up to and beyond plastic hinge formation will occur. This forms the basis of the capacity design philosophy, wherein the remaining elements of the structure are proportioned to resist the maximum loads that can be developed by the ERS. However, when the ERS is expected to remain essentially elastic even at the upper level ground motions, proportioning the remainder of the structure for the full plastic capacity of the ERS may require an impractically large set of design loads and a resulting design that is excessively costly. This would seem to argue for the abandonment of capacity protection principles when the structure is designed for elastic performance during the upper level ground motions. However, a critical look at the performance of bridges during past earthquakes would indicate that a certain amount of humility regarding the ability to predict the magnitude of future events and the performance of the built environment when subjected to seismic motions is in order. This leads to two options: one, require at least some form of capacity protection even when elastic performance is provided or, two, include an additional factor to account for uncertainties that are normally covered by conservatism in the displacement capacities calculated and the over-strength material factors used. The approach taken in the Guidelines is to strongly encourage the adoption of the capacity protection philosophy and requirements of the Seismic Guide Specifications even when elastic performance is targeted. If the designer chooses not to utilize capacity protection design, then an additional factor of 1.5 is applied to the loads from the demand analysis. This factor is largely based on judgment. However, some rational basis should perhaps be provided that could account for bridge size, importance, or some other attribute. Because many major or significant bridges are often designed for project-specific criteria that may require elastic response for a 2500 year return period ground motion, perhaps the factor should be the ratio of the 2500 year site-adjusted 1-second spectral acceleration to that of the 1000 year site-adjusted 1-second spectral acceleration. This will vary according to tectonic, geologic, and topographic settings, but the intent would be to have enough capacity to withstand the 2500 year ground motion elastically if capacity protection is not used. Design Examples The proposed design examples were developed under Task 9. Because PBSD is an iterative process and many of the key decisions can involve owner input and conflicting goals and priori- ties, they were developed as if an actual design for a bridge were being conducted. The proposed design examples include some nonlinear directionality to exhibit the expected path that PBSD projects may take. In addition to the design examples, a comparative study of a simple SDOF bridge structure was undertaken to explore the reasonableness of the proposed methodology at sites across the country, for representative column dimensions and loadings, and using traditional as well as DDBD methods of analysis. This study is included with this report and titled Appendix A.
