Integrated Superstructure-Substructure Load Rating forBridges with Foundation Movements

Nathan T. Davis, S.M.ASCE1; Ehssan Hoomaan, S.M.ASCE2; Masoud Sanayei, M.ASCE3;Anil K. Agrawal, M.ASCE4; and Farrokh (Frank) Jalinoos, M.ASCE5

Abstract: Superstructures of highway bridges are load rated regularly as a part of the National Bridge Inspection Standards (NBIS). It is wellknown that the load-carrying capacity of a superstructure is affected by foundation movements; however, the current load rating frameworkdoes not explicitly include these effects. In the current framework, foundation movement could be treated as structural condition change andconsidered as a permanent load. In this paper, the authors propose an integrated framework for load rating of superstructures and substructuresin the presence of continuing foundation movements and geohydraulic hazards. The approach is based on the modification of the load ratingequation to include foundation movements and effects of loads other than dead and live loads that can affect the load capacity of a bridge. Amethodology for load rating elements loaded in biaxial moment and axial load, commonly experienced by piers, columns, and piles, has alsobeen proposed. The term substructure functionality index (SFI) has been proposed to account for the effect of foundationmovement on the func-tionality of critical elements such as bearings. Applications of the proposed integrated superstructure-substructure load rating and SFI have beendemonstrated through two examples of actual bridges. It has been demonstrated that the load rating produced can be nonconservative if theeffects of foundation movement are neglected.DOI: 10.1061/(ASCE)BE.1943-5592.0001232.© 2018 American Society of Civil Engineers.

Author keywords: Bridge load rating; Superstructure; Substructure; Settlement; Foundation.

Introduction

Load rating of superstructure components is a procedure commonlyused in the United States to evaluate the operational capacity ofbridge components carrying dead and live loads (Mertz 2005;Chajes et al. 1997; Sanayei et al. 2016). Load rating of all bridges(bridge is defined as any structure that carries a highway load andhas a total length greater than 20 ft) is required in compliance withNational Bridge Inspection Standards (NBIS) and is performed bybridge owners to better maintain the existing inventory and toensure safe usage of aging infrastructure. Typical load rating ofbridge superstructures is performed by developing analytical mod-els using approximate load distribution methods and structural andgeometrical details from design drawings or on-site inspections(Gao 2013). Load rating based on field testing is performed whenanalytical models are not reliable because of the presence of phys-ical damages to bridge components or because of unreliable/insufficient information on structural or geometrical details ofbridge components (Cai and Shahawy 2003). The result of a

traditional load rating is a “rating factor” (RF), which defines themaximum safe carrying load for a component as a multiple of thedesign or rating truck load.

Generally, load rating procedures have been limited to super-structure elements, although substructures are routinely evaluatedfor capacity when deterioration of structural elements or the soilsystem is noted. The 2011 AASHTO Manual for Bridge Evaluation(MBE) (AASHTO 2011) provided the following guidance on theconsideration of substructures in load rating procedures: “Wheredeemed necessary by the owner, load rating of substructure ele-ments and checking stability of substructure components such asabutments, piers, and walls should be done using all permanentloads and loads due to braking and centrifugal forces, but neglectingother transient loads such as wind or temperature.” State DOTs pro-vide varying requirements with limited guidance on the load ratingof substructure elements. For example, MassDOT (2013) requiredpile bents to be load rated. FDOT (2016) stated that the substruc-ture, specifically “rotted piles, settlement, excessive scour, and dis-tressed pile caps” should be considered. IDOT (2014) required areevaluation of substructures with condition factors below 4.MaineDOT (2015) stated that substructures need not be routinelyanalyzed as part of the load rating procedure.

The main objective of the research presented in this paper is toinvestigate and propose amethodology for load rating bridges includ-ing the effects of foundation movements, such as vertical settlement,horizontal translation, or rotation. This approach uses integratedmodeling of the superstructure-substructure system to perform loadrating of both superstructure and substructure elements consideringfoundation movement and other foundation loads. The superstructureand substructure load rating process returns a RF in the same wayas the conventional load rating approach. Additionally, an index,referred to as the substructure functionality index (SFI), is alsoproposed to quantify the functionality of bridges after foundationmovement. This index is similar to the condition rating com-monly applied to bridge components during routine bridge

1Ph.D. Candidate, Dept. of Civil & Environmental Engineering,Tufts Univ., Medford, MA 02155.

2Ph.D. Candidate, Dept. of Civil Engineering, The City College ofCUNY, New York, NY, 10031.

3Professor, Dept. of Civil & Environmental Engineering, Tufts Univ.,Medford, MA 02155 (corresponding author). E-mail: masoud.sanayei@tufts.edu

4Professor, Dept. of Civil Engineering, The City College of CUNY,New York, NY, 10031.

5Research Structural Engineer, Federal Highway Administration,Office of Infrastructure R&D, McLean, VA 22101.

Note. This manuscript was submitted on May 23, 2017; approved onNovember 21, 2017; published online on March 12, 2018. Discussion pe-riod open until August 12, 2018; separate discussions must be submittedfor individual papers. This paper is part of the Journal of BridgeEngineering, © ASCE, ISSN 1084-0702.

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inspections. It ranges from zero to 10, with 10 indicating no foun-dation movement, and zero indicating loss of functionality.

Background

Bridge load rating provides an assessment of the live load-carryingcapacity of superstructure components and is commonly performedfor two levels of loads: (1) inventory rating that corresponds toloads that can be safely carried by the bridge for an indefinite periodand (2) operating rating that corresponds to the maximum permissi-ble live load that can be placed on the bridge, although with poten-tial adverse effects on life span. AASHTO guidelines on load andresistance factor rating (LRFR) seek to achieve a reliability index(b) of 3.5 for inventory load rating and 2.5 for operating load rating,which is achieved by using factors of 1.75 and 1.35 on the live loadfor inventory and operational load rating, respectively. Load ratingis initially performed with an HL-93 load rating vehicle at the in-ventory or operating level. If the RF for the design truck is below1.0, load rating is then performed with state legal loads, which moreclosely match the operating condition. Evaluation at these load lev-els is performed with the different live-load factors prescribed in theMBE (AASHTO 2011). If the load rating is below 1.0 for state legalloads, then the bridge is posted at the value that is the product of theRF and the gross vehicle weight of the rating truck. Load rating canalso be performed for permit vehicles that exceed the normal trucksize and weight limits to ensure that they do not overstress bridgesalong the routes they propose to operate over.

The MBE (AASHTO 2011) presented a detailed guideline onload rating of bridges. The following general expressions are usedto determine the load RF of each element subjected to a single loadeffect using the LRFRmethod:

RF ¼ C � gDCDC � gDWDW6g pP

gLL LLþ IMð Þ (1)

C ¼ capacity ¼ w cw swRn Strength Limit State

fR Service Limit State

((2)

where ƒR = allowable stress specified in AASHTO (2014) or asstated; Rn = nominal member resistance (as calculated); DC = deadload effect due to structural components and attachments; DW =dead load effect due to wearing surface and utilities; P = permanentloads other than dead loads; LL = live-load effect; IM = dynamicload allowance; gDC = LRFD load factor for structural componentsand attachments; gDW = LRFD load factor for wearing surfaces andutilities; gP = LRFD load factor for permanent loads other than deadloads; gLL = LRFD load factor for live-load factor (different foroperating and inventory levels); and w , w c, and w s are the LRFD re-sistance factor, condition factor, and system factor, respectively.

The resistance factors, w , w c, and w s, in Eq. (2) are applied toaccount for the uncertainty in calculating the capacity, uncertaintydue to deterioration, and a decrease in reliability for less redundantsystems, respectively. Typical values of the system factor, w s, rangefrom 0.85 to 1.0, and are provided in Table 6A.4.2.4-1 of the MBE,whereas LRFR values for the condition factor, w c, are provided inTable 6A.4.2.3-1 of theMBE.

The only permanent loads specifically mentioned in the MBEare the secondary effects from posttensioning. Other transient,semipermanent, or permanent loads that can impact a bridge duringoperation (e.g., wind, water, earth pressure, or settlement) are typi-cally neglected during load rating. The proposed methodology in

this paper will consider some of these additional permanent loads inthe rating equation.

The load factors used in LRFR have been derived from load fac-tors and load combinations common to LRFD design. The loadcombinations that need to be applied during LRFR depend on thetype of superstructure and common design checks for the compo-nent being rated. The load cases considered for LRFR are presentedin Table 6A.4.2.2-1 of the MBE (AASHTO 2011) and includestrength, service, and fatigue load cases. The strength load cases usefactors of 1.25, 1.50, and 1.75 for the dead loads, wearing surfaceloads, and live loads, respectively.

Impact of Substructure Movement on Load Rating

Regardless of the underlying cause, vertical foundation settlementwill result in force and moment redistribution in girders, bearings,and other superstructure elements. The magnitude of force andmoment created by foundation movement is affected by details andcharacteristics of the bridge superstructure, such as the type of gird-ers present, the layout of the superstructure (vertical and horizontalcurves, skew, and superelevation), and the details of their connec-tion to the pier or abutment undergoing movement. Only differen-tial movements from one foundation element to the next or across afoundation element will induce forces or moments in superstructureelements. Simple span bridges provide a discontinuity in the girdersover the piers, allowing rotation that reduces load redistributionresulting from differential settlement. Continuous girders will expe-rience positive moment demand over settling piers and negativemoment demand over the adjacent pier or abutment during differen-tial settlement. Abutments often undergo a combination of verticalsettlements, horizontal translation, and rotation. These movementscan induce forces and moments in the girders, although the magni-tude will depend on the details of the girder to abutment connection.

Because the current load rating procedure does not regard theforces and moments resulting from settlement, the load rating forsome superstructure elements may not be conservative for bridgesthat have undergone substantial foundationmovements. The approachpresented in this paper incorporates these effects in the standard loadrating procedure. The proposed research is not recommended to beapplied to all bridges. Rather, the proposed approach is recommendedto be used only for bridges in which substantial foundation movementthat may lower the load rating is observed during inspection.

Literature Review

Sayed et al. (2013) proposed amethod for load rating bridge piers sub-jected to scour. ARFwas assigned to the individual piers by determin-ing the amount of live load that could be carried without the pierundergoing excessive settlement. To represent the ultimate conditionat failure, the dead and live loads were factored by 2.5 and applied to amodel created in FB-Pier (2015). P-Y curves were used to representsoil behavior and were removed to simulate scour. This methodologyonly considered foundations in their worst-case scoured condition,and not necessarily their current condition, as is typical with load rat-ing practice. Only vertical settlements were considered, and limitswere based on empirical findings from the literature (Bozozuk 1978;Grover 1978; Wahls 1990; Walkinshaw 1978). These limits weresummarized by Barker et al. (1991) and are shown in Table 1.

These settlement limits are based on studies of large populationsof bridges and may not represent conditions for a particular bridgethat is being load rated. Wang et al. (2011) studied the changes inpositive and negative moments due to support settlements for

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continuous span steel girder, concrete girder, and slab bridges. Itwas shown that the reliability indices for prestressed concrete girderand slab bridges undergoing foundation movement are significantlylower than those for steel girders due to the increased stiffness ofslab bridges, indicating that these bridges are more sensitive tofoundation movement.

It is well known that the differential movement of foundations(including settlement or rotation) cause ride quality and serviceabilityissues as well as cause damage to abutments, piers, railings, curbs,sidewalks, bearings, and anchor bolts, and can result in significantstresses and cracking in concrete components (DiMillio 1981;Moulton et al. 1985). The acceptable limit on movements depends onthe characteristics of the bridge being analyzed. Furthermore, thesecriteria ignore horizontal movement and rotation, whereas it wasnoted by Moulton et al. (1985) that “most types of structural damageappear to occur for those bridges with both vertical and horizontalmovements occurring simultaneously.” Moulton et al. (1985) pro-posed limits on differential vertical settlement rather than total settle-ment, whichwere adapted by AASHTO (2014), as shown in Table 2.

Andrawes and Caiza (2012) presented a method for load ratingthe structural capacity of eccentrically loaded timber piles by sub-tracting the dead load stresses from the total stress capacity anddividing by the stresses induced by the live load. Kim andAndrawes (2017) have extended this methodology to include fiber-reinforced polymer (FRP) retrofitted timber piles.

Dupont andAllen (2002) studied the causes and effects of approachsettlement and effectiveness of construction techniques in mitigatingthis issue. Paikowsky and Lu (2006) examined the reliability of serv-iceability criteria in the LRFD code, considering the observationsfromMoulton et al. (1985), to propose new settlement criteria for vari-ous bridge types.Modjeski andMasters, Inc. (2015) examined service-ability requirements for bridges, including settlement criteria for shal-low and deep foundations. Changes to the LRFD code were proposedthat included appropriate gSE terms for settlement predicted using vari-ous methods. Proposed gSE factors ranged from 1.0 to 1.25 dependingon the prediction technique used. The primary source of uncertaintyin these calculations was related to the prediction of settlement prior toit occurring. Factors for measured settlement were not proposed.

Moon et al. (2018) studied the impacts of foundation movementon bridge superstructures, finding pier and abutment settlement cancause superstructures to exceed Strength or Service limit criteria,especially for continuous multispan steel girder and prestressedconcrete bridges. The worst-case movements were found to be dif-ferential settlement between adjacent piers/abutments, and differen-tial settlements across single elements.

ProposedMethodology

As discussed previously, the MBE left the evaluation of substructureelements, including the evaluation of stability of substructure compo-nents, such as abutments, piers, and walls, up to the discretion of the

bridge owners. The MBE also did not require the consideration oftransient loads, such as wind or temperature. Although permanentloading on superstructure elements is generally limited to prestressingforces, “permanent” loading on abutments is present in the form ofvertical or horizontal earth pressures. Water loads are typicallyregarded as transient loads, but bridge foundations that see significantwater loading during daily operational traffic should have these loadsincluded as well. The water loads to be used during load rating shouldnot represent a flood or abnormal condition; rather, they should be theloads present on a semipermanent basis.

Because the load rating procedures outlined in the MBE werecentered on the rating of superstructure components, the procedurefor load rating members in eccentric axial loading is not explicitlyspecified. Instead, the rating equation shown in Eq. (1) defines theRF as the capacityminus the dead load and wearing surface demandsdivided by the anticipated live-load demand. For a structural compo-nent in uniaxial bending, the capacity is the factored nominalmoment/shear capacity, and the demands are the factored moment/shear demands on the component for each load case. Similarly, axi-ally loaded components are rated based on the factored axial capacityand factored axial demands. For both types of loading, the RF is thepercentage of the factored live-load demand on the remainingcapacity after the permanent loading has been taken into account.

Unlike superstructure components, many substructure compo-nents, especially pier columns and long piles, must be designed toresist significant simultaneous axial force and bending momentdemands (eccentric axial loading). Although pier columns are pri-marily comprised of reinforced concrete, piles can be made of rein-forced concrete, prestressed concrete, steel, or timber. Piles and col-umns can be square, rectangular, or circular in shape.

For many bridges undergoing foundation movements, the mostprominent concern is not the strength of superstructure components;instead, it is the rideability and functionality of the bridge.Excessive settlement can result in damage to bearings that can leadto unseating of girders from bearings, discontinuities in bridgedecks, cracking of deck or girder concrete, or girders contactingabutments. In these circumstances, the primary concerns are inde-pendent from the magnitude of live load applied. A load rating pro-cedure intended to provide the maximum load permissible does notaid in the evaluation of these issues. Although the concept of loadrating does not fully apply to rideability and functionality concerns,there is an ongoing necessity to document the performance of thesesubstructures in a consistent manner.

The proposed integrated load rating methodology has three maincomponents: (1) superstructure load rating considering the effects ofsubstructure movement, (2) load rating of substructure elements, and(3) defining the functionality of the structure concerning an observedsettlement. The superstructure and substructure load rating proceduresreturn a rating value in the sameway as current load rating procedures.The functionality of the bridge considering settlement is quantifiedthrough the newly developed SFI. This value should not be interpretedas a load rating; rather, it should be seen as akin to a condition ratingcommonly applied to components during routine bridge inspections.The SFI can range from 0 to 10, with 10 indicating no foundationmovement, and zero indicating loss of functionality.

Table 1. Empirical Limits on Vertical Settlement (Data from Barker et al.1991)

Settlementmagnitude Basis for recommendation Reference

50 mm Not harmful Bozozuk (1978)60 mm Ride quality Walkinshaw (1978)>60 mm Structural distress Walkinshaw (1978)100 mm Ride quality and structural distress Grover (1978)100 mm Harmful but tolerable Bozozuk (1978)>100 mm Usually intolerable Wahls (1990)

Table 2. Angular Distortion Limits in LRFD Code (Data from AASHTO2014)

Tolerable settlement (d ) Type of bridge

0.004 La Continuous span bridges0.008 L Simple span bridges

aL is span length.

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Superstructure Load Rating considering SubstructureMovement

For superstructure elements, the primary difference between tradi-tional load rating and the proposed integrated load rating is the addi-tion of a settlement term to the rating equation. The settlement term,SE, represents the additional moment, force, or stress demand onthe component being rated due to foundation movement. It is pro-posed that load cases (except fatigue) include the effects of settle-ment when it is considered significant and agencies have performedmeasurements of foundation movements, relative displacements, orconnection distortion. For all load cases except fatigue, the RFequation in Eq. (1) can be revised to include the effects of settle-ment, as shown in Eq. (3)

RFsup ¼ C � gDC DCð Þ � gDW DWð Þ6gP Pð Þ � gSE SEð ÞgLL LLþ IMð Þ (3)

The definition of parameters in Eq. (3) is the same as in Eq. (1).At present, gSE is taken to be 1.0, which is consistent with LRFDspecifications. The LRFD load factor of 1.0 is prescribed to be usedwith predicted settlement, whereas the proposed load rating wouldbe based on measured settlements. Moulton et al. (1985) have sug-gested that a linear elastic analysis of loads from measured settle-ments will conservatively estimate demands (actual demands willbe lower) due to creep and relaxation. Hence, it is expected thatusing a gSE of 1.0 will produce conservative load ratings. Furtherresearch and test data would be required to determine appropriategSE values for measured settlements that account for the variabilityof loads resulting from settlement, the variability of settlement mea-surement, and the effects of creep and relaxation.

Substructure Load Rating

Additional Loads on SubstructuresIn traditional load rating of superstructures, the primary operationaldemand results from dead and live loads. Loads from other sources,such as wind, water, ice, and earth pressure, are not included in theload rating equations due to their relative insignificance. Earthquakeloadingwas considered in the LFRD approach as an “extreme event”that does not coincide with operational loading.

Wind loading was evaluated in the LRFD using four load cases:Strength III, Strength V, Service I, and Service IV. The Strength IIIand Service IV wind load cases had no live load and should be eval-uated separately from load rating when deemed necessary. TheStrength V and Service I operational (occurring with live load on

the bridge) load cases used an 89-kph (55-mph) wind with factorsof 1.35 and 1.0 on the live load, respectively. The authors haveinvestigated the significance of these load cases on the load ratingof substructure elements and have not identified an example inwhich they control the load rating. It is expected that these loadcases can control the load rating for tall substructures in which lat-eral deck loading can generate a large moment in the pier.

For abutments and wing walls, lateral earth pressure loads areessentially permanent loads that need to be considered when evalu-ating demands. Pier elements in moving water have a lateral loadapplied to submerged elements. Although lateral load during flood-ing can be considered an extreme event case, normal streamflowunder operational conditions can impart significant loads onaffected bridge components. Ice loading due to extreme event iceforces has not been considered in this research. Table 3 presentsLRFD factors for loading that are not typically considered in LRFR,but they are considered in this research.

Water LoadingWater loading on bridge piers can act transversely or parallel to thedirection of traffic. Water loads are excluded from superstructureload rating because superstructures experience water loads (for exam-ple, during submergence) only during extreme flooding cases. InAASHTO (2014), the water loads were included in all strength, serv-ice, and extreme event load cases. A design flood, which is based onminimum return frequency (i.e., 100-year return period), is used forstrength and service load cases, whereas a check flood, which is basedon a 500-year return period, is used for extreme event load cases.

For the purposes of load rating, it is proposed that the normalstreamflow (or expected maximum during the evaluation interval)be considered as load on the bridge. The proposed water load isdetermined by considering the current state of the bridge founda-tion in terms of scour and hydrological conditions. Many stateDOTs already have requirements for scour vulnerability evalua-tion, following HEC-18 (Arneson et al. 2012), that should not besuperseded by the proposed load rating procedure.

Proposed Load Cases for SubstructuresBecause of the additional loads experienced by substructures, addi-tions to Table 6A.4.2.2-1 are proposed and are listed alongside thecurrent LRFR factors in Table 4.

The equation for load rating of substructures, including founda-tions, can be modified to include effects of earth pressure, waterloading, and settlement, as in Eq. (4)

RFsup ¼ C � gDC DCð Þ � gDW DWð Þ � gSE SEð Þ � gEH EHð Þ � gEV EVð Þ � gWA WAð ÞgLL LLþ IMð Þ (4)

Table 3. LRFD Load Factors Not Typically Used during LRFR Load Rating

Load Symbol in LRFD Typical factor in LRFD code

Settlement SE gSE = 1.0 (Strength I, II, III, IV, often avoided by limiting settlement)Vertical earth pressure EV gEV = 1.00–1.35 (retaining walls and abutments),

gEV = 0.9–1.30 (rigid buried structures),gEV = 1.0 (stability)

Horizontal earth pressure EH gEH = 0.9–1.50 (active earth pressure),gEH = 0.9–1.35 (passive earth pressure)

Water load WA gWA = 1.0 (all strength, service, and extreme event)

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It is proposed that gSE be equal to 1.0 for the reasons mentionedpreviously. It is also proposed that gWA be equal to 1.0 for thisresearch, primarily to provide consistency with existing LRFDstandards. Reliability-based factors would need to consider the vari-ability of streamflow over the load rating interval as well as the like-lihood of those flows occurring simultaneously with heavy truckloading. It is expected that these values would be specific to individ-ual bridges, and calibration of these factors beyond the LRFD valuesis believed to be beyond the scope of this research. Furthermore,Turkstra (1970) has found that extreme values of loading occurwhen one load reaches its extreme, whereas the others are near theirexpected mean (Nowak 1999). Because load rating is an attempt toconsider the maximum permissible live load, it is rational to onlyconsider the expected (nonfactored) water load, especially if a con-servative value is chosen.

Combined Axial-Moment Load RatingSubstructures will typically contain elements that are subjected toboth axial forces and bending moments (eccentric loading).Determining the available resistance of a pier during eccentric load-ing is a more involved procedure that generally requires evaluationof both the moment capacity and axial capacity, or a simultaneousevaluation of both. The equations governing the available capacityof elements in eccentric axial loading can be found in AASHTO(2014), and they vary depending on element type. Applicable limitstates can be found in Section 5.7.4.5 of AASHTO (2014) for rein-forced concrete elements, Section 6.9.2.2 for steel elements, andSection 8.10.1 for timber elements. Specific limit states can befound in Eqs. (S1)–(S7) in the Supplemental Data.

Because the previously mentioned equations are more complexthan those governing the capacity of elements loaded purely in com-pression or uniaxial bending, Eq. (4) cannot be used to load rateeccentrically loaded columns. Furthermore, because the dead loadand live load will not necessarily have the same eccentricity, it isnot possible to subtract the permanent load effects from the capacityand divide by the live-load demands to determine a load rating.Instead, the proposed methodology determines the multiple of liveload that can be applied until the failure criterion is met. This isachieved by separately determining the permanent load effects andlive-load effects, including the axial load and moments about bothaxes. The resultant load effects are then a function of the multiple(m), as shown in Eq. (5) for axial load

P mð Þ ¼ gDC PDCð Þ þ gDW PDWð Þ þ gSE PSEð Þ þ gWA PWAð Þþ gEV PEVð Þ þ gEH PEHð Þ þ mð ÞgLL PLLð Þ (5)

where P = axial load; and the subscripts follow the previouslydescribed AASHTO conventions. Eq. (5) also applies to the twomoments, Mx and My, which can also be written as functions of m.The relevant limit state equation can then be a function of m by

using P(m), Mx(m), and My(m). The multiple of live load (m) thatcauses the limit state to be reached is then analogous to the RFobtained from Eq. (4). Fig. 1 depicts this methodology applied to acircular reinforced concrete column. The solid curved line is thefactored interaction surface that represents failure, as determined byACI (2015). The horizontal line is x-axis that divide tension andcompression, the star is the factored permanent load effects, thecircle represents the point of failure, and the dashed line representsthe load path the total load effects take as m is increased. The direc-tion of the dashed line is a result of the eccentricity of the worst-case live loading, which is defined as the case in which the lowestmultiple causes the failure surface to be reached.

The path shown in Fig. 1 is only a two-dimensional (2D) projec-tion of the three-dimensional (3D) path taken by the live-loadeffects between the permanent load effects and failure. As such, thelength of the line in 2D space is not particularly meaningful. Whenmoment reversals (i.e., permanent load effects produce a momentwith an opposite sign of the live-load moment) occur during liveloading, a turn in the live loading line will be visible, as shown inFigs. 2(a and b), which show the cause of this to be a moment rever-sal about the y-axis because the live load has the opposite sign of thedead load. It should be noted that although the path taken in Fig. 2appears longer than the path taken in Fig. 1, Fig. 2 (in this case,although not generally) represents a lower load rating because thelive-load effects in Fig. 2 are of greater magnitude.

SFI

Many issues related to excessive bridge settlement will not bestrength based; therefore, they will not be directly dependent on thelive loads. Because the live-load forms the denominator of the RFequation, a RF cannot meaningfully characterize these issues. Forthese scenarios, a new form of load rating, defined in this paper asthe SFI, is proposed. The SFI is a positive number from 0 to 10,which is similar to the condition rating applied during bridgeinspection. An SFI of 10 indicates that the bridge has experiencedno differential movements, whereas an SFI of 0 indicates that thesuperstructure is no longer functional. If the settlement is greaterthan the allowable value, a negative SFI is mathematically possible.It is proposed that zero be the minimum value of SFI because it cor-responds to a loss of functionality. The SFI can be applied to anyconnection or detail, but the index should be viewed as a rating onthe substructure performance. The overall SFI of the bridge is gov-erned by the lowest SFI of any component. The SFI of each compo-nent will inherently account for the simultaneous movements of allfoundation components. Unlike a load rating, the SFI is notintended in any way to estimate the magnitude of live load that canbe safely applied. At low SFIs, the bridge still may be functional,although significant usability issues may exist. How detrimental alow SFI is will depend on the component being rated, details of the

Table 4. Load Cases Applicable to LRFR Factors for Substructures

Limit state

Dead load Wearing surface

Design load

Legal load Permit load Settlement Water loadVertical earth

pressureHorizontal earth

pressureInv Oper

gDC gDW gLL gLL gLL gLL gSE gWA gEV gEH

Strength I 1.25 1.50 1.75 1.35 1.30–1.45 — 1.0 1.0 gEV gEH

Strength II 1.25 1.50 — — — 1.10–1.40 1.0 1.0 gEV gEH

Service I 1.00 1.00 — — — 1.00 1.0 1.0 gEV gEH

Service II 1.00 1.00 1.30 1.00 1.30 1.00 1.0 1.0 gEV gEH

Service III 1.00 1.00 0.80 — 1.00 — 1.0 1.0 gEV gEH

Note: Inv = inventory; Oper = operating.

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bridge, and how the limit criteria have been defined. Quantitatively,the SFI is expressed as

SFI ¼ Allowablemovement� ObservedmovementAllowablemovement

� 10 (6)

Allowable settlement can be calculated by the following threeapproaches. The most simplistic approach is to define “allowable”movement using existing AASHTO or state DOT guidelines. The“observed” movement should be estimated from field measure-ments. This method is likely to be overly conservative becauseguidelines are applicable to many bridges. These guidelines also donot typically restrict lateral movement, rotation, or consider theinteraction of translation, rotation, and settlement. Hence, these lim-its will not be appropriate for foundations with several simultaneousmovements.

The second approach to calculating allowable movement is tomodel the bridge including the foundation and subject the foun-dation elements to the observed movements. The distortion invarious connections and details would then be the “observedmovement,” whereas the “allowable movement” can be deter-mined from the capabilities of those connections or details (e.g.,how far a girder can move before impacting an abutment, howmuch an elastomeric bearing pad can deform, how much a rollerconnection can rotate, etc.). This approach allows the inclusionof the effects of all measured or estimated movements into theSFI equation.

The third approach proposed is to measure the actual relativemovement in a specific detail (e.g., girder translation relative toabutment or pier cap). This allows for direct and simple observationof the actual areas of concern without worrying about modeling theentire bridge. The allowable movement would still need to be

0 0.5 1 1.5 2-0.2

-0.1

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

Pu/P

0

Mu/M0

Factored interaction diagramPermanent load effectsDirection of Live LoadingFailure Point

Fig. 1. Path traveled between permanent loading and failure surface

Fig. 2. Live-load loading path when stress reversal is present in (a) PU-MU space and in (b)MX-MY space

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determined using the knowledge of the connection details and engi-neering judgment, but foundation movements would not necessarilyneed to be measured. The resulting SFI would still be a measure oftotal foundation performance, assuming foundation movements arethe only source of deformations.

The SFI can be implemented into the traditional load rating para-digm by first determining which bridges are undergoing significantenough movement to warrant consideration of the impacts of settle-ment on functionality. On these bridges, critical details or connec-tions can be identified for continuous ongoing monitoring. A limit toobservable settlement, connection rotation, or differential movementcan be defined following the previously mentioned approaches.Observations of the settlement or connection distortion can be per-formed with the regular inspection interval to provide an objectivemeasure of the remaining functionality of the substructure. The SFIwould be reported alongside the RF to indicate the severity of thecurrent movement.

Modeling Techniques

Two different modeling techniques are investigated in this paper.The first is a common approach in which the foundation is not mod-eled alongside the rest of the superstructure and substructure.Instead, boundary conditions are applied to the model, often at theground surface for interior bents or at the bearing location for abut-ments. In this modeling approach, observed settlements are applieddirectly to the boundary conditions as a separate load case. As longas the bridge behavior can be modeled elastically, the settlementload case can be added to the other permanent loading on the bridge.This approach is described in greater detail in a subsequent section.

The second design approach is to model the entire foundation,substructure, and superstructure in a single model. Pile-soil interac-tion in this approach is represented by nonlinear P-Y (lateral force-lateral displacement), T-Z (axial displacement-skin friction), T-u(twisting-rotational resistance), and Q-Z (tip displacement-tip re-sistance) springs. A description of these springs and their governingequations can be found in the FB-Pier program manual (FB-Pier2015). This approach allows complete modeling of foundation ele-ments, including modeling of soil behavior, and scour. For thismodeling approach, the order the loads are applied is importantbecause the soil springs are nonlinear. Generally, the model shouldbe loaded with the dead and other permanent loads, then the settle-ment load, and last the live load. Only nonfactored loads were usedin the model, and the effects from each load were factored outsideof the modeling. This modeling approach automatically includesthe effects of settlements that occur from dead and live loading,although additional settlements can be modeled by converting theQ-Z tip spring to a fixed end and applying a displacement.

Field Examples

The application of the proposed integrated substructure-superstructure load rating approach has been demonstratedthrough two example bridges. Both bridges are in Pinellas County,Florida, but they have very different foundations and superstruc-tures. One bridge is a 3-span continuous steel girder bridgewith sin-gle column piers, whereas the other bridge is a 3-span slab bridgewith two pile bent piers with nine precast concrete piles (PCPs)each. The selection of these two bridges is expected to highlight dif-ferent applications of the proposed methodology. The continuousgirder bridge is expected to experience load redistribution in thegirders and tall pier columns due to foundation movement. In con-trast, the simple span bridge is not expected to experience

significant load redistribution due to uniform foundation move-ment. However, the piles within the pier bents are expected to expe-rience load redistribution during scour or water loading.

Three-Span Continuous Steel Girder Bridge

The I-275 southbound in Pinellas County crosses over I-275 north-bound and 34th Street south with a 3-span, continuous girderbridge. There are five steel girders in composite action with a 190-mm (7.5-in.) thick reinforced concrete deck. The girders areapproximately 2.5 m (99 in.) deep with span lengths of 67, 70, and62 m (220, 230, and 203 ft) along the centerline. The bridge iscurved with a radius of 537 m (1,763 ft) and has a superelevation of6.4%. The two intermediate bents in the bridge are hammerheadpiers consisting of 2.1-m (7-ft) diameter concrete columns, longitu-dinally reinforced with 44 #11 bars. The piers are founded on a 2-m(6.5-ft) thick underground pile cap connected to 460� 460-mm(18� 18-in.) square PCPs, approximately 21.3 m (70 ft) long.The ends of the bridge are founded on reinforced concrete stubabutments supported by eight PCPs each, ranging from 27.4 to29 m long (90 to 95 ft). The soil conditions at all bents consist of18.3–21.3 m (60–70 ft) of medium to dense sand with trace silt,underlain by a thin layer of soft clay above hard limestone.

A finite-element model of the bridge (Fig. 3) was created usingthe software package CSiBridge. The girders, pier caps, and col-umns are modeled with frame elements. The deck is modeled withshell elements. The pile caps, piles, and soil are not modeled;instead, a fixity in which movements can be prescribed is applied atthe ground surface. The model is linear elastic, and the force redis-tribution from foundation movements are calculated in a separateload case. References to the “outer” portion and the “inner” portionof the bridge refer to the outside and inside of the curvature,respectively.

Two damage scenarios have been simulated using this bridgemodel. The first modeled damage scenario (SE-1) has 102mm (4 in.)of pure vertical settlement in a single pier, with no movement at theadjacent pier or abutments. The selection of 102 mm is arbitrary, butit is an amount of settlement expected to generate concerns whilestill being well below the limit of 0.004 L (280 mm, 11 in.) fromAASHTO (2014). A second damage scenario (SE-2) considers acase in which piles under one of the piers do not settle uniformly.

Fig. 3. (a) Google Earth image of the I-275 bridge (image © 2017Google) and (b)CSiBridgemodel of the I-275 bridge

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In the simulated scenario, there is 51 mm (2 in.). of settlement onthe outer (with respect to girder curvature) edge of the pier,102 mm (4 in.) of settlement on the inner edge, and 25 mm (1 in.)of translation in plane with the pier cap toward the center of thecurvature. The second load case is applied to the model as 153 mm(3 in.) of downward settlement, 51 mm (1 in.) of horizontal trans-lation, and 0.637° of transverse rotation at the base of the column.The load rating of the superstructure and the load rating of the piercolumn and SFI are calculated by considering these effects.

Superstructure Load RatingSuperstructure load rating was performed considering the two set-tlement cases (SE-1 and SE-2). The resulting negative momentsover the adjacent pier and the girder negative moment capacities forthree different conditions of girder (i.e., good, fair, and poor) areshown in Table 5.

Fig. 4 shows the RFs for the negative moment region over theadjacent pier for the Strength I load case for all five girders, assum-ing poor condition with w c = 0.85.

The critical girder from Fig. 4 is Girder 3, which has the low-est initial RF. In good condition, the RF for Girder 3 drops from2.04 to 1.83 with 102 mm (4 in.) of vertical settlement. In poorcondition, this RF drops from 1.25 to 1.05. The load case withvertical settlement, rotation, and horizontal translation has a

smaller impact than pure vertical settlement, except for Girder 5.Girder 5 still does not control the load rating of the superstruc-ture when the foundation undergoes these movements. In themethodology presented by Sayed et al. (2013), the largest sug-gested settlement limit is 100 mm (4 in.), indicating excessiveconservatism. The proposed methodology allows the considera-tion of girder condition, nonvertical movement, and design andloading details.

Substructure Load RatingThe column in Pier 2 (Pier Column 2; PC2) has an initial load ratingof 3.98. The first step in finding the failure condition is determiningthe critical live-load effects (in this case, when the rating vehiclepasses over Pier 2 on the inside lane, producing the maximummoment in the column). The live loads from the critical case arethen multiplied by a factor,m, which is increased until the limit stateequation is met. The total loads at failure can be found using Eq.(5), and the RF is the m that causes the limit state to be met. Thedirection of loading as m is increased is shown in Pu-Mu space bythe dashed line in Fig. 5, and the failure condition is shown by thecircle. Although this process can be solved using the closed-formsolution, in the experience of the authors, a solution with three digitsof precision can be converged on very quickly by trial and error(<10 iterations).

Table 5. Girder Negative Moments over Adjacent Pier for Strength I Load Case Including Settlement Loads

Load case

Factored moments (kN · m) Capacity (kN · m)

DC DW SE-1 SE-2 LL Good Fair Poor

Girder 1 −8,893 −6,162 −920 −161 −4.354 −31,184 −29,625 −26,506Girder 2 −10,832 −7,469 −1,101 −479 −5.396 −31,184 −29,625 −26,506Girder 3 −11,349 −7,765 −1,197 −887 −5.926 −31,184 −29,625 −26,506Girder 4 −9,825 −6,759 −1,220 −1,238 −5.856 −31,184 −29,625 −26,506Girder 5 −7,229 −6,759 −1,135 −1,374 −5.090 −31,184 −29,625 −26,506

0.00

0.50

1.00

1.50

2.00

2.50

3.00

Girder 1 Girder 2 Girder 3 Girder 4 Girder 5

Ra�

ng F

acto

r

No Se�lement SE-1 (ver�cal se�lement) SE-2 (Ver�cal + Rota�on)

Fig. 4. RFs for girders with no settlement, settlement Scenario 1 (SE-1), and settlement Scenario 2 (SE-2) for each girder in poor condition

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The load rating procedure was then applied with both settlementcases, as shown in Figs. 6(a and b).

Fig. 6 shows the load rating of PC2 after settlement has occurred.The vertical settlement imposed in the first settlement load caselowers the rating from 3.98 to 3.77. The second settlement load caselowers the load rating to 2.48. All load ratings assume a columncondition factor of 1.0; a lower condition factor would require fac-toring of both the nominal moment resistance and nominal axial re-sistance when forming the interaction surface.

SFIThe angular distortion criterion of 0.004 L fromAASHTO (2014) isapplicable to the load case with vertical settlement only. Applyingthis criterion to this bridge gives

0:004� 70m ¼ 0:28m ¼ 280mm 11 in:ð Þ (7)

Using the 280-mm (11-in.) limit from AASHTO (2014) for theSFI equation in Eq. (6) gives

SFI ¼ 280mm� 102mm280mm

� 10 ¼ 6:36 (8)

Another possible criterion includes limiting translation in theelastomeric bearing pads to 64mm (2.5 in.), which is approximatelyhalf of the thickness of the bearing pad. In the SE-1 load, five bear-ing pads connecting Pier 2 to the girders experience a maximum of2.8 mm (0.11 in.) of displacement (under the innermost girder)from the first settlement load case. During the second settlementload case, the middle girder experiences 89 mm (3.5 in.) of

0 0.5 1 1.5 2-0.2

-0.1

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

Pu/P

0

Mu/M0

Factored interaction diagramDead load effectsDirection of Live Loading3.98 times factored Live Load

Fig. 5. Load rating of PC2with no settlement

Fig. 6. Load rating of PC2 during (a) settlement and (b) settlement, rotation, and translation

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displacement. These movements are translated to an SFI for the firstand second settlement load cases in Eqs. (9) and (10), respectively

SFISE1 ¼ 64mm� 2:8mm64mm

� 10 ¼ 9:56 (9)

SFISE2 ¼ 64mm� 89mm64mm

� 10 � 0 (10)

These indices provide a simple measure of the remaining func-tionality of the substructure. It is important to note the differencesbetween Eqs. (8) and (9), which are for the same load case. The0.004-L limit on vertical differential is based on total performancecriteria including strength and serviceability issues; thus, the SFIfound from bearing pad deformation is not expected to match theSFI from the AASHTO (2014) limit. The SFI for the second settle-ment case in Eq. (10) shows that the movement observed at the bot-tom of the pier column has exceeded the functionality of the bearingpad. A real-life inspection could directly measure the bearing padtranslation and not bother with estimation of foundation movementandmodeling of the bridge.

Three-Span Prestressed Concrete Simple Span Bridge

State Road 595 crosses over Stevenson Creek in Pinellas County. Itis a 3-span simple span bridge, with each span comprised of 18 rec-tangular prestressed concrete box beams. The girders are notspaced; instead, they are connected transversely using postten-sioned steel rods. A cast-in-place unit takes the place of a 19thgirder and connects the two halves of the bridge. The asphalt wear-ing surface was placed directly onto the prestressed concrete sec-tions. All three spans are 11.8 m (38 ft, 8 in.) in length, for a total of35.4 m (116 ft) of bridge length. The interior piers are pile bentswith a 760-mm (30-in.) deep reinforced concrete pile cap supportedby nine 460-mm (18-in.) square prestressed concrete piles. The outertwo piles on each bent are battered at 1/12 toward the outsides of thebent. The abutments are also supported on nine 460-mm (18-in.)square prestressed concrete piles. The girders are connected to thepiers and abutments by elastomeric bearing pads. The piles are drivenapproximately 1.2 m (4 ft) into soft limestone. Above the limestoneis approximately 1.8 m (6 ft) of firm to stiff marine clay, and abovethe clay is a 2.1-m (7-ft) deep layer of sand with shells. Previousscour analysis estimated a potential scour depth of 13 feet at thisbridge.

Two models of this bridge were created with identical super-structures. The deck was modeled with shell elements with proper-ties matching each of the girders. A discontinuity with separatebearing pads on each side is provided over the piers. Prestressingsteel for each girder is represented by a single tendon with the sametotal area and eccentricity as the total prestressing steel. The firstmodel, shown in Fig. 7(b), has the pile for each pile bent modeled tothe top of ground surface, with a pin boundary condition preventingtranslation and rotation at the ground surface. Rotation was allowedat these connections to prevent overconstraining themodel. A frameelement was placed underneath the abutment bearing pads to allowfor a prescribed abutment displacement to be input. This model wasused to model two damage scenarios: 102 mm (4 in.) of uniformvertical settlement of one of the pile bents and 51 mm (2 in.) of uni-form horizontal movement of one of the abutments.

The second model is identical to the first model, except with theaddition of the remaining portions of pile below the ground surface.In this model, nonlinear P-Y, T-Z, and T-u springs were used torepresent the soil conditions around the piles, and Q-Z springs wereused to represent the tip resistance of the piles. This model was used

to determine the loading on piles including scour and water flows atvarious scour depths.

Superstructure Load RatingBecause the SR 575 Bridge is a simple span bridge, vertical piermovement does not have a significant impact on the load ratingof the bridge superstructure. The only moment transferred intothe girders comes from the stiffness of the bearing pads restrain-ing rotation. Because the abutments have neoprene bearing pads,the horizontal movement does not impart significant momentdemands on the superstructure outside of a small negativemoment in the end region near the abutment. Only a slight longi-tudinal stress was imparted on these girders, which means loadrating of the Strength I and Service I conditions will be relativelyunaffected by foundation movement. Fig. 8 shows the plot of themoment demands resulting from dead and wearing surface loads,HL-93 live load, vertical pier settlement, and horizontal abut-ment movement. Fig. 8 shows that the moment demands frompier settlement or abutment movement are insignificant com-pared with live and dead load demands.

Because the superstructure load rating was mostly unaffected bythe substructure behavior, it was not investigated using the secondmodel. The modeling technique that uses soil springs can be usedfor superstructure load rating, although settlement would need to beapplied to the bottom of the piles, requiring a fixed condition ratherthan a Q-Z spring.

Substructure Load RatingSubstructure load rating was only performed with the model includ-ing P-Y springs. This model allowed for the successive removal ofnonlinear springs, accompanied by a water load of 1.75 N/mm (0.12kip/ft) on the exposed underwater pile sections. The stream pressurewas calculated in accordance with Eq. 3.7.3.1-1 of AASHTO(2014) and applied as a distributed load to the submerged pile sec-tions above the ground surface. The piles were load rated using thelimit state equation given by Eq. 5.7.4.5-3 of AASHTO (2014) asshown in Eq. (11)

Mux

Mr

� �þ Muy

Mr

� �� 1:0 (11)

where Mux and Muy are the moments about the X- and Y-axes,respectively; andMr = effective moment capacity considering theapplied axial load. Eq. (11) is applicable for these piles because

Fig. 7. (a) SR 595 bridge (image courtesy of Amir Ghiasi) and (b) SR595 bridge model with piles cut off at ground elevation

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the factored axial load is less than 10% of the gross axial capacity.The RFs were found by iterating the RF until the left side ofEq. (11) equaled 1.0.

The addition of water load to the exposed piles primarily caused areduction in compressive loading on the upstream piles and anincrease in compressive loading on the downstream piles. Because thepiles on this bridge were lightly loaded in axial compression, the criti-cal effect from water loads was on the piles in which the axial loadwas reduced because this reduction reduced the effective momentcapacity. As scour increases, all pier piles experienced greatermoment demands from the live load. The critical pile is the secondpile from the upstream side of the bridge that experienced 11.2-kN(2.5-kip) and 66.2-kN (14.9-kip) reduction in compressive load fromthe water load in the as-built and fully scoured condition. The criticallive load was a single truck passing over the pier in the lane farthest tothe downstream side of the bridge because this produced a tensileaxial load and the largest moment on the critical pile. Table 6 providesthe factored loads obtained for the critical pile in the nonscoured andfully scoured condition. Table 7 shows how the RF is affected byscour up to the maximum possible depth. The considered scour depthsinclude removal of P-Y springs representing half of the sand beingscoured, all of the sand being scoured, the entire sand and half of theclay layers being scoured, and all of the clay and sand being scouredwith only the soft limestone embedment remaining.

SFIThe bearing pad distortion limit chosen for this bridge was 13 mm(0.5 in.). The maximum translational bearing pad distortion for theload case with 102 mm (4 in.) of vertical pier settlement was 2 mm(0.082 in.). The distortion in the bearing pads connecting to theabutment with 51 mm (2 in.) of movement was 39.6 mm (1.56 in.).

The maximum bearing pad distortion observed from the model dur-ing the fully scoured condition with water loads was 1.78 mm (0.07in.). Table 8 provides a summary of the functionality indices basedon bearing pad deformation.

Conclusions and FutureWork

A framework for integrated superstructure-substructure load rat-ing of bridges with foundation movements and an index to quan-tify functionality of bridges in the presence of foundation move-ment has been proposed and illustrated through two examplebridges. It was shown through the example bridges that verticalsettlement could substantially impact the load rating of super-structure and substructure elements. In the bridges studied, hori-zontal and rotational movements did not substantially impact thesuperstructure load rating, but did reduce the substructure loadrating and the proposed SFI, which quantifies the amount of toler-able movement. Applying this methodology to bridges with notedsettlement, scour, or substructure deterioration issues can allow

-0.05

0

0.05

0.1

0.15

0.2

0.25

0.3

0 5 9 13 18 22 26 31

Mom

ent D

eman

d (M

N-m

)

Distance Along Bridge (m)

Dead Load

Wearing Surface

Se�lement

Abutment Transla�on

Live Load

Fig. 8. Moment demands from various load cases

Table 6. Calculated Factored Loads without Scour and with Full Scour

Load

No scour 2.44 m of scour Full scour

P (kN) M2 (kN · m) M3 (kN · m) P (kN) M2 (kN · m) M3 (kN · m) P (kN) M2 (kN · m) M3 (kN · m)

DCþDW −428.5 0.4 2.4 −474.3 0.2 3.8 −486.3 0.2 5.4WA 11.2 −6.9 −0.9 57.7 1.1 −0.9 66.2 −4.5 −1.1HL-93þ IM 50.6 −29.4 −170.1 110.3 −8.7 −251.5 113.1 −10.2 −358.0Total −366.7 −35.9 −168.6 −306.2 −7.5 −248.6 −307.0 −14.5 −353.6

Table 7. RFs for the Critical Pile with Varying Scour

Load case Rating factor

No scour, no water load 1.70No scour with water load 1.651.27 m of scour 1.422.44 m of scour 1.283.47 m of scour 0.95Maximum scour to limestone (4.88 m) 0.91

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bridge managers to objectively qualify foundation issues andinform management decisions. Load rating foundation capacityand performance can aid preliminary decision making when con-sidering a foundation for reuse.

In conclusion, the following are the primary findings of thisresearch:1. Load rating of superstructures may be nonconservative if foun-

dation movement has occurred and is not considered.2. Foundation movement and additional loading sources like

water or earth pressure may lower the load rating of foundationelements.

3. The functionality of substructures can be objectively quantifiedthrough use of the SFI.Further investigation is needed into how the RF of various types

of substructures, bearings, and superstructures depend on move-ment. Time-dependent properties, such as creep or relaxation,should be investigated to determine the time dependency of settle-ment loads. For substructure load rating, investigation into the loadrating of damage scenarios and strengthened components needs tobe performed. Investigation should be performed to assess theappropriate inspection and rating interval for substructure move-ment, as well as the appropriate water flows to consider and theirfactors during that interval. Further investigation is also needed toidentify components that will govern the SFI of bridges undergoingfoundation movement.

Acknowledgments

This material is based upon work supported by Federal HighwayAdministration under Contract DTFH61-14-D-00010. Any opinions,findings, and conclusions or recommendations expressed in thispublication are those of the authors and do not necessarily reflect theviews of the Federal Highway Administration.

Supplemental Data

Additional information on limit states typical for bridge founda-tion design can be found in Eqs. S1–S7, which are available onlinein the ASCE Library (www.ascelibrary.org).

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Table 8. Functionality Index Based on Bearing Pad Deformation forThree Damage Scenarios

Damage scenario SFI

102 mm of vertical settlement under one of the piers 8.4651 mm of abutment translation 0Maximum scour and water loading on pier 8.63

© ASCE 04018022-12 J. Bridge Eng.

J. Bridge Eng., 2018, 23(5): 04018022

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