Engineering Structures 36 (2012) 27–38

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Engineering Structures

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Integrated analysis of the performance of pile-supported bridgesunder scoured conditions

Cheng Lin, Caroline Bennett ⇑, Jie Han, Robert L. ParsonsCivil, Environmental, & Architectural Engineering (CEAE) Department, The University of Kansas, 2150 Learned Hall, 1530 W. 15th Street, Lawrence, KS 66045, United States

a r t i c l e i n f o

Article history:Received 17 August 2010Revised 28 July 2011Accepted 8 November 2011Available online 27 December 2011

Keywords:ScourBridgePile foundationSoil–structure interactionStructural analysis

0141-0296/$ - see front matter � 2011 Elsevier Ltd. Adoi:10.1016/j.engstruct.2011.11.015

⇑ Corresponding author.E-mail address: crb@ku.edu (C. Bennett).

a b s t r a c t

Evaluation of scour effects on bridge performance helps predict the safety of bridges under criticalscoured conditions, and as a result, may help prevent unnecessary losses. However, very few studies havebeen conducted on scour evaluation involving an integrated analysis of interactions between water, soils,pile foundations, and bridge structures. In this study, integrated analyses were conducted based on thefollowing procedure: (1) nonlinear soil-structure interactions were considered for foundation analyses;(2) superstructure analyses were conducted by considering a bridge model under design flood conditions;and (3) integration of foundation and superstructure analyses was achieved based on iterative calcula-tions of the stiffness matrices between the two models. The integrated analysis technique described inthis paper enables bridge engineers to model the substructure and superstructure elements separatelyusing software well-suited for the respective analyses, and to link the separate results using an iterativeapproach, forming a complete integrated analysis.

Kansas Bridge 45 was selected as a case study to evaluate scour performance using the developedintegrated analysis technique. Results show that scour increased lateral deflections of pile caps in anexponential manner. Greater lateral load was supported by the abutments as scour proceeded, whilethe resistance of pile foundations to lateral loads decreased at interior piers. Scour resulted in highershear force and bending moment exerting on the pile foundation, and consequently increased the possi-bility of the failure of piles.

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1. Introduction

Scour is the leading cause of bridge failures in the United States,with 60% of bridge failures reported to be due to scour and flood-con-dition failures [1]. Pile foundation capacities can be greatly reduceddue to removal of streambed materials by scour, affecting the capac-ity and stability of the overall bridge system. It is critical for stateDepartments of Transportation (DOTs) to be able to quickly andeffectively determine which bridges in their inventories are scour-critical, enabling responsible management of those bridges duringand after scour events. As this is an important issue facing all stateDOTs, it is of clear benefit to identify and explore analytical methodsfor determining bridge system susceptibility to scour events.

Extensive research has been performed to characterize thebehavior of scour; however, only limited research has examinedhow to evaluate the effects of scour on piles and bridge systems.Avent and Alawady [2] presented a case study showing that afterscour the bridge was susceptible to buckling failure due to the wash-ing out of soils around the pile foundations and the deterioration ofpiles. Daniels et al. [3] investigated the pushover failure of pile bent

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bridges under extreme flood/scour conditions. Hughes et al. [4,5]evaluated the performance of bridges with pile bents in terms ofbuckling and pushover in scour events, and the effectiveness of brac-ing systems used to mitigate scour damage to bridges. Bennett et al.[6] examined the effects of scour depths on the behavior of a laterallyloaded bridge pile group with respect to shear forces, bending mo-ments, and lateral movements of pile groups under the impact ofscour and flood. McConnell and Cann [7] monitored the Indian RiverInlet Bridge under scour, and numerically analyzed scour effects onthe pushover capacity of the substructure and capacity of the super-structure of the bridge. Lin et al. [8] illustrated the scour effects onthe pile-soil interactions.

Research described in the literature [2–8] has been generallylimited to either: detailed analysis of the superstructure with sim-plified substructure analysis, or detailed analysis of the substruc-ture while simplifying the influence of the superstructure. Forexample, scour-affected bridges with pile bents are often analyzedusing simplified conditions for the pile foundation, such as assum-ing 50 for the boundaries, while pile foundations under scour areoften evaluated by neglecting the superstructure. However, scouralters the soil conditions and increases the unsupported pilelength. Such changes in pile foundations will influence thebehavior of the bridge superstructure. Therefore, a more accurate

28 C. Lin et al. / Engineering Structures 36 (2012) 27–38

analysis should account for interaction between water, soil, pilefoundation, and the bridge superstructure elements. An integratedanalysis such as this has not been reported in the literature, but issorely needed to more accurately determine which bridges aremost susceptible to scour, and to more effectively manage thosebridges before, during, and after a scour event.

When bridge engineers are concerned with the performance ofa constructed bridge system under the effects of scour, there arecurrently no good tools available that make scour analysisstraight-forward. It is clear that scour analyses must accuratelyconsider both substructure and superstructure interaction, how-ever, the simplifying assumptions often used cannot necessarilybe considered to be valid in a scour analysis. Thus, a bridge engi-neer currently has few realistic options for analysis that can becompleted in a timely manner with good accuracy. One option thatthe bridge engineer has is to model the entire bridge system (thesuperstructure and the substructure) using only one piece of anal-ysis software. However, commercially-available software packagesare primarily suited for modeling either the superstructure or sub-structure, and are not well-suited to perform both aspects of thetotal analysis. Therefore, this is not always a practical solution. Asecond option is that the bridge engineer could model the super-structure with a tool well-suited for that analysis (STAAD, SAP,RISA, etc.), and model the substructure separately with a toolwell-suited for that analysis (LPILE, FB-MultiPier, etc.). This canresult in accurate results for the superstructure and substructurecomponents of the analysis. However, there is no existing descrip-tion in the literature as to how these separate analyses resultsmight be unified in an efficient, iterative manner to integrate theseparate analyses. Therefore, the intention of this paper is to de-scribe a procedure for implementation of this type of integratedanalysis approach.

This paper proposes an integrated analysis technique which isprimarily aimed at gaging scour effects on the performance ofexisting bridges, but the technique can also improve the accuracyof bridge design. For example, the integrated analysis can easilyand more accurately incorporate foundation loads than the tradi-tional techniques commonly used in the current practice. In prac-tice, foundation loads are commonly obtained by either crudelyassuming the bridge to be fixed at the base of piers or usingDavisson and Robison’s method [9] to generate an approximate fix-ity boundary condition. Neither of these simplified approaches canadequately account for the soil-pile interaction.

In addition to enabling engineers to obtain more realistic foun-dation loads, spring stiffnesses between bridge piers and founda-tions can also be determined based on the integrated analysis,which are useful information for structural engineers designingor analyzing bridges. The spring stiffnesses obtained in this man-ner are expected to better reflect the actual interaction betweenpiers and foundations than the rigid supports commonly assumedin current practice. Therefore, the integrated analysis has signifi-cant implications for the design of pile-supported bridges. It shouldbe pointed out that the integrated analysis is based on equivalentstatic loads, which are already commonly adopted in practice.

In this paper, an integrated analysis for a scour-affected bridgehas been developed and described. Using the developed integratedprocedure, Kansas Bridge 45 was examined as a case study to evalu-ate its performance under scour conditions. This case study was con-ducted to illustrate how the integrated analysis procedure might beused to investigate scour-susceptibility of existing bridges. Lateralresponses of the bridge deck and foundation were investigated atvarious scoured depths. Stiffness of spring supports to the super-structure was also determined, as these values may be of interestto structural engineers when designing the bridge superstructure.Second order effects (referred to as P-delta effects) of the pile foun-dation were considered after scour reached a certain depth.

2. Integrated analysis technique

The objective of this study was to develop an analytical tech-nique able to capture interaction effects between soil, structure,and water to enable bridge engineers to more accurately and effi-ciently determine bridge susceptibility to scour. Furthermore, itwas an objective of the study to accomplish the integration in sucha manner that the general technique could be applied by bridgeengineers for a multitude of pile-supported bridges, using com-monly available foundation and structural analysis software pack-ages. Therefore, it was not desired to use advanced finite elementor finite difference software for the structural or foundation analy-ses (i.e. ABAQUS, ANSYS, FLAC3D), but rather, modeling softwarethat may be more commonly found in design office settings.

The following procedure, which can be readily implemented bystructure engineers, was developed to accurately capture the soil–structure–water interaction: (1) Nonlinear soil-pile interactionwas considered for the foundation analysis; (2) Loads under floodswere considered in the analysis of the bridge superstructure, whichis defined herein as including piers, girders, and concrete deck; and(3) Integration of the foundation and superstructure analyses wasachieved based on iterative calculations of stiffness matrices. Astiffness matrix was generated at the pile cap from the analysisof the pile group, and was then used to define the spring supportsin the superstructure analysis. Loads were applied to the super-structure, and the resulting reactions at the spring-supported basewere then applied to the substructure model as the foundationloads at the pile cap. Based on the new foundation loads, the stiff-ness matrix was updated in the foundation analysis, and was thenused in the superstructure model as new spring supports for fur-ther analysis. Convergence was identified based on equilibriumand compatibility of the superstructure and the pile foundation.During the integrated analysis, the software package FB-MultiPierwas used to analyze the soil-pile interaction while STAAD Pro.was used to analyze the bridge superstructure.

Soil-pile interaction analyses were conducted using the finiteelement analysis program, FB-MultiPier, which has been widelyused to analyze pile foundations with nonlinear soil models for lat-eral, axial and torsional behaviors [4,10,11]. FB-MultiPier is capableof considering multiple bridge piers interconnected by girders;however it has many limitations in structural analysis in compar-ison with STAAD Pro, the latter of which is widely used in structuralanalysis and design [12,13]. For example, FB-MultiPier is only capa-ble of analyzing bridge structures below the girder elevation, and itcannot directly provide design results. However, FB-MultiPier iscapable of considering nonlinear soil effects on pile buckling resis-tance, which is a feature that is difficult to accurately capture instructural analysis software packages such as STAAD Pro, with com-pounding levels of difficulty when second-order effects are desiredwithin the overall system analysis. Therefore, it was determinedthat to accurately capture soil-structure interaction an integratedapproach would be utilized, in which the strengths of two com-monly-used software packages, FB-MultiPier and STAAD Pro, wouldbe harnessed by analytically linking iterative analyses results atthe pile cap boundary separating the substructure analysis (per-formed in FB-MultiPier) from the superstructure analysis (per-formed in STAAD Pro). It should be noted that while this paperdemonstrates integrating two specific software packages, the inte-grated technique is applicable when used with other robust foun-dation and structural analysis software packages.

2.1. Soil and pile interaction

In FB-MultiPier, the ‘‘p–y’’, ‘‘t–z’’, and ‘‘t–h’’ methods were usedto characterize lateral, axial, and torsional soil-pile interactions

C. Lin et al. / Engineering Structures 36 (2012) 27–38 29

respectively. Each of these methods is based on the use of nonlin-ear springs to represent the resistance of the surrounding soil tothe piles. These nonlinear springs are incorporated into the gov-erning equations to model piles interacting with the surroundingsoil. The ‘‘p–y’’ curve originally developed by Matlock and Reese[14] was used to describe the resistance to lateral displacementprovided to the piles by the surrounding soil. The characterizationof ‘‘p–y’’ curve is dependent on different types of soil including softclay, stiff clay, sand, and rock. The ‘‘t–z’’ curve describes soil resis-tance provided to an axially loaded pile (frictional and end bearingresistance) against corresponding vertical (axial) displacement.The ‘‘t–z’’ curve depends on the construction of piles, and isdescribed differently for driven piles [15] and for drilled shafts[16]. Similarly, torsional soil-pile interaction was evaluated usinga ‘‘t–h’’ curve, which is modeled by a hyperbolic curve and pre-sents soil resistance against pile torsional displacement [17]. Eachof these methods was originally developed based on the results offull-scale tests, and they have been widely used to evaluate soiland structure interactions. In FB-MultiPier, these methodologiesare applied by dividing the underground portions of each pileevenly into 16 discretized elements, and applying non-linearsprings for each curve at the 17 nodes to capture the soil resis-tance to the piles.

Piles in a bridge foundation are often installed in groups todevelop the necessary bearing capacity. The resistance of a pilegroup subjected to lateral and/or axial loads is generally less thanthe sum of the individual pile resistances. This is due to a well-doc-umented group effect [18], wherein close spacing between pilestends to result in overlapping regions of soil support for each indi-vidual pile. Accordingly, reduction factors for soil resistance (p-mul-tipliers) were used in the FB-MultiPier analyses to account for the pilegroup effect [17].

2.2. Integration procedure

The procedure used for the integration of the superstructureelements (bridge deck, girders, and piers) and the substructure(pile cap and piles) is summarized in Fig. 1. The procedure is dis-cussed here in a step-wise manner, for clarity:

1. The first step of the integrated analysis was to analyze thebridge superstructure using fixed boundary conditions at thebridge pier bases and abutments using the software STAADPro. 2007. Loads were applied to the ‘‘fixed’’ superstructuremodel as discussed in Section 3.2. Reactions at the bases ofthe piers and abutments (just above the pile cap) were thenobtained from the STAAD Pro. Analysis.

2. Reactions calculated in Step 1 were next used as foundationloads applied to the pile cap in FB-MultiPier to achieve an inte-grated analysis. An analysis of the substructure stiffness wasperformed using FB-MultiPier, which is able to compute flexibil-ity matrices and stiffness matrices for an internally-generatedequivalent point on the pile cap [17]. The stiffness matrix gen-erated in FB-MultiPier included 6 � 6 elements.

3. Since STAAD Pro. 2007, like many other structural analysis soft-ware packages, is only capable of accepting six total spring sup-ports at a point: three axial springs (KFX, KFY, and KFZ) and threerotational springs (KMX, KMY, and KMZ), six spring constants werederived for the superstructure analysis as follows. The equiva-lency method used was as follows: a 6 � 6 flexibility matrixwas first generated in FB-MultiPier, which was then multipliedby the applied loads to calculate corresponding displacementsof the pile cap. The equivalent stiffness of the substructurewas then obtained by dividing the loads by the correspondingdisplacements. This procedure is further illustrated in Fig. 2.

4. Next, the equivalent stiffness of the substructure obtained fromthe FB-MultiPier analysis was used as spring supports for thesuperstructure, replacing the fixity supports used for the initialstep of the bridge superstructure analysis.

5. New base reactions at the spring supports in the superstructureanalysis were next calculated under the originally-applied loadsin the superstructure model.

6. The new reactions from the superstructure analysis were thenassigned to the pile foundation as new foundation loads.

7. New spring stiffnesses were generated after each pile foundationanalysis, and the spring supports in STAAD Pro. were updated ateach iterative step to reflect the revised stiffness from thefoundation.

8. Iterations were performed between the superstructure and thepile foundation until the difference between displacements atthe base of the superstructure (i.e., the bottom of the pier)and at the top of the substructure (i.e., the pile cap) was insig-nificant, or the change between two successive stiffness valuesduring the iteration was considerably small. The convergencedisplacement tolerance was set to be 1 � 10�4 unit (in formovement and rad for rotation), which was consistent withthe internal settings of STAAD Pro. [19].

The integrated analysis using the abovementioned proceduretakes full advantage of the features of the structural analysis andfoundation software packages, in terms of evaluating bridge super-structures and pile foundations. As a result, the complete analysisof a bridge under scoured conditions can be accomplished usingthe proposed integration analysis. A limitation of this integrationanalysis technique is that the ground surface should not be locatedhigher than the elevation of the pile cap, because the superstruc-ture analysis in STAAD Pro.2007 cannot consider the effects of soilunless the engineer chooses to make the soil material equivalentto multilinear springs. Therefore, for bridges with a significant por-tion of the pile foundation embedded into soil, the proposed inte-gration analysis may no longer be suitable, unless additional effortis made to transform the soil into multilinear springs within theSTAAD Pro. analysis. The interested reader is referred to work byLin et al. [20], which describes a method for simplifying surround-ing soil into multilinear springs. Another consideration is thatsome bridge abutments have main walls and wing walls. Whenevaluating pile-supported abutment stiffnesses, the contributionsof main wall, wing wall foundations, backfill soil, and main wallcharacteristics as well as wing wall stiffness are important and de-serve a comprehensive study, thus are beyond the scope of this pa-per. In the case study (Bridge 45) discussed below, the bridgeabutments consisted of only pile bents and pile caps without amain wall or wing wall.

3. Case study

3.1. Bridge description

Bridge 45 is situated in Jewell County, Kansas and carries StateHighway K14 over a local creek. The five-span bridge was con-structed in 1956 and has a total length of 112 m (367 ft). FourW33x141 steel girders with the spacing of 2.3 m (7.5 ft) supportthe bridge deck, as shown in Fig. 3. Bridge 45 has eight piers (fourbents), and each pier is supported by a group of eight HP10x42piles as shown in Fig. 4. Each abutment sits on a pile group consist-ing of 14 vertical and seven battered HP10x42 piles, as shownFig. 5. In Figs. 4 and 5, c = unit weight of soil; c’ = effective unitweight of soil; Cu = undrained shear strength; / = effective frictionangle of soil; e50 = strain value of soil at 50% of maximum stress;K = modulus of subgrade reaction.

Apply forces (reactions from superstructure

analysis ) to pile cap in substructure analysis

Obtain 6 x 6 stiffness matrix

from substructure analysis

Make 6 x 6 stiffness matrix equivalent to 6

spring supports for input in superstructure

analysis

Obtain superstructure reactions at base of piers and

at abutments

Apply gravity and lateral loads to superstructure

START: Superstructure with fixed supports at pier bases

and at abutments

Update spring supports in superstructure analysis

Girders and bridge deck

Pier

All superstructure supports initially fixed ; spring supports used at pier bases in subsequent iterations

Pile Cap

Superstructure Analyses

Substructure Analyses

Fig. 1. Procedure for the integration of substructure and superstructure.

30 C. Lin et al. / Engineering Structures 36 (2012) 27–38

The connections within the superstructure, such as the deck togirders and girders to piers, were assumed rigidly connected orpartially connected. The partial connection considered the effectsof bearings between girders and piers or abutments, for example,pin connections at pier three and roller connections at abutmentsand other piers. The bridge piers, which are tapered, were discret-ized into columns with different sized cross-sections when mod-eled in Staad Pro. 2007 as depicted in Fig. 3.

3.2. Load treatment

Loads considered in the integrated analysis included flood loadswith debris and wind loads, while vertical loads included self-weight of the bridge. Vehicular loads were considered as part ofa buckling analysis. All applied loads above were combined usingload factors of 1.0 to reflect the actual behavior of the existingbridge system. The loads used in this case study represent onecombination of lateral and gravity loads that a bridge would belikely to experience during a scour event, and it should be notedthat different loads and load combinations could be easily accom-modated in the procedure described in this work.

Water loads were calculated using Eq. 1 based on equationC3.7.3.1-1 from the 4th Edition AASHTO-LRFD Bridge Design Spec-ifications [21], provided here in metric units.

p ¼ CDcV2 � 10�6=2 ð1Þ

where V = water velocity (m/s); CD = drag coefficient; c = density ofwater (kg/m3); p = water pressure (MPa).

The design 100-year flood for the case study bridge was taken atthe design elevation of 12.5 m (39.4 ft) above the base of piers. Thedesign flood velocity used in the calculation was 3.66 m/s (12 ft/s).In addition to water loads, debris forces were calculated by multi-plying the water pressure (Eq. 1) by the area of debris accumula-tion at a pier based on Section C3.7.3.1 of the AASHTO-LRFDBridge Design Specifications [21]. The dimension of debris-accumulation was simplified as an inverted triangle in whichthe width was taken as half the sum of adjacent span lengths,but not greater than 13.5 m (45 ft), and the depth was taken as halfthe water depth, not greater than 3.0 m (10 ft). Debris forces wereapplied only to the upstream piers of the bridge due to the rela-tively short distance between upstream and downstream piers(6.90 m [22.6 ft]) as compared with the width of debris at a pier(13.7 m [44.9 ft]).

Debris loads were applied to piers as concentrated loads, whilewater loads were applied as pressure to piers below the maximumdepth of debris-accumulation. Water loads were also consideredfor the exposed pile foundation as scour progressed. However,the hydraulic force was equivalent to a concentrated load appliedto the base of the pier as a part of the superstructure analysis, asshown in Fig. 6. An additional moment would be expected to occuras the centroid location of the hydraulic load moved from theexposed piles up towards the base of the pier, as indicated inFig. 6. Hence, an equal negative moment was added to the baseof the pier to counteract this effect.

Wind loads were calculated using Eqs. 2 and 3, which are basedon Equations 3.8.1.2.1-1 and 3.8.1.1-1 from the 4th Edition AASH-

Fig. 2. Determination of equivalent stiffness.

12.5 m(41ft)

112 m (368 ft)

13.9 m(45.5 ft)

1.1 m(3.5 ft)

PierdiscretizationV V

Ft

Ft

Streamdirection

Upstreampier

downstream pier

M M

2.3 m(7.5 ft)

2.3 m(7.5 ft)

19.5 m (64 ft)

2.3 m(7.5 ft)

24.4 m (80 ft)

Pier#1

Pier#2

Pier#3

Pier#4

Abutment#2

Abutment#1

24.4 m (80 ft)24.4 m (80 ft)19.5 m (64 ft)

Fig. 3. Bridge K45 superstructure.

C. Lin et al. / Engineering Structures 36 (2012) 27–38 31

Fig. 4. Cross section of the pile foundation at piers and scour depths investigated.

Fig. 5. Pile foundation at abutments.

32 C. Lin et al. / Engineering Structures 36 (2012) 27–38

Fe

Me = -Fe(he)

Ground li

Water loads

Centroid positionof water loads

he

Offset fromcentroid position

Pile cap

Pier

Fig. 6. Equivalent system of hydraulic loads at the pile group to the base of the pier.

C. Lin et al. / Engineering Structures 36 (2012) 27–38 33

TO-LRFD Bridge Design Specifications [21], provided here in metricunits.

PD ¼ PBðVDZ=VBÞ2 ð2Þ

Where

VDZ ¼ 2:5V0ðV10=VBÞInðZ=Z0Þ ð3Þ

In Eqs. 2 and 3, PD = wind pressure (MPa); PB = base wind pres-sure (MPa); VDZ = design wind velocity at design elevation (km/hr);VB = base wind velocity, typically taken as 160 km/hr; Z = height ofstructure at which wind loads are calculated (mm); V0 = frictionvelocity (km/hr); V10 = wind velocity at 10,000 mm above lowground (km/hr); and Z0 = friction length of upstream fetch (mm).

Wind loads were calculated above the flood level and wereapplied as concentrated loads to bridge girders at the location of

Fig. 7. Equivalency approach for reaction force

piers. The concentrated wind loads were determined by multiply-ing the tributary area of the bridge deck and fascia girder normal towind loads by the wind pressure calculated using Eq. 2.

3.3. Application of integration procedure in case study

The top of the pile cap was taken at the same elevation as theground line for all the piers for simplicity, which is reasonablebecause pile heads are usually embedded less than 3 m (10 ft) be-low grade [22]. Embedment depths greater than 3 m are usuallynot recommended because excessive embedment of pile head willincrease excavation costs and will not offer much benefit inincreasing the lateral capacity of piles [22]. Five scour depths wereinvestigated in this study, as illustrated in Fig. 4. The soil profiles

s at abutments shown in two dimensions.

Table 1Displacements and rotations of the superstructure and pile foundation from iterations for the upstream row (Scour depth = 0 m).

Iteration No. Dx mm Dy mm Dz mm hx 10�3 rad hy 10�3 rad hz 10�3 rad

Displacement of pile cap1 5.00 �1.08 �0.14 �0.0863 0.931 �1.762 4.95 �1.08 �0.07 �0.0509 0.140 �1.573 4.98 �0.97 �0.08 �0.0546 0.221 �1.584 4.98 �0.97 �0.08 �0.0526 0.201 �1.58

Displacement of pier base1 0 0 0 0 0 02 5.36 �1.02 �0.1 0 0 �2.003 4.95 �0.97 �0.08 �0.0500 0.190 �1.584 4.98 �0.97 �0.08 �0.0500 0.210 �1.58

Relative difference (%)1 100 100 100 100 100 1002 8 6 52 100 100 283 1 1 3 8 14 04 0 0 0 5 4 0

Note: Dx, Dy, and Dz represent displacements along x, y, and z axis respectively; hx, hy, and hz are rotations about the x, y, and z axes respectively.

(a)

(b)

0.0

1.0

2.0

3.0

4.0

5.0

6.0

0 10 20 30 40 50 60 70

Scou

r de

pth

(m)

Pile cap deflection (mm)

Rigid connection_abutment pile groupPartial connection_abutment piel groupRigid connection_downstream pile groupPartial connection_downstream pile groupRigid connection_upstream pile groupPartial connection_upstream pile group

0.0

1.0

2.0

3.0

4.0

5.0

6.0

0 200 400 600 800

Scou

r de

pth

(m)

Shear forces at pile cap (kN)

Upstream pile group

Downstrream pile group

Abutment pile group

Fig. 8. Responses of pile cap at different scour depths, (a) displacement, (b) shearforces.

34 C. Lin et al. / Engineering Structures 36 (2012) 27–38

used for pile foundations at the piers and abutments are shown inFigs. 4 and 5.

The integration of the abutments and their corresponding pilefoundations was performed differently than that for piers. As previ-ously mentioned, one-point reactions are computed in FB-MultiPier(an internally generated equivalent point in FB-MultiPier). However,four girders were supported directly on the pile cap of each abut-ment, and thus six reactions at each of the four girders at each abut-ment could be calculated from the superstructure analysis, asillustrated in Fig. 7. Fig. 7 only shows three degrees of freedomfor each support for the purpose of showing the equivalence pro-cess; the calculation performed considered three dimensional ef-fects (six degrees of freedom for each support). Therefore, it wasnecessary that reaction forces for each of the individual girders (4girders � 6 degrees of freedom each = 24 reactions) be made equiv-alent to a single reaction point (6 reactions) to conduct the founda-tion analysis for the abutments. A similar issue is presented whenreversing the analysis, in that the pile foundation analysis was onlyable to generate stiffness values at a single point (6 spring stiffnessvalues). However, as mentioned, six spring supports should be ap-plied to each of the four girders at each abutment for the super-structure portion of the analysis.

First, four reaction point-loads were transformed into one equiv-alent point-load reaction in a standard coordinate system, as de-tailed in Fig. 2. Lateral loads including wind and flood loads wereapplied to the bridge in positive direction of the x axis (the positivecoordinate system is shown in Fig. 2). Equivalent forces for each pilecap in x, y, and z directions were equal to the total of the reactionforces from the four girders in the corresponding directions. Equiv-alent moments about each axis included moments due to the fourpoint loads, plus concentrated moments. Next, each value in anequivalent spring stiffness matrix (1 � 6 matrix) computed fromthe pile group at each abutment was divided by four. The resultingstiffness matrix was then used as spring supports for each of fourgirders at the abutment. This was an approximate approach to esti-mating the spring supports for the girders. The main concern for thesuperstructure in a scour investigation generally focuses on inves-tigating lateral system behavior, and rotation about the z-axiswas considered negligible (0.0001 degree, in this case). The lowmagnitude of z-axis rotation contributed little to horizontal deflec-tion, and therefore, similar horizontal deflections of each girder andhence similar spring stiffness were reasonably assumed.

3.4. Application of buckling analysis in case study

As scour continually removes the soils surrounding bridge pilefoundations, piles experience greater unsupported lengths and

become increasingly susceptible to buckling failure. Therefore, inaddition to the integrated analyses, a buckling capacity analysis

-15

-10

-5

0

5

10

15

- 200 - 100 0 100 200

Ele

vati

on(m

)

Shear force (kN)

Original ground line

Scour depth(m)

- 15

- 10

- 5

0

5

10

15

- 1000 - 600 - 200 200 600 1000

Bending moment (kN-m)

02.14.3

Fig. 9. Distribution of shear forces and bending moments along the upstream pier and pile foundation.

C. Lin et al. / Engineering Structures 36 (2012) 27–38 35

was performed for a pile group at the pier with increasing scourdepths of 2.1 m (6.9 ft), 3.2 m (10.5 ft), 4.3 m (14.1 ft), and 5.3 m(17.4 ft). In this study, piles and the pile cap were rigidly con-nected. The boundary condition of the pile cap was taken as free.Second-order effects (P � D effects) were considered within theFB-MultiPier analysis. The pile group configuration is shown inFig. 4. A constant lateral water load of 89 kN was applied to the pilecap; this water load was calculated based on a water velocity of1.8 m/s which was assumed as a normal water velocity in thisstudy. An axial load was then added incrementally until the con-vergence in FB-MultiPier could not be reached. The axial load atthe failure of the convergence is defined as the buckling capacityof the pile group. The buckling capacity obtained was then com-pared to the total gravity load applied to the bridge system, includ-ing self-weight and vehicular live loading. This approach was alsoused by Hughes et al. [4] to determine the buckling capacity of asingle pile.

4. Results and discussion

Integration between the pile foundation and the bridge super-structure was performed for the upstream piers, downstream piers,and abutments. Convergence was identified as having beenachieved when the difference between the displacements of thebase of the pier and the pile cap was within 5% of the pile cap dis-placement which ensured the convergence displacement toleranceat 1 � 10�5 unit (in for movement and rad for rotation). The resultspresented below were mainly based on rigid connections betweengirders and piers or abutments, while other results of displace-ments at the pile cap and the bridge deck considering partial con-nections were presented for comparison purposes. Rigidconnections had full six degrees of freedom as compared with par-tial connections which released one or two degrees of freedom andresulted in an easier calculation. Table 1 presents the displacementat the upstream piers during iterations when scour depth was zero,using standard coordinate system shown in Fig. 2. It can be seenthat displacement differences gradually decreased and converged

after four iterations. Convergence was generally achieved after fouror five iterations. Since lateral stability is likely to be a primaryconcern for the integrity of the bridge at flood events, the lateralresponse of the pile foundation and superstructure was investi-gated and presented here as an example. Similar responses fromother directions can be obtained in a similar manner, but are notdiscussed in this paper.

4.1. Lateral response of pile foundations

Pile foundations at the upstream piers, downstream piers, andabutments were investigated. Fig. 8(a) shows that lateral deflec-tions of the pile cap at upstream and downstream pile groupsincreased exponentially with scour depth, e.g. from 5.0 to66.4 mm at the scour depth increasing from 0 to 5.3 m. It can beobserved that the deflections of the pile cap were almost the samewith rigid connections and as with partial connection. This result isanticipated because the partial connection released degrees offreedom in the longitudinal direction and had little effect on thedeflections in the transverse direction. If 38 mm (1.5 in.) of lateraldeflection is considered an upper limit for allowable horizontalmovement [23], then scour depth for the bridge studied shouldnot exceed 4.3 m (14.1 ft). Upstream pile groups underwent great-er deflections at the pile cap than downstream pile groups; thiswas because debris loads were not applied to downstream piers.In contrast to upstream and downstream pile groups, deflectionsof the abutment pile caps were negligible. Little change was ob-served at the abutments while scour depth increased.

To examine the lateral loads transferred from the superstruc-ture to the foundations, shear forces and bending moments werealso calculated, as presented in Figs. 8(b) and 9. The calculationof shear forces at the pile cap was based on the computation of pierbase reactions in the superstructure analysis. In Fig. 8(b), it can beseen that shear forces at upstream and downstream pile capsdecreased with scour depth, while they increased with scour depthat abutment pile caps, e.g. from 152 kN (S = 0 m) to 63.3 kN(S = 5.3 m) for upstream pile caps, and from 489.3 kN (S = 0 m) to783 kN (S = 5.3 m) for abutment pile caps. This result indicates that

0.0

1.0

2.0

3.0

4.0

5.0

6.0

30 40 50 60

Scou

r de

pth

(m)

Maximum deflection of bridge deck (mm)

Rigid connection

Partial connection

Fig. 10. Maximum lateral deflection of bridge deck at different scour depths.

36 C. Lin et al. / Engineering Structures 36 (2012) 27–38

as scour proceeded, fewer loads were borne by the foundationstowards the middle of the bridge while more loads were carriedby abutment foundations. This finding also indicates that the resis-tance of pile groups to lateral loads decreased towards the middleof the bridge when scour occurred. Fig. 9 depicts the shear forcesand bending moments (with respect to z axis in the standard coor-dinate system) along the upstream pier and pile foundation. Threescour depths (i.e. 0 m, 2.1 m, and 4.3 m) from the original groundsurface were examined for the purpose of comparison. Shear forcesand bending moments of individual piles were summed to beequivalent to those of a pile group. Shear forces at the pierdecreased while shear increased at the pile foundation as scourprogressed; in addition, the location of the maximum shear forceof the pile group moved downward as scour progressed, e.g. from4.3 to 7.3 m measured from the top of the pile cap when scourdepth increased from 0 to 4.3 m. Similarly, bending moments atthe pier decreased but increased at the pile group as the scourdeveloped, and the location of the maximum moment also loweredwith deepening scour. These results show that scour resulted inhigher shear force and bending moment moving deeper into thepile foundation, and hence increasing risk of the failure of piles.

Table 2Results of spring support to the superstructure.

Scour depthm

KFX

MN/mKFY

MN/mKFZ

MN/mSupports to upstream row of piers0 30.5 1250 59.41.1 18.9 1130 33.82.1 11.4 1020 15.73.2 7.35 902 7.74.3 4.44 763 3.725.3 2.52 611 2.17

Spring supports to downstream row of piers0 30.6 1230 491.1 19.4 1140 26.52.1 11.7 1030 11.73.2 7.4 904 5.974.3 4.64 793 3.065.3 2.63 631 1.17

Spring supports to abutments0 65.2 884 �0.161.1 65.3 884 �0.152.1 63.7 881 �0.043.2 62.5 880 �0.134.3 59.6 879 �0.455.3 58 878 �0.44

Note: KFX, KFY, and KFZ are spring stiffnesses in the x, y, and z axis directions respectively; K

4.2. Response of bridge superstructure

Fig. 10 shows the maximum lateral deflection of the bridge deckfor both different scour depths, and for both rigid and partialgirder-to-pier connections. Connections had a minimal effect onthe transverse deflections of the bridge deck and the pile cap; par-tial connections resulted in 1–3 mm larger deflection of the bridgedeck than did rigid connections. This result indicated that connec-tion conditions between girders and piers or abutments affectedthe deflection of the bridge deck to a greater extent than the deflec-tion of piles. As would be expected, the maximum lateral deflectionof the bridge deck increased as scour depth increased. Perhapsmore surprising, it can also be seen that the maximum lateraldeflection of the bridge deck increased more slowly with theincreasing depth of scour than the deflections of the pile cap(Fig. 8(a)). This result may be associated with the strong lateralresistance from abutments and the high lateral stiffness of thesuperstructure.

Spring supports at the bases of the bridge piers and abutmentswere calculated as shown in Table 2. The results are expressed inthe standard coordinate system shown in Fig. 2. Spring stiffnesseswere obtained by using equivalency of a 6 � 6 stiffness matrix tosix spring supports as discussed. Table 2 illustrates how scourreduced the stiffness of the spring supports to the bridge super-structure. Consider the stiffness of the upstream pile foundationsas an example. The horizontal stiffness (KFX) and rotational stiff-ness (KMX) decreased from 30.5 MN/m (2089.8 kip/ft) to 7.35 MN/m (503.6 kip/ft) and 9.51 MN-m/deg (7013.9 kip-ft/deg) to5.27 MN-m/deg (3886.8 kip/ft), respectively, when scour depthincreased from 0 m (0 ft) to 3.2 m (10.5 ft). The degradation ofspring stiffness from pile foundations was caused by the fact thatpile foundations towards the middle of the bridge experienced de-creased support from surrounding soils due to scour.

4.3. Buckling of pile foundation

Buckling capacities of the pile group, Pcr, at different scour depthsare shown in Fig. 11. Fig. 12 illustrates that when the pile groupreached the buckling capacity, the downstream piles in the groupcarried the largest axial load, followed by the middle piles, whilethe upstream piles had the lowest axial load. In Fig. 11, it can be seen

KMX

MN-m/degKFY

MN-m/degKMZ

MN-m/deg

9.51 1.53 98.02 0.69 7.056.61 0.26 4.985.27 0.13 2.723.40 0.07 0.342.82 0.03 �0.20

9.94 1.71 8.748.82 0.71 7.057.57 0.30 4.996.3 0.15 2.845.31 0.07 0.694.17 0.03 �0.05

10.1 11 7.8410.1 11 7.7710.1 10.7 7.6210 10.5 7.49

9.93 9.71 6.539.9 9.5 6.35

MX, KMY, and KMZ are the rotational stiffnesses about the x, y, and z axes respectively.

0

2

4

6

8

10

120 50 100 150 200

Dep

th m

easu

red

from

pile

cap

(m

)

Deflection of pile group (m)

2.1

3.2

4.3

5.3

Scour depth (m)

Pcr =8900 kNPcr =8233 kN

Pcr = 6453 kNPcr = 5118 kN

Fig. 11. Buckling capacity of pile group at different scour depths.

0

1

2

3

4

5

6

100 150 200 250 300

Scou

r de

pth

(m)

Buckling loads for individual piles (kN)

Upstream piles in the pile group

Middle piles in the group

Downstream piles in the pile group

Fig. 12. Buckling capacity of individual piles in the pile group at different scourdepths.

C. Lin et al. / Engineering Structures 36 (2012) 27–38 37

that buckling capacity decreased significantly with scour depth, e.g.the capacity decreased by 42% when the scour depth increased from2.1 m (6.9 ft) to 5.3 m (17.4 ft). However, the axial loads exerted onthe pile cap were approximately 1335 kN (255.2 kips) dead load and369 kN (83 kips) live load, which when combined, was considerablysmaller than 5118 kN (1151 kips), the buckling capacity of the pilegroup at the scour depth of 5.3 m (6.9 ft). As previously discussed,the scour depth should not be allowed to exceed 4.3 m (14.1 ft) forpile foundations based on lateral movement limitations for pilefoundations [23]. Therefore, while buckling of pile groups is a veryimportant parameter when considering the capacity of scour-dam-aged pile foundations, it was not found to be the controlling limitstate for the case study examined.

5. Conclusions

A procedure for integrating superstructure and substructureanalyses, accounting for water–soil–substructure–superstructureinteractions, has been presented. Substructure and superstructure

elements were analyzed in a holistic fashion through use of an iter-ative process that took advantage of the strengths of commonly-used geotechnical and structural analysis software packages. Theintegration method described may be readily applied by bridgeengineers to evaluate the susceptibility of bridges to scour, before,during, or after a scour event. Furthermore, the integrated analysisalso provides useful information regarding foundation loads andspring stiffness for bridge analysis that are also applicable to engi-neers designing new bridge structures. The overall integrated ap-proach may also be extended to analyze different types ofbridges not described in the case study.

A case study was carried out to demonstrate how the describedprocedure may be applied by bridge engineers in practice. In the casestudy, the lateral responses of the bridge were evaluated, and thebuckling capacity of the pile group was determined. The followingconclusions can be drawn from the case study, which may be ofuse to bridge engineers applying the integrated analysis technique:

� Connections between girders and piers or abutments had littleinfluence on the transverse deflection of the pile cap and thebridge deck.� Deflection of pile caps at the piers increased exponentially with

scour depth, e.g. from 5.0 to 66.4 mm at scour depth (S) increasingfrom 0 to 5.3 m; however, the pile caps at the abutments experi-enced little deflection even though scour increased significantly.� Scour resulted in reduced shear forces on the pile caps at piers

e.g. from 152 kN (S = 0 m) to 63.3 kN (S = 5.3 m), but increasedshear forces on the pile caps at the abutments, e.g. from489.3 kN (S = 0 m) to 783 kN (S = 5.3 m). This result indicatedthat greater lateral loads would be supported by abutmentfoundations than at interior pier foundations.� Increasing scour depths corresponded to higher shear forces

and bending moments exerting on the piles, and consequentlyincreased the possibility of pile failure.� The bridge deck deflected laterally as scour depth increased, but

the rate of deflection at the deck was lower than that noted atpile caps. The reason was due to the high stiffness of superstruc-ture and the large lateral resistance provided by bridge abut-ments, which were able to restrain lateral deflections of thebridge deck. This is important to recognize because it impliesthat the visible deflections at the bridge superstructure arenot a linear indicator of the deflections that are hidden fromview (pile cap).� The rate of degradation of spring support stiffness of the pile

foundations to the superstructure was very large at small scourdepths, and then gradually decreased as scour proceeded. Theloss of soil support and interaction between soil and pileaccount for the mode of degradation.� Scour could potentially significantly reduce the buckling resis-

tance of a pile group, e.g. from 8900 kN (S = 2.1 m) to 5118 kN(S = 5.3 m); however, for the case study examined, bucklingcapacity was not found to be the controlling mode of failure.

This paper has presented an integrated technique for analyzingbridge substructures and superstructures in an iterative fashion,such that bridge engineers can more accurately use specialized soft-ware without making over-simplifying assumptions about either thesubstructure or superstructure analysis. The integrated analysistechnique presented can be used to efficiently and accurately capturethe effects of scour on bridge system performance, allowing bridgeengineers to better identify and manage bridges susceptible to scour.

Acknowledgements

Research described in this article was funded by the KansasDepartment of Transportation (KDOT), through the KTRANS pro-

38 C. Lin et al. / Engineering Structures 36 (2012) 27–38

gram. The authors would like to express their appreciation to KDOTfor this support. The results and opinions presented in this paperare the authors’ and do not reflect the policy or recommendationof KDOT.

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