Research Article Development of a Vehicle-Bridge-Soil Dynamic Interaction Model...

Research ArticleDevelopment of a Vehicle-Bridge-Soil Dynamic InteractionModel for Scour Damage Modelling

L J Prendergast1 D Hester2 and K Gavin1

1School of Civil Structural and Environmental Engineering University College Dublin Newstead Belfield Dublin 4 Ireland2School of Planning Architecture and Civil Engineering Queenrsquos University Belfast University Road Belfast BT7 1NN UK

Correspondence should be addressed to L J Prendergast lukeprendergastucdconnectie

Received 1 July 2015 Revised 19 August 2015 Accepted 23 August 2015

Academic Editor Ruqiang Yan

Copyright copy 2016 L J Prendergast et alThis is an open access article distributed under theCreativeCommonsAttribution Licensewhich permits unrestricted use distribution and reproduction in any medium provided the original work is properly cited

Damage detection in bridges using vibration-based methods is an area of growing research interest Improved assessmentmethodologies combined with state-of-the-art sensor technology are rapidly making these approaches applicable for real-worldstructures Applying these techniques to the detection and monitoring of scour around bridge foundations has remainedchallenging however this area has gained attraction in recent years Several authors have investigated a range of methods butthere is still significant work required to achieve a rounded and widely applicable methodology to detect and monitor scour Thispaper presents a novel Vehicle-Bridge-Soil Dynamic Interaction (VBSDI) model which can be used to simulate the effect of scouron an integral bridgeThe model outputs dynamic signals which can be analysed to determine modal parameters and the variationof these parameters with respect to scour can be examined The key novelty of this model is that it is the first numerical model forsimulating scour that combines a realistic vehicle loadingmodel with a robust foundation soil responsemodelThis paper provides adescription of the model development and explains the mathematical theory underlying the model Finally a case study applicationof the model using typical bridge soil and vehicle properties is provided

1 Introduction

11 Motivation for Modelling Damage in Civil EngineeringStructures Farrar andWorden [1] give a very useful overviewof the area of structural healthmonitoring (SHM)They pointout that the motivation for governments and private compa-nies implementing this technology is due to the economic andpotentially lifesaving impact it can have Dimarogonas [2]points out that online damage detectionmonitoring startedin the early 1970s when power companies started lookingat developing ways of identifying defects in rotating shaftswhile machinery was in use To date this kind of conditionmonitoring of rotatingmachinery has been themost success-ful application of SHM and it is almost entirely non-modelbased [1] Effectively these machines have quite a narrowrange of operating behaviours so anomalies are relativelyeasy to identify As there were many of these machines inservice over time it was thus possible to develop databasesthat allowed specific types of damage (eg chipped gear teethor damaged bearings) to be identified fromparticular features

of the machinersquos vibration signature This concept of lookingfor damage-sensitive features in a response signal is centralto SHM Typically an SHM algorithm works by seekinga damage feature in a response signal or by identifyinga change in some characteristic of the structure when itis damaged for example natural frequency mode shapesor damping For rotating machinery these damage featurescould be identified relatively easily through experiments orby correlating monitoring data with subsequent servicingrecords The first instance of applying the SHM philosophyto large scale civil engineering structures was in the 1970sand 80s when the oil industry began attempting to apply thistechnology to offshore platforms In comparison to damagearising in rotating machines this time the structures werelarge and multiple damage locationsseverities were possibleso the nature of the damage features was typically unknownTherefore it was necessary to simulate candidate damagescenarios using numerical models in order to for exampleobserve how that damage affected the frequency of theplatform The idea behind this was that if this frequency was

Hindawi Publishing CorporationShock and VibrationVolume 2016 Article ID 7871089 15 pageshttpdxdoiorg10115520167871089

2 Shock and Vibration

subsequently observed in the field it could be correlated to agiven damage scenario In general the challenges of applyingvibration-based SHM to offshore platforms are significant asfactors such as variations in the mass of the structure dueto changes in the mass of the storage tanks and changes inthe amount of marine growth on the structure can proveproblematic

The development of SHM tools for bridge engineeringfaces the same challenges as the oil industry in that it isvery rare that one can take a full size test piece and applydamage for the purpose of developing monitoring tools Infact it is practically unheard of in bridge engineering asthe structures themselves are just too valuableimportant tointerfere with Therefore when researchers wish to try anddevelop a new SHM algorithm to detect a particular type ofdefect in the structure the first task is to try and understandhow damage affects the response of the structure To establishthis their options (broadly speaking) are to use a computermodel [3] andor a laboratory experiment using a scaledmodel of the structure [4] Occasionally it will be possibleto test at full scale when a bridge is due to be retrofittedfor example a scoured but retrofitted bridge in Italy see [5]However in many cases the first option is a computer modelto undertake simulations of candidate damage scenariosThe challenge therefore is to develop a model that outputsrealistic results A numerical model that outputs signals thatare representative of those likely to be encountered on thereal structure is a very useful tool when trying to developnew SHM algorithms This paper aims to develop just sucha model as by including vehicle-bridge interaction and soil-structure interaction every effort ismade tomake the loading(applied to the bridge) and the (soil) boundary conditions ofthe model as realistic as possible It should be noted that theaim of this paper is not to develop a new SHM technique forscour detection but to present the basis of a model to make iteasy for others to test emerging SHM techniques by allowingthem to generate realistic bridge response signals occurringdue to foundation scour Section 12 gives some examples ofnumerical models developed to simulate damage in beam-like structures where the model outputs (eg accelerationvelocity or displacement signals) were subsequently used asinputs to damage detection algorithmsThis section also pro-vides a discussion on previous works focussed on modellingscour damage

12 Modelling Structural Damage for SHM Algorithm Devel-opment Over the past two decades several authors haveprepared models of damaged structures with a view todeveloping SHM algorithms to detect this type of damage Aparticular focus has been given to models which representlocalised damage in a structure (eg cracking or sectionloss) Ostachowicz and Krawczak [6] describe the differentmethods commonly used to model structural stiffness lossdue to damage Friswell and Penny [7] give a very usefuloverview on crack modelling for SHM They point out thatapproaches for modelling cracks in beam type structurestypically fall into three categories local stiffness reduction[8] discrete spring models [9] and complex models in twoor three dimensionsThey compare the three approaches and

broadly speaking they conclude that for structural healthmonitoring which utilises low frequency vibration simplemodels of crack flexibility based on beam elements areadequate

Other authors have developed models to simulate theresponse signals of damaged beam structures to movingloads and then used the signals from these models as inputsto SHM algorithms A number of authors have simulatedthe structure as having a localised loss in stiffness andthen calculated the response to a moving point force [10]Hester and Gonzalez [11] modelled a similar type of damagehowever they modelled the moving load as a sprung vehicleto incorporate vehicle-bridge interaction effects that is tomake the simulated response signals as realistic as possibleThis is important when numerically testing the versatility ofa new SHM algorithm before applying it to a real structureOthers have postulated that the occurrence of damage willaffect the damping of the bridge and prepared numericalmodels to simulate this by analysing the vehicle accelerationsignals output from the model [12] that is this is an indirectmonitoring approach as the vehicle response passing over adamaged bridge is used to detect the damage feature

In terms of scour modelling several authors have inves-tigated the effect of scour on the static and dynamic prop-erties of bridges using numerical methods The principleunderlying these approaches is that during scour loss ofsoil contact occurs which leads to higher applied stress overthe area of soil remaining in contact with the foundationThis coupled with the nonlinear stiffness of soils leadsto lower operational system stiffness [13] Therefore scourpresence should be detectable as a change in the dynamicproperties of the structure Ju [14] developed a 3D FE modelof a bridge incorporating soil-structure and fluid-structureinteraction to assess the magnitude of the change in naturalfrequency of the bridge with increasing scourThey validatedthe bridge natural frequencies from the model against a full-scale field experiment and then used the numerical modelto study various scour conditions and how it affected thebridgersquos natural frequency They concluded that scour causesa reduction in bridge natural frequency but the magnitudeof the frequency change with scour is affected by varyingfoundation geometry and layering in foundation soils Chenet al [15] developed a full FE model of a cable-stayedbridge with a pylon and a pier They updated the modelproperties to obtain a match tomodal data obtained from theactual structure They then used known data about the pylonfoundation condition to obtain representative soil stiffness(matching the stiffness of the actual soil) The numericalmodel was then used to update the scour depth around thepier until the predicted frequency data matched the observeddata In this case the numerical model was used to ascertainthe actual scour condition around the real pier and this paperserves as a successful real-life application of a vibration-basedscour detectionmethod Klinga and Alipour [16] developed anumerical model to assess the effect of scour on various staticand dynamic performance features of a bridge They usedtheir model to perform pushover analyses buckling analysesandmodal analyses under extreme scour conditions to assessthe effect of scour on the various bridge elements such as

Shock and Vibration 3

the piles and columnsThey present a number of case studiesof affected performance features due to scour

Unlike authors working in the area of bridge damage viacracking and so forth for the purpose of scour detectionmany authors have developed models to specifically performa single task only that is to establish the depth of scouraround a foundation element or assess the change in bridgeperformance under scoured conditions No authors to datehave developed a model capable of rapidly modelling avariety of bridge scour scenarios with the flexibility to testemerging SHM techniques This paper aims to develop anumerical model that can generate dynamic signals (dis-placement velocity and acceleration) from a bridge undera variety of input loadingscour scenarios in order to allowusers to develop andor test SHM algorithms Because ofthe increasing popularity of integral bridges the structuremodelled in this paper is a two-span integral bridge Detailsabout this type of bridge are given in Section 21 Section 13summarises the aims of the model presented in this paper

13 Generic Algorithm for Modelling Integral Bridge Scour

131 Method In order to develop a representative vehicle-bridge interaction model for the purpose of simulating theeffect of scour on the dynamic response of an integralbridge a number of key assumptions are made In the firstinstance to aid in the rapid generation of dynamic datathe integral bridge is assumed to act as a 2D frame systemThe reason behind this is twofold (i) it is assumed thatthe dynamic movements of interest for scour on an integralbridge predominately take place in the longitudinal direction(it is acknowledged that this assumption may not hold truefor other bridge types eg [15] found that for a cable-stayedbridge the first horizontal flexural and second torsional modeof the pylon were the most sensitive to scour) and (ii) 3Dnumerical modelling is very user and computationally costlyand the resulting signals of interest are not expected to varysignificantly from those in a 2D system For these reasonstransverse and torsional motion of the integral bridge isneglected The benefit of a 2D frame system is that a varietyof representative bridges can be rapidly modelled as the useronly has to specify a relatively small number of parameters(bridge element structural and geometric properties vehicleparameters such as axle spacing and mass) For the purposeof generating signals to test emerging SHM concepts this isdeemed adequate

Scour can be modelled around both the central pier andthe left and right abutments of the bridge and is considered asthe increase in effective length of the bridge pierabutmentscorresponding to a decrease in bed elevation level Thestiffness of the soil can be varied to be representative ofsoils from loose to dense in situ conditions that are typicalof the range of ground conditions encountered in riverineenvironmentsThe foundation scourmodel used in this paperis derived from previously validated work undertaken by theauthors (see Section 132) The method for modelling thevarious bridge elements namely deck abutments pier andsoil is discussed in detail in Section 2

minus1

minus2

minus3

minus4

minus5

minus6

minus70 5 10 15 20 25 30 35

0

Frequency (Hz)

Scou

r dep

th (m

)

Experimental frequencyNumerical (shear wave) frequencyNumerical (CPT) frequency

Figure 1 Frequency change with scour for experimental andnumerical models [17]

132 Validation of Scour Model The greatest uncertaintywith regard to bridge input parameters relates to the soilstiffness It is imperative to specify soil properties that ade-quately reflect the boundary stiffness effects of the soil likelyto be encountered in the field for the purpose of accuratescour modelling The method for deriving soil stiffness forscour evaluation comes from an experimental investigationundertaken by [17] In this work the authors measured thechange in the natural frequency of a full-scale pile tomanuallyinduced scour The field measurements were compared tonumerical models developed using a Winkler spring-beammethodology (see Section 23) Two different methods wereused to estimate the soil stiffness the first derived soil stiffnessbased on the shear modulus of the soil obtained from theMultichannel Analysis of Surface Waves (MASW) (see [18])the second method used estimates of shear modulus froma correlation to measured Cone Penetration Test (CPT) tipresistance (119902

119888) data measured at the experimental site The

results of the frequency change with scour are reproduced inFigure 1

Figure 1 shows that the experimental data and the numer-ical predictions from both numerical models match wellTherefore for the purpose of scour modelling the methoddeveloped in [17 19] is used to generate representative soilprofiles (and corresponding spring stiffness coefficients) fora range of soil density states This is further discussed in thenext sections

2 Structural Model Development

Thenumerical model is developed in theMATLAB program-ming environmentThe various components of themodel aredescribed in the following subsections Section 21 describesthe integral bridge to be modelled Section 22 describesthe mathematical modelling philosophy Sections 23 and 24describe how the interaction effects with foundation soil andvehicle are considered respectively

21 Integral Bridges Integral bridges are becoming increas-ingly popular as they do not require a conventional expansion


Bank seatBridge deck

Abutment

Pile caps

Abutment

Bridge U-beams (exposed)

Crosshead

Central

Central

columns

Abutment columns

piles

Abutment piles

pier

pier piles

Figure 2 3D rendering showing typical structural arrangement of a two-span integral bridge with flexible abutment supports

joint The desire to (where possible) avoid using expansionjoints is due to the fact that they tend to give maintenanceproblems For example after surveying approximately twohundred concrete highway bridges in the UK Wallbank(1989) (cited in [20]) found that expansion joints werea source of costly and disruptive maintenance work Inresponse to this finding in 1996 the UK Highways Agencypublished Technical Note BA 42 which recommended (withsome exceptions) that for new bridges up to 60m in lengthintegral construction should be considered

The Steel Construction Institute (2015) [21] gives a usefulsummary on the different types of integral bridges thathave been used over the years Broadly speaking integralbridges can be split into 4 types (i) frame abutments thisis when the abutments form a portal frame with the bridgesuperstructure (ii) bank pad abutments in this type thebank pad end support is integral to the deck and the bankpad is able to slide and rotate on the soil (iii) flexiblesupport abutments this is where the bank pad is supportedby pilescolumns that are not in contact with the soil thatis they have an annular space around them and this makesthem more flexible and therefore better able to absorb thethermal movements of the bridge deck and (iv) semi-integral(screen end abutments) in this case there is an end screenwall (at the end of the deck) which is integral to the deckbeams however this wall does not provide support to thebeams Instead support is provided by some other structuralelement (eg a piled bank seat) and bearings are used toaccommodate deck movements

In this paper the flexible support abutment type ismodelled as this form of construction is most commonlyused Figure 2 shows an annotated schematic 3D renderingof a typical two-span integral bridge with flexible abutmentcolumns The deck is formed from prestressed concrete U-beams and an in situ slab The outline of the ends of thebeams can be seen at the left hand end of the deck wherethe beams are cast into an end diaphragmbank seat that issupported on the flexible columns The deck beams can beseen on the right hand span (the deck slab is removed forillustrative purposes) No dimensions are indicated on thefigure as the numerical model that is developed is intendedto model bridges of this type but span length pile length

section modulus and so forth can be defined by the user Inthis model the longitudinal stability of the bridge is providedprimarily by the central pier which is significantly stiffer(longitudinally) than the abutment columns Figure 3 showsan integral bridge (flexible abutment type) in its completedstate For aesthetic reasons the abutment columns are oftenhidden from view in the completed structure typically usingreinforced earth which is the approach used on the bridgeshown in Figure 3

22 Bridge Elements The bridge structure is modelled as a2D frame whereby grouped geometric properties are usedto model the various structural elements namely the deckabutments central pier and the foundation piles The bridgeelements are modelled using 6-degree-of-freedom (6-DOF)Euler-Bernoulli frame elements [22] The individual bridgeelements are assembled together to create global mass [M

119866]

and stiffness [K119866] matrices for the full structure using the

assembly procedure outlined in [22] The dynamic responseof the bridge is governed by the second-order matrix differ-ential equation shown in

[M119866]

x1(119905)

x2(119905)

x119873(119905)

+ [C119866]

x1(119905)

x2(119905)

x119873(119905)

+ [K119866]

x1(119905)

x2(119905)

x119873(119905)

=

F1(119905)

F2(119905)

F119873(119905)

(1)

where [M119866] [C119866] and [K

119866] are the (119873 times 119873) global mass

damping and stiffness matrices for the model respectivelyand119873 is the total number of degrees of freedom in the systemThe vector x(119905) describes the displacement of every degreeof freedom for each time step in the analysis Similarly thevectors x(119905) and x(119905) describe the velocity and accelerationof every degree of freedom for each time step The vector


F(119905) describes the external forces acting on each of thedegrees of freedom for a given time step in the numericalmodel The damping matrix [C

119866] is calculated assuming a

Rayleigh approach in line with the recommendations of [23]The time-domain dynamic response of the system is obtainedby solving (1) using numerical integration In the modeldescribed in this paper the Wilson-120579 integration scheme isemployed which is a special case of the linear accelerationmethod [24]

23 Winkler Soil Modelling Dynamic soil-structure inter-action covers a broad spectrum of applications from large-strain cyclic load-displacement regimes to small-strain lowamplitude vibrations Soil behaviour is highly nonlinear andin particular its stiffness changes nonlinearly with strainTheresponse of soil-structure systems is heavily dependent on themagnitude and the nature of external loading and a variety ofmethods exist that aim to accurately capture the behaviourof foundation systems In this paper it is assumed that theexternal loading from vehicles passing over the bridge willlead to very small lateral strains being imparted into thesoil surrounding the piles Therefore it is assumed that thestrains remain within the ldquosmall-strainrdquo linear-elastic regionof the soil response curve This means the discretised soilimpedances can be characterised by fixed value constantsindependent of the strain The methods for modelling thecontribution of the soil are discussed in the following sub-sections namely the mathematical assumptions underlyingthe process (Section 231) and the derivation of representativesoil stiffness coefficients (Section 232)

231 Mathematical Assumptions The bridge foundationcomprises piled foundation elements embedded in soil Thesoil is modelled using a Winkler framework whereby thecontinuous soil layers are replaced by representative discretemutually independent and closely spaced spring elements[25 26]These spring elements have two translational degreesof freedom (2 DOFs) and permit one-dimensional uniaxialmovement along the longitudinal axis of the spring For thepurpose of dynamic interaction modelling with the bridgestructure the soil springs are assumed to provide dynamicimpedance only and inertial effects are ignored In modellingterms the springs have a null mass matrix The stiffnessmatrix formulation [K

119904119894] for these spring elements is shown

in

[K119904119894] = 119896119904119894

[1 minus1

minus1 1] 119896

119904119894ge 0 (2)

where 119896119904119894is the stiffness coefficient of the 119894th spring element

As discussed previously 119896119904119894remains constant with strain in

the spring due to the assumption of linear-elasticity withsmall soil displacements These springs are addedintegratedinto the global stiffness matrix [K

119866] (for the full bridge

structure) by couplingldquoattachingrdquo one end of the spring tothe pile nodes in the model that is the pile nodes locatedbelow the assumed ground line The free end of each springis restricted frommotion to model the confining effect of thesoil by setting the permissible displacement of each of these

Reinforced earth

Figure 3 Two-span integral bridge with flexible abutment supports

degrees of freedom to zero Effectively every spring added tothe model adds one extra degree of freedom to the globalmatrices [M

119866] [C119866] and [K

119866] A visualisation of the spring

elements is shown in Figure 5

232 Derivation of Soil Spring Stiffness Coefficients (119896119904119894)

Using a discrete spring modelling framework as per theWinkler regime it is imperative to specify spring stiffnesscoefficients that accuratelymodel the small-strain continuumsoil behaviour at the soil-pile interfaces In this paper themethod described in Prendergast et al [19] is used to calculaterepresentative soil stiffness coefficients for a range of soilstates from loose to very dense sand

The process involves (i) generating synthetic Cone Pene-tration Test (CPT) 119902

119888profiles that correspond to the stresses

measured when a cone tip passes through a loose mediumdense and dense sand deposit (Section 232(1)) (ii) corre-lating these CPT 119902

119888profiles to profiles of the small-strain

shear modulus (1198660) for the three soil profiles adopted (Sec-

tion 232(2)) and (iii) converting the shear modulus profilesinto profiles of modulus of subgrade reaction (119870) and henceinto individual spring coefficients (119896

119904119894) (Section 232(3))

(1) Hypothetical CPT 119902119888Profile As part of a standard

geotechnical site investigation Cone Penetration Tests areoften carried out whereby an instrumented cone is pushedinto the soil at a constant rate and the tip stresses and sidesleeve friction aremeasured at discrete depth intervals Lunneand Christoffersen [27] proposed an expression relating thecone tip resistance 119902

119888value with the soilrsquos effective stress

(1205901015840V) and relative density (119863119903) A rearranged version of this

expression is shown in

119902119888= 60 (120590

1015840

V)07

exp (291119863119903) (3)

Using (3) a hypothetical CPT 119902119888profile can be derived from

effective stress and relative density conditions 119863119903values

of 03 (30) 05 (50) and 08 (80) are assumed tocorrespond to the properties of a loose medium denseand dense sand deposit respectively [28] and are assumedconstant with depth for uniform soils The vertical effectivestress can be calculated assuming values of bulk unit weight(120574119887) of 18 19 and 20 kNmminus3 to approximate loose medium

dense and dense sand deposits and the bulk unit weight ofwater (120574

119908) is assumed as 10 kNmminus3 Although these synthetic

CPT 119902119888profiles are idealised they do conform quite well

to the values expected for the given soil conditions [29]


0 5 10 15 20 25

0D

epth

(m)

qc medium denseqc dense

qc loose

minus5

minus10

minus15

CPT qc (MPa)

(a)

Dep

th (m

)

0 20 40 60 80 100 120

0

G0 medium denseG0 dense

G0 loose

minus5

minus10

minus15

G0 (MPa)

(b)

Dep

th (m

)

0 100 200 300 400

0

K (MPa)

K medium denseK dense

K loose

minus5

minus10

minus15

(c)

Dep

th (m

)

0 05 1 15 2

0

minus5

minus10

minus15

ks (N mminus1) times108

ks medium denseks dense

ks loose

(d)

Figure 4 Example soil profiles (a) CPT 119902119888profiles for loose medium dense and dense sand (b)119866

0profiles (c)modulus of subgrade reaction

(119870) profiles and (d) individual 119896119904values for loose medium dense and dense sand

Figure 4(a) shows typical 119902119888profiles generated using this

approach

(2) Convert CPT 119902119888to Profiles of 119866

0 There are a number

of correlations linking the CPT 119902119888value to the small-strain

shear modulus (1198660) for a given soil deposit In this paper the

expression suggested in the Imperial College design method(IC-05) for driven piles in sand and clays [30] is used Thisexpression was originally suggested by Baldi et al [31] and isshown in

1198660= 119902119888[119860 + 119861120578 minus 119862120578

2

]minus1

(4)

where 119860 = 00203 119861 = 000125 119862 = 1216119864 minus 6 and120578 = 119902119888(1198751198861205901015840

V)minus05 with 119875

119886= 100 kPa and 120590

1015840

V = vertical effectivestress (kPa) Using (4) the synthetic 119902

119888profiles for loose

medium dense and dense sand may be converted to profiles

of the small-strain shear modulus An example of this for a15m deep stratum is shown in Figure 4(b)

(3) Calculate Modulus of Subgrade Reaction (119870) Profile Thefirst step in calculating the modulus of subgrade reactionfrom119866

0is to convert119866

0data to small-strain Youngrsquosmodulus

(1198640) data using the relation shown in

1198640= 21198660(1 + V) (5)

where ] Poissonrsquos ratio is assumed as 01 Using 1198640profile for

the soil the modulus of subgrade reaction (119870) for the soil-pile interface may be calculated using the expression shownin [17 32]

119870 =101198640

1 minus V2[11986401198634

119864119901119868119901

]

112

(6)

where 119863 is the effective diameter of the pile group (m) 119864119901

is Youngrsquos modulus of the pile material (Nmminus2) and 119868119901is


xxx

middot middot middot middot middot middot

Mb Ip o

yb

y2 y1

Ks2 Ks1

Kt2

mw2 mw1Kt1

Cs1Cs2

E I 120588 A

kSN kSN kSN

kS2 kS2 kS2

kS1 kS1 kS1

SS1S2

120593pDirection of motion

1

4

2

5

3

6

Road profile Classes ldquoArdquo to ldquoErdquo

Figure 5 Continuum model of half car crossing an integral bridge(not to scale)

the effective moment of inertia of the pile group (m4) Theeffective diameter of the pile group is obtained by summingthe diameters of the individual piles in the group and theeffective moment of inertia of the pile group is obtained inthe same way Individual soil stiffness coefficients (119896

119904119894) are

calculated by multiplying 119870 value at a given spring depth bythe spacing between springs at that depth

An example of converting 1198660data from Figure 4(b)

into a profile of the modulus of subgrade reaction (119870) isshown in Figure 4(c) and hence that into individual springcoefficients (119896

119904119894) is shown in Figure 4(d) In this figure the

effective diameter of the pile group is taken as 6m (8 piles times075m diameter each) and the pile material is assumed to beconcrete

24 Vehicle Model and Interaction

241 Overview of Vehicle-Bridge Interaction (VBI) ProblemHaving developed a finite element model of bridge-soilinteraction the next step toward implementing a Vehicle-Bridge-Soil Dynamic Interaction (VBSDI) model is to modelhow the vehicle applies loading to the bridge as it passes overit The important point to note is that as a vehicle passes overa bridge the loading it applies to the bridge is not constant asit is affected by the road profile (surface roughness) the speedof the vehicle and the properties of the vehicle

The fundamental challenge with vehicle-bridge interac-tion modelling is that the movement of the bridge influ-ences movements of the vehicle which in turn influencemovements of the bridge When studying vehicle-bridgeinteraction problems two sets of equations can be writtenone set for the vehicle and one set for the bridge To satisfycompatibility the contact forces in both subsystems must bethe same and it is these contact forces that make the twosets of equations coupled Yang et al [23] give an overviewof the problem as well as a description of some commonlyused techniques such as the iterative method the dynamiccondensation method and Yangrsquos VBI element Each of the

Table 1 Typical parameters for truck model

Dimensional data

Dimensions(m)

Wheel base (119878) 55Dist from centre of mass to front axle (119878

1) 366

Dist from centre of mass to rear axle (1198782) 184

Mass and inertia

Mass (kg)Front wheelaxle mass (119898

1199081) 700

Rear wheelaxle mass (1198981199082) 1100

Sprung body mass (119898119887) 13300

Inertia (kgm2) Pitch moment of inertia of truck (119868119901) 41008

SuspensionSpring stiffness(kNmminus1)

Front axle (1198701199041) 400

Rear axle (1198701199042) 1000

Damping(kN smminus1)

Front axle (1198621199041) 10

Rear axle (1198621199042) 10

Tyre stiffness(kNmminus1)

Front axle (K1199051) 1750

Rear axle (K1199052) 3500

methods has certain advantages and disadvantages howeverfor the purposes of this study the iterative approach wassuitable Iterative techniques have been used by Green andCebon [33] and Yang and Fonder [34] and are described inmore detail in Section 244

Before describing how vehicle-bridge interaction isimplemented it is first useful to look at the bridge-vehiclemodel see Figure 5 In this arrangement the vehicle has4 degrees of freedom the pitch of the sprung body mass120593119901(119905) the displacement of the sprung body mass y

119887(119905) the

displacement of unsprung mass 1 y1(119905) and the displacement

of unsprung mass 2 y2(119905) Unsprung masses 1 and 2 represent

the masses of the front and rear axle assembly

242 Vehicle Properties In this study the vehicle modelledis a two-axle truck The geometry of the test truck can betailored by the user to represent any type of two-axle truckthat is the sprung body mass axle spacing unsprung axlemass suspension damping and stiffness and so forth can allbe modified by the user Harris et al [35] give the typicalsuspension and tyre properties for this kind of vehicle andTable 1 gives a summary of the vehicle properties that wereused in this study

243 Generating a Road Profile The road profile is simply anarray of numbers that defines the height of the road surfaceat discrete intervals along the length of the bridge (eg every1 cm) The length of road profile necessary depends on thespan of the bridge the wheel base of the vehicle and thedesired approach distance The purpose of modelling themovement of the vehicle as it approaches the bridge is to allowit to reach a steady state of vibration before it reaches thebridge thereby making its subsequent interaction with thebridge more realistic A typical approach length used is of theorder of 100m Cebon [36] describes how the topography ofa given road profile can be classified in accordance with the


ISO standard for example a road profile can be classified asldquovery goodrdquo ldquogoodrdquo ldquoaveragerdquo ldquopoorrdquo or ldquovery poorrdquo Cebonalso describes how an artificial road surface topography ofa given roughnessclassification can be generated for use intime-domain vehicle vibration simulations While the roadprofile generator defines the height of equally spaced pointsalong the road (eg spatially distributed every 1 cm) it isinappropriate to use these heights directly in the model Thereason for this is that the wheel of the truck is not supportedby just one road profile ordinate Typical truck tyres spanapproximately 24 cm therefore the wheel rests upon 24 roadprofile ordinates simultaneously (for ordinates spaced at 1 cmintervals) To take account of this fact the road profile used inthe model is obtained by applying a moving average filter tothe road profile given by the road profile generator to obtainthe average ordinate height over the span of the wheel Finallyit is necessary to extract from the global road profile theroad profile experienced by the front axle on the approachsection 119903

1119860(119905) and on the bridge section 119903

1(119905) and to do

the same for the rear axle (The road profile is generatedspatially however for simulation purposes the importantthing to know is the height of the road profile ordinateunder each axle at each time step) It is also important tonote that the purpose behind incorporating a road profilein the model is to afford a more realistic treatment of thevehicle-bridge interaction problem and to allow researchersto test the resilience of emerging SHM techniques under avariety of conditions Road profiles are generated randomlyaccording to the specified road profile classification and it isnot intended to model the road profile of a specific bridgeFigure 6 shows example road profiles generated for a 50mlong bridge span The road surface roughness is varied fromClass ldquo119860rdquo (very good) toClass ldquo119864rdquo (very poor) for the purposeof illustration

244 Iterative VBI Procedure By using the equations ofFryba [37] it is possible to develop a stiffness [KV] mass[MV] and damping [CV] matrix for the vehicle The dynamicresponse of the vehicle is modelled as shown in

[MV]

119901(119905)

y119887(119905)

y1(119905)

y2(119905)

+ [CV]

119901(119905)

y119887(119905)

y1(119905)

y2(119905)

+ [KV]

120593119901(119905)

y119887(119905)

y1(119905)

y2(119905)

= FV

(7)

where FV is the vector of forces acting on the vehicle degreesof freedom for a given time step In the first instance thevehicle is run across the bridge assuming the bridge does notexperience any deflection The displacement of each vehicleaxle y

1(119905) and y

2(119905) is then obtained using the Wilson-120579

method applied to (7) and the contact forces between thevehicle and the road surface for each time step are calculatedin

F1(119905)

F2(119905)

= [K1199051

00 K

1199052

]y1(119905)

y2(119905)

(8)

0 5 10 15 20 25 30 35 40 45 50

0

002

004

006

008

01

Distance (m)

Hei

ght (

m)

Class ldquoArdquoClass ldquoBrdquoClass ldquoCrdquo

Class ldquoDrdquoClass ldquoErdquo

minus002

minus004

Figure 6 Example road profiles Class ldquo119860rdquo to Class ldquo119864rdquo for a 50mlong bridge

where K1199051

and K1199052

are the front and rear tyre stiffnessrespectively The contact forces obtained in (8) can thenbe applied to the FE model of the bridge This is achievedby defining F(119905) in (1) using Hermitian shape functionsto apportion the axle loads F

1(119905) and F

2(119905) to the bridge

nodes since the position of the loads x(119905) at every timestep is known Once F(119905) has been populated the Wilson-120579 method is used to calculate the displacement of each ofthe bridge degrees of freedom at each time step Since thefirst run of the vehicle assumed no bridge displacementthe process must be iterated to take account of the bridgedisplacement changing the height of the road profile experi-enced by each axle at each time step The latest road profileaffects the contact forces which in turn affect the bridgedisplacement which affects the road profile and so forthTheroad profile is continually updated by subtracting the bridgedisplacements until convergence is achieved Guidance onconvergence for simulations of this type is given in [33]Convergence in this study is deemed to have occurred whenthe maximum difference in displacement (for all degrees offreedom) between the current time step and the previous timestep is less than 1 of the max displacement of the bridgesee

10038161003816100381610038161003816100381610038161003816

Δ119894minus Δ119894minus1

Δmax

10038161003816100381610038161003816100381610038161003816le 001 (9)

3 Modelling Algorithms

31 Scour Modelling In this section the output of signals ofinterest from the system and the postprocessing required tomake them ldquoanalysis readyrdquo is discussed As mentioned inprevious sections themodel is capable of outputting dynamicdisplacement velocity and acceleration signals from amulti-tude of points on the bridge structure Moreover the modelis also capable of outputting dynamic displacement velocityand acceleration signals from the vehicle model as it traversesthe bridge Using the signals arising on the bridge structureitself allows the user to test direct SHM techniques that ismethods that rely on sensors being placed on the actual


Define soil stateloose medium

dense and dense

Specify geometricand structural

properties for bridgeelements and

dynamic properties

Specify number ofspringslevel ofscour around

foundation elements

Define vehicle propsand assemble

Specify vehiclevelocity and

generate roadroughness profile

Assemble global

matrices for bridgemodel

Run vehicle overbridge to generate

Process signals

(i) Add free vibration(ii) Add noise

Remove top springincrement scour

depth

Prearrangedscour depth

reached

No

Yes

Output signals ofinterest from the

model

Vehicle model properties

Desiredmodel conditions

checked

Yes

Scour algorithm

No

Bridge model properties

Itera

te if

nece

ssar

y

= minus 1

[Kv] matrices[Cv] and stiffness

x 998400 and 998400998400

displacementsvelocities andaccelerations

[C] and stiffness [K]mass [M ] damping

mass [Mv] damping

Ns

Ns Nsx x

x998400x

998400998400 x

sand

Figure 7 Scour modelling algorithm to generate analysis signals

structure to detect damage features Using the signals arisingon the vehicle system allows the user to test indirectmethodsof damage detection which use sensors placed on the vehicle(ie axles body) to detect damage on the bridge as ittraversesThe generic algorithm to generate signals of interestfrom the bridge is shown in the flow diagram in Figure 7In order to create usable signals for analysis it is oftennecessary to simulate damped free vibration of the bridgeafter the vehicle has departed the structure (this is becausehigh vehicle speeds can result in very short signals which isoften problematic from a signal processing point of view)The model also has the facility to add ldquomeasurement noiserdquothat would be present in real signals This is discussed inSection 32 Scour is modelled as the removal of springs fromaround the foundation element of interest (pier abutments)starting with the spring nearest the top

32 Adding Noise to Numerical Signals Signals recorded ona real structure will contain measurement noise therefore forthe purpose of a fair assessment of a given SHM algorithmthe presence of noise in the numerically generated signalsshould be accounted for The model developed in this paperallows for two different methods to add noise to the ldquocleanrdquonumerical signals The first method is based on Zhu andLaw [10] and the second method is based on Lyons [38]The Zhu and Law approach allows the user to specify

a percentage noise level to be added to the signal of interestand is formulated as follows

sigNOISE = sigCLEAN + 119864119901119873NOISE120590 (sigCLEAN) (10)

where sigNOISE is the noisy (corrupted) signal 119864119901is the

percentage of added noise 119873NOISE is a standard normaldistribution vector with zero mean value and unit standarddeviation sigCLEAN is the calculated signal from the modeland 120590(sigCLEAN) is the standard deviation Specifying 119864

119901

values of 001 to 005 adds 1 to 5 of noise respectively tothe clean signal for example

The second method used to add noise is based on thesignal-to-noise ratio (SNR) given in [38]

SNR = 10 log10

Signal PowerNoise Power

(11)

where SNR is the ratio of the strength of a signal carryinginformation equating to that of unwanted interference Thisequation can be rearranged to give

120590119873

= radicNoise Power = radicSignal Power

exp ((SNR sdot log119890(10)) 10)

(12)

where 120590119873

is the variance of the noise Using (12) noisesignals with different signal-to-noise ratios can be added to


Table 2 Case study bridge properties

Bridge deckYoungrsquos modulus (119864) (MPa) 35000 X-sectional area (m2) 9516Moment of inertia (m4) 29487 Concrete density (kgmminus3) 2400Spans 2 Span length (m) 25

Bridge abutment columnsYoungrsquos modulus (119864) (MPa) 35000 Total X-sectional area (m2) 17671Total moment of inertia (m4) 00276 Concrete density (kgmminus3) 2400Number of columns 9 Column length (m) 6

Bridge pierYoungrsquos modulus (119864) (MPa) 35000 Total X-sectional area (m2) 722Total moment of inertia (m4) 1137 Concrete density (kgmminus3) 2400Number of columns 2 Column length (m) 6

Abutment pilesYoungrsquos modulus (119864) (MPa) 35000 Total X-sectional area (m2) 2827Total moment of inertia (m4) 00636 Concrete density (kgmminus3) 2400Number of piles 10 Pile length (m) 15

Pier pilesYoungrsquos modulus (119864) (MPa) 35000 Total X-sectional area (m2) 3534Total moment of inertia (m4) 01243 Concrete density (kgmminus3) 2400Number of piles 8 Pile length (m) 15

the original ldquocleanrdquo signal obtained directly from the numer-ical model This process is shown in

SigNOISE = 120590119873[rand] + SigCLEAN (13)

The addition of noise to the signals allows for a more robusttesting of a given SHM scheme as in general measurementnoise can inhibit the accuracy of a given SHM scheme

4 Example Signals from Developed Model

In this section some example signals simulated by the modeland their response features are shown Section 41 displayssome typical bridge signals and Section 42 displays somevehicle signals calculated when the vehicle is crossing thebridgeThe case study bridge modelled is a two-span integralbridge with flexible abutments each span is 25m in length(Figure 2 shows a 3D schematic of the bridge) The bridgedeck is formedusing nineU10 bridge beams [39] supporting a200mm thick deck slabThebridge abutments are formulatedwith nine concrete columns supporting the bridge beamseach column 500mm in diameter and spaced at 1900mmcentres Two stiff piers support the deck at the centre andhave plan dimensions of 1375mm times 2625mmThe abutmentcolumns rest on a pile cap under which ten 15m long (06mdiameter) bored concrete piles are placed A loose sand soilprofile is generated as per the analysis in Section 232 For thepurpose ofmodelling scour around an individual foundationelement is assumed to be uniform along the transverse lengthof a given support As mentioned previously the model isidealised as a 2D frame with group properties adopted forthe various structural members The structural propertiesshown in Table 2 are used for the simulations presented inthis section

41 Bridge Signals Some typical response signals from thebridge due to the vehicle crossing are shown in Figure 8For this analysis the vehicle (properties shown in Table 1)traverses the bridge at 50 kmhrminus1 over a Class ldquo119860rdquo roadsurface (shown in Figure 6) and a zero scour condition isassumed Ten seconds of free vibration is also calculated andthe analysis assumes damped vibration at 2The three plotson the left side of the figure (ie (a) (c) and (e)) showthe vertical displacement velocity and acceleration of themidpoint of the left span (span 1) of the bridge resulting fromthe passage of the vehicle across the bridgeThe displacementresponse in part (a) of the figure is dominated by the staticbridge response When the truck is on span 1 the spandeflects downwards and while there are some dynamicmovements evident their amplitude is small relative to thestatic displacement As the truck passes onto span 2 the mid-span of span 1 deflects upwards slightly Once the truck leavesthe bridge at time 119905 = 4 seconds the deck goes into freevibration but the amplitudes of the displacements are verysmall relative to the static displacement Figure 8(c) showsthe corresponding vertical velocity response at the mid-spanof span 1 While the static movements are still evident inthe velocity signal the dynamic movements are much clearerFigure 8(e) shows the vertical acceleration response of themid-span of span 1 This time the dynamic movements ofthe bridge dominate the signal and high amplitude localisedpeaks are visible in the acceleration signal as the front andrear axles enterleave the bridgeThe logarithmic decay of theacceleration signal when the bridge goes into free vibrationis also evident in part (e) of the figure The three plots onthe right side of the figure (ie (b) (d) and (f)) show thehorizontal displacement velocity and acceleration of the topof the pier resulting from the passage of the vehicle across


0 5 10

0

2

Time (s)

Disp

lace

men

t (m

)

Mid D1 VERT

Free vibrationVehicle

times10minus4

minus2

(a)

Disp

lace

men

t (m

)

0 5 10

0

1

2

Time (s)

Pier top LAT

Free vibrationVehicletimes10minus4

minus1

minus2

(b)

0 5 10

0

1

2

Time (s)

Mid D1 VERT

times10minus3

minus1

minus2

Velo

city

(msminus

1)

(c)

0 5 10

0

2

4

Time (s)

Pier top LAT

times10minus4

minus2

minus4

Velo

city

(msminus

1)

(d)

0 5 10

0

005

01

Time (s)

Mid D1 VERT

Front axle enters

Front axle leaves

Rear axle enters

Rear axle leavesAcce

lera

tion

(msminus

2)

minus005

minus01

(e)

0 5 10

0

0005

001

Time (s)

Pier top LAT

Front axle enters

Front axle leaves

Rear axle entersRear axle leavesAc

cele

ratio

n (m

sminus2)

minus0005

minus001

(f)

Figure 8 Example signals from model for vehicle traversing at 50 kmhrminus1 with 10 seconds of free vibration and a Class ldquo119860rdquo road profile (a)Vertical displacement response at mid-span of span 1 (b) horizontal displacement at top of pier (c) vertical velocity response at mid-span ofspan 1 (d) horizontal velocity at top of pier (e) vertical acceleration response at mid-span of span 1 (f) horizontal acceleration at top of pierAll signals are damped at 2

the bridge When the vehicle is on span 1 the head of thepier moves to the left (negative displacement) and whenthe vehicle is on span 2 the head of the pier moves to theright (positive displacement) Although there is little dynamicmovement evident when the vehicle is on the bridge oncethe bridge goes into free vibration the dynamic movementsare clearly evident The horizontal velocity signal shown inpart (d) of the figure shows a clear dynamic componentand the frequency is noticeably lower than the frequency

evident in the plot of vertical mid-span velocity (Figure 8(c))Figure 8(f) shows the horizontal acceleration response atthe top of the pier and again the peaks due to the axlesenteringleaving the bridge are evident

For the purpose of scour detection the lateral bridgeresponse is often the response of most interest in that this isthe response typically affected by scour in bridges of this type[16 40] Therefore it is of interest to examine the parametersthat affect the ability for a vehicle traversing the bridge to


0 2 4 6 8 10 12 14

0

001

002

Time (s)

Free vibration Vehicle

minus002

minus001

Acce

lera

tion

(msminus

2)

0 05 1 15 2 25 3 35 4

0

001

002

Time (s)

minus002

minus001

Acce

lera

tion

(msminus

2)

Class ldquoArdquoClass ldquoCrdquoClass ldquoErdquo

(b)

(a)

Figure 9 Effect of road surface roughness on lateral pier topacceleration response (a) forced and free vibration for Classes 119860119862 and 119864 and (b) forced vibration only

excite the lateral response of the structure Figures 8(b)8(d) and 8(e) show the lateral displacement velocity andacceleration response of the pier top due to the passage of avehicle over a Class ldquo119860rdquo road surface The effect of increasedroad surface roughness on the lateral pier top accelerationis examined in Figure 9 The vehicle traverses the bridge at50 kmhrminus1 and 10 seconds of free vibration (damped at 2)is assumed after the vehicle leaves the bridge

Figure 9 shows the effect of increasing road surfaceroughness from 119860 to 119862 to 119864 on the resulting lateral accelera-tion response at the pier top (see Figure 6 for road profiles)The effect of increasing the surface roughness leads to highermagnitude acceleration responses for both the forced and freevibration components of the response signal As the forcedvibration component is difficult to see in Figure 9(a) part (b)shows only the forced component of the signal

The effect of scour on the lateral acceleration response ofthe pier top is examined in Figure 10 whereby 5m of scour isinduced around the central pier foundation For this analysisthe vehicle once again traverses the bridge at 50 kmhrminus1 overa Class ldquo119860rdquo road surface with 10 seconds of subsequent freevibration

Figure 10 shows the effect of 5m of pier scour on thelateral acceleration response measured at the pier top due tothe passing vehicle at 50 kmhrminus1 In this figure the period ofthe signal has increased with scour (see the insert showing azoomed-in portion of the signal between 45 and 7 seconds)This is sensible as the effect of scour is to increase the effectivelength of the pier thusmaking it more flexible so an increasedperiod is expected The amplitude of the scoured signal hasreduced in the free vibration The reason for this is twofold(i) The effect of scour reducing the confining stiffness effect


0 2 4 6 8 10 12 14

0

0005

001

0015

002

Time (s)

Zero scour

45 5 55 6 65 7

minus0015

minus0005

minus001

Acce

lera

tion

(msminus

2)

5m pier scour

Figure 10 Difference in lateral pier top acceleration for 0 and 5mscour

of the soil leads to higher lateral translation of the pier atlower depths meaning the pier top translation is lessenedThismanifests itself as a lower pier top dynamic displacementand acceleration for increased pier scour (ii) Interactioneffects between the bridgersquos natural oscillation period and thevelocity of the vehicle lead to differences in the free vibrationamplitude depending on where the vehicle is on the bridge ata given time increment relative to the (lateral) oscillation stateof the bridge itselfThe location of the vehicle at a certain timemeans it can either increase or diminish the bridgersquos naturaloscillatory response

In terms of damage detection using vibrations manySHM algorithms can be sensitive to the presence of measure-ment noise as well as other external disturbances Figure 11shows the effect of artificially adding noise to the simulatedacceleration signals For this analysis the process outlinedin (11)ndash(13) is used whereby noise is added by utilising thesignal-to-noise ratio (SNR) as per [38] Once again thisanalysis is for a vehicle traversing at 50 kmhrminus1 a Class ldquo119860rdquoroad profile loose sand profile 10 seconds of free vibrationzero scour and the lateral acceleration generated at the piertop SNRs of 20 10 and 5 are used to show the increasingeffect of noise on the time-domain acceleration signals

Figure 11 shows the effect of increasing the noise levelpresent in the lateral acceleration response at the top ofthe bridge pier In Figure 11(a) the characteristics of thesignal are easily discernible and the individual oscillationsin the free vibration can be seen clearly On the contrary inFigure 11(d) with a SNR = 5 the individual oscillations aredifficult to identify and it is clear that the addition of noisehas significantly reduced the clarity of the signalThe additionof noise to the signals allows researchers to test the resilienceof emerging SHM algorithms under increasingly challengingconditions that might be experienced in the field

42 Vehicle Signals In this section some typical vehicleresponse signals are shown The purpose of using vehiclesignals as mentioned previously is to allow researchers totest indirect methods of SHM whereby the response of the


0 5 10

0

001

002

Time (s)

No noise

minus002

minus001

Acce

lera

tion

(msminus

2)

(a)SNR = 20

0 5 10

0

001

002

Time (s)

minus002

minus001Acce

lera

tion

(msminus

2)

(b)

SNR = 10

0 5 10

0

001

002

Time (s)

minus002

minus001

Acce

lera

tion

(msminus

2)

(c)SNR = 5

0 5 10

0

001

002

Time (s)

minus002

minus001Acce

lera

tion

(msminus

2)

(d)

Figure 11 Effect of noise on lateral pier acceleration response (a) Noise-free signal (b) signal with SNR = 20 (c) signal with SNR = 10 (d)signal with SNR = 5

0 1 2 3 4 5 6

0

5

Time (s)

Zero scour

Rear axle enters bridge

Front axle leaves bridge

minus5

minus10

times10minus3

Acce

lera

tion

(msminus

2)

5m pier scour

(a)

0 1 2 3 4 5 6

0

1

Time (s)

Zero scour Class ldquoArdquo

Acce

lera

tion

(msminus

2)

5m pier scour Class ldquoArdquo

minus05

05

(b)

Figure 12 Effect of road roughness on vehicle body accelerations (a) Vertical body acceleration over smooth road surface for zero and 5mscour (b) vertical body acceleration over Class ldquo119860rdquo road surface for zero and 5m scour

vehicle is used to infer the damage condition of the bridge Forexample a number of authors have inferred the condition ofthe bridge deck by analysing the vehicle response as it crossedthe bridge [41 42] The vehicle response is sensitive to theroad profile therefore in this section the effect of road surfaceroughness is examined in terms of detecting the presence ofscour Figure 12 shows the vertical acceleration response ofthe vehicle body as it traverses a bridge at 30 kmhrminus1 for zeroand 5m of pier scour To make the simulation as realisticas possible the vehicle commences motion at an approach

distance of 100m from the start of the bridge however hereonly the portion of the response when the vehicle is on thebridge is shown A loose sand profile is adopted in the bridgemodel and the vehicle traverses a smooth road surface inFigure 12(a) and a Class ldquo119860rdquo road surface in Figure 12(b) (seeFigure 6 for road profile)

Figure 12 shows the effect of the road surface roughnesson the clarity of the vertical acceleration response detectedon the vehicle body as it traverses the bridge at 30 kmhrminus1Figure 12(a) shows the difference in vehicle body vertical


acceleration for zero and 5m pier scour as it traverses asmooth road surface Figure 12(b) shows that the differencebetween zero scour and 5m pier scour vertical vehicle bodyaccelerations is difficult to observe in the presence of a Classldquo119860rdquo road surface The presence of a road profile may causedifficulty with some SHM schemes aiming to use vehiclemeasurements to detect damagescour

5 Conclusion

In this paper the development of a novel Vehicle-Bridge-SoilDynamic Interaction (VBSDI)model formodelling the effectof scour around integral bridge foundations is presentedThemodel is capable of rapidly modelling the scour response ofintegral bridges and incorporates realistic (validated) repre-sentations of the foundation soil stiffness as well as a realisticvehicle loadingmodelThis paper discusses themathematicaltheory and assumptions underlying the model The modelis capable of outputting dynamic displacements velocitiesand accelerations from any point on the bridge as well ason the vehicle with a view to allowing researchers to testemerging structural health monitoring techniques Signalsfrom the bridge can be used to test direct methods of healthmonitoring whereby sensors are placed on the actual bridgestructure Signals measured on the vehicle as it traverses thebridge can also be used to test indirect methods of healthmonitoring which rely on the bridgersquos damage feature beingdetected in the vehicle response The model can vary the soilconditions from loose sand to dense sand and vary the roadsurface roughness from Class ldquo119860rdquo (very good) to Class ldquo119864rdquo(very poor) The effects of measurement noise can also beincorporated using two separate methods to afford a morerigorous assessment of a particular SHM technique aimingto use real (noisy) signals Finally some typical response datafrom both a bridge and a two-axle vehicle are presented byway of a case study

The model developed in this paper is intended to aidresearchers working in the area of scour detection usingvibration-based methods to test emerging algorithms thatthey may have in development While every effort has beenmade to ensure the signals from the model are as realistic aspossible it is recommended where possible to test developedtechniques on actual structures The current model aimsto serve as a preliminary tool for researchers to test theirtechniques under a range ofmodelling scenarios prior to fielddeployment

Conflict of Interests

The authors declare that there is no conflict of interestsregarding the publication of this paper

Acknowledgments

The authors would like to acknowledge the support ofthe Earth and Natural Sciences (ENS) Doctoral StudiesProgramme funded by the Higher Education Authority(HEA) through the Programme for Research at Third LevelInstitutions Cycle 5 (PRTLI-5) cofunded by the European

Regional Development Fund (ERDF) the European UnionFramework 7 Project SMARTRAIL (Project no 285683) andthe University College Dublin (UCD) Earth Institute

References

[1] C R Farrar and K Worden ldquoAn introduction to structuralhealth monitoringrdquo Philosophical Transactions Series A Math-ematical Physical and Engineering Sciences vol 365 no 1851pp 303ndash315 2007

[2] A D Dimarogonas ldquoVibration of cracked structures a state ofthe art reviewrdquo Engineering Fracture Mechanics vol 55 no 5pp 831ndash857 1996

[3] E A Johnson H F Lam L S Katafygiotis and J L BeckldquoPhase I IASC-ASCE structural health monitoring benchmarkproblem using simulated datardquo Journal of Engineering Mechan-ics vol 130 no 1 pp 3ndash15 2004

[4] SDykeD Bernal J Beck andCVentura ldquoExperimental phaseII of the structural health monitoring benchmark problemrdquo inProceedings of the 16th ASCE EngineeringMechanics ConferenceSeattle Wash USA July 2003 httpauthorslibrarycaltechedu342261Report bldg shm exp2pdf

[5] S Foti and D Sabia ldquoInfluence of foundation scour on the dy-namic response of an existing bridgerdquo Journal of Bridge Engi-neering vol 16 no 2 pp 295ndash304 2011

[6] W Ostachowicz andM Krawczak ldquoOn modelling of structuralstiffness loss due to damagerdquo in Proceedings of the 4th Inter-national Conference Damage Assessment of Structures (DAMASrsquo01) Cardiff UK 2001

[7] M I Friswell and J E T Penny ldquoCrack modeling for structuralhealth monitoringrdquo Structural Health Monitoring vol 1 no 2pp 139ndash148 2002

[8] C P Ratcliffe ldquoDamage detection using a modified laplacianoperator on mode shape datardquo Journal of Sound and Vibrationvol 204 no 3 pp 505ndash517 1997

[9] M A Mahmoud ldquoEffect of cracks on the dynamic responseof a simple beam subject to a moving loadrdquo Proceedings of theInstitution of Mechanical Engineers Part F Journal of Rail andRapid Transit vol 215 no 3 pp 207ndash215 2001

[10] X Q Zhu and S S Law ldquoWavelet-based crack identificationof bridge beam from operational deflection time historyrdquoInternational Journal of Solids and Structures vol 43 no 7-8pp 2299ndash2317 2006

[11] D Hester and A Gonzalez ldquoA wavelet-based damage detectionalgorithm based on bridge acceleration response to a vehiclerdquoMechanical Systems and Signal Processing vol 28 pp 145ndash1662012

[12] A Gonzalez E J Obrien and P J McGetrick ldquoIdentificationof damping in a bridge using a moving instrumented vehiclerdquoJournal of Sound and Vibration vol 331 no 18 pp 4115ndash41312012

[13] L J Prendergast and K Gavin ldquoA review of bridge scour moni-toring techniquesrdquo Journal of Rock Mechanics and GeotechnicalEngineering vol 6 no 2 pp 138ndash149 2014

[14] S H Ju ldquoDetermination of scoured bridge natural frequencieswith soil-structure interactionrdquo Soil Dynamics and EarthquakeEngineering vol 55 pp 247ndash254 2013

[15] C-C Chen W-H Wu F Shih and S-W Wang ldquoScourevaluation for foundation of a cable-stayed bridge based onambient vibration measurements of superstructurerdquo NDT amp EInternational vol 66 pp 16ndash27 2014


[16] J V Klinga and A Alipour ldquoAssessment of structural integrityof bridges under extreme scour conditionsrdquo Engineering Struc-tures vol 82 pp 55ndash71 2015

[17] L J Prendergast D Hester K Gavin and J J OrsquoSullivan ldquoAninvestigation of the changes in the natural frequency of a pileaffected by scourrdquo Journal of Sound and Vibration vol 332 no25 pp 6685ndash6702 2013

[18] S Donohue M Long K Gavin and P OrsquoConnor ldquoShearwave stiffness of Irish glacial tillrdquo in Proceedings of the 2ndInternational Conference on Site Characterization pp 459ndash466Porto Portugal 2004

[19] L J Prendergast K Gavin and P Doherty ldquoAn investigationinto the effect of scour on the natural frequency of an offshorewind turbinerdquo Ocean Engineering vol 101 pp 1ndash11 2015

[20] S M Springman A R M Norrish and C W W Ng ldquoCyclicloading of sand behind integral bridge abutmentsrdquo TRL Report146 Transport Research Laboratory Wokingham UK 1996

[21] Steel Construction Institute ldquoIntegral bridgesrdquo 2015 httpwwwsteelconstructioninfoIntegral bridgesReferences

[22] Y W Kwon and H Bang The Finite Element Method usingMATLAB CRC Mechanical Engineering Series CRC PressBoca Raton Fla USA 2nd edition 2000

[23] Y Yang J Yau and Y Wu Vehicle-Bridge Interaction DynamicsWorld Scientific 2004 httpwwwworldscientificcomdoipdf1011429789812567178 fmatter

[24] J W Tedesco W G McDougal and C Allen Ross StructuralDynamics Theory and Applications AddisonWesley Longman1999

[25] E Winkler Theory of Elasticity and Strength Dominicus Pra-gue Czech Republic 1867

[26] S C Dutta and R Roy ldquoA critical review on idealizationandmodeling for interaction among soilndashfoundationndashstructuresystemrdquo Computers and Structures vol 80 no 20-21 pp 1579ndash1594 2002

[27] T Lunne and H P Christoffersen ldquoInterpretation of conepenetrometer data for offshore sandsrdquo in Proceedings of theOffshore Technology Conference Houston Tex USA 1983

[28] API ldquoRecommended practice for planning designing andconstructing offshore platformsmdashworking stress designrdquo APIRP2A American Petroleum Institute Washington DC USA2007

[29] Fugro ldquoGuide for estimating soil type and characteristicsusing cone penetration testingrdquo Cone Penetration Tests 2011httpwwwfescoukdownloadsCPT-generalpdf

[30] R J Jardine F C Chow R F Overy and J Standing ICPDesignMethods for Driven Piles in Sands and Clays Thomas TelfordPublishing London UK 2005

[31] G Baldi R Belottini V N Ghionna N I Jamiokowski andD C F Lo Presti ldquoModulus of sands from CPTs and DMTsrdquoin Proceedings of the 12th International Conference on SoilMechanics and Foundation Engineering (ICSMFE rsquo89) vol 1 pp165ndash170 Rio de Janeiro Brazil August 1989

[32] S A Ashford and T Juirnarongrit ldquoEvaluation of pile diametereffect on initial modulus of subgrade reactionrdquo Journal ofGeotechnical and Geoenvironmental Engineering vol 129 no 3pp 234ndash242 2003

[33] M F Green and D Cebon ldquoDynamic interaction betweenheavy vehicles and highway bridgesrdquoComputers and Structuresvol 62 no 2 pp 253ndash264 1997

[34] F Yang and G Fonder ldquoAn iterative solution method fordynamic response of bridgendashvehicles systemsrdquo Earthquake

Engineering amp Structural Dynamics vol 25 no 2 pp 195ndash2151996

[35] N K Harris E J OBrien and A Gonzalez ldquoReduction ofbridge dynamic amplification through adjustment of vehiclesuspension dampingrdquo Journal of Sound and Vibration vol 302no 3 pp 471ndash485 2007

[36] D Cebon Handbook of Vehicle-Road Interaction Swets ampZeitlinger Lisse The Netherlands 1999

[37] L FrybaVibration of Solids and Structures UnderMoving LoadsThomas Telford London UK 1999

[38] R LyonsUnderstanding Digital Signal Processing Prentice HallBoston Mass USA 3rd edition 2011

[39] Concast Civil Engineering Solutions Civil Engineering Solu-tions 2014 httpwwwconcastprecastcoukimagesuploadsbrochuresConcast Civilpdf

[40] A Elsaid Vibration based damage detection of scour in coastalbridges [PhD thesis] North Carolina State University RaleighNC USA 2012

[41] J Keenahan E J OBrien P J McGetrick and A GonzalezldquoThe use of a dynamic truck-trailer drive-by system to monitorbridge dampingrdquo Structural HealthMonitoring vol 13 no 2 pp143ndash157 2014

[42] A Malekjafarian and E J OBrien ldquoIdentification of bridgemode shapes using short time frequency domain decomposi-tion of the responsesmeasured in a passing vehiclerdquoEngineeringStructures vol 81 pp 386ndash397 2014

International Journal of

AerospaceEngineeringHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

RoboticsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014


Active and Passive Electronic Components

Control Scienceand Engineering

Journal of



RotatingMachinery


Hindawi Publishing Corporation httpwwwhindawicom

Journal ofEngineeringVolume 2014

Submit your manuscripts athttpwwwhindawicom

VLSI Design



Shock and Vibration


Civil EngineeringAdvances in

Acoustics and VibrationAdvances in



Electrical and Computer Engineering

Journal of

Advances inOptoElectronics


Volume 2014

The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014

SensorsJournal of


Modelling amp Simulation in EngineeringHindawi Publishing Corporation httpwwwhindawicom Volume 2014


Chemical EngineeringInternational Journal of Antennas and

Propagation




Navigation and Observation



DistributedSensor Networks



subsequently observed in the field it could be correlated to agiven damage scenario In general the challenges of applyingvibration-based SHM to offshore platforms are significant asfactors such as variations in the mass of the structure dueto changes in the mass of the storage tanks and changes inthe amount of marine growth on the structure can proveproblematic

The development of SHM tools for bridge engineeringfaces the same challenges as the oil industry in that it isvery rare that one can take a full size test piece and applydamage for the purpose of developing monitoring tools Infact it is practically unheard of in bridge engineering asthe structures themselves are just too valuableimportant tointerfere with Therefore when researchers wish to try anddevelop a new SHM algorithm to detect a particular type ofdefect in the structure the first task is to try and understandhow damage affects the response of the structure To establishthis their options (broadly speaking) are to use a computermodel [3] andor a laboratory experiment using a scaledmodel of the structure [4] Occasionally it will be possibleto test at full scale when a bridge is due to be retrofittedfor example a scoured but retrofitted bridge in Italy see [5]However in many cases the first option is a computer modelto undertake simulations of candidate damage scenariosThe challenge therefore is to develop a model that outputsrealistic results A numerical model that outputs signals thatare representative of those likely to be encountered on thereal structure is a very useful tool when trying to developnew SHM algorithms This paper aims to develop just sucha model as by including vehicle-bridge interaction and soil-structure interaction every effort ismade tomake the loading(applied to the bridge) and the (soil) boundary conditions ofthe model as realistic as possible It should be noted that theaim of this paper is not to develop a new SHM technique forscour detection but to present the basis of a model to make iteasy for others to test emerging SHM techniques by allowingthem to generate realistic bridge response signals occurringdue to foundation scour Section 12 gives some examples ofnumerical models developed to simulate damage in beam-like structures where the model outputs (eg accelerationvelocity or displacement signals) were subsequently used asinputs to damage detection algorithmsThis section also pro-vides a discussion on previous works focussed on modellingscour damage

12 Modelling Structural Damage for SHM Algorithm Devel-opment Over the past two decades several authors haveprepared models of damaged structures with a view todeveloping SHM algorithms to detect this type of damage Aparticular focus has been given to models which representlocalised damage in a structure (eg cracking or sectionloss) Ostachowicz and Krawczak [6] describe the differentmethods commonly used to model structural stiffness lossdue to damage Friswell and Penny [7] give a very usefuloverview on crack modelling for SHM They point out thatapproaches for modelling cracks in beam type structurestypically fall into three categories local stiffness reduction[8] discrete spring models [9] and complex models in twoor three dimensionsThey compare the three approaches and

broadly speaking they conclude that for structural healthmonitoring which utilises low frequency vibration simplemodels of crack flexibility based on beam elements areadequate

Other authors have developed models to simulate theresponse signals of damaged beam structures to movingloads and then used the signals from these models as inputsto SHM algorithms A number of authors have simulatedthe structure as having a localised loss in stiffness andthen calculated the response to a moving point force [10]Hester and Gonzalez [11] modelled a similar type of damagehowever they modelled the moving load as a sprung vehicleto incorporate vehicle-bridge interaction effects that is tomake the simulated response signals as realistic as possibleThis is important when numerically testing the versatility ofa new SHM algorithm before applying it to a real structureOthers have postulated that the occurrence of damage willaffect the damping of the bridge and prepared numericalmodels to simulate this by analysing the vehicle accelerationsignals output from the model [12] that is this is an indirectmonitoring approach as the vehicle response passing over adamaged bridge is used to detect the damage feature

In terms of scour modelling several authors have inves-tigated the effect of scour on the static and dynamic prop-erties of bridges using numerical methods The principleunderlying these approaches is that during scour loss ofsoil contact occurs which leads to higher applied stress overthe area of soil remaining in contact with the foundationThis coupled with the nonlinear stiffness of soils leadsto lower operational system stiffness [13] Therefore scourpresence should be detectable as a change in the dynamicproperties of the structure Ju [14] developed a 3D FE modelof a bridge incorporating soil-structure and fluid-structureinteraction to assess the magnitude of the change in naturalfrequency of the bridge with increasing scourThey validatedthe bridge natural frequencies from the model against a full-scale field experiment and then used the numerical modelto study various scour conditions and how it affected thebridgersquos natural frequency They concluded that scour causesa reduction in bridge natural frequency but the magnitudeof the frequency change with scour is affected by varyingfoundation geometry and layering in foundation soils Chenet al [15] developed a full FE model of a cable-stayedbridge with a pylon and a pier They updated the modelproperties to obtain a match tomodal data obtained from theactual structure They then used known data about the pylonfoundation condition to obtain representative soil stiffness(matching the stiffness of the actual soil) The numericalmodel was then used to update the scour depth around thepier until the predicted frequency data matched the observeddata In this case the numerical model was used to ascertainthe actual scour condition around the real pier and this paperserves as a successful real-life application of a vibration-basedscour detectionmethod Klinga and Alipour [16] developed anumerical model to assess the effect of scour on various staticand dynamic performance features of a bridge They usedtheir model to perform pushover analyses buckling analysesandmodal analyses under extreme scour conditions to assessthe effect of scour on the various bridge elements such as







minus1

minus2

minus3

minus4

minus5

minus6

minus70 5 10 15 20 25 30 35

0

Frequency (Hz)

Scou

r dep

th (m

)












Abutment

Pile caps

Abutment


Crosshead

Central

Central

columns

Abutment columns

piles

Abutment piles

pier

pier piles







119866]



[M119866]

x1(119905)

x2(119905)

x119873(119905)

+ [C119866]

x1(119905)

x2(119905)

x119873(119905)

+ [K119866]

x1(119905)

x2(119905)

x119873(119905)

=

F1(119905)

F2(119905)

F119873(119905)

(1)

where [M119866] [C119866] and [K










in

[K119904119894] = 119896119904119894

[1 minus1

minus1 1] 119896

119904119894ge 0 (2)






Reinforced earth



119866] [C119866] and [K











119904119894) (Section 232(3))






119902119888= 60 (120590

1015840

V)07

exp (291119863119903) (3)









0 5 10 15 20 25

0D

epth

(m)


qc loose

minus5

minus10

minus15

CPT qc (MPa)

(a)

Dep

th (m

)

0 20 40 60 80 100 120

0


G0 loose

minus5

minus10

minus15

G0 (MPa)

(b)

Dep

th (m

)

0 100 200 300 400

0

K (MPa)


K loose

minus5

minus10

minus15

(c)

Dep

th (m

)

0 05 1 15 2

0

minus5

minus10

minus15



ks loose

(d)





approach






1198660= 119902119888[119860 + 119861120578 minus 119862120578

2

]minus1

(4)

where 119860 = 00203 119861 = 000125 119862 = 1216119864 minus 6 and120578 = 119902119888(1198751198861205901015840


119886= 100 kPa and 120590

1015840









1198640= 21198660(1 + V) (5)



119870 =101198640

1 minus V2[11986401198634

119864119901119868119901

]

112

(6)




xxx


Mb Ip o

yb

y2 y1

Ks2 Ks1

Kt2

mw2 mw1Kt1

Cs1Cs2

E I 120588 A

kSN kSN kSN

kS2 kS2 kS2

kS1 kS1 kS1

SS1S2


1

4

2

5

3

6




119904119894) are










Dimensional data

Dimensions(m)


1) 366


Mass and inertia


1199081) 700


Sprung body mass (119898119887) 13300



Front axle (1198701199041) 400

Rear axle (1198701199042) 1000


Front axle (1198621199041) 10

Rear axle (1198621199042) 10


Front axle (K1199051) 1750

Rear axle (K1199052) 3500



119887(119905) the









1(119905) and to do



[MV]

119901(119905)

y119887(119905)

y1(119905)

y2(119905)

+ [CV]

119901(119905)

y119887(119905)

y1(119905)

y2(119905)

+ [KV]

120593119901(119905)

y119887(119905)

y1(119905)

y2(119905)

= FV

(7)


1(119905) and y



F1(119905)

F2(119905)

= [K1199051

00 K

1199052

]y1(119905)

y2(119905)

(8)

0 5 10 15 20 25 30 35 40 45 50

0

002

004

006

008

01

Distance (m)

Hei

ght (

m)



minus002

minus004


where K1199051

and K1199052


1(119905) and F



10038161003816100381610038161003816100381610038161003816


Δmax

10038161003816100381610038161003816100381610038161003816le 001 (9)





dense and dense



dynamic properties


foundation elements




Assemble global



Process signals



depth


reached

No

Yes


model



checked

Yes

Scour algorithm

No


Itera

te if

nece

ssar

y

= minus 1


x 998400 and 998400998400



mass [Mv] damping

Ns

Ns Nsx x

x998400x

998400998400 x

sand








119901



SNR = 10 log10


(11)


120590119873


exp ((SNR sdot log119890(10)) 10)

(12)

where 120590119873
















0 5 10

0

2

Time (s)

Disp

lace

men

t (m

)

Mid D1 VERT


times10minus4

minus2

(a)

Disp

lace

men

t (m

)

0 5 10

0

1

2

Time (s)

Pier top LAT


minus1

minus2

(b)

0 5 10

0

1

2

Time (s)

Mid D1 VERT

times10minus3

minus1

minus2

Velo

city

(msminus

1)

(c)

0 5 10

0

2

4

Time (s)

Pier top LAT

times10minus4

minus2

minus4

Velo

city

(msminus

1)

(d)

0 5 10

0

005

01

Time (s)

Mid D1 VERT

Front axle enters

Front axle leaves

Rear axle enters


lera

tion

(msminus

2)

minus005

minus01

(e)

0 5 10

0

0005

001

Time (s)

Pier top LAT

Front axle enters

Front axle leaves


cele

ratio

n (m

sminus2)

minus0005

minus001

(f)






0 2 4 6 8 10 12 14

0

001

002

Time (s)


minus002

minus001

Acce

lera

tion

(msminus

2)

0 05 1 15 2 25 3 35 4

0

001

002

Time (s)

minus002

minus001

Acce

lera

tion

(msminus

2)


(b)

(a)







0 2 4 6 8 10 12 14

0

0005

001

0015

002

Time (s)

Zero scour

45 5 55 6 65 7

minus0015

minus0005

minus001

Acce

lera

tion

(msminus

2)

5m pier scour







0 5 10

0

001

002

Time (s)

No noise

minus002

minus001

Acce

lera

tion

(msminus

2)

(a)SNR = 20

0 5 10

0

001

002

Time (s)

minus002

minus001Acce

lera

tion

(msminus

2)

(b)

SNR = 10

0 5 10

0

001

002

Time (s)

minus002

minus001

Acce

lera

tion

(msminus

2)

(c)SNR = 5

0 5 10

0

001

002

Time (s)

minus002

minus001Acce

lera

tion

(msminus

2)

(d)


0 1 2 3 4 5 6

0

5

Time (s)

Zero scour



minus5

minus10

times10minus3

Acce

lera

tion

(msminus

2)

5m pier scour

(a)

0 1 2 3 4 5 6

0

1

Time (s)


Acce

lera

tion

(msminus

2)


minus05

05

(b)







5 Conclusion





Acknowledgments



References















































RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation















minus1

minus2

minus3

minus4

minus5

minus6

minus70 5 10 15 20 25 30 35

0

Frequency (Hz)

Scou

r dep

th (m

)












Abutment

Pile caps

Abutment


Crosshead

Central

Central

columns

Abutment columns

piles

Abutment piles

pier

pier piles







119866]



[M119866]

x1(119905)

x2(119905)

x119873(119905)

+ [C119866]

x1(119905)

x2(119905)

x119873(119905)

+ [K119866]

x1(119905)

x2(119905)

x119873(119905)

=

F1(119905)

F2(119905)

F119873(119905)

(1)

where [M119866] [C119866] and [K










in

[K119904119894] = 119896119904119894

[1 minus1

minus1 1] 119896

119904119894ge 0 (2)






Reinforced earth



119866] [C119866] and [K











119904119894) (Section 232(3))






119902119888= 60 (120590

1015840

V)07

exp (291119863119903) (3)









0 5 10 15 20 25

0D

epth

(m)


qc loose

minus5

minus10

minus15

CPT qc (MPa)

(a)

Dep

th (m

)

0 20 40 60 80 100 120

0


G0 loose

minus5

minus10

minus15

G0 (MPa)

(b)

Dep

th (m

)

0 100 200 300 400

0

K (MPa)


K loose

minus5

minus10

minus15

(c)

Dep

th (m

)

0 05 1 15 2

0

minus5

minus10

minus15



ks loose

(d)





approach






1198660= 119902119888[119860 + 119861120578 minus 119862120578

2

]minus1

(4)

where 119860 = 00203 119861 = 000125 119862 = 1216119864 minus 6 and120578 = 119902119888(1198751198861205901015840


119886= 100 kPa and 120590

1015840









1198640= 21198660(1 + V) (5)



119870 =101198640

1 minus V2[11986401198634

119864119901119868119901

]

112

(6)




xxx


Mb Ip o

yb

y2 y1

Ks2 Ks1

Kt2

mw2 mw1Kt1

Cs1Cs2

E I 120588 A

kSN kSN kSN

kS2 kS2 kS2

kS1 kS1 kS1

SS1S2


1

4

2

5

3

6




119904119894) are










Dimensional data

Dimensions(m)


1) 366


Mass and inertia


1199081) 700


Sprung body mass (119898119887) 13300



Front axle (1198701199041) 400

Rear axle (1198701199042) 1000


Front axle (1198621199041) 10

Rear axle (1198621199042) 10


Front axle (K1199051) 1750

Rear axle (K1199052) 3500



119887(119905) the









1(119905) and to do



[MV]

119901(119905)

y119887(119905)

y1(119905)

y2(119905)

+ [CV]

119901(119905)

y119887(119905)

y1(119905)

y2(119905)

+ [KV]

120593119901(119905)

y119887(119905)

y1(119905)

y2(119905)

= FV

(7)


1(119905) and y



F1(119905)

F2(119905)

= [K1199051

00 K

1199052

]y1(119905)

y2(119905)

(8)

0 5 10 15 20 25 30 35 40 45 50

0

002

004

006

008

01

Distance (m)

Hei

ght (

m)



minus002

minus004


where K1199051

and K1199052


1(119905) and F



10038161003816100381610038161003816100381610038161003816


Δmax

10038161003816100381610038161003816100381610038161003816le 001 (9)





dense and dense



dynamic properties


foundation elements




Assemble global



Process signals



depth


reached

No

Yes


model



checked

Yes

Scour algorithm

No


Itera

te if

nece

ssar

y

= minus 1


x 998400 and 998400998400



mass [Mv] damping

Ns

Ns Nsx x

x998400x

998400998400 x

sand








119901



SNR = 10 log10


(11)


120590119873


exp ((SNR sdot log119890(10)) 10)

(12)

where 120590119873
















0 5 10

0

2

Time (s)

Disp

lace

men

t (m

)

Mid D1 VERT


times10minus4

minus2

(a)

Disp

lace

men

t (m

)

0 5 10

0

1

2

Time (s)

Pier top LAT


minus1

minus2

(b)

0 5 10

0

1

2

Time (s)

Mid D1 VERT

times10minus3

minus1

minus2

Velo

city

(msminus

1)

(c)

0 5 10

0

2

4

Time (s)

Pier top LAT

times10minus4

minus2

minus4

Velo

city

(msminus

1)

(d)

0 5 10

0

005

01

Time (s)

Mid D1 VERT

Front axle enters

Front axle leaves

Rear axle enters


lera

tion

(msminus

2)

minus005

minus01

(e)

0 5 10

0

0005

001

Time (s)

Pier top LAT

Front axle enters

Front axle leaves


cele

ratio

n (m

sminus2)

minus0005

minus001

(f)






0 2 4 6 8 10 12 14

0

001

002

Time (s)


minus002

minus001

Acce

lera

tion

(msminus

2)

0 05 1 15 2 25 3 35 4

0

001

002

Time (s)

minus002

minus001

Acce

lera

tion

(msminus

2)


(b)

(a)







0 2 4 6 8 10 12 14

0

0005

001

0015

002

Time (s)

Zero scour

45 5 55 6 65 7

minus0015

minus0005

minus001

Acce

lera

tion

(msminus

2)

5m pier scour







0 5 10

0

001

002

Time (s)

No noise

minus002

minus001

Acce

lera

tion

(msminus

2)

(a)SNR = 20

0 5 10

0

001

002

Time (s)

minus002

minus001Acce

lera

tion

(msminus

2)

(b)

SNR = 10

0 5 10

0

001

002

Time (s)

minus002

minus001

Acce

lera

tion

(msminus

2)

(c)SNR = 5

0 5 10

0

001

002

Time (s)

minus002

minus001Acce

lera

tion

(msminus

2)

(d)


0 1 2 3 4 5 6

0

5

Time (s)

Zero scour



minus5

minus10

times10minus3

Acce

lera

tion

(msminus

2)

5m pier scour

(a)

0 1 2 3 4 5 6

0

1

Time (s)


Acce

lera

tion

(msminus

2)


minus05

05

(b)







5 Conclusion





Acknowledgments



References















































RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation











Abutment

Pile caps

Abutment


Crosshead

Central

Central

columns

Abutment columns

piles

Abutment piles

pier

pier piles







119866]



[M119866]

x1(119905)

x2(119905)

x119873(119905)

+ [C119866]

x1(119905)

x2(119905)

x119873(119905)

+ [K119866]

x1(119905)

x2(119905)

x119873(119905)

=

F1(119905)

F2(119905)

F119873(119905)

(1)

where [M119866] [C119866] and [K










in

[K119904119894] = 119896119904119894

[1 minus1

minus1 1] 119896

119904119894ge 0 (2)






Reinforced earth



119866] [C119866] and [K











119904119894) (Section 232(3))






119902119888= 60 (120590

1015840

V)07

exp (291119863119903) (3)









0 5 10 15 20 25

0D

epth

(m)


qc loose

minus5

minus10

minus15

CPT qc (MPa)

(a)

Dep

th (m

)

0 20 40 60 80 100 120

0


G0 loose

minus5

minus10

minus15

G0 (MPa)

(b)

Dep

th (m

)

0 100 200 300 400

0

K (MPa)


K loose

minus5

minus10

minus15

(c)

Dep

th (m

)

0 05 1 15 2

0

minus5

minus10

minus15



ks loose

(d)





approach






1198660= 119902119888[119860 + 119861120578 minus 119862120578

2

]minus1

(4)

where 119860 = 00203 119861 = 000125 119862 = 1216119864 minus 6 and120578 = 119902119888(1198751198861205901015840


119886= 100 kPa and 120590

1015840









1198640= 21198660(1 + V) (5)



119870 =101198640

1 minus V2[11986401198634

119864119901119868119901

]

112

(6)




xxx


Mb Ip o

yb

y2 y1

Ks2 Ks1

Kt2

mw2 mw1Kt1

Cs1Cs2

E I 120588 A

kSN kSN kSN

kS2 kS2 kS2

kS1 kS1 kS1

SS1S2


1

4

2

5

3

6




119904119894) are










Dimensional data

Dimensions(m)


1) 366


Mass and inertia


1199081) 700


Sprung body mass (119898119887) 13300



Front axle (1198701199041) 400

Rear axle (1198701199042) 1000


Front axle (1198621199041) 10

Rear axle (1198621199042) 10


Front axle (K1199051) 1750

Rear axle (K1199052) 3500



119887(119905) the









1(119905) and to do



[MV]

119901(119905)

y119887(119905)

y1(119905)

y2(119905)

+ [CV]

119901(119905)

y119887(119905)

y1(119905)

y2(119905)

+ [KV]

120593119901(119905)

y119887(119905)

y1(119905)

y2(119905)

= FV

(7)


1(119905) and y



F1(119905)

F2(119905)

= [K1199051

00 K

1199052

]y1(119905)

y2(119905)

(8)

0 5 10 15 20 25 30 35 40 45 50

0

002

004

006

008

01

Distance (m)

Hei

ght (

m)



minus002

minus004


where K1199051

and K1199052


1(119905) and F



10038161003816100381610038161003816100381610038161003816


Δmax

10038161003816100381610038161003816100381610038161003816le 001 (9)





dense and dense



dynamic properties


foundation elements




Assemble global



Process signals



depth


reached

No

Yes


model



checked

Yes

Scour algorithm

No


Itera

te if

nece

ssar

y

= minus 1


x 998400 and 998400998400



mass [Mv] damping

Ns

Ns Nsx x

x998400x

998400998400 x

sand








119901



SNR = 10 log10


(11)


120590119873


exp ((SNR sdot log119890(10)) 10)

(12)

where 120590119873
















0 5 10

0

2

Time (s)

Disp

lace

men

t (m

)

Mid D1 VERT


times10minus4

minus2

(a)

Disp

lace

men

t (m

)

0 5 10

0

1

2

Time (s)

Pier top LAT


minus1

minus2

(b)

0 5 10

0

1

2

Time (s)

Mid D1 VERT

times10minus3

minus1

minus2

Velo

city

(msminus

1)

(c)

0 5 10

0

2

4

Time (s)

Pier top LAT

times10minus4

minus2

minus4

Velo

city

(msminus

1)

(d)

0 5 10

0

005

01

Time (s)

Mid D1 VERT

Front axle enters

Front axle leaves

Rear axle enters


lera

tion

(msminus

2)

minus005

minus01

(e)

0 5 10

0

0005

001

Time (s)

Pier top LAT

Front axle enters

Front axle leaves


cele

ratio

n (m

sminus2)

minus0005

minus001

(f)






0 2 4 6 8 10 12 14

0

001

002

Time (s)


minus002

minus001

Acce

lera

tion

(msminus

2)

0 05 1 15 2 25 3 35 4

0

001

002

Time (s)

minus002

minus001

Acce

lera

tion

(msminus

2)


(b)

(a)







0 2 4 6 8 10 12 14

0

0005

001

0015

002

Time (s)

Zero scour

45 5 55 6 65 7

minus0015

minus0005

minus001

Acce

lera

tion

(msminus

2)

5m pier scour







0 5 10

0

001

002

Time (s)

No noise

minus002

minus001

Acce

lera

tion

(msminus

2)

(a)SNR = 20

0 5 10

0

001

002

Time (s)

minus002

minus001Acce

lera

tion

(msminus

2)

(b)

SNR = 10

0 5 10

0

001

002

Time (s)

minus002

minus001

Acce

lera

tion

(msminus

2)

(c)SNR = 5

0 5 10

0

001

002

Time (s)

minus002

minus001Acce

lera

tion

(msminus

2)

(d)


0 1 2 3 4 5 6

0

5

Time (s)

Zero scour



minus5

minus10

times10minus3

Acce

lera

tion

(msminus

2)

5m pier scour

(a)

0 1 2 3 4 5 6

0

1

Time (s)


Acce

lera

tion

(msminus

2)


minus05

05

(b)







5 Conclusion





Acknowledgments



References















































RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation
















in

[K119904119894] = 119896119904119894

[1 minus1

minus1 1] 119896

119904119894ge 0 (2)






Reinforced earth



119866] [C119866] and [K











119904119894) (Section 232(3))






119902119888= 60 (120590

1015840

V)07

exp (291119863119903) (3)









0 5 10 15 20 25

0D

epth

(m)


qc loose

minus5

minus10

minus15

CPT qc (MPa)

(a)

Dep

th (m

)

0 20 40 60 80 100 120

0


G0 loose

minus5

minus10

minus15

G0 (MPa)

(b)

Dep

th (m

)

0 100 200 300 400

0

K (MPa)


K loose

minus5

minus10

minus15

(c)

Dep

th (m

)

0 05 1 15 2

0

minus5

minus10

minus15



ks loose

(d)





approach






1198660= 119902119888[119860 + 119861120578 minus 119862120578

2

]minus1

(4)

where 119860 = 00203 119861 = 000125 119862 = 1216119864 minus 6 and120578 = 119902119888(1198751198861205901015840


119886= 100 kPa and 120590

1015840









1198640= 21198660(1 + V) (5)



119870 =101198640

1 minus V2[11986401198634

119864119901119868119901

]

112

(6)




xxx


Mb Ip o

yb

y2 y1

Ks2 Ks1

Kt2

mw2 mw1Kt1

Cs1Cs2

E I 120588 A

kSN kSN kSN

kS2 kS2 kS2

kS1 kS1 kS1

SS1S2


1

4

2

5

3

6




119904119894) are










Dimensional data

Dimensions(m)


1) 366


Mass and inertia


1199081) 700


Sprung body mass (119898119887) 13300



Front axle (1198701199041) 400

Rear axle (1198701199042) 1000


Front axle (1198621199041) 10

Rear axle (1198621199042) 10


Front axle (K1199051) 1750

Rear axle (K1199052) 3500



119887(119905) the









1(119905) and to do



[MV]

119901(119905)

y119887(119905)

y1(119905)

y2(119905)

+ [CV]

119901(119905)

y119887(119905)

y1(119905)

y2(119905)

+ [KV]

120593119901(119905)

y119887(119905)

y1(119905)

y2(119905)

= FV

(7)


1(119905) and y



F1(119905)

F2(119905)

= [K1199051

00 K

1199052

]y1(119905)

y2(119905)

(8)

0 5 10 15 20 25 30 35 40 45 50

0

002

004

006

008

01

Distance (m)

Hei

ght (

m)



minus002

minus004


where K1199051

and K1199052


1(119905) and F



10038161003816100381610038161003816100381610038161003816


Δmax

10038161003816100381610038161003816100381610038161003816le 001 (9)





dense and dense



dynamic properties


foundation elements




Assemble global



Process signals



depth


reached

No

Yes


model



checked

Yes

Scour algorithm

No


Itera

te if

nece

ssar

y

= minus 1


x 998400 and 998400998400



mass [Mv] damping

Ns

Ns Nsx x

x998400x

998400998400 x

sand








119901



SNR = 10 log10


(11)


120590119873


exp ((SNR sdot log119890(10)) 10)

(12)

where 120590119873
















0 5 10

0

2

Time (s)

Disp

lace

men

t (m

)

Mid D1 VERT


times10minus4

minus2

(a)

Disp

lace

men

t (m

)

0 5 10

0

1

2

Time (s)

Pier top LAT


minus1

minus2

(b)

0 5 10

0

1

2

Time (s)

Mid D1 VERT

times10minus3

minus1

minus2

Velo

city

(msminus

1)

(c)

0 5 10

0

2

4

Time (s)

Pier top LAT

times10minus4

minus2

minus4

Velo

city

(msminus

1)

(d)

0 5 10

0

005

01

Time (s)

Mid D1 VERT

Front axle enters

Front axle leaves

Rear axle enters


lera

tion

(msminus

2)

minus005

minus01

(e)

0 5 10

0

0005

001

Time (s)

Pier top LAT

Front axle enters

Front axle leaves


cele

ratio

n (m

sminus2)

minus0005

minus001

(f)






0 2 4 6 8 10 12 14

0

001

002

Time (s)


minus002

minus001

Acce

lera

tion

(msminus

2)

0 05 1 15 2 25 3 35 4

0

001

002

Time (s)

minus002

minus001

Acce

lera

tion

(msminus

2)


(b)

(a)







0 2 4 6 8 10 12 14

0

0005

001

0015

002

Time (s)

Zero scour

45 5 55 6 65 7

minus0015

minus0005

minus001

Acce

lera

tion

(msminus

2)

5m pier scour







0 5 10

0

001

002

Time (s)

No noise

minus002

minus001

Acce

lera

tion

(msminus

2)

(a)SNR = 20

0 5 10

0

001

002

Time (s)

minus002

minus001Acce

lera

tion

(msminus

2)

(b)

SNR = 10

0 5 10

0

001

002

Time (s)

minus002

minus001

Acce

lera

tion

(msminus

2)

(c)SNR = 5

0 5 10

0

001

002

Time (s)

minus002

minus001Acce

lera

tion

(msminus

2)

(d)


0 1 2 3 4 5 6

0

5

Time (s)

Zero scour



minus5

minus10

times10minus3

Acce

lera

tion

(msminus

2)

5m pier scour

(a)

0 1 2 3 4 5 6

0

1

Time (s)


Acce

lera

tion

(msminus

2)


minus05

05

(b)







5 Conclusion





Acknowledgments



References















































RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation










0 5 10 15 20 25

0D

epth

(m)


qc loose

minus5

minus10

minus15

CPT qc (MPa)

(a)

Dep

th (m

)

0 20 40 60 80 100 120

0


G0 loose

minus5

minus10

minus15

G0 (MPa)

(b)

Dep

th (m

)

0 100 200 300 400

0

K (MPa)


K loose

minus5

minus10

minus15

(c)

Dep

th (m

)

0 05 1 15 2

0

minus5

minus10

minus15



ks loose

(d)





approach






1198660= 119902119888[119860 + 119861120578 minus 119862120578

2

]minus1

(4)

where 119860 = 00203 119861 = 000125 119862 = 1216119864 minus 6 and120578 = 119902119888(1198751198861205901015840


119886= 100 kPa and 120590

1015840









1198640= 21198660(1 + V) (5)



119870 =101198640

1 minus V2[11986401198634

119864119901119868119901

]

112

(6)




xxx


Mb Ip o

yb

y2 y1

Ks2 Ks1

Kt2

mw2 mw1Kt1

Cs1Cs2

E I 120588 A

kSN kSN kSN

kS2 kS2 kS2

kS1 kS1 kS1

SS1S2


1

4

2

5

3

6




119904119894) are










Dimensional data

Dimensions(m)


1) 366


Mass and inertia


1199081) 700


Sprung body mass (119898119887) 13300



Front axle (1198701199041) 400

Rear axle (1198701199042) 1000


Front axle (1198621199041) 10

Rear axle (1198621199042) 10


Front axle (K1199051) 1750

Rear axle (K1199052) 3500



119887(119905) the









1(119905) and to do



[MV]

119901(119905)

y119887(119905)

y1(119905)

y2(119905)

+ [CV]

119901(119905)

y119887(119905)

y1(119905)

y2(119905)

+ [KV]

120593119901(119905)

y119887(119905)

y1(119905)

y2(119905)

= FV

(7)


1(119905) and y



F1(119905)

F2(119905)

= [K1199051

00 K

1199052

]y1(119905)

y2(119905)

(8)

0 5 10 15 20 25 30 35 40 45 50

0

002

004

006

008

01

Distance (m)

Hei

ght (

m)



minus002

minus004


where K1199051

and K1199052


1(119905) and F



10038161003816100381610038161003816100381610038161003816


Δmax

10038161003816100381610038161003816100381610038161003816le 001 (9)





dense and dense



dynamic properties


foundation elements




Assemble global



Process signals



depth


reached

No

Yes


model



checked

Yes

Scour algorithm

No


Itera

te if

nece

ssar

y

= minus 1


x 998400 and 998400998400



mass [Mv] damping

Ns

Ns Nsx x

x998400x

998400998400 x

sand








119901



SNR = 10 log10


(11)


120590119873


exp ((SNR sdot log119890(10)) 10)

(12)

where 120590119873
















0 5 10

0

2

Time (s)

Disp

lace

men

t (m

)

Mid D1 VERT


times10minus4

minus2

(a)

Disp

lace

men

t (m

)

0 5 10

0

1

2

Time (s)

Pier top LAT


minus1

minus2

(b)

0 5 10

0

1

2

Time (s)

Mid D1 VERT

times10minus3

minus1

minus2

Velo

city

(msminus

1)

(c)

0 5 10

0

2

4

Time (s)

Pier top LAT

times10minus4

minus2

minus4

Velo

city

(msminus

1)

(d)

0 5 10

0

005

01

Time (s)

Mid D1 VERT

Front axle enters

Front axle leaves

Rear axle enters


lera

tion

(msminus

2)

minus005

minus01

(e)

0 5 10

0

0005

001

Time (s)

Pier top LAT

Front axle enters

Front axle leaves


cele

ratio

n (m

sminus2)

minus0005

minus001

(f)






0 2 4 6 8 10 12 14

0

001

002

Time (s)


minus002

minus001

Acce

lera

tion

(msminus

2)

0 05 1 15 2 25 3 35 4

0

001

002

Time (s)

minus002

minus001

Acce

lera

tion

(msminus

2)


(b)

(a)







0 2 4 6 8 10 12 14

0

0005

001

0015

002

Time (s)

Zero scour

45 5 55 6 65 7

minus0015

minus0005

minus001

Acce

lera

tion

(msminus

2)

5m pier scour







0 5 10

0

001

002

Time (s)

No noise

minus002

minus001

Acce

lera

tion

(msminus

2)

(a)SNR = 20

0 5 10

0

001

002

Time (s)

minus002

minus001Acce

lera

tion

(msminus

2)

(b)

SNR = 10

0 5 10

0

001

002

Time (s)

minus002

minus001

Acce

lera

tion

(msminus

2)

(c)SNR = 5

0 5 10

0

001

002

Time (s)

minus002

minus001Acce

lera

tion

(msminus

2)

(d)


0 1 2 3 4 5 6

0

5

Time (s)

Zero scour



minus5

minus10

times10minus3

Acce

lera

tion

(msminus

2)

5m pier scour

(a)

0 1 2 3 4 5 6

0

1

Time (s)


Acce

lera

tion

(msminus

2)


minus05

05

(b)







5 Conclusion





Acknowledgments



References















































RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation










xxx


Mb Ip o

yb

y2 y1

Ks2 Ks1

Kt2

mw2 mw1Kt1

Cs1Cs2

E I 120588 A

kSN kSN kSN

kS2 kS2 kS2

kS1 kS1 kS1

SS1S2


1

4

2

5

3

6




119904119894) are










Dimensional data

Dimensions(m)


1) 366


Mass and inertia


1199081) 700


Sprung body mass (119898119887) 13300



Front axle (1198701199041) 400

Rear axle (1198701199042) 1000


Front axle (1198621199041) 10

Rear axle (1198621199042) 10


Front axle (K1199051) 1750

Rear axle (K1199052) 3500



119887(119905) the









1(119905) and to do



[MV]

119901(119905)

y119887(119905)

y1(119905)

y2(119905)

+ [CV]

119901(119905)

y119887(119905)

y1(119905)

y2(119905)

+ [KV]

120593119901(119905)

y119887(119905)

y1(119905)

y2(119905)

= FV

(7)


1(119905) and y



F1(119905)

F2(119905)

= [K1199051

00 K

1199052

]y1(119905)

y2(119905)

(8)

0 5 10 15 20 25 30 35 40 45 50

0

002

004

006

008

01

Distance (m)

Hei

ght (

m)



minus002

minus004


where K1199051

and K1199052


1(119905) and F



10038161003816100381610038161003816100381610038161003816


Δmax

10038161003816100381610038161003816100381610038161003816le 001 (9)





dense and dense



dynamic properties


foundation elements




Assemble global



Process signals



depth


reached

No

Yes


model



checked

Yes

Scour algorithm

No


Itera

te if

nece

ssar

y

= minus 1


x 998400 and 998400998400



mass [Mv] damping

Ns

Ns Nsx x

x998400x

998400998400 x

sand








119901



SNR = 10 log10


(11)


120590119873


exp ((SNR sdot log119890(10)) 10)

(12)

where 120590119873
















0 5 10

0

2

Time (s)

Disp

lace

men

t (m

)

Mid D1 VERT


times10minus4

minus2

(a)

Disp

lace

men

t (m

)

0 5 10

0

1

2

Time (s)

Pier top LAT


minus1

minus2

(b)

0 5 10

0

1

2

Time (s)

Mid D1 VERT

times10minus3

minus1

minus2

Velo

city

(msminus

1)

(c)

0 5 10

0

2

4

Time (s)

Pier top LAT

times10minus4

minus2

minus4

Velo

city

(msminus

1)

(d)

0 5 10

0

005

01

Time (s)

Mid D1 VERT

Front axle enters

Front axle leaves

Rear axle enters


lera

tion

(msminus

2)

minus005

minus01

(e)

0 5 10

0

0005

001

Time (s)

Pier top LAT

Front axle enters

Front axle leaves


cele

ratio

n (m

sminus2)

minus0005

minus001

(f)






0 2 4 6 8 10 12 14

0

001

002

Time (s)


minus002

minus001

Acce

lera

tion

(msminus

2)

0 05 1 15 2 25 3 35 4

0

001

002

Time (s)

minus002

minus001

Acce

lera

tion

(msminus

2)


(b)

(a)







0 2 4 6 8 10 12 14

0

0005

001

0015

002

Time (s)

Zero scour

45 5 55 6 65 7

minus0015

minus0005

minus001

Acce

lera

tion

(msminus

2)

5m pier scour







0 5 10

0

001

002

Time (s)

No noise

minus002

minus001

Acce

lera

tion

(msminus

2)

(a)SNR = 20

0 5 10

0

001

002

Time (s)

minus002

minus001Acce

lera

tion

(msminus

2)

(b)

SNR = 10

0 5 10

0

001

002

Time (s)

minus002

minus001

Acce

lera

tion

(msminus

2)

(c)SNR = 5

0 5 10

0

001

002

Time (s)

minus002

minus001Acce

lera

tion

(msminus

2)

(d)


0 1 2 3 4 5 6

0

5

Time (s)

Zero scour



minus5

minus10

times10minus3

Acce

lera

tion

(msminus

2)

5m pier scour

(a)

0 1 2 3 4 5 6

0

1

Time (s)


Acce

lera

tion

(msminus

2)


minus05

05

(b)







5 Conclusion





Acknowledgments



References















































RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation












1(119905) and to do



[MV]

119901(119905)

y119887(119905)

y1(119905)

y2(119905)

+ [CV]

119901(119905)

y119887(119905)

y1(119905)

y2(119905)

+ [KV]

120593119901(119905)

y119887(119905)

y1(119905)

y2(119905)

= FV

(7)


1(119905) and y



F1(119905)

F2(119905)

= [K1199051

00 K

1199052

]y1(119905)

y2(119905)

(8)

0 5 10 15 20 25 30 35 40 45 50

0

002

004

006

008

01

Distance (m)

Hei

ght (

m)



minus002

minus004


where K1199051

and K1199052


1(119905) and F



10038161003816100381610038161003816100381610038161003816


Δmax

10038161003816100381610038161003816100381610038161003816le 001 (9)





dense and dense



dynamic properties


foundation elements




Assemble global



Process signals



depth


reached

No

Yes


model



checked

Yes

Scour algorithm

No


Itera

te if

nece

ssar

y

= minus 1


x 998400 and 998400998400



mass [Mv] damping

Ns

Ns Nsx x

x998400x

998400998400 x

sand








119901



SNR = 10 log10


(11)


120590119873


exp ((SNR sdot log119890(10)) 10)

(12)

where 120590119873
















0 5 10

0

2

Time (s)

Disp

lace

men

t (m

)

Mid D1 VERT


times10minus4

minus2

(a)

Disp

lace

men

t (m

)

0 5 10

0

1

2

Time (s)

Pier top LAT


minus1

minus2

(b)

0 5 10

0

1

2

Time (s)

Mid D1 VERT

times10minus3

minus1

minus2

Velo

city

(msminus

1)

(c)

0 5 10

0

2

4

Time (s)

Pier top LAT

times10minus4

minus2

minus4

Velo

city

(msminus

1)

(d)

0 5 10

0

005

01

Time (s)

Mid D1 VERT

Front axle enters

Front axle leaves

Rear axle enters


lera

tion

(msminus

2)

minus005

minus01

(e)

0 5 10

0

0005

001

Time (s)

Pier top LAT

Front axle enters

Front axle leaves


cele

ratio

n (m

sminus2)

minus0005

minus001

(f)






0 2 4 6 8 10 12 14

0

001

002

Time (s)


minus002

minus001

Acce

lera

tion

(msminus

2)

0 05 1 15 2 25 3 35 4

0

001

002

Time (s)

minus002

minus001

Acce

lera

tion

(msminus

2)


(b)

(a)







0 2 4 6 8 10 12 14

0

0005

001

0015

002

Time (s)

Zero scour

45 5 55 6 65 7

minus0015

minus0005

minus001

Acce

lera

tion

(msminus

2)

5m pier scour







0 5 10

0

001

002

Time (s)

No noise

minus002

minus001

Acce

lera

tion

(msminus

2)

(a)SNR = 20

0 5 10

0

001

002

Time (s)

minus002

minus001Acce

lera

tion

(msminus

2)

(b)

SNR = 10

0 5 10

0

001

002

Time (s)

minus002

minus001

Acce

lera

tion

(msminus

2)

(c)SNR = 5

0 5 10

0

001

002

Time (s)

minus002

minus001Acce

lera

tion

(msminus

2)

(d)


0 1 2 3 4 5 6

0

5

Time (s)

Zero scour



minus5

minus10

times10minus3

Acce

lera

tion

(msminus

2)

5m pier scour

(a)

0 1 2 3 4 5 6

0

1

Time (s)


Acce

lera

tion

(msminus

2)


minus05

05

(b)







5 Conclusion





Acknowledgments



References















































RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation











dense and dense



dynamic properties


foundation elements




Assemble global



Process signals



depth


reached

No

Yes


model



checked

Yes

Scour algorithm

No


Itera

te if

nece

ssar

y

= minus 1


x 998400 and 998400998400



mass [Mv] damping

Ns

Ns Nsx x

x998400x

998400998400 x

sand








119901



SNR = 10 log10


(11)


120590119873


exp ((SNR sdot log119890(10)) 10)

(12)

where 120590119873
















0 5 10

0

2

Time (s)

Disp

lace

men

t (m

)

Mid D1 VERT


times10minus4

minus2

(a)

Disp

lace

men

t (m

)

0 5 10

0

1

2

Time (s)

Pier top LAT


minus1

minus2

(b)

0 5 10

0

1

2

Time (s)

Mid D1 VERT

times10minus3

minus1

minus2

Velo

city

(msminus

1)

(c)

0 5 10

0

2

4

Time (s)

Pier top LAT

times10minus4

minus2

minus4

Velo

city

(msminus

1)

(d)

0 5 10

0

005

01

Time (s)

Mid D1 VERT

Front axle enters

Front axle leaves

Rear axle enters


lera

tion

(msminus

2)

minus005

minus01

(e)

0 5 10

0

0005

001

Time (s)

Pier top LAT

Front axle enters

Front axle leaves


cele

ratio

n (m

sminus2)

minus0005

minus001

(f)






0 2 4 6 8 10 12 14

0

001

002

Time (s)


minus002

minus001

Acce

lera

tion

(msminus

2)

0 05 1 15 2 25 3 35 4

0

001

002

Time (s)

minus002

minus001

Acce

lera

tion

(msminus

2)


(b)

(a)







0 2 4 6 8 10 12 14

0

0005

001

0015

002

Time (s)

Zero scour

45 5 55 6 65 7

minus0015

minus0005

minus001

Acce

lera

tion

(msminus

2)

5m pier scour







0 5 10

0

001

002

Time (s)

No noise

minus002

minus001

Acce

lera

tion

(msminus

2)

(a)SNR = 20

0 5 10

0

001

002

Time (s)

minus002

minus001Acce

lera

tion

(msminus

2)

(b)

SNR = 10

0 5 10

0

001

002

Time (s)

minus002

minus001

Acce

lera

tion

(msminus

2)

(c)SNR = 5

0 5 10

0

001

002

Time (s)

minus002

minus001Acce

lera

tion

(msminus

2)

(d)


0 1 2 3 4 5 6

0

5

Time (s)

Zero scour



minus5

minus10

times10minus3

Acce

lera

tion

(msminus

2)

5m pier scour

(a)

0 1 2 3 4 5 6

0

1

Time (s)


Acce

lera

tion

(msminus

2)


minus05

05

(b)







5 Conclusion





Acknowledgments



References















































RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation























0 5 10

0

2

Time (s)

Disp

lace

men

t (m

)

Mid D1 VERT


times10minus4

minus2

(a)

Disp

lace

men

t (m

)

0 5 10

0

1

2

Time (s)

Pier top LAT


minus1

minus2

(b)

0 5 10

0

1

2

Time (s)

Mid D1 VERT

times10minus3

minus1

minus2

Velo

city

(msminus

1)

(c)

0 5 10

0

2

4

Time (s)

Pier top LAT

times10minus4

minus2

minus4

Velo

city

(msminus

1)

(d)

0 5 10

0

005

01

Time (s)

Mid D1 VERT

Front axle enters

Front axle leaves

Rear axle enters


lera

tion

(msminus

2)

minus005

minus01

(e)

0 5 10

0

0005

001

Time (s)

Pier top LAT

Front axle enters

Front axle leaves


cele

ratio

n (m

sminus2)

minus0005

minus001

(f)






0 2 4 6 8 10 12 14

0

001

002

Time (s)


minus002

minus001

Acce

lera

tion

(msminus

2)

0 05 1 15 2 25 3 35 4

0

001

002

Time (s)

minus002

minus001

Acce

lera

tion

(msminus

2)


(b)

(a)







0 2 4 6 8 10 12 14

0

0005

001

0015

002

Time (s)

Zero scour

45 5 55 6 65 7

minus0015

minus0005

minus001

Acce

lera

tion

(msminus

2)

5m pier scour







0 5 10

0

001

002

Time (s)

No noise

minus002

minus001

Acce

lera

tion

(msminus

2)

(a)SNR = 20

0 5 10

0

001

002

Time (s)

minus002

minus001Acce

lera

tion

(msminus

2)

(b)

SNR = 10

0 5 10

0

001

002

Time (s)

minus002

minus001

Acce

lera

tion

(msminus

2)

(c)SNR = 5

0 5 10

0

001

002

Time (s)

minus002

minus001Acce

lera

tion

(msminus

2)

(d)


0 1 2 3 4 5 6

0

5

Time (s)

Zero scour



minus5

minus10

times10minus3

Acce

lera

tion

(msminus

2)

5m pier scour

(a)

0 1 2 3 4 5 6

0

1

Time (s)


Acce

lera

tion

(msminus

2)


minus05

05

(b)







5 Conclusion





Acknowledgments



References















































RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation










0 2 4 6 8 10 12 14

0

001

002

Time (s)


minus002

minus001

Acce

lera

tion

(msminus

2)

0 05 1 15 2 25 3 35 4

0

001

002

Time (s)

minus002

minus001

Acce

lera

tion

(msminus

2)


(b)

(a)







0 2 4 6 8 10 12 14

0

0005

001

0015

002

Time (s)

Zero scour

45 5 55 6 65 7

minus0015

minus0005

minus001

Acce

lera

tion

(msminus

2)

5m pier scour







0 5 10

0

001

002

Time (s)

No noise

minus002

minus001

Acce

lera

tion

(msminus

2)

(a)SNR = 20

0 5 10

0

001

002

Time (s)

minus002

minus001Acce

lera

tion

(msminus

2)

(b)

SNR = 10

0 5 10

0

001

002

Time (s)

minus002

minus001

Acce

lera

tion

(msminus

2)

(c)SNR = 5

0 5 10

0

001

002

Time (s)

minus002

minus001Acce

lera

tion

(msminus

2)

(d)


0 1 2 3 4 5 6

0

5

Time (s)

Zero scour



minus5

minus10

times10minus3

Acce

lera

tion

(msminus

2)

5m pier scour

(a)

0 1 2 3 4 5 6

0

1

Time (s)


Acce

lera

tion

(msminus

2)


minus05

05

(b)







5 Conclusion





Acknowledgments



References















































RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation










0 5 10

0

001

002

Time (s)

No noise

minus002

minus001

Acce

lera

tion

(msminus

2)

(a)SNR = 20

0 5 10

0

001

002

Time (s)

minus002

minus001Acce

lera

tion

(msminus

2)

(b)

SNR = 10

0 5 10

0

001

002

Time (s)

minus002

minus001

Acce

lera

tion

(msminus

2)

(c)SNR = 5

0 5 10

0

001

002

Time (s)

minus002

minus001Acce

lera

tion

(msminus

2)

(d)


0 1 2 3 4 5 6

0

5

Time (s)

Zero scour



minus5

minus10

times10minus3

Acce

lera

tion

(msminus

2)

5m pier scour

(a)

0 1 2 3 4 5 6

0

1

Time (s)


Acce

lera

tion

(msminus

2)


minus05

05

(b)







5 Conclusion





Acknowledgments



References















































RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation











5 Conclusion





Acknowledgments



References















































RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation








































RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation









Research Article Development of a Vehicle-Bridge-Soil Dynamic Interaction Model...

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