ORIGINAL RESEARCH Open Access Soil-structure ...2F2008-6695...Long-span bridges, such as cable-stayed bridge structural systems, provide a valuable environment for the nonlinear behavior

Raheem and Hayashikawa International Journal of AdvancedStructural Engineering 2013, 5:8http://www.advancedstructeng.com/content/5/1/8

ORIGINAL RESEARCH Open Access

Soil-structure interaction modeling effects onseismic response of cable-stayed bridge towerShehata E Abdel Raheem1,2* and Toshiro Hayashikawa3

Abstract

A nonlinear dynamic analysis, including soil-structure interaction, is developed to estimate the seismic responsecharacteristics and to predict the earthquake response of cable-stayed bridge towers with spread foundation. Anincremental iterative finite element technique is adopted for a more realistic dynamic analysis of nonlinearsoil-foundation-superstructure interaction system under great-earthquake ground motion. Two different approachesto model soil foundation interaction are considered: nonlinear Winkler soil foundation model and linear lumped-parameter soil model. The numerical results show that the simplified lumped-parameter-model analysis provides agood prediction for the peak response, but it overestimates the acceleration response and underestimates the upliftforce at the anchor between superstructure and pier. The soil bearing stress beneath the footing base isdramatically increased due to footing base uplift. The predominant contribution to the vertical response at footingbase resulted from the massive foundation rocking rather than from the vertical excitation.

Keywords: Soil-structure interaction, Cable-stayed bridge towers, Linear lumped-parameter model, Uplift, Seismicdesign, Nonlinear Winkler soil model, Time history analysis

IntroductionLong-span bridges, such as cable-stayed bridge structuralsystems, provide a valuable environment for the nonlinearbehavior due to material and geometrical nonlinearitiesof the structures of relatively large deflection andforces (Ali and Abdel-Ghaffar 1995; Abdel Raheem andHayashikawa 2003; Committee of Earthquake Engineering1996). The Hyogoken-Nanbu (Kobe, Japan) earthquake on17 January 1995 led to an increased awareness concerningthe response of highway bridges subjected to earthquakeground motions. The dynamic analyses and ductilitydesign have been reconsidered by Japan Road Association(Committee of Earthquake Engineering 1996; Japan RoadAssociation 1996a, 1996b). Necessity has arisen to developmore efficient analysis procedures, which can lead to athorough understanding and a realistic prediction of thenonlinear dynamic response of the bridge structuralsystems, to improve the bridge seismic performances.Current design practice does not account for the

nonlinear behavior of soil-foundation interface primarily

* Correspondence: [email protected] University, Medina, Saudi Arabia2Civil Engineering Department, Faculty of Engineering, Assiut University,Assiut 71516, EgyptFull list of author information is available at the end of the article

© 2013 Raheem and Hayashikawa This is an OpAttribution License (http://creativecommons.orin any medium, provided the original work is p

due to the absence of reliable nonlinear soil-structureinteraction modeling techniques that can predict thepermanent and cyclic deformations of the soil as well asthe effect of nonlinear soil-foundation interaction on theresponse of structural members. Safe and economicseismic designs of bridge structures directly depend onthe understanding level of seismic excitation and theinfluence of supporting soil on the structural dynamicresponse. Long-span bridges are more susceptible torelatively severe soil-structure interaction effect duringearthquakes when compared to buildings due to theirspatial extent, varying soil condition at different supports,and possible incoherence in the seismic input. The neces-sity of incorporating soil-structure interaction in the designof a wide class of bridge structures has been pointed out byseveral post-earthquake investigations, experimental, andanalytical studies (Committee of Earthquake Engineering1996; Vlassis and Spyrakos 2001; Trifunac and Todorovska1996; Megawati et al. 2001). Recently, several cable-stayedbridges have been constructed on relatively soft ground,which results in a great demand to evaluate the effect ofsoil-structure interaction on the seismic behavior of bridgesand properly reflect it on seismic design to accurately

en Access article distributed under the terms of the Creative Commonsg/licenses/by/2.0), which permits unrestricted use, distribution, and reproductionroperly cited.

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capture the response, enhance the safety level, and reducedesign and construction costs.Due to material and geometrical nonlinearities, the

dynamic characteristics of soil-structure system arechanged during a severe earthquake. These nonlinear-ities are sometimes treated using an equivalent linearmodel (Abdel Raheem et al. 2002; Chaojin and Spyrakos1996; Spyrakos 1997). However, the dynamic characteristicsof soil-structure system are dependent on the soil stresslevel during a severe earthquake (Ahn and Gould 1992;Gazetas and Dobry 1984; Kobayashi et al. 2002). Founda-tion rocking and uplifting are important for short-periodstructures on a relatively soft soil site (Yim and Chopra1984; Harden et al. 2006). For nonlinear structures, effectsof soil-structure interaction due to rocking can resultin significantly larger ductility demands under certainconditions (Tang and Zhang 2011; Zhang and Tang 2009).These findings necessitate the evaluation of structuralresponses considering soil-structure interaction usingfoundation models that can realistically capture thenonlinear force, displacement behaviors, and energy dissi-pation mechanisms. Nonlinear foundation movements andassociated energy dissipation may be utilized to reduceforce and ductility demands of a structure, particularly inhigh-intensity earthquake events (Raychowdhury 2011).The purpose of this study is to assess the effects of

soil-structure interaction on the seismic response anddynamic performance of the cable-stayed bridge towerswith spread foundation. An incremental iterative finiteelement technique for a more realistic dynamic ana-lysis of nonlinear soil-foundation-superstructure systemsubjected to earthquake ground motion is developed.Two different modeling approaches, nonlinear Winklersoil model and linear lumped-parameter soil model,for the soil foundation interaction are investigated.The seismic responses of the nonlinear Winkler soilmodel are compared to those of the simplified linearlumped-parameter model. In the lumped-parametersoil model, the soil-structure interaction is simulatedwith translational, rotational, and their coupling linearsprings acting at the centroid of the spread foundationat footing base level. While in the nonlinear Winklersoil model, the soil structure interaction is simulatedwith continuous spring system (Winkler) along theembedded depth of tower pier and underneath thespread foundation. Soil strain-dependent materialnonlinearity is considered through hysteretic element,while geometrical nonlinearity by basemat uplift is con-sidered through a gap element. The massive pier ofthe tower model activates rocking response of thespread foundation under strong earthquake groundmotion, hence, results in the foundation uplift andyield of the underlying soil (Kawashima and Hosoiri2002; Gelagoti et al. 2012). The results of the nonlinear

Winkler-soil-model approach are compared with thosefrom the linear lumped-soil-model approach.

MethodsFinite element analysis procedureThree-dimensional beam element tangent stiffnessA nonlinear dynamic finite element technique is developedto analyze the elastoplastic dynamic response of framestructures under strong earthquake excitation, in which thenonlinear three-dimensional beam elements are employed.A three-dimensional beam element has six degrees of free-dom at each node, in which all couplings among bending,twisting, and stretching deformations for the beam elementare incorporated according to the geometrical nonlinearbeam theory. The element nodal displacement vector inlocal coordinate system is given as follows:

d ¼ �ui �vi �wi�θxi �θyi �θzi �uj �vj �wj

�θxj �θyj �θzj� �T

: ð1ÞThe displacements u, v, and w of a general point (x, y,

and z) in the beam can be written as follows:

u ¼ �u� y⋅d�v=dx� z⋅d�w=dx; v ¼ �v;w ¼ �w; ð2Þwhere �u , �v , and �w are the displacements of a point inthe centroid axis of a beam corresponding to x-, y-, andz-axes, respectively. �θ is the cross-sectional rotationabout the x-axis. The displacement transformation matrixof the beam element relates the element internal displace-ment to the nodal point displacement:

�u ¼ �u �v �w �θ� �T ¼ N

—x N

—y N—z N—θ

� �Td; ð3Þ

N—x ¼ N1 0 0 0 0 0 N2 0 0 0 0 0½ �;

N—y ¼ 0 N3 0 0 0 N4 0 N5 0 0 0 N6½ �;

N—z ¼ 0 0 N3 0� N4 0 0 0 N5 0� N6 0½ �;

N—θ ¼ 0 0 0 N1 0 0 0 0 0 N2 0 0½ �: ð4Þ

The shape functions Ni (i = 1 to 6) are assumed forthe local element displacements and given as follows:

N1 ¼ 1� ζ;N2 ¼ ζ;N3 ¼ 1� 3ζ2 þ 2ζ3; ζ ¼ x=l;N3 ¼ ζ � 2ζ2 þ ζ3

� �l;N5 ¼ 3ζ2 � 2ζ3;N6 ¼ �ζ2 þ ζ3

� �l;

ð5Þ

in which l is the original length of the beam element.

d�udx

¼ Bxd;d2�vdx

¼ B2d;d2�wdx

¼ B3d;d�vdx

¼ B4d;d�wdx

¼ B5d ;d�θdx

¼ B6d: ð6Þ

The strain in the deformed configuration εt can beexpressed in terms of the displacement at the equilibriumstate at any specified point in the beam cross section (x, y,and z) that defines the state of strain at any arbitrary point.


The strain displacement equation (Green-Lagrange repre-sentation of axial strain εt) is given in the following:

εt ¼ dutdx

þ 12

dutdx

� 2

þ 12

dvtdx

� 2

þ 12

dwt

dx

� 2

; ð7Þ

where ut, vt, and wt are the element displacement vectors inx-, y-, and z-axis directions, respectively; it is assumed thatdut/dx << 1. Thus, (dut/dx)

2 is ignored compared to itslinear term. The normal strain εt is then calculated. Theunknown strain in t + 1 configuration can be writtenincrementally from configuration t as follows:

εtþ1 ¼ dutþ1

dxþ 12

dvtþ1

dx

� 2

þ 12

dwtþ1

dx

� 2

; ð8Þ

δεtþ1 ¼ dδudx

þ dvtdx

⋅dδvdx

þ dwt

dx⋅dδwdx

þ 12δ

dvdx

� 2

þ 12δ

dwdx

� 2

¼ BL þ BNLð Þδd; ð9Þ

BL ¼ B1 � yB2 � zB3;

BNL ¼ BT4 B4 þ BT

5 B5� �

=2;

B1 ¼ Bx þ dvtdx

B4 þ dwt

dxB5: ð10Þ

From the principle of energy, the external work is equiva-lent to the internal work. The equilibrium equation in thedeformed configuration t + 1 can be expressed in terms ofthe principle of virtual displacements:

δU � δW ¼ 0:; ð11ÞZV

σ tþ1 δ εtþ1 dV þZl

Tsv⋅ dθ=dxð Þdx

þ 12

Zl

GJ dθ=dxð Þ2dx�ZS

f Ttþ1 δ dtþ1 dS ¼ 0; ð12Þ

where U is the internal work, W is the external virtualwork, σt+1 is the axial Couchy stress,V is the volume, δis the virtual quantity, f is the external applied force,and θ is the cross-sectional rotation about the x-axis.The unknown configuration is t + 1 which can be writtenincrementally from configuration t consistently with anonlinear Lagrangian scheme as follows:

ZV

σ t þ σð Þ δ εtþ1 dV þZl

Tsvdθdx

dxþ 12

Zl

GJdθdx

� 2

dx

�ZS

f Tt þ f T� �

δ dt þ dð Þ dS ¼ 0; ð13Þ

where σ is the second Piola-Kirchhoff axial stress:

ZV

σ BL þ σ tBNLf gdVþ 12

Zl

GJdθdx

� 2

dx�ZS

f Tδd dS

¼ZS

f Tt δd dS�ZV

σ tBLdV�Zl

Tsvdθdx

dx; ð14Þ

ZV

σ BL þ σ tBNLf gdVþ0:5Zl

GJ dθ=dxð Þ2dx

¼ δdTZ

fE1BT1 B1 � E2 BT

2 B1 þ BT1 B2

� �þ E3BT

2 B2 � E4 BT3 B1 þ BT

1 B3� �þ E5BT

3 B3

þ E6 BT2 B3 þ BT

3 B2Þ� �

ddx

þ δdTZl

Fx BT4 B4 þ BT

5 B5� �

dxd

þ δdTZl

GJ BT6 B6

� �ddx ð15Þ

ZV

σ t BLdV þZl

Tsv dθ=dxð Þdx

¼ δdTZV

σ t BT1 � yBT

2 � zBT3

� �dV þ δdT

Zl

TsvBT6 dx

¼ δdTZl

FxBT1 �MzBT

2 �MyBT3 þ TsvBT

6

� �dx;

ð16Þ

E1 ¼ ET

Zdydz; E2 ¼ ET

Zydydz; E3 ¼ ET

Zy2dydz;

E4 ¼ ET

Zzdydz; E5 ¼ ET

Zz2ydydz; E6 ¼ ET

Zzydydz;

Fx ¼Z

σ tdydz; Mz ¼Z

σ tydydz; My ¼Z

σ tzdydz

ð17Þwhich can be determined through numerical integrationover the cross section of fiber segments. The tangentstiffness can be written as follows:

kt ¼Z

fE1BT1 B1 � E2 BT

2 B1 þ BT1 B2

� �þ E3B

T2 B2 � E4 BT

3 B1 þ BT1 B3

� �þ E5BT3 B3

þ E6 BT2 B3 þ BT

3 B2� �þ Fx BT

4B4þBT5B5

� �þGJ BT

6B6Þ� �

dx: ð18Þ

In order to capture the spread of plastic zone inindividual element, the beam element is divided along its


length and over its cross section directions. The stiffnessquantities of the section are calculated based on the stressstates of integration points over the cross section. Theelement stiffness quantities are then obtained by integratingalong the length of the beam, where the plastic devel-opment of the material is automatically considered.The stiffness matrix calculations of the elements arecompleted by a numerical integration procedure. Afterobtaining the stiffness matrix of the elements withrespect to the local coordinate system, the elementcoordinates are transformed from the local coordinatesystem to the global coordinate system. The stiffnessmatrix of the elements is then assembled using standardprocedures and by getting the global stiffness matrix. In thenonlinear incremental analysis, the structure tangent stiff-ness matrix, which is assembled from the element tangentstiffness matrices, is used to predict the next incrementaldisplacements under a loading increment.

Soil-structure interaction formulationThe interaction between the soil and the structureis simulated with translational, rotational, and theircoupling spring system and equivalent viscous damping.The spring constants of the lumped-parameter modelin both bridge axis and right-angle directions arecalculated based on foundation geometry and soil profileunderneath and along the embedded depth of the foun-dation, as specified in Japanese Highway Specification(Committee of Earthquake Engineering 1996; Japan RoadAssociation 1996a). Soil properties from the standardpenetration test (SPT) data and logs of boreholes at thetower site are used to determine the coefficients of verticaland horizontal subgrade reactions that are used in aspread foundation design. A set of spring elements alongall the six degrees of freedom and the coupling of lateraland rotational directions constitutes the linear lumped soilmodel, and it is connected to the foundation centroidnode at the footing base level. The influence of the soilflexibility in the global dynamic response is consideredthrough the assembling of the stiffness matrix of the soilspring system using standard procedures getting the globestiffness matrix (Abdel Raheem 2009; Abdel Raheem et al.2002, 2003).In the nonlinear Winkler soil model, three types of soil

resistance displacement models could describe the soilcharacteristics: the first type represents the lateral soilpressure against the pier and the corresponding lateralpier displacement relationship, the second type representsthe skin friction and the relative vertical displacementbetween the soil and the pier relationship, and the thirdtype describes the bearing stress beneath the spreadfoundation and settlement relationship. All three typesassume the soil behavior to be nonlinear and can be devel-oped from the basic soil parameters. The soil-structure

interaction is simulated with nonlinear spring-dashpotsystem along the embedded depth of the pier. Bothstrain-dependent material nonlinearity and geometricalnonlinearity by basemat uplift are considered through abeam on nonlinear Winkler soil element connected inseries with gap element spring system (Abdel Raheemet al. 2002, 2003; Kobayashi et al. 2002). The springconstants in both bridge axis directions are calculatedbased on foundation geometry and soil profile under-neath and along the embedded depth of the founda-tion as specified in Japanese Highway Specification(Committee of Earthquake Engineering 1996; JapanRoad Association 1996a). The nonlinear soil-foundationmodel is described as the Winkler model that has nonlinearsprings distributed along the embedded depth in the threedirections of the local coordinate system. The reactiondisplacement model of the tensionless foundation atbase level is considered.The contribution of soil reactions to the foundation

element equivalent nodal forces vector and the elementtangent stiffness of the foundation, {fsoil} and [ksoil],respectively, can be given as follows:

fsoilf g ¼ �Zl

N½ �T rf gdx ð19Þ

and

ksoil½ � ¼ � δ fsoilf gδ df g ¼

Zl

N½ �T δ rf gδ df g dx

¼Zl

N½ �T k½ � N½ �dx; ð20Þ

where

δ rf g ¼kx

kykz

24

35 δ�u

δ�vδ�w

8<:

9=; ¼ k½ �δ �uf g

¼ k½ � N½ � df g: ð21Þ

Equation of motionThe governing nonlinear dynamic equation of the towerstructure response can be derived using the principle ofenergy, i.e., the external work is absorbed by the internal,inertial, and damping energy for any small admissiblemotion that satisfies compatibility and boundary condition.By assembling the element dynamic equilibrium equationat time t + Δt over all the elements, the incremental finiteelement method dynamic equilibrium equation (AbdelRaheem 2009; Chen 2000) can be obtained as follows:

M½ � u̇̇f gtþΔt þ C½ � u̇f gtþΔt þ K½ �tþΔt Δuf gtþΔt

¼ Ff gtþΔt � Ff gt ; ð22Þ

34.00 34.00

36.0

06 8

.00

68.0

036

.00

8 x 11.5 = 92.00 34.50 34.50 8 x 11.50 = 92.00 31.00 8 x 11.50 = 92.00 34.50 34.50 8x 11.5 = 92.00

74.30 115.00 284.00 115.00 81.10

Figure 1 Schematic representation of bridge elevation (m).

III

III

IV

11.00

18.00

X

Z

Y18.00

68.0

036

.00

3.50

7.50

1.00

34.00

17.0

014

.50

36.5

0

7.50

1.00

2.40

13.00

2.70

14.504

5.00

24.0

037

.50

1.50

2 0.0

04 8

.00

2 7.5

08 .

50

36.0

068

.00

36.00

3.003.00

18.00

a) Tower geometry

z B

yy

A

t11b

t22

t1

t2a

t1

z

t2

b) Cross section

Figure 2 Tower geometry (a) and cross section (b) of steel tower of cable-stayed bridge.


5.85 3.15 3.15 5.85

1.1

7.5

1.0

2.2

4.4

5.0

12.0

6.0

6.0

2.5

35.0

1.5

Rigid element

Superstructure

Substructure

Steel element

Concrete element

Figure 3 Finite element model of bridge tower.

Table 1 Cross section dimension of different towerregions

Tower parts Cross section dimensions (cm)

Outer dimension Stiffener dimension

A B t1 t2 a b t11 t22

I 240 350 2.2 3.2 25 22 3.6 3.0

II 240 350 2.2 3.2 22 20 3.2 2.8

III 240 350 2.2 2.8 20 20 2.8 2.2

IV 270 350 2.2 2.6 31 22 3.5 2.4


where [M], [C], and [K]t+Δt are the system mass, damping,and tangent stiffness matrices at time t + Δt, respectively; ü,u̇ and Δu are the accelerations, velocities, and incre-mental displacement vectors at time t + Δt, respectively.{F}t+Δt − {F}t is the unbalanced force vector. It can benoticed that the dynamic equilibrium equation of motiontakes into consideration the different sources of nonlinear-ities (geometrical and material nonlinearities), which affectthe calculation of the tangent stiffness and internal forces.The implicit Newmark step-by-step integration method isused to directly integrate the equation of motion, and thenit is solved for the incremental displacement using theNewton–Raphson iteration method, in which the stiffnessmatrix is updated at each increment to consider thegeometrical and material nonlinearities and to speedthe convergence rate.The tower structure damping mechanism is adapted to

the Rayleigh damping; the damping coefficient is taken tobe 2% for steel materials of tower superstructure and 10%for concrete materials of embedded pier substructure(Committee of Earthquake Engineering 1996; Japan RoadAssociation 1996a, 1996b). Vibration periods of 2.5 and0.50 s are considered to represent a broad range of highparticipation modes and the softening that takes place asthe columns and soil yield. A common design approachof maintaining elastic behavior in the substructure isconsidered to avoid inelastic behavior below the groundsurface, where the damage would be difficult to detect orto repair. A nonlinear dynamic analysis computer programis developed based on the above-mentioned formulation topredict the vibration behavior of framed structures as wellas the nonlinear response under earthquake loadings.The program has been validated through a comparisonwith different commercial software EDYNA, DYNA2E,and DYNAS (Japanese software).

Input excitationIn the dynamic response analysis, the seismic motion byan inland direct-strike type earthquake that wasrecorded during the 1995 Hyogoken-Nanbu earthquakeof high intensity but short duration is used as an inputground motion to assure the seismic safety of the bridges.

Table 2 Stiffness values of linear lumped-parameter soil model

Stiffness values Lateral stiffness KL Rotational stiffness KR Coupling stiffness KC Vertical stiffness KV Torsional stiffness KT

(kN/m) (kN m/rad) (kN/rad) (kN/m) (kN·m/rad)

Bridge axis 1.798 × 107 2.778 × 109 2.747 × 107 3.084 × 107 3.075 × 109

Right-angle axis 1.739 × 107 3.454 × 109 2.552 × 107 3.071 × 107 3.075 × 109

+ 17.27

+ 5.40

- 11.23

- 18.73

KR

KV

KC

KL

Figure 4 Linear lumped-parameter soil model.


The horizontal and the vertical accelerations recordedat the station of JR-Takatori observatory (Committee ofEarthquake Engineering 1996; Japan Road Association1996a, 1996b) are used for the dynamic response analysisof the cable-stayed bridge tower at a soil of type II, wherethe fundamental period of the site ranges from 0.2 to 0.6 s,and the mean value of shear wave velocity of 30 m ofthe soil deposit ranges from 200 to 600 m/s (JapanRoad Association 1996a). It is considered to be capableof securing the required seismic performance duringthe bridge service life. The selected ground motion hasmaximum acceleration intensities of its components of642 (N-S), 666 (E-W), and 290 gal (U-D). The kinematicinteraction can be modeled by a transfer function, whichcan be used to modify a free-field ground motion so thatan effective input motion for a soil-structure system canbe obtained. A simple model based on analytical modelingof rigid foundation is adopted, in which the effectiveseismic motion is obtained starting from the free-fieldmotion by an approximate analytical solution (Harada et al.1981; Ganev et al. 1995) for embedded foundation with itsbase resting on a stiffer layer.

Finite element modeling of tower structureThe steel tower of a three-span continuous-cable-stayedbridge located in Hokkaido, Japan is considered, inwhich the main span length is equal to 284 m. Figure 1shows a schematic representation of the bridge elevation.The towers are H-shaped steel structures as shown inFigure 2. Each tower is founded on a spread foundationon good soil layer, and it consists of two steel legs andhorizontally connected beam. The cross section of eachleg has a hollow rectangular shape with an interiorstiffener; the cross-sectional size varies over the heightof the tower. Cable-stayed bridges represent highlyredundant and mechanically nonhomogeneous struc-tural systems; the tower, deck, and cable stays affectthe structural response in a wide range of vibrationmodes (Ali and Abdel-Ghaffar 1995; Abdel Raheemand Hayashikawa 2003). The tower is taken out of thecable-stayed bridge, and a finite element model isconstructed based on the design drawings, as shown inFigure 3. A flexural fiber element is developed for thetower characterization; the element incorporates bothgeometric and material nonlinearities. A bilinear model isadopted to describe the stress–strain relationship of theelement. The yield stress and the modulus of elasticity are

equal to 355 MPa (SM490) and 200 GPa, respectively; theplastic region strain hardening is 0.01. The nonlinearity ofinclined cables is idealized using the equivalent modulusapproach (Karoumi 1999). The nonlinearity of the cablesoriginates with an increase in the loading followed by adecrease in the cable sag, resulting in an increase of thecable apparent axial stiffness. In this approach, eachcable is simulated by a truss element with equivalenttangential modulus of elasticity Eeq that is given by(Ernst 1965) as follows:

Eeq ¼ E= 1þ EA wLð Þ2=12T 3� �

; ð23Þ

+ 17.27

+ 5.40

- 11.23

- 18.73Gap element

Soil nonlinear elementkv

kh

Figure 5 Winkler model for soil-structure interaction.


where E is the material modulus of elasticity, L is thecable horizontal projected length, w is the weight perunit length of the cable, A is the cross section of thearea of the cable, and T is the tension force in the cable.This tower has nine cables in each side of the tower.The stiffening girder dead load is considered to beequivalent to the vertical component of the pretensionforce of the cables acting at their joints and the two verticalcomponents at stiffening girder-tower connection at thesubstructure top level. The tower steel superstructure has arectangular hollow steel section of different dimensionsalong the different parts of the tower, as indicated in Table 1.In the numerical analysis, steel superstructure is modeledas a three-dimensional elastoplastic beam element, whileconcrete substructure is modeled as an elastic element.

GG0

max

Skeleton curve

Hysteresis curve

Figure 6 Hardin-Drnevich model and Masing rulehysteresis loop.

Modeling of soil-structure interactionA crucial goal of current seismic foundation design,particularly as entrenched in the respective codes(European Committee for Standardization 1998), is toavoid full mobilization of strength in the foundation byguiding failure to the aboveground structure. The designermust ensure that the (difficult to inspect) belowgroundsupport system will not even reach a number of thresholdsthat would statically imply failure: mobilization of the soilbearing capacity, significant foundation uplifting, and slid-ing or any of their combination are prohibited or severelylimited. To this end, following the norms of capacity design,overstrength factors and safety factors (explicit or implicit)are introduced against those failure modes.

Linear lumped-parameter soil modelIn the linear lumped-parameter soil model, the interactionbetween the soil and the structure is simulated withtranslational, rotational, and their coupling springsystem. The spring stiffness values in both bridge axisand right-angle directions are given in Table 2. Thestiffness is calculated based on foundation geometry andsoil profile underneath and along the embedded depthof the foundation, as specified in Japanese HighwaySpecification (Japan Road Association 1996a, 1996b)and as shown in Figure 4.

Nonlinear Winkler model for soil-structure interactionThe soil-structure interaction is simulated with nonlinearspring-dashpot system along the pier embedded depth.Strain-dependent material nonlinearity is implementedusing the nonlinear Hardin-Drnevich soil model (Hardinand Drnevich 1972a, 1972b). Geometrical nonlinearity

10 -6 10 -5 10 -4 10 -3 10 -2 10 -1

0

0.5

1 Sand Clay Gravel

Strain

G/G0

h

Shea

r mod

ulus

ratio

& d

ampi

ng

Figure 7 Strain-dependent soil material nonlinearity (rigidity and damping).

w w /2

Figure 8 Hysteretic damping of soil.


by basemat uplift is considered through nonlinear soilelement connected in series with gap element springsystem, as shown in Figure 5. The spring constants inboth bridge axis directions are calculated based onfoundation geometry and soil profile underneath andalong embedded depth of foundation, as specified inJapanese Highway Specification (Japan Road Associ-ation 1996a, 1996b). Soil properties from the SPT dataand logs of boreholes at the tower site are used to deter-mine the coefficients of vertical and horizontal sub-grade reactions. The subgrade reaction coefficientsare obtained from the ground stiffness correspondingto the deformation caused in the ground during anearthquake.

Soil nonlinearity idealization One of the most importantfactors in the analysis of soil-foundation interactivebehavior is the nonlinear constitutive laws of the soil(material nonlinearity). In this study, the Hardin-Drnevichmodel is proposed to represent the soil materialnonlinearity that is often used for its capacity to trace thedegradation of stiffness. The parameters used to define theskeleton curve and family of hysteresis stress–strain curvesare indicated in Figure 6. The skeleton curve is expressedas follows:

τ ¼ G0γ= 1þ γ=γr � �

; γr ¼ τmax=G0; ð24Þ

where G0 is the initial shear modulus, τ is the general-ized soil shear stress, τmax is the shear stress at failure,γr is the reference strain, and γ is the generalized strain.

The hysteretic curve can be constructed using theMasing rule (Masing 1926) and is given as follows:

τ � τm ¼ G0 γ � γm� �

= 1þ γ � γm� �

=2γr � �

; ð25Þ

where τm and γm indicate the coordinates of the originof the curve, that is, the point of the most recent loadreversal. The hysteresis curve is the same in shape asthe skeleton curve but is enlarged twice. The nonlineardynamic soil parameters including the dynamic shearmoduli and the damping ratios for the employed soilmodels in this study are modulated based on the shearstrain-dependent relationships for gravel, sand, and clayshown in Figure 7. Soil exhibits nonlinear nature even

Viscous dashpot analog

1-D wave propagation

Infinitely long rod

P-waves

= Mass density of rod

rod ends

viscous dashpotC = AV

P-waves

S-w

aves

x = 0

x = 0

S-w

aves

Figure 9 One-dimensional radiation-damping model.


at small strains. The shear modulus (G) can be de-scribed as follows:

G=G0 ¼ 1= 1þ γm=γr� �

: ð26ÞThe soil element stiffness is idealized by the Winkler

model. For practical use, frequency-independent spring co-efficients are computed based on Japanese Specification forHighway Bridges (Japan Road Association 1996a, 1996b).Each spring consists of a gap element and a soil element.The gap element transmits no tensile stress, which canexpress the geometrical nonlinearity of basemat uplift.

Soil damping idealization The hysteretic damping charac-teristic of the soil, which resulted from the deformationsproduced by interaction with the pier, is represented by

-2000

-1000

0

1000

2000

Acc

eler

atio

n (g

al)

Case

0 5 10 15 20-2000

-1000

0

1000

2000

Acc

eler

atio

n (g

al)

Case I

Time (sec)

Figure 10 Acceleration time history and response spectra at tower to

nonlinear viscous dashpots. The damping ratio of the soildashpot strain-dependent material nonlinearity is describedby a simple relationship between the shear modulus anddamping, as shown in Figure 8.

h ¼ Δw=wð Þ=2π

¼ 2=πð Þ�2G0=Gð Þ

�γr=γm� �� γr=γm

� �2log 1þ gr=gmð Þ

� 1

�:

ð27Þ

The material-damping ratio h is defined as follows:

h ¼ Cm=Cr;Cr ¼ 2 k=mð Þ0:5; ð28Þ

in which Cm is the coefficient of material damping, Cr isthe coefficient of material critical damping, and k and m

I

25

I0

0.1

0.2

0.3

0.4

0.5

Fou

rier

spe

ctra

l am

plit

ude

0 1 2 3 40

0.1

0.2

0.3

0.4

0.5

Fou

rier

spe

ctra

l am

plit

ude

Frequency (Hz)

p.

-1

0

1

Mom

ent r

atio

Case I

0 5 10 15 20 25

-1

0

1

Mom

ent r

atio

Time (sec)

Case II

Figure 11 Moment ratio time history at towersuperstructure base.

-20

0

20

40

For

ce (

MN

)

Case I

0 5 10 15 20 25

-20

0

20

40

For

ce (

MN

)

Case II

Time (sec)

Figure 12 Vertical force time history at tower superstructure base.


are the soil spring stiffness and pier mass per unitlength, respectively. The coefficient of material dampingof the soil Csoil is obtained as follows:

Csoil ¼ 2hmax 1� k=k0ð Þ k=mð Þ0:5: ð29Þ

The radiation-damping characteristic of soil is repre-sented through an approximation of a para-axial boundary,where viscous dampers can be used to represent a suitabletransmitting boundary for many applications involving bothdilatational waves and shear waves. A one-dimensionalviscous boundary model is selected for this study. It isassumed that a horizontally moving pier cross sectionwould solely generate one-dimensional P waves traveling inthe direction of shaking and one-dimensional S waves inthe direction perpendicular to shaking, as shown in Figure 9.Based on the previous assumption, the coefficient ofviscous dashpot that will absorb the energy of the wavesoriginating at soil-pier interface is evaluated.

Results and discussionTo study the effects of soil-foundation-structure inter-action on the seismic behavior of the cable-stayed bridgetowers, two different approaches for soil-foundation-interaction modeling (nonlinear Winkler model andlinear lumped-parameter model) are considered. The soil-foundation-superstructure model with Winkler hypothesisfor soil idealization is compared to a simplified lumped-parameter model, and dynamic response simulation isconducted by applying acceleration at the base level ofthe foundation. The following two different cases ofsoil idealization are analyzed:Case I Seismic response with soil material and geomet-

rical nonlinearities: nonlinear Winkler model.Case II Seismic response of tower model with linear

lumped-parameter soil model.

Soil-structure interaction modeling effects on globalresponsesThe acceleration time history at the tower top, wherethe tower acceleration response is significantly decreaseddue to degradation of soil stiffness and energy dissipationthrough soil hysteresis, clarifies the effects of soilnonlinearity. The reduction of acceleration response ofWinkler model (case I) related to soil nonlinearities(material and geometrical) approaches about 60% ofthat of the simplified model (case II), as illustrated inFigure 10. Moreover, the acceleration time history ofcase II is characterized by large peak acceleration that isassociated with a short duration impulse of high frequency(acceleration spike). The Fourier acceleration responsespectrum clarifies the significant contribution of high-frequency modes to the tower seismic response.

The displacement, moment ratio, and vertical forcetime histories of Winkler model (case I) at the towersuperstructure base show the response nature to strongexcitation. The moment ratio is defined as the ratio ofmoment demand to the moment capacity at the firstyield of the cross section. The large pulse in the groundmotion produces two or three cycles of large forceresponse with rapidly decaying amplitudes of displace-ment, moment, and force after the peak excursions. Thepredominant contribution to the vertical force response

0 5 10 15 20 25-0.005

0

0.005D

ispl

acem

ent

(m)

Footing base extreme right Footing base extreme left

Time (sec)

Figure 13 Vertical displacement time history of footing extreme right and left at footing base level.


at the tower superstructure base results from the in-planerocking vibration rather than from the vertical excitation,and it is dominated by long-period in-plane vibration andslightly affected by high-frequency vertical excitation andvibration, as shown in Figures 11 and 12. However, thelumped-parameter-model analysis (case II) for towersuperstructure base moment and axial force displaysslight attenuation after peak response excursions, andthe time history response is characterized by high-frequency spike. The simplified lumped-parameter-modelanalysis provides a good prediction for peak response butoverestimates the acceleration response and underesti-mates the uplift force at the anchor between superstruc-ture and pier. It can be obviously seen that foundationuplifting and plasticity have a significant effect on thereduction of seismic force of bridge tower. The founda-tion allowed uplifting, and yielding in design willprotect tower pier and superstructures. The value of re-duction of seismic force increases with the increase ofseismic intensity.

0 5 10-3

-2

-1

0

1

For

ce (

MN

/m)

Footing base extreme right

Ti

Figure 14 Vertical force per unit length time history of footing extrem

Soil nonlinearity effects on tower responseThe uplift of the tower footing is investigated throughvertical deformation and force resistance of the basementsoil at the extreme right and left sides of the footing base(case I). Two aspects of foundation response to seismicexcitation, rocking deformation and the accumulationof the permanent settlement can be distinguished. Thepermanent settlement was found to be the less significantin the total vertical displacement at the footing base level,as shown in Figures 13 and 14. It can be concluded thatseparation of the soil from the structure occurs under largedynamic loads leading to changes in the predominantvibration of the system. As a result of the decrease in soilsupport at the sidewalls of the foundation by stiffnessdegradation due to hysteresis, the stress caused by thestructural weight on the bottom soil is increased duringearthquakes. The reduction of the foundation width incontact during uplift induces an increase of the stressesunder the foundation. This leads to a larger soil yielding,which itself modifies the uplift behavior of the foundation.

15 20 25

Footing base extreme left

me (sec)

e right and left at footing base level.

0 5 10 15 20 25

-0.04

-0.02

0

0.02

0.04

Time (sec)

Dis

plac

emen

t (m

)

Case I

Figure 15 In-plane displacement time history at superstructure base.


The maximum uplift of not more than 5 mm clarifies thatthe tower foundation almost has sufficient structuralloading to minimize the uplift. The soil layer at thefooting base level has sufficient bearing capacity to preventfoundation excessive settlement.Since the foundation structure is very rigid compared

to the underlying foundation soil, the rocking motion ofthe foundation is significantly observed, which affectsthe characteristics of the foundation motion. The limitedshear strength of soil also causes sliding of the foundationblock, which could alter the characteristics of the founda-tion motion. In addition to the inertial soil-foundationinteraction due to the existence of foundation mass, thesize and stiffness of the foundation could also affect thefoundation motion characteristics. From superstructurebase (steel superstructure and concrete substructureconnection joint) displacement time history (case I) asshown in Figure 15, it could be seen that the displacementcould reach around 3.0 cm for soil-structure interactionmodel of the tower with both material and geometricalnonlinearities; this effect is totally ignored for fixed basemodel assumption. The limited shear strength of basementsoil causes sliding of the foundation, which could beunderestimated by elastic and linear soil assumption, asshown in Figure 16.

0 5 10

-0.005

0

0.005

Dis

plac

men

t (m

)

T

Figure 16 Foundation sliding time history at footing base level.

From the Fourier spectra study of tower accelerationresponse at different levels of tower for nonlinearsoil-foundation-superstructure interaction model (case I),it is shown that there is amplification of different modesover a wide frequency range, as seen in Figures 17 and 18.The in-plane superstructure base response spectrum islarger than that at the footing base at a spectral frequencyless than 2.0 Hz because of amplification induced byflexible superstructure and massive rigid substructureinteraction, while at high frequency above 2.0 Hz, theresponse spectra are slightly attenuated due to inertialinteraction. The tower top response spectra are signifi-cantly amplified at low-frequency range and are almosttotally attenuated at high-frequency range due to towersuperstructure flexibility, as seen in Figure 18. Themassive foundation has the effect of amplifying theresponse over a wide frequency band. The verticalacceleration response at the footing base level showsrelatively high-frequency amplification as the responsespectra within the frequency range of 2 to 3 Hz areslightly amplified at the superstructure base level, andthey are dramatically amplified at the tower top. Onthe other hand, the response spectrum at high-frequencyrange is attenuated by superstructure flexibility filter of thetower response. The nonlinear seismic response of bridge

15 20 25

Case I

ime (sec)

-1000

0

1000

Acc

eler

atio

n (g

al)

Tower top level

-1000

0

1000

Acc

eler

atio

n (g

al)

Tower superstructure base level

0 5 10 15 20 25-1000

0

1000

Acc

eler

atio

n (g

al)

Time

Footing base level

0

0.1

0.2

0.3

0.4

0.5

Fou

rier

spe

ctra

l am

plit

ude

0

0.1

0.2

0.3

0.4

0.5

Fou

rier

spe

ctra

l am

plit

ude

0 2 4 60

0.1

0.2

0.3

0.4

0.5F

ouri

er s

pect

ral a

mpl

itud

e

Frequency (Hz)

Figure 17 In-plane acceleration time history and response spectra (case I).


piers is distinctly different from that of the linear response.There is a great difference whether it is in vibrationamplitude or in frequency property. The nonlinearproperties of foundations make the stiffness of thestructure low, the response of rotational angle increase, andthe response of bending moment decrease.

ConclusionsA finite element model to study the effects of soil-foundation-superstructure interaction on the seismicresponse of a cable-stayed bridge tower supported onspread foundation was presented, in which an incrementaliterative technique was adopted for a more realistic analysisof the nonlinear soil-foundation-superstructure interaction.The problem was analyzed, employing the finite elementmethod and taking account of material (soil, steel

superstructure) and geometric (uplifting and P-Δ effects)nonlinearities. Two different modeling approaches for soilfoundation interaction, nonlinear Winkler model and linearlumped-parameter model, were investigated. The seismicresponses of Winkler soil model were compared tothose of the simplified linear lumped-parameter model.In the lumped-parameter soil model, the soil-structureinteraction is simulated with translational, rotational,and their coupling spring system acting at centroid ofspread foundation at the footing base level while in theWinkler soil model, the soil-structure interaction issimulated with continuous spring system (Winkler)along embedded depth of tower pier and underneaththe spread foundation. Soil yielding under the founda-tion and along the embedded depth was modeled usingthe Hardin-Drnevich model to express nonlinear soil

-400

-200

0

200

400

Acc

eler

atio

n (g

al)

Tower top level

-400

-200

0

200

400

Acc

eler

atio

n (g

al)

Tower superstructure base level

0 5 10 15 20 25-400

-200

0

200

400

Acc

eler

atio

n (g

al)

Time

Footing base level

0

0.2

Four

ier

spec

tral

am

plitu

de0

0.2

Four

ier

spec

tral

am

plitu

de

0 2 4 60

0.2

Four

ier

spec

tral

am

plitu

de

Frequency (Hz)Figure 18 Vertical acceleration time history and response spectra (case I).


characteristics. The contact nonlinearity induced bythe uplift of the foundation was integrated using gapelement. Radiation damping associated with wavepropagation was accounted for implicitly throughviscous damping while the energy dissipation throughsoil material nonlinearity was explicitly modeled. Theinteraction effects generated by the normal and tan-gential resistance of the soil against all active sides ofthe footing were taken into account. The followingconclusions can be drawn as follows:The analysis with simplified linear lumped-parameter

model provides a good prediction for the peak response butoverestimates the acceleration response and underestimatesthe uplift force at the anchor between superstructure andpier. The nonlinear soil-foundation interaction effect is veryremarkable when uplifting and yielding of supporting soilare considered. The analysis using the nonlinear interaction

Winkler model shows that the foundation uplift alterstower displacement seismic response and reduces structuralmember forces. Compared with the linear analysis, thestiffness of the tower-soil system degrades in eachcycle after considering uplifting and yielding. Thenonlinear analysis displays larger rotational angles andsmaller bending moments compared with the linearlumped-parameter-model analysis. The inclusion ofmassive foundation and nonlinearity of soil effectsleads to the amplification of higher modes of vibrationand activates the high-frequency translational motionof the input ground motion and generates foundation-rocking responses. The rocking vibration dominates thelateral bearing stress for the soil along the embedded depthof the tower pier. The predominant contribution to thevertical response at the footing base resulted from themassive foundation rocking rather than from the vertical


excitation; the permanent settlement is found to be lesssignificant. The soil bearing stress demand beneath thespread foundation is significantly increased due to footingbase uplift. The bearing stress under the foundation shouldbe checked considering both soil material and geometricalnonlinearities with an appropriate factor of safety to avoidcatastrophic foundation failure. The soil at the foundationlevel should have sufficient bearing capacity to preventfoundation excessive settlement.From the nonlinear Winkler soil model, it is concluded

that the soil interaction effect is very remarkable whenuplifting and yielding of supporting soil are considered.Compared with the linear lumped soil model, the stiffnessof tower foundation-soil model degrades in each cycleafter considering uplifting and yielding. It is shown thatthe nonlinear analysis can get larger rotational angles andsmaller bending moments compared with the linearanalysis. The nonlinear modeling of soil-foundationinterface shows that the soil structure interaction effectmay play an important role in altering the force anddisplacement demand, indicating the necessity for consid-eration of foundation behavior in the modern design codesto accomplish a more economic yet safe structural design.For more general and versatile conclusions, different inputexcitations and different ground conditions at bridgeconstruction site should be considered.

Competing interestsThe authors declare that they have no competing interests.

Authors’ contributionsSEAR carried out the finite element modeling and numerical simulations forthe extensive parametric study, which is presented in the research work, anddrafted the manuscript. SEAR and TH discussed the idea and the importantsystem parameters, which are included for the numerical study and alsohave checked the manuscript before submission. Both authors read andapproved the final manuscript.

Authors’ informationSEAR is an associate professor in Earthquake, Bridge, Structural andGeotechnical Engineering since 2009 at the Civil Engineering Department inAssiut University, Egypt. He acquired his Doctorate in Engineering in 2003and was a Japan Society for the Promotion of Science fellow in 2006 inHokkaido University, Japan. He was an Alexander von Humboldt fellow in2005 in Kassel University, Germany. He has published more than 60 papers inthe field of structural engineering, structural analysis, earthquakeengineering, soil structure interaction, seismic pounding, structural control,and nonlinear dynamic of offshore structures. He is a previous member ofthe Japan Society of Civil Engineers. He reviewed many papers forinternational journals. He is currently working as an engineering counselor atthe general project management of Taibah University, Medina, Saudi Arabia.TH is a professor in Earthquake, Bridge, Structural and GeotechnicalEngineering since 2004. He acquired his Doctorate in Engineering in 1984 inHokkaido University, Japan. He was a visiting research fellow at PrincetonUniversity, USA in 1985. His research works/interests include Response ofCable-Stayed Bridges under Great Earthquake Ground Motion; SeismicIsolation Design; Energy Dissipation System and Performance-Based Designof Steel Structures; Damage Identification of Highway Bridge; and BridgeManagement System Vibration Control and Intelligential Structure of SteelBridges. He is a fellow member of the Japan Society of Civil Engineers. Hereviewed many papers for international journals.

Author details1Taibah University, Medina, Saudi Arabia. 2Civil Engineering Department,Faculty of Engineering, Assiut University, Assiut 71516, Egypt. 3GraduateSchool of Engineering, Hokkaido University, Sapporo, Japan.

Received: 27 September 2012 Accepted: 20 February 2013Published: 22 March 2013

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doi:10.1186/2008-6695-5-8Cite this article as: Raheem and Hayashikawa: Soil-structure interactionmodeling effects on seismic response of cable-stayed bridge tower.International Journal of Advanced Structural Engineering 2013 5:8.

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ORIGINAL RESEARCH Open Access Soil-structure ...2F2008-6695...Long-span bridges, such as cable-stayed bridge structural systems, provide a valuable environment for the nonlinear behavior