Raheem and Hayashikawa Internationa Journa of Advanced Structura Engineering 213, 5:8 ORIGINAL RESEARCH Open Access Soi-structure interaction modeing effects on seismic response of cabe-stayed bridge tower Shehata E Abde Raheem 1,2* and Toshiro Hayashikawa 3 Abstract A noninear dynamic anaysis, incuding soi-structure interaction, is deveoped to estimate the seismic response characteristics and to predict the earthquake response of cabe-stayed bridge towers with spread foundation. An incrementa iterative finite eement technique is adopted for a more reaistic dynamic anaysis of noninear soi-foundation-superstructure interaction system under great-earthquake ground motion. Two different approaches to mode soi foundation interaction are considered: noninear Winker soi foundation mode and inear umpedparameter soi mode. The numerica resuts show that the simpified umped-parameter-mode anaysis provides a good prediction for the peak response, but it overestimates the acceeration response and underestimates the upift force at the anchor between superstructure and pier. The soi bearing stress beneath the footing base is dramaticay increased due to footing base upift. The predominant contribution to the vertica response at footing base resuted from the massive foundation rocking rather than from the vertica excitation. Keywords: Soi-structure interaction, Cabe-stayed bridge towers, Linear umped-parameter mode, Upift, Seismic design, Noninear Winker soi mode, Time history anaysis Introduction Long-span bridges, such as cabe-stayed bridge structura systems, provide a vauabe environment for the noninear behavior due to materia and geometrica noninearities of the structures of reativey arge defection and forces (Ai and Abde-Ghaffar 1995; Abde Raheem and Hayashikawa 23; Committee of Earthquake Engineering 1996). The Hyogoken-Nanbu (Kobe, Japan) earthquake on 17 January 1995 ed to an increased awareness concerning the response of highway bridges subjected to earthquake ground motions. The dynamic anayses and ductiity design have been reconsidered by Japan Road Association (Committee of Earthquake Engineering 1996; Japan Road Association 1996a, 1996b). Necessity has arisen to deveop more efficient anaysis procedures, which can ead to a thorough understanding and a reaistic prediction of the noninear dynamic response of the bridge structura systems, to improve the bridge seismic performances. Current design practice does not account for the noninear behavior of soi-foundation interface primariy * Correspondence: shehataraheem@yahoo.com 1 Taibah University, Medina, Saudi Arabia 2 Civi Engineering Department, Facuty of Engineering, Assiut University, Assiut 71516, Egypt Fu ist of author information is avaiabe at the end of the artice due to the absence of reiabe noninear soi-structure interaction modeing techniques that can predict the permanent and cycic deformations of the soi as we as the effect of noninear soi-foundation interaction on the response of structura members. Safe and economic seismic designs of bridge structures directy depend on the understanding eve of seismic excitation and the infuence of supporting soi on the structura dynamic response. Long-span bridges are more susceptibe to reativey severe soi-structure interaction effect during earthquakes when compared to buidings due to their spatia extent, varying soi condition at different supports, and possibe incoherence in the seismic input. The necessity of incorporating soi-structure interaction in the design of a wide cass of bridge structures has been pointed out by severa post-earthquake investigations, experimenta, and anaytica studies (Committee of Earthquake Engineering 1996; Vassis and Spyrakos 21; Trifunac and Todorovska 1996; Megawati et a. 21). Recenty, severa cabe-stayed bridges have been constructed on reativey soft ground, which resuts in a great demand to evauate the effect of soi-structure interaction on the seismic behavior of bridges and propery refect it on seismic design to accuratey 213 Raheem and Hayashikawa This is an Open Access artice distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/icenses/by/2.), which permits unrestricted use, distribution, and reproduction in any medium, provided the origina work is propery cited.
Raheem and Hayashikawa Internationa Journa of Advanced Structura Engineering 213, 5:8 Page 2 of 17 capture the response, enhance the safety eve, and reduce design and construction costs. Due to materia and geometrica noninearities, the dynamic characteristics of soi-structure system are changed during a severe earthquake. These noninearities are sometimes treated using an equivaent inear mode (Abde Raheem et a. 22; Chaojin and Spyrakos 1996; Spyrakos 1997). However, the dynamic characteristics of soi-structure system are dependent on the soi stress eve during a severe earthquake (Ahn and Goud 1992; Gazetas and Dobry 1984; Kobayashi et a. 22). Foundation rocking and upifting are important for short-period structures on a reativey soft soi site (Yim and Chopra 1984; Harden et a. 26). For noninear structures, effects of soi-structure interaction due to rocking can resut in significanty arger ductiity demands under certain conditions (Tang and hang 211; hang and Tang 29). These findings necessitate the evauation of structura responses considering soi-structure interaction using foundation modes that can reaisticay capture the noninear force, dispacement behaviors, and energy dissipation mechanisms. Noninear foundation movements and associated energy dissipation may be utiized to reduce force and ductiity demands of a structure, particuary in high-intensity earthquake events (Raychowdhury 211). The purpose of this study is to assess the effects of soi-structure interaction on the seismic response and dynamic performance of the cabe-stayed bridge towers with spread foundation. An incrementa iterative finite eement technique for a more reaistic dynamic anaysis of noninear soi-foundation-superstructure system subjected to earthquake ground motion is deveoped. Two different modeing approaches, noninear Winker soi mode and inear umped-parameter soi mode, for the soi foundation interaction are investigated. The seismic responses of the noninear Winker soi mode are compared to those of the simpified inear umped-parameter mode. In the umped-parameter soi mode, the soi-structure interaction is simuated with transationa, rotationa, and their couping inear springs acting at the centroid of the spread foundation at footing base eve. Whie in the noninear Winker soi mode, the soi structure interaction is simuated with continuous spring system (Winker) aong the embedded depth of tower pier and underneath the spread foundation. Soi strain-dependent materia noninearity is considered through hysteretic eement, whie geometrica noninearity by basemat upift is considered through a gap eement. The massive pier of the tower mode activates rocking response of the spread foundation under strong earthquake ground motion, hence, resuts in the foundation upift and yied of the underying soi (Kawashima and Hosoiri 22; Geagoti et a. 212). The resuts of the noninear Winker-soi-mode approach are compared with those from the inear umped-soi-mode approach. Methods Finite eement anaysis procedure Three-dimensiona beam eement tangent stiffness A noninear dynamic finite eement technique is deveoped to anayze the eastopastic dynamic response of frame structures under strong earthquake excitation, in which the noninear three-dimensiona beam eements are empoyed. A three-dimensiona beam eement has six degrees of freedom at each node, in which a coupings among bending, twisting, and stretching deformations for the beam eement are incorporated according to the geometrica noninear beam theory. The eement noda dispacement vector in oca coordinate system is given as foows: d ¼ u i v i w i θxi θyi θzi u j v j w j θxj θyj θzj T : ð1þ The dispacements u, v, and w of a genera point (x, y, and z) in the beam can be written as foows: u ¼ u y dv=dx z dw=dx; v ¼ v; w ¼ w; ð2þ where u, v, and w are the dispacements of a point in the centroid axis of a beam corresponding to x-, y-, and z-axes, respectivey. θ is the cross-sectiona rotation about the x-axis. The dispacement transformation matrix of the beam eement reates the eement interna dispacement to the noda point dispacement: u ¼ u v w θ T ¼ N x N y N z N Td; θ ð3þ N x ¼ ½N 1 N 2 ; N y ¼ ½ N 3 N 4 N 5 N 6 ; N z ¼ ½ N 3 N 4 N 5 N 6 ; N θ ¼ ½ N 1 N 2 : ð4þ The shape functions N i (i = 1 to 6) are assumed for the oca eement dispacements and given as foows: N 1 ¼ 1 ζ; N 2 ¼ ζ; N 3 ¼ 1 3ζ 2 þ 2ζ 3 ; ζ ¼ x=; N 3 ¼ ζ 2ζ 2 þ ζ 3 ; N5 ¼ 3ζ 2 2ζ 3 ; N 6 ¼ ζ 2 þ ζ 3 ð5þ ; in which is the origina ength of the beam eement. du dx ¼ B xd; d2 v dx ¼ B 2d; d2 w dx ¼ B 3d; dv dx ¼ B 4d; dw dx ¼ B 5 d ; d θ dx ¼ B 6d: ð6þ The strain in the deformed configuration ε t can be expressed in terms of the dispacement at the equiibrium state at any specified point in the beam cross section (x, y, and z) that defines the state of strain at any arbitrary point.
Raheem and Hayashikawa Internationa Journa of Advanced Structura Engineering 213, 5:8 Page 3 of 17 The strain dispacement equation (Green-Lagrange representation of axia strain ε t ) is given in the foowing: ε t ¼ du t dx þ 1 du 2 t þ 1 dv 2 t þ 1 dw 2 t ; ð7þ 2 dx 2 dx 2 dx where u t, v t,andw t are the eement dispacement vectors in x-, y-, andz-axis directions, respectivey; it is assumed that du t /dx << 1. Thus, (du t /dx) 2 is ignored compared to its inear term. The norma strain ε t is then cacuated. The unknown strain in t + 1 configuration can be written incrementay from configuration t as foows: ε tþ1 ¼ du tþ1 dx þ 1 dv 2 tþ1 þ 1 dw 2 tþ1 ; ð8þ 2 dx 2 dx δε tþ1 ¼ dδu dx þ dv t dx dδv dx þ dw t dx dδw dx þ 1 2 δ dv 2 þ 1 dx 2 δ dw 2 dx ¼ ðb L þ B NL Þδd; ð9þ B L ¼ B 1 yb 2 zb 3 ; B NL ¼ B T 4 B 4 þ B T 5 B 5 =2; B 1 ¼ B x þ dv t dx B 4 þ dw t dx B 5: ð1þ From the principe of energy, the externa work is equivaent to the interna work. The equiibrium equation in the deformed configuration t + 1 can be expressed in terms of the principe of virtua dispacements: δu δw ¼ :; σ tþ1 δ ε tþ1 dv þ V þ 1 2 GJðdθ=dxÞ 2 dx T sv ðdθ=dxþdx S f T tþ1 δ d tþ1 ds ¼ ; ð11þ ð12þ where U is the interna work, W is the externa virtua work, σ t+1 is the axia Couchy stress, V is the voume, δ is the virtua quantity, f is the externa appied force, and θ is the cross-sectiona rotation about the x-axis. The unknown configuration is t + 1 which can be written incrementay from configuration t consistenty with a noninear Lagrangian scheme as foows: V ðσ t þ σþδ ε tþ1 dv þ S f T t þ f T dθ T sv dx dx þ 1 dθ 2 GJ dx 2 dx δ ð dt þ dþ ds ¼ ; ð13þ where σ is the second Pioa-Kirchhoff axia stress: V σ B L þ σ t B NL f gdvþ 1 2 ¼ V V S ft T δd ds V fσ B L þ σ t B NL gdvþ:5 dθ 2 GJ dx dx f T δd ds S dθ σ t B L dv T sv dx dx; ð14þ GJðdθ=dxÞ 2 dx ¼ δd T fe 1 B T 1 B 1 E 2 B T 2 B 1 þ B T 1 B 2 þ E 3 B T 2 B 2 E 4 B T 3 B 1 þ B T 1 B 3 þ E5 B T 3 B 3 þ E 6 B T 2 B 3 þ B T 3 B 2Þ ddx þ δd T F x B T 4 B 4 þ B T 5 B 5 dxd þ δd T σ t B L dv þ ¼ δd T V ¼ δd T E 1 ¼ E T dydz; E 4 ¼ E T zdydz; F x ¼ σ t dydz; GJ B T 6 B 6 ddx ð15þ T sv ðdθ=dxþdx σ t B T 1 ybt 2 zbt 3 dv þ δd T T sv B T 6 dx F x B T 1 M zb T 2 M yb T 3 þ T svb T 6 dx; ð16þ E 2 ¼ E T E 5 ¼ E T M z ¼ ydydz; z 2 ydydz; σ t ydydz; E 3 ¼ E T E 6 ¼ E T M y ¼ y 2 dydz; zydydz; σ t zdydz ð17þ which can be determined through numerica integration over the cross section of fiber segments. The tangent stiffness can be written as foows: k t ¼ fe 1 B T 1 B 1 E 2 B T 2 B 1 þ B T 1 B 2 þ E 3 B T 2 B 2 E 4 B T 3 B 1 þ B T 1 B 3 þ E5 B T 3 B 3 þ E 6 B T 2 B 3 þ B T 3 B 2 þ Fx B T 4 B 4þB T 5 B 5 þgj B T 6 B 6Þ dx: ð18þ In order to capture the spread of pastic zone in individua eement, the beam eement is divided aong its
Raheem and Hayashikawa Internationa Journa of Advanced Structura Engineering 213, 5:8 Page 4 of 17 ength and over its cross section directions. The stiffness quantities of the section are cacuated based on the stress states of integration points over the cross section. The eement stiffness quantities are then obtained by integrating aong the ength of the beam, where the pastic deveopment of the materia is automaticay considered. The stiffness matrix cacuations of the eements are competed by a numerica integration procedure. After obtaining the stiffness matrix of the eements with respect to the oca coordinate system, the eement coordinates are transformed from the oca coordinate system to the goba coordinate system. The stiffness matrix of the eements is then assembed using standard procedures and by getting the goba stiffness matrix. In the noninear incrementa anaysis, the structure tangent stiffness matrix, which is assembed from the eement tangent stiffness matrices, is used to predict the next incrementa dispacements under a oading increment. Soi-structure interaction formuation The interaction between the soi and the structure is simuated with transationa, rotationa, and their couping spring system and equivaent viscous damping. The spring constants of the umped-parameter mode in both bridge axis and right-ange directions are cacuated based on foundation geometry and soi profie underneath and aong the embedded depth of the foundation, as specified in Japanese Highway Specification (Committee of Earthquake Engineering 1996; Japan Road Association 1996a). Soi properties from the standard penetration test (SPT) data and ogs of borehoes at the tower site are used to determine the coefficients of vertica and horizonta subgrade reactions that are used in a spread foundation design. A set of spring eements aong a the six degrees of freedom and the couping of atera and rotationa directions constitutes the inear umped soi mode, and it is connected to the foundation centroid node at the footing base eve. The infuence of the soi fexibiity in the goba dynamic response is considered through the assembing of the stiffness matrix of the soi spring system using standard procedures getting the gobe stiffness matrix (Abde Raheem 29; Abde Raheem et a. 22, 23). In the noninear Winker soi mode, three types of soi resistance dispacement modes coud describe the soi characteristics: the first type represents the atera soi pressure against the pier and the corresponding atera pier dispacement reationship, the second type represents the skin friction and the reative vertica dispacement between the soi and the pier reationship, and the third type describes the bearing stress beneath the spread foundation and settement reationship. A three types assume the soi behavior to be noninear and can be deveoped from the basic soi parameters. The soi-structure interaction is simuated with noninear spring-dashpot system aong the embedded depth of the pier. Both strain-dependent materia noninearity and geometrica noninearity by basemat upift are considered through a beam on noninear Winker soi eement connected in series with gap eement spring system (Abde Raheem et a. 22, 23; Kobayashi et a. 22). The spring constants in both bridge axis directions are cacuated based on foundation geometry and soi profie underneath and aong the embedded depth of the foundation as specified in Japanese Highway Specification (Committee of Earthquake Engineering 1996; Japan Road Association 1996a). The noninear soi-foundation mode is described as the Winker mode that has noninear springs distributed aong the embedded depth in the three directions of the oca coordinate system. The reaction dispacement mode of the tensioness foundation at base eve is considered. The contribution of soi reactions to the foundation eement equivaent noda forces vector and the eement tangent stiffness of the foundation, {f soi } and [k soi ], respectivey, can be given as foows: and ff soi g ¼ ½k soi where δfg¼ r ½N T fgdx r ¼ δ f f soig δfdg ¼ ¼ 2 4 ½N T δfg r δfdg dx ð19þ ½N T ½k½Ndx; ð2þ k x k y ¼ ½k½Nfdg: k z 38 5 δu 9 < = δv : ; ¼ ½ k δ f u g δ w ð21þ Equation of motion The governing noninear dynamic equation of the tower structure response can be derived using the principe of energy, i.e., the externa work is absorbed by the interna, inertia, and damping energy for any sma admissibe motion that satisfies compatibiity and boundary condition. By assembing the eement dynamic equiibrium equation at time t + Δt over a the eements, the incrementa finite eement method dynamic equiibrium equation (Abde Raheem 29; Chen 2) can be obtained as foows: ½Mfu g tþδt þ ½Cfg u tþδt þ ½K tþδt fδu ¼ ffg tþδt ffg t ; g tþδt ð22þ
Raheem and Hayashikawa Internationa Journa of Advanced Structura Engineering 213, 5:8 Page 5 of 17 74.3 115. 284. 115. 81.1 8 x 11.5 = 92. 34.5 34.5 8 x 11.5 = 92. 31. 8 x 11.5 = 92. 34.5 34.5 8x 11.5 = 92. 36. 68. 36. 68. Figure 1 Schematic representation of bridge eevation (m). 34. 34. 3.5 2.4 13. 5. 68. 36. 11. 36.5 14.5 17. I II III X IV 2.7 14.54 18. 37.5 24. 1.5 27.5 48. 2. 36. 68. Y 7.5 1. 7.5 1. 8.5 34. a) Tower geometry z a 3. 18. 18. 36. t2 3. b y t22 t11 y A t1 z B t1 t2 b) Cross section Figure 2 Tower geometry (a) and cross section (b) of stee tower of cabe-stayed bridge.
Raheem and Hayashikawa Internationa Journa of Advanced Structura Engineering 213, 5:8 Page 6 of 17 5. 12. Tabe 1 Cross section dimension of different tower regions Tower parts Cross section dimensions (cm) Outer dimension Stiffener dimension A B t 1 t 2 a b t 11 t 22 I 24 35 2.2 3.2 25 22 3.6 3. II 24 35 2.2 3.2 22 2 3.2 2.8 III 24 35 2.2 2.8 2 2 2.8 2.2 IV 27 35 2.2 2.6 31 22 3.5 2.4 6. 1.5 2.5 35. 6. 1. 1.1 7.5 4.4 2.2 Rigid eement Superstructure Stee eement Substructure Concrete eement 5.85 3.15 3.15 5.85 Figure 3 Finite eement mode of bridge tower. where [M], [C], and [K] t+δt are the system mass, damping, and tangent stiffness matrices at time t+δt, respectivey; ü, u and Δu are the acceerations, veocities, and incrementa dispacement vectors at time t+δt, respectivey. {F} t+δt {F} t is the unbaanced force vector. It can be noticed that the dynamic equiibrium equation of motion takes into consideration the different sources of noninearities (geometrica and materia noninearities), which affect the cacuation of the tangent stiffness and interna forces. The impicit Newmark step-by-step integration method is used to directy integrate the equation of motion, and then it is soved for the incrementa dispacement using the Newton Raphson iteration method, in which the stiffness matrix is updated at each increment to consider the geometrica and materia noninearities and to speed the convergence rate. The tower structure damping mechanism is adapted to the Rayeigh damping; the damping coefficient is taken to be 2% for stee materias of tower superstructure and 1% for concrete materias of embedded pier substructure (Committee of Earthquake Engineering 1996; Japan Road Association 1996a, 1996b). Vibration periods of 2.5 and.5 s are considered to represent a broad range of high participation modes and the softening that takes pace as the coumns and soi yied. A common design approach of maintaining eastic behavior in the substructure is considered to avoid ineastic behavior beow the ground surface, where the damage woud be difficut to detect or to repair. A noninear dynamic anaysis computer program is deveoped based on the above-mentioned formuation to predict the vibration behavior of framed structures as we as the noninear response under earthquake oadings. The program has been vaidated through a comparison with different commercia software EDYNA, DYNA2E, and DYNAS (Japanese software). Input excitation In the dynamic response anaysis, the seismic motion by an inand direct-strike type earthquake that was recorded during the 1995 Hyogoken-Nanbu earthquake of high intensity but short duration is used as an input ground motion to assure the seismic safety of the bridges.
Raheem and Hayashikawa Internationa Journa of Advanced Structura Engineering 213, 5:8 Page 7 of 17 Tabe 2 Stiffness vaues of inear umped-parameter soi mode Stiffness vaues Latera stiffness K L Rotationa stiffness K R Couping stiffness K C Vertica stiffness K V Torsiona stiffness K T (kn/m) (kn m/rad) (kn/rad) (kn/m) (kn m/rad) Bridge axis 1.798 1 7 2.778 1 9 2.747 1 7 3.84 1 7 3.75 1 9 Right-ange axis 1.739 1 7 3.454 1 9 2.552 1 7 3.71 1 7 3.75 1 9 The horizonta and the vertica acceerations recorded at the station of JR-Takatori observatory (Committee of Earthquake Engineering 1996; Japan Road Association 1996a, 1996b) are used for the dynamic response anaysis of the cabe-stayed bridge tower at a soi of type II, where the fundamenta period of the site ranges from.2 to.6 s, and the mean vaue of shear wave veocity of 3 m of the soi deposit ranges from 2 to 6 m/s (Japan Road Association 1996a). It is considered to be capabe of securing the required seismic performance during the bridge service ife. The seected ground motion has maximum acceeration intensities of its components of 642 (N-S), 666 (E-W), and 29 ga (U-D). The kinematic interaction can be modeed by a transfer function, which can be used to modify a free-fied ground motion so that an effective input motion for a soi-structure system can be obtained. A simpe mode based on anaytica modeing of rigid foundation is adopted, in which the effective seismic motion is obtained starting from the free-fied motion by an approximate anaytica soution (Harada et a. 1981; Ganev et a. 1995) for embedded foundation with its base resting on a stiffer ayer. Finite eement modeing of tower structure The stee tower of a three-span continuous-cabe-stayed bridge ocated in Hokkaido, Japan is considered, in which the main span ength is equa to 284 m. Figure 1 shows a schematic representation of the bridge eevation. The towers are H-shaped stee structures as shown in Figure 2. Each tower is founded on a spread foundation on good soi ayer, and it consists of two stee egs and horizontay connected beam. The cross section of each eg has a hoow rectanguar shape with an interior stiffener; the cross-sectiona size varies over the height of the tower. Cabe-stayed bridges represent highy redundant and mechanicay nonhomogeneous structura systems; the tower, deck, and cabe stays affect the structura response in a wide range of vibration modes (Ai and Abde-Ghaffar 1995; Abde Raheem and Hayashikawa 23). The tower is taken out of the cabe-stayed bridge, and a finite eement mode is constructed based on the design drawings, as shown in Figure 3. A fexura fiber eement is deveoped for the tower characterization; the eement incorporates both geometric and materia noninearities. A biinear mode is adopted to describe the stress strain reationship of the eement. The yied stress and the moduus of easticity are equa to 355 MPa (SM49) and 2 GPa, respectivey; the pastic region strain hardening is.1. The noninearity of incined cabes is ideaized using the equivaent moduus approach (Karoumi 1999). The noninearity of the cabes originates with an increase in the oading foowed by a decrease in the cabe sag, resuting in an increase of the cabe apparent axia stiffness. In this approach, each cabe is simuated by a truss eement with equivaent tangentia moduus of easticity E eq that is given by (Ernst 1965) as foows: E eq ¼ E= 1 þ EAðwLÞ 2 =12T 3 ; ð23þ + 17.27 + 5.4-11.23-18.73 KR KV Figure 4 Linear umped-parameter soi mode. KL KC
Raheem and Hayashikawa Internationa Journa of Advanced Structura Engineering 213, 5:8 Page 8 of 17 + 17.27 + 5.4-11.23-18.73 Gap eement kv Soi noninear eement kh Figure 5 Winker mode for soi-structure interaction. where E is the materia moduus of easticity, L is the cabe horizonta projected ength, w is the weight per unit ength of the cabe, A is the cross section of the area of the cabe, and T is the tension force in the cabe. This tower has nine cabes in each side of the tower. The stiffening girder dead oad is considered to be equivaent to the vertica component of the pretension force of the cabes acting at their joints and the two vertica components at stiffening girder-tower connection at the substructure top eve. The tower stee superstructure has a rectanguar hoow stee section of different dimensions aong the different parts of the tower, as indicated in Tabe 1. In the numerica anaysis, stee superstructure is modeed as a three-dimensiona eastopastic beam eement, whie concrete substructure is modeed as an eastic eement. Hysteresis curve max G G Skeeton curve Figure 6 Hardin-Drnevich mode and Masing rue hysteresis oop. Modeing of soi-structure interaction A crucia goa of current seismic foundation design, particuary as entrenched in the respective codes (European Committee for Standardization 1998), is to avoid fu mobiization of strength in the foundation by guiding faiure to the aboveground structure. The designer must ensure that the (difficut to inspect) beowground support system wi not even reach a number of threshods that woud staticay impy faiure: mobiization of the soi bearing capacity, significant foundation upifting, and siding or any of their combination are prohibited or severey imited. To this end, foowing the norms of capacity design, overstrength factors and safety factors (expicit or impicit) are introduced against those faiure modes. Linear umped-parameter soi mode In the inear umped-parameter soi mode, the interaction between the soi and the structure is simuated with transationa, rotationa, and their couping spring system. The spring stiffness vaues in both bridge axis and right-ange directions are given in Tabe 2. The stiffness is cacuated based on foundation geometry and soi profie underneath and aong the embedded depth of the foundation, as specified in Japanese Highway Specification (Japan Road Association 1996a, 1996b) and as shown in Figure 4. Noninear Winker mode for soi-structure interaction The soi-structure interaction is simuated with noninear spring-dashpot system aong the pier embedded depth. Strain-dependent materia noninearity is impemented using the noninear Hardin-Drnevich soi mode (Hardin and Drnevich 1972a, 1972b). Geometrica noninearity
Raheem and Hayashikawa Internationa Journa of Advanced Structura Engineering 213, 5:8 Page 9 of 17 Shear moduus ratio & damping 1.5 G/G h Sand Cay Grave 1-6 1-5 1-4 1-3 1-2 1-1 Strain Figure 7 Strain-dependent soi materia noninearity (rigidity and damping). by basemat upift is considered through noninear soi eement connected in series with gap eement spring system, as shown in Figure 5. The spring constants in both bridge axis directions are cacuated based on foundation geometry and soi profie underneath and aong embedded depth of foundation, as specified in Japanese Highway Specification (Japan Road Association 1996a, 1996b). Soi properties from the SPT data and ogs of borehoes at the tower site are used to determine the coefficients of vertica and horizonta subgrade reactions. The subgrade reaction coefficients are obtained from the ground stiffness corresponding to the deformation caused in the ground during an earthquake. Soi noninearity ideaization One of the most important factors in the anaysis of soi-foundation interactive behavior is the noninear constitutive aws of the soi (materia noninearity). In this study, the Hardin-Drnevich mode is proposed to represent the soi materia noninearity that is often used for its capacity to trace the degradation of stiffness. The parameters used to define the skeeton curve and famiy of hysteresis stress strain curves are indicated in Figure 6. The skeeton curve is expressed as foows: The hysteretic curve can be constructed using the Masing rue (Masing 1926) and is given as foows: τ τ m ¼ G γ γ = 1 þ γ m γm =2γr ; ð25þ where τ m and γ m indicate the coordinates of the origin of the curve, that is, the point of the most recent oad reversa. The hysteresis curve is the same in shape as the skeeton curve but is enarged twice. The noninear dynamic soi parameters incuding the dynamic shear modui and the damping ratios for the empoyed soi modes in this study are moduated based on the shear strain-dependent reationships for grave, sand, and cay shown in Figure 7. Soi exhibits noninear nature even w w / 2 τ ¼ G γ= 1 þ γ=γ r ; γr ¼ τ max =G ; ð24þ where G is the initia shear moduus, τ is the generaized soi shear stress, τ max is the shear stress at faiure, γ r is the reference strain, and γ is the generaized strain. Figure 8 Hysteretic damping of soi.
Raheem and Hayashikawa Internationa Journa of Advanced Structura Engineering 213, 5:8 Page 1 of 17 Infinitey ong rod = Mass density of rod 1-D wave propagation P-waves S-waves x = P-waves rod ends viscous dashpot C = AV Viscous dashpot anaog S-waves x = Figure 9 One-dimensiona radiation-damping mode. at sma strains. The shear moduus (G) can be described as foows: G=G ¼ 1= 1 þ γ m =γ r : ð26þ The soi eement stiffness is ideaized by the Winker mode. For practica use, frequency-independent spring coefficients are computed based on Japanese Specification for Highway Bridges (Japan Road Association 1996a, 1996b). Each spring consists of a gap eement and a soi eement. The gap eement transmits no tensie stress, which can express the geometrica noninearity of basemat upift. Soi damping ideaization The hysteretic damping characteristic of the soi, which resuted from the deformations produced by interaction with the pier, is represented by noninear viscous dashpots. The damping ratio of the soi dashpot strain-dependent materia noninearity is described by a simpe reationship between the shear moduus and damping,asshowninfigure8. h ¼ ðδw=wþ=2π ¼ ð2=πþ ð2g =GÞ 2og γ r =γ m γr =γ m ð 1 þ gr =g m Þ The materia-damping ratio h is defined as foows: 1 : ð27þ h ¼ C m =C r ; C r ¼ 2ðk=mÞ :5 ; ð28þ in which C m is the coefficient of materia damping, C r is the coefficient of materia critica damping, and k and m Acceeration (ga) Acceeration (ga) 2 1-1 -2 2 1-1 Case I Case II -2 5 1 15 2 25 Time (sec) Figure 1 Acceeration time history and response spectra at tower top. Fourier spectra ampitude Fourier spectra ampitude.5.4.3.2.1.5.4.3.2.1 1 2 3 4 Frequency (Hz)
Raheem and Hayashikawa Internationa Journa of Advanced Structura Engineering 213, 5:8 Page 11 of 17 are the soi spring stiffness and pier mass per unit ength, respectivey. The coefficient of materia damping of the soi C soi is obtained as foows: C soi ¼ 2h max ð1 k=k Þðk=mÞ :5 : ð29þ Moment ratio 1 Case I The radiation-damping characteristic of soi is represented through an approximation of a para-axia boundary, where viscous dampers can be used to represent a suitabe transmitting boundary for many appications invoving both diatationa waves and shear waves. A one-dimensiona viscous boundary mode is seected for this study. It is assumed that a horizontay moving pier cross section woud soey generate one-dimensiona P waves traveing in the direction of shaking and one-dimensiona S waves in the direction perpendicuar to shaking, as shown in Figure 9. Based on the previous assumption, the coefficient of viscous dashpot that wi absorb the energy of the waves originating at soi-pier interface is evauated. Resuts and discussion To study the effects of soi-foundation-structure interaction on the seismic behavior of the cabe-stayed bridge towers, two different approaches for soi-foundationinteraction modeing (noninear Winker mode and inear umped-parameter mode) are considered. The soifoundation-superstructure mode with Winker hypothesis for soi ideaization is compared to a simpified umpedparameter mode, and dynamic response simuation is conducted by appying acceeration at the base eve of the foundation. The foowing two different cases of soi ideaization are anayzed: Case I Seismic response with soi materia and geometrica noninearities: noninear Winker mode. Case II Seismic response of tower mode with inear umped-parameter soi mode. Soi-structure interaction modeing effects on goba responses The acceeration time history at the tower top, where the tower acceeration response is significanty decreased due to degradation of soi stiffness and energy dissipation through soi hysteresis, carifies the effects of soi noninearity. The reduction of acceeration response of Winker mode (case I) reated to soi noninearities (materia and geometrica) approaches about 6% of that of the simpified mode (case II), as iustrated in Figure 1. Moreover, the acceeration time history of case II is characterized by arge peak acceeration that is associated with a short duration impuse of high frequency (acceeration spike). The Fourier acceeration response spectrum carifies the significant contribution of highfrequency modes to the tower seismic response. Moment ratio -1 1-1 Case II 5 1 15 2 25 Time (sec) Figure 11 Moment ratio time history at tower superstructure base. The dispacement, moment ratio, and vertica force time histories of Winker mode (case I) at the tower superstructure base show the response nature to strong excitation. The moment ratio is defined as the ratio of moment demand to the moment capacity at the first yied of the cross section. The arge puse in the ground motion produces two or three cyces of arge force response with rapidy decaying ampitudes of dispacement, moment, and force after the peak excursions. The predominant contribution to the vertica force response Force (MN) Force (MN) 4 2-2 4 2-2 Case I Case II 5 1 15 2 25 Time (sec) Figure 12 Vertica force time history at tower superstructure base.
Raheem and Hayashikawa Internationa Journa of Advanced Structura Engineering 213, 5:8 Page 12 of 17 Footing base extreme right Footing base extreme eft Dispacement (m).5 -.5 5 1 15 2 25 Time (sec) Figure 13 Vertica dispacement time history of footing extreme right and eft at footing base eve. at the tower superstructure base resuts from the in-pane rocking vibration rather than from the vertica excitation, and it is dominated by ong-period in-pane vibration and sighty affected by high-frequency vertica excitation and vibration, as shown in Figures 11 and 12. However, the umped-parameter-mode anaysis (case II) for tower superstructure base moment and axia force dispays sight attenuation after peak response excursions, and the time history response is characterized by highfrequency spike. The simpified umped-parameter-mode anaysis provides a good prediction for peak response but overestimates the acceeration response and underestimates the upift force at the anchor between superstructure and pier. It can be obviousy seen that foundation upifting and pasticity have a significant effect on the reduction of seismic force of bridge tower. The foundation aowed upifting, and yieding in design wi protect tower pier and superstructures. The vaue of reduction of seismic force increases with the increase of seismic intensity. Soi noninearity effects on tower response The upift of the tower footing is investigated through vertica deformation and force resistance of the basement soi at the extreme right and eft sides of the footing base (case I). Two aspects of foundation response to seismic excitation, rocking deformation and the accumuation of the permanent settement can be distinguished. The permanent settement was found to be the ess significant in the tota vertica dispacement at the footing base eve, as shown in Figures 13 and 14. It can be concuded that separation of the soi from the structure occurs under arge dynamic oads eading to changes in the predominant vibration of the system. As a resut of the decrease in soi support at the sidewas of the foundation by stiffness degradation due to hysteresis, the stress caused by the structura weight on the bottom soi is increased during earthquakes. The reduction of the foundation width in contact during upift induces an increase of the stresses under the foundation. This eads to a arger soi yieding, which itsef modifies the upift behavior of the foundation. Footing base extreme right Footing base extreme eft 1 Force (MN/m) -1-2 -3 5 1 15 2 25 Time (sec) Figure 14 Vertica force per unit ength time history of footing extreme right and eft at footing base eve.
Raheem and Hayashikawa Internationa Journa of Advanced Structura Engineering 213, 5:8 Page 13 of 17.4 Case I Dispacement (m).2 -.2 -.4 5 1 15 2 25 Time (sec) Figure 15 In-pane dispacement time history at superstructure base. The maximum upift of not more than 5 mm carifies that the tower foundation amost has sufficient structura oading to minimize the upift. The soi ayer at the footing base eve has sufficient bearing capacity to prevent foundation excessive settement. Since the foundation structure is very rigid compared to the underying foundation soi, the rocking motion of the foundation is significanty observed, which affects the characteristics of the foundation motion. The imited shear strength of soi aso causes siding of the foundation bock, which coud ater the characteristics of the foundation motion. In addition to the inertia soi-foundation interaction due to the existence of foundation mass, the size and stiffness of the foundation coud aso affect the foundation motion characteristics. From superstructure base (stee superstructure and concrete substructure connection joint) dispacement time history (case I) as shown in Figure 15, it coud be seen that the dispacement coud reach around 3. cm for soi-structure interaction mode of the tower with both materia and geometrica noninearities; this effect is totay ignored for fixed base mode assumption. The imited shear strength of basement soi causes siding of the foundation, which coud be underestimated by eastic and inear soi assumption, as showninfigure16. From the Fourier spectra study of tower acceeration response at different eves of tower for noninear soi-foundation-superstructure interaction mode (case I), it is shown that there is ampification of different modes over a wide frequency range, as seen in Figures 17 and 18. The in-pane superstructure base response spectrum is arger than that at the footing base at a spectra frequency ess than 2. Hz because of ampification induced by fexibe superstructure and massive rigid substructure interaction, whie at high frequency above 2. Hz, the response spectra are sighty attenuated due to inertia interaction. The tower top response spectra are significanty ampified at ow-frequency range and are amost totay attenuated at high-frequency range due to tower superstructure fexibiity, as seen in Figure 18. The massive foundation has the effect of ampifying the response over a wide frequency band. The vertica acceeration response at the footing base eve shows reativey high-frequency ampification as the response spectra within the frequency range of 2 to 3 Hz are sighty ampified at the superstructure base eve, and they are dramaticay ampified at the tower top. On the other hand, the response spectrum at high-frequency range is attenuated by superstructure fexibiity fiter of the tower response. The noninear seismic response of bridge Dispacment (m).5 -.5 Case I Figure 16 Foundation siding time history at footing base eve. 5 1 15 2 25 Time (sec)
Raheem and Hayashikawa Internationa Journa of Advanced Structura Engineering 213, 5:8 Page 14 of 17 Acceeration (ga) Acceeration (ga) Acceeration (ga) 1-1 1-1 1 Tower top eve Tower superstructure base eve Footing base eve -1 5 1 15 2 25 Time Figure 17 In-pane acceeration time history and response spectra (case I). Fourier spectra ampitude Fourier spectra ampitude Fourier spectra ampitude.5.4.3.2.1.5.4.3.2.1.5.4.3.2.1 2 4 6 Frequency (Hz) piers is distincty different from that of the inear response. There is a great difference whether it is in vibration ampitude or in frequency property. The noninear properties of foundations make the stiffness of the structure ow, the response of rotationa ange increase, and theresponseofbendingmomentdecrease. Concusions A finite eement mode to study the effects of soifoundation-superstructure interaction on the seismic response of a cabe-stayed bridge tower supported on spread foundation was presented, in which an incrementa iterative technique was adopted for a more reaistic anaysis of the noninear soi-foundation-superstructure interaction. The probem was anayzed, empoying the finite eement method and taking account of materia (soi, stee superstructure) and geometric (upifting and P-Δ effects) noninearities. Two different modeing approaches for soi foundation interaction, noninear Winker mode and inear umped-parameter mode, were investigated. The seismic responses of Winker soi mode were compared to those of the simpified inear umped-parameter mode. In the umped-parameter soi mode, the soi-structure interaction is simuated with transationa, rotationa, and their couping spring system acting at centroid of spread foundation at the footing base eve whie in the Winker soi mode, the soi-structure interaction is simuated with continuous spring system (Winker) aong embedded depth of tower pier and underneath the spread foundation. Soi yieding under the foundation and aong the embedded depth was modeed using the Hardin-Drnevich mode to express noninear soi
Raheem and Hayashikawa Internationa Journa of Advanced Structura Engineering 213, 5:8 Page 15 of 17 Acceeration (ga) Acceeration (ga) Acceeration (ga) 4 2-2 -4 4 2-2 -4 4 2-2 Tower top eve Tower superstructure base eve Footing base eve -4 5 1 15 2 25 Time Figure 18 Vertica acceeration time history and response spectra (case I). Fourier spectra ampitude Fourier spectra ampitude Fourier spectra ampitude.2.2.2 2 4 6 Frequency (Hz) characteristics. The contact noninearity induced by the upift of the foundation was integrated using gap eement. Radiation damping associated with wave propagation was accounted for impicity through viscous damping whie the energy dissipation through soi materia noninearity was expicity modeed. The interaction effects generated by the norma and tangentia resistance of the soi against a active sides of the footing were taken into account. The foowing concusions can be drawn as foows: The anaysis with simpified inear umped-parameter mode provides a good prediction for the peak response but overestimates the acceeration response and underestimates the upift force at the anchor between superstructure and pier. The noninear soi-foundation interaction effect is very remarkabe when upifting and yieding of supporting soi are considered. The anaysis using the noninear interaction Winker mode shows that the foundation upift aters tower dispacement seismic response and reduces structura member forces. Compared with the inear anaysis, the stiffness of the tower-soi system degrades in each cyce after considering upifting and yieding. The noninear anaysis dispays arger rotationa anges and smaer bending moments compared with the inear umped-parameter-mode anaysis. The incusion of massive foundation and noninearity of soi effects eads to the ampification of higher modes of vibration and activates the high-frequency transationa motion of the input ground motion and generates foundationrocking responses. The rocking vibration dominates the atera bearing stress for the soi aong the embedded depth of the tower pier. The predominant contribution to the vertica response at the footing base resuted from the massive foundation rocking rather than from the vertica
Raheem and Hayashikawa Internationa Journa of Advanced Structura Engineering 213, 5:8 Page 16 of 17 excitation; the permanent settement is found to be ess significant. The soi bearing stress demand beneath the spread foundation is significanty increased due to footing base upift. The bearing stress under the foundation shoud be checked considering both soi materia and geometrica noninearities with an appropriate factor of safety to avoid catastrophic foundation faiure. The soi at the foundation eve shoud have sufficient bearing capacity to prevent foundation excessive settement. From the noninear Winker soi mode, it is concuded that the soi interaction effect is very remarkabe when upifting and yieding of supporting soi are considered. Compared with the inear umped soi mode, the stiffness of tower foundation-soi mode degrades in each cyce after considering upifting and yieding. It is shown that the noninear anaysis can get arger rotationa anges and smaer bending moments compared with the inear anaysis. The noninear modeing of soi-foundation interface shows that the soi structure interaction effect may pay an important roe in atering the force and dispacement demand, indicating the necessity for consideration of foundation behavior in the modern design codes to accompish a more economic yet safe structura design. For more genera and versatie concusions, different input excitations and different ground conditions at bridge construction site shoud be considered. Competing interests The authors decare that they have no competing interests. Authors contributions SEAR carried out the finite eement modeing and numerica simuations for the extensive parametric study, which is presented in the research work, and drafted the manuscript. SEAR and TH discussed the idea and the important system parameters, which are incuded for the numerica study and aso have checked the manuscript before submission. Both authors read and approved the fina manuscript. Authors information SEAR is an associate professor in Earthquake, Bridge, Structura and Geotechnica Engineering since 29 at the Civi Engineering Department in Assiut University, Egypt. He acquired his Doctorate in Engineering in 23 and was a Japan Society for the Promotion of Science feow in 26 in Hokkaido University, Japan. He was an Aexander von Humbodt feow in 25 in Kasse University, Germany. He has pubished more than 6 papers in the fied of structura engineering, structura anaysis, earthquake engineering, soi structure interaction, seismic pounding, structura contro, and noninear dynamic of offshore structures. He is a previous member of the Japan Society of Civi Engineers. He reviewed many papers for internationa journas. He is currenty working as an engineering counseor at the genera project management of Taibah University, Medina, Saudi Arabia. TH is a professor in Earthquake, Bridge, Structura and Geotechnica Engineering since 24. He acquired his Doctorate in Engineering in 1984 in Hokkaido University, Japan. He was a visiting research feow at Princeton University, USA in 1985. His research works/interests incude Response of Cabe-Stayed Bridges under Great Earthquake Ground Motion; Seismic Isoation Design; Energy Dissipation System and Performance-Based Design of Stee Structures; Damage Identification of Highway Bridge; and Bridge Management System Vibration Contro and Inteigentia Structure of Stee Bridges. He is a feow member of the Japan Society of Civi Engineers. He reviewed many papers for internationa journas. Author detais 1 Taibah University, Medina, Saudi Arabia. 2 Civi Engineering Department, Facuty of Engineering, Assiut University, Assiut 71516, Egypt. 3 Graduate Schoo of Engineering, Hokkaido University, Sapporo, Japan. Received: 27 September 212 Accepted: 2 February 213 Pubished: 22 March 213 References Abde Raheem SE (29) Pounding mitigation and unseating prevention at expansion joint of isoated muti-span bridges. Engineering Structures 31 (1):2345 2356 Abde Raheem SE, Hayashikawa T (23) Parametric study on stee tower seismic response of cabe-stayed bridges under great earthquake ground motion. Structura Engineering and Earthquake Engineering - JSCE 2(1):25 41 Abde Raheem SE, Hayashikawa T, Hashimoto I (22) Study on foundation fexibiity effects on stee tower seismic response of cabe-stayed bridges under great earthquake ground motion. 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