Proceeding of te 9t International Conference on Structural Dnamic, EURODYN 04 Porto, Portugal, 30 June - Jul 04 A. Cuna, E. Caetano, P. Ribeiro, G. Müller (ed.) ISSN: 3-900; ISBN: 978-97-75-65-4 Tunnel-oil-ile interaction in te rediction of ibration from underground railwa: alidation of te ub-model W.I. Hamad, H.E.M. Hunt, M.F.M. Huein, J.P. Talbot Deartment of Engineering, Unierit of Cambridge, Trumington Street, Cambridge, CB PZ, UK Intitute of Sound and Vibration Reearc, Unierit of Soutamton, Higfield, Soutamton, SO7 BJ, UK email: wi@cam.ac.uk, em@cam.ac.uk, m.uein@oton.ac.uk, t000@cam.ac.uk ABSTRACT: Ti aer rooe a metod for calculating te ibration leel from an underground tunnel, adacent to a iledfoundation, embedded in a omogeneou alf-ace on te bai of trong couling. Te metod relie on ueroing te ibration field generated b te tunnel wit tat generated b te iled-foundation. Te oil in ti aer i modelled utiliing te boundar element metod, wile te tunnel i modelled uing tin-ell teor and te iled-foundation i modelled b adoting te elatic bar and Euler beam teorie. Onl te reult of te ub-model (tunnel and iled-foundation) are reented erein and comared wit reiou work in te literature. Te current tunnel model i contrated to te well-known PiP model werea te iled-foundation model i alidated againt a reiou boundar element model. Te comarion reeal good agreement between te reult of te current model and toe of te reiou model. Te robutne of te current model a been igligted b eamining te reone of te tunnel at oint on te free urface wen it i ubect to a oint armonic load at it inert. Te reone of te iled-foundation to oriontal and ertical oint load on te ile-ead are alo inetigated, in addition to te dilacement field on te free urface due to a ertical oint load. KEY WORDS: Ground-borne ibration; Boundar element metod; Soil-tructure interaction, Tunnel; Piled-foundation INTRODUCTION Underground railwa noie and ibration can be a maor ource of diturbance to occuant in cloe roimit. Vibration i generated at te weel-rail interface, due to weel and track irregularitie, and roagate troug oil to nearb building. Wilt tee ibration ma not induce tructural damage, teir effect can imair uman comfort and actiit leading to long-term imlication [, ] or can caue malfunctioning of enitie equiment. Te roblem of ground-borne ibration a caugt te attention of reearcer during te at decade. To better undertand te tranmiion of ibration from underground railwa, different numerical imulation tecnique ae been eloited. Tee tecnique are eentiall aimed at identifing wa to tackle unaccetable leel of ibration from eiting a well a future railwa line. In te literature, tere eit a number of model to calculate ibration from railwa tat are baed on ace dicretiation and ueroition of elatic wae. Model baed on ace dicretiation emlo boundar element (BE) and finite element (FE) metod to imulate te dnamic oil-tunnel interaction, were te FE metod i ued to model te tunnel wall, and te urrounding oil i imulated b te BE metod. In te lat decade, tee metod were often couled togeter to roide more rigorou, efficient comutation. Ti wa acieed b auming omogeneit in te track direction allowing for te imlementation of a two-and-a-alf-dimenional (.5D) or waenumber FE-BE model [3], or b incororating eriodicit of te tunnel and oil wit te Floquet tranform [4, 5]. Te eriodicit aroac wa alo utilied witin te contet of a BE metod to model oil-iled foundation dnamic interaction [6]. Model baed on ueroition of elatic wae, on te oter and, are deemed to roide comutationall efficient tool. A model tat i articularl oular i te ie-in-ie (PiP) model, wic i a emi-analtical tree-dimenional (3D) model accounting for te dnamic oil-tunnel interaction [7, 8]. Te main model account for a tunnel embedded in a full-ace b uing te elatic wae equation for two concentric ie wit infinite lengt. Te PiP model a been alo augmented to conider a tunnel embedded in a alf-ace or a multi-laered alf-ace [9]. Deite te reearc effort deoted to te toic of underground railwa ibration, imlifing aumtion remain necear in all numerical model due rimaril to comutational limitation. A common imlifing aumtion i to neglect te interaction between neigbouring tructure. It mut be mentioned, oweer, tat tere eit in te literature a few tudie inetigating te dnamic interaction between neigbouring tunnel [0, ], and between an underground tunnel and tri-foundation [] or iledfoundation [3, 4]. In te tudie of tunnel/iledfoundation interaction [3, 4], a ub-domain modelling aroac wa adoted in wic te dilacement and traction generated b te tunnel ibration were ued a inut ariable for te iled-foundation. Put differentl, te reence of ile in te oil wa neglected wen calculating ibration field due to te moement of a train in a tunnel. Ti aroac reult in a weak couling, and it tereb doe not redict accuratel te beaiour of te couled tem. Ti aer reort on a noel tecnique for modelling te dnamic interaction of a full couled underground tunnel and a iled-foundation embedded in a omogeneou alface. Te urrounding oil i modelled uing te BE metod adoting alf-ace Green function, werea te tin-ell 767
Proceeding of te 9t International Conference on Structural Dnamic, EURODYN 04 teor i ued to imulate te tunnel wall and te iledfoundation i modelled uing te bar formulation for aial deformation and beam formulation for bending. Te tecnique aciee te trong couling b ueroing te ibration field generated b te tunnel wit tat generated b te iledfoundation. Te laout of te aer i a follow. Section decribe te modelling trateg for te couled tem and it comonent, along wit te formulation ued to erform te calculation. Section 3 roide te model arameter and briefl decribe te reiou model in te literature ued to alidate te current model. Section 4 reent te modelling arameter and comare te reult wit reiou work in te literature. Finall, te finding are igligted togeter wit work to follow in ection 5. MODELLING STRATEGY embedded in a full-ace from te olution of a ingle tunnel. In ti aer, te dilacement field, for eac ub-model, due to force acting on a ingle cait, be te oriontal or ertical, can be calculated at it interface and alo at te interface of te irtual cait. Te ibration reone of te couled tem can be written a te ueroition of te two dilacement field (U, U). One dilacement field i te reult of force acting on a ingle cait, werea te oter dilacement field i te reult of te interaction between te two caitie. Likewie, te total force alied to te couled tem (F, F) are equal to te ummation of te force acting on one cait wit toe rereenting te motion induced b te neigbouring cait. Ti i illutrated b te following equation, U = U + U F = F + F Te model reented ere aim to tud te influence of an eiting iled-foundation on te ibration field generated b an underground tunnel. Te rooed tem comrie a oriontal tunnel embedded at a det (d) from te free urface and a ertical iled-foundation, wic i at a oriontal ditance () from te tunnel centreline, ee Figure. Te rooed tem i modelled b firt imulating te ertical and oriontal caitie and ten couling tem to te tunnel wall and iled-foundation. U = U + U, F = F + F in wic te ubcrit refer to te ub-model and uercrit refer to te orientation of te cait, were denote oriontal and rereent ertical. From ub-model in Figure, relationi between te force (F) in te oriontal cait and it dilacement (U) a well a te dilacement (U) and traction (Q) in te irtual ertical cait read, U H F U H F, Figure. Te laout of te model for a couled tunnel-iled foundation tem. Te ueroition metod i ued to ole te tem in Figure, b breaking it into two ub-model. Firt, a model of a oriontal cait embedded in a alf-ace, witout a ertical cait. Second, a model of a ertical cait embedded in a alf-ace, witout a oriontal cait. Ti i illutrated in Figure, were te daed line in ub-model rereent te oition of te ertical cait and te daed line in ubmodel refer to te oition of te oriontal cait from te original roblem in Figure. Tee are own to aid in elaining te metod. Figure. Te ueroition metod ued for oling te couled tem, owing te ub-model. Te ueroition metod ued in ti work i imilar to tat alied b Kuo et al. [] to model a twin-tunnel tem 768 () Q G F were H i te frequenc reone function (FRF) matri between te oriontal cait force and dilacement, and H and G are te FRF matrice between te oriontal cait force and irtual ertical cait dilacement and traction reectiel. Te force (F) are obtained b integrating te traction (Q). Similarl for ub-model in Figure, relationi between te force on te interface of te ertical cait (F) and it dilacement (U) in addition to te dilacement (U) and traction (Q) on te irtual oriontal cait ield, () U H F U H F, Q G F (3) in wic H i te FRF matri between te ertical cait force and dilacement, and H and G are te FRF matrice between te ertical cait force and te irtual oriontal cait dilacement and traction reectiel. Te force (F) are obtained b integrating te traction (Q). Te FRF matrice (H, H, H and H) are obtained b aling a unit force at eac degree of freedom (DoF) of te cait (F and F) and calculating te dilacement at all DoF of te cait (U and U) a well a te irtual cait (U and U). Te FRF matrice (G and G) are acquired from te dilacement at te DoF of te irtual cait a follow:
Proceeding of te 9t International Conference on Structural Dnamic, EURODYN 04 u, u k, e(ik )dk, calculate train from dilacement calculate tree from train uing contitutie relationi calculate traction from tree uing Cauc formula Now, tere are 0 DoF unknown and 0 DoF equation reented in ()-(3), wic could be combined togeter to ole te couled tem in Figure. Te olution of te equation ield te FRF matri of te couled oriontal and ertical caitie tem. Ti FRF matri can ten be couled wit matrice of a tunnel and a iled-foundation auming comatibilit and equilibrium at te interface. In te following ub-ection, te formulation adoted for modelling te oil, te tunnel and te iled-foundation are reented. were te.5d Green function of EDT are ued for te fundamental olution of te BE formulation. For te cenario of te iled-foundation (ertical cait), a 3D BE me i utilied uing 3D Green function for te fundamental olution. In ti cae, a FRF matri decribing te 3D beaiour of te ertical cait at te frequenc of interet i obtained and i couled wit te FRF matri of te iled-foundation in order to calculate te reone of te couled tem. It a been made ure trougout te BE anali tat tere are more tan i contant element er waelengt to atif Domingue [6] recommendation... Te oil model Te BE metod i ued to model te oil, were Green function for a omogeneou alf-ace oil are ued a fundamental olution in te formulation. Te alf-ace Green function are calculated wit te aid of te ElatoDnamic Toolbo (EDT) [5]. Te EDT i baed on te direct tiffne metod and te tin laer metod in order to model wae roagation in laered media. Te BE model conit of a total of N contant element in wic traction and dilacement are aumed to be uniform and equal to te alue at teir central node. For eac of te N node of te BE me, tere are tree alue of dilacement and traction. Tee ariable are related b, Hu = G, { N... u N u N }T N N, N (5) T } were u and are te dilacement and traction ector of node reectiel. Equation (4) can be rearranged a, u H G, Te tunnel model Clindrical tin-ell teor i ued to model te tunnel, wic i aumed to be inariant in te longitudinal direction, allowing for te formulation of te equation of motion in te waenumber-frequenc domain. In linear ibration teor, if te alied loading comrie armonic traction comonent in ace and time, te equation of motion are atified b imilarl armonic dilacement comonent. Hence, te modal dilacement at te mean radiu (a) of te clinder due to alied force in te radial, tangential and longitudinal direction read,, (8) (4) were H and G are 3N 3N matrice decribing te beaiour of te oil in term of it denit ( ), ear modulu ( ), Poion ratio ( ), daming ratio ( ), ear wae eed (C), reure wae eed (C) and frequenc of interet (f). Te 3N u and ector are aembled from te comle dilacement and traction amlitude of eac node a follow, u {u u u u u u... u (7) (6) u H were H i te oil FRF matri relating dilacement and traction at te frequenc of interet. Ti FRF matri i couled wit te FRF matrice of te tunnel and iledfoundation in order to crutinie te oil-tructure interaction. For te cenario of te embedded tunnel (oriontal cait), it i aumed tat te tem i inariant in te longitudinal direction allowing for te ue of.5d aroac. In ti aroac, te calculation are erformed in te waenumber domain (k), allowing for rereenting te 3D reone of te tructure and te radiated wae field on a two-dimenional (D) me. Hence, a FRF matri for a D cait i calculated at te frequenc of interet and couled to te FRF matri of te tunnel wall. After tat, te couled reone i tranformed back to te ace domain b mean of inere Fourier tranform, a were E i te Young modulu, i te tickne, and te coefficient of matri A can be found in [] for mmetric and antimmetric cae. Te radial (U rn) and longitudinal (U n) dilacement are aociated wit conθ, wile te tangential (U θn) dilacement i aociated wit innθ. Since, te tunnel in ti aer i ubect to a oint armonic load at it inert, it i necear to decomoe te oint load into it ace-armonic comonent before finding te correonding dilacement. Te ariation of te load can be written a a linear combination of te ring mode (n) b mean of a Fourier erie, a ( ) (9) co n bn co n, a a n a n on te interal -, were ( ) i te Dirac-delta function. Uing te rereentation of te oint load in (9), te inut force can be written in a form tat uit te tin-ell formulation in order to calculate te reone of mmetric and antimmetric force for a gien ring mode (n). In order to coule te tunnel to te oil cait, te FRF matri of te tunnel i needed. Ti i formulated b uing te dnamic tiffne aroac, in wic te ell i diided into a number of node. Eac node a tree DoF rereenting te longitudinal, tangential and radial direction (ee Figure 3). Wit te aid of te tin-ell formulation in (8) and te rereentation of oint load in (9), a FRF matri relating te reone at eac DoF to te alied force read, (0) U = Ht F, were te ie of matri Ht i 3N 3N. 769
Proceeding of te 9t International Conference on Structural Dnamic, EURODYN 04 Figure 3. Cro-ection of a tin-ell diided into N node. Before combining te tem in (6) and (0), two tranformation are carried out. Firt, te oil FRF matri i modified to relate dilacement to force intead of traction b diiding it b te area of te element in te BE me. Second, te tunnel FRF matri i modified (H c t) to relate dilacement and force in te Carteian coordinate rater tan in te clindrical coordinate, a H c t T H T, () r t r were te ie of te tranformation matri T r i 3N 3N. Now, te two tem can be couled in te waenumber domain b aling comatibilit of dilacement and equilibrium of force at te interface. Te equation read, U U F t H F U c t t U H F F a c H t c H H tfa, () were F a i te alied force into te tunnel and F i te reulting force alied into te oil. B knowing F, te reone at an oint in te oil can be calculated..3 Te iled-foundation model Te iled-foundation i imulated b an elatic bar for aial loading and an Euler-Bernoulli beam for tranere loading. Te ile i rereented b it centroid ai, wic a N l equall aced node, ee Figure 4. At eac of tee node, tere are i DoF rereenting dilacement and rotation in te tree direction. Te ile i aumed to be contraint free at it end and an local deformation of te cro-ection i neglected. Figure 4. Pile centroid (drawn oriontall) were te circle rereent te node at wic te force are alied and te reone are calculated. Onl te - lane i own. Te reone of te ile to a unit armonic force wit angular frequenc alied in te longitudinal direction () at node i calculated a follow: u u were I I I, u A co B in for 0, u A co B in for L E, (3), te uercrit I and indicate te ection aboe and beneat te node and coefficient A I, B I, A, B are found from te boundar condition. Te general reone of te ile to a unit armonic force or moment wit angular frequenc alied in/around te tranere direction (, ) at node read u u,, I I I i I I i, u, A e B e C e D e for 0, (4) i i u,, A e B e C e D e for L 4 were A and te coefficient A I, B I, C I, D I, A, EPI B, C, D are found from te boundar condition. In order to obtain te rotation around te tranere direction equation (4) i differentiated wit reect to. Te general olution of te ile to a unit armonic torque wit angular frequenc alied around te longitudinal direction () i, I I I, A co B in for 0, (5), A co B in for L in wic and coefficient A I, B I, A, B are G found from te boundar condition. Likewie te tunnel, te FRF matri of te ile centroid (H l) can be aembled wic a a ie of 6N l 6N l. Ti matri i ten tranformed to gie te FRF matri (H ) of te ile node around te circumference a, H T H T, (6) r l r were te matri H a a ie of 3N 3N and te ie of te tranformation matri T r i 6N l 3N. To ti end, te tem in (6) and (6) can be couled in te ame wa a in (). 3 MODEL PARAMETERS AND COMPARISONS In ti aer, onl te reult of te uncouled tem, i.e. ub-model and in Figure, are reented. Te model of te tunnel i alidated againt te PiP model [9], wic carrie out te comutation auming tat te tunnel near field dilacement i not influenced b te free urface. Te PiP imulate te ibration of a tunnel embedded in a alf-ace in tree te. Firt, te model calculate te dilacement at te tunnel-oil interface uing a model of a tunnel embedded in a full-ace. It ten calculate equialent internal force in a model of a full-ace, witout a tunnel, tat roduce te ame dilacement at te tunnel-oil interface a comuted in te firt te. Finall, te PiP conider a alf-ace model, witout a tunnel, and multilie it Green function b te equialent force in te econd te. For comarion, a cenario of a tunnel embedded at a det of 5m and ubect to a armonic oint load at it inert i conidered. Te reone are calculated in te frequenc 770
Proceeding of te 9t International Conference on Structural Dnamic, EURODYN 04 range -80H. Te number of element in te BE me, wic i 40 contant node-collocated element of equal ie, conform to te number of element in te tunnel. Te arameter ued in modelling are ummaried in Table. Table. Tunnel and oil arameter ued for calculating te reult of current model and PiP model. Parameter Smbol Value Tunnel Radiu a.75m Denit 500kg/m 3 Young modulu E 50GPa Poion ratio 0.3 Daming lo factor 0.03 Soil Radiu r 3m Denit 800kg/m 3 Sear wae eed C 00m/ Preure wae eed C 400m/ Daming lo factor 0.04 Te model of te iled-foundation (ub-model ) i contrated to te model of Talbot and Hunt [6], wic utilied te BE metod for te oil aling te fundamental olution of full-ace Green function. Ti a led to te dicretiation of te free urface in order to account for te alf-ace beaiour. Anoter feature of Talbot and Hunt model i tat it rereented te circular cro-ection of te ile b four element in order to eae te dicretiation of te free urface uing rectangular element. Te current model a 6 contant node-collocated element in it circumference and 6 contant node-collocated element in te longitudinal direction. Te number of element in te BE me i equal to tat in te ile model. Te reone of te ile due to aial and tranere loading are conidered in ti aer. Tee are reented in te form of fleibilit coefficient F i = I i + ij i, wic are obtained b normaliing te driing-oint FRF to teir tatic alue. Table gie te arameter ued in modelling te iledfoundation. Table. Piled-foundation and oil arameter ued for calculating te reult of te current model and Talbot and Hunt model. Parameter Smbol Value Piled-foundation Lengt L 7.5m Radiu r 0.35m Denit 687kg/m 3 Young modulu E 5GPa Poion ratio 0.5 Soil Radiu r 0.35m Denit 50kg/m 3 Sear wae eed C 00m/ Preure wae eed C 490m/ Daming lo factor 0.03 4 RESULTS AND DISCUSSION In ti ection, te reult of te current model are reented and comared againt reiou model in te literature. 4. Te tunnel model reult Te firt et of te reult conider te ertical dilacement on te free urface ( = 0) at te oint (0m, 0m, 0m) and (0m, 0m, 0). Suc reult are articularl imortant for racticing engineer to ae underground railwa and deign mitigation. Figure 5 deict te modulu of te ertical dilacement (U ) at te oint (0m, 0m, 0m), calculated wit te current model and te PiP model. Some difference between bot olution can be een in te frequenc range of -0H and alo in te range of 60-80H. Howeer, at mid-range frequencie (5-55H) te model comare reaonabl well. Te ertical dilacement (U ) modulu comuted b te two model at te oint (0m, 0m, 0m) on te free urface i reented in Figure 6. Te model ow at ome frequencie reaonable agreement. Howeer, difference of about 0dB are obered around te frequenc range 0-30H. Te reaon of tee dicreancie in Figure 5 and Figure 6 could be attributed to a number of reaon. One i tat te PiP model imulate te tunnel uing continuum teor, wic i more robut tan te tin-ell teor adoted in te current model. Anoter reaon tat could caue uc difference i te reflection of wae from te free urface. Te PiP model doe not include a free urface. A tird could be due to te dicretiation rule followed in deeloing te BE model and alo in te waenumber amling. Deite te difference between bot model in Figure 5 and Figure 6, te rediction of te current model are romiing and could be furter imroed following more inetigation. It i eential to enure tat te current model of te tunnel roide adequate rediction for te ibration leel before roceeding to te net te of couling te tunnel to te iled-foundation. Te tunnel wall could alo be modelled a a continuum (i.e. tick-wall teor) intead of uing te tin-ell teor. Howeer, ti i unlikel to make a difference oer te frequenc range under conideration. Figure 5. Modulu of te ertical dilacement at te oint (0m, 0m, 0m) on te free urface comuted b te current model and te PiP model. 77
Proceeding of te 9t International Conference on Structural Dnamic, EURODYN 04 Figure 7. Real art of te oriontal dilacement on te free urface at (a) 0H and (b) 50H comuted b te couled tin-ell-be model. Figure 6. Modulu of te ertical dilacement at te oint (0m, 0m, 0m) on te free urface comuted b te current model and te PiP model. Te econd et of reult deal wit dilacement field on te free urface at frequencie 0H and 50H. Tee are onl reented for te current model. Wae generated at te tunnel due to te armonic load at it inert roagate troug te oil and reult in Raleig wae at te urface of te alface. In Figure 7, te oriontal dilacement field i illutrated for bot frequencie. It can be obered tat te dilacement troug te ero -ai equal ero due to mmetr. Te dilacement at oter mmetr oint are equal in magnitude and ooite in direction. Figure 8 ow te longitudinal dilacement field for bot frequencie. All dilacement troug te lane of ero - ai equal ero due to mmetr. Along te oriontal ai, te dilacement are equal in magnitude and in te ame direction, werea along te longitudinal ai te dilacement are equal in magnitude and ooite in direction. Te ertical dilacement field i own in Figure 9. It can be een tat te waefront on te urface of te alf-ace are not clindrical due to te nature of te ource and te dnamic interaction between te oil and te tunnel. In ti figure te dilacement at te mmetr oint are equal in magnitude and ooite in direction. Baed on te arameter roided in Table, te Raleig wae eed i about 90m/. Ti reult in a Raleig waelengt for te frequenc 0H of about 9m and for te frequenc 50H of aroimatel 3.8m. Indeed, tee alue are calculated baed on te ingle ource of a oint armonic load, wic i not te cenario for te reult reented in Figure 7 - Figure 9. It can alo be dicerned from Figure 7 - Figure 9 tat te magnitude of te longitudinal dilacement (Figure 8) i le tan tat of te tranere dilacement. Figure 8. Real art of te longitudinal dilacement on te free urface at (a) 0H and (b) 50H comuted b te couled tin-ell-be model. Figure 9. Real art of te ertical dilacement on te free urface at (a) 0H and (b) 50H comuted b te couled tin-ell-be model. 4. Te iled-foundation model reult Te firt art of tee reult i concerned wit reenting te fleibilit coefficient at te ile-ead againt non-dimenional frequencie (a 0=r/C ) range from 0 to 0.5. Ti i te range tat wa conidered in reiou work on modelling oil-ile interaction for eimic uroe, in wic iger frequencie are not conidered. 77
Proceeding of te 9t International Conference on Structural Dnamic, EURODYN 04 Figure 0 comare te oriontal ile-ead fleibilit comuted b te current model wit toe redicted b Talbot and Hunt [6]. Te model agree well for bot real and imaginar art at low non-dimenional frequencie. Howeer, mall dicreancie are obered at iger frequencie, tat are belieed to be due to te difference in te ie of te BE me between te two model. Talbot and Hunt model ued four element in te circumference werea te current model utilie 6 element. Figure illutrate te ertical ile-ead fleibilit due to a unit armonic aial load comuted b bot model. For te real art fleibilit, te difference between te two model i almot contant at all non-dimenional frequencie. For te imaginar art fleibilit, oweer, dicreancie between te model become clearer at frequencie beond a 0=0.5. a it conform to te requirement of te me ie recommended b Domingue [6]. Te current model i alo able to redict te dnamic beaiour of te iled-foundation wen te ile i ubect to torion a te of loading tat i likel to occur in a full couled tunnel-iled-foundation tem. Te econd art of te iled-foundation reult reent te dilacement field at te free urface wen a unit armonic ertical oint load i alied to te ile-ead at a nondimenional frequenc a 0=0.5. Figure (a) ow te ertical dilacement field at te free urface, were concentric circular waefront are obered. Ti confirm te correctne of te model, a it i eected to ae uc waefront wen te iled-foundation i ubect to a ertical load on it ead. Figure (b) ow a ertical ection troug te free urface of te dilacement field at te location of te ile centroid. Te figure indicate te Raleig waelengt to be aroimatel 4.m. Ti agree well wit te teoretical Raleig waelengt for te arameter in Table, wic i 4.m at a 0=0.5. Tee finding confirm again te accurac of te current model in redicting te dnamic oil-ile interaction. Figure 0. Comarion of te oriontal ile-ead fleibilit coefficient redicted b te current model wit toe redicted b Talbot model. Figure. Comarion of te ertical ile-ead fleibilit coefficient redicted b te current model wit toe redicted b Talbot model. Gien te difference between te current model and Talbot and Hunt model in Figure 0 and Figure, it can be generall aid tat te two model are in a good agreement. In eence, te BE me of te current model i more adequate Figure. (a) Te ertical dilacement field redicted b te current model wen ubect to a oint armonic load on te ile-ead at a non-dimenional frequenc a 0 = 0.5, (b) ertical ection troug te free urface at te location of te ile centroid. 773
Proceeding of te 9t International Conference on Structural Dnamic, EURODYN 04 5 CONCLUSION AND FUTURE WORK Ti aer a rooed a noel tecnique for modelling te dnamic interaction between an underground tunnel and iled-foundation. Te metod i baed on ueroition of ibration waefield generated b te tunnel and iledfoundation. Te oil in ti work i modelled uing te BE metod were alf-ace Green function are ued a fundamental olution. Te tunnel i modelled uing tin-ell teor, werea te iled-foundation i modelled uing an elatic bar for aial deformation and an Euler-Bernoulli beam for bending deformation. Te aer a firt reented te reult of te dnamic interaction between a tunnel and oil and comared tem againt te rediction of te PiP model. Te comarion ae reealed tat te reult of bot model agree well at mot frequencie. Howeer, ome difference between te two model are obered at a number of frequencie. Tee difference are attributed to te reflection of free urface wae tat are not adequatel redicted b te PiP model, and alo to te dicretiation rule followed in te BE model. Te aer a alo reented te reult of te dnamic interaction between te iled-foundation and oil. Te model rediction are comared againt te BE model of Talbot and Hunt [6] b mean of te fleibilit coefficient. Te comarion include te reone of te iled-foundation to a oriontal and ertical oint load on te ile-ead. It i reealed tat bot model agree well for te oriontal loading cenario, eeciall at low frequencie. For te ertical loading cenario, mall difference are obered, in articular at iger frequencie. In general, te reented reult ae igligted te abilit of te ub-model in adequatel redicting te dnamic interaction between te tunnel-oil and oil-iled-foundation. Terefore, te work can now be moed to te net te were bot ub-model can be couled togeter. Te reult will ten be contrated to te work of Huein et al. [4], wic emloed te ub-modelling tecnique to inetigate te dnamic interaction between a railwa tunnel and iledfoundation on te bai of weak couling. [5] G. Degrande, D. Clouteau, R. Otman, M. Arnt, H. Cebli, R. Klein, P. Catteree and B. Janen, A numerical model for ground-borne ibration from underground railwa traffic baed on a eriodic finite element-boundar element formulation, J. Sound Vib., 93, 645-666, 006. [6] J. Talbot and H. Hunt, A comutationall efficient iled-foundation model for tuding te effect of ground-borne ibration on building, Proc. Int. IMecE Part C: J. Mec. Eng. Sci., 7, 975-989, 003. [7] J. Forret and H. Hunt, A tree-dimenional model for calculation of train-induced ground ibration, J. Sound Vib., 94(4-5), 678-705, 006. [8] M. Huein, H. Hunt, A numerical model for calculating ibration from a railwa tunnel embedded in a full-ace, J. Sound Vib., 305, 40-43, 007. [9] M. Huein, H. Hunt, L. Rike, S. Guta, G. Degrande, J. Talbot, S. Francoi and M. Sceenel, Uing te PiP model for fat calculation of ibration from a railwa tunnel in a multi-laered alf-ace, Note on Numerical Fluid Mecanic and Multidicilinar Deign, 99/008, 36-4, 008. [0] X. Seng, C. Jone and D. Tomon, Modelling ground-ibration from railwa uing waenumber finite- and boundar-element metod, Proc. R. Soc. A: Matematical, Pical and Engineering Science, 46, 043-070, 005. [] K. Kuo, H. Hunt and M. Huein, Te effect of a twin tunnel on te roagation of ground-borne ibration from an underground railwa, J. Sound Vib., 330, 603-6, 0. [] P. Coulier, G. Degrande, G. Lombaert, Te influence of ource-receier interaction on te numerical rediction of traffic induced ibration, Proc. of Adance in Enironmental Vibration: Fift International Smoium on Enironmental Vibration, Cengdu, Cina, 0- October, 0. [3] P. Coulier, G. Degrande, K. Kuo and H. Hunt, A comarion of two model for te ibration reone of iled foundation to inertial and underground-railwa-induced loading, Proc. of te 7 t International Congre on Sound & Vibration, Cairo, Egt, 8- Jul, 00. [4] M. Huein, H. Hunt, K. Kuo, P. Cota and J. Barboa, Te ue of ubmodelling tecnique to calculate ibration in building from underground railwa, Proc. Int. IMecE. Part F: J. Rail Raid Tranit, 0(0), -, 03. [5] M. Sceenel, S. Francoi and G. Degrande, An ElatoDnamic Toolbo for MATLAB, Comut. Geoci., 35(80): 75-754, 009. [6] J. Domingue, Boundar Element in Dnamic, Comutational Mecanic Publication and Eleier Alied Science, Soutamton, 993. ACKNOWLEDGMENTS Te autor would like to acknowledge te generou funding of te EPSRC (grant reference no. EP/K006665/) roided to conduct ti reearc. Te reult reented ere are art of te MOTIV (Modelling Of Train Induced Vibration) roect. Te autor would like alo to tank te contribution of te Unierit of KU Leuen for roiding te EDT and alo for ome function of BEMFUN ued in te BE model. REFERENCES [] S. Fidell, D. Barber and T. Scult, Udating a doage-effect relationi for te realence of annoance due to general tranortation noie, J. Acout. Soc. Am, 89(), -33, 99. [] M. Ferrara and L. De Gennaro, How muc lee do we need?, Slee Med. Re., 5(), 55-79, 00. [3] X. Seng, C. Jone and D. Tomon, Prediction of ground ibration from train uing te waenumber finite and boundar element metod, J. Sound Vib., 93, 575-586, 006. [4] D. Clouteau, M. Arnt, T. Al-Huaini and G. Degrande, Freefield ibration due to dnamic loading on a tunnel embedded in a tratified medium, J. Sound Vib., 83, 73-99, 005. 774