Available online at ScienceDirect. Procedia Engineering 153 (2016 )

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1 Avalable onlne a ScenceDrec Proceda Engneerng 5 (6 ) XXV Polsh Russan Slova Semnar Theorecal Foundaon of Cvl Engneerng Vbraon of embedded foundaon a mul-layered base ang no accoun non-lnear and rheologcal properes of sols Ter-Marrsyan Z.G. a, Ter-Marrsyan A.Z. a *, Sobolev E.S. a a Moscow Sae Unversy of Cvl Engneerng (Naonal Research Unversy), 6 Yaroslavsoye Shosse, Moscow, 97, Russa Absrac Calculaon scheme of sold mul-layered base of he embedded foundaon s offered for descrpon of sysem vbraon foundaon s a mul-layered base. I s shown ha n hs case consderaon of apparen mass of he sold mul-layered base, as well as foundaon sde surface frcon leads o non-perodcal (non-harmonc) damped vbraon of he foundaon. Dfferen conac models ncludng elasc, non-lnear and rheologcal ones wh regard o srenghenng hroughou he me are consdered as for calculaon for soluon of problem of sysem vbraon. I s shown ha consderaon of sol srenghenng and sde surface frcon of he embedded foundaon grealy nfluence he nensy of vbraon dampng hroughou he me. 6 Publshed The Auhors. by Elsever Publshed Ld. by Ths Elsever s an open Ld. access arcle under he CC BY-NC-ND lcense Peer-revew (hp://creavecommons.org/lcenses/by-nc-nd/4./). under responsbly of he organng commee of he XXV Polsh Russan Slova Semnar Theorecal Foundaon Peer-revew under of Cvl responsbly Engneerng. of he organng commee of he XXV Polsh Russan Slova Semnar Theorecal Foundaon of Cvl Engneerng. Keywords: vbraons, base, sol, rheologcal properes, nonlneary.. Inroducon I s nown ha when desgnng he foundaon for machne and equpmen wh dynamc loads, ground base s consdered as a massless and s characered by sffness coeffcen K, Kx and. Such a smplfed model of he base, nown as Wnler model, enables us o smplfy consderably he soluon of dfferenal equaons of foundaon vbraon a compressble base regardless o vscous ressance [, 4, 5, ]. * Correspondng auhor. Tel.: E-mal address: gc-mgsu@mal.ru Publshed by Elsever Ld. Ths s an open access arcle under he CC BY-NC-ND lcense (hp://creavecommons.org/lcenses/by-nc-nd/4./). Peer-revew under responsbly of he organng commee of he XXV Polsh Russan Slova Semnar Theorecal Foundaon of Cvl Engneerng. do:.6/j.proeng.6.8.7

2 748 Z.G. Ter-Marrsyan e al. / Proceda Engneerng 5 ( 6 ) One uses he models whch ae no accoun dampng properes of he sol, ncludng Kelvn-Vog model and Maxwell model when s necessary o accoun non-elasc ressance of he base []. Ths paper presens he problem of vbraon of he embedded foundaon a he sold (neral) mul-layered base ang no accoun vscous properes of base sols and sde surface frcon [8, 9]. Frs aemps o accoun he apparen mass of base sols are made by E. Ressner, hen by O.Ya.Sheher []. One consdered he problem of forced vbraons of he round plae a he elasc sold semspace nfluenced by harmonc dsurbng force. Accoun of neral forces of base sols resuls n he fac ha vbraon amplude does no urn no nfny anywhere ha s here s no resonance, provded ha he ncrease n Posson s rao leads o he ncrease of energy emsson from vbrang foundaon o he sol, consequenly, he dampng of sysem vbraons. Besdes, accoun of nera of base sols resuls n aperodc foundaon vbraon ha s here s no vbraon moon of he foundaon. In hs respec, neral properes of base sols nfluence more he foundaons of low hegh and large se han he foundaons of hgh hegh and relavely small base square. The models wh he apparen mass are currenly used for soluon of praccal problems wh dfferen mehods ncludng s seng o he sol volume conaned n he acve deformaon area of he base. When calculang wde foundaons, dynamc load s consdered o be ransferred o he ground base as a load-bearng pos, concal (rapeodal) sold mass and semspace.. Vbraon of embedded massve foundaon a he mul-layered sold vsco-elasc base I s nown [, 7] ha n case of neral base, he dynamc equlbrum of he foundaon wh one degree of freedom under he nfluence of vbraon power can be expressed wh he equaon: m F sn( ) = p sn( ω) (), where s a vercal dsplacemen; m s a foundaon mass; F s a sde surface frcon force. The equaon sysem of ype (5) mus be solved n case of sold mul-layered base wh several degrees of freedom. The number of equaons mus concde wh he number of degrees of freedom of hs sysem. Reacve and neral forces, as well as sde surface frcon force of foundaon and sol appear n case of vbraon of he embedded foundaon a he sol sold mul-layered base. These forces can consderably nfluence he characer of foundaon vbraon, ncludng amplude and vbraon frequency, exclude resonance possbly and enable he accumulaon of foundaon resdual selemen and nclnaon. The problem of vbraon on elasc and neral unform base s consdered n paper [] ncludng he approxmae calculaon scheme where he dynamc load s consdered o be ransferred o: exclusvely load-bearng prsmac sol pos; load-bearng sold mass n he form of fne (rapeodal) sold mass and semspace. One also nows he approxmae calculaon scheme where base nera s aen no accoun by way of jonng of acve one sol mass o foundaon mass. All hese calculaon schemes lead o decrease of vbraon amplude and exclude resonance. Ths paper offers he approxmae calculaon scheme of vbraon of he embedded foundaon a sold mullayered base wh regard o sde surface frcon of foundaon and sol, as well as elasc and vscous sol properes. Sol base s shown as sold layers of fne hcness joned by elasc and elasc and vscous elemens. In hs case, each layer wh mass m wll vbrae ndvdually and, consequenly, here wll be a sysem wh mulple degree of freedom equal o he number of layers (fg. ). Soluon of sffness coeffcen of each layer, s mass m and mean value of sac load p, as well as sress dsrbuon angle of sascal load are defned for mahemacal descrpon of vbraon of such a sysem. The las n he frs approxmaon can be defned on he bass of dampng sress coeffcen under he foundaon of he cenral axs by ables [] dependng on foundaon ype n plan (recangle, square, crcle). There s dependence beween he dsrbuon angle and sress dampng coeffcen as follows: b( α ) an λ =, () α Z a

3 Z.G. Ter-Marrsyan e al. / Proceda Engneerng 5 ( 6 ) FOUNDATION where b and l are he breadh and he lengh of he recangular foundaon, respecvely; Z a s he lower bound of he compressble foundaon hcness defned from he condon p =,5 g [6, 7]. Thus, for example, for recangular foundaon wh breadh b = m, and lengh l = 8m a he deph = m, he value maes =.46. Then an =.58,. Havng he values, one can defne he dmensons of he -h layer n plan, ha s b = b l an, where h s he hcness of he -h layer. Values p and can be defned by formulas: bl b p = p ; p = ; S S p β h = ; () E where E s he module of lnear deformaon of he -h layer; S s of he selemen of he -h layer; ν β =,8. (4) ν where s a coeffcen of Posson s rao of he -h layer. Le s consder he smples suaon. Imagne he vbraon calculaon scheme of he sysem foundaon s a valuable base wh hree degrees of freedom consderng ha he foundaon wh mass m co-operaes wh valuable wo-layered base wh mass m and m, whch cener of gravy s on one hrd of he hegh of layers h and h (fg. ). In hs case, here s a possbly of only vercal dsplacemen of he foundaon. If n he frs approxmaon one does no accoun energy absorpon, hen he dfferenal equaon of forced vbraons of such a sysem can be represened as follows:

4 75 Z.G. Ter-Marrsyan e al. / Proceda Engneerng 5 ( 6 ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) sn sn = = = m m p F m ω. (5) Fg.. Vbraon calculaon scheme of he sysem foundaon s a valuable wo-layered base wh hree degrees of freedom where,, are vercal dsplacemens of he foundaon and ceners of gravy of he frs and he second layers of he foundaon, respecvely; m, m, m are he masses of foundaon, he frs and he second layers of ground bases, respecvely; s a sffness coeffcen of he base, where ( ) ( ) = ; s a vscous ressance coeffcen of sols, where ( ) ( ) = ; F s a sde surface frcon force of he foundaon. Equaon soluon (5) can be obaned by numercal mehod wh he help of sofware MahCAD. The resuls of he soluon are shown n fg. ang no accoun sol srenghenng, ha s a e β =, e α = and a foundaon mass m=8 ons, dameer 8 m under nfluence of dsurbng mpulse force P()=p, a layer hcness h =h =5m. FOUNDATION

5 Z.G. Ter-Marrsyan e al. / Proceda Engneerng 5 ( 6 ) Vercal dsplacemen(m) () () ().5.5 Fg.. Curves of vbraons of he sysem foundaon s a wo-layered base wh hree layers of freedom ploed based on equaon soluon (5) wh he help of sofware MahCAD ang no accoun srenghenng and frcon of sols by sde surface of he embedded foundaon; foundaon ( ), frs layer ( ) and second layer ( ) Tme(s) I s apparen n case of absence of harmonc vbraon and foundaon resdual selemen. Ths problem s solved also n elasc approach boh n soluon (5) and sofware PLAXIS. Benchmarng of hese soluons (fgures 4, 5, 6) demonsraes ha here s a sasfacory convergence. Consequenly, he proposed calculaon model (fg. ) can be used for calculaon of vbraon sysem foundaon s a mul-layered valuable base wh he help of sofware MahCAD. 5 Vercal dsplacemen(m) () () () Tme(s) Fg. 4. Curves of vbraons of he sysem foundaon s a wo-layered base wh hree layers of freedom ploed based on soluon (5) wh he help of sofware MahCAD ang no accoun he elasc sol model; foundaon ( ), frs layer ( ) and second layer ( )

6 75 Z.G. Ter-Marrsyan e al. / Proceda Engneerng 5 ( 6 ) Vercal dsplacemen[m] 5e- -5e- -. Pon A Pon B Tme[s] Pon C Fg. 5. Curves of vbraons of foundaon (Pon A), ceners of he frs (Pon B) and he second (Pon C) layers of sols ang no accoun elasc properes of foundaon sols ploed based on he resuls of numercal calculaon of plane problem n sofware PLAXIS Vercal dsplacemen [m] -5e- -. Pon A -.5 Pon B Tme [s] Pon C Fg. 6. Curves of vbraons of foundaon (Pon A), ceners of he frs (Pon B) and he second (Pon C) layers ang no accoun elasc and plasc properes of foundaon sols ploed based on he resuls of numercal calculaon of plane problem n sofware PLAXIS. Conclusons. The proposed calculaon scheme (fg. ) wh adequae accuracy descrbes he vbraon of he embedded foundaon a sold mul-layered base.. The examples of problems soluons on vbraon of he sysem foundaon s a base on he ground of he proposed calculaon scheme of he sold mul-layered base wh several degrees of freedom and her comparson wh he resuls of numercal problem soluon n sofware PLAXIS showed her sasfacory convergence.. Accoun of wegh of base sols and sde surface frcon of he embedded foundaon n he proposed model (fg. ) has consderable nfluence on he characerscs of foundaon vbraon ncludng amplude and accumulaon of foundaon resdual selemen.

7 Z.G. Ter-Marrsyan e al. / Proceda Engneerng 5 ( 6 ) Acnowledgemens Ths wor was fnancally suppored by he Mnsry of Russan Educaon (sae as #4/4; # /K). References [] E.A.Vonesensy Sol Dynamc Insably. Moscow: Edoral, 999. page 64 [] Yu.K. Zaresy, V.N. Lombardo Sascs and Dynamcs of Sol Dams. Moscow: Energoaomda, 98. page 56 [] N.D. Krasnov Dynamc Properes of Sols and Mehods of her Deermnaon. Lenngrad: Sroyda, 97. page 9 [4] E. Rausch Machne Foundaons. Moscow: Sroyda, 965. page 48 [5] O.A. Savnov Modern Consrucons of Machne Foundaons and her Calculaons. Moscow: Sroyda, 979. page 79 [6] SP... Foundaons of Buldngs and Srucures. Revsed edon SNP..-8* Moscow: Mnsry of Regonal Developmen of Russa,. page 6 [7] SP 6... Foundaons for Machnes wh Dynamc Loads. Revsed edon SNP Moscow: Mnsry of Regonal Developmen of Russa, page 66 [8] L.R. Savnser Sesmc Ressance of Basemens and Foundaons. Moscow: ASB,. page 447 [9] Z.G. Ter-Marrsyan Sol Mechancs. Moscow: ASB, 9. page 55 [] Sol Mechancs, Basemens and Foundaons / S.B. Uchov, V.V. Semenov, V.V. Znamenovsy, Z.G. Ter-Marrsyan, S.N. Chernyshev eded by S.B. Uchov rd edon. Moscow: Vysshaya Shola, 4. page 566 [] O.Ya. Sheher Dynamc Calculaon of Ples Jon by Rgd Foundaon Frame on Top // Collecon of Wors of he Research Esablshmen of Foundaons and Basemens, No.. Moscow: 948. pages 4-5 [] M. Nova Sae of he Ar n Analyss and Desgn of Machne Foundaons // Sol-Srucure Ineracon pages 55-67