01 IACSIT Coimbtor Confrns IPCSIT ol. 8 (01 (01 IACSIT Prss, Singpor Formultion of Sismi Ati Erth Prssur of Inlind Rtining Wll Supporting -Ф Bkfill Sim Ghosh 1 nd Strup Sngupt + 1 Assistnt Profssor, Ciil Engg. Dprtmnt, Ntionl Institut of Thnology M.Th Studnt, Ciil Engg. Dprtmnt, Ntionl Institut of Thnology, Agrtl, PIN 799055 Abstrt. An ffort is md to lut th formultion of sismi ti rth prssur bhind nonrtil rtining wll supporting -Ф bkfill. Th formultion is don to gt singl ritil wdg surf for simultnous tion of wight, surhrg, ohsion nd dhsion. Th fft of rious prmtrs iz. intrnl frition (Φ, ngl of wll frition (δ, wll inlintion ngl(α, ohsion (, dhsion (, sismi lrtions (k h, k, surhrg loding (q, unit wight (γ, hight ( r lso tkn into ount to proid th rition of sismi ti rth prssur offiint. Kywords: sismi ti rth prssur, psudo-stti, rtining wll, -Φ bkfill, singl wdg, wll inlintion. 1. Introdution Th pionring work in dtrmining th stti rth prssur ws don by Coulomb (1773. Mononob- Okb xtndd th thory inluding rthquk lods introduing horizontl nd rtil inrti fors for rtining wll hing ohsionlss bkfill. Th Coulomb s thory is furthr xtndd to lut sismi ti rth prssur onsidring -φ bkfill by Prksh nd Srn (1966, Srn nd Prksh (1968, Srn nd Gupt (003. In ll ths mthods thr sprt wdg surfs gnrtd for th indiisul tion of unit wight, surhrg nd ohsion onsidring unit dhsion is qul to unit ohsion. This ssumption is not t ll tru. Thrftr, Shukl t l. (009 ws th first prson who gi th id to xtnd this Mononob-Okb onpt for -Φ bkfill in suh wy to gt singl ritil wdg surf. Thrfor this ppr imd to gi stisftory formultion to lut sismi ti rth prssur inluding th influn of both dhsion nd ohsion for non-rtil rtining wll.. Mthod of Anlysis q pr unit lngth A (W+Qk h D (W+Q(1±k P δ α θ φ R B + Corrsponding uthor. Tl.: + 919774596933. E-mil ddrss: strups@yhoo.om. 08
Fig. 1: Fors ting on rtining wll soil wdg systm during ti stt of quilibrium A shmti digrm of sismi ti rth prssur is shown in th fig.1. r rigid rtining wll of hight supporting -Φ bkfill of unit wight γ, unit ohsion, unit dhsion, ngl of wll frition δ, ngl of soil frition Φ, rtining wll inlintion ngl α is shown. On th top of th bkfill surhrg lod of intnsity q pr unit lngth is ting. At ny stg of rthquk (hing sismi lrtion offiints k h nd k during ti stt of quilibrium, if th plnr wdg surf BD gnrts n ngl θ with th rtil, thn th fors ting on th wdg systm s shown in Fig.1, P nd R bing th for on th rtining wll nd rtion offrd by th rtind rth on th sliding wdg ABD t th f BD rsptily. Th othr fors r totl ohsion C = sθ, totl dhsion C = Sα, wight of wdg, W = {γ (tnθ+tnα}/, surhrg lod, Q = q (tnθ+tnα, horizontl inrti for = (W+QK h nd rtil inrti for = (W+QK. Applying th quilibrium onditions, = 0 nd V = 0 w gt rsptily, ( φ + θ + tnθ tn = ( W Q k h ( φ + θ + + = ( W + Q( k P os( α + δ R os α + P sin( α + δ + Rsin 1± On simplifition of Eqn 1 nd substituting th lus of C, Q, W t. w gt, q (tnθ + tnα P sin( α + φ + δ + θ = γ + k os( φ + θ ψ sθ os α + φ + θ s ( α Rpling (γ+q/ by γ, Eqn 3 n b writtn s, Substituting P = γ k = n nd (tnθ + tnα os os γ k = m ( φ + θ ψ ( α + φ + θ sin sα ( α + φ + δ + θ γ k sθ γ k γ k [ sin( α + θos ( ( φ + θ ψ n osα m osθ os( α + φ + θ ] 1± k sin( α + φ + δ + θ osθ osα P = γ (5 whih n lso b writtn s P = γ k k (6 whr, [ sin( α + θ os( φ + θ ψ n osα m osθ os( α + φ + θ ] k = (7 sin α + φ + δ + θ osθ os ( α In Eqn 7, ll th trms r onstnt xpt θ. On optimizing this offiint for sismi ti rth prssur w gt th lu of θ whih is rprsntd hr s θ nd gin by Whr ( r + s s + t + t s 1 θ = os (8 ( s + t ( ψ + δ osδ + t r r = sin m (9 (1 ( (3 (4 09
3. Prmtri Study ( α + φ + δ s = n osα os + m osδ + sin( φ ψ os(α + φ + δ + sin( φ + δ os( φ ψ (10 t = osα sin( α + φ + δ [ sin( φ ψ + n ] (11 Prmtri is don to lrify th ffts of diffrnt soil nd wll prmtrs on th rition of sismi ti rth prssur offiint K.Fig.. shows th rition of sismi ti rth prssur offiint (K with K h for diffrnt lu of Φ. From th plot it is lr tht inrs in Φ drss th mgnitud of sismi ti rth prssur offiint K but inrs in sismi lrtion offiint K h inrss th mgnitud of sismi ti rth prssur offiint K. Fig.3. shows th rition of sismi ti rth prssur offiint (K with K h for diffrnt lu of δ. From th plot, it is sn tht K drss with inrs in δ from Φ/ to 0. But for inrs in δ from φ/ to φ, K rmins onstnt upto rtin ll of K h = 0.1 thn inrss with inrs in K h. Fig.4. shows th rition of sismi ti rth prssur offiint (K with K h for diffrnt rtio of K /K h. From th plot, it is lr tht K is onstnt upto rtin ll of K h =0.15 pproximtly ftr tht inrs in K /K h rtio inrss th mgnitud of sismi ti rth prssur offiint K. Fig.5. shows th rition of sismi ti rth prssur offiint (K with K h for diffrnt lus of unit ohsion. From th plot, it is sn tht ohsion drss th mgnitud of sismi ti rth prssur offiint. For xmpl, for K h = 0.4, du to inrs in ohsion from 0 to 10 KN/m nd 0 to 0 kn/m, sismi ti rth prssur offiint K drss by 7.78% nd 44.5% on = 0 lu. Fig.6. shows th rition of sismi ti rth prssur offiint (K with K h for diffrnt rtio of /. Thr is ry nominl drs in sismi ti rth prssur offiint du to th 10
inrs in / rtio. Th rt of drs gin boms lssr for highr lu of K h. Fig.7. shows th rition of sismi ti rth prssur offiint (K with K h for diffrnt lu of loding q ffts signifintly th mgnitud of k. Fig.8 shows th rition of sismi ti rth prssur offiint (K with K h for diffrnt lu of unit wight. From th plot, it is sn ffts signifintly th mgnitud of k. K inrss with th inrs in th lu of γ. For xmpl t K h = 0., du to hng in γ from 10 to 0 KN/m 3, K inrss by 30.0% on γ = 10 KN/m 3 lu. Fig.9 shows th rition of sismi ti rth prssur offiint (K with K h for diffrnt hight of rtining wll. From th plot, it is sn tht hight of th rtining wll ffts signifintly th mgnitud of K. For smllr hight of rtining wll fft of K h is smll. Fig.10 shows th rition of sismi ti rth prssur offiint (K with K h for diffrnt wll inlintion ngl (α. From th plot, it is sn tht th fft of wll inlintion ngl is ry prominnt ftor for th dtrmintion of sismi ti rth prssur offiint (K. In th s of luting sismi ti rth prssur th ritil wdg ngl is th mximum ngl md by th filur surf. Th wdg ngl is prsntd grphilly in Fig.11. for diffrnt lu of φ. θ drss with th inrss in th lu of φ whih mns lssr prtiiption of soil mss in ibrtion du to inrs in Φ. 4. Comprison of Rsults Tbl 1 shows th omprison of rsults s obtind from prsnt with Shrm nd Ghosh 010. Tbl. 1: Comprison of th rsults obtind from prsnt with Shrm nd Ghosh'010 [Φ = 0, δ = Φ/3, γ = 18kN/m3, q = 15 KN/m, = 10 m, i= 0, α=30 ] Vlu of ohsion nd dhsion Shrm nd Ghosh(010 K h =0, K =0 K h =0.1, K =0.05 K h =0., K =0.1 Shrm nd Ghosh(010 Shrm nd Ghosh(010 = = 0.6 0.569 0.698 0.663 0.88 0.81 10 KN/m = = 0.50 0.395 0.578 0.467 0.695 0.58 0 KN/m 11
5. Conlusion Th prsnt dsribs n nlytil formultion for th offiint of totl ti for on th bk of rtining wll supporting -Φ bkfill onsidring simultnous tion wight, surhrg, dhsion nd ohsion to gt singl ritil wdg ngl. Dpnding on th dlopd formultion, thorough prmtri is don for th rition of diffrnt soil nd wll prmtrs. From th bsis of prmtri, it is sn sismi rth prssur offiint shows n inrs rltion with th ngl of soil intrnl frition, ohsion, / rtio. On th othr hnd, it inrss with th inrs in th lu of K /K h rtio, surhrg loding, unit wight of bkfill mtril. Th fft of K is grtr for high rtining wll nd it inrss du to hng of wll inlintion from ngti to positi. 6. Rfrns [1] Coulomb, C. A. (1773, Essi sur un pplition ds rgls ds mximis t minimis qulqu problms d sttiqu rltifs 1 rhittur, Mmoirs d Admi Roy. Prs. Dirssnts.7. [] Mononob, N. nd Mtsuo,. (199, On th Dtrmintion of Erth Prssur during Erthquks, Prodings, World Engg. Confrn, Vol. 9, 176 p. [3] Okb, S. (196, Gnrl Thory of Erth Prssur, J. of th Jpns Soity of Ciil Enginrs, Tokyo, Jpn, 1(1. [4] Srn, S. nd Gupt, R. P. (003, Sismi Erth Prssur Bhind Rtining Wlls, Ind. Goth., 33(3, 195-13. [5] Prksh, S. nd Srn, S. (1966, Stti nd dynmi rth prssurs bhind rtining wlls, Pro., 3 rd Symposium on Erthquk Enginring, Unirsity of Roork, Roork, Vol. 1, pp. 77-88. [6] Srn, S. nd Prksh, S. (1968, Dimnsionlss Prmtrs for Stti nd Dynmi Erth Prssur Bhind Rtining Wlls, Indin Gothnil J., 7(3, 95 310. [7] Shukl, S. K., Gupt, S. K. nd Sikugn, N. (009, Ati rth prssur on rtining wll for Φ soil bkfill undr sismi loding ondition, J of Gothnil nd Gonironmntl Enginring, Vol. 135, No.5. 1