PSEUDO-STATIC PASSIVE RESPONSE OF RETAINING WALL SUPPORTING c-φ BACKFILL

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1 IJET: Iteatoal Joual of eeach Egeeg ad Techology ISSN: PSEUDO-STATIC PASSIVE ESPONSE OF ETAINING WALL SUPPOTING c-φ BACKFILL Sma Ghoh ad Sume Deb Atat Pofeo, PG tudet, Cl Egeeg Depatmet, Natoal Ittute of Techology Agatala, Tpua, Ida, Abtact Pae etace a gfcatly mpotat facto fo ucceful deg ad pefomace of aou tuctue le acho, bulhead, etag wall etc. Seeal aalytcal method hae bee toduced tme to tme to pedct the pae etace fo etag wall uppotg ol a the bacfll. Mot of thee method fo the aaly ae baed o lea falue cteo. Wheea; expemetal etgato, theoetcal aaly ad faled tuctue hae dcated that the uptue uface uppoed to be olea fo the mot pactcal eomet. Thu, the aumpto of plaa ldg uface uppoed to udeetmate the lateal eath peue o the acte de, whch may mae etag wall uatfactoly deged at the pae de fo uppot depedg o eath peue. Fo th eao, the olea aalye wee toduced the eath peue theoe. The methodologe fo olea aaly ude emc loadg codto ae motly baed o the aumpto of log pal falue uface. Emet eeache hae pedcted the falue uface to be a combato of log pal ad taght le. I th pape a effot ha bee made to dee the aalytcal expeo of pae eath peue coeffcet o the etag wall fom the c- bacfll ubjected to both hozotal ad etcal emc coeffcet. The oluto ha bee caed out by ug Hozotal Slce Method HSM ad lmt equlbum pcple to geeate a o-lea falue uface. Peudo-tatc appoach ha bee ued to deteme the emc pae eath peue. Geealzed equato ha bee deeloped to fd the oluto. eult hae bee pepaed tabula fom codeg aato of paamete. The eult hae duly bee compaed wth peou tude to jutfy the peet aaly. Detaled paametc tudy ha bee made fo the aato of dffeet paamete le agle of teal fcto Φ, agle of wall fcto δ, wall clato agle α, Hozotal ad etcal emc coeffcet h ad, coheo c, adheo c a ad heght of etag wall H. Idex Tem:- Peudo-tatc, emc pae eath peue, c-φ bacfll, gd etag wall, Wall clato, olea falue uface *** INTODUCTION The pae etace efe to a codto whch eable the etace of a ma of ol agat the moemet of the tuctue. The cocept ey mpotat fo the tablty of aou tuctue le acho, bul head ad alo fo beag capacty of foudato etc. I commo pactce, the total tatc pae eath peue o foce fom ol bacfll calculated ug the method baed o ae 857 o Coulomb 776 aalytcal expeo. But, etag wall ae expoed to the exteme ufaoable effect of eathquae ad t tog dyamc wae. The ey ft expeo fom Oabe 96 ad Mooobe-Matuo 99 aaly ha poded the oluto fo dyamc eath peue codeg the wall bacflled by Φ atue of ol. They exteded Coulomb wedge 776 theoy fo ealuatg dyamc eath peue by copoatg the emc acceleato a eta foce. Kuma ad Subba ao 997 adopted a method of lce to pedct the pae eath peue co-effcet. Ghoh ad Segupta ad Shama ad Ghoh hae uggeted eetal oluto fo c-φ atue of bacfll ude emc loadg codto. Thee aalye ae maly baed o lea atue of falue uface. Tezagh 943 ha ge a oluto by codeg log pal falue fo the aaly of lateal eath peue to how the oleaty of falue uface. The log pal method wa adopted by Kuma, whee the pae eath peue co-effcet fo a cled etag wall ha bee computed by tag the falue uface a a combato of a logathmc pal ad a taght le. Subba ao ad Choudhuy 5 aalyzed the emc eath peue ol ug the lmt equlbum method baed o peudo-tatc appoach ad codeg the effect of coheo c ol. Wheea, Azad et. al. 8 ad Ghaba ad Ahmadabad hae ge the oluto by codeg the Hozotal Slce Method wth lea d of falue uface. The pae etace fom coheole bacfll ha bee aalyzed by Choudhuy ad Nmbala 5 codeg the cocept of phae dffeece due to fte hea wae popagato ug peudo-dyamc method. Fom the eale tude, t eeal that pecally, cae of pae codto, o-lea falue uface geeate moe acceptable oluto compao to lea falue uface Volume: Iue: 3 Ma-3, 54

2 IJET: Iteatoal Joual of eeach Egeeg ad Techology ISSN: aalye. Theefoe, th tudy, a attempt ha bee made to geeate a o-lea falue uface. To do th aaly, Hozotal Slce Method ued.. ANALYTICAL SOLUTION C = Coheo actg o the falue uface. C a = Adheo actg o the wall uface. h = Hozotal emc coeffcet. = Vetcal emc coeffcet. Fo the aaly, let u code a etag wall cled at a agle, α wth the etcal a how Fg.. The wall of heght, H eta a hozotal c-φ bacfll ad the falue uface of the etag wall codeed to be o-lea a how the fgue. The falue uface mae the agle of θ wth the etcal at bottom ad θ wth the etcal at the top a how Fgue. P C a δ α W ± V H V W h θ C ΔH SLICE - SLICE - Ѳ V - H - H C a Pp δ SLICE - Ѳ +Ѳ W h ψ W± V Φ C H P C a δ α W K h W ±K V H V θ +- θ C ΔH SLICE- α Ѳ LAYE - Fg. Batteed face etag wall ude pae peudo-tatc tate of equlbum C a V - H - W h C The falue wedge dded to umbe of lce wth equal thce of ΔH a how Fg.. The aumpto fo aou paamete elated to lce hae bee detaled Fg.. The ate of chage of clato of falue uface wth the etcal θ to θ ha bee aumed a θ = {θ ~ θ / - }. Fee Body Dagam of etag wall-bacfll ytem ude pae peudo-tatc tate of equlbum ha bee elaboated Fg.. P δ W ± V α θ SLICE - Fg.: Showg the foce actg o wedge lce dug pae tate of equlbum << ΔH The foce actg o the wall ha bee calculated by codeg the followg paamete: H -, H = Hozotal hea actg o the top ad bottom of the th lce. W = Weght of the falue wedge of th lce. V -, V = Vetcal load UDL o top ad bottom of th lce. Φ = The agle of teal fcto of ol. P = Pae eath peue o th lce. = The eacto of the etaed ol o th lce. δ = The agle of wall fcto. 3. DEIVATION OF FOMULATIONS CONSIDEING PASSIVE STATE OF EQUILIBIUM Applyg the foce equlbum codto fo t lce fom Fg., we ca ole the equato the followg patte: H ; Volume: Iue: 3 Ma-3, 55

3 IJET: Iteatoal Joual of eeach Egeeg ad Techology ISSN: P co co ta ta c ca co co {ta ta... ta ta c ta ta } V ; P ta ta c co ca co co co Solg thee equato ad, we get, [{ta ta ta co } N co co M co co ta {ta ta ta N ta ta }] PP Whee, h 3 h ta 4 I the peet tudy N ad M Value hae bee toduced fo the aaly of lce, whee N = H /ΔHN c 5 M = H /ΔHM c 6 Whee, N c = c / γh 7 M c = c a / γh 8 Applyg the ame pocedue fo d lce, we get, P P [{3ta ta ta co } N co M co co co ta {ta... ta ta ta ta N ta ta }] Smlaly, fo th lce, we get, H ; P co {ta ta } c ca co co V ; co {[ ta ta m ] m ta ta c ta ta } P ta ta c co c co h 9 a co co Volume: Iue: 3 Ma-3, 56

4 IJET: Iteatoal Joual of eeach Egeeg ad Techology ISSN: Volume: Iue: 3 Ma-3, 57 ta ta ta ta ta co co co co co ta ta ta P N K M N K P Thu, Total pae etace of the bacfll ca be tated a, P p = P p +P p +P p3 + +P p 3 Now the geealzed equato fo th lce ca be oted out a follow, H ; } ta ta ta ta ta ta ta { co co } ta {ta co co m a h c m c c P 4 V ; co co co co ta ta a c c P 5 Solg the aboe equato 4 ad 5, the geealzed equato fo th lce ca be fomulated a follow: } ta ta { } ta ta ta ] ta {[ ta co co co co co ta ta ta m P N m M N P 6 The codto to ue Eq. 6 at, =, we hae to tae, ta m 7 Fom all the aboe equato, the pae eath peue coeffcet ca be mplfed a, H P p p 8

5 IJET: Iteatoal Joual of eeach Egeeg ad Techology ISSN: ESULTS AND DISCUSSIONS O optmzato of p wth epect to θ ad θ, we get the emc pae eath peue co-effcet whch deoted hee a K p. Lt of alue obtaed o optmzato hae bee peeted tabulated fom heewth Table- to Table-8. Table-: Pae eath peue coeffcet K p fo N c =., h =. δ M c = = h/ α=- α= α= + α= - α= α= / / / N c/ N c N c/ N c N c/ N c N c/ N c N c/ N c N c/ N c N c/ N c N c/ N c N c/ N c Hee, a detaled paametc tudy ha bee coducted to fd the aato of emc pae eath peue co-effcet wth a wde age of aato of paamete le agle of teal fcto, agle of wall fcto δ, wall clato agle α, coheo c, adheo c a, emc acceleato h,, ad the heght of etag wall H. The alue hae bee optmzed fo the th lce codeg pae peudo-tatc tate of equlbum. Vaato of paamete codeed ae detaled below: =, 3 ad 4 ; δ =, Φ/ ad Φ; α = +, ad - ; h =,. ad.; =, h /, h ; N c =.,.; M c =, N c /, N c ; H = 5m, 7.5m ad m. Table-: Pae eath peue coeffcet K p fo N c =., h =. δ M c 3 4 / / / = h α=- α= α= N c / N c N c / N c N c / N c N c / N c N c / N c N c / N c N c / N c N c / N c N c / N c Volume: Iue: 3 Ma-3, 58

6 IJET: Iteatoal Joual of eeach Egeeg ad Techology ISSN: Table-3: Pae eath peue coeffcet K p fo N c =., h =. Table-4: Pae eath peue coeffcet K p fo N c =., h =. = = h/ δ M c = h α=- α= α=+ δ M c α=- α= α= + α= - α= α= N c/ N c / N c N c / N c / / N c/ N c N c N c / N c/ N c N c N c / N c/ N c / / N c N c/ N c N c/ N c N c/ N c N c/ N c N c/ N c / / N c / N c N c / N c N c / N c N c / N c N c / N c Volume: Iue: 3 Ma-3, 59

7 IJET: Iteatoal Joual of eeach Egeeg ad Techology ISSN: Table-5: Pae eath peue coeffcet K p fo N c =., h =. Table-6: Pae eath peue coeffcet K p fo N c =., h =. δ M c α=- α= = = h/ α= + α= - α= α= + = h δ M c α= - α= α= N c / N c/ N c N c / Nc/ / Nc/ N c N c N c / N c/ N c N c N c / N c/ N c N c / N c / / N c/ N c N c N c / N c/ N c N c N c / / N c/ N c N c/ N c / N c N c / N c N c / N c N c/ N c Volume: Iue: 3 Ma-3, 6

8 IJET: Iteatoal Joual of eeach Egeeg ad Techology ISSN: Table-7: Pae Eath peue coeffcet K p fo N c =., h =. Table-8: Pae Eath peue coeffcet K p fo N c =., h =. = = h/ δ M c α= - α= α= + α= - α= α= N c/ N c δ / M c = h α= - α= α= N c / N c N c / N c / N c/ N c N c / N c/ N c N c N c / N c N c/ / N c / / N c N c/ N c N c / N c N c N c / N c/ N c N c/ / N c N c / N c N c N c / N c / N c/ N c N c/ N c Effect of Wall Iclato Agle α Fg.3 how the aato of pae eath peue coeffcet wth epect to ol fcto agle Φ at dffeet wall clato agle α= -,, fo N c =., M c =N c, δ = Φ/, h =. ad = h /. Fom the plot, t ee that the magtude of emc pae eath peue co-effcet K p deceae wth the ceae wall clato agle α. Volume: Iue: 3 Ma-3, 6

9 IJET: Iteatoal Joual of eeach Egeeg ad Techology ISSN: Effect of Sol Fcto Agle Fg.5 how the aato of acte eath peue coeffcet K p wth epect to wall clato agle α fo dffeet ol fcto agle at N c =., M c =N c, h =., = h /. The ceae clato mpog geate amout of bacfll ol, thu the pae etace gettg educed. Fo example, at =, δ=φ/ ad h =., = h /, N c =., M c =N c, the magtude of K p.966 at α = whch educe to K p =.599 at α = +. Aga, at = 3, δ = Φ / ad h =., = h /, N c =., M c =N c, the magtude of K p at α = - whch deceae upto K p = 3.8 at α =. 4. Effect of Wall Fcto Agle δ Fg.4 how the aato of pae eath peue coeffcet wth epect to ol fcto agle at dffeet Wall fcto agle δ=, /, fo N c =., M c =N c, α=, h =., = h /. It obeed that the ceae the alue of ceae the pae etace. The eao behd that the elf etace of ol ceae fo hghe alue of. 4.4 Effect of h ad Fg.6 how the aato of pae eath peue coeffcet K p wth epect to etcal emc acceleato coeffcet fo h =.,.,.3 at = 3, δ= /, α = +, N c =., M c =N c ad = h /. Fom the plot, t ee that due to the ceae δ, pae peue co-effcet K p ceaed. The fcto betwee wall ad ol ceag the pae etace. Fo example, at = 3, α =+, N c=., M c =N c, h =. ad = h /, the magtude of K p ceae fom. to.93 fo δ = / oe δ =. Aga, the alue ceaed upto K p = 4.4 fo δ = Φ wth all othe codto emag uchaged. Fom the fgue, t ee that the magtude of emc pae eath peue co-effcet K p deceaed due to the ceae hozotal emc acceleato h. Fg.7 how the aato of pae eath peue coeffcet K p wth epect to ol fcto agle fo dffeet alue of h at Volume: Iue: 3 Ma-3, 6

10 IJET: Iteatoal Joual of eeach Egeeg ad Techology ISSN: = h /, α = +, δ=/, N c =. ad M c =N c. Wth the ceae the alue of, the pae etace ceae. Fo example, at = 3, δ = Φ/, α = +, N c =., M c =N c ad = h / the magtude of K p deceaed fom 3.67 to.735 fo h =. oe h =.. Fg.9 how the aato of pae eath peue coeffcet K p wth epect to ol fcto agle Φ at dffeet alue of N c fo M c =N c, δ = Φ/, h =. ad = h /. Fo the alue of M c beg, N c / ad N c at N c =., δ= /, h =., = h / ad α = +º the alue of K p gadually ceae wth the ceae of N c alue. Aga fo, =, the alue of K p ae.87 ad.48 fo h =. ad h =. epectely. Fg.8 Show the aato of pae eath peue coeffcet K p wth epect to ol fcto agle fo dffeet alue of at h =., α =, δ= / N c =.ad M c =N c. Coheo ceae the temolecula attacto, thu the pae etace alo ceae. Fo example, at Φ =3, M c = N c /, δ= /, h =., = h / ad α = + the alue of K p ae.547, ad.663 epectely fo N c =. ad.. Fg. how the aato of pae eath peue coeffcet K p wth epect to ol fcto agle Φ at dffeet alue of M c fo N c =., δ=φ/, h =. ad = h /. Fom the plot, t ee that due to the ceae K, the pae peue co-effcet K p gog to be deceaed. Fo example, at = 4, δ = /, α = +, N c =., M c =N c ad h =., the magtude of K p 4.7 at = h / whch educed upto K p = 4.5 fo = h. A the emc acceleato ceae, the dtubace bacfll ol ad wall alo ceae, thu the pae etace of the bacfll ol educe. 4.5 Effect of Coheo c ad Adheo ca Fo example, at Φ =, N c =., δ= /, h =., = h / ad α = + the alue of K p.3 fo M c =N c /, wheea the alue ceae upto.9 fo M c =N c all othe codto emag uchaged. Thu, t obeed that the ceaed cohee ad adhee popety of ol mateal ehace the emc pae etace of the etag wall. Volume: Iue: 3 Ma-3, 63

11 IJET: Iteatoal Joual of eeach Egeeg ad Techology ISSN: Effect of Heght H Fg. how the aato of pae eath peue coeffcet K p wth epect to ol fcto agle h fo dffeet heght at N c =., M c =N c, δ = Φ/, h =. ad = h /. The compaate eult hae bee put codeg the heght of wall to be 5m, 7.5m ad m. Fom the fgue t obeed that the alue of K p gadually deceae wth ceae heght of etag wall. The falue le lea fo Ghoh ad Segupta aaly. Fo example, at α =+ fo Φ =3º, δ= Φ/, N c =., M c =N c ad h =., = h / the alue of falue uface clato wth the etcal at bottom 63 ad agle at the top 7, wheea; at α = - the alue of the clato of falue uface wth etcal at bottom 74 ad agle at the top 86. It ee that the clato of the falue uface wth etcal educe wth the ceae the wall clato agle whe the clato of the wall away fom the bacfll. 5. COMPAISON OF ESULTS Fg.3 how the compao of eult fo aato of pae eath peue coeffcet wth epect to ol fcto agle Φ at α = +, δ= /, h =. ad = h /, N c =. ad M c =N c. It alo ee that the magtude of K p ceaed wth the ceae ol fcto agle Φ fo a cotat heght of etag wall. Hghe etag wall uppot geate amout of bacfll ad thu the pae etace uppoed to deceae. 4.7 Noleaty of Falue Suface Fg. how the compao betwee falue uface of bacfll fo wall clato, α = + at = 3, δ= /, h =. ad = h /, N c =. ad M c =N c. It obeed that the falue uface culea atue fo peet aaly. The peet alue ae compaable wth extg eath peue theoe. Hee, the gaph plotted to compae the eult obtaed fom peet tudy wth the eult of Ghoh ad Shama aaly. The compao of the alue how that the peet alue of K p aoud 5-% malle tha the alue of Ghoh ad Shama aaly. CONCLUSIONS I th tudy, the Hozotal Slce Method of aaly wth peudo tatc appoach ha bee codeed to deteme the emc pae etace of the etag wall wth o-lea falue uface. The peet tudy how that the o-leaty of the falue uface affectg the ealuato of emc pae eath peue. It alo oted that the atue of the falue uface chage wth the chage wall clato agle ad the hape of the falue uface aggg atue. The detaled paametc tudy how that the eult ae compaable to othe utable method etablhed eale. The peet tudy how that the emc pae eath peue co- Volume: Iue: 3 Ma-3, 64

12 IJET: Iteatoal Joual of eeach Egeeg ad Techology ISSN: effcet K p ceae due to the ceae wall fcto agle δ, ol fcto agle Φ, coheo c ad adheo c a ; at the ame tme the alue of K p deceae wth the ceae wall clato α, wall heght H, ad emc acceleato h,. The clato of the falue uface wth etcal ceae wth the deceae wall clato α, wall fcto agle δ, ol fcto agle Φ ad heght of etag wall H. Wheea, the clato of the falue uface wth etcal deceae wth the ceae wall clatoα, ol fcto agle Φ, coheo c, adheoc a ad wall fcto agle δ. The geeato of aggg atue of uptue uface pae codto howg culea epoe the detemato pae eath peue coeffcet actg o the etag wall. NOTATIONS Φ = Sol fcto agle. δ = Wall fcto agle. α = Wall clato agle wth the etcal. P p = Pae eath peue. h = Hozotal emc co-effcet. = Vetcal emc co-effcet. = Sol eacto foce. γ = ut weght of ol. K p = Pae eath peue coeffcet c = coheo c a = adheo EFEENCES: []. Azad, A, Shahab Yaob, S, Pa, A. 8, Acte Peue Dtbuto Htoy Behd gd etag Wall, Sol Dyamc ad Eathquae Egeeg []. Choudhuy, D ad Nmbala, S, 5, Semc Pae etace by Peudo-dyamc Method, Geotechque; 559: [3]. Coulomb, C.A. 776, Ea Su Ue Applcato De Maxm et Mm a Queque poblem De Statque elatfa Achtectue, Nem. D. Sa.Acad, Sc.Vol.7. [4]. Ghaba, A ad Ahmadabad, M., Peudo- Dyamc Acte Eath Peue Aaly of Icled etag Wall Ug Hozotal Slce Method, Taacto A: Cl Egeeg Vol. 7, No., pp. 8-3 Shaf Uety of Techology. [5]. Ghoh, S. ad Segupta, S., Fomulato of Pae etace o o etcal etag wall bacflled wth c-φ, Cl ad Eometal eeach ISSN Pt ISSN 5-54 Ole, Vol, No.,. [6]. Ghoh, S. ad Shama,. P., Peudo-Dyamc Ealuato of Pae epoe o the Bac of A etag Wall Suppotg c-φ Bacfll, Geomechac ad Geoegeeg: A Iteatoal Joual, Vol. 7, No., Jue, 5. [7]. Kuma J, Subba ao K. S, 997, Pae Peue detemato by method of Slce, It J Num Aal Method Geomech USA : [8]. Kuma, J., Semc Pae Eath Peue Coeffcet fo Sad, Ca. Geotech. J., Ottawa, 38, pp: [9]. Mooobe, N. ad Matuo, H. 99, O the Detemato of Eath Peue Dug Eathquae Poc. of the Wold Egeeg Coge, Toyo, 9, pp []. Oabe, S. 96, Geeal Theoy of Eath Peue, J. Japa Soc. Cl Eg.,. []. ae, W. J. M. 857, O the Stablty of Looe Eath, Phl. Ta. oyal Socety Lodo. []. Shula, S. K ad Habb, D., Dyamc Pae Peue fom c- Sol Bacfll, Sol Dyamc ad Eathquae Egeeg [3]. Subbaao, K. S, ad Choudhuy, D. 5, Semc Pae Eath Peue Sol, Joual of Geotechcal ad Geoeometal Egeeg, ASCE 5; 3; 3-5. [4]. Tezagh, K, 943, Theoetcal Sol Mechac : Joh Wley & So, New Yo, 5 p. BIOGAPHIES: Sma Ghoh peetly wog a a Atat Pofeo at NIT Agatala, INDIA a cotet Gold medalt BE Cl fom Tpua Egeeg College ow NIT Agatala 994 ad M. Tech Geotechcal Egeeg fom IIT, ooee. She ha completed he PhD Geotechcal Egeeg ad became the ey ft peo to atta the PhD Degee ce the cepto of PhD coue at NIT Agatala. She ha a wde age of publcato woldwde Iteatoal ad Natoal Joual cludg ASCE, SPINGE, ELSEVIE, TAYLO & FANCIS, EJGE, IGJ etc. He peet eeach wo clude emc epoe of etag wall, eathquae egeeg, emc beag capacty ad mcozoato. Sume Deb a fal yea M. Tech tudet of Geotechcal Egeeg at NIT Agatala dog the wo o Semc epoe of etag wall ad watefot etag wall. Apat fom th, he a Egee Cl eg ude ual Deelopmet Depatmet of Goemet of Tpua, INDIA fo the lat te yea. Volume: Iue: 3 Ma-3, 65