Ultimate lateral load resistance of laterally loaded pile

Transcription

1 Ultimat latral load rsistanc of latrally loadd pil Md. M. Rahman Assistant Profssor, Dpartmnt of Civil Enginring, RUET, Rajshahi, Bangladsh Md. R. arim, A. L. Baki & D.. Paul Lctr, Dpartmnt of Civil Enginring, RUET, Rajshahi, Bangladsh ABSTRACT: Svral mthods ar availabl for prdicting ultimat latral load rsistanc of latrally loadd pil. Ths mthods oftn produc significantly diffrnt ultimat latral rsistanc. This maks it difficult to slct an appropriat mthod in dsigning/prdicting ultimat latral rsistanc of pil. This papr prsnts a rviw of two diffrnt mthods; Myrhof and Patra & Pis for prdicting latral rsistanc of pil. Thn, th prdictd ultimat latral rsistancs by ths two mthods ar compard with th xprimntal rsults. It is found that Myrhof s mthod givs bttr prdiction for singl pil with smallr L/d ratio whras Patra & Pis mthod givs bttr prdictions for pil groups with highr L/d. Thus, non of ths mthods can b applicabl univrsally for all possibl conditions. Also th paramtric study on ultimat latral rsistanc rvald that lngth to diamtr ratio, pil spacing, pil configation in a pil group ar important paramtrs for prdiction of latral load rsistanc. 1 INTRODUCTION Thr ar svral approachs ar availabl in th litrat to stimat latral load rsistanc of pil in sand and clay (Broms 1964; Myrhof t al. 1981; Myrhof and Ranjan 197; Myrhof and Sastry 1985; Myrhof and Yalcin 1984; Sastry 1977; Sastry and Myrhof 1986; Zhang t al. 5). Also som simplifid mthods ar proposd by Myrhof t al. (1988) and Patra & Pis (1) for cohsionlss soil. Howvr, ths mthods oftn produc significantly diffrnt ultimat latral load rsistanc valu (Zhang t al. 5). This maks it difficult to slct appropriat mthod whn dsigning latrally loadd pil in cohsionlss soil. A comparativ study has bn mad in this papr btwn Mayrhof and Patra & Pis mthods and xprimntal rsults with th intnsion that it could add som valu on th undrstanding of practicing nginrs. Also a paramtric study is don on ultimat latral load rsistanc. Thy ar discussd in coming sctions. ULTIMATE LATERAL LOAD RESISTANCE Th simplifid mthods proposd by Myrhof t al. (1988) and Patra & Pis (1) has bn brifly rviwd in this sction. Ths mthods ar approximat with considrabl assumptions. Thy ar discussd in coming subsctions..1 Myrhof s mthod Th ultimat latral rsistanc of rigid pil, is xprssd by Myrhof t al.(1981) as =.1γdL (1) b Whr γ is avrag unit wight of sand; d is th diamtr of pil; L is mbddd lngth of pil; b is cofficint of nt passiv arth prss on pil using an avrag angl of skin friction δ = ϕ/3. Whr ϕ is th angl of intrnal friction. Howvr th ultimat latral load rsistanc of flxibl pil was prsntd by Myrhof t al. (1988) as =.1γdL () b Whr L is th ffctiv mbddd lngth of flxibl pil. Myrhof and Yalcin (1984) suggstd that if rlativ stiffnss ratio rs is lss than 1-1 to 1 - thn th pil can b considr as flxibl pil. Howvr, th rlativ stiffnss, rs can b prsntd as E I E L = 4 (3) rs p p h Whr E p is modulus of lasticity of pil; I p is momnt of inrtia of pil; E h is horizontal soil modulus at pil tip; L is mbddd lngth of pil. Myrhof t al. (1988) rportd that L /L has an approximat functional rlationship with rlativ stiffnss rs and it can b prsntd as

2 L L = (4) rs Howvr, Rahman t al. (3) rportd that L /L can b rprsnt by following rlation as L L = (5) rs. Patra & Pis mthod Patra & Pis (1) modifid th Myrhof s quation by multiplying a constant shap factor of 3 with th lin of Broms (1964) = 3.1γdL (6).3 Pil group b Patra & Pis (1) rportd that th ultimat rsistanc of th pil group can b rprsntd by Lg = + P P (7) Whr, Lg is ultimat latral rsistanc of th pil group, is frictional rsistanc on th vrtical plan along th sid of th pil group of width qual to cntr to cntr distanc btwn xtrnal pils and mbddd lngth L and passiv arth prss for th front pil as shown in ig 1..4 Group fficincy Th fficincy of ultimat latral rsistanc of pil group can b xprssd as Lg η = (11) n1n Ls Whr Lg is th ultimat latral capacity of pil group; Ls is th ultimat latral capacity of singl pil; n 1 is th numbr of rows in th pil group and n is th numbr of columns in th pil group. 3 EXPERIMENTATION An xprimntal program was dsignd for th vrification and comparison of th abov mntion mthods. Th dtails of th xprimntal program and matrial proprtis such as sand, pil, pil cap tc. ar givn in following subsctions. 3.1 oundation Rajshahi sand (availabl in north-wst rgion in Bangladsh) is usd as foundation mdium. All modl pil tsts wr don on a concrt tank of on mtr in hight, on mtr in width and on mtr in dpth. Sand had a placmnt dnsity of 95 lb/ft3 or 15kN/m 3 and th angl of intrnal friction was 37.9º. Spcific gravity of th sand usd in th modl tank was 1.8. Lg Lg ig 1. r body diagram of latrally loadd pil group lxibl Wir Pil cap Vrtical Gaug Horizontal Gaug Th frictional rsistanc along th sid of th pil group could b approximatly found as 1 = γ L S S (8) Whr, s is cofficint of arth prss along th sid of th pils group govrning frictional rsistanc [( 1 sinϕ) tanδ ]. Thus, ultimat latral rsistanc of pil group, x1 is [ S +. d ] Lg = γ L s 36 b (9) And th ultimat rsistanc of pil group, x can b xprssd as [ S +. d ] Lg = γ L s 7 b (1) Applid Load, (N) Tank Sand Pil ig. Exprimntal arrangmnt for latrally loadd pil 3. Pil and pil cap Aluminum alloy tub of 19mm outr diamtr and.81mm wall thicknss wr usd as modl pil. To incras th pil wall friction angl, sand was addd around th pil by adhsivs. Th avrag outsid diamtr of th rough pils wr mm. Th mbdmnt lngth-to-diamtr ratios, L/d wr, 3, and 35. Stl plat of.64cm thicknss was usd as pil cap. Th pils wr attachd with th pil cap by scrw. Th dtails of sand and pils proprtis can

3 b found in (Rahman t al. 3). Th pil groups usd in this study had configations of x1 and x. 3.3 Exprimntal procd Th arrangmnt of tst program is shown in ig. Th Loading arrangmnt was mad in such a way that it actd latrally to pil or pil cap. Howvr, it was not possibl to apply continuous loading but load is applid by stpping. To maintain a uniform dnsity all through th tank dpth, sand was placd in th tank from a constant hight of about.5m. Aftr filling th tank, th uppr sfac of sand was lvld and thn th pil was pushd into sand. Pil cap was thn fixd on th pil top with scrw connctions. A 4 hos of rst priod was allowd bfor applying any load on pil stup. Th latral load was applid to th pil cap through a pully arrangmnt with flxibl wir. Th othr nd of th wir was attachd to th loading apron. Load was applid by dad wight ovr th loading pan starting form th smallst with gradual incras in stps. To mas th latral and vrtical dflction dial gaugs with a snsitivity of.1 mm wr usd. Whn stp by stp latral loads wr applid on th pil or pil group, thy wr dflctd in th dirction of th latral load and th dial gaug radings and th corrsponding loadings wr rcordd. 4 RESULTS Th ultimat latral load rsistanc of th pil was workd out by plotting th rcordd data, thus load Vs dflction cv was obtain which was non-linar in nat. Ultimat latral rsistanc of th pil was obtaind from th cv by doubl tangnt mthod (DTM) or th point whr th cv show a gratr dflction without fthr incras in any load. Th dtail can b found in (Rahman t al. 3). Th cvs prsntd in this papr ar only showing th gnral trnds. Th ultimat load rsistanc bhavios of singl pil and th pil group ar prsntd in coming subsctions. 4.1 Singl pil Th ultimat latral load rsistanc of singl pil incrass with incras in L/d ratio as shown in ig 3. Th ultimat load rsistanc of a singl pil for L/d= is about 17N whras 115.N prdictd by Myrhof s mthod and 7N by Patra & Pis mthod. Thus, Patra & Pis mthod dosn t prdict wll for singl pil and th prdiction by Myrhof s mthod is vry closd to th xprimntal obsrvation. Howvr, in highr L/d, Patra & Pis mthod givs bttr prdiction. Th ultimat latral load rsistanc of L/d=35 is about 5N and Patra & Pis mthod prdictd 1.7N whras Myrhof s prdiction dviat by 5N in highr sid. 4. Pil group, x1 Th ultimat latral load rsistanc of pil group, x1 incrass with incrasing L/d as shown in ig 4. It is about 117.N for L/d= and 16N, 5N for L/d=3, L/d=35 rspctivly. Howvr, whn th obsrvd ultimat latral rsistanc is compard with Mayrhof and Patra & Pis mthods, it is found that th ultimat latral load rsistanc prdictd by Patra & Pis mthod givs a bttr prdiction for pil group. Tabl 1. shows th dtaild rsults for L/d=. Tabl 1. Comparison of latral load rsistanc of pil group, x1 with Patra & Pis mthod and obsrvd valu. L/d ratio Spacing (d) Obsrvd rsistanc (N) Thortical rsistanc (N) Pil group, x Th load dflction cv for pil group, x is shown in ig 5. This fig only shows two diffrnt L/ds and it clarly shows that ultimat latral load rsistanc of pil incrass with its L/d ratio. Th ultimat latral load rsistancs ar N and N for L/d= and L/d=3 rspctivly. Howvr, th ultimat latral load rsistancs prdictd by Patra-Pis mthods ar 19N and 8N rspctivly. Again, it indicats that this mthod could bttr and consrvativ prdiction. Applid forc on pil top, (N) L/d=, Singl L/d=3, Singl L/d=35, Singl Dflction on pil top, y (mm) ig 3. Load dflction cv for singl pils for diffrnt L/d ratios.

4 4.4 Effct of pil spacing in group ig 6 shows that th cntr to cntr distanc of pils in a group has strong influnc on th ultimat latral rsistanc of pil; it incrass with incrasing in pils c/c distanc. Howvr, th variation with c/c distanc of pils is not linar. ig 7 shows that th incrmnt of latral rsistanc for 3.d to 4.5d is highr than th incrmnt for 4.5d to 6.d. Applid forc on pil top, (N) S=3.d, L/d=, x1 S=3.d, L/d=3, x1 S=3.d, L/d=35, x Dflction on pil top, y (mm) ig 4. Load-dflction cv for pil group, x1 Applid forc on pil top, (N) S=3.d, L/d=, x S=3.d, L/d=3, x Dflction on pil top, y (mm) ig 5. Load-dflction cv for pil group, x 4.5 Group fficincy Th fficincy of latral load rsistanc for pil group is calculatd by th Equation 11 and thy ar prsntd in ig 7. It shows that th incrmnt of group fficincy for 3.d to 4.5 is maximum and it rducs from 4.5d to 6.d. This trnd is sn in both groups of x1and x. Howvr, it is intrsting to not that group fficincy for th group of x is lss than for th group of x1. Thus, it indicats that pil spacing also vry important for ultimat latral rsistanc of pil. Applid forc on pil top, (N) S=3.d, L/d=, x1 S=4.5d, L/d=, x1 S=6.d, L/d=, x Dflction on pil top, y (mm) ig 6. Th ffct of cntr to cntr distanc btwn pils in group, x1. Efficincy, η (%) x1 x Pil spacing, S (d) ig 7. Variation of pil group fficincy with pil spacing btwn group, x1 and group, x. 5 CONCLUSIONS Th following conclusions ar drawn from th prsnt study: o Th ultimat latral load rsistanc of pil group dpnds on th lngth to diamtr ratio of pil, pil friction angl, pil group gomtry, spacing of pils in a group and sand placmnt dnsity. Th quantitativ and

5 qualitativ influnc of thos paramtrs has bn invstigatd. o Th ultimat rsistanc of pil group incrass with an incras in pil spacing. It has bn found that rsistanc at 3d spacing is lss than that of 4.5d spacing. Again rsistanc at 4.5d spacing also lss than that of 6d spacing. o Group fficincy of pil incrass with an incras in pil spacing. It has also bn found that th fficincy at 3d spacing is lss than that of 4.5d and 6d spacing. o inally, th prdiction by Patra & Pis mthod can giv bttr prdiction for pil groups whras Myrhof s mthod givs bttr prdiction for singl pil. Thus, non of ths can b univrsally usd for th prdiction of latral load rsistancs of pil or pil group. 6 REERENCES Broms, B. B Latral rsistanc of pils in cohsionlss soils. Jonal of th Soil Mchanics and oundations Division, ASCE, 9(SM3): Myrhof, G. G., Math, S.., and Valsangkar, A. J Latral Rsistanc and Dflction of Rigid Walls and Pils in Layrd Soils. Canadian Gotchnical Jonal, 18(): Myrhof, G. G., and Ranjan, G Th baring capacity of rigid pils undr inclind load in sand. I. Vrtical Pils. Canadian Gotchnical Jonal, 9, Myrhof, G. G., Sastry, V., and Yalcin, A. S Latral Rsistanc and Dflction of lxibl Pils. Canadian Gotchnical Jonal, 5(3): Myrhof, G. G., and Sastry, V. V. R. N Baring capacity of rigid pils undr ccntric and inclind loads. Canadian Gotchnical Jonal,, Myrhof, G. G., and Yalcin, A. S Pil capacity for ccntric inclind load in clay. Canadian Gotchnical Jonal, 1, Patra, N. R., and Pis, P. J. 1. Ultimat latral rsistanc of pil groups in sand. Jonal of Gotchnical and Gonvironmntal Enginring, 17(6): Rahman, M. M., Alim, M. A., and Chowdhy, M. A. S. 3. Invstigation of latral load rsistanc of latrally loadd pil in sandy soil. 4th Intrnational Confrnc on Bord and Augr Pils, BAPIV, Ghnt, Blgium, Sastry, V. V. R. N Baring capacity of pils in layrd soil, PhD Thsis, Tchnical Univrsity of Nova Scotia, Halifax, NS. Sastry, V. V. R. N., and Myrhof, G. G Latral soil prsss and displacmnts of rigid pils in homognous soils undr ccntric and inclind loads. Canadian Gotchnical Jonal, 3, Zhang, L., Silva,., and Grismala, R. 5. Ultimat Latral rsistanc to pils in cohsion lss soils. Jonal of Gotchnical and Gonvironmntal Enginring, 131(1):