Effect of soil profile modulus distribution on pile head lateral stiffness

Transcription

1 Proc. 18 th NZGS Geotechnicl Symposium on Soil-Structure Interction. d. CY Chin, Aucklnd Michel Pender University of Aucklnd, New Zelnd eywords: pile hed stiffness, effect of pile shft size, soil modulus distribution with depth, site investigtion dt ABSTRACT The effect of pile shft dimeter nd soil Young s modulus distribution with depth on unrestrined pile hed lterl nd rottionl stiffnesses of long piles is considered. Anlysis of field test dt for lterl lod tests on piles of different dimeters t prticulr sites hd led to the suggestion tht modulus of subgrde rection ppers to increse with incresing pile shft dimeter. This is contrry to the usul understnding tht the modulus of subgrde rection is independent of pile shft dimeter. This puzzle is resolved in the relistion tht only if the soil modulus is constnt with depth is constnt modulus of subgrde rection pproprite. A corollry of the work is tht ccurte estimtes of pile hed stiffness require better thn routine site investigtion dt. Included in the pper is discussion of the effect of the vrition with pile shft dimeter of the unrestrined pile hed lterl nd rottionl stiffnesses for three distributions of soil modulus with depth, s well s the effect of the pile hed moment to sher rtio. 1 INTRODUCTION When pile foundtions re to be constructed it is not uncommon to construct test pile(s) to evlute the cpcity nd lso the stiffness. Sometimes these piles re t reduced scle nd in others they re t prototype scle. There re in the literture only few cse studies in which the lterl pile hed stiffness is mesured on piles of different dimeters t one site. The clssic pper of Terzghi (1955) considered lterl pile stiffness from the point of view of the Winkler spring model of pile-soil interction (constnt stiffness soil-pile springs). The conclusion is tht s the dimeter of the pile increses the coefficient of subgrde rection (units FL -3 ) for the soil decreses linerly with pile shft dimeter nd consequently the modulus of subgrde rection (units FL -2 ) is independent of pile dimeter. As will be seen below n importnt prt of this rgument is tht the ground in which the pile is embedded hs constnt properties with depth. The writer hs been wre of n pprent effect of pile shft dimeter on lterl stiffness of piles since the thesis of Crter (1984) in which published dt from lterl lod testing of piles of differing dimeters t prticulr sites were exmined. Such dt re sprse, but the few cse histories vilble led to the finding tht the modulus of subgrde rection ppers to increse with incresing pile dimeter. The results of the evlution of the initil lterl stiffness of free hed piles re plotted in Fig. 1. Most of the dt from which the points in these digrms were derived re from bck nlysis of the field test dt of Gill (1968), Gill nd Demrs (197), Reese et l (1974), Reese nd Welch (1975), nd Dunvnt nd O Neil (1985). The left prt of Fig. 1 shows tht the constnt modulus of subgrde rection ideliztion does not give the correct modeling for different dimeter piles. A similr observtion is lso mde by Reese nd Vn Impe (21). The dt in Fig. 1 were clculted on the ssumption of constnt modulus of subgrde rection. The filure of this idelistion to model the observed chnge in pile stiffness with chnge in pile dimeter presents something of qundry s simple dimensionl nlysis indictes tht the 1

2 Rtio of predicted to mesured deflection Rtio of predicted to mesured deflection 1.5 b Pile dimeter (m) Pile dimeter (m) Figure 1: vidence of the pprent size effect on pile lterl stiffness: () Unstisfctory modelling when the modulus of subgrde rection is independent of pile dimeter, (b) stisfctory modelling when the modulus of subgrde rection increses linerly with pile dimeter. Terzghi conclusion must be sound. Fig. 1b presents stisfctory modelling of the lterl stiffness of different dimeter piles. This is chieved by incresing the modulus of subgrde rection s the pile dimeter increses. Severl possible explntions were investigted for this puzzling dimeter effect, including three-dimensionl finite element studies to investigte the ction of sher stresses mobilised t the interfce between the pile shft nd surrounding soil, Stywn (2). None of these indicted ny size effect. However, eventully settle simple explntion ws found. Nmely tht if the soil modulus increses with depth, lrger dimeter piles will hve greter lterl stiffness thn one would expect from extrpoltion of lterl lod test dt on smller dimeter piles nd vice vers. It is the purpose of this pper to explin this in more detil. The min vehicle for our explntion is group of expressions for the components of the pile hed stiffness mtrix given by Gzets (1991), which re bsed on numericl clcultion of the response of n elstic pile embedded in n elstic soil. 2 PIL HAD STIFFNSS MATRIX FOR LONG PILS In considering long piles the ctive length concept is useful, Gzets (1991). This is the length of pile shft beyond which deflections nd rottions induced by hed loding re negligible. Intuitively one cn to think of this s the mximum depth which the pile reches into the soil profile to mobilise lterl resistnce. The ctive length depends on the dimeter of the pile shft, the Young s modulus of the pile shft reltive to tht of the soil in which it is embedded, nd the profile of the soil Young s modulus with depth. Gzets gives expressions for the ctive lengths nd the components of the pile hed stiffness mtrix in soil profiles hving constnt modulus, modulus incresing from zero t the ground surfce s the squre root of the depth, nd modulus incresing linerly with depth from zero t the ground surfce. The definition digrms for these three cses re given in Fig. 2 nd Tble 1 gives expressions for the ctive lengths nd components of the pile hed stiffness mtrix. The ctive length equtions in Tble 1 re for dynmic lterl loding, equtions re given elsewhere for the ctive lengths under sttic loding, the vlues obtined re similr to those for dynmic loding. The pile hed stiffness mtrix reltes lterl nd rottionl displcements of the pile hed induced by sher forces nd moments pplied to the pile hed s follows: 2

3 D s sd s =mz z z s = sd z/d z Figure 2: The three soil profile stiffness models used herein. (D pile shft dimeter, sd soil Young s modulus t depth of one pile dimeter.) Tble 1: Components of the pile hed stiffness mtrix for the soil profiles shown in Fig. 1 Model L HH HM MM p 36. Constnt = L = 2D = D.21 =.22D 2.5 =.1D HH s HM s MM s s p 2. Liner = L = 2D.6D.35 HH sd md 3.75 = D =.17 =.15D HM sd MM sd Prbolic = p sd 22. L = 2D =.8D.28 D =.24 =.15D HH sd HM sd MM sd H HH HM u = M MH MM θ (1) where: H nd M re the sher force nd moment pplied to the pile hed, u nd θ re the lterl displcement nd rottion of the pile hed, nd HM = MH. As field testing is usully done on piles with unrestrined heds, the unrestrined pile hed lterl nd rottionl stiffnesses re given by: h 2 = - HH MM HM -e (2) MM H M 2 - HH MM HM = θ - / e (3) HH H M where: h θ e is the unrestrined horizontl stiffness of free hed pile, is the unrestrined rottionl stiffness of free hed pile, is the rtio M/H. 3

4 b 4 3 h 3 2 Liner Squre root 2 Liner 1 Constnt 1 Constnt Figure 3: Pile hed stiffness rtio s function of pile shft dimeter rtio for M/H rtio =.1. (The strting vlue for the curves is 1..) (Sher wve velocity of the constnt modulus soil profile 5 m/sec.) b h Liner Constnt 8 4 Liner Constnt Figure 4: Pile hed stiffness rtio s function of pile shft dimeter rtio for M/H rtio = 1. (The strting vlue for the curves is 1..) (Sher wve velocity of the constnt modulus soil profile 5 m/sec.) 3 XPLANATION Using equtions 2 nd 3 the effect of pile dimeter on pile hed stiffness for the vrious distributions of soil Young s modulus with depth cn be investigted. Pile dimeters between.2 m nd 2. m were considered nd the Young s modulus ws set t vlue for reinforced concrete pile. Two limiting cses for the soil profile stiffness, sher wve velocities of 5 nd 75 m/sec, were used. As only the initil prts of the lod - displcement nd moment - rottion curves re discussed herein, the sher wve velocity is used to chrctise the soil s this gives the soil stiffness tht controls the liner portion t the beginning of the pile lterl response. Assuming vlue of.5 for the Poisson s rtio of the soil, the Young s modulus cn be obtined from the sher wve velocity. For the liner nd prbolic modulus distributions this Young s modulus is for depth of one pile dimeter. With the vrying pile dimeters the prmeters were djusted so tht the modulus distribution with depth ws the sme for ll pile dimeters. It is pprent from equtions 2 nd 3 tht the pile hed stiffnesses depend on the rtio of the sher to moment pplied t the pile hed. We will consider the results with M/H =.1 nd M/H = 1.. 4

5 The unrestrined pile hed lterl nd rottionl stiffnesses re plotted s rtios of the stiffness t given dimeter pile divided by the corresponding stiffness for the smllest dimeter pile. The stiffness rtios re denoted by h nd θ nd the rtio of the dimeter of the current pile to the dimeter of the smllest pile s. In Fig. 3 for dt re for the cse where M/H =.1, nd in Fig. 4 the sme stiffness rtios re plotted for the cse where M/H = 1. Since stiffness rtios re plotted in Figures 3 nd 4 the effect of the sher wve velocity, which is reflected in much lrger stiffness vlues for the piles in the 5 m/sec soil profile, is not pprent s the rtios re very nerly the sme for sher wve velocities of 75 nd 5 m/sec. Figs. 3 nd 4 show tht the unrestrined pile hed rottionl stiffness is more sensitive to pile dimeter thn the lterl stiffness; consequence of the MM terms in Tble 1 being function of D 3, wheres the HH terms depend on D. Figures 3 nd 4 provide the explntion for the pprent pile size effect. The figures show tht s the pile shft dimeter increses the unrestrined pile hed stiffnesses increse for ll three distributions of soil modulus. However, the stiffnesses for the liner nd squre root profiles increse t fster rte thn those for the constnt modulus profile. The modelling on which Fig. 1b is bsed is equivlent to using liner soil modulus distribution with depth. Although the clcultions were bsed on constnt vlue for the modulus of subgrde rection, the increse in modulus with incresing pile dimeter mens, in effect, tht vlue from deeper in the soil profile is used s representtive vlue s the dimeter increses. Thus the puzzle in Fig. 1 is resolved in the relistion tht it ws not pproprite to model the soil profiles in which the piles were embedded s hving constnt modulus of subgrde rection with depth. As explined bove the ctive lengths specified in Tble 1 give n indiction of how fr into the soil profile the pile reches to mobilise lterl stiffness. As the ctive lengths increse with incresing pile shft dimeter, the depth of n equivlent constnt modulus lso increses. The lesson from this is tht if the lterl stiffness of piles is required, more thn cursorily routine site investigtion will be needed to estimte the pile stiffness dequtely. One very well documented nd executed field test cse history, which supports the need for good rther routine soil profile dt, is reported by Ashford nd Juirnrongrit (23). At this site sher wve velocities indicte n upper lyer bout 6 metres deep, with n pproximtely constnt sher wve velocity of 315 m/sec., below which the velocity increses (interestingly SPT dt do not give such cler picture). Reinforced concrete piles.4 m to 1.2 m in dimeter were constructed nd subject to dynmic lterl loding. From the vlues for the nturl periods of these piles the Young s modulus of the soil profile ws estimted. The results indicted tht the chnge in stiffness with pile dimeter could be modelled by ssuming constnt soil modulus with depth. This result is consistent with the clcultion of the ctive lengths for the vrious dimeter piles, using eqution 2 for the constnt modulus soil profile nd pile Young s modulus of 25 GP, ll of which fll within the upper constnt modulus prt of the soil profile. Further discussion of the bove effects is given by Pender et l (27). 4 CONCLUSIONS The following conclusions re reched: (i) The pprent pile size effect on unrestrined pile hed lterl stiffness, highlighted by Crter (1984), Pender (1993) nd investigted further by Prnjoto (2), is consequence of the distribution of soil modulus with depth. If the soil modulus increses with depth, then clcultions bsed on constnt modulus distribution will 5

6 (ii) (iii) underestimte the increse in lterl stiffness s the pile shft dimeter is incresed. This conclusion is bsed on Figs. 3 nd 4. Figs. 3b nd 4b show how the unrestrined pile hed rottionl stiffness increses with pile shft dimeter. As for the lterl stiffnesses, the vlues of the rottionl stiffnesses for the squre root nd liner modulus distributions increse fster thn those for the constnt modulus profile. A corollry of (i) nd (ii) is tht good qulity soil profile dt is impertive for mking relible estimtes of the initil pile hed lterl nd rottionl stiffnesses. The work of Ashford nd Juirnrongrit (21) shows tht sher wve velocity profile gives better indiction of soil stiffness properties thn Stndrd Penetrtion Test vlues. RFRNCS Ashford nd Juirnrongrit (23). vlution of Pile Dimeter ffect on Initil Modulus of Subgrde Rection, Proc ASC, Jnl. Geotechnicl nd Geoenvir. ng. 129, No. 3, Crter, D P (1985). A nonliner soil model for predicting lterl pile response, Mster of ngineering thesis, University of Aucklnd. Dunvnt, T W nd O Neil, M W (1989). xperimentl p-y model for submerged stiff cly, Journl of Geotechnicl ngineering Division, ASC 11, No. GT7, Gzets, G. (1991). Foundtion vibrtions, in Foundtion ngineering Hndbook, 2nd. edition, H- Y Fng editor, Vn Nostrnd Reinhold, Gill, H L (1968). Soil behviour round lterlly loded piles, Technicl Report R-571, Nvl Civil ngineering Lbortory, Port Hueneme, Cliforni Gill, H.L. nd.r. Demrs (197.) Displcement of Lterlly Loded Structures (piles) in Nonlinerly Responsive Soil, Technicl Report R-67, Nvl Civil ngineering Lbortory, Port Hueneme, Cliforni Pender, M J (27) rthquke resistnt design of foundtions. Course notes uropen School for Advnced Studies in Reduction of Seismic Risk. Instituto Universitrio & Studi Superiori, Pvi, Itly. Pender, M J., Prnjoto, S., & Crter, D P., (27) Dimeter effects on pile hed lterl stiffness nd site investigtion requirements for pile foundtion design. Journl of rthquke ngineering, 11 Supplement 1, 1-12 Prnjoto, Stywn (2). The effects of gpping on pile behviour under cyclic lterl loding, PhD thesis, University of Aucklnd. Reese, L C; Cox, W R; oop, F D (1974). Anlysis of lterlly loded piles in snd, Proc. 6th Annul Offshore Technology Conference, Houston, pper OTC 28, Reese, L C; Cox, W R; oop, F D (1975). Field testing nd nlysis of lterlly loded piles in stiff cly, Proc. 7th Annul Offshore Technology Conference, Houston, pper OTC 2312, Reese, L C nd Welch, R C (1975). Lterl loding of deep foundtions in stiff cly, Journl of Geotechnicl ngineering Division, ASC 11, No. GT7, Reese, L C & Vn Impe, W F (21). Single piles nd pile groups under lterl loding, Rotterdm: Blkem, p. 64. Terzghi,. (1955). vlution of coefficients of subgrde rection, Geotechnique 5, No. 4,