LATERAL DISPLACEMENT RESPONSE OF PILES INSTALLED IN NEAR SURFACE IMPROVED COARSE-GRAINED SOILS

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1 ateral Displacement Respnse f Piles Installe in near Surface Imprve Carse-Graine Sils IGC 9, Guntur, INDIA ATERA DISPACEMENT RESPONSE OF PIES INSTAED IN NEAR SURFACE IMPROVED COARSE-GRAINED SOIS V. Pamavathi Assistant Prfessr, JNTUH Cllege f Engineering, Hyeraba, Inia. vpama7@gmail.cm M.R. Mahav Emeritus Prfessr, JNTUH Cllege f Engineering, Hyeraba, Inia. mahavmr@gmail.cm E. Saibaba Rey Registrar & Prfessr in Civil Engineering, JNTUH, Hyeraba, Inia. sbrey@yah.c.in ABSTRACT: Piles especially fr near-shre an ffshre funatins freuently penetrate thrugh lse sil epsits which are prne t excess isplacement at grun level uner lateral las. Pamavathi et al. (7) presente analysis f single rigi free hea pile in chesinless sils base n kinematics an subgrae reactin apprach. In this paper, the effect f increase in stiffness by ensificatin f the surficial chesinless sil n the behaviur f rigi pile base n kinematics an nn-linear subgrae respnse with hyperblic mel has been stuie. The reuctin in the isplacement f the pile at the surface ue t increase in the stiffness f the near surface sil as a cnseuence f ensificatin is uantifie.. INTRODUCTION Piles are cmmnly selecte as an ptin fr the supprt f high-rise structures, highway an infrastructure. These structural members are ften subjecte t cnsierable lateral frces such as ue t win las in hurricane prne areas, earthuake las in areas f seismic activity, an wave las in ffshre envirnments. Hansen (96), Brms (964a), Meyerhf et al. (98), Prasa & Chari (999), Zhang et al. (5), etc., prpse theries fr the estimatin f ultimate capacities f piles, piers an ples in chesinless sils uner varius pile-hea an base cnitins. Pamavathi et al. (7) presente analysis f single rigi free hea pile in chesinless sils base n kinematics an subgrae reactin apprach. With the same cnsieratins as mentine abve, the effect f increase in stiffness f the surficial sil ue t ensificatin n the behaviur f rigi pile using hyperblic apprach has been stuie. In this analysis, bth subgrae mulus an ultimate sil pressure vary linearly with epth. Anther imprtant cnsieratin in this analysis is that the sil es nt mbilie any pressure clse t the pint f rtatin because the isplacement there is er.. PROBEM DEFINITION A rigi pile f length,, an iameter,, is installe in a carse graine sil. A lateral frce, H, is acting at an eccentricity, e, which creating a mment, M (= e.h), at the grun level (Fig. ). The pile is unrestraine an rtates thrugh an angle, θ, abut a pint, O at epth,, frm the grun surface. The isplacement at grun line is ue t the rtatin f the pile. Mulus f hrintal subgrae reactin, k s, ultimate lateral sil pressure, max, unit weight, γ, angle f internal frictin, φ are the relevant prperties f the sil. The isplacements at grun level may be t high frm structural cnsieratins in many f the cases. The near surface sil can be ensifie s that the sil mulus increases in that prtin an the isplacements get reuce. The mulus an maximum sil pressure fr the imprve sil ver the epth,, frm grun level are cnsiere as k s an max respectively (Fig. b). The prblem is euivalent t that f laterally lae pile in ense san verlying lse san. H e G θ k s γ φ O se San H e Densifie GGrun θ k s γ φ Fig. : Original Grun Imprve Sil ayer near the Grun Surface O k s γ φ se San 79

2 ateral Displacement Respnse f Piles Installe in near Surface Imprve Carse-Graine Sils. Variatins f Stiffness an Strength f the Sil The isplacements vary linearly with epth. The respnse f the sil n t the pile is represente by nn-linear Winkler type respnse with mulus f hrintal subgrae reactin, k s, an ultimate lateral sil pressure, max. The lateral stress,, is relate (Fig. ) t the lateral isplacement,, as = k s /(+ k s / max ) () where is the isplacement f the pile at epth,, frm grun surface. Bth k s an max are assume t increase linearly with epth as shwn in Figures & respectively. k s = α k / () an max = α / () where α k an α are the rates f increase f the mulus f hrintal subgrae reactin an the maximum lateral sil pressure with epth respectively. The epth t the pint f rtatin,, an the angle f rtatin, θ, f the pile are the tw unknwns. Fr euilibrium, the applie lateral frce, H, is euate t the ttal respnse frm the sil as, H = k (4) s k + s + max max Taking mments abut the pint f applicatin f the la M = He = + max + max Where = ( ) tanθ an = ( ) tan θ are isplacements abve an belw the pint f rtatin at epth. an θ can be btaine by slving Es. (4) an (5). ateral Displacement, Fig. : Nn-inear Hyperblic Respnse f the Sil k s ateral Stress, k s max Fig. : Variatin f Parameters with Depth, Hrintal Subgrae Mulus Ultimate ateral Resistance max α k α (5) The imprve sil cnsists f subgrae mulus, k s, an maximum sil pressure, max. The variatins f subgrae mulus an maximum sil pressure alng the length f the pile are as shwn in Figures 4 & respectively. Base n these variatins the frce euatin becme ks H = + k k s s k + s + + max max/ max/ (6) The nrmalie euatins fr frce an mment are H H = = α an M + r k r ( ) tan θ + + μ ( ) tan θ M He = = α α k r (αk / αk ) ( ) tan θ + μ ( ) tan θ (αk / αk ) ( ) tan θ + μ ( ) tan θ k r ( ) tan θ + μ ( ) tan θ k s α k α k G Fig. 4: Variatin f Hrintal Subgrae Muli an Ultimate ateral Sil Pressure with Depth, (αk / αk ) ( ) tan θ + μ ( ) tan θ = (8) (αk / αk ) ( ) tan θ + μ ( ) tan θ where = / the nrmalie epth, = / nrmalie epth f pint f rtatin, r = / an nrmalie la, H = H αk The parameters µ an µ, an the rati, α kr are efine as μ = k s / max = α k /α ; μ = k s / max = α k /α an α kr = α k /α k. Ieally, the epth f rtatin,, an the rtatin, θ, are t be estimate fr given lateral frce, H, an mment, M. Hwever, it wul be an iterative prcess an very teius. Fr given values f μ, μ, α kr an θ, an H can be btaine by slving Es. (7) an (8). Knwing an θ, the nrmalie eflectin at grun level, = tan θ, is evaluate crrespning t the nrmalie applie la, H.. DISCUSSIONS The variatins f nrmalie la, H, with nrmalie isplacement at grun level,, are evaluate base n the prpse mel fr ifferent cmbinatins f μ an μ max α α (7) 74

3 ateral Displacement Respnse f Piles Installe in near Surface Imprve Carse-Graine Sils values ranging frm t 7 with intermeiate values f, 5,,, 5,, an 5; stiffness ratis, α kr f 5, 5,, 5, an, nrmalise thickness f imprve sil frm grun level, r varying frm t.7 an nrmalise la eccentricity, e/ values spanning ver,.,.4,.6,.8,, an 4. Figure 5 shws the la versus isplacement at grun level, respnse curves fr the pile fr μ =, μ =, α kr = 5 an θ =.. Stiffness rati f the sils is 5, which crrespns t the stiffness f the imprve grun being five times mre than the riginal ne. The nrmalie la increases with increase in the epth f the imprve sil. Nrmalise a, H The nrmalise la fr a pile fr epth f imprvement.5, is abut % cmpare t that prir t the imprvement f the sil. Nrmalise a, H.E-4 5.E-5.5E-4.5E-4 μ = r =.4.8 Nrmalise Displacement, Fig. 5: Nrmalie a, H vs Nrmalie Displacement, at Grun evel fr μ =, μ = an α kr = 5 Effect f r,,7,.4.8 Nrmalise Displacement at G, Fig. 6: Nrmalie a, H vs Nrmalie Displacement, at Grun evel fr μ =,, r =.4, e/ = an α kr = 5 Effect f μ Figure 6 presents the variatin f nrmalise la with nrmalise isplacement f the pile fr ifferent values f μ fr μ =,, r =.4, e/=, α kr = 5 an θ =.. The nrmalise las are.4 4, an t.5 5 an crrespn t nrmalise isplacements f.6,.4 an.78 fr μ = 5, 5 an 7, respectively an θ =.. The isplacement increases by abut times fr μ increasing frm 5 t 7, an rtatin.. The initial slpes f the la-isplacement curves fr stiff sils (lwer μ values) are high an reuce fr sft sils (higher μ values). The variatins f nrmalise isplacements at the tp with nrmalise imprve sil thickness an fr ifferent stiffness ratis, α kr = t is illustrate in Figure 7 fr μ =,, μ =,, θ =., e/ =. The isplacements f the piles at the grun line ecrease with increase in r, fr the case f stiffer upper surface. The isplacement ecreases frm.77 t.5 fr r increasing frm t.5, fr α kr =. The minimum value f isplacement f the pile tp epens n α kr. Fr example, the nrmalise isplacement is minimum near r values f.5,.6,.67 an.7 fr α kr =, 5, an respectively. The percentage ecrease in isplacement is maximum at r =.5 fr α kr =. The maximum ecrease in isplacement ccurs fr r between.5 an.7 fr α kr in the range t. The maximum ecrease in isplacement is abut % fr α kr = 5. Nrmalise Displacement, r Fig. 7: Variatins f Nrmalise Displacements with r, fr μ =,, μ =, an θ =.-Effect f α kr Figure 8 presents the nrmalise sil pressure istributins alng the length f the pile, fr ifferent values f μ r μ, μ = μ, r =.4, α kr = 5 an θ =.. The nrmalise sil pressure belw the epth f imprve sil ( r ) is significantly less because it is 5 times weaker than the imprve sil. The ifference in nrmalise sil pressures between the curves fr tw values f μ is mre in stiffene sil, while it is less in riginal sil. The variatins f rati f ultimate lateral capacity the pile in imprve sil t that in riginal grun (H u /H u ) is als stuie with respect t r, α kr an presente in Figure 9 fr μ =,, μ =,, / = 4 an e/ =. The increase in nrmalise ultimate pile capacity is high fr values f r between an.5. The ultimate lateral capacity rati H u /H u remains nearly cnstant fr r between.5 an.7 except fr α kr =. 5 α kr = 74

4 ateral Displacement Respnse f Piles Installe in near Surface Imprve Carse-Graine Sils Nrmalise Sil Pressure,.E- 5.E-4 5.E-4.E- 6. Nrmalise Depth, / 7,.5, 5 α kr = μ =5 µ =5 7,, 5 Fig. 8: Variatins f Nrmalise Pressures alng the ength f the Pile, fr r =.4, μ = μ, e/ = an α kr = 5 stiffness f the near surface sil. The maximum ecrease in pile tp isplacement ccurs fr r between.5 an.7. The ecrease in isplacement is abut % fr stiffness rati f.. The preicte la-isplacement plts cmpare well with the measure values reprte by Meyerhf et al. (98) fr piles in tw-layere sils. Nt nly isplacement, but the ultimate carrying capacity f the pile in ensifie grun is als imprve. ateral a, kn.4. exp. Prpse H u /H u Fig. 9: Variatin f Rati f Ultimate ateral Capacity f Pile after an Prir t Imprvement f the Sil, H u an H u with r fr µ =,, µ =,, / = 4 - Effect f α kr Meyerhf et al. (98) cnucte tests n piles installe in tw-layere sils. The ense an the lse sans have the fllwing prperties an cnitins. Unit weights, γ, are 5. an 4 kn/m an angles f internal frictin, φ, are 5 an 5 respectively. ength f the pile,, is. mm, iameter f the pile,, is.5 mm, eccentricity f la (e/ = ) an r =.5 an.75 fr ense san verlying lse san. This ata is applicable fr the present prblem an facilitates cmparisn f the present analysis with experimental results. Figure shws the cmparisn f measure an prpse la-isplacement curves fr the pile respnse, fr ense san verlying lse san fr r =.5. The preicte values agree clsely with the measure nes. 4. CONCUSIONS Present thery preicts the ultimate las as well as the la -isplacement respnses at wrking las f piles installe in ensifie grun. The isplacements at grun line get reuce significantly as can be expecte with increase in the r 5 Displacement at G, mm Fig. : Cmparisn f Preicte an Measure (Meyerhf et al. 98) a-displacement Curves fr Pile in Tw-ayere San: Dense San ver se San, r =.5 REFERENCES Brms, B.B. (964b). ateral Resistance f Piles in Chesinless Sils, Jl. Sil Mech. Fun. Div., ASCE, 9(): 56. Hansen, J.B. (96). The Ultimate Resistance f Rigi Piles against Transversal Frces, Bulletin N., Danish Getechnical Institute, Cpenhagen, Denmark, pp Meyerhf, G.G., Mathur, S.K. an Valsangkar, A.J. (98). ateral Resistance an Deflectin f Rigi Wall an Piles in ayere Sils, Canaian Getechnical Jurnal, Vl. 8(): Pamavathi, V., Saibaba Rey, E. an Mahav, M.R. (7). Analysis f aterally ae Rigi Piles in Sans base n Kinematics an Nn-linear Sub-grae Respnse, Inian Getechnical Jurnal, Vl. 7(): 9 9. Prasa, Y.V.S.N. (997). Stanar Penetratin Tests an Pile Behaviur uner ateral as in Clay, Inian Getechnical Jurnal, Vl. 7():. Zhang,., Silva, F. an Grismala, R. (5). Ultimate ateral Resistance t Piles in Chesinless Sils, Jl. Getechnical & Geenvirnmental Engrg., ASCE, Vl. ():

5 ateral Displacement Respnse f Piles Installe in near Surface Imprve Carse-Graine Sils 74