Displacement and deformation analysis for uplift piles Displacement and deformation analysis for uplift piles

Displacement and deformation analysis for uplift piles

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J. Cent. South Univ. Technol. (2008) 15: 906- 910包SpringerDOI: 10.1007/511771-008- 0165-xDisplacement and deformation analysis for uplift pilesYANG Xia-l(杨小礼),ZOU Jin-feng(邹金锋)(School of Civil and Architectural Engineering, Central South University, Changsha 410075, China)Abstract: On the assumptions that the shear resistance increases linearly with increasing shear displacement between the uplift pileand surrounding soil, that the axis force is distributed as parabola along the pile length, that elastic distortion occurs when the pile isloaded, that the displacement of pile is in accord with that of the soil, and that the uplift pile failure is regarded as the soil failure, arational calculation method was proposed for calculating the deformation, ultimate displacement and shear resistance of piles. Thedistributions of frictional resistance and the shear displacement along the pile length were obtained with the method. Thecomparisons were made between the measurement results and the present results. The present theoretical results agree well with themeasurement results, with the average difference being less than 12% before failure. The comparisons show that the proposedmethod is reasonable for uplift design and engineering construction of piles.Key words: uplift pile; load transfer mechanism; displacement; deformationinformation related to the working status of the uplift pile,1 Introductionwhich is a reasonable basis for the adjustment of thedesign.The uplift pile has been widely used as an effectiveIn order to overcome the above defects, anreinforcement in civil engineering for long time.analytical model based on an improved model for upliftHowever, the interaction mechanism between the pilepile was developed. The development of the model isand the soil mass is not well understood, and the upliftbased on the interaction behavior description that thepile design is still empirical so far, especially theshear resistance increases linearly with increasing sheardeformation and the displacement. A common method to .displacement between the uplift pile and the surroundingverify part of the uplift pile design is the pullout test, butsoil, that the axis force is distributed as parabola alongit is difficult and expensive, and the working conditionsthe pile length, that only elastic distortion occurs whenof the rock and soil around the pile are alwaysthe load is operated on the pile, and that the displacementunknowable. Many researchers have worked on this field.of pile is in accord with that of the soil. A back analysisFor example, HUANG et al' proposed a theoreticalmethod was proposed to calculate the shear displacementmethod to predict the displacement of pile, andand friction force of the interface media. By using theLEHANE et a1[2] and CAIRO and CONTE'3] provideddeveloped model, the interaction behavior of the upliftthe model of frictional pile. However, the literature of theile and the surrounding soil mass was investigated,pile displacement and deformation is limited, which iswhich provides a way of evaluating the supportingcontributedhe fact that the deformation anperformance quantitatively.displacement are restricted by not only the material madeof the pile but also the parameters of the soil and rock.2 Theoretic modelThe deformation and displacement are more uncertainthan the load capacity of pile. In order to improve the2.1 Basic assumptionsuplift pile design, it is necessary to have a goodAccording to the previously published achievements,understanding about the calculation of deformation anthe load is supported by pile and soil when the upliftthe ultimate displacerment in the uplift pile, especially inworks'1. The deformation between the pile and the soil isthe important projects+-o. At the same time, the limitharmoniousu-. The failure of pile is regarded aanalysis has been developed rapidlyl-9!. The ultimatefailure of the soil that strength is up to the ultimatedisplacement of uplift pile in soil is helpful for the designstrength.the major theoretic hypotheses are asbecause the ultimate displacement provides the essentialfollows.中国煤化工Foundation item: Project(05-0686) supported by the Program for New Century Excellent Tale.MYHCNMHGuppotedbytheFoundation for the Author of National Excellent Doctoral Dissertation of ChinaReceived date: 2008- 01- 08; Accepted date:2008-04- -20Corresponding author: Y ANG Xiao-li, Professor; Tel: +86- -731- 2656248; E-mail: yxnc@yahoo.com.cn.J. Cent. South Univ. Technol. (2008) 15: 906- 9109071) It is assumed that there is only shear resistance atelement of dr in the uplift pile isthe surface of the pile embedded in soil mass.Px2Consequently,the potential contribution of the shaf8.=-5 dx(3)resistance of the ground, which may lie above the soil, isEgA.L2not taken into account, and neither is the possiblewhere Ac is the cross section area, Ac=rD-/4, D is thecontribution of the pile tip.diameter of the uplift pile, and Ea is the effective elastic2) The strength at the interface between the soil andmodulus of the uplift pile composed of steel bar andpile is assumed to be the soil strength. This means thaconcrete, which can be expressed asthere are not disturbance, modification, alteration of thesurface of the soil in contact with the uplift pile. It alsoE.A.+ E。A.,means that the strength of the material that the pile is .A. +A.made of concrete or steel is greater than the strength ofwhere Es, E。and As are the elastic modulus of the steelbar, the elastic modulus of the concrete, and the cross3) The shear resistance increases linearly with thesection area of steel bar, respectively. Integrating Eqn.(3)shear displacement between the pile and the surroundingleads to the following expressionsoil. The axis force supported by the tension pile isPIdistributed as parabola along the uplift pile.S。=f% δdr=;(5)3EgAc2.2 Deformation of uplift pileSince the axial force is known at the pullout end,According to the assumptions, the ultimateind the other end carries no axial force, the boundarydisplacement of uplift pile can be expressed ascondition can be described as follows (see Fig.1).S=S&+Ss[P(x)|._ =Pwhere S, Se and Ss are the ultimate displacement of the(6)|P(x)_L =0uplift pile, the elastic deformation of the pile and theshear displacement between the soil and the uplift pile,respectively.2.3 Shear displacement between uplift pile and soilAccording to the assumptions, the deformation ofThe interaction demonstration of the uplift pile anduplift pile is mostly the elastic deformation when thethe soil mass is sketched in Fig. 2.uplift load acts on the pile. The loads equal P and 0 at thetop and the bottom of the pile, respectively. Therelationship is shown in Fig. 1._Pix, '北lSeLqdx↓↓dP(x)_P+P|x1)b)Fig.2 Load transfer mechanism of tension pile: (a) TotalFig.1 Parabolic distribution of axial force supported by tensiondistribution of stresses; (b) Element stressespileAccording to the balance of an infinitesimal elementAccording to Hooke 's law, there exists an axis forceof the uplift pile in Fig.2, the following formula isP(x) at point x, as shown in Fig.1.established:P(x)=(2)(7L2lx中国煤化工where P(xr) and L are the axial force of the rock bolt atwhere qis the.MH.. CNM H Ga. Accordingthe position x and the length of uplift pile, respectively.0 Hooke's law, tne relationsnip Derween elasticSimilarly,the deformation of δx in an infinitesimaldeformation of and the axis pressure ofP is.908J. Cent. South Univ. Technol. (2008) 15: 906- -910πD2E。dS。expressed as(8)dPLcosh(uL/D)(19)Combining Eqns.(7) with (8), q can be expressed as3πE。D2 cosh(uL/D)-1πD2E。d'S。 ,It can be seen from Eqn.(19) that the displacement(94 d2xcan be calculated if the material parameters of the upliftAccording to assumption 3) in Section 2.1, we canpile, the geometry of the uplift pile and the parameters ofthe soil are known. Furthermore, the shear resistance andhavethe shear displacement between pile and soil are relatedq= tDr=G,Ss(10)to the diameter and length of the pile, the ratio of lengthwhere T and Gs are the shear stress on the uplift pileto diameter of the pile, the elastic modulus of the pileand the shear modulus of the soil, respectively.and the characteristic of the soil.Combining Eqn.(9) with Eqn.(10), the differentialfunction of elastic displacement can be expressed as3 Discussion and comparison with measureddatad2s。4G,S。(11)dx 2πD2E。3.1 DiscussionSimilarly, combining Eqn.(9) with Eqn.(10) andIn order to investigate the distribution character ofignoring the higher-order terms, the differential functionfriction resistance and the shear displacement along theof shear displacement is expressed aspile length, the numerical simulation was adopted here.The parameters for numerical simulation were as follows:d2sg 4G。S、E。=110 GPa,L=6.0 m, D=0.5 m, P=350 kN. Figs.3 and 4dx2πD2 Egshow the friction resistance and the shear displacementAccording to the boundary conditions8(P(x)._=P and Pp(x)._, =0 and the expression of。- G.=0.5GPa70↑一G3= 1.0GPaμ=√↓4G./(πE。) (u is the Poisson ratio), the shear*- G-=2.0GPadisplacement of S(x) and the friction force of t(x) along6the uplift pile can be expressed as客5CS(x)=-_4P_ cosh[(L -x)D](13)πDEgMsinh(μL/D)40-4PG。cosh[u(L - x)/D](πD)2 Egusinhb(μuL/D)30|If order x=0 and x=L, the displacements of up and202345bottom pile are respectivelyx/Fig.3 Distribution of friction resistance along pile lengthS(0)=-- cosh(μuL/D)(15)πDEgμ0.164PS(L)=-πDEgμ sinh(uL/D)(16),GELOGPaG-15GPa0.12-. G-=2.0GPaCombining Eqn.(15) with Eqn.(16), the relationshipbetween the bottom displacement and the updisplacement can be obtained.0.08S(0)=S(L)cosh(uL)(17)Similarly, combining Eqns.(1) with (16), we can0.04cosh(μuL)中国煤化工s=S。-- . S(L)S(0)=Secosh(uL- 1)(18)MHCNM HGSo the ultimate displacement of uplift pile can beFig.4 Distribution of shear displacement along pile length.J. Cent. South Univ. Technol. (2008) 15: 906- 910909along the pile length with different shear moduli,parison between the theoretic values in this work and therespectively.test data is shown in Fig.6. The theoretic value S=0.391From Fig.3, it can be seen that the friction resistancemm is more nearly to the test data of S= =0.398 mm.attenuates from the top to the bottom of the pile with0.45non-linearity. The maximum and minimum frictionresistances appear at the top and the bottom of the pile,■- - Measurement●- Calculationrespectively. The larger the shear modulus, the more thenonlinearity. If the shear modulus exceeds a certain value,0.30-the shear resistance will be centralized on the 2/3 of pilelength. These results correspond to the fact that frictionresistance is fully exerted for piles in rock masses, andthat the shear resistance is concentrated on top and the0.15shear resistance is distributed uniformly for piles in softsoils.From Fig.4, it is found that the shear displacementdistribution is similar to the friction resistance426distribution. The effect of shear modulus on the shearQ/MNdisplacement is smaller than that on the frictionFig.6 Q- S curves of pier uplift pileresistance. At the same time, it can be seen that the sheardisplacement only offers a lttle to the wholeFrom the comparison between the theoretic valuesdisplacement in the 1/3 length at the bottom of pile. Thisin this work and the test data, it can be seen that thetheoretical conclusion agrees with the field monitoringpresent results obtained with this method agree with thedata obtained in Ref.[1].monitoring data favorably, with the average differencebeing less than 12%. The comparison proves the3.2 Comparison with measured datatheoretic reliability and validity presented in this work,In order to validate the reliability of the aboveso it can provide consult for uplift pile design. Themethod, a model and a pier uplift pile test data werecausation of errors between the theoretical calculationtaken as examples for comparison.and the monitoring data come from other factors such asFor the model test pier pile, the model parametersthe pile length, the pile diameter, the strength of the soilwere as follows: L=4.5 m, D=0.18 m, E=-110 GPa, G;=around the pile and so forthl2 . The effects of these2.179 MPa, μ=0.18. The grade loading was adopted. Theinfluencing factors on the displacement and deformationmaximum loading was 32 kN. The relationship betweenof uplift pile demand more study.the top pile settlement S and the uplift force Q is shownin Fig.5. The theoretic value S=12.044 mm is more4 Conclusionsnearly to the test data of S= 12.216 mm.1) The distribution of the friction resistance is40nonlinear for the uplift pile. Rational calculation method'一Measurementis presented for calculating the deformation, ultimateTheoretic calculationdisplacement and shear resistance of the uplift pile30embedded in rock and soil. The interaction behaviorbetween the pile and soil mass is described by shear20modulus, which is determined by the interaction mediumbetween the pile and the soil.2) The maximum and minimum friction resistances1(appear at the top and the bottom of the pile, respectively.If the shear modulus exceeds a certain value, the frictionresistance will be centralized on the 2/3 of pile length.10152()25303:The results of theoretical solutions and those of testsQMNshow generally favorable agreement, which proves thatFig.5 Q- -S curves of model tension pilethe present method is reasonable for uplift designs.中国煤化工For the pier uplift pile, the maximum pullout forceReferencesis 18 MN. The parameters were as follows: L=10.0 m,MYHCNM HGD=1.5 m, E。=100 GPa, G-=4.7 MPa, μ=0.245. The com-[1] HUANG Feng, LI Guang-xin, LU He. Analysis of deformation oftension in sand soil []. China Civil Engineering Jourmal, 1999, 32(2):.910J. Cent. South Univ, Technol. (2008) 15: 906- -91031-36. (in Chinese)[2] LEHANE B M, JARDINE R J, BOND A J, FRAND R. Mechanismsslopes with a modified Hoek-Brown failure criterion [].of fiction in sand from instrumented pile tests [J]. Joumal ofInternational Joumal for Numerical and Analytical Methods inGeotechnical Engineering, 1993, 119(1): 19-35.Geomechanics, 2004, 28(2): 181-190.[3] CAIRO R, CONTE E. Stlement analysis of pile groups in10] EMMETT K. Pile disturbance in layered ground []. Groundlayered soils []. Canadian Geotechnical Journal, 2006, 43(8):Engineering, 2005, 38(12): 30- 32.788- -801.WANG Tao, LIU Jin-li. Tests on influence of pile-soil-pile[4] ZHANG C, YIN J. Field static load tests on drilled shaft founded oninteraction [J]. Chinese Journal of Geotechnical Enginering, 2008,or socketed into rock [] Canadian Geotechnical Jourmal, 2000, 37(5):30(1): 100-105. (in Chinese)1283-1294.12] ZHAO P, JI s. Refinement of shear-lag model and its aplication [0].[5] SERRANO A, OLALLA C. Tensile resistance of rock anchors [I].Tectonophisics, 1997, 279(1): 37-53.Intemnational Journal of Rock Mechanics and Mining Sciences, 1999,13] YANG Xiao-li. Seismic displacement of rock slopes with nonlinear36(3): 449 -474.Hock- Brown failure criterion []. International Journal of Rock[6] HOEK E, BROWN E T. Practical estimnates of rock masses strengthMechanics and Mining Sciences, 2007, 44(6) 948 -953.[] International Journal of Rock Mechanics and Mining Sciences,14] ABRAMENTO M, WHITTLE J A. Analysis of pulut tests for1997, 34(7): 1165 -1186.planar reinforcements in soil []. Journal of Getechnical[7] YANG Xiao-li, YIN Jian-hua. Slope stability analysis with nonlinearEngineering, 1995, 121(6): 476- -485.failure criterion []. Journal of Engineering Mechanics, 2004, 130(3):15] LEE K M, XIAO Z R. A simplified nonlinear approach for pile group[8] YANG Xiao-li, LI Liang, YIN Jian-hua. Seismic and static stabilitysettlement analysis in mulilayered soils []. Canadian Geotechnicalanalysis for rock slopes by a kinematical approach [J]. Geotechnique,Journal, 2001, 38(5): 1063-1080.2004, 54(8): 543- -549.(Edited by CHEN Wei-ping)中国煤化工MHCNMH G.

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