NON-LINEAR BENDING CHARACTERISTICS OF PHC PILES UNDER VARYING AXIAL LOAD

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1 13 th World Conferene on Earthquake Engineering Vanouver, B.C., Canada August 1-6, 24 aper No. 356 NON-LINEAR BENDING CHARACTERISTICS OF HC ILES UNDER VARYING AXIAL LOAD Toshihiko ASO 1 Fusanori MIURA 2 Takehiro INOUE 3 Masashi YAMAMOTO 4 SUMMARY This paper desribes the bending harateristis of HC piles up to ultimate state, when suh piles are subjeted to ompressive and tensile axial fores. Monotoni loading tests of atual HC piles were arried out for several levels of axial fore. The relationship between moments-defletions and bending moments-urvatures are examined with respeted to the axial fores. Numerial analysis was onduted in order to simulate the pile s nonlinear bending behavior obtained from the test results. The results of the analysis agree well with the results of the loading tests. Earthquake response analyses of strutures with pile foundations are performed. A omparison of the response analysis results, with and without onsideration of varying axial load, demonstrates the need to inlude varying axial load within the analysis. INTRODUCTION During severe earthquakes, plasti deformations may develop not only in bridge piers but also in the pile foundations. Many types of pile foundations were severely damaged during the Hyogo-ken Nanbu earthquake, whih ourred on January Sine that time, muh effort has gone toward improving the seismi resistane of pile foundations. The seismi design of Highway Bridge is shifting to the ultimate state design method, whih onsiders the deformation ability. Ultimate state design method requires exat estimation of ation fores and deformation harateristis of members under the earthquake. Due to the diffiulty of damage investigation and the prompt managements, seuring the seismi safety of foundations is a serious problem. There are many types of foundations, however pile is the most popular foundation for bridges. re-stressed high strength onrete piles (HC pile) are used at many sites due to its advantages of allowable stress, i.e. allowable stress of HC piles is greater than RC piles. Hoshikuma [1] studied non-linear bending harateristis of a HC pile. It proposed a method for defining the relationship between bending moment and urvature to onsider non-linearity in dynami analysis. On the other hand, a pile foundation is onsists of a group of piles. In this ase, due to a rotation of substruture 1 Assoiate professor, Yamaguhi University, Ube, Japan. aso@yamaguhi-u.a.jp 2 rofessor, Yamaguhi University, Ube, Japan. 3 Engineer, Kawada Industries, In., Osaka, Japan. 4 Graduate student, Yamaguhi University, Ube, Japan.

2 of bridge, ompressive fore and tensile fore ats to both sides of pile. Therefore, it is neessary to onsider flutuant axial fore, when alulating a non-linear dynami behavior of piles. There are few researhes about non-linear bending harateristis of a HC pile under tensile axial fore. This paper desribes the bending harateristis of HC pile under varying axial fores. Bending tests of real HC pile under several axial fores were arried out to observe the bending behavior. Numerial simulation onsidering with the relationship between bending moment and urvature were performed. The results of the analysis agree well with the results of the bending tests. Earthquake response analysis of soil-pile-substruture system was also alulated. The results of response analysis learly demonstrate the need to onsider varying axial load in the analysis. BENDING TEST OF A HC ILE Bending test of HC piles with several axial fores ware performed. Diameters of test piles are 4mm, 6mm and 8mm. Table 1 shows dimensions of piles and onditions of bending tests. Loads at the entral two points on the simple supported pile auses bending as shown in Fig. 1. Compression axial fores are installed as reation of tension rod that was plaed at inside the pile hollow and that was hauled by jak. On the other hand, tensile axial fore was given by hauling of pile through tension rod attahed at both ends of pile. In this ase, the frame that was onstruted around the pile supports the reations of jaks. The monotoni step load was applied to a pile until the pile was broken. No. Table 1 Dimensions of test piles C Rods Diameter Length Thikness Diameter Number Set radius Axial fore (mm) (m) (mm) (mm) (mm) (kn) Load Displaement gauge ile Support Support (mm) Fig.1 Bending test

3 The relationship between load magnitude and displaements at the enter of pile were observed as shown in Fig. 2. In the ase of pile diameter 4mm, the maximum defletion under tensile axial fore is smaller than that with ompression axial fore. On the other hand, in the ase of 6mm diameter pile, the maximum defletion under tensile axial fore is larger than that with ompression axial fore. From these results, it ould be onfirmed that the axial fore affets deformation ability of piles signifiantly Displaement (mm) Displaement (mm) Displaement (mm) N=kN N=12kN N=kN N=26kN N=kN N=4kN N=6kN N=-5kN N=13kN N=-1kN N=2kN (a) D=4mm (b) D=6mm () D=8mm Fig.2 Relationship between displaement and load RELATIONSHI BETWEEN BENDING MOMENT AND CURVATURE OF HC ILE The following assumptions are onsidered in alulating the relationships between bending moment and urvature; refer to Oiwa [2]. (1) The setion of a HC pile holds a onstant plane until destrution. (2) Bending moment M orresponds to the raking strain at the outermost tensile side of onrete. (3) Bending moment M y orresponds to the yield strain at the outermost tensile side C rod. (4) Bending moment M u orresponds to the ultimate strain at the outermost ompression side of onrete. (5) Stress and strain relationships of onrete are shown in Fig.3 (a). That of C rod is shown in Fig.3 (b). (6) It is assumed that all ross setions of onrete are effetive until M. After M, tensile stress of onrete is disregarded. (7) At the neutral line, ompression strain of onrete is zero. (8) C rods are substituted as equivalent thin-wall steel pipe. Bending moment M and urvature φ are expressed with following formula. I e N M M = σ e + σ bt + φ = (1) r Ae EIe Where, I e : equivalent moment of inertia, σ bt : bending tensile strength of onrete, N : axial fore, e r : radius to enterline of thikness, A : equivalent ross setional are. σ e : effetive pre-stress,

4 The position of neutral line after M must be deided by numerial alulation. Referring to Fig.4, ompression fore C () i and bending moment M () i of onrete with assumed arbitrary neutral axis position are expressed by Eq.(2) and Eq.(3). σ σ.85σu σsy ε.2 εu ε Es E σy εsy ε (a) Conrete (b) C Fig.3 Stress and strain relationships e(i)=e(l) s(i)= s(l) Δy θi(j) θ(j) y(j) y(n) y(l) xi(j) x(j) Fig.4 Analytial model C M 4D = i (2) n D i = 4 2 osθ j σ j { Dsinθ j d sinθi j } n (3) () i σ ( j) { D sinθ ( j) d sinθ ( j) } () ( ) ( ) ( ) ( ) Where, D : diameter of pile, d : internal diameter of pile, n : number of elements, σ ( j) stress of j th element, θ ( j) : enter angle of outside irle of j th element. : ompressive Tensile fore T () i and bending moment M () i of C rod with assumed arbitrary neutral axis position are expressed by Eq. (4) and Eq. (5). T () i = ( A m) σ ( k ) (4) M Where, () i ( A m) σ ( k ) osθ ( k ) = (5) A : total ross setional area of C rods, m : number of division of equivalent thin-wall steel k θ k : enter angle of thin-wall steel pipe of k th element. pipe, σ ( ): tensile stress of k th element, ( )

5 The position of neutral line is deided from aording to the following ondition. * N ( i) = C( i) T ( i) (6) Here, bending moment and urvature are obtained by equations (7) and (8), respetively. M ( i) = M ( i) M ( i) (7) C ε ( i) ( i) ε t φ = (8) 2r Where, ε (i) : strain of the outermost ompressive side of the pile, ε t : strain of the outermost tensile side of the pile. COMARISON OF ANALYSIS AND BENDING TEST The relationships of bending moment and urvature are alulated. Geometrial onditions and physial harateristis of the piles are shown in Table 2. Figure 5 shows the omparison of test results and alulated value. These figures indiate that the rak moment, yield moment and ultimate moment strength inrease with the axial fore. In the ase when tensile axial fore ats, the urvature inreases. When high ompression axial fore ats in piles of diameter 6mm and 8mm, M y beomes greater than M u. This shows that ompression side onrete is in an ultimate state before C rods yield. Comparisons of analysis and test results are shown in Fig.6 and Fig.7. In this figure, irle marks indiate results of analysis and solid line is results of bending test. Analytial results and test results shows good orrelation in all axial fores. Thus, validity of the analysis was onfirmed. Table 2 Geometrial onditions and physial harateristis of the pile Outside diameter (mm) D Inside diameter (mm) d C rods set radius (mm) r Number of C rods n Angle of C rods (rad) θ i Elasti modukus of onrete (N/mm 2 ) E Elasti modukus of C rod (N/mm 2 ) Es 21 Cross setional area pf onrete (mm 2 ) A Cross setional area of C rods (mm 2 ) A s re-stress (N/mm 2 ) σ e Crak strain of onrete ε.125 Yield strain pf C rod ε sy.7158 Ultimate strain of onrete ε u.245

6 D=4mm D=6mm D=8mm N=-5kN N=kN N=6kN N=-1kN N=13kN N=kN N=12kN N=kN N=26kN N=2kN Fig.5 Relationship between bending moment and urvature N=4kN N= 13 kn N= 26 kn N= -1 kn Fig.6 Comparison of moment-urvature relationships (D=6mm) N= 13 kn Displaement (mm) Displaement (mm) Analysis N= 26 kn Test results N= -1 kn Displaement (mm) Fig.7 Comparison of load-displaement relationships (D=6mm) EARTHQUAKE RESONSE ANALYSIS Earthquake response analysis in onsideration of flutuant axial fore is performed using the M φ relationships that are obtained in this researh. In the analysis, it arries out about the model of the bridge pier - foundation - ground system as shown in Fig. 8. Figure 9 shows the soil property and Fig.1 is the sketh of pier and foundation. The bottom of the ground was set as a fixed boundary, and the sides have

7 visous boundary in order to onsider the energy dissipation. The Hardin-Drnevih model was used for the nonlinearity of the ground. A nonlinearity of pile bending is taken as bi-linear defined by its rak and ultimate point. On the other hand, when onsidering the flutuant axial fore into nonlinearity of pile, the relationship between axial fore and bending moment were set as shown in Fig.11. The damping ratio of ground was 2% and that of strutures is 2%. The input seismi wave is sown in Fig. 12. This is generated based on the standard seismi wave desribed in Highway Speifiations in Japan and the soil properties. The standard wave was JR Takatori, whih was reorded in Hyougoken Nanbu earthquake. Time histories of axial fore that was observed at pile No.1 and No.3 are shown in Fig.13. Large flutuant axial fore ats in pile No.1, however, axial fore on No.3 ontains initial axial fore only. This is aused by rotation of footing. Figure 14 displays distribution of maximum bending moment along the pile No.3. Differene of maximum bending moment appears at upper part of pile. Most of the points show that the bending moment under M-N-f is greater than that of M-N. Relationship between bending moment and urvature at the point.3m below pile top is displayed in Fig.15. From this figure, hysteresis loop is appeared when flutuant axial fore was onsidered. This suggests that flutuant axial fores must be onsidered in earthquake response analysis. 122 Visous boundary Fig.8 FEM model ST-N Value = = (mm) = Fig.9 Soil property Fig.1 Sketh of the pier

8 Bending Moment(kNm) M Mu Axial Fore(kN) Fig.11 M-N relationships Aeleration(gal) eriod(se) Fig.12 Input seismi wave Axial Fore(kN) 15 1 No M-φ -1 M-N-φ Time (se) Axial Fore(kN) No.3 M-φ M-N-φ Time (se) Fig.13 Axial fores M- N- f M- f Bending moment (knm) Fig.14 Distribution of Bending moment Bending Moment(kNm) E-3-2.E-3.E+ 2.E-3 4.E-3 Curvature(1/m) Fig.15 Moment-urvature relationships CONCLUSION This study presented the bending moment urvature urve of HC pile under flutuant axial fores based on bending test results of atual piles ated by tensile axial fores. Results revealed that the analyti

9 results showed good orrelation with test results. The bending moment urvature urves and load displaement relationships under bending load of both were similar, thus, bending behavior was well simulated. Furthermore, this paper suggest the onsideration of flutuant axial fores in seismi design sine it was onfirmed that due to flutuant axial fores, bending behavior of piles hanges signifiantly. REFERENCES 1. Hoshikuma J., Otsuka H., Tsuda K. and Nagaya K. A seismi evaluation for flexural dutility of prestressed high strength onrete pile. Journal of Strutural Mehanis and Earthquake Engineering, 1997, No.57: (in Japanese) 2. Oiwa K., Tsuda K. The relationship between bending moment & urvature on preast onrete piles, and the shearing strength of HC piles. Bridge and Foundation Engineering, 1998, 98(2): (in Japanese)

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