Horizontal Biaxial Loading Tests on Sliding Lead Rubber Bearing System

Transcription

1 Horizontal Biaxial Loading Tet on Sliding Lead Rubber Bearing Sytem M. Yamamoto, H. Hamaguchi & N. Kamohita Takenaka Reearch and Development Intitute, Japan. M. Kikuchi & K. Ihii Hokkaido Univerity, Japan. 217 NZSEE Conference T. Wake Oile Corporation, Japan. ABSTRACT: The author have propoed a high-afety-margin eimic iolation ytem for large earthquake that exceed deign bai earthquake (DBE). Thi ytem conit of a lead rubber bearing (LRB) and a liding bearing in erie. The ytem function a a conventional LRB under earthquake maller than DBE; under thoe larger than DBE, the liding bearing lide and prevent the failure of the LRB. Dynamic loading tet of the ytem were conducted. The target ize of the LRB in the ytem wa 9 9 mm. The tet pecimen, reduced.5 time in length from the original ize, meaured 2 2 mm. Horizontal diplacement were applied under variou axial force condition with contant average tree of, 8, and 12 MPa. A diplacement-dependent cae wa tudied with average tre varying between and 12 MPa. The horizontal loading were applied uniaxially and biaxially a circle and ellipe. Tet reult howed that the previouly reported deign equation of friction force wa applicable for both biaxial and uniaxial loading. However, biaxial loading caued torional deformation in the LRB, which increaed the hear train relative to that under correponding uniaxial loading. The ytem wa analytically modelled and implemented in OpenSee oftware. Thi analytical model imulated the tet reult preciely for variou frequencie, variou axial force, and both uniaxial and biaxial horizontal loading. 1 INTRODUCTION Recently, damage of building tructure under unexpected large earthquake ha become apparent. Behaviour of eimically iolated (SI) building under large earthquake that exceed deign bai earthquake (DBE) have been tudied. The author have propoed and tudied a eimic iolator ytem with a high afety margin for large earthquake exceeding DBE. The ytem comprie a lead rubber bearing (LRB) and a liding bearing connected in erie (Hamaguchi et al. 21). Horizontal bidirectional characteritic are alo a growing concern in eimic iolation. Experimental tudie on LRB (Nakamura et al. 212) and elatic liding bearing (Yamamoto et al. 212a; Kamohita et al. 21) have been conducted. Thee tudie revealed that the retoring force of the bearing wa highly affected by horizontal bidirectional loading, while the hear train of a rubber bearing wa increaed by torional deformation induced by bidirectional loading. The propoed iolation ytem wa alo affected by horizontal bidirectional loading. Hence, dynamic loading tet, including horizontal bidirectional loading tet, of the propoed iolator were conducted uing reduced model. In addition, an analytical model wa formulated and validated baed on the tet reult. Thee experimental and analytical reult are decribed in the following. 2 LEAD RUBBER BEARING SYSTEM WITH FAIL-SAFE MECHANISM The author have propoed a eimic iolation ytem with a liding mechanim that maintain the

2 deformation of a rubber bearing within a certain allowable value. The ytem conit of a rubber bearing with damping capability, uch a an LRB or high damping rubber (HDR) bearing, and a liding bearing with a high friction coefficient. The two bearing are connected in erie. In thi tudy, an LRB wa ued a the rubber bearing. The ytem function a a conventional LRB during earthquake maller than DBE. The liding bearing lide under earthquake larger than DBE, preventing the failure of the LRB a well a the exceive deformation of the building. Thi ytem i imilar to a conventional elatic liding bearing (Hibino et al. 212) and to the iolator that wa ued in the Koeberg nuclear power plant (Guéraud et al. 1985). The iolator in Koeberg wa a combination of a chloroprene rubber bearing and liding bearing. The propoed ytem differ from thee iolator in that it ue a rubber bearing with damping capability and a fail-afe of a liding bearing in order to prevent the failure of the rubber bearing. 3 DYNAMIC LOADING TESTS Yamamoto et al. (212b) reported that hear train developed under torional deformation caued by horizontal bidirectional loading of an HDR bearing, and that the local hear train wa increaed under bidirectional loading compared to that formed under unidirectional loading. Thi behaviour i caued by the damping force of the iolator. The propoed ytem alo generate a damping force; therefore, horizontal bidirectional loading tet were conducted for reduced-ize pecimen to clarify the bidirectional characteritic of the propoed ytem. 3.1 Tet Specimen The real ize of the ytem are 9 9 mm and mm. The pecimen were both reduced to 2 2 mm in ize, a hown in Table 1. Specification of the tet pecimen are hown in Figure 1. While only one LRB for each ize wa ued in all tet, four et of the lider part (polytetrafluoroethylene (PTFE) plate and tainle teel liding plate) for each LRB, eight et in total, were placed and replaced for every vertical preure condition. Table 1. Specification of tet pecimen Item Specimen No.1 Specimen No.2 Nominal ize mm 2 (9)* 2 (15) * Thickne of rubber heet mm 1.29 (5.8) *.93 (7.) * LRB Number of rubber heet 3 (3) * 29 (29) * Thickne of inner teel plate mm 1.2 (.3) * 1.2 (.3) * Number of lead plug 1 () * 1 () * Slider Total area mm 2 38,35 (755,5) * 38,35 (2,11,) * * Value in round bracket indicate that for correponding aumed full-ize bearing. 65 mm Slider ( mm) Sliding plate ( mm) Lead core (φ mm) Sliding bearing LRB 25 mm Figure 1 - Section of tet pecimen. 2

3 3.2 Input Excitation Tet were conducted uing a three-axi teting machine (Yamamoto et al. 212a). Tet parameter were the horizontal loading orbit (Figure 2), vertical preure (Figure 3) on the lider, and loading frequency. Tet cae are lited in Table 2 according to thee parameter. A break-in loading wa conducted after replacing the lider part before tarting the tet erie in Table 2. Tet cae* i-j-1 / i-j-2 Vertical preure** (MPa) Horizontal orbit Unidirectional Table 2. Tet cae Frequency (Hz) Maximum velocity (mm/) Maximum diplacement (mm) 25.1 / (.)*** i-j-3 / i-j- :1 ellipe 2. / (8.5)*** i-j-5 / i-j-6, 8, 12, var 2:1 ellipe.2 / / (89.)*** i-j-7 / i-j-8 Circle 17.8 / (11.)*** i-j-9 / i-j-1 Unidirectional 25.1 / (.)*** * i (= 1, 2) repreent pecimen No.; j (=, 8, 12, var) repreent vertical preure. ** Condition var varie vertical preure according to major axi diplacement, a hown in Figure 3. *** Value in round bracket indicate maximum diplacement in the minor axi. 2 Repeated cycle Diplacement in minor axi (mm) Diplacement Diplacement Diplacement Diplacement in major axi (mm) in major axi (mm) in major axi (mm) in major axi (mm) 3.3 Meaured Item (a) Unidirectional (b) :1 Ellipe (c) 2:1 Ellipe (d) Circle Vertical preure (MPa) Figure 2 - Horizontal loading orbit MPa 8 MPa MPa Normalized major axi diplacement to maximum loading diplacement Figure 3 - Vertical preure pattern. The actuator diplacement and ix force component meaured by load cell were provided by the teting machine. In addition to thee meaurement, potentiometer-type diplacement tranducer were intalled to meaure the deformation of the rubber part directly. By uing four diplacement tranducer, torional deformation a well a two horizontal deformation were obtained (Yamamoto et al. 212a; Kamohita et al. 21). A thermocouple wa intalled at the centre of the liding plate from the rear ide. 3

4 3. Evaluation Method 3..1 Sliding Velocity, Vertical Preure, and Friction Coefficient Hereafter, ubcript of x, y, and z indicate that the value correpond to the major, minor, and vertical axe, repectively. Sliding velocity wa etimated at the centre of the lider urface to the liding plate. Vertical preure wa the vertical force, F z, meaured by the load cell divided by the lider urface area, A. The friction coefficient μ wa etimated a the horizontal force, F = (F x, F y), meaured by the load cell and divided by F z, and a a compenated value at 2 C (Hamaguchi et al. 213). Repreentative value for each tet cae were evaluated a the average value of the meaured item at the time when the diplacement in the major axi of lider part wa changed from poitive to negative, and later from negative to poitive. It i noted that the loading began a a poitive diplacement for all cae Shear Strain of LRB A torional deformation formed from a moment in the vertical axi, generated according to the horizontal bidirectional loading. The average hear train induced by torional deformation at the corner of the LRB, γ tor_ave, i etimated uing the oberved torional angle θ: ( d / 2) h (1) tor _ ave / where d and h are the diagonal length and total rubber thickne, repectively, of the LRB. Conidering the equilibrium of force hown in Figure (a), and auming the ditribution of moment and hear train a Figure (b), the hear train, γ tor_fix and γ tor_lider, at the fixed and liding end of the LRB at the corner are given by the following equation (Kamohita et al. 21): tor _ fix tor _ lider (2) tor_ ave tor _ ave tor_ dif (3) tor _ dif tor _ dif ( F F ) d /(GI ) () x y y x p where G and I p are the hear modulu and polar modulu, repectively, of the LRB. d F x M fix F y 3.5 Tet Reult Slider end Fixed end F y δ y δ x M lider F x (a) Equilibrium of force θ M fix Moment M lider tor_lider tor_ave Shear train Slider end Fixed end tor_fix Height of rubber part (b) Ditribution of moment and hear train by torional deformation Figure - Aumed condition. h Friction Characteritic of Slider Bearing The initial friction coefficient for tet cae No.i-j-1 and 2, and the rate of change of the final friction coefficient for the tet cae No.i-j-9 and 1 to the correponding initial friction coefficient are ummarized in Table 3. In the cae of j = var, conducted under variable vertical preure, the coefficient i etimated when the vertical preure i 8 MPa. The change of the friction coefficient i

5 not ignificant even after experiencing variou bidirectional loading. Figure 5 how a comparion of the friction coefficient under variou loading pattern from tet cae No.i-j-1 8 (i = 1, 2; j =, 8, 12). The following deign equation of the friction coefficient (Hamaguchi et al. 213) at 2 C i alo plotted in the figure: (, V ) ln(16 / V ) for V 16.2 (, V ).32 for V 16 (5) where V i the velocity of the lider part with unit of mm/. The unit of the vertical preure σ i MPa. The friction coefficient are almot equal under every loading pattern for both pecimen, and agree well with equation (5). Vertical preure (MPa) Table 3. Initial friction coefficient and change rate from initial to final Specimen No.1 Specimen No.2 Frequency (Hz) Change rate Initial Coefficient Initial Coefficient Change rate.2.16.% % % % % % % % %.19.7% % % var % %.2.13.% % Friction coefficient MPa 8 MPa 12 MPa Unidirectional :1 Ellipe 2:1 Ellipe Circle Sliding peed (mm/) 25 3 (a) Specimen No.1 Friction coefficient Figure 5 - Comparion of friction coefficient. MPa 8 MPa 12 MPa Unidirectional :1 Ellipe 2:1 Ellipe Circle Sliding peed (mm/) 25 3 (b) Specimen No Shear Strain in LRB The maximum hear train of LRB, γ centre, γ tor_fix, and γ fix under variou loading pattern and vertical preure are ummarized in Table. The value γ centre indicate the hear train at the centre of the LRB, which doe not include train due to torional deformation. The value γ fix i the ummation of γ centre and γ tor_fix; however, the maximum value of γ fix were etimated in the time domain, and hence did not match the ummation of the maxima of γ fix and γ centre. The reult for pecimen No.2 at.2 Hz (No.2-j-2,, 6, 8) are ued in the table, becaue the reult are almot the ame between pecimen No. 1 and 2, and at the frequencie.2 and.2 Hz. Bidirectional loading alo increaed γ centre from that meaured under unidirectional loading, a Yamamoto et al. (212a) reported for a conventional elatic liding bearing. The ratio of γ fix under bidirectional loading to that under unidirectional loading i calculated and lited in Table. The ratio i reduced with the vertical preure. 5

6 Photograph of the deformed LRB and the time-hitorie of γ centre, γ tor_fix, and γ fix are hown in Figure 6. For horizontal biaxial loading of circular hape under the vertical preure of MPa (Figure 6(b)), a large torional deformation of the rubber i oberved in the lider end of the LRB. In thi cae, the fixation degree of the lider end eem to be mall. However, for loading under the vertical preure of 12 MPa (Figure 6(d)), the fixation degree of the lider end eem ufficiently high to contrain the torional deformation at the end. Loading pattern* Vertical preure (MPa) Table. Shear train γ centre γ tor_fix γ fix Increae** Vertical preure (MPa) γ centre γ tor_fix γ fix Increae** Uni : % % 12 2: % % Circle % % Uni : % % 8 var 2: % % Circle % % * Uni: Unidirectional; :1: :1 Ellipe; 2:1: 2:1 Ellipe. ** Increae ratio of γ fix under bidirectional loading to unidirectional loading. Shear train γ fix γ γ tor_fix fix γ centre γ γ tor_fix γ centre centre γ tor_fix γ tor_fix Time () Time () Time () Time () (a) Unidirectional; MPa (b) Circle; MPa (c) Unidirectional; 12 MPa (d) Circle; 12 MPa γ fix γ centre Figure 6 - Photograph of deformed LRB and time-hitorie of hear train. γ fix SIMULATION ANALYSIS.1 Analytical Model An analytical mechanical model of the propoed bearing wa developed by modifying the model for an elatic liding bearing preented by Kamohita et al. (21). The propoed bearing model mut include the elato-platic behaviour of LRB, which wa not conidered in the previou model. Figure 7 how an illutration of the developed model. Thi model ha three node, which are repreentative of the fixed-end flange plate of the LRB (point P), the lider (point Q), and the liding plate (point O). Horizontal retoring force characteritic of the LRB were implemented between point P and Q. The LRB, which wa implemented between point P and Q, wa modelled a a multiple hear pring (MSS) model in which the elemental pring were modelled by the Kikuchi-Aiken model, a in Nakamura et al. (212). The liding bearing, implemented between point Q and O, wa modelled a a bidirectional friction element contituted by equation (5). The friction element and the LRB model affect each other intricately. In order to addre thi, the 6

7 following equation wa introduced. By iterating uing the equation, the parameter α and then the incremental diplacement of the friction element Δq x and Δq y are obtained: q q x y d x f x / kx ( 1 ) (6) d y f y / k y where d, f, and k denote the deformation, force, and tiffne of the LRB model, repectively. The parameter β wa et a.5 in thi tudy. The above analytical mechanical model wa implemented in the OpenSee oftware program (Open Sytem for Earthquake Engineering Simulation; Sliding plate Slider Q O Multiple hear pring Flange plate P.1. Simulation Reult Figure 7 - Analytical mechanical model. In the following, the tet reult from pecimen No.2 were ued for comparion. Figure 8(a) how the imulation reult for the force diplacement relationhip in the tet cae under the contant vertical preure of 8 MPa (No.2-8-1, 2, 5, 6). Figure 8(b) how the reult for the tet cae under varied vertical preure (No.2-var-1, 2, 5, 6). Conidering the effect of repeated loading on the pecimen, the econd tiffne and yield trength of the LRB model were adjuted by multiplying 1. and 1.3 time for the 8-MPa preure tet cae, and by.8 and 1.2 time for the varied-preure tet cae, repectively. The propoed model imulate the force diplacement relationhip well for both unidirectional and bidirectional loading, for both contant 8 MPa and varied preure, and for frequencie of both.2 and.2 Hz. 5 CONCLUSIONS A eimic iolation ytem with a high afety margin for large earthquake that exceed DBE wa propoed in thi paper. Thi ytem conit of a LRB and a liding bearing with a high friction coefficient connected in erie. Dynamic loading tet were conducted uing reduced-ize pecimen of 2 2 mm. The reult howed that the friction characteritic were almot equal among all teted loading pattern and agreed well with a deign equation identified baed on previou unidirectional loading tet reult. However, local hear train were increaed by bidirectional loading. Thi increaed hear train tendency wa dominant when the vertical preure wa mall. An analytical model of the propoed iolation ytem wa developed. Simulation analyi reult howed that the developed model imulated the force diplacement relationhip of the ytem well for both unidirectional and bidirectional loading, even under varied vertical preure. 6 ACKNOWLEDGEMENTS Thi reearch wa partially upported by the Japan Society for the Promotion of Science, Grant-in-Aid for Scientific Reearch (A), 15H227, 216. The author would like to expre their thank to thoe organization. Dynamic loading tet in thi paper were conducted at the Oile Corporation, Japan. The author would like to expre their thank to Mr. Nagata, Dr. Kouchiyama, and Dr. Nakamura of the Oile Corporation for their advice on the tet. The author would like to alo expre their thank to Dr. McKenna of the Univerity of California, Berkeley, for hi advice on the development of the imulation model. 7

8 Unidirectional 2:1 Ellipe Retoring force in major axi (kn) Retoring force in major axi (kn) Retoring force in minor axi (kn) 8 - Tet Analyi.2 Hz.2 Hz Diplacement in major axi (mm) Diplacement in major axi (mm) Hz.2 Hz Diplacement in minor axi (mm) Diplacement in minor axi (mm) (a) Tet under 8 MPa (tet cae No , 2, 5, 6) Retoring force in major axi (kn).2 Hz.2 Hz Diplacement in major axi (mm) Diplacement in major axi (mm) Hz.2 Hz.2 Hz.2 Hz - Retoring force in major axi (kn) Retoring force in minor axi (kn) Tet Analyi 8.2 Hz.2 Hz (b) Tet under varied vertical preure (tet cae No.2-var-1, 2, 5, 6) Figure 8 - Simulation reult. REFERENCES Guéraud, R. Noël-Leroux, J.P., Livolant, M. & Michalopoulo, A. P. 1985: Seimic iolation uing lidingelatomer bearing pad, Nuc. Eng. and De., 8(3): Hamaguchi, H., Yamamoto, M., Higahino, M. & Taniguchi, H. 21. A propoal of a eimic iolation ytem with high afety margin for unexpected input ground motion (part 1) Outline, Summ. Tech. Pap. Annu. Meet., AIJ, B2:37-38 (in Japanee). Hamaguchi, H., Yamamoto, M., Wake, T. & Miyazaki, M A propoal of a eimic iolation ytem with high afety margin for unexpected input ground motion (part 8) Evaluation of the dynamic friction factor of a uggeting bearing, Summ. Tech. Pap. Annu. Meet., AIJ, B2:83-8 (in Japanee). Hibino, H., Maeki, R., Nii, A., Minewaki, S., Yamamoto, M., Yoneda, H., Takayama, M., Kikuchi, M. & Iiba, M Safety verification of eimic iolation ytem uing liding bearing againt long period earthquake motion, 15th World Conf. Earthq. Eng., Libon, Portugal. Kamohita, N., Yamamoto, M., Minewaki, S., Kikuchi, M., Ihii, K., Kouchiyama, O. & Nakamura, T. 21. Horizontal bidirectional characteritic of elatic liding bearing under variou fluctuant vertical loading condition, J. Struct. Contr. Eng. AIJ, 79:53-6 (in Japanee). Nakamura, T., Kikuchi, M., Ihii, K. & Kouchiyama, O Hyterei propertie of lead rubber bearing under horizontal bi-directional deformation, J. Struct. Contr. Eng. AIJ, 77: (in Japanee). Yamamoto, M., Minewaki, S., Kamohita, N., Kikuchi, M., Ihii, K., Kouchiyama, O. & Nakamura, T. 212a. Behavior of a liding rubber bearing under horizontal bidirectional loading, 15th World Conf. Earthq. Eng., Libon, Portugal. Yamamoto M., Minewaki S., Yoneda, H. & Higahino, M. 212b. Nonlinear behavior of high-damping rubber bearing under horizontal bi-directional loading: Full-cale tet and analytical modelling, Earthq. Eng. Struct. Dyn., 1: