NONLINEAR SEISMIC RESPONSE OF BASE-ISOLATED BUILDINGS CONSIDERING POUNDING

Transcription

1 8CUEE CONFERENCE PROCEEDINGS 8th Internationa Conference on Urban Earthquake Engineering March 7-8,, Tokyo Institute of Technoogy, Tokyo, Japan NONLINEAR SEISMIC RESPONSE OF BASE-ISOLATED BUILDINGS CONSIDERING POUNDING Deepak Raj Pant ) and Ani C. Wijeyewickrema ) ) Graduate Student, Department of Civi and Environmenta Engineering, Tokyo Institute of Technoogy, Japan ) Associate Professor, Department of Civi and Environmenta Engineering, Tokyo Institute of Technoogy, Japan pant.d.aa@m.titech.ac.jp, wijeyewickrema.a.aa@m.titech.ac.jp Abstract: Previous studies have shown that pounding of seismicay isoated buidings during earthquakes coud significanty affect the performance of these buidings. In this paper anaysis of seismic pounding of a typica 4-story base-isoated reinforced concrete (RC) buiding with retaining was at the isoation eve is presented. A modified Kevin-Voigt impact force mode, which does not have the imitations of the conventiona mode, is used to simuate impact. Geometric and materia noninearities are considered in the anaysis. The effect of seismic pounding on the performance of the buiding is evauated based on drift demands and damage indices. The findings of the study are expected to assist design and evauation of typica mid-rise base-isoated RC buidings.. INTRODUCTION Seismic pounding refers to coision between adjacent structures during earthquakes. It occurs when structures with different dynamic characteristics, having insufficient separation between them vibrate out of phase. Earthquake reconnaissance surveys have reported that seismic pounding of fixed-base buidings may ead to severe damage and even resut in compete coapse (Rosenbueth and Mei 986, Kasai and Maison 997). At east one case of seismic pounding of base-isoated buidings has been reported viz. the Fire Command and Contro (FCC) buiding in Los Angees experienced one-sided pounding with the entry bridge during the 994 Northridge earthquake. Increased story shear, drift and acceeration demands on the stee structure were evident due to pounding (Nagarajaiah and Sun ). Athough seismic pounding of fixed-base buidings has been studied extensivey (Maison and Kasai 99, Pant et a. ) for two decades, it is ony recenty that the seismic pounding of base-isoated buidings has drawn the attention of researchers (see for exampe Matsagar and Jangid 3, Poycarpou and Komodromos ). A previous studies reated to seismic pounding of base-isoated buidings have been carried out where the buidings were modeed as eastic or eastopastic shear beams or eastic muti-degree-of-freedom umped mass systems. However, these simpified modes cannot incorporate characteristics of the reaistic buiding materias such as reinforced concrete (RC). Therefore, the response of a base-isoated RC buiding considering seismic pounding is not we understood. Owing to the increasing use of base isoation technoogy for seismic protection of mid-rise RC buidings around the word, it is important to study the seismic pounding response of such buidings. In this study, seismic pounding of a typica mid-rise base-isoated RC buiding with retaining was at the base is studied. The effect of seismic pounding on the performance of the buiding is assessed using three-dimensiona noninear finite eement (FE) anaysis.. IMPACT SIMULATION The contact eement approach is widey used for the simuation of impact between structures, due to its cear physica meaning and simpe agorithm. The appropriate force-deformation reationship of the contact eement is one of the important issues in pounding simuations. Hence, there have been numerous efforts to deveop various impact force modes for these contact eements. Athough noninear impact force modes are aso avaiabe, the inear impact force modes provide a good baance between simpicity and accuracy. The Kevin-Voigt (KV) mode, which can be represented by the combination of a spring and a dashpot in parae, is the most widey used impact force mode. In this mode, the impact force F between the impacting bodies is, kδ + cδ δ >, F = () δ, where k is stiffness of spring eement, c is damping coefficient and indentation δ and reative veocity of impact δ are given by,

2 δ = u u d, δ = u u, () i j g i j where u i and u j are dispacements and u i and u j are veocities of impacting nodes i and j, respectivey and d g is at-rest gap distance between the impacting nodes. The damping coefficient c in Eq. () can be expressed in terms of the coefficient of restitution r, which is defined as the ratio of the reative veocity after impact to the reative veocity before impact. The expression for the damping coefficient in the KV mode is (Anagnostopouos 4), ( ) c ξ km, (3) = eff where the stiffness k in the absence of experimenta studies is determined based on the axia stiffness of coiding bodies and the effective mass m eff and damping ratio ξ are given by, m mm n( r),, m + m π + (n( r)) eff = ξ = where m and m are masses of the coiding bodies. Athough the mode is attractive due to its simpicity, the imitations are: (i) Due to a constant damping coefficient, it shows a sudden jump in the impact force at the beginning of impact, which is not reasonabe for concrete-to-concrete impact (Fig. ). This sudden jump in the force induces unreaistic high acceerations in the impacting bodies. (ii) Due to the dashpot being activated even in the restitution phase, the coiding bodies exert tension on each other just before the separation (Fig. ), which has no physica meaning. Hence, a modification to the KV mode referred to as the Modified Kevin-Voigt (MKV) mode was proposed by Pant et a.. The MKV mode is based on the assumption that most of the energy during impact is dissipated in the compression phase. Hence, the energy dissipated in the restitution phase can be negected. This assumption aows for the remova of the dashpot from the spring-dashpot assemby in the restitution phase. The impact force F between the impacting bodies can be expressed as, (4) beginning of impact, the damping coefficient c is taken to be directy proportiona to the indentation δ as, c = ξδ. (6) This eads to a new reationship between ξ and r as, ( r ) 3k ξ = r δ where δ is reative veocity before impact. The reationship between impact force and indentation for the MKV mode is shown schematicay in Fig.. It is cear from Fig. that the sudden jump in impact force at the beginning of impact and the tensie impact force just before the separation of the KV mode are no onger present. Thus, a the major imitations of the KV mode are eiminated in the MKV mode, whie maintaining the simpicity and cear physica meaning of the KV mode. Furthermore, the mode is impemented in FE program OpenSees in the form of a uniaxia materia and is used to simuate seismic pounding of a base-isoated buiding in subsequent sections. It is noted that other researchers have aso proposed different modifications to the KV mode. However, a comparison of these modes with the MKV mode has shown that the MKV mode is more rationa for seismic pounding simuation of muti-story buidings (Pant ). To verify the correctness of the derived formua (Eq. (7)) and its proper impementation in OpenSees, numerica verification is conducted by simuating the first instance of impact between a spherica ba and a stationary rigid surface. A ba of mass m =. kg is dropped freey from a height h =.5 m on a stationary rigid surface (Fig. ). Different vaues of coefficient of restitution r pre are specified, pounding simuations are performed and the coefficient of restitution from the simuation r post are obtained and compared with the pre-specified vaues. In OpenSees, the simuation is conducted using two-dimensiona FE method. The FE mode of the probem is shown in Fig.. The stationary rigid surface and the spherica ba are modeed as node and node, respectivey. Node is fixed and node is free to move F k F, k (7) kδ + δ δ > and c δ >, F = k δ δ > and δ, (5) δ. δ δ In order to avoid a sudden jump in the impact force at the Fig.. Schematic force-indentation curve for one instance of impact for: KV mode; MKV mode.

3 spherica ba h m stationary rigid surface Fig.. Drop weight impact simuation: schematic diagram; finite eement ideaization. Tabe. Comparison of pre-defined and simuated vaues of coefficient of restitution using MKV mode. ony in the vertica direction. A contact eement needs to be paced between the nodes to simuate the pounding phenomenon. Here, a so caed zero-ength eement avaiabe in OpenSees is chosen. With the zero-ength eement, end nodes of the eement can have same coordinates. Particuar choice of zero-ength eement as contact eement becomes very advantageous whie performing a arge number of numerica simuations of seismic pounding between structures with various at-rest gap distances. The noda coordinates of the adjacent structures need not to be revised for each gap case; rather the gap parameter in the associated uniaxia materia ony needs to be changed. For the present simuation, the MKV mode is assigned to the aforementioned contact eement. The 7 stiffness of spring eement k is set to. N/m. In the free fa condition, node has a constant acceeration of g in downward direction. Hence, a uniform acceeration oading is appied at node. To be consistent with the seismic pounding simuations going to be discussed in forthcoming sections, the appied acceeration is treated from the viewpoint of uniform ground acceeration. The resuting system of noninear equations is soved using Newmark s method of constant acceeration ( β =.5, γ=.5), where Modified Newton-Raphson node node r pre r post Reative error (%) uniform acceeration g contact eement method is used for iterative soution. The anayses are performed for.35 sec with a time step of 7 sec. The vaues of r post obtained from pounding simuation are compared with r pre and reative error is computed as rpre rpost r pre. The comparison is shown in Tabe. The reative error reduces with increasing r. The coefficient of restitution used to simuate structura pounding ranges from.5 to.75 (Jankowski 5). It is cear from Tabe that the reative error is sma for the vaues of coefficient of restitution in this range. This shows that the reationship between ξ and r given by Eq. (7) is correct and hence can be used for rationa simuation of structura pounding. 3. SEISMIC POUNDING CASES A 4-story, -bay by -bay base-isoated RC buiding is considered to investigate the effect of pounding on the response of a typica mid-rise structure. The bay widths and story heights are 6 m and 3.6 m, respectivey. The buiding is supposed to be used as an eementary schoo such that substantia hazard to human ife is expected in case of faiure. The buiding is assumed to be ocated at a stiff soi site. Two cases of seismic pounding of this buiding are examined: (i) Pounding with the retaining wa on one side (Fig. 3), (ii) Pounding with the retaining was on both sides (Fig. 3). The retaining wa extends from ground eve up to the isoation eve (Fig. 3). The buiding was designed foowing the 9 Internationa Buiding Code (ICC 9). According to the code, an equivaent atera force procedure was used for the design of this buiding. ACI 38-8 (ACI 8) was foowed for the design of the structura concrete. Compressive strength, unit weight and moduus of easticity 3 of concrete are taken as 8 MPa,.76 kn/m and 4.5 MPa, respectivey. The yied strength of main stee reinforcement bars and ties are taken as 4 MPa and 3 MPa, respectivey. The unit weight and moduus of easticity of stee are assumed to be base-isoated buiding retaining wa Fig. 3. The base isoated buiding with: retaining wa on one side; retaining was on both sides.

4 kn/m and.99 MPa, respectivey. Live oads on foors and roofs are assumed to be 4.79 kn/m and.96 kn/m, respectivey. Tota wa thickness is taken as 3 mm with a unit weight of approximatey 3 5. kn/m. The sab thickness is mm. For the foor finish, a mm thick porceain tie with a unit weight 3 of 3.57 kn/m is taken. Seismic force-resisting system of the buiding is chosen as specia moment-resisting frame (SMRF). The ead rubber bearing (LRB) isoation system is seected for the buiding. Bearings are designed for gravity and earthquake oads using SAP (9) and Microsoft Exce spreadsheets. Identica circuar bearings of 75 mm diameter and 57 mm height are provided under each of the 9 coumn bases. A tota of 3 ayers of rubber with a ayer thickness of 5 mm are used. Stee shim thickness is taken as mm. The design dispacement D D and tota maximum dispacement D TM of the isoation system are 5 mm and 46 mm, respectivey. Figure 4 shows the cross-section of the bearing. In order to investigate the infuence of separation, the structures are assumed to be separated by different at-rest gap distances d g in both of the pounding cases. It is considered that the gap between buidings can be as sma as haf of the design dispacement D D. Therefore, ratio of at-rest gap distance to the design dispacement is taken as.,.9,.8,.7,.6 and.5. For performance evauation, four earthquake ground motions are seected from 968 Hachinohe, 94 E Centro, 995 Kobe and 994 Northridge earthquakes (see Tabe for detais of ground motions). The earthquake ground motions are matched to the design response spectrum at 5% damping using waveet adjustments. The program RspMatch5 (Hancock et a. 6) is used to match the ground motions simutaneousy to the design acceeration response spectrum (Fig. 5) and the design dispacement response spectrum for natura periods up to 6 sec. 4. NUMERICAL MODELING AND ANALYSIS A macromode-based approach is adopted for three-dimensiona modeing of seismic pounding of the base-isoated buiding in OpenSees. There are three Fig. 4. Cross-section of the bearing (a dimensions are in mm) Tabe. Detais of earthquake ground motions. Earthquake Date Station PGA (g) Hachinohe 968/5/6 Hachinohe city.39 E Centro 94/5/9 E Centro Array #9.33 Kobe 995//7 JMA Kobe.8 Northridge 994//7 Rinadi Receiving Station.85 Pseudo acceeration (g) Design E Centro Hachinohe Northridge Kobe Natura period (sec) Fig. 5. Comparison of eastic pseudo acceeration response spectra of matched ground motions with design acceeration response spectrum. modeing issues to be addressed viz. modeing of structura members which are beams, coumns, ead rubber bearings and sabs, modeing of retaining was and modeing of impact. Reinforced concrete beams and coumns are modeed using force-based, fiber beam-coumn eements, which are considered as most accurate and robust distributed pasticity eements. In fiber beam-coumn eements, the eement response is evauated at certain number of integration points i.e. sections aong the ength of the eement and each section is discretized into unconfined concrete, confined concrete and stee fibers (Fig. 6, 7). Uniaxia materias with noninear constitutive reationship are assigned to these fibers. Section constitutive reationship is derived from the integration of constitutive reationship of fibers. There are severa materia modes to describe noninear constitutive reationship of concrete and stee under monotonic as we as cycic oading. In this study the modified Kent and Park mode (Park et a. 98) is used for the response of concrete in compression. In tension, a inear eastic branch is foowed by a inear softening branch up to zero stress (Fig. 8). For reinforcing stee, the constitutive mode of Menegotto and Pinto (Menegotto and Pinto 973) is used (Fig. 8). Lead rubber bearings are modeed using eastomeric bearing eements. A biinear hysteretic mode (Fig. 8(c)) is used to describe shear force-deformation reationship of these eements. Foor and roof sabs are not modeed expicity; rather their restraining effect is accounted for by assuming an in-pane rigid diaphragm response. Retaining was are modeed as rigid objects. Backfi soi-structure

5 integration points Fig. 6. A fiber beam-coumn eement. = + + RC section unconfined concrete fibers confined concrete fibers stee fibers Fig. 7. Discretization of RC section into unconfined concrete, confined concrete and stee fibers. σ σ F ε ε δ (c) Fig. 8. Stress-strain reationship of concrete; stress-strain reationship of reinforcing stee; (c) biinear hysteretic mode of eastomeric bearing eements. interaction is considered outside the scope of this study. Impact is modeed using zero ength eements, which are used as contact eements between structures at foor eves (Fig. 3). The materia property of the contact eements is based on the MKV mode. The coefficient of restitution r is taken as.65 and stiffness of spring eement k is assessed based on the axia stiffness of a sab. Noninear time-history anayses are performed. Time integration of equations of motion is accompished using Newmark s method of constant acceeration. A time step of.5 sec is used for a the cases. The noninearity of the probem demands an iterative soution procedure. At the beginning of each time step modified Newton-Raphson method is empoyed for the iterative soution and the method is changed if the convergence is not achieved in the time step. There are many aternatives to modified Newton-Raphson method in OpenSees such as Newton with ine search or Broyden method. The convergence of the soution is based on energy increment. For damping in the buiding, stiffness proportiona damping is appied to the superstructure ony. A damping ratio of 5% is used for the first mode of the isoated structure. The accuracies of impact force mode and FE modeing have been vaidated using an avaiabe impact experiment and a shake tabe test of a base-isoated RC buiding, respectivey. Detais of the vaidation are shown esewhere (Pant ). 5. RESULTS AND DISCUSSION Inter-story drift ratio and overa damage index (ODI) based on Park and Ang damage index (Park et a. 985) are presented to iustrate the infuence of pounding on the structura performance of the base-isoated buiding.

6 Tabe 3. Vaues of inter-story drift ratios and overa damage indices for performance evauation of RC buidings. Degree of damage Physica appearance Inter-story drift ratio (%) ODI No damage Minor ocaized cracking drift ratio <.5 ODI <. Minor to moderate damage Severe damage Light cracking throghout to extensive cracking and ocaized spaing of concrete Extensive crushing of concrete and exposure of bucked reinforcement.5 drift ratio <.5. ODI <.4.5 drift ratio < 3..4 ODI <. Tota coapse Compete oss of oad carrying capacity drift ratio 3. ODI. Foor eve R 3F F F B 3 Inter-story drift ratio (%) No pounding d g /D D =. d g /D D =.9 d g /D D =.8 d g /D D =.7 d g /D D =.6 d g /D D =.5 ODI No pounding d g/d D =. d g/d D =.9 d g/d D =.8 d g/d D =.7 d g/d D =.6 d g/d D =.5 Fig. 9. Response of the base-isoated buiding considering pounding with the retaining wa on one side: peak inter-story drifts; overa damage indices. Foor eve R 3F F F B 3 Inter-story drift ratio (%) No pounding d g /D D =. d g /D D =.9 d g /D D =.8 d g /D D =.7 d g /D D =.6 d g /D D =.5 ODI No pounding d g/d D =. d g/d D =.9 d g/d D =.8 d g/d D =.7 d g/d D =.6 d g/d D =.5 Fig.. Response of the base-isoated buiding considering pounding with retaining was on both sides: peak inter-story drifts; overa damage indices. The damage can be cassified as no damage, minor to moderate damage, severe damage and tota coapse based on inter-story drift ratio and ODI as shown in Tabe 3. Note that to highight the trends in the response, the resuts presented represent maximum responses generated due to a four earthquake excitations. When the pounding of the base-isoated buiding is considered with the retaining wa on one side, the peak inter-story drift ratio, which is ess than.5% at the first story when there is no pounding, becomes more than.% due to pounding (Fig. 9). This impies that the base-isoated buiding experiencing no damage without any interaction with adjacent structures undergoes minor to moderate damage due to pounding. In genera, the inter-story drift demand increases with reduction in the gap. In addition, the maximum inter-story drift occurs at the first story and graduay reduces at upper stories. The minor to moderate damage to the buiding is aso evident from Fig. 9, where ODI remains ess than.4. A cear pattern of overa damage is aso observed from Fig. 9. Overa damage index increases rapidy for the gaps up to 7% of the design dispacement and becomes neary constant for further reduction in the gap. Significant increase in the demands is observed in case

7 of pounding with the retaining was on both sides compared to one-sided pounding (Fig. ). The peak inter-story drift demand at the first story ceary exceeds.5% for the gaps smaer than 8% of design dispacement, denoting severe damage to the story. Imminent coapse of the story is evident at a gap equa to 6% of the design dispacement. The infuence of pounding is ess severe at upper stories. Fig. shows cear trend in the overa damage to the buiding for various gaps. With decreasing gap, the ODI first increases and then reduces with further reduction of the gap. This impies that there exists a critica at-rest gap distance causing maximum damage to the base-isoated buiding. 6. CONCLUDING REMARKS This study investigates the performance of a typica mid-rise base-isoated RC buiding considering seismic pounding. It is found through series of numerica anayses that the seismic pounding has detrimenta effects on the response of a base-isoated RC buiding. Whie one-sided pounding with a retaining wa at the base causes minor to moderate damage to the base-isoated buiding, two-sided pounding with retaining was at the base coud even ead to its coapse, depending upon the cear space maintained around the buiding. The present study ony focuses on the evauation structura damage to the buiding due to pounding. Evauation of the non-structura damage, which requires accurate estimation of foor acceerations in the buiding, coud be studied in the future. Furthermore, the present study is ony focused on the seismic performance evauation of base-isoated buidings. The mitigating measures against pounding shoud aso be studied in the future. Acknowedgements: The first author is peased to acknowedge a Monbukagakusho (Ministry of Education, Cuture, Sports, Science and Technoogy, Japan) schoarship for graduate students. Financia support from the Center for Urban Earthquake Engineering (CUEE) through the GCOE Program Internationa Urban Earthquake Engineering Center for Mitigating Seismic Mega Risk, is gratefuy acknowedged. Engineering and Structura Dynamics, 34, Kasai, K. and Maison, B. (997), Buiding pounding damage during the 989 Loma Prieta earthquake, Engineering Structures, 9, Maison, B.F. and Kasai, K. (99), Dynamics of pounding when two buidings coide, Earthquake Engineering and Structura Dynamics,, Matsagar, V.A. and Jangid, R.S. (3), Seismic response of base-isoated structures during impact with adjacent structures, Engineering Structures, 5, Menegotto, M. and Pinto, P. (973), Methods of anaysis for cycicay oaded R/C frames, Proceedings of the Symposium of Resistance and Utimate Deformabiity of Structure Acted by We Defined Repeated Load, IABSE, Lisbon, Portuga. Nagarajaiah, S. and Sun, X. (), Base-isoated FCC buiding: impact response in Northridge earthquake, Journa of Structura Engineering, ASCE, 7(9), OpenSees (), Open system for earthquake engineering simuation. < Pant, D.R. (), Seismic Pounding of a Base-Isoated Buiding with Adjacent Structures, M. Eng. Thesis, Tokyo Institute of Technoogy. Pant, D.R., Wijeyewickrema, A.C. and Ohmachi, T. (), Three dimensiona noninear anaysis of seismic pounding between muti-story reinforced concrete buidings, Proceedings of the Seventh Internationa Conference on Urban Earthquake Engineering (7CUEE) and Fifth Internationa Conference on Earthquake Engineering (5ICEE), March 3-5, Tokyo, Japan, Park, R., Priestey, M.J.N. and Gi, W.D. (98), Ductiity of square-confined concrete coumns, Journa of Structura Engineering, ASCE, 8, Park, Y., Ang, A.H. and Wen, Y.K. (985), Seismic damage anaysis of reinforced concrete buidings, Journa of Structura Engineering, ASCE, (4), Poycarpou, P.C. and Komodromos, P. (), Earthquake-induced poundings of a seismicay isoated buiding with adjacent structures, Engineering Structures, 3, Rosenbueth, E. and Mei, R. (986), The 985 earthquake: causes and effects in Mexico City, Concrete Internationa (ACI), 8, SAP (9), Integrated finite eement anaysis and design of structures, Computers and Structures, Inc., Berkeey, CA. References: ACI (8), Buiding Code Requirements for Structura Concrete (ACI 38-8) and Commentary (ACI 38R-8), ACI Committee 38, American Concrete Institute, Farmington His, MI. Anagnostopouos S.A. (4), Equivaent viscous damping for modeing ineastic impacts in earthquake pounding probems, Earthquake Engineering and Structura Dynamics, 33, Hancock, J., Watson-Lamprey, J., Abrahamson, N.A., Bommer, J.J., Markatis, A., Mccoy, E. and Mendis, R. (6), An improved method of matching response spectra of recorded earthquake ground motion using waveets, Journa of Earthquake Engineering, (Sp. ), Internationa Code Counci (ICC) (9), Internationa Buiding Code, IBC 9, Country Cub His, Iinois. Jankowski, R. (5), Non-inear viscoeastic modeing of earthquake-induced structura pounding, Earthquake