Seismic Protection of Structures with Base Isolation

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Paper regarding Base Isolation presented by myself at the 2009 Concrete Institute of Australia Biennial

Paper regarding Base Isolation presented by myself at the 2009 Concrete Institute of Australia Biennial

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  • 1. Concrete Solutions 09 Paper 7a-3 Seismic Protection of Structures with Modern Base Isolation Technologies Luis Andrade1 and John Tuxworth2 1 Senior Structural Engineer, Green Leaf Engineers 2 Director, Green Leaf EngineersSynopsis: Increased resistance to earthquake forces is not always a desirable solution for buildingswhich house contents that are irreplaceable or simply more valuable than the actual primary structure (egmuseums, data storage centres, etc). Base isolation can be employed to minimize inter-story drifts andfloor accelerations via specially designed interfaces at the structural base, or at higher levels of thesuperstructure.This paper presents the design comparison of two isolation systems (lead-rubber bearings, and frictionpendulum bearings) for a five-story reinforced concrete framed building. The response of the base-case,fixed-structure, and isolated systems is compared for dynamic analysis to actual historical records for fivesignificant seismic events.Keywords: bearing, concrete, damping, dissipation, drift, isolation, inter-storey, lead-rubber, pendulum,seismic.1. IntroductionConventionally, seismic design of building structures is based on the concept of increasing resistanceagainst earthquake forces by employing the use of shear walls, braced frames, or moment-resistantframes. For stiff buildings these traditional methods often result in high floor accelerations, and large inter-story drifts for flexible buildings. With both scenarios building contents and nonstructural components maysuffer significant damage during a major event, even if the structure itself remains basically intact.Obviously this is an undesirable outcome for buildings which house contents that are irreplaceable, orsimply more costly and valuable than the actual primary structure (eg museums, data storage centers,etc).The concept of base isolation is increasingly being adopted in order to minimize inter-story drift and flooraccelerations. In this instance the control of structural forces and motion is exercised through speciallydesigned interfaces at the structural base — or potentially at a higher level of the superstructure — thusfiltering out the actions transmitted from the ground. The effect of base isolation is to essentially uncouplethe building from the ground.This paper presents the design comparison of two isolation systems — Friction Pendulum System (FPS)and Lead-Plug Bearings (LPB) — for a five-story reinforced concrete framed building. The response of thefixed-base structure is compared to base-isolated cases for five different historical time-history records forsignificant earthquake events.2. Base Isolation SystemsThere are two common categories of large-displacement base (or seismic) isolation hardware: SlidingBearings and Elastomeric Bearings. This paper considers Friction Pendulum Systems (FPS) and Lead-Plug-Bearings (LPB), which belong to the first and second categories respectively.2.1 Friction Pendulum System (FPS)A FPS is comprised of a stainless steel concave surface, an articulated sliding element, and cover plate.The slider is finished with a self-lubricating composite liner (e.g. Teflon). During an earthquake, thearticulated slider within the bearing, travels along the concave surface, causing the supported structure tomove with gentle pendulum motions as illustrated in Figure 1(a) and 1(b). Movement of the slider 1
  • 2. Concrete Solutions 09 Paper 7a-3generates a dynamic frictional force that provides the required damping to absorb the earthquake energy.Friction at the interface is dependent on the contact between the Teflon-coated slider and the stainlesssteel surface, which increases with pressure. Values of the friction coefficient ranging between 3% to 10%are considered reasonable for a FPS to be effective, Wang (1).The isolator period is a function of the radius of curvature (R) of the concave surface. The natural period isindependent of the mass of the supported structure, and is determined from the pendulum equation:T = 2π R / g (1)where g is the acceleration due to gravity.The horizontal stiffness (KH) of the system, which provides the restoring capability, is provided by:kH = W / R (2)where W is the weight of the structure.The movement of the slider generates a dynamic friction force that provides the required damping forabsorbing earthquake energy. The base shear V, transmitted to the structure as the bearing slides to adistance (D), away from the neutral position, includes the restoring forces and the friction forces as can beseen on the following equation, where μ is the friction coefficient: WV = μW + D (3) RThe characterised constant (Q) of the isolation system is the maximum frictional force, which is defined as:Q = μW (4)The effective stiffness (keff) of the isolation system is a function of the estimated largest bearingdisplacement (D), for a given value of μ and R, and is determined by: μW Wk eff = V / D = + (5) D RA typical hysteresis loop of a FPS can be idealized as shown in Figure 1(c). Force Vmax 1 Q kH keff (a) 1 Dmax Displacement (b) (c) Figure 1. Motion in a FPS (a) initial condition, (b) displaced condition at maximum displacement, (c) Idealized Hysteresis Loop of a FPSThe dissipated energy (area inside the hysteretic loop) for one cycle of sliding, with amplitude (D), can beestimated as:E D = 4 μWD (6)Thus the damping of the system can be estimated as: 2
  • 3. Concrete Solutions 09 Paper 7a-3 ED 2 μβ= = (7) 4πk eff D 2 π D/R+μ2.2 Lead-Plug Bearings (LPB)The elastomeric LPB which are generally used for base isolation of structures consist of two steel fixingplates located at the top and bottom of the bearing, several alternating layers of rubber and steel shims,and a central lead core as shown in Figure 2(a). The elastomeric material provides the isolationcomponent with lateral flexibility; the lead core provides energy dissipation (or damping), while the internalsteel shims enhance the vertical load capacity whilst minimizing bulging. All elements contribute to thelateral stiffness. The steel shims, together with the top and bottom steel fixing plates, also confine plasticdeformation of the central lead core. The rubber layers deform laterally during seismic excitation of thestructure, allowing the structure to translate horizontally, and the bearing to absorb energy when the leadcore yields.The nonlinear behavior of a LPB isolator can be effectively idealized in terms of a bilinear force-deflectioncurve, with constant values throughout multiple cycles of loading as shown on Figure 2(b). Force Vmax 1 kd Q keff ki 1 Dmax Dy Displacement (a) (b) Figure 2. LPB isolator (a) components, (b) Idealized Hysteresis Loop of a LPBThe natural period of the isolated LPB system is provided by: WT = 2π (8) k eff gThe characterised strength (Q) is effectively equal to the yield force (Fy,) of the lead plug. The yield stressof the lead plug is usually taken as being around 10MPa. The effective stiffness (keff ) of the LPB, at ahorizontal displacement (D) being larger than the yield displacement (Dy) may be defined in terms of thepost-elastic stiffness (kd,) and characteristic strength (Q), with the following equation:k eff = k d + Q / D (9)As a rule of thumb for LPB isolators, the initial stiffness (ki) is usually taken as 10 x kd , Naeim et al (2).The energy dissipated for one cycle of sliding, with amplitude (D) can be estimated as:E D = 4Q ( D − D y ) (10)Following on from this assumption, it has been shown by Naeim et al (2) that the effective percentage ofcritical damping provided by the isolator can be obtained from: 3
  • 4. Concrete Solutions 09 Paper 7a-3 ED 2 Q ( D − Q / 9k Iβ= = (11) 4πk eff D 2 π (k i D + Q) D3. Model-building ConfigurationA reinforced concrete moment-resisting frame was adopted as the structural system for the analysisbuilding. Figure 3 (a) and 3(b) show the structural configuration of the building in plan. (a) (b) Figure 3. Structural configuration plans (a) 1st to 3rd floors. (b) 4th and 5th floors.Self weight of the structure was based on a concrete density (γ ) = 24 kN/m3. Super-dead loads of 1 kN/m2was also applied to represent floor finishes, and 140 mm thick, 2.5-m high hollow masonry partitions witha density of (γ ) = 15 kN/m3 were considered to contribute as a line-load along beams of 4.9 kN/m. Theimposed (live) load applied in each floor was taken as 2 kN/m2. Story heights were taken as 3 m.The Universal Building Code was considered in relation to seismic classification and variables, so as toenable consistency of symbols and nomenclature throughout the paper. Most international standardsincluding AS 1170.4:2007 are either based on, or align significantly with, UBC 1997(3). It was assumedthat the building ‘model’ was located in a Seismic Zone 4 of source Type A, and rests on a soil profileType C.4. Design ParametersAccording to Mayes et al (4), an effective seismic isolation system should have the followingcharacteristics:• sufficient horizontal flexibility to increase the structural period and accommodate spectral demands of the installation (except for very soft soil sites),• sufficient energy dissipation capacity to limit displacement to a practical level,• adequate rigidity to enable the building structure to behave similarly to a fixed base building under general service loadings.As recommended by both Naeim et al (2) and Mayes et al (4), a target period (T) of 2.2 seconds wasadopted for the isolated structure — approximately 3 times the fixed-base fundamental period (TF ) of 0.7seconds.Following UBC 1997, the target design displacement can be calculated as: 4
  • 5. Concrete Solutions 09 Paper 7a-3 ( g / 4π 2 )C VD TDD = (12) BDwhere CVD is a seismic coefficient, and BD is a damping coefficient which is a function of the effectivedamping β.From UBC 1997 Table 16-R, CVD = 0.56. An affective damping of 15% was assumed for both LPB andFPS — to be confirmed at the end of the design. From Equation 12, the design displacement = 220 mm.The effective stiffness for both bearing types was calculated following the formulas presented previously.Properties including damping, hardness, modulus of rigidity, modulus of elasticity and poisons ratio (forLPB), and friction coefficient (for FPS) were adopted from manufacturer’s data.As the performance of LPB isolators is weight dependant, three different sizes were incorporated in themodel. The positions nominated in Figure 5 were adopted to promote an economical design. Final designparameters and details for each isolator type are provided following.Detailed design calculations have been omitted for clarity, however iterative calculation is required toascertain effective stiffness and effective damping as both are typically displacement dependent.Figures 4(a) & 4(b) display cross-sectional details for isolator characteristics summarised in Tables 1 and2 respectively. R=1200mm (a) (b) Figure 4. Geometrical characteristics of Base Isolators (a) FPS. (b) LPB Type A Table 1. Design Parameters of FPS isolators. Symbol Value Nomenclature T (sec) 2.2 (Design Period) β (%) 15 (Effective damping) BD 1.38 (Damping factor) DD (mm) 220 (Design displacement Eq. 12) R (mm) 1200 (radius of curvature, calculated from Eq. 1) μ 0.057 (friction coefficient) (Force reduction factor, UBC 1997 Table A-16-E, Concrete special moment RI 2.0 resisting frame) W (kN) 7318 (Total weight of the building) Keff (kN/m) 7961 (Total effective stiffness Eq. 5) kH (kN/m) 6085 (Non-linear stiffness Eq. 2 ) 31033 ki (kN/m) (Elastic stiffness, taken as 51kH) 0 Q (kN) 416 (Frictional force Eq. 4) Dy (m) 1.4 (Yield displacement calculated as Q / ( ki- kH ) β (%) 14.9 (Check of assumed effective damping Eq. 7) 5
  • 6. Concrete Solutions 09 Paper 7a-3 Table 2. Design Parameters of LPB isolators. Parameter Value Nomenclature T (sec) 2.2 (Design period) β (%) 15 (Effective damping) BD 1.38 (Damping factor) DD (mm) 220 (Design displacement Eq. 12) G (MPa) 0.45 (Shear modulus) T (sec) 2.2 (Design period) Isolator Nomenclature Parameter Type A Type B Type C Wi (kN) 1030 740 510 (Axial load on isolator) Keff (kN/m) 840 604 416 (Effective stiffness calculated from Eq. 8) ED (kN-m) 38.9 28.0 19.3 (Global energy dissipated per cycle, calculated from Eq. 11) Q (kN) 43.9 31.5 21.7 (Short term yield force, calculated form Eq. 10) Kd (kN/m) 642 461 318 (Inelastic stiffness, calculated form Eq.9) Ki (kN/m) 6422 4614 3180 (Elastic stiffness, taken as 10kd) Kd / Ki 0.10 0.10 0.10 (Stiffness ratio) Dy (mm) 7.6 7.6 7.6 (Yield displacement, calculated as Q/9 kd) Fy (kN) 48.8 35.0 24.1 (Yield Force calculated as kiDy) Figure 5. Location of LPB isolators Type A, B and C.5. Modal AnalysisSAP2000 structural analysis software is capable of Time History Analysis, including Multiple BaseExcitiation. SAP2000 facilitates the dynamic modeling of base isolators as link elements, which can beassigned various stiffness properties. This stiffness values for both FPS and LPB isolators were calculatedas detailed in previous sections of this paper. Calculations associated with the following summary andtotaling some one-hundred pages have been excluded from the paper.Table 3 provides the fundamental period for the three cases studied: structure with fixed base; with FPSisolators; and with LPB isolators, as derived from an SAP2000 modal analysis. It can be seen that theperiods obtained for both types of isolator are close to the target period (T = 2.2 sec) recommended byNaeim et al (2) and Mayes et al (4). Figure 6 shows the shape of the first mode of vibration for the 3models. In addition to influencing fundamental period Figure 6 shows the isolators’ influence on modalshape. Table 3. Fundamental Periods Model Fundamental Period, T (sec) Fixed Base 0.73 LPB 2.23 FPS 2.05 6
  • 7. Concrete Solutions 09 Paper 7a-3 (a) (b) (c) Figure 6. First mode of vibration for (a) fixed base building, (b) FPS isolated building and (c) LPB isolated building.6. Time History AnalysisA nonlinear analysis was carried out in SAP2000 in order to test the response of the structural systems,and to validate isolator functionality. The models were subjected to the following historical seismic time-history records: • 1940 Imperial Valley Earthquake, El Centro Record (Richter Scale 7.1), • 1979 Imperial Valley Earthquake, El Centro Record, Array #5 (Richter Scale 6.4), • 1989 Loma Prieta Earthquake, Los Gatos Record (Richter Scale 7.1), • 1994 Northridge Earthquake, Newhall Record (Richter Scale 6.6), • 1995 Aigion Earthquake, Greece (Richter Scale approx. 5)A seismologist is of invaluable assistance when selecting applicable time-histories, however guidance forselecting scaling records can be gleaned from codes, Kelly (5). The events chosen for consideration inthis paper represent several of the major earthquakes in recorded history, with the 1995 AigionEarthquake in Greece being of similar magnitude to the Newcastle earthquake of 1989 (Richter Scale 5.6)Figure 7 shows maximum response values for each of the earthquake records for roof acceleration,elastic base shear, inter-storey drift, and isolator displacements.Maximum roof acceleration is dominated by the 1989 Loma Prieta earthquake record which yields a valueof about 36 m/sec2 for the fixed base structure, while for the isolated structures is in the order of 8.5m/sec2 (76% reduction) (see Figure 7(a)).Maximum elastic base shears are dominated also by the 1989 Loma Prieta earthquake. An elastic baseshear of approximately 120%W (where W is the building’s weight) for the fixed base building is reduced to35%W (68% reduction) and 45%W (63% reduction) for LPB and FPS isolators respectively (see Figure7(b)).Maximum Inter-storey drifts for fixed base and isolator cases are again generated by the 1989 LomaPrieta Earthquake, with values of about 129mm for the fixed base structure and 25mm (81% reduction)and 35mm (73% reduction) for LPB and FPS respectively (see Figure (c)). The drift ratio derived for Level-1 of the fixed base structure is 4.3%, about twice the maximum limit of 2% imposed by the UBC 1997. TheFPS isolated structure displays a value of 1.15% which is well under the limit.Figure 7(d) shows maximum isolator displacements in the order of 473mm and 469mm. It can be seen inFigure 7(e) that these values are round 215% of the isolator design displacement of 220 mm, indicatingthat both isolator systems would fail during the 1989 Loma Prieta Earthquake and 1994 NorthridgeEarthquake. 7
  • 8. Concrete Solutions 09 Paper 7a-3Force-Displacement hysteresis loops for the FPS and LPB isolator (Type A), as subjected to the 1989Loma Prieta earthquake record, are provided in Figures 8(a) and 8(b). These curves follow themathematical models presented in section 2 of this paper. Elastic and post-elastic stiffness can beobtained as the slopes of the first two initial segments. Roof Acceleration Elastic Base Shear 40 140 35 LBS LRB 120Acceleration (m/sec/sec) FPS FPS 30 V / W (%) Fixed Base 100 25 Fixed Base 80 20 60 15 40 10 20 5 0 0 1940 El 1979 El 1989 Loma 1994 1995 Aigion 1940 El 1979 El 1989 Loma 1994 1995 Aigion Centro Centro Prieta Northridge Centro Centro Prieta Northridge Earthquake Record Earthquake Record (a) (b) 1st Floor Inter - Story Drift Isolator Displacement 140 500 LRB LRB 450 Isolator Displacement (mm) 120 FPS FPS 400 100 350 Fixed Base 300 Drift (mm) 80 250 60 200 40 150 100 20 50 0 0 1940 El 1979 El 1989 Loma 1994 1995 Aigion 1940 El 1979 El 1989 Loma 1994 1995 Aigion Centro Centro Prieta Northridge Centro Centro Prieta Northridge Earthquake Record Earthquake Record (c) (d) Time History Displacement / Design Value 250% LRB FPS 200% 150% 100% 50% 0% 1940 El 1979 El 1989 Loma 1994 1995 Aigion Centro Centro Prieta Northridge Earthquake Record (e) Figure 7. Comparison of Response to the 5 earthquake records (a) roof acceleration, (b) elastic base shear (c) 1st floor inter-story drift, (d) isolator displacement, (e) time history displacement / design value utilization ratio. 8
  • 9. Concrete Solutions 09 Paper 7a-3The energy dissipated by each isolator is provided by the area inside each loop cycle. Effective dampingcan be calculated using Equations 7 or 11 and compared with the assumed design value. Note that thereis seemingly an anomaly present in Figure 8 (a), as maximum ‘-ve’ deflection for the FPS isolatorcorresponds to a reduction in elastic base shear. This anomaly was evident only for the Loma Prietaearthquake, and further study is required to ascertain why this issue occurred. (a) (b) Figure 8. 1989 Loma Prieta Earthquake Record. Force-displacement hysteresis loops for (a) FPS isolator (b) LPB isolator Type A. Lead Plug Bearing Friction Pendulum System Fixed Base 40.0 Acceleration (m/sec/sec) 20.0 0.0 -20.0 -40.0 0 5 10 15 20 25 30 Time (sec) Lead Plug Bearing Friction Pendulum System Fixed Base 9000 Base Shear (kN) 4500 0 -4500 -9000 0 5 10 15 20 25 30 Time (sec) Lead Plug Bearing Friction Pendulum System 500Isolator Displacement 250 (mm) 0 -250 -500 0 5 10 15 20 25 30 Time (sec) Figure 9. Time-history results for 1989 Loma Prieta earthquake record. (a) Roof acceleration, (b) elastic base shear, (c) isolator displacement. 9
  • 10. Concrete Solutions 09 Paper 7a-3Finally, time-history results for the Loma Prieta earthquake record are shown in Figure 9. It can be noticedfrom Figures 9(a) and 9(b) how the response in time of the isolated system is significantly less than thefixed base structure, specially between the first 10 to 15 seconds of the seismic excitation. Figure 9(c)compares the two types of isolators’ lateral displacements, which appears to be less for the FPS.7. Conclusions & RecommendationsIt can be seen that resultant accelerations, elastic base shears and inter-storey drifts were all effectivelyreduced by the adoption of Lead-Plug and Friction-Pendulum isolator systems, resulting in significantimprovement in modeled building performance, and a very likely minimisation of post-event losses. Forthe ground conditions and sway-frame structural system adopted, LPB & FPS base isolation would beexcellent options to reduce structural and non-structural damage, and to protect building contents. Boththe LPB and FP systems provided a comparative reduction in roof level accelerations (up to 76%);however the LPB provided the best reduction in elastic base shear, and inter-storey drift (at first floor). Forthe adopted bearing characteristics, the FPS provided greatest control of isolator displacement — asignificant serviceability constraint with respect to boundary conditions.Response of the isolated structural framing systems was dominated by the time-history record of the 1989Loma Prieta Earthquake. The second highest intensity experienced by the test structure was due to 1994Northbridge earthquake. The isolator design displacement (being a function of the nominated isolatorcharacteristics) of both systems was exceeded by these earthquakes, indicating alternate properties/sizeswould be required to accommodate higher intensity events.Further work is recommended to establish applicability of these base-isolation systems for the commonbraced-frame structural framing paradigm, and also to confirm suitability (or lack thereof) for high-riseconstruction, and or use on deep alluvial soil strata as evident in Australian centers such as Newcastle.8. References 1. Wang, Yen-Po, “Fundamentals of Seismic Base Isolation”, International Training programs for Seismic Design of Building Structures. 2. Naeim, F. & Kelly, J. M., “Design of Seismic Isolated Structures: From Theory to Practice”, John Wiley & Sons, Inc. 1999. 3. International Conference of Building Officials, ICBO (1997), “Earthquake Regulations for Seismic- Isolated Structures”, Uniform Building Code, Appendix Chapter 16, Whittier, CA. 4. Mayes, R. & Naeim, F., “Design of Structures with Seismic Isolation”, Earthquake Engineering Handbook, University of Hawaii, CRC Press, 2003. 5. Kelly, T. E., “Base Isolation of Structures Design Guidelines”, Holmes Consulting Group Ltd, July 2001. 10