Effect of bearing characteristics on the response of friction pendulum base-isolated buildings under three components of earthquake excitation

Effect of bearing characteristics on the response of friction pendulum base-isolated buildings under three components of earthquake excitation M.Rabiei Department of Civil Engineering, University of AmirKabir, Tehran, Iran. 2008 NZSEE Conference ABSTRACT: This investigation has been conducted to examine the effect of bearing characteristics on the response of friction pendulum base-isolated buildings under three components of earthquake excitation. The structure is idealized as a three-dimensional single-story building resting on a friction pendulum bearing. The coupled differential equations of motion for the isolated system are derived and solved in the incremental form using Newmark s step-by-step method of integration. The response of this system subjected to three components (including vertical component), two components (excluding vertical component) and single component (excluding vertical component and no interaction between orthogonal directions) of Tabas 1940 and two records of Northridge 1994 earthquakes are investigated. The effect that the vertical component of the earthquake has on the peak values of both the bearing displacement and the base shear of the isolated structure is investigated. This includes variation of the bearing characteristics, such as the isolation period and friction coefficient of the sliding surface. It is demonstrated that bearing characteristics could significantly influence the response of friction pendulum base-isolated structure subjected to three components of earthquake excitation. 1 INTRODUCTION Seismic isolation is the separation of the building (or any other type of structure) from the harmful motions of the ground by providing flexibility and energy dissipation capability through the insertion of the so-called isolators between the foundation and the superstructure. It is not a long time since the first application of the isolators. The first base-isolated building in the United States of America was built in 1985 (Zayas et al., 1987). In terms of behaviour, isolators are classified in two major groups: elastomeric and frictional isolators. Kelly (Kelly et al., 1986), Su (Su et al., 1989). and Skinner (Skinner et al., 1993) provided comprehensive reviews on isolation devices and techniques. The use of base isolation systems has two major advantages. First, the vertical and horizontal loads are resisted in different ways. This results in a more stable structural system and eliminates the need for a mechanism to dissipate energy while preventing structural collapse. Second, in the presence of a small restoring force, the sliding systems are (practically) insensitive to frequency content of the base excitation and always limit the transmitted shear force to the building. This feature (insensitivity to frequency content of the base excitation) is the most important benefit of a sliding system. A significant amount of the past research in the area of base isolation has focused on the use of frictional elements to concentrate flexibility of the structural system and to add damping to the isolated structure. The simplest sliding system device is a pure-friction (P-F) system without any restoring force (Mostaghel et al., 1983 & Yang et al., 1990). The P-F system supporting a relatively rigid superstructure is very effective for a wide range of frequency input and transmits a limited earthquake force equal to the maximum limiting frictional force (Mostaghel et al., 1983). However, the large sliding and residual displacement in the P-F system render it unsuitable for practical applications to important structures. To overcome this, the sliding systems with restoring force had been proposed and studied such as the resilient-friction base isolator (R-FBI) system (Mostaghel et al., 1987), the Electricite de France (EDF) system (Gueraud et al., 1985) and the friction pendulum system (FPS) (Zayas et al., 1990). 1

Housing Plate Slider Figure 1. Cross section of a Friction Pendulum (FP) system The friction pendulum (FP) system is a sliding type seismic isolation system which uses its surface curvature to generate the restoring force from the pendulum action of the weight of the structure on the FPS (Fig. 1). The natural period of the isolated structure becomes independent of the mass of the superstructure, as it only depends on the radius of the sliding surface. This behaviour allows the superstructure to avoid changes in the natural period with the varying mass as in a liquefied natural gas tank. Another important mechanism is the energy dissipation mechanism related to the velocity dependent friction between the articulated sliding surface and the composite material on the slider (Tsopelas et al., 1996). This study investigates the effect of bearing characteristics on the response of a three-dimensional base-isolated structure, using the friction pendulum bearing under different earthquakes. The specific objectives of the study are: (i) Examining the effects of the bearing characteristics, such as isolation period, bearing's friction coefficient, on the response of the isolated structures with friction pendulum bearings. (ii) Examining the effect of the interaction between horizontal components of bearing displacement on the maximum values of the isolated structures response. (iii) Examining the extent of the effect of vertical component of earthquake on the peak values of the isolated structure responses 2 MATHEMATICAL MODELING OF FRICTION PENDULUM BEARINGS The force-displacement relationship of FP bearing undergoing unidirectional excitation can be described by (Zayas et al., 1987): N F b = ub + µ N sgn( u& b ) (1) R Where u b is the bearing displacement, N is the normal load on the bearing, R is the radius of curvature of sliding surface, µ is coefficient of friction, and sgn is the signum function. If the FP bearing is subjected to a bi-directional motion then the force-displacement relationship can be expressed by the following equation (Mosqueda et al., 2004): F F Where [ xb yb = ] T x u y N R u u xb yb 1 u& xb + µ N (2) u& b u& yb u, [ u & & ] T and [ ] T x u y F are the bearing displacement, velocity and resisting xb F yb force vectors respectively. The coefficient of sliding friction between the PTFE and stainless steel is known to be velocity dependent, which can be modeled as (Mokha et al., 1988): ( f f ) ( & ) µ = f exp a u t (3) max max min Sliding Surface Where f min is the coefficient of friction at a large sliding velocity, f max is the coefficient of friction at 2

a low sliding velocity, u& t is the total sliding velocity, and a is a constant that controls the variation of the coefficient of friction with sliding velocity. In this study f min and a are considered to be constant and equal to 0.03 and 100 s/m, respectively (Fenz et al., 2006). Also the period of the fixed-base structure is Kept constant and equal to 0.1sec. The isolation period ( T i ) of the structure isolated with friction pendulum system is independent of the superstructure weight and can be expressed by the following equation (Al-Hussaini et al., 1994): T i R = 2π (4) g 3 MODELING OF BASE-ISOLATED BUILDING Figure 2 represents the assumed structural system, which is an idealized three-dimensional singlestory building model, mounted on a friction pendulum bearing. The top mass m s and base mass m b are rigid decks supported on axially inextensible mass-less columns. The superstructure is assumed to be linear elastic. This is a reasonable assumption, since the purpose of the base isolation is to reduce the earthquake forces on the structure. The center of mass (CM) of the top deck and the base deck are assumed to be vertically aligned. As a result, there is no torsional coupling. β Represents the ratio between the vertical and horizontal vibration frequency of the structure - typical values for β in frame buildings range between 5 and 15 and β = 7 is selected for the present study (Almazan et al., 1998). The dynamic behaviour of the investigated system subjected to earthquake excitation can be described by the following six degrees of freedom: u xs, u ys and u zs are the displacement of the superstructure at the center of top deck relative to the base deck and u xb, u yb and uzb are the base displacement at the center of base deck relative to the ground in x -, y - and z - directions, respectively. The equation of motion for the structure in vertical direction can be expressed in matrix form as: ms ms zs u 2 β c 0 & zs β k 0 uzs ws + + = (5) 0 mb zg + zb uzg + u 2 β c 0 & & zb β k 0 uzg + uzb N wb Where w s is the weight of superstructure deck and w b is the weight of base deck; u zg and u& zg are displacement and velocity of the ground in vertical direction, respectively; and u& & zb is the acceleration of base slab relative to the ground in vertical direction which can be written in the following form: Where u & = v&& + v& (6) v& zb x v& y x y & 2 uxb uxb uxb = xb sin cos (7) & 2 u yb u yb u yb = yb sin cos (8) Where u xb, u& xb and u& & xb are displacement, velocity and acceleration of the base slab relative to the ground in x direction and u yb, u& yb and u& & yb are displacement, velocity and acceleration of the base slab relative to the ground in y direction; and R is the radius of curvature of the sliding surface. The corresponding equation of motion for the top deck can be expressed by: ms 0 xs c 0 u& xs k 0 uxs ms 0 xb + xg + + = 0 ms ys 0 c u& ys 0 k u ys 0 ms yb + yg (9) 3

u zs u ys m s u xs k c β c 2 β k u zb u yb k c m b u xb u& & zg u& & yg u& & xg R Figure 2. Idealized three-dimensional single-story structure resting on FP bearing. Also the equation of motion for the base deck can be written in the form of m 0 s xs xb + xg mb 0 xb + xg Fxb + + + = 0 0 0 (10) ms ys yb + yg mb yb + yg Fyb Where [ F ] T xb F yb is the bearing resisting force vector according to equation 2. Equations 5-10 are the governing equations of motion for whole system. Finally, these coupled equations are solved in the incremental form using Newmark s average acceleration method of integration. 4 NUMERICAL STUDY The effect of the bearing characteristics on the response of the three-dimensional structure mounted on friction pendulum system subjected to three, two and single component of earthquake excitations has been investigated. Response quantities of interest for the system under consideration are the base shear of the superstructure and the relative bearing displacement. The above response quantities are of importance because the base shear is an index of exerted forces to the structure due to the earthquake excitations and the latter is a measure of displacement between the isolated structure and the ground, which is crucial in design of friction pendulum system. In this study, the bearings friction coefficient and isolation period are considered as the variable parameters of the bearings, and attempt is made to examine the impact of the variation in these parameters on the peak values of the response of the isolated structures. Along with the examination of the impact of the bearing characteristic on the structure response, this study tries to examine the effect of using one or two earthquake component instead of the three of them. 4

Table 1. Earthquake characteristics records. Item Name of Earthquake record Name Station of Peak acceleration in x-direction(g) Peak acceleration in y-direction(g) Peak acceleration in vertical direction(g) 1 Northridge 1994 Sylmar 0.604 0.843 0.535 2 Tabas 1978 Tabas 0.836 0.852 0.688 3 Kobe 1995 Takarazuka 0.693 0.694 0.433 Bearing Displacement in X direction (cm) 30 20 10 0-10 -20-30 -40 30 Bearing Displacement in Y direction (cm) 20 10 0-10 -20-30 3 5 7 9 11 13 15 17 19 Time(s) Figure 3. Time history of base displacement under Tabas 1995 earthquake ( T i = 2s, f max = 0. 10 ). Three real earthquake records are considered and applied to the isolated structure. The characteristics of these earthquake records are shown in Table 1. These earthquakes are selected as they have strong vertical component and different soil type. The damping ratio of the structure is assumed to be 2% of critical damping. For the present study the mass ratio m s mb is held constant with m s m b = 1. After many trails, it was found that a time interval of t = 0. 001s would yield accurate results and In figure 3 the time variation of the base displacement in x and y directions is plotted for single, two and three components of Tabas 1978 earthquake. The parameters of the isolated structure considered are: T i = 2s and f max = 0. 10. This figure indicates that the nature of variation of the base 5

displacement is almost the same for all of three cases. But it can be seen that the base displacement for single-component ground motion is obviously more as compared to two- and three- component ground motion. Figure 4 shows the normalized peak base shear changes chart (by the total structure weight) versus the isolation period. The general trend of these charts is descending, and this shows the fact that with the increase in the isolation period, the function of the superstructure becomes similar to a rigid body and hence the decrease in the drift and the base shear of the structure. The other point is that, based on these charts, if all three earthquake components are not incorporated in the determining of the maximum value of the base shear, the calculated value will be less than the real value. Figure 5 shows the peak bearing displacement changes chart versus the isolation period. These charts clearly show that, first, a lack of incorporation of the interaction between the horizontal components leads to an overestimation of the peak bearing displacement, and, second, the impact of the vertical component of earthquake on the peak bearing displacement is insignificant. Figure 6 shows the variation of the normalized peak base shear against the maximum friction coefficient of the bearing. A look at these charts shows that when the friction coefficient increases, the distance between the charts pertaining to the two and three components of the earthquake gradually increases, and this means that the error caused by failing to incorporate the vertical component in determining the maximum base shear of the isolated structure increases with the increase in the bearings friction coefficient. This chart also confirms the necessity for the use of all three earthquake components in determining the maximum value of the base shear of the isolated structures with friction pendulum system. Figure 7 shows the chart for the variation of the peak bearing displacement against the maximum friction coefficient of the bearing. The general trend in the charts is ascending and this shows that with the increase in the maximum friction coefficient of the bearings the sum of the times when bearing is sliding decreases and as a result of which the peak bearing displacement decreases too. The other point is that in the lower maximum friction coefficients, the peak bearing displacement obtained in the single-component mode is less than that of the two- or three-component modes. However, the reverse happens with the increase in the maximum bearings friction coefficient, and the obtained value in the single-component mode becomes more than the other two modes. 5 CONCLUSIONS The influence of bearing characteristics on the response of friction pendulum base-isolated structures subjected to three, two and single components of different input motions is investigated. The key conclusions of the study are: 1. Failing to use all three earthquake components in determining the maximum value of the base shear leads to its underestimation compared to its real value. 2. Neglecting the interaction between the horizontal components of the bearing displacement leads to an overestimation of the bearing displacement. 3. The increase of the isolation period decreases the base shear of the structure. 4. The impact of the vertical component of the earthquake on the peak bearing displacement is insignificant. 6

6 REFERENCES Al-Hussaini TM, Zayas VA, Constantinou MC. 1994. Seismic isolation of multi-storey frame structures using spherical sliding isolation system. Technical Report No. NCEER-94-0007, National Center for Earthquake Engineering Research, State University of New York at Buffalo, Buffalo, New York. Almazan, J. L., De la llera, J. C., Inaudi, J. A. 1998. Modeling aspects of structures isolated with the frictional pendulum system. Earthquake Engineering and Structural Dynamics; Vol. 27, pp. 845-867. Fenz DM, Constantinou MC. Behaviour of the double concave friction pendulum bearing. 2006. Earthquake Engineering and Structural Dynamics;35:1403 24. Gueraud R, Noel-leroux J-P, Livolant M, Michalopoulos AP. 1985. Seismic isolation using sliding elastomer bearing pads. Nuclear Engineering and Design; 84:363 77. Kelly JM. 1986. Aseismic base isolation: review and bibliography. Soil Dynamics and Earthquake Engineering. 5(3):202 216. Mokha, A., Constantinou, M. C., Reinhorn, A. M. 1988. Teflon bearings in aseismic base isolation: experimental studies and mathematical modeling. Technical Report No. NCEER-88-0038, National Center for Earthquake Engineering Research. State University of New York at Buffalo, Buffalo, New York. Mosqueda, G., Whittaker, A. S., Fenves, G. L. 2004. Characterization and modeling of friction pendulum bearing subjected to multiple components excitations. J Structural Engineering, ASCE; Vol. 130, No. 3: 433-442. Mostaghel N, Khodaverdian M. 1987. Dynamics of resilient-friction base isolator (R-FBI). Earthquake Engineering and Structural Dynamics;15:379 90. Mostaghel N, Tanbakuchi J. 1983. Response of sliding structures to earthquake support motion. Earthquake Engineering and Structural Dynamics;11:729 48. Skinner RI, Robinson WH, McVerry GH. 1993. An Introduction to Seismic Isolation. Wiley; Chichester. Su L, Ahmadi G, Tadjbakhsh IG. 1989. A comparative study of performance of various base isolation systems, Part I: shear beam structures. Earthquake Engineering and Structural Dynamics; 18:11 32. Tsopelas P, Constantinou MC, Kim YS, Okamoto S. 1996. Experimental study of FPS system in bridge seismic isolation. Earthquake Engineering and Structural Dynamics; 25:65 78. Yang YB, Lee TY, Tsai IC. 1990. Response of multi-degree-of-freedom structures with sliding supports. Earthquake Engineering and Structural Dynamics; 19:739 52. Zayas VA, Low SS, Mahin SA. 1987. The FPS earthquake resisting system. Experimental Report No. UCB/EERC 87/01, EERC, University of California, Berkeley, California. Zayas VA, Low SS, Mahin SA. 1990. A simple pendulum technique for achieving seismic isolation. Earthquake Spectra;6:317 33. 7

Peak Normalized Base shear 0.50 0.40 0.30 0.20 0.10 Ti (Sec) Peak Normalized Base shear 0.4 0.35 0.3 0.25 0.2 0.15 (a) 0.1 Ti (Sec) Peak Normalized Base Shear 0.35 0.30 0.25 0.20 0.15 0.10 (b) Three components 0.05 Ti(Sec) (c) Figure 4. The variation of the peak normalized base shear versus isolation period under (a) Northridge, (b) Tabas and (c) Kobe earthquakes ( f max = 0. 10 ). 8

Peak Bearing Displacement (cm) 50 47 44 41 38 35 Ti(Sec) (a) Peak Bearing Displacement (cm) 55 45 35 25 15 Ti(Sec) (b) Peak Bearing Displacement (cm) 40 35 30 25 20 Ti (Sec) (c) Figure 5. The variation of the peak base displacement versus isolation period under (a) Northridge, (b) Tabas and (c) Kobe earthquakes ( f max = 0. 10 ). 9

Normalized Peak Base Shear 0.40 0.35 0.30 0.25 0.20 (a) Normalized Peak Base Shear 0.45 0.40 0.35 0.30 0.25 0.20 0.15 (b) Normalize Peak Base Shear 0.30 0.26 0.22 0.18 0.14 (c) Figure 6. The variation of the normalized peak base shear versus maximum coefficient of friction under (a) Northridge, (b) Tabas and (c) Kobe earthquakes ( T i = 2 s ). 10

Peak Bearing Displacement (cm) 80 70 60 50 40 30 (a) Peak Bearing Displacement (cm) 75 60 45 30 15 (b) Peak Bearing Displacement (cm) 55 45 35 25 15 (c) Figure 7. The variation of the peak base displacement versus maximum coefficient of friction under (a) Northridge, (b) Tabas and (c) Kobe earthquakes ( T i = 2 s ). 11