Design Principles of Seismic Isolation

In earthquake resistance design of structures, two general concepts have been used. The first is to increase the capacity of the structures to resist the earthquake load effects (mostly horizontal forces) or to increase the dynamic stiffness such as the seismic energy dissipation ability by adding damping systems (both devices and/or structural fuses). The second concept includes seismic isolation systems to reduce the input load effects on structures. Obviously, both concepts can be integrated to achieve an optimal design of earthquake resilient structures. This chapter is focused on the principles of seismic isolation. It should be pointed out that from the perspective of the structural response control community, earthquake protective systems are generally classified as passive, active and semi-active systems. The passive control area consists of many different categories such as energy dissipation systems, toned-mass systems and vibration isolation systems. This chapter addresses only the passive, seismic isolation systems [Soong and Dargush, 1997; Takewaki, 2009; Liang et al, 2011] Using seismic isolation devices/systems to control earthquake induced vibration of bridges and buildings is considered to be a relatively matured technology and such devices have been installed in many structures world-wide in recent decades. Design guidelines have been established and they are periodically improved as new information based on research and/or field observations become available during the past 20-30 years [ATC 1995; SEAONC 1986; FEMA 1997; IBC 2000; ECS 2000; AASHTO 2010, ASCE 2007, 2010]. Besides the United States, base isolation technologies are also used in Japan, Italy, New Zealand, China, as well as many other countries and regions. [Naiem and Kelly, 1999; Komodromos, 2000; Christopoulos, C. and Filiatrault 2006] Affiliated with the increased use of seismic isolation systems, there is an increased demand of various isolation devices manufactured by different vendors. This growth of installing seismic isolation devices in earthquake engineering has been following the typical pattern experienced in structural engineering development, which begins from a “statics” platform by gradually modifying the design approach to include the seismic effects based on structural dynamics principles as they develop and new field observations on the responses of real-world structures. The process is typically slow because most studies and laboratory observations have been concentrated on the performances of the devices with scaled-down experiments. Results could not be readily scaled-up for design purposes. At the same time, there were very limited field data on the actual performances of seismically isolated


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structures. In recent years, some limited successful stories were reported in the literature on the seismic performance of base-isolated bridges and buildings during real earthquakes, as well as reports of unsuccessful cases including the failure of isolation bearings and falling spans of bridges and magnification (rather than reduction) of vibration levels of buildings. These structural failures have not been systematically examined for their contributing factors. Some of them include: construction quality, improper choice of the type of isolation bearings, incomplete design principles and methods, unknown ground motion and soil characteristics, etc. In summary, current practice is mainly based on past research and observations on the performance of the isolation devices themselves, with minimum information on the dynamic performance of the structure-device as a system. The working principle of seismic isolation may be explained in several ways. It is a general understanding that isolation devices/systems are used to reduce the seismic force introduced base shear. Designers often understand the working principles from the viewpoint of design spectrum in that, when the vibration period of a structure is longer than a certain level, continue to increase the period will reduce the magnitude of the spectral value and thus reduce the base shear accordingly. To qualitatively explain the working principle of seismic isolation in this manner is reasonable, but it is insufficient to use it in actual design. Refinements and additional design principles are necessary. Another commonly used explanation of seismic isolation is the "decoupling" of the superstructure vibration from the ground motions excitations to reduce the vibration of structures. This statement again requires quantitative elaborations from the viewpoint of isolation design. In general, an isolation device/system can be viewed as a low-pass mechanical filter of the structure being isolated, to filter out excitations with the undesirable high frequencies to reduce the level of acceleration. In order to establish the cut-off frequency the period of the isolation system must be carefully addressed, and this requires a basic design principle to guide the design. In order to reduce the base shear, an isolation system must be allowed to deform. This relative displacement cannot be filtered like the absolute acceleration. In general working range, the longer the relative displacement associated with longer periods, the more reduction in base shear can be achieved, except for the fact that the latter will introduce certain negative effects. The most significant issue of large relative displacement is the large P-delta effect and for falling spans in bridges. In this regard, a design principle is needed to achieve the best compromise in seismic isolation design. In reality, the only approach to effectively reduce the relative displacement is to increase damping, which, in turn, will result in higher level of acceleration. This conflicting demand of controlling acceleration and acceptable displacement in essence defines the limiting range of the effectiveness of seismic isolation systems. Quantitatively this issue can be addressed, and this is an important design principle to be conceptually discussed in this chapter. In Section 2 of this chapter, several important design issues (e.g. P-delta effect, vertical motions, etc.) will be discussed and seismic isolation design principles will be described. In Section 3, the quantitative basis of treating seismically-isolated structures will be briefly reviewed and simplified models will be established for the dynamic analysis and design of the structure-device system. Design methods will be briefly discussed in Section 4, and a newly developed seismic isolation device to address some of the issues facing today's practice is briefly introduced in Section 5. Finally, the key issues and parameters in seismic isolation is summarized and future research needs are briefly noted.

Some issues and principles of seismic isolation
In this section, the theories, design and practical considerations of seismic isolation are briefly discussed.

State-of-practice on seismic isolation
The principle of base isolation is typically conceptually explained by using figure 2.1.   (b) show a structure without and with base isolation, respectively. It is seen that the major difference between (a) and (b) is that in (b), the structure is set on top of isolation several bearings. When the ground moves with acceleration A g , the superstructure will move accordingly with a displacement , and a reduced level of absolute acceleration, denoted by A a , rather than the original level A a0 . This principle has been the basis for many research and development efforts in design guidelines and devices for seismic isolation. These have been many important contributions during the past 25 years led by Kelly and his associates at Berkeley and Constantinou and his associates at Buffalo as well as many others. (See references listed at the end of this chapter.)

Basic concept
The major purpose of using the seismic isolation is to reduce the base-shear of the structure. Physically, large base shear is one of the main reasons of structural damages due to strong horizontal ground accelerations. Thus, to reduce the lateral acceleration is a basic principle. From the viewpoint of design, many aseismic codes use the base shear as a control parameter. For example, if the base shear of a building is reduced, then the upper story lateral forces floor drifts are also reduced. In the case of a bridge, base shear reduction will minimize damage to the piers. where f Lj is the later force of the j th story of the structure. Base isolation is intended to reduce f Lj simultaneously, so that the base shear will be reduced, in addition

Base shear
where K b is the lateral stiffness of the bearing system; is the nominal relative displacement of the bearing. The stiffness K b of the bearing system will be much smaller than the structure without the bearing, so that the base shear is reduced.

Lateral acceleration
In equation (2.1), C s is in fact the normalized lateral absolute acceleration a A , which is in general zero-valued unless earthquake occurs.
where M is the total mass and g = 9.8 m/s 2 is the gravity. In equation (2.2), f Lj is also caused by lateral absolute acceleration a aj of the j th story, that is where m j is the mass of the j th floor. From (2.5) and (2.6), it is seen that, it is difficult to change or reduce the mass M or m j in a design; however, if the acceleration can be reduced, the lateral forces will be reduced. Therefore, we will focus the discussion on the acceleration.

Issues of base isolation
Seismic isolation is considered as a relatively matured technology as evidenced by the many practical applications. These applications have been designed based on codes and provisions that have been established incrementally over time. In the following, seismic isolation principles are examined from a structural dynamics perspective with an objective to suggest additional future research needs.

Absolute acceleration vs. relative displacement
Seen in figure 2.1, to achieve the goal of acceleration reduction, in between the ground and the super structure, there will be installed in a group of bearings, which have much soft stiffness so that the period of the total system will be elongated.
Thus, to achieve acceleration reduction, a major sacrifice is the relative displacement between base and structure must be significantly large. Due to nonlinearities of isolation system, the dynamic displacement can be multiple-centered, which can further notably enlarge the displacement. In addition, permanent residual deformation of bearing may worsen the situation. Generally speaking, the simplest model of a base isolation system can be expressed as where C v(t) is the viscous damping force and C is the damping coefficient; v(t) is relative velocity.
In most civil engineering structures, the damping force is very small, that is Thus, (2.7) can be re-written as where A a and are amplitudes of the absolute acceleration a a (t) and relative displacement d(t).
Equation (2.9) describes the relationship between acceleration and displacement of a singledegree-of-freedom (SDOF) system, which can be used to generate the design spectra. Since the damping force is omitted, the generated acceleration is not exactly real, which is referred to as pseudo acceleration, denoted by A s . That is, the weaker the stiffness is chosen, the smaller value of A s can be achieved, which is the basis for current design practice of seismic isolation. From the above discussion, it seems that, as long as K b is smaller than a certain level, the base isolation would be successful. A more accurate model will unveil that, to realize the base isolation, only one parameter, say A a or , is not sufficient. This is because A a and  are actually independent. In fact, both of them are needed. That is, whenever a claim of the displacement being considered in an isolation design, as long as they are not treated as two independent parameters, the design is questionable. Later, why they must be independent will be explained. Here, let us first use certain group of seismic ground motions as excitations applied on a SDOF system, the ground motion are suggested by Naiem and     .2 (a) shows the accelerations of SDOF systems as functions of period for selected damping ratios. When the period becomes larger, the accelerations do reduce, especially when T b > 2 (s). The responses are all smaller than 0.4 (g) and namely, the acceleration is reduced. Figure 2.2 (b) shows the displacements. It is seen that, when the periods increase, the displacements can become rather large. When T b > 2 (s), the responses can be larger than 0.1 (m), especially if the damping ratio is small, say, 5%.
In figure 2.2 the parameter, damping ratio denoted by is defined by b ξ C / 2 MK  (2.18)

Displacement and center position
Another seismic isolation design issue is the self-centering capacity. Because the SDOF system used to generate the response is linear, and many commercially available bearings are nonlinear systems, the displacement time history can be multiple centered. Figure 2.3 shows examples of a bi-linear (nonlinear) system under Northridge earthquake excitations. The plot in Fig. 2.3 (a) is the displacement time history of the bi-linear system with load and unload stiffness ratio = 0.1 and damping ratio = 0.01. Here the damping ratio is calculated when the system is linear. The plot in Fig 2.3 (b) is the same system with damping ratio = 0.2. It is seen that, the biased deformations exist in both cases. This example illustrates that center shifting can enlarge the displacement significantly, even with heavy damping. In the above equations, A is the input level of ground acceleration; S is the site factor; D, instead of , is used to denote the dynamic amplitude and B is called the numerical damping coefficient. Approximately B = 3 + 0.9 (2.21) Equations (2.19) and (2.20) will work for most (but not all) situations but cannot handle the position shifting which is a nonlinear response. Some of the nonlinear modeling issues are discussed in Section 3.

SDOF and MDOF models
Many analyses and design of seismic isolations are based on SDOF model, whereas realistic structures are mostly MDOF systems. The acceleration of a higher story of an MDOF system can be much more difficult to reduce. Equation (2.15) is based on a SDOF system, when the superstructure can be treated as a lumped mass. Namely, the relative deformation among different stories of the structure is negligible. Realistically, such a case is rare; therefore, the acceleration a aj at different stories can be different. A conventional idea is to decouple a MDOF system into several vibration modes. Each mode is treated as a SDOF system. Furthermore, for multi-story structures, an additional parameter, mode shape, is needed to distribute the acceleration and displacement at different levels. By denoting the mode shape by P i , which is a vector with the j th element representing the model displacement p ji . The acceleration vector A si is given as where a ji is the acceleration of the i th mode at the j th story and  i is the i th modal participation factor. The displacement vector is given by where d ji is the displacement of the i th mode at the j th story. www.intechopen.com

Acceleration of higher stories
One of the shortcomings of approximately a MDOF system by a SDOF model is the inability to estimate the responses at the higher levels of a MDOF structure. Typically, through SRSS, the acceleration of the j th story of MDOF system can be calculated as And the displacement of the j th story is The reduction of MDOF accelerations is discussed in the literature. The general conclusion is that, (2.25) and (2.27) may not work well so that the acceleration of the higher story a sj may not be calculated correctly. In fact, a sj can be significantly larger. The reasons of this inaccuracy mainly come from several factors. The first is the damping effect. The second is the error introduced by using only the first mode for design simplicity (the triangular shape function) as illustrated in figure 2.4 In addition, seen from figure 2.4, even through the acceleration of the base, denoted by p b is rather small by using isolators, the top story will have a rather large acceleration.

Cross effects
Another shortcoming of using SDOF models is the inability to estimate the cross effect. Typical MDOF structures have "cross effects" in their dynamic responses. Different from a single member of a structure, which has principal axes, a three-dimensional structure often does not have principal axes. This is conceptually shown in figure 2.5, which is a two story structure. Suppose the first story does have its own principal axes, marked as x 1 -y 1 , and the second story also has its own principal axes, marked as x 2-y 2. However, from the top view, if x 1 and x 2 are not pointing exactly the same direction, say, there exists an angle , then the entire structure will not have principal axes in general. In this case, the inputs from any two perpendicular directions will cause mutual responses. The resulted displacement will be further magnified. This the third reason of large displacement. At present, there are no available methods to quantify cross effects associated with seismic responses, although in general this effect in base isolation design may be small for regularly shaped structures.

Overturning moment
The product of large vertical load and large bearing displacement forms a large P- effect, conceptually shown in figure 2.6.

Fig. 2.6. Isolation P- effect
This large displacement will result in an overturning moment, given by where, the vertical load P is a product of the total weight and the vertical acceleration, the vertical acceleration is the sum of gravity g and earthquake induced acceleration A v . For example, suppose the total mass is 1000 (ton), the displacement is 0.5 (m), and the additional vertical acceleration is 0.4 (g), the total overturning moment will be 6.86 (MN-m). This is a large magnitude, which requires special consideration in the design of foundations, structure base as well as bearings.

Horizontal and vertical vibrations
As mentioned above, the primary purpose of base isolation is to reduce the horizontal load and/or acceleration. By installing bearings, the lateral stiffness will be significantly reduced so the horizontal vibration can be suppressed. Moreover, by using bearings, the vertical stiffness can also be reduced to a certain level and the vertical vibration can be magnified. Since the earthquake induced vertical load is often not significantly large, the vertical vibration is often ignored in design. However, due to the magnification of vertical acceleration as well as the above-mentioned large overturning moment, care must be taken to check the vertical load. In the worst scenario, there can be an uplift force acting on bearings with many of them not manufactured to take the uplift load (e.g. rubber bearings).

Dynamics of seismically isolated MDOF systems
In this section, base isolation is examined from a different perspective, as a second order mechanical filter of a dynamic system. The working principle of base isolation system is to increase the dynamic stiffness of acceleration without sacrifice too much "dynamic stiffness." Dynamic stiffness is a function of effective period and damping.

Models of isolation systems 3.1.1 Linear SDOF model
The linear SDOF model is used here to provide a platform to explain the essence of isolation systems under sinusoidal excitation. A more detailed base isolation model can be rewritten as where a(t) and a g (t) are respectively the relative and ground accelerations. Note that ag a (t) a(t) a (t)  where the overhead dot and double dot stand for the first and the second derivatives with respect to time t. Let the ground displacement d g (t) be sinusoidal with driving frequency  f , The ground acceleration is Here, D g and A g are respectively the amplitudes of the displacement and acceleration. The amplitude of steady state responses of the relative displacement D can be written as and d β is the dynamic magnification factor for the relative displacement Note that r = 0 means the driving frequency  f =0 and the system is excited by static force only. In this case, D(r =0) = 0. The amplitude of steady state responses of the absolute acceleration A a can be written as and A β is the dynamic magnification factor for the relative displacement Note that when the driving frequency  f = 0 and the system is excited by static force only.
A a (r =0) = A g . If there exist a static force F SA so that Then, when r ≠ 0 or  f ≠ 0, the dynamic response of the acceleration can be seen as where β M is called apparent mass or dynamic mass and That is, the value of the dynamic response A a can be seen as a static force divided by a dynamic mass. From (3.12), SA β a F M= A (3.14) The essence described by (3.14) is that the "dynamic mass" equals to a force divided by response. Generally speaking, this term is stiffness. Since the response is dynamic, it can be called a dynamic stiffness, K dA . In this particular case, the dynamic stiffness is the apparent mass.
Similarly, the relationship between a static force F Sd and a dynamic displacement D can be written as It can be seen that Both the dynamic stiffness and the dynamic factors are functions of frequency ratio r. It can be proven that, the proportional coefficients for (3.17) and (3.18) are constant with respect to r. That is, we can use the plots of dynamic magnification factors to shown the variations of the dynamic stiffness with respect to r. It can be seen from figure 3.1(a), the plot of A β , when the frequency ratio varies, the amplitude will vary accordingly. Note that, That is, if the driving frequency is given, then the frequency ratio r is proportional to the natural period T b . Therefore, the horizontal plot can be regarded as the varying period. Recall figure 2.2(a) where x-axis is also period. We can realize the similarity of these two plots. First, when the period increases, the amplitudes in both plot increases. After a certain level, these amplitudes start to decrease. It is understandable that, the target of acceleration reduction should be in the region when the accelerations being smaller than a certain level. In figure 3.1 (a), we can clearly realize that this region starts at r = 1.414, which is called rule 1.4. To let the isolation system start to work, the natural period should be at least 1.4 times larger than the driving period T f =  f . In the case of earthquake excitation, due to the randomness of ground motions, there is no clear-cut number. However, from figure 2.2 (a), it seems that this number should be even larger than 1.4. In fact, with both numerical simulations and shaking Additionally, different damping will result in different response level. In figure 3.1(a), it is seen that, when r > 1.4, larger damping makes the reduction less effective. In figure 2.2 (a), it can be seen that when the period becomes longer, increase damping still further reduce the responses, but the effectiveness is greatly decreased. Note that, this plot is based on statistical results. For many ground excitations, this phenomenon is not always true. That is, increasing damping can indeed reduce the effectiveness of reduction. Now, consider the displacement. From figure 3.1(b), when the period is near zero, the relative displacement is rather small. Then, as the period increases, the displacement will reach the peak level and then slowly decreases. However, it will never be lower than 1, which means that, the displacement will never below the level of ground displacement. Increasing the damping, however, will help to reduce the large displacement. This may be seen from Fig. 2.2(b) and it is true for both sinusoidal and earthquake excitations.

Nonlinear SDOF model
The above discussion is based on a linear model. Nonlinear system will have certain differences and can be much more complex to analyze. Generally speaking, many nonlinear systems considerably worsen the problem of large displacement. In the working region, increasing the period will decrease the acceleration but the displacement will remain at a high level. Increasing the damping will help to reduce the displacement but does not help the acceleration.

Effective system
It is well understood that, in general, a nonlinear dynamic system does not have a fixed period or damping ratio. However, in most engineering applications, the effective period T eff and damping ratio  eff are needed, and are calculated from where E d is the energy dissipation of the nonlinear system during a full vibration cycle. From (3.21) and (3.22), it is seen that, to have the effective values, the key issue is to establish the effective stiffness K eff . In the following, the bi-linear system is used to discuss the effective stiffness, for the sake of simplicity. Although this system is only a portion of the entire nonlinear systems, the basic idea of conservative and dissipative forces seen in the bilinear system can be extended to general nonlinear systems. And, in many cases, nonlinear isolation is indeed modeled as a bi-linear system. Figure 3.2 shows (a) the elastic-perfectly-plastic (EEP) system and (b) the general bi-linear system. Conventionally, the secant 'stiffness" is taken to be the effective stiffness. That is where D is the maximum displacement and f N is the maximum nonlinear force. In the following, since the system is nonlinear and the .response is random, we use lower case letters to denote the responses in general situations, unless these responses will indeed reach their peak value.

Fig. 3.2. Secant stiffness
In figure 3.2, d y and d N are the yielding and the maximum displacements. f y and f N are the yielding and the maximum forces. K d and K u are the loading and unloading stiffness. If the system remains elastic, then we will have a linear system when the displacement reaches the maximum value D, the force will be f L . However, since the system is nonlinear, the maximum force f N will be smaller. Thus the corresponding effective stiffness will be affected. For seismic isolation, the measurement of the effective stiffness can be considerably overestimated. To see this point, let us consider the definition of stiffness in a linear system. It is well known that the stiffness denotes capability of how a linear system can resist external force. Suppose under a force f L , the system has a deformation d, and then the rate defines the stiffness. That is When the load f L is released, the linear system will return to its original position. Thus, the stiffness also denotes the capacity for how a system can bounce back after the force f L is removed, for at displacement d, the linear system will have a potential energy E p Therefore, we can have alternate expression for the stiffness, which is Apparently, in a linear system, the above two expressions of the stiffness, described by (3.24) and (3.26), are identical. This is because the potential energy can be written as f N = f d = q Namely, the EPP system does not have a conservative force. Its restoring force is zero. From another example of the general bilinear system shown in figure 3.2 (b In this case, using (3.24) and (3.26) will contradict each other. In order to choose the right formulae to estimate the effective period and damping, the estimation of effective stiffness must be considered more precisely. Generally speaking, a nonlinear system will have the same problem as the above-mentioned bi-linear system, that is, the restoring force is smaller than the maximum force, as long as the nonlinear system has softening springs.

Estimation of effective period
From the above-discussion, when we use an effective linear system to represent a nonlinear system, the effective stiffness should satisfy the following: By using (3.30) as well as (3.31), the effective stiffness k eff will be smaller than the secant stiffness k sec . Furthermore, it can be seen that, vibration is caused by the energy exchange between potential and kinetic energies. The natural frequency of a linear system can be obtained by letting the maximum potential energy equal the maximum kinetic energy, that is, through the relation In other words, considering the dynamic property of a nonlinear system, we should not use the secant stiffness as the effective stiffness. Following this logic, the effective stiffness should be defined in a nonlinear system by considering the restoring potential energy as follows.
In the bi-linear case (see the shaded areas in Figure 3.3), when the system moves from 0 to d, the potential energy is Note that, the term a is smaller than unity and  is larger than unity. Therefore, from (3.42), it is seen that the period can be notably underestimated by using the secant stiffness. For example, suppose a = 0.2 and = 4, the factor will be greater than 2. Similar to the estimation of effective period, the term K eff will also affect the measurement of the effective damping ratio. Using the same logic, the damping ratio can also be underestimated. These double underestimations may cancel each other to a certain degree for acceleration computation, but will certainly underestimate the displacement. For a detailed discussion on structural damping, reference is made to Liang et al (2012).

MDOF models
Now, let use consider a linear n-DOF systems along one direction, say the X-direction. The governing equation can be written as Here M, C and K are nxn mass, damping and stiffness matrices, J = {1} nx1 is the input column vector and     where d j (t) is the displacement at the j th location. If the following Caughey criterion hold The system is proportionally damped, which can be decoupled into n-SDOF systems, which are referred to as n-normal modes, so that the analysis of SDOF system can be used. In base isolation, to regulate the displacement, large damping must be used. When the damping force is larger, isolation system is often not proportionally damped. That is, (3.45) will no longer hold and the system cannot be decoupled into n SDOF normal modes. In this case, it should be decoupled in 2n state space by using the state equations.
Configuration of MDOF structures and non-proportional damping will both affect the magnitude of the accelerations of higher stories. However, the acceleration of the base, as well as the relative displacement between the base and the ground will not be significantly affected by using the normal mode approach. Practically speaking, more accurately estimate the displacement is important then the computation of the acceleration of higher stories. Furthermore, when the isolation system is non-linear, its first "effective" mode will dominate. Thus, we can use its first "effective" mode only to design the system. However, care must be taken when the cross effect occurs. It is seen that, if both the motion of both X and Y directions, which are perpendicular, are considered, we can have where a xg and a yg are ground accelerations along X and Y directions respectively, which are time variables and for the sake of simplicity, we omit the symbol (t) in equation (3.46). The subscript X and Y denote the directions. The subscript XX means the input is in x direction and the response is also in X direction. The subscript XY means the input is in X direction and the response is in Y direction, and so on. In (3.46), M X = M Y are the mass matrices. It is seen that, both C XY = C YX T and K XY = K YX T are the cross terms. Generally speaking, if the system is rotated with the help of rotation matrix we can minimize the cross terms C XY and K XY .
The angle can be chosen from 0 to 90 0 . However, in this case no matter how the angle  is chosen, at least one of C XY and K XY is not null and hence, the input in X direction will cause the response in Y direction. That is defined here as the cross effect, which implies energies of ground motions from one direction is transferred to another. There are many reasons to generate the cross effect. In certain cases, the cross effect can considerably magnify the displacement.

Bearings and effect of damping 3.2.1 Role of damping
From the above discussion, it is seen that there are several possible inaccuracies that may exist in estimating the displacement. The results can often be underestimation of displacement in isolation design. As pointed out earlier, the only way to reduce the displacement in the working range of isolation systems is to increase the damping. For example, from figure 2.2(b), it is seen that, at 3 second period, if the damping ratio is taken to be 50%, the displacement is about 0.2 (m) whereas using 5% only can cause about 0.5 (m) displacement, which is about 2.5 times larger.

Damping and restoring stiffness
Often base isolators or isolation bearings are designed to provide the required damping. Practically speaking, damping can be generated by several means.
The first kind of damping is material damping, such as high damping rubber bearings, leadcore rubber bearings as well as metallic dampers. The damping mechanism is generated through material deformations. Note that, high damping rubbers often do not provide sufficient damping. The second is surface damping. The damping mechanism is generated through surface frictions of two moving parts, such as pendulum bearings, friction dampers. Note that, surface damping often is insufficient and can have a significant variation from time to time.
The third type of damping is viscous damping, which is often provided by hydraulic dampers. This kind of damping is more stable but with higher cost. Closely related to damping generated by isolator is the restoring stiffness, since both of them are provided by bearings. In fact, the type of method of proving restoring stiffness and damping classifies the type of bearings. The restoring stiffness can be generated by material deformations, including specific springs, which relies on the deformation to restore potential energy. Releasing of such potential energy can make the bearing return to its center position. Rubber bearings, including high damping rubber bearings, lead core rubbers bearings, steel-rubber-layered bearings fall into this category. Bearings with sliding surface and elastomeric springs also use restoring force generated by material deformation. Bearings with metal ribs which provide both stiffness and damping also fall into this category. The restoring stiffness can also be generated by geometric shaped. Generally, when horizontal motion occurs, such bearings generate vertical movement which can also restore potential energy. Again, release of potential energy enables the bearing return to its center position. Pendulum sliding bearing falls into this category. Recently, a newly type of roller bearing is developed, which guarantees a low level constant horizontal acceleration, and will be described in Section 5.

Design windows
As mentioned earlier, the key issue in design of isolation system is an optimal compromise of the acceleration and the displacement, within an acceptable range of the period called "design window" period. The reason to consider the concept of design window is to avoid possible undesired displacement, which in general is independent to acceleration.

Lower bond of period
In order to reduce the acceleration, the period of the isolation system cannot be shorter than a given value. Although this value depends upon the site, it can be roughly estimated to be 1.5 to 2 seconds. This value actually establishes the left boundary of the design windows on the design spectrum. This lower limit is well understood. Because of the assumption of negligible damping, acceleration is taking as directly proportional to the displacement. Thus in typical design practice, it is assumed that displacement bound is given once the acceleration limit is established. This is not always true, because acceleration and displacement are in general independent.

Upper bond of period
In order to limit the displacement to a reasonable value, the period of the isolation system cannot be too long. This defines the right side boundary of the design window. In figure 4.1, the design spectrum and the design window for the isolation system is conceptually illustrated. .1 illustrates that if the design has a period that falls outside this "window," it is unacceptable. Within this window, reductions of the acceleration and tolerance displacement must be considered simultaneously. In this sense, a proper isolation system is an optimally compromised design. It should be noted that, when damping is large, the reduction of acceleration will be reduced. When damping is too low, the displacement will be increased. Thus, the proper damping will have upper and lower period bonds from the viewpoint of isolation design.

Left boundary of the design window, acceleration related parameters 4.2.1 Design force
In a typical aseismic design, the base shear V typically needs to be designed by where [V] is the allowable base shear and s A is a factor of safety. The base shear V can be determined by several ways. One is that given by (2.1), which is repeated here.
To determine the seismic response factor C s , the effective stiffness K eff , or K eff in the case of MDOF system is required. The effective stiffness often should not be determined by using the secant stiffness, as previously explained. At the same time, the base shear is equal to the product of the lateral stiffness K b and the displacement D of the bearing system plus the damping force F d measured at the maximum displacement. bd V = K D + F (4. 3) The specifications related to the damping force for isolators are provided by bearing vendors. For bi-linear damping, the damping force is roughly the dissipative force or the characteristic strength q (see fig. 3.2b). Using the maximum value of q, denoted by Q, For friction damping where  is the friction coefficient.
For multi-story structures, base on the SRSS method, where, f Lj is the lateral force of the j th story and in which m j is the mass of the j th story and a ji is the absolute acceleration of the i th mode at the j th story. Note that, for an n-DOF system, there will be n-modal accelerations, and, usually the first few modes will contain sufficient vibration energy of the system. To be on the safe side, the desirable number of modes to be considered is S = S r + S f (4.8) where S r is the number of the first few modes that contain 90~95% vibration energy and S f = 1~3, (4.9) as an extra safety margin particularly for irregular structures. This should not add too much computational burden.
To determine S r , modal mass ratio  i is often needed, (4.10) and S r can be determined by In (4.7) the absolute acceleration a ji is the j th element of the i th acceleration vector a i , which is determined by The term C si is the i th seismic coefficient, which can be determined through the building or bridge code. The modal participation factor  i is given by Equations (4.10), (4.12) and (4.13) contain the mode shape function P i which can be a triangular approximation, or more precisely, be given by the following eigen-equation with the normalization by letting the roof modal displacement equal to unity.
 i 2 P i = (M -1 K) P i (4.14) Note that, the base shear calculated from (4.2) only considers the first mode, which may not be sufficiently accurate. Equation (4.3), is theoretically workable but practically speaking, the dissipative force F d is difficult to establish. Note that, in (4.12), the mode shape P i is obtained through (4.14), however, P i is the displacement mode shape but not necessarily the acceleration mode shape. Therefore, cares must be taken by using (4.12) to calculate the modal acceleration; otherwise a design error can be introduced. For the limited space, the detailed explanation is not discussed in this chapter. Interested reader may see Liang et al 2012.

Overturning moment
Because of the potentially large P- effect, base isolation design must carefully consider the overturning moment to ensure that the uplifting force is not magnified. Furthermore, most bearings cannot take tensions, whereas the overturning moment can generate uplift tension on bearings. If the structure has notable plan irregularity, the additional moment due to the asymmetric distribution of mass must also be considered.
With the help of M T and knowing the geometric dimensions of the isolated structure, the uplift force can be calculated, and the corresponding criterion can be set up as where s M is a safety factor and [M T ] is allowable moment. The above two criteria define the left side boundary of the design window (see fig 4.1).

Right boundary of design window: Independency of displacement 4.3.1 Independency of displacement
That the displacement D and the acceleration A a are independent parameters mentioned previously will be briefly explained here. For linear system, from (2.7) we have For large amount of damping, consider the peak values, we have Additionally, for nonlinear system, softening behavior often occurs, so that the maximum force is not proportional to the maximum displacement. As a result, one cannot simply calculate D due to the nonlinearity of the most isolation systems, as In design, the bearing displacement is as important as the acceleration related parameters. Due to the uncertainties illustrated above, a safety factor should be used before further research results are available.
where s D is a safety factor and [D] is allowable displacement.

Right boundary due to displacement
Since the displacement needs to be regulated, the right boundary of the design window is defined. Because of the above-mentioned reasons, by using the safety factor s D , the right boundary will further shift leftwards.
It is seen that, the resulted window can be rather narrow.

Probability-base isolation design
In recent years, the probability-based design for civil engineering structures against natural and man-made load effects attracts more and more attentions. The basic idea is to treat both the loads and resistance of structures as random variables and to calculate the corresponding failure probability, based on which the load and resistant factors are specified, (see Nowak and Collins, 2000). Probability-based design for base isolation systems should be one of the frontier research areas for earthquake engineering researchers.

Failure probabilities of base-isolated structures
In the above discussions of seismic isolation, the design process is a deterministic approach because it is established on deterministic data. A base-isolated building or bridge is a combination of civil engineering structures and mechanical devices, the bearings. In most cases of mechanical engineering devices, the safety factors are considerably larger than those used by civil engineers. The main reason, among many, is that the civil engineering structures have much larger redundancy. Mechanical devices, on the other hand, do not have such a safety margin. This raises an interesting issue on safety factors for seismically isolated structures. Take the well known design spectrum, for example. Its spectral value is often generated by the sum of mean value plus one standard deviation. However, the maximum value can be much larger than the spectral value. For example, consider under 99 earthquake statistics of a structure with period = 2 second and damping ratio = 20%. The mean-plus-one standard deviation value of acceleration is 0.24 (g) whereas the maximum value is 0.47 (g Here, the subscripts f A and f D stand for failure of acceleration and failure of displacement respectively. Symbol [(.)] means the allowable value of (.).  The failure probability can be calculated as

Computation of failure probabilities
The integral is also the shadow area. From figure 4.3 (b), we can also see that, this failure probability is not small either. Note that, in this case, the allowed value being 0.29 (m) is satisfied by using the mean-pulse-one-standard-deviation value. Generally, the computations can be described as follows  The failure probability implies the chance of not meeting the design requirement. For acceleration, because of the structural redundancy of earthquake resilience, the allowed failure probability can be higher. Anyhow, 15% chance of failure may not acceptable by the owners of the structures (e.g. seismic isolation systems for nuclear reactors). For displacement, usually a bearing cannot tolerance virtually any exceedance. Thus, the allowed failure probability should also be lower. This brief discussion above suggests that the design safety considerations for the combined civil engineering structures with mechanical devices may be examined by using a probability-based principle and approach.

Seismic isolation bearings
There are several types of isolation bearings commercially available, such as lead-rubber, high damping rubber as well as sliding bearings. Generally speaking, as long as the bearing system can satisfy the requirement of the above-mentioned design windows in the service life time of the isolation system, any bearing may be employed. Interested readers can consult Komodromos, P.I. (2000). In seismic isolation design, it is suggested that the allowed bearing displacement be used as the primary criterion; the effective period obtained via effective stiffness as the second criterion and providing the proper amount of damping as the third criterion for bearing selections. Because of the difficulty to choose correct type of bearings within the design window, a new type of bearing is introduced as described in Section 5. . In the literature, certain non-traditional approaches of using relatively inexpensive bearings are reported. Many inexpensive bearings do not allow large displacements and have very limited service life. Therefore, they should not play an important role in seismic isolation design for bridges. Furthermore, the cost of the isolation bearing is often a smaller fraction of the total cost of bridge construction. In most cases, using inexpensive bearings may not be a good choice.

A new seismic isolation device
The above discussion on seismic isolation technology suggests that there are many aspects which require further research and development efforts, especially in the area to establish quantitative boundaries of design period in order to achieve optimal designs. In fact, among all commercially available base isolators, none seems to provide a good balance between acceleration reduction and reasonable cost. A recent development, the roller bearing, is briefly explained in this section. It has the promise to utilize damping to achieve desirable compromise in isolative design.

Concept of roller bearing
The core component of this device is the rolling assembly, which generates a desired low and constant acceleration of the superstructure regardless of the magnitude of the ground excitations. To explain the principle of constant acceleration, consider the simplified sketch of a roller traveling on an inclined surface shown in figure 5.1.
In figure 5.1, the inclined surface shown has a constant slope with an angle  measured from the horizontal axis. The motion has an absolute acceleration in the horizontal direction, denoted by a h . The roller has a relative acceleration a r along the sloping surface, which has a vertical component a v and a horizontal component a rh . g A is the ground acceleration which is acting in the horizontal direction without a vertical component: In other words, the roller will have an absolute vertical acceleration, which is a v . where  is the rolling friction coefficient.
The relative vertical and horizontal accelerations relationships are respectively given by Because the quantities and g are all constant, the horizontal absolute acceleration is a constant. Note that the ground acceleration, g A , does not appear in equation (5.6) [Lee et al 2007]. In other words, the amplitude of the acceleration of the superstructure will be constant. The first objective of having a constant and low amplitude acceleration of the superstructure thus may be achieved. Next, if the friction is sufficiently small,  <<  then, a h θ g  (5.8) The rotation friction coefficient of the rolling motion will only be a fraction of one percent. However, with θ less than 5 0 , the angle will be several percent (unit in radians). That is,  will be about ten times larger than  The condition   << is then satisfied. Next, the vertical acceleration can be given as a v g A t a n θ (5.9) Since tan  is for very small angles, the vertical acceleration due to the horizontal ground excitation g A is very small and can be shown quantitatively that it is negligible [Ou et al 2009].

Design parameters
The major design parameters for the roller isolation bearing are listed as follows: where y σ = specified minimum yield strength of the weakest material at the contact surface E s = Young's modulus for material P r = load asymmetrical coefficient c =1 for single direction rolling bearing c = 0.7 for double direction rolling bearing Fig. 5.2 shows the configuration of a prototype roller bearing assembly which was manufactured for laboratory studies. Details on the performance and design of roller isolation bearings may be found in publications by the authors and their colleagues that are given in the references.

Roller bearing implementation
With the support of a Federal Highway Administration grant, the new roller isolation bearing has been installed in an actual bridge to observe the constructability and other related issues in Rhode Island. As of August 2011, the installation is completed and the bridge is open to traffic. C ertain monitoring systems are installed so that in time the performance of the roller isolation bearings under ambient live loads can be evaluated. Figure 5.3 contains a number of the New Street Bridge in RI which is the first bridge in the US implemented with the new roller bearings.

Summary
Although seismic isolation is considered to be a relatively matured technology, there are several issues need to be further explored. The main concern is that in general, the targeted acceleration reduction and the bearing displacement are independent parameters. That is, giving one does not automatically define the other. While for most available isolation systems today, the design practice has been based on the assumption that they are dependent parameters. For this assumption works for many cases, it does not yield adequate design for special situations that can exist. Therefore, principles and approaches to deal with these two independent parameters are needed. This chapter first discussed several design issues of seismic isolation followed by an explanation of the cases where current design approaches may introduce large errors.
Certain key parameters for isolation design are discussed and some research needs are identified. The references provided are selected representative publications by many contributors. No intention was given in this chapter to provide a careful literature review on the subject of seismic isolation. The main control parameter of the seismic induced vibration is the natural period or effective period of the isolation system. To reduce the acceleration, longer period is needed. However, the longer the period is the larger displacement will be resulted. Thus, isolation design is viewed from the perspective of compromising between acceleration reduction and displacement tolerance. The second important parameter is the effective damping ratio, because displacement can only be regulated by damping. The issue becomes complicated because adding damping will affect the acceleration reduction. A base-isolated structure is typically a combination of civil engineering structure with mechanical engineering devices. The former is often designed with sufficient safety redundancy. However, the isolation devices are "precision" mechanical parts that do not have large tolerance of displacement uncertainty. By using the concept of probability based design, the safety margin for base isolation systems may be established with more confidence. This chapter emphasizes the importance of a design window to consider the demand of acceleration and the displacement. Since large displacement may induce many engineering problems, such as large artificial P- effect, etc. the displacement has to be carefully regulated or controlled. This will narrow the available design window. In some cases, no window is available for a reasonable design of base isolation system, suggesting that for such a case it is not effective to use isolation bearings.