Effects of Shape Memory Alloys on Response of Steel Structural Buildings within Near Field Earthquakes Zone

Base isolation is one of the effective ways for controlling civil engineering structures in seismic zone which can reduce seismic demand. Also is an efficient passive control mechanism that protects its superstructure during an earthquake. However, residual displacement of base-isolation systems, resulting from strong ground motions, remain as the main obstacle in such system’s serviceability after the earthquake. Shape Memory Alloys (SMA) is amongst the newly introduced smart materials that can undergo large nonlinear deformations with considerable dissipation of energy without having any permanent displacement afterward. This property of SMA may be utilized for designing of base isolation system to increase the structure’s serviceability. Here, a proposed semi-active isolation system combines laminated rubber bearing system with shape memory alloy, to take advantage of SMAs high elastic strain range, in order to reduce residual displacements of the laminated rubber bearing. Merits of the system are demonstrated by comparing it to common laminated rubber bearing isolation systems. It is found that the optimal application of SMAs in base-isolation systems can significantly reduce bearings’ residual displacements. In this study, OpenSees program for a three dimensional six-storey steel frame building has been used by locating the isolators under the columns for investigating the feasibility of smart base isolation systems, i.e., the combination of traditional Laminated Rubber Bearing (LRB) with the SMA, in reducing the structure’s isolated-base response to near field earthquake records are examined. Also, a new configuration of SMAs in conjunction with LRB is considered which make the system easier to operate and maintain.


Introduction
Earthquake is one of the most destructive phenomena which caused catastrophic destruction. Annually, earthquakes take thousands lives, and bring about significant financial loss all over the world. Today, civil engineers concern is to design structures to withstand under earthquake forces and to dissipate the input earthquake energy through in-elastic deformations [1]. Generally, structures are designed according to codes with criteria based on structural collapse prevention. This approach allows for the forces due to ground motion to be transmitted into the structure; and relies only on strength and ductility of the structure to resist these forces. Hence, large motion can occur at higher floors of the structure, causing severe damage to the building. Seismic base isolation system change structure's response by allowing the ground to undergo relatively large displacements without transmitting forces into the isolated structure. In fact, in most isolation designs, the structure generally moves as a rigid body. This means that ground accelerations signals that pass through the isolators remains relatively constant along structure's height [2], i.e. the acceleration of the top floors differ slightly from the accelerative motion imposed at lower level. It has been pointed out by Markris and Aghagholizadeh (2019), for reducing the earthquake forces acting on a structure or to absorb a part of the seismic energy, innovative systems and devices have been developed [3]. Seismic isolation systems are able to reduce the natural frequency created by the seismic load applied to the structures. Over the last few decades, several types of seismic isolators have been proposed and developed and are often divided into elastomeric and friction isolators, i.e. low damping natural rubber bearing, lead rubber bearing, high damping natural rubber bearing, pure-friction and friction pendulum system [4,5]. Several studies have also focused on the evaluation of the seismic performance of highway bridges with seismic isolators using yielding steel dampers and laminated rubber bearings in comparison with other popular isolation systems [6,7].
Recently, advanced materials have been used for seismic isolator and damping systems [8]. A group of metals that have the ability to dissipate energy through repeated cyclical loading, without significant permanent deformations is known as Shape Memory Alloys (SMAs). It has been pointed out by Wesolowskyi and Wilson (2004), shape memory alloys as compared to other metals, have a wide usable strain range; up to about 8%; thus, requiring a smaller volume of material in order to produce the comparable damping capacity. Furthermore, they have needed ability, i.e. providing stiff elastic resistance under large displacements [9]. A numerical parametric study carried out by Asgharian et al. (2016) for self-centering hybrid damper [10]. In this study, steel pipe used as a vertical link for energy dissipation and two transverse pairs of shape memory alloy wires as for re-centering components. Tian et al. (2018) used shape memory alloy tuned mass damper for seismic vibration control of power transmission tower in order to assess nonlinear time history analysis method [11]. Ghasemi et al. (2019) pointed out that as the shape memory alloy is highly capable of dissipation energy, which can control the vibrations created by wave-induced of the offshore jacket platforms [12]. Also base isolation systems can have an extensive applications in different types of tall structures in order to reduce the lateral displacements, drifts and natural frequencies [13,14].
In this study, a three dimentional six stroey steel frame building has been cosidered. The base isolation system has been design according to ASCE7 code requirements. Their charecteristics dependent on the weight and period of its superstructure. The near field earthquke data from Northridge records are selected and scaled in order to carry the response history analysis; by generating design response spectrum which is specialized for the site. The structure is modeled in OpenSees package, which is based on finite element method. By definining the base isolation materials from OpenSees library, fixed-based structure and base isolation system in a 3D model are analysed. SMA bars are implemented into the base isolation system's model and the structural response due to earthquake records are computed and compared.

Base Isolation and Shape Memory Alloys Concept
Shape memory alloys are earthquake-resistant in civil engineering structures which can dissipate significant energy and are able to to return to their previous shape after being severely deformed. It has been pointed out by Nakashima et al. (2004) that designing of base isolation in any structures should follows two objectives, achieving life safety and limiting damage due to a significant earthquake [15]. To achieve these objectives, the base isolation should be stable and sustain forces and displacements with significant earthquake [16]. Base isolation system has a limited ductility and a significant inelastic response which meet the second performance objective of damage control [17,18]. A lead rubber bearing, manufactured from layers of rubber, bonded with layers of steel and in middle of bearing a solid lead core ted shown in Figure 1 [19].

Figure 1. Lead rubber bearing [19]
Design of isolators is based on the ASCE7, the following procedures such as equivalent lateral static force and dynamic analysis for time-history can be used. For design of isolators, some requirements such as structural site with S 1 and site class A, B, C, or D. Effective period of isolated structure at the maximum displacement, T M , and the effective period of the isolated structure at the design displacement, T D , can be obtained [20]. Also, the base isolation system should meet the following criteria [21]:  Effective stiffness at the design displacement is greater than one-third of the effective stiffness at 20 percent of the design displacement.  Base isolation system is capable of producing a restoring force.
 Maximum considered earthquake displacement to less than the total maximum displacement.
The following steps are illustrated for dynamic analysis procedure:  First step: the target period assumed to be not less than at least three times of the fixed base period of structure (T D > 3 T fix ).
 In the second step, design displacement (D D ) and maximum considered earthquake response displacement (D M ), at the center of rigidity of the isolation system can be calculated by Equations 1 to 4.
Where [11]: Where; W: weight of structure above the base isolator. Where : minimum effective stiffness of base isolation at the design displacement in the horizontal direction and : minimum effective stiffness of base isolation at the maximum considered earthquake response displacement in the horizontal direction can be obtained by Equations 5 and 6 respectively: As shown in Equations 5 and 6, minimum effective stiffness of the isolators can be obtained by using parameters such as ∑| + | & ∑| − | from testing the isolators, so value for , can be assumed to be 3.0 sec.  Second step: the modified displacement can be obtained using Equations 7 and 8.
 Third step: the total of design displacement and maximum considered earthquake response displacement (D TD and D TM ), can be obtained by Equations 9 and 10 respectively:  Fourth step: the base shear can be evaluated using Equations 11 and 12.
Where; is the ratio of secondary stiffness to primary stiffness of isolator.
The R I factor is based on the type of seismic force-resisting system used for the structure above the isolation system and should be 0.375 of the value of R given in ASCE 7, Table 12.2-1, with a maximum value not greater than 2.0 and a minimum value not less than 1.0. It should be noted that in this study the isolated structure R I = 2.  Fifth step: controlling drift and base shear limit which shall not exceed the following limits: 1. Maximum storey drift of the structure above the isolation system shall not exceed 0.015h sx .
2. Maximum storey drift of the structure above the isolation system shall not exceed 0.020hsx.
The value of base shear, V S shall not be taken as less than one of the following limits: 1. Base shear corresponding to the factored design wind load.
2. Lateral seismic force required to fully activate the isolation system multiplied by 1.5.
The isolators make a reduction in forces created by earthquake in the design of structures and also reduce floor displacement and accelerations which can be apply into the new and retrofitting of existing structures. Recently, the performance of the isolator in the base of structures has been used in near-fault earthquakes, long period and large velocity pulses in the velocity history of ground motion can be characterized. For the isolated base structure, if the period of the mentioned pulses coincides with the period of the structure, the seismic response of the system will be amplified. The base isolation structure will be influenced with normal to the fault ground motion such that, the isolator effects will be reduced or maybe negative. To solve this type of problems with the isolation systems, shape memory alloys can be applied in vibration control of structures. The shape memory alloys has two unique properties: shape memory effect and super elastic effect. Both of these properties acting on the solid-solid phase transformation first more ordered phase named austenite and less ordered phase named martensite. To transfer from the one mentioned phase to another, it is necessary to exist the variation in temperature or stress which the transformation due to temperature variation called shape memory effect and due to the stress variation called super elastic effect.
The super elastic effect can be considered in base isolator residual displacement problem. It can fully reenter the original shape of the isolator, and this shape recovery is also compeer with significant hysteresis loop which leads to energy dissipation. Combination of the isolators and these smart materials can lead to an intelligent solution for the mentioned problems with isolators in a near-fault earthquake. Residual displacements of the isolators can be removed with a re-centring force which was generating by the SMA bars due to the ground motion. In this study to meet the mentioned purpose, two principal part of isolators (top and below flange of isolator) should be linked with the SMA bars as shown in Figure 2.

Figure 2. Combination LRB isolators with the SMA bars
Several key parameters on the hysteresis loop have be determined for shape memory alloys as illustrated and shown in Figure 3 which indicate the energy dissipation and restoration after unloading.

Time History Analysis and Structural Model
As suggested by ASCE 7, in time-history analysis, at least three different strong ground motions will be needed to apply the structural model and the scaled ground motion [21] . Seven ground motions which are the maximum value of each response parameter have been used for design as listed in Table 1, are taken for the response-history analysis. All of the selected records are near field record as shown in Table 1. In this study several combinations of scaling factors have been defined for three 6-storey structural models and assumed to be located in California zone. The details of steel structural building are shown in

. Beams and columns of 6-storey model in X & Y direction
The dynamic properties of steel building are listed in Table 2.

Table 2. 6-storey model, dynamic properties (Natural period in sec)
The site class of soil considered to be C (very dense soil and soft rock) base on ASCE 7 code, and is residential structures. The design parameters for the models are as follow [21]: Importance Factor (I e ) was defined as 1 in this study concerning the risk category.
Site location, evaluate S 1 and S S (acceleration parameters), S 1 =0.82g and S S =1.61g Site class, to evaluate properties of soil at a given site.

Site categorized are as site class A, B, C, D, E and F.
For this study site classification C has been selected (C: Very dense soil and soft rock).
For moment resisting frames category (D), behavior factor of ( ) = 8 and the seismic response coefficient, C S , can be obtained using Equation 16.
The approximate fundamental period (Ta), in s, can be calculated by Equation 17.
= . ℎ (17) Where h n is the structural height from the base, C t and x are determined from ASCE 7 [21].
The following flowchart is given to show procedures of research methodology:

Results and Comparisons
In this study, displacement and acceleration responses of the model have been presented and compared with each other in such a ways to illustrate the significant differences which exist in displacement and acceleration responses between the fixed base and isolated base and isolated base equipped by shape memory alloys material in isolators:

Fixed Base Results
Displacement response for an ordinary building subjected to Northridge record is shown in Figures 6 to 9.   According to Figures 6 to 9, in a 6-storey steel structure, displacement graphs demonstrate a response for an ordinary building where the maximum displacement in the first storey is 2.09 cm and 1.88 cm in X and Y directions. In sixth storey, maximum displacement is 17.6 cm and 19.3 cm in X and Y direction respectively. So, the building has a noticeable relative displacement in stories. The period of the structure is same as conventional steel moment frames.

Isolated Base Results
Displacement response for an ordinary building subjected to Northridge record is shown in Figures 10-13. Compared to the fixed base, the relative displacement decreased from 4.02 cm to 0.59 cm and from 3.17 cm to 0.83 cm in X and Y direction respectively. The relative displacement shown in Figure 14, indicate a reduction since isolators have been used. However, after earthquake, a significant residual displacement can be observed in base isolation devices, which consequently alter the performance of the isolators afterwards.

X Direction
Fixed Base Isolated Base

Isolated Base Equipped with SMA Results
As observed in the base isolation system, there is a negligible residual displacement compare to the base-isolated system equipped with shape memory alloys, the residual displacement in the X direction is 0.53 cm compared to the base isolation system with 7.96 cm and in the Y direction is 0.29 cm compared to 8 cm. The stiffness of shape memory alloys has an insignificant effect on dissipating energy and the relative displacement is slightly different from base isolation systems. According to Figures 14 and 19, the relative displacement difference is negligible in comparison with the base isolation system with the maximum relative displacement of 0.79 cm and 0.67 cm in X and Y direction compared to 0.59 cm and 0.83 cm. The period of the structure is almost same for both cases. The results maximum displacement, residual displacement and maximum relative displacement for three cases of fixed base, isolated base and isolated base equipped with shape memory alloys are listed in Table 5.

Conclusion
In this study, a three dimensional six-storey steel structural building was modelled in OpenSees program by locating the isolators under the columns in order to investigate the feasibility of smart isolation systems. Initially, fixed-based results are observed which shows that their responses are same as conventional buildings; with significant storey drifts and vulnerable in near-field earthquake excitations with noticeable acceleration at first story and shear force consequently. Base isolation system results are compared to fixed-based results. Maximum relative displacement of base isolation system has been reduced to 85 percent compared to fixed-based where the period of the structure became 3 times greater than fixed-based structure. Considering the results, in the base-isolated system equipped with shape memory alloys, the residual displacement decreased up to 94 percent in the X direction and up to 97 percent in the Y direction. It can be concluded that the efficient function of a base isolation can be reserved for the future and the maintenance costs of the structure. The importance of the structure and considering the high price pf shape memory alloys, the economic values of these types of structures should be considered. The indicated system significantly elevates the durability of base isolation during service level of earthquakes over the time which may reduce base isolation maintenance and replacement expenditures.