Introduction
Seismic isolation is an effective solution to reduce the vulnerability of new and existing structures. Isolation can mitigate the negative impact of an earthquake because it shifts the period of the structure in the range of the spectrum where the spectral acceleration is low. Seismic isolators are especially needed for masonry structures in developing countries. Masonry is a common building method in developing countries because of its low cost and simplicity of construction, but its poor tensile strength ultimately leads to low horizontal loading capacities \cite{murtyl2004twin,feng2011seismic}. In high seismicity regions such as Indonesia, many affordable housing structures are built with masonry and experience severe damage during an earthquake. This consequently results in many avoidable casualties \cite{boen2006yogya}. The importance of conceiving new low-cost seismic isolation systems is therefore paramount.
An elastomeric isolator is a well-known and relatively cheap seismic isolation device. Typically, it consists of several layers of high-damping rubber (pads) and reinforced by steel lamina interposed between pads. The reinforcement has the role of limiting only vertical deformations. The horizontal deformations can be large and are controlled by the small shear stiffness of the pads. This system can isolate the energy transmission of the earthquake from the foundation to the upper-structure. However, a massive application of commercial elastomeric isolators in developing regions is not easy to be realized. It still costs too much for its widespread utilization in low-class housing, due to the need of using steel reinforcements and rigid steel plates for isolation supports.
Glass or carbon fiber lamina is now being used as an alternative reinforcement \cite{van2012horizontal,das2016shake}. A glass fiber is much cheaper than its steel counterpart but has a comparable reinforcement effect. Furthermore, one may think to remove the stiff still plates connecting the isolator to ground and superstructure, so conceiving a so called unbonded device , also known as Unbonded Fiber Reinforced Elastomeric Isolator (UFREI). Experimental works reveal the advantages of the UFREI application \cite{toopchi2008testing,spizzuoco2014innovative}.Its effective horizontal stiffness is considerably lower than that of a bonded device, decreasing the seismic force demands. This softening effect is notable in the stiffness variation of UFREIs that is caused by a roll-over deformation of the UFREI (Fig. \ref{887768}), which is a sort of quasi rigid rotation occurring at large deformation under strong earthquakes.
Another remarkable feature of a UFREI is the so called hardening at large deformation. This occurs when the vertical edges of the bearing, due to increased roll-over, touch the superstructure and the ground. It is considered as an advantageous effect because it plays an important role in limiting the shear displacement during a maximum seismic motion \cite{van2016structural}. An innovative method was proposed to accelerate the full-contact mechanism of a UFREI by modifying the geometry of the upper and bottom supports \cite{van2016structural}. However, this method seems to significantly increase the construction cost. The hardening feature is also found in an expensive isolation system that employs a stopper device to control the displacement \cite{chaudhary2001performance,wilde2000base}.
UFREIs have been already applied for seismic isolation of low-rise masonry prototypes tested in the laboratory \cite{das2016shake}. The experimental results show a desired behavior of the isolated structure with a significant reduction of the roof acceleration and inter-story drift. This excellent performance is also followed by an easy technical detail of the connection between the isolators and the structures. Consequently, advanced and complicated construction methods can be avoided. Basing on such promising results, a first full-scale masonry building isolated with UFREIs has been recently built in Tawang, India, a well know high seismicity region \cite{thuyet2017mitigation}.
UFREI specimens in the literature \cite{toopchi2008testing,calabrese2015shaking,van2017evaluation} mostly consist of many thin rubber pads (15-20 pads), resulting in high shape factors, defined as known as the ratio between the load area to the force-free area of a single pad. Employing many thin pads, consequently, increases the price because of the need for adhesive on rubber-fiber interfaces. Thus, in this work, a UFREI with significantly fewer rubber pads is proposed to result in a cheaper isolation system.
Effective numerical modeling of unbonded rubber isolation for masonry housing
Another important issue is the modelling of UFREIs in structural analysis. The non-linearity model of this isolator, including the softening and hardening, is not found in the most structural analyses software available \cite{simulia2013abaqus,csi20108}. Some works implemented a numerical model of UFREIs only up to the softening mode \cite{das2016comparison,manzoori2017application}. The hardening branch was usually excluded because it was considered as the unstable part.
First of all, a detailed 3D model of a single isolator is implemented into ABAQUS and its hysteretic behavior is numerically analyzed. A preliminary validation is provided assuming as reference some existing experimental data obtained on a standard UFREI subjected to hysteretic cycles. The proposed UFREI is then identified with a single DOF system constituted by a spring exhibiting softening during a cycle, this latter is quite low and can be disregarded without meaningful errors for structural applications. The identification of the 3D model behavior with a single DOF system (non-linear spring with damping) is mandatory to perform large scale non-linear dynamic analyses on isolated full scale buildings.
A numerical model of fiber reinforced elastomeric isolator (FREI)
Fig. \ref{207728} shows the isolators considered in the present work. UFREI-200 is the reference specimen \cite{Toopchi_Nezhad_2008} to calibrate the material properties, and UFREI-175 is the proposed device with a much fewer number of pads. The isolator is used in unbonded type (UFREI), where the upper and lower edges do not exhibit any bond with the supports. Under moderate shear forces, such frictional limited strength allows the isolator to roll-over and facilitates larger deformations, see fig \ref{887768}. Unlike a bonded model, the peak tensile stress on the rubbers and interfaces significantly decreases. Thus, delamination at high deformation can be avoided.