Introduction

Rapid urbanization increases the number of structures that have been built using non-engineering methods without following the seismic provisions. Also, some structures constructed before the introduction of seismic codes are defined as seismically vulnerable. By lowering the seismic demand, the failure of these impaired structures can be prevented. For this purpose, base isolation has been practiced for earthquake-resistance design. The most common base isolator is the steel-reinforced elastomeric isolator (SREI). The shortcomings of SREI are the large weight and production cost (Kelly, 2002). That is why SREIs are used in large and expensive structures only (May, 2002; Pan et al., 2005). To extend the earthquake-resistant design strategies for masonry structures, residential and public buildings, the cost reduction and simplicity of the design principles are of great concern. As an alternative, numerous innovative aseismic tools made with locally available and inexpensive materials have been proposed (Kelly & Takhirov, 2002; Llera et al., 2004; Xiao et al., 2004; Turer & Özden, 2007; Tsang et al., 2012). The fiber-reinforced elastomeric isolator, which is called FREI, was proposed by Kelly (Kelly, 1999). In FREI, fiber reinforcement is utilized instead of the steel shim used in SREI. The FREI can be used without the endplates, which are required for installation of SREIs (Konstantinidis & Kelly, 2007). The unbonded FREI exhibits superior performance, high damping, and shear deformability (Toopchi-Nezhad et al., 2008a, b, 2009a, b, 2011, and 2014) compared with the bonded one. However, due to a lack of raw materials, manufacturing facilities, and a high cost, its application and acceptance in developing countries is limited.

As an alternative, an isolator made from scrap automobile tires has been proposed by Turer and Özden (2007), Spizzuoco et al. (2014), and Mishra et al. (2013). Automobile tires are made by vulcanizing natural or synthetic rubber with interleaved steel cords. These steel cords are expected to have similar functions to that of the steel shims in SREI. An STRP isolator has an effective damping ratio in the range of 10 ~ 22% and a vertical-to-horizontal stiffness ratio exceeding 150 (Mishra, 2012). The shear modulus of tire pads is around 1.0 (Turer & Özden, 2007; Mishra et al., 2013), which is comparable to natural rubber, 0.55 ~ 1.20 MPa (AASHTO-LRFD). These properties of the tire pad match with the required properties of isolation material (Kelly, 1997; Eurocode8, 2004). The STRP is cheap since the material cost is nearly zero, and it needs only cost for sizing and adhesive. The STRP is considered eco-environmental and suitable for isolating low to medium-rise buildings (Turer & Özden, 2007; Spizzuoco et al., 2014; Calabrese et al., 2015). The positive aspect of STRP is that it can be utilized without any mechanical fastening to structures. The flexible twisted cord allows an unbonded STRP to deform freely, as like FREI (Toopchi-Nezhad et al., 2011), without generating tensile stress. Besides, the rollover deformation significantly decreases the lateral stiffness, which lengthens the isolation period (Toopchi-Nezhad et al., 2008a). It is claimed that isolators made with recycled-tire chips and fiber mesh (RR-FRB) are advantageous to the SREIs or FREIs (Calabrese et al., 2015).

A precise understanding of the nonlinear behavior of the STRP base-isolated (BI) building remains unknown. The seismic design codes for bridges and buildings (JSSI, 1995; JRA, 1998; AASHTO LRFD, 2014) suggest time-history nonlinear dynamic analysis for BI structures. In current practice, the inelastic properties of isolators in a nonlinear dynamic analysis are assumed through a simple bilinear model (Naeim & Kelly, 1999). This model is unable to represent the nonlinear elastoplastic behaviors, especially the rate-dependency of the elastomer (Abe et al., 2004a, b; Bhuiyan et al., 2009). Besides, the effects of vertical compression and horizontal displacement on the seismic performance of a BI building need to be considered. Since experimental investigation for a BI building is costly and impractical, the FE simulation is more practical. The FE simulation of the LRB base-isolated building conducted by Ohsaki et al. (2015) is a pragmatic example of inelastic analysis of BI structures.

From the literature review, there are few studies on the unbonded application of base isolator. Toopchi-Nezhad et al. (2009b) conducted a shaking table test on a 1/4th scaled two-story frame supported on unbonded FREI isolators. Das et al. (2016) investigated a two-story 1/5th scaled un-reinforced masonry building rested on unbonded FREI isolators. Both concluded that the unbonded FREI has high potential for reducing the seismic demand. The shaking table test of RR-FRB base-isolated buildings (Calabrese et al., 2015; Maddaloni et al., 2017; Losanno et al., 2019) shows that roof acceleration and story drift are substantially lower than that of the fixed base structure. The unboned isolators also show good re-centering capabilities. However, there is no experimental or FE study that focuses on the effectiveness of unbonded STRP isolation in real structures or any study on the serviceability of unbonded isolation compared with bonded or conventional methods.

Previous studies (Mishra and Igarashi, 2013; Mishra et al., 2013) focused on the stiffness and damping of STRP isolators. Besides, a pseudo-dynamic test on a 1/3rd scale STRP isolator was carried out by Mishra et al. (2014) under constant pressure and a moderate level of acceleration. A numerical simulation of a three-story STRP BI building that ignored the friction-based unbonded boundary condition was performed (Mishra, 2012). Later, (Zisan, 2021; Zisan and Iarashi, 2020, 2021a, b, 2022) investigated the lateral performance, deformation capacity, hysteresis force model of unbonded square and strip-shaped STRP isolators under combined axial and lateral loads. The seismic vulnerability of masonry building supported by STRP isolator is investigated by Zisan et al. (2022). These studies considered the influence of the length-to-width ratio and bearing height on the horizontal stiffness, damping, and seismic demand at different levels of earthquake. Since the unbonded isolator relies on friction and rollover deformation, the overturning of the superstructure or high vertical ground motion should be considered. The superstructure uplifting depends on the type of input motion, the aspect ratio and weight of the structure, and the vertical stiffness and horizontal displacement capacity of the isolator (Ehsani & Toopchi-Nezhad, 2017). These factors were not considered in the previous studies of the unbonded STRP isolator. Besides, to assess the practicability of the unbonded STRP isolator, its effectiveness needs to be assessed with an analogous conventional system and a FB structure.

Therefore, the scope of the research includes the following objectives:

  • A systematic design procedure for an unbonded STRP isolator.

  • An outline for the FE simulation of a BI building, including a 3-D model for seismic isolators.

  • Seismic performance of BI building and isolation systems for different base connections: SREI, B-STRP, U-STRP, and FB.

  • A comparative study among the SREI, B-STRP, U-STRP, and FB systems.

Super structure modeling

A hypothetical four-story-reinforced concrete building resting on nine square-shaped isolators is considered. Since the scope of this study is to assess the effectiveness of STRP base-isolation, the structural components and geometry of the building are assumed to be based on the conventional design. The building is a two-by-two bay in the plan with a total width of 12 m and a height of 12 m, as shown in Fig. 1. The column and beam sizes are 500 × 500 mm and 300 × 500 mm, respectively, and the slab is 150 mm thick. There is no rigid slab at the base level since most low-to-medium-rise structures are built above the grade beam with no firm floor to save money. Therefore, isolators are placed below the grade beam at beam-column intersections. These columns are extended from the rigid foundation. An inverted T-shape rigid floor around the column and below the beam-column intersection section that sandwiched the STRP between superstructure and foundation can be used to prevent the STRP from being moved beyond the center of the column. The unit mass of concrete and that of the infilled wall is 2400 and 1950 kg/m3, respectively. The mass of the 130 mm thick infill wall (760.5 kg/m) is added to the mass of the beam. Isolator mass is negligible and ignored. The total mass of the superstructure is 686.2 tons, distributed as 69.7 tons at the base level, 164.4 tons at each floor level, and 125.1 tons at the top floor level. The elastic modulus and Poisson's ratio for a 35.0 MPa concrete are 32.1 GPa and 0.20, respectively (ACI, 2008). The approximate lateral stiffness of the frame structures is 668.7 kN/mm, the same in the vertical direction. The beams and columns are assumed to be linear isotropic elastic–plastic elements and the floor slab as a shell element. Figure 2 and Table 1 show the mode shape and period of the FB building obtained from FE analysis.

Fig. 1
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Plan and elevation of 4-storied BI building

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Fig. 2
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Mode shape of FB building

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Table 1 Modal characteristics of 4-storied building
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Earthquake ground motions

For a FB structure, the adopted earthquake accelerogram should meet a critical loading condition. In contrast, the period of a BI structure should be more separated from the predominant period of the same seismic events. The ground accelerations are modelled based on the design response spectrum. The design response spectrum is determined using ASCE 7–22 specifications based on the level of seismicity. Because no precise site for the assumed building is assumed, the efficacy of the STRP-base-isolated building is investigated for three possible degrees of seismicity: low, medium, and strong. These response spectrum represent the seismic intensity level at class B, C, and D sites. Figure 3a and b are the accelerograms and 5%-damped elastic response spectrum of the earthquakes at the DBE level. The acceleration and corresponding response spectrum at the MCE level are 1.5 times that of the DBE level. Based on the input design response spectrum, the ground motion is calculated using the PEER ground motion database. The input accelerations are Kobe (KB), the Northridge (NR), and the Imperial Valley (IV), as shown in Fig. 3a. Figure 3b shows the site class coefficient for a short period and a 1-s period. The IV and NR earthquakes are suitable to produce a substantially greater difference in response between the FB and BI buildings than that of the KB earthquake. Table 2 gives the ground motion parameters at the DBE level. The peak ground acceleration (PGA) of the KB, IV, and NR earthquakes is 0.345, 0.47, and 0.569 g, respectively. The peak ground velocity (PGV) of the respective motions is 27.7, 44.5, and 51.8 cm/s, respectively. In the case of the IV earthquake, the peak ground displacement (PGD) is 19.5 cm, and about 9.0 in the case of the KB and NR earthquakes. The damage potentiality measured by Housner Intensity (Clough & Penzien, 2003) of IV and NR earthquakes is comparable and higher than that of the KB earthquake.

Fig. 3
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Acceleration and 5%-damped response spectrum at DBE level of input earthquakes

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Table 2 Input earthquake parameters at DBE level
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Isolator models

The STRP is a 12 mm thick tire pad made from a Bridgestone 385/65R22.5 tire. It has five reinforcement layers oriented at ± 70° to the carcass steel direction. The STRP isolator is made by stacking individual STRP layers one above another and then bonding them with an adhesive. A detailed description of the preparation of the STRP isolator can be found in Mishra (2012). The HDR-C bearing, here called the steel-reinforced elastomeric isolator (SREI), was experimentally studied by Abe et al. (2004a). Figure 4 shows the geometric properties of the SREI and STRP isolator that have been used in the loading test and FE model validation. In SREI, the thickness of each elastomer and reinforcement layer is 5 and 2.3 mm, respectively. In the STRP isolator, the equivalent thickness of the elastomer layer and that of the steel cord is 2.40 and 0.4 mm, respectively.

Fig. 4
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Experimental models used in the FE model validation. a SREI b STRP isolator

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Table 3 indicates the properties of the reinforcement in the SREI and STRP isolator. The hyperelasticity of rubber material is expressed by the Mooney-Rivlin material constant. Table 4 shows the material constants for rubber in the STRP isolator (Mishra et al., 2013; Zisan & Igarashi, 2021a) and SREI (Yoshida et al., 2004a, b). The viscoelasticity of rubber is assumed using the Prony series viscoelastic shear response parameters. Numerous FE analyses of high damping rubber bearings (HDRB) have been carried out based on the hyperelastic and viscoelastic material models (Fuller et al., 1993; Matsuda, 2002; Yoshida et al., 2004b; Amin et al., 2015). The same is employed in modeling and analyzing the SREI. The degradation of rubber is assumed using a phenomenological model called Mullin's effect. The rebar position, size, and orientation are given in Table 3. In the case of SREI, the steel shims are modeled by a membrane element that has bending stiffness. A detailed explanation of the finite element modelling and determination procedure of material constants can be found in Zisan and Iarashi, (2020, 2021a).

Table 3 Properties of reinforcing cord and steel shim
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Table 4 Properties of the elastomer in STRP and SREI
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Validation of FE models

Table 5 represents the loadings that were used in the experiments for STRP-4 (Mishra et al., 2014) and HDR-C (Abe et al., 2004b) isolators. The displacement in the quasi-static test consists of three fully reversed cycles for each displacement amplitude, which is linear in the case of the STRP-4 isolator and sinusoidal in the case of the SREI. The pseudo-dynamic test of the full-scale STRP isolator was designed for a mass of 29.9 tons, and it gives a mass equal to 1107.4 kg for the 1/3rd scaled model. Abe et al. (2004b) conducted a bidirectional hybrid simulation test for SREI using Kobe Marine Meteorological Observatory data from the Kobe 1995 earthquake. In that simulations, the input acceleration was scaled by 1/3rd to limit the shear displacement to 150%.

Table 5 Loading conditions in quasi-static and dynamic loading tests
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The boundary conditions used in the loading test of the STRP-4 isolator is shown in Fig. 5. The upper loading block supplies rigid mass to the tested specimen. The loading system consists of one, three, and five actuators in the x, y, and z directions, respectively. Three actuators are connected with the reaction frame and the rigid block through pin connections and provide reactions Fx, Fy, and Fz or displacements ux, uy, and uz. Four actuators are used to restrain the rotation about the x and y-axes and the remaining two constraint rotations about the z-axis. The STRP-4 isolator is placed between two steel plates as shown in Fig. 5b without any bond between the plate and the specimen. During the test, actuator Fz controls the vertical compression on the specimen, and actuator Fx controls the cyclic displacement or lateral load. Fy is used to constrain out-of-plane movement.

Fig. 5
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Pseudo-dynamic test conditions (Mishra et al., 2014)

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Figure 6 demonstrates the FE model, which is analogous to the quasi-static and dynamic test conditions. In quasi-static conditions, all degrees of freedom of the bottom plane and rotational degree of freedom of the top plane are restrained. In dynamic analysis, the vertical degree-of-freedom of the bottom plane is restrained, whereas both the bottom and top planes are allowed horizontal and rotational degrees of freedom. The MASS elements, or column nodes, are also glued to the top rigid plane. The MASS, or column node, shares the same degree of freedom as the top rigid plane. The contact surface between the rubber and rigid surfaces is specified as touch contact using the bilinear Coulomb friction model with a friction coefficient of 0.80. Details of the modelling and analysis procedure can be found in Zisan and Iarashi, (2020, 2021a, b).

Fig. 6
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Boundary conditions and lateral load used in the FE model (STRP-4)

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Table 6 shows the horizontal stiffness of the SREI and STRP-4 isolator found from the loading tests and the FE analysis. The stiffness between the experiment and the FE analysis matched very well. Figure 7 indicates that the hysteresis curve found from the FE analysis and experiment is comparable. The effective damping ratios also show good agreement. An average effective damping ratio obtained by FE analysis is approximately 14% higher in the STRP isolator and about 16% lower in the SREI than that of the experimental value.

Table 6 Horizontal stiffness and damping: Experimental and FE analysis
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Fig. 7
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FE Model validation: quasi-static test

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Figures 8 and 9 present the restoring force–time history and hysteresis loop of the SREI and STRP-4 isolator, respectively. It shows that the FE analysis result matched the experimental result well. Besides, the peaks of the restoring force and the lateral displacement between the FE analysis and the experiment are very close. Figure 10 shows that the FE model is capable of stimulating the rollover deformation observed in the experiment. Therefore, it can be concluded that the FE model of the isolators acceptably represents the practical model.

Fig. 8
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STRP-4 FE Model validation: pseudo-dynamic test

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Fig. 9
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SREI model validation: bidirectional dynamic test

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Fig. 10
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Deformation of STRP-4 isolator at 100% shear strain

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Design of base isolators

Based on the axisymmetric mass and stiffness, the base isolators in the assumed building are grouped into corner isolators (B1, B3, B7, B9) as A-type, periphery-middle isolators (B2, B4, B6, B8) as B-type, and the central one (B5) as C-type. The axial load on each A, B, and C-type isolator due to building weight is 540.6, 864.1, and 1344 kN, respectively. The geometric properties of the SREI and STRP isolators are determined based on the pressure on bearing and target period of the BI-structure. Table 7 indicates the average size of the isolators found from the preliminary design as described in Fig. 11 (Zisan, 2021b). The period and displacement determined by the flowchart are based on a single-degree-of-freedom system and 5%-damped spectral acceleration. The procedure used the equivalent lateral force (ELF) procedure described in ASCE 7–22 specifications. An average pressure of 3.97 MPa is assumed for all isolators. The aspect ratio, R, is kept at 3.0, and for the square-shaped isolator, the length-to-width ratio, r, is 1.0. Other parameters such as Ef, tf, υf, G, te, tri are given in Tables 3 and 4. The spectral accelerations at an isolation period of 1.78 s and at 100% shear level are listed in Table 7. The damping constant is 1.20, corresponding to 10% effective damping. The design is initiated with an initial value of pressure, p and R. The minimum value of R is 2.5, while the same is greater than 1.0 MPa for p. It is found that an U-STRP isolator experiences no sliding until 200% shear under 1.5 MPa pressure. TB = α1TF, where TB and TF are the periods of BI and FB buildings, respectively, and α1 is the magnification factor. The tolerance is assumed to be 5%. Table 7 shows the displacement and period of the U-STRP isolation system for different input motions. The period of a STRP-base-isolated building is found in the range of 1.5 ~ 1.85 s, which is sufficiently larger than 0.75 s, the period of the same building with a fixed base condition. Since a typical earthquake ground motion record contains a substantial amount of energy within a period range of 0.1 ~ 1.0 s and a maximum in the range of 0.2 ~ 0.6 s, the period 1.5 ~ 1.85 s assumed to be sufficient for the assumed building. Here, the average size of each isolator is assumed to be 440 × 440 × 146 mm. The period can be lengthened by increasing the thickness of the isolator. Since compressive forces for isolators are different, Table 8 shows the actual size of each isolator group utilized in the FE analysis and is deduced based on pressure and aspect ratio of 3.0.

Table 7 Preliminary design of STRP isolators for earthquake load
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Fig. 11
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Flow chart for the preliminary design of the STRP isolator

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Table 8 Geometric properties of STRP and LRB isolators (mm)
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The static pressure within the isolators varies between 2.89 and 5.16 MPa, while the average pressure remains at 4.0 MPa. These pressures are about 5.0 MPa, which is accepted until 200% shear displacement and tension below 2G ~ 3G. The shear modulus of U-STRP isolators under 3.3 ~ 10 MPa pressure and 100% shear strain is 0.48 ~ 0.75 MPa (Mishra et al., 2014), and the effective damping ratio is 12 ~ 16%. The shear modulus at 100% shear and 3.97 MPa pressure is assumed to be 0.60 MPa. The lateral stiffness and period of U-STRP BI-building using a 144 mm thick isolator are 9.05 kN/mm and 1.78 s, respectively, at 100% shear level. The shear modulus of the rubber in SREI at 100% shear estimated using the AASHTO definition is 0.71 MPa. The stiffness and period of SREI BI-building are 12.13 kN/mm and 1.52 s, respectively, at 100% shear strain.

Modeling and nonlinear analysis of BI building

Figure 12 shows the FE model of the U-STRP BI building resting on a bottom rigid plane. The bottom plane can move horizontally in the direction of input acceleration. A top plane that distributes the column force is placed between each isolator and the column. Figure 12b shows an enlarged view of the central isolator. The bottom node of each column maintains contact between the superstructure and the rigid top plane. Both the column node and the top plane have the same degree of freedom. The contact model between the isolator and the fixed planes is the same as described in the model validation section. There is no contact between the beams and the top rigid plane. The Single-Step Houbolt operator, γ1 = 1.5 and γ = -0.5 is used for numerical integration. The Newton–Raphson iteration procedure with a relative force and displacement tolerance of 0.1 N and 0.1 mm, respectively, is used. The time step is kept between 0.001 and 0.0025. The FE model of BI-building has 27 individual contact interactions. The Multifrontal Sparse solver with four multiple threads and a CPU of 2.10 GHz is used, and it needs a computational time of 40 ~ 50 h for each analysis.

Fig. 12
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FE Model of 5-storied U-STRP BI building

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Analysis result

The response of the BI building and that of isolators is determined for two levels of design earthquake: DBE and MCE levels. The response of a 5%-damped linear elastic FB structure is determined to assess the effectiveness of STRP base isolation. The effectiveness of isolation is expressed in terms of response attenuation or reduction factors, defined as below:

$${\text{Attenuation factor}} = {\text{Response of BI building}} \div {\text{Response of FB building}}$$
$${\text{Response of FB building}} = \left( {1 - {\text{attenuation factor}}} \right) \times 100\%$$

Floor acceleration and displacement are taken at the center of the mass of each floor. The lateral displacement of the isolator and that of the floor is measured by subtracting the horizontal displacement of the bottom plane from the lateral displacement of each story. The vertical distribution of lateral load is estimated from the inertia force, which is a product of floor mass and floor acceleration. All floor accelerations are taken at the same time instant when base shear is maximum. The hysteresis curves, lateral displacement, and rocking motion in each isolation system are included for comparison purposes.

Responses of the building

The displacement time histories at the top floors of the FB, SREI, B-STRP, and U-STRP BI buildings at DBE and MCE level design earthquakes are depicted in Fig. 13. The displacement time history among the BI-buildings is comparable. A significant reduction is observed in the IV and NR earthquakes in comparison with the FB building. Figure 14a and c shows the maximum lateral displacement at each floor level at the DBE and MCE levels, respectively. The top floor displacements of the FB building vary in the range of 40 ~ 98.2 mm and 61.1 ~ 147.2 mm at DBE and MCE levels, respectively. The corresponding value in the BI building is substantially lower and in the range of 25.0 ~ 43.8 and 39.0 ~ 69.3 mm, respectively. The lower limit of this displacement range is due to the KB earthquake. The floor displacements are minimum in the U-STRP BI building and comparable to the SREI BI building. Floor displacements of SREI and B-STRP BI buildings due to KB input are 0.86 ~ 0.96 and 1.03 ~ 1.08 times that of the U-STRP BI building. In the IV and NR earthquakes, the respective displacements are 1.0 ~ 1.15 and 1.23 ~ 1.59 times. It implies that U-STRP isolation is more effective, and its efficiency increases with an increase in seismicity. Figure 14b and d shows the displacement attenuation factor. It indicates that U-STRP isolations are more efficient than the SREI isolation, and the SREI is more efficient than the B-STRP. For example, the top floor displacement is reduced by 61 ~ 63%, 58 ~ 59%, and 41 ~ 53% in U-STRP, SREI, and B-STRP BI buildings, respectively, in the case of IV the earthquake. In the NR input, these reductions are between 47 ~ 48 and 44 ~ 49, and 32 ~ 35%, respectively. In the KB earthquake, top floor displacement reduction is 14 ~ 20, 23 ~ 25, and 12 ~ 13% in U-STRP, SREI, and B-STRP BI buildings, respectively.

Fig. 13
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Top floor displacement time-history

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Fig. 14
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Superstructure displacement and displacement attenuation

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Figure 15a and c presents the inter-story drift. The inter-story drift in the FB building is larger than 0.01hx, which is the limiting value for risk category IV (ASCE 7–10, 2010). The maximum drift in the BI building is within the safe limit. Figure 15b and d indicates that the drift attenuation factors in SREI and U-STRP BI buildings are comparable and lower than those of the B-STRP BI buildings. At the DBE level, the average drift reduction in U-STRP, SREI, and B-STRP BI buildings is 30 ~ 70, 38 ~ 67, and 27 ~ 62%, respectively, compared to the FB building. At the MCE level, the corresponding reductions are 31 ~ 67, 35 ~ 65, and 27 ~ 52%. The lower limit of these ranges is the lateral drift due to the KB earthquake. It implies that base isolation effectively reduces inter-story drift and U-STRP isolation is as good as SREI isolation.

Fig. 15
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Inter-story drift and drift attenuation

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Figure 16 shows the top floor acceleration time histories of FB, U-STRP, SREI, and B-STRP BI buildings. Acceleration response in the BI building is substantially reduced in comparison with the FB building. Figure 17a and c shows the normalized value of the peak floor acceleration along with the height at DBE and MCE levels, respectively. The peak floor accelerations are normalized with respect to PGA. It should be noted that the peak acceleration of all floors does not occur at the same instant of time. The normalized accelerations in FB buildings drastically increase along with the height. At the DBE and MCE levels, normalized acceleration at the top floor of FB-building is about 1.50, 2.06, and 3.04 due to KB, NR, and IV earthquakes, respectively. Alternatively, these accelerations in BI buildings are lower than unity and almost constant along the height of the building. It indicates the rigid body motion of the building. The normalized acceleration within the floors varies in the range of 0.43 ~ 0.75, 0.50 ~ 0.69, and 0.53 ~ 0.86 in the U-STRP, SREI, and B-STRP BI buildings, respectively, at the DBE level. At the MCE level, the same values are 0.45 ~ 0.76, 0.54 ~ 0.70, and 0.56 ~ 0.92, respectively. Figure 17b and d indicates the acceleration attenuation factor. An average reduction of acceleration is 38 ~ 69% in the U-STRP BI building, whereas it is 47 ~ 65 and 38 ~ 60% in SREI and B-STRP isolations, respectively, at the DBE level. At the MCE level, acceleration is reduced by 46 ~ 62, 45 ~ 63, and 37 ~ 51% in U-STRP, SREI, and B-STRP BI buildings, respectively.

Fig. 16
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Acceleration time history at the top floor

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Fig. 17
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Floor normalized acceleration and acceleration amplification

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Bearing response and base shear

Figure 18 shows the base-shear time history of BI and that of the FB buildings at DBE and MCE levels. Base shear between the B-STRP and U-STRP buildings is comparable. Table 9 lists the magnitude of base shear in terms of the seismic response coefficient, the ratio between the peak of base shear and seismic dead load (V/W). The seismic response coefficient for the BI building is substantially lower than that of the FB building. At low levels of seismicity, such as the KB input, base shear among the systems is comparable, and its average is 0.2 and 0.33 W at the DBE and MCE levels, respectively. Base shear reduction increases with the level of seismicity, and the U-STRP BI exhibits the highest efficiency. For example, due to the DBE level input of the IV earthquake, the maximum base shear in SREI, B-STRP, and U-STRP BI buildings is 0.27, 0.30, and 0.24 W, respectively, and the corresponding reduction is 68, 64, and 71%, respectively. At the MCE level, the maximum reduction of base shear in the U-STRP, SREI, and B-STRP is approximately 73, 56, and 67%, respectively. The lower limit of the base shear is due to the KB earthquake.

Fig. 18
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Base shear time histories

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Table 9 Base shear (V/W) (W = 686.2 ton)
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Figure 19 illustrates the hysteresis loops for SREI, B-STRP, and U-STRP BI buildings under the DBE and MCE levels. It shows that each isolation system exhibits positive incremental force-resisting capacity and no slippage at the DBE level. The same is true at the MCE level, except for the U-STRP system that experienced minor dislocation due to the IV earthquake. Table 10 indicates the lateral displacement of the isolation systems found from the preliminary design and the FE analysis. The displacement determined from the preliminary design is comparable with the FE analysis results in the cases of U-STRP and SREI systems. It is observed that the displacement in the SREI isolator is lower than that of the B-STRP and U-STRP isolators, and the U-STRP isolators experience the highest displacement. The displacement in the case of the NR earthquake is 110, 133, and 154 mm in SREI, B-STRP, and U-STRP systems, respectively, at the DBE level. At the MCE level, the corresponding values are 159, 179, and 208 mm, respectively. Similarly, the U-STRP system undergoes a displacement of 150, 208, and 204 mm at the MCE level of KB, NR, and IV earthquakes, respectively, and 110, 154, and 130 mm due to the DBE level input. Displacement due to the KB earthquake is considerably lower than that in the NR and IV earthquakes.

Fig. 19
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Hysteresis curves for B-STRP, U-STRP, and SREI base-isolation

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Table 10 Displacement (mm) and shear strain (%) of the isolation system
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Figure 20 shows the lateral deformation of individual isolators due to the NR earthquake at MCE level. Lateral deformation in SREI is similar to that of the B-STRP isolator as shown in Fig. 20b. In the case of the U-STRP isolator, as shown in Fig. 20a, shear deformation within the isolator at the same instant of time varies with the location. It is due to the change in contact pressure caused by the overturning of the superstructure. The isolators B1, B2, and B3 experience higher rollover deformation than those of B7, B8, and B3. Besides, Fig. 20a shows that columns on the B7, B8, and B9 isolators are dislocating from their center positions. Therefore, a partially bonded STRP isolator can be utilized to avoid slippage.

Fig. 20
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Lateral displacement of isolators due to the NR earthquake at MCE level

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Figure 21 shows the energy dissipation in different isolation systems, which is obtained by integrating the force–displacement relationship given in Fig. 19. The SREI isolation dissipates higher energy than the U-STRP and B-STRP. Nevertheless, the dissipating energy in the U-STRP isolation system is greater than the B-STRP isolation.

Fig. 21
figure 21

Energy dissipation in the different isolation systems at DBE and MCE levels

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The effectiveness of the U-STRP isolator depends on the effective compressive force. Due to the symmetric mass and stiffness, the hysteresis loops of B2, B5, and B9 under the DBE and MCE levels of the IV earthquake are shown in Fig. 22. The hysteresis loop shown in Fig. 19 does not represent the behavior of the corners (B1, B3, B7, and B9) or periphery (B2, B8) bearings. For example, Fig. 22 shows that the U-STRP isolators that are located at the corner or perimeter (B2 and B9) experience no slippage at the DBE level but undergo substantial slippage at the MCE level. Slippage in corner isolators is significant because the effective compression becomes less than 0.8 MPa. Again, the instant when isolators (B1, B2, and B3) on one side of the building undergo slippage, the isolators on the opposite side (B7, B8, and B9) have zero slippage. The overturning of the building and the rocking motion of the isolator affect the net compression of the isolator. Besides, the vertical component of the ground motion is another crucial factor for the U-STRP isolator and needs to be considered. Therefore, the minimum compression should be defined for the STRP isolator. In addition, a partially bonded isolator can be used to avoid slipping.

Fig. 22
figure 22

Restoring-force displacement of bearings subjected to the IV earthquake

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Figure 23 presents the vertical force–time histories of U-STRP isolators under the DBE and MCE levels of the NR earthquake. It shows that effective compression within the corner (B1, B3, B7, and B9) or periphery (B2 and B8) isolators is substantially reduced compared to the isolators on the axis of rotation (B4, B5, and B6). The possible reasons are the rocking motion and the overturning. Figure 24 shows the maximum and minimum values of axial force amplification factors for the SREI and B-STRP isolators. In addition, the isolators SREI and B-STRP subjected tension in the MCE level earthquake. At the DBE level, the amplification factor in U-STRP, B-STRP, and SREI isolators falls in the range of 0.32 ~ 1.74, 0.20 ~ 1.91, and 0.33 ~ 1.75, respectively. At the MCE level, the respective values are 0.19 ~ 2.1, – 0.25 ~ 2.38, and – 0.14 ~ 2.21, respectively. The minima of each range represent the compressive force in the corner and periphery (B2 and B8) isolators. In U-STRP isolators, the minimum axial force amplification factors are 0.32 ~ 0.54 and 0.19 ~ 0.42 at the DBE and MCE levels, respectively. These factors correspond to 0.92 ~ 1.56 MPa and 0.55 ~ 1.22 MPa vertical compression, respectively. At this compression level, the corner isolators do not participate in seismic isolation since there is no contact friction. Therefore, the height of a building and the lowest effective compression to avoid the slip of unbonded STRP isolators need to be studied.

Fig. 23
figure 23

Axial force in each bearing of U-STRP bearing under the NR earthquake

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Fig. 24
figure 24

Amplification of axial force in U-STRP and LRB bearings

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Rocking motion

The flexible steel cord and low vertical stiffness cause the rocking motion of the U-STRP base isolation. A typical rocking angle time history of the U-STRP BI building under the KB earthquake is shown in Fig. 25. The rocking angle is determined by the vertical displacement difference divided by the horizontal displacement between the two isolators. Figure 26 shows the peak of the rocking angle in each isolation system at the DBE and MCE levels. At the DBE level, rocking angles in different isolation systems are comparable. At the MCE level, rocking motion in STRP isolation is high, and the U-STRP isolators experience the highest rocking displacement. The SREI, B-STRP, and U-STRP systems exhibit a maximum rocking displacement of 2.01 × 10–4 ~ 2.86 × 10–4, 1.99 × 10–4 ~ 3.09 × 10–4, and 2.11 × 10–4 ~ 3.65 × 10–4 rad, respectively, at the DBE level. At the MCE level, the respective rocking displacements are 2.75 × 10–4 ~ 4.13 × 10–4, 3.14 × 10–4 ~ 5.66 × 10–4, and 6.30 × 10–4 ~ 13.0 × 10–4 radians. The relative vertical displacement between two U-STRP isolators due to the rocking motion is between 2.50 and 5.2 mm. For a risk level category of IV, ASCE-SEI-7–10 recommends a rocking angle within 10% of the inter-story drift (0.01hx) which is 7.5 × 10–4 rad. The U-STRP isolator exceeds this limit at the MCE level. A high rocking angle can reduce the effective compression on the STRP isolator to zero or lower than the minimum compression, which is expected to cause residual displacement of the STRP isolator. Again, due to vertical ground acceleration and the high height-to-length ratio of the building, these rocking motions could be different, which is needed for further study. Therefore, to avoid the residual displacement of the STRP isolator due to rocking motion, a partially bonded STRP isolator can be considered.

Fig. 25
figure 25

Rocking motion due to KB earthquake

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Fig. 26
figure 26

Rocking angle motion due to IV earthquake

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Conclusion

This paper describes the seismic protection effectiveness of the STRP base isolation system installed below a four-story building. A three-dimensional building model including four different base connections: SREI, B-STRP, U-STRP isolations, and FB is analyzed for two design levels of earthquake. The effectiveness of STRP isolation is assessed through a comparative study with SREI base isolation and FB condition. Both SREI and STRP isolations are geometrically identical, and the accuracy of these models is validated with past experimental results. The findings of the FE analysis are summarized as follows:

  • (i) The seismic performance of U-STRP isolators is comparable to that of SREI and sometimes superior in reducing floor displacement, inter-story drift, and floor acceleration. The seismic performance of the U-STRP isolator is preferred over that of the B-STRP isolator, and its efficacy increases with the level of the seismicity.

  • (ii) The reduction in floor displacement in U-STRP, SREI, and B-STRP is 6163%, 5859%, and 4153%, respectively. The U-STRP isolation reduces the inter-story drift by 30 ~ 70% which is 35 ~ 67% and 22 ~ 62% in the SREI and B-STRP isolations respectively. The floor acceleration is reduced by 38 ~ 69% in the U-STRP isolation, whereas it is 47 ~ 65% and 38~60% in SREI and B-STRP isolations, respectively.

  • (iii) At low seismicity, the seismic response coefficients of the BI systems are comparable, but significantly lower at high seismicity. At the DBE level earthquake, the maximum base shear reduction in SREI, B-STRP, and U-STRP BI buildings is 68, 64, and 71%, respectively. At the MCE level, these reductions are 67, 56, and 73%, respectively.

  • (iv) A preliminary design procedure can be applied to predict the displacement of the U-STRP isolator for a known spectral acceleration. Displacement determined from the proposed procedure is comparable with the FE analysis results. The lateral displacement of the U-STRP isolation system is higher than that of the B-STRP and SREI isolations. The U-STRP lateral displacement is 208 mm, equal to 173% shear strain only. The U-STRP isolators experienced slippage under the MCE level design earthquake while well performed at the DBE level.

  • (v) The compressive force in U-STRP isolator reduced to 0.55 ~ 1.22 MPa that nullifies the isolation purpose at MCE level earthquake. Therefore, the minimum compressive force, the aspect ratio of the building, and its effect on effective compression on the U-STRP isolator need to be studied. The amplification of vertical compression in U-STRP isolators is lower than that of the SREI. Axial force in the corner U-STRP isolator is in the range of 1.50~1.70 and 2.10 ~ 2.20 at DBE and MCE levels, respectively. The same amplification in SREI is 1.80 ~ 2.15 and 2.15 ~ 2.70, respectively.

  • (vi) At low seismicity, rocking angles in different isolation systems are comparable. STRP isolators show higher rocking displacement than that of the SREI. Rocking displacement in U-STRP isolators remains below the limiting value for a risk level category of IV under the DBE level earthquake. However, it crossed the limit at the MCE level design earthquake, which indicates a partially bonded STRP isolator can be used.

This research work is carried out through FE analysis based on experimental elastomer properties. For a comprehensive understanding of seismic protection effectiveness of unbonded STRP base isolation, an experimental study on unbonded STRP base-isolated building should be carried out.