Seismic performance of an LRB-isolated structure with EIMD under near-fault pulse-like ground motions

Abstract

Under near-fault pulse-like ground motions, base-isolated structures (BIS) are prone to isolation bearing failure due to excessive base floor displacement. To mitigate this risk, hybrid base isolation systems, which incorporate passive dampers with isolation bearings, offer a promising solution. This paper proposes a novel hybrid base isolation system that combines an electromagnetic inertial mass damper (EIMD) with a lead-rubber bearing (LRB), aiming to reduce the base floor displacement while further improving the isolated superstructure’s seismic performance. Firstly, the force-displacement relationship of the bearing is described by the Bouc-Wen hysteretic model and a linear damping model, while a linearized mechanical model is adopted for the EIMD. The motion equations of a 10-storey LRB-isolated building model with EIMD are subsequently established. Next, the influence of the inertance-to-mass ratio on the natural period of the LRB-isolated building model with EIMD is investigated. Then, based on the average seismic responses of the LRB-isolated building model with EIMD subjected to 18 near-fault pulse-like ground motions, the control law of EIMD on the base floor displacement, superstructure interstory drift and absolute acceleration is studied. Finally, the nonlinear time-history responses of the LRB-isolated building model with EIMD and with viscous damper (VD) are compared, and the superiority of EIMD’s performance is demonstrated.

Keywords

near-fault pulse-like ground motion electromagnetic inertial mass damper lead-rubber bearing natural period seismic performance

Introduction

Base isolation technology prolongs the period of the structure, shifting it out of the strong amplification range of the earthquake acceleration response spectrum. Thus, the earthquake will not be transmitted to the isolated superstructure, and the structural seismic response is greatly reduced (Du et al., 2021; Kelly, 1993; Qi et al., 2025). Typically, the acceleration response of the isolated superstructure decreases to 1/4∼1/8 of that of the original fixed-base structure. However, large deformations caused by earthquakes occur at the base floor, possibly reaching hundreds of millimeters under near-fault pulse-like ground motions. Unlike far-field earthquakes, near-fault pulse-like ground motions contain velocity pulses with large amplitude and long period, which are mainly caused by forward directivity and permanent translation (Baker, 2007; Du et al., 2020; Mavroeidis et al., 2003). Research shows that the base floor displacement of the BIS under near-fault pulse-like ground motions is considerably greater than that under the earthquakes without velocity pulse components (Pan et al., 2018).

The hybrid base isolation system, composed of passive dampers and isolation bearings, is one of the methods to reduce the excessive base floor displacement of the BIS under strong earthquakes. Scholars have considered applying Viscous Damper (VD), Tuned Mass Damper (TMD), and Magnetorheological Damper (MRD) to base-isolated structures. However, each of these devices has certain limitations. Studies indicate that an excessive damping coefficient of VD (exceeding 0.5) may excite higher-mode responses of base-isolated structures, thereby increasing the interstory drifts and floor accelerations of the superstructure (Kelly, 1999). TMD is prone to frequency detuning and requires a large mass and stroke to achieve a superior control performance (Li et al., 2003; Sladek et al., 1983; Taniguchi et al., 2008). For MRD, the sedimentation stability of the magnetorheological fluid remains a concern, and the damper’s reliability and actual control performance under strong earthquakes require further investigation (Zhu et al., 2022).

An inerter is a two-terminal mechanical element whose output force is proportional to the relative acceleration between its two terminals (Smith, 2002). In recent years, inerter-based dampers composed of inerter, damping, and stiffness elements have demonstrated excellent dynamic response control performance in building and bridge engineering (Nakamura et al., 2014; Shen et al., 2019; Song et al., 2023). As depicted in Figure 1, the electromagnetic inertial mass damper (EIMD) comprises an inerter element and an electromagnetic damper element in parallel. Compared with other types of inerter-based dampers, EIMD features a simple manufacturing process and low cost. Furthermore, it deliver superior damping stability, robust temperature adaptability, and tunable damping force and coefficient, rendering it ideally suited for complex service environments. Sun et al. (Sun et al., 2019) derived analytical solutions for the optimal inertance-to-mass ratio and damping ratio of the EIMD to minimize the H₂ norm of the superstructure interstory drift. Numerical simulations of a multi-story base-isolated structure under actual earthquake motions demonstrated that EIMD can effectively reduce base floor displacement, superstructure interstory drift, and floor acceleration, outperforming the viscous damper (VD) in some cases. Wang et al. (Wang et al., 2021) examined the influence of EIMD parameters on the natural frequencies, mode shapes, modal participation factors, and dynamic amplification factors of a two degree of freedom base-isolated structure. They found that the inerter element can prolong the fundamental period of the isolated structure without decreasing its static lateral stiffness. An excessively high inertance-to-mass ratio may excite higher-mode responses of the isolated structure, thereby amplifying the responses of the superstructure. Stochastic response analyses of the hybrid base isolation system with EIMD under different soil conditions revealed that, whether with linear or nonlinear isolation bearings, the system achieves better control performance on soft soil conditions than on hard soil conditions, and also outperforms the hybrid base isolation system with VD (Wang et al., 2022; 2023a; 2023b). To date, few studies have studied the seismic response of base-isolated structures (BIS) with inerter-based dampers under near-fault pulse-like ground motions (Li et al., 2021), and the control effectiveness of EIMD in such ground motions remains unclear.

Figure 1.

Configuration of the LRB-isolated building model with EIMD: (a) MDOF model of the LRB-isolated building model with EIMD; (b) Configuration of the EIMD; (c) Mechanical model of EIMD.

To address the literature gap, a numerical simulation of an LRB-isolated structure with EIMD is conducted. Firstly, the motion equations of a 10-storey LRB-isolated building model with EIMD are established. Next, the influence of the inertance-to-mass ratio on the natural period of the LRB-isolated building model with EIMD is investigated. Then, using the Runge-Kutta method, the average responses of the building model with different EIMD parameters subjected to 18 near-fault pulse-like ground motions is calculated. The control laws and response mitigation ratios of EIMD on BIS are studied, including base floor displacement, superstructure interstory drifts and absolute acceleration. Finally, the time-history responses of the LRB-isolated building model with optimized EIMD and with optimized VD are compared.

Motion equations

This section establishes the motion equations of an LRB-isolated building model with EIMD under earthquakes. Figure 1(a) shows the multiple degrees of freedom (MDOF) dynamical system. Figure 1(b) shows the EIMD prototype, whose details and operation principles are referred to in previous studies (Zhu et al., 2019).

The bearing’s force-displacement relation is established by the Bouc-Wen hysteretic model and a linear damper model. The output force is expressed as follows (Jangid, 2010)

f_{b} = c_{b} {\dot{υ}}_{b} + α k_{b} υ_{b} + (1 - α) k_{b} υ_{yb} Z

(1)

υ_{yb} \dot{Z} = A {\dot{υ}}_{b} - γ | {\dot{υ}}_{b} | {| Z |}^{η - 1} Z - β {\dot{υ}}_{b} {| Z |}^{η}

(2)

where the non-dimensional parameters

A

γ

β

η

have a relation to both the smoothness and shape of the hysteresis loops.

This study adopts the linearized model of EIMD (Figure 1(c)), whose restoring force is

f_{EIMD} = m_{e} {\ddot{υ}}_{b} + c_{d} {\dot{υ}}_{b}

(3)

Figure 2 shows the theoretical (Equation (3)) and measured hysteresis curves of EIMD, and it can be seen that they match well, which shows the feasibility of the linearized model.

Figure 2.

Validation of the EIMD model (Parameters of the EIMD prototype: $m_{e} = 5.8 ton$ ; $c_{d} = 132.4 kN \cdot s / m$ ; $R_{load} = 0 Ω$ , sinusoidal excitation frequency: 0.5 Hz, displacement amplitude: 8 mm): (a) Experimental setup; (b) Comparison of predicted and measured hysteretic curve of the EIMD.

The equations of motion of the LRB-isolated building model with EIMD under earthquake ${\ddot{u}}_{g}$ are expressed in the form

M \ddot{υ} + C \dot{υ} + K υ + H = F

(4)

where

M = [\begin{array}{c} (m_{b} + \sum_{i = 1}^{n} m_{i}) + m_{e} & m_{1} & m_{2} & \dots & \dots & m_{n} \\ m_{1} & m_{1} & 0 & \dots & \dots & 0 \\ m_{2} & 0 & m_{2} & \dots & \dots & 0 \\ ⋮ & ⋮ & ⋮ & ⋱ & ⋮ \\ ⋮ & ⋮ & ⋮ & ⋱ & 0 \\ m_{n} & 0 & 0 & \dots & 0 & m_{n} \end{array}], C = [\begin{array}{c} c_{b} + c_{d} & 0 & 0 & \dots & \dots & 0 \\ 0 & c_{1} + c_{2} & - c_{2} & \dots & \dots & 0 \\ 0 & - c_{2} & c_{2} + c_{3} & - c_{3} & \dots & 0 \\ ⋮ & ⋮ & ⋮ & ⋱ & ⋮ \\ ⋮ & ⋮ & ⋮ & ⋱ & - c_{n} \\ 0 & 0 & 0 & \dots & - c_{n} & c_{n} \end{array}], K = [\begin{array}{c} α k_{b} & 0 & 0 & \dots & \dots & 0 \\ 0 & k_{1} + k_{2} & - k_{2} & 0 & \dots & 0 \\ 0 & - k_{2} & k_{2} + k_{3} & - k_{3} & \dots & 0 \\ ⋮ & ⋮ & ⋮ & ⋱ & ⋮ \\ ⋮ & ⋮ & ⋮ & ⋱ & - k_{n} \\ 0 & 0 & 0 & \dots & - k_{n} & k_{n} \end{array}], H = [\begin{array}{c} (1 - α) k_{b} υ_{yb} Z \\ 0 \\ 0 \\ ⋮ \\ ⋮ \\ 0 \end{array}], υ = [\begin{array}{c} υ_{b} \\ υ_{1} \\ υ_{2} \\ ⋮ \\ ⋮ \\ υ_{n} \end{array}], F = [\begin{array}{c} - (m_{b} + \sum_{i = 1}^{n} m_{i}) {\ddot{u}}_{g} \\ - m_{1} {\ddot{u}}_{g} \\ - m_{2} {\ddot{u}}_{g} \\ ⋮ \\ ⋮ \\ - m_{n} {\ddot{u}}_{g} \end{array}]

(5)

The Runge-Kutta method can solve the above nonlinear motion equations. As shown in equations (4) and (5), the inertance of EIMD changes the mass matrix of the system, thereby altering the system’s dynamic characteristics. Importantly, the EIMD’s inertance is an equivalent mass coefficient and not a true physical mass, so it will not increase the seismic loads acting on the structure, which is one of the significant advantages of EIMD.

In this study, a 10-storey steel frame building model is selected as the analytical model, and its detailed parameters are shown in Table 1. Only horizontal degrees of freedom are considered for each floor, and the superstructure is in a linear elastic state during seismic excitation. The LRB parameters are as follows:

υ_{yb} = 0.015 m

;

α = 0.1

;

A = 1

γ = β = 0.5

η = 1

(Wang et al., 2023b).

Table 1.

Parameters of the LRB-isolated building model.

Floor	Height (m)	Mass (ton)	Stiffness (kN/m)	Damping (kNs/m)
10	3.00	500	1000000	6000
9	3.00	500	1000000	6000
8	3.00	500	1000000	6000
7	3.00	500	1000000	6000
6	3.00	500	1000000	6000
5	3.00	500	1000000	6000
4	3.00	500	1000000	6000
3	3.00	500	1000000	6000
2	3.00	500	1000000	6000
1	3.00	500	1000000	6000
Base floor	$-$	1250	274156	1309

The natural period of the fixed-base structure is 0.94 s. The natural period of the LRB-isolated building model can be calculated by

T_{b} = \frac{2 π}{ω_{b}} = \frac{2 π}{\sqrt{\frac{α_{b} k_{b}}{m_{b} + \sum_{i = 1}^{10} m_{i}}}} = 3 s

(6)

Therefore, the ratio of the natural period between the LRB-isolated building model and the fixed-base building model is 3.19.

The damping ratio of the LRB is given by

ξ_{b} = \frac{c_{b}}{2 {(m_{b} + \sum_{i = 1}^{10} m_{i}) ω}_{b}} = \frac{c_{b}}{2 (m_{b} + \sum_{i = 1}^{10} m_{i}) \sqrt{\frac{α_{b} k_{b}}{m_{b} + \sum_{i = 1}^{10} m_{i}}}} = 0.05

(7)

Influence of inertance on the natural period

The natural period $T_{b}^{'}$ of the LRB-isolated building model with EIMD is defined as

T_{b}^{'} = \frac{2 π}{\sqrt{\frac{α_{b} k_{b}}{(m_{b} + \sum_{i = 1}^{10} m_{i}) + m_{e}}}}

(8)

The period ratio of $T_{b}^{'} / T_{b}$ is given by

\frac{T_{b}^{'}}{T_{b}} = \sqrt{1 + \frac{m_{e}}{m_{b} + \sum_{i = 1}^{10} m_{i}}}

(9)

Figure 3 shows the variation of the period ratio $T_{b}^{'} / T_{b}$ with the inertance-to-mass ratio $m_{e} / (m_{b} + \sum_{i = 1}^{10} m_{i})$ . As the inertance-to-mass ratio increases from 0 to 10, the inertance can lengthen the natural period of the isolated structure by a factor from 1 to 3.32, demonstrating a significant period adjustment capability.

Figure 3.

Period ratio $T_{b}^{'} / T_{b}$ varies with inertance-to-mass ratio $m_{e} / (m_{b} + \sum_{i = 1}^{10} m_{i})$ .

Earthquake ground motions selection

For the simulations, a set of 18 near-fault pulse-like ground motion records is selected. To ensure the generalizability of the analysis results, these ground motion records are chosen from various site types and cover a range of pulse periods. The selected records satisfy the following criteria (Pan et al., 2023): 1. An improved energy-based approach is adopted to select the ground motions containing only one typical pulse (Chang et al., 2016); 2. The fault distance is no greater than 60 km; 3. The earthquake magnitude is not less than 6. Table 2 summarizes the detailed information of the selected ground motions. Figure 4 shows the acceleration response spectra and their average spectrum of the 18 ground motions. It can be found that the maximum spectrum value of each record occurs in distinctly different period ranges, which is attributable to the differences in soil conditions.

Table 2.

Information of the near-fault pulse-like ground motions.

Record sequence	Event	Year	Magn-itude	Component	Pulse period (s)	Rjb (km)	PGA(g)	PGV (m/s)
RSN-161	Imperial Valley-06	1979	6.53	H-BRA225	4.2	8.54	0.1626	0.366
RSN-171	Imperial Valley-06	1979	6.53	H-EMO000	2.5	0.07	0.3172	0.729
RSN-173	Imperial Valley-06	1979	6.53	H-E10050	3.3	8.6	0.1731	0.507
RSN-178	Imperial Valley-06	1979	6.53	H-E03140	2.5	10.79	0.2674	0.479
RSN-182	Imperial Valley-06	1979	6.53	H-E07140	3.1	0.56	0.3408	0.517
RSN-184	Imperial Valley-06	1979	6.53	H-EDA270	3.3	5.09	0.3526	0.755
RSN-503	Taiwan SMART1 (40)	1986	6.32	40C00EW	1.5	58.69	0.1736	0.336
RSN-725	Superstition Hills-02	1987	6.54	B-POE270	2.5	11.16	0.4750	0.411
RSN-766	Loma prieta	1989	6.93	G02090	1.7	10.38	0.3227	0.404
RSN-767	Loma prieta	1989	6.93	G03090	2.0	12.23	0.3682	0.454
RSN-803	Loma prieta	1989	6.93	WVC000	2.0	8.48	0.2575	0.420
RSN-1084	Northridge-01	1994	6.69	SCS052	2.9	0.0	0.6230	1.162
RSN-3744	Cape mendocino	1992	7.01	BNH270	4.1	8.49	0.1774	0.679
RSN-3746	Cape mendocino	1992	7.01	CBF270	1.7	16.44	0.3181	0.495
RSN-4875	Chuetsu-oki, Japan	2007	6.8	65058EW	2.8	0.0	0.3600	1.025
RSN-4896	Chuetsu-oki, Japan	2007	6.8	SG01EW	2.3	0.0	0.4444	1.252
RSN-6911	Darfield, New Zealand	2010	7.0	HORCN18 E	2.2	7.29	0.4501	1.059
RSN-8130	Christchurch, New Zealand	2011	6.2	SHLCS40 W	1.9	5.58	0.3178	0.748

Figure 4.

Acceleration response spectra of near-fault pulse-like ground motions.

Parametric study

This section studies the control laws of EIMD on the seismic responses of the LRB-isolated building model for three performance indicators. These performance indicators are: (a) Maximum value of superstructure interstory drift; (b) Maximum value of superstructure absolute acceleration; and (c) Maximum value of base floor displacement. The corresponding reduction ratio for each performance indicator is defined as follows

J_{1} = 1 - \frac{\max (\max (| υ_{1} |), \max (| υ_{2} - υ_{1} |), \max (| υ_{3} - υ_{2} |), \dots, \max (| υ_{10} - υ_{9} |))}{υ_{s 0}}, J_{2} = 1 - \frac{\max (\max (| {\ddot{υ}}_{b} + {\ddot{υ}}_{1} + {\ddot{u}}_{g} |), \max (| {\ddot{υ}}_{b} + {\ddot{υ}}_{2} + {\ddot{u}}_{g} |), \dots, \max (| {\ddot{υ}}_{b} + {\ddot{υ}}_{10} + {\ddot{u}}_{g} |))}{{\ddot{u}}_{s 0}}, J_{3} = 1 - \frac{\max (| υ_{b} |)}{υ_{b 0}}

(10)

among them, $υ_{s 0}$ , ${\ddot{u}}_{s 0}$ and $υ_{b 0}$ are respectively the maximum value of superstructure interstory drift, the maximum value of superstructure absolute acceleration, and the maximum value of base floor displacement of the BIS without EIMD.

The inertance-to-mass ratio and damping ratio of EIMD are defined as

μ = \frac{m_{e}}{m_{b} + \sum_{i = 1}^{10} m_{i}}, ξ = \frac{c_{d}}{2 (m_{b} + \sum_{i = 1}^{10} m_{i}) ω_{b}}

(11)

Figure 5 illustrates the seismic response control laws of the EIMD on the LRB-isolated building model under different parameters. The value ranges of the EIMD’s inertance-to-mass ratio and damping ratio are $0 \leq μ \leq 1$ , $0 \leq ξ \leq 0.5$ , respectively. As shown in Figure 5(a), there exists an optimal set of $μ$ and $ξ$ that minimizes the peak superstructure interstory drift. The optimal parameters are determined as $μ = 0.22$ , $ξ = 0.12$ , with which a 19.8% reduction ratio of the peak superstructure interstory drift is achieved. As illustrated in Figure 5(b), the reduction ratio of the peak superstructure absolute acceleration also has a maximum value. When $μ = 0.14$ , $ξ = 0.10$ , the EIMD reaches the optimal control level, and the corresponding reduction ratio is 22.9%. In addition, it is observed that the reduction ratio of the peak superstructure absolute acceleration is more sensitive to the variations in the inertance-to-mass ratio. Figure 5(c) shows that the reduction ratio of the peak base floor displacement is positively correlated with both $μ$ and $ξ$ , with a maximum reduction ratio of the peak base floor displacement by 61.8%. From a practical engineering perspective, minimizing the base floor displacement will require a high cost (output force of the damper). Therefore, it is reasonable to optimize the EIMD parameters for controlling the superstructure seismic response.

Figure 5.

Relationship between the reduction ratios of system response and the EIMD parameters: (a) Peak interstory drift of superstructure; (b) Peak absolute acceleration of superstructure; (c) Peak displacement of base floor.

Nonlinear time history analysis

In this section, the EIMD parameters are set as $μ = 0.14$ , $ξ = 0.10$ , under which the EIMD achieves the best control effect for the superstructure absolute acceleration. The average reduction ratios of the maximum value of the base floor displacement, superstructure interstory drift and absolute acceleration of the dynamic system under 18 near-fault pulse-like ground motions are 25.7%, 19.2% and 22.9%, respectively. For the LRB-isolated building model with optimized VD ( $ξ = 0.10$ ), the corresponding reduction ratios are 20.7%, 10.7% and 4.9%, respectively.

Figure 6(a) shows a typical near-fault pulse-like ground motion accelerogram (RSN-1084 Northridge-01, PGA = 0.6230 g), while Figure 6(b) and (c) present the corresponding velocity time history and the acceleration response spectrum, respectively. Figure 7(a) and (b) present the hysteretic curves of VD and EIMD under the Northridge earthquake, respectively. The maximum damping force of the VD is 3299 kN and that of the EIMD is 6071 kN. The strokes of the two dampers are similar, but the EIMD’s output force is 1.84 times that of the VD. It is observed that the EIMD shows an obvious negative slope in the second and fourth quadrants, indicating a considerable inertance effect.

Figure 6.

A typical near-fault pulse-like ground motion (RSN-1084 Northridge-01, PGA = 0.6230 g): (a) Acceleration time history; (b) Velocity time history; (c) Acceleration response spectrum.

Figure 7.

Force-displacement curves of the damper under the Northridge earthquake: (a) VD; (b) EIMD.

Figure 8 shows a comparison of the time-history responses of the LRB-isolated building model without a damper, with a supplemental VD and with a supplemental EIMD under the Northridge earthquake. For the LRB-isolated building model with EIMD, the maximum value of base floor displacement, the maximum value of superstructure interstory drift and absolute acceleration are reduced by 35.9%, 31.4% and 32.1%, respectively. When the LRB-isolated building mode is equipped with VD, the corresponding reduction ratios are respectively 32.1%, 23.4% and 17.4%. This indicates that the EIMD achieves further performance improvements over the VD by 3.8%, 8.0%, and 14.7% in the three response indicators, respectively. Figure 9 compares the peak seismic response of the LRB-isolated building model without a damper, with a supplemental VD and with a supplemental EIMD under 4 selected ground motion records. It is consistently observed that the EIMD exhibits superior seismic control performance to the conventional VD.

Figure 8.

Comparison of seismic responses of the three cases subjected to the RSN-1084 earthquake record: (a) Interstory drift at the first floor of the superstructure; (b) Absolute acceleration at the roof; (c) Base floor displacement.

Figure 9.

Comparison of the control performances of the EIMD and VD for the LRB-isolated building model subjected to earthquake records: (a) Peak superstructure interstory drift; (b) Peak superstructure absolute acceleration; (c) Peak base floor displacement.

Table 3 summarizes the peak response reduction ratio of the VD and EIMD for the LRB-isolated building model under 18 ground motion records. The following observations can be made: (1) The control effect of the EIMD on the superstructure absolute acceleration is significantly better than that of the VD. Across all 18 ground motion records, the reduction ratio of the superstructure absolute acceleration achieved by the EIMD is consistently higher than that of the VD. Notably, under ground motion records RSN-182, RSN-725, and RSN-767, the reduction ratio of the EIMD exceeds that of the VD by more than 30%. For instance, under ground motion record RSN-725, the VD leads to an amplification of 4.7% (i.e., a reduction ratio of −4.7%), whereas the EIMD achieves a reduction ratio of 42.2%. (2) In terms of controlling the superstructure interstory drift, the EIMD is generally better than the VD, with only minor performance degradation observed under a limited set of ground motions. For the majority of the seismic records, the reduction ratio of interstory drift achieved by the EIMD is higher than that of the VD. Only under the ground motion records RSN-171, RSN-178, and RSN-182, EIMD performs worse than VD. (3) The EIMD and VD exhibit comparable control effectiveness on base floor displacement, with the EIMD being slightly more effective overall.

Table 3.

Comparison of the peak response of the LRB-isolated building model with VD and EIMD under 18 near-fault pulse-like ground motions.

Earthquake	Performance indicators	LRB	LRB + VD	LRB + EIMD
RSN-161, imperial Valley-06	Base floor displacement (m)	0.1087	0.0958 (11.9%)	0.0965 (11.2%)
	Superstructure interstory drift (m)	0.0059	0.0054 (8.5%)	0.0054 (8.5%)
	Superstructure absolute acceleration (m/s²)	1.7827	1.6734 (6.1%)	1.5137 (15.1%)
RSN-171, imperial Valley-06	Base floor displacement (m)	0.2078	0.1828 (12.0%)	0.1833 (11.8%)
	Superstructure interstory drift (m)	0.0085	0.0087 (−2.4%)	0.0091 (−7.1%)
	Superstructure absolute acceleration (m/s²)	3.1696	3.2323 (−2.0%)	2.5888 (18.3%)
RSN-173, imperial Valley-06	Base floor displacement (m)	0.1285	0.1168 (9.1%)	0.1149 (10.6%)
	Superstructure interstory drift (m)	0.0061	0.0058 (4.9%)	0.0054 (11.5%)
	Superstructure absolute acceleration (m/s²)	1.9363	1.7675 (8.7%)	1.7441 (9.9%)
RSN-178, imperial Valley-06	Base floor displacement (m)	0.1581	0.1228 (22.3%)	0.1211 (23.4%)
	Superstructure interstory drift (m)	0.0069	0.0066 (4.3%)	0.0068 (1.4%)
	Superstructure absolute acceleration (m/s²)	2.8968	3.0973 (−6.9%)	2.8312 (2.3%)
RSN-182, imperial Valley-06	Base floor displacement (m)	0.1277	0.1147 (10.2%)	0.1109 (13.2%)
	Superstructure interstory drift (m)	0.0066	0.0066 (0%)	0.0067 (−1.5%)
	Superstructure absolute acceleration (m/s²)	3.2123	3.3467 (−4.2%)	2.2705 (29.3%)
RSN-184, imperial Valley-06	Base floor displacement (m)	0.1543	0.1313 (14.9%)	0.1317 (14.6%)
RSN-184, imperial Valley-06	Superstructure interstory drift (m)	0.0070	0.0067 (4.3%)	0.0064 (8.6%)
	Superstructure absolute acceleration (m/s²)	2.6598	2.9526 (−11.0%)	2.4426 (8.2%)
Earthquake	Performance indicators	LRB	LRB + VD	LRB + EIMD
RSN-503, Taiwan SMART1 (40)	Base floor displacement (m)	0.1146	0.1049 (8.5%)	0.1028 (10.3%)
	Superstructure interstory drift (m)	0.0059	0.0064 (−8.5%)	0.0063 (−6.8%)
	Superstructure absolute acceleration (m/s²)	2.4790	2.5809 (−4.1%)	1.9906 (19.7%)
RSN-725, superstition Hills-02	Base floor displacement (m)	0.0801	0.0754 (5.9%)	0.0694 (13.4%)
	Superstructure interstory drift (m)	0.0057	0.0058 (−1.8%)	0.0052 (8.8%)
	Superstructure absolute acceleration (m/s²)	3.2743	3.4282 (−4.7%)	1.8930 (42.2%)
RSN-766, loma prieta	Base floor displacement (m)	0.1709	0.1556 (9.0%)	0.1461 (14.5%)
	Superstructure interstory drift (m)	0.0077	0.0071 (7.8%)	0.0067 (13.0%)
	Superstructure absolute acceleration (m/s²)	3.0675	3.1179 (−1.6%)	2.6928 (12.2%)
RSN-767, loma prieta	Base floor displacement (m)	0.1740	0.1549 (11.0%)	0.1483 (14.8%)
	Superstructure interstory drift (m)	0.0081	0.0073 (9.9%)	0.0068 (16.0%)
	Superstructure absolute acceleration (m/s²)	3.0357	3.1246 (−2.9%)	2.2097 (27.2%)
RSN-803, loma prieta	Base floor displacement (m)	0.1604	0.1451 (9.5%)	0.1375 (14.3%)
	Superstructure interstory drift (m)	0.0070	0.0064 (8.6%)	0.0062 (11.4%)
	Superstructure absolute acceleration (m/s²)	2.6691	2.6495 (0.7%)	2.1839 (18.2%)
RSN-1084, Northridge-01	Base floor displacement (m)	0.6891	0.4678 (32.1%)	0.4415 (35.9%)
RSN-1084, Northridge-01	Superstructure interstory drift (m)	0.0188	0.0144 (23.4%)	0.0129 (31.4%)
	Superstructure absolute acceleration (m/s²)	5.0773	4.1962 (17.4%)	3.4454 (32.1%)
Earthquake	Performance indicators	LRB	LRB+VD	LRB+EIMD
RSN-3744, cape mendocino	Base floor displacement (m)	0.2383	0.1950 (18.2%)	0.1892 (20.6%)
	Superstructure interstory drift (m)	0.0093	0.0084 (9.7%)	0.0073 (21.5%)
	Superstructure absolute acceleration (m/s²)	2.7222	2.4124 (11.4%)	2.0991 (22.9%)
RSN-3746, cape mendocino	Base floor displacement (m)	0.1450	0.1287 (11.2%)	0.1260 (13.1%)
	Superstructure interstory drift (m)	0.0074	0.0068 (8.1%)	0.0065 (12.2%)
	Superstructure absolute acceleration (m/s²)	2.6774	2.6728 (0.2%)	2.0424 (23.7%)
RSN-4875, chuetsu-oki, Japan	Base floor displacement (m)	1.0873	0.7580 (30.3%)	0.6879 (36.7%)
	Superstructure interstory drift (m)	0.0275	0.0208 (24.4%)	0.0176 (36.0%)
	Superstructure absolute acceleration (m/s²)	6.8866	5.0430 (26.8%)	4.3305 (37.1%)
RSN-4896, chuetsu-oki, Japan	Base floor displacement (m)	0.8730	0.6770 (22.5%)	0.5964 (31.7%)
	Superstructure interstory drift (m)	0.0227	0.0199 (12.3%)	0.0155 (31.7%)
	Superstructure absolute acceleration (m/s²)	5.4953	5.2048 (5.3%)	4.3755 (20.4%)
RSN-6911, darfield, New Zealand	Base floor displacement (m)	0.5122	0.4184 (18.3%)	0.3890 (24.1%)
	Superstructure interstory drift (m)	0.0152	0.0145 (4.6%)	0.0112 (26.3%)
	Superstructure absolute acceleration (m/s²)	4.2300	3.7595 (11.1%)	3.3438 (21.0%)
RSN-8130, christchurch, New Zealand	Base floor displacement (m)	0.2456	0.2211 (10.0%)	0.2029 (17.4%)
	Superstructure interstory drift (m)	0.0095	0.0084 (11.6%)	0.0075 (21.1%)
	Superstructure absolute acceleration (m/s²)	3.1694	3.2051 (−1.1%)	2.6082 (17.7%)

Conclusions

This paper investigates the performance of a 10-story hybrid base isolation system composed of LRB and EIMD under a set of near-fault pulse-like ground motions. Numerical simulations show that:

(1) As the inertance-to-mass ratio increases from 0 to 10, the inertance can lengthen the natural period of the LRB-isolated building model by a factor from 1 to 3.32, demonstrating a significant period adjustment capability.

(2) There are optimal values of inertance-to-mass ratio and damping ratio of EIMD that minimize the maximum value of superstructure interstory drift and absolute acceleration. The reduction ratio of base floor displacement is positively correlated with the EIMD’s inertance-to-mass ratio and damping ratio.

(3) When $μ = 0.14$ , $ξ = 0.10$ , the EIMD achieves the best control effect on the superstructure absolute acceleration. Compared with the LRB-isolated building model without a damper, the average reduction ratios of the maximum value of base floor displacement, superstructure interstory drift and superstructure absolute acceleration of the LRB-isolated building model with EIMD under 18 near-fault pulse-like ground motions are 25.7%, 19.2% and 22.9%, respectively. For the LRB-isolated building model with optimized VD ( $ξ = 0.10$ ), those reductions are 20.7%, 10.7% and 4.9%, respectively. Overall, EIMD outperforms VD.

Footnotes

ORCID iDs

Wenai Shen

Heng Wang

Funding

The authors disclosed receipt of the following financial support for the research, authorship, and/or publication of this article: This research was partially supported by Scientific Research Fund of Institute of Engineering Mechanics, China Earthquake Administration (Grant No. 2021D37), and National Key R&D Program of China (Grant No. 2024YFC3012802).

Declaration of conflicting interests

The authors declared no potential conflicts of interest with respect to the research, authorship, and/or publication of this article.

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