Experimental and Numerical Study on the Seismic Performance of Base-Suspended Pendulum Isolation Structure

Abstract

This paper proposes a novel suspended seismic structure system called Base-suspended Pendulum Isolation (BSPI) structure. The BSPI structure can isolate seismic action and reduce structural seismic response by hanging the structure with hanger rods set at the base. The viscous dampers are installed in the isolation layer to dissipate earthquake energy and control the displacement. Firstly, the configuration of suspension isolation layer and mechanical model of the BSPI structure are described. Then, an equivalent scaled BSPI structure physical model was tested on the shaking table. The test results demonstrate that the BSPI structure has a good isolation effect under earthquakes, and the viscous dampers had an obvious control effect on the structure’s displacement and acceleration response. Finally, numerical simulation of the tests was carried out. The accuracy of the numerical models are confirmed by the good agreement between the simulation and test results. The numerical models for the BSPI structure and conventional reinforced concrete (RC) frame structure are built and analyzed using the commercial software ABAQUS. Research results indicate that the lateral stiffness of the BSPI structure is reduced greatly by installing the suspension layer, and the acceleration response of BSPI structure is significantly reduced under rare earthquakes, which is only 1/2 of that of the RC frame. The inter-story displacement of the BSPI structure is less than 1/100, which meets the seismic fortification goal and is reduced to 50% of that of the BSPI structure without damper under rare earthquakes.

1. Introduction

Earthquakes have consistently posed a significant threat to structural integrity, resulting in substantial economic losses. Traditional seismic design methods rely on structural deformation and ductile members to absorb and dissipate earthquake energy. However, ductile member may sustain damage from excessive deformation during major earthquakes, posing a challenge for repairing destroyed components [1,2,3]. During the First Planning Meeting for the Second Phase of NEES/E-Defense in January 2009, American and Japanese scholars introduced the “Resilient City” concept as a comprehensive overarching theme [4]. Designing a structure that can resist earthquakes without any damage or with damage that can be repaired quickly will become a pivotal research direction of earthquake engineering [5,6,7].

Over the past few decades, isolation structures have gained increasing prominence in the field of resilient structures [8]. Evidence suggests that structures equipped with a base isolation system demonstrate superior performance during huge earthquake [9]. The primary objective of base isolation is to uncouple the structure from the detrimental effect of earthquakes by shifting the structural fundamental period to long period range along with enhancing energy dissipation capabilities. Structural isolation enables precise control of the structural response, leading to a reduction in both acceleration and lateral forces transmitted to the building. At present, base isolators are mainly classified into rubber-based isolators and sliding-based isolators, and they have been widely studied and applied in engineering structures. A representative example of the sliding-based isolator is the friction pendulum system (FPS). Drawing inspiration from pendulum motion, Zayas et al. [10] proposed the friction pendulums for seismic isolation of buildings. The supported structure responds to earthquake motions with small amplitude pendulum motions and friction damping absorbs the earthquake energy. Paolo et al. [11] conducted an analysis of the impact of FPS isolator properties on the seismic performance of base-isolated structures through theoretical modeling. In 2002, Pranesh et al. [12] introduced the variable frequency pendulum isolator to address limitations related to restoring force characteristics and period. Tsai et al. [13,14] investigated the performance of multiple friction pendulum system (MFPS) on seismic mitigation through shaking table tests. However, some problems limit the application of the FPS system, such as the response to high vertical accelerations [15,16] and the relevance of residual displacement [17].

The suspension structure is an example of the isolation structure that utilizes a pendulum isolation mechanism. The suspension structure was first used in bridge engineering, such as modern suspension bridges and cable-stayed bridges [18,19]. With the development of suspended-floor buildings, suspension structure has been applied in large-span and high-rise buildings [20]. The suspension structure consists of the main supporting structures and the suspended substructures. The main supporting structures, namely core tube or mega-frame, bear all horizontal and vertical loads. The suspended substructures are connected to the main structure by rigid hangers. Nowadays, research on suspension structures mainly focuses on the core-tube-suspended building structure [21,22] and the mega-frame suspended building structure [23,24]. Yutaka et al. [25,26] proposed a new core-suspended isolation (CSI) system consisting of a reinforced concrete core, a multilevel structure and rubber bearings. The seismic isolation performance of the system was verified through shaking table tests of a scale model and quasi-static loading tests, and the effects of the CSI system are revealed via the observed earthquake records. Du et al. [27] designed a 1:20 scaled two-segment 19-story mega-frame suspended structure and evaluated its seismic performance through shaking table tests. The suspended floors can adjust the natural frequencies of structures similar to larger mass pendulums, like tuned mass dampers (TMD) [28].

However, suspension structure also has some disadvantages in practical application. Compared to conventional structures, the load mode of suspension structure increases the load paths, leading to a reduction in force transmission efficiency and an increase in the amount of material used in the structure [29]. In addition, because the lateral stiffness of the suspended layer is relatively small, the story drift of the suspended layer may exceed the elastic limit [30], and the structure enters the plastic deformation stage under a rare earthquake. Therefore, excessive deformation will likely damage rigid hangers [31,32].

To address the shortcomings of traditional suspended seismic isolation buildings, some researchers have proposed a new type of seismic isolation structure in which the suspension layer is suspended from the foundation. Bakhshi et al. [33] proposed the Suspended Pendulum Isolation (SPI) system and evaluated its seismic behavior via a nonlinear program based on the Runge–Kutta algorithm and an experimental test of a 4:25-scale model. The invented SPI system had similar isolation mechanisms as the above base device isolation and was equipped with a lead damper to absorb earthquake energy. Tan et al. [34] performed an experimental study on the symmetrical suspension pendulum and found the possibility of developing an isolation system based on the feature that non-parallel symmetry pendulum could adjust its natural period.

On the other hand, the viscous damper has gained popularity in the field of passive energy dissipation systems and is widely employed in seismic isolation structures to control structural deformation [35]. The viscous damper can offer additional damping and dissipate energy, without significantly improving structural stiffness [36]. Viscous dampers and diagonal steel braces were applied, replacing the steel bars in suspension structures [37]. The results of numerical analysis verify the feasibility of the new suspension structure. Cai et al. [38] carried out a series of shaking table tests of a ten story concrete suspended structure equipped with viscous dampers. The test results show that the maximum strain response was decreased by 42.3–72.7% for the damping suspended structure compared with the suspended structure without damper.

This paper proposes a new seismic isolation structure, Base-suspended Pendulum Isolation (BSPI). It realizes the effect of seismic isolation by suspending the superstructure on the foundation while avoiding the shortcomings of FPS and main-substructure suspension system. The BSPI system operates by suspending the superstructure from the foundation using hanger rods, allowing it to move like a pendulum. This motion reduces the lateral stiffness of the structure and decouples the superstructure from seismic ground motions. Energy dissipation is achieved through viscous dampers installed in the isolation layer, which absorb earthquake energy by converting kinetic energy into heat. The damping force is velocity-dependent, helping to reduce accelerations and displacements during seismic events. The structural configuration and motion equations of BSPI are presented. Based on the theoretical analysis, a shaking table test of a single-mass BSPI model was conducted. Finite element models of the BSPI structure and the conventional reinforced concrete frame (RCF) structure are established, and dynamic time-history comparative analysis is carried out on the seismic performance of these two types of structures.

2. Horizontal Isolation Mechanism of BSPI

2.1. Configuration of BSPI

The BSPI structure consists of two primary parts: the superstructure and the isolation layer. The superstructure is a conventional frame structure, and the isolation layer consists of suspension rods, column-bottom plates, and dampers, as shown in Figure 1. The entire superstructure is suspended from the rigid foundation using suspension rods, and the viscous dampers are installed in the isolation layer to dissipate earthquake energy and reduce isolation layer displacement.

Since the superstructure is suspended, it can move like a pendulum, giving it a self-centering capability. Moreover, the structure reduces its lateral stiffness through suspension, which reduces the seismic action of the superstructure. At the same time, dampers can be positioned between the rigid foundation and the column-bottom plate to control the displacement of the seismic isolation layer. In addition, the dampers can be replaced after the earthquake, thus realizing the resilience of the entire structure.

2.2. Mechanical Model of the BSPI Structure

According to the features of the BSPI structure, the mechanical model can be simplified into a single pendulum, as shown in Figure 2.

According to the principle of a single pendulum [39], the horizontal restoring force is calculated by the following equation:

$$F=\tan \theta \cdot mg={\displaystyle \frac{(x_b / l)}{\sqrt{1-{(x_b / l)}^2}}}\cdot mg$$

(1)

where x_b is the lateral displacement at the pendulum base, l represents the length of the rod, m denotes the mass of the superstructure, θ is the rod’s rotation angle, and g represents the gravity acceleration. According to Equation (1), the relationship between restoring force and displacement is obtained, as shown in Figure 3.

According to Equation (1), the horizontal stiffness of the system, k_iso, can be calculated by Equation (2):

$$k_{iso}=\tan \theta \cdot mg / x_b={\displaystyle \frac{mg}{l\cos \theta }}={\displaystyle \frac{mg}{l\sqrt{1-{(x_b / l)}^2}}}$$

(2)

When the rod’s rotation angle θ is less than 5°, the natural period T of BSPI structures can be equated with that of the single pendulum [31]:

$$T=2\pi \sqrt{{\displaystyle \frac{l}{g}}}$$

(3)

2.3. Equation of Motion of the BSPI Structure

The ideal BSPI N-story structure is shown in Figure 4. Each floor and the base mass have one degree of dynamic lateral freedom. The N-story building’s dynamic freedom degree is therefore N + 1.

The motion control equation for the BSPI structural model can be stated as follows, based on Figure 4:

$$M{\ddot{x}}_{iso}+c_{iso}{\dot{x}}_{iso}+k_{iso}{x}_{iso}+{\displaystyle \sum _{i=1}^N{m}_i}{\ddot{x}}_i=-M{\ddot{x}}_g$$

(4)

where M is the total mass of the entire BSPI building, and x_i is the displacement of the ith floor of the superstructure relative to the column-bottom plates that represent the vector {x} component. x_iso represents the relative displacement of the column-bottom plates to the base. k_iso is the stiffness of the isolation layer, c_iso is the damping coefficient of the isolation layer, and x_g is the ground motion. A dot on top of the letters denotes a time derivation and {I} is a unity column vector.

The motion control equation for the superstructure model is as follows:

$$\left[m\right]\left\{\ddot{\mathbf{x}}\right\}+\left[c\right]\left\{\dot{\mathbf{x}}\right\}+\left[\mathbf{k}\right]\left\{\mathbf{x}\right\}=-\left[m\right]\left\{I\right\}({\ddot{\mathbf{x}}}_{\mathbf{g}}+{\ddot{\mathbf{x}}}_{\mathbf{iso}})$$

(5)

The matrices [m], [c], and [k] stand for the superstructural mass matrices, damping matrices, and stiffness matrices, respectively:

$$\left[m\right]=\left[\begin{array}{ccccc}{m}_1& & & & \\ & m_2& & & \\ & & \ddots & & \\ & & & m_{N-1}& \\ & & & & m_N\end{array}\right],$$

$$\left[c\right]=\left[\begin{array}{ccccc}{c}_1+c_2& -c_2& & & \\ -c_2& c_2+c_3& -c_3& & \\ & -c_3& \dots & \dots & \\ & & \dots & c_{N-1}+c_N& -c_N\\ & & & -c_N& c_N\end{array}\right],$$

$$\left[k\right]=\left[\begin{array}{ccccc}{k}_1+k_2& -k_2& & & \\ -k_2& k_2+k_3& -k_3& & \\ & -k_3& \dots & \dots & \\ & & \dots & k_{N-1}+k_N& -k_N\\ & & & -k_N& k_N\end{array}\right].$$

3. Shaking Table Test Program

3.1. Test Prototypes and Similarity Relationships

The test prototype superstructure was a three-story RC frame structure. The plane layout of the prototype building was 13.5 m wide and 13.5 m long, as shown in Figure 5. Every story in the building was 3.5 m high. The seismic fortification intensity was VIII according to Chinese seismic code [40]. The weight of the superstructure was 600 t. Since the lateral stiffness of the superstructure was much greater than the stiffness of the seismic isolation layer, the prototype frame can be equivalent to a mass block with a total mass of 600 t in this test [41,42].

The test was conducted on a 4 m × 4 m shaking table. Based on the model material and the size of the shaking table, three controlling parameters (S_l, S_a, S_E) were selected. To ensure the validity and representativeness of the scaled physical model, standard scaling laws, including length scaling, mass scaling, and acceleration scaling, were applied. The length scaling factor S_l was set to 1:5 to ensure the dimensions of the scaled model met the requirements for shaking table testing. For material properties, C40 concrete and HRB400 steel were used, ensuring that the material scaling factor was set as S_σ = S_E = 1. The acceleration scaling factor S_a was determined as 1, ensuring accurate representation of seismic loading conditions. These scaling considerations are essential for ensuring that the experimental findings reflect the true dynamic response of the full-scale structure under seismic forces. The other scale factors were then calculated from the three controlling factors, as shown in

Table 1. Similitude scale factors.

Variable	Expression	Scale Factors
Length	Sl	1/5
Density	$S_{\rho }$	1
Elastic Modulus	$S_E$	1
Mass	$S_m=S_{\rho }{S}_l^3$	1/125
Frequency	$S_f=\sqrt{S_g/S_l}$	$\sqrt{5}$
Time	$S_t=\sqrt{S_l/S_g}$	$\sqrt{5}$
Velocity	$S_v=\sqrt{S_l{S}_a}$	$\sqrt{5}$
Acceleration	$S_a$	1
Gravitational acceleration	$S_g$	1

.

3.2. Design of the Test Specimen

The BSPI model utilized a mass block with a weight of 4.8 t (calculated as 600 t/125) to simulate the superstructure. The schematic drawing of the BSPI model is shown in Figure 6, and the photograph of the model is shown in Figure 7. Steel supports are equivalent to rigid foundations, and the mass block was suspended from the steel support by four steel rods. As shown in Figure 7d, the 1.6 × 1.6 × 0.78 m concrete block was positioned on a platform plate consisting of steel box beams. The rod length of the prototype seismic isolation layer was established at 5 m. According to the dynamic mechanism in Section 2.1, the calculated theoretical natural period T is 4.4 s. Based on the similarity law, the designed length of the test rod was set at 1.0 m.

In the test, hanger steel rods with a diameter of 30 mm and a tensile strength of 345 MPa were employed. The steel box beams used to support the mass block, as depicted in Figure 7e, were made of Q345 steel. Hanger steel rods were connected to the steel support through ball hinges, as shown in Figure 7b,c. Before the test, a 2 t axial pressure test was conducted on the ball hinges to verify the axial load-bearing capacity.

3.3. Design of Dampers

The viscous dampers were employed as displacement control and energy dissipation devices. The damping parameters were determined using the displacement control inversion method. Initial results showed a maximum displacement angle of 1/12 without damping, and the damping coefficient was calculated based on an energy equivalence method. After iteration, the final damping coefficient was set to 1200 N/(m/s), corresponding to an equivalent damping ratio of 15%, which satisfies the displacement angle limit requirement. The dampers were concentrated at the bottom of the isolation layer beneath the bearings to optimize displacement control. The placement also ensured structural feasibility, as finite element analysis showed minimal deviation in damper axis, satisfying the required installation accuracy standards. The viscous damper was tested under cyclic loading to examine its mechanical properties and energy dissipation capacity by the MAS-100 electro-hydraulic servo actuator. Due to the MAS-100 actuator’s inability to meet the test requirements in terms of maximum loading speed, the lever principle was employed to amplify the stroke loading by a factor of six, as shown in Figure 8. The test results indicate that the damping coefficient C of the viscous damper is 1165 N/(m/s)^0.32, and the velocity index is 0.32.

3.4. Test Program

3.4.1. Instrumentation

As shown in Figure 9, the measurement devices comprised stress gauges, linear voltage displacement transducers (LVDT), and accelerometers. On the shaking table platform, two accelerometers (A1, A2) were mounted in order to record the actual input excitation. The horizontal acceleration of model was measured by two accelerometers (A3, A4) that were positioned on two sides of the mass block. Four LVDTs (L1~L4) were employed to capture the specimen’s lateral deformations. Stress gauges (S1~S4) were placed on the hanger rods to measure the internal forces acting on the hanger rods.

3.4.2. Earthquake Records and Loading Protocol

Two natural earthquakes were selected as ground motions and obtained from the database [43], as listed in

Table 2. Details of the input ground motions.

Record	Magnitude	Year	PGA/g	Duration/s
El centro-EW	7.1	1940	210.1	53.48
Taft-NS	7.7	1957	152.7	54.38

. Figure 10a presents the normalized acceleration time histories of the two chosen ground motions, while Figure 10b depicts the corresponding acceleration response spectra with 5% damping. The test model was subjected to two seismic motions with an intensity level of VIII. The maximum accelerations of the input natural earthquakes were 0.07 g, 0.20 g, and 0.40 g, aligning with Chinese code’s classification of frequent, fortified, and rare earthquakes, respectively. The loading protocol for the shaking table test is detailed in

Table 3. Loading protocol in shaking table test.

Run Cases	Peak Acceleration/g	Remarks
White noise	0.05	Measure natural frequency and damping ratio
El Centro	0.07	Frequent earthquake
Taft	0.07
El Centro	0.20	Fortification earthquake
Taft	0.20
El Centro	0.40	Rare earthquake
Taft	0.40

. Before input the ground motions, white noise scans were conducted to determine the natural period and damping ratio of the BSPI structure.

4. Shaking Table Test Results

4.1. Dynamic Characteristics

The natural frequency of the BSPI structure can be obtained from the results of white noise scans. This method involves applying a white noise signal to the system and measuring the corresponding acceleration response. The frequency response function is then derived, and the natural frequencies are identified as peaks in the function. The damping ratio is determined using the half-power method, based on the bandwidth of the identified peaks.

Table 4. Dynamic characteristics of the BSPI structure.

Test Model	PGA/g	Natural Frequency/Hz	Damping Ratio
BSPI without damper	0.05	0.750	0.058
BSPI with viscous damper	0.05	0.875	0.198

presents the dynamic characteristics of the BSPI with dampers and the BSPI without damper. Regardless of increasing input ground vibration amplitudes, the test results show that the BSPI without damper had a constant natural frequency of 0.75 Hz. However, the theoretical natural frequency of the test model is 0.5 Hz, indicating that the ball hinges at both ends of the rod contribute additional stiffness. Furthermore, the measured damping ratio of the BSPI without damper was 0.058, whereas the BSPI with viscous dampers installed demonstrated a much higher damping ratio of 0.198. This suggests that the installed damper improved the damping ratio of the BSPI structure.

4.2. Measured Acceleration

Figure 11 compares the acceleration time histories recorded by an accelerometer mounted on the mass block with the input acceleration of the shaking table. When the maximum acceleration of the El Centro motion input to the shaking table was 0.40 g, the maximum acceleration of the BSPI structure with viscous dampers was 0.081 g. The acceleration responses of the BSPI structure were reduced compared with input ground motion, indicating that the BSPI structure has adequate seismic isolation effect.

Figure 12 compares the maximum acceleration responses of the BSPI structure without damper and the BSPI structure with viscous dampers. Removing viscous dampers from the BSPI structure results in a small alteration in the structural acceleration response. The BSPI structure generally demonstrates a substantially reduced acceleration response compared to the input acceleration in the shaking table test. Between 58% and 79% of vibrations can be reduced with BSPI technology.

4.3. Displacement Response Measured Displacement

The relative displacement of the structural model is the displacement between the structure and the shaking table. Inter-story drift is defined as the value of relative displacement divided by the length of the hanger rod. The maximum relative displacement responses of the BSPI structure under the El Centro earthquake are displayed in

Table 5. Maximum displacement responses of the two structures under El Centro earthquake.

Structure Type	PGA (g)	Relative Displacement (mm)	Inter-Story Drift
BSPI without damper	0.07	11.25	1/89
BSPI with viscous dampers	0.07	5.31	1/188
BSPI without damper	0.2	25.38	1/39
BSPI with viscous dampers	0.2	12.53	1/79
BSPI without damper	0.4	41.02	1/24
BSPI with viscous dampers	0.4	26.71	1/37

. The inter-story drift of the BSPI with dampers under El Centro earthquake with a PGA of 0.4 g is 1/37, which is less than 1/20 of the length of the rod.

The maximum relative displacement of the BSPI structure with dampers was reduced by 35% from 41.02 mm to 26.71 mm compared to that without damper when the input shaking motion was El Centro earthquake with a PGA of 0.4 g. The relative displacement of the BSPI structure with dampers was smaller than that of the BSPI structure without damper. The installed lateral damper device can dissipate earthquake energy and control the structural displacement effectively.

4.4. Forces of Rods

In order to investigate the effects of seismic activity on the internal forces in the rods, stress sensors were installed on the rods to monitor the variations in internal force under different ground motions. Figure 13 illustrates the internal forces experienced by the rods of the structure when exposed to El Centro motion. A consistent rise in the maximum internal force of the rods is observed as the intensity of the acceleration input escalates.

The internal force in the rod of the BSPI with dampers is smaller than that of the structure without dampers, indicating that incorporating dampers can reduce rod internal forces by decreasing the relative displacement of the structure. The internal forces of the four rods are slightly different under the same loading case, mostly due to construction errors. The resulting stress was found to be 28.29 MPa, which is significantly below the yield strength of the steel (345 MPa).

4.5. Numerical Simulation Methods and Verification

4.5.1. Numerical Simulation Methods

The seismic isolation performance of the BSPI frame is further investigated by numerically modeling BSPI structures in the finite element analysis software ABAQUS 6.11, as shown in Figure 14. Hanger rods and steel beams were modeled using B31 elements. For the superstructure, a SOLID element was used. The material properties are defined to match the shaking table test. To simulate the rotation stiffness of the joints connecting rods and foundation beams accurately, HINGE elements were used to simulate the joints. A CARTESIAN connection is used to directly add damping to the dampers, and the Rayleigh damping model is adopted. The full Newton–Raphson method with automatic step increments is adopted in the ABAQUS simulations to ensure accurate and stable solutions [44].

The Newton–Raphson method is adopted in the ABAQUS simulation to ensure accurate and stable solutions. The Kent–Park model [45] is employed to simulate the concrete material. A bilinear constitutive model is utilized to simulate the nonlinear behavior of the steel bars under seismic loading.

4.5.2. Verification of the Simulation Model of BSPI

The BSPI structural finite element model was subjected to seismic motions used in the shaking table test. The seismic reaction time-history comparison between the test and the results of the numerical calculation is shown in Figure 15 and Figure 16. The numerical results of comparing the structural displacements and accelerations during the El Centro earthquake demonstrate a strong correlation with the test data. This indicates that this study’s finite element modeling method is accurate and reliable.

5. Finite Element Analysis of the BSPI Frame

The suspension system of BSPI weakens the structure’s lateral stiffness, thereby lengthening the structure’s natural period and consequently mitigating the structural acceleration response. However, this also causes an increase in the displacement of the structure. In order to further investigate the seismic isolation performance of the BSPI frame, as well as to study the effects of the length of the suspension rod and the damping ratio on the seismic isolation effectiveness, a finite element model of the BSPI frame was established and analyzed.

5.1. Model Overview

Figure 17a displays the plane configuration of a three-story prototype building (unit: mm). The height of each story is 3.6 m. The building has three spans in depth and seven spans in width. A dead load of 5.0 kN/m² and a live load of 2.0 kN/m² are intended for the building. The reinforcement design follows Chinese seismic design code GB5011-2010 [32]. As shown in Figure 17b, only two transverse frames are separated for nonlinear analysis in order to increase analysis efficiency. The dynamic analysis of the model was performed only in the Y-direction. The suspension rod of the seismic isolation layer adopts a Q345 steel rod with a length of 1.3 m and a diameter of 30 mm, and four rods are arranged at the bottom of each column. There are two viscous dampers positioned transversely at the bottom of each column, with damping coefficient C of 40 kN/(m/s)^0.3 and damping index α of 0.3.

The numerical models of the BSPI structure and the RCF structure were established using ABAQUS finite element software, as shown in Figure 17. Modeling of the seismic isolation layer was carried out using the modeling approach in Section 4.5.1. The properties of the isolation model used in the numerical study are summarized in

Table 6. Detailed properties of the isolation layers.

Components	Material Properties	Element Names	Remarks
Hanger rods	Steel	T3D2	The hanger rods are only subjected to tensile forces
Column-bottom plates	Steel	S4R	SHELL element (S4R) can be used for simulation of plate members
Dampers	/	CARTESIAN	Applying damping with CARTESIAN
Hinge	/	HINGE	The isolation layers are connected using HINGE element that accurately imitate rotation at the joints
Gravitational restoring force	/	AXIAL	The gravity restoring force is simulated by defining behavior through AXIAL element at the column-bottom plates

. The hanger rods are simulated using the ABAQUS software’s TRUSS element (T3D2), while the B31 element simulates the superstructure’s beams and columns. The HINGE element is used to model the movement of the joints between the hanger rods and column-bottom plates. This allows for the exact simulation and assurance of the joints’ rotatable properties. The restoring force of the seismic isolation layer provided by gravity is defined by the behavior of the AXIAL element.

To address the variability in ground motion, a range of seismic records representing different intensities—frequent, fortification, and rare earthquakes—was considered. The performance of the BSPI structure was analyzed under each of these scenarios to assess its resilience across a spectrum of seismic activities.

5.2. Natural Vibration Frequencies of Structures

The natural period of the BSPI structure and the RCF in the Y direction were determined through computational analysis using the ABAQUS finite element software. The BSPI structure exhibited a natural period of 2.305 s, while the RCF demonstrated a natural period of 0.415 s. This suggests that positioning the suspension layer in the BSPI structure reduced the overall structural stiffness, consequently extending the structure’s natural period. The seismic response spectrum for an intensity level of VIII is shown in Figure 18. According to seismic response spectrum theory, extending the structural period can reduce the acceleration response. It is evident that the BSPI structure exhibits excellent seismic isolation capabilities in terms of its natural vibration period.

5.3. Acceleration Response

In addition to the El-Centro and Taft records, the SH09-1 wave was introduced to enhance the validation of the BSPI structure’s seismic performance. This approach aligns with the guidelines set forth in the Chinese Seismic Design Code for Seismic Isolation of Structures (GB 50011-2010), which permits the use of two natural seismic records and one artificial record for time-history analysis. Figure 19, Figure 20 and Figure 21 depict the structure’s acceleration responses at each floor under the three input ground motions. The dynamic amplification coefficient K is defined as the ratio of the maximum acceleration of floor to the input PGA.

Table 7. Maximum acceleration response of the BSPI structures and RCF.

Seismic Events	PGA/g	Structural Types	${\mathit{a}}_{\mathbf{max}}/(\mathbf{m}\cdot {\mathbf{s}}^{-2})$			$\mathit{K}$
			1st Floor	2nd Floor	3rd Floor	1st Floor	2nd Floor	3rd Floor
El Centro	0.20	RCF	5.03	4.07	4.33	2.51	2.04	2.16
		BSPI without damper	1.57	1.56	1.62	0.79	0.78	0.81
		BSPI with viscous dampers	0.99	0.91	1.02	0.50	0.46	0.51
	0.40	RCF	4.60	5.36	5.20	1.15	1.34	1.30
		BSPI without damper	2.79	2.87	2.89	0.70	0.72	0.72
		BSPI with viscous dampers	1.81	1.84	1.98	0.45	0.46	0.49
Taft	0.20	RCF	3.72	3.82	4.25	1.86	1.91	2.12
		BSPI without damper	0.59	0.62	0.65	0.30	0.31	0.32
		BSPI with viscous damper	0.54	0.58	0.61	0.27	0.29	0.31
	0.40	RCF	4.99	5.48	5.48	1.25	1.37	1.37
		BSPI without damper	1.21	1.24	1.28	0.30	0.31	0.32
		BSPI with viscous damper	1.15	1.17	1.21	0.29	0.29	0.30
SH09-1	0.20	RCF	4.1	4.32	4.84	2.05	2.16	2.42
		BSPI without damper	1.92	1.98	1.92	0.96	0.99	0.96
		BSPI with viscous damper	1.18	1.14	1.24	0.59	0.57	0.62
	0.40	RCF	4.92	4.92	5.76	1.23	1.23	1.44
		BSPI without damper	3.64	3.72	3.84	0.91	0.93	0.96
		BSPI with viscous damper	2.2	2.12	2.28	0.55	0.53	0.57

lists the peak acceleration response of the BSPI structure and the dynamic amplification coefficient (K). The acceleration response of the BSPI structure is smaller than that of the RCF, which is due to the suspended seismic isolation layer weakening the overall stiffness of the structure, indicating that the BSPI structure has an obvious seismic isolation effect.

The acceleration response of the BSPI structure is reduced when equipped with viscous dampers compared to its undamped structure. Specifically, the maximum floor acceleration response during rare earthquakes is approximately 70% lower in the BSPI damped structure. This reduction is attributable to the incorporation of viscous dampers in the seismic isolation layer, which enhances the damping capacity of the BSPI structure and effectively diminishes its acceleration response by dissipating energy.

5.4. Displacement Response

The BSPI structure represents an innovative seismic isolation system that requires the definition of seismic objectives for assessing its seismic performance. According to the Chinese code GB50011-2010, it is recommended to set an inter-story drift limit of 1/400 for fortification earthquakes and 1/100 for rare earthquake in the superstructure of the isolated system. Considering both the structural functional requirements and the stress restrictions of the hanger rod, it is recommended that the displacement of the seismic isolation layer be less than 10% of the length of the rod and the maximum value of 300 mm at the same time during rare earthquake.

The displacement reduction factor η is the ratio of the inter-story displacements in the BSPI structure to those in the RCF structure.

Table 8. Inter-story displacement of the BSPI structures and RCF.

Seismic Events	PGA/g	Structural Types	Δmax/mm			$\mathit{\eta }$
			1st Floor	2nd Floor	3rd Floor	1st Floor	2nd Floor	3rd Floor
El Centro	0.20	RCF	29.99	17.72	6.40	—	—	—
		BSPI without damper	5.94	3.38	1.68	0.20	0.19	0.26
		BSPI with viscous dampers	2.19	1.75	0.95	0.07	0.10	0.15
	0.40	RCF	97.14	30.93	10.90	—	—	—
		BSPI without damper	23.45	10.20	3.55	0.24	0.33	0.33
		BSPI with VD dampers	6.32	3.91	1.97	0.07	0.13	0.18
Taft	0.20	RCF	16.11	13.23	5.73	—	—	—
		BSPI without damper	1.70	1.19	0.63	0.11	0.09	0.11
		BSPI with viscous dampers	1.54	1.03	0.56	0.10	0.08	0.10
	0.40	RCF	46.81	28.72	9.85	—	—	—
		BSPI without damper	3.65	2.47	1.27	0.08	0.09	0.13
		BSPI with viscous dampers	2.97	2.09	1.12	0.06	0.07	0.11
SH09-1	0.20	RCF	24.16	16.22	5.97	—	—	—
		BSPI without damper	6.19	3.35	1.32	0.26	0.21	0.22
		BSPI with viscous dampers	2.47	2.18	1.26	0.10	0.13	0.21
	0.40	RCF	85.71	27.07	11.36	—	—	—
		BSPI without damper	25.35	18.46	7.76	0.30	0.68	0.68
		BSPI with viscous dampers	8.67	5.56	2.58	0.10	0.21	0.23

displays the displacement reduction factor and the maximum inter-story displacement response Δ_max for each floor in the three structures subjected to three different seismic motions. The inter-story displacement response of the BSPI structure is substantially smaller than that of the RCF structure, as seen in Figure 22, Figure 23 and Figure 24. The displacement reduction factor of the BSPI structure without damper ranges from approximately 0.1 to 0.6 under rare earthquakes, whereas it ranges from 0.1 to 0.2 for the BSPI structure equipped with dampers. The maximum inter-story displacement of the BSPI structure with dampers under fortification earthquakes and rare earthquakes is about 1/1400 (<1/400) and 1/415 (<100), respectively, which meets displacement design objectives for seismic isolation.

The implementation of viscous dampers in BSPI structures enhances seismic performance. Under fortification earthquakes, the inter-story displacements decreased by 47.8%, 57.9%, and 64.5% when compared to undamped BSPI structures. Similarly, the reductions were 48.0%, 54.8%, and 54.4% under rare earthquakes. This confirms that viscous dampers can improve the additional effective damping ratio of the BSPI structure and control the displacement response of the seismic isolation layer. Furthermore, the isolation layer displacement of the BSPI structure with dampers is less than 1/10 and 300 mm of the hanging rod length, meeting the seismic objectives.

5.5. Analysis of the Rod Length and Damping Ratio

Adjust the length of BSPI structure model’s hanger rods from 0.1m to 2 m, and adjust the damping ratio to 0.05, 0.1, 0.15, 0.2, 0.25, and 0.3, respectively, to analyze the influence of the rod length and damping ratio on the structure. Inputting El Centro and Taft ground motions for dynamic time-history analysis, the effects of damping ratio and rod length on the maximum roof acceleration response of the structure and the maximum displacement response of the isolation layer are shown in Figure 25 and Figure 26.

The maximum roof acceleration response of the BSPI structure varies with changes in rod lengths and damping ratios, as illustrated in Figure 25. As the rod length extends from 0.1 to 2 m, the acceleration response of the structure becomes smaller. For instance, under the El-Centro seismic wave and maintaining a constant damping ratio of 0.3, the acceleration response is reduced from 2.1 m/s² to 0.85 m/s² when the rod length is increased from 0.1 to 2 m. Furthermore, the rate of decrease in acceleration is more pronounced when the rod length varies from 0.1 m to 1 m, while changes beyond 1 m in rod length have a lesser impact on acceleration. As the rods’ length increases, the seismic isolation’s displacement response increases. It shows that the increase in the horizontal stiffness weakening of the isolation layer causes an increase in the horizontal displacement of the isolation layer under seismic action.

As the damping ratio increases, there is a corresponding decrease in the structure’s acceleration response. As the damping ratio rises from 0.05 to 0.30, the acceleration response under El-Centro motion decreases from 1.862 m/s² to 1.007 m/s², while the rod length remains unchanged at 1 m. For the same rod length, the increase in damping ratio reduces the displacement response of the seismic isolation layer. The maximum inter-story displacement under the El-Centro motion decreased by 35.2% when the damping ratio increased from 0.05 to 0.3, at which time the rod length was 2 m, indicating that an appropriate increase in damping ratio can control the displacement of the seismic isolation layer in the BSPI structure.

The analysis of parameter sensitivity showed that increasing the rod length reduced the structure’s acceleration response, while an increase in damping ratio led to reductions in both displacement and acceleration responses. These variations emphasize the critical role of damping and rod length in optimizing the seismic performance of the BSPI structure.

6. Conclusions

This paper proposes a Base-suspended Pendulum Isolation system, composed of superstructure, hanger rods, viscous dampers, and foundation. The seismic performance of the BSPI structure was verified through theoretical analysis, shaking table tests, and numerical simulations. The main conclusions are drawn as follows:

(1)

The self-centering mode of the BSPI system is similar to that of a pendulum, and the natural period mainly depends on the length of the hanger rods. The lateral stiffness of the structure is weakened, and the natural period of the structure is prolonged by suspending the superstructure from the foundation.

(2)

The utilization of BSPI technology effectively reduces the acceleration demands of the structure. The shaking table test findings indicate a decrease in the acceleration response of the BSPI model under El-Centro and Taft motion compared to the input from the shaking table. The effectiveness of BSPI technology on vibration reduction ranges between 58% and 79%.

(3)

The incorporation of viscous dampers into the isolation layer mitigates the deformation requirements of the BSPI structure. Finite element analysis results show that the inter-story displacement of the superstructure of the BSPI structure is reduced by about 50%, attributable to the viscous dampers.

(4)

The seismic performance of BSPI structures is affected by the rod length and damping ratio. As the hanger rod’s length increases, the structure’s acceleration response decreases and displacement response increases. When the damping ratio was adjusted from 0.05 to 0.3, the maximum inter-story displacement under the El-Centro motion decreased by 35.2%.

While the small-scale tests and simplified numerical models demonstrate promising reductions in acceleration and displacement responses, these findings remain preliminary and test-specific. Given the inherent limitations of model scaling and numerical simplifications, the generalizability of the results warrants cautious interpretation. Further validation through large-scale physical testing and sophisticated numerical simulations is essential to comprehensively evaluate the BSPI structural system’s performance across diverse seismic scenarios.