An 8-story reinforced concrete frame structure is established with a seismic fortification intensity of 8° and a structural damping ratio of 0.05. The isolation story is positioned at the top of the three stories. The building structure has a plane size of 24 m × 15 m, and each story has a height of 3.3 m. The slab thickness measures 150 mm, while the beam and slab have a concrete strength grade of C30. The column’s concrete strength grade is C40, and the reinforcement is of strength grade HRB400 for the main bars and HPB300 for the stirrups. The concrete cover has a thickness of 30 mm. Nonlinear material properties are assigned to the concrete with a strength grade of C40 using the Takeda hysteresis type. At the same time, HRB400 steel reinforcement is defined with the Kinematic hysteresis type. The frame columns are designated PMM plastic hinges, whereas the frame beams and beam connections are labeled M3 plastic hinges. Table 1 provides detailed information on each story’s section dimensions and reinforcement of the beams and columns.

The finite element model of the inter-story isolation structure considering the SSI effect is established using SAP2000 software. Figure 2 illustrates the model, where the upper structure is simulated using frame elements, thick shell elements represent the raft foundation, and the foundation soil is modeled using solid elements. The foundation size is ten times the structure size, with a plane size of 240 m × 150 m. The upper structure’s raft foundation is embedded in the soil layer, and a layered model with a thickness of 30 m is employed to capture the foundation soil’s characteristics better. Table 2 presents the parameters of the foundation soil, and an artificial viscoelastic boundary is set around the foundation soil boundary.

The SAP2000 software extracts the column bottom reaction f under the standard gravity load to determine the number and type of isolation support. The total horizontal yield force is estimated as 2% of the column bottom reaction under the standard gravity load, which helps determine the required isolation supports. The inter-story isolation structure employs LRB600 isolation bearings; their parameters are listed in Table 3. The arrangement of the isolation bearings can be seen in Figure 3. The rubber isolator and gap elements are used in the isolation bearings to capture the vertical tension and compression nonlinear stiffness. To accurately represent the restoring force characteristics of the isolation story in the subsequent time history analysis, the Bouc-Wen model is employed.

This paper investigates the response of the inter-story isolation structure to three selected seismic waves. Table 4 provides the ground motion information, while Figure 4 illustrates the acceleration response spectrum of these seismic waves. The maximum acceleration input of the three-dimensional seismic wave is adjusted based on the ratio of X direction, Y direction, and Z direction, set explicitly at 1:0.85:0.65. To align with the base-isolation seismic intensity of 8° during rare earthquakes, the peak acceleration of the seismic wave is adjusted to 400 cm/s².

The research on dynamic characteristics of isolated structures primarily focuses on inter-story displacement and inter-story shear. Assessing a building’s seismic capability involves examining the shear force variation between floors, which accurately reflects the seismic performance of each floor in the seismic isolation structure. To analyze the effects of soil-structure interaction (SSI), elastic-plastic time-history analysis is conducted on both staggered structures with and without SSI. Figure 6 compares inter-story displacement values between these two isolated structures.

Figure 5 reveals that the inter-story displacements of both types of inter-story isolated structures, subjected to three-dimensional seismic wave input, are greater than those under one-dimensional and two-dimensional seismic input. Additionally, considering the SSI effect, the inter-story seismic structure’s inter-story displacement values show more significant variations across different seismic wave input dimensions compared to the results of the inter-story seismic structure without considering SSI.

Figure 6 compares inter-story shear values between the two isolated structures. It can be observed that the inter-story shear values of structures with varying story intervals under the influence of three-dimensional seismic wave input are consistently more extensive than those under one-dimensional and two-dimensional seismic inputs. Furthermore, the inter-story shear value of the inter-story seismic structure considering the SSI effect is greater than that of the inter-story seismic structure without considering SSI across different seismic wave input conditions. Please refer to Figure 7 for a visual representation.

An elastic-plastic time history analysis is conducted on the inter-story isolation structure, considering the SSI effect. The outcomes of story displacement and story shear are illustrated in Figures 7A, B, respectively. It is evident from both figures that when considering the SSI effect, the seismic response of the lower isolation structure under three-dimensional ground motion exhibits greater significance compared to that under one-dimensional and two-dimensional seismic inputs.

Figure 8A illustrates the hysteresis curve of the recovery force-displacement for the isolation bearing subjected to underground motion input. The figure demonstrates that the hysteresis curve exhibits chaotic behavior when subjected to ground motion input. Along with the distinct hysteretic characteristics, it also displays specific viscous properties, indicating a correlation between the anisotropic responses following ground motion input. Consequently, the hysteresis curve of the support assumes an irregular shape. The restoring force model employed for the isolation bearing is depicted as a bilinear relationship, as illustrated in Figure 8B.

In accordance with the seismic design code for buildings (Code for Seismic Design of Buildings, 2010), the maximum horizontal displacement of isolation bearings during rare earthquakes should not exceed the smaller value between 0.55 times the bearing diameter and three times the total thickness of rubber layers. For this study, LRB600 bearings are utilized, resulting in a horizontal displacement limit of 330 mm (600 × 0.55). Based on the time history analysis results, the maximum horizontal displacement of the inter-story isolation structure bearing, considering the SSI effect under different input conditions, is measured at 249.98 mm, which falls within the prescribed limit.

To ensure the effective performance of the inter-story isolation structure’s bearings under an 8-degree rare earthquake, it is essential to evaluate both the tensile and compressive stress experienced by the approaches. As per the specifications, the tensile stress of the isolation bearing should not exceed 1 MPa, while the compressive stress should not exceed 30 MPa.

Figure 9A illustrates the compressive stress curve of the inter-story isolation structure’s bearings. It is evident from the figure that the compressive stress generated by the Kobe and Hollister waves remains below 30 MPa. However, some bearings experienced compressive stress exceeding 30 MPa during the El Centro wave earthquake, and notably, bearing 18 exhibited the highest compressive stress, measuring 39.7 MPa, surpassing the specified limit.

The tensile stress curve of the bearings in the story isolation structure is presented in Figure 9B. Analysis of Figure 9B reveals that several bearings surpass the standard limit for tensile stress under each seismic wave. Notably, bearing 18 experienced maximum tensile stress of 2.2 MPa during the Kobe wave earthquake, exceeding the standard limit by more than twice. Similarly, under the El Centro wave earthquake, bearing 15 reaches a maximum tensile stress of 1.4 MPa, while under the Hollister wave earthquake, support 15 exhibits an ultimate tensile stress of 1.5 MPa.

Based on the analysis of the bearing stress curve, it can be concluded that when considering the SSI effect under three-dimensional ground motion, the conventional horizontal isolation bearing used in the story isolation structure fails to isolate vertical ground motion effectively. Furthermore, specific bearings encounter issues of tensile and compressive stress exceeding the limits. To address this problem, the implementation of a vertical isolation device is proposed.

A three-dimensional isolation structure model incorporating a vertical isolation bearing is constructed in this study. For the vertical isolation story, a steel spring with a stiffness of 8 × 10³ kN/m is chosen as the vertical isolation bearing. It is complemented by parallel viscous dampers, represented by the Damper element. The seismic response of traditional horizontal and three-dimensional isolation structures is compared and analyzed under three-dimensional ground motion excitations.

Modal analysis is performed on both the three-dimensional and traditional horizontal isolation structures, and the results for the first six natural vibration periods are presented in Table 5. It is evident from Table 5 that the three-dimensional isolation structure exhibits longer natural vibration periods compared to the traditional horizontal isolation structure. This can be attributed to the presence of an additional vertical isolation device in the three-dimensional structure, which enhances the system’s flexibility and further extends the natural vibration period of the structure.

Moreover, the three-dimensional isolation structure’s fourth, fifth, and sixth modes experience a more pronounced increase in their natural vibration periods when compared to the traditional horizontal isolation structure. This significant extension of the natural vibration periods for these modes contributes to an enhanced damping effect within the isolation structure, particularly for the respective methods mentioned.

The bearing pressure stress curve of the three-dimensional isolation structure is illustrated in Figure 11A. It is evident from Figure 11A that the maximum compressive stress experienced by the three-dimensional isolated structure under different seismic waves is 28.9 MPa, which is below the allowable limit specified in the code.

Figure 11B depicts the tensile stress of the isolation bearing. Figure 11B shows that the maximum tensile stress of the three-dimensional isolation structure under various seismic waves is 0.9 MPa, lower than the ultimate tensile stress the specifications allow. Furthermore, the maximum tensile stress of the bearing after incorporating the vertical isolation device is reduced by 59% compared to the maximum tensile stress of the isolation bearing in the traditional horizontal isolation structure. This optimization of stress in isolation bearing effectively addresses the issue of tensile stress exceeding limits in the conventional horizontal isolation structure under three-dimensional ground motion, thereby achieving the desired damping effect.

A three-dimensional isolation structure’s effectiveness lies in its superior damping effect and in considering the stress imposed on the foundation soil as a crucial criterion for evaluating its overall isolation performance. Figure 12 illustrates the comparison of the maximum soil stress between the two isolation structures under three-dimensional ground motion input. As depicted in Figure 12, incorporating the three-dimensional isolation bearing results in lower soil stress on the foundation than the traditional horizontal isolation bearing. Reducing soil stress is advantageous for the foundation and facilitates better design.

Based on the soil characteristics of the stories, two distinct sites are established in the inter-story seismic model that accounts for the soil-structure interaction (SSI) effect. Site 1 represents hard soil, while Site 2 represents soft soil. The selected parameters for the soils at these two sites are presented in Table 7. The subsequent analysis focuses on examining the disparity in response and isolation effectiveness between traditional horizontal isolation structures and three-dimensional isolation structures when considering the SSI effect at each site.

This paper establishes an inter-story isolation structure model considering the soil-structure interaction (SSI) effect. Various ground motion scenarios, including one-dimensional, two-dimensional, and three-dimensional inputs, are applied to compare the seismic responses of inter-story isolation structures. A three-dimensional isolation device is introduced to address the issue of tensile and compressive stress exceeding the limits in isolation bearings under three-dimensional seismic input. The seismic response results of traditional horizontal isolation structures are analyzed and compared. The following conclusions are drawn from the study.

(1) considering the SSI effect, the inter-story isolation structure exhibits larger inter-story displacement and inter-story shear values than the two-dimensional and one-dimensional seismic inputs under three-dimensional seismic conditions.

Inter-story isolation, as an emerging seismic isolation technology, has been implemented in numerous inter-story isolation engineering examples both domestically and internationally. However, the theoretical framework for this system is still not sufficiently developed, and the relevant literature is relatively scarce. Furthermore, there has been no research on inter-story isolation considering the Soil-Structure Interaction (SSI) effects under three-dimensional seismic conditions. This paper focuses on the response of inter-story isolated structures considering SSI effects during three-dimensional seismic events. Numerical simulation analysis is conducted to investigate the seismic response under four influencing factors: SSI effects, the dimension of seismic input, the type of seismic input, and the type of isolation bearings. Modal analysis and time-history analysis are employed for seismic response comparison. The impact of both stiff and soft soil layers on the response of inter-story isolated structures considering SSI effects under three-dimensional seismic input conditions is explored, offering valuable insights for further in-depth research on inter-story isolation structures.

In comparison to base isolation, inter-story isolation may lead to severe consequences and significant losses if the isolation layers are damaged, potentially resulting in the overall collapse of the superstructure. Thus, further exploration and protection measures regarding the performance requirements of isolation layers are necessary. The scope of this study is limited to the response of regular framed inter-story isolation structures considering SSI effects. If the structural configuration is altered, the response of irregular structures with inter-story isolation under three-dimensional seismic conditions and their effectiveness in reducing seismic effects warrant further investigation. Additionally, the seismic input for inter-story isolation structures consists of two horizontal components and one vertical component. However, real seismic effects also include torsional components, and it remains a subject of further research to examine the changes in response patterns when considering torsional effects in inter-story isolated structures.