MODELING OF BUILDINGS USING TRIPLE FRICTION PENDULUM-TYPE FLUOROPLASTIC SEISMIC ISOLATORS

УДК 721

ABSTRACT

The article studies the effectiveness of triple friction pendulum-type fluoroplastic seismic isolators in order to increase the seismic strength of buildings. As part of the study, their dynamic properties were studied based on a comparison of computational models of buildings with and without seismic isolation. The modeling results showed that when isolation is used, the natural oscillation period of the building increases from 0.63 s to 1.20 s. It was found that the shear forces in the X direction decreased from 17564 kN to 4328 kN, which is a decrease of 75%. Also, accelerations and inter-storey displacements decreased significantly, and the main deformations were observed at the foundation level. The results obtained indicate that triple friction pendulum-type isolators effectively reduce earthquake energy.

АННОТАЦИЯ

В статье исследуется эффективность сейсмических изоляторов маятникового типа с тройным трением на основе фторопласта с целью повышения сейсмостойкости зданий. В рамках исследования динамические характеристики изучены на основе сравнительного анализа расчетных моделей зданий с применением и без применения сейсмической изоляции. Результаты моделирования показали, что при использовании изоляции собственный период колебаний здания увеличивается с 0,63 с до 1,20 с. Установлено, что поперечные силы в направлении X уменьшаются с 17564 кН до 4328 кН, что составляет снижение на 75%. Также наблюдается значительное снижение ускорений и межэтажных перемещений, при этом основные деформации сосредоточены на уровне фундамента. Полученные результаты свидетельствуют о том, что изоляторы маятникового типа с тройным трением эффективно снижают воздействие сейсмической энергии.

Keywords: triple friction pendulum isolator, fluoroplastic seismic isolators, building modeling, seismic action, dynamic analysis, shear force, acceleration, interstory displacement, vibration period, seismic resistance.

Ключевые слова: изолятор маятникового типа с тройным трением, фторопластовые сейсмические изоляторы, моделирование зданий, сейсмическое воздействие, динамический анализ, поперечная сила, ускорение, межэтажное перемещение, период колебаний, сейсмостойкость.

Introduction

Today, the expansion of the construction of multi-storey buildings and structures of special importance in seismically active regions around the world makes the issue of ensuring their seismic resistance one of the most urgent and priority matter [1]. Traditional seismic protection methods, that is, resistance to seismic effects by increasing the rigidity of building structures, in many cases lead to an increase in the dead weight of the structure and the occurrence of excessive stresses and damage to structural elements under the influence of dynamic loads [2].

In this regard, the use of seismic isolation systems based on the principle of dynamic separation of the upper part of the building from the foundation is of great scientific and practical importance in modern construction practice. Scientific research in this area has widely covered the effectiveness of seismic isolation systems. In particular, James M. Kelly developed the theoretical foundations of seismic isolation systems based on elastomeric supports [3], while Roberto Villaverde studied in depth the dynamic properties of isolated buildings and their response to earthquakes [4]. Also, the studies of Constantin M. Constantinou [5] and Anil K. Chopra [6] developed calculation methods for seismic isolation devices and their practical applications.

In recent years, pendulum-type seismic isolators based on sliding supports made of fluoroplastic layer have attracted particular attention. The operating principle, energy absorption capacity and re-centering properties of such systems were studied by Maurizio Dolce [7]. However, the operation of triple friction pendulum-type isolators based on fluoroplastic layer under complex dynamic vibrations, heat dissipation on friction surfaces and their effect on the overall vibration characteristics of the building have not yet been sufficiently studied [8]. Mathematical modeling of nonlinear deformations of these systems, especially under conditions of strong seismic effects, is one of the urgent scientific issues [9].

The main objective of this study is to evaluate the seismic performance of buildings using triple friction pendulum-type fluoroplastic seismic isolators based on their modeling [10]. In the research process, the slip coefficient of the fluoroplastic layer was taken as a variable parameter, and the dynamic response of the building structure under seismic loads of different intensities was analyzed, and the results obtained were compared with the performance of an uninsulated building. The operating principle of a triple friction pendulum-type seismic isolator is based on the mechanism of energy dissipation through pendulum motion and friction forces. This isolator is a complex mechanical system installed at the base of a structure, between the foundation and the superstructure of a building, which ensures the controlled occurrence of relative displacement between the building and the foundation during earthquake. As a result, the seismic forces transmitted to the upper part are significantly reduced. The structural scheme of a triple friction pendulum-type isolator is presented in Figure 1 [11].

The working principle of the isolator occurs in three stages, depending on the intensity of the seismic impact [12]:

1. Low-intensity seismic effects (first layer). At this stage, mainly internal sliding surfaces are active. The system has high sensitivity and effectively absorbs small amplitude vibrations.

2. Seismic effects of medium intensity (second layer). As the earthquake intensity increases, the sliding surfaces in the middle layer are activated. As a result, the equivalent stiffness of the system decreases and the period of vibration of the building increases, which leads to a decrease in seismic effects.

3. High-intensity seismic effects (third layer). In conditions of strong earthquakes, all sliding surfaces move simultaneously. At this stage, maximum relative displacement is observed and energy is dissipated to the greatest extent.

1. Low-intensity seismic effects (first layer).

2. Seismic effects of medium intensity (second layer).

3. High-intensity seismic effects (third layer).

Figure 1. Triple friction pendulum

Research methodology

Description of seismic impact

The study used the Santa Monica earthquake accelerogram as a seismic impact. This earthquake occurred with high intensity (IX on the MSK-64 scale) in the Santa Monica area, located approximately 21 km from the epicenter. According to studies, this natural disaster is associated with geological faults located approximately 3 km underground, as a result of which an increase in high-frequency seismic waves was observed. As a result of this earthquake, many multi-storey buildings and structures were seriously damaged, some reinforced concrete structures were collapsed, and some elements of the transport infrastructure failed. Therefore, this accelerogram was chosen as a load representing a real seismic impact.

Computational model of the building

As part of the research, a spatial model of a 6-story reinforced concrete frame residential building was created. Modeling work was carried out in the ETABS software package, designed for modern engineering calculations. The building was designed in accordance with the conditions of a score of 9 seismic zone (on the MSK-64 scale). The main geometric and structural indicators of the building are presented in Table 1.

Table 1.

Main parameters of the model

The modeled building is a 6-story reinforced concrete frame structure, the main load-bearing elements of which are columns, beams and floor slabs, were adopted in accordance with standard geometric dimensions widely used in practical construction and regulatory requirements.

The loads used in the modeling were adopted in accordance with the requirements of current regulatory documents, and the seismic effects were determined in accordance with the conditions of the area with a score of 9 on the MSK-64 scale. Based on these loads, the dynamic properties of the building and its impact on the main seismic parameters were comprehensively analyzed.  The selected structural solution is aimed at ensuring sufficient strength, stability and operational reliability of the building frame. The values of the loads adopted in the calculations are given in Table 2.

Table 2.

Loads

An overview of the computational models of buildings with and without seismic isolation is presented in Figure 2.

Figure 2. Overview of the computational models of the building:(a) Model with seismic isolation; (b) Model without isolation (rigidly fixed).

Results and discussion

Oscillation period analysis

According to the results of the analysis, the first-order natural vibration period (T) of the building has changed significantly. In particular, in the model without seismic isolation, the vibration period was 0.63 s, while in the model with seismic isolation, this indicator increased to 1.20 s. This indicates an increase in the vibration period by 90.4%. An increase in the vibration period has a positive effect on the dynamic properties of the building, i.e., it leads to a decrease in the horizontal inertia forces that arise during an earthquake. As is known, earthquake waves are characterized mainly by short-period vibrations. If the vibration period of the building coincides with the earthquake vibration period, a resonance phenomenon can occur, which can lead to serious damage to the structure. One of the main tasks of the seismic isolation system is to reduce the risk of resonance by extending the vibration period.

Analysis of shear forces occurred on the building

The shear forces occurred by along floors in two buildings with a rigidly fixed foundation and triple friction pendulum-type fluoroplastic seismic isolators were compared. The results obtained are presented in Tables 2 and 3. The results of the analysis showed that the use of seismic isolation significantly reduces the shear forces occurred on the building foundation. While the maximum shear force on the foundation in the X direction was 17564 kN in the model without isolation, after the application of isolation this value decreased to 4328 kN. This represents a reduction of approximately 75%. While the shear force on the foundation in the Y direction was 29691 kN in the model without isolation, this figure decreased to 13469 kN in the isolated model, which is equal to 53.8% reduction. These results indicate that the seismic isolation system absorbs a large portion of the earthquake energy at the foundation level and significantly reduces the forces transmitted to the upper part. The shear forces in the cross-section of the floors in the x direction are given in Table 3.

Table 3.

Shear forces in the cross-section of floors in the X direction

In particular, the maximum shear force at the base decreased from 17,564 kN to 4,328 kN, reduced 75%. This indicates that the seismic isolation system effectively absorbs earthquake energy. The results obtained in the Y direction also confirm the positive effect of the seismic isolation system. The shear forces on all floors were significantly reduced by the application of seismic isolation. The shear forces on the floor sections in the Y direction are presented in Table 4.

Table 4.

Shear forces in the cross-section of floors in the Y direction

The reduction of shear forces in this direction is slightly less than in the X direction, but in the model where the isolation is applied, a reduction in loads is observed on all floors. This indicates that the isolation system is effective in the spatial performance of the building.

Maximum displacement and interstory displacement analysis

The results of the maximum displacements at the stories showed that there was a significant difference between the models with and without seismic isolation. In the rigidly fixed model, the displacements at the stories increased sharply from the lower stories to the upper stories. The graphs of the maximum displacements at the stories are presented in Figure 3, which shows (a) the model with seismic isolation and (b) the model without isolation (rigidly fixed).

Figure 3. Maximum displacements by floor:(a) Model with seismic isolation; (b) Model without isolation (rigidly fixed)

In particular, the maximum displacement at the top story was 121.13 mm and was observed in a curved shape at the stories. As a result, large bending moments were generated at the nodes where the columns and beams meet. In the model with seismic isolation, the maximum displacement values by floor were almost the same, ranging from 132 to 133 mm. The main deformation was concentrated in the isolation layer installed at the foundation level, where the displacement was 129.63 mm. Comparative analysis shows that while in the model without isolation, the deformations increase along the height of the building, in the isolated model, the deformations are mainly concentrated at the foundation level. As a result, inter-floor displacements on the upper floors are sharply reduced, and the internal stresses generated in the structural elements are significantly reduced. This feature clearly confirms the effectiveness of the seismic isolation device, in other word the earthquake energy is dissipated at the foundation level, ensuring that the main elements of the building frame operate in an elastic state. This not only increases the seismic resistance of the structure, but also ensures its post-earthquake operational suitability.

The analysis of accelerations in the X direction shows that the maximum acceleration observed in a simple (non-isolated) building was +22.40 m/s², and the minimum value was –12.55 m/s², while in the model with isolation these indicators did not exceed +7.27 m/s² and –5.26 m/s². The acceleration graph in the X direction of buildings with and without seismic isolation under the influence of an earthquake is shown in Figure 4.

Figure 4. X-direction acceleration graph of buildings with and without seismic isolation under earthquake impact

In non-isolated buildings, the vibrations were of high intensity and uneven nature, with sharp maximum values occurring in a short time interval. This means that the earthquake impact is transmitted through the structure almost without loss. The analysis of the acceleration graph in the Y direction shows that the use of seismic isolation significantly reduces the response of the building to dynamic impacts. In a simple building without seismic isolation, the maximum acceleration value was +29.48 m/s² (t = 10.24 s), and the minimum value was –37.40 m/s² (t = 9.94 s). In the case of seismic isolation, these indicators were +17.66 m/s² (t = 9.8 s) and –14.76 m/s² (t = 9.68 s), respectively. This indicates a decrease in acceleration in the positive direction by approximately 40%, and in the negative direction by approximately Unversium%. The acceleration graph in the Y direction of buildings with and without seismic isolation under the influence of an earthquake is shown in Figure 5.

Figure 5. Y-direction acceleration graph of buildings with and without seismic isolation under earthquake impact

In the absence of isolation, earthquake vibrations are fully transmitted to the structure, which causes large-amplitude, sharply changing vibrations. This process leads to the emergence of high inertia forces in structural elements. In a building with seismic isolation, vibrations are significantly reduced, their amplitude is lower, and the vibrations are relatively stable. In addition, the isolation system absorbs the main part of the earthquake energy at the foundation level, limiting its transfer to the upper floors. Due to this, the overall dynamic characteristics of the building are improved and the reliability of the structure increases.

Conclusion

1. As a result of the conducted studies, it was found that the use of triple friction pendulum-type fluoroplastic seismic isolators has a significant positive effect on the dynamic properties of the building. In particular, the first-order natural vibration period of the building was 0.63 s without isolation, but after the isolation was applied, it increased to 1.20 s, which is an increase of almost 90%. This reduces the likelihood of the structure entering a resonance state and reduces the negative consequences of earthquakes.

2. The results of the shear force analysis also showed the high efficiency of the isolation. While the maximum shear force at the base in the X direction was 17564 kN in the model without isolation, it was found that after the isolation was applied, it decreased to 4328 kN, a decrease of 75%. A significant decrease was also observed in the Y direction, with the maximum values ​​decreasing by about 53–55%.

3. Analysis of inter-storey displacements showed that, while in the model without isolation, the maximum displacement on the upper floors reached 121.13 mm, when isolation was applied, the main deformation was concentrated in the insulation layer, and the displacements on the floors were distributed at almost the same value (~132–133 mm). This ensures the movement of the building close to a solid body and prevents excessive deformations in the structural elements.

4. The results obtained on accelerations also confirm the effectiveness of the isolators. While the maximum acceleration in the X direction in the building without isolation was +22.40 m/s² and the minimum value was –12.55 m/s², in the isolated model these indicators decreased to +7.27 m/s² and –5.26 m/s², respectively. In the Y direction, the maximum acceleration was observed to decrease from +29.48 m/s² to +17.66 m/s², and the minimum value decreased from –37.40 m/s² to –14.76 m/s². These results indicate a significant reduction in inertial forces.

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