Performance of Dynamic Energy Absorbers in Multi-storey Structures with Incorporating Soil Structure Interaction

The moderate to high-intensity seismic events can cause catastrophic outcomes in buildings and other structures due to the level of structural harm. This type of damage can affect both the structural and non-structural components and under certain instances, can even cause injuries. Thus, the structures such as buildings and bridges need to be designed and constructed to resist seismic events, which will ultimately reduce the risk of damage and injury [1]. In the last several years, researchers try to discover some effective ways of controlling seismic loads to ensure people's lives and minimize the earthquake damage level [2, 3]. Seismic design is aimed at developing structures that are earthquake-resistant as well as durable, reliable, and above all, minimize the risk of death or injury. Special techniques and technologies, which include the ability to control the response of structures during earthquakes, as well as a decrease in the risk of damage and failure are a must [4-8]. Historically, energy dissipation was conceived through the deformation and damage of structure elements [9, 10]. Several methods and approaches are used in the construction of structures like bridges, buildings, and dams, which are aimed at dissipating energy and conserving the structural integrity of the structures. To illustrate this, engineers use displacement-based design while including enough ductility for the energy dissipation [11-16]. The other method is employing control systems such as seismic isolation that are normally used in the critical facilities to limit seismic response and enable the facilities to stay in operation during and after the earthquake [17-19].

Not long ago, conventional structural design is determined to be inadequate for purposes of preventing buildings and other structures from collapsing during earthquakes. As a consequence, it is necessary to employ solution which allow for fast reoccupation of buildings and minimise the need for repairs and disturbance of function even after strong to large earthquakes [20]. An efficient solution to the above is using control systems with the structures, which reduces the displacements and seismic forces. Utilization of control systems as an alternative to designing new structures or retrofitting existing ones will now be classified as standard practice in building codes, i.e., ASCE 7-16 and Eurocode [21]. This is especially important because some buildings and other structures may not always be fully secured using the regular structural designs after the occurrence of at least moderate to strong earthquakes. However, it is the time for alternatives to be adopted that allow for immediate occupancy, reduce the extent of repairs and minimization of the destroyed functions [22]. Previous research has demonstrated that implementing control systems can decrease the overall expense of a structure during its lifetime, in comparison to traditional design methods. This is due to the fact that control systems decrease damage, ensure post-earthquake functionality, and lower the requirement for repairs [23].

Control systems are widely adopted in many buildings worldwide to enhance their dynamic performance during earthquakes. Some notable examples include the Churchill Hotel in San Diego, CA, USA, the St. Francis Towers in Mandaluyong, Philippines, the Opera House in San Francisco, CA, USA, the King County Court House in Seattle, Washington, USA, and 3Com in Foster City, CA, USA [24, 25]. Though this, traditional structure engineering is usually not given attention to the influence of soil structure interactions. While the dynamic behavior of structures is studied by structural mechanics, the application of equations of motion and discrete elements makes it possible to correctly calculate displacements and stresses [26]. In the application of soil mechanical analysis, the soils' effect is also taken into account, hence the displacement and stress of the underground structure are different [27]. The mentioned interaction between structural system and soil is called as "Soil-Structure Interaction" (SSI). As it is not easy to give the comprehensive concept of SSI, it describes the interactions between the ground and the construction which is more rigid [28].

For example, when doing dynamic SSI analysis, amplification of seismic waves in the ground and the dynamic interaction between different soil layers should be consider as a factor. Additionally, dynamic SSI analysis also requires accounting for the dynamic behavior of the structure in response to the soil motion. This includes analyzing the transfer of forces between the structure and soil, as well as the effect of soil deformation on the structural response [29].

Other studies have demonstrated that the dynamic response of structures can be significantly impacted by dynamic SSI considerations. This impact is almost seen in three aspects: i) the increasing in damping within the system due to the transference of the structure's energy into the ground; ii) the change in the dynamic characteristics of the soil-structure system such as frequencies and modes of vibration; and iii) the soil moving properties influence the analysis [30]. Recent studies have shown that dynamic SSI effects have a significant impact on structural response in terms of base shear, performance levels and drift when supported by soft ground [31-33].

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Figure 1. Overview of the flowchart of the research process

In order to evaluate the impact of dynamic SSI on a steel frame with a viscous damper device, a 12-story steel 3D frame was analyzed with and without the control system installed. Seven representative seismic records were selected based on representative features such as frequency content, and these records were matched with the corresponding response spectra of the high seismic hazard zone as defined by the design criteria. The matched records were then filtered through the modeled soil profile to obtain surface records. Using the same profile data, the foundation stiffness was calculated at ground level and a more accurate structural and soil analysis was performed in the transition zone between both systems. The analysis considered the ground stiffness and earthquakes acting at the surface. The structure's analytical model was created using the finite element software ETABS, with the objective of analyzing its seismic performance [34]. The analysis comprised four cases: fixed base and flexible base with and without viscous dampers. The results were presented in terms of storey displacement, maximum storey displacement, inter-story drift, maximum inter-story drift, top storey acceleration, and maximum storey acceleration with and without viscous dampers. Figure 1 shows the flowchart of the research processes.

A 12-story frame is modeled in ETABS considering the geometry shown in Figure 6, both with and without viscous dampers. The loads applied on the model is: Dead load is 6 kN/m² and the live load is 4 kN/m².

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Figure 6. A 12-story steel frame

A viscous damper was incorporated into the model using a link element with a nonlinear exponential damper [43]. Non-linear properties were introduced following the methodology considering moderate damage levels for moderate-height buildings [44]. First, calculate the response reduction factor B as follows:

$B=\frac{D_{\max }}{D_{o b j}}$             (4)

where, $D_{\text {max }}$ is the maximum drift obtained in the structural analysis and $D_{o b j}$ is the target drift. In this case, the FEMA moderate damage level of 0.0051 . A target of 35% effective damping of the structure is set. This means that the viscous damper should contribute 30% of the total structural damping. The damping coefficient $C$ calculated for each floor using the following formula:

$C=\zeta \frac{k_i}{\mu_i} * \frac{T}{\pi} * \frac{1}{\cos _{\theta_j}^2}$              (5)

where, $\zeta$ is the damping ratio, $k_{i}$ is the stiffness of the ith floor, $\mu_{\mathrm{i}}$ is the number of viscous dampers per floor, $T$ is the fundamental period of the structure, and $\theta_j$ is the tilt angle of the viscous dampers. The following nonlinear properties of the viscous damper have been determined: Damping coefficient $C$ $=2553.59 \mathrm{kN}-\mathrm{seg} / \mathrm{m}$, velocity exponent $\alpha=0.5$, brace stiffness $K=202630.16 \mathrm{kN} / \mathrm{m}$, physical properties of HEB200 taken from the axial stiffness equation of the brace element steel section. Maximum damping force can be determined using the following formula:

$F=C(V)^\alpha$            (6)

$V=\frac{2 \pi}{T} 0.02 \times H_{\text {story }} \times \operatorname{Cos}(\theta)$              (7)

where, $F$ is the damping force, $V$ is the velocity, $T$ is the fundamental period, $H_{\text {story}}$ is the analyzed story height, and $\theta$ is the damper inclination angle.

The SSI effect of a steel 3D frame structure implementing a viscous damper has been investigated. The following conclusions for 12-story 3D framed building that were used as a case study:

1. It is very important to consider the impact of SSI when performing a global analysis of any kind of structure, even more so if the structure falls into a category of high importance to the community. This is because there is a notable difference in the results when considering the effects of SSI in the analysis. In this case study, the displacement increases for selected properties of the soil supporting the structure.
2. The results of this study show that using a damper has an inverse effect on the acceleration and displacement response. The maximum displacement decreased by about 26% on average, while the acceleration response shows a small noticeable increase of less than 13%.
3. Despite the use of dampers and the inclusion of soil-structure interaction, the acceleration values vary between the upward and downward motions. This variation can be attributed to the nature and frequency content of the ground motion, as well as the response characteristics of the model to the ground motion.
4. The inclusion of soil-structure interaction in the building leads to an increase in relative lateral displacement. This is due to the additional flexibility and reduction in stiffness resulting from the interaction with the soil.
5. Comparing the fixed-base and flexible-base models, the average floor-to-floor drift increased by about 32.95% when considering the SSI.
6. The use of viscous dampers allows for dynamic control during seismic events, potentially reducing the amount and level of damage that both structural and nonstructural elements can withstand. This is a result of the additional capacity to dissipate the energy provided by the control system.
7. Including the effect of soil structure interaction in the modeling representation is an absolute necessity because it reflects the reality of the structure’s behavior, and the designers of structure must also have the decision to choose the materials used in construction based on the SSI response effect in terms of lateral displacement and the change in the natural frequency of the structure.