Autors: Burak Ismail AtesMoritz Wittmann Chi-Chia Tung
Earthquakes pose a significant threat to the built environment, leading to catastrophic loss of life, property, and infrastructure. According to the United States Geological Survey (USGS), on average, there are approximately 500,000 earthquakes annually, with about 1000 of them causing damages, making it imperative to develop and implement strategies that can minimize the associated risks [1]. The economic toll of earthquake-induced destruction is staggering.
"Earthquakes can cause massive damage to infrastructure, as was seen in the 2011 earthquake and tsunami in Japan which resulted in US$ 239 billion in economic losses, the highest figure in any disaster event on record [1]."
The World Bank estimates that earthquakes have caused over US$ 3.5 trillion in damages globally over the past two decades [1]. This economic burden is not only a result of direct physical damage but also encompasses indirect costs such as business interruption, healthcare expenses, and post-disaster recovery efforts [2]. But the adoption of advanced protection systems is not just a matter of preserving economic stability but is also a critical component in safeguarding lives in earthquake-prone regions. The earthquake cited above, for example, led to the reactor accident in Fukushima, one of the biggest humanitarian crises in history. As urbanization continues to surge and populations concentrate in seismically active regions, the need for robust earthquake protection systems becomes paramount.
For this reason, there are a large number of earthquake protection systems, some of which have very different principles of operation. This report deals with the modelling and simulation of base isolated buildings, especially by curved surface sliders. First, a brief overview of earthquake protection systems will be presented before the basic technical principle of curved surface sliders is discussed. Building on this, the model for modelling and simulating actual seismic events will be presented and applied.
1. Base Isolators
There are many different methods of protecting a building or structure from an earthquake. Figure 1 provides an overview of them. In this paper the seismic isolation of a building will be discussed. Therefore, the aim is not to reinforce the building structure itself, but to decouple and dampen dynamic force excitation. Hysteretic and hydraulic dampers can be considered for this purpose, but the focus of this report will be on the base isolators presented below.
As part of the project, three different base isolators will be discussed, the functionality of which is briefly described below.
"Hereby, a proper isolation system must be capable of appropriately ensuring the following four main functions: Vertical load transmission, lateral flexibility (decoupling + period elongation), energy dissipation (damping) and re-centring capability [3]."
In all three cases, the structure is initially treated as a rigid mass that is to be decoupled from the seismically active subsoil or whose vibration is to be damped by means of a base isolator.
1.1. Elastomeric Isolators
There are various versions of elastomeric bearings that must be selected or dimensioned according to the area of application. In general, elastomeric isolators are made of layered rubber, whereby a distinction is made between unreinforced and reinforced bearings. Figure 2 shows a cut-away elastomer bearing reinforced with a lead core (LRB: Lead Rubber Bearing). Non-linear damping is primarily due to plastic lead core deformation.
"The isolators transfer the vertical loads from the structure to the foundation while at the same time allowing for rotation and elastic re-centring. [...] When subjected to horizontal deformation, the lead core produces significantly greater hysteretic damping than Low and High Damping Rubber Isolators. The resulting force displacement loop is much fatter, i.e. much more energy is dissipated per cycle, which is the reason why LRBs are the most commonly used Elastomeric Isolators [4]."
A more detailed description of the elastic dampers is not provided here, as the focus is on the following curved surface sliders. For further information on LRBs, we recommend [7] and [8].
1.2. Sliding Isolators
As with elastomer bearings, there are various versions of curved surface sliders (CSS), also known as friction concave isolators or friction pendulum bearing. This paper will primarily deal with curved sliding isolators, which in turn are divided into two types. Figures 3 and 4 show a single curved slider (SCS) on the left and a double curved slider (DCS) on the right.
Both displayed sliders have a concave (primary) sliding plate, which is the upper grey object. While the system shown on the left has only one upper sliding surface and rests on the calotte at the bottom, the glider moves between two concave main sliding surfaces in the case on the right. The elements shown in gray in the illustration are typically made of stainless steel which are polished on their sliding surfaces. The sliding elements are also fabricated out of stainless steel and coated with high-bearing-capacity polymer composites such as polytetrafluoroethylene (PTFE) or other designs of self-lubricating, thermoplastic polymers [5]. According to [5], the sliding materials in particular have been greatly improved in recent years, not only with regard to better friction degradation but also thermoplastic sliding friction losses have been reduced.
Figure 5 illustrates the basic mechanical principle of a CSS. It shows a simplified building as a rigid body, which stands on a spherical sliding surface with the radius R_{geo} of a SCS.
The above diagrams illustrates that one distinguishes between a geometrical radius R_{geo} and an effective radius R_{eff}. R_{geo} describes the actual geometric radius of one of the sliding surfaces, as shown in figure 5. Figure 6 shows, however, that this is not necessarily the effective radius. R_{eff} describes the mechanically effective radius, which refers to the center of mass (centre of gravity) of the idealized pendulum. This can deviate from R_{geo}, as illustrated in Figure 6, where R_{geo} is visibly smaller than R_{eff}. The difference becomes particularly clear when considering double curved surface sliders. As described at the beginning, there are two concave friction surfaces whose geometric radii are both added together to form an effective radius. This leads to a relevant difference between the two radii. R_{eff} is used for the following calculations.
Figure 5 indicates, that the coupling stiffness is indirectly proportional to R_{eff}. In the model shown, this relationship is entered as the equivalent spring stiffness k_B in equation (1):
| (1) | \begin{equation} k_B = \frac{N_S}{R_{eff}} \end{equation} |
This function can be derived using the known dynamics of a pendulum such as depicted in figure 6.
The graph shows the displacement x along a segment of the circle, which describes the damping-effective path. The building load results in the gravitational force N_S. Using the the known ratio k = \frac{\text{force}}{\text{displacement}} = \frac{f_T}{x} one can now derive the force F_R:
| (2) | F_R = N_S \cdot \frac{x}{R_{eff}} = x \cdot \frac{N_S}{R_{eff}} |
Given this relation, it is possible to plot the equation (1) in a force-displacement diagram which produces a diagonal line with slope k_B. In order to generate a hysteresis loop from this, the friction damping must now also be taken into account. The Coulomb friction force is the product of the friction coefficient \mu and the vertical load.
| (3) | F_\mu = N_S \cdot \mu \cdot sign(\dot x) |
In the force-displacement diagram, this product forms a rectangle.
Analogously, the indirect displacement-proportional sliding friction stiffness can also be derived:
| (4) | k_\mu = \mu \cdot \frac{N_S}{x} |
Combining the derived formulas, the dynamics of a CSS can be described the following way:
| (5) | k_{eff} = k_B + k_\mu = \frac{N_S}{R_{eff}} + \mu \cdot \frac{N_S}{x} |
| (6) | F_{eff} = F_R + F_\mu = \frac{N_S}{R_{eff}} \cdot x + \mu \cdot N \cdot sign(\dot x) |
It should be noted that this calculation makes two assumptions: a constant vertical loadN_Sand constant coefficient of sliding friction\mu(Coulomb simplified theory). In reality, this approximation does not hold for greater total sliding paths. Typically, the coefficient of sliding friction decreases roughly logarithmically with increasing temperatures [5], which occur as an effect of the movement (second law of thermodynamics). This dependency was neglected in the model shown.
The equations (5) and (6) can also be indicated in the hysteretic loop, which combines the diagonal line with slope k_B and the rectangular shape of the friction to a parallelogram as depicted in figure 7 to the right.
The small peaks that can be seen at the top left and bottom right of the hysteresis loop are the result of the transition from static to dynamic friction [4].
A major difference between the LRB and CSS is the duration of the isolation period. T_{iso, LRB} = 2 \pi \sqrt{\frac{m}{k_{eff}}} is calculated as a function of mass and spring stiffness. T_{iso, CSS}, on the other hand, can be derived from the kinematics of a thread pendulum. According to [4], using the small angle approximation T_{iso, CSS} results in
| (7) | T_{iso, CSS} = 2 \pi \sqrt{\frac{R_{eff}}{g}} |
WhileT_{iso, LRB} increases with increasing mass, T_{iso, CSS} is independent of the weight of the structure. According to [4], an extension of the isolation period is generally expedient. If the isolation period were the only selection criterion for the type of support, one could generally say that CSSs are suitable for light structures and LRBs for heavier buildings. However, the choice also depends on other factors (excitation spectra, construction, costs, etc.) and typically several insulators are installed, so that the building mass is also distributed here. The isolation period is therefore one of many selection criteria for seismic protection systems that must be taken into account by the planning engineer.
2. Analysis Method and Data Acquisition
The solution approach for the equation of motion and the data needed for the solution is the core part of the analysis and design. Several methods exist in practice and literature to analyze the response of a structure under earthquake excitation.
It's important to start by revisiting the equation of motion for a root point excited single degree of freedom (SDOF) system to understand where the ground motion data is required. Then, we will briefly summarize the most common analysis methods in the literature, including the time history method, which we used in this project. Afterward, we'll discuss the steps we took to gather and preprocess the necessary data.
2.1. Equation of Motion for a Single Degree of Freedom (SDOF) System
Seismic actions, induced by human activities (e.g., gas extraction) or tectonic movements, introduce accelerations to the existing superstructure. As the base to which the building is attached accelerates during an earthquake, Newton's second law of motion applies to the structure, and d'Alambert inertia forces become relevant. These lateral forces are the primary cause of building collapse during earthquakes. Since these forces result from ground acceleration rather than a real horizontal force, the building is considered root point excited. The equation of motion for a root point excited SDOF system under root point excitation(8) is provided below to refresh readers' memories.
| (8) | m\ddot{w_r}+c\dot{w_r}+k{w_r} = -m\ddot{w_g} |
The right-hand side of equation (8) represents d'Alambert inertia forces. There are two acceleration terms in the equation, namely $\ddot{w_r}$ and $\ddot{w_g}$. The former refers to the acceleration of the structure, while the latter refers to the ground acceleration. To obtain the displacement $w_r$, velocity $\dot{w_r}$, and acceleration $\ddot{w_r}$ of the structure, we need to know the ground acceleration term $\ddot{w_g}$. This term can be determined from a design response spectra as a single value in terms of peak ground acceleration (PGA) for an equivalent static force analysis or can be entered into the equation as time-dependent acceleration for a time history analysis. This time dependent accelerations can either be acquired from a ground motion database [14] or generated artificially [15].
Static and dynamic analysis techniques are utilized to obtain the structure's response under earthquake excitation. Eurocode-8 section 4.3.3 suggests several methods, including linear equivalent static analysis, modal response spectra analysis, nonlinear static analysis (such as pushover analysis), and time-history analysis.
The equivalent static force analysis, prescribed in any seismic design code, involves considering only the fundamental mode of the structure and its corresponding PGA value from the design response spectra. The base shear is then calculated based on this acceleration value and distributed non-uniformly along the structure's height. The corresponding displacement for each floor is obtained from a static analysis. Pushover analysis, another form of static analysis, incorporates nonlinearity in the structure's components and redistributes the load in each iteration.
Modal response spectra analysis, applicable for linear models, involves superposing all dominant modes in the structure's response. For our structure analysis, we employed a dynamic analysis so-called time-history analysis, which consider the dynamic behavior of the structure under seismic excitation. While time-history analysis considers the entire time history of ground acceleration and provides the temporal history of the structure's response during the earthquake, modal analysis focuses on the structure's natural modes of vibration. Also it's possible to perform nonlinear analysis in time-history method. For further reading and application, reference may be made to any seismic design code [11], [12] or a text book [13]
Ten representative earthquake records were utilized as input for the time-history analysis. We will explain the steps for data acquisition and preprocessing in the following section.
2.2. Data Acquisition and Preprocessing
In the previous section, we stated that we do the analysis in the time domain using the time history method. To accomplish this, the time history of a statistically significant number of earthquakes must be gathered, and simulations must be run for these earthquakes. We selected ten earthquakes whose acceleration response spectra are compatible with the design response spectra for our structure. Subsequently, we averaged the maximum absolute displacements of the base isolator for each simulation to design the base isolator.
The data was obtained from the Pacific Earthquake Engineering Research Center's (PEER) database[14]. Parameters for the earthquake records entered into the database search engine included:
- Magnitude: 6-7
- $V_{s30}$= 180-360 m/s (Soil Class C according to Eurocode 8)
- Time until 95 % of earthquake energy dissipated = 30 seconds
- Number of records = 100
Based on these parameters, 100 earthquake records were provided by the database. However, not all of these earthquakes were compatible with our design response spectra. Therefore, data preprocessing was necessary before running the simulation.
Before preprocessing the data, it's beneficial to understand what a response spectra is. In equation (8), if we divide both sides by $m$ and rearrange the equation, we can rewrite it in terms of damping ratio $\zeta$ and natural frequency $\omega_N$ (see equation (9)).
| (9) | \begin{equation} \ddot{w_r}+2\zeta\omega_N\dot{w_r}+\omega_N^2{w_r} = -{w_g} \end{equation} |
The acceleration response spectra are obtained by solving equation (9) for structures with varying natural periods $T_n=[0.01,4]$ and a fixed damping ratio of $\zeta=0.05$. It should be noted that the accelerogram remains the same for any $T_n$. The maximum absolute acceleration response value is then obtained for the corresponding natural period. Thus, the graph demonstrates the PGA for the SDOF system with the corresponding natural period.
To fit the data to our design response spectra where our base isolator's period corresponds, we first plotted the design response spectra and acceleration response spectra of the real earthquakes (see Figure 8 ).
The design spectrum is plotted according to Eurocode 8 specifications. We assumed the structure is located in earthquake zone 1 in Italy with reference ground acceleration 0.3g, as depicted in Figure 9.
The soil class is considered as class C, and the structure is classified as a residential building with importance class II and a damping ratio of 0.05. The corresponding parameters for the calculation of design response spectra is given in table 1.
Zone | Reference Ground Acceleration (g) | Soil Class | Importance Factor | Damping Ratio |
|---|---|---|---|---|
I | 0.3 | C-180-360 m/s | 1.0 | 0.05 |
Table 1: Parameters for design response spectra according to Eurocode-8
The goal of the base isolator is to shift the natural period of the nonisolated structure (possibly in the high demand area) to the tail of the spectra where lower acceleration values are observed. Therefore, the base isolated structure's natural period (T_{iso}) is determined as 3 seconds arbitrarily. To make the accelerogram compatible with the design response spectra at $T=T_{iso}$, we rescaled the acceleration time history by a scaling factor $\alpha$. The $\alpha$ is determined as:
| (10) | \begin{equation} \alpha=\frac{a_{design}}{a_{actual}} \end{equation} |
Where:
$\alpha_{design}=$ PGA at $T=3s$ on the design response spectra
$\alpha_{actual}=$ PGA at $T=3s$ on real earthquake's response spectra
In summary, the time history method is chosen for the simulation, and the acceleration time history was needed to solve the equation of motion. We acquired the data from PEER's database and preprocessed it to make it compatible with our design response spectra, which are drawn according to Eurocode 8. After obtaining the compatible accelerograms, we built the model in the Matlab Simulink environment and ran the simulation for ten different earthquakes in $x$ and $y$ directions. In the next section, we will explain how the model is built and implemented in Simulink.
3. Equations of Motion for Multi-Storey Buildings with Base Isolation
Figure 10 shows a building model, with multiple (n) stories. Such structure can now be accelerated by an earthquake, causing the individual floors to vibrate in a horizontal direction. When considering seismic events, the vertical movement is generally not as relevant as horizontal directions, as buildings primarily fail due to shear [4]. A horizontal displacement x_i relative to the ground movement is therefore defined for each storey. Their first and second derivatives are then the corresponding velocity \dot{x}_{i} and acceleration \ddot{x}_{i} respectively. Displacement, velocity and acceleration in the other direction are denoted as y_i, \dot{y_i} and \ddot{y_i}.
In our model, it is assumed that motion in x and y direction does not cause any torsional effect. Because of this assumption, motion in both directions can be superposed [9]. Therefore, equations of motion of highest floor n can be written as:
| (11) | \begin{equation} \ddot{x}_{n}+\ddot{x}_{g}= \frac{1}{m_n} [-c_n(\dot{x}_{n}-\dot{x}_{n-1}) -k_n({x}_{n}-{x}_{n-1}) ] \end{equation} |
| (12) | \begin{equation} \ddot{y}_{n}+\ddot{y}_{g}= \frac{1}{m_n} [-c_n(\dot{y}_{n}-\dot{y}_{n-1}) -k_n({y}_{n}-{y}_{n-1}) ] \end{equation} |
where c_nandk_n are damping and stiffness on storey n.
The equations of motion for the second floor to the (n-1)th floor can be written as:
| (13) | \begin{equation} \ddot{x}_{n}+\ddot{x}_{g}= \frac{1}{m_n} [-c_n(\dot{x}_{n}-\dot{x}_{n-1}) -k_n({x}_{n}-{x}_{n-1}) +c_{n+1}(\dot{x}_{n+1}-\dot{x}_{n}) + k_{n+1}({x}_{n+1}-{x}_{n}) ] \end{equation} |
| (14) | \begin{equation} \ddot{y}_{n}+\ddot{y}_{g}= \frac{1}{m_n} [-c_n(\dot{y}_{n}-\dot{y}_{n-1}) -k_n({y}_{n}-{y}_{n-1}) +c_{n+1}(\dot{y}_{n+1}-\dot{y}_{n}) + k_{n+1}({y}_{n+1}-{y}_{n}) ] \end{equation} |
The equations of motion for the fundament plate(Fundamentplatte, the floor structure connected to the base isolator) are presented below:
| (15) | \begin{equation} \ddot{x}_{b}+\ddot{x}_{g}= \frac{1}{m_b} [-F_{Rx}-F_{\mu x} +c_{1}(\dot{x}_{1}-\dot{x}_{b}) + k_{1}({x}_{1}-{x}_{b}) ] \end{equation} |
| (16) | \begin{equation} \ddot{y}_{b}+\ddot{y}_{g}= \frac{1}{m_b} [-F_{Ry}-F_{\mu y} +c_{1}(\dot{y}_{1}-\dot{y}_{b}) + k_{1}({y}_{1}-{y}_{b}) ] \end{equation} |
where F_{Ry} , F_{Rx} , F_{\mu x} and F_{\mu y}are restoring force and friction force in x and y direction. In 2D cases, restoring force F_{Ry}andF_{Rx} can be computed by using equation (2) and superposed to compute the total restoring force.
| (17) | \begin{equation} \begin{bmatrix}F_{Rx} \\ F_{Ry}\end{bmatrix} = \begin{bmatrix} x \cdot \frac{N_S}{R_{eff}} \\ y \cdot \frac{N_S}{R_{eff}} \end{bmatrix} \end{equation} |
To compute friction forces of base isolator in 1D cases, equation (3) is used but is modified in this model. In simulations, sign function should be approximated by other function because of numerical integration and tangent hyperbolic is a good approximation [4]. Therefore, the sign function in equation(3) is replaced with tangent hyperbolic function with a scaling factora and the friction forces F_{\mu x}andF_{\mu y} in 1D cases are computed by the equation below:
| (18) | \begin{equation} \begin{bmatrix}F_{\mu x} \\ F_{\mu y}\end{bmatrix} = \begin{bmatrix} N_S \cdot \mu \cdot \tanh{(a \cdot \dot x)} \\ N_S \cdot \mu \cdot \tanh{(a \cdot \dot y)} \end{bmatrix} \end{equation} |
In 2D cases, the influence of interdependency between both direction on friction forces F_{\mu x}andF_{\mu y} should be considered to prevent overestimation of forces and energy dissipation [10]. In this model, equations for 2D cases are used when velocity in both direction are larger than 10^{-4}(m/s). The equations for computing friction forces F_{\mu x}andF_{\mu y} then become:
| (19) | \begin{equation} \begin{bmatrix}F_{\mu x} \\ F_{\mu y}\end{bmatrix} = \frac{1}{\sqrt{{\dot x}^2 + {\dot y}^2}} \begin{bmatrix} N_S \cdot \mu \cdot \dot x \\ N_S \cdot \mu \cdot \dot y \end{bmatrix} \quad for \quad \dot y > 10^{-4} m/s \quad and \quad \dot x > 10^{-4} m/s \end{equation} |
4. Models Setup
Initially, a model without base isolator is set up which consists of 9 stories and each storey has identical mass m(kg). The stiffness between each floor is set to be k(N/m) to make the period of the first eigenmode be on the plateau region of design spectra. The damping used is stiffness proportional damping, so the damping value is computed by c=\beta k. In order to give a reasonable damping ratio to a building without base isolator, the coefficient \beta is computed so that the damping ratio of first eigenmode is 5%. The computation can be done by the following equation based on the Rayleigh damping method[10]:
| (20) | D_j=\frac{1}{2} \beta \omega_j |
In the next step, the same model is placed on a base isolator model to assess the performance of it. To compute the friction force, the friction coefficient \muis determined. The base isolator is able to lengthen the period to T_{iso}(s) and the effective radius can be computed by the following equation[4]:
| (21) | R_{eff}=g(\frac{T_{iso}}{2\pi})^2 |
Both model are set up in Simulink and the equations are solved by the inbuilt ordinary differential equations solver ode15s. A pseudo model of a storey in a building shows roughly how the equations can be implemented, which is depicted in figure 11.
The table below shows the parameters used in simulations. The friction coefficient is not included in table 2 because it is tuned for the investigation of its influence on the results, which is presented later in table 4.
m(kg) | k(N/m) | \beta | T_{iso}(s) | Number of Isolators | a(Scaling factor for friction force in eq. 16) |
|---|---|---|---|---|---|
8.16\cdot10^5 | 6\cdot10^7 | 0.04 | 3 | 36 | 10^4 |
Table 2: Simulation parameters for building structure and base isolator
5. Results and Discussion
This section will compare a 9-story building with and without single curved surface sliders. Quantitative comparisons will be made regarding interstorey drifts and maximum accelerations for both structures. Additionally, recentering error will be discussed. Finally, the search for an economic and safe slider will be explored through several simulations with varying friction coefficients.
The concept behind using curved surface sliders is to decouple the superstructure from the ground to reduce inertia forces acting on it. Consequently, we anticipate observing smaller interstorey drifts, reduced accelerations per floor, and nearly rigid body translation. Figures 12 and 13 depict the maximum displacements for each floor. It's important to note that these maximum displacements may not occur simultaneously. Nonetheless, it's intuitive to comprehend that the base-isolated structure exhibits nearly rigid body motion.
In Table 3, we compared the interstorey displacements and accelerations for each structure along with the corresponding Eurocode limitations and peak ground acceleration for the given earthquake. It's evident that the non-isolated structure exhibits very high interstorey drifts, surpassing the serviceability criteria and posing safety concerns by inducing second-order effects. The interstorey drift is significantly reduced by the base isolation, which also falls below the Eurocode-8 limitation for a structure with a 3m height. Additionally, upon examining the acceleration response of the structure and the PGA, we observe that the response of the conventional structure exceeds the PGA, whereas the isolated structure's acceleration is below the PGA, indicating smaller internal forces.
| Maximum relative displacement between base and first floor (mm) | Maximum of the peak accelerations of the floors ($m/s^2$) |
Non-isolated | 13.7 > 6 | 5.87 > 2.6478 |
Isolated | 2.84 < 6 | 2.03 < 2.6478 |
Table 3: Comparison of nonisolated and base isolated structure in terms of interstorey drifts and accelerations.
Last but not least, it is worth mentioning that the friction of the base isolator introduces additional damping to the structure. Higher friction values are desired for economical reasons, as smaller displacements on the isolation plate lead to cost savings. However, very high friction values tend to converge to the non-isolated structure, resulting in higher acceleration values and undesired effects. Therefore, there is a balance between the economy and safety of the structure. We conducted several simulations to estimate the optimum value for friction and corresponding re-centering error. The value for minimum re-centering error, which is the percentage error between the friction force (see equation (3)) and the spring force (see equation (2)) is obtained for $\mu=0.04$. The results of these simulations are tabulated in Table 4 below. Additionally, it can be observed that as the friction coefficient increases, the acceleration response of the structure and interstorey displacements increase, while the base plate displacement decreases.
Friction coefficient (μ) | Expected maximum acceleration (m/s2) | Expected maximum displacement of the base plate (mm) | Expected maximum interstorey drift (mm) | Recentering Error (%) |
|---|---|---|---|---|
| 0.02 | 0.8747 | 119.56 | 2.1 | 62.6 |
| 0.03 | 1.1011 | 93.92 | 2.1 | 28.59 |
| 0.04 | 1.3394 | 84.13 | 2.2 | 6.29 |
| 0.05 | 1.4625 | 78.78 | 2.3 | 41.89 |
0.06 | 1.6182 | 73.54 | 2.5 | 82.40 |
| 0.07 | 1.7557 | 70.07 | 2.7 | 123.34 |
Table 4: Mean maximum accelerations and displacements for different $\mu$ values and corresponding recentering error. The minimum is obtained with $\mu=0.04$.
6. Conclusion
In summary, this work presents the fundamental principles of base isolation, deriving the necessary equations for its application. Following this, the process of acquiring and preprocessing ground motion data for simulation purposes is demonstrated. Subsequently, the modeling of multi-degree-of-freedom systems with base isolators is discussed, with assumptions of Coulomb friction. Furthermore, the discussion is expanded to include a 2D model.
The study then compares the performance of structures with and without base isolation to assess the effectiveness of base isolators. It is evident that base isolation systems (also referred to as curved surface sliders, or CSS) are proven methods for effectively securing buildings against seismic events.
The modeling and simulation of multi-storey buildings with base isolation have shown significant improvements in structural performance. Non-isolated buildings under earthquake loading often exceed the limits permitted by Eurocode 8 by more than double, while CSS-isolated structures experience less than half the horizontal deflection permitted by EC8. Similar trends are observed for the maximum peak acceleration of floors, with CSS-isolated buildings experiencing only around a third of the acceleration compared to non-isolated structures.
These results highlight the effectiveness of CSSs in mitigating the impact of seismic events. However, there is a continual need for improvement and refinement of this technology, especially in developing thermo-mechanical models to address earthquakes with long duration. Engineering solutions that effectively enhance seismic resilience can significantly reduce the economic, social, and humanitarian impact of disasters.
In conclusion, the modeling and simulation of seismic protection systems demonstrate the significant role that curved surface sliders can play in improving safety in earthquake-prone regions.
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