A Comparative Analysis of International Standards on Curved Surface Isolators for Buildings

Abstract

This study presents a comprehensive comparative analysis of a hospital located in Costa Rica, examining the performance of sliding pendulum isolators under different international seismic design standards. The standards considered in this research include the U.S. code ASCE/SEI 7-22 and various European standards, namely EN 15129, EN 1337, and EN 1998-1. The case study employs the Equivalent Linear Analysis method, as prescribed by Eurocode 8, alongside the Equivalent Lateral Force procedure from ASCE/SEI 7-22. The seismic action is defined using the acceleration response spectrum from the Costa Rican Seismic Code (CSCR-10, 2010). However, certain limitations must be acknowledged when applying the equivalent linear analysis approach. One key restriction is that the isolation system must be modeled with equivalent viscoelastic behavior, which is feasible for sliding pendulum isolators. Despite being a simplified method, this approach proves valuable in the initial selection and optimization of an isolation system, particularly for practitioners. It is recommended that this method be applied as a preliminary step before performing more advanced nonlinear analyses. After determining the optimized parameters for the friction pendulum system, the detailed design of the isolators will be conducted following the provisions of the selected international standards. This process includes verifying compliance with key performance requirements such as self-recentering capability, type testing procedures, deformation verification, and partial load verification on the concrete pedestal, where the isolators are assumed to be installed. These requirements ensure that the isolation system meets the necessary structural performance criteria, providing reliable seismic protection while adhering to international engineering best practices.

1. Introduction

Earthquakes remain one of the most destructive natural hazards, with the potential to cause widespread loss of life, property damage, and long-term disruption to critical infrastructure. In seismically active regions, the development of resilient structural systems is a priority for safeguarding both human life and the post-disaster functionality of essential facilities. Among modern seismic protection strategies, seismic isolation has emerged as a highly effective approach for decoupling structures from ground shaking. By inserting flexible, energy-dissipating devices between the foundation and superstructure, isolation systems significantly reduce the seismic demand on the structure [1,2,3,4,5]. The use of Friction Pendulum Isolators (FPIs) has proven to be particularly effective in seismic isolation due to their ability to support vertical loads while simultaneously allowing lateral flexibility in the horizontal plane [6,7]. These isolators provide substantial energy dissipation through friction and possess a self-centering capability, which helps restore the structure to its original position after a seismic event. The fundamental mechanism of FPIs relies on a concave sliding surface and an articulated slider, which work together to generate a controlled pendulum motion, reducing seismic forces transmitted to the superstructure [8,9,10,11].

The effectiveness of seismic isolation has been unequivocally demonstrated through the outstanding performance of isolated structures in major earthquakes, such as the 1994 Northridge [12] and 1995 Hyogoken-Nanbu and Kobe events [12,13]. Conversely, the severe damage observed in buildings, infrastructure, and industrial facilities during seismic events, including the 2009 L’Aquila [14,15,16,17], 2012 Emilia [16,17,18,19] and 2016 earthquakes in Italy [16,19], the 1997/2000 Jabalpur [20,21,22] and 2001 Bhuj earthquakes in India [23,24,25], and the 2013 and 2016 earthquakes in New Zealand [26,27,28], highlighted the vulnerabilities of conventional construction techniques. Post-earthquake assessments revealed recurring failure patterns across multiple seismic events [16], indicating that many structures, including those made of reinforced concrete [16,29,30,31], precast elements [16,32,33], lightweight concrete/infill [34,35,36] and steel [16,37,38,39], were originally designed using outdated seismic provisions that did not adequately address modern seismic demands.

These observations have reinforced confidence in seismic isolation as a reliable protective strategy and validated analytical models predicting its performance. As a result, the adoption of isolation techniques has expanded, both for new constructions and retrofit applications [40,41,42]. Seismic isolation functions by incorporating flexible elements, such as elastomeric bearings, sliding interfaces, or rolling mechanisms, positioned between a structure’s superstructure and its foundation [43,44]. Often, these components are combined with damping devices to absorb and dissipate seismic energy, thereby lengthening the building’s natural period and reducing resonance effects with high-frequency ground motions. Recent advancements in seismic isolation have further extended its application to more flexible structures, such as silos [45,46], leading to reduced accelerations and displacements. This has allowed for the optimization of structural design, minimizing the dimensions of load-bearing elements, mitigating damage potential, and ensuring continued functionality post-earthquake, particularly for critical facilities housing essential services or sensitive equipment [47,48,49,50,51].

The core benefits of implementing seismic isolation in structural design, whether for new or existing buildings, can be summarized as follows:

• Enhanced flexibility and period shift: seismic isolation increases structural flexibility, effectively shifting the fundamental period of the building away from the high-energy frequency range of seismic ground motions. This shift significantly reduces seismic design forces, especially in structures with shorter natural periods. In contrast, structures with inherently longer periods experience a comparatively smaller effect. This flexibility is particularly advantageous for safeguarding non-structural components, such as mechanical systems [47,48,49,50,51] and precision instruments [52,53], which are highly susceptible to seismic accelerations.
• Controlled inelastic deformation: although seismic isolation increases overall structural displacements, it ensures that inelastic deformations occur primarily within the isolation system itself, preserving the integrity of the main structural and nonstructural components [47,48,49,50,51,52,53]. As a result, the primary structure remains within the elastic range even during strong ground motions, reducing the likelihood of significant damage and minimizing post-earthquake repair costs.
• Energy dissipation and improved damping: seismic isolation systems not only provide flexibility but also enhance energy dissipation, which is crucial for mitigating seismic forces. Some isolation devices exhibit inherent damping characteristics due to their material properties, while hybrid systems integrate additional damping mechanisms at the isolation interface to further attenuate seismic energy. By increasing damping, these systems help limit displacement demands on isolators and enhance the overall resilience and safety of the structure.

A wide range of isolation technologies is available in the market, each designed to fulfill the essential requirements of vertical load-bearing capacity, lateral flexibility, and energy dissipation efficiency [54]. The selection of an appropriate isolation device depends on several factors, including cost, availability, and the specific technical requirements dictated by the building’s location, function, and design constraints.

This research focuses specifically on FPIs, a widely utilized class of seismic isolation devices. Furthermore, this study presents a comparative analysis of international design standards governing the application of FPIs, using a case study of a hospital located in San José, Costa Rica. Given the varying seismic environments worldwide, different countries have established their own regulatory frameworks to ensure the effective implementation of seismic base isolation systems. In Europe, standards such as EN 15129:2018 [55], EN 1337-2:2004 [56], and the Eurocodes (EN 1998-1:2004—Eurocode 8, EC8) [57] provide specific guidelines for the design, testing, and application of FPIs. Likewise, in the United States, similar standards exist, including the Minimum Design Loads and Associated Criteria for Buildings and Other Structures (ASCE/SEI 7-22) [58] and the AASHTO Guide Specification for Seismic Isolation Design (AASHTO-GSID-14) [59].

While seismic isolation is widely used, its implementation is governed by national and international standards, each offering different approaches to design, analysis, and safety verification. Notably, ASCE/SEI 7-22, adopted in the United States, and Eurocode 8 (EN 1998-1 and EN 15129), adopted across Europe, present substantial methodological differences in how isolation systems are modeled, how damping and displacement demands are calculated, and how re-centering capability is ensured. These discrepancies can lead to significantly different design outcomes, even for the same structure. Despite the widespread adoption of both standards, comparative studies examining their implications on isolated system performance remain limited, particularly in the context of friction pendulum isolators.

Understanding and systematically comparing these regulatory frameworks is crucial for ensuring the efficient and reliable design of FPIs, particularly when adapting isolation strategies to different seismic hazard levels and construction practices. By examining the key provisions of each standard, this study aims to highlight their strengths, limitations, and practical implications, ultimately contributing to a more informed approach to seismic isolation system design across diverse global regulatory contexts.

2. Case Study Building and Seismic Action

This study examines a case involving a ten-story hospital building situated in San José, Costa Rica, designated as an essential facility. This designation highlights the hospital’s critical function in ensuring continuous medical services, particularly during and after seismic events. The structural analysis of the hospital was performed using ETABS (v.21) [60], a widely recognized structural analysis software. The hospital, covering a total area of approximately 4150 m², is designed as a reinforced concrete frame structure. The building has a total height of 35 m, with plan dimensions of 46.35 m in the $X$-direction and 93.72 m in the Y-direction. The building employs a dual system consisting of reinforced concrete columns and beams forming moment-resisting frames, with reinforced concrete slabs acting as rigid diaphragms to ensure effective in-plane distribution of lateral forces. The columns are predominantly rectangular and symmetrically reinforced, measuring 600 mm × 600 mm at the lower levels (basement to 3rd floor) and reducing to 500 mm × 500 mm from the 4th to the 10th floor. Longitudinal reinforcement consists of 12 to 16 bars of ϕ25 mm (Grade 500 MPa), arranged to provide balanced capacity under biaxial bending. Transverse reinforcement is provided in the form of closed stirrups and seismic hoops with ϕ10 mm diameter spaced at 100 mm centers near potential plastic hinge regions and 200 mm in the remaining regions, ensuring confinement as per ductility requirements. Beams span between columns and are generally 400 mm wide and 700 mm deep. They are reinforced with four to five top and three to four bottom bars of ϕ20 mm in typical spans, depending on the moment envelope. Stirrups of ϕ10 mm are spaced at 100 mm near supports and at 150–200 mm in midspan regions. Additional top bars are provided over intermediate supports to resist negative moments and maintain continuous reinforcement. All longitudinal bars are anchored with standard hooks or mechanical couplers, and lap splices are avoided in high-moment zones. The floor system is composed of 200 mm thick precast, prestressed hollow-core slabs with a cast-in-place topping of 60 mm reinforced with a light mesh (ϕ8 mm @ 150 mm in both directions). The slabs act as horizontal diaphragms and are mechanically connected to primary beams using cast-in-place concrete keys and shear connectors. Vertical elements are monolithically connected to the foundation, which is a 1.2 m thick reinforced concrete mat foundation designed to distribute loads evenly over variable subsoil conditions. The seismic weight at the level of the isolation interface is estimated to be approximately 746,673.25 kN. Figure 1 illustrates a three-dimensional representation of the hospital structure, modeled from the foundation to the roof level. The isolation system is incorporated at the first story, where the interface between the superstructure and the isolation units is defined.

Seismic action, also referred to as seismic hazard, is typically characterized using the acceleration response spectrum. While various seismic codes and regulations prescribe different methodologies for deriving this spectrum, the underlying principle remains consistent. For this case study, the seismic action was defined based on Costa Rica’s specific seismic conditions, despite the fact that international standards such as ASCE/SEI 7-22 [58] and EN 1998-1:2004 [57] also provide methodologies for estimating seismic action. Costa Rica is situated in Central America along the Pacific Ring of Fire and experiences significant seismic activity due to the subduction interactions between the Caribbean, Cocos, Nazca, and North American tectonic plates [61]. As a result, the region is prone to both shallow and intermediate-depth seismic events [62], with earthquakes ranging in magnitude from 5.5 to 8.0 ($M_w$) originating from interplate and intraplate sources [63].

The country has developed its own seismic code, known as the Costa Rican Seismic Code (CSCR-10 Rev. 2014—CFIA, 2010) [64], which has been in effect since 1974. Chapter 5 of the CSCR-10 outlines the procedure for calculating the seismic coefficient ($C$), which defines the horizontal seismic demand and corresponds to the spectral design acceleration for given levels of ductility and damping. The seismic coefficient is computed using the following equation [64]:

$$C={\displaystyle \frac{I{·a}_{\mathrm{ef}}·FED}{SR}}$$

(1)

where:

• $a_{\mathrm{ef}}$ represents the effective peak ground acceleration at the base of the structure, expressed as a fraction of gravitational acceleration ($g$). This value is obtained from Table 2.3 of the CSCR-10 [64], based on the seismic zone and the site conditions. The concept of effective peak acceleration originates from ACT 3-06 (1981) [65] and represents the spectral acceleration values within the period range of 0.1 to 0.5 s, where maximum spectral accelerations typically occur. It is determined by averaging the spectral acceleration ordinates at 5% damping and dividing by a factor of 2.5;
• $I$ is the importance factor, which is specified in Table 4.1 of CSCR-10 [64] based on the function and occupancy of the structure. This parameter ensures that essential facilities, such as hospitals, are designed to withstand higher seismic demands in accordance with the performance objectives stated in Section 4.1.b of the code [64];
• $FED$ is the dynamic spectral factor, which defines the shape of the acceleration spectrum based on site conditions, seismic zones, and the assigned global ductility level;
• $SR$ represents the overstrength factor, which accounts for the difference between the actual and nominal seismic resistance capacity of the structure. According to CSCR-10 [64], the overstrength factor reflects an inherent increase in structural capacity. Instead of directly comparing the actual resistance to the seismic demand, the code evaluates the nominal capacity of the structure against the demand reduced by the factor $SR$. This approach justifies the presence of $SR$ in the denominator of Equation (1).

To provide a comprehensive summary of the key assumptions and parameters used in defining seismic actions for this study,

Table 1. Assumptions for seismic parameters based on site-specific conditions in Costa Rica, used for developing the input spectra required for the design of the isolation system.

Parameter	Assumed Value
Effective peak ground acceleration $a_{\mathrm{ef}}$	0.36 $\mathrm{g}$
Importance factor $I$	1.25
Dynamic spectral factor $FED$	Table E.7 in CSCR-10 [64]
Overstrength factor $SR$	1.0

presents a concise overview of the selected values and their corresponding criteria.

Moving from the seismic coefficient ($C$ in Equation (1)), the response spectrum from the Costa Rican Seismic Code (CSCR-10) [64] is represented on a logarithmic scale in Figure 2. While the formulation and description of the response spectrum in CSCR-10 differ from those presented in ASCE/SEI 7-22 [58] and Eurocode 8 [57], the fundamental concept remains the same. However, significant differences exist in how these standards define the elastic response spectrum, particularly in terms of reference return periods and the anchoring of spectral ordinates used for the computation of the design spectrum. As discussed in [1,2,66], these variations stem primarily from the different approaches adopted by each standard in defining seismic hazard levels.

In Eurocode 8 [57], seismic action is specified for a reference exceedance probability of 10% in 50 years, which translates to a return period of 475 years. This value can be adjusted using the importance factor ($I$) to reflect the importance classification of structures. The peak ground acceleration (PGA) serves as the reference seismic intensity, also associated with an exceedance probability of 10% in 50 years. The importance factor is similarly based on a reference return period of 475 years, ensuring that structures are designed to meet the no-collapse requirement, meaning they should not experience either local or total failure under the design seismic action. The shape of the elastic response spectrum defined in Eurocode 8 is illustrated in Figure 3a.

In contrast, ASCE/SEI 7-22 [58], in Chapter 11 “Seismic Design Criteria”, defines the response spectrum using two different methods, as described in Section 11.4.5 of the same standard. The first approach relies on the multi-period design response spectrum, which provides a more detailed representation of the frequency content of design ground motions and is considered the preferred characterization of spectral response. The second approach, known as the two-period design response spectrum, offers a simplified representation based on seismic parameter values. Unless a site-specific ground motion study is performed, the two-period spectrum can be used for design purposes. Due to its simplicity and ease of application, this second method is adopted in this study, with Figure 3b presenting the corresponding two-period design response spectrum as described in ASCE/SEI 7-22 [58].

These differences in the definition of response spectra across CSCR-10, EC8, and ASCE/SEI 7-22 highlight the variation in seismic hazard characterization and design methodologies. While all three standards aim to achieve structural safety, their differences in reference return periods, spectral anchoring, and methodology for defining design ground motions can lead to variations in seismic demand predictions, ultimately affecting the design of base-isolated structures.

3. Design Procedures

In seismic isolation systems, two primary strategies are employed to reduce the impact of seismic forces on structures: increasing the natural period and enhancing energy dissipation (damping), as illustrated in Figure 4. These two mechanisms are fundamental in ensuring the effectiveness of a seismic isolation system. The natural period of the structure is extended by incorporating an isolation layer between the superstructure and substructure, effectively acting as a harmonic oscillator. This forces the superstructure to oscillate according to the natural frequency of the isolator, thereby reducing the transmission of high-frequency seismic energy. On the other hand, energy dissipation plays a critical role in seismic isolation by transforming the mechanical energy induced by seismic motion into heat. This heat generation results in localized temperature increases, necessitating dynamic testing to assess potential material degradation under cyclic loading. Seismic isolators primarily function as harmonic oscillators, classified into two main categories: Spring-based isolators with a characteristic stiffness constant $K$; pendulum-based isolators, where the restoring force is determined by the pendulum length $R$. Among these, FPIs are a widely used category of pendulum-based isolators. FPIs have four key functional characteristics. First, they provide lateral flexibility, enabling controlled horizontal displacement during seismic events. Second, they offer vertical load-bearing capacity, which ensures overall structural stability. Third, they have the self-centering capability, allowing the structure to return to its original position after shaking. Finally, they enable energy dissipation through friction, where the sliding interface converts kinetic energy into heat.

This study focuses primarily on single FPIs. However, it is important to note that the kinematic behavior of both single and double friction pendulum systems is essentially equivalent. The single pendulum (Figure 5) consists of a single sliding surface that provides lateral flexibility and energy dissipation through friction, with the restoring force governed by the curvature of the sliding surface. In contrast, the double pendulum (Figure 5) includes an internal articulated slider mechanism that allows for two sequential sliding surfaces, enabling greater displacement capacity and more complex hysteretic behavior. While the two systems differ in complexity and performance characteristics, their kinematic behavior is fundamentally equivalent, particularly under the assumptions adopted in the equivalent linear analysis applied in this research.

The key parameters defining FPIs include: equivalent radius ($R_{\mathrm{eq}}$ or $R$); dynamic coefficient of friction ($\mu$); maximum design displacement ($D$); seismic weight of the structure ($W$); effective equivalent stiffness ($K_{\mathrm{eff}}$); effective equivalent period ($T_{\mathrm{eff}}$) and damping that is an essential aspect of oscillatory systems, serving to attenuate, constrain, or completely suppress vibrations. In seismic isolation, equivalent viscous damping ($\xi$) is commonly used to approximate the behavior of nonlinear single-degree-of-freedom (SDOF) systems. This is completed by equating the energy dissipated in a nonlinear system to that of a linear system with an equivalent viscous damping ratio. For conventional reinforced concrete and steel structures, damping ratios are typically assumed to be 5% and 2%, respectively. Moreover, international seismic standards such as EC8 [57] and ASCE/SEI 7-22 [58] standardize their acceleration response spectra for a default damping value of 5% for building structures.

Based on the above key parameters, the allowable analytical procedures for evaluating base-isolated structures differ between European and U.S. standards, as outlined below:

• European Standard (EN 1998-1—Eurocode 8) [57]

• Equivalent Linear Analysis;
  • Simplified Linear Analysis;
  • Modal Simplified Linear Analysis;

• Nonlinear Time–History Analysis.

2.

United States Standard (ASCE/SEI 7-22) [58]

• Equivalent Lateral Force Procedure (ELF);
• Dynamic Analysis Procedure;
  • Response Spectrum Procedure;
  • Response History Procedure (Time–History Analysis).

For the scope of this study, we focus on the Equivalent Linear Analysis (ELA) approach. Specifically, we apply:

• The Simplified Linear Analysis method as per Eurocode 8 (EC8) [57].
• The Equivalent Lateral Force (ELF) Procedure as prescribed in ASCE/SEI 7-22 [58].

3.1. European Standard Approach

The European standard (EN 1998-1—Eurocode 8) [57] follows the ELA method for the design and assessment of seismically isolated structures. This approach relies on an iterative procedure, where an initial displacement assumption is made ($D_i$), and calculations are refined until the final displacement converges to the initial assumption. To achieve this convergence, it is necessary to determine the key mechanical parameters that characterize FPIs, including:

• Initial displacement $D_i$:

  $$D_i=400\mathrm{nm}$$

  (2)
• Equivalent stiffness ($K_{\mathrm{eff}}$), which governs the dynamic response of the isolation system (where $W$ is the seismic weight of the structure, equivalent radius ($R_{\mathrm{eq}}$ or $R$), $D_i$ the initial displacement in Equation (2), and $\mu$ the dynamic coefficient of friction):

  $$K_{\mathrm{eff}}=\mathrm{W}\left({\displaystyle \frac{1}{R}}+{\displaystyle \frac{\mu }{D_i}}\right)=233.34\mathrm{kN}/\mathrm{mm}$$

  (3)
• Equivalent stiffness ($T_{\mathrm{eff}}$), representing the effective oscillation period of the isolated structure:

  $$T_{\mathrm{eff}}=2\mathsf{\pi }\sqrt{{\displaystyle \frac{W}{g{K}_{\mathrm{eff}}}}}=3.59\sec$$

  (4)
• Equivalent viscous damping (${\xi }_{\mathrm{eff}}$), which accounts for energy dissipation in the system:

  $${\xi }_{\mathrm{eff}}=\mathrm{m}\mathrm{i}\mathrm{n}\left({\displaystyle \frac{2\mu }{\pi \left(\mu +\frac{D_i}{R}\right)}}\right)=12.73\%$$

  (5)
• Reduced spectral acceleration, adjusted by the damping factor ($\eta$), to incorporate the effects of increased damping in the isolation system:

  $$\eta =\mathrm{m}\mathrm{a}\mathrm{x}\left(\sqrt{{\displaystyle \frac{10}{5+\xi }}},0.55\right)=0.75$$

  (6)

This expression is derived by equating the energy dissipated per cycle by frictional sliding to the energy dissipated in a linear viscous damper. The formula effectively captures the hysteretic energy dissipation of the isolator in terms of an equivalent damping ratio that can be used with linear response spectra. The radius $R$ controls the restoring stiffness, while the coefficient of friction $\mu$ directly governs the level of energy dissipation, with higher values of $\mu$ resulting in greater damping.

Since the CSCR-10 response spectrum does not provide a direct mathematical equation to estimate spectral acceleration ($S_a$) for a given period, unlike the EC8 [57] and ASCE/SEI 7-22 [58] standards, an approximation method is required for regions of interest. To address this limitation, a curve-fitting tools has been developed to derive an approximate equation for spectral acceleration, ensuring accurate interpolation at the equivalent period of interest. This approach allows for a practical estimation of $S_a\left(T\right)$ in regions where the response spectrum lacks explicit analytical formulation. Figure 6 presents the CSCR-10 [64] response spectrum for Zone III, considering soil type S3, ductility factor $\mu =2$, and overstrength factor $SR=1$. To enhance clarity, Figure 6a provides a zoomed-in view of the portion of the spectrum where the natural period is higher, along with the approximate equations (Figure 6b) corresponding to the constant velocity and constant displacement branches of the spectrum. This approach ensures that the spectral acceleration estimation remains consistent with engineering standards, providing reliable input for further structural analysis.

Therefore, the seismic coefficient ($C$), which corresponds to the spectral acceleration, can be determined based on the required period in the response spectrum, considering the previously defined seismic parameters. The spectral acceleration is estimated as a function of the selected period, ensuring consistency with the response spectrum and seismic design criteria:

$$0.5s\le T_{\mathrm{eff}}\le 3.78s \to C=0.3219x^{-1}$$

(7)

$$3.78s\le T_{\mathrm{eff}}\le 10s \to C=1.2274x^{-2.007}$$

(8)

where $x$ is the natural period variable. For the first iteration, since the period is less than 3.78 s, the acceleration can be determined using the approximate equation corresponding to the constant velocity region of the response spectrum:

$$C=0.3219x^{-1}=0.66{\displaystyle \frac{\mathrm{m}}{{\mathrm{s}\mathrm{e}\mathrm{c}}^2}}\approx 0.0673 g$$

(9)

As previously mentioned, one of the key objectives in reducing seismic action is to increase damping, thereby enhancing energy dissipation. To account for this, the reduced spectral acceleration is obtained by applying the damping factor as a multiplier. From this, the maximum displacement $D_{\max }$ and the maximum horizontal force $F_{\mathrm{m}\mathrm{a}\mathrm{x}}$ can be derived:

$$A=C·\eta =0.37{\displaystyle \frac{\mathrm{m}}{{\mathrm{s}\mathrm{e}\mathrm{c}}^2}} \approx 0.037 g$$

(10)

$$D_{\max }={\left({\displaystyle \frac{T_{\mathrm{e}\mathrm{f}\mathrm{f}}}{2\pi }}\right)}^2=215.46 \mathrm{m}\mathrm{m}$$

(11)

$$F_{\mathrm{m}\mathrm{a}\mathrm{x}}=W\left({\displaystyle \frac{D}{R}}+\mu \right)=5886.56 \mathrm{k}\mathrm{N}$$

(12)

Since this is an iterative procedure, the calculated displacement must converge with the initially assumed displacement, as mentioned at the beginning of this section. After several iterations, convergence is achieved, and the resulting values are presented and compared across different codes in

Table 2. Comparison between the European standard (EC8) and the American standard (ASCE/SEI 7-22) in terms of the key parameters governing isolator design and the percentage differences observed.

Parameter	Eurocode 8	ASCE/SEI 7-22	[%]
Displacement $D_i$ [mm]	136.62	157.23	15.35
Equivalent stiffness $K_{\mathrm{eff}}$ [kN/mm]	323.60	305.39	5.63
Equivalent period $T_{\mathrm{e}\mathrm{f}\mathrm{f}}$ [sec]	3.05	3.14	2.95
Equivalent viscous damping ${\xi }_{\mathrm{eff}}$ [%]	26.94	24.75	8.13
Damping factor $B_M$	0.56	1.59	12.30
Acceleration $A$	0.059	0.064	8.62
Maximum displacement $D_{\max }$ [mm]	136.32	157.23	15.35
Maximum horizontal force $F_{\mathrm{m}\mathrm{a}\mathrm{x}}$ [kN]	44,113.84	48,017.53	8.85

.

3.2. US Standard Approach

The American standard ASCE/SEI 7-22 [58] adopts the ELF procedure, a method used to estimate seismic forces acting on a structure based on its fundamental period and site-specific seismic parameters. This approach follows a similar procedural sequence to that of the European standard (EC8) [57], ensuring consistency in methodology. The fundamental relationships outlined in Equations (2)–(9) remain applicable in this context. The procedure begins with an updated formulation in Equation (10), which accounts for the specific spectral acceleration, damping adjustments, and effective period of the isolated structure as prescribed by ASCE/SEI 7-22:

$$A={\displaystyle \frac{C}{B_M}}=0.895{\displaystyle \frac{\mathrm{m}}{{\mathrm{s}\mathrm{e}\mathrm{c}}^2}} \approx 0.091 \mathrm{g}$$

(13)

$$D_{\max }={\left({\displaystyle \frac{T_{\mathrm{e}\mathrm{f}\mathrm{f}}}{2\pi }}\right)}^2=229.17 \mathrm{m}\mathrm{m}$$

(14)

$$F_{\mathrm{m}\mathrm{a}\mathrm{x}}=W\left({\displaystyle \frac{D}{R}}+\mu \right)=73206.57 \mathrm{k}\mathrm{N}$$

(15)

where the damping factor $B_M=0.982$ derived from ASCE/SEI 7-22 [58].Since this is an iterative procedure, the calculated displacement must converge with the initially assumed displacement, as mentioned at the beginning of this section. After several iterations, convergence is achieved, and the resulting values are presented and compared across different codes in Table 2.

3.3. Bounding Considerations

According to ASCE/SEI 7-22 Appendix 17-A (Section 17.2.1), the modification of isolator design properties, such as the friction coefficient, is required for bounding analyses using Upper Bound Design Properties (UBDP) and Lower Bound Design Properties (LBDP). Similarly, EN 15129 (Clause 6.6.3.3.3) stipulates that variation of mechanical properties must be accounted for in the analysis to ensure safety under expected uncertainties due to aging, temperature, and loading rate. These provisions provide the basis for applying friction modification factors (e.g., ${\lambda }_{\max }$ and ${\lambda }_{\min }$) as used in the case study to represent realistic bounds on isolator behavior under seismic loading. It is important to emphasize that the friction coefficient values used in seismic isolation design represent nominal (average) values. In real-world conditions, the dynamic coefficient of friction can vary due to several factors. These include temperature changes, material aging, pressure applied to the sliding surface, and the number of dynamic loading cycles [8]. To account for these variations, the friction coefficient is adjusted using property modification factors (${\lambda }_{\max }$ and ${\lambda }_{\min }$), which define the upper and lower bounds of the friction coefficient. This ensures a more robust and realistic evaluation of the seismic isolation system’s behavior. For this case study, the UBDP and LBDP were determined based on experimental test results [9,10,11], ensuring high material quality and performance consistency. These values were selected following the European approach (EC8 [57] in case of ELA). In this analysis, only the coefficient of friction ($\mu$) is modified by the property factors:

• Upper Bound Design Properties—UBDP: $\mu$ = 2.5% with ${\lambda }_{\max }$ = 4%;
• Lower Bound Design Properties—LBDP: $\mu$ = 2.5%, with ${\lambda }_{\min }$ = 2%.

The final results are presented in

Table 3. Comparison between Upper Bound Design Properties and Lower Bound Design Properties in the framework of the European standard (EC8) in terms of the key parameters governing isolator design.

Parameter	Eurocode 8	UBDP	LBDP
Displacement $D_i$ [mm]	136.62	113.72	163.11
Equivalent stiffness $K_{\mathrm{eff}}$ [kN/mm]	323.60	449.3	278.22
Equivalent period $T_{\mathrm{e}\mathrm{f}\mathrm{f}}$ [sec]	3.05	2.59	3.29
Equivalent viscous damping ${\xi }_{\mathrm{eff}}$ [%]	26.94	37.31	20.95
Damping factor $B_M$	0.56	0.55	0.62
Acceleration $A$	0.059	0.068	0.061
Maximum displacement $D_{\max }$ [mm]	136.32	113.72	163.11
Maximum horizontal force $F_{\mathrm{m}\mathrm{a}\mathrm{x}}$ [kN]	44,113.84	51,094.24	45,380.43

after performing an iterative analysis, ensuring convergence between the initial displacement $D_i$ and the maximum displacement $D_{\max }$, following the same procedure used for the nominal friction coefficient case.

It is also important to assess whether the observed percentage differences across standards hold practical engineering relevance. For example, the 15.35% difference in displacement estimates between EC8 and ASCE/SEI 7-22 (as shown in Table 2) is consistent with the 15% displacement amplification required by ASCE/SEI 7-22 to account for accidental torsional effects. Moreover, Eurocode 8 allows variability in mechanical properties of isolators, including equivalent stiffness and damping, up to ±20% through property modification factors [EN 15129, Clause 6.3.3]. Given this regulatory context, the percentage differences reported in Table 2 and Table 3 fall within the range of engineering tolerances accepted by international standards.

Historically, similar levels of variability in isolation system performance have been documented in both full-scale experiments and post-earthquake assessments of isolated buildings [12,54]. Therefore, while the differences are numerically significant, they are not unusual nor necessarily indicative of poor design and should instead be considered as expected deviations arising from different underlying design philosophies and approximations.

4. Discussion

The maximum displacement obtained from the ELA is initially estimated at the center of mass of the structure, considering earthquake excitation in a single direction. However, for design purposes, the total displacement must account for the combination of earthquake effects in both orthogonal directions. As per standard practice, this is completed by adding 30% of the displacement in the perpendicular direction to the main directional displacement. For the structural model, the calculated displacements are $D_{\mathrm{x}}=154.55$ mm and $D_{\mathrm{y}}=139.21$ mm. A key advantage of FPIs compared to other isolation systems, such as High-Damping Lead Rubber Bearings (HDRBs), is their inherent ability to ensure that the center of mass and the center of stiffness always coincide. This is because the stiffness of FPIs is directly proportional to the supported weight, ensuring automatic alignment with the building’s mass distribution. In contrast, HDRBs require careful design adjustments to ensure that the gravity center of the building and the stiffness centroid of the isolators are aligned. If they are not, accidental torsional effects may arise, necessitating additional design considerations. To account for such torsional effects, ASCE/SEI 7-22 [58] requires a minimum amplification of 15% on the maximum displacement. Therefore, the maximum design displacement is computed as:

$$\begin{gathered} D_{\mathrm{E}\mathrm{d}.\mathrm{x},\mathrm{m}\mathrm{a}\mathrm{x}}=\sqrt{{\left(D_{\mathrm{x}}\right)}^2+{\left({0.3·D}_{\mathrm{y}}\right)}^2}+D_{\mathrm{x}}·0.15=183.13\mathrm{mm} \\ {D}_{\mathrm{E}\mathrm{d}.\mathrm{y},\mathrm{m}\mathrm{a}\mathrm{x}}=\sqrt{{\left(D_{\mathrm{y}}\right)}^2+{\left({0.3·D}_{\mathrm{x}}\right)}^2}+D_{\mathrm{y}}·0.15=168.51\mathrm{mm} \end{gathered}$$

It is important to note that Eurocode standards do not explicitly require displacement amplification to account for accidental torsion. However, in this study, the ASCE/SEI 7-22 approach has been adopted to ensure a more conservative design.

According to the above findings, an essential requirement for any seismic isolation system is its self-centering capability, also referred to as the restoring force in U.S. design standards. This characteristic is crucial to prevent significant residual displacements after an earthquake, ensuring that the structure returns to its original position. If excessive permanent deformations remain, the functionality of the structure may be compromised, and the maximum displacement capacity of the isolators could be exceeded, potentially leading to structural failure [67]. All international seismic isolation standards mandate that a structure must return to its initial position (or close to it) after an earthquake. However, the European (EN 15129) [55] and American (ASCE/SEI 7-22) [58] standards adopt fundamentally different approaches to addressing the recentering capability of seismic isolators. These differences are a key aspect of seismic isolation design and require careful consideration when comparing design methodologies across different regulatory frameworks.

The re-centering capability of seismic isolation systems is a fundamental performance requirement that ensures the structure returns to its original position after an earthquake, minimizing residual displacements and preserving post-event functionality. In essence, re-centering reflects the system’s ability to restore equilibrium without requiring external intervention. This property is particularly critical for essential facilities, such as hospitals, where operability after a seismic event is vital.

In base isolation systems, re-centering is achieved through the restoring force generated by the geometry of the isolator (e.g., the curvature in sliding systems) or the elasticity of the materials (e.g., in elastomeric bearings). The primary parameters influencing re-centering are the radius of curvature in pendulum-type isolators, the friction coefficient, which opposes re-centering, and the displacement demand imposed by seismic loading. The ASCE/SEI 7-22 standard defines a minimum requirement for restoring force by stipulating that, at the design displacement, the restoring force must exceed the restoring force at 50% displacement by at least $\mathrm{W}$/40, where $\mathrm{W}$ is the seismic weight. This criterion, while simple and enforceable, does not explicitly account for the effects of friction, which can significantly hinder the re-centering behavior in systems with high frictional resistance. On the other hand, the European standard EN 15129 introduces a more refined approach based on the energy balance principle, specifically requiring that the reversibly stored elastic energy be at least 25% of the hysteretically dissipated energy. This condition ensures that even in systems with substantial energy dissipation, a sufficient elastic restoring force remains available to bring the structure back toward its original position. In friction-based isolators, re-centering capability depends on the balance between the geometrically induced restoring force and the opposing frictional resistance. While low-friction systems tend to exhibit excellent re-centering performance, high-friction systems may experience permanent offsets unless carefully controlled. Therefore, it is crucial to assess this performance aspect not only through force-based checks but also via energy-based evaluations, particularly in cases involving high friction coefficients or complex loading conditions. In this study, re-centering capability has been carefully evaluated under both code frameworks. The results suggest that while both standards aim to prevent large residual displacements, the energy-based approach adopted by EN 15129 offers a more transparent and physically consistent methodology, especially for isolators with significant nonlinearity or frictional behavior. Conversely, the ASCE/SEI 7-22’s restoring force criterion may lead to underestimation of residual drift, particularly in systems where friction dominates the response.

In U.S. seismic design standards, the restoring force of an isolation system is assumed to depend on three key parameters: the isolated structure’s fundamental period; the yield friction level of the isolator; the yield displacement of the isolation system. The ASCE/SEI 7-22 specifies that the restoring force at the design displacement must be at least $W$/40 greater than the restoring force at 50% of the design displacement, where $W$ represents the total seismic weight of the structure. This ensures that the isolation system possesses adequate self-centering capability, minimizing residual displacements after an earthquake. Similarly, the AASHTO Guide Specifications for Seismic Isolation Design (AASHTO-GSID-14) [59] imposes comparable criteria, reinforcing the necessity of a sufficient restoring force to prevent excessive permanent deformations. One of the primary requirements of this standard is to guarantee that the isolation system can return the structure to its near-original position post-earthquake, thereby preserving the functionality and integrity of the building:

• The isolation system must be designed to generate a lateral restoring force such that the period corresponding to its tangent stiffness, at any displacement up to the total design displacement, remains below 6 s:

  $$T=2\pi \sqrt{{\displaystyle \frac{R}{g}}}<6 \sec \cong R<8900 \mathrm{mm}$$
• The restoring force must be greater than the restoring force at 50% of the design displacement by at least $W$/80, where $W$ represents the seismic weight. For a sliding pendulum isolator, the variation in force is given by:

  $$\mathsf{\Delta }F=K·D$$

  where $D$ is the design displacement and $K$ the lateral stiffness of the frictionless pendulum base isolator. Therefore, by the previous requirement it may be satisfied that:

  $$\begin{gathered} \mathsf{\Delta }F=K·D·0.5 \ge {\displaystyle \frac{W}{80}} \\ \mathsf{\Delta }F={\displaystyle \frac{W·D}{R·2}} \ge {\displaystyle \frac{W}{80}} \end{gathered}$$

An equivalent requirement can be derived based on the equivalent radius ($R$) from the previous relation:

$$\begin{gathered} {\displaystyle \frac{W·D}{R·2}} \ge {\displaystyle \frac{W}{80}}\equiv {\displaystyle \frac{80·W·D}{W·2}} \ge R \\ 40·D \ge R \end{gathered}$$

In the case of ASCE/SEI 7-22, the restoring force at the design displacement must be greater than the restoring force at 50% of the design displacement by at least W/40. This requirement is determined using the same procedure:

$$20·D \ge R$$

The EN 15129 [55] approach differs significantly as it is based on an energy-based methodology. This approach was originally proposed in the theoretical studies in [68], where over 100 time–history analyses of base-isolated structures utilizing various types of isolators were conducted. It is also important to note that energy dissipation and self-centering capability are inherently opposing functions. Their relative significance primarily depends on the specific case under examination, as highlighted in [68]. The energy balance approach in seismic isolation design is based on the following fundamental expression:

$$E_i=E_S+E_H+E_V$$

(16)

where $E_i$ represents the mechanical energy transferred to the structure due to seismic excitation; $E_S$ is the reversibly stored energy (elastic strain energy and potential energy) within the isolation system and any structural elements influencing its response; $E_H$ accounts for the energy dissipated through hysteretic deformation or friction within the isolators; and $E_V$ denotes the energy dissipated through viscous damping mechanisms.

According to EN 15129 [55], the re-centering capability requirement is applicable only when using the ELA. The standard mandates that the stored elastic energy ($E_S$) must satisfy the following condition relative to the energy dissipated by hysteretic mechanisms ($E_H$):

$$E_S\ge 0.25E_H$$

(17)

This requirement ensures that the isolation system retains sufficient restoring force, preventing excessive residual displacements after an earthquake. By maintaining an adequate balance between stored and dissipated energy, the structure remains functional and returns to its original position, preserving the effectiveness of the isolation system.

The elastically stored energy ($E_S$) and the energy ($E_H$) dissipated through hysteretic deformation or friction for the sliding pendulum isolator can be expressed, respectively, as follows:

$$E_S={\displaystyle \frac{F·D}{2}}={\displaystyle \frac{R·D·D}{2}}={\displaystyle \frac{W·D^2}{R·2}}$$

(18)

$$E_H=\mu ·W·D$$

(19)

and by proper substitution into Equation (17):

$$E_S\ge 0.25E_H \equiv {\displaystyle \frac{2·D}{R}}\ge \mu$$

(20)

This implies that the energetic approach outlined in EN 15129 [55] imposes a limitation on the friction coefficient of sliding pendulum isolators, whereas US standards do not address this aspect, as they follow a different approach. After analyzing both standards in terms of recentering capability, considered as restoring force in the case of ASCE/SEI 7-22, the verifications for the given case study ($D$ = 200 mm, $R$ = 4000 mm, and $\mu$ = 2.5%) are as follows:

$$\mathrm{ASCE} 7/22 \mathsf{\Delta }F={\displaystyle \frac{W·D}{R·2}} \ge {\displaystyle \frac{W}{40}} \to 20·D\ge R \to 4000 \mathrm{m}\mathrm{m}\ge 4000 \mathrm{m}\mathrm{m}$$

$$\mathrm{E}\mathrm{N} 15129 E_S\ge 0.25E_H \to {\displaystyle \frac{2·D}{R}}\ge \mu \to 10\%\ge 2.5\%$$

5. Conclusions

This research presents a comprehensive comparative analysis between two internationally recognized seismic design codes, Eurocode 8 (EN 15129) and ASCE/SEI 7-22, specifically focusing on their application to seismically isolated structures. The study objectively evaluates each code’s approach to base isolation design, highlighting both its strengths and limitations. The findings provide valuable insights into how different engineering assumptions influence seismic performance predictions and the subsequent design choices for base-isolated buildings.

One of the most critical differences identified in this study pertains to re-centering capability, a fundamental requirement in seismic isolation design. The European standard (EN 15129) adopts an energy-based approach, where the re-centering capability is inherently linked to the level of friction. This implies that as friction increases, the system must store more elastic energy to ensure successful re-centering. In contrast, the ASCE/SEI 7-22 standard determines re-centering solely based on the isolator’s radius, without considering the influence of frictional resistance. This divergence raises significant concerns, particularly in high-friction scenarios where the ASCE model may overestimate the ability of an isolator to return to its original position. While a frictionless system would re-center automatically, the presence of friction can make re-centering difficult or even impossible, a factor that ASCE/SEI 7-22 does not fully account for in its framework.

Additionally, the comparison revealed a systematic difference of approximately ±12% in the values of the damping reduction factor ($\eta$) and its inverse (1/$B_M$) between the two codes. This difference is directly related to the higher displacements and accelerations observed when applying the ASCE/SEI 7-22 methodology. Such discrepancies emphasize the sensitivity of seismic response predictions to the assumptions embedded within each standard. The ASCE code, by yielding higher displacement and acceleration estimates, tends to lean toward a more conservative design philosophy. However, this conservatism may lead to increased structural costs or suboptimal design choices in cases where excessive displacement predictions result in over-designed systems that may not reflect the actual seismic demands on the structure.

Beyond numerical differences, this study highlights the fundamental philosophical distinctions between the two codes. Eurocode 8 integrates friction into its design approach, recognizing its effect on system behavior, while ASCE/SEI 7-22 assumes an idealized restoring force mechanism. These contrasting methodologies underscore the need for engineers to critically assess which framework best aligns with the specific site conditions, structural characteristics, and isolation system used in a given project.

From a practical perspective, the findings of this study emphasize that choosing between EN 15129 and ASCE/SEI 7-22 should not be based solely on regulatory compliance but rather on a thorough understanding of the fundamental principles underlying each approach. Designers must carefully consider whether the ASCE/SEI 7-22’s higher displacement and acceleration estimates, coupled with its neglect of friction in re-centering calculations, align with the practical realities of seismic isolation system performance. Conversely, the Eurocode approach, while more explicit in its treatment of friction and damping, may still require careful validation through advanced nonlinear analyses to ensure its applicability to specific seismic isolation configurations.

About possible future research directions, while this study has provided valuable insights into the differences between ASCE/SEI 7-22 and EN 15129, further research is necessary to:

• Validate these findings through full-scale experimental testing of isolated structures designed according to each standard, providing empirical data on re-centering behavior and displacement demands;
• Investigate the implications of different damping models on seismic response, particularly in highly damped systems where standard assumptions may no longer be valid;
• Extend the comparison to include other seismic isolation technologies, such as hybrid isolators and nonlinear time–history analysis approaches, to evaluate their impact on seismic performance predictions.

Specifically, the comparative analysis reveals that the maximum design displacement estimated using ASCE/SEI 7-22 is approximately 15% higher than that derived using Eurocode 8. Similarly, the equivalent damping values differ by nearly 8%, while the equivalent period estimates are within 3% of each other. These variations translate into an 8.9% higher base shear force when using the American standard, emphasizing its more conservative nature. Furthermore, the analysis of bounding properties showed that variations in the coefficient of friction could lead to displacement differences up to 49 mm, reinforcing the importance of considering upper and lower bound behavior in isolation system design. These results highlight how the selection of a specific standard can influence not only the technical performance but also the overall design philosophy and cost-efficiency of seismically isolated structures.

While the ELA method provides a convenient and computationally efficient approach for the preliminary design of base-isolated structures, it presents notable limitations when applied to complex seismic scenarios and certain structural configurations. The fundamental assumption behind ELA is that nonlinear hysteretic behavior—such as that exhibited by friction pendulum isolators—can be adequately represented by an equivalent viscous damping ratio. This simplification may yield acceptable results under moderate, far-field seismic motions; however, its accuracy deteriorates under more demanding conditions. In particular, ground motions characterized by near-fault effects or velocity pulses often produce abrupt energy input and large displacements, which ELA does not fully capture. Furthermore, structural systems with pronounced flexibility, irregular stiffness or mass distribution, or soft-story characteristics may respond in ways that deviate significantly from the linear assumptions embedded in the ELA framework. In such cases, the interaction between the isolation system and the superstructure becomes more complex, potentially activating higher modes and generating torsional effects not accounted for in linear analysis.

Another source of uncertainty in ELA arises from the estimation of equivalent damping. Since spectral accelerations are sensitive to the assumed damping ratio, even small deviations, such as the 8% difference reported in this study, can result in non-negligible changes in predicted displacements and base shear demands. For instance, our comparative analysis between EC8 and ASCE/SEI 7-22 reveals displacement differences of approximately 15%, largely influenced by the treatment of damping. These discrepancies, while within acceptable engineering tolerances, underscore the inherent limitations of simplified methods. As such, ELA should be viewed primarily as a tool for initial sizing and design iteration. For final validation, especially in high-importance structures or in regions with complex seismic hazards, more advanced methods such as Nonlinear Time History Analysis (NLTHA) are essential. In a related study by the authors [42], it was shown that ELA may underpredict displacement demands by over 20% when compared to NLTHA under pulse-type ground motions. This highlights the importance of supplementing simplified procedures with more refined nonlinear analyses to ensure a comprehensive and accurate assessment of seismic performance.

Ultimately, this study underscores that the selection of a seismic isolation design standard is not merely a regulatory decision but a strategic choice that must be informed by the specific engineering requirements of a project. The differences in damping reduction, displacement predictions, and re-centering assumptions must be carefully considered to ensure that the selected approach provides both safety and efficiency in real-world seismic events. By acknowledging and addressing the strengths and weaknesses of each methodology, engineers can make more informed decisions that lead to resilient and cost-effective seismically isolated structures.