1 Background

Seismic engineering has progressed quickly over the last 50 years, owing to the various experiments employed to study and clarify the basic response mechanisms of different structures at different levels of seismic excitation. The experimental observations have been used to develop numerical models and extend the knowledge gained through experiments, leading to improved design codes.

Despite the extensive progress in earthquake engineering, there are still several issues that require further experimental and analytical studies. One is the seismic response of medium- to high-rise reinforced concrete (RC) buildings, which exhibit unique responses compared with lower low-rise structures. Experiments dealing with the seismic response of such buildings have mainly focused on the response of individual structural components or substructures. The tests of entire structures are rare and have typically been performed on a small scale because they are costly; they require capable technical equipment and highly trained personnel, which are only available in the largest testing centres in the world. Thus, tests have generally been conducted based on certain assumptions, limiting the scope of the studies. For example, owing to the reduced scale, some properties of the specimens have been distorted, demanding proper interpretations of the results and often requiring more assumptions. The full-scale experiments on seismically isolated mid-rise buildings are even rarer.

Past earthquakes (e.g., in Chile in 2010) have also revealed the lack of knowledge concerning the seismic response of mid- and high-rise buildings. Numerous issues, such as the seismic response of RC walls, dual structures, RC joints, the effective width of RC slabs, etc., demand more attention and research.

Notably, it is not clear how effective the various numerical models may be for analysing seismic responses in mid- to high-rise structures or how appropriate the design requirements may be in different design standards, let alone when and how they should be updated.

2 Objective and scope

In 2015, unique full-scale shaking table tests of 10-story buildings were performed at the world’s largest and most advanced shake table facility, the E-Defense research centre in Japan. Such tests had never been performed before. Two sets of experiments were carried out, one on the structure using classical foundations and one on the base-isolated structure using the base-slip mechanism. The heavily instrumented specimens (654 data channels) provided comprehensive information about the seismic response of the buildings and their structural components (e.g., beams, columns, slabs, beam-column joints, walls, etc.).

In 2019, an international research team was established to analyse the response of the tested buildings. The members have been addressing various issues, which are overviewed in the next section, and the outcomes of that work are presented in this Special Issue. The contributions of research teams from Japan, South Korea, the USA, Taiwan, Italy, Slovenia, and China, enabled a balanced discussion of different numerical solutions and standards used worldwide.

Considering the results, the range of applicability and shortcomings of current numerical models are assessed for the frame and dual structural systems, including various numerical models of RC beams, columns, joints, walls, slabs, and base-slip isolation devices. Additionally, possible model improvements and directions for future research are identified. This Special Issue presents the observations related to system-level behaviour and its 3D modelling. Several shortcomings concerning the requirements of different design codes are presented, and improvements are proposed.

3 Overview of the contributions

This Special Issue includes nine papers, starting with the paper that initially describes the experiments and several observations regarding the response (Sect. 3.1). In the following five papers, various models for the tested structures are presented, and different parameters influencing the response are discussed. The last three papers are mainly focused on specific aspects, including the response of the beam-column joints (BCJs), the effective width of the slabs, the shear-force amplification owing to higher vibration modes, and the requirements of different codes related to these issues.

In this section, an overview of the numerical models used for specific structural elements is followed by proposals for their modifications and an overview of other modelling assumptions that require an explanation and discussion. Numerical models used for BCJs, beams and columns, walls, slabs, isolation devices used in the tested building, and viscous damping are presented in Sect. 3.2–3.7.

Most of the presented studies have predicted the maximum response quantities with reasonable accuracy, particularly the maximum top displacements and maximum drifts, using the standard parameters of the employed numerical models. However, the demand distribution over the height of the building was estimated with a wide range of accuracy. The response and modelling of BCJs significantly influenced this distribution, but the response also depended on the ratio of the stiffness and the strength of BCJs versus beams, columns, and walls, as well as the ratio of the energy dissipated in these structural elements. Important parameters that influenced the response are summarised in Sect. 3.8.

3.1 Tested buildings and the observed response

The experiments, which were the focal point of all the studies considered in this Special Issue, are described in detail by Kang et al. 2023. The tests of a full-scale 10-story RC building were performed considering different boundary conditions at the foundations: (a) a base-isolated system and (b) a conventionally fixed building. The total height of the building was 27.45 m, and the typical floor dimensions were 13.5 m x 9.5 m. The structural system along the longer floor side (i.e., frame direction) consisted of RC frames. In the perpendicular direction (i.e., wall direction), a dual structural system was employed, consisting of RC walls extending from the basement to the seventh floor and RC columns and beams extending for the entire height of the building.

The primary aims of the tests were to evaluate and define the appropriate numerical models and design procedures, to support the development of advanced technologies for seismic isolation based on cast-iron plates, and to compare the seismic response of isolated and conventional buildings.

Two structures were tested. First, the building supported using a free-standing base-sliding system consisting of 16 cast-iron plates was subjected to a series of seismic excitations with increasing intensities. The isolation device was designed considering a friction coefficient of 0.2–0.25. After these tests, the isolation devices were removed, the building was fixed to the foundations, and another series of tests on the conventionally fixed building were performed.

The tested building was designed according to the Architectural Institute of Japan (AIJ) standard for the design of RC structures (AIJ 2010) and the Technological standard for building structures from 2007 (MLIT 2010). The design was conducted in two phases. First, the allowable stress design was performed considering a shear-force coefficient of 0.2. Then, a detailed analysis was performed considering a specific level of lateral load capacity. The seismic forces were reduced using a structural characteristic coefficient Ds (the parameter inverse to the response reduction factor R and the behaviour factor q used in USA and Europe) of 0.30–0.35 in the frame direction. In the wall direction, Ds values in the range of 0.35–0.40 and the value of 0.3 were considered in the bottom seventh floors and the rest of the building, respectively.

Both buildings were excited based on the accelerations recorded at the Japan Meteorological Agency (JMA) Kobe observatory during the Kobe earthquake in 1995. Three components were considered: the north-south component with a maximum acceleration of 8.18 m/s2, the east-west component with a maximum acceleration of 6.17 m/s2, and the vertical component with a maximum acceleration of 3.32 m/s2. In both the isolated and conventional building, the intensity of the imposed seismic excitation was gradually increased: 10%, 25%, 50%, and 100% of the acceleration recorded at JMA Kobe. The conventional building was subjected to an additional excitation of 60% JMA Kobe to examine the aftershock response.

The isolated building only exhibited slight cracking, and the response was predominantly elastic. On the contrary, the conventional structure was considerably damaged, particularly in the frame direction. Significant damage was observed in weak BCJs, particularly on the 3rd − 5th floors. Columns and beams at bottom stories also exhibited nonlinear deformations but were notably smaller than those in the joints. The damage was less severe in the wall direction but was still significant, mainly localised at the bottom of the walls and columns.

The applied isolation devices significantly reduced the maximum story drifts and shear forces in both directions. At 100% JMA Kobe, the maximum story drifts were 0.3% and 0.6% in the wall and frame directions, respectively. In the conventional building, similar drifts were observed at 25% JMA Kobe. At 100% JMA Kobe, the conventional building exhibited 1.5% and 3.05% drift in the wall and frame directions, respectively. In the isolated building, the maximum story base shear forces were reduced to 40% and 60% of those detected in the wall and the frame direction of the conventional structure.

Considerable sliding of the isolated building was observed when the shear-force coefficient was between 0.15 and 0.2, which was initiated under 25% JMA Kobe. The maximum values of the average sliding displacements were approximately 16 and 11 cm in the wall and frame directions, respectively. The table and the first-floor velocities were similar as long as sliding did not occur. When the sliding displacements were large (e.g., at 50% JMA Kobe), the first-floor velocity was approximately half that of the table.

The regression analysis of the measured data was performed. It was concluded that the global rotation stiffness ratio of the equivalent single degree of freedom system and the equivalent story stiffness ratio of the multi-story building could be related to the cumulative value of the peak velocity for the shaking table.

3.2 Beam-Column joints (BCJs)

BCJs were among the crucial structural elements influencing the response of the tested buildings. Owing to their weak reinforcement, the main damage, particularly in the fixed-base structure, was mainly concentrated at the BCJs. Explicit modelling of their nonlinear response was necessary to accurately simulate the building response.

In most of the papers dealing with numerical modelling (Janevski et al. 2023; Di Domenico et al. 2023; Kolozvari et al. 2023; Sun et al. 2023), the BCJs were modelled as proposed by Alath and Kunnath 1995, using the scissor numerical model, which consists of a rotational spring and its rigid connections with beams and columns. Kabeyasawa et al. 2023 considered the BJCs to be rigid.

OpenSees (McKenna et al. 2010) software was used in most of the presented studies, except for Kabeyasawa et al. 2023, who used the CANNY programme (Li 2007). In OpenSees, the rotational springs were modelled using zero-length elements, which were assigned by a specific type of response envelope and hysteretic response. Different approaches were used to define these envelopes. Janevski et al. 2023, Sun et al. 2023, and Di Domenico et al. 2023 modelled the nonlinear response of the BCJs using the model and recommendations proposed by Kim et al. 2009. All these studies concluded that the models required certain modifications owing to the weak reinforcement of the BCJs. Possible modifications are proposed by Janevski et al. 2023.

Kolozvari et al. 2023 modelled the nonlinear response of the BCJs in two ways: (a) as defined in ASCE/SEI 41 − 17 (ASCE/SEI 41 2017) and (b) according to Shiohara et al. 2013. The second option approximated the experiment more accurately because the ASCE/SEI 41 − 17 model overestimated the rate of strength loss with increasing demand. In all previously mentioned models, the nonlinear response of the BCJs was modelled using Pinching4 material (Lowes and Mitra 2003), as defined in OpenSees.

The need for explicit modelling of the nonlinear response of BCJs was demonstrated by Janevski et al. 2023 and Sun et al. 2023, where the responses of the structures modelled with and without the nonlinear response of BCJs were compared. The importance of modelling the nonlinear response of BCJs was confirmed by Di Domenico et al. 2023 and Kolozvari et al. 2023, where the responses of models with the nonlinear and linear behaviours of BCJs were compared.

A comprehensive and detailed study of the role of BCJs in the tested building has been presented by Del Vecchio et al. 2023. This study was used to define the appropriate numerical model of joints in the numerical analysis presented by Di Domenico et al. 2023. A detailed comparison between analytical and experimental responses of BCJs was performed, and their damage was classified, concluding that the damage state was DS0 (crack widths > 0.5 mm and reinforcement yielding) and DS3 (spalling of the concrete > 80% and concrete crushing) in the base-isolated and fixed-base structures, respectively. Moreover, the responses of the BCJs designed according to different standards, namely AIJ (AIJ 2003), ACI-318 (ACI 318 2019), EC8 (CEN 2005), and NZS (NZS 3101 2006), were compared. As a result, the American, European, and New Zealand standards required a considerably larger amount of BCJ reinforcement in the tested structure than the AIJ standard. According to ACI-318, in the tested building BCJs should be reinforced by minimal reinforcement; however, this amount of reinforcement exceeds that required by all other codes. The paper also presented an excellent and comprehensive state-of-the-art regarding the seismic analysis and design of BCJs.

Overall, it can be concluded that the weakly reinforced BCJs, which are weaker than adjacent beams and columns, can considerably influence the global response of the building, increasing its demand, particularly the displacements and story drifts, as well as the distribution of the demand along the building height. In such cases, which can primarily be expected in older buildings, the nonlinear response of BCJs should be explicitly modelled during their seismic assessment. Otherwise, incorrect information about the critical parts of the building may be obtained, and inadequate solutions for the strengthening and retrofit may be carried out.

Although extensive research activities regarding the seismic response of BCJs were performed and presented in the literature (for more details, see Del Vecchio et al. 2023), further studies are required concerning the seismic response, appropriate modelling, and design of BCJs, particularly to assess substandard BCJs in older buildings and determine their strengthening and retrofit requirements.

3.3 Beams and columns

Various numerical models with different levels of complexity were used for analysing the beams and columns. Kabeyasawa et al. 2023, Janevski et al. 2023, and Di Domenico et al. 2023 used Giberson’s lumped plasticity model (Giberson 1967). The nonlinear response was modelled by placing rotational springs at the ends of the elements (e.g., using zero-length elements, as defined in OpenSees). However, different approaches were used to describe the nonlinear hysteretic responses of these springs. Janevski et al. 2023 and Kabeyasawa et al. 2023 described the hysteretic response using modified Takeda hysteretic rules (Takeda et al. 1970), whereas Di Domenico et al. 2023 used a modified Ibarra–Medina–Krawinkler deterioration model with peak-oriented hysteretic response (Ibarra et al. 2005), which was a part of the H model (i.e., hinged model).

Di Domenico et al. 2023 conducted an additional analysis using another type of model referred to as the F model, where beams and columns were modelled using the distributed plasticity model. Specifically, the force-based-beam-column element (Scott and Fenves 2006) was used, as defined in OpenSees. The cross-sections of the beams and columns were divided into concrete and steel fibres, where the nonlinear response was described using the nonlinear stress-strain relationship of the fibres, using Concrete04 (Popovics 1973) and Steel02 (Menegotto and Pinto 1973) materials for the concrete and steel fibres, respectively.

Kolozvari et al. 2023 and Sun et al. 2023 also used the distributed plasticity model for beams and columns; however, the model type was different. Instead of the force-based element, a displacement-based element was used, which follows the standard finite element procedure (Zienkiewicz and Taylor 2000). The concrete material model was also different, specifically, Concrete02 was used (Yassin 1994).

3.4 Walls

Varying complexity was also used for modelling the walls. Di Domenico et al. 2023 modelled walls similarly to beams and columns using the distributed plasticity model with the forced-based beam-column element, in both the H and F models. Kabeyasawa et al. 2023, Janevski et al. 2023, and Kolozvari et al. 2023 used models developed specifically for RC walls. Kabeyasawa et al. 2023 used the original version of the multiple-vertical-line-element model - MVLEM (Otani et al. 1985; Kabeyasawa et al. 1984), which was later modified by different researchers. One of these modifications, developed at the University of Ljubljana, was the 3D force-displacement-based MVLEM (Fischinger 2004, Isakovic 2019) which is available in the local UL version of OpenSees. It has been used by Janevski et al. 2023. Kolozvari et al. 2023 used the stress-strain-based 3D MVLEM model (Kolozvari et al. 2021), which is included in the official version of OpenSees. Sun et al. 2023 used the most complex model for walls, specifically ShellDKGQ (Lu et al. 2017), which involves a multilayer shell section and PlaneStressUserMaterial.

3.5 Slabs

Slabs were mostly modelled as rigid diaphragms, except for those in the F model used by Di Domenico et al. 2023, where the bending response of the slab was explicitly considered using the ShellMITC4 model (Dvorkin and Bathe 1984) with nDMaterials (i.e., Concrete01 proposed by Scott et al. 1982, and Steel02). Other studies implicitly considered the bending response of the slabs, using certain effective widths of slabs when modelling the beams. This is one of the issues that require additional research attention, as discussed in Sect. 3.8.1.

3.6 Isolation devices

Three numerical models employed for describing the cast-iron plates used to isolate the tested building were analysed by Kabeyasawa et al. 2023. The same model used to analyse the fixed building (see previous sections) was employed used to model the structure above the isolation devices. Instead of the pushover analysis, a dynamic response history analysis was performed.

The simplest model of isolation devices consisted of two uncoupled springs, the response of which depended on the shear-force coefficient. The second model, referred to as the multidirectional spring model, consisted of coupled springs. In both models, the strength was constant because the variation of the axial forces due to the vertical excitations and eventual uplifts were neglected. Then, the third model was defined as an upgrade of the second model by introducing the variable strength of the device and capabilities for uplift analysis.

The response of the superstructure was simulated reasonably well using all the proposed models. However, the estimation of the response for the sliding devices themselves requires further improvement.

In other previously mentioned studies, the base-isolated building was analysed without explicit modelling of the isolation devices by loading the structure with either displacements (Di Domenico et al. 2023) or accelerations (Sun et al. 2023), which were registered at the top of the isolation devices, or the base-isolated building was not analysed (Janevski et al. 2023; Kolozvari et al. 2023).

3.7 The viscous damping

In general, when simulating the experiments, it is feasible to reduce the viscous damping because test specimens do not contain non-structural elements that are typical in real buildings. This observation has been reported in multiple references (N. Ile and J.M. Reynouard 2003, Gilles and McClure 2012, Fischinger et al. 2017, and Karaton et al. 2021).

This was also recognised by Janevski et al. 2023, Kolozvari et al. 2023, and Sun et al. 2023. The first two research groups considered 2% mass and stiffness-proportional Rayleigh damping. The third group considered a 2.5% mass, revealing that the average damping ratio was 2.5% and 1.6% in the wall and the frame direction, respectively.

Although a consensus was almost obtained regarding the amount of damping, the type of stiffness-proportional damping can be the subject of the debate. Di Domenico et al., Kolozvari et al., and Sue et al. considered the tangent stiffness-proportional damping. Janevski et al., however, accounted for the initial stiffness-proportional damping, excluding the very rigid elements to reduce the spurious forces.

Ultimately, both solutions can be employed in the analysed building. In general, both options have pros and cons, and the user must decide based on the model of the structure and their personal experiences. Useful observations and recommendations regarding the modelling of viscous damping have been reported by Ibarra and Krawinkler 2005 and Chopra and McKenna 2016.

3.8 Important parameters influencing response of the tested buildings and some directions for future research

3.8.1 The effective width of slabs

In most of the models, the bending response of the slabs was modelled implicitly by considering the specific effective widths of the slabs while modelling the beams. In the initial studies, the effective widths of the slabs were defined based on the requirements of various standards: (a) according to AIJ standards (Kabeyasawa et al. 2023), (b) Eurocode 2 - CEN 2004 (Janevski et al. 2023), (c) Eurocode 8 (Di Domenico et al. 2023), (d) ASCE/SEI 41 − 17 (Kolozvari et al. 2023; Unal et al. 2023), and (e) Chinese design codes (GB 50010-2010 2015) (Sun et al. 2023). It has been found that the effective width, activated for larger drifts at the most loaded beams, was larger than the values mentioned above. These observations agreed with previous evidence from the literature, suggesting that the effective width can be significantly underestimated for large drift demands (Pantazopoulou and French 2001; Kabeyasawa et al. 2017, Isakovic et al. 2021).

Kabeyasawa et al. 2023 and Janevski et al. 2023 increased the effective width of slabs to the entire span to analyse the effects of this parameter, and they observed improvements in the response due to this enlargement. Kabeyasawa et al. 2023 conducted a 3D pushover analysis according to the Japanese practice, whereas Janevski et al. 2023 performed a complete dynamic response history analysis.

Kabeyasawa et al. 2023 studied the effective width of the slabs further. They tested the methodology used for estimating this effective width by employing the model of the Timoshenko beam (Timoshenko 1922), as previously described (Kabeyasawa et al. 2017). The proposed methodology overestimated the slab reinforcement strains at the outer spans of the tested building, but a fair correlation between the measured and calculated slab strains was obtained when the analytical beam reinforcement strains were consistent with the measured values.

Other research teams reported that the effective width of the slabs had limited effects on the overall response, which might also be related to the different models that were used for the analysis and the different procedures used to define the properties of these models. Differing conclusions have been expressed by different research teams, and thus the effective width of the slabs requires additional research attention, especially considering that it can change the type of the response mechanism in some structures (Isakovic et al. 2021).

3.8.2 The shear-force amplification due to the higher vibration modes

In taller and more flexible buildings, considerable shear-force magnifications can be expected as a result of the higher vibration modes. A detailed study of the shear-force magnification in the tested building was presented by Unal et al. 2023. The requirements of the ACI 318 − 19 (ACI 318 2019) standard were assessed, revealing that the new requirements estimated the wall shear amplifications reasonably well, but they significantly underestimated the shear demand in RC columns in the frame direction. In the studied structure, a considerably more accurate estimation of the column’s shear forces was obtained using alternative procedures from NZS 3101 2006, NIST 2016, and that reported by Visnjic et al. 2017.

3.8.3 The ratio of dissipated energy in BCJs, beams, and columns

In the fixed-base structure, mainly the BCJs were considerably damaged. The damage pattern in the building was influenced primarily by the ratio of the strengths of hinges, beams, and columns. However, Janevski et al. 2023 noted that the distribution of the damage over the structure also depended on the energy dissipated in these structural elements, which was mainly dissipated in BJCs. That is why the energy dissipated in the beams of columns was reduced by changing the standard hysteretic response, reducing the dissipated energy by employing a lower unloading stiffness.

3.8.4 The initial stiffness and sequential application of the ground motions

As previously mentioned, Janevski et al. 2023 and Kolozvari et al. 2023 did not study the base-isolated building, which was tested before the base was fixed and tested again. Although the base-isolated building only exhibited some cracking, its stiffness was reduced. This stiffness reduction should be appropriately modelled when analysing the fixed-base structure without prior analysis of the isolated one. Furthermore, the sequential analysis of the fixed building, considering all the successive excitations is necessary to properly evaluate the cumulative damage in different test runs. This is typical for simulations of experiments where structures enter the nonlinear range.

Additionally, it should be considered that some reduction of the initial stiffness can occur because of the assembly, transportation, and handling of the tested specimens. The reduction in the initial stiffness typically has a more significant influence on the response under weaker excitations and becomes less important in the nonlinear range. A more substantial reduction in the initial stiffness can be expected in structures with lower axial forces, owing to the force of gravity.

Janevski et al. 2023 reduced the initial stiffness of the fixed structure by threefold (compared with the stiffness corresponding to the gross cross-section of the structural elements) to capture the initial periods defined based on the white-noise tests. This reduction is consistent with the requirements of some codes (e.g., ASCE/SEI 41 − 17), according to which the initial stiffness of the elements subjected to low axial forces is approximately one-third of that corresponding to the gross cross-section.

The importance of considering the sequential excitations when simulating the experiments was demonstrated by Kolozvari et al. 2023. When the tested structure entered the nonlinear range, the sequential excitations primarily influenced the damage distribution over the building, rather than the absolute maximum values of the displacements, story drifts, or accelerations.

3.8.5 Pushover analysis and estimation of design floor accelerations

In most studies, dynamic response history analyses were performed. Chiou et al. 2023 evaluated the accuracy of the pushover analysis according to the Taiwan Earthquake Assessment for Structures by Pushover Analysis, and the procedure for estimating the design floor acceleration has been proposed.

4 Concluding remarks

The iron-plate isolation devices efficiently reduced the seismic demand in the tested building, which only exhibited some cracking when it was isolated. Significant damage was observed when the base was fixed, primarily in the weakly reinforced BCJs.

Because a large portion of the seismic energy was dissipated in the BCJs, their explicit modelling was required to properly simulate the seismic response and the damage pattern over the entire building. The damage pattern depended on the strength ratio and the amount of energy dissipated in the joints, beams, and columns. Furthermore, standard numerical models of the joints, beams, and columns had to be modified somewhat in the tested building with weak column joints.

A variety of different modelling solutions were used. Without attempting to determine the best modelling elements or solutions, this Special Issue aims to provide detailed information about various modelling options for high-rise buildings and highlight the presented models’ capabilities, in addition to clarifying the necessary modifications that were implemented, compared with the basic assumptions used in their original development. This information may be particularly useful when assessing the seismic response of older buildings, where the BCJs are typically weakly reinforced, as well as in risk studies where the information about modelling parameters near collapse is needed.

Moreover, several issues require additional attention and are worth emphasising: (a) modelling of iron-plate isolation devices while considering the uplifts, (b) modelling weak BCJs, (c) estimation of the effective width of slabs activated under larger drift demands, (d) the shear-force magnification due to the higher vibration modes, and (e) relationships between peak velocity at the shake table (peak ground velocity) and the global rotation stiffness ratio of the equivalent SDOF system and the equivalent story stiffness ratio of the multi-story building.