1. Introduction
The importance of this research stems from the need to reevaluate the level of protection of existing structures against seismic actions and to determine the seismic requirement for the retrofitting process. The current approach to the assessment of existing buildings is based on an evaluation of the strength of structural elements and performance ratios. First, the critical elements are identified by an expert, based on engineering standards, and then, they are checked against the prescribed performance criteria. Finally, these critical elements are treated in the proposed seismic upgrade. As these local measures can only marginally affect the capacity and stiffness of the whole building [
1], this approach often leads to disproportionate levels of retrofit demand that greatly exceed the requirements of the current seismic provisions. In general, the assessment of individual components is more time-intensive and it does not provide the quantified assessment of retrofit needs.
In this paper, we propose a displacement-based model that treats the structure as a whole object without evaluating its components. This approach allows for the quantitative assessments of the earthquake resistance of existing buildings and a level of the required seismic retrofit.
Nowadays, the legal provisions in many countries require a reassessment of the earthquake resistance of existing structures that were designed for gravity loads only or to substandard design codes. The deficiency of seismic resistance in these buildings is due to the lack of ductility rather than the lack of strength, which is a result of poor reinforcement detailing and inadequate design methods [
2]. Moreover, these sub-standard buildings suffer from the corrosion of reinforcement, lack of concrete cover, joint problems [
3], and poor design of weak and flexible stories [
4]. The identification of sufficient levels of seismic upgrade for these buildings is complicated by high uncertainties in the evaluation of real existing conditions, which in turn limits the possibility of the quantitative assessment of required retrofit levels.
The procedures for the assessment of the earthquake resistance of existing buildings can be broadly classified into two categories: force-based and displacement-based methods. The force-based assessment approaches start from the assessment of member and joint-strength capacities, which define the elastic period and a class of the building frame. The base shear demands are then calculated and used to evaluate the members’ strength demands [
2]. The displacement-based approaches are the performance-based methods defining the ultimate response of a structure in terms of the displacement parameters, such as roof displacements, inter-story drift ratios, rotations at joints, and ductility ratios. These parameters are assessed against the ones associated with the specific levels of the seismic hazard. The main advantage of the displacement methods is that it accounts for the ductility of the system [
2,
5,
6,
7]. The displacement-based methods assume definitions of the target displacements for each assessment case (building) independently. The most common method that defines the target displacement is the Capacity Spectrum Method (CSM), which predicts the maximum response of the structures based on the corresponding earthquake design spectrum [
6,
7,
8,
9,
10]. Another common approach is the Displacement Coefficient Method (DCM), which estimates the peak displacement based on the spectral response of an elastic system and defines it using a series of coefficients depending on the effective fundamental period of the structure [
10]. Lately, a simplified Direct Displacement-Based Assessment (DDBA) has been proposed for the seismic design of concrete buildings [
2]. This method was originally developed by Priestley and colleagues [
2,
5,
11]. It was demonstrated that the Nonlinear Static Pushover Analysis (NSPA) can be applied to the seismic assessment of RC buildings and evaluations of the limit displacements under various structural conditions. It was also shown that DDBA can be used to evaluate the effectiveness of various retrofit scenarios. The assessment of integrated solutions for combined energy efficiency improvement and the seismic strengthening of existing buildings was also discussed in [
12]. The rapid seismic damage assessment of RC frames via a performance-based approach was presented in [
13].
Few studies are dedicated to the development of various specific assessment models. Binda and colleagues suggested applying the NSPA to assess the capacity of masonry structures [
14]. Zamppieri et al. used the nonlinear time–history analysis to examine the safety ratios for arch bridges subjected to different earthquake scenarios [
15]. Mendes et al. reviewed assessment approaches to the rehabilitation of historic buildings, which focus on damage evaluation in the components of the main stability system [
16]. The displacement-based criteria for possible seismic retrofitting scenarios were discussed in [
17,
18]. The dissipation energy-based method for the seismic retrofit of existing frames was presented in [
19,
20]. A seismic retrofit approach based on general stiffening of the building and displacement-based evaluation was proposed in [
21,
22,
23]. Another approach to reducing the cumulative damage in existing sub-standard buildings by introducing viscous dampers was presented in [
24].
The current provisions of various international standards for assessing the seismic performance of existing structures are diverse. The New Zealand Standard [
25] utilizes classical methods for evaluating the resistance of existing buildings. It includes displacement-based methods and performance models and recommends the use of a time–history analysis. Japanese provisions [
26,
27] focus on changing the properties of the structure to increase ductility and stiffness. It emphasizes the use of base isolation devices for low-energy absorption and an improved seismic response. The US standards are based on the performance theory. ASCE provisions [
28] require examining the structure as a collection of components rather than a whole object. It provides guidelines for evaluating the seismic performance of existing structures. FEMA-27 [
29] emphasizes improving ductility by restoring capacity in various connectors of the structure. It also considers changes in damping levels as the structure moves between different positions.
In general, the developed methodologies for the earthquake-resistance assessment of the existing buildings are summarized in
Table 1. One can see a variety of methods involving different underlying principles that have been proposed in the literature. However, most of these methods do not provide a quantitative measure for the lack of resistance and cannot be used for the evaluation of the efficiency of retrofit procedures.
The retrofit procedures for upgrading RC buildings that have been developed in recent decades can be classified into two main groups. The first group includes the methods that upgrade the structure at local levels of individual elements, while the approaches from the second group deal with the structure as a whole object by introducing so-called global measures [
46]. The most popular local treatment is the jacketing of existing RC members, which can be performed using concrete, steel, or composite materials [
10,
23,
47,
48]. This local reinforcement improves the load-bearing capacity and ductility of critical structural elements. The global measures, on the other hand, aim at enhancing the lateral resistance of the building or decreasing the seismic demand. Bracing systems, cables, steel exoskeletons, and shear and infill walls are among the structural systems used to improve lateral resistance [
23]. The seismic demand can be decreased by using base isolation [
43] and various energy dissipation systems [
41].
In this study, we assess the global earthquake resistance of buildings through the displacement-based approach. The proposed procedure will allow for an evaluation of the seismic demand of the tested building. Here, we translate this demand into the amount of lateral stiffening required to provide the sub-standard building with sufficient earthquake resistance. In the verification case study, this additional stiffening is supplied using the external shear walls, which are proportioned based on the estimated demand. A similar retrofitting solution for RC sub-standard buildings was discussed in [
23,
38,
49,
50]. It was shown that the shear walls were very efficient in controlling lateral drifts and reducing damage to frame members. The main drawback of this method is that the existing foundation system needs to be strengthened to resist the increased overturning moment and the larger weight of the structure. The advantages of applying this external upgrade included lower installation costs when compared to local repairs, no need to shut down the building, and the use of conventional construction materials. The efficient application of retrofitting through external stiffening requires reliable estimates of the amount of shear wall that is needed to achieve the desired level of resistance. To the best of the author’s knowledge, none of the existing assessment methods can provide this evaluation. The current study aims to address this research gap. It is expected that the same procedure can also be applied when additional stiffness is provided externally through exoskeletons or external braces. In the case of internal braces or infill walls, the necessary stiffening can be similarly estimated using standard methods of structural analysis.
The method we propose here capitalizes on several ideas explored in the previous studies. Firstly, we utilize the idea of the displacement limit by introducing a safety target displacement for the existing building. Then, we employ the fact that the yield displacements vary little with respect to the structural stiffness. Since the yield displacement is essentially defined by the geometry of the structure and material it is built of, it can be assumed that it is independent of the stiffness of the structure [
1,
23,
38,
51]. As a result, we can reasonably assume that the yield displacement of the existing building is not significantly affected by the stiffness added to the structure during the retrofitting process. Finally, we use the energy balance to define the resistance factor for the building as reviewed in [
42,
52]. The main challenge of the proposed procedure is the definition of the safety target displacement for existing buildings that is not presently available in the literature. The ability to evaluate the displacement limits will allow us to determine the seismic demand for a specific structure and thus assess the retrofitting efficiency.
To determine the displacement limits, the building structure is described as a whole object, while the overall resistance is assessed using equilibrium force-displacement curves. The ability of the structure to resist seismic loads is examined using the Nonlinear Static Pushover Analysis (NSPA). The seismic loads are defined based on the requirements and recommendations of the relevant standards. The additional seismic demand is determined in terms of the additional stiffness required to maintain the displacement limits.
The paper is structured as follows.
Section 2 deals with the characterization of typical sub-standard buildings that require seismic upgrades.
Section 3 discusses the applicability of available procedures to provide the safety displacement limits for typical structures.
Section 4 presents the derivations of the proposed method and discusses the assessment of the seismic demands for sub-standard existing buildings.
Section 5 is devoted to the definition of the resistance factor, which is based on the safety displacement limits and the energy balance.
Section 6 presents a case study that demonstrates the ability of the developed method to evaluate the earthquake capacity of existing buildings and predict the efficiency of retrofitting procedures.
2. Characterization of Typical Sub-Standard Structures
To define a benchmark structure for the evaluation of the applicability limits of various assessment procedures for the earthquake resistance of existing buildings, we start with a review of typical sub-standard reinforced concrete (RC) buildings. We surveyed 18 seismically sub-standard buildings with similar structural systems built in Israel between 1960 and 1980. The survey included the geometry, inspection of the structural system, and a series of non-destructive tests to measure the material properties of concrete and reinforcement steel and the reinforcement ratios of all structural components. The seismic deficiency of these buildings was broadly recognized, but the actual level of seismic resistance had never been assessed [
53]. All of these buildings are conventional RC structures with three to four stories and an open floor. The structural arrangements consist of two to four RC load-bearing frames and non-bearing infill walls. The RC frames are made of drop edge beams and small section columns that were originally designed for gravity loads only. The connectors between beams and columns exhibit limited resistance to bending moments and interstory drifts. The structural features of the surveyed RC frames are summarized as follows:
Cross-sections of the columns and beams range from 20/30 to 20/50 cm;
The concrete strength is 18 MPa;
Concrete sections are not confined and have very few links;
The reinforcement ratio (RR) in the cross-sections of the beams and columns ranges from 0.3% to 1.25%;
The frames are on pinned supports due to the very limited resistance to bending. Connecting beams between the columns are provided at the ground level, but these beams do not contribute to the connection between the columns and the foundation;
The strength of the reinforcement steel is 200 MPa;
The infill walls add weight, but do not serve as a part of the stability system.
The detailed characteristics of the surveyed buildings can be found in [
53].
Based on this survey, we define three typical benchmark frames that will be used in the following sections for the evaluation of various assessment models. These frames are two-, three-, and four-bay RC frames that represent a four-story building; see
Figure 1. The structural parameters of these frames only differ in the number of spans, which leads to different levels of lateral stiffness. The ductility in these frames depends upon the available level of reinforcement. In the following numerical simulations, three values of the reinforcement ratios in the beams and the columns are considered as 0.3, 0.8, and 1.25%. Note that for the sake of simplicity, the infill walls are not included in the structural analysis, and the connections between the beams and columns are assumed to be rigid.
As a first step toward the development of the proposed procedure, three benchmark structures are analyzed using the mode-superposition method using the commercial computational package ATIR [
54]. Note that this procedure is recommended by the Israeli standard [
55]. The compliance of the structures with the resistance criteria prescribed by [
56] is checked by examining the story drifts and stability factors. The interstory drifts are assessed based on the maximum obtained value (Δ) and maximum Interstory Drift Ratio (IDR
max). These indicators are commonly used for seismic performance assessments (e.g. [
57,
58]). The detailed building specifications and seismic loads are presented in
Appendix A, while the results of this analysis are given in
Appendix B and are summarized below as follows.
The interstory drifts are greater than what is allowed by Israeli standards [
56]. The first floor is particularly vulnerable, as indicated by its high stability coefficient (see
Table A3,
Table A4 and
Table A5). When compared to FEMA-356 guidelines [
59], the IDR
max of the 1st floor exceeded the acceptable limit for buildings to remain occupied immediately after an earthquake (Immediate Occupancy Performance Level [
59]). Due to the uniform rigidity of all stories and the absence of infill walls, which leads to equal story shear strength, no weak or soft stories appear in these cases. This outcome is not surprising as it is commonly accepted that these buildings would not withstand any strong ground motion. Yet, this evaluation does not provide a quantitative measure for the lack of their earthquake resistance and the degree of vulnerability of these buildings. In the next section, we discuss the ways for such assessments.
5. Resistance Factor for the Assessment of Existing Buildings
Assessment of the earthquake resistance of existing structures in different geophysical locations requires a quantitative factor that can help a decision-maker to determine retrofitting and demolition policies and recommendations that will improve the safety status of the buildings in the given area. As discussed in
Section 3, the CSM and DCM models that are widely accepted as the methods of choice in the literature are unable to describe the earthquake resistance of low ductility structures, nor are they able to derive the resistance factor from the true properties of the structure. Several attempts have been made to define the resistance factor as a ratio between the original capacity of a structure and the required capacity [
7,
61]. However, the definition of a target structure and the assessment of the capacity demands were not given in these studies. On the other hand, the methodology proposed in the current study allows for the qualitative assessment of the resistance through a comparison of the capacity curves of an existing structure with a corresponding ideal TDC of the same structure. This comparison can be expressed as a ratio between the energy the existing structure is capable of dissipating to the amount of energy the ideal target structure would be able to dissipate, whereas both energies can be calculated using the curves established in
Section 3 and
Section 4 as follows. The amount of energy the ideal target structure should be able to dissipate,
, is defined as the integral of TDC, which is graphically represented in
Figure 8 as the shaded area below the curve. The amount of energy the actual structure dissipates under the earthquake loading is obtained using its capacity curve (CC); see
Figure 4a. However, in practice, we suggest limiting this value by using a safety target displacement (STD) defined at the right integration boundary, as shown in
Figure 8, where this reduced energy amount is illustrated by a cross-hatched area. This energy reduction will provide a margin of safety and account for joints’ detailing, which is not considered in the analysis. Thus, the resistance factor, RF, will be defined as the ratio between the reduced energy,
Ered and
Edemand, as
It can be seen from Equation (16) that the RF varies as 0 <
RF < 1.0.
RF→0 defines an engineering structure with a very low level of earthquake resistance. This type of structure with no actual stability system was discussed in [
39]. At the upper limit of
RF = 1.0, we see the upgraded structure that is retrofitted using the methodology developed in the current study. This resistance factor can be used to compare the seismic performance of similar structures located in different seismic regions, to assess the retrofit costs and to define the amount of retrofitting required. It can also be an inductive factor for decision-making, such as upgrading or demolition when it is implemented along with cost estimates.
7. Conclusions
In a range of the methods used for the assessment of existing buildings, the displacement-based methods are among the most reliable ones. However, the commonly used CSM and DCM models for the evaluation of earthquake resistance have limited ability to provide a quantitative measure for the lack of such resistance. Moreover, it has been shown that these methods are not suitable for the assessment of low-ductility structures. In such cases, these methods might only be able to provide the seismic demand estimate for higher damping levels.
The outcomes of the current study can be summarized as follows:
An alternative approach to the identification of the seismic demands and corresponding resistance factors has been developed. The building is considered as a whole object and the structural capacity is evaluated in terms of the base shear force–top floor displacement equilibrium curve.
The seismic retrofit is achieved through global stiffening of the existing structure without the treatment of individual components.
The ideal target structure is obtained by defining the limit target displacement, which is determined through the energy balance.
The seismic resistance factor is expressed as a ratio between the amounts of energy the existing structure is able to dissipate to those an ideal (upgraded) structure would be able to dissipate.
The amount of stiffening required to achieve the ideal energy-absorbing capacity defines the seismic demand. Both seismic demand and resistance factors depend on the structural properties of the existing structure and the seismic conditions of the location.
The minimum ductility in the existing structures that ensures the formation of a performance point depends on the available level of reinforcement. Underenforced structures or those with heavily corroded steel reinforcements will have high levels of critical ductility and thus cannot be assessed using the CSM or DCM methods, as the performance point cannot be determined.
The ability of the developed procedure to assess an existing building is demonstrated through a case study by applying the method to a real RC building.
The case study has been carried out for a low-ductility structure, which cannot be analyzed using the commonly accepted DCM and CSM models. First, it is shown, using the mode-superposition method, that the structure lacks adequate earthquake resistance. Then, the non-linear pushover analysis is used to determine the resistance factor and seismic demand for the target structure. The retrofit scenario has been proposed based on the obtained results. The upgraded structure has been checked and deemed to satisfy the seismic requirements.
It has been demonstrated that the developed limit displacement model provides a reliable approach for the quantitative assessment of existing buildings. This method can be used for evaluations of a wide range of existing buildings and the comparative assessment of sub-standard structures. The resistance factor derived here provides a quantitative measure of the amount of required retrofit for any structure regardless of the geophysical location or specific site conditions. Since this factor is independent of a particular retrofit scenario, it allows for the grading of existing buildings for the profitability of potential upgrades. This grading system would assist policymakers in creating tiered incentive programs where buildings with high profitability scores receive large grants or tax breaks for retrofit. This would also encourage building owners to undertake retrofits when they might otherwise hesitate due to uncertainties in upfront costs.
The case study presented in this paper validates that the seismic upgrade of subs-standard low-rise RC buildings can be performed by upgrading the global stiffness of the building rather than improving the capacity and ductility of individual structural members. To allow for the use of the method by design engineers, it is recommended to include, in future studies, the effects of the infill walls and bracing systems, to investigate the effects of different types of foundations, and to verify the method for medium-rise buildings.