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Seismic Repair Cost-Based Assessment for Low-Rise Reinforced Concrete Archetype Buildings through Incremental Dynamic Analysis

Juan Patricio Chicaiza-Fuentes
1,2 and
Ana Gabriela Haro-Baez
Department of Earth Sciences and Construction, Universidad de las Fuerzas Armadas ESPE, Avenue General Rumiñahui s/n, Sangolquí 171103, Ecuador
Research Group of Structures and Constructions (GIEC), Universidad de las Fuerzas Armadas ESPE, Avenue General Rumiñahui s/n, Sangolquí 171103, Ecuador
Author to whom correspondence should be addressed.
Buildings 2023, 13(12), 3116;
Submission received: 19 October 2023 / Revised: 20 November 2023 / Accepted: 29 November 2023 / Published: 15 December 2023
(This article belongs to the Special Issue Achieving Resilience and Other Challenges in Earthquake Engineering)


This study presents the performance-based seismic assessment of low-rise reinforced concrete archetype buildings, considering repair costs for ordinary moment-resistant frames (OMF) and dual systems consisting of OMF plus special shear walls (SSW). Historically, the OMF systems, conceived for residential purposes in Ecuador resulting from informal construction, have reported poor responses under seismic forces. This study analyzes damage levels through fragility curves as a function of the maximum global drift reached through incremental dynamic analysis. For this, two archetypes with OMF and two with a similar configuration, including structural walls, are modeled to define a loss function and annual collapse probabilities. As a result, it is noted that systems with structural walls significantly reduce repair costs by between 75 and 90% of the total cost of the building, and prevent collapse. Systems with ordinary moment frames report total losses, implying their use should be limited in areas of high seismicity.

1. Introduction

Ecuador is located in an area of high seismicity. On its coasts, the Nazca plate moves under the South American continental plate, producing the phenomenon of subduction, where seismic events of various magnitudes and depths occur. Likewise, crustal faults cross some main cities, raising awareness among their inhabitants [1]. The most recent devastating event was the 16 April 2016 earthquake on the northern coast, with a magnitude of 7.8 Mw that lasted 48 s [2]. The fatalities were estimated to exceed 673 deaths, while according to government entities, the economic losses reached USD 3 billion [3].
In recent years, various studies have been developed in the region to determine the seismic risk of buildings, highlighting the South America Risk Assessment (SARA) project [4]. In this project, a survey for different structural typologies was carried out in Quito, Ecuador, reporting 77% for the taxonomy established as CR+CIP/LFLSINF+DNO. According to the seismic risk report of the Global Earthquake Model Foundation [5], this corresponds to a non-ductile frame structure with a solid or lightened flat cast-in-situ concrete slab. Historically, this typology has registered inadequate seismic performance, which justifies the application of cutting-edge assessment methodologies to reduce economic and social losses after an earthquake. In this context, the FEMA P-58 methodology [6] highlights the next-generation performance-based approach [7], which aims to determine the damage caused to a building due to seismic demands. The results are expressed as a function of the probability of occurrence, including possible occupancy loss, reconstruction, repair time, environmental impact, and costs for structural and non-structural components. Furthermore, with adequate information, potential fatalities, injuries, or casualties affecting the occupants are identified [6].
One of the most important events that has driven the need to develop new methodologies in the evaluation of seismic performance was the Northridge earthquake in 1994, where, although the structures were designed with the codes of the time and did not collapse, the owners were not satisfied with the times and costs required to repair and reoccupy their businesses and homes [8].
In the last decade, research has been conducted to determine the seismic performances of buildings. For example, Ref. [7] used FEMA P-58 to estimate economic and social losses from earthquakes for four reinforced concrete structures intended for educational occupancies in Iraq. This study established that buildings could report repair costs of more than 60% of their total cost. Furthermore, the research carried out in [9] presents an approach to the evaluation of economic losses of reinforced concrete buildings with infill masonry, where it was concluded that the monetary losses, even if the building does not collapse, could be so high that it would be more convenient to rebuild the structure than to repair it. In addition, a more novel application of the FEMA P-58 is developed in [10], where, using BIM tools and the economic loss prediction method, an algorithm is created to visualize, in a complete 3D model, the elements that would be affected after the earthquake.
On the one hand, research has also been carried out in the region where dynamic incremental analysis [11] is applied together with FEMA P-58 to evaluate structures. For instance, in El Salvador [12], fragility curves are obtained for buildings with structural walls, and in Mexico [13], a comparison study has been carried out between simplified seismic and dynamic incremental analyses to find a relationship between the capacity curves of each method. On the other hand, there is relatively little research on this topic in Ecuador. One of these studies is presented in [14], where medium and high-rise structures are qualified using the REDITM system and the FEMA P-58 methodology, allowing the definition of population models and structural parameters typical of the dynamic analysis developed.
Considering the previous analysis, it is necessary to disseminate the repair costs of an Ordinary Moment Frame (OMF) typology structure, which are significantly higher than in OMF + Special Shear Wall (SSW) structures. Using incremental dynamic analysis to evaluate both typologies, questions arise for the final decision of the owners or promoters of a project about the importance and benefit of developing safer structures [9]. For this purpose, four analysis models framed in the CR+CIP/LFLSINF+DNO taxonomy have been created [5]. Two models correspond to structures formed with OMF frames; the other two also consider SSW. In this regard, a point of comparison states that repair costs are reduced after an earthquake if the initial project involves adequate design and construction processes. Indeed, safer structural systems reduce time costs and life losses [15].
The numerical models created do not consider the influence of partitions or any other non-structural element. However, for the repair costs analysis, the impact of non-structural components is taken directly from the FEMA P-58 database through a given fragility according to the analysis results related to the ordinary moment-resistant frames.

2. Materials and Methods

2.1. Methodology

The seismic performance is quantified through the probability of suffering accidents, repair and replacement costs, repair time, environmental impacts, and resulting unsafe non-structural elements. The performance evaluation is carried out for a particular earthquake scenario or intensity, and the probability of occurrence of all earthquakes is also considered during a specific period [6]. Figure 1 summarizes the performance-based seismic analysis procedure applying the FEMA P-58 methodology. In step one, the installation is defined (D), that is, identifying the structural system, the location of the structure, and the possible hazards. The annual exceedance frequency for the seismic event is the function λ[IM], given by the seismic hazard. The intensity measurement (IM) is the specific level of excitation that could be caused by an earthquake and is used for structural analysis. The engineering demand parameter (EDP) defines the seismic response of structural and non-structural components, such as accelerations, drifts, and rotations. Step 4 evaluates the structural elements’ damage measure (DM) based on the fragility functions and the corresponding EDP. For the loss analysis, the probability of exceeding the decision variable (DV) is estimated, directly related to the damage level. Generally, money, fatalities, repair costs, and downtime are the decision variables most used by interested parties, who evaluate whether the quantified and calculated risk is acceptable [9]. To define the seismic hazard, 11 pairs of seismic records are selected and scaled to an objective spectrum corresponding to a return period of 475 years [16] in a type D soil commonly observed on the Ecuadorian coast. The simplest way to check that the scaled spectra fit the target spectrum is to calculate the average spectrum of the 11 records, which must work in a range of periods from 0.5 T to 1.50 T, where T is the fundamental period of the structure [16].
The FEMA P-58 methodology recommends using a lognormal distribution function that is given by (1) as follows:
P D M D M i I M = Φ 1 β D M ln I M θ
where Φ is the cumulative standard normal distribution function, DMi is the damage measure state according to the discrete point i, IM is the measure seismic intensity, θ is the mean of the parameter selected to evaluate the structures, and βPE is the standard deviation [6].
The first data are obtained from the IDA curves. An IDA curve is a graph that records the DM state calculated by dynamic incremental analysis versus the IM that describes the scaled accelerogram used [17]. Since the maximum drift is the evaluating parameter, the data are tabulated to group them according to the ranges defined by FEMA P-48.
Figure 2 presents the usual flowchart for decision-making based on evaluating costs, time, and possible building replacement based on the prices calculated for each scenario [18].

2.2. Description of the Typologies


Two structural typologies consider lightened cast-in-situ concrete flat slabs with band beams, typical in low-income housing, and part of the CR+CIP/LFLSINF+DNO taxonomy of the SARA project [4]. This structural configuration exhibits fragile behavior, with exposed failure at the base of the columns. The geometry of these two numerical models is obtained through information collected on-site by [2], which exhibited significant damage for this building type after the 2016 Ecuador earthquake.
On the other hand, structural walls provide greater lateral rigidity when placed in specific and symmetrical places in the structure with an appropriate design. In addition, they resist lateral loads cost-effectively when included as a retrofit alternative for existing buildings [19]. Consequently, an OMF + SSW structural typology is considered for the reinforced version of the original ones, as described in Table 1.
Figure 3 shows the numerical models used in this study. Figure 3a and Figure 3b represents the TE-1 and TE-2 typologies, respectively. In contrast, the buildings with structural walls, TE-1RF and TE-2RF, are shown in Figure 3c and Figure 3d, respectively.
In addition, the beam–column elements are also modeled with the inelastic force-based frame element type, the infrmFB class element implemented in SeismoStruct. This force-based 3D model allows the simulation of spatial frames with geometric nonlinearities. The nonlinear uniaxial material response is obtained from the individual fibers into which the section is divided [20]. Conceptually, the infrmFB elements are more precise because they capture the inelastic behavior throughout the entire element extension. The analytical results of plastic hinges and rotations are related to the verifications of seismic codes such as FEMA-356 and ATC-40 [20].
Table 2 presents the properties of the structures. Note that the TE-1RF and TE-2RF typologies are similar to the TE-1 and TE-2 typologies, but include structural walls for comparison purposes.

2.3. Materials

2.3.1. Concrete

The Mander model is applied to concrete, and is a uniaxial nonlinear constant confinement model. This model was initially programmed by [21]. It follows the constitutive relationship proposed by [22] and the cyclic rules proposed by [23].

2.3.2. Steel

The Menegotto–Pinto model is used for reinforcing steel. This is a uniaxial steel model initially programmed by [24], based on a simple but efficient stress–strain relationship proposed by [25], together with isotropic hardening rules proposed by [26]. Its use should be limited to modeling reinforced concrete structures, particularly those subject to complex loading histories, where significant load reversals may occur. As analyzed in [27], with correct calibration, this model, which was initially developed with ribbed reinforcing bars, can also be employed for modeling smooth bars, which are often found in relatively old existing structures [20].

3. Structural Analysis

3.1. Capacity Curves

The capacity curve or pushover curve allows for evaluating the seismic response of a building incurring in the inelastic range. It represents the lateral shear force versus lateral displacement measured in the last mass-representative level of the structure. In addition, it enables the identification of the performance points when a plastic hinge is formed [28].
The graphs obtained for the TE-1 and TE-1RF typologies are shown in Figure 4a, where the damage states are calculated from the ultimate displacement and the performance levels defined as Operational (OP), Immediately Occupational (IO), Life Safety (LS), and Collapse Prevention (CP), specified by ASCE 41-17 [29]. Structural collapse is reached when the maximum lateral displacement at the roof of the building achieves 4% of its total height. Thus, the control displacement for TE-1 is 43.20 cm, and for TE-2 it is 28.80 cm.
Figure 4b shows that the capacity curve for TE-2 is significantly lower than the capacity curve for the TE-2RF typology. It also shows the performance points associated with the damage states later described. These preliminary results show that the structural performance enhancement is significant in buildings with OMF+SSW systems, evidenced by increased resistance to lateral forces and greater stiffness. As also known, structural walls generate an economic advantage when carrying out structural reinforcement since the capacity to withstand lateral forces produced by earthquakes is considerably increased, all with a relatively small construction intervention area [30].

3.2. Seismic Records

The target response elastic spectrum is built according to the Ecuadorian Construction Code (NEC-15) with the following parameters: soil type D and zone factor V, representing a high seismic hazard zone with a 0.4 g factor. The soil amplification coefficients are defined for the short period zone (Fa), the elastic spectral response in rock (Fd), and the nonlinear behavior of soil (Fs), taking values of 1.20, 1.19, and 1.28, respectively. The ratio between spectral acceleration and PGA (ɳ) is 1.80, and the relationship between the project’s geographical location and the type of soil r is 1.0 for coastal cities [31].
The characteristics of the seismic sources correspond to the fault zones associated with a seismotectonic region. These fault zones are represented as source areas to simplify the difficulty of generalizing all the seismic hazard identification factors, which becomes a limitation when relating seismic records from different source zones [32].
Using the PEER Ground Motion Database [33] in conjunction with factors associated with the source zones, it is possible to filter the compatible records through a range of parameters such as distance, site characteristics, source data, wave speed, and expected magnitude.
Ten pairs of seismic records are selected, plus the 2016 Ecuador earthquake, as detailed in Table 3. This database reports the seismic records of surface-active tectonic regimes worldwide.
Applying the scaling factors, the spectra are adjusted to the target spectrum, as shown in Figure 5a, in such a way that the weighted average of all of them is over the range of interest from 0.2 T to 1.5 T [16], as shown in Figure 5b.
Applying the intensity of Arias [34], the records were considerably reduced in size concerning the duration. With this, analysis times are optimized by focusing on the significant range wherein the main effects on the structures occur. Table 4 summarizes the data obtained on the effective duration for the incremental dynamic analysis.

3.3. IDA Curves

The IDA curves represent the maximum response for the evaluated parameter. In this case, the global or maximum roof drift is determined at each seismic intensity. This study uses ten seismic intensities of the PGA ranging from 0.10 to 1.0 for each record [35].
Eight hundred and eighty analyses corresponding to the four studied structures, the eleven seismic records selected in each orthogonal direction, and the ten variation intensities are performed. As a result, the global drift values measured on the terrace of the building are obtained, as shown in Figure 6 for each record.
One way to evaluate whether the IDA analysis was performed correctly is to superimpose the pushover and IDA curves [11], standardized to represent the basal cutoff value versus the maximum displacement. As shown in Figure 7, the curves follow a similar pattern for each typology, indicating that the dynamic incremental analysis and the scale factors used for the ground motions are correct.

3.4. Fragility Functions

3.4.1. Acceleration

Through incremental dynamic analysis, the average collapse intensity is determined. The average collapse capacity takes a value of the spectral acceleration where at least 50% of the seismic records produce collapse. The collapse can be identified by parameters such as simulated collapse, engineering criteria, numerical instability, or excessive lateral drift, for which the fragility function before collapse must be developed to allow the evaluation of repair costs against engineering parameters such as the maximum spectral acceleration at each seismic intensity and its corresponding maximum global drift [6]. Within the data analysis, it must be clarified that each IDA curve is specific, mainly due to differences in the frequency contents of seismic records. Figure 8 shows the fragility curves for the structures TE-1 and TE-1RF, where the average probability of collapse is reached for spectral accelerations of 0.157 g and 0.14 g, respectively.
Figure 9 shows the collapse probability fragility curves for the TE-2 and TE-2RF structures, where the average collapse probability is reached at 0.155 g and 0.145 g spectral accelerations.
Consequently, determining the average probability of collapse through spectral acceleration relates the fragilities of the non-structural components with the repair costs shown next.

3.4.2. Drift

The fragility curves obey the lognormal distribution function shown in (1). In addition, the FEMA-P-58 methodology offers its formulations to calculate the statistical parameters of median and standard deviation through (2) and (3) [6]:
l n θ = 1 n n = 1 n l n P E n
β = 1 n 1 n = 1 n l n P E n θ 2
where θ is the median value, PE is the evaluator parameter, n is the data number for an associated damage state, and β is the standard deviation.
A numerical example for constructing a fragility curve, with the limits for one of the OMF systems, is shown in Table 5. Firstly, the maximum drift data for the RSN-864 record are classified according to the indicated limits. Then, using Equations (2) and (3), the results shown in Figure 10 are obtained. Finally, with the values of θ and β, the lognormal distribution is applied to graph the curves according to the calculated damage state.
The range for the distribution is given by the expected drifts between 0.1% and 5%, with probabilities of occurrence from 0% to 100%. Thus, damage limits are established to identify the seismic performance states of the structure, which are shown in Table 5, thereby tabulating the information obtained from the IDA analysis.
In Figure 11a, the global drifts are plotted against the probability of collapse for each damage state, resulting in the fragility curves for the TE-1 typology.
The analysis indicates that for the TE-1 structure, there is a 100% probability of reaching a life safety state (DS3) for a global drift of 2%. The probability of achieving the collapse prevention state (DS4) is 60% for the same drift value. It is concluded that the structure will suffer considerable damage that will entail a high repair cost or even a total loss. In contrast, the TE-1RF structure reaches low values of global drift, presenting a probability of around 83% of attaining an immediate occupational damage state (DS2), and it does not present a probability of collapse that compromises the structural integrity, that is, damage states DS3 and DS4 do not exist, as shown in Figure 11b.
In the case of the TE-2 structure, Figure 12a shows a 92% probability of reaching 2% drifts, which indicates a collapse prevention state (DS4). When analyzing TE-2RF, it is observed that the DS4 level is practically zero. In this case, Figure 12b shows the DS1 and DS2 levels in the normative range for drifts of 2%, which is expected to result in the need for minor repairs after an earthquake.

4. Results

Repair Costs

The current costs per square meter of construction are compared to the prices in the United States, in California, in 2011 [14]. According to research, the construction price per square meter is USD 1076.37/m2 [36]. An equivalence factor calculated by dividing the cost per square meter of construction in Ecuador by the price per square meter in the USA must be obtained [37]. It is clarified that these prices do not include indirect costs such as administrative expenses, unforeseen expenses, utilities, or the values of land or implementation sites [36]. The factors calculated for each structure are presented in Table 6.
A summary of the repair costs calculated at each level of seismic intensity is presented in Table 7. For the TE-1 typology, there is a total loss scenario based on seismic intensity 7, corresponding to a cost of USD 195,036.03, equivalent to a total loss of the structure. The same table shows how the losses range from 5.36% at seismic intensity 1 for an average acceleration of 0.068 g to 77.42% before the total loss of the building, with an average collapse acceleration of 0.392 g. All this is related to the total construction cost.
On the other hand, for the TE-1RF typology, the repair cost values range from USD 2222.22 and start at seismic intensity 2, with an average acceleration of 0.059 g, up to USD 54,666.66 at seismic intensity 10, with an acceleration of 0.221 g. In percentage terms, these values represent between 1.05% and 25.86% of the total replacement cost of the analyzed structure.
While for the TE-2 and TE-2RF typologies, the results are shown in Table 8, for the ordinary moment frame structure, there is a total loss scenario based on seismic intensity 8, that is, USD 176,097.95, with probable accelerations of 0.302 g. On the other hand, for TE-2, the cost is significantly reduced, reaching a maximum of 20,625.00 USD at seismic intensity 10, corresponding to accelerations of 0.212 g. The results are shown in Figure 13.
The calculated repair costs include all the elements that constitute the structure—structural and non-structural. The non-structural components show that the most affected are the masonry partitions, which were not included in the numerical models but were considered in the used method as a fragility component to calculate global and specific repair costs.
Graphically, these values are expressed in a bar diagram where the reduction in repair costs is clearly shown compared to a non-reinforced typology and one that is reinforced.
The costs for losses are presented as the probability for each seismic intensity level. Figure 14a shows a representation on a 3D surface of how the costs increase sharply from seismic intensity 3, with probable damage of 60% for around USD 50,000.00. It is observed that for TE-1, there is a 100% probability that with any level of seismic intensity, there will be some cost due to losses, making these typologies highly vulnerable.
Figure 14b represents the cost surface for the TE-1RF typology, while Figure 15a,b show the loss curves for the TE-2 and TE-2RF typologies, respectively. In general, a reduction in loss costs is observed for typologies reinforced with structural walls. This means the building can remain functional after a seismic event, and the interventions or rehabilitations will decrease.
The probability that a building reinforced with structural walls will incur high repair costs is relatively low if we compare it with the initial investment that must be made, since it is highly advisable to invest more capital in the initial phases of the project instead of facing scenarios of costly repairs or total losses.

5. Conclusions

This work has presented the differences between repair costs for OMF and OMF+SSW typologies by evaluating seismic performance using incremental dynamic analysis. Typical structural typologies framed within the CR+CIP/LFLSINF+DNO taxonomy have been used, built with minimum sections and reinforcement, which has led to weak performance in the face of a seismic event. The analysis has shown that in the long term, an increase in the initial investment of 10%, on average, can prevent total losses of buildings during their useful life. Indeed, a design with an initially adequate level of safety is more expensive. Still, in the long term, it is offset by reduced repair costs or even the total loss of the structure.
The fragility curves obtained for each typology have shown probabilistically the expected behavior in the face of a seismic event. In the case of the TE-1 structure, there is a 63% to 100% probability that the structure will suffer extensive damage. Conversely, for the TE-1RF typology, the chance of collapse has been significantly reduced, considering the 2% drift limit according to the NEC-15. Probabilities of up to 15% have been obtained for the DS3 damage state, improving seismic performance and facilitating rehabilitation work.
In the case of typology TE-2, it was noted that the probability of collapse for a maximum drift of 2% is between 55% and 100%. Furthermore, the fragility curves show that the damage state DS3 has a probability of occurrence between 95% and 100% for the analyzed structure. Similar to the case of the TE-1RF structure, for TE-2RF, the likelihood of collapse is considerably decreased, obtaining values around 95% for the damage state DS2. This implies that the structure could be occupied immediately after the seismic event. On the other hand, it has been found that the probability of entering the damage state DS3 for a 2% drift is less than 10% for practically all the cases analyzed.
Regarding the quantification of repair costs, a clear improvement was evident when comparing the TE-1 and TE-1RF systems. Thus, a 75% reduction in the repair cost was observed after the same seismic event, and there was no damage to the structural elements of the reinforced structure. A 90% reduction in the repair cost was obtained if the TE-2 and TE-2RF typologies were compared. Consequently, it was shown that using structural walls represents a rapid and safe solution to reinforce buildings, since they provide higher stiffness with relatively low investment and reduced architectural impact.
The typologies analyzed in this study correspond to the typical systems generally used as housing in the region, with easily understood terminologies for communicating the results with various stakeholders. This study constitutes a supporting action to facilitate the transition to seismic resilience, focusing on terms like repair costs to avoid high economic and social impacts.
Finally, future research should focus on developing fragility functions that include the region’s materials. In this way, a specific database of structural and non-structural components could be created to obtain results adjusted to the realities of Ecuador.

Author Contributions

Conceptualization, J.P.C.-F. and A.G.H.-B.; methodology, J.P.C.-F.; software, J.P.C.-F.; validation, J.P.C.-F. and A.G.H.-B.; formal analysis, J.P.C.-F.; investigation, J.P.C.-F.; resources, J.P.C.-F.; data curation, J.P.C.-F.; writing—original draft preparation, J.P.C.-F. and A.G.H.-B.; writing—review and editing, A.G.H.-B.; visualization, J.P.C.-F. and A.G.H.-B.; supervision, A.G.H.-B. All authors have read and agreed to the published version of the manuscript.


This work is part of the project 2023-PIS-004 from the Research Groups Propagation, Electronic Control, and Networking (PROCONET) and Structures and Constructions (GIEC) of Universidad de las Fuerzas Armadas ESPE.

Data Availability Statement

The data presented in this study are available on request from the corresponding author. The data are not publicly available due to privacy between authors and sponsor.


The authors thank Diego Arcos for writing assistance and proofreading.

Conflicts of Interest

The authors declare no conflict of interest.


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Figure 1. Performance-based analysis phases.
Figure 1. Performance-based analysis phases.
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Figure 2. Decision variables for determining performance.
Figure 2. Decision variables for determining performance.
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Figure 3. Schemes of the analysis models used. (a) Structural typology 1 without retrofit; (b) Structural typology 2, without retrofit; (c) Structural typology 3, with retrofit; (d) Structural typology 4, with retrofit.
Figure 3. Schemes of the analysis models used. (a) Structural typology 1 without retrofit; (b) Structural typology 2, without retrofit; (c) Structural typology 3, with retrofit; (d) Structural typology 4, with retrofit.
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Figure 4. (a) TE-1 and TE-1RF capacity curves for the X and Y directions; (b) TE-2 and TE-2RF capacity curves for X and Y directions.
Figure 4. (a) TE-1 and TE-1RF capacity curves for the X and Y directions; (b) TE-2 and TE-2RF capacity curves for X and Y directions.
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Figure 5. (a) Scaled response spectra; (b) average spectrum of the 11 selected seismic records.
Figure 5. (a) Scaled response spectra; (b) average spectrum of the 11 selected seismic records.
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Figure 6. (a) IDA curves for TE-1 and TE-1RF; (b) IDA curves for TE-2 and TE-2RF.
Figure 6. (a) IDA curves for TE-1 and TE-1RF; (b) IDA curves for TE-2 and TE-2RF.
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Figure 7. (a) IDA and pushover curves for TE-1 and TE-1RF; (b) IDA and pushover curves for TE-2 and TE-2RF.
Figure 7. (a) IDA and pushover curves for TE-1 and TE-1RF; (b) IDA and pushover curves for TE-2 and TE-2RF.
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Figure 8. Cumulative distribution function for spectral acceleration. (a) Collapse fragility curve, TE-1; (b) collapse fragility curve, TE-1RF.
Figure 8. Cumulative distribution function for spectral acceleration. (a) Collapse fragility curve, TE-1; (b) collapse fragility curve, TE-1RF.
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Figure 9. Cumulative distribution function for spectral acceleration. (a) Collapse fragility curve, TE-2; (b) collapse fragility curve, TE-2RF.
Figure 9. Cumulative distribution function for spectral acceleration. (a) Collapse fragility curve, TE-2; (b) collapse fragility curve, TE-2RF.
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Figure 10. Drift dispersion over time, RSN-864 record with an example of a numerical calculation.
Figure 10. Drift dispersion over time, RSN-864 record with an example of a numerical calculation.
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Figure 11. (a) RSN-864 fragility curves for TE-1; (b) RSN-864 fragility curves for TE-1RF.
Figure 11. (a) RSN-864 fragility curves for TE-1; (b) RSN-864 fragility curves for TE-1RF.
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Figure 12. (a) RSN-864 fragility curves for TE-2; (b) RSN-864 fragility curves for TE-2RF.
Figure 12. (a) RSN-864 fragility curves for TE-2; (b) RSN-864 fragility curves for TE-2RF.
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Figure 13. Cost comparison between (a) TE-1 and TE-1RF and (b) TE-2 and TE-2RF.
Figure 13. Cost comparison between (a) TE-1 and TE-1RF and (b) TE-2 and TE-2RF.
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Figure 14. Repair costs by intensities for (a) TE-1 and (b) TE-1RF.
Figure 14. Repair costs by intensities for (a) TE-1 and (b) TE-1RF.
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Figure 15. Repair costs by intensities for (a) TE-2 and (b) TE-2RF.
Figure 15. Repair costs by intensities for (a) TE-2 and (b) TE-2RF.
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Table 1. Denomination of structural typologies.
Table 1. Denomination of structural typologies.
Structural typology 1 TE-1—without retrofit
Structural typology 2TE-2—without retrofit
Structural typology 3TE-1RF—with retrofit
Structural typology 4TE-2RF—with retrofit
Table 2. Model properties.
Table 2. Model properties.
Number of floors4.
Floor height (m)2.702.402.702.40
Number of spans in X direction4.
Span length in X direction (m)
Number of spans in Y direction2.
Span length in Y direction (m)
Slab thickness (m)
Columns (m)0.30 × 0.300.25 × 0.250.30 × 0.300.25 × 0.25
Beams (m)0.35 × 0.250.30 × 0.200.35 × 0.250.30 × 0.20
Structural walls (m)--0.20 × 1.200.20 × 1.20
Concrete compressive strength, f′c (MPa)21.00
Concrete elastic modulus, Ec (MPa)21,538.11
Steel yielding strength, fy (MPa)420.00
Steel elastic modulus, Es (MPa)200,000.00
Table 3. Seismic records and scale factors.
Table 3. Seismic records and scale factors.
Seismic RecordIDFactorYearMw
San Fernando RSN-883.1819716.61
Irpinia_ Italy-01 RSN-2862.7019806.90
Loma Prieta RSN-7403.5319896.93
Cape Mendocino RSN-8272.0119927.01
Landers RSN-8641.5919927.28
Northridge-01 RSN-10832.1219946.69
Manjil_ Iran RSN-16331.1719907.37
Chuetsu-oki_ Japan RSN-48431.8220076.80
Iwate_ Japan RSN-57751.5620086.90
Darfield_NZ RSN-69711.7120107.00
Pedernales 16APED 16-A1.2620167.60
Table 4. Significant duration of seismic records.
Table 4. Significant duration of seismic records.
Seismic RecordDuration (s)Significant Range (s)Effective Duration (s)
PED 16-A1754.65–34.5629.91
Table 5. Damage states, according to story drifts.
Table 5. Damage states, according to story drifts.
Structural SystemOperational DS1Immediately Occupational DS2Life Safety DS3Collapse Prevention DS4
Ordinary moment-resistant frames0.20%0.50%1.00%>1.00%
Structural walls1.00%2.20%2.60%3.60%
Table 6. Cost multiplier factor.
Table 6. Cost multiplier factor.
Structure TipologyCost/m2Factor
TE-1USD 406.33USD 1076.370.38
TE-1RFUSD 440.420.41
TE-2USD 434.810.40
TE-2RFUSD 479.230.45
Table 7. Repair costs in USD TE-1 and TE-1RF.
Table 7. Repair costs in USD TE-1 and TE-1RF.
Seismic IntensityStructural Typology
USD 195,036.03
% LossesTE-1RF
USD 211,401.93
% Losses
1USD 10,461.545.36%USD 0.000.00%
2USD 32,600.0016.71%USD 2222.221.05%
3USD 52,777.7727.06%USD 7000.003.31%
4USD 64,666.6633.16%USD 14,833.337.02%
5USD 90,666.6646.49%USD 21,375.0010.11%
6USD 151,000.0077.42%USD 32,125.0015.20%
7USD 195,036.03100.00%USD 37,400.0017.69%
8USD 195,036.03100.00%USD 44,600.0021.10%
9USD 195,036.03100.00%USD 47,545.4522.49%
10USD 195,036.03100.00%USD 54,666.6625.86%
Table 8. Repair costs in USD for TE-2 and TE-2RF.
Table 8. Repair costs in USD for TE-2 and TE-2RF.
Seismic IntensityStructural Typology
USD 176,097.96
% LossesTE-2RF
USD 194,086.95
% Losses
1USD 9200.005.22%USD 0.000.00%
2USD 27,100.0015.39%USD 0.000.00%
3USD 38,285.7121.74%USD 598.130.31%
4USD 47,727.2727.10%USD 2653.061.37%
5USD 66,000.0037.48%USD 5272.722.72%
6USD 104,500.0059.34%USD 8727.274.50%
7USD 142,000.0080.64%USD 11,083.335.71%
8USD 176,097.95100.00%USD 14,375.007.41%
9USD 176,097.95100.00%USD 18,384.619.47%
10USD 176,097.95100.00%USD 20,625.0010.63%
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Chicaiza-Fuentes, J.P.; Haro-Baez, A.G. Seismic Repair Cost-Based Assessment for Low-Rise Reinforced Concrete Archetype Buildings through Incremental Dynamic Analysis. Buildings 2023, 13, 3116.

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Chicaiza-Fuentes JP, Haro-Baez AG. Seismic Repair Cost-Based Assessment for Low-Rise Reinforced Concrete Archetype Buildings through Incremental Dynamic Analysis. Buildings. 2023; 13(12):3116.

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Chicaiza-Fuentes, Juan Patricio, and Ana Gabriela Haro-Baez. 2023. "Seismic Repair Cost-Based Assessment for Low-Rise Reinforced Concrete Archetype Buildings through Incremental Dynamic Analysis" Buildings 13, no. 12: 3116.

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