Performance-based seismic assessment method for medium-rise RC buildings

Severe earthquakes registered in Turkey over the last five decades have shown that most of the existing buildings exhibit low resistance to earthquake action. In this study, a simplified version of the performance based rapid seismic assessment method (PERA) is proposed for the analysis of medium-size reinforced-concrete buildings. The influence of a critical storey is also considered when evaluating performance of the entire building. Good agreement is obtained between predictions by the simplified method, the PERA method, and the code based structural performance assessment procedures.

The Japanese Seismic Index Method [11], Hassan and Sozen method [12], Yakut [13], P25 method [14], and the New Zealand Society for Earthquake Engineering method [15], can be used for the analysis in cases when the building density is too high, and when the time and material resources are limited. There are many studies in the literature aiming to adapt the Japanese Seismic Index Method to Turkish buildings [16][17][18][19][20]. Favvata et al. [21], Ni [22] and Ozmen and Inel [23] assessed the inelastic effect of rapid screening parameters on seismic performance of RC buildings. Priestley [24], Chandler and Mendis [25], Lervolino et al. [26], Ruiz-Garcia and Miranda [27] and Jeong et al. [28] proposed seismic evaluation methods taking into account probabilistic approaches. Other researchers compared various assessment methods (Lupoi et al. [29] and Kalkan and Kunnath [30]) Also, methods for analysing seismic performance of existing buildings are given in appropriate codes and guidelines (e.g., TSC 2007; NZSEE 2012 Eurocode 8 Part 3; ASCE 41) [1,15,31,32]. The details of these approaches are given in Ilki et al. [33].
In addition to detailed structural analyses that can take considerable time and computing resources, on-site inspection studies are also required when applying these methods for large stocks of vulnerable buildings in developing countries. Ilki et al. [33] proposed a simpler method that minimizes the scope of field investigations. This method involves a simpler approach and is more reliable compared to other methods proposed in the literature. The first vibration mode of earthquake effect is proposed for dominant reinforced concrete frame structures. This method is based on the member tributary area concept and GRAĐEVINAR 71 (2019) 8, 663-672 On performance-based seismic assessment method for medium-rise RC buildings includes various simplifications and assumptions related to the structural analysis and performance-based evaluation. It makes use of the Muto principles [34] and performance criteria given in TSC 2007 [1]. Some assumptions about the type of elements, diameter and spacing of longitudinal and transverse reinforcing bars, the shear and axial-flexural capacities of columns, concrete quality, geometric ratio, and locations of columns, are considered. Since the seismic safety assessment is based on TSC 2007 [1], potential problems such as non-compliance with the code of conduct, likely to occur if other quick evaluation methods are used, are reduced to minimum [33].

PERA procedure
The data collected from recent earthquake clearly show that most of the structures situated in earthquake zones are vulnerable to seismic load [33]. In order to avoid catastrophic consequences of earthquakes, it is necessary to sort the buildings susceptible to seismic action and take the necessary precautions. In this respect, a performance-based quick and low-cost evaluation procedure should be presented and compared to conventional code-based seismic evaluation procedures. Most of these assumptions are mentioned in this method for many RC frame structures in Turkey. However, modifications might be in order for use in other countries. Nevertheless, the methodology of Ilki et al. [33] is useful in all seismic regions where reinforced concrete buildings are widespread. The seismic performance of RC frame buildings was evaluated according to TSC 2007 performance-based assessment principles in the method of Ilki et al. [33]. TSC 2007 [1]consider irregularities of the building and detailed structural characteristics, together with local soil class and the earthquake zone in which the building is located. The demand/capacity ratios of structural elements should be obtained to determine the building performance. The elastic internal force demands and capacities are first determined, and the demand/capacity ratios are then calculated for each building element. This is followed by determination of member damage levels depending on the demand/capacity ratios and inter-storey drifts. The expected failure modes of structural elements, confinement properties, and levels of axial and shear forces, are taken into account when determining the damage levels. And, finally, the level of seismic performance of the building is determined. According to its approach, the PERA (Performance Based Rapid Seismic Assessment) method [33] is similar to the method proposed in TSC 2007 [1]. In this method, the duration of site inspections is significantly reduced, and the stages of analysis and evaluation are simplified. This method estimates damage levels of the columns of the ground storey and its inter-storey. The flexural strength and moment capacity of the beams are estimated based on reinforcement rates and beam measurements and observations at typical building structures. In addition, the method assumes the reinforcement configuration of the columns.
Structural irregularities shown in Table 1 as per TSC 2007 [1] are considered through penalty coefficients in the PERA method [33]. The amount of data required is lower compared to the data needed in the above-mentioned rapid and preevaluation methods. Thanks to the determination of concrete quality with a limited number of tests, appropriate stirrup spacing and type of reinforcing bars, and use of different modes of comparison, the algorithm used is more realistic compared to classical method. The PERA method [33] assumes that the ground storey of the building is the critical storey, as defined in the RDRS [2] with regard to seismic loads. The base shear force (V b ) is given in Eq.
(1), where A o (Table 2) is the effective ground acceleration, W is the building weight (G + 0.3Q), G and Q are the dead and live loads, respectively. The spectrum coefficient S(T) is defined in TSC 2007 ( Figure 3). The T A and T B are corner periods ( Table 3). The natural vibration period of the building is estimated by Eq.
(2). A coefficient of 0.85 is used in Eq. (1) to take into account the effects of high vibration modes used in the TSC 2007 approach. The 'n' used in Eq. (2) is the number of stories contributing to the first vibration mode on the investigation side. Detailed calculations should be done to calculate the natural period of construction in a more complex way.   Table 3.

Spectrum characteristic periods (T A , T B ) (TSC 2007) [1]
V ij is the column shear force (Eq. 3) where h i and I i are heights and the moment of inertia of the ground storey columns, respectively. The y coefficient is a summation of values and is calculated by Eq. (4) where is the inflection point coefficient.
(3) y = y 0 + y 1 + y 2 + y 3 (4) In the PERA method [33], it is assumed that, while coefficients are ignored. y 0 values are given in Muto (Table 4) [34] for sway loading for wind and seismic loading separately. The stiffness ratio ( ) is given in Eq. (5). k 1 and k 2 are beam stiffness values, and k c is the column stiffness. As to the effect of cracking on stiffness, the beam section is assumed to be a rectangular section. Most of these assumptions are made to enable quick assessment of the building, and to speed up and simplify site investigations [33].
(for exterior columns) (for interior columns) In the PERA method [33], the first and last (exterior) axes are marked as x 1 , x 2 in the x-direction and y 1 , y 2 and in the y-direction of the structure. The corner columns are marked as x 1 y 1 , x 2 y 1 , etc. (Figure 4).
In Eqs (10) and (11), r1 i and r2 i are demand-capacity ratios of the columns. Damage levels are determined using Table 5. In this table, MN, SL and FL denote the minimum damage, safety and failure limit, respectively. The damage boundary is determined according to the relative storey drift ratio (Table 6). (10)

Proposed method
PERA [33] has been modified in the scope of this study. Thus, the present study is an alternative to the PERA method [33] for reinforced concrete frame buildings.. The proposed methodology makes use of the approaches presented in the very well-known Smith method [35]. The contra-flexure point occurs in the middle of all members of the frame in Smith method [35], as shown schematically in Figure 5. An approach for estimating inflection point of beams and columns is presented in the Smith method [35]. The basic assumptions made in the development of the Smith method  In the Smith method [35], the inflection point coefficient is taken as y = y 0 + y 1 + y 2 + y 3 = 0.50, giving the location of   On performance-based seismic assessment method for medium-rise RC buildings the point of zero moment at the mid height of the column from the base of the column, as shown in figures 5 and 6. This assumption is very important to prevent the possibility of using a wrong value by practicing engineers, and to save time for calculating individual values y 0 + y 1 + y 2 + y 3 .  Figure 7, and main characteristics of buildings B1-B15 are presented in Table 7. As shown in this table, all buildings are located in Earthquake Zone 1. The Earthquake Zone 1 is defined as a high seismic-risk zone. Number of stories of the buildings varies between three and four. Most of the building were built between 1975 and 2000 in accordance with TSC 1975 [38].

Results and discussion
The grade S220 steel was used for reinforcing bars of older buildings, constructed before 2000, while the steel grade S420 was used for the remaining buildings. The buildings were subjected to horizontal load along two principal inplane axes. The compressive strength values of concrete amounting to 10, 14, and 20 MPa, were assumed. Z2 and Z3 local soil classes were separately considered in the analysis (Table 3).  Table 12.
The results of the analyses using the PERA method [33] are given in Table 9 and compared with the rigorous analysis by TSC 2007 [1]. If estimations given in TSC 2007 [1] are accepted as reference values, as given in Table 9, the results of the PERA method [33]  On performance-based seismic assessment method for medium-rise RC buildings Figure 8 shows the effect of several parameters such as concrete compressive strength values (C10, C14, and C20), shear reinforcement (confinement, no confinement), and soil conditions (stiff, soft), on TSC 2007 [1] predictions. In this figure, the horizontal x-axis corresponds to concrete compressive strength, the vertical y-axis corresponds to percentages of unsafe cases in each parameter group. The percentage of unsafe cases generally decreases with an increase in concrete compressive strength.
In addition to an overall comparison between TSC 2007 [1] and the proposed method, the effect of the concrete compressive strength, presence of sufficient confinement, and soil conditions, on the performance of the proposed method is evaluated in Figure 9. In this figure, the confinement status (confinement, no confinement) and soil conditions (stiff, soft), are defined as data series corresponding to four parameter groups. The vertical axis now corresponds to the percentage of the analysis results for the safe case according to TSC 2007 [1]. These results were predicted successfully by the proposed method. According to Figure 9, highly successful prediction rates relative to the TSC 2007 [1] results were obtained for two out of four parameter groups.

Conclusions
A simplified version of the PERA method for rapid evaluation of seismic safety of the existing medium-rise reinforced concrete frame structures is proposed in the paper. The performance based rapid seismic assessment method (PERA) is modified in this study. The analysis steps of the PERA procedure were used by replacing the Muto method with the Smith method. The integrity of the presented method is validated for common medium-rise reinforced concrete frame structures for which the first mode of vibration is dominant. The proposed method exhibits an acceptable level of agreement for both safe and unsafe cases. A good agreement is obtained between the proposed method, the PERA method and conventional detailed seismic safety assessment analyses carried out for 720 different cases representing typical medium-rise reinforced concrete frame buildings in Turkey. A comparison of building performance for 720 cases using the rigorous TSC 2007 [1] approach and the proposed method is also presented. The predictions of the proposed method result in 337 safe and 383 unsafe cases, or 47 % and 53 % of the 720 cases, respectively. These values point to an acceptable level of correspondence between the values of the proposed method and TSC 2007 [1] (34 % and 66 %, respectively). It should be noted that the pace of application of the proposed method is remarkably higher compared to conventional structural performance assessment methods. Not only the accuracy of the presented method is acceptable for structures with limited structural irregularities, but also the pace of implementation is considerably higher in comparison with current conventional structural performance assessment methods. Further study is required to evaluate and improve reliability of the proposed rapid seismic assessment method for structures with significant irregularity defined in conventional structural performance assessment methods, and structures with shear walls in two principal directions.