1. Introduction

The precast construction has a great potential to help overcoming the construction industry from several challenges such as aging infrastructures, reduced population and labor, high construction cost etc. The cost effectiveness and high-quality construction have resulted in its widespread use, including the countries with high seismicity (Kurama et al. 2018)⁽²²⁾. The construction industry in Korea is also adopting new trends of pre-fabrication through industrial automation with reduced manpower and improved construction quality and efficiency. However, the design standards practiced in precast construction industry were initially developed for cast-in-place construction. Specially, regarding the seismic design for the precast concrete structures, the Korean Standards (KCI 2017)⁽¹⁹⁾, stipulates that the “precast special moment frames shall satisfy the relevant design criteria”.

However, the code does not specify the appropriate response modification factor, system overstrength factor and displacement amplification factor etc. for precast concrete frames as it does case of cast-in place concrete frames.

The precast structures are developed by connecting pre- fabricated RC elements on site, the performance of precast structures under seismic excitation is highly dependent on the strength, stiffness, and deformation capacity of the connections. The connections of precast structures usually become the weaker points, hence the poor seismic performance of precast buildings in past earthquakes has often been attributed to poorly designed and built connections (FIB 2003)⁽¹⁶⁾. Several studies (Englekirk 1986; Hawkins and Englekirk 1987; Park 1995; ACI-ASCE 2001)^(4,13,28) emphasized on special attention to the connections of the precast concrete structures for safe and economical seismic design. Seo and Lee (1999)⁽³²⁾, Lee et al. (2009)⁽²³⁾ and Choi et al. (2010)⁽¹⁰⁾ conducted experiments on various types of joints to evaluate the structural performance of the connections of precast concrete frames.

The seismic performance of precast structural systems and elements including connections, have actively been investigated in different parts of the world. Specially the research efforts under the US-Japan cooperative research program on precast seismic structural systems (PRESSS) provided a base for several seismic design guidelines (Priestley 1991)⁽²⁹⁾. Restrepo et al. (1995)⁽³⁰⁾ tested six types of sub assemblages of moment resisting frames located at the perimeter of buildings. Connections between the prefabricated elements were realized at beam midspan or at the beam-to-column joint region with cast in- place concrete.

The experimental results showed that the connection details can be successfully designed and constructed to emulate cast-in- place construction. In Europe, a collaborative five-year research project called SAFECAST was conducted to study the behavior of precast concrete buildings under earthquake loading.

In Korea, the guidelines for precast concrete building structure were first published by the Architectural Institute of Korea (AIK 1992)⁽⁵⁾. The code recommended that the seismic analysis of the precast concrete members shall be carried out with reduced modulus of elasticity (1/4 of the general concrete) considering influence of the weaker performance of precast member joints. Additionally, the code suggested to use a response correction factor of 3.0, 4.5, 4.0 or 5.0 for the bearing wall structural system, moment resistance frame, and dual precast structural systems, respectively. On the other hand, in the KCI (2017)⁽¹⁹⁾, moments frames are classified into ordinary, intermediate, and special moment frames for cast-in place RC structures, but the code doesn’t include any specifications for seismic design of precast moment frames. Similarly, the Building Structural Standards (KBC 2016)⁽⁶⁾ also doesn’t recommend any seismic design guidelines for precast concrete structures, which causes difficulties for the practicing engineers. The current ACI 318-19 (ACI Committee 318 2019)⁽¹⁾ standards stipulates the details of the connections for precast special moment frames, but no special rules are set for precast intermediate moment frames. Other guideline on precast concrete structures (ACI T1 2001, 2003; ACI-ASCE 2001)^(2,3,4) allow the use of the similar seismic coefficients for precast concrete structure with similar performances to that of the cast-in-place concrete structure. The basic concepts of seismic design standards practiced in Korea are similar to the ACI 318-19 (ACI Committee 318 2019)⁽¹⁾ standard, but there are few regulations that can actually review the performance of precast concrete structures. Therefore, if the concept of seismic design for precast concrete based on ACI 318-19 (2019)⁽¹⁾ is introduced in the Korean Building Code AIK (2016)⁽⁶⁾, a separate restriction condition is required to ensure safety. Therefore, in this study, the performance of the connection between the precast concrete intermediate moment frame and the special moment frame was examined by adjusting the seismic load size of the design load combination.

Although, the design codes allow emulative connections for precast concrete structures which can be simulated as equivalent cast-in-place monolithic connections. However, studies (Khoo et al. 2006; Saghi and Shariatmadar 2016)^(20,31) suggest that due to difficulties in construction process, the precast joints can hardly achieve strength and stiffness similar to cast-in-place monolithic connections and under seismic events substantial inelastic deformations are noticed in precast connection regions. Considering such strength, deformation and energy dissipation capacity reduction of precast connections compared to cast-in- place monolithic joints, the RC frames with different levels of deformation capacities were analyzed, in this study. The analyses were conducted first on two RC intermediate moment resisting plane frames without considering the performance reduction due to precast construction in order to set a base for further analysis. In the second stage, the RC frames with reduced ultimate strength and deformation capacity were considered for analysis so called the potential performance reduction in precast concrete frames connection can be accounted for. The two frames with reduced performance had deformation capacities equal to 75 % and 50 % of those for the initial frame based on the FEMA 356 (FEMA 2000)⁽¹⁵⁾. Finally the response modification factors for the selected structures were calculated using the method suggested in ATC-19 (1995)⁽⁸⁾ guidelines.

2. Response Modification Factor

The conventional force-based design approaches are suitable for designing the structures with permanently applied actions. The current seismic design procedures follow the similar design approach, while keeping allowance for the inelastic deformations utilized to absorb seismic energy which leads to reduction in the design level forces. These codes carry out this design process by allowing the use of a response modification or force reduction factor, hereafter called R-factor, to reduce the elastic shear force demand to the design level shear force. The R-factor accounts for several important parameter such as material and system over- strength, seismic energy absorption and dissipation, indeterminacy of structural systems to redistribute seismic forces from highly deformed regions to low deformed regions etc. This factor is quite unique for every structural system. Therefore, for each structural system, a unique R-factor is needed and assigned for calculating the design base shear. Fig. 1 shows the definitions given in ASCE 7 (ASCE 2002)⁽¹²⁾ for response modification factor. If the structures are designed to remain within the elastic range, the relationship between the base shear and roof displacement will follow a linearly elastic response, as shown with dotted line in Fig. 1. However, the actual structural responses deviate from the linear elastic line after a certain force-deformation level, depending on the material and system configurations. When the base shear reaches a level slightly higher than the design base shear ($V_{d}$), the inelastic deformations or the plastic hinges develop. The systems dissipate energy through inelastic deformations until the base shear reaches a maximum value ($V_{\max}$).

In the design process, the elastic force demands are reduced to the design level force by using the R-factor, which the seismic design guidelines justify by relying on the reserve strength and ductility of the structural systems. The ATC-19 (1995)⁽⁸⁾ suggests that the R-factor assigned to any structural system shall account for three parameters; the strength, ductility and the system redundancy. The assigned R-factors are determined by separately calculating the values of each component. However, studies (Zafar 2010)⁽³³⁾ system redundancy can be considered as a parameter contributing to overstrength. Adopting the similar approach, in this study, the response modification factor for the precast concrete moment frames is calculated by accounting for the two parameters, the ductility and over-strength. Thus, the definition of R-factor adopted in this study is given as;

Fig. 1. Definition of response modification factor

where, $R_{u}$ is the parameter accounting for the ductility and $R_{o}$ factor considers the system over-strength.

The ductility factor reduces the elastic demand force ($V_{e}$) to the level of maximum force ($V_{\max}$), which may be represented as follows;

The ductility related factor ($R_{u}$) depends on the global ductility ($\mu$) of the well-detailed structural systems where $\mu$ is the ratio of the maximum roof displacement to the roof displacement at yield. Several methods (Newmark and Hall 1982; Krawinkler and Nassar 1992; Miranda and Bertero 1994; Borzi and Elnashai 2000)^(9,21,25,26) are developed to relate the ductility related factor ($R_{u}$) to the global structural ductility demand factor ($\mu$). In this study, Newmark and Hall’s method (Newmark and Hall 1982)⁽²⁶⁾ is adopted which is given as;

where, $T$ is the pre-yield vibration period of idealized single- degree of freedom (SDOF) system.

On the other hand, the overstrength parameter ($R_{o}$) accounts for the material as well as system overstrength resulting from factors such as low gravity load at the time of seismic load application, use of strength reduction factors, higher actual material strengths than the specified values, redundancy of the structural systems etc. This parameter can be defined as the ratio of the maximum base shear ($V_{\max}$) to the design level base shear ($V_{d}$) which is given as;

3. Model Structures

In this study, the analytical models for the 8-story plane precast RC intermediate moment resisting frames were developed using software program PERFORM-3D. PERFORM-3D is specialized software package developed for the damage assessment, specifically intended for performance-based seismic assessment of structures (Mamun and Saatcioglu 2017⁽²⁴⁾. The program allows monitoring the inelastic behavior of structural components with different level of deformation. Since the precast structures are developed by connecting pre-fabricated RC elements on site, the connections of such structures usually become the weaker points. Although, the design codes (FEMA 1997; IBC 1997; ACI Committee 318 2019)^(1,14,17) allow emulative connections for precast concrete structures which can be simulated as equivalent cast-in-place monolithic connections. However, studies (Khoo et al. 2006; Saghi and Shariatmadar 2016)^(20,31) suggest that due to difficulties in construction process, the precast joints can hardly achieve strength and stiffness similar to cast-in-place monolithic connections and under seismic events substantial inelastic deformations are noticed in precast connection regions. In order to analyze the connection details, material model should include bonding between concrete and reinforcement bars in the joint sections. But bonding performance varies widely depending on the type of joints. So in this study, analyzing structure model was taken into place to evaluate the overall performance of the PC frame. Considering such strength, deformation and energy dissipation capacity reduction of precast connections compared to cast-in-place monolithic joints, the RC frames with different levels of deformation capacities were analyzed. The analyses were conducted first on two RC intermediate moment resisting frames (X-X’ and Y-Y’ frames), selected from the 3-dimensional frame given in Fig. 2, without considering the performance reduction due to precast construction in order to set a base for other analysis. This initial frame is represented as B-IMRF which stands for “basic intermediate moment resisting frame”. In the second stage, the RC frames with reduced ultimate strength and deformation capacity were considered for analysis so called the potential performance reduction in precast concrete frames connection can be accounted for. The model frames with reduced performance had strength and deformation capacities equal to 75 % and 50 % of those for the basic frame based on the FEMA 356 (FEMA 2000)⁽¹⁵⁾. The models were named as 75B-IMRF and 50B-IMRF, where the numbers 75 and 50 represent the percentage of strength and deformation considered.

Fig. 2. Basic plan and elevations of selected frame for analysis

The plan of the selected structures is given in Fig. 2(a). Two plane frames (Frame X-X’ and Y-Y’) where chosen for the analysis to assess the performance of structure in X- and Y-directions. The selected plane frames had 5 bays each with widths of 10.8 m and 8.4 m for X-X’ and Y-Y’ frames respectively. The reinforcement arrangement and cross-sectional details of beams and columns are given in Table 1 and 2. The concrete compressive strength ($f_{c}'$) of 24 MPa and reinforcement yielding strength ($f_{y}$) of 400 MPa and 500 MPa for D16 rebars and D19 and above were used, respectively. The buildings were modelled as a bare frame, neglecting any possible contributions from non-structural elements. The beams were modeled as FEMA beam concrete type, with bi-linear force-deformation curve considering the strength loss and deformation capacities based on the modelling parameters and numerical acceptance criteria for nonlinear analysis defined in FEMA 356 (FEMA 2000)⁽¹⁵⁾. The selected FEMA beams had symmetrical sections at the ends. The compound beam elements were considered to be under equal and opposite moments at the ends resulting from the self-weight and element load with an inflection point at the midspan. The compound beams were divided into two segments, with each segment modelled as an inelastic FEMA beam element. The width of beam integral with the attached column was modelled as a rigid segment having 10 times more the rigidity of the beam element in order consider a rigid beam-column joints. The columns were also modeled using FEMA concrete column elements. Similar to the beam element, FEMA columns also comprised of two inelastic columns segment. The force-deformation (moment-rotation) backbone curves for beams and columns were developed based on the FEMA 356 guidelines (FEMA 2000)⁽¹⁵⁾ as shown in the Fig. 3. The yielding and ultimate moment capacities were calculated using a sectional analysis program and the rotation deformation/rotation capacities were calculated using the code guidelines (FEMA 2000)⁽¹⁵⁾ according to the sectional and material properties of the members. In order to account for the reduction in the strength and deformation performance of RC precast moment connections, the strength and deformation values were reduced by 75 % and 50 % of the initial frames.

Fig. 3. Adopted load-deformation relationship of FEMA beam/column elements of intermediate moment resisting frame models

4. Nonlinear Static Pushover Analysis

Fig. 4. Base shear vs. Roof drift ratio of frame

The nonlinear static analyses were conducted on the structural models discussed above using PERFORM-3D. One of the important things to consider in the pushover analysis is the selecting a load distribution pattern. The FEMA standards (FEMA 2000)⁽¹⁵⁾ suggest to use uniform or triangularly distributed load pattern. The program PERFORM-3D provides three options for pushover load patterns including; 1) distribution based on nodal load pattern, 2) load distribution based on the masses and a specified displacement variation over the structural height, and 3) distribution of loads based on the masses and mode shapes of the structures (CSI 2006)⁽¹¹⁾. In this study, the pushover load distribution pattern based on the masses and mode shapes was selected. Fig. 4(a) and Fig. 4(b) compare the results of the pushover analysis in terms of base shear vs. roof displacement of the model frames X-X’ and Y-Y’, respectively. The maximum base shear of structure B-IMRF in X-X’ and Y-Y’ direction was noticed to be 3,694 kN and 3,894 kN, respectively. For frames 75B-IMRF and 50B-IMRF the base shear for X-X’ direction was 3,440 and 3,084 kN, while for Y-Y’ direction it was 3,545 kN and 3,083 kN, respectively. It can be observed that with reducing the section strength as discussed above, the base shear was decrease, whereas the ultimate roof deflections were increased. The bi-linearized backbone curves of all analyzed frames are given in Fig. 5.

5. Calculation for Response Modification Factor

As discussed above the response modification factor is calculated in this study as a product of factor accounting for structural ductility ($R_{u}$) and the system overstrength ($R_{o}$). For calculating the ductility related factor Newmark and Hall’s approach (Newmark and Hall 1982)⁽²⁶⁾ was used which involves the roof displacement ductility ratio ($\mu$) and the fundamental period of vibration ($T$). The vibration period was calculated through code specified formula, which was greater than 0.50 sec. The roof displacement ductility ratio ($\mu$) was taken as the ratio of the ultimate roof displacement to the roof displacement at idealized yielding. The idealized yielding displacement ($\Delta_{y}$), was determined by using the method suggested by (Pan and Moehle 1989)⁽²⁷⁾, as shown in Fig. 3. In this method, a secant line was drawn to intersect the base shear-deflection response curve at $0.75V_{\max}$ ($V_{\max}$is the base shear). The secant line was extended to intersect a horizontal line corresponding to the maximum base shear, and then projected on the horizontal axis in order to obtain the yield deflection ($\Delta_{y}$). While the ultimate roof displacement capacity of the model structures was taken as the displacement capacity corresponding to the life safety (LS) drift limit of structure. The displacement capacity corresponding to the LS limit states was computed in accordance with the FEMA 356 (FEMA 2000)⁽¹⁵⁾, which is taken as 0.75 of the drift corresponding to the collapse prevention limit state. Ultimate displacement capacity was divided to the yield displacement to calculate the ductility ratio $\mu$, which in the present case is equal to the ductility factor $R_{\mu}$. Finally, the response modification factor $R$ was quantified for all frames in X-X’ and Y-Y’ direction by multiplying the ductility factor $R_{\mu}$ to the overstrength factor $R_{s}$. The final value of R-factor for each frame was taken as average value of response modification factor in both directions. The calculated seismic response parameters are shown in Table 3.

Fig. 5. Bilinearized backbone curve

The calculated $R$ factor for B-IMRF frame was found to be approximately 6.5. In case of frames with reduced strength and deformation capacities, the calculated $R$ factor was 6.3 in case of frame 75B-IMRF and 5.4 in case of frame 50B-IMRF. Table shows the base shear at yield, maximum based shear, ductility related factor, overstrength factor and the response modification factors for all the selected structures.

6. Conclusions

In this study, the response modification factor of precast RC moment resisting frame was determined by analyzing RC frames with different strength and deformation capacities through PERFORM-3D. The analyses were first conducted on the precast RC frame with strength and deformation capacities equivalent to a monolithic cast-in place intermediate moment. In next phase of analysis, the frames with reduced strength and deformation capacities in accordance with FEMA 356 standards were investigated. The R-factor was finally calculated by evaluating a ductility related factor and system overstrength factor which accounts for material overstrength and redundancy of the structural system. The calculated value of R-factor for frame B-IMRF, 75B-IMRF and 50B-IMRF were 6.5, 6.3 and 5.4, respectively.