Volume 7, Issue 3 e13114

RESEARCH ARTICLE

Open Access

Seismic Evaluation of Plan Asymmetry Effects in an Older Infill Framed Reinforced Concrete Building Structures

Aslam F. Mohammad,

Corresponding Author

Aslam F. Mohammad

[email protected]

orcid.org/0000-0002-2552-5466

Department of Civil Engineering, NED University of Engineering and Technology, Karachi, Pakistan

Correspondence:

Aslam F. Mohammad ([email protected])

Contribution: Conceptualization, Investigation, Writing - original draft, Writing - review & editing, Methodology, Software

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Marco Faggella,

Marco Faggella

CONSTRUCT-LESE, Faculty of Engineering (FEUP), University of Porto, Porto, Portugal

Contribution: Conceptualization, Writing - review & editing, Methodology

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Rashid A. Khan,

Rashid A. Khan

Department of Earthquake Engineering, NED University of Engineering and Technology, Karachi, Pakistan

Contribution: Conceptualization, Writing - review & editing, Methodology

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Sami U. Haq,

Sami U. Haq

Department of Civil Engineering, NED University of Engineering and Technology, Karachi, Pakistan

Contribution: Writing - review & editing, Methodology, Software

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Muhammad Saim,

Muhammad Saim

Department of Earthquake Engineering, NED University of Engineering and Technology, Karachi, Pakistan

Contribution: Conceptualization, Methodology, Writing - review & editing

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Aslam F. Mohammad,

Corresponding Author

Aslam F. Mohammad

[email protected]

orcid.org/0000-0002-2552-5466

Department of Civil Engineering, NED University of Engineering and Technology, Karachi, Pakistan

Correspondence:

Aslam F. Mohammad ([email protected])

Contribution: Conceptualization, Investigation, Writing - original draft, Writing - review & editing, Methodology, Software

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Marco Faggella,

Marco Faggella

CONSTRUCT-LESE, Faculty of Engineering (FEUP), University of Porto, Porto, Portugal

Contribution: Conceptualization, Writing - review & editing, Methodology

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Rashid A. Khan,

Rashid A. Khan

Department of Earthquake Engineering, NED University of Engineering and Technology, Karachi, Pakistan

Contribution: Conceptualization, Writing - review & editing, Methodology

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Sami U. Haq,

Sami U. Haq

Department of Civil Engineering, NED University of Engineering and Technology, Karachi, Pakistan

Contribution: Writing - review & editing, Methodology, Software

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Muhammad Saim,

Muhammad Saim

Department of Earthquake Engineering, NED University of Engineering and Technology, Karachi, Pakistan

Contribution: Conceptualization, Methodology, Writing - review & editing

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First published: 18 March 2025

https://doi.org/10.1002/eng2.13114

Funding: This work was supported by Computers and Structures, Inc (csiamerica).

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ABSTRACT

Several earthquake events revealed the severity of damage in reinforced concrete (RC) building structure mainly from the irregular placement of masonry infill and negligence of code compliant detailing provisions in structural components on building response. This study aims to evaluate the detrimental effects of nonuniform placement of infill panels in building structures constructed in regions susceptible to high seismic risk. Therefore, a finite element model (FEM) model of an older infilled frame RC building employed herein with various combinations of infill placement along with noncompliant detailing in structural components including bond-slip effects in plastic region of frame components and the short column effects from frame infill interaction. Results are presented in terms of modal periods and confirm that the period obtained from theoretical or empirical models reported in literature provides a good estimate. Furthermore, the interstory drift ratio (IDR) at ultimate limit states obtained from nonlinear static and dynamic analyses depict the poor performance of in-plan irregular configurations compared with the counterpart. Moreover, in irregular configurations, the roof displacement calculated from N2 and Extended N2 methods miscalculate the roof displacement obtained from nonlinear dynamic analysis and the difference in results increases from serviceability to ultimate limit states.

1 Introduction

It has been recognized from past earthquakes that buildings with asymmetric configuration are at high seismic risk compared with their symmetric counterparts [1] and these typologies are generally affected by large displacement demand at the flexible side of the structure. A building structure can be asymmetric in one-way or two way, the seismic response of one-way asymmetric building has been evaluated by several researcher [2-4]. However, the presence of complex interaction between translation and rotation components of earthquake, limited research reported on the two-way in-plan asymmetric RC structure subjected to the bidirectional seismic effects [5].

RC buildings with unreinforced masonry infills (URMIs) are commonly used around the world for low to mid-rise buildings, including high seismic zones. The URMIs interaction with frame components can develop fragile failure mechanism [6, 7]. Generally, the interaction between URMIs and the fragile frame components can lead to localized failures, including short or captive column effects [8], brittle failure of the beam-column joint or panel zone element, and soft or weak storey mechanisms, also noticed in uniformly distributed URMIs in elevation and not necessary damage initiated from the first storey. Whereas, in some cases for example the use of weaker URMI in comparison to frame components can attribute larger stiffness and strength, eventually decreasing the interstorey drift demand and delaying the process of soft-storey mechanism compared with the response of a bare frame [9]. In general, the damage observed in past events as a result of the interaction of URMIs with fragile frame components (beam and column). The F presence of soft-story, short-column effects, in-plan accidental torsional effects, thus increasing the damage even under moderate ground motions (GMs) [10].

Reported literature shows the abundant experimental and analytical database available on the response of infilled frame RC building structures and confirmed the expected inherent weaknesses of these systems, few are listed in Table 1.

TABLE 1. Reported experimental and analytical work on infilled frame structures.

Authors (year)	Salient features
Experimental studies
Mehrabi et al. (1996) [11]	According to Mehrabi experimental study, infill panels can greatly raise the efficiency of RC frames. In terms of load resistance and energy-dissipation capacity, specimens with strong frames and weak panels performed better than those with weak frames and strong panels.
Al-Chaar et al. (2002) [12]	The findings showed that, compared with bare frames, infilled RC frames have significantly greater ultimate strength, residual strength, and initial stiffness without sacrificing any ductility in the load-deflection response.
Anil and Altin (2007) [13]	Anil concluded from the experimental study, partially infilled RC frames exhibited significantly higher strength and stiffness than the bare frame. Furthermore, strength and stiffness are directly proportion to the aspect ratio of the URMIs.
Kakaletsis and Karayannis (2007) [14]	Based on these findings, it can be concluded that masonry infills with eccentrically positioned openings have been found to improve the strength, stiffness, ductility, and energy dissipation of the bare RC frames' seismic performance.
Analytical studies
Crisafulli et al. (2000) [15]	Crisafulli introduces a novel multi-strut formulation-based macro-model for the assessment of the structure's overall response. The model, uses a double truss mechanism and a shear spring in each direction to independently account for the compressive and shear behavior of URMI.
Al-Chaar and Mehrabi (2008) [16]	Al-Chaar investigated a finite element formulation for smeared cracks and a cohesive interface model to portray the behavior of the frame-to-panel interface as well as the behavior of mortar joints between masonry units.
Mosalam and Günay (2015) [17]	In a new method presented by Mosalam, URM infill walls' in-plane and out-of-plane interactions are considered in simulations of progressive collapse. The infill wall effect to cause column shear failure is also studied using a nonlinear shear spring modeling strategy.
Asteris et al. (2016) [18]	P. G. Asteris proposed a mathematical macro-model that can be utilized as a practically viable tool to determine the equivalent compressive strut width in the presence of opening in URMI.

There are no such design guidelines mentioned in the most recent seismic codes due to the significant randomness observed in experimental and analytical investigations relating to infilled frame buildings. However, past seismic events revealed that detrimental effects are significant in plan asymmetrical configurations generally induces due to the nonuniform arrangement of masonry infills in the plan and/or in elevation [19, 20].

Mondal et al. investigate the vertical irregularities and thickness variation effects on a six-story three bays RC infill framed structure. Mondal et al. [21] conducted parametric study using nonlinear static analysis (NSA) and concluded the effects of vertical irregularities by employing the response surface method.

Faggella et al. [22] investigated, several seismic codes prescribed design guidelines related to torsional behavior as a result of inherent and accidental eccentricities, these provisions enabled different sources of asymmetry in building structures. Furthermore, presence of plan asymmetry develops torsional effects at global level, which locally increases the unbalanced demand on structural components and eventually leading to collapse in strong seismic events.

Due to the irregular arrangement of infills, Eurocode 8 [23, 24] mandates increasing the seismic forces on frame components. Ferraioli et al. [25] investigated the efficacy of the EC-8 design provisions for plan asymmetry RC buildings generally induced by the use of irregular URMI and observed the shear demand imposed on frame components underpredicted by the code provisions in several cases. Additionally, the nonuniform placement of URMI in plan and elevation increases the eccentricity between the center of mass and the center of rigidity, eventually generating significant torsional and higher modes effects in major seismic events. When comparing the outcomes from the bare frame model with an accidental eccentricity of 10%, Ferraioli et al. suggested that the asymmetry in the plan be considered by increasing the accidental eccentricity by a factor of 2.0.

According to Fardis et al. [26], plan-eccentric infills alter the response of symmetric and uniform structure into torsionally unstable, while reducing or eliminating infill masonry in a storey may cause an increase in inelastic deformation demands in the corresponding columns and trigger a soft-storey mechanism.

The shear demand is greatly increased, especially in the columns of the outer frames, as a result of the torsional effects from the dynamic response of a structure that does not meet the uniformity criterion in both plan and elevation, as noted by Fardis [27].

Similarly, Messaoudi et al. [28] examined the effect of the nonuniform distribution of URMIs over the height of the building and concluded the fragile response of structure.

The nonductile response of irregular building structures was due to the inadequate interaction of URMIs with structural components, which eventually caused torsion and resulted in the collapse of the entire building structure [10].

The contribution of masonry infills is not considered in the design of structures because of the inherent uncertainties in their behavior; however, when evaluating the capacity of existing structures, the interaction of URMIs should not be disregarded (Moretti et al. [29-31]).

In addition, some other construction defects are also responsible for significant damage in building structures observed in past events. These defects include poor quality concrete, lack of shear reinforcement in panel-zone element or beam-column joints, poor confinement in plastic zones of columns, weak-column–stronger-beam formations, inadequate seismic/expansion joints, lap splice inadequacies, buckling of longitudinal column reinforcement, soft-story [32] or weak-story irregularities and short columns effects [33, 34].

In comparison to the nonlinear dynamic analysis (NDA), conventional nonlinear static methods, such as the pushover with N2 approach [35], significantly underestimate the demand on plan asymmetric structures, particularly on the stiffer side. To this end, several researchers (include [2, 36-42], Fujii et al. [38]), investigate the true seismic demand on the asymmetric building and among those Fajfar et al. [43] developed an extended version of N2 method named as N2ext for torsionally asymmetric (Torsionally stiff/flexible) structures due to the presence of URMI. Furthermore, Fajfar et al. recommend combining the outcomes of linear dynamic spectral analysis and pushover analysis (POA) on a 3D structural model. The findings of the linear dynamic spectrum analysis are used to define the torsional amplifications, while the NSA of a 3D structure is used to regulate the performance point and the displacement pattern over the height of the building.

Later on, Dolsek and Fajfar [44], proposed a simplified approach for the assessment of plan-asymmetric structures, which is based on the PEER probabilistic framework, in which the computationally expensive incremental dynamic analysis (IDA), is replaced by the Incremental N2 (IN2) analysis. Fajfar et al. concluded that the layout of the infills causes in-plan irregularity, which increases the lateral displacement of the joints near the infill-free areas. Consequently, substantial damage was observed close to the joints on the flexible sides of the building.

A simplified dynamic-based pushover analysis for plan asymmetric (DPPA) Buildings was developed by Rofooei et al. [45] and Mirjalili et al. [46] considering the consequences of considerable torsional behavior including higher modes effects in the applied lateral load distribution over the height of the building. According to [45], DPPA-based results are well correlated with modal pushover, N2ext method and nonlinear time history analyses. The author also noted that the plan-wise distribution of maximum normalized lateral displacement (u/u_CM) differs significantly between torsionally rigid (TS) and flexible (TF) systems. The maximum normalized displacement (u/u_CM) in TS systems is > 1.0 at the flexible edge and < 1.0 at the stiff edge, whereas in TF systems the maximum normalized displacement is > 1.0 at both the rigid and flexible edges (Figure 1).

Details are in the caption following the image — **FIGURE 1**
Open in figure viewer PowerPoint

In-plan envelope of target displacement for (a) torsionally stiff or Rigid (TS) and (b) torsionally flexible (TF) structural systems.

Several renowned studies and their salient features reported in literature on plan-asymmetry effects, listed in Table 2.

TABLE 2. Reported literature on plan-asymmetry infilled frame structures.

Methods (Reference)	Salient features
Multimodal pushover (MMPA) [47]	In this method, capacity spectrum method (CSM) has been employed to check the capacity of structure corresponding to the induced seismic demand based on each and every mode.
Adaptive POA [48]	This approach attempts to gradually update the load vectors in order to consider the change in the system's modal properties during the inelastic phase of structural response.
Modal pushover (MPA) [49, 50]	In MPA, multiple pushover analyses have been carried out, considered different load distribution corresponding to different vibrational modes.
Equivalent load pattern [51]	In this approach, pushover analysis has been performed by an equivalent load vector developed from the translational and torsional displacements acquired from the response spectrum analysis.
Lateral load and torsional torque [52]	According to this method, the corresponding SDOF systems' base shear force and base torque versus roof displacement/rotation curves were produced using the lateral load and torsional torque calculated from response spectra analysis.
Extended N2 method (Fajfer et al. [53])	The torsional amplification of lateral displacements is recommended using this method designed for plan asymmetrical building structures. In this approach, a correction factor is calculated as the difference between the normalized displacement derived from a linear RSA and the *POA*.
Energy-based pushover [54]	This method fixes the problems associated with the original MPA by sign-reversing the higher-mode effects.
Adaptive modal combination (AMC) procedure [55]	The AMC approach combines the effects of varying dynamic properties during the inelastic response through its adaptive feature and accounts for higher mode contributions by integrating the response of distinct modal pushover analyses.
Efficacy of nonlinear static procedure [56]	The change in response characteristics with an increase in seismic intensity appears to have been somewhat better tracked using the Adaptive capacity spectrum method (ACSM).
Corrective eccentricities approach [57, 58]	In order to evaluate nonlinear asymmetric models, this method offered an analogous plan eccentricity known as corrective eccentricity. The corrective eccentricity of an irregular structure as determined by its elastic and inelastic characteristics.
Modified N2ext method [59]	This approach is based on the N2ext method with four adjustments that take into consideration of the displacement at performance point, interstory drift ratio (IDR), higher mode effects in plan and elevation.
Bidirectional pushover [39, 40]	For asymmetric buildings subject to bidirectional seismic effects, Fuiji proposed a method in which the final response was calculated as the total of the outcomes of pushover analyses with the first two modes' load patterns carried out in the corresponding directions.
Modified dynamic pushover Mirjalili and Rofooei [60]	This method uses the modified load pattern developed from the story-drift ratio obtained from RSA.
Graphical method [61, 62]	To forecast the directional earthquake response for two-ways plan-asymmetric buildings, Faggella suggested a graphical dynamic model. The suggested approach makes accurate forecasts of the critical angle and maximum response using directed combination methods.
Torsional and directivity effects [63]	It is a simplified technique, which predicts torsional effects on asymmetric seismically isolated buildings under the influence of bidirectional earthquake components.

2 Research Significance and Methodology

In the current contribution, the work is continued evaluating the safety of RC buildings built in Italy before the 1970s [64] with a focus on quantifying the decrease in seismic performance caused by some of the typical loss of regularity.

This is accomplished by evaluating the effects of irregularities induced by the nonuniform arrangement of infill in plan and elevation and their asymmetrical effects on the seismic performance of existing older RC-framed structures. To this end, a nonlinear finite element model (FEM) of a three-story 3D-framed prototype structure developed on OpenSees [65] and OpenSeesMP [66-68] interfaces with different configuration of infills placement designed for vertical (dead and live) loads only. To investigate the effects of nonuniform placement of URMI, the research methodology opted herein has been divided into three phases based on three types of analyses. When forecasting a building's seismic behavior and choosing the best retrofitting strategy in the event of damage, dynamic properties are crucial. The fundamental period of a structure is one of its most important dynamic features. Therefore, in the initial phase, modal analysis has been performed to determine the natural mode shapes (Eigen-vectors) and frequencies of different configurations due to the irregular placement of infills during free vibration. Modal or eigenvalue analysis (EVA) uses the total seismic weight (mass) and stiffness of the case-study prototype structure to examine different periods at which it will naturally resonate considering the different configurations of infill and compared with existing empirical models of period-height relationships reported in literature in the seismic performance evaluation of existing RC framed structures (Table 3). However, URMIs increase the stiffness and mass of the structure, causing considerable changes in the period of vibration, the majority of the empirical models (period-height and period-stories relationships) do not take their presence into account. However, limited research reported in literature [69-72] considered the presence of masonry infill (cracked and uncracked, with and without opening) in the assessment of existing RC framed structures.

TABLE 3. Fundamental period based on empirical and analytical/numerical models.

Existing models	Formulation
Building codes models
UBC-70, 82	T = 0.1 N
BOCA-75	T = 0.1 N
Costa Rican Code-86	T = 0.08 N
BOCA-87, 96	T = 0.075 H^0.75
UBC-88, 94, 97
ASCE 7–98
CEN, EC-8 [23]
NEHRP-94, 97
NEHRP-2000	T = 0.0466 H^0.9
ASCE 7-02, 05	T = 0.0466 H^0.9
Empirical models
Goel and Chopra [73]	T = 0.052 H^0.9
Chopra [74]	T = 0.067 H^0.9
[75]	T = 0.037 N—0.039 N
Navarro and Oliveira [76]	T = 0.042 N—0.044 N
Hong and Hwang [77]	T = 0.0294 H^0.804
Guler [78]	T = 0.026 H^0.9
Gallipoli et al. [79]	T = 0.016H
Oliveira and Navarro [80]	T = 0.015H—0.017H
Hatzigeorgiou and Kanapitsas [81]	T = 0.073 H^0.745
Analytical/numerical models
Crowley [82]	T = 0.1 H
Crowley and Pinho [69]	T_GBF = 0.054H	T_GFIF = 0.025H	T_GFWO = 0.034H
	T_YBF = 0.089H	T_YFIF = 0.031H	T_YFWO = 0.043H
	T_CIF = 0.055H
Masi et al. [70]	T_G = 0.050H	T_Y = 0.055H

Note: Where T_BF, T_FIF, T_FWO, T_e, T_y, H, and N represent bare frame period, fully infilled frame period, period of frame with opening in masonry infill, elastic period, yield period, height (meters), and number of stories, respectively.

In the second phase, nonlinear static analyses have been performed in the longer/X-direction only based on conventional pushover approach with uniform load distribution over the height. To this end, performance point on different configurations have been calculated by employing conventional N2 [35] and Extended N2 [43] methods (Figure 2). The seismic demand is computed using inelastic spectra and depends on the period of the idealized equivalent SDOF system in the N2 approach, this approach was developed at the University of Ljubljana and used in Eurocode 8. The transformation from the multi-degree of freedom (MDOF) to an equivalent single-degree of freedom (SDOF) system assumes of a time-invariant displacement shape. It functions well when there is little effect from higher modes in planar structural models. An approach considering higher mode effects in plan, which can be used for plan-asymmetric buildings, was proposed by Fajfar et al. [43] named as extended N2 (N2ext) method. By using a correction factor (CF > 1.0) applied at the level of individual story, the results of the N2ext approach are scaled to the target roof displacement from those of the conventional pushover method and the standard elastic modal analysis. Reported literature [83] shows that a significant influence of higher modes effects on storey drifts in the upper parts of the medium to high-rise buildings. Furthermore, the N2ext (Fajfer et al. [53]) procedure provides slightly larger estimates as compared to the counterpart NDAs employed mean values. In general, the estimated storey drifts obtained by different approximate methods such as N2 and N2ext methods are within the range between the mean and mean ± σ values obtained by NDA.

Finally, multiple-strip nonlinear dynamic analyses (MNDAs) have been performed (Figure 3) on OpenSeesMP, OpenSeesMP is an extension of the Open System for Earthquake Engineering Simulation (OpenSees) software framework, which is designed to perform parallel numerical simulations of structural and geotechnical engineering problems. OpenSeesMP is specifically designed to take advantage of high-performance computing (HPC) resources, such as parallel clusters, multicore processors, and graphical processing units (GPUs), to speed up the solution of large-scale engineering problems [66, 68]. In this contribution, MNDA have been performed corresponding to four different HLs of earthquakes with probability of exceedance (POE) 81%, 63%, 10%, and 5% and compared with code mandated serviceability (SLO-Operational, SLD-Limited damage) and ultimate limit states (SLV-Life safety, and SLC-Collapse prevention) based on seismic safety assessment matrix (Figure 4).

This study mainly focusses on in-plane effects of masonry in plan or elevation and neglect the out-of-plane failure effects. In addition, all the analyses are carried out in the longer direction (X-direction) only considering the torsionally balanced prototype reinforced concrete (RC) building structures (both directions) in which lateral-torsional coupling may develop due to the strongly eccentric layout of infills masonry. As a result, the undesirable soft-story mechanism and short column failure may occur in existing RC building stock. Therefore, the main question addressed herein to what extent the seismic demand on RC elements increases due to the asymmetrical layout of masonry infill (in plan and elevation) compared with the counterpart (regular structures).

3 Prototype Structure and Infill Configurations

The prototype structure used herein was widely discussed in several reported studies [64, 84]. It is an older 3-story RC framed building with two uniform bays (length of 4.0 m) in the smaller side (Y-direction) and three nonuniform bays (length of 4.5, 2.0, and 3.0 m) in the longer side (X-direction). A C20/25 concrete and a rebar of yield strength (f_y) of 340 MPa are used as base materials, since these mechanical characteristics are reasonably estimate with those of the materials used in the pre-1970s construction practices [64]. The values assumed for the concrete and steel Young's moduli are respectively 20 and 210 GPa. The typical sizes of beams and columns are 300 × 500 mm and 300 × 300 mm, respectively. The total floor masses are 78 tons at first and second floor levels, and 62 tons at roof level. The reinforcement details are shown in Figure 5 and identical in all three frames in X-direction. Whereas, in Y-direction peripheral beams reinforcement details of section a and section b are used for exterior and interior ends, respectively.

The building is an aseismic and designed for vertical loads only, and having URMIs of 145 mm thickness on the periphery and a bare frame on the interior/central grid. To investigate the randomness associated with irregular placement of masonry infill, six variant configurations are used herein among those three are regular and three irregulars in plan or elevation in X-direction only. These configurations are categorized based on the selection of different types of frames include bare frame, pilotis frame (soft-story at first floor only) and fully infilled frame. For example, in regular configurations, Configuration-01 has bare frames at interior and at periphery, Configuration-02 has bare frame at interior and pilotis frames (soft-story at first floor only) at periphery, Configuration-03 has bare frame at interior and fully infilled frame at periphery as shown in Figure 6. Similarly, in irregular configurations, all three configurations have bare frame at interior, one peripheral side supported by fully infilled frame and remaining periphery is supported by bare frame (Conf-04), pilotis frame (Conf-05), and fully infilled frame (Conf-06) as shown in Figure 7. In addition, the material characteristics for URMIs include cement-sand mortar type, compressive strengths (σ_mo), shear strength(τ_mo), modulus of elasticity (E_m), and brick thickness (t) are given in Table 4. Further details of URMIs and frame component sizes with material strengths can be found in Liberatore [85] and Gigliotti [84].

TABLE 4. Properties of URMIs.

Brick thickness (mm)	σ_mo (MPa)	τ_mo (MPa)	E_m (MPa)
	Mechanical properties
145	2.1	0.4	1880

4 Finite Element Model

A comprehensive 3D FEM model has been developed in OpenSees [65] with different sources of nonlinearities such as (a) axial-moment interaction [86, 87], (b) infill-frame interaction ([88-90], Mohammad [91]), (c) nonlinear shear interaction in frame components [89, 92] and (d) bond–slip effects close to the beam-column joints attributed from the use of plain bars [93] which are common sources of nonlinearities observed in pre-1970s construction practices.

A thorough description of the elements and sections, material models, seismic weight, damping, solution algorithm, diaphragm, and analysis direction are given below.

Elements and sections—Force-based fiber-section (Figure 8a) beam-column elements [94, 95] employed with P-Delta geometric transformation [96, 97] for all nonlinear elements in the model. A total of five integration points has been assigned on each element [98]. At the section level, rectangular shaped fiber section with different model parameters for confined and unconfined concrete fibers are assigned along with the section aggregator command in OpenSees to depict the nonlinear-shear response from a nonlinear shear constitutive model. Whereas an eccentric single strut truss element (ASCE 41-06) is used to model the masonry infill panel between the frame components.
Material models—The stress–strain relationships proposed by Kent and Park [99] (Figure 8b) are employed herein for concrete elements with confined and unconfined concrete fibers. The stress–strain model proposed by Giuffrè–Menegotto–Pinto [CEB1996] is used for the rebar steel fibers (Figure 8c). For masonry infill panels, the idealized bilinear hysteretic model obtained from ASCE41 guidelines and applied to eccentric bi-diagonal truss elements (Figure 8d). Whereas a nonlinear shear law (Figure 8f) is applied on column elements [100] near the beam-column joint, to simulate the short-column effects in frame components resulted from the interaction with masonry infill panels.
Seismic weight—Lumped masses at the nodes are used to model the structure's seismic weight. The entire dead load, including the self-weight (slab, beam and column weight) and the superimposed dead loads (masonry panels and floor finishes), are directly calculated as a seismic weight. In addition, according to EC8 [23, 24], 30% contribution of live load also considered as seismic weight.
Damping—According to Smyrou et al. [101], the mass and stiffness proportional damping characteristics of the building are modeled at 3% of the critical damping. In order to do this, the initial elastic stiffness matrix and periods of two modes determined from the EVA have been used.
Solution algorithm—With coefficients of 0.50 and 0.25 and a time step of 0.01 s, the Newmark-β method is utilized as the time integrator. According to Mohammad et al. [93], the Newton–Raphson solution algorithm is employed to solve the nonlinear equilibrium equations. Depending on the convergence of the solution, other algorithms might be employed.
Diaphragm-A rigid diaphragm is introduced at each floor level to calculate the contribution of the floors [102].
Direction of analysis-all analyses in this case study have been done in one way and exclusively in parallel to the longer route.

An eccentric bi-diagonal truss element with a uniaxial bilinear elastoplastic hysteretic constitutive model suggested by ASCE-41 (ASCE/SEI 41-06) has been used to represent the URMI panel (Figure 8e). According to the Equation (1) presented by Smith [103-105] and the Equation (2) presented by Mainstone et al. [106] as stated in FEMA356 [107], the equivalent strut width (b_w) was calculated. The strength (σ_w) assigned to the strut accounts for the least amount of the possible panel failures when compared with the potential panel failure modes (Equations 3-6), such as diagonal compression (σ_w1), corner crushing (σ_w2), bed-joint sliding (σ_w3), and diagonal tension (σ_w4) failures [108] shown in Figure 9.

λ = \sqrt[4]{\frac{E_{W} t_{W} \sin 2 θ}{4 E_{C} I_{P} H}}

(1)

b_{w} = 0.175 {(λ H)}^{- 0.4} d_{w}

(2)

σ_{w 1} = \frac{1.16 σ_{mo} tanθ}{K_{1} + K_{2} λ H}

(3)

σ_{w 2} = \frac{1.12 σ_{mo} sinθ cosθ}{K_{1} {(λ H)}^{- 0.12} + K_{2} {(λ H)}^{0.88}}

(4)

σ_{w 3} = \frac{1.2 u sinθ + 0.45 u \cos θ + 0.3 σ_{o}}{K_{1} {(λ H)}^{- 1} + K_{2}}

(5)

σ_{w 4} = \frac{0.6 τ_{mo} + 0.3 σ_{o}}{K_{1} {(λ H)}^{- 1} + K_{2}}

(6)

In above equations, the story height represented by H; the masonry infill modulus of elasticity denoted by E_w; infill strut angle of inclination by θ; Flexural stiffness of RC columnsby E_cI_p; Masonry panel diagonal length by d_w; the compressive strength by σ_mo and the shear strength by τ_mo obtained from Liberatore [85], the resistance to sliding of the joints (u) approximately equal to 0.7τ_mo; the axial stress on the vertical panel from gravity load (zero for this study) by σ_o; K1 and K2 are constants with values equal to (0.47–1.3) and (−0.178 to 0.04), respectively (average value of K1 and K2 employed in this study).

Based on the in-plane size of the infill panels, three types of struts in the case-study frame are designated as St-A (4.5 m wide), St-B (2.0 m wide), and St-C (3.5 m wide). The force in the infill strut (F_y) is obtained from Equation (7) using the minimum σ_w for all panel sizes from the bed-joint sliding failure mechanism.

F_{y} = σ_{w} A_{w}

(7)

Whereas, the displacement capacity of equivalent strut depends upon the ratios of shear strength (Q_f/Q_inf) in frame to the masonry panel and reported in ASCE 41 (ASCE 41-06) as modeling parameters d and e. The modeling parameters d = 0.9% and e = 1.5% used herein to calculate the displacement capacity at yield (D_y) and maximum (D_max) from Equations (8-10).

k = \frac{A_{w} E_{w}}{d_{w}}

(8)

D_{y} = \frac{F_{y}}{k}

(9)

D_{\max} = d h_{eff}

(10)

The localized shear failure of the column caused by infill-frame interaction has been traced herein from the response of the Timoshenko [109] beam theory. Initially, adopted by Martino et al. [110] and later on Marini et al. have further developed a modified approach in which section stiffness is uncoupled from shear deformations and only depending upon flexural and axial effects whereas, to incorporate the shear–moment interaction, bending forces are integrated with shear effects at the element or component level only since the equilibrium is imposed at the element level. Therefore, in this study, a phenomenological V–γ law is employed on the section aggregation command in OpenSees with zero-length nonlinear shear spring. The shear strength of column used in V–γ law calculated from CNR DT [111] approach (Equations 11-17).

V_{R} = V_{Rdc} + V_{Rds}

(11)

V_{Rdc} = τ_{Rd} k (1.2 + 40 ρ_{l}) bd

(12)

ρ_{l} = \frac{A_{l}}{bd}

(13)

τ_{Rd} = 0.25 f_{ctm}

(14)

f_{ctm} = 0.3 {(f_{ck})}^{\frac{2}{3}}

(15)

k = 1.6 - \frac{d}{1000}

(16)

V_{Rds} = \frac{A_{sh} f_{yh} d}{s}

(17)

In the above equations, terms

V_{Rdc}

V_{Rds}

τ_{Rd}

k,

ρ_{l},

b

, d, A_l

f_{ck}

, A_sh, and s represent the concrete shear strength, rebar shear strength, design shear stress, coefficient depending upon the depth of cross-section, longitudinal reinforcement ratio, section width, section depth, longitudinal rebar area, concrete compressive strength, shear reinforcement area, and hoops spacing, respectively. In the present investigation, the building's damping properties used mass and stiffness proportional damping of 3% of the critical damping (Equation 18). Since the structural model is nonlinear and the material laws already consider hysteretic response, a 3% damping ratio (ξ) was used herein.

C = a_{o} M + a_{1} K

(18)

a_{1} = \frac{2 ξ}{(ω_{1} + ω_{2})}

(19)

a_{o} = ω_{1} ω_{2} a_{1}

(20)

In the above equations, terms M, K, C, a_o, a₁, ω₁, and ω₂ represent mass matrix, stiffness matrix, damping matrix, coefficient for stiffness-proportional damping obtained from Equation (19), coefficient for mass-proportional damping obtained from Equation (20), frequency of first mode, and frequency of second mode, respectively. As aforementioned, MNDA are also carried out corresponding to four different intensities of earthquakes such as 81%, 63%, 10%, and 5% POE (Table 5). Therefore, a group of 14 unscaled GM records has been identified (Figure 10a) using REXEL beta ([93, 112, 113]), based on the site-specific location Mormanno, Calabria, Italy, with magnitude 4–7.5 and distance deaggregation in 0–40 km, as summarized in Table 6. The unscaled GMs are extracted from the European Strong Motion database and matched to the Italian Code NTC (NTC-2018), site-specific target spectrum within a code specified period range (0.2–2.0 T). Unscaled records are then uniformly intensity-scaled over a range of four HLs (Figure 10b) consistent with the probabilistic hazard curve of PGA available from INGV [114]. The number of 14 GMs was chosen herein as a reasonable tradeoff between: (a) the 7 GMs normally prescribed by “deterministic” design-oriented performance-based codes which aim to capture mean response values of EDPs to perform design checks as per NIST [67], and (b) the 11 GMs prescribed in the probabilistic risk-oriented performance-based frameworks like FEMA P-58 based on scaling/conditioning on Sa(T₁) (FEMA P-58, 2012) [68]. Furthermore, the spectrum coherence in terms of average response under unscaled GMs used herein with moderate-strong nonlinearities inherent to the different models.

TABLE 5. Seismic HLs for different probability of exceedance (POE) and corresponding limit states.

NTC-18 limit states		For 50 years design life	IM-PGA (g)
		Hazard levels (HLs) with POE
Serviceability	SLO	81%	0.056
Serviceability	SLD	63%	0.076
Ultimate	SLV	10%	0.25
Ultimate	SLC	5%	0.34

TABLE 6. Suite of unscaled 14 ground motions [113].

Earthquake	Year	Mw	Fault	R (km)	Site class
Friuli (aftershock)	1976	6	Thrust	14	B
Montenegro	1979	6.9	Thrust	21	A
Campano Lucano	1980	6.9	Normal	25	A
Alkion	1981	6.6	Normal	20	C
Lazio Abruzzo	1984	5.9	Normal	22	A
Lazio Abruzzo	1984	5.9	Normal	36	B
Kalamata	1986	5.9	Normal	11	B
Kyllini	1988	5.9	Strike slip	36	B
Mataranga	1992	5.2	—	34	B
Kozani (aftershock)	1995	5.2	Normal	16	B
Umria Marche	1997	5.7	Normal	25	C
Izmit (aftershock)	1999	5.8	Oblique	15	A
South Iceland	2000	6.5	Strike slip	21	B
Bingol	2003	6.3	Strike slip	14	A

Different limit state acceptance criteria are described in the literature for evaluating the performance of structures; in this study, acceptance criteria based on interstory drift ratios (IDRs) are applied. In order to achieve this, the maximum IDRs, which correspond to the aforementioned HLs for both regular and irregular building layouts, are obtained and evaluated against the limit state acceptability requirements. The immediate occupancy (IO), life safety (LS), and collapse prevention (CP) performance levels described in FEMA356 and indicated in Table 7 are the basis for these limit states acceptance criteria.

TABLE 7. FEMA356 proposed interstory drift ratios (IDRs) acceptance criteria for RC buildings.

Building types	IO	LS	CP
	IDR (%) limit states
Bare frame	1	2	4
Infilled frame	0.1	0.5	0.6

Moreover, for the completeness of results the roof displacements at different HLs are also obtained and compared from NSA and MNDA.

5 Results and Findings

5.1 Eigenvalue Analysis

An important step in earthquake design and evaluation methodology is determining the natural period of vibration of an RC building structure. This single feature can be used to gain a better understanding of the overall demands on a structure under a specific seismic input.

Despite the fact, the evaluation of existing buildings is shifting towards a displacement-based approach, seismic design for new buildings all over the world still uses a force-based methodology. In force-based design, it is best to develop conservative estimations of the period of vibration such that the total shear at the base can be conservatively projected from a code specified site-specific acceleration spectrum. As a result, it may be appropriate to employ gross cross-section (uncracked section) stiffness in analytical calculations.

In contrast, the only stiffness that can be considered with confidence for the members of an existing RC frame is the yield or cracked stiffness. In this study, using EVA, the uncracked and cracked periods of existing RC structures with infills of regular and irregular placement are analytically determined. For both the uncracked and cracked states of the structural components, OpenSees was used to calculate all the results from the EVA. The modal periods for cracked and uncracked states along with mode shape for all the case-study configurations are shown in Figure 11.

Results illustrated, in plan symmetrical Configurations 1–3, all are having different modes of vibration and there is no evidence of lateral-torsional coupling of vibration modes. Whereas, in plan asymmetrical Configurations 4–6 all are significantly affected by the coupling of lateral-torsion vibration. Furthermore, the average period calculated corresponds to the longer or X-direction for all the configurations from EVA and compared with building code models (EC-8 and ASCE 7-05), empirical models ([73]; Chopra [74]), and numerically [69, 70] proposed models of fundamental period estimation. Results illustrated, building codes period estimation models overestimated the building response 5%–10% based on uncracked state and underestimated 5% in case of cracked state of structural components. Similarly, empirical models overestimated the building response 20%–25% based on uncracked state and 10%–15% in case of cracked state of structural components. Whereas numerical models overestimated the building response 25%–30% based on uncracked state and 15%–20% based on cracked state of structural components (Figure 12).

5.2 Nonlinear Static Analysis

In the second phase, results obtained from the NSA performed on six variant configurations (in longer/X-direction only) and presented in terms of capacity curves for individual frame (exterior/interior frame) and the entire 3D structure. Furthermore, performance points have been calculated for different intensities of HLs including POE81%, POE63%, POE10%, and POE5% by employing N2 [35] and Extended N2 [43] methods. Subsequently, for each performance point, the interstory drift and floor displacement profiles are obtained for the assessment of structural response corresponding to limit states compliance/acceptance criteria based on interstory drift ration imposed on every configuration as stated in FEMA 356.

Results show that the response of individual bare, pilotis and fully infilled frame is almost identical to reported in past studies [89, 92]. Also, the overall capacity (Figure 13a,b) of the entire structure in Conf-01 and Conf-02 is quite similar, whereas in other configurations (Conf-03 to Conf-06), the overall capacity and initial stiffness (Figure 13c–f) are increased due to the presence of masonry infill. Furthermore, performance points for serviceability and ultimate limit states are highlighted corresponding to different intensity levels in tersms of SLO, SLD, SLV, and SLC limit states. Results illustrated, Configuration-01 which is the bare frame configuration, structure response is compliant for all the considered mandatory limit states (Figure 14a). In Configuration-02, comprised of bare frame at interior and pilotis frames (frame with soft-story at first floor) at periphery, by imposing limit state criteria based on bare frame the structure response seems to be compliant, whereas structure response seems to be highly vulnerable at the first story level (Figure 14b) by considering compliance criteria of infilled frame particularly at ultimate limit states (SLV/SLC). Similarly, unsatisfactory results observed at SLC limit state on first floor only for masonry infilled frame Configuration-03 (Figure 14c). As compared to the counterpart, in irregular configurations, it is observed that all configurations are vulnerable particularly at the first story level (Figure 14d–f) based on ultimate limit states criteria (SLV/SLC).

In general, bare frame configuration (Conf-01) is typicaly used in the design of RC structure based on that results are presented in terms of percentage variation in roof drift and base shear at incremental performance levels with respect to Conf-01. Results are summarized in Tables 8 and 9, and shown in Figure 15a.b. The presence of infill increases the overall stiffness of Configurations 2–6. As a result, there is a significant reduction in roof drift and increment in internal forces on components or base shear have been observed from serviceability (SLO/SLD) to ultimate (SLV/SLC) limit states. The maximum percentage reduction in roof drift is 20%, 60%, 35%, 45%, and 40% observed in Conf-02, Conf-03, Conf-04, Conf-5, and Conf-06, respectively. Whereas, the maximum percentage increase in base shear is 25%, 65%, 35%, 45%, and 25% found in Conf-02, Conf-03, Conf-04, Conf-5, and Conf-06, respectively.

TABLE 8. Roof drift at different limit states.

Limit states	Conf-01	Conf-02	Conf-03	Conf-04	Conf-05	Conf-06
	Roof drift (%)
	Symmetrical (1–3)			Asymmetrical (4–6)
SLO	0.112	0.088	0.044	0.074	0.061	0.067
SLD	0.153	0.122	0.063	0.104	0.086	0.093
SLV	0.620	0.500	0.233	0.413	0.345	0.372
SLC	0.908	0.731	0.340	0.603	0.504	0.558

TABLE 9. Base-shear at different limit states.

Limit states	Conf-01	Conf-02	Conf-03	Conf-04	Conf-05	Conf-06
	Base-shear (kN)
	Symmetrical (1–3)			Asymmetrical (4–6)
SLO	166.0	210.0	236.8	187.5	215.0	180.9
SLD	201.2	256.5	332.5	256.5	295.0	250.6
SLV	391.5	420.0	604.0	537.7	570.0	440.0
SLC	431.3	438.4	422.5	566.0	450.8	441.0

Figure 16 illustrated the roof displacement variation along the frame lines in X-direction only plan asymmetrical configurations (Configurations 4–6) of infilled frames. As aforementioned, in all configurations, frame-01 (Fr-01) is stiffer than frame-03 (Fr-03) and located on the periphery whereas, frame-02 (Fr-02) is central or interior frame and close to the center of the mass (CM) of entire structure. Roof displacement at frame Fr-03 is greater than roof displacement at frame Fr-01 in asymmetrical configurations. This discrepancy is caused by the different stiffnesses of the individual frames, and evidenced from the reported literature. Furthermore, results obtained from N2ext method at Fr-03 location are larger than the results obtained from conventional N2 method in all three configurations by applying the CFs based on response spectrum analysis. Also, it is noticed that the difference in results obtained from N2 and N2ext increases from serviceability (SLO, SLD) to ultimate limit states (SLV, SLC). The maximum calculated CFs corresponding to SLC limit states are 1.20, 1.28, and 1.48 for Conf-04, Conf-05, and Conf-06, respectively at the peripheral frame (Fr-03).

5.3 NSA and MNDA

In this section, results are presented (Figure 17) for MNDA corresponding to HLs having probability of exceedance (POE) 81%, 63%, 10%, and 5%. To this end, Configuration-05 has been employed and analyzed for a suite of 14 unscaled GMs and results presented in terms of roof displacement with respect to the location of frames (Fr-01, Fr-02, and Fr-03). Subsequently, compared with NSA results obtained from N2 and N2ext methods as stated in previous section. Results show that roof displacement obtained from 14 GMs increases at flexible side (Fr-03) as per increasing the intensity of HLs. Furthermore, N2 and N2ext methods provide conservative estimates of roof displacement as compared to the NDA. Results illustrated (Figure 18), N2 and N2ext methods slightly underestimate the roof displacements at stiffer side (Fr-01) and significantly overestimate at flexible side (Fr-03) corresponding to POE 81%, 63%, 10% and 5%. Whereas, at stiffer side (Fr-01) ratios of roof displacements based on N2ext method are close to unity as compared to the conventional N2 method.

6 Conclusions and Recommendations

The plan asymmetry induced by the irregular arrangement of masonry infill increases the vulnerability of existing nonconforming building structures located in seismically active regions. To this end, an FEM model of case-study building used herein with different (regular and irregular) configurations of infill placement along with nonconforming materials, noncompliant detailing in structural components and include the short column effects produced from the infill-frame interaction typically observed in past events. In the current contribution, both for regular and irregular configurations, the key concluding remarks obtained from results based on EVA, NSA, and MNDA performed on detailed FEM model illustrated as:

The EVA-based results depict that the building code period-height relationships provide a good estimate for the assessment of existing infilled frame structures both for cracked and uncracked states of building components compared with the numerical and analytical estimates reported in the literature. Results illustrated, building codes period estimation models overestimated the building response 5%–10% based on uncracked and cracked state of structural components. Whereas empirical models overestimated the building response 10%–25% based on uncracked and cracked state of structural components. Similarly, numerical models overestimated the building response 15%–30% based on uncracked and cracked state of structural components.
The capacity curves obtained from NSA reveal the significance of plan asymmetrical effects induce from irregular arrangement of masonry infill as compared with the counterpart. Results show the poor performance of plan asymmetrical configurations (Conf-4–6) at ultimate limit states (SLV/SLC) based on IDR compliance criteria.
Furthermore, in plan asymmetrical configurations, the N2-method underestimates the roof displacement demand at flexible side compared with the N2ext-method for all limit states. Also, the difference in roof displacement demand increases from serviceability (SLO/SLD) to ultimate limit states (SLV/SLC). The maximum calculated CFs from N2ext-method corresponding to SLC limit states are 1.20, 1.28, and 1.48 for Conf-04, Conf-05, and Conf-06, respectively at the peripheral frame (Fr-03).
Moreover, building response at serviceability limit states, both from N2 and N2ext methods slightly unconservative at stiffer side and overestimate the roof displacement at flexible side compared with the MNDA. Whereas, at stiffer side for higher hazard level, ratios of roof displacement demand from multiple strip analysis based on N2 and N2ext methods are close to unity. Furthermore, results depict the use of simplified POA with N2 and N2ext method is conservative at flexible side in comparison with MNDA.
In general, it is concluded from this study, the overall seismic risk and the vulnerability of existing RC building structures can be minimized by analyzing the effects of existing plan asymmetry based on the irregular placement of masonry infill. However, to obtained more rational results, bidirectional plan asymmetry effects should also be investigated by considering the different characteristics of infill panels and the structure layout.

Author Contributions

Aslam F. Mohammad: conceptualization, investigation, writing – original draft, writing – review and editing, methodology, software. Marco Faggella: conceptualization, writing – review and editing, methodology. Rashid Ahmed Khan: conceptualization, writing – review and editing, methodology. Sami U. Haq: writing – review and editing, methodology, software. Muhammad Sami: writing – review and editing.

Acknowledgments

We are writing to formally acknowledge the receipt of the financial grant awarded to Computers and Structures, Inc (csiamerica). We are extremely grateful for your generous support, which will significantly contribute to the success of our work.

Conflicts of Interest

The authors declare no conflicts of interest.

Open Research

Data Availability Statement

The data that support the findings of this study are available on request from the corresponding author. The data are not publicly available due to privacy or ethical restrictions.

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Volume7, Issue3

March 2025

e13114

Seismic Evaluation of Plan Asymmetry Effects in an Older Infill Framed Reinforced Concrete Building Structures

ABSTRACT

1 Introduction

2 Research Significance and Methodology

3 Prototype Structure and Infill Configurations

4 Finite Element Model