Improving Earthquake Resilience—The Role of RC Frame Asymmetry Under Successive Events: Nonlinear Dynamic Insights for Safer Building Codes ^†

Abstract

This study addresses a critical gap in seismic design by quantifying how plan asymmetry and multiple earthquake sequences interact to affect the nonlinear reaction of reinforced concrete (RC)-framed models. While earthquake-resistant design provisions have evolved, most current codes are based on single-event assumptions and simplified symmetry considerations, overlooking the cumulative effects of repeated ground motions observed in recent international studies. In this research, symmetrical and asymmetrical low-rise RC buildings are analyzed through nonlinear dynamic simulations, with both single- and multiple-event ground excitations considered for comparison. The analyses incorporate three-dimensional ground motions in horizontal and vertical orientations, while explicitly modeling the nonlinear inelastic response of RC sections under severe seismic demands. The evaluation of elastoplastic findings relies on normalized indices, by considering a simple dimensionless parameter to quantify the physical symmetry or asymmetry of the RC models. Results show that increasing plan asymmetry amplifies inter-story drift, torsional rotations, and plastic hinge concentrations, particularly under successive earthquake sequences. These findings indicate that existing design provisions may underestimate the vulnerability of irregular RC buildings. This work is among the first to integrate plan asymmetry and multi-event seismic loading into a unified evaluation framework, offering a novel tool for refining earthquake-resistant design standards.

1. Introduction

The symmetry/asymmetry of building structures is recognized as an essential parameter in seismic response, e.g., as mentioned by Das et al. [1] and Bento et al. [2]. Reinforced concrete (RC) is the most widely investigated structural material, as evidenced by the work of Lazaridis et al. [3] and Fardis [4], while current codes address the detailing and dimensioning of RC structures [5]. The effect of successive earthquake occurrences on dynamic performance response remains unidentified in current seismic codes [6], although it has been identified as critical by research [6,7,8]. Recent studies have also explored physics-informed neural networks for structural mechanics and reliability analysis [9,10]. Although these methods represent an important emerging research direction, the present work employs conventional nonlinear dynamic analysis to investigate the cumulative damage effects in asymmetric RC frame structures directly. The target of the current investigation is the role of RC frame asymmetry in successive events to improve earthquake resilience.

2. Description of RC Buildings and Analysis

Practical RC ordinary models are selected for detailing and in-depth analysis, to provide broader application of the current work. One-story RC analyzed frames are presented in Figure 1, with a typical height of 4.0 m and consisting of one RC slab measuring 5.0 × 4.0 m² and 15 cm thick, acting as a rigid diaphragm. This RC slab rests on four external RC beams with a 25 × 60 cm² cross section and four RC end-supporting columns. The three columns feature a constant cross section of 40 × 40 cm², while the last one, labeled “wall” here, has a variable cross section ranging from 40 × 40 cm² to 30 × 200 cm². In this manner, an in-plan geometric asymmetry is imposed on the three-dimensional one-story RC building models.

Comparable three-story buildings are developed (Figure 2), sharing the same first-story configuration as the one-story frames. The second and third stories of the three-story models resemble the one-story model, with a floor level at 3.0 m above the base level. The three columns at the second and third levels have a uniform cross section of 35 × 35 cm². The last column, hereafter referred to as the “wall” exhibits a stepwise increase in cross-sectional dimensions in the range of 35 × 35 cm² to 30 × 200 cm², implementing a planar imbalance. The beams’ sectional area is constant at 25 × 60 cm² at all models. The slabs of the three-story 3D-framed buildings are 15 cm thick and serve as rigid diaphragms.

Following the current regulation [11], the applied loadings refer to typical domestic/residential, office use, mentioned here for convenience as the slab design load consisting of a dead load of 2.0 kN/m² and a moving load of 0.6 kN/m² and the wall permanent load of 3.6 kN/m². The RC models are made of concrete type C20/25 reinforced with B00c steel. The frames are dimensioned according to the design codes [5,6,11] for the fixed-base assumption, with typical parameters: a_g = 0.36 g, γ_Ι = 1.00, ξ = 5%, soil type C, and ductility class medium (DCM). In compliance with the current codes [6], the behavior factor of each frame is assessed individually. Capacity design rules from current codes [5,6] are applied to detail the primary structural components and their shear connections, with seismic code combos utilizing the 30% instruction and 5% accidental eccentricity [6].

In the nonlinear time-history (NLTH) analyses conducted here, working with the computer program ETABS [12] for better accuracy [13], the considered successive ground motions (Figure 3) are downloaded by [14] as “Chalfant Valley” [14], consisting of two single occurrences; “Coalinga” [14], respectively, with two occurrences; “Imperial Valley” [14] with two occurrences; “Whittier Narrows” [14], with two occurrences; and “Mammoth Lakes” [14], with five occurrences. By subjecting the models to the first stage of the “Mammoth Lakes” earthquake, the potential impact of several earth motions on a single one is examined over the time frame 0–50 sec, referred to here as “Mammoth-1st”. Earthquake excitations are considered at 0°, 90°, and 45° angles, aligned with the two horizontal geometric axes and roughly along the geometrical diagonal, following ref. [13].

In the analysis model of [12], elastoplastic point hinges are positioned at the structural components’ finishes, representing essential attributes such as geometry, material quality, section detailing, strength and stiffness limits, bending moment and curvature capacities, and plastic rotation angles following the model of ref. [15]. The possible vulnerability of RC sections to shear is analyzed in accordance with the current code requirements [5,6]. More details on the mechanistic nonlinear behavior of the RC elements are available in the Refs. [3,8,15], but these are not included here because of additional respective modeling assumptions and result interpretations that are outside the intended scope of this manuscript. The chosen analysis work procedure serves for the current target, which is the plan asymmetry effect on the RC frame response under multiple seismic events.

3. Structural Response Results

The structural response results are evaluated by the following selected parameters for comparison of the nonlinear behavior of the RC buildings:

• The simple geometrical asymmetry discusses the relative asymmetry and symmetry among the supporting columns to the wall as far as the sectional area and stiffness, technically indicated as a mathematical division of the wall’s section to columns’ one, denoted as “A-ratio”, to characterize the plan asymmetry for comparative nonlinear response analysis. The interest of this work lies in the investigation of the relative imbalance of the stiffness and mass of the vertical structural elements that governs torsional coupling effects.
• Plots of “inter-story drift ratio” (“IDR”) on each building floor are displayed versus the “performance levels” (“FEMA-356”) [16], with code limits: 1% concerning the “Immediate Occupancy (IO) level” [16], 2% at the “Life Safety (LS) level” [16], 4% at the “Collapse Prevention (CP) level” [16].
• Plots displaying the “peak floor acceleration to the peak ground acceleration” (“PFA/PGA” [17]) ratio help to evaluate the elastoplastic structure performance, whereas the associated thresholds are not found in the existing literature.

Due to space limitations, only selected typical response charts will appear here.

3.1. One-Story RC Buildings

Starting from the one-story RC models, the IDR on both axes tends, as shown in Figure 4, to variably slightly decrease along with the increase in the A-ratio, within the 2% limit, with higher values noted concerning the “Chalfant Valley” excitation and lower for the “Whittier Narrows” one, considering the 90° orientation. The IDR on the Y-axis plot values for the “Mammoth-1st” motion are notably smaller than for the “Mammoth Lakes” sequential motion (Figure 4b).

The PFA/PGA ratio rises alongside the increase in the A-ratio on both axes, as depicted in Figure 5, presenting higher values regarding the “Imperial Valley” ground motion, and lower values regarding the “Mammoth-1st” motion. Some deliberate plotline gaps in the IDR and PFA/PGA plots (Figure 4 and Figure 5) indicate a structural failure in the model case with identical column and wall sections.

3.2. Three-Story RC Models

Continuing the evaluation of the three-story RC models, the IDR increases with a growing inclination toward larger wall sections on both axes, as shown in Figure 6 and Figure 7. The IDR values are higher on the first story and lower in general on the third story (Figure 6 and Figure 7). Smaller IDR values are depicted for the single occurrence ground motion of Mammoth-1st in comparison to the sequential earthquakes (Figure 6 and Figure 7).

Respectively, the PFA/PGA plots (Figure 8 and Figure 9) show variable increases in the higher wall sections, with higher values in the third story than in the first. The gaps in the plotlines of the IDR and PFA/PGA ratios indicate a structural failure due to the lack of RC models for A-ratio values exceeding the “wall” limit of the current earthquake code [8].

4. Conclusions

The nonlinear dynamic analyses conducted in this study demonstrate that the elastoplastic behavior of reinforced concrete frames is highly sensitive to both structural symmetry and the sequencing of ground motions. When subjected to multiple seismic events, even low-rise structures exhibiting modest vertical imbalance experience cumulative damage effects that are not apparent under single-event excitation. The used asymmetry index, the A-ratio, is for comparative response outcomes that are not sensitive to this index.

These findings highlight the importance of recognizing progressive degradation—a distinctly nonlinear phenomenon—in future seismic design provisions. The results show that asymmetry in the stiffness distribution leads to amplified lateral drifts, earlier yield initiation, and larger residual deformations during sequential ground motions.

Symmetric configurations, while performing more predictably, are still susceptible to strength deterioration after the first event, indicating that current design practices based solely on single-event demand may underestimate the actual structural vulnerability.

Given the current evaluations, the following statements are drawn.

• The IDR demands increase as wall sections become larger; however, all observed values remain within acceptable seismic performance limits for reinforced concrete structures.
• The PFA/PGA ratio shows a clear upward trend with increasing wall dimensions and building height in the evaluated RC models.
• Symmetrical one-story RC buildings exhibit heightened vulnerability under sequential earthquake loading compared to single-event excitations. A similar sensitivity is also observed in asymmetrical three-story RC frame–wall systems with large wall sections that exceed the “wall” dimensional limits prescribed by current seismic codes.
• Analyses that consider only single-event ground motions consistently underestimate the structural response, yielding smaller response quantities than those produced by the respective sequential ground motion scenarios.
• An earthquake orientation of 45° produces the most critical structural response in the examined frame models, although the 0° and 90° orientations also remain essential for comprehensive seismic assessment.
• By integrating current nonlinear performance considerations into future seismic codes, design practice can move toward a more realistic safety-oriented representation of building behavior under complex earthquake scenarios.