Progressive Collapse and Robustness Analysis of Multi-Story Reinforced Concrete Structures ^†

Abstract

Progressive collapse is a critical structural phenomenon where local damage triggers a chain reaction and potentially leads to disproportionate failure of the entire system. In this study, the progressive collapse behavior of multi-story reinforced concrete (RC) structures is investigated using numerical analysis methods. This situation poses a serious danger, especially for high-risk types of structures. In the study, the effect on the collapse tendency is evaluated by considering different structural models. Numerical analyses are performed using a nonlinear finite element method. This study offers a general exploration of the progressive collapse behavior of multi-story RC frames, focusing on robustness evaluation under various structural scenarios. The aim of this study is to improve the understanding of structural responses and to support the development of safer, more durable design strategies.

1. Introduction

Earthquakes occurring in areas with high seismic risk can cause varying levels of damage to structures or the collapse of different structural elements. In general, the characteristics of earthquakes, the design and construction features of buildings, and local soil conditions play a critical role in the behavior of buildings under earthquake impact. Structural features such as the geometry of the structure, type of structural system, material quality, presence of structural irregularities, stiffness distribution, damping ratio, etc., also play a decisive role in seismic performance. Soft/weak story formation, torsional irregularities, insufficiently detailed joint areas, short columns, strong beam–weak columns, insufficient interlocking between structural elements, pounding effects, and heavy overhangs significantly reduce the earthquake resistance capacity of structures. In addition, inadequate engineering services and deficiencies in building inspection processes can lead to increased structural damage during earthquakes and the deterioration of structural integrity [1,2,3,4,5,6]. Buildings with damaged structural integrity may be subject to partial, progressive, and/or total collapse [7,8,9,10,11,12,13,14,15,16]. Progressive collapse describes a failure mechanism where local damage, such as the sudden loss of a column, leads to a chain reaction of structural failures, potentially resulting in the partial or total collapse of a building. Unlike conventional structural analyses, which assume that localized damage remains contained, progressive collapse analysis investigates how such damage might spread through the system. It addresses a critical question: can a structure redistribute loads and remain stable after losing a key element? Triggers of progressive collapse are varied, ranging from explosions and fires to earthquakes and hidden design flaws. What unites these events is not the cause but the outcome—unexpected, disproportionate failure due to insufficient structural robustness. Historic failures like Ronan Point (1968), as well as more recent collapses linked to seismic activity and construction deficiencies, underscore that this risk is global and ongoing [17,18,19,20,21,22,23,24]. Modern guidelines, such as GSA (2016) [25] and UFC 4-023-03 [26], provide systematic approaches to evaluate structural resilience under sudden loss scenarios. These frameworks emphasize alternative load paths and demand-capacity checks to ensure that localized failures do not escalate into catastrophic collapse.

In 2023, a sequence of twin earthquakes with magnitudes of 7.8 and 7.6 struck Kahramanmaraş, Türkiye, causing extensive structural damage [27]. These earthquakes directly affected 11 provinces in the country [28] and once again highlighted numerous issues, including insufficient material strength, irregularities in plan and elevation, poor workmanship, short columns, soft soil [29], and inadequate foundations, as well as soft-story problems [30]. The recent earthquakes in Türkiye also offered a stark reminder: progressive collapse considerations must be integrated into seismic assessments, especially in regions with aging and vulnerable building stock revealed that many buildings failed not solely due to seismic demands, but due to their inability to remain stable after localized damage (Figure 1). This underscores the need to complement seismic analysis with progressive collapse assessment [31,32,33,34,35,36,37,38,39]. Where robustness is found lacking, targeted structural strengthening should be implemented to prevent disproportionate failure and ensure post-event integrity. Figure 1 shows typical collapse examples observed after the 6 February 2023 Kahramanmaraş earthquakes.

Structures with low seismic performance or existing damage require effective retrofitting strategies to prevent collapse and enhance overall resilience [40]. The use of seismic isolators has proven effective in reducing structural demands and preventing collapse during strong ground motions [41,42]. In reinforced concrete buildings, the addition of shear walls can significantly improve lateral strength and stiffness, offering an efficient strengthening solution for existing structures [43]. Alternatively, bracing systems, including conventional steel braces, viscous damping braces, and buckling-restrained braces, have been widely studied and successfully applied to enhance seismic performance and energy dissipation capacity [44,45,46,47]. Moreover, fiber-reinforced polymer (FRP) composites have emerged as a practical technique for strengthening reinforced concrete elements, providing improved ductility and load-bearing capacity [48].

2. Materials and Methods

In this study, the structural response was simulated using the Applied Element Method (AEM), a discrete-based computational technique that integrates aspects of both finite element and discrete element methods. In AEM, the structure is idealized as an assembly of small rigid elements interconnected by sets of normal and shear springs distributed along their faces. These springs represent the actual mechanical behavior of the material, including elasticity, cracking, crushing, and separation. As external loads are applied, the springs deform, allowing the simulation of both in-plane and out-of-plane responses. Moreover, the springs respond to stress redistribution, allowing the simulation to capture local failures, such as connection fractures or member buckling, and their propagation throughout the structure. Once a predefined failure criterion is met, such as tensile or shear capacity, corresponding springs are removed, thus enabling the method to capture progressive damage, element separation, and collapse mechanisms [49,50,51]. The stiffness of a normal spring Is calculated [52,53].

Main Model

The analyzed structure consists of a 5 × 5 reinforced concrete frame grid system with a uniform bay spacing of 5.5 m in both orthogonal directions, yielding an overall plan dimension of 22.6 m × 22.6 m. Each column is located at the grid intersections, resulting in a total of 36 columns across the base. The structures used S420 steel reinforcement and C30 concrete. Columns were uniformly 40 × 40 cm, beams 30 × 50 cm, and slabs 20 cm thick, with stirrups spaced every 10 cm. Lap splices followed TBEC 2018 [54], and the reinforcement ratio was 4% for both columns and beams. The mesh accounted for plastic hinge zones, dividing beams into 7, columns into 44, and slabs into 49 segments, ensuring compatibility at interfaces. Thin structures and shear locking correction (TSCF) were applied in slabs, maintaining beam continuity. The building comprises 10 stories, with each story having a uniform height of 3 m, resulting in a total height of 30 m. The elevation views highlight two configurations: one representing the bare frame structure without infill walls (Figure 2), and another including masonry infill walls placed only along the perimeter bays (Figure 3). In both structural configurations, column removal was applied at three distinct locations at the ground floor level, and the displacement response of the roof apex was recorded over a 2 s time interval after each removal. Three column removal cases were performed for the scenario without walls: corner column, edge column, and the column at the geometric center (Figure 2).

The same procedure was applied for the scenario with walls. For each column removal, two displacement values were recorded: at the removal point on the first floor and at the geometric center of the top floor (10th floor) (Figure 3). In the analyses, conventional brick masonry infill walls were included in the model as solid elements. The sudden column removal was simulated through a nonlinear time-history dynamic analysis with a time step of 0.001 s. The nonlinear behavior was inherently captured by the Applied Element Method (AEM), which accounts for material cracking, crushing, and separation through the progressive failure of discrete elements and contact interactions.

3. Results and Discussion

The removal of critical load-bearing columns produced varying displacement responses based on column position and wall presence. The bare frame exhibited consistently higher transient and residual displacements than the wall-included case. Among all cases, center column removal in the bare frame generated the highest vertical displacement at the 10th story (max: −6.57 mm; residual: −3.56 mm), indicating a severe progressive collapse potential without wall contribution.

Table 1. Maximum transient and residual vertical displacements (in mm) for different column removal scenarios.

Removal Scenario	Story	Wall-Included Max	Wall-Included Residual	Bare Frame Max	Bare Frame Residual
Corner column	1st Story	−2.21	−1.40	−2.33	−1.44
	10th Story	−4.47	−2.43	−5.20	−2.95
Edge–middle	1st Story	−1.91	−1.25	−2.74	−1.71
	10th Story	−4.52	−2.45	−5.73	−3.23
Center column	1st Story	−2.19	−1.29	−3.13	−1.78
	10th Story	−4.73	−2.54	−6.57	−3.56

summarizes the maximum transient and residual vertical displacements recorded following the removal of different columns. The simulation results reveal that the presence of structural walls significantly reduces both the maximum transient and residual displacements across all investigated column removal scenarios (Table 1). In both models, the most severe responses were observed following the removal of the center column, particularly in the bare frame configuration. For instance, the vertical displacement at the 10th-story center reached −6.57 mm (transient) and −3.56 mm (residual) in the bare frame case, compared to −4.73 mm and −2.54 mm in the wall-included model. Removal of the corner and edge–middle columns led to relatively smaller displacements, indicating a lower collapse vulnerability. Wall-included models consistently demonstrated improved energy dissipation and reduced residual deformations, confirming the beneficial role of infill walls in progressive collapse resistance. It should be noted that in the wall-included model, masonry infill walls were placed only along the perimeter frames; no internal infill walls were present. Figure 4, Figure 5, Figure 6 and Figure 7 illustrate the vertical displacement responses of the structure under sudden column removal when walls are included in the model.

As shown in Figure 4, the labels (a) and (b) indicate the measurement points at the first and 10th stories, respectively, where the displacement responses were evaluated following column removal. The corresponding displacement data at these locations are presented in graphical form in Figure 5, Figure 6 and Figure 7 and Figure 8, Figure 9, Figure 10 and Figure 11.

Figure 8, Figure 9, Figure 10 and Figure 11 illustrate the vertical displacement responses of the structure subjected to sudden column removal under bare frame conditions.

The results corresponding to different column locations (corner, edge–middle, and center) and story levels (1st and 10th) are summarized in Table 1.

4. Conclusions

This study evaluated the progressive collapse potential of a mid-rise reinforced concrete structure subjected to sudden column removal, with and without structural walls. Three critical column locations were considered: a corner column, an edge–middle column, and a center column. For each case, the vertical displacements were tracked both at the removal point on the first story and at the geometric center of the 10th story.

The findings highlight the following:

• Structural walls, even when limited to the perimeter, significantly enhance collapse resistance by limiting vertical displacements and contributing to post-event stability.
• Center column removal resulted in the most critical scenario, especially in the bare frame configuration, emphasizing the need to protect key interior supports.
• Bare frame structures showed greater vulnerability across all scenarios, with higher transient and residual displacements.
• The inclusion of walls improved the load redistribution capacity and reduced residual deformation, supporting their role in robust and resilient design strategies.

Limitations and Future Work

A key limitation of this study is that infill walls were only modeled along the perimeter frames, while no internal partitions were considered. This representation may underestimate the overall stiffness and energy dissipation capacity of real buildings, particularly in the central bays. Future work should incorporate the distribution of infill walls, including internal partitions. Such enhancements would provide a more comprehensive understanding.