Assessment of Damage Progression in Corner Buildings with Infill Walls During an Intraplate Earthquake in Mexico

Abstract

On 19 September 2017, an intraplate earthquake with a magnitude of Mw = 7.1 occurred in Mexico. Visual inspection reports following the earthquake indicated that 11% of high-risk structures and 35% of collapsed buildings were situated at block corners in Mexico City. This study analyzes the statistics on corner buildings damaged by the 2017 earthquake. Three numerical models of reinforced concrete buildings were developed, featuring four, six, and eight floors with a waffle flat slab floor system. The study focuses on collapsed corner buildings and examines their seismic responses using a series of real unscaled accelerograms from the 19 September 2017 earthquake recorded at seismic stations near these buildings. The nonlinear dynamic analysis showed that seismic demands are concentrated at the more flexible corners of buildings with plan stiffness irregularity, which may result in a collapse at drift ratios lower than those required for more regular structures, indicating low seismic resilience. The study analyzed the progression of seismic demands and damage to corner buildings throughout the 19 September 2017 earthquake, allowing for a numerical verification of the observed damages. Damage indices and the distribution of seismic demands on the buildings clearly correlated with the observed partial and total collapses during the earthquake.

1. Introduction

Mexico experiences significant seismic activity, especially along the Pacific coast, from Jalisco to Chiapas. The country has four primary sources of seismic activity: interplate (subduction), intraplate, cortical, and, in the northern region, the transform seismic source [1]. Mexico City is one of the regions in Mexico that experiences significant damage during large-magnitude earthquakes, whether they originate from the Pacific coast (interplate) or the central region of the continent (intraplate). The soil near downtown consists of highly compressible clays with a high water content, as Lake Texcoco formerly occupied this area. Consequently, seismic movements in this region are amplified, often damaging buildings.

The subsoil of Mexico City is categorized into three zones: hard soil (zone I), transition soil (zone II), and soft soil (zone III). Zone III is divided into four subdivisions based on the soil depth: zone IIIa, IIIb, IIIc, and IIId [2]. Zone IIIa has the smallest soft soil thickness, while zone IIId is the thickest, reaching depths of up to 70 m [2,3].

On 19 September 2017, a magnitude 7.1 intraplate earthquake struck at a depth of 57 km. The epicenter was located 120 km from Mexico City, on the border between the states of Morelos and Puebla. This seismic event damaged over 1000 buildings, classified according to visual inspections at different damage levels [4,5].

Torsional effects in buildings have been the focus of various investigations for decades, with increased attention towards the end of the 1970s [6]. Researchers such as Tso [7], Goel [8], and Chandler [9] contributed valuable insights into the linear and nonlinear behavior of systems that exhibit plan asymmetry. However, early studies primarily concentrated on single-floor systems and the effects of ground movement in only one direction.

Research on torsion in buildings has increased significantly, leading to new proposals for analysis, design, and rehabilitation considerations. De Stefano [10] and Das [11] compiled information from studies focused on torsion in buildings, revealing under-researched areas such as passive control mechanisms to enhance torsional behavior. Chakroborty [12] emphasized the importance of soil parameters, including ground motion duration, frequency content, and the statistical dependence of the two horizontal components, along with the dynamic properties of the building and its lateral–torsional coupling. De la Colina [13] introduced a new method for addressing accidental torsion based on amplification factors derived from a Monte Carlo simulation.

For decades, buildings with irregular plan configurations or elevations have been considered vulnerable to seismic activity. Damage statistics from the earthquake that struck Mexico City on 28 July 1957 revealed that 40% of the affected structures were located at corners, while 50% exhibited plan layout irregularities [14]. Buildings damaged or collapsed after a large-magnitude earthquake commonly exhibit irregularities or asymmetries in their structural configuration. During the 19 September 1985 earthquake in Mexico, it was reported that 42% of the damaged buildings were located at corners [15]. Recent earthquakes have also highlighted the relevance of structural pathology, as seen during the earthquakes in Turkey and Syria on 6 February 2023. Torsion resulting from plan asymmetry or geometric irregularity significantly contributed to partial and total building collapses [16,17].

Corner buildings typically feature glass partitions on their facades to enhance lighting. They often include masonry walls connected to the columns along the two perimeter axes adjacent to neighboring buildings. These designs result in an irregular floor plan due to the eccentricity between the center of mass and the center of rigidity caused by the lateral stiffness provided by the walls. This eccentricity generates torsional moments that place increased demands on the structural elements farthest from the center of rigidity.

Although most studies on buildings with torsion problems, including this work, focus on quantifying the expected damage to the structural elements of the building, other studies also relate to the amplification of floor accelerations in these structures [18]. Quantifying the demand for floor acceleration is crucial for assessing the expected behavior of building contents and is highly relevant in hospitals. Ruggieri and Vukobratovic [18] analyzed low-rise reinforced concrete archetypes, inducing torsion by varying the eccentricity between the center of mass and the center of rigidity. The authors reported increases in the acceleration demands of nodes located far from the center of mass, on the flexible side of the building, by as much as 50% in the elastic analyses and up to 20% in the inelastic analyses.

This study aimed to thoroughly analyze the nonlinear behavior of numerical models representing damaged corner buildings in Mexico City during the 19 September 2017 earthquake. Based on the results, we examine the damage process to explain partial and total collapses of corner buildings during the seismic event. The variability of uncertain parameters in the nonlinear dynamic analysis can be reduced by utilizing data from post-earthquake building inspections collected immediately after the earthquake and accelerograms recorded near seismic stations.

2. The 19 September 2017 Earthquake

The seismic event was recorded by 61 accelerographic stations located throughout the city’s various seismic zones, managed by the Seismic Instrumentation and Registration Center (CIRES), along with seven stations from the Engineering Institute (II) of UNAM. The number of instruments that recorded the event on 19 September 2017 was significantly higher than the number of accelerographic stations that provided records 32 years earlier during the 19 September 1985 earthquake (M = 8.1). In 1985, records were obtained from nine accelerographs in Mexico City, and along with the significant damage that occurred, an urgent need arose to instrument the city seismically. After the 1985 earthquake, the number of seismological stations in Mexico City significantly increased, and is now close to 150. The significance of this extensive seismological network has become evident in understanding the dynamic response of the city’s soils, which has resulted in continuous updates to the seismic design regulations. Thus, seismic regionalization now enables the determination of design spectra, incorporating site effects, for any specific location in Mexico City. The impact of the 2017 earthquake on the city was significantly less than that of 1985, partly due to the knowledge gained from seismic networks and updates of regulations. Seismic networks are limited across the rest of the country, and many regions have insufficient seismological stations. The experience in mitigating seismic risk in Mexico City encourages the expansion of seismic networks in other cities throughout the Mexican Republic.

Mexico City is situated on the old side of Texcoco, covering an area of approximately 700 km². The soil primarily consists of volcanic material, highly plastic soft lacustrine clays, thin silt, and sand layers, and has a high water content [3]. The saturated soft clay layers have very low shear wave speeds, ranging from 40 to 90 m/s. The Mexico City building code defines zone I, known as the Hill Zone, as being composed of generally firm rocks or soils deposited outside of the lake area, where sandy materials may exist superficially or interbedded deposits. Zone II, referred to as the Transition Zone, is a type of soil where deep firm deposits are located at a depth of 20 meters or less, primarily made up of sandy layers interspersed with clay layers. Finally, zone III, the Lake Zone, consists of highly compressible clay deposits separated by sandy layers with varying silt or clay content. These sandy layers are moderate to very compact, with thicknesses ranging from centimeters to several meters. Lacustrine deposits are often covered at the surface by alluvial soils, dry materials, and artificial fills. The thickness of this layer can exceed 50 m.

The lowest peak ground acceleration (PGA) recorded in Mexico City was 0.05 g (where g is the acceleration of gravity) at station MT50 in zone I (firm ground). In contrast, the CH84 station presented the highest PGA value of 0.23 g in zone IIIa (flexible soil). The highest PGA values were found in zones II (transition soil) and IIIa and IIIb (soft soils).

Figure 1 displays the pseudo-acceleration response spectra from the accelerograms recorded in each seismic zone [19]. It also includes the mean values and the mean ± one standard deviation. In zone I (firm soil), the maximum spectral intensities ranged from 0.25 to 0.38 g for periods between 0.2 and 1 s. CH84 station (zone IIIa) presented the highest spectral amplitude, reaching 1.57 g for a period of 1.4 s.

The dominant periods of the seismic records and the amplifications of ground motion depend on the thickness of the clay strata. Zone I has a clay layer less than 10 m thick, while zone II reaches a thickness of 15 m, and zones IIIa, IIIb, IIIc, and IIId have thicknesses of 30 m, 40 m, 50 m, and 60 m, respectively [3].

The spectral intensities in the two horizontal directions, N-S and E-W, were comparable across the different stations. However, the E-W component exhibited slightly greater spectral amplitudes in all areas except for zone IIId. According to the response spectra, zones II, IIIa, and IIIb displayed the highest amplitudes for periods ranging from 0.7 to 2 s.

The substantial number of seismic records collected since 1985 across various soil types in Mexico City has enabled the development of more refined models to assess the hazards and risks produced by natural phenomena in the city, considering urban growth and climate change. Among other aspects, it has been proven that the consolidation phenomena of the city’s soils, evaluated in the last 40 years, have modified the soft soils’ dynamic properties and vibration frequencies, which modifies seismic risk assessment.

3. Damage Statistics of Corner Buildings

The 19 September 2017 earthquake caused significant damage to buildings near the epicenter and in Mexico City, which is 120 km away. This damage was mainly due to the characteristics of the subsoil in the city and the great density of buildings. The seismic damage to structures was influenced by several factors, including the year of construction, structural configuration, geometry, location, and soil type. Hernandez [20] found that 91% of the buildings that collapsed in Mexico City were constructed before 1987. This suggests that these older buildings were designed to withstand lower seismic demands than those in the current seismic code, making them more vulnerable than those built under more recent regulations.

The Puebla-Morelos earthquake caused significant damage to hundreds of buildings in Mexico City. Figure 2 shows damaged corner buildings. In response to the earthquake, the Institute for Construction Safety of Mexico City (ISCDF) [21] organized working groups to conduct visual inspections and assess the extent of the damage. The reports included information regarding the location of the building, a description of the structural system (such as concrete or steel frames, concrete masonry walls, etc.), the floor system (like flat slab, solid slab, etc.), infill walls, a description of the observed damage (including damage density in beams, columns, and walls), loss of verticality, and conservation state (such as humidity and water leakages). After compiling the information, the buildings were cataloged in a specific group. The institute compiled more than 1200 reports and classified the structures into five categories: total or partial collapse, high risk of collapse (designated for demolition), high risk, medium risk, and low risk. The following statistics relate to 281 documents regarding structures classified as total, partial, and high risk of collapse.

The teams prepared detailed reports with information about each building, including its location, number of floors, building use, a general structure description, and the observed damage. According to these reports, 11% of the buildings were classified as high risk, and 35% of the collapsed structures were located at the corners of blocks.

The reports indicated that 44 constructions collapsed, 31 of which were buildings. Analyzing these data along with the Google Earth tool identified structural pathologies (Figure 3), including torsion in corner buildings (35.5%) and soft-story buildings (38.7%). The primary structural pathologies associated with the collapses during the Puebla-Morelos earthquake were essentially the same as those identified during the September 19 1985 earthquake (Magnitude 8.1), as noted by Galvis et al. [22].

Table 1. Collapsed corner buildings.

Building Id	Address	Number of Stories	Seismic Zone
CE1	4 Edimburgo & Escocia, Colonia del Valle.	8	II
CE2	4 Escocia & Gabriel Mancera, colonia del Valle Centro.	5	II
CE3	1503 Concepción Beistegui, colonia Narvarte Poniente	5	II
CE4	173 Niños Héroes & Galicia, colonia Niños Héroes	6	IIIb
CE5	56 Emiliano Zapata, Colonia Portales	7	IIIa
CE6	915 Prolongación Petén, colonia emperadores	6	IIIa
CE7	106 Viaducto Presidente Miguel Alemán & Torreón, colonia Piedad Narvarte.	2	IIIa
CE8	480 Calzada del Hueso & Canal de Miramontes Ave., colonia Los Girasoles	3	IIIa
CE9	México & Lázaro Cárdenas, colonia San Gregorio Atlapulco	6	II
CE10	176 Medellín & San Luis Potosí, colonia Roma Norte	8	IIIa
CE11	107 Ámsterdam & Laredo, colonia Hipódromo	8	IIIa

provides information on corner buildings that collapsed during the 19 September 2017 earthquake. The most common structural system involved concrete frames with masonry walls connected to columns on two perimeter sides, and the floor systems were constructed using solid and waffle slabs (see Figure 4).

Figure 5 shows that the collapsed buildings were mainly in zones II, IIIa, and IIIb (Figure 5a), had between two and nine floors (Figure 5b), and were situated on city soils with periods ranging from 1.0 to 2.0 s.

4. Numerical Models

The information about collapsed buildings and those at risk of collapse located at a corner [19,23] was analyzed to determine the typology of the damaged buildings for the numerical models. Most buildings were rectangular, with masonry walls on the two perimeter neighboring sides and windows on both corner facades. The Google Earth program [24] was utilized to evaluate the geometric characteristics of the damaged buildings. This assessment included determining the plan dimensions, structural system, number of bays, number of stories, building’s use, and the type of masonry used in the walls.

Figure 6 shows the selected typology, which comprises four bays in the longitudinal direction and three bays in the transverse direction. Each bay has a span length of five meters in both directions. The structural system features flat waffle-reinforced concrete (RC) slabs supported by columns. The concrete has a compressive strength of f′c = 24.5 MPa and an elasticity modulus of Ec = 15,505 Mpa [25]. The reinforcing steel has a yield strength of fy = 411.9 MPa and an elastic modulus of steel of Es = 196,133 MPa. The neighboring sides have masonry infill walls with a compressive strength of f*m = 1.9 MPa and an elastic modulus of Em = 1118 MPa. The numerical model includes four-, six-, and eight-story buildings designed for residential occupancy. Although only two collapsed buildings in a corner had a waffle slab floor system (Figure 4b), according to Reinoso [26], 47% of a suite of 543 damaged buildings had this floor system during the 19 September 2017 earthquake.

The deformability of the floor system is one factor that can alter the distribution of inertial forces in the resistance elements of the building. The flexibility of the floor diaphragm can, in some cases, increase the acceleration demand in shear walls, and assuming a rigid diaphragm is not necessarily conservative when the building has flexible floor diaphragms [27]. The authors reached this conclusion by studying structures primarily consisting of timber floor systems. According to numerical models of floor systems traditionally used in Mexico [28], the flexibility of the waffle slab floor system is more pronounced when the size of the slab void is large, when the ratio of the longest to the shortest side of the building exceeds three, and when the distance between columns exceeds six meters. Additionally, other authors [29,30] have concluded that when the building is supported on reinforced concrete frames, the assumption of a rigid floor diaphragm is acceptable, particularly for moderate spans between columns. These authors conclude that the flexibility of the floor system is particularly relevant when shear walls support the building.

In the present study, the ratio of the largest to smallest span is 1.33, the length between columns is five meters, and the slab voids are small (0.45 m), so not including the flexibility of the floor system in the analysis was considered appropriate. However, in future works, this effect could be included and analyzed in the seismic response of this type of building.

Statistics showed that most of the collapsed buildings were constructed before 1985. Therefore, this study designed the structures based on the regulations in force at that time, corresponding to those established in 1976 [25,31].

The amplitudes of the gravitational loads, dead and live loads, for residential use were obtained from the construction regulations [31]. A dynamic modal spectral analysis was conducted using the design spectrum proposed in the same regulation [31] for a Group B structure located on soft soil (zone III). Figure 7 illustrates the elastic design spectrum in effect in 1976 for zone III, along with the reduced spectra for three values of the Q factor, known as the ductility factor in those regulations. A reduction factor of Q = 4 was used, commonly employed at that time for designing this type of building.

Figure 8, Figure 9 and Figure 10 illustrate the cross-sections and the longitudinal and transverse reinforcement for the four-, six-, and eight-story numerical models. The regulations proposed confinement zones in the columns, with stirrup spacing at half the value determined by the shear force demand. The confinement zones at both ends of the columns measured 0.60 m.

The slab’s thickness was 0.25 m, and the ribs were categorized into three groups: central ribs (RibP), which run through the center of the column; secondary ribs (RibS), located on either side of the RibP; and tertiary ribs (RibT), formed by the remaining ribs of the slab. According to the design code, solid heads were employed at the columns to support the penetration forces. Additionally, the masonry walls had a thickness of 0.15 m.

Table 2. Vibration periods and mass participation factors (PFs) of the buildings.

Building Model	Mode 1				Mode 2
	Period (s)	PF UX	PF UY	PF RZ	Period (s)	PF UX	PF UY	PF RZ
N4	1.09	21.92%	40.21%	22.38%	0.54	50.95%	35.39%	0.79%
N6	1.42	20.94%	38.78%	21.94%	0.77	48.87%	34.13%	0.83%
N8	1.77	20.16%	37.73%	21.37%	1.02	47.57%	33.18%	0.88%
	Mode 3				Mode 4
N4	0.34	1.41%	3.33%	65.67%	0.31	15.39%	12.43%	1.06%
N6	0.45	9.35%	5.59%	62.10%	0.44	7.39%	9.71%	1.99%
N8	0.61	13.22%	9.26%	60.27%	0.55	3.37%	5.80%	2.37%

presents the dynamic properties of four-, six-, and eight-story buildings obtained using the SAP2000v23 program [32]. The table includes the first four vibration modes and their corresponding mass participation factors in the longitudinal direction UX, in the transverse direction UY, and rotation about the vertical axis. The fundamental periods range from 1.09 to 1.77 s within a region that exhibits high amplitudes in the response spectra, as shown in Figure 1. Due to the presence of infill walls connected to the columns, the modes significantly participate in the degree of freedom RZ (rotation around the vertical Z-axis).

5. Nonlinear Analysis

Nonlinear dynamic analyses were conducted using Perform 3D v8 software [33]. The numerical models were subjected to the 5–95% Arias intensity [34] of the two horizontal components from 36 unscaled accelerograms recorded in zones II, IIIa, and IIIb. First, the E-W seismic record was applied in the longitudinal direction of the building, and the N-S record was used in the transverse direction. Then, the accelerograms were reversed to maximize the structural element demands. Material nonlinearity was modeled using concentrated plasticity, with plastic hinges assigned at both ends of the elements (Figure 11). The hinge length, Lph, was determined according to Priestley’s proposal [35]. Moment–curvature diagrams that describe material nonlinearity were created based on the constitutive models for reinforced concrete proposed by Mander, Priestley, and Park [36], and for reinforcing steel following the proposal of Park and Paulay [37]. The masonry walls were modeled with biarticulated diagonals working in compression [38].

The hysteretic behavior was characterized by a linear envelope [39], which describes the stiffness in the elastic range, the yield strength and deformation, the stiffness in the post-yield range, the maximum strength, and the subsequent decrease in strength (Figure 12a). Cyclic degradation of stiffness and strength was considered, with an envelope that concludes with a residual strength and maximum deformation of the element [40,41]. Performance 3D uses four parameters to define material degradation. This study adopted the values proposed in the study [41].

The nonlinear behavior of the masonry walls was modeled as trilinear, following the guidelines set by the Masonry Committee [38]. Figure 12b shows the compression stress–strain behavior of the equivalent diagonals representing the walls under lateral loads. When failure occurs due to diagonal tension (ideal behavior), the walls exhibit a higher deformation capacity (dashed line). In this study, the shear resistance of the walls against diagonal tension, crushing, and separation was calculated, following the standards indicated by the masonry NTC-20 [42]. A brittle failure, corresponding to crushing, was identified (represented by the solid line in Figure 12b).

The displacement demands for the buildings at the four corners of the roof were assessed to evaluate the impact of torsion on their nonlinear response. The resulting drift ratios were then used to estimate the expected building damage. Figure 13 displays the corners Cor1 through Cor4 of the roof, where the displacement demands were determined.

Cor1 is the corner where two perimeter infill walls meet. Cor2 and Cor4 are the corners where a frame connects to a wall, while the perpendicular frame has no wall. Cor3 is the facade corner with no walls linked to the column. The building’s facades are on the sides from Cor2 to Cor3 and Cor3 to Cor4.

5.1. Damage Index

The damage index proposed by Park et al. [43] was employed to evaluate the overall building damage (Equation (1)). A pushover analysis assessed the ultimate displacement capacity (${\delta }_u$) and the basal yield shear ($Q_y$) under monotonic loading. Additionally, the maximum displacement demand (${\delta }_M$) and the dissipated hysteretic energy ($E_h$) were determined based on the results of the nonlinear dynamic analysis. The $\beta$ coefficient accounts for the impact of the applied cyclic load.

$$DI={\displaystyle \frac{{\delta }_M}{{\delta }_u}}+{\displaystyle \frac{\beta }{Q_y{\delta }_u}}\int d{E}_h$$

(1)

Kalateh-Ahani et al. [44] modified Equation (1) for multi-story buildings based on the roof displacement demand (Equation (2)).

$$DI={\displaystyle \frac{D_M-D_y}{D_u-D_y}}+{\displaystyle \frac{\beta E_h}{V_y{D}_u}}$$

(2)

$D_y$, $D_u$, and $V_y$ represent the yield displacement capacity, ultimate displacement, and basal yield shear, respectively. These values were determined using a pushover analysis. The $\beta$ coefficient was assumed to be 0.15 [44].

Kalateh-Ahani [44] proposed damage limit states based on the damage indices. A maximum displacement ($D_M$) value less than the yield displacement ($D_y$) indicates that the structure remains within the elastic range and no damage is anticipated, allowing for immediate use ($DI$ < 0.11). When the structure reaches the life safety limit state (LS), it would require rehabilitation before it can be occupied again (0.11 ≤ $DI$ < 0.4). The collapse prevention level (CP) signifies a structure that has sustained significant damage (0.4 ≤ $DI$ < 0.77), making rehabilitation economically unfeasible. Finally, the collapse condition occurs for $DI$ ≥ 0.77.

The buildings were subjected to the two horizontal components of seismic records from zones II, IIIa, and IIIb. Initially, the north–south (N-S) component was applied in the transverse direction (Y), while the east–west (E-W) component was used in the building’s longitudinal direction (X). After this, the damage indices for each corner of the building in both the X and Y directions were computed.

Next, the N-S component was applied in the longitudinal direction (X), and the E-W component was applied in the transverse direction (Y). Again, the damage indices were determined. Finally, the quadratic mean of the damage indices in both directions was assessed. Figure 14, Figure 15 and Figure 16 show the mean damage indices for corner 1 (Cor1) and corner 3 (Cor3) of the four-, six-, and eight-story buildings. Corners 2 and 4 experienced displacement demands similar to those of corners 1 and 3.

Corner damage is mainly observed in columns without masonry infill walls. The expected damage at corners 3 and 4 is comparable in the longitudinal direction, while corners 2 and 3 show similar damage in the transverse direction. Corner 3 showed the highest damage indices, and the building was most vulnerable in the transverse direction (Y). Conversely, the lowest damage index was recorded at corner 1, which features masonry infill walls connected to the columns in both directions.

Figure 14 presents the results for the four-story building. The highest damage indices were observed in the building’s transverse direction (Y). In zone II, 50% of the seismic records indicated demands that placed the building within the immediate occupancy (IO) limit state, 30% in life safety (LS), 0% in collapse prevention (CP), and 20% in collapse (C). In zone IIIa, the distribution was 0% in IO, 12.5% in LS, 25% in CP, and 62.5% in C. Conversely, zone IIIb had 50% in IO, 44% in LS, 0% in CP, and 6% in C. Thus, zone IIIa generated the highest damage indices, while zone IIIb had the lowest. Notably, the seismic records CH84, JC54, and MI15, which exhibited the highest spectral intensities in zone IIIa, caused the building to reach the collapse limit state.

Figure 15 illustrates the damage indices for the six-story building. In zone II, 70% of the seismic records classify the building in immediate occupancy, 20% in LS, 0% in CP, and 10% in C. In zone IIIa, the percentages are 0% in IO, 12.5% in LS, 50% in CP, and 37.5% in C. Meanwhile, in zone IIIb, 5.5% of the recordings fall under IO, 66.7% in LS, 11.1% in CP, and 16.7% in C. Overall, the building exhibited the highest damage indices in zone IIIa and the lowest in zone II.

Figure 15d illustrates the impact of torsion on damage at the corners of the structure. For instance, corner 1 is in the life safety (LS) limit state when subjected to seismic records JC54, LV17, SI53, and UC44, whereas corner 3 has reached the collapse prevention (CP) limit state. These variations in damage indices indicate higher concentrations of damage in the elements near the facade corner, which increases the risk of partial collapses in that building area.

Figure 16 illustrates the damage indices for the eight-story building. In zone II, 90% of the accelerograms resulted in demands that placed the building in the immediate occupancy (IO) state, while 0% resulted in life safety (LS), 0% in collapse prevention (CP), and 10% in collapse (C). In zone IIIa, 12.5% of the seismic records led to the IO state, 50% to LS, 37.5% to CP, and 0% to C. Lastly, none of the accelerograms from zone IIIb situated the building in the IO limit state; instead, 27.8% of the seismic records produced demands to place the structure in LS, 27.8% reached CP, and 44.4% reached C. Overall, zones IIIb and II produced the highest and lowest damage indices for this building, respectively.

According to previous results, the four-story building subjected to the accelerograms of zone IIIa experienced the highest proportion of seismic records that placed it in the collapse limit state (C), with a percentage of 62.5%. As the number of stories increased, the rate of records leading to collapse in this zone decreased to 37.5% for six-story buildings and dropped to 0% for eight-story buildings. In zone II, collapse occurred for 20% of the seismic records in the four-story building, while it occurred for 10% in both the six- and eight-story buildings. Finally, in zone IIIb, the percentages of accelerograms leading to collapse were 5.6%, 16.7%, and 44.4% for the four-, six-, and eight-story buildings, respectively.

The corner damage indices showed more closely aligned values as the building’s stories increased. The columns’ cross-sections increased with building height, increasing lateral stiffness in the frames. However, the masonry walls maintained the same thickness, which meant their lateral stiffness remained unchanged. Consequently, the eccentricity was reduced, leading to a lower demand for torsional moments.

The expected damage depended on the buildings’ dynamic properties and the soils’ dominant periods. The performance level in different seismic zones reflected the observed damage of structures classified as high risk, including those that collapsed during the seismic event. Zone IIIa experienced the highest number of collapses during the earthquake, as illustrated in Figure 5. The numerical analyses indicated that most of the accelerograms recorded in this zone caused four- and six-story buildings to reach limit states of collapse prevention (CP) and collapse (C). Additionally, post-earthquake evaluations revealed more collapses in six-story buildings compared to eight-story buildings, a trend also confirmed by the results of the numerical analyses.

The varying damage limit states at the corners explained the partial collapses observed during the earthquake [23]. The differences in seismic demands at the corners were caused by the stiffness asymmetry in the plan area.

5.2. Inter-Story Drift Ratios and Performance Levels

The previous section identified damage indices that correlated with building performance levels. In addition, this section shows the drift ratio demands at the facade corner and the corner with infill walls that led to the different performance levels. Figure 17a–c display the average maximum drift ratios for corners 1 and 3 of the four-, six-, and eight-story buildings with the performance limit states when subjected to a set of seismic records from zones II, IIIa, and IIIb. The difference in drift ratio demands between corners 1 and 3, and the drift ratios that led to collapse (C), is most pronounced in the four-story model, with a maximum distortion of 0.032. This difference decreases as the number of stories increases. Additionally, the results for the six- and eight-story buildings showed less variability than those for the four-story building.

Figure 17d illustrates the average drift ratio demands for each damage limit state at corners 1 and 3 of the three buildings. The figure also includes curves representing the mean ± one standard deviation. The results indicate an almost linear behavior at both corners. However, when corner 3 reaches the collapse level (C), corner 1 only slightly exceeds the life safety level (LS). This highlights the significant impact of torsion on the expected damage, especially at the intersection of the building facades.

Table 3. Drift ratio intervals and the performance levels.

Performance Level	Drift Ratio
Elastic (EL)	Δ < 0.0100
Immediate operation (IO)	0.0100 ≤ Δ < 0.0140
Life safety (LS)	0.0140 ≤ Δ < 0.0190
Collapse prevention (CP)	0.0190 ≤ Δ < 0.0240
Collapse (C)	0.0240 ≤ Δ

summarizes the drift ratio intervals required to reach the performance levels for the corner with the highest seismic demands (Cor3) based on the average results of the three buildings.

Akbari [45] proposed the following expected damages as a function of drift ratios: almost no damage for Δ < 0.005, slight damage from Δ = 0.005, moderate damage from Δ = 0.015, extensive damage from Δ = 0.025, and complete damage for Δ ≥ 0.05. These values closely align with the performance level achieved in this study, except for the no damage and complete damage scenarios at a drift ratio of 0.01 and 0.05, respectively. An average value of 0.0240 was determined in this study.

The higher necessary drift ratio to achieve the limit state of no damage (0.01) was due to the initial contribution of the masonry walls, which delayed the onset of damage. The relatively low drift ratio that led to the collapse of the buildings in this study (Δ = 0.024) can be attributed to two main factors: (1) the existing buildings, constructed in the 1970s, were designed according to standards that differed significantly from current regulations, resulting in a lower deformation capacity of the structural elements; and (2) the torsion effect placed increased demands on the structure, concentrating damage in the elements near the flexible corner (Cor3). This concentration also increased the demand for hysteretic energy in that area. These findings indicate that buildings with stiffness irregularity can collapse at drift ratios lower than those required for more regular structures.

5.3. Damage Evolution

The building damage assessment during the seismic event was determined by analyzing the damage index over time. Three collapsed buildings near seismic stations were selected for this analysis. Figure 18a illustrates the locations of the buildings designated as CE4 (five stories), CE10 (six stories), and CE11 (eight stories). The dynamic analyses were conducted using seismic records from the closest seismic stations to the collapsed buildings: CI05, CJ03, CJ04, SI53, and PE10. Among these, stations CI05, CJ03, CJ04, and PE10 are in seismic zone IIIb, while station SI53 is in seismic zone IIIa. As shown in Figure 18a, building CE4 is positioned very close to the boundary between zones IIIa and IIIb.

Figure 18b (four-story building) and Figure 19 (six- and eight-story buildings) display the evolution of damage over time in the transverse direction (Y) for buildings subjected to the closest seismic records. The damage index is presented for corner 1 (Cor1), where the infill walls intersect, and corner 3 (Cor3), where the facades meet. Since no collapsed four-story buildings were found at a corner during the earthquake, CE4 building was analyzed using the four-story numerical model results. Figure 18b shows the behavior of the four-story building subjected to two different seismic records: SI53 (zone IIIa) and PE10 (zone IIIb). Although the seismic stations are near one another, the impact on the building was markedly different. The PE10 record positioned the building’s performance at the life safety state, whereas the SI53 record pushed it to the collapse limit state. This disparity highlights how variations in the frequency content and ground motion amplitudes can lead to significantly different demands on buildings. Figure 18b also shows that when the building was subjected to the SI53 accelerogram, it took only seven seconds to reach the limit state of collapse prevention and just over 20 s to achieve total collapse.

Figure 19 displays that the maximum damage index was attained within the first 20 s of the seismic activity for both the six- and eight-story buildings. This indicates that the structures collapsed rapidly. Notably, the column at the corner of the facade (Cor3) showed more damage than at the opposite corner (Cor1). These findings align with the damage observed in corner buildings, where the torsional forces led to partial or total collapse of the column at the facade corner.

Figure 20 displays the response spectra of seismic records SI53 and PE10 in the north–south (N-S) and east–west (E-W) directions. The response spectrum of the PE10 seismic record reveals a lower maximum amplitude than the SI53 accelerogram and exhibits different frequency contents. The accelerogram PE10 exhibits a dominant period of 2 s in both directions, while the SI53 seismic record has a dominant period of slightly less than 1.5 s. The fundamental period of the four-story building was 1.09 s, resulting in a moderate spectral acceleration demand of 0.2 g when the structure was subjected to the PE10 accelerogram. The evolution of the damage index shown in Figure 18b indicates that the PE10 record generated a seismic demand that kept the building primarily within the elastic range of behavior. In contrast, the SI53 record produced spectral acceleration demands between 0.32 and 0.4 g, which pushed the building into the inelastic behavior range. This transition increased the building’s period, leading to spectral zones with greater amplitude that eventually caused the structure to collapse.

Figure 21 displays the response spectra for the seismic stations CI05, CJ03, and CJ04. The highest amplifications are observed for periods exceeding 1.4 s. Six-story and eight-story buildings have fundamental periods of 1.4 s and 1.8 s, respectively. The spectral acceleration demands for the fundamental periods of the structures led the buildings into the range of inelastic behavior. The CI05 record caused the six-story building to exceed the collapse prevention limit state in just over 10 s. However, it did not reach collapse until the end of the signal duration, which lasted 50 s. Although seismic records CJ03 and CJ04 delayed the building’s entry into the collapse prevention limit state, they finally led to its collapse at the end of the seismic event.

In summary, corner buildings with infill walls constructed in the 1970s and earlier exhibit a high vulnerability to damage and/or collapse due to ground motions. During those decades, the minimum amount of longitudinal reinforcement in the columns was 0.5%, using No. 2 hoops was permitted, and a reduction factor Q of 1 to 6 was allowed. Currently, the regulations require a minimum of 1% longitudinal reinforcement, stirrups must be at least No. 3, and the reduction factor Q is limited to 4. Additionally, while there were no specific requirements for this type of structure in the past, buildings currently facing torsion problems should reduce the maximum allowable drift ratio by 20% to 50% of that for regular buildings. Furthermore, the current seismic regulations state that when a structure is classified as strongly irregular due to torsional effects, step-by-step nonlinear analyses must be conducted. All of the above will undoubtedly contribute to reducing seismic risk; however, future studies should quantify the effects of these regulatory changes on the expected behavior of buildings based on detailed nonlinear analyses.

6. Conclusions

The earthquake that struck on 19 September 2017 caused significant damage to buildings in Mexico City, particularly in seismic zones II, IIIa, and IIIb. The height of the collapsed corner buildings typically ranged from two to nine stories and these buildings were situated in seismic zones with the highest spectral accelerations for periods between 1 and 2 s. This study examined typical collapsed corner building typologies through nonlinear dynamic analysis to assess how torsion affected the damage evolution process. Based on these analyses, the following conclusions are drawn.

The buildings subjected to the accelerograms recorded in zones II and IIIa presented the lowest and highest damage indices, respectively. Zone IIIa had the highest demands for four- and six-story buildings, while zone IIIb, with fewer building collapses, had the highest demands for eight-story buildings. The results demonstrated a strong correlation with the damage observed during the earthquake.

The impact of infill masonry walls was more significant in low-rise buildings, and this influence diminishes as building height increases. These walls’ inter-story stiffness remains constant, regardless of the number of stories, since the wall thickness does not change. In contrast, the stiffness of the column frames increases as their cross-sectional area enlarges. As the columns’ stiffness increases, the walls’ contribution to the overall inter-story stiffness decreases. Consequently, the eccentricity between the centers of mass and rigidity reduces in taller buildings.

The damage in the buildings, regardless of their height, was primarily concentrated in the corner with the lowest stiffness, which lacked infill walls connected to the column (Cor3). This corner is situated at the intersection of the two facades. Such concentration of damage led to partial collapses, a phenomenon observed in several buildings during the 19 September 2017 earthquake. This behavior highlighted that buildings with plan stiffness irregularities may collapse at drift ratios lower than those required for more regular buildings.

Numerical analyses indicate that the story level most affected by torsion varies depending on the number of floors in a building. The first, second, and third inter-stories were the most impacted in models of four-, six-, and eight-story buildings. These findings were confirmed during the earthquake on 19 September 2017, when low-rise buildings experienced total collapse. In contrast, several buildings with more than five stories exhibited partial collapse, with the first story remaining intact after the seismic event.

This study also presented drift ratio demands to achieve various performance levels for existing buildings. The proposed drift ratios are related to the corner of the facades (Cor3) along the short direction of the building. These values were derived from the average drift ratios obtained from all the nonlinear analyses conducted for different performance levels. However, the results are limited to the specific types of structures studied, where torsion occurs due to the inclusion of infill walls on two perimeter sides of the building. Since the numerical models analyzed in this work do not account for the floor’s flexibility or the effect of record-by-record variability on the damage index, this could be a subject for analysis in future studies.

Based on the results, infill walls in corner buildings create torsion that can ultimately lead to damage and/or collapse along the axis of the façade corner columns. In an existing corner building analyzed from its conception without considering the infill walls, separating the infill walls might improve the expected future seismic behavior. However, for existing buildings designed with seismic considerations that include the infill walls in their structural analysis, new analyses should be conducted before deciding to separate the infill walls.