A numerical study on the seismic retrofit of Haitian reinforced concrete building frames Open Access

On 12 January 2010, a 7.0-magnitude earthquake, with its epicenter in the city of Léogâne, 17 km from the capital Port-au-Prince, struck Haiti and left 105,000 buildings collapsed, 208,000 buildings damaged, over 217,000 people killed, and an additional 300,000 injured (Earthquake Engineering Research Institute [EERI], 2010). Another major earthquake with a magnitude of 7.2 and its epicenter close to Petit Trou de Nippes struck the southern part of Haiti on 14 August 2021. The intensity of this earthquake in the Modified Mercalli Intensity Scale was IX (violent) in the city of Les Cayes, leading to a death toll of over 2000 and more than 12,000 injured people (Tracy et al., 2021). The locations of the epicenters for both the 2010 and 2021 earthquakes are shown in Figure 1.

The extensive building damage and high casualty rates from past earthquakes in Haiti are largely due to inadequate seismic design standards and the widespread use of low-quality construction materials (Desroches et al., 2011; Mix et al., 2011; Miyamoto et al., 2011; Paultre et al., 2013). A large portion of the buildings in Haiti are made of reinforced concrete (RC) frames (Laguerre et al., 2024; Paultre et al., 2013; Whitworth et al., 2022). Many of the RC buildings built before 2010 are seismically vulnerable and pose a major threat to both human lives and economic activities. Considering the high seismicity of Haiti, it is necessary that the existing Haitian non-ductile RC buildings be effectively retrofitted.

Over the past decade, a few studies have been conducted to identify Haiti’s geological faults and assess their associated seismic hazard (Frankel et al., 2011; Saint Fleur et al., 2015). However, research into the seismic performance of Haitian RC buildings has been primarily limited to the case studies following the two recent major earthquakes in 2010 and 2021 (EERI, 2010; Tracy et al., 2021). Some research has utilized post-earthquake data to derive fragility curves and evaluate the vulnerability of existing buildings (Hancilar et al., 2013; Laguerre et al., 2024; Molina et al., 2014). However, there has not been a comprehensive study conducted with the specific objective of retrofitting these structures. As a result, the purpose of this study is, first, to evaluate the seismic performance of typical non-ductile RC building frames in Haiti, and second, to evaluate the seismic retrofit of those frames through various methods using numerical models. The findings of this study will help improve the seismic resilience of the Haitian communities against future seismic events.

The remainder of this article is organized as follows. It starts with identifying the construction practices and assessing the seismic hazard of the country. The types of failure encountered in the recent earthquakes are used in this assessment to identify the major deficiencies of these buildings. Four building archetypes are considered: R1 for residential one-story buildings, R2 for residential two-story buildings, NR2 for non-residential two-story buildings, and NR3 for non-residential three-story buildings. After that, five different retrofit measures are used to strengthen these buildings: RC jacket, RC shear wall, prestressed cable, steel braces, and buckling-restrained braces (BRBs). To evaluate the hysteretic behavior and damage of the original columns and joints, three-dimensional (3D) finite element (FE) models are developed in LS-DYNA. Then, two-dimensional (2D) FE models built in OpenSees are used to evaluate the seismic performance of the frame archetypes through nonlinear time-history analyses.

Before the recent strong earthquakes in Haiti, RC buildings were essentially designed by architects and engineers that had little to no seismic design training. In addition, there were no national building codes or material standards, and no enforcement bodies. As a result, the RC buildings were either non-engineered at all or designed based on inadequate codes, such as the old French RC design code, BAEL 91, which does not include any seismic criteria (Paultre et al., 2013). In the following, the typical characteristics of the older Haitian RC buildings and their engineering flaws gathered from reconnaissance studies are briefly reviewed.

The Haitian buildings are mostly low-rise, typically having one or two stories (Paultre et al., 2013). According to the Haitian Institute of Statistics and Informatics (IHSI), the majority of Haitian buildings are one-story houses (73%) and a much smaller portion are multi-story houses and apartments (5%) (Desroches et al., 2011). In addition, a survey of 170 buildings in Port-au-Prince and Léogâne indicated that 12% were of one story and 57% were of two stories (O’Brien et al., 2011).

The roof and floors in the Haitian RC buildings, particularly in those of multiple stories, are mostly made of two-way RC slabs. The thickness of the slab varies, typically ranging from 150 to 300 mm (Eberhard et al., 2010; EERI, 2010; Lang and Marshall, 2011; Marshall et al., 2011; Paultre et al., 2013). Considering that no lateral load resisting system would be considered in the design, the slabs are not generally supported by any beams in the residential RC buildings (Desroches et al., 2011; O’Brien et al., 2011). However, in some multi-story buildings, the slabs may be supported by spandrel beams (Eberhard et al., 2010).

In the older Haitian RC buildings, columns are typically made of square cross-sections and their sizes range from 150 to 350 mm (see Table 1). The typical longitudinal reinforcement comprises 4 #3 or #4 bars located at the cross-section corners, which are sometimes smooth (Lang and Marshall, 2011; Marshall et al., 2011). In multi-story buildings, the longitudinal bars are usually lap-spliced right above the floors (Paultre et al., 2013). The transverse reinforcement along the columns and into the joints typically consists of #2 ties spaced at 150–300 mm (see Table 1). The ties are generally made of smooth bars and have short 90° hooks rather than 135° seismic hooks (Mix et al., 2011). Table 1 summarizes the column sizes and reinforcement details reported in several reconnaissance studies after the 2010 Haiti earthquake. According to some reconnaissance studies (Holliday and Grant, 2011; Marshall et al., 2011), there is not significant differences between the column sizes and reinforcement details of residential and non-residential buildings.

Although beams are rarely present in residential RC buildings, they are present in some multi-story non-residential buildings (Marshall et al., 2011). The beam cross-sections are typically larger than the columns’, which would lead to undesirable weak-column–strong-beam conditions (Paultre et al., 2013). However, very limited information on the typical sizes and reinforcement details of the beams in Haitian RC buildings was found in the literature.

Concrete in Haiti is often of poor quality because it is usually made at the construction sites without using any sieving/mixing machines and often does not have the right mixture of water and cement (Lang and Marshall, 2011). This leads to inconsistent concrete mixtures with low compressive strengths. For example, a reconnaissance team tested three concrete cylinders made in Haiti, and the obtained compressive strengths were 2.8, 8.7, and 12.1 MPa (Lang and Marshall, 2011). Some other tests on Haitians concrete cylinders resulted in a mean compressive strength of 9 MPa and a standard deviation of 4 MPa (Desroches et al., 2011). As seen in Figure 2, all the reported compressive strengths are lower than the minimum acceptable strength per ACI 318, that is, 17 MPa (ACI 318-19) [American Concrete Institute (ACI, 2019)]. A reconnaissance team also tested several smooth and deformed rebar samples with various sizes obtained from the RC buildings in Haiti. The measured yield strengths ranged from 296 to 393 MPa, and the measured ultimate strengths ranged from 455 to 565 MPa (Lang and Marshall, 2011). These values correspond to Grades 40 and 60 reinforcing steels used in the United States.

Four two-dimensional RC frame archetypes with the typical design and material properties of Haitian buildings were selected for the evaluations. The selected frame archetypes belong to: (1) a residential one-story building (R1), (2) a residential two-story building (R2), (3) a non-residential two-story building (NR2), and (4) a non-residential three-story building (NR3). The building plans and frame elevations are shown in Figure 3. The column sizes and reinforcement details were chosen based on the reconnaissance reports (see the previous section). However, their agreement with the BAEL 91 code was also verified. For all the columns in all four frame archetypes, irrespective of their sizes, 4 #4 smooth bars comprised the longitudinal reinforcement, and #2 ties spaced at 200 mm comprised the transverse reinforcement. The slab thickness was specified as 150 mm for the residential buildings (R1 and R2) and 200 mm for the non-residential buildings (NR2 and NR3). All the slabs were reinforced with #4 bars spaced at 150 mm. Beams were only used in the non-residential buildings (NR2 and NR3). Since there was little information about the beams in the reconnaissance studies (see the previous section), the BAEL 91 code was used to design the beams for the non-residential archetype frames. The beam sizes and reinforcement details are shown in Figure 3. The material properties were also chosen based on the reconnaissance studies. Specifically, the concrete was assigned a compressive strength of 9 MPa, while the reinforcing steel was set to a yield strength of 344 MPa.

In local practices for creating joints between beams, columns, and slabs, it is usual to have the main rebar continue through the connection point without additional confining ties, as noted by Lang and Marshall (2011). For a deeper insight into how anchorage works, the BAEL guidelines were reviewed. It is a common technique to use straight bars with different types of anchorage, such as hooks bent at 180, 90, 135, or 120 degrees (Perchat and Roux, 1997). Consequently, this research is based on the premise that 90-degree hooks are used for longitudinal bars, and it excludes confining ties at the junctions. This approach is demonstrated in the illustrations for the footing in Figure 4a and for the beam–column connection in Figure 4b. The approach for slab–column connections mirrored that of the beam–column connections, distinguished by the omission of 90-degree hooks, as shown in Figure 4c.

In general, seismic retrofit methods are aimed at either strengthening (i.e. increasing lateral load resistance), stiffening (i.e. reducing displacement demands), energy dissipation supplementation (as a way to reduce displacement demands), or a combination of those (Bai and Hueste, 2007; Park et al., 2011; Saingam et al., 2021). Choosing effective retrofit methods for a given building depends on its main deficiencies, the targeted performance objectives (dependent on seismic hazard), and the available budget. In the case of older Haitian RC buildings, according to the reconnaissance data reviewed earlier and as will be demonstrated through numerical simulations later, the primary deficiencies are the inadequacy of lateral load resistance and low ductility. These deficiencies mainly stem from the small column cross-section sizes, the inadequate longitudinal reinforcement in the columns, the inadequate transverse reinforcement in the columns and joints, and the low concrete strength. As a result, the selected retrofit methods needed to provide both stiffness and strength enhancements. Although supplemental energy dissipation devices could additionally help reduce the displacement demands of the Haitian RC frames, currently, their application was deemed economically and technically impractical in Haiti. Therefore, for the seismic retrofit of the archetype frames, five different methods were considered: (1) installation of prestressed cable (as braces), (2) installation of steel braces, (3) RC jacketing of columns, (4) addition of RC shear walls, and (5) installation of BRBs. Considering their implementation costs, the first two methods were only applied to the residential frame archetypes and the last two methods were only applied to the non-residential frame archetypes, while the third method (RC jacketing) was applied to all the frame archetypes.

The retrofit designs followed the ASCE/SEI 41-23 (2023) guidelines, aiming to achieve a specific building performance level in response to a defined seismic hazard level. The hazard level and the target building performance level selected here were 2% probability of exceedance in 50 years and “life safety,” respectively. The life safety (LS) performance level allows damage to the structural components, yet it provides some safety margin against partial or total collapse. The earthquake intensity corresponding to the chosen hazard level was taken from the hazard curve of a site in Port-au-Prince (see Figure 5). The displacement capacities representing the performance level of LS are obtained through nonlinear pushover analyses performed via the FE models as described in section “Pushover analysis.”

Adding steel braces to an existing structure is a common way to increase its lateral strength and stiffness. Various concentric configurations of steel braces could be used for this purpose, including V braces, inverted V braces, cross braces, and K braces. Several studies have demonstrated the effectiveness of steel braces in the seismic retrofit of RC frames (Hueste and Bai, 2007; Park et al., 2011). Through a number of experiments on half-scale non-ductile RC frames, Park et al. showed that both cross braces and K braces could significantly enhance the strength and stiffness of the frames. The X braces were connected to a gusset in the middle and other gussets welded to joint connector plates. The K braces were connected to the beams and columns by steel connector plates. For this study, steel braces are used as a retrofit measure for the frame archetypes R1 and R2. The braces were diagonally installed as inverted V braces in the two bays of each story (Figure 6). The section used for the steel braces in both frames was HSS-3×3×1/8 for R1 and HSS-5×3×1/8 for R2, conforming with ASTM A36/A36M (ASTM International, 2014). The steel braces are welded to gusset plates which are bolted to the RC frame to ensure a monolithic connection.

An alternative for steel braces is the use of BRBs. Unlike normal steel braces, to prevent its buckling, the yielding steel member in a BRB is encased in concrete that is confined by a steel tube (Black et al., 2004). Although the cost of BRBs is higher than normal steel braces, they can provide lateral load resistance even when they go in compression. Several studies have shown the effectiveness of BRBs for seismic retrofit (Dunn and Pantelides, 2022; Mahrenholtz et al., 2015). Dunn and Pantelides experimentally tested a single-bay single-story frame retrofitted with a BRB and showed that it can increase the maximum base shear resistance of the frame by more than 100%. In that study, the BRB was connected to gusset plates that were connected to U plates. However, BRBs could be connected to RC frames via other types of connection, such as L plates (Mahrenholtz et al., 2015), too. In this study, BRBs are used in the frame archetypes NR2 and NR3, and they are placed as shown in Figure 7. The cross-section area of the BRBs’ cores is 1000 mm² for NR2 and 2500 mm² for NR3, and they are made of Grade 60 steel. The BRB are bolted to gusset plates which are bolted to the RC frame to ensure a monolithic connection.

In the context of Haiti, BRBs are not affordable for all homeowners. As a result, their use for seismic retrofit was limited to non-residential building archetypes, specifically NR2 and NR3, which represent more expensive buildings with higher seismic risk that can justify the investment. For residential buildings, more cost-effective retrofitting solutions were considered to ensure broader accessibility for homeowners while still enhancing seismic performance.

Using prestressed cables is another retrofitting approach that can address the buckling-related issues of normal steel braces. Prestressed high-strength steel cables can be used as diagonal or cross braces to increase the lateral stiffness and strength of RC frames (Carriere, 2007; Molaei, 2014; Shalouf, 2005). For example, Molaei (2014) experimentally evaluated the effectiveness of seismic retrofit of non-ductile single-bay single-story RC frames through diagonal prestressed cables. The cables were connected to the RC frame specimens either through holes or threaded bolts. The experiments showed that prestressed cables could significantly increase the lateral load resistance and the initial stiffness of the frames. However, because of the prestressing and the lower ultimate strain of high-strength steel cables relative to steel braces, prestressed cables cannot measurably improve the ductility of the retrofitted frames.

For this research, a cable with a cross-section of 112 mm² was used for models R1 and R2. Two cables were used for each brace in R1, and three cables for each brace in R2. The cables are placed as V braces (Figure 8). The yield stress was 1862 MPa, and the prestressed force is 40% of the yield force. To optimize the installation of post-tensioned cables, they should be added only after RC jackets are added to the columns. Since the as-built columns are thin and constructed from low-strength concrete, the addition of prestressed cables can increase the gravity load, increasing the stress in the columns. Strengthening the columns with RC jackets first ensures they can better support the additional load imposed by the prestressed cables.

RC jacketing is an effective technique to increase the strength and ductility of the RC columns with flexural and/or shear strength deficiencies. The RC jacket’s longitudinal bars are usually anchored in holes drilled in the foundation/slab via epoxy resins (Chang et al., 2014). Bousias et al. (2007) investigated the effectiveness of RC jacketing to retrofit RC columns with square cross-sections made with deformed and smooth bars through experiments. The concrete used in the jacket was of a greater strength than that of the original specimens. Their test results showed that RC jacketing could adequately increase both the strength and the ductility of the tested columns. Júlio et al. (2005) and Júlio and Branco (2008) investigated the influence of interface treatment before adding RC jackets. Their results showed that a monolithic behavior can be achieved even without surface treatment for jackets of thickness smaller than 17% of the column width. In this study, RC jacketing was adopted for all the columns in the four archetypes. A 25-MPa concrete is used for the jackets, and Grade 60 steel was used as reinforcement. The jackets’ thickness is half of the column size. More details for each column are given in Figure 9.

Similar to braces, shear walls may be added to the existing RC building structures to increase their lateral load resistance and reduce their displacement demands under earthquake excitation. For example, through cyclic tests, Bahadır et al. (2013) demonstrated that using external shear walls can increase the maximum base shear resistance of a one-bay two-story non-seismic RC frame by an order of magnitude. Hueste and Bai (2007) numerically showed that adding an RC shear wall to a five-story RC frame can almost triple its maximum base shear resistance and significantly increase its stiffness. The additional base shear resistance and stiffness provided by the shear walls could significantly reduce the likelihood of failure in shear-critical RC columns and joints due to their low displacement capacities. Shear walls can also be installed both externally to minimize the disruption of activities in the building (Bahadır et al., 2013; Kaplan et al., 2011) or internally, that is, as infill walls (Gkournelos et al., 2021). For this study, two shear walls were designed for NR2 and NR3 models as described in Figure 10. A concrete strength of 25 MPa was used with Grade 60 steel rebar.

In the context of Haiti, not all retrofitting techniques are equally adaptable or easy to construct. The most adaptable methods are the installation of RC jackets and RC shear walls, which use familiar techniques for RC members, with the exception of drilling into existing concrete to apply epoxy or cementitious grout to anchor new longitudinal rebars. In contrast, retrofits involving prestressed cables, steel braces, and BRBs require the installation of gusset plates, which can be connected to the existing RC frames through bolts or welded jackets. This step requires careful execution to ensure a monolithic and robust connection, which can be practically achieved as many experiments have shown (Dunn and Pantelides, 2022; Molaei, 2014; Park et al., 2011). Since the goal of this study is to assess whether these retrofits can achieve mechanical effectiveness when properly installed, the FE modeling discussed in the next section simplifies the handling of connections by assuming that they do not control the failures of the retrofitted frames. Although these connections present more challenges than those for RC components, they can still be implemented in Haiti because steel frames are already used in the construction of some industrial buildings (Eberhard et al., 2010), and steel sections are readily available in the local market (Burlotos et al., 2021). Depending on the post-tensioning level, the post-tensioning of the prestressed cables can be achieved through turnbuckles or hydraulic jacks, which are not advanced technologies and are available in Haiti. The retrofit steel elements also need protection against corrosion through proper coating, which is already accessible in Haiti.

Two different sets of FE models were used to evaluate the selected frame archetypes before and after retrofit. The first set consisted of 3D continuum-based FE models built in LS-DYNA (Livermore Software Technology Corporation [LSTC], 2021). The second set consisted of 2D macroscopic FE models built in OpenSees (McKenna et al., 2000), which will be explained later. The continuum-based models were used to (1) evaluate the hysteretic response and damage in the columns and the beam-to-column joints in the original frames and (2) to calibrate the macroscopic FE models. The continuum-based modeling approach is described and validated in the following.

Continuum-based models were developed in LS-DYNA for the columns and the beam-to-column joints of the original frame archetypes (Figure 11). In the column models, considering the inflection point’s approximate location, only 0.6 times the column height is considered. With a similar approach, in the joint models, only half of the connected columns and beams are considered. Concrete was modeled as constant stress solid elements using the Winfrith material model (Schwer, 2010). Both longitudinal and transverse reinforcing steel bars were explicitly modeled as beam elements with the piecewise linear plasticity material model (MAT024). The modeled transverse bars could directly capture their shear resistance and potential concrete confinement effects. To account for the interactions more accurately between the longitudinal steel bars and their surrounding concrete in the column longitudinal bars (i.e. bond-slip effects), the bond-slip model developed by Murcia-Delso et al. (2013) was implemented in LS-DYNA. Figure 12 shows sample bond stress versus slip responses obtained using the above model for a deformed steel bar and a smooth one embedded in an elastic material. The gravity loads were applied as load on the surfaces resisting those. All the analyses were performed using the implicit solver of LS-DYNA.

To validate the described modeling approach, it was used to simulate a cyclic test on an RC column. The selected RC column was specimen 9L-0.2 from Boonmee et al. (2018) and Rodsin et al. (2020), which had similar properties to the Haitian columns. The column’s dimensions and reinforcement details are shown in Figure 13. Both the longitudinal and transverse reinforcement bars were smooth. The yield strengths of the longitudinal and transverse steel were 354 and 511 MPa, respectively. The concrete’s compressive strength was 5.4 MPa. The column was subjected to 58.86 kN of axial load and quasi-static cyclic lateral displacement with a maximum drift ratio amplitude of 4%.

The hysteretic responses obtained from the test and the respective continuum-based FE model are compared in Figure 14a. It is observed that the FE model could accurately capture the overall characteristics of the column’s response, such as strength degradation and pinching behavior (mainly due to the use of smooth longitudinal bars). Most importantly, the FE model could predict the column’s maximum base shear and stiffness values in both directions with less than 10% error—the maximum base shears obtained from the test and the FE model were 11.8 and 12.4 kN, respectively. According to Figure 14b, which displays the column specimen’s plastic hinge region after the test, the column’s strength degradation was mainly caused by flexure-induced concrete damage rather than shear failure. Despite using the Winfrith material model to simulate concrete, which has been shown capable of effectively capturing cracking and strength degradation in shear- and shear-flexure critical RC elements (Asgarpoor et al., 2021), the simulated hysteretic response exhibits a slightly lower cyclic degradation rate than the experimental response. In Figure 14c, the crack pattern predicted by the FE model under the maximum displacement (4% of drift ratio) is in reasonable agreement with the experimental findings, demonstrating the model’s ability to acceptably capture the orientations and the spread of cracks in the Haitian RC columns.

The response of column assemblies to lateral forces is considerably influenced by the choice of bond-slip models. These models range from the idealized perfect bond between concrete and steel to those that simulate slip due to friction—often associated with non-deformed bars—and models that consider the combined effects of friction and bearing, as found with deformed bars. An analysis comparing these different scenarios, as shown in Figure 15, reveals that the perfect bond assumption tends to predict higher peak loads. This can be attributed to the assumed enduring strength of the bond that does not deteriorate over repeated loading. When the bond-slip model accounts for both bearing and friction, the peak load predictions are notably higher than for friction-only models, highlighting the stronger bond between deformed bars and concrete. For this study, the bond-slip model will be employed to evaluate the cyclic response of the case study frames, considering friction alone for smooth bars while both bearing and friction will be accounted for in the case of deformed bars.

Before analyzing the entire frames and designing the retrofit measures, the continuum-based FE models described earlier are used to evaluate the cyclic responses and the damage of the first-story columns in all of the selected frame archetypes and the exterior beam-to-column joints in the non-residential building frames (NR2 and NR3). Only the columns located at the first story and the exterior beam-to-column joints were examined here because of their higher vulnerability under seismic loading.

Each of the simulated columns was subjected to a constant gravity load and a cyclic lateral displacement protocol. The gravity loads were 100, 250, 480, and 800 kN for the most loaded columns of the frame archetypes R1, R2, NR2, and NR3, respectively. The equivalent drift ratio amplitudes of the lateral load increased from 0.5% to 5.0%, and each amplitude was repeated once to allow examination of cyclic degradation effects (Figure 16). The analysis was stopped when a sudden significant strength drop occurred, corresponding to more than 20% strength drop.

The predicted lateral load–displacement responses of the columns are shown in Figure 17. The general shapes of the hysteretic responses indicate that the lateral load resistances of the columns are controlled by flexure and their longitudinal steel, which is expected due to the slenderness of the columns and their low longitudinal reinforcement ratios. The inadequate concrete confinement due to the large spacing of the transverse reinforcement also manifests itself in the column ductilities being less than ∼4. It is observed that the base shear capacities of the columns are very small. Specifically, the base shear capacities of the first-story columns belonging to the frame archetypes R1, R2, NR2, and NR3 are only 3.3, 8.8, 15.3, and 24.7 kN, respectively. The drift ratio amplitudes during which the columns of the frame archetypes R1, R2, NR2, and NR3 fail are 2.5%, 2.0%, 1.5%, and 1.0%, respectively. Based on these results, it is generally observed that as the column dimensions increase without changing the reinforcement (see Figure 3) and their axial/gravity loads increase, their lateral strengths significantly increase. On the contrary, the same reasons lead to a significant decrease in the column ductility capacities. All the columns showed significant cracking at failure at their bottom part, as can be seen in Figure 18.

Each of the simulated beam-to-column joints was subjected to a constant gravity load (applied at the column top) and a cyclic vertical displacement (applied at the beam’s end). The gravity loads were 480 and 800 kN for the joints of the frame archetypes NR2 and NR3, respectively. Similar to the columns’ loading, the drift angle amplitudes increased from 0.5% to 5%, and each amplitude was repeated once.

The achieved force–displacement responses are shown in Figure 19. The results showed that their flexural-shear capacity is less than 25 kN but higher than the column flexural-shear capacity. The maximum shear force observed was 23.0 and 21.8 kN, respectively, for the beam–column joint of NR2 and NR3 (Figure 19). For the NR2 beam–column joints, failure occurred at 4% drift, and the load abruptly dropped. For the NR3 beam–column joint, crack starts at 0.3% drift; the peak strength was reached at 3% drift. All the beam-columns also showed significant crack at failure, as can be seen in Figure 20. Cracks appear both at the column joint and at the beam.

In LS-DYNA, the concrete in the RC jackets was modeled via solid elements assuming a perfect bond with the original concrete. The perfect bond assumption was demonstrated by Laguerre (2024) to be accurate in modeling RC jacketing, using experimental data from Júlio and Branco (2008), where the columns were jacketed after surface preparation with sandblasting. This surface preparation or a similar condition would be required when implementing this retrofit method to ensure a proper bond between the original and jacketed concrete. Notably, the bond-slip model parameters were different for the jacket, with a t_max equaling 10 MPa because of the higher 25 MPa strength of the concrete comprising the jacket.

The RC jacketing was the only member-level retrofit used, and it led to a significant increase in shear capacity for all the models. As can be seen in Figure 21, the jacketed columns of NR2 and NR3 exhibit slight pinching in their hysteretic responses. However, all jacketed columns demonstrate stable, repeatable loops with high ductility. It is further noted that the “bow tie” shape of the achieved hysteretic responses, especially those of the NR2 and NR3 columns, is typical for ductile well-confined RC columns because of the inability of the concrete in tension to contribute to the flexural resistance of the column during the unloading paths. The maximum shear forces observed were significantly higher for the RC jacket retrofits, which were 60.3, 104.8, 167.1, and 348.0 kN, respectively, for R1, R2, NR2, and NR3. The maximum displacement significantly increased from 2.5% to 4% for R1, from 2% to 3% for R2, from 1.5% to 3% for NR2, and from 1% to 3% for NR3. These showed that RC jacketing is an efficient retrofit solution for these columns.

The bottom story frame for each prototype was also analyzed on LS-DYNA. A constant vertical load is applied on the frame, and a monotonic lateral load is applied at the column top end. The resulting pushover curves are illustrated in Figure 22. The maximum shear force was observed at 3.1% drift, 2.7% drift, 2.0% drift, and 1.8% drift, respectively, for the frames of R1, R2, NR2, and NR3. The drift limits used are based on ASCE/SEI 41-23 drift limit approach. LS is the limit considered for the retrofit performance, and it was taken as 75% of the collapse prevention (CP) drift limit. The drift corresponding to the maximum shear force was taken as the CP limit. Table 2 gives the drift limits for the four models.

The residential (R1 and R2) and non-residential (NR2 and NR3) models exhibited some comparable behaviors in their pushover curves but contrasting behavior in their failure modes. In the early stage, the frame stiffness in all the models gradually decreased, and prior to reaching the LS drift limit, hairline cracks appeared at the joint. With the progressive application of load, the joint experienced the development of additional cracks, leading to the yielding of both the tension and compression rebars, eventually reaching the specified CP drift threshold. Figure 23 presents the strain contour at the LS and CP drift limits for R1 and NR2, indicating a higher strain concentration in the columns. However, the cracking pattern was different in the residential and non-residential models. Model R1 displayed significant cracks at the column-slab connection resembling punching shear failure at the LS and CP drift limits, whereas model NR2 was not susceptible to punching shear failure due to the presence of beams.

Given that running nonlinear pushover and time-history analyses on the entire RC frames using the continuum-based FE models would be computationally impractical, macroscopic FE models built in OpenSees (McKenna et al., 2000) were used for such analyses. The frame analyses were used to evaluate the seismic performance of both the original and retrofitted frames. In the following sections, the general approaches taken to model the original and retrofitted RC frames in OpenSees are described.

The RC frames and the frames retrofitted through RC jacketing for NR2 and NR3 are modeled using force-based gradient inelastic (GI) beam-column elements as schematically shown in Figure 24a. The GI elements can generate objective softening responses without strain localization issues associated with conventional force-based elements (Salehi and Sideris, 2017; Salehi et al., 2020; Sideris and Salehi, 2016). To define the fiber sections used in the GI elements, each column cross-section is discretized into five groups of uniaxial fibers representing (1) unconfined jacket concrete, (2) confined jacket concrete, (3) confined original concrete, (4) jacket’s longitudinal rebar, and (5) original longitudinal rebar (Figure 24b). The concrete and steel bars were represented via the Kent–Scott–Park model (Scott et al., 1982) and the Giuffre–Menegotto–Pinto model (Giuffre, 1970), respectively. The beam-to-column joints were modeled as rotational springs. The modified Ibarra–Medina–Krawinkler (IMK) deterioration model with pinched hysteretic response was used for this purpose and was calibrated based on the cyclic responses obtained from the continuum-based models calibrated using the cyclic analysis results from LS-DYNA. P-Delta effects were accounted for by using co-rotational geometric transformations.

Each RC frame for R1 and R2 was simulated using a group of GI beam–column elements, elastic elements, and nonlinear zero-length spring elements (Figure 25a). The approach described in section “Frames with slabs and beams” is the same used for modeling the columns in the flat slab frames. However, the flat slabs were modeled as elastic elements with rotational springs representing the joints. The springs were calibrated using the cyclic analysis of the column–slab joint on LS-DYNA. The assumption of adding spring at the column–slab joint was because damage happens more significantly at this location from the LS-DYNA pushover analysis (as seen in Figure 23).

In the FE models of the frames retrofitted with braces or shear walls, the frames were modeled similarly to the original frames, but other elements were added to simulate braces or shear walls. The steel braces were modeled using truss elements; however, their axial load was checked to not exceed their buckling capacity. Each BRB was modeled using a single co-rotational truss element with the same constitutive model used for the steel braces. Prestressed cables were modeled using co-rotational truss elements, too, but using an elastic-perfectly plastic material model with an initial strain. Shear walls are modeled using GI beam–column elements. The fiber sections representing the shear wall cross-sections are discretized into three groups of fibers, including unconfined concrete, confined concrete, and longitudinal bars. The concrete and steel bars were represented via the Kent–Scott–Park model (Scott et al., 1982) and the Giuffre–Menegotto–Pinto model (Giuffre, 1970), respectively.

A total of 11 ground motions were selected for this study, sourced from the PEER website and from the database of Ayiti Seismes (Calais et al., 2022). The number of scaled ground motions was selected in accordance with ASCE/SEI 7-22, which recommends using a minimum of 11 ground motions for nonlinear response history analysis. These ground motions were spectrally matched to the adopted response spectrum (see Figure 26), which was constructed based on the seismic hazard curve selected from a site in Port-au-Prince, using the program SeismoMatch (SeismoSoft, 2022). The accelerations corresponding to 2% of exceedance probability in 50 years from Figure 5 were used for the PGA and PSAs. A site of class C was considered, and the response spectrum was developed according to ASCE/SEI 7-22.

Time-history analysis was conducted using OpenSees for the as-built frames and all the retrofitted frames to evaluate the effectiveness of the retrofit techniques. A damping ratio of 0.03 was employed in the analysis. The unretrofitted frames performed poorly, showing their interstory drift reaching the LS limit as shown in Figure 27. Each global retrofit technique was then combined with RC jacketing to assess their combined effectiveness.

The results of the retrofits or retrofit combinations are presented in Figure 28, showing significant reduction of the interstory drift compared to the as-built frames in Figure 27. A retrofit measure is considered successful here if the median of the maximum interstory drift remains below the LS drift limit. For the four archetypes—R1, R2, NR2, and NR3—different retrofitting options show varying levels of effectiveness in minimizing the maximum interstory drift. In the R1 model, the steel brace combined with RC jackets proves to be the most effective, with a median of 0.08% for the maximum interstory drift obtained in the time-history analyses. The prestressed cable braces combined with RC jacket retrofit perform also well with a median of 0.48%, but not as effectively as the steel braces. The RC jacket retrofit in R1 with no braces results in a higher drift of 1.65%, but still below the LS limit of 2.3%. For R2 buildings, the RC jacket retrofit with no braces has a median drift of 1.88%, which is greater than the LS limit of R2 archetypes. However, the steel braces and prestressed cables, combined with RC jacket had medians of 0.18% and 0.63%, respectively. Overall, for residential buildings, the steel braces combined with RC jackets proved to be the most effective in reducing the maximum interstory drift demand. It is worth noting that the maximum compressive forces of the steel braces were confirmed not to exceed their buckling limits in any of the time-history analyses.

For non-residential archetypes, the BRB combined with RC jackets proved to have the best performance in reducing the maximum interstory drift demand. In NR2 structures, BRB combined with RC jackets had a median drift of 0.97%, while shear walls combined with RC jackets had a median drift of 1.10%. Finally, in NR3 buildings, BRB combined with RC jackets had a median drift of 1.18%, while shear walls combined with RC jackets had a median drift of 1.22%. Overall, BRB braces with RC jackets show the best performance in minimizing maximum interstory drift in non-residential buildings. Note that the maximum shear forces in the shear walls were checked in all the analyses to ensure they did not exceed the shear capacities of the designed shear walls.

This study presents a comprehensive numerical analysis of Haiti’s RC structures and uses five techniques for effectively strengthening them against earthquakes. An investigation was conducted to assess the implementation of RC jacketing as a retrofit strategy at the member level, combined with global retrofit methods such as steel braces, BRB, prestressed cables, and RC shear walls. The RC buildings in Haiti were represented using four archetypes: R1 for residential one-story buildings, R2-residential two-story, NR2 for non-residential two-story, and NR3 for non-residential three-story buildings. The analysis in this study utilized both continuum-based FE models in LS-DYNA and macroscopic FE models in OpenSees to assess the effectiveness of the retrofitting techniques. These analyses led to the following key findings:

• The as-built frames had very low shear capacity, and their maximum interstory drift went beyond the LS and CP limit states when subjected to time-history analysis with the unscaled ground motions.

• The RC jacketing proved to be a highly effective member-level retrofit of the typical Haitian columns. It increased both the shear capacity and drift limit of columns across all building archetypes, demonstrating a substantial improvement in structural stability. It increased the base shear force 18 times for the archetype R1, 12 times for R2, 11 times for NR2, and 13 times for NR3.

• The global retrofitting techniques, comprising steel braces, BRBs, prestressed cables, and RC shear walls, were shown to significantly reduce the interstory drift demand when they are combined with RC jacketing. The steel braces led to lower drift demand for residential buildings, and the BRBs led to lower drift demand for non-residential prototypes.

Given the significant vulnerability of Haitian RC structures, there is a clear and pressing need for widespread retrofitting across the country. By addressing both the structural deficiencies and the practical challenges of retrofitting, this study can serve as an important guide for engineers and policymakers working toward a more resilient built environment in Haiti. With the right implementation strategy, these retrofitting measures could play a crucial role in safeguarding Haitian communities from future seismic events. It is important to note, however, that this study employed a deterministic approach, relying on mean values for building properties. As such, a comprehensive exploration of the uncertainties associated with these properties remains an essential step for gaining a deeper understanding of the retrofit effectiveness. In addition, experimental evaluation of metallic brace connections to the existing Haitian RC frames should be considered in the future studies.

The authors extend their gratitude to Dr Ioannis Koutromanos for his assistance in implementing the bond-slip model in LS-DYNA. The authors also thank Dr Eric Calais and his team for their facilitation in obtaining ground motions from the 2021 earthquake in Haiti.