Retrofit scheme of FRP jacketing system for blast damage mitigation of non-ductile RC building frames

Composite Structures 228 (2019) 111328

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Retrofit scheme of FRP jacketing system for blast damage mitigation of nonductile RC building frames Jiuk Shina, Jong-Su Jeonb,

T

⁎

a

Department of Building & Urban Research at the Korea Institute of Civil Engineering and Building Technology (KICT), 283 Goyang-daero, Ilsanseo-gu, Goyang-si, Gyeonggi-do 10223, South Korea b Department of Civil and Environmental Engineering, Hanyang University, Seoul 04763, South Korea

ARTICLE INFO

ABSTRACT

Keywords: Blast performance Non-ductile reinforced concrete frame Fiber-reinforced polymer jacketing system Retrofit scheme

Non-ductile reinforced concrete building structures built before the 1970s have been significantly damaged and collapsed under man-made disasters (e.g., blast loads) due to their inadequate column details. The structural deficiencies can be mitigated by a fiber-reinforced polymer jacketing system. This research investigated the blast performance of a low-rise non-ductile building frame strengthened with the jacketing system. Based on the investigation, a retrofit scheme was established to mitigate the blast-induced damage and maximize the effectiveness of the retrofit system. The retrofitted models varied with the main parameters of the retrofit system associated with the confinement effect and flexural stiffness, and blast simulation was performed under various loading scenarios. The retrofit effect was examined in terms of confinement and stiffness ratios. Since the effects of the retrofit parameters on the blast performance depend on the blast loads, the retrofit scheme needs to be established in terms of expected blast loading scenarios.

1. Introduction Before the 1970s, many reinforced concrete (RC) building structures in the United States were designed and constructed with structurallydeficient details. Thus, existing building structures are structurally vulnerable to natural and man-made disasters, such as earthquakes and blast loads [1–4]. Such disasters have led to significant damage of the main structural elements (e.g., columns) because the building structures were designed for only gravity loads. This design practice resulted in the following inadequate detailing of RC columns: (1) small-diameter transverse reinforcement, (2) wide spacing between column ties, and (3) 90 degree hooks in a rectangular column [1–4]. These insufficient design details result in poor confinement and low shear capacities of RC columns under extreme loading conditions (seismic and blast loads), which can induce structural/element failure in a brittle manner. In particular, previous researchers [5,6] have pointed out that the structurally-deficient RC columns suffered brittle failure modes against blast loads as well as earthquake loads, including diagonal shear failure, and axial failure. The diagonal shear failure mode is closely related to inadequate transverse reinforcement details, which can often be observed at the bottom and top of the columns. This shear failure mode exposed the concrete core in RC columns. After that, the exposed columns suddenly lost their axial load carrying capacity because the inadequate ⁎

column details cannot fully confine the exposed columns. The damaged columns suffered axial failure. Then, the column failure can trigger the progressive collapse of building structures, which has led to many human casualties [7,8]. For example, the 1995 bombing (04/19/1995) of the Alfred P. Murrah Federal Building located in Oklahoma City is an example. The Murrah Building constructed in the 1970s had seismically-deficient column details (i.e., insufficient blast resistance in RC columns). The Oklahoma City bombing led to significant structural damage to the Murrah Building. The main load-bearing columns of the building structure, which directly faced the blast effects, failed in shear, and the column shear failure triggered the subsequent progressive collapse. This blast event killed 87% (153 out of 175) of the people in the collapsed area [5]. To prevent such catastrophic losses and strengthen the blast performance, previous studies [6–15] have recommended strengthening existing RC columns using column retrofit techniques with steel and fiber-reinforced polymer (FRP) materials. The FRP retrofits have been widely used to upgrade the lateral-resisting capacities since the mid-1980s in an earthquake engineering field. In particular, an FRP column jacketing system can ensure the ductile behavior of RC columns with the seismically-deficient details because it provides additional confinement to the existing RC columns. To upgrade the blast resistance of RC columns, column retrofits using the FRP materials started around 1995. The retrofit effects have been

Corresponding author. E-mail addresses: [email protected] (J. Shin), [email protected] (J.-S. Jeon).

https://doi.org/10.1016/j.compstruct.2019.111328 Received 24 April 2019; Received in revised form 4 July 2019; Accepted 16 August 2019 Available online 24 August 2019 0263-8223/ © 2019 Elsevier Ltd. All rights reserved.

Composite Structures 228 (2019) 111328

J. Shin and J.-S. Jeon

demonstrated by several existing experimental and numerical studies against blast loads. After the Murrah building bomb, a series of studies for FRP-retrofitted columns were conducted by Karagozian & Case (K& C). Previous researchers [9–15] demonstrated that column retrofits using an FRP jacketing system for non-ductile building structures with shear-critical columns can effectively reduce the lateral deformation and prevent building collapse. Crawford et al. [9,12] carried out the full-scale field tests for non-retrofitted and FRP-retrofitted columns in an RC frame building. Note that the non-retrofitted column has structurally-deficient design details. Since the FRP retrofit provided sufficient shear capacity and ensure ductile behavior, the retrofitted RC column avoided brittle shear failure, and thus remained elastic without permanent deformation under blast loads. Rodriguez-Nikl [15] tested non-ductile and FRP-retrofitted RC columns under blast-like shock loading, using ultra-fast hydraulic actuators. The FRP-retrofitted RC column specimens behaved in a ductile manner without any significant damage, whereas the non-ductile RC column specimens suddenly failed in diagonal shear. Additionally, the previous researchers [9–14] proposed and validated a retrofit design procedure using FRP materials based on full-scale blast field tests. While this retrofit design procedure focuses on ensuring sufficient shear capacities, a retrofit design standard specified in the American Society of Civil Engineers (ASCE) 59-11 [16] addresses confinement requirements for FRP-retrofitted RC columns to ensure the ductility capacity under design against blast loads. This blast-resistance building standard has ductility-based damage thresholds with respect to low-to-high performance levels (level of protection, LOP). Since such damage thresholds are composed of deformation-based damage demands (i.e., displacement ductility), the effects of the number of inelastic cycles induced by blast loading are not included for the blast-resistant design and performance evaluation of as-built/retrofitted columns. A recent study [17] proposed a hybrid performance criterion by combining the seismic and blast damage thresholds using energy absorption demands, which were computed using the Park-Ang damage model [18]. Since a concept of structural performance evaluation with energy demands has been widely used against extreme loads (e.g., earthquake), the energy-based thresholds can be adopted to a blast performance evaluation method. This research used the energy-based blast damage thresholds in the hybrid performance criterion to determine the blast damage level of the retrofitted RC frame in this paper. The goal of this study was to investigate the effectiveness of an FRP column jacketing system for an existing low-rise RC building frame under blast loads. Based on the investigation, the retrofit scheme of the FRP jacketing system was proposed to minimize the blast damage or maximize the retrofit effects. To achieve the research goals, a finite element (FE) column model was developed using LS-DYNA to simulate blast responses [19]. This model was validated with existing experimental results performed by Woodson and Baylot [20]. The validated modeling technique was implemented into a non-ductile, two-story frame model retrofitted using the FRP jacketing system. For a set of retrofitted frame models, comparative parametric studies for the retrofit system were carried out to investigate the effect of retrofit parameters, such as jacket thickness, jacket strength, size of section enlargement, and grout material strength. Note that the blast performance of the retrofitted models was evaluated in terms of energy-based thresholds, and the effectiveness of the retrofit system was quantified by comparing energy damage demands between as-built and retrofitted frame models.

(MM-ALE) method [21], and (3) a coupled method between LBE and MM-ALE (coupled LBE-ALE) [22]. The LBE method produced an air blast pressure using an empirical blast equation and directly applied the blast pressure to the segments on a given surface of the target structure. Therefore, the LBE method is computationally efficient. However, the LBE method cannot generate blast wave interactions (e.g., merging reflected waves by a target structure, diffracted blast waves in front of a target structure, and the effect of trailing vortices along the back sides of a target structure) because the air blast pressure produced by the LBE model is directly applied on the blast-facing surfaces of the target structure [23–26]. To overcome this limitation, blast loads can be modeled with the MM-ALE modeling method. This method requires a Lagrangian mesh and two separate Eulerian meshes; the target structure serves as the Lagrangian mesh, while explosive and surrounding air models function as the Eulerian meshes [27]. The surrounding air meshes are fully coupled with the Lagrangian target structure using a fluid-structure interface (FSI) algorithm, which allows air to flow on and around the structure. In other words, the coupled air mesh serves as a compressible medium between the explosive and the target structures, making it possible to transfer the blast waves to the target structure immediately after the explosive charge occurs. Therefore, the incident waves produced by the detonation of the explosive material interact with any reflected waves from ground and target surfaces while traveling in the air mesh. However, the MM-ALE modeling method is more computationally expensive than the LBE modeling method. This is mainly due to the large number of elements in the air, the small mesh size of the explosive model, and the reduction in time step size required for coupling computations [23–26]. To ensure a good balance between accuracy and computational efficiency in blast simulations, this research selected a coupled method using both the empirical blast load function (LBE method) and the MMALE method. The coupled LBE-ALE method is composed of a Lagrangian target structure, an air model, and a single layer of ambient elements. The air model surrounding the target structure and the ambient element immediately adjacent to the air model are modeled with an ALE domain. The ambient air element transfers a blast pressure timehistory computed by the LBE method to the air model surrounding the target structure. The ALE air model allows the blast wave to travel and interact with the target structure by coupling using the FSI algorithm, which can simulate the blast wave interaction in a manner similar to the MM-ALE method. Additionally, the coupled LBE-ALE method can eliminate the explosive model and reduce the air model as compared to the MM-ALE method. Thus, the coupled LBE-ALE method can generate accurate responses in an efficient way. 2.2. Model development 2.2.1. Previous studies To investigate blast responses, Woodson and Baylot [20] designed, constructed, and tested quarter-scaled RC frame structures, which are commonly found in low seismic regions. Fig. 1 illustrates the experimental setup for the quarter-scaled RC frame specimen. Reaction walls, which were constructed behind the specimen, restrained the horizontal motions of structural slabs to investigate the blast effects of a center front column. As shown in Fig. 1, a 7.1 kg hemisphere of C4 was detonated at a standoff distance (RD) of 1.07 m and a standoff height (RH) of 305 mm above the ground surface. These blast loading parameters (charge weight, RD and RH) were determined by matching the scaled distance of the quarter-scale model with that of the full-scale model. The blast experimental study measured displacement time history responses at the mid-height of the first story exterior column, peak pressure, and impulse on the column’s front surface. Note that this research validated the FE numerical model for the blast-faced column (the center front column in the first story) because the blast load mainly impacted the studied column, and the lateral displacement of the column was marginally affected by other structural elements (e.g.,

2. Numerical column model 2.1. Blast loads Blast loads can be simulated by several modeling methodologies provided in LS-DYNA: (1) the Load Blast Enhanced (LBE) modeling method [19], (2) the Multi-Material Arbitrary Lagrangian-Eulerian 2

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Table 1 Dimensions of the RC column model. Parameter

Dimension (mm)

Column Column Column Spacing

900 89 89 100

height (H) width (b) depth (h) of column and cross ties (s)

height (H), width (b), depth (h), and clear spacing (s) of the column and cross ties. The dimensions of the RC column are provided in Table 1. The boundaries at the header reproduced the structural slabs in the quarter-scaled RC frame specimen, which were constrained against horizontal motions (X- and Y-directions) by the reaction walls. The footing was restrained in all directions to represent a fixed condition. The concrete element was modeled using 25 mm (i.e., 25 mm mesh size) solid elements. The mesh size for the target structure was determined based on sensitivity analyses. The beam truss elements were used to model steel reinforcing bars. The column ties and cross ties were directly linked to the concrete mesh nodes. That is, the linked nodes between the column/cross ties and the surrounding concrete were fully bonded. Since the concrete surface damage caused bond-slip effects between the longitudinal reinforcing bars and surrounding concrete, longitudinal rebars were separate from the concrete mesh nodes. These separate nodes were connected using a one-dimensional (1D) slide line model provided in LS-DYNA, which can transfer interfacial forces from slave (steel rebars) to master (concrete) nodes. The interfacial forces can be reproduced by simple bilinear behavior with bond stress degradation. In this study, the parameters in the 1D slide line models were defined using the CEB-FIP Model Code [30], which provides the model parameters in terms of the failure modes and bonding conditions. This modeling method can reproduce bond slip behavior after concrete damage [30,31]. The bond-slip effects of the studied column were characterized by a splitting failure mode and poor condition because the column has seismically-deficient detailing.

Fig. 1. Schematic view of the test setup for a quarter-scale RC frame specimen, reproduced from Woodson and Baylot [20].

minor damage was detected on the two exterior first-story columns), and only permanent vertical displacement was observed on the firststory slab due to the reaction walls that provided a lateral restraint on the slab. In the previous numerical studies, the experimental responses measured by Woodson and Baylot [20] were used to validate their numerical modeling methodology under blast loading. Baylot and Bevins [28] simulated entire quarter-scale specimens with and without infill walls to reproduce the experimental responses of the first story exterior column and investigate the effects of the infill walls. Additionally, Shi et al. [29] validated their RC column model under blast loads with the experimental responses. They modeled the quarterscaled exterior columns in the first story and implemented bond-slip models along the column rebars in their model. Compared to Baylot and Bevins’s numerical simulation, Shi et al.’s column model showed a better correlation with the experimental results. 2.2.2. Structural geometry model To validate the numerical modeling technique used in this study, the experimental responses measured by Woodson and Baylot [20] were compared to the numerical simulation results reproduced by LSDYNA. Fig. 2 shows a numerical model of the first story exterior RC column. This figure also includes brief information on the column

2.2.3. Material model The concrete behavior was modeled using the Karagozian & Case (K &C) concrete model (KCC model). This KCC model can generate concrete damage using a default parameter of the unconfined compressive

Fig. 2. Details of the RC column model selected in the quarter-scale RC frame (unit: mm). 3

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concrete strength (fc'), which reflects concrete hardening and softening, shear dilation, and confinement effects. Among these, the shear dilation effect can be reproduced by a parameter ϖ in the KCC model. Since the parameter captures the concrete expansion when concrete cracks were detected, the parameter allows the prediction of reasonable confinement effects [14]. A previous study [32] proposed values of the ϖ parameter as follows: (1) ϖ = 0.9 for the FRP-strengthened columns and (2) ϖ = 0.5 or 0.75 for the seismically-deficient columns. This research modeled concrete behavior using the fc' of 42 MPa and the ϖ of 0.5 in the KCC model for the numerical column model. The stress-strain curve of longitudinal rebars was reproduced using a bilinear model with strain hardening (elasto-plastic material model). The main parameters (elastic modulus, yielding strength, and strain hardening ratio) of the elasto-plastic material for the ϕ 3.2 longitudinal bars were assumed to be 2000 GPa, 399 MPa, and 0.002, respectively. The above main parameters for the ϕ 1.6 column ties were assumed to be 2000 GPa, 449 MPa, and 0.002, respectively. To determine the strain rate effects in the material models induced by high-speed blast loads, the concrete and steel material models included a dynamic increase factor (DIF), which is a ratio of the dynamic to static strength related to strain rates. The DIFs, which are characterized as a function of the strain rate, were incorporated into the KCC model to determine the concrete strain rate effects. The DIF function modifies the failure surface of the KCC model to reflect apparent changes in strength due to high loading speeds. The DIF functions for the concrete compressive and tensile strengths can be derived as in Eqs. (1) and (2) [14], respectively, where = strain rate in s−1 (1/ second), sc = 30 × 10−6 s−1 for a static strain rate in compression, −6 −1 s for a static strain rate in tension, fc' = static compressive st = 10 strength of concrete in MPa, log(γs) = 6.156αs − 2, αs = 1/(5 + 0.9fc'), log(β) = 6δ − 2, and δ = 1/(1 + 0.8fc').

DIF =

DIF =

( / sc )1.026 s ,

for

1/3 , s ( / sc )

for

( / st ) , ( /

st

for

)1/3 ,

for

s

s s

1

> 30s

1.0s > 1.0s

WTNT) = 0.54 m/kg1/3. The peak blast pressure and impulse generated from the coupled LBE-ALE method were 6680 kPa and 1082 kPa-msec, respectively. These simulated blast loading parameters were slightly underestimated compared to the measured peak pressure and impulse on the column front surface in a previous experiment [20]. Before modeling the blast load, the mesh sizes of the ambient air model and the ALE air model were determined by performing mesh sensitivity analyses for the various mesh densities until the blast responses remained constant. To transfer the blast load produced from the LBE method to the air meshes, the ambient layer initially impacted by the blast load was merged with the air meshes. The air meshes were fully coupled with the target structure using an FSI algorithm, which can follow the incident wave transferred from the ambient layer and the reflected waves through the air meshes. Non-reflecting boundaries were applied to the exterior boundaries on the numerical air models as shown in Fig. 3 to prevent the overestimation of the blast pressure and impulse due to the unpredictable reflected waves in the air models. Fig. 4 compares the displacement time histories at the middle height of the RC column between the simulation and experiment results. This figure also includes the simulated responses from the numerical models developed by previous studies [28,29] (referred to as the “Baylot model” and “Shi model”) to compare their responses to those of the coupled LBE-ALE model performed in this study. These numerical models simulated the blast loads using the MM-ALE method, which implements the high explosive materials and air meshes described in Section 2.1. As shown in Fig. 4, the variation in the peak displacement between the coupled LBE-ALE model and experimental data was approximately 3%. In addition, the coupled LBE-ALE model showed a better correlation than the Baylot and Shi models in terms of the peak displacement and the time when the displacement is maximized. This is

1

30s

s

Fig. 3. Implementation of the coupled LBE-ALE method to the RC column model.

(1)

1 1

(2)

The PLASTIC_KINEMATIC steel material model can be incorporated with the DIF. The DIF amplifies yield and ultimate stresses of the steel materials as given in Eq. (3) [33], where fy = static yielding stress of the steel material in MPa, fu = static ultimate stress of the steel material in MPa, αs = 0.074–0.04 fy/414 for yielding stress of the steel material, and αs = 0.019–0.009 fu/414 for the ultimate stress of the steel material. Note that the equation is only valid for reinforcement with yield stresses between 290 MPa and 710 MPa.

DIF = ( /10 4)

s

(3)

2.3. Model validation The blast load was simulated using the coupled LBE-ALE. The coupled LBE-ALE method was implemented into the target structure (RC column model). Fig. 3 illustrates the numerical column model with the blast loading model reproduced by the coupled LBE-ALE method. The blast load produced by the LBE model impacted the single layer of the ambient air model (mesh size = 12.5 mm), and the ALE air model (mesh size = 12.5 mm) transferred the blast waves to the surrounding column model. The LBE method used for producing the blast load in the coupled method generates air blast pressures using an equivalent mass of TNT (i.e., WTNT over gravity acceleration) with stand-off distances in the X-, Y- and Z-directions (i.e., X-, Y- and Z-coordinates of the charge center, respectively). The blast load in the LBE method was set to 8.0 kg of the WTNT (about 1.13 times the C4 charge weight), with a 1.07 m stand-off distance (RD = 1.07 m) and 0.23 charge height (RH = 305 mm), corresponding to a scaled distance (Z = RD/

Fig. 4. Comparison of mid-span displacements of simulations and experiment. 4

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mainly due to the following modeling methods used in the coupled LBEALE model: (1) implementation of the bond-slip effects between the surrounding concrete and longitudinal reinforcing bars compared to the Baylot model, and (2) better prediction of the blast wave interaction using the coupled LBE-ALE method compared to the Shi model. The residual displacement of the coupled LBE-ALE column model is slightly underestimated compared to the measured responses in the test specimen. This underestimation is associated with the modeling assumptions. A steel material model with elasto-plastic behavior was used in this column, under the assumption that the steel reinforcing bars did not fail after reaching their ultimate strength. Additionally, the bondslip properties used in the 1D slide line model were determined based on the CEB-FIP Model Code [30]. This model code defines the bond-slip properties using the average values of each parameter (e.g., maximum bonding stress, residual bonding stress, and slip displacement) for a broad range of cases, and the residual bonding stress retains the maximum bonding stress of 15% after the ultimate slip displacement. These modeling assumptions can result in underestimation of the residual displacement of the numerical column model. This research validated the maximum displacement from the numerical model using experimental results; this is because ASCE 59-11 [16] specifies displacement ductility limits for the performance levels using the ratio of maximum displacement over yielding displacement, and this research also used the energy-based limits derived from the ductility limits. Fig. 5 shows the damage propagation of the coupled LBE-ALE column model under the blast load from the initiation of shear damage to permanent damage on the model after the blast effects. This figure does not consider the ambient layer or air meshes in order to observe the damage patterns on the column model. The damage propagation illustrated in Fig. 5 is correlated with the blast damage observed from previous experiments [19]. Therefore, the blast modeling technique presented in this study provides reasonable predictions. To predict blast responses of the full fame models in as-built and retrofitted frame configurations, this modeling technique was incorporated into their FE frame models.

3. Numerical frame model 3.1. Model development To simulate the blast response of the full-fame models, the blast modeling approach used for model validation was implemented to model as-built and retrofitted frame models. This research selected nonductile two-story RC frame structures in as-built and retrofitted configurations. The frame structures represent a typical low-rise RC office building constructed in the 1950–1970s, which was designed in accordance with the gravity loads. In past studies [3,34], full-scale shaker testing for the as-built and retrofitted RC frames was performed to measure realistic responses and investigate the applicability and effectiveness of the retrofit system. Based on the experimental results, asbuilt and retrofitted FE frame models were developed using LS-DYNA, and the simulated responses from the FE frame models were compared with the experimental results. The FE frame models reasonably predicted the seismic responses within approximately 12% [35]. The FE models reproduced the measured seismic responses, and prediction accuracy was improved through the implementation of proper bondslip effects in the possible bond-slip zones (column lap-splice and exterior beam-column joint areas). The bond-slip behavior was determined based on the measured bond-slip performance from the fullscale tests. In this study, the blast modeling approach validated with the past blast experimental study in Section 2 was implemented into the FE frame models. To generate the reasonable blast responses, the FE frame models additionally included the concrete and steel materials with the strain rate effects and blast loading simulation models (e.g., single layer of the ambient air model, the ALE air model, explosive model, and reflected and non-reflected boundary conditions). Fig. 6 illustrates the details of a full-scale RC frame specimen, including column and beam reinforcing details, and section views. Among them, the A-A' section view for the first story column of the retrofitted test frame specimen includes carbon FRP (CFRP) jacketing system

Fig. 5. Damage propagation of coupled LBE-ALE column model. 5

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Fig. 6. Details of two-story, two-bay non-ductile RC specimens (unit: mm) [34].

Fig. 7. Retrofitted FE frame model.

details (e.g., jacket thickness, FRP and grout material properties, and section size), which were designed for seismic loads to ensure a target ductility of 4.5. This target ductility is approximately twice as high as that of the RC column in the as-built test frame [34]. Here, the ductility of the as-built column is 2.20. For the FRP jacketing system, the compressive strength of the non-shrink grout material used for the section enlargement is 40 MPa, and the tensile strength of the CFRP sheet wrapped around the columns is 1080 MPa, corresponding to an ultimate strain of 0.011 [34]. Based on the test frame details, the numerical frame models were developed using a half-symmetry condition to reduce the computational efforts, as illustrated in Fig. 7. This figure includes the FE frame model strengthened using an FRP jacketing system and a detail modeling view of the FRP-retrofitted column and bond-slip conditions in the first and second columns. This frame model was utilized as a target structure in a blast simulation model. The foundation bases were modeled as a fixed boundary condition. The concrete column and beam models in the longitudinal direction (main structural elements) utilized solid elements. All steel reinforcing bars surrounding

the solid elements were modeled using beam elements. Fig. 7 also illustrates the model of the FRP jacketing system, which is composed of non-shrink grout materials for modifying sectional shapes and FRP materials for providing additional confining pressures to the existing RC columns. The FRP jacketing system was modeled with two different elements: non-shrink grout using solid elements and an FRP jacket using shell elements. As shown in Fig. 7, two contact surfaces between the existing concrete and grout models and between the grout models and FRP shells, and the interface surfaces were reproduced using a surface-to-surface contact function provided in LS-DYNA [36]. The concrete behavior was captured using the KCC model to simulate concrete damage. The parameters were set as given in Table 2 [34,35]. For the longitudinal reinforcing bars, the material behavior was captured using a piecewise linear plasticity model in LS-DYNA. This material model allows the user to input an arbitrary stress-strain curve [35]. Based on the past experimental studies, the parameters of the steel reinforcing bars were assumed, as summarized in Table 3 (ultimate strain = 0.15). This research utilized an orthotropic material 6

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Table 2 Summary of concrete material parameters [33,34]. Story levels

Element

As-Built FE frame

Retrofitted FE frame

Concrete strength (MPa)

Concrete strength (MPa)

First story

Column Beam

31.5 25.0

0.5 0.5

32.8 26.5

0.9 0.5

Second story

Column Beam

28.5 23.5

0.5 0.5

30.3 23.5

0.5 0.5

Table 3 Summary of steel material parameters [33,34]. Rebar

Yield strength (MPa)

Ultimate strength (MPa)

Elastic modulus (GPa)

ϕ10 bar ϕ19 bar ϕ25 bar

520 445 541

739 734 663

197 194 209

Fig. 9. FE frame model with the coupled LBE-ALE blast modeling method.

the FE model were set up using the lap-splice failure and good bonding conditions in the model code. Using a similar modeling approach, the bond stress-slip relationships represented by the one-dimensional slide line model were incorporated into the all possible areas where bond-slip would occur under blast loads. To simulate blast loading, this research utilized the coupled LBEALE approach described in Section 2.1. Fig. 9 illustrates the FE frame model combined with the coupled LBE-ALE blast modeling approach. To determine the element mesh sizes for the target structure and ALE air models, mesh sensitivity analyses were performed under a given blast loading scenario: a charge weight (WTNT) = 680 kg, stand-off distance (RD) = 7.0 m, and scaled-distance (Z) = 0.80 m/kg1/3. The minimum element mesh sizes were determined as follows: 12.5 mm for the target structure and 38 mm for the ALE air model. The ALE air model extended from the corners of the target structure by 100 mm, except for the symmetric boundaries in the XZ-plane, based on previous studies [37,38]. The single layer of ambient air was directly modeled at the end surface of the air model in the YZ-plane. The ALE air model was coupled with the frame model using the FSI algorithm described in Section 2.1. To eliminate the blast wave reflections from the boundaries of the air model in the XY-, XZ-, and YZ-planes, non-reflecting boundaries were introduced around the outer perimeter of the air medium. The non-reflecting boundary in the base of the XY-plane activated the reflection of shear and dilatational waves from the ground surface to reproduce the wave reflections from the ground surface. The frame models were subjected to the blast loading scenario. The retrofit effect (reduction in peak blast displacement) was investigated

model in LS-DYNA to describe FRP material behavior. This model has been commonly used for modeling composite materials. As mentioned in Section 2, the bond-slip effects between the longitudinal reinforcing bars and surrounding concrete were simulated using the one-dimensional slide line model in LS-DYNA in all the possible bond-slip areas. The bonding condition and failure modes for the as-built and retrofitted frame models were determined based on the trend of the measured strain values in the bond-slip areas. Shin et al. [35] measured reinforcing bar strains in all the possible bond-slip areas during the fullscale dynamic tests to identify the bond-slip effects using the relationships between the peak beam/column hinge rotations and the reinforcing bar strains. Fig. 8 shows the relationships between the peak column hinge rotations and the reinforcing bar strains for the as-built (Fig. 8(a)) and retrofitted test frames (Fig. 8(b)). As shown in Fig. 8(a), the rebar strains in the first story columns of the as-built test frame tended to decrease with an increase in the shaker force before the longitudinal reinforcing bars yielded, i.e., bond-slip failure was detected. Based on the measured responses, the bond stress-slip relationship of the first story columns was modeled with lap-splice failure and poor bonding conditions in the CEB-FIP Model Code [30]. This model code provides bond stress-slip relationships in terms of the failure modes and the bonding conditions. However, the rebar strains in the first story columns of the retrofitted test frame continuously increased until the ultimate loading sequence of the full-scale dynamic tests, as shown in Fig. 8(b). This indicates that the retrofit system delayed the bond-slip failure in the first story columns. Thus, the bond-slip properties of the retrofitted column in

Fig. 8. Relationships between column hinge rotation and rebar strain [35]. 7

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Fig. 10. Comparison of blast responses between as-built and retrofitted numerical models.

Fig. 11. Comparison of blast damage patterns between as-built and retrofitted numerical models.

by comparing the displacement time histories of the as-built and retrofitted frame models. Fig. 10 shows the displacement time histories and column deformed shapes at the time when the maximum displacement occurred in the blast-faced columns for the FE frame models. The peak displacement in the as-built case was 62 mm, while the peak displacement in the retrofitted case was 46 mm. The FRP column jacketing system thus reduced the peak displacement by 27%. Additionally, the retrofit system resulted in a 41% decrease in the residual displacement. This reduction in the peak displacement is attributed to an increase in the flexural stiffness by the section enlargement of the column using the grout material, as well as an increase in the confining pressure produced by the FRP jackets. The FRP jackets restrained the column dilation and provided additional confining pressure on the column. The confining pressure enhanced the concrete strength, contributing to a reduction in the peak displacement compared to the asbuilt frame model. Fig. 11 compares the damage pattern of the as-built FE frame model and the retrofitted frame model using effective plastic strains, which illustrate the concrete damage under tension and compression on the basis of the three types of shear failure surfaces (yield, maximum, and residual surfaces) of the concrete material model. In this figure, the contour of the fringe in the effective plastic strains indicate damage levels from 0.0 to 2.0; (1) the values from 0.0 to 1.0 indicate the damage progress from the initial yield failure surface to the

maximum failure surface; (2) the values from 1.0 to 2.0 indicate progress from the maximum failure surface to the residual failure surface; and (3) a value of 2.0 in the fringe level refers to concrete cracks in tension or concrete crushing during compression [39]. As shown in Fig. 11(a), the blast load mainly impacted the first story exterior column of the frame model and led to permanent damage on the column. However, the FRP jacketing system helped minimize the permanent damage on the blast-faced column of the retrofitted model. This retrofit effect was also demonstrated by the reduced residual displacement on the front surface of the column. The effectiveness of the retrofit system can be changed by varying specific retrofit parameters, such as FRP jacket thickness, FRP material properties, size of the section enlargement, and grout material properties. The effect of these main parameters will be described in the following section. 3.2. Main parameters for the retrofit system A typical FRP jacketing system is composed of grout materials and FRP shells. To maximize the confining area in existing RC columns, the column sectional shape is enlarged and modified from the original rectangular/square sectional shape to an elliptical/circular sectional shape by adding the grout material. The addition of grout material improves their flexural capacity (e.g., flexural stiffness and strength) by 8

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blast pressures and impulses, varied from 0.4 m/kg1/3 to 1.6 m/kg1/3. This research selected three blast loading scenarios (Z = 0.4, 0.8, and 1.6 m/kg1/3), which were classified as near contact, near-field, and farfield charges, respectively. The blast loading parameters for the charge weight (WTNT) and standoff height (RH) were fixed as 680.4 kg and 0.9 m, respectively, and the standoff distance (RD) varied from 3.7 m to 14.0 m. The parameters WTNT and RH were determined based on the size and capacity of the vehicle as specified in FEMA-426 [44]; the selected values represent typical vehicle bombs ranging from sedans to vans. This research mainly focused on an environment of external blast loads generated away from the target structure. That is, this research did not consider direct contact charges. Additionally, previous studies [6,9–13,45] revealed that the heat generated from the blast load does not significantly affect the FRP-retrofitted columns. For these reasons, this research did not model the damage of FRP jackets.

section enlargement [34], and thus the inner diameter (ID) of the column section and the grout strength (fg) were regarded as the main parameters for the FRP column jacketing system. Additionally, the FRP shells wrapped around the existing RC columns restrain the concrete dilation under axial loading and provided additional confining pressure (σR) to the existing columns. The additional confining pressure produced from the FRP jackets improved the concrete compressive strength (fcc', confined concrete strength) and ultimate axial strain (εcu) [39–43]. This improvement in concrete material behavior enhanced the shear resistance capacity of the existing RC columns, ensuring ductile behavior of the RC columns. The confining pressure was computed using Eq. (4) [40,41], where fju = ultimate tensile strength of the FRP jacket, tj = thickness of the FRP jacket, and r = radius of the FRP jacket: R

= f ju t j / r

(4)

The confined concrete strength (fcc') is a function of the unconfined concrete strength (fc') and the confining pressure (σR) [40,41]:

fcc = fc 2.254 1 +

7.94 fc

R

2 R fc

1.254

4. Blast performance evaluation 4.1. Energy-based performance threshold

(5)

To design structural elements ensuring the blast resistance capacity of structures, ASCE 59-11 [16] provides blast performance thresholds for structural elements, which are quantified by the displacement ductility or support rotation in terms of three damage levels (level of protection, LOP): superficial, moderate, and heavy damage. Since ductility-based thresholds exclude the effect of the number of inelastic cycles, energy-based limits were proposed under seismic and blast loads [17]. Shin [17] developed FE models that can reasonably capture experimental results and utilized them to create 161 sample cases, including datasets with multiple inputs (load, geometry, and material parameters) and outputs (code-defined demands and energy-based demands). After that, the sample cases were used to train, validate, and test artificial neural network (ANN) models. The ANN models rapidly and reliably generated extensive seismic and blast datasets. Using these datasets, the energy-based thresholds corresponding to the current code-defined limits for seismic and blast loads were derived with respect to the three performance levels [17]. In this study, energy-based blast performance thresholds were recomposed based on the extensive blast datasets created from the work of Shin [17], as presented in Table 5. The blast performance thresholds were utilized to evaluate the blast performance of the as-built and retrofitted frame models.

Based on these equations, the two main confinement-related parameters, i.e., FRP material properties (fju) and FRP jacket thickness (tj), were also selected as main parameters. To summarize, this research selected four geometric and material parameters for the retrofit system: (1) FRP material properties (fju), (2) jacket thickness (tj), (3) column inner diameter enlarged by grout material (ID), and (4) grout material properties (fg). Table 4 summarizes the parametric models associated with the above main parameters. This table includes the confinement ratio (CR), computed from σR/fc', and stiffness ratio (SR), defined as the initial stiffness ratio of the retrofitted column to the as-built column. It should be noted that the initial stiffness in this study was simply calculated as the product of the gross moment of inertia (Ig) and elastic modulus (Ec and Eg) for concrete and grout materials, respectively. A parametric study was performed to examine the effect of the main retrofit parameters on the blast performance. The range of each parameter was determined on the basis of commercially available datasheets for the FRP and grout materials, confinement effects for the jacket thickness, and constructional practices used for section enlargement. Detailed information on the range of each parameter can be found in Shin [17]. For the blast loads, the scaled distance (Z = RD/WTNT1/3), which affects Table 4 Summary of the parametric models for an FRP jacketing system. Group

Model

Blast loads (kg/ m1/3)

Jacket strength (fju, MPa)

Jacket thickness (tj, mm)

Inner diameter (ID, mm)

Grout strength (fg, MPa)

Confinement ratio (CR)

As-built

As-built

Z = 0.4, 0.8, 1.6

None

None

None

None

0 (assumed)

Retrofitted

R-F1 R-F2 R-F3 R-T1 R-T2 R-D1 R-D2 R-G1 R-G2 R-FD1 R-FDT1

166 419 1380 419 419 419 419 419 419 166 419

3.6 3.6 3.6 0.7 6.5 3.6 3.6 3.6 3.6 3.6 6.5

444 444 444 444 444 502 559 444 444 559 559

42.9 42.9 42.9 42.9 42.9 42.9 42.9 13.8 89.3 42.9 42.9

0.08 0.20 0.66 0.04 0.36 0.18 0.16 0.20 0.20 0.06 0.29

As-built: non-retrofitted model, R-F#: retrofitted models varying the fju parameter of the retrofit system, R-T#: retrofitted models varying the tj parameter of the retrofit system, R-D#: retrofitted models varying the ID parameter of the retrofit system, R-G#: retrofitted models varying the fg parameter of the retrofit system, R-FD#: retrofitted model varying the fju and ID parameters of the retrofit system, and R-FDT#: retrofitted model varying the fju, ID and tj parameters of the retrofit system. 9

Stiffness ratio (SR) 1.00 2.91 2.91 2.91 2.91 2.91 4.85 7.54 2.08 3.75 7.54 7.54

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Table 5 Energy-based performance thresholds for FRP-retrofitted frame structure. Level (i)

Blast performance level (PLi)

Ductility-based damage threshold (μi)

Energy-based damage threshold (Di)

Description No permanent deflection No element failure, some permanent deflection, repairable No element failure, significant permanent deflection, not repairable Element failure

1 2 3

PL1 PL2 PL3

Superficial Moderate Heavy

≤1.0 ≤3.0 ≤6.0

≤0.28 ≤0.79 ≤1.86

4

PL4

Hazardous

> 6.0

> 1.86

Fig. 14. CR-DE relationship under Z = 1.6 m/kg1/3.

Fig. 12. CR-DE relationship under Z = 0.4 m/kg1/3.

(CR-II), and (3) CR ≥ 0.15 (CR-III). These levels were determined using the minimum value of the confinement ratio (CRmin) and modified confinement ratio (MCRmin) derived from previous experimental studies. The MCR was computed using Eq. (6), where r = corner radius; and fco = unconfined concrete strength.

4.2. Parametric studies This section describes the effects of the retrofit parameters (fju, tj, ID, and fg) on the blast performance in terms of the CR and SR. As given in Eqs. (4) and (5) in Section 3.2, the CR is affected by the parameters fju, tj, and ID. The parameter SR, which is associated with the column section enlargement resulting from the addition of grout materials, varied from 2.08 to 7.54.

MCR =

2r · R ID fco

(6)

Mirmiran et al. [46] recommended an MCRmin of 0.15, which means that the ultimate confined concrete strength (fcu') is equal to or greater than the peak confined concrete strength (fcc'). For circular columns, the MCR can be expressed as σR/fco, i.e., the confinement ratio (CR). A minimum threshold of the CR was proposed as 0.07 (CRmin = 0.07) for the FRP column jacketing system, which indicates that the ultimate confined concrete strength (fcu') will be less than the unconfined concrete strength (fco) [47]. The R-T1 and R-FDT1 models indicated in the figures represent the lowest and highest blast performances, respectively. As shown in Fig. 12, the as-built model has a hazardous performance level under the near contact charge (Z = 0.4 m/kg1/3), indicating element failure. Although the retrofit system that produced CRII (CR = 0.06) was installed on the first story columns in the frame model, the blast performance of the retrofitted model (R-T1) was evaluated as a heavy level. The blast performance for the retrofitted models higher than a CR of 0.15 (CR-III) was significantly enhanced from hazardous to moderate levels. After the CR-III level, the increase in the parameters fju and/or tj only marginally reduced the variation of DE (i.e., the variation between the minimum and maximum retrofit effects is less than approximately 12%). In particular, the R-FDT1 model with CR-II and an SR of 7.54 showed a lower energy-based damage demand than the numerical model that had the highest value of CR (=0.63) and an SR of 2.91. This performance enhancement is attributed to the stiffness change within the CR-III. Fig. 13 illustrates the CR-DE relationship subjected to the Z = 0.8 blast load (near-field charge). While the R-T1 model with a minimum value of CR-I (CR = 0.03) experienced a heavy damage level, the frame models with CR-II and CR-III showed a moderate performance level. This indicates that the retrofit scheme for

4.2.1. Effect of confinement ratio Figs. 12 through 14 show the relationship between the parameter CR and energy-based damage demands (DE) under three blast loading scenarios. To investigate the blast performance for each numerical model, these figures include the energy-based performance thresholds given in Table 5. As illustrated in the figures, the parameter CR was classified as three levels: (1) CR < 0.07 (CR-I), (2) 0.07 ≤ CR < 0.15

Fig. 13. CR-DE relationship under Z = 0.8 m/kg1/3. 10

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the FRP column jacketing system should be determined based on blast loading conditions. For the frame models within the CR-III level, the CR-DE relationship under the Z = 0.8 blast load showed a similar trend with the CR-DE relationship under Z = 0.4, i.e., showing marginal effects on the energy-based damage demand associated with the increase in the parameters fju and tj within the CR-III. Fig. 14 reveals that the FRP-retrofitted models have a superficial damage level regardless of the CR levels. This is attributed to the fact that the blast loading scenario (far-field charge) produced no bonding failure between the FRP column jacketing system and existing RC column. For this reason, the retrofit system improved the flexural stiffness and reduced the maximum displacement despite the insufficient CR (less than CR-I level, e.g., CR = 0.03 and 0.06). Overall, the blast performance was enhanced in accordance with the increase in the confinement effect by increases in the parameters fju and tj. In particular, the blast performance of the retrofitted models with CRIII reached a moderate level. The effect of the CR on the energy-based demand within CR-III was marginal. Although the confinement effect was improved by the increase in the parameters fju and tj, several cases among the retrofitted models increased the energy demand. Such an observation was examined using the relationship between SR and DE in the following section.

Fig. 16. SR-DE relationship under Z = 0.8 m/kg1/3.

4.2.2. Effect of stiffness ratio Figs. 15 through 17 show the relationships between SR and DE with the energy-based performance thresholds subjected to three blast loading scenarios (Z = 0.4, 0.8 and 1.6 m/kg1/3). These relationships examined the blast performance of the numerical frame models according to the increase in flexural stiffness resulting from the addition of the grouting materials. Among the 12 numerical models, the lowest (R-T1) and highest (R-FDT1) blast performance results were marked in the figures. As illustrated in Fig. 15, the improvement in SR (i.e., increase in ID and/or fg) marginally affected the blast performance of the retrofitted frame models for the loading scenario of Z = 0.4 m/kg1/3. The retrofitted models for SR = 2.91 and 7.54 showed a significant change in the blast performance from heavy to moderate levels because of the increases in the parameters fju and tj. For example, since the R-T1 with the lowest CR (=0.03) among the parametric models produced an insufficient confining pressure, the blast performance of the R-T1 model is lower than other retrofitted models in which SR = 2.91. This is due to the fact that the bonding surface between the jacketing system and existing column failed under the near contact charge (Z = 0.4 m/kg1/3), and the ductility capacity was rapidly reduced due to the low CR. Since the R-FDT1 model with SR = 7.54 is within the CR-III level, it has the highest blast performance among all the parametric models. Similar to the SR-DE relationship for the Z = 0.4 m/kg1/3, Fig. 16 shows no

Fig. 17. SR-DE relationship under Z = 1.6 m/kg1/3.

significant effect on the blast performance due to the stiffness increase without a sufficient confining pressure (CR-I level, less than a CR of 0.07). For example, the R-T1 model has a heavy performance level. The retrofitted models that have higher confinement than the CR-II level (CR = 0.08 to 0.63) reached a moderate level blast performance subject to the near-field charge (Z = 0.8 m/kg1/3). In addition, the models with the CR-III level had a marginal effect on the reduction in the DE values from 0.27 to 0.50 based on the increase in the flexural stiffness. Fig. 17 reveals that the blast performance of the parametric models was improved from moderate to superficial levels by an increase in the SR regardless of the range of the CR. This is due to the fact that the retrofit system increased the flexural stiffness with no bonding failure under the far-field charge (Z = 1.6 m/kg1/3). The DE values for the parametric models were continuously reduced by the increase in flexural stiffness. Based on the numerical results, the SR-related parameters (ID and fg) are more critical than the CR under a given blast loading scenario. Overall, the confinement effects on the blast performance were more significant than the stiffness effects when the near contact and near-field charges produced bonding failure at the blast-faced columns. However, the blast performance was governed by the effect of the flexural stiffness under the far-field charge (Z = 1.6 m/kg1/3). As such, the retrofit scheme depends on the blast loading scenarios. 4.3. Effectiveness of the retrofit system To quantify the effectiveness of the FRP column jacketing system for various parameters, the DE values for the retrofitted models were

Fig. 15. SR-DE relationship under Z = 0.4 m/kg1/3. 11

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(40% for R-T1 versus 62% for R-FD1) due to the increased flexural stiffness. Fig. 19 illustrates the effectiveness of the retrofit system for the parametric models with the identical SR values (SR = 2.91 and 7.54) in terms of the CR. The retrofitted models with the identical SR values increased the retrofit effects in accordance with the increase in the CR values. However, the difference of the reduction in the DE values among the retrofitted models with a CR > 0.15 is marginal when subjected to Z = 0.4 m/kg1/3 (e.g., 63% energy reduction for a CR of 0.19 versus 67% energy reduction for a CR of 0.63). Additionally, the increase in SR values contributes significantly to the improvement in blast performance for Z = 1.6 m/kg1/3 (retrofit effects on average = 47% for an SR of 2.91 versus 77% for an SR of 7.54). A retrofit scheme for the blast performance needs to be established depending on the expected blast loading scenarios to maximize the effectiveness of the retrofit system. According to Mirmiran et al. [46], the CR for the FRP jacketing system should be greater than 0.15 under near contact and near-field charges. The SR-related parameters are more critical than the other retrofit parameters (fju and tj) under the far-field charge.

Fig. 18. Effectiveness of the retrofit system for a range of confinement ratios.

compared to those for the as-built model. The retrofit effect (i.e., reduction in DE values) was computed using the following equation.

Retrofit effect = (DEA

DER )/ DEA × 100 (%)

5. Conclusions This research evaluated the blast performance of low-rise seismicallyvulnerable RC building frames retrofitted using an FRP column jacketing system, and examined the effectiveness of the retrofit system to identify the critical retrofit parameters under various blast loading scenarios (near contact, near-field and far-field charges). Based on the investigation, a retrofit scheme of the FRP jacketing system for a low-rise RC building frame was proposed. To achieve the main goals of this study, finite element numerical models in as-built and retrofitted configurations were developed using a blast modeling method. This modeling method includes bond-slip effects between longitudinal reinforcing bars and the surrounding concrete determined based on measured responses from fullscale dynamic tests as well as an advanced blast load modeling technique, which can ensure a good balance between computational efficiency and accurate prediction. The modeling method used in this study has a better correlation between the experimental and simulated results based on a comparison of the blast experiment results and numerical results performed by previous researchers (i.e., less than 5% variation). The retrofitted models were developed by varying the main parameters (e.g., jacket strength, jacket thickness, grout strength, and inner diameter of the retrofit system) that affect confinement and flexural stiffness. The blast performance for the retrofitted frame models was evaluated using energy-based damage thresholds proposed by a past researcher, and the effectiveness of the retrofit system was examined in terms of the confinement ratio and the stiffness ratio. Based on the parametric study, the following conclusions can be drawn:

(7)

where DEA = energy-based damage demand for the as-built model and DER = energy-based damage demand for the retrofitted models. Based on the DE reduction, the effectiveness of the retrofit system was examined in terms of the range of the confinement effects (CR-I, CR-II and CR-III levels) in Fig. 18 and flexural stiffness (minimum and maximum SR values = 2.91 and 7.94) in Fig. 19. Fig. 18 shows the effectiveness of the retrofit system for the CR-I, CR-II and CR-III levels. While the retrofitted models within the CR-I level exhibited an approximately 20% reduction in the DE under the blast loading scenarios with Z = 0.4 and 0.8 m/kg1/3, the effectiveness of the retrofit system under the Z = 1.6 m/kg1/3 blast load (far-field charge) is nearly twice as large as those under the near contact and near-field charges. The effectiveness of the retrofit system with the CR-I and CR-II levels for Z = 0.4 and 0.8 m/kg1/3 were 32% and 35% on average, respectively. Compared to these retrofit effects, the parametric models with the CR-III level significantly reduced energy demand (e.g., retrofit effects on average = 65% for Z = 0.4 m/kg1/3). The DE values for all parametric models under the Z = 1.6 m/kg1/3 blast load were reduced by more than 40% regardless of the CR range. In particular, the two retrofitted models with the CR-I under the Z = 1.6 m/kg1/3 have roughly 1.5 times higher effectiveness compared to the retrofit system

(1) The blast performance of retrofitted frame models with a confinement ratio higher than 0.15 (CR-III level, CR ≥ 0.15) was improved in accordance with the increase in values of the confinement ratio, which was controlled by the jacket strength and/or thickness parameters under near-contact and near-field charges (e.g., element failure to moderate levels under Z = 0.4 m/kg1/3, and heavy to superficial levels under Z = 0.8 m/kg1/3). However, a retrofit system with a confinement ratio below 0.07 (CR-I level, CR < 0.07) had no significant effect on the blast performance of the retrofitted frame models. This is due to the fact that bonding failure between the retrofit system and existing columns occurred at the blast-faced columns under the high and moderate blast loads if the retrofit system produced low confining pressures. (2) When subjected to a low blast loading scenario (far-field charge, Z = 1.6 m/kg1/3), the blast performance of the retrofitted frame models were enhanced from moderate to superficial levels due to the increase in flexural stiffness-related parameters (e.g., grout strength and inner diameter), regardless of the confinement limits.

Fig. 19. Effectiveness of the retrofit system for the stiffness ratio (SR) and confinement ratio (CR). 12

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Since the blast loading scenario does not trigger the bonding failure at the blast-faced columns, the stiffness-related parameters have more critical effects on the blast performance than the confinementrelated parameters (i.e., jacket strength and thickness). (3) A comparison of the energy-based blast demands between as-built and retrofitted frame models showed that an increase in confinement-related parameters (i.e., jacket strength and/or thickness) decreased the energy-based damage demands under high and moderate blast loading scenarios (near contact and near-field charges, i.e., Z = 0.4 and 0.8 m/kg1/3). Among the retrofitted models with a confinement ratio higher than 0.15 (CR-III level, CR ≥ 0.15), the increase in confinement-related parameters marginally affected the reduction in the variation of the energy-based damage demands. In addition, the energy-based demands were significantly reduced by an increase in flexural stiffness (i.e., increases in grout strength and inner diameter parameters) when subjected to a low blast loading scenario (far-field charge, i.e., Z = 1.6 m/kg1/3). (4) Based on the investigation of the retrofit effects, the retrofit scheme of the FRP jacketing system should be established for blast loading scenarios. For high and moderate blast loading scenarios, it was found that critical parameters (jacket strength and/or thickness) for the confinement ratio should be designed such that the confinement ratio is greater than 0.15. For a low blast loading scenario, the stiffness-related parameters (grout strength and inner diameter) were more critical rather than other parameters. The retrofit system with the maximum strength ratio can reduce the blast responses more than 60%, although the retrofit system has the minimum confinement ratio. Note that this retrofit scheme was proposed based on an investigation of the retrofit effects for low-rise nonductile RC building frames. Based on this study, additional retrofit schemes for mid-rise and high-rise building structures under various blast loading scenarios are being proposed.

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