Sensitivity analysis of parameters affecting the seismic performance of RC columns strengthened by fabric-reinforced cementitious mortar

In recent years, fabric-reinforced cementitious mortar (FRCM) has emerged as a popular choice for strengthening reinforced concrete and masonry structures due to several advantages over conventional fiber-reinforced polymer (FRP) composites. Particularly, the enhancement of Reinforced Concrete (RC) columns using FRCM composites has garnered significant attention. While experimental investigations are crucial for assessing the effectiveness of FRCM, physical experiments are often resource-intensive and time-consuming. Therefore, this study seeks to investigate the impact of various design parameters on the performance of RC columns strengthened with FRCM under low-amplitude cyclic loads simulating earthquakes through Finite Element (FE) analysis. The FE model, incorporating columns and FRCM strengthening materials, was developed using the DIANA 10.5 program. To assess the reliability of the model, analytical results were compared with experimental findings from a previous study, focusing on lateral strength, hysteresis behavior, and failure modes. The validation outcomes demonstrated a reasonable correlation between the test and numerical results. Subsequently, a sensitivity analysis was conducted to explore the influence of input parameters, such as concrete compressive strength, fabric reinforcement quantity, longitudinal reinforcement ratio of the columns, and pre-axial loading levels, on the seismic performance of RC columns reinforced with FRCM. The findings of the sensitivity analysis were discussed in detail.


Introduction
Fiber-reinforced polymer (FRP) composites have been used to enhance the compressive, shear, and flexural performance of reinforced concrete structures, including externally bonded composite fabrics for bridge components, jackets on beams, columns, and bridge decks, etc [1][2][3][4][5][6][7].However, over more than 55 years of implementation in the construction industry, FRP composites have shown some limitations due to the use of organic adhesive materials.These limitations include poor performance at relatively high temperatures, incompatibility with epoxy resin and substrate materials such as masonry walls, formation of vapor barriers and difficulty in application on wet surfaces, difficulty in construction in low temperatures, risks to installers, sensitivity to radiation, low reversibility, which makes it challenging to evaluate post-earthquake damage to reinforced concrete structures behind the undamaged FRP layer, and the relatively high cost of epoxy resin [8][9][10][11].Therefore, numerous studies have developed fabric-reinforced cementitious matrix (FRCM) composites in the past two decades to overcome the limitations of FRP materials, as analyzed above [8,[12][13][14][15], with the ultimate goal of finding a better alternative to FRP.Curbach and Jesse [16] laid the first foundation for this material type.Nowadays, FRCM has become a favored alternative to FRP composites in reinforced concrete structures [11,17].There are currently three commercially available FRCM product lines: Glass (G)-FRCM [18], polyparaphenylene benzobisoxazole (PBO)-FRCM [19], and Carbon (C)-FRCM [20].The superior features of FRCM over FRP will be discussed in detail below.
Several studies have shown that FRCM is better compatible with the original concrete substrate compared to externally-bonded FRP using epoxy resin [21], especially FRCM composites exhibit better compatibility with masonry walls compared to FRP composites [17,22,23].For flexural elements such as beams, FRCM is more effective in limiting deformation than FRP sheets [24].Particularly, the performance of FRCM-reinforced components increases significantly with the increase in the number of corresponding reinforcement layers compared to FRP reinforcement [24].Due to the nature of FRCM embedded in binding mortar that can withstand high temperatures, it can work in an environment with exceptional high temperatures and exhibit superior fire resistance compared to its epoxy resin FRP counterpart [25][26][27].FRCM composites are very effective in limiting deformation cycles (such as cyclic loads during earthquakes), energy dissipation, and delaying the instability of steel bars in columns [28].In this aspect, FRCM composites exhibit similar effectiveness to FRP reinforcement layers [28].Therefore, it is considered a promising composite material for strengthening RC components, masonry walls, and for constructing slender, lightweight, modular, and freeform structures.Various studies have explored the application of the FRCM system in diverse contexts such as flexural strengthening [29][30][31][32][33], shear strengthening [34][35][36][37][38], confinement of axially loaded concrete [39][40][41][42][43][44], seismic retrofitting of RC members [45][46][47], and masonry infilled RC frames [48][49][50][51][52].
Numerous studies have been conducted regarding the application of FRCM composites in seismic structural rehabilitation of RC columns [46,53,54].Bournas et al [28] conducted experimental investigations into the seismic performance of columns with deficient reinforcement details, retrofitting them with FRCM jackets.Results indicated that FRCM jackets effectively enhanced the cyclic deformation capacity and energy dissipation of poorly detailed RC columns, delaying bar buckling and preventing splitting bond failures in columns with lap-spliced rebars.Additionally, Koutas et al [48] explored the use of FRCM for retrofitting a three-story reinforced concrete frame filled with masonry under seismic loading conditions.The study revealed a 56% increase in lateral load-carrying capacity and a 52% improvement in deformation capacity corresponding to ultimate load in the retrofitted frame compared to the non-retrofitted one.Comert et al [55] conducted an investigation into the behavior of RC columns subjected to a constant axial load and cyclic lateral displacement reversals, both before and after retrofitting with jackets made of basalt mesh-reinforced sprayed Glass-Fiber Reinforced Concrete (GFRC).In a recent study by Guo et al [56], FRCM optimized with short Polyvinyl Alcohol (PVA) fibers was employed as a strengthening material for seismically deficient RC columns.The study specifically explored the impacts of the reinforcing ratio of carbon textile and axial load ratio on the seismic performance of columns retrofitted with the FRCM system.The findings indicated a notable increase of 54.3%-55.2% in shear capacity and 40.34%-78.62% in deformability of the RC columns after strengthening with the optimized FRCM system.
To assess the effectiveness of FRCM for confining RC columns in seismic performance evaluation for performance-based design, experimental investigations are essential.However, physical experiments are often time-consuming and costly.Recently, with the development of many efficient and highly reliable computational analysis algorithms, Finite Element Analysis (FEA) has been used to analyze the effectiveness and behavior of FRCM in strengthening structures, and has been verified with high accuracy [37,45,[57][58][59].Hence, in this study, FEA is an effective choice to provide the opportunity for virtual experiments, which are cost-efficient and time-saving, assuming well-calibrated models.However, the FEA analysis of FRCM-confined columns subjected to cyclic load is still limited.
Therefore, the primary objective of this research is to investigate the sensitivity of various input design parameters for RC columns and FRCM materials in confining concrete columns using FEA.The FE model was developed using the commercial DIANA 10.5 program and validated against experimental results from a previous study, considering strength, hysteresis behavior, and failure modes.Subsequently, a sensitivity study was conducted to elucidate the influence of input parameters such as concrete compressive strength, amount of fabric reinforcement, and pre-axial loading levels on the seismic performance of RC columns enhanced by FRCM.The discussion of the sensitivity analysis is presented in detail.

Development of finite element model 2.1. Three-dimensional model
The FEA of RC columns strengthened with FRCM jackets was conducted to validate and discuss findings in comparison with a prior experimental study by Dinh et al [60].The FE models of the specimens were established using the commercial DIANA 10.5 program [61].A 20-node isoparametric solid element (CHX60), available in the DIANA program, was employed to represent the 3D concrete elements of the column and the mortar elements of the FRCM composite.This element, based on quadratic interpolation and Gauss integration, provided accurate modeling.Steel rebars of RC members were modeled using a 3D bond-slip truss element.The CFRP mesh was represented using a 3D embedded truss element, assuming perfect bonding between the textile mesh and the surrounding mortar.Furthermore, a typical surface-to-surface connected interface element (CQ48I) was utilized to model the interaction between FRCM and concrete.The 25 mm-meshed FE model for the FRCM-strengthened column is depicted in figure 1.The foundation block was subjected to fixed boundary conditions by restraining translations in the X, Y, and Z directions.A constant vertical load of P 10% n (where P n is the nominal axial strength of the column) was applied through a loading steel block.The horizontal lowamplitude cyclic load, conforming to the experimental setup simulating earthquake [60], was applied at the top of the column, as per figure 1.

Material constitutive law
In the DIANA software, two primary methodologies have conventionally been utilized to simulate the cracking behavior of concrete: the discrete crack model and the smeared crack model, as explained by Rots [62] and Bažant et al [63].For this investigation, the mortar of FRCM and concrete material was represented using the smeared crack approach and analyzed using the total strain rotating-crack method integrated into the DIANA software [61].This model deals with the average stress-strain approach to obtain the fracture energy within the element, which was established based on the modified compression field theory originally developed by Vecchio and Collins [64] and further improved by Selby and Vecchio (1995) [65], to extend its applicability to 3D elements.This method independently delineates the tensile and compressive characteristics of the cementitious model through a stress-strain relationship.
For unconfined concrete material, the uniaxial compressive model curve presented by Thorenfeldt and the tension-softening law proposed by Hordijk were employed in DIANA.Equations (1) and (2) [61] outline the expression of the compressive stress-strain curve as per Thorenfeldt's model: In this equation, f c represents the concrete compressive strength, o e is the corresponding strain, and E c denotes the elastic modulus of concrete.
The tensile behavior of concrete is modeled by tension-softening law of concrete following the Hordijk's model.The stress-crack opening law is expressed by equations (3) through (5) [61]:

= ⋅ +
In this equation, c 1 is equal to 3.0 and c 2 is equal to 6.93.Moreover, G f represents fracture energy, and h denotes crack bandwidth, which depends on the size of the solid concrete element.The parameters of the concrete materials used in the FE analysis are summarized in table 1.To further simulate the confining effect of the FRCM jacket on the RC column, the DIANA program incorporated a user-defined multi-linear compressive stress-strain curve illustrated in figure 2. This requires the provision of stress and strain values as essential inputs for formulating the compressive stress-strain relationship of FRCM-confined concrete.The values were derived from the confined concrete model based on ACI 549.4R-13 [66] and the work of Triantafillou et al [39], as shown in figure 3. The outcomes of the confinement models, varying with the number of textile layers, are illustrated in figure 3.
The von Mises plasticity model incorporating isotropic strain hardening behavior governs the steel rebars constitutive law, which is implemented in DIANA to characterize uniaxial tensile stress-strain response, as illustrated in figure 4(a).Here, E s denotes the elastic modulus, f y and f u represent the yield strength and ultimate strength of steel rebars, respectively, and the modulus during the hardening stage is stipulated as E 0.01 s [67].Moreover, for the Carbon Fiber Reinforced Polymer (CFRP) mesh, a linear elastic model is employed to delineate the uniaxial tensile stress-strain response of the carbon fiber, as depicted in figure 4(b).Here, E f and fu e denote the elastic modulus and ultimate tensile strain of the carbon fiber, respectively.The input parameters derived from rebar testing and carbon filaments are detailed in table 2.
When it comes to RC members subjected to cyclic loading conditions, it is essential to characterize the bondslip phenomenon between the reinforcement and concrete to elucidate cracking behavior and the pinching effect.To achieve this, the finite element (FE) model in DIANA incorporates a bond-slip model for the concretereinforcement interface based on the FIB model code 2010 [68], as depicted in figure 5.Here are the bond-slip equations:  were utilized based on [67] and [68].A 3D embedded truss element was utilized to model the CFRP mesh, assuming that there was ideal adhesion between the textile mesh and the surrounding mortar.In addition, a nonlinear interface element (CQ48I) was utilized to simulate the interface between the FRCM and concrete, with no-tension and shear stiffness reduction.As we consider that the FRCM jackets were applied to the columns in a fully wrapped manner, thereby assuming perfect bonding between FRCM and concrete, the normal and shear stiffness values of the interface element were assigned according to Chai et al's work [69].The parameters of the interface that were used in the finite element model are outlined in table 3.

Model validation
Figures 6 and 7 present a comparative analysis between numerical simulations and experimental results, with regard to crack patterns and hysteresis curves of the column specimens.The crack patterns were plotted using the contour of 'crack width' in the output of nonlinear analysis, which is defined as the product of the crack strain and the crack bandwidth.Figure 6 specifically illustrates the crack propagation in the control specimen FC-1, which was not strengthened, as the drift increases, by comparing numerical predictions with experimental observations.FC-1 was designed to undergo flexure-shear failure.In the initial stage, at a drift of 1.26%, fine flexural cracks initiated and subsequently developed along the column's length, connecting to form diagonal cracks.After the yielding of stirrups at around 2.20% drift, numerous diagonal cracks appeared on the column web.At the ultimate stage of the cyclic test, a combination of several flexural cracks and macro-diagonal shear cracks was noticeable, resulting in severe concrete crushing.Moreover, the shear also reached the yield stage, as validated by the numerical results.In summary, the finite element model demonstrated good correlation with the experimental outcomes.Figure 7 indicates a strong correlation between the FE model and the experimental outcomes for specimen FC-2, which was reinforced with the FRCM jacket.In this instance, FC-2 was confined with four textile layers in the plastic hinge region, which exhibited a significant improvement in the failure mode compared to FC-1.Fine diagonal cracks appeared on the FRCM jacket and the column web at a drift of 2.10%.By the time the drift   reached 3.89%, the critical diagonal cracks had propagated beyond the confined region in the plastic hinge region, leading to the strength degradation of the specimen.Figure 8 compares the hysteresis behavior of the lateral load-drift relationship for FC-1 and FC-2.The results show good agreement between the numerical and experimental findings regarding the strength and deformation capacity of both the control specimen FC-1 and the strengthened specimen FC-2.FC-2, reinforced with FRCM, exhibited a significant improvement in ductility compared to FC-1, evidenced by minimal degradation in loadcarrying capacity at approximately 4.5% drift.Regarding lateral strength, the disparities between the test and finite element results were 3.7% and 2.3% for specimens FC-1 and FC-2, respectively.Moreover, the implementation of the bond-slip model for the concrete-reinforcement interface facilitated the observation and accurate reproduction of the pinching effect, aligning well with the experimental outcomes.

Sensitivity analysis
By using the FE model, a sensitivity analysis was conducted to examine the influence of key design parameters on the structural performance of RC columns strengthened by FRCM jackets.Three primary parameters were investigated, namely the levels of axial force acting on the columns, the amount of textile reinforcement, and the longitudinal reinforcement.

Effect of magnitude of axial load
Figure 9 illustrates the effect of axial force on the lateral load-drift curves of FRCM-strengthened columns.Analytical columns were strengthened with 4 layers of fabric and subjected to varying axial load levels ranging from 10% to 70% of the nominal axial capacity of the column ( ) P , n which was calculated as: Here, f c refers to the concrete compressive strength, A g is the gross section of the column, and A s and f y refer to the total area and yield strength of the longitudinal reinforcement of the column, respectively.These design parameters were similar to those used in the previous study by Dinh et al [60].
From figure 9, it is evident that the axial load significantly influences the effectiveness of the FRCM jackets.An increase in the applied axial load corresponds to a higher lateral load-carrying capacity of the column.However, a reduction in ductility is observed, attributed to the increase in the plastic moment capacity of the column crosssection and compression zone due to the axial load.For columns exposed to low axial load levels  ( ) P P 0.3 , n the FRCM jacket demonstrates high efficacy in significantly improving the column's ductility.Nevertheless, this efficacy diminishes for columns subjected to higher axial load levels  ( ) P P 0.5 .
n The FE results imply a heightened need for textile reinforcement in strengthening RC columns under substantial axial loads.

Effect of textile reinforcement amount
Figure 10 illustrates the effect of different numbers of fabric layers on the lateral load-drift curves of FRCMstrengthened columns.In this investigation, an axial load level of P 10% n was used for analysis.The analytical results indicate that a higher number of fabric layers employed for the FRCM composite to confine the concrete  column leads to higher lateral load-carrying capacity.Additionally, the ductility was significantly improved.Compared to the control specimen without strengthening, the columns strengthened with FRCM using 2, 4, and 6 layers show improved lateral strength of 21.17%, 31.63%, and 46.27%, respectively.Such improvements could result from the high confinement effects associated with the use of a high textile reinforcement ratio.analytical results indicate that for control specimens, using higher longitudinal reinforcement ratios leads to a higher lateral load-carrying capacity of the column.However, insignificant increase was observed between 3.44% r = and 4.50%, r = with the difference of 5.45%.For FRCM strengthened specimens, the FRCM jacket was very effective, regardless of the longitudinal reinforcement ratio, improving both the strength and deformation capacity of the columns.For a column with r of 1.76%, the strength improvement is 14.46%.For columns with r of 3.44% and 4.50%, these values were 14%, and 18%, respectively.

Conclusions
In this study, the influence of various parameters on the performance of RC columns reinforced with FRCM under low-amplitude cyclic loads simulating earthquakes was investigated using FE analysis.The FE model simulating the RC column confined with FRCM composite in the plastic hinge region was developed using the DIANA 10.5 program.To assess the reliability of the model, analytical results were compared with previous experimental results.Subsequently, a sensitivity analysis was conducted to explore the influence of input parameters.The main conclusions are as follows: • The FE model, based on DIANA commercial software, showed good correlation with the test results from the previous study concerning failure mode, crack patterns, lateral load-carrying, and deformation capacity.The FE model can simulate well the development of diagonal cracks and severe concrete crushing of the unstrengthened specimens and improve crack patterns after FRCM retrofitting.
• Regarding lateral strength results, the disparities between the test and finite element results were 3.7% and 2.3% for specimens FC-1 and FC-2, respectively.
• Axial load significantly influences the efficacy of FRCM jackets.An increase in applied axial load corresponds to a higher lateral load-carrying capacity of the column.However, a reduction in ductility is observed, attributed to the increase in the plastic moment capacity of the column cross-section and compression zone due to the axial load.The FE results imply a heightened need for fabric reinforcement in strengthening RC columns under substantial axial loads.
• A higher number of fabric layers used for the FRCM composite to confine the concrete column leads to a higher lateral load-carrying capacity.Compared to the control specimen without strengthening, the columns strengthened with FRCM using 2, 4, and 6 layers show improved lateral strength of 21.17%, 31.63%, and 46.27%, respectively.Additionally, the ductility was significantly improved.
• The FE results indicate that for control specimens, using higher longitudinal reinforcement ratios leads to a higher lateral load-carrying capacity of the column.However, insignificant increase was observed between 3.44% r = and 4.50%, r = with a difference of 5.45%.For FRCM-strengthened specimens, the FRCM  jacket was very effective, regardless of the longitudinal reinforcement ratio, improving both the strength and deformation capacity of the columns.
• For the capability for application to other materials and tests, the current model can be adapted for various materials and loading scenarios, however, the calibration and understanding of material behaviour are essential for reliable results.

Figure 1 .
Figure 1.FE model of RC column strengthened by FRCM jackets.

Figure 2 .
Figure 2. Constitutive laws used for total strain crack model of concrete in DIANA.

Figure 5 .
Figure 5. Bond-slip model of the concrete-reinforcement according to FIB model code 2010.

Figure 7 .
Figure 7.Comparison of failure modes and crack patterns of FC-2 specimen between test and FEA.

Figure 6 .
Figure 6.Comparison of failure modes and crack patterns of FC-1 specimen between test and FEA.

Figure 11
illustrates the effect of different longitudinal reinforcement ratios ( ) r of the column on the efficacy of the FRCM jacket.In the analysis, an axial load level of P 10% n and 4 textile layers were used.The longitudinal reinforcement ratios of the columns were ( )

Figure 8 .
Figure 8. Numerical versus test result of hysteresis curve of FC-1 and FC-2.

Figure 9 .
Figure 9.Effect of axial force on lateral load-drift curves of FRCM strengthened columns.

Figure 10 .
Figure 10.Effect of number of fabric layers on lateral load-drift curves of FRCM strengthened columns.

Figure 11 .
Figure 11.Effect of column longitudinal reinforcement ratios on the effectiveness of the FRCM jacket.
The value of s 3 is equal to c clear [=7 mm], which represents the clear distance between the ribs.In the FE model, a In the mentioned bond-slip equations, b t represents the local shear bond stress, s is the slip displacement (mm), and s s 0.10 mm 1 2 = = for hot-rolled deformed rebars, which is the slip occurring at .b max t

Table 1 .
Concrete material parameters for FEA.

Table 2 .
Steel reinforcement material parameters for FEA.