PREDICTIVE MODELS OF BEHAVIOR AND CAPACITY OF FRP REINFORCED CONCRETE COLUMNS

P.O


INTRODUCTION
Fiber Reinforced Polymer (FRP) composite bars have emerged through the years as an efficient substitute for conventional steel reinforcing bars, due to their exceptional corrosion resistance, as well as other advantageous properties. Conventional reinforced concrete (RC) structures deteriorate in harsh conditions due to the corrosion of the reinforcing steel [1]. FRP bars could result in significant cost savings when compared to the replacement or rehabilitation of deteriorated RC elements. FRP materials possess many characteristics that improve their performance as a reinforcement substitute: a low elastic modulus (in comparison to steel reinforcing bars), a high strength-to-weight ratio, and a linear stress-strain relationship [2]. FRP bars are composed of aligned fibers embedded in a resin matrix and have a brittle stress-strain curve with an elastic modulus that varies depending on the fiber's type. Concrete structural members reinforced with GFRP bars, for example, demonstrate superior durability and strength [3]. Over the past twenty years, extensive analytical and experimental investigations have been carried out to study the behavior of FRP-RC beams flexural and shear loads [3,4]. The outcomes of the research studies were used to establish design guidelines (ACI 440.1R-15 [5], CAN/CSA S806-12 [6]) for FRP-reinforced flexural elements. Accordingly, FRP bars have been utilized in bridge girders and beams [4]. However, the design guidelines (ACI 440.1R-15 and CAN/CSA S806-12) related to the use of FRP in compression regions disregard the contribution of FRP bars in beams and columns, resulting in a conservative estimation of capacity, and thus paving the way for more research in this context. In this paper, genetic expression programming is utilized to introduce two models to simulate the axial capacity of FRP-RC columns loaded concentrically and eccentrically. In this paper, two new GEP models are proposed to predict the axial capacity and behavior of FRP-RC columns. The required experimental data for short and long, concentrically and eccentrically loaded FRP-RC columns is gathered O N L I N E F I R from the literature and used to formulate the two GEP models for columns reinforced with different types of fibers. The genes influencing the performance of the GEP models are defined and analyzed, with a parametric study conducted to evaluate the effect of each variable on the proposed models. A comparison is carried out between the results obtained in this paper and those of empirical models previously suggested and available in the literature, where the results of the comparison indicate the superiority of the proposed models in determining the axial capacity of eccentrically and concentrically loaded FRP-RC columns.

PREVIOUS STUDIES
As was already indicated, the unpredictability in estimating that contribution causes the present design codes to ignore the compressive contribution of FRP bars in columns. Several studies were devoted to investigating the FRP bars' behavior in axially loaded columns. De Luca et al. (2010) studied the performance of concentrically loaded GRFP-RC columns. The study indicated that the behavior of GFRP-RC columns behaves similarly to typical steelreinforced columns with just a little reduction in axial capacity when the reinforcement ratio equals one percent [7]. Alsayed et al. (1999) reported a thirteen percent reduction in axial capacity with direct replacement of longitudinal steel reinforcement with GFRP reinforcement, maintaining a similar reinforcement ratio [8]. By comparing many scientific contributions in the literature, there appears to be no mutual agreement regarding the determination of the FRP contribution in the column capacity. Elchalkani and Ma (2017) [9], Hadhood et al. (2017) [10], and De Luca et al. [7] measured the contribution of GFRP longitudinal bars within five percent of the column nominal compressive strength. Tobbie et al. (2012) [11]. and Afifi et al. (2014) [12] noticed that the steel reinforcement contribution is 12 percent, whereas the GFRP contribution is between 5 and 10 percent. Guérin et al. (2018a) performed 12 large-scale GFRP-RC columns under a wide range of eccentricity levels. The study showed that the capacity and behavior of the GFRP in particular and the reinforced column, in general, were significantly affected by the eccentricity level. Additionally, the study discovered that, for the same amount of eccentricity, FRP-RC and steel-RC columns behaved similarly, with no discernible difference for the FRP manufacturer. When compared to standard steel-RC specimens, GFRP RC columns with eccentricity values ranging from 6 to 27 percent have a lower capacity, and a compression-ductile failure was the primary failure mechanism. [13]. Guérin et al. reported the contribution of GFRP bars as a function of the load eccentricity: on average, the load carried by GFRP bars was 3%, 5%, and 13% of peak load for specimens with low eccentricity ( / e h = 0.1 to 0.2), moderate eccentricity ( / e h = 0.4), and high eccentricity ( / e h = 0.8), respectively.
Another experimental program was conducted by Guérin et al. (2018b) to investigate the contribution of the FRP reinforcement ratio to the performance and capacity of eccentrically FRP-RC columns. The results showed that increasing the reinforcement ratio from one to three percent increased the capacity by almost ten percent for columns with low eccentricity ( / e h = 0.1 to 0.2) and 35% for columns with high eccentricity ( / e h = 0.8). In addition, the parametric investigation revealed that the failure envelope considerably increased when concrete compressive strength raised from 30 to 60 MPa (approximately 100%). The study's results indicated that correct predictions are obtained when the GFRP's contribution in compression is taken into account [14]. Understanding the behavior of FRP-RC columns can be more complicated than steel-RC columns, particularly in the case of eccentric loading mainly due to the different contributing variables such as elastic modulus of FRP bars, concrete compressive strength, reinforcement ratio, slenderness ratio, and column dimensions for each experiment. The existing empirical models for the FRP-RC columns were built using regression analysis and a limited number of experimental data, therefore researchers were unable to account for all possible combinations and interrelations of the variables in order to create an accurate model (Raza et. al 2020) [15]. Furthermore, there is a lack of research studies when considering eccentric axial load and column slenderness in predicting the capacity of FRP-RC columns. Artificial intelligence techniques have seen great attention recently, as they are implemented to understand the complex nature of various phenomena and generalizations, by breaking down sophisticated mathematical relations into simple operations [16]. The utilization of artificial intelligence techniques has been extended to various applications in structural and civil engineering. For instance, Solhmirzaei et al. in 2020 developed a machine learning framework utilizing gene expression programming (GEP), an artificial neural network (ANN), and a large experimental database that is capable to predict strength and failure for ultra-high-performance concrete beams [17]. In 2021 Tarawneh et al. utilized GEP to develop a strength model for the shear capacity of steel-fiber-reinforced concrete based on a large experimental database [18]. The developed model provided superior accuracy compared to other models proposed in the literature. In civil engineering applications, Imam et al. (2021) developed a Pavement Condition Index from International Roughness Index using Gene Expression Programming [19]. The higher accuracy achieved by machine learning tools and their ability in pattern recognition is very crucial in the design process for different reasons. First, developing a machine learning-based model is considered a faster and easier tool in developing robust models compared to simple regression that may not accurately account for some affecting variables. Secondly, an accurate model means a higher safety level. An accurate prediction model with a low coefficient of variation and standard deviation allows for increasing the strength reduction factor in the design process while maintaining the same safety level which is described by the reliability index. Finally, this will allow for better utilization and economic use for structural members. This study utilizes a GEP technique to understand and predict the behavior of FRP-RC columns by considering the individual contribution and the effect of each of the column properties, such as reinforcement ratio, FRP bars elastic modulus, concrete compressive strength, eccentricity level, and column dimensions.

DATA-DRIVEN GENE EXPRESSION MODEL DEVELOPMENT
This section describes the development of the machine GEP model and surveyed experimental database.

Experimental Data
Any gene expression model that aims to learn, be able to recognize patterns, and forecast performance needs a data set for training. A survey and collection of experimental data on FRP-RC columns carrying concentric and eccentric loads has been done as a result. The data set consists of 247 experimentally tested columns with a variety of parameters, including eccentricity level( / e h ), reinforcement ratio ( ρ ), FRP elastic modulus ( E ), concrete An overview of the experimental data for concentric and eccentric FRP-RC columns is presented in Table 1.

Gene Expression Programming
Typically, Gene Expression Programming (GEP) is a tool for finding the best mathematical expression using a random set of data that has been wildly used. In general, data used in GEP should consist of a number of inputs used to predict an output value. Each input represents a variable. The program generates several models which are potential solutions to the problem. The models are compared with the correlation coefficient R 2 and the Root-Mean-Square Error (RMSE). A variety of sized and shaped expression trees can then be used to depict the best model. The trees, known as GEP Expression Trees (ETs), may be represented as a mathematical function, as demonstrated in Fig. 1. Two GEP models are developed to study both concentric and eccentrically loaded columns. Concentrically loaded columns data set consists of 69 tests. The main database has been divided into two parts; Training dataset and validation dataset. Randomly divided, 46 data points (66.6%) were selected for the training dataset, and the remaining 23 data points (33.3%) were considered for the validation data set. On the other hand, for eccentric columns, the data set gathered from literature consists of 178 tests. Additionally, this entire data set is randomly split into training and testing data sets. For the training dataset, 118 data points (66.6%) were chosen at random, while the remaining 60 data points (33.3%) were taken into account for the testing dataset.  The linking function between ETs Addition A training phase and a testing phase are involved in creating a gene expression model. In the training phases, the input information is entered in multiple mathematical processes and is adjusted to reduce the difference in inaccuracy between the input and output layers. Gene expression models evaluate error using RMSE. The training procedure is continued until the RMSE error has stabilized across a number of iterations.

PROPOSED GEP MODEL
The GEP algorithm discussed previously has been applied along with the experimental database to develop prediction models for concentrically and eccentrically loaded FRP-RC columns. The developed two GEP models are presented in form of expression trees as shown in Figures 2 and 3. The models consist of three sub-trees (ET) linked by addition for concentric loading and multiplication for eccentric loading. In the presented ET for concentrically ' c f , ρ , E , and l/r, respectively, for eccentrically loaded columns. Table 3 Fig. 4. shows the predicted versus experimental capacities for concentric loading (Fig. 4 (a)) and eccentric loading ( Fig. 4 (b)) and the associated coefficient of determination (R 2 ). It can be seen that both models resulted in a high R 2 . It is observed that the concentric and eccentric axial capacities estimated using the GEP models have RMSE of (231, 167.8) N, respectively, and COV of (9%, 19%), respectively, and 1.0 in terms of average axial load values ( / tested predicted P P ). Based on these statistical values, it is observed that the proposed models accurately predict the axial load, due to the consideration of all influencing parameters and the use of a large set of data in this study. Additionally, the model accuracy can be assessed by studying the ratio / tested predicted P P for all affecting parameters as shown in Fig. 5 and Fig. 6. The slope of the trendline represents the consistency of the prediction with respect to each variable. The ratio of / tested predicted P P for concentric model resulted in nearly flat slopes for all variables, which indicates consistency in prediction over all variable ranges. Regarding the eccentric loading model, the prediction also resulted in a nearly flat slope for all variables except the eccentricity level. The negative slope in Figure 6 (a) indicates an overestimation in the predicted axial strength at a high eccentricity level. It should be noted that the prediction models are only applicable within the ranges of the variables.

Comparison with existing models
An evaluation of the proposed model prediction with respect to other existing models (Table 4) for concentrically loaded columns has been performed and shown in Figure 7. Due to the lack of proposed models in literature for eccentrically loaded columns, the comparison is carried out for concentric columns only. The first model in comparison is adopted by the ACI 440-15 (Eq. 3) which approximates the FRP compression contribution with concrete, and accordingly, assumes the entire cross-section is concrete. This approximation is justified due to the low elastic modulus of FRP bars. The prediction model adopted by CSA-S806 neglects the FRP compression contribution as shown in Equation 6.   Figure 7: Comparison between the empirical equations shown in Table 3 and the proposed model

Parametric Analysis
To determine the impact of each of the model's variables discussed above on the axial capacity, a parametric analysis is carried out using the two GEP models that have been established. The 247 columns in the original database made it easier to evaluate variables with a broad range of values. The analysis is conducted by selecting one variable at a time and then assigning different values for that specific variable while keeping all other variables fixed at their average values obtained by studying the entire data set of 247 columns.  [Tarawneh et. al., 2022] reported a consistent concrete crushing failure mode, and no FRP bars ruptures were reported even for columns with high eccentricity [42]. This will also explain the negligible effect of FRP bars as will be shown later. Fig. 8 shows almost similar behavior for both concentric and eccentric loads.

Effect of FRP elastic modulus
The effect of changing the FRP elastic modulus ( E ) on the axial load capacity for both concentrically and eccentrically loaded columns is shown in Fig. 9. An increment of the FRP elastic modulus equal to 50 MPa is used during the investigation, and the results show that the FRP elastic modulus effect was insignificant, especially for the eccentric axial load.

Effect of reinforcement ratio
The effect of the reinforcement ratio ( ρ ) on the axial load capacity for both concentrically and eccentrically loaded columns is seen in Fig. 10. The influence of changing the column reinforcement ratio was different depending on load type. For concentric loading, the effect of the reinforcement ratio (Fig. 10a) decreases with increasing the reinforcement ratio. On the other hand, the reinforcement ratio in the eccentrically loaded column is negligible. The model ignores the reinforcement ratio effect in the eccentrically loaded column as its contribution is minimal compared to the concrete compressive strength, FRP elastic modulus, slenderness ratio, and eccentricity level as shown later  Fig. 11 shows the influence of varying the slenderness ratio (l/r) on the axial load capacity for both concentrically and eccentrically loaded columns. The figure shows that the axial load capacity decrease as the slenderness ratio is increased. Figure 11: Effect of the slenderness ratio (l/r) on the predicted axial load capacity (a) Concentric load (b) Eccentric load

Effect of eccentricity level
Fig . 12 shows the influence of varying the eccentricity level ( / e h ) on the axial load capacity for the eccentric axial loads. As shown in Fig. 12, the capacity is dramatically influenced by the eccentricity level with nonlinear relation.

MODEL LIMITATION AND RECOMMENDATION
Although the proposed model yielded a higher accuracy compared to other proposed procedures, data-driven machine learning models are only valid within the range of variables used to develop the models and should not be used for cases outside the range. Therefore, it is recommended to reexamine the proposed model with a larger database and a wider range of variables to validate its applicability.

CONCLUSIONS
In this study, gene expression programming is utilized with a database of 247 tested FRP-RC columns to generate prediction models for the axial capacity of concentrically and eccentrically loaded columns. The prediction models are applicable for concentric and eccentric loading, short and slender columns, different types of FRP reinforcement, and circular and rectangular cross-sections. In order to evaluate the sensitivity of each influencing parameter, a parametric study was also conducted. contribution with concrete, and accordingly, assumes the entire cross-section is concrete while the CSA-S806 equation neglects the FRP compression contribution. However, the proposed model by Mohammad et al. 2014 accounts directly for the FRP compression contribution using Hook's law with an assumed strain of 0.002 in FRP bars. As expected equations 3 and 4 resulted in a higher average than other models due to neglecting FRP compression contribution. However, they resulted in a lower COV compared to other models. In contrast, It is observed that the proposed model provided the lowest COV and RMSE. 3. Based on the parametric study performed in this study, it shows a strong positive correlation between increasing the concrete compressive strength and the carrying load capacity. The results also show that the FRP elastic modulus effect was insignificant, especially for the eccentric axial load. In addition, the effect of the reinforcement ratio decreases with increasing the reinforcement ratio for concentric loading while the reinforcement ratio in the eccentrically loaded column is negligible. The axial load capacity decrease as the slenderness ratio is increased. As shown before the capacity is significantly influenced by the eccentricity level with nonlinear relation.