# Estimation of the Ultimate Strength of FRP Strips-to-Masonry Substrates Bond
###### Abstract  
Fiber-Reinforced Polymers (FRP) were developed as a new method over the past decades due to their many beneficial mechanical properties, and they are commonly applied to strengthen masonry structures. In this paper, the Artificial Neural Network (ANN), K-fold Cross-Validation (KFCV) technique, Multivariate Adaptive Regression Spline (MARS) method, and M5 Model Tree (M5 MT) method were utilized to predict the ultimate strength of FRP strips applied on masonry substrates. The results obtained via ANN, KFCV, MARS, and M5 MT were compared with the existing models. The results clearly indicate that the considered approaches have better efficiency and higher precision compared to the models available in the literature. The correlation coefficient values for the considered models (i.e., ANN, KFCV, MARS, and M5 MT) are promising results, with up to 99% reliability. Fiber-Reinforced Polymers Artificial Neural Network K-fold Cross-Validation Multivariate Adaptive Regression Spline M5 Model Tree +
Footnote †: journal: Applied Sciences  
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Moreover, researchers investigated the effect of different bonded lengths of FRP sheets on the calcarenite stone behavior [28]. In other studies [29; 30; 31], experimental tests were applied to present mathematically based models to define the behavior of strengthened materials with FRP sheets. [PERSON] et al., considered the micro-mechanical and macroscopic models used to study the behavior of FRP-reinforced and unreinforced masonry structures. The proposed models utilized different yielding criteria and constitutive laws [29]. There are arch and curved masonry structures that need to be retrofitted using FRP strips. [PERSON] and [PERSON] [32] utilized the FRP sheets to enhance the capability to transform the tensile stress between the arch masonry and FRP sheets. Finally, they proposed a closed-form model. [PERSON] et al. [33] proposed a numerical model to study the responses of curved masonry structures retrofitted using fiber-reinforced cementitious matrix. They concluded that the numerical model needs fewer mechanical properties and computational costs and has high accuracy [33]. [PERSON] et al. [34] performed experimental tests that retrofitted masonry walls using carbon fiber-reinforced polymer embedded in the mortar joint. They concluded that the combined structure failed on the shear mode via a diagonal configuration [34]. Recently, a model has been proposed in [35] which may reasonably predict the joint sliding for the masonry buildings retrofitted using pultruded FRP. [PERSON] et al. [35] found that FRP-transfer length significantly affects the maximum monotonic load capacity of strengthened masonry panels. They also showed that the optimal transfer length depends on the average tensile strength of support and FRP stiffness per width. In [36], it was shown that a similar pattern for the transfer mechanism occurs in the masonry members strengthened with FRP sheets compared to the concrete members. They also proved that the strain path along the FRP sheets obeys different laws based on the magnitude of the applied load. A new method was also proposed to solve or delay the inopportune debonding of FRP sheets from the masonry wall surface [37]. [PERSON] et al. [37] applied different strengthening methods (i.e., nailing, surface preparation, grooving, plaster, and boring) to mount the CFRP and GFRP sheets to the wall surfaces, and showed a 110% increase in the ductility index of reinforced walls. Furthermore, the ductility of reinforced walls improved by 26% and 53% for the surface preparation and boring methods, in combination with the nailing method, respectively [37]. In addition, the results showed that the ductility of the reinforced wall increased by 30% when the groove dimensions were 4 mm and 7 mm in width and depth, respectively. Finally, the cement plaster had no tangible effects in terms of improving the ductility of the wall.