# Novel Predictive Model of the Debonding Strength for Masonry Members Retrofitted with FRP
## 1 Introduction  
Masonry buildings have been utilized from time immemorial and, these days, because of aging, material degradation, and structural variations, members' performances often need to be strengthened. In this case, fiber reinforced polymer (FRP) composites in the form of bonded laminates attached to the outside can be a lasting strengthening solution provided that they comply with the cultural value of the building [1]. The use of FRP material, however, causes novel and significant modeling problems [2; 3], in spite of various material modeling plans that were extended in previous years achieving reproduction of the structural behavior of both un-strengthened and FRP-strengthened masonry structures [4; 5]. A diversity of FRP strengthening systems has been indicated to develop the out-of-plane load-carrying capacity of masonry elements (e.g., [6; 7; 8; 9; 10; 11; 12; 13; 14; 15]). Many experimental investigations have been performed with the purpose of studying the capability of using FRP in the strengthening of masonry structures (e.g., [16; 17; 18]). Similar experimental tests for monotonic or cyclic loading have been performed by [PERSON] et al. [16], [PERSON] [19], [PERSON] et al. [20], and [PERSON] et al. [21]. [PERSON] et al. [22] proposed a local bilinear shear stress-slip law (bond behavior) between CFRP strips and calcarenite stone using an experimental study with three different bonded lengths (\(l_{b}\)):50, 100, and 150 mm. Moreover, mathematical models have also been developed for improving the existing models to fit the experimental results better ([3; 5; 23]). [PERSON] and [PERSON] [24] proposed the use of neural networks and neuro-fuzzy models for modeling the debonding strength of retrofitted masonry elements. Failure modes observed in these investigations contain debonding of the FRP laminate from the masonry layer, tensile rupture of the FRP laminate, masonry crushing in the compression area, flexural-shear fracture near the support, sliding shear fracture along a bed joint, and localized masonry collapse. A very common fracture is created by bond loss of the FRP reinforcement, called as debonding failure. Debonding happens when the FRP is no longer adhered to the element because of a crack or separation of the fiber matrix and bond junction. This failure mode is often referred to as intermediate crack (IC) debonding [25]. The adhesive bonded joint analyzed, illustrated in Figure 1, can be noticed as a simple and generic model of FRP-strengthened structures to understand stress transfer and debonding behavior. There are various analytical models for calculating the debonding strength of members with FRP shear retrofit in the literature (e.g., models in Section 2 of this paper). In the area of empirical modeling, soft computing methods can be assumed as the effective superseded to usual techniques. Genetic programming (GP) [26] is a rather new soft computing method for the treatment modeling of structural engineering problems. GP is a development of genetic algorithms (GA). The major benefit of the GP-based procedures is their capability to create estimation equations without presuming a prior form of the relation. Genetic programming (GP), and its deployment of gene expression programming (GEP), may be applied as an alternative to a physical model. In the last decade, new procedures based on GEP have been applied to civil engineering problems. [PERSON] et al. [27] proposed a new formula for bond strength of FRP-to-concrete composite joints using GEP. [PERSON] [28] introduced a simple model to compute the concrete shear strength of FRP-reinforced concrete slender beams without stirrups using GEP. [PERSON] et al. [29] used GEP to predict the slump flow of high-performance concrete by using seven concrete components. [PERSON] [30] used several soft computing approaches for predicting strength enhancement of FRP confined concrete cylinders. Additionally, [PERSON] et al.