## 2 Improved Cohesive Model
### Numerical Benchmark  
Masonry wallette is widely used in civil engineering. Experiments conducted by [PERSON] et al. (2010, 2012) on a Masonry wallette was chosen to verify the correctness and effectiveness of the improved cohesion-friction mode ([PERSON] et al., 2014; [PERSON] et al., 2016). Both the bonding of the masonry and the bonding of the steel-concrete structure is provided by cement mortar. The related failure modes can be simplified to be quasi-brittle, although the material and production method used for the cement mortar may lead to differences in the mechanical parameters. Hence, after verification by the shear slip behavior between the bricks, the established model can be applied to characterize the mechanical behavior of the interface between steel and concrete in CCFSTs. As shown in Figure 4a, there are three bricks bonded by mortar; the middle brick is also constrained by two rigid bricks on the upper surface. In addition, the bilateral bricks are applied with the vertical displacement load on the lower surfaces to achieve a shear effect. Pressure is applied on the two outer vertical surfaces to ensure the friction effect. Figure 4: Numerical verification of the masonry wallette: (**a**) experiment configuration ([PERSON] et al., 2010, 2012) ([PERSON] et al., 2014; [PERSON] et al., 2016); (**b**) numerical configuration. Figure 3: Coupling method between friction and tangent tractions: (**a**) effect of the friction growth shape parameter, \(s\), on the response factor, \(\kappa\); (**b**) relationship between tangential stress and tangential displacement. Different numerical models have been used to simulate the experiment of [PERSON] et al. (2010, 2012) [45; 46]. As [PERSON] and [PERSON] (2015) [41], [PERSON] (2013) [47], and [PERSON] (2019) [48] utilized the symmetric half model, as depicted in Figure 4a,b; this same model is adopted here for an accurate comparison. Initially, different normal pressures of 0.2, 0.4, and 0.65 MPa are applied to the right surface of the specimen and maintained at a constant level during the shearing process. Then, a vertical displacement load of 10 mm is applied to the lower side of the right brick, while a vertical constraint is imposed on the upper surface of the light brick. Consequently, the mortar interface is in a coupled state of compression and shear during loading. This study used the ABAQUS (R2017) software to simulate the above experiment. A static solving algorithm was used. Three-dimensional (3D) eight-node linear elements (C3 DBR) were chosen to describe the mechanical behavior of the masonry, and eight-node cohesive elements (COH3D8) were inserted into the mortar interface between the bricks. Considering that the strength of the masonry was significantly higher than that of the mortar, the linear elastic model was used for the masonry. The experimental case cited in this study has been widely simulated using various numerical methods, with the masonry often assumed to be elastic bodies [41; 47; 48]. The mortar material was characterized by the improved cohesive model, and the model was embedded into ABAQUS as the user-defined model. Based on the MC strength criterion, the peak shear stress can be separated into two components. The first component, contributed by cohesion, is approximately 0.2295 MPa, while the second component, contributed by friction, is around 0.308 MPa. Given a normal pressure of 0.4 MPa, the friction coefficient was calculated to be 0.77. The material properties of the bricks and joint mortar are listed in Table 1. Furthermore, it is assumed that the brick behaves as a linear elastic material with an elastic modulus of 14,000 MPa and a Poisson's ratio of 0.15. The critical results of the improved PPR model demonstrate good agreement with the experimental results.