# Numerical and Experimental Investigation of Recycled Brick Coarse Aggregate Concrete
## 2 Materials and Methods
### Numerical Simulation on RBAC Uniaxial Compress Test  
Concrete is a three-phase composite material consisting of aggregate, mortar, and the interface between aggregate and mortar. Fine aggregate and coarse aggregate accounted for 60% to 75% of the total volume of concrete, of which coarse aggregate accounts for 40% to 50% [33]. In order to obtain the internal damage process and morphology of concrete under external load and other factors, a finite element model of random recycled aggregate was presented to reflect the concrete microstructure. The random aggregate algorithm was written based on Python, and the modeling and numerical analysis of two-dimensional recycled aggregate concrete were conducted using ABAQUS. Concrete was graded in three levels, and the thickness of the interface transition zone was determined at 0.5 mm in the numerical simulation [34]. Figure 5 shows the load and boundary conditions of the model, and the model dimension is 100 mm by length and 100 mm by width. Vertical constraints were set at the bottom of the model and horizontal constraints at the bottom's midpoint to simulate the  
Figure 4: Microcomputer controlled electrohydraulic servo universal testing machine. Figure 3: RBCA concrete specimens: (**a**) RB-0, (**b**) RB-25, (**c**) RB-50, (**d**) RB-75, (**e**) RB-100. specimen's bottom constraints in the compression test. A displacement load of \(-0.05\) mm was applied on the top to simulate the compression of the loading plate of the testing machine. A total of 23,480 CPS3 units with an average size of 1.0 mm were used to mesh the mortar matrix, aggregate, and interface transition zone. Furthermore, mortar matrix, aggregate, and interfacial transition zone were connected by merging. The mechanical behavior of the mortar matrix and the interface transition zone was similar to the mechanical behavior of concrete [21; 22]. The plastic damage constitutive relationship of concrete proposed by [PERSON] and [PERSON] [35] was adopted to describe its mechanical behavior in this study. RBCA is characterized by a rough surface, sharp edges, high water absorption, and low strength [36; 37; 38]. The failure mode of RBCA concrete is different from that of ordinary concrete, mainly existing in the mortar matrix and interface transition zone. The aggregate itself can be crushed and fractured. Research on RBCA's constitutive relationship has previously been carried out. The modified plastic damage intrinsic model proposed in the literature [21] is used in this paper to describe the damage behavior of red brick particles. The constitutive formula adds the parameter \(r\) to consider the content of recycled aggregate, which is more accurate for numerical simulation of RBCA concrete. Furthermore, the elastoplastic constitutive relation is adopted for NCA concrete and has high strength. The constitutive model of RBCA concrete is as follows:  
\[\sigma=E_{r}\epsilon\exp\left[1-(\frac{\epsilon}{a})^{b}\right] \tag{1}\]  
The total damage variable \(D\) of recycled concrete with different replacement levels:  
\[D=1-\frac{E_{r}}{E_{0}}\exp\left[-(\frac{\epsilon}{a})^{b}\right] \tag{2}\]  
\[a=\frac{\epsilon_{p}}{\left(\frac{1}{b}\right)^{\frac{1}{b}}} \tag{3}\]  
\[b=\frac{1}{\ln(\frac{E_{r}\epsilon_{p}}{\sigma_{p}})} \tag{4}\]  
In Formulas (1) and (2), \(E_{0}\) is the elastic modulus of concrete with a 0% recycled aggregate replacement rate, \(Er\) is the elastic modulus of concrete with a replacement rate of \(r\%\), and the parameters \(a\) and \(b\) are distribution parameters of the Weibull distribution, which can be obtained by combining the peak strain with Formulas (3) and (4). Figure 5: Two-dimensional mesounmerical model. It is necessary to determine the mechanical parameters of three-phase materials (RBCA particles, mortar matrix, and interfacial transition zone) in the mesoscopic numerical simulation of RBCA concrete.