# Lattice Fracture Model for Concrete Fracture Revisited: Calibration and Validation
## 4 Validation
### Uniaxial Compression Test  
Uniaxial compressive test conducted by [PERSON] et al. [47] was used for the validation of fracture analysis under compressive loading. In the experiment, cubic samples with size \(50\,\mathrm{mm}\times 50\,\mathrm{mm}\times 50\,\mathrm{mm}\) were subjected to compressive loads actuated by two steel plates at opposite faces of the cube. To model this loading boundary, \(x\) and \(y\) displacement were restrained and the prescribed displacement was applied along with \(z\)-direction (Figure 4a,b). The element mechanical properties \(E,f_{\rm c},\) and \(f_{\rm t}\) can also be calibrated by fitting the experimental stress-strain curve, as shown in Table 3.  
Figure 4: Uniaxial compressive test (**a**) crack pattern at a point, (**b**) crack pattern at b point (red-cracked element), (**c**) stress-strain response. Figure 4a,b show the crack patterns under uniaxial compressive loading in different stages and Figure 4c shows a comparison between the experimental and numerical results. Due to the local confinement near the boundaries provided by friction of the loading platens (zones 1 and 2 in Figure 4a), the cone-shaped inner part of the specimen remained uncracked. A majority of cracks initiated from areas marked as 3 and 4. This numerical result shows the same tendency as experiments [47]. According to previous research [4; 50], the slenderness and boundary conditions significantly influence the crack pattern and load-displacement curve of concrete subjected to uniaxial compressive loading. To understand their influence, the relevant numerical analyses were performed. The input parameters used are listed in Tables 3 and 4. Figure 5 shows the typical crack patterns for the specimens under uniaxial compressive loading from the experimental and numerical perspectives. For the high friction boundary condition, the cone shape inner parts of the specimens remained uncracked. For taller specimens, the boundary restraint influenced less. As a result, the cracks mainly occured in the middle zone of the specimen and less cracking occured in the area close to the top and the bottom surface. This explains the fact that simulations of samples with decreasing slenderness show higher load-carrying capacity. Figure 5: Crack patterns for (**a**) high friction boundary condition in numerical analysis, (**b**) high friction boundary condition from the literature [51]. Reproduced from [51]. Copyright 1996, Wiley Online Library. (**c**) low friction boundary condition in numerical analysis, (**d**) low friction boundary condition from the literature [51] (red-cracked element). Reproduced from [51]. Copyright 1996, Wiley Online Library. For the low friction boundary condition, the failure mode was characterized by localized cracks which were almost parallel to the applied load. Specifically, a large number of elements in the upper and lower surfaces were broken. In contrast, for the high friction boundary condition, the failure mode was characterized by inclined cracks that left the simulated sample ends almost undamaged. Furthermore, for low friction boundary conditions, many micro-cracks occured on the top and bottom area during the fracture process. This is in agreement with experimental observations [4]. In Figure 6a,b, the stress-strain curves with different slenderness and boundary conditions are plotted. For the high friction boundary condition, the slenderness significantly influenced the peak load. Specifically, increasing slenderness resulted in lower strength and lead to more brittle softening behavior. For the low friction boundary condition, increasing slenderness showed less influence on the peak load but resulted in a more brittle softening part behavior. According to the numerical results, high friction boundary condition provided a higher bearing capacity than the low friction boundary. This can be explained by the cohesion in the boundary which constrains the lateral deformation and improved the load-bearing capacity. The numerical results are in accordance with the literature [4].