# Lattice Fracture Model for Concrete Fracture Revisited: Calibration and Validation
## 4 Validation
### Tensile Splitting Test  
Brazil splitting tests conducted by [PERSON] et al. (2018) were simulated in this section. In their experiments, cylindrical specimens with different diameters \(D\) (19 mm, 38 mm, 76 mm, 152 mm) are tested. The thickness of the specimens was kept constant (\(B\) = 51 mm), as shown in Figure 7a. Since the loading condition is not specified in this publication, an assumption that the specimens are loaded through steel loading platens is made herein. In the numerical analysis, the prescribed displacement was applied to the vertical direction and the displacements in other directions were set to 0 to model the experimental loading condition, as shown in Figure 7b. In this section, the input parameters in Table 5 were calibrated by fitting the peak load of the experimental sample with a diameter of 38 mm. Specimens of other sizes were utilized to evaluate the LBM ability on tensile splitting fracture analysis. Furthermore, since the publication only provides tensile splitting strength rather than the whole stress displacement curve, the elastic modulus was assigned as 25 GPa without calibration.  
Figure 7: (**a**) Setup for tensile splitting test, (**b**) failure mode for splitting tensile test, (**c**) crack patterns for splitting tensile test (red-cracked element).  
Figure 8a reports the nominal stress, defined as 2_P_/(\(\pi BD\)), versus displacement curves obtained by the numerical analyses. The peak load of the nominal stress was the tensile splitting strength. The peak nominal stress for splitting tensile test decreased as the size increased. It can be observed from Figure 8b that the numerical results agree well with experimental results for specimens with diameters ranging from 19 to 152 mm. Note that the numerical result for the digital specimen with a diameter of 19 mm showed lower strength than the experiment, which is attributed to the relatively large element size compared to specimen size and boundary condition. Specifically, the cell size (2.5 mm) was utilized to avoid size effect, nevertheless mesh size was not enough to produce accurate calculations. To model the loading condition of the experiments, a displacement was prescribed in the vertical direction at the nodes belonging to the loading area in the simulation. Due to the influence of cell size, for the smallest digital sample, with diameter of 19 mm, it was difficult to apply the load with the same width as others. Therefore, stress concentration may have occurred in the smallest modeled sample, resulting in a lower simulated strength. For the specimen with a diameter equal to 152 mm, LBM overestimated the experimental strength, which was induced by the different failure mechanisms. Specifically, in the experimental campaign, most samples failed due to a splitting crack initiating in the center of the specimen, while for the specimen with a size of 152 mm, there was significant damage underneath the loading platen (2018). For the numerical procedure, all models followed a comparable crack pattern. Yet accurately, some micro-cracks occured within the loading area, and then a splitting crack initiated in the center of the model and propagated to the top and bottom boundaries. Finally, the modeled sample gradually lost the capacity to bear the load. Thus, the deviation for the largest model can be well explained by the different types of dominant cracking modalities.