# Meso-Scale Simulation of Concrete Based on Fracture and Interaction Behavior
## 6 Parametric Study  
### The Effect of Mode II Fracture Energy  
Since mode I fracture was considered as the dominant form in tension damage, single fracture energy was adopted to describe the interface fracture behavior in the previous concrete tension simulation. In this method, the fracture energies of the interface elements are fixed values regardless of fracture type. Moreover, since the compression failure of concrete is mostly due to shear fracture [41], modeling with one specific fracture energy is unable to simulate the fracture behavior of concrete both under tension and compression. Due to the multiphase and heterogeneous property of concrete, the mixed-mode fracture would occur inevitably in concrete failure, even under uniaxial tension conditions. Mixed-mode fracture energy is determined by mode I and mode II fracture energy, and the two pure-mode fracture energies both have influences on concrete tensile and compressive behavior.  
Figure 15: The relationship between global strain and the sum of length of (**a**) ITZ elements and (**b**) MII elements with different damage degree.  
In this section, the effect of mode II fracture energy on the performance of concrete under tension and compression is studied.  
As mentioned in Section 2, the experiment results show that there is a relationship between mode I and II fracture energy. In this section, mode I fracture energy is fixed. The ratio of mode II and mode I fracture energy (\(\xi\)) is taken as the variable to investigate the effect of mode II fracture energy. The ratio \(\xi\) is calculated by the following equation:  
\[\xi=G_{s}^{C}/G_{n}^{C} \tag{8}\]  
The tension simulation result of varying \(\xi\) is shown in Figure 15(a). The influence on the ultimate tensile strength is negligible. It is noteworthy that the mode II fracture energy influences the specimen's tensile behavior in the softening stage. The mixed-mode fracture accounts for a large proportion. In the case that the mode II fracture energy equals the mode I fracture energy (\(\xi=1\)), the total fracture energy is 48.2% lower than that of the standard model (\(\xi=25\)). It can be inferred that the mixed-mode fracture energy caused by the difference of the two pure-mode fracture energy accounts for about half of the total fracture energy.  
The compression simulation result of varying the multiple is shown in Figure 15(b). The ultimate compressive strength is significantly influenced by the mode II fracture energy, which is different from tensile strength. When the mode II fracture energy equals the mode I fracture energy (\(\xi=1\)), the compressive strength and total fracture energy is 44.7% and 82.2% lower than that of the standard model (\(\xi=25\)), respectively. As described in Sections 3 and 4, the crack initiates before and after the specimen reaches the ultimate bearing capacity state under compression and tension, respectively. Low mode II fracture energy will limit interface elements' shear deformation under compression, while it has a relatively low influence on the interface elements' tensile deformation under tension. It can be noticed that with the increase of mode II fracture energy, the growth of compressive strength decreases. The limit of compressive strength gradually translates from deformation ability to the shear strength of interface elements.