# Meso-Scale Failure of Freezing-Thawing Damage of Concrete under Uniaxial Compression
## 5 Conclusions  
Based on the uniaxial compression test of freezing-thawing-damaged concrete, a numerical model was established using particle flow discrete element theory to study the influence of freezing-thawing damage on the meso-scale failure mode of concrete. The following conclusions are drawn.  
As the difference between the uniaxial compression axial deformation of the freezing-thawing concrete model and that of the numerical simulation was less than 1%, the model of freezing-thawing concrete and the selected parameters is accurate.  
Through analysis of the contact force between particles in two different stage points of the numerical model, we found that the softening effect of concrete after the peak force is considerably weakened by the freezing-thawing effect on concrete. From 75 to 150 cycles of freezing-thawing, the softening effect after peak decreased by 39.7%. At the same time, by controlling the termination condition of uniaxial compression of the concrete numerical model, the contact force between particles at any point on the stress-strain curve can be used to estimate the damage degree of the concrete structure at different points.  
Figure 17: Failure states of concrete at the third stage point under different freezing–thawing cycles. (**a**) Failure state concrete without freeze–thaw; (**b**) Failure state of 25 freezing–thawing concrete; (**c**) Failure state of 50 freezing–thawing concrete; (**d**) Failure state of 75 freezing–thawing concrete; (**e**) Failure state of 100 freezing–thawing concrete; (**f**) Failure state of 125 freezing–thawing concrete; (**g**) Failure state of 150 freezing–thawing concrete.  
With the increase in freezing-thawing cycles, the number of cracks increased significantly. In the second stage point, the crack growth rate from 75 to 150 cycles of freezing-thawing was 6.8%; in the third stage point, the crack growth rate from 75 to 150 cycles of freezing-thawing was 12.2%. In the third stage point, the crack growth rate was significantly higher than that in the second stage point, which indicated that the failure of concrete mainly occurred in the post-peak softening stage. By controlling the termination condition of uniaxial compression of the numerical model of concrete, the number of cracks at any point on the stress-strain curve is obtained to predict the degree of concrete damage.  
With the increase in freezing-thawing cycles, the number of concrete fragments increased gradually, and the damage worsened. From 125 to 150 cycles of freezing-thawing, the growth rate of concrete fragments was the highest, with an increase of 48.1; the fragmentation after 150 cycles of freezing-thawing was the most serious. Therefore, testing the mechanical properties of concrete is necessary when concrete has undergone more than 125 cycles of freezing and thawing. At the same time, the number of concrete fragments and the final failure morphology are used to predict the failure mode and the damage degree of concrete in macroscopic physical test.  
Conceptualization, Z.S.; Data curation, X.D.; Formal analysis, Z.S. and X.D.; Investigation, X.D. and L.H.; Project administration, L.H. and Y.L.; Resources, Z.S., L.H. and Y.L.; Validation, Y.L. All authors have read and agreed to the published version of the manuscript.  
This study was financially supported by the National Natural Science Foundation of China (Nos. 51879217, 51409207, and 51609200) and the National Science Foundation for Post-Doctoral Scientists of China (No. 2015M582765 XB).  
The author would like to thank the reviewers for their comments.  
The authors declare no conflict of interest.