“…Different methods are adopted to improve the concrete properties, such as the C-S-H seed enhanced concrete (Chen et al, 2020g;Li et al, 2020), the fiber-reinforced concrete (Chen et al, 2018d;Liu et al, 2020;Zhang et al, 2021) and the self-healing concrete (Yang et al, 2009). The self-healing material can repair the concrete's (micro-) cracks and (micro-) voids automatically, which can cause damage to the material (Li et al, 2018;Li et al, 2020aLi et al, , 2020bWhite et al, 2001;Yang et al, 2009;Zhou et al, 2017). Meanwhile, through extending the traditional continuum damage mechanics (CDM) framework (Ju, 1989(Ju, , 1991Ju and Lee, 1991;Ju et al, 1989;Kachanov, 1987;Krajcinovic, 1984;Voyiadjis and Kattan, 1999), the researchers proposed the continuum damage-healing mechanics (CDHM) in the literatures to describe the damage-healing behavior (Barbero et al, 2005;Miao et al, 1995;Voyiadjis and Kattan, 2014;Voyiadjis et al, 2011Voyiadjis et al, , 2012aVoyiadjis et al, , 2012b.…”