Quantitative Solution On Dosage Of Self-healing In Different Cracks Via Set Theory

The service life of concrete is reduced due to the crack propagation.In order to prolong the service life of structure,self-healing technology via embedded capsule with repairing agent has been developed in the past few decades.And,the self-healing technology via embedded capsule has been prevailed.However,the research that how to determine the dosage of capsules is still few.And,a mathematical model has been established to acquire the analytical solution of capsule's dosage in different crack patterns,which combined the knowledge of integral geometry and stereology.On the basic,several crack patterns have been discussed.On the basis of the previous study,this paper presents a set methodology on analytical solution of the required capsule dosage in the crack patterns.And,the key of method is that the polygons crack networks are decomposed into discrete angels and sides.According to the set theory,the crack-hitting probability and capsule's dosage by linear capsules for arbitrary two-dimensional convex crack network can be calculated.Afterwards,the idea of set theory is also used in the capsule's dosage of three-dimensional crack network.By means of the “vertical sectioning”,a relationship has been established between the three-dimensional crack and two-dimensional crack.On the basis of the relationship,the crack-hitting probability and capsule's dosage have been calculated,including parallel plane,two sets of planes and the straight prism crack pattern.Then,the reliabilities of the crack-hitting probability models by capsules has been verified via numerical simulation.Meanwhile,the crack-hitting probability of multi-shaped crack is also verified by this way.Besides,both the computer image processing technology and abstracting the crack method are described,so as to get the crack pattern in the picture.In the image processing,image scaling,binaryzation and denoising are introduced in detail.After the image processing,the corresponding coordinates of the crack are extracted and the linear fitting of the crack is achieved.According to the research,a novel calculation method has been presented to make sure the dosage of capsules in the different crack pattern.Meanwhile,a new idea has been shown in how to get the information of the crack pattern.