The Scaling Law And The Realization Of Fractal Interpolation Of The Crack Development Of RC Member

The appearance and expansion of cracks is the most visible information of concretestructure damage, and the development situation of fracture will directly influence themechanical properties of reinforced concrete members. So researching the developmentof surface cracks in reinforced concrete members has a practical application value instudying and evaluating the safety state of the reinforced concrete members.In this paper, the development mechanism of cracks has been researched furtherbased on the four-point bending tests and reinforced concrete member stretch numericalexperiments, and on the basis of previous studies, fractal geometry and scale theory isapplied to study the following problems, from theory and experiment both aspects, suchas the corresponding relation between the mechanical propertise of reinforced concretebeam and the development of cracks in the surface of members, the scaling law of thecrack development, the relationship of crack development of reinforced concretemember and its mechanical parameters, the fractal interpolation calculation of crack ofreinforced concrete members. The main objectives of the research are as follows:(1) In this paper, the research train of thought is raised based on the existingproblems and the insufficiency in current research of fractal theory and scale theory inthe domestic and foreign, and the application in crack development of concrete member,and carrying on a feasibility analysis;(2) Through the four-point bending test of reinforced concrete beam, fractalgeometry theory is selected to study the development law of surface crack in reinforcedconcrete beam in order to get the relationship between fractal dimension of thedevelopment distribution of the fracture and the mechanical properties of concretemembers, such as the crack width, the deflection of beam mid-span, and the fractaldimension can be as an indicator to measure the performance of reinforced concretemember;(3) With the help of reinforced concrete member tensile numerical experiments,fractal method is applied to study the relationship between the law of crack development of reinforced concrete member and the basic mechanical parameters.Based on the above results, a mathematical expression is established, and verified thatthe surface cracks in reinforced concrete member with fractal characteristics;(4) Based on the Studying of the scaling law problem of the crack development,the fact that the crack development has a characteristic of scaling law under the scalingtransformation throughing calculating, then puts forward a scale criterion of concretecomponent damage state, to judge the damage states of the reinforced concrete member;(5) MATLAB, a numerical calculation software, and the fractal interpolationmethod are adopted to achieve the fractal interpolation algorithm of the cracksdevelopment of the length and type in members. and this method has been applied in thedetection and identification of concrete structures.