Scaling Law Characteristics And Parameters Estimation Of Inhomogeneous Brittle Materials Before Destruction

The damage of earthquakes, mountain landslides and large civil engineering structures all belong to the category of Inhomogeneous brittle material failure. Because of the brittleness of the materials itself and the non uniformity of the internal structure, it leads to the destruction of the uncertainty and unpredictability. Once it happens, it will bring huge losses to people’s lives and production. Therefore, in the engineering and scientific community, it causes a big concern about the catastrophic failure mechanism and failure prediction of inhomogeneous brittle materials. In this paper, three aspects of Inhomogeneous brittle materials are studied from theory, numerical analysis and experimental verification. Scaling law characteristics are described in detail before the material’s damage occurred. Besides the key parameters related to the scaling law characteristics are also estimated accurately.Firstly, based on the theory of damage mechanics and the integral mean field approximation, the complex inhomogeneous brittle material is idealized as a continuous threshold model. By using the uniform distribution function and the Weibull distribution function, the heterogeneity of the threshold of the micro element in the theoretical model is described. The theoretical results of a power-law singularity characteristic of the inhomogeneous brittle materials can be obtained. And the power exponent is estimated.Secondly, through the Monte Carlo method, Inhomogeneous brittle materials are dispersed for one-dimensional fiber bundles model. And the stress loading control is simulated. In the process of nominal stress increasing and tending to the maximum value, the response or response function of fiber bundles model in damage evolution also appears the same power-law singularity characteristics of theoretical results.An then, The results above will be verified by experiments. There surely exhibits a power-law singularity characteristics between deformation rate and loading control(testing machine loading displacement or load time variables) but showing different exponential results in two kinds of destructive test.Finally, In two different failure test of granite, the deformation of the specimen with the loading process showing three different phases: the first stage for deformation rate decreasing rapidly; The second stage for deformation rate stably constant; the third stage for deformation rate increasing unstably. In addition, the stable stage and sample destruction of specimen damage evolution process exist a relationship. Through statistical analysis of large amounts of sample results, the linear variation characteristics is found between the deformation rate of stable stage and the average deformation rate of the tests with the different slopes in different tests.