Modeling of rocks with spatial distributed fractures by random medium theory

摘要

By using the Spectrum expanding theory of random process and Hudson's crack model, we developed a random medium model for rocks with spatial random distributed number density of cracks. This model could connect the micro parameters of the cracks (the number density of crack) with the macro mechanical properties (the elastic constants), and can be effectively applied to model the real inhomogeneous medium. Numerical example indicates that the random distribution characters could be different for different elastic constants under the same random distribution of number density of cracks. By change the value of the autocorrelation length pair, it is possible to model the difference of the distribution in the two coordinate directions.