A numerical simulation of seepage structure surface and its feasibility

PENG Kang(彭康), LI Xi-bing(李夕兵), WANG Ze-wei(王泽伟), LIU Ai-hua(刘爱华)

(School of Resources and Safety Engineering, Central South University, Changsha 410083, China)

Abstract:According to Cubic law and incompressible fluid law of mass conservation, the seepage character of the fracture surface was simulated with the simulation method of fractal theory and random Brown function. Furthermore, the permeability coefficient of the single fracture was obtained. In order to test the stability of the method, 500 simulations were conducted on each different fractal dimension. The simulated permeability coefficient was analyzed in probability density distribution and probability cumulative distribution statistics. Statistics showed that the discrete degree of the permeability coefficient increases with the increase of the fractal dimension. And the calculation result has better stability when the fractal dimension value is relatively small. According to the Bayes theory，the characteristic index of the permeability coefficient on fractal dimension P(D_fj︱R_i) is established. The index, P(D_fj︱R_i)，shows that when the simulated permeability coefficient is relatively large，it can clearly represent the fractal dimension of the structure surface，the probability is 82%. The calculated results of the characteristic index verify the feasibility of the method.

Key words:fractal theory; numerical simulation; representative elementary volume (REV); random brown function; permeability coefficient; fractal dimension