Chaotic Analysis on Extended State of Crack in Brittle Rock

Abstract: Through the fracture mechanics theory, two-dimensional analytic solution of stress field and displacement field on the tip of crack had been obtained. And expression of crack's stress intensity factor, which is a measure of the crack expansion tendency and the crack expansion propelling force, was inferred. Destruction mechanism of rock included crack under compressive stress condition had been discussed. If elliptical shape immerged crack's long axis is obviously greater than minor axis in project rock mass, then it will be allowed to simplify to be a breakthrough ellipse crack on processing. The expression of effective crack length was deduced. And concept of crack expansion rate was proposed. And rock's test physical mechanical parameters which are useful for theoretical analysis and numerical experiment were got by experimental method. The theoretical values of effective crack length and crack expansion rate under the different compressive stress were calculated.Through finite element software FLAC3D numerical experiment, the crack's expansion rule and stress concentration situation under different compressive stress are analyzed. And then the crack dehiscence direction had been obtained. Further more, time series were extracted from the crack's the stress field. The crack plastic condition had indicated crack's destruction form, and the plastic area scope increases along with the compressed stress increases. The experiment value of crack expansion rate, contrasting with theoretical value, is basically concordance under different compressive stress. The impressive stress isoclines indicates between the biggest principal stresses in crack concentrates region and the crack's horizontal direction presents a angle, and it increases along with compressed stress under the model increases.Through reconfiguration of time series' phase space, the biggest Lyapunov exponent was extracted from the horizontal stress and the vertical stress's time series. All of exponents are positive, which indicates this system is chaotic. Then the stress condition of tip of crack is in chaos. Finally the level of chaos about stress of crack is evaluated by Kolmogorov entropy. The extended state of rock crack is much more chaotic under higher stress while is less under lower stress…
Key words: stress intensity factor; effective crack length; crack expansion rate; stress isoline; chaos; time series

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