Abstract: In this study, the Lyapunov index method is adopted to study time series under each loading strain level during the experiment on an evolving stress relaxation system of the deep coal seam. Through reconstructing phase space of deep seams, phase locus corresponding to each strain level presents an evolution on encircling its historic stress median no-repeatedly. By analyzing the time series with the fractal geometrics method, self similarities among different evolving stages of the stress relaxation system have been determined quantitatively. In addition, the relationship between classic mechanics and nonlinear science is also reflected. Nonlinear dynamical indexes of the evolving stress relaxation system are obtained to verify that it is a complicated system with typical chaotic properties. Moreover, the chaotic degree and complicated degree might descend with the development of the stress relaxation system of deep coal seams. It is found that the most obvious chaotic degree appears at the critical stage when the competition between softened factors and the enhanced ones for mechanical features of coal seam is the most drastic. Whereas after macroscopic failure the system shows the lowest chaotic and complicated degrees.

Key words: nonlinear dynamics, stress relaxation, evolving system, deep coal seam, chaos, fractal, phase space