Study On Chaos And Bifurcation Characteristics Of Instability And Fracture Of Rocks And Rock-bursts

Instability and failure of rocks during different loading conditions are always important concerns in rock mechanics and engineering. On the basis of an extensive experimental program of conventional triaxial compression, plain strain and CT tests, the formation and orientation of a localization band in the sandstone, the chaotic characteristics of rock fracturing, the CT evolution of the coal rock and rockbursts occurring at deep coal mines were studied using discontinuous bifurcation theories and chaos theories. The results could be summarized as follows:1. A new plain strain apparatus for testing mild rocks were designed and built and a series of plain strain tests on sandstone have been performed. The comparison of plain strain experimental results of sandstone to that under conventional triaxial compression shows that the constitutive responses of rocks differ greatly for various loading conditions. Questionable predictions may arise when data obtained from axi-symmetric tests are applied to two dimensional problems.2. The unloading-reloading cycles in triaxial tests at different confining pressures have been undertaken to investigate the stress-dependent elasticity of sandstone. The analysis of experimental results show that the elasticity of sandstone is not only stress sensitive but also coupled to the plasticity, manifesting strong nonlinearity.3. All sandstone specimens in our test program failed by a single plane called a shear band when subjected to confining pressures lower than 40MPa regardless of loading conditions. The measurements of shear band inclinations of failed specimens indicate that the orientations are decreasing with increasing confining pressures under conventional triaxial compression, while that of specimens subjected to plain strain conditions seem unaffected by varying confining pressures.4. The onset and orientation of a localization band formed in sandstone was studied theoretically within the framework of equilibrium bifurcation theory. Corresponding elastoplasitc constitutive models with nonlinear yield and potential functions were developed from plain strain and conventional triaxial compression experiments. The inclinations of shear bands and the bifurcation points were predicted using so-called acoustic tensor method. Comparison of computation results with experimental results indicates that the initiation of a shear band predicted by the three dimensional model occurs closely after the peak axial stress, while the two dimensional model predicts bifurcation will happen within the strain hardening region, i.e. prior to the peak stress.5. A model characterizing the CT evolution of coal rocks during uniaxial loading was developed on the basis of CT test on coal rock. Dynamical analysis of the model shows the model behaves chaotically, implying there possibly exists chaotic characteristics in the process of coal rock fracturing.6. The acoustic emission time series obtained from conventional triaxial testing on sandstone at different confining pressures was analyzed by use of nonlinear time series techniques including the phase space reconstruction, the correlation dimension analysis and the evaluation of the largest Lyapunov exponent. The analysis concludes that the acoustic emission time series is a chaotic one, and the smallest dimensions of the embedding spaces is 16, indicating the instability process of rocks could be a complex nonlinear dynamical system.7. On the basis of the previous analyses of CT evolution model for coal rock and acoustic emission time series of sandstone in connection with damage mechanics and dissipation structure theories, a new definition on damage of rocks is first presented, which is called chaotic damage, and it is thought that damages in rocks during loading may develop in a chaotic way.8. The single state variable model, two state variables model, corresponding to a single degree of freedom elastic system, and the two degrees of freedom elastic system are introduced to model the rockbursts occurring frequently at many deep coal mines based on the investigation into the conditions triggering rockbursts. The models'dynamical behaviors and their applicability are discussed in detail.