Bifurcation Analysis Of Rock Under Different Loading Conditions

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 tests, the formation and orientation of a localization band in the sandstone, were studied using discontinuous bifurcation 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 show 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 of the triaxial tests have been undertaken to investigate the stress-dependent elasticity of sandstone. The analysis of experimental results shows that the elasticity of sandstone is not only stress sensitive but also coupled to the plasticity, manifesting strong nonlinearity.3. All sandstone 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 show that the orientations are decreasing with increasing confining pressures under conventional triaxial compression, while the orientations of specimens subjected to plain strain conditions seems unaffected by varying confining pressures.4. The initiation 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 inclination of the shear band and the bifurcation point 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 happen within the strain hardening region, i.e. prior to the peak stress.