Research On The Fundamentals Of Stability And Control Of Non-equilibrium Evolution Of Rock Mass Structures

Natural rocks cut by joints and fissures form rock masses, which further constructlarge-scale rock engineering structures. Due to the rapid growth of the scale andcomplexity of rock engineering in China, the stability of rock engineering structures ispotentially threatened. In this paper, the stability and control of rock mass structures arestudied from the perspective of non-equilibrium evolution. An integrated researchframework is proposed, whose mathematical and mechanical fundamentals are focusedin this paper. The major achievements are listed as below:(1) Non-equilibrium thermodynamics: It is proved that the degrees of a set ofhomogeneous Onsager fluxes must be identical and thus the Rice’s normalitystructure based on homogeneous Onsager fluxes is equivalent to Ziegler’sprinciple of maximum rate of dissipation. Such conclusion means that thethermodynamic basis for the constitutive relations of geomaterials must beestablished in the range of rotational thermodynamic fluxes.(2) Orientation distribution function (ODF) and fabric tensor: The mostgeneralized type of ODF is proposed as the tensor-valued ODFs. Integrated fabrictensor algebra for tensor-valued ODFs is established, including the analytical solutionsfor asymmetric and symmetric fabric tensors of any orders, the convergence andaccuracy analysis for the fabric tensor expansion and the relationship between fabrictensors of different orders.(3) The Kachanov-Rabotnov (K-R) damage effective stress: Amicroplane-based model for3D anisotropic K-R damage effective stress isproposed based on vector-valued ODFs, which fulfills rigorous geometryequivalence between the micro and macro scopes. The model clarifies some basic issuesin continuum damage mechanics such as the applicability of some frequently usedanisotropic and isotropic effective stress models and the positive definiteness and Voigtsymmetry of the damage effect tensor.(4) Generalized Hamilton’s principle: A generalized Hamilton’s principlefor dissipative material bodies is established in thermodynamics with internalvariables. Compared with the classical Hamilton’s principle for elastic bodies, the generalized form has the elastic strain energy replaced by the summation ofthe specific internal energy and the inelastic dissipation work. The generalizedHamilton’s principle is the continuum mechanical basis for the followingLyapunov theory for stability and control.(5) The Lyapunov theory for stability and control of Rice inelastic bodies:Based on the Lyapunov’s second method for stability, the principle of minimumflow potential for perfect Rice inelastic bodies is proved, which is thenincorporated with damage effects to reveal the non-equilibrium evolution lawsof continuum structures. Effective methods for stability evaluation and controlare proposed based on the evolution laws. The theoretical bases are clarified forsome important practical principles in geotechnical engineering such as the NewAustrian Tunneling Method and the Pan’s principles of soil and rock stability.(6) The deformation reinforcement theory: Based on the Lyapunov theoryestablished above, the deformation reinforcement theory is proved as a specialcase, through which the Lyapunov theory is applied to stability evaluation andreinforcement design for engineering structures. Combined with numericalexamples using finite element method, some fatal issues in geotechnicalengineering is preliminarily studied, such as global structural stability, effectand efficiency of reinforcement measures, monitoring and forecasting forlong-term stability of engineering structures.