A continuous-discontinuous cellular automaton method for cracks growth and coalescence in brittle material

A method of continuous-discontinuous cellular automaton for modeling the growth and coalescence of multiple cracks in brittle material is presented. The method uses the level set to track arbitrary discontinuities, and calculation grids are independent of the discontinuities and no remeshing are required with the crack growing. Based on Grif- fith fracture theory and Mohr-Coulumb criterion, a mixed fracture criterion for multiple cracks growth in brittle mate- rial is proposed. The method treats the junction and coales- cence of multiple cracks, and junction criterion and coales- cence criterion for brittle material are given, too. Besides, in order to overcome the tracking error in the level set ap- proximation for crack junction and coalescence, a dichotomy searching algorithm is proposed. Introduced the above the- ories into continuous-discontinuous cellular automaton, the present method can be applied to solving multiple crack growth in brittle material, and only cell stiffness is needed and no assembled global stiffness is needed. Some numerical examples are given to shown that the present method is efficient and accurate for crack junction, coalescence and percolation problems.

UNCERTAINTY ANALYSIS OF ROCK FAILURE BEHAVIOUR USING AN INTEGRATION OF THE PROBABILISTIC COLLOCATION METHOD AND ELASTO-PLASTIC CELLULAR AUTOMATON

The Karhunen-Loeve （KL） expansion and probabilistic collocation method （PCM） are combined and applied to an uncertainty analysis of rock failure behavior by integrating a self- developed numerical method （i.e., the elastic-plastic cellular automaton （EPCA））. The results from the method developed are compared using the Monte Carlo Simulation （MCS） method. It is concluded that the method developed requires fewer collocations than MCS method to obtain very high accuracy and greatly reduces the computational cost. Based on the method, the elasto- plastic and elasto-brittle-plastic analyses of rocks under mechanical loadings are conducted to study the uncertainty in heterogeneous rock failure behaviour.

DEVELOPMENT AND APPLICATIONS OF THE ELASTO-PLASTIC CELLULAR AUTOMATON

The paper presents the advancement and applications of the elasto-plastic cellular automaton （EPCA）, a simulator for rock mechanics and rock engineering. The most significant feature of EPCA lies in its ＇down-top＇ way of dealing with nonlinear behaviors of rocks. The theory, the basic idea and associated developments, including the definition of cellular automaton, the heterogeneous material model, constitutive relations, failure criteria, the post-yield softening scheme, the thermo-hydro-mechanical coupling process, are described. The applications are presented to show the ability of EPCA to model the rock failure process, fluid flow, heat transfer, and the coupled thermo-hydro-mechanical （THM） process etc.

Numerical study on coupled thermo-mechanical processes in sp Pillar Stability Experiment

This paper presents a study of the full three-dimensional thermo-mechanical （TM） behavior of rock pillar in,Aspo Pillar Stability Experiment （APSE） using a self-developed numerical code TM-EPCA3D. The transient thermal conduction function was descritized on space and time scales, and was solved by using cellular automaton （CA） method on space scale and finite difference method on time scale, respectively. The advantage of this approach is that no global, but local matrix is used so that it avoids the need to develop and solve large-scale linear equations and the complexity therein. A thermal conductivity versus stress function was proposed to reflect the effect of stress on thermal field. The temperature evolution and induced thermal stress in the pillar part during the heating and cooling processes were well simulated by the developed code. The factors that affect the modeling results were discussed. It is concluded that, the complex TM behavior of Aspo rock pillar is significantly influenced by the complex boundary and initial conditions.