Homogenization Numerical Analysis And Applications In Layered Rock Masses Based On Cosserat Medium Theory

Layered rock masses are very common in pratical engineering, which are often computated and analyzed by the explicit joint element or the anisotropy equivalent model based on the classical continua medium mechanics. The traditional continua medium theory FEM can't provide satisfying interpretation on sliding, bending, buckling, flexural toppling failure phenomena, especially in case of the sharp stress gradients. The paper aims at analyze the bending mechanical properties of the layer rock masses, which combining the Cosserat medium theory into the asymptotic homogenization method, and solve the engineering practical problem in geotechnical engineering, mining engineering and correlative engineering aspects. The research results have no doubt the great theoretical significance, to improve the accuracy and credibility for the engineering application analysis also has the guiding sense.The innovative research results in the paper are as follows:1,A new Cosserat medium equivalent model was established in the paper, which connected the Cosserat medium theory with the homogenization method. At first, the layered rock mass was regarded as a composite with representative element volume (unit cell) periodic repetition rank. The representative element volume contained the rock layers and the joints,two or more different physical and mechanical characteristics the rock layers, which considering the rock material itself resist-bend ability. Satisfied with the periodic boundary conditions of unit cell,micro-displacement of all nodes can be obtained by micro homogenization analyzed at first, then a Cosserat medium equivalent model can be got by solving the macro elastic module formula educed from the homogenization process.2,Based on the conventional medium homogenized, the new displacement function applying to the Cosserat medium is constructed. Then Young's modulus of the macro - formula can be solved from the corresponding generalized stress and strain elationships, such as the normal stress, the shear stress, couple stress and the corresponding normal strain, the shear strain and the curvature. For the formula including the relationship between the couple stress and the curvature, so it can be reflected the bending properties of the Cosserat medium materials.3,The main functions program of Cosserat medium used in the homogenization methods were workouted in the MATLAB platform with help of the macro elastic modulus formula. Then the results were compared between the Cosserat medium equivalent model and the numerical method computated by the software FLAC showing the validity of the program.4,To study the surrounding rock displacement and couple-stress, such as bending deformation impacted by the rock layers thickness, dip, ground stress and the cavern height and other factors in the different-shaped caverns in the layered rock masses for the finite element method numerical simulation. In addition, a large hydroelectric dam on the intake to high slope on the left bank and the slope on the right bank were a natural tendency to state the numerical simulation to study the layered rock slope with lower angle and the layered rock slope with steep dip performanced different characteristics of bending deformation and failure.According to the numerical analysis, either in case of the layer thickness is very small (high strain gradient) produced or two or more interbedding layered rock masses, the new Cosserat models can reflect the bending characteristics of the layered rock masses. The results were compared between the Cosserat medium equivalent model and the conventional continuum model showing the feasibility and validity of the new method.