| There are many geotechnical engineering problems involved in the practice of civil construction, water conservancy and hydroelectric structures, railway and highway project, mine exploitation, cultural relic protection, geological hazard prevention, energy exploiture and national defence works etc, especially the problems for the stability, strength and deformation of the rock mass. And the rock mass as the main object of most engineering practice is developed by all kinds of geotechnical action and force in the long geology history to the complex characteristic of continuous medium, crannied medium and granular medium, to the anisotropic and heterogeneous entity with elasticity, plasticity, viscidity, creepocity and rheology. At the meantime, the rock mass may alternate between loading and unloading and it exists in certain kind of liquid, such as surface water, unconfined water, confined water etc for its intrinsic crannies. The practical rock mass concerned project must solve the key stability problem after the understanding of the complicated mechanical characteristic and the deformation trends to guide the following project design and construction for the demand of security, economy, feasibility and validity. However, the intrinsic nonlinearness and complexity of the engineering rock mass become the main difficulty to predict the stability and deformation, the corresponding structure design must ensure enough safety with all the determinate or random force combination, so a model without the geometry distortion and constitutive equation warp is necessary to be built for the quantificational analysis of practical structure's stress, for the simulation of the real process and for the determinate evaluation system and optimization. It is also indispensable to direct the design, construction, operation, maintenance and management of specific rock mass concerned project. Discontinuities of rock mass are the primary challenge for theoretically analysis and numerical model based on the traditional continuous medium mechanics theory, and sharply increase the cost, extend the period of the physical modeling. And the geotechnical engineering concerned problems are typical data limited and understanding limited issues. All available theoretically analysis methods, simple or complex, qualitative assessment and prediction by experience, physical modeling and numerical modeling can not solve these problems solely. However, numerical modeling can make use of the result of physical modeling and theoretically analysis and its result can be compared with the practical monitoring data to verify the validity of theoretically analysis and it may decrease the cost of physical modeling. The most advantage of numerical modeling is its wide solution scope and its repetition. So the study on the numerical manifold method for geotechnical engineering problem is an important subject of academic and applied value for practical projects.Numerical Manifold Method (NMM) is a thorough new numerical modeling method for geotechnical engineering in past decade. Manifold, as the main theme of differential geometry and analysissitus, has a basic structure composed of finite cover system and contact functions betweencovers, which could be overlapped or even folded. There are two type meshes, mathematic mesh and physical mesh for the general definition of manifold. Mathematic mesh is composed of folded covers and could be random set by final user, and physical mesh is composed of real material boundary, joints or discontinuities, phase interfaces etc and couldn't be artifical. Traditional finite element method's mesh can be used as the mathematic mesh for the NMM. And NMM is a promising numerical method to solve both the continuous and discontinuous deformation problem of rock mass and to unify the finite element method(FEM),discontinuous deformation analysis(DDA) and analytic method.This paper will focus on the generation of finite cover system for the numerical manifold method, distance and angle criteria for contact jud...
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