Kriging Interpolation Meshless Method Based On Finite Cover Technique And Its Application In Fracture Analyses Of Rock Mass

As a type of geomaterials naturally formed, rock mass is usually composed of manynatural joints and cracks or other types of intact discontinuities due to long-term deformationand damage. When loaded, cracks will be initiated and expand in the rock mass and the thenmechanical properties of rock mass will change. The actual deformation and failure process ofgeo-materials and geo-structures is a complex progressive evolution involving initially elasticdeformation, crack propagation, large-scale displacement and even movement of a discretesystem. The study on the crack expansion is very important for the evaluation of damage andstability of rock masses.At present, the main techniques applied to investigating rock mass problems areexperimental method and numerical analysis method. Through numerical analyses, a largenumber of usable data can be obtained. Howerer, restricting because of time and space, it isnot convenience to apply this method, and it needs much manpower and financial resources.Numerical analyses can analyze problems of rock mass quickly. In this paper, crack expansionof rock mass is analyzed and computed with Kriging interpolation meshless based on finitecovers technique.Discontinuous deformation calculating and numerical modelling of the process for rockdeforming and failure are blue topic in rock mass mechanics and engineering region. Byvirtue of the finite cover technique of manifold, manifold method integrates conventionalfinite element methods, discontinuous deformation analysis and analytical methods in a unitedmathematical framework and can deal with both continuous and discontinuous deformationproblems such as contact and multi-body interaction. Howerer, the action of dual-mesh inMM is both sides. On the one hand, it is the feature of MM, on the other hand, it bringstroubles in pre-process and difficulties in simulating crack growth. Meshless method based onmoving least square method is very effective in simulating crack propagation which is a keyissue in modeling failure or/and damage behavior of structures or materials without meshingas required in MM. The kernel of manifold method is finite cover technique while the mainfeature of meshless/mesh-free approximation is that only nodes are need in interpolation anddoes not need to join nodes into any element. Manifold method and meshless method haveown advantages in handling discontinuous deformation problems.To simulatet the discontinuous grwth in the fractured rockmass, Kriging interpolationmeshless method base on finite covers technique and Kriging interpolaton method is presented. The method can conquer the disadvantages of the remeshtechnique treating withthe discontinuous growth problems in the manifold method. The finite cover technology isapplied in the proposed method. And some difficulites in the meshless methods, such as thetrial function due to the discontinuity in the displacement, are avoided and nodal arrangementis morefree near the discontinuous. The Kriging interpolation meshless method is well suitedto problems involving crack propagation due to the absence of any predefined manifoldelement connectivity. The main purpose of the paper is to explore the possibility to work out anew numerical method by combining the finite-cover technique and meshless concepttogether. Presented method is a meshless method, which can treat with continuous anddiscontinuous problems in a uniform mathematic approach space.Rock mass is composed of rock piece and structure face, and its failure always begins atthe discontinuous surface, so the stability of rock mass depends on the characters of structuresurface in the rock. Fracture mechanics of rock mass explain the mechanical characteristicnby the theory of fracture mechanics, and the joint and slit in rock are simplified crack. Hence,rock mass is discontinuous and anisotropy. The crack initiation, propagation and cuttingthrough until the local failure of rock can be simulated by fracture mechanics of rock massand numerical method.The fundamental principle of static fracture mechanics is stated and stress intensityfactor (SIF) is calculated and the criterion of crack growth is presented. The method isnumerically implemented and numerical analyses for a number of benchmark problems aremade. The Kriging interpolation meshiess method is demonstrated comprehensively in thisthesis. Then, the possibilities of applying the Kriging interpolation meshless method tonumerical analyses of fracture behavior and crack expansion of rock masses are discussed.The treatments for the related special issues are given. The static fracture mechanics is usedfor analysis, in which the growth rule of crack is mainly taken into account by staticequilibrium condition: The simulated results by the proposed method have a good aggrementwith the test and other numerical method. Concrete is a kind of heterogeneous, anisotropic artificial composite material. Based onfracture mechanics and damage mechanics, and supposing that physics parameter of rock andconcrete complying Weibull distribution. Numerical simulation of crack propagation isimplemented under meshless frame for heterogeneous and discontinuous material, such asrock or concrete. By comparing with experimental results and other numerical results, theresults have a good agreement with known solution. A new approach for analyzing suchmaterial is offered in this thesis.The stress field in vicinity of Crack is singularity field. To capture the singularity of crackand make the crack problems can be simulated better, the base function is proper extendedwith special functions and enriched Kriging interpolation meshless method based on finitecover technique is proposed, the capability to solve discontinuous problem is enhanced andthe precision of exploring crack problem is increased. The validity and accuracy of this method are illustrated by numerical examples.In summary, a numerical method with a computer code based on the proposed methodand fracture theory is developed for assessing the fracture behavior and predicting initiation,development and arresting of crack in rock masses. Finally, a comprehensive summary isgiven and some issues for further studies are discussed.