A 2-D meshless model for jointed rock structures

Abstract

SUMMARYAccording to the characteristic structural features of jointed rock structures, a meshless model is proposed for the mechanics analysis of jointed rock structures based on the moving least-squares interpolants. In this model, a jointed rock structure is regarded as a system of relatively intact rock blocks connected by joints or planes of discontinuity; these rock blocks are modelled by general shaped anisotropic blocks while these joints and planes of discontinuity are modelled by interfaces. The displacement ÿeld of each block is constructed by the moving least-squares interpolants with an array of points distributed in the block. To deal with the discontinuities of rock structures, the displacement ÿelds are constructed to be discontinuous between blocks. The displacement ÿelds and their gradients are continuous in each block, hence no post processing is required for the output of strains and stresses. The ÿnite element mesh is totally unnecessary, so the time-consuming mesh generation is avoided. The rate of convergence can exceed that of ÿnite elements signiÿcantly, and a high resolution of localized steep gradients can be achieved. Furthermore, the discontinuities of rock structures are also fully taken into consideration. The present method is developed for two-dimensional linear elastic analysis of jointed rock structures, and can be extended to three-dimensional and non-linear analysis.

A moving Kriging interpolation-based meshfree method for free vibration analysis of Kirchhoff plates

“…Because of this inequality, the enforcement of the essential boundary conditions is quite awkward and not treated as straightforward as in the FEM. Thus, many efforts have been devoted to the subject and various special techniques have been proposed to overcome this difficulty in several ways such as direct collocation methods [14,15], Lagrange multipliers [3,16], penalty methods [17][18][19], modified variational principles [14,20], coupling with the traditional FEM [21][22][23][24][25][26], d'Alembert's principle [27], discrete form of essential boundary conditions [28], transformation method [29,30], displacement constraint equations method (DCEM) [31], etc.…”

Overview of the numerical methods for the modelling of rock mechanics problems

“…Many meshless methods have been developed, but some of the mostly used ones are: Smoothed particle hydrodynamics [59], Diffuse element method [60], Element-free Galerkin method [61], Reproducing kernel particle methods [62], Moving least-squares reproducing kernel method [63], hp-cloud method [64], the method of finite spheres [65], Finite point method [66] etc. For the specific purpose in rock mechanics, where the treatment of the fractures is of essential influence, the meshless approach has significant potential which is shown by Zhang et al [67].…”

Modelling 3D jointed rock masses using a lattice spring model

“…Such modelling is directly related to the design and stability analysis of rock engineering structures that are built in or on jointed rock. Many numerical methods have been developed or further developed to address this problem, including the finite element method (FEM), [1] eXtended FEM (XFEM), [2] discrete element method (DEM), [3] discontinuous deformation analysis (DDA), [4] elementfree Galerkin method (EFG), [5] natural element method, [6] smoothed particle hydrodynamics (SPH), [7] and boundary element method (BEM) [8]. In fact, the numerical methods used in rock engineering have been categorised into continuum-based and discontinuum-based methods according to their ability to solve jointed rock mass problems.…”

“…[4] However, many studies have been also performed to enhance the ability of existing methods to model jointed rock masses as well (e.g., Refs. [1,2,[5][6][7][8]). …”