Guoyang Fu

A COMPARISON BETWEEN THE NMM AND THE XFEM IN DISCONTINUITY MODELING

Discontinuities such as voids, cracks, material interfaces, and joints widely exist in nature. Conventional finite element method (FEM) requires the finite element mesh to coincide with the discontinuities, which often complicates the meshing task. When evolution of discontinuities are necessary, remeshing is inevitable, which makes the simulation tedious and time-consuming. In order to overcome such inconveniences, the extended finite element method (XFEM) and the generalized finite element method (GFEM) were developed by incorporating special functions into the standard finite element approximation space based on partition of unity. The finite element mesh is allowed to be totally independent of the discontinuities and remeshing is totally avoided for discontinuity evolution. The numerical manifold method (NMM) can also be viewed as an extension or generalization to the conventional FEM. Different from the XFEM/GFEM, the approximation in the NMM is based on covers. The NMM models discontinuities by its dual cover system. In this paper, a detailed comparison between the NMM and the XFEM in discontinuity modeling is presented. Their advantages and disadvantages are pointed out. How the dual cover system in the NMM favors the complex crack modeling is emphasized. Potential extensions to the XFEM and the NMM are suggested.

3D ROCK MASS GEOMETRICAL MODELING WITH ARBITRARY DISCONTINUITIES

This paper describes an algorithm to generate the realistic numerical representation of three-dimensional rock masses. The discontinuities can be treated as infinite or finite planes with or without thickness. A finite plane is represented by a polygon and defined using centroid of the polygon, orientation, geometry in 2D plane, the angle between strike line and reference line and other properties including cohesion, friction angle, tensile strength and aperture. Through 3D discontinuity network simulation, the information of discontinuities is obtained as the input data for block generation. The block generation process includes boundary planes cutting, discontinuities cutting and block integration. The results are also verified by graphical check, topological and geometrical properties of a polyhedron. The algorithm we adopt is convenient to be developed into a computer program. The generated model, in which the blocks and loops of blocks could be convex or concave, can be used for single block stabilit...

Efficiency and Accuracy Verification of the Explicit Numerical Manifold Method for Dynamic Problems

The original numerical manifold method (NMM) employs an implicit time integration scheme to achieve higher computational accuracy, but its efficiency is relatively low, especially when the open–close iterations of contact are involved. To improve its computational efficiency, a modified version of the NMM based on an explicit time integration algorithm is proposed in this study. The lumped mass matrix, internal force and damping vectors are derived for the proposed explicit scheme. A calibration study on P-wave propagation along a rock bar is conducted to investigate the efficiency and accuracy of the developed explicit numerical manifold method (ENMM) for wave propagation problems. Various considerations in the numerical simulations are discussed, and parametric studies are carried out to obtain an insight into the influencing factors on the efficiency and accuracy of wave propagation. To further verify the capability of the proposed ENMM, dynamic stability assessment for a fractured rock slope under seismic effect is analysed. It is shown that, compared to the original NMM, the computational efficiency of the proposed ENMM can be significantly improved.

Coupled Time Domain Integration Algorithm for Numerical Manifold Method

AbstractA temporal coupled explicit–implicit time integration algorithm is proposed to improve the computational efficiency of the numerical manifold method (NMM) for seismic stability analysis of rock slope. It includes a coupled time integration scheme, a phase transfer criterion, and an associated contact algorithm. To calibrate the proposed algorithm, a block sliding along a slope under seismic excitation and a block rocking under half-sine pulse shaking are simulated. The traditional limit equilibrium method (LEM) for slope stability analysis determines the factor of safety (FoS) without considering the time-dependent effect. The developed algorithm is able to simulate jointed rock slope seismic stability taking advantage of the NMM for continuous and discontinuous deformation analysis. An open-pit mine slope excited by the El Centro earthquake wave is studied. The simulated results are in good agreement with the results based on the traditional NMM, whereas the computational efficiency is improved s...

A Copula-Based Method for Estimating Shear Strength Parameters of Rock Mass

The shear strength parameters (i.e., the internal friction coefficient and cohesion ) are very important in rock engineering, especially for the stability analysis and reinforcement design of slopes and underground caverns. In this paper, a probabilistic method, Copula-based method, is proposed for estimating the shear strength parameters of rock mass. The optimal Copula functions between rock mass quality and , and for the marbles are established based on the correlation analyses of the results of 12 sets of in situ tests in the exploration adits of Jinping I-Stage Hydropower Station. Although the Copula functions are derived from the in situ tests for the marbles, they can be extended to be applied to other types of rock mass with similar geological and mechanical properties. For another 9 sets of in situ tests as an extensional application, by comparison with the results from Hoek-Brown criterion, the estimated values of and from the Copula-based method achieve better accuracy. Therefore, the proposed Copula-based method is an effective tool in estimating rock strength parameters.

A rational and realistic rock mass modelling strategy for the stability analysis of blocky rock mass

Due to the importance of a realistic rock mass model for the achievement of accurate and reliable results from numerical analysis of blocky rock mass, a probability based rock mass geometrical model is proposed in the present study. The rock mass geometry is built based on site investigation data and stochastic analysis of the discontinuity mapping results. The discontinuities and/or sets of them, either finite or infinite in size, planar or non-planar, convex or concave in shape, can be implemented in the three-dimensional rock mass model. Key block analysis and support design are then suggested to the stochastic rock mass models. To achieve a realistic stability analysis of the rock mass with the proposed probabilistic rock mass model, a few suggestions have also been made. These include the adoption of realistic constitutive models to intact rock and rock discontinuities, use of numerical model to technically handle numerical difficulties and development of a realistic modelling strategy to achieve realistic and affordable computational cost, etc.