International Journal of Computational Methods

This study assessed the relevance of numerical modeling with respect to the mechanical properties of specific rock and investigated the applicability of submarine landslide simulation using discontinuous deformation analysis (DDA). To predict the dynamic behavior of submarine landslides, we developed a way to model a jointed rock mass for the evaluation of rock slope instability and an original DDA approach using an energy loss model that incorporates energy loss caused by collision between blocks and seawater resistance as a viscous force. We applied the developed model to estimate the dynamic behavior of actual submarine landslides. The simulations assessed seawater resistance and energy loss due to collision between blocks, reproducing past events and suggesting the behavior of vulnerable slopes. The results demonstrate that the model can clarify the energy loss caused by slope absorbability and seawater resistance, and that the improved DDA is very useful for submarine land analysis.

The speed and stability of three-dimensional (3D) discontinuous deformation analysis (DDA) are strongly dependent on the efficiency and correctness of contact detection and the definition algorithm, which affects the simultaneous equilibrium equations solved in every open–close iteration (OCI) retry. In particular, the definition of vertex-to-vertex contacts in a tangled zone may abruptly change the entrance planes, even in the case of very small displacement of the objects. This study proposes a new contact-definition algorithm using an inscribed sphere virtually installed in every contacting vertex. The suggested algorithm generates virtual entrance planes in the case of a vertex-to-vertex contact, and controls the accuracy of the contact definition process by adjusting the sphere size. Verification tests of the proposed algorithm indicate an increase in the efficiency and stability of 3D DDA.

In the conventional discontinuous deformation analysis (DDA) method, the contact conditions are enforced by the penalty function method. Improperly selected penalty parameters might cause numerical problems. In order to evade the introduction of the penalty parameters and to avoid "open–close iteration" that can not assure convergence, this study reformulates the DDA as a variational inequality problem. Based on the fact that the solution of a variational inequality is a fixed point of a natural projection map, the problem is reduced to the solution of nonsmooth equations with weak nonlinearity. Then, the Path Newton Method (PNM) is utilized to solve the equations. Some practical examples originally designed by Shi are reanalyzed, which demonstrates that the new DDA method is feasible.

The meshless methods are particularly suitable for modeling problems with discontinuities such as joints in rock mass. The meshless Shepard and least squares (MSLS) method is a newly developed meshless method, which overcomes some limitations with other meshless methods. In the present paper, the MSLS method is extended for modeling jointed rock mass and the joint is modeled as discontinuity governing the near-field stress. A substantial high rock slope by the dam shoulder of Jinping Hydropower Station is analyzed by the developed method. Safety factors are evaluated based on the stress results along potential slip surfaces and compared with the conventional slice methods. The results demonstrate the feasibility of using the MSLS method in rock slope stability analysis and also reveal some interesting differences from the conventional slice methods. Some findings and outstanding issues demonstrated in this study are discussed in the end, which can be the topics for future development.

Wenchuan earthquake, Ms 8.0 in magnitude and occurred on May 12, 2008 in Sichuan Province, China, triggered a lot of landslides, rock collapses, debris flow, etc. The Tangjiashan landslide, with its total volume 20.37 million m³, was the biggest and the most notable one for its effects. Based on the field geological investigation and the typical acceleration records of the main shock obtained in the period of the earthquake, numerical simulation of the whole sliding process of Tangjiashan landslide has been carried out by DDA method. It is shown that the Tangjiashan landslide was a high-speed landslide, behaved with nonlinear features in the whole sliding process. The total duration of the landslide was about 30 s while nearly all of their slipping displacements were carried out in the beginning 25 s, with the maximum sliding velocity about 30 m/s, and the average 15–17 m/s in the beginning 25 s. The crash of rock blocks induced a much higher stresses near the middle and lower parts of the landslide, with the maximum value of 6–7 MPa. The dynamic earthquake load caused an incessant deformation of the landslide, resulting in the reduction of mechanical parameters, especially the shear strength on the sliding surface and the ratio of friction coefficient on sliding surface in kinematical and static conditions are no more than 0.35. DDA simulation considering the displacement-based parameter reduction has been developed in the original DDA code, and its results primarily reflect the evolvement process of a landslide under strong seismic loads.

In this paper, the stability including stress distribution of two ancient masonry structures, the pyramid of the Pharaoh Khufu, Egypt and the Pont of Gard, were analyzed using discontinuous deformation analysis (DDA) and numerical manifold method (NMM). For the simulation using NMM, the newly developed four-node isoparametric element was used. The stress distributions/concentration were calculated and compared between the two methods. The calculated results show qualitative agreement with observations. DDA and NMM are applicable to simulate the physical phenomena of masonry structures.

Drill and blast method has been widely used as an effective excavation method for underground rock caverns or tunnels. To achieve a good blast design, an understanding on the rock dynamic response and rock fragmentation process is important. In this paper, numerical simulations are performed on a typical parallel hole cut blasting based on the discontinuous deformation analysis (DDA). The blast loading is obtained from the explicit FEM code LS-DYNA and the dynamic response of the rock mass is modeled by the DDA. Different influence factors on rock fragmentation under the blast loading are investigated, including the different delay time and various rock mass properties. Such a study will have potential applications for better drill and blast designs.

In deep mines, the way of excavation, depositing packs, and the mechanical properties as well as the velocity of mining belong to the most decisive phenomena for the threat of bumps. In this paper, time-dependent hereditary creep problem in terms of free hexagon distinct element method (DEM) is formulated and solved for assessment of bumps occurrence in deep mines. The time factor as an impact of the velocity of mining is involved here in a natural way in the model of discrete elements. Inside of these elements, the material behavior is described by the boundary element method. Mutual coupling of the velocity and the way of deposition of packs can principally influence the safety against bumps. For the correct understanding, the behavior of the rock aggregate (coal seam and the overburden) and the nucleation of cracks finally leading to the bumps have to be treated as time depended and creep and viscoplasticity in the overburden should be considered. In the coal seam, brittle material is adopted. According to the new experiments on scale models and results from accessible literature those effects will be involved into the formulations.

An overview of modeling arbitrary discontinuities within the numerical manifold method (NMM) framework is presented. The NMM employs a dual cover system, namely mathematical covers (MCs) and physical covers (PCs), to describe a physical problem. MCs are constructed totally independent of geometries of the problem domain, over which a partition of unity is defined. PCs are the intersections of MCs and the problem domain, over which local approximations with unknowns to be determined are defined. With such a dual cover system, arbitrary discontinuities involving jumps, kinks, singularities, and other nonsmooth features can be modeled in a convenient manner by constructing special PCs and designing tailored local approximations. Several typical discontinuities in solid mechanics are discussed. Among them are the simulations of material boundaries, voids, brittle cracks, cohesive cracks, material interfaces, interface cracks, dislocations, shear bands, high gradient zones, etc.