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The unstable dynamic propagation of multistage hydrofracturing fractures leads to uneven development of the fracture network and research on the mechanism controlling this phenomenon indicates that the stress shadow effects around the fractures are the main mechanism causing this behaviour. Further studies and simulations of the stress shadow effects are necessary to understand the controlling mechanism and evaluate the fracturing effect.

In the process of stress-dependent unstable dynamic propagation of fractures, there are both continuous stress fields and discontinuous fractures; therefore, in order to study the stress-dependent unstable dynamic propagation of multistage fracture networks, a series of continuum-discontinuum numerical methods and models are reviewed, including the well-developed extended finite element method, displacement discontinuity method, boundary element method and finite element-discrete element method.

The superposition of the surrounding stress field during fracture propagation causes different degrees of stress shadow effects between fractures and the main controlling factors of stress shadow effects are fracture initiation sequence, perforation cluster spacing and well spacing. The perforation cluster spacing varies with the initiation sequence, resulting in different stress shadow effects between fractures; for example, the smaller the perforation cluster spacing and well spacing are, the stronger the stress shadow effects are and the more seriously the fracture propagation inhibition arises. Moreover, as the spacing of perforation clusters and well spacing increases, the stress shadow effects decrease and the fracture propagation follows an almost straight pattern. In addition, the computed results of the dynamic distribution of stress-dependent unstable dynamic propagation of fractures under different stress fields are summarised.

A state-of-art review of stress shadow effects and continuum-discontinuum methods for stress-dependent unstable dynamic propagation of multiple hydraulic fractures are well summarized and analysed. This paper can provide a reference for those engaged in the research of unstable dynamic propagation of multiple hydraulic structures and have a comprehensive grasp of the research in this field.

The purpose of this paper is to introduce the numerical methods in tunnel engineering and their capabilities to indicate the fracture and failure in all kinds of tunneling methods such as New Austrian Tunneling Method, tunnel boring machine and cut‐cover. An essential definition of numerical modeling of tunnels to determine the interaction between geo‐material (soil and rock) surrounding the tunnel structure is discussed.

Tunnel geo‐material (soil and rock) interaction requires advanced constitutive models for the numerical simulation of linear, nonlinear, time‐dependent, anisotropic, isotropic, homogenous and nonhomogeneous behaviors. The numerical models discussed in this paper are developed in finite element method (FEM), finite deference method (FDM), boundary element method and discrete element method and these tools are used to illustrate the behavior of tunnel structure deformation under different loads and in complicated conditions. The disadvantage of this method is the tunnel lining assumed an independent structure under fixed load which is unable to model soil‐lining interaction. Predicting the effect of all natural factors on tunnels is the most difficult method. The above‐mentioned numerical methods are very simple and quick to use and the results are conservative and practical for users. One of the most significant advantages of the numerical method is in predicting the critical area surrounding the tunnel and the tunnel structure before making the tunnel construction due to different loads.

Numerical modeling is used as control method in reducing the risk of tunnel construction failures. Since some factors such as settlement and deformation are not completely predictable in rock and soil surrounding the tunnel, using numerical modeling is a very economical and capable method in predicting the behavior of tunnel structures in various complicated conditions of loading. Another benefit of using numerical simulation is in the colorful illustrations predicting the tunnel behavior before, during and after construction and operation.

There are not many conducted studies using numerical models to tunnel structures that estimate the critical zones. As some of the methods available have limitation in simulating and modeling the whole tunnel design factors, numerical modeling seems to be the best option, because it is fast, economical, accurate and more interesting in predicating critical zones in tunnel. However, what softwares predict are not always the same as real ground nature conditions in which there is tunnel.

This paper discusses the issues involved in the development of combined finite/discrete element methods; both from a fundamental theoretical viewpoint and some related algorithmic considerations essential for the efficient numerical solution of large scale industrial problems. The finite element representation of the solid region is combined with progressive fracturing, which leads to the formation of discrete elements, which may be composed of one or more deformable finite elements. The applicability of the approach is demonstrated by the solution of a range of examples relevant to various industrial sections.

This paper outlines a dynamic domain decomposition‐based parallel strategy for combined finite/discrete element analysis of multi‐fracturing solids and discrete systems. Attention is focused on the parallelised interaction detection between discrete objects. Two graph representation models for discrete objects in contact are proposed which lay the foundation of the current development. In addition, a load imbalance detection and re‐balancing scheme is also suggested to enhance the parallel performance. Finally, numerical examples are provided to illustrate the parallel performance achieved with the current implementation.

This paper aims to propose a shape factor for granular materials based on particle shape. The scientific goal is to investigate the influence of particle shape on the mechanical properties of rockfill materials.

The method of generating four regular-shaped particles is based on the observation that most rockfill grains are regarded as like-triangle, like-rhombus, like-square and like-hexagon. A shape factor F that is developed using the Blaschke coefficient and a concave–convex degree is proposed. A biaxial compression test on rockfill materials under stress path is numerically simulated by discrete element method. The evolution of the shape factor F under the simulated stress paths is analyzed, and particle breakage rate, peak intensity and peak-related internal friction angle for rockfill materials are derived. A method of determining the shape factor F involved in the two functions is proposed.

A new micro-parameter is calibrated using the test data of one rockfill material. Particle shape greatly affects the particle breakage rate, peak intensity and peak-related internal friction angle for rockfill materials. The final experimental grading curves all approach the particle breakage grading curve proposed by Einav (the fractal dimension is 2.7).

This study proposes a shape factor F, which describes the geometric features of natural rockfill particles. The proposed shape factor F has a simple structure, and its parameters are easy to determine. The method provides an opportunity for a quantitative study on the particle shape of granular materials, and this study helps to better understand the influence of particle shape on the mechanical characteristics of rockfill materials.

A generalized weighted residual method is used to formulate the discrete element method (DEM) for rigid or deformable bodies. It is shown that this approach provides a unified methodology for deriving many of the different discrete element techniques in current use today. This procedure is used to develop a number of different element formulations for use in problems in which the distinct bodies exhibit complex deformation behaviour such as beam or plate flexure, membrane action, and additional reinforcement of a jointed discontinuum. A covergence proof for the two‐dimensional beam element is given for mathematical validation. A number of examples are also presented which illustrate the usefulness of different discrete element types in engineering analyses of discontinuum problems.

We present the preliminary results from a parameter study investigating the stability of underground structures in response to explosion‐induced strong ground motions. In practice, even the most sophisticated site characterization may lack key details regarding precise joint properties and orientations within the rock mass. Thus, in order to place bounds upon the predicted behavior of a given facility, an extensive series of simulations representing different realizations may be required. The influence of both construction parameters (reinforcement, rock bolts, liners) and geological parameters (joint stiffness, joint spacing and orientation, and tunnel diameter to block size ratio) must be considered. We discuss the distinct element method (DEM) with particular emphasis on techniques for achieving improved computational efficiency, including the handling of contact detection and approaches to parallelization. We introduce a new approach for simulating deformation of the discrete blocks using the theory of a Cosserat point, which does not require internal discretization of the blocks. We also outline the continuum techniques we employ to obtain boundary conditions for the distinct element simulations. We present results from simulations of dynamic loading of several generic subterranean facilities in hard rock, demonstrating the suitability of the DEM for this application. These results demonstrate the significant role that joint geometry plays in determining the response of a given facility.

Continua and discontinua coexist in natural rock materials. This paper aims to present an improved approach for addressing the mechanical response of rock masses based on the combined finite-discrete element method (FDEM) proposed by Munjiza.

Several algorithms have been programmed in the new approach. The algorithms include (1) a simpler and more efficient algorithm to calculate the contact force; (2) An algorithm for tangential contact force closer to the actual physical process; (3) a plastic yielding criterion (e.g. Mohr-Coulomb) to modify the elastic stress for fitting the mechanical behavior of elastoplastic materials; and (4) a complete code for the mechanical calculation to be implemented in Matrix Laboratory (MATLAB).

Three case studies, including two standard laboratory experiments (uniaxial compression and Brazilian split test) and one engineering-scale anti-dip slop model, are presented to illustrate the feasibility of the Y-Mat code and its ability to deal with multi-scale rock mechanics problems. The results, including the progressive failure process, failure mode and trajectory of each case, are acceptable compared to other corresponding studies. It is shown that, the code is capable of modeling geotechnical and geological engineering problems.

This article gives an improved FDEM-based numerical calculation code. And, feasibility of the code is verified through three cases. It can effectively solve the geotechnical and geological engineering problems.

The purpose of this paper is to propose a novel combined finite-discrete element method (FDEM), based on the cohesive zone model, for simulating rockslide problems at the laboratory scale.

The combined FDEM is realized using ABAQUS/Explicit. The rock mass is represented as a collection of elastic bulk elements glued by cohesive elements with zero thickness. To reproduce the tensile and shear micro-fractures in rock material, the Mohr-Coulomb model with tension cut-off is employed as the damage initiation criterion of cohesive elements. Three simulated laboratory tests are considered to verify the capability of combined FDEM in reproducing the mechanical behavior of rock masses. Three slope models with different joint inclinations are taken to illustrate the application of the combined FDEM to rockslide simulation.

The results show that the joint inclination is an important factor for inducing the progressive failure behavior. With a low joint inclination, the slope failure process is observed to be a collapse mode. As the joint inclination becomes higher, the failure mode changes to sliding and the steady time of rock blocks is shortened. Moreover, the runout distance and post-failure slope angle decrease as the joint inclination increases.

These studies indicate that the combined FDEM performed within ABAQUS can simulate slope stability problems for research purposes and is useful for studying the slope failure mechanism comprehensively.

The purpose of this paper is to model the strain localization in J₂ materials with damage evolution using embedded strong discontinuity modes.

In this procedure, an heuristic bandwidth scale is adopted to model the damage evolution in the shear bands. The bifurcation triggering conditions and band growth directions are studied for these materials.

The resulting formulation does not require a specific mesh refinement to model a localization, provides mesh independent results also insensitive to element distortions and allows calibration of the model response using experimental data. The formulation capability is shown embedding the strong discontinuity modes into quadrilateral and higher order elements.

The work described in this paper extends the use of strong discontinuity modes to materials with damage evolution.