Assessment of strain bursting in deep tunnelling by using the finite-discrete element method

Rockbursting in deep tunnelling is a complex phenomenon posing significant challenges both at the design and construction stages of an underground excavation within hard rock masses and under high in situ stresses. While local experience, field monitoring, and informed data-rich analysis are some of the tools commonly used to manage the hazards and the associated risks, advanced numerical techniques based on discontinuum modelling have also shown potential in assisting in the assessment of rockbursting. In this study, the hybrid finite-discrete element method(FDEM) is employed to investigate the failure and fracturing processes, and the mechanisms of energy storage and rapid release resulting in bursting, as well as to assess its utility as part of the design process of underground excavations.Following the calibration of the numerical model to simulate a deep excavation in a hard, massive rock mass, discrete fracture network(DFN) geometries are integrated into the model in order to examine the impact of rock structure on rockbursting under high in situ stresses. The obtained analysis results not only highlight the importance of explicitly simulating pre-existing joints within the model, as they affect the mobilised failure mechanisms and the intensity of strain bursting phenomena, but also show how the employed joint network geometry, the field stress conditions, and their interaction influence the extent and depth of the excavation induced damage. Furthermore, a rigorous analysis of the mass and velocity of the ejected rock blocks and comparison of the obtained data with well-established semi-empirical approaches demonstrate the potential of the method to provide realistic estimates of the kinetic energy released during bursting for determining the energy support demand.

Characterizing the influence of stress-induced microcracks on the laboratory strength and fracture development in brittle rocks using a finite-discrete element method-micro discrete fracture network FDEM-μDFN approach

Heterogeneity is an inherent component of rock and may be present in different forms including mineralheterogeneity, geometrical heterogeneity, weak grain boundaries and micro-defects. Microcracks areusually observed in crystalline rocks in two forms： natural and stress-induced; the amount of stressinducedmicrocracking increases with depth and in-situ stress. Laboratory results indicate that thephysical properties of rocks such as strength, deformability, P-wave velocity and permeability areinfluenced by increase in microcrack intensity. In this study, the finite-discrete element method （FDEM）is used to model microcrack heterogeneity by introducing into a model sample sets of microcracks usingthe proposed micro discrete fracture network （mDFN） approach. The characteristics of the microcracksrequired to create mDFN models are obtained through image analyses of thin sections of Lac du Bonnetgranite adopted from published literature. A suite of two-dimensional laboratory tests including uniaxial,triaxial compression and Brazilian tests is simulated and the results are compared with laboratory data.The FDEM-mDFN models indicate that micro-heterogeneity has a profound influence on both the mechanicalbehavior and resultant fracture pattern. An increase in the microcrack intensity leads to areduction in the strength of the sample and changes the character of the rock strength envelope. Spallingand axial splitting dominate the failure mode at low confinement while shear failure is the dominantfailure mode at high confinement. Numerical results from simulated compression tests show thatmicrocracking reduces the cohesive component of strength alone, and the frictional strength componentremains unaffected. Results from simulated Brazilian tests show that the tensile strength is influenced bythe presence of microcracks, with a reduction in tensile strength as microcrack intensity increases. Theimportance of microcrack heterogeneity in reproducing a bi-linear or S-shape failure envelope and itseffects on the mechanisms leading to spalling damage near an underground opening are also discussed.

TIME-DISCRETIZATION PROCEDURE FOR FINITE ELEMENT APPROXIMATION OF COMPRESSIBLE MISCIBLE DISPLACEMENT IN POROUS MEDIA

We’ll consider the model of two-phase compressible miscible displacement in porous media which includes molecular diffusion and dispersion in one dimensional space. Time-discretization procedure is established and analysed. The optimal error estimate in L2 norm is proved by introducing a new interpolation operator R.

Discrete element and finite element coupling simulation and experiment of hot granule medium pressure forming

The granule medium of discreteness is supposed to be continuous（Drucker-Prager model） in the existing finite element simulation analysis on the hot granule medium pressure forming（HGMF） process, so the granule medium may produce tensile stress in the process of pressure-transferring and flowing, which does not coincide with the reality. The analysis method, discrete element and finite element（DE-FE） coupling simulation, is proposed to solve the problem. The material parameters of simulation model are obtained by the pressure-transfer performance test of granule medium and the hot uniaxial tensile test of sheet metal. The DE-FE coupling simulation platform is established by adopting Visual Basic language. The features in the process that AA7075-T6 conical parts are formed by the HGMF process are analyzed and verified by the process test. The studies show that the results of DE-FE coupling simulation coincide well with the test results, which provides a new analysis method to solve the mechanics problem in the coupling of discrete and continuum.

PARALLEL ANALYSIS OF COMBINED FINITE/DISCRETE ELEMENT SYSTEMS ON PC CLUSTER

A computational strategy is presented for the nonlinear dynamic analysis of large- scale combined finite/discrete element systems on a PC cluster.In this strategy,a dual-level domain decomposition scheme is adopted to implement the dynamic domain decomposition.The domain decomposition approach perfectly matches the requirement of reducing the memory size per processor of the calculation.To treat the contact between boundary elements in neighbouring subdomains,the elements in a subdomain are classified into internal,interfacial and external elements.In this way,all the contact detect algorithms developed for a sequential computation could be adopted directly in the parallel computation.Numerical examples show that this implementation is suitable for simulating large-scale problems.Two typical numerical examples are given to demonstrate the parallel efficiency and scalability on a PC cluster.

Transient analysis of 1D inhomogeneous media by dynamic inhomogeneous finite element method

The dynamic inhomogeneous finite element method is studied for use in the transient analysis of one dimensional inhomogeneous media. The general formula of the inhomogeneous consistent mass matrix is established based on the shape function. In order to research the advantages of this method, it is compared with the general finite element method. A linear bar element is chosen for the discretization tests of material parameters with two fictitious distributions. And, a numerical example is solved to observe the differences in the results between these two methods. Some characteristics of the dynamic inhomogeneous finite element method that demonstrate its advantages are obtained through comparison with the general finite element method. It is found that the method can be used to solve elastic wave motion problems with a large element scale and a large number of iteration steps.

FINITE ELEMENT METHOD ON NUMERICAL SIMULATION OF STRATUM CORNEUM'S PENETRATION PROPERTY

How the outer substance could penetrate through the skin lies in the stratum corneum, because it is the main barrier in the multi-layers of the skin. Supposing the keratin cell with a special geometry as tetrakaidecahedron, the penetration property of stratum corneum was the key problem which was numerically simulated with finite element method. At first the discretization of the stratum corneum region was given in two steps： first, the discretization of the keratin cell; second, the discretization of fattiness that surrounds the keratin. Then there was the work of numerical simulation. In this procedure, the finite element method and the multi-grid method were used. The former was to obtain the discretization of basic elements; the latter was to decrease the high frequency error. At last the visualization of the numerical simulation was shown.

Assessing fracturing mechanisms and evolution of excavation damaged zone of tunnels in interlocked rock masses at high stresses using a finitediscrete element approach

Deep underground excavations within hard rocks can result in damage to the surrounding rock mass mostly due to redistribution of stresses.Especially within rock masses with non-persistent joints,the role of the pre-existing joints in the damage evolution around the underground opening is of critical importance as they govern the fracturing mechanisms and influence the brittle responses of these hard rock masses under highly anisotropic in situ stresses.In this study,the main focus is the impact of joint network geometry,joint strength and applied field stresses on the rock mass behaviours and the evolution of excavation induced damage due to the loss of confinement as a tunnel face advances.Analysis of such a phenomenon was conducted using the finite-discrete element method (FDEM).The numerical model is initially calibrated in order to match the behaviour of the fracture-free,massive Lac du Bonnet granite during the excavation of the Underground Research Laboratory (URL) Test Tunnel,Canada.The influence of the pre-existing joints on the rock mass response during excavation is investigated by integrating discrete fracture networks (DFNs) of various characteristics into the numerical models under varying in situ stresses.The numerical results obtained highlight the significance of the pre-existing joints on the reduction of in situ rock mass strength and its capacity for extension with both factors controlling the brittle response of the material.Furthermore,the impact of spatial distribution of natural joints on the stability of an underground excavation is discussed,as well as the potentially minor influence of joint strength on the stress induced damage within joint systems of a non-persistent nature under specific conditions.Additionally,the in situ stress-joint network interaction is examined,revealing the complex fracturing mechanisms that may lead to uncontrolled fracture propagation that compromises the overall stability of an underground excavation.

Development of quadrilateral spline thin plate elements using the B-net method

The quadrilateral discrete Kirchhoff thin plate bending element DKQ is based on the isoparametric element Q8, however, the accuracy of the isoparametric quadrilateral elements will drop significantly due to mesh distortions. In a previous work, we constructed an 8-node quadrilateral spline element L8 using the triangular area coordinates and the B- net method, which can be insensitive to mesh distortions and possess the second order completeness in the Cartesian co- ordinates. In this paper, a thin plate spline element is devel- oped based on the spline element L8 and the refined tech- nique. Numerical examples show that the present element indeed possesses higher accuracy than the DKQ element for distorted meshes.

Towards a Micromechanical Understanding of Landslides—Aiming at a Combination of Finite and Discrete Elements with Minimal Number of Degrees of Freedom

In this paper, we propose a combination of discrete elements for the soil and finite elements for the fluid flow field inside the pore space to simulate the triggering of landslides. We give the details for the implementation of third order finite elements (“P2 with bubble”) together with polygonal discrete elements, which allows the formulation with a minimal number of degrees of freedom to save computer time and memory. We verify the implementation with several standard problems from computational fluid dynamics, as well as the decay of a granular step in a fluid as test case for complex flow.

Three-dimensional combined finite-discrete element approach for simulation of single layer powder compaction process

The application of a combined finite-discrete element modeling approach to simu late the three-dimensional microscopic compaction behavior of single-layer met al powder system was described. The process was treated as a static problem,wit h kinematical component being neglected. Due to ill condition,Cholesky’s metho d failed to solve the system equations,while conjugate gradient method was trie d and yielded good results. Deformation of the particles was examined and compar ed with the results of physical modeling experiments. In both cases,the inner p articles were deformed from sphere to polygonal column,with the edges turning f rom arc to straight line. The edge number of a particle was equal to the number of particles surrounding it. And the experiments show that the ductile metal par ticles can be densified only by their plastic deformation without the occurrence of rearrangement phenomenon.

Numerical simulation of hydraulic fracturing and associated microseismicity using finite-discrete element method

Hydraulic fracturing （HF） technique has been extensively used for the exploitation of unconventional oiland gas reservoirs. HF enhances the connectivity of less permeable oil and gas-bearing rock formationsby fluid injection, which creates an interconnected fracture network and increases the hydrocarbonproduction. Meanwhile, microseismic （MS） monitoring is one of the most effective approaches to evaluatesuch stimulation process. In this paper, the combined finite-discrete element method （FDEM） isadopted to numerically simulate HF and associated MS. Several post-processing tools, includingfrequency-magnitude distribution （b-value）, fractal dimension （D-value）, and seismic events clustering,are utilized to interpret numerical results. A non-parametric clustering algorithm designed specificallyfor FDEM is used to reduce the mesh dependency and extract more realistic seismic information.Simulation results indicated that at the local scale, the HF process tends to propagate following the rockmass discontinuities; while at the reservoir scale, it tends to develop in the direction parallel to themaximum in-situ stress. 2014 Institute of Rock and Soil Mechanics, Chinese Academy of Sciences. Production and hosting byElsevier B.V. All rights reserved.

Dynamic Analysis of a Centrifugal Compressor by Finite Element Method

This paper mainly deals with dynamic analysis of rotor-bearing system in a centrifugal compressor. A finite element model of the rotor-bearing system has been developed. The considered factors of the model include the rotary inertia of solid elements, stiffness and damping of hydrodynamic bearing. In the calculating, ANSYS software was used. Both calculated and measured results are in good agreement.

Discrete formulation of mixed finite element methods for vapor deposition chemical reaction equations

The vapor deposition chemical reaction processes, which are of extremely extensive applications, can be classified as a mathematical model by the following governing nonlinear partial differential equations containing velocity vector, temperature field, pressure field, and gas mass field. The mixed finite element （MFE） method is employed to study the system of equations for the vapor deposition chemical reaction processes. The semidiscrete and fully discrete MFE formulations are derived. And the existence and convergence （error estimate） of the semidiscrete and fully discrete MFE solutions are demonstrated. By employing MFE method to treat the system of equations for the vapor deposition chemical reaction processes, the numerical solutions of the velocity vector, the temperature field, the pressure field, and the gas mass field can be found out simultaneously. Thus, these researches are not only of important theoretical means, but also of extremely extensive applied vistas.

Fifty years of finite elements——a solid mechanics perspective

The finite element method has been considered as one of the most significant engineering advances of the twentieth century. This computational methodology has made substantial impact on many fields in science and also has profoundly changed engineering design procedures and practice. This paper, mainly froln a solid mechanics perspective, and the Swansea viewpoint in particular, describes very briefly the origin of the methodology, then summaries selected milestones of the technical developments that have taken place over the last fifty years and illustrates their application to some practical engineering problems.

The Numerical Integration of Discrete Functions on a Triangular Element

With the application of Hammer integral formulas of a continuous function on a triangular element, the numerical integral formulas of some discrete functions on the element are derived by means of decomposition and recombination of base functions. Hammer integral formulas are the special examples of those of the paper.

Fracture Response of Reinforced Concrete Deep Beams Finite Element Investigation of Strength and Beam Size

This article presents a finite element analysis of reinforced concrete deep beams using nonlinear fracture mechanics. The article describes the development of a numerical model that includes several nonlinear processes such as compression and tension softening of concrete, bond slip between concrete and reinforcement, and the yielding of the longitudinal steel reinforcement. The development also incorporates the Delaunay refinement algorithm to create a triangular topology that is then transformed into a quadrilateral mesh by the quad-morphing algorithm. These two techniques allow automatic remeshing using the discrete crack approach. Nonlinear fracture mechanics is incorporated using the fictitious crack model and the principal tensile strength for crack initiation and propagation. The model has been successful in reproducing the load deflections, cracking patterns and size effects observed in experiments of normal and high-strength concrete deep beams with and without stirrup reinforcement.

A multithreaded parallel upwind sweep algorithm for the S_(N) transport equations discretized with discontinuous finite elements

The complex structure and strong heterogeneity of advanced nuclear reactor systems pose challenges for high-fidelity neutron-shielding calculations. Unstructured meshes exhibit strong geometric adaptability and can overcome the deficiencies of conventionally structured meshes in complex geometry modeling. A multithreaded parallel upwind sweep algorithm for S_(N) transport was proposed to achieve a more accurate geometric description and improve the computational efficiency. The spatial variables were discretized using the standard discontinuous Galerkin finite-element method. The angular flux transmission between neighboring meshes was handled using an upwind scheme. In addition, a combination of a mesh transport sweep and angular iterations was realized using a multithreaded parallel technique. The algorithm was implemented in the 2D/3D S_(N) transport code ThorSNIPE, and numerical evaluations were conducted using three typical benchmark problems:IAEA, Kobayashi-3i, and VENUS-3. These numerical results indicate that the multithreaded parallel upwind sweep algorithm can achieve high computational efficiency. ThorSNIPE, with a multithreaded parallel upwind sweep algorithm, has good reliability, stability, and high efficiency, making it suitable for complex shielding calculations.

Finite Volume Element Method for Solving the Elliptic Neumann Boundary Control Problems

Solving optimization problems with partial differential equations constraints is one of the most challenging problems in the context of industrial applications. In this paper, we study the finite volume element method for solving the elliptic Neumann boundary control problems. The variational discretization approach is used to deal with the control. Numerical results demonstrate that the proposed method for control is second-order accuracy in the L2 (Γ) and L∞ (Γ) norm. For state and adjoint state, optimal convergence order in the L2 (Ω) and H1 (Ω) can also be obtained.

Application of the DEM to screening process:a 3D simulation

The discrete element method(DEM) has been widely used to simulate microscopic interactions between particles.Screening is a deeply complicated process when considering the law of motion for the particles,themselves.In this paper,a numerical model for the study of a particle screening process using the DEM is presented.Special attention was paid to the modeling of a vibrating screen that allows particles to pass through,or to rebound,when approaching the screen surface.Inferences concerning screen length and vibrating frequency as they relate to screening efficiency were studied.The conclusions were:three-dimensional simulation of screening efficiency along the screen length follows an exponential distribution;when the sieve vibrates over a certain frequency range the screening efficiency is stable;and,higher vibration frequencies can improve the handling capacity of the screening machine.