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.

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.

Adaptive discontinuous finite element quadrature sets over an icosahedron for discrete ordinates method

The discrete ordinates(S N)method requires numerous angular unknowns to achieve the desired accu-racy for shielding calculations involving strong anisotropy.Our objective is to develop an angular adaptive algorithm in the S N method to automatically optimize the angular distribution and minimize angular discretization errors with lower expenses.The proposed method enables linear dis-continuous finite element quadrature sets over an icosahe-dron to vary their quadrature orders in a one-twentieth sphere so that fine resolutions can be applied to the angular domains that are important.An error estimation that operates in conjunction with the spherical harmonics method is developed to determine the locations where more refinement is required.The adaptive quadrature sets are applied to three duct problems,including the Kobayashi benchmarks and the IRI-TUB research reactor,which emphasize the ability of this method to resolve neutron streaming through ducts with voids.The results indicate that the performance of the adaptive method is more effi-cient than that of uniform quadrature sets for duct transport problems.Our adaptive method offers an appropriate placement of angular unknowns to accurately integrate angular fluxes while reducing the computational costs in terms of unknowns and run times.

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.

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.

Rock Cutting Analysis Employing Finite and Discrete Element Methods

The petroleum industry has shown great interest in the study of drilling optimization on pre-salt formations given the low rates of penetration observed so far. Rate of penetration is the key to economically drill the pre-salt carbonate rock. This work presents the results of numerical modeling through finite element method and discrete element method for single cutter drilling in carbonate samples. The work is relevant to understand the mechanics of drill bit-rock interaction while drilling deep wells and the results were validated with experimental data raised under simulated downhole conditions. The numerical models were carried out under different geometrical configurations, varying the cutter chamfer size and back-rake angles. The forces generated on the cutter are translated into mechanical specific energy as this parameter is often used to measure drilling efficiency. Results indicate that the chamfer size does not change significantly the mechanical specific energy values, characteristic. Results also show there is a significant increase although the cutter aggressiveness is influenced by this geometrical in drilling resistance for larger values of back-rake angle.

岩石类材料直接拉伸破坏的FDEM数值模拟

有限元-离散元耦合算法(FDEM)在岩石裂纹扩展模拟中广泛应用,尤其在直接拉伸模拟中用于参数校核。然而,模拟结果通常受到拉伸速率和网格尺寸的影响。本文首先阐述FDEM基本原理;然后,建立直接拉伸数值计算模型,探究拉伸速率、网格尺寸及高径比对破坏模式和力学参数的影响;最后,给出直接拉伸模拟中建议采用的拉伸速率和网格尺寸。研究结果表明:随着拉伸速率增加,试样抗拉强度、破坏程度和峰值应变率增加,而平均弹性模量减小;在较低拉伸速率下(v≤0.01 m/s),试样仅产生1条主拉伸裂缝;当拉伸速率较高时,有分支裂缝出现在主拉伸裂缝上侧。网格尺寸对抗拉强度、峰值应变率和平均弹性模量的影响较小,但对破坏模式和破坏程度的影响较显著。随着高径比增加,试样的抗拉强度、破坏程度和峰值应变率增大,但平均弹性模量呈相反趋势,并且高径比对破坏程度的影响较为显著。建议在直接拉伸模拟中使用0.01 m/s的拉伸速率,并将网格尺寸限制在1.5 mm以内。

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.

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.

孔洞形状对层状岩石力学特性影响的FDEM数值模拟研究

为揭示孔洞形状对层状岩石力学性质和破坏模式的影响,采用有限元-离散元耦合数值模拟方法(FDEM)开展系列数值模拟研究。首先,阐述FDEM模拟层状岩石的基本原理,然后,开展不同层理倾角完整试样的单轴压缩模拟,并与试验结果进行对比验证。最后,对含有圆形、椭圆形、三角形、矩形和方形孔洞的层状岩石试样(β为0°、30°、45°、60°和90°)进行单轴压缩模拟研究。研究结果表明:对于不同孔洞形状的试样,抗压强度和试样破坏程度随层理倾角的增大呈V字型变化趋势,且均在层理倾角为0°时抗压强度取得最大值,在90°时破坏程度最为严重;孔洞的存在严重削弱了试样的力学性能,且削弱幅度与孔洞形状密切相关,其中方形和圆形孔洞对抗压强度的削弱能力最弱。将含不同形状孔洞试样的破坏模式随层理倾角的变化主要分为穿层理面拉剪混合破坏(β=0°)、沿层理面与穿层理面混合拉剪破坏(β=30°)、沿层理面剪切破坏(β=45°和60°)和沿层理面拉剪劈裂破坏(β=90°)。

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 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.

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.

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.

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.

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.

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.

基于FDEM数值模拟的软岩隧洞大变形预测

软岩隧洞收敛变形量预测对隧洞施工方法、设备选型和支护设计具有重要意义。采用有限元-离散元耦合数值模拟方法(FDEM)对软岩隧洞掘进过程开展了模拟研究,并调研了地应力量值对隧洞收敛变形量的影响。结果表明:隧洞大变形机理为开挖卸荷引起径向应力降低、切向应力升高,升高的切向应力造成围岩发生共轭剪切破坏,并持续向深处完整围岩扩展,深部破裂块体对浅部碎裂岩块的接触挤压产生宏观空隙,造成体积增大,发生具有碎胀效应的挤压大变形;随着围岩强度应力比的降低,围岩收敛变形量呈指数函数增大,相关系数高达0.996,为软岩隧洞收敛变形量预测提供了经验公式。

基于DEM-FDM耦合的过渡段膨胀诱发钢轨上拱研究

研究目的:为分析涵洞过渡段地基膨胀引起的钢轨上拱响应,基于现场测试、室内膨胀试验数据,开展DEM-FDM耦合数值模拟,分析某涵洞附近路基土在膨胀范围为16 m,膨胀中心距离涵洞中心分别为0 m、5 m、10 m这三种工况下,不同膨胀率时基床填料的运动规律及钢轨的上拱响应。研究结论:(1)涵洞对于钢轨上拱位移的传递存在阻断作用,但会增大钢轨上拱的峰值,原位膨胀率下工况二的钢轨上拱峰值达到46 mm,当路基膨胀率为0.3%时钢轨上拱位移量达到无砟轨道钢轨可调节临界值(4mm);(2)过渡段钢轨上拱处同时产生轴向应力集中,其中原位膨胀率下工况二轴向应力峰值达到14.4 MPa;(3)对于膨胀区域位于涵洞下方的工况,钢轨轴向应力呈现出来的分布规律为钢轨上拱拱顶处为主拉应力状态,拱脚处为主压应力状态,因此一共包括三个压应力峰值点以及两个拉应力峰值点;(4)本文研究可为高铁涵洞过渡段路基膨胀病害解决方案的确定提供理论依据。

三维可变形圆化多面体离散单元法

为真实模拟岩体的变形特性与运动形态,将圆化多面体离散元法与有限单元法结合,提出一种三维可变形圆化多面体离散单元法。该方法既能真实表征块体的不规则特征,又降低了接触判断的难度,同时能准确反映块体的变形特性。在求解切向接触力时,将接触判断对象从接触对简化为单元整体,显著提高了计算效率。为分析块体变形特性,在块体离散单元内部划分有限元网格,将最外层有限元网格作为最小接触单元。采用直接平均法,将接触力转化为等效节点力,并采用非线性有限单元法实现对单元变形特性的精确模拟,克服了圆化多面体无法反映单元变形的缺陷。通过5个算例论证了新方法在捕捉单元变形、运动形态以及其力学特征等方面的准确性和高效性。