Zoned finite strip method and its applications in geomechanics

The technique of Finite Strip method has been extended for zoned strips. One strip can have several different materials in horizontal direction including dummy materials. The new developed zoned Finite Strip (Z.F.S.) method has many engineering applications, particularly in geomechanical problems. The formulation is presented and three different geotechnical problems have been solved using the new Z.F.S. method, which could not be solved by the original Finite Strip method. The results are compared with the solution for the same problems obtained by analytical and/or numerical (Finite Element) methods. The reduced input and output for the Z.F.S. method compared to the Finite Element method makes this method attractive particularly for practising engineers. However the results can be as good as the well known Finite Element method.     

A multiresolution strategy for solving landslides using the Particle Finite Element Method

We present an approach for the simulation of landslides using the Particle Finite Element Method of the second generation. In this work, the multiphase nature (granular phase and water) of the phenomenon is considered in a staggered fashion using a single, indeformable Finite Element mesh. A fractional step and a monolithic strategy are used for the water flow and granular phase, respectively. In this way, the maximum accuracy with minimal computational times is reached. The method is completed by adding the interaction terms due to drag and pressure forces, together with a moving mesh strategy to reduce the size of the computational domain.     

‘Infinite domain’ elements in finite element analysis of underground excavations

The Finite Element Method is frequently used to analyse problems involving an ‘infinite domain’. A typical problem is an underground excavation in prestressed infinite medium in either tunnelling or mining operations or a foundation in an infinite half space. This paper examines the implications of mesh truncation on the accuracy of the accuracy of the solution. At the same time, a more economical and accurate method of analysing these problems using special ‘infinite domain’ Finite Elements is presented.     

Compatible algorithm for integrations on a block domain of any shape for three-dimensional discontinuous deformation analysis

This work calculates the integrations of convex and concave polyhedrons in three-dimensional discontinuous deformation analysis (3D DDA) using a novel method. With this novel method, mathematical topology is applied to the integration, and the numerical mesh used by the Finite Element Method (FEM) is not needed to subdivide polyhedrons into tetrahedrons or hexahedrons. Examples demonstrate the accuracy of the proposed method for integrating convex and concave polyhedrons with planar boundaries.     

复合单元法在求解有自由面渗流问题中的应用

论文指出了在有限元分析过程中地下水自由面上、下的区别,提出可采用复合单元法处理常应变交截单元,并以四面体单元为例,推导出了自由面与单元交截的截面方程,详细说明了复合单元法的原理、系数矩阵的求解方法、推导出体积分和曲面积分的求解公式。     

Numerical Reliability for Mixed Methods Applied to Flow Problems in Porous Media

This paper is devoted to the numerical reliability and time requirements of the Mixed Finite Element (MFE) and Mixed-Hybrid Finite Element (MHFE) methods. The behavior of these methods is investigated under the influence of two factors: the mesh discretization and the medium heterogeneity. We show that, unlike the MFE, the MHFE suffers with the presence of badly shaped discretized elements. Thereat, a numerical reliability analyzing software (Aquarels) is used to detect the instability of a matrix-inversion code generated automatically by a symbolic manipulator. We also show that the spectral condition number of the algebraic systems furnished by both methods in heterogeneous media grows up linearly according to the smoothness of the hydraulic conductivity. Furthermore, it is found that the MHFE could accumulate numerical errors if large jumps in the tensor of conductivity take place. Finally, we compare running-times for both algorithms by giving various numerical experiments.     

Forecast of creep settlements of heavy structures using pressuremeter tests

This paper presents a new method proposed for the prediction of long term settlement of very heavy structures based on a numerical interpretation of long term pressuremeter creep tests. The constitutive model used for the modelling of the soil creep is described. The constants of the constitutive model are determined by fitting a simulated curve, given by a simple Finite Element Method, to the results of a long term pressuremeter creep test. The calculation of long term settlement under nuclear power plants, using the soil parameters defined by this method, is presented and compared with the in situ measured values.     

线源二维瞬变电磁场的正演计算新方法

首先应用有限元直接迭代法,在频域中实现了线源二维电磁场正演计算,然后利用频时转换中较为简便且有效的数字滤波法,实现了频域到时域的转换,从而实现了线源二维瞬变电磁场的正演模拟。该方法具有编程简单,占用内存小,运算速度快和模型输入方便等特点。模拟结果与理论计算结果对比表明,该方法具有较高的计算精度。另外,该方法对复杂条件下的瞬变电磁勘探方法的研究和二维瞬变电磁反演有重要意义。      

Nonlinear analysis of NATM tunnel construction with the boundary element method

This paper presents a novel approach to the simulation of NATM tunnel construction using the Boundary Element Method (BEM) as principal numerical method. This new approach has the advantage that only the excavation surface, the possible plastic zones and the tunnel lining have to be discretised. The whole rock mass is represented by the BEM whereas the Finite Element Method (FEM) is used to represent the tunnel lining only. Thus, a general coupling strategy for coupling three-dimensional boundary elements with shell finite elements (shotcrete) and beam finite elements (steel arches) is presented. To achieve realistic results the effect of hydration of the shotcrete and yielding of the steel arches is considered in the excavation process. Furthermore, the nonlinear rock behaviour is modelled more realistically by using a powerful hierarchical constitutive model which considers a large range of rock materials. The combination of these ideas results in higher user-friendliness and efficiency. Some verification tests and practical applications in tunnelling are presented.     

Online conservative generalized multiscale finite element method for highly heterogeneous flow models

Computational Geosciences - In this work, we consider an online enrichment procedure in the context of the Generalized Multiscale Finite Element Method (GMsFEM) for the two-phase flow model in...     

Boundary element analysis methods for ground stress field of rock masses

Basing on the principle of the Boundary Element Method, the authors of this paper present two computational methods for the analysis of ground stress field of rock masses, namely, the Boundary Element Regression Method and the Boundary Direct Integral Method. If the stress values of certain points in the rock masses have been known, we can find the solution of the entire ground stress field using either of these two methods. In this paper, these two methods have been used in conducting practical engineering computations. A critical comparison is made of the results obtained using these two methods with those of Finite Element Regression Method and Photoelastic Model Experiment, and the results are all in agreement. This shows that the above two methods are both feasible for implementation and easy for operation.     

Mathematica软件在计算有限单元法系数矩阵中的应用

以一维分层连续介质大地电磁有限元模拟为例,应用Mathematica软件计算系数矩阵。节约了大量的推导时间。确保快速、准确地得到有限元系数矩阵。展示了mathematica软件在计算有限单元系数矩阵中的强大功能。     

A basal slip model for Lagrangian finite element simulations of 3D landslides

A Lagrangian numerical approach for the simulation of rapid landslide runouts is presented and discussed. The simulation approach is based on the so‐called Particle Finite Element Method. The moving soil mass is assumed to obey a rigid‐viscoplastic, non‐dilatant Drucker–Prager constitutive law, which is cast in the form of a regularized, pressure‐sensitive Bingham model. Unlike in classical formulations of computational fluid mechanics, where no‐slip boundary conditions are assumed, basal slip boundary conditions are introduced to account for the specific nature of the landslide‐basal surface interface. The basal slip conditions are formulated in the form of modified Navier boundary conditions, with a pressure‐sensitive threshold. A special mixed Eulerian–Lagrangian formulation is used for the elements on the basal interface to accommodate the new slip conditions into the Particle Finite Element Method framework. To avoid inconsistencies in the presence of complex shapes of the basal surface, the no‐flux condition through the basal surface is relaxed using a penalty approach. The proposed model is validated by simulating both laboratory tests and a real large‐scale problem, and the critical role of the basal slip is elucidated. Copyright © 2016 John Wiley & Sons, Ltd.     

Particle finite element analysis of large deformation and granular flow problems

A version of the Particle Finite Element Method applicable to geomechanics applications is presented. A simple rigid-plastic material model is adopted and the governing equations are cast in terms of a variational principle which facilitates a straightforward solution via mathematical programming techniques. In addition, frictional contact between rigid and deformable solids is accounted for using an approach previously developed for discrete element simulations. The capabilities of the scheme is demonstrated on a range of quasi-static and dynamic problems involving very large deformations.     

A Simple Method for Analysis of Point Anchored Rockbolts in Circular Tunnels in Elastic Ground

Summary. A simple analytical method for the analysis of point anchored rockbolts is presented in this paper. The solution has been derived for elastic ground and rockbolts, for plane strain conditions, and for tunnels with circular cross section. The method provides accurate results for the rockbolts’ loads and displacements and explicitly includes the connection of the rockbolts to the surrounding ground. The addition of such details to a Finite Element numerical model is critical; otherwise the solution obtained may be dependent on the discretization used and on the stiffness of rockbolts and ground. As an alternative to including details of the rockbolt head and anchor point in the numerical model, which could be computationally very expensive, an equivalent spring constant is proposed. The spring constant is obtained by matching numerical with analytical results for a simple case, but keeping the geometry, material properties, and discretization unchanged.     

The Andra Couplex 1 Test Case: Comparisons Between Finite-Element, Mixed Hybrid Finite Element and Finite Volume Element Discretizations

We present here results for the Andra Couplex 1 test case, obtained with the code Cast3m. This code is developped at the CEA (Commissariat l'nergie atomique) and is used mainly to solve problems of solid mechanics, fluid mechanics and heat transfers. Different types of discretization are available, among them finite element, finite volume and mixed hybrid finite element method. Cast3m is also a componant of the platteform Alliances (co-developped by Andra, CEA), which will be used by Andra for the safety calculation of an underground waste disposal in year 2004. We solve the Darcy equation for the water flow and a convection–diffusion transport equation for the Iodine 129 which escapes from a repository cave into the water. The water flow is calculated with a MHFE discretization. It is shown that this method provides sharp results even on relatively coarse grids. The convection–diffusion transport equation is discretized with FE (Finite Element), MHFE (Mixed Hybrid Finite Element) and FV (Finite Volume) methods. In our comparison, we point out the differences of these methods in term of accuracy, respect of the maximum principle and calculations cost. Neither the finite element nor the mixed hybrid finite element approach respects the maximum principle. This results in the presence of negative concentrations near the repository cave, whereas FV calculations respect the monotonicity. We show that mass lumping techniques suppress this problem but with strong restrictions on the grid. FE and MHFE approaches are more accurate than FV for the diffusion equation, but the overall results are equivalent since the advective terms are dominant in the far field and are discretized with centered schemes. We conclude by studying the influence of the grid: a very fine grid near the repository solves almost all the problems of monotonicity, without employing mass lumping techniques. We also observed a very important increase of the accuracy on a structured grid made up of rectangles.     

A numerical solution to seepage problems with complex drainage systems

Seepage problems with complex drainage systems are commonly encountered in civil engineering, with strong non-linearity. A numerical solution based on the Finite Element Method combining the substructure technique with a variational inequality formulation of Signorini’s type is proposed to solve these problems. The aims of this work are to accurately characterize the boundary conditions of the drainage systems, to reduce the difficulty in mesh generation resulting from the drainage holes with small radius and dense spacing, and to eliminate the singularity at the seepage points and the resultant mesh dependency. Numerical stability and robustness of the proposed method are guaranteed by an adaptive procedure for progressively relaxing the penalized Heaviside function associated with the formulation of the discrete variational inequality. Two challenging numerical examples are presented to validate the effectiveness and robustness of the proposed method.     

平面有限元计算结果等值线的绘制

有限元的计算结果常需要用等值线表示出来。Surfer是一应用得十分广泛地作等值线的软件,但它仍有不足,如有的等值线所代表的值无法判断等。基于有限元网格和线性插值的方法及其他一些处理技巧,可有效地克服Surfer等软件的缺点,通过VBA语言编程可直接将等值线画在常用的制图软件AutoCAD界面里。所编的程序在平面有限元计算结果的等值线绘制中运用效果良好。     

地下水数值模型三维可视化研究

探讨了利用OpenGL技术实现含水层三维可视化的原理和方法,基于地下水数值模型的有限元三角网格和含水层顶底板信息,构建含水层三维实体模型,并将地下水数值模型计算结果通过三维表面动画的形式进行动态显示。本项研究为全方位、多视角地展示地下水系统进行了有益的尝试,将三维可视化技术成功地应用到地下水模拟研究。      

接触预压式元件钻孔变形法地应力测量数值处理

在现有的采用接触预压式元件的钻孔变形法地应力测量中,不论是用哈斯特率定法还是围压率定法,在计算孔壁的折算位移时都存在着不足。1984年潘立宙首先指出了这些不足,并给出了计算孔壁折算位移的精确公式[1]。但由于公式中的某些参数不能直接获得,所以公式一时无法应用于实际测量。本文通过有限元法的数值计算,确定了文献[1]的计算公式中的参数值,从而得出了用以往方法计算折算位移所产生的误差。又经过数值的量级比较,明确了文献[1]的公式中所考虑的那些对计算折算位移有影响的因素的主次。