结构-地基动力相互作用的时域模型

结构-地基动力相互作用是结构地震响应分析及安全评估的一个非常重要课题。基于比例边界有限元法,提出了一种新颖的结构-地基动力相互作用的时域模型,即采用比例边界有限元子域模拟近场有限域部分,采用高阶透射边界模拟远场无限域部分。通过采用连分式展开和引入辅助变量,有限域的动力方程采用高阶的静力刚度矩阵和质量矩阵表示。高阶透射边界精确满足无限远处的辐射边界条件,具有全局精确、时间局部和收敛速度快等优点。它是基于改进的连分式法求解无限域动力刚度矩阵而建立的,在时域里表示为一阶常微分方程组。通过联立有限域和无限域的运动方程,建立了结构-地基相互作用的标准动力学方程,采用Newmark法可直接求解。3个算例结果表明,该算法在时域里比黏弹性边界更精确、有效。     

Some aspects of coupled FEBEM analysis of underground openings

The finite element method (FEM) and the boundary element method (BEM) are two well established numerical methods used for the analysis of underground openings. The advantages of both the methods are utilized by adopting FEBEM in which finite elements are coupled with boundary elements. A coupling procedure is presented in this paper. In using FEBEM, the effect of the location of interface boundary between finite element and boundary element regions, effect of Poisson's ratio and effect of stress ratio are discussed. It is shown that Poisson's ratio and stress ratio have significant effect on the accuracy of the results. Different discretization schemes are discussed to study their effect on accuracy and computation time. The use of different material properties in the FE region is presented. A comparative study is made with FEM for all the cases. It is shown that use of FEBEM is more advantageous than FEM.     

Calculation of the volume of an alluvial fan

Calculation of the volume of a lithostratigraphic unit within an alluvial fan allows a longterm denudation rate to be calculated for the fan's catchment, where sediment is not transported beyond the fan. The calculation of denudation rates in this case depends upon accurate estimates of the volume of sediment in a lithostratigraphic unit of known age. Two methods of volume calculation and their approximations are presented. The first method sums the volume of discrete blocks used to approximate a variety of fan shapes. The second method integrates a quadratic function that approximates both the surface and lower boundary of a lithostratigraphic unit where the edges of the fan are assumed to be vertical. For fans that satisfy these restrictive assumptions, the integration method should be more accurate than the summation method. However, the summation method is more generally applicable and calculations using the two methods, and their approximations, yield remarkably similar results.     

Probabilistic assessment of the impact of coal seam gas development on groundwater: Surat Basin,Australia

Modelling cumulative impacts of basin-scale coal seam gas (CSG) extraction is challenging due to the long time frames and spatial extent over which impacts occur combined with the need to consider local-scale processes. The computational burden of such models limits the ability to undertake calibration and sensitivity and uncertainty analyses. A framework is presented that integrates recently developed methods and tools to address the computational burdens of an assessment of drawdown impacts associated with rapid CSG development in the Surat Basin, Australia. The null space Monte Carlo method combined with singular value decomposition (SVD)-assisted regularisation was used to analyse the uncertainty of simulated drawdown impacts. The study also describes how the computational burden of assessing local-scale impacts was mitigated by adopting a novel combination of a nested modelling framework which incorporated a model emulator of drawdown in dual-phase flow conditions, and a methodology for representing local faulting. This combination provides a mechanism to support more reliable estimates of regional CSG-related drawdown predictions. The study indicates that uncertainties associated with boundary conditions are reduced significantly when expressing differences between scenarios. The results are analysed and distilled to enable the easy identification of areas where the simulated maximum drawdown impacts could exceed trigger points associated with legislative ‘make good’ requirements; trigger points require that either an adjustment in the development scheme or other measures are implemented to remediate the impact. This report contributes to the currently small body of work that describes modelling and uncertainty analyses of CSG extraction impacts on groundwater.     

Determination of plastic regions around underground openings by a coupled boundary-element-characteristics method

A two-dimensional hybrid method for solving elastoplastic problems in engineering is presented by coupling two existing methods, namely, the boundary element method and the characteristics method. The formulation of this method is presented, as well as an excellent procedure for the determination of the boundary between elastic and plastic regions. It is shown not only that this method is a powerful and accurate method for evaluating the shape and extent of the plastic region around rock caverns, which is of prime importance for the construction of rock caverns, but also applicable to a given range of the initial stress field ratio where only compressive failure occurs. Then, some typical examples are solved in order to check the accuracy of the solution by this method. Furthermore, its successful applications are presented and discussed to determine the shape and the extent of the plastic regions around parallel, circular and rectangular openings.     

A general method for simulating reactive dissolution in carbonate rocks with arbitrary geometry

The two-scale continuum model is widely used in simulating the reactive dissolution process and predicting the optimum injection rate for carbonate reservoir acidizing treatment. The numerical methods of this model are currently based on structured grids, which are not applicable for complicated geometries. In this study, a general numerical scheme for simulating a reactive flow problem on both structured and unstructured grids is presented based on the finite volume method (FVM). The convection and diffusion terms involved in the reactive flow model are discretized by using the upwind scheme and two-point flux approximation (TPFA), respectively. The location of the centroid node inside each control volume is moved by using an optimization algorithm to make the connections with the surrounding elements as orthogonal as possible, which systematically improves the accuracy of the TPFA scheme. Additionally, in order to avoid the computational complexity resulting from the discretization of the non-linear term, the mass balance equation is only discretized in the spatial domain to get a set of ordinary differential equations (ODEs). These ODEs are coupled with the reaction equations and then solved using the numerical algorithm on ODEs. The accuracy and efficiency of the proposed method are studied by comparing the results obtained from the proposed numerical method with previous experimental and numerical results. This comparison indicates that, compared with the previous methods, the proposed method predicts the wormhole structure more accurately. Finally, the presented method is used to check the effect of the domain geometry, and it is found that the geometry of the flow domain has no effect on the optimum injection velocity, but the radial domain requires a larger breakthrough volume than the linear domain when other parameters are fixed.     

A generic approach to modelling flexible confined boundary conditions in SPH and its application

In this paper, a new approach to applying confining stress to flexible boundaries in the smoothed particle hydrodynamics (SPH) method is developed to facilitate its applications in geomechanics. Unlike the conventional SPH methods that impose confining boundary conditions by creating extra boundary particles, the proposed approach makes use of kernel truncation properties of SPH approximations that occur naturally at free-surface boundaries. Therefore, it does not require extra boundary particles and, as a consequence, can be utilised to apply confining stresses onto any boundary with arbitrary geometry without the need for tracking the curvature change during the computation. This enables more complicated problems that involve moving confining boundaries, such as confining triaxial tests, to be simulated in SPH without difficulties. To further enhance SPH applications in elasto-plastic computations of geomaterials, a robust numerical procedure to implement Mohr-Coulomb plasticity model in SPH is presented for the first time to avoid difficulties associated with corner singularities in Mohr-Coulomb model. The proposed approach was first validated against two-dimensional finite element (FE) solutions for confining biaxial compression tests to demonstrate its predictive capability at small deformation range when FE solutions are still valid. It is then further extended to three-dimensional conditions and utilised to simulate triaxial compression experiments. Simulation results predicted by SPH show good agreement with experiments, FE solutions, and other numerical results available in the literature. This suggests that the proposed approach of imposing confining stress boundaries is promising and can handle complex problems that involve moving confining boundary conditions.     

Grid adaptation for the Dirichlet–Neumann representation method and the multiscale mixed finite-element method

A Dirichlet–Neumann representation method was recently proposed for upscaling and simulating flow in reservoirs. The DNR method expresses coarse fluxes as linear functions of multiple pressure values along the boundary and at the center of each coarse block. The number of flux and pressure values at the boundary can be adjusted to improve the accuracy of simulation results and, in particular, to resolve important fine-scale details. Improvement over existing approaches is substantial especially for reservoirs that contain high-permeability streaks or channels. As an alternative, the multiscale mixed finite-element (MsMFE) method was designed to obtain fine-scale fluxes at the cost of solving a coarsened problem, but can also be used as upscaling methods that are flexible with respect to geometry and topology of the coarsened grid. Both methods can be expressed in mixed-hybrid form, with local stiffness matrices obtained as “inner products” of numerically computed basis functions with fine-scale sub-resolution. These basis functions are determined by solving local flow problems with piecewise linear Dirichlet boundary conditions for the DNR method and piecewise constant Neumann conditions for MsMFE. Adding discrete pressure points in the DNR method corresponds to subdividing faces in the coarse grid and hence increasing the number of basis functions in the MsMFE method. The methods show similar accuracy for 2D Cartesian cases, but the MsMFE method is more straightforward to formulate in 3D and implement for general grids.     

Finite element modeling of wave propagation problems in multilayered soils resting on a rigid base

A new finite element scheme is proposed, in this paper, for solving two-dimensional wave propagation problems in multilayered soils resting on a rigid base. The multilayered soils are treated as multiple horizontal layers of lateral infinite extension in geometry. Since these horizontal layers can be truncated by two artificially truncated vertical boundaries, two high-order artificial boundary conditions are applied for propagating the incoming waves from the interior domain into the far field of the system. Both the semi-analytical method and the truncated boundary migration procedure are used to derive the high-order artificial boundary conditions, which are comprised of a physically meaningful dashpot and a generalized energy absorber. The main advantage of using the proposed finite element scheme is that the derived artificial boundary condition can be straightforwardly implemented in the finite element analysis, without violating the band/sparse structure of the conventional finite element equation. The related numerical examples have demonstrated that the proposed finite element scheme is of high accuracy in dealing with wave propagation problems in multiple horizontal layers.     

Efficient solution of 3-D geomechanical problems by indirect BEM using iterative methods

The research herein primarily addresses to geomechanical problems of underground constructions in Mining and Civil Engineering. The problems are solved using the Indirect Boundary Element Method (IBEM). Although the geometry of the constructions themselves is usually very complicated, it will become much more complicated if we were to draw the existing joints. The computational problem therefore is how to deal with huge amount of equations and find out efficient methods of their formation and solution keeping in mind restraints of the computer memory and calculation time. Several approaches are used to enhance the performance of the Indirect Boundary Element Method. One of them deals with application of efficient equation solvers. It is shown that Krylov-type methods like CGS and GMRES with simple Jacoby preconditioning appear to be efficient and robust. In addition, adaptive integration on the boundary elements, together with diagonal dominance of equationsmake it possible to accelerate convergence of the iterative procedure. Some of the problems discussed allow a substantial reduction of matrix entries that leads to a very cheap iterative solution keeping reasonable accuracy of the results. © 1998 John Wiley & Sons, Ltd.     

地震分析中人工边界处理与地震动输入方法研究

基于柱面波波动方程,推导建立了适用于土-结构地震动力相互作用分析的地震动输入和人工边界的处理方法.其中,地震动的输入是通过在人工边界上施加等效节点力来实现的,等效节点力的大小与入射地震波波速成正比;而人工边界的处理方法使得人工边界条件不仅在时间上是局部的,而且在空间上也是局部的.这种处理方法简单、有效,物理意义清晰,且很容易在有限元法中实现,结合Newmark时间积分是无条件稳定的.为了验证方法的有效性和精度,给出了两个算例,分别用于检验人工边界条件的性能以及地震动输入方法的正确性.算例分析结果表明,所提出的方法是十分有效的.     

局域地应力场获取的插值平衡方法

针对由整体地应场插值计算局域地应力场的问题计算量大、受地质结构的影响大、不过分追求高精度等特点,改进了反距离加权插值法,考虑了单元体积的影响,提高了该方法在此问题中的适用性。基于此,提出了平面问题、三维地面和地下工程局域地应力场的求取策略,建议了边界全平动约束和法向约束两种边界条件,并验证了其合理性和适用场合。最后,在大型水电工程深切河谷坝肩边坡分析中进行了应用分析。结果表明：该插值方法简单实用,能够满足工程分析的精度要求;局域地应力场的求取策略计算效率高,计算精度能够满足工程分析的要求。     

An analytical solution for one-dimensional contaminant diffusion through multi-layered system and its applications

An analytical solution for one-dimensional contaminant diffusion through multi-layered media is derived regarding the change of the concentration of contaminants at the top boundary with time. The model accounts for the arbitrary initial conditions and the conditions of zero concentration and zero mass flux on the bottom boundary. The average degree of diffusion of the layered system is introduced on the basis of the solution. The results obtained by the presented analytical solutions agree well with those obtained by the numerical methods presented in the literature papers. The application of the analytical solution to the problem of landfill liner design is illustrated by considering a composite liner consisting of geomembrane and compacted clay liner. The results show that the 100-year mass flux of benzene at the bottom of the composite liner is 45 times higher than that of acetone for the same composite liner. The half-life of the contaminant has a great influence on the solute flux of benzene diffused into the underlying aquifer. Results also indicates that an additional 2.9–5.0 m of the conventional (untreated) compacted clay liner under the geomembrane is required to achieve the same level of protection as provided by 0.60 m of the Hexadecyltrimethylammonium (HDTMA)-treated compacted clay liners in conjunction with the geomembrane. Applications of the solution are also presented in the context of a contaminated two-layered media to demonstrate that different boundary and initial conditions can greatly affect the decontamination rate of the problem. The method is relatively simple to apply and can be used for performing equivalency analysis of landfill liners, preliminary design of groundwater remediation system, evaluating experimental results, and verifying more complex numerical models.     

Accelerating strategies to the numerical simulation of large‐scale models for sequential excavation

In this paper, a novel combination of well‐established numerical procedures is explored in order to accelerate the simulation of sequential excavation. Usually, large‐scale models are used to represent these problems. Due to the high number of equations involved, the solver algorithm represents the critical aspect which makes the simulation very time consuming. The mutable nature of the excavation models makes this problem even more pronounced. To accomplish the representation of geometrical and mechanical aspects in an efficient and simple manner, the proposed solution employs the boundary element method with a multiple‐region strategy. Together with this representational system, a segmented storage scheme and a time‐ordered tracking of the changes form an adequate basis for the usage of fast updating methods instead of frontal solvers. The present development employs the Sherman–Morrison–Woodbury method to speed up the calculation due to sequential changes. The efficiency of the proposed framework is illustrated through the simulation of test examples of 2D and 3D models. Copyright © 2006 John Wiley & Sons, Ltd.     

二阶声波方程频域PML边界条件及频域变网格步长并行计算

研究了二阶声波方程频域PML边界条件和频域变网格并行计算技术。PML边界是一种较为理想的吸收边界方法,多用在求解时域应力速度方程中,但对于频域声波正演,二阶位移方程更常用。从一阶声波方程PML吸收边界条件导出频域二阶位移方程PML边界条件,模拟算例得到的频率切片、时间切片和地震记录对比都说明该边界条件吸收效果很好。频域单炮正演不同频率间是独立的,据此低频部分采用大网格计算,高频采用小网格,实现变网格步长计算技术,这是较时间域正演的一个优势,在保证模拟质量的同时,减少计算量和内存消耗。     

Discrete element method for bearing capacity analysis

Analysis based on Discrete Element Method (DEM) is presented for estimating bearing capacity of foundations. Soil mass in the present model is treated as comprising of blocks which are connected by elasto-plastic Winkler-springs. By considering the conditions of compatibility, the boundary stresses on the failure surface and the ultimate bearing capacity of shallow foundations can be obtained. The computed boundary stresses from the present method satisfy equilibrium conditions and do not exceed the material strength. Formulation of the method is presented. Examples are shown to demonstrate the applicability of the method to the analysis of bearing capacity of shallow foundations. Effects of stiffness of Winkler-springs and mesh pattern on the computed results are investigated. The present method is shown to be a useful tool for analyzing bearing capacity of foundations with unusual geometry and loading conditions.     

Equivalent Permeability and Simulation of Two-Phase Flow in Heterogeneous Porous Media

The problem of calculating equivalent grid block permeability tensors for heterogeneous porous media is addressed. The homogenization method used involves solving Darcy's equation subject to linear boundary conditions with flux conservation in subregions of the reservoir and can be readily applied to unstructured grids. The resulting equivalent permeability tensor is stable as defined relative to G-convergence. It is proposed to use both conforming and mixed finite elements to solve the local problems and compute approximations from above and below of the equivalent permeability, respectively. Comparisons with results obtained using periodic, pressure and no-flux boundary conditions and the renormalization method are presented. A series of numerical examples demonstrates the effectiveness of the methodology for two-phase flow in heterogeneous reservoirs.     

Boundary Element based Discontinuous Deformation Analysis

A Boundary Element based Discontinuous Deformation Analysis (BE‐DDA) method is developed by implementing the improved dual reciprocity boundary element method into the open close iterations based DDA. This newly developed BE‐DDA is capable of simulating both the deformation and movement of blocks in a blocky system. Based on geometry updating, it adopts an incremental dynamic formulation taking into consideration initial stresses and dealing with external concentrated and contact forces conveniently. The boundaries of each block in the discrete blocky system are discretized with boundary elements while the domain of each block is divided into internal cells only for the integration of the domain integral of the initial stress term. The contact forces among blocks are treated as concentrated forces and the open–close iterations are applied to ensure the computational accuracy of block interactions. In the current method, an implicit time integration scheme is adopted for numerical stability. Three examples are used to show the effectiveness of the algorithm in simulating block movement, sliding, deformation and interaction of blocks. At last, block toppling and tunnel stability examples are conducted to demonstrate that the BE‐DDA is applicable for simulation of blocky systems. Copyright © 2016 John Wiley & Sons, Ltd.     

Non-rigid disk-based DDA with a new contact model

In this paper, a new disk-based DDA formulation is presented. In the original disk-based DDA, disks are considered to be rigid and the penalty method is used to enforce disk contact constraints. In order to improve the accuracy of the disk-based DDA, new formulations of stiffness and force matrices for non-rigid disks using a new efficient contact model are presented in this paper. Blocks are considered deformable without need to do more computations for contact detection. In the proposed contact model, disk–disk and disk–boundary contacts are transformed into the form of point-to-line contacts and normal spring, shear spring and frictional force sub-matrices are derived by vector analysis. The penalty method is quite simple to implement, but has some major disadvantages. In the presented contact model, not only the simplicity of the penalty method is retained but also the limitations are overcome by using the augmented Lagrangian method. Moreover, unlike the contact model used in the original disk-based DDA, reference line can be obtained directly by using only coordinates of disk centers and their radii, and no more computations are needed. The validity and capability of the new disk-based DDA formulation are demonstrated by several illustrative examples.