济南泉域岩溶地下水三维等参有限元数值模拟

基于济南泉群研究区域岩溶水贮存和运动特征,建立了三维有限元数学模型,并利用等参有限元方法求解,再根据2001年、2002年的水文资料,识别模型参数,进一步对济南泉域内岩溶地下水的开采方案进行评价,探讨了济南市“保泉”与“供水”的可行性,为科学管理济南市泉群区域内地下水资源提供依据。      

A new development of the scaled boundary finite element method for wave motion in layered half-space

The scaled boundary finite element method (SBFEM) developed by Wolf and Song has shown certain parallels to the finite element method (FEM) and boundary element method (BEM). Because of its semi-analytical nature, SBFEM is particularly suitable for the analysis of wave propagation in unbounded domains. This paper makes a certain modification of the standard SBFEM. A new idea of scaling surface instead of a scaling center is introduced to formulate the governing SBFE equations for the analysis of wave propagation in multilayered half-space, which leads to simplifying the modeling and saving considerably the computational effort. In addition, by employing the proposed approach, some problems encountered in engineering practice, which are difficult to deal with by the conventional SBFEM, for example, 3D foundation impedance on half-space with irregular geographical features, can be effectively solved. The proposed approach also helps to simplify the solution of shell structures. Numerical examples are provided to validate the accuracy and efficiency of the proposed approach.     

Efficiency of heavy mass technology in traffic vibration reduction: Experimental and numerical investigation

Vibrations induced by traffic and construction activities cause serious environmental problems. The reduction of the impact of these vibrations on the nearby environment constitutes an important challenge, mainly in urban area. This paper presents both experimental investigation and 3D numerical modeling of the performance of heavy masses technology for scattering the ground vibrations. The efficiency of this method is compared to that of the trench barriers, largely studied in the literature. Analyses show that the heavy mass constitutes an efficient technology for the attenuation of the traffic induced vibrations. The performance of this method depends mainly on the mass weight. An amplitude reduction ratio up to 70% can be reached using this technology.     

Numerical modeling of traffic-induced ground vibration

Ground vibrations due to road traffic constitute a major environmental problem. This paper presents a numerical model for the analysis and prediction of the ground vibrations due to the road traffic. A car model with four degrees of freedom is used for the determination of the load due to the road traffic. The load is then introduced in a 3D finite difference model for the determination of the traffic-induced ground vibrations. The numerical model is validated using field data. Numerical analyses show that both the amplitude and frequency of the traffic-induced vibrations are mainly affected by the vehicle speed, the road unevenness and the vehicle suspension system. Some recommendations are suggested for the reduction of these vibrations.     

饱和地基上列车运行引起的地面振动隔振分析

利用推导出的频域内饱和土的以土骨架位移u和孔隙水压力p表示的u-p格式的2.5维有限元方程,分析列车低速和高速运行条件下不同隔振措施的隔振效果,包括空沟、填充沟（混凝土墙）和混凝土板（波阻板）。其中轨道被简化为饱和地基上的Euler梁,通过沿轨道方向的波数变换将三维空间问题降为平面应变问题,对求解的结果进行Fourier反变换,获得三维时域-空间域内的解。研究表明：弹性地基和饱和地基上设置空沟和填充沟隔振效果相差不大,而设置波阻板隔振效果存在较大差异。列车低速运行时,空沟基本无隔振效果,填充沟在一定范围内有隔振效果,波阻板隔振效果最好;列车高速运行时,空沟在较大沟宽和较深沟深条件下才能达到较好隔振效果,填充沟和波阻板只需较小尺寸就能达到理想的隔振效果     

A nonlinear HHT-α method with elastic–plastic soil–structure interaction in a coupled SBFEM/FEM approach

This article presents a new method for the calculation of elastic–plastic building ground deformations and elastic–plastic building ground failure including wave propagation in the ground. The presented procedure is a hybrid method, based on several common calculation methods. Included is a nonlinear calculation with the finite element method (FEM), a nonlinear HHT-alpha method with full Newton–Raphson iteration and the scaled boundary finite element method (SBFEM). The presented method can be used as a tool for the accurate calculation of building ground deformations and the stability of the subsoil with included dynamic loading.     

Multigrid preconditioned conjugate-gradient solver for mixed finite-element method

The mixed finite-element approximation to a second-order elliptic PDE results in a saddle-point problem and leads to an indefinite linear system of equations. The mixed system of equations can be transformed into coupled symmetric positive-definite matrix equations, or a Schur complement problem, using block Gauss elimination. A preconditioned conjugate-gradient algorithm is used for solving the Schur complement problem. The mixed finite-element method is closely related to the cell-centered finite difference scheme for solving second-order elliptic problems with variable coefficients. For the cell-centered finite difference scheme, a simple multigrid algorithm can be defined and used as a preconditioner. For distorted grids, an additional iteration is needed. Nested iteration with a multigrid preconditioned conjugate gradient inner iteration results in an effective numerical solution technique for the mixed system of linear equations arising from a discretization on distorted grids. Numerical results show that the preconditioned conjugate-gradient inner iteration is robust with respect to grid size and variability in the hydraulic conductivity tensor.     

饱和土半解析边界元法及在双排桩被动隔振中的应用

针对均质饱和地基中双排桩远场被动隔振问题,首先,基于饱和多孔介质的边界元法,建立了以薄层法（TLM）基本解作为动力Green函数的饱和土半解析边界元法,该方法可有效地分析饱和半空间的土-结构动力相互作用问题。在此基础上,根据双排桩与周围土体的邻接条件,推导了双排桩对Rayleigh波散射的三维边界元方程;运用上述边界元方程,对双排桩的远场被动隔振问题进行了研究。结果表明：双排桩能够有效地降低屏障后的位移振幅,其隔振效果要优于单排桩;排间净距对隔振效果影响不大,而桩间净距则对双排桩隔振效果起控制作用。     

频率域航空电磁三维矢量有限元正演模拟

目前有限元技术的开发及在电磁勘查技术中的应用已日趋成熟.然而,有限元正演模拟主要集中于地面和海洋电磁,航空电磁三维有限元模拟尚没有受到足够重视.以前人工作为基础,利用结构化网格实现了航空电磁系统的三维矢量有限元正演模拟.从二次场双旋度矢量非齐次亥姆霍兹方程出发,应用广义变分原理推导出变分方程,并采用六面体单元剖分,将场置于单元棱边上,对每个单元应用线性插值,最后合成含有稀疏矩阵的线性方程组.针对航空电磁多源性问题,利用MUMPS(multifrontal massively parallel sparse direct solver)直接求解器进行求解,在保证精度的前提下大幅度提高计算速度.利用单个异常体模型检验算法的精度和软件的稳定性,进而通过典型地电模型的模拟验证算法的有效性.对不同地下电性结构正演模拟结果进行对比分析,进一步研究了覆盖层和垂直接触带等典型构造对航空电磁响应的影响特征.      

时频～炮检距域面波衰减方法及应用

面波以低频强能量为特征,数据处理中常用的面波衰减技术有:频率滤波、F-K滤波和速度滤波等.由于面波特殊的频散现象,使得上述方法的应用效果受到一定的影响.基于面波的特征随炮检距变化这一特点,提出一种时频～炮检距域面波衰减方法:①对单炮记录中的面波区域做Fourier变换或时频分析,了解面波频率随时间和炮检距的变化规律;②...     

基于子结构法的成层场地中沉积河谷的散射分析

土层场地对地震动的影响明显,研究成层场地局部复杂地形的波动场特性,对于抗震设防具有重要意义。基于土-结构相互作用理论,含有局部复杂地形的成层场地,可分解成广义结构（即近场复杂地形及其周围土体）和具有规则开挖边界的成层无限地基（即远场）。远场的格林函数可通过精细积分求解频域-波数域内的对偶波动方程获得,利用傅里叶逆变换得到频域-空间域内的柔度矩阵。近场可采用比例边界有限元进行模拟,通过高性能连分式的传递边界求解动刚度。自由场波动可通过传递矩阵法求得,将动刚度和自由场波动位移代入控制方程即可得到散射场的动力响应。数值算例验证了方法的准确性,并利用提出的方法讨论含有软夹层场地局部复杂场地的波动场特性。     

2D finite-element elastic models of transtensional pull-apart basins

A set of two-dimensional finite-element elastic models are presented to provide insights on the evolution of transtensional pull-apart basins between two right-stepping, right-lateral fault segments. Three representative fault segment interaction geometries are modelled, showing underlapping, neutral and overlapping segments. Despite the simplifications of the 2D model, overall results are obtained that might help understanding the formation of pull-apart basins. Firstly, the orientations of the local σ₁ and σ₃ tensional stress directions markedly depend on the segment's position. Secondly, the mean normal stress is extensional in a transtensional basin between segments, while the region outside the step is characterized by more compressive mean normal stresses. Thirdly, the angle of offset between the fault segments is one of the most important parameters controlling the geometries of the transtensional pull-apart basins: connected depocenters with basin high and lozenge shape in the case of underlapping steps, spindle shape or lazy S or Z shape in the case of neutral steps, and broadly elongate rhomboidal to sigmoidal basins in the case of overlapping steps. Generally, en-échelon basin margin system, dual opposing asymmetric depocenter, intrabasin relative structural high, and wide basin width can be used as indicators that a pull-apart basin is developing in transtension zones.     

A tentative fault propagation description by three-dimensional finite-element analysis

A 3-dimensional finite-element analysis is used to describe the behavior of a block affected by an incipient fault and subjected to a tectonic thrust which is oblique in relation to the fault.The aim of this study is to describe computed fault evolution, stress modifications induced in the whole block by this evolution and possible effects of these stresses.Some of the results obtained match well enough with observations made on the zone from which the model was derived; some other results are not in agreement with observations and thus emphasize the limitations of this kind of computing.     

A Feasibility Study on Controlling Ground Vibrations Caused by Blasts in Malmberget Underground Mine

In order to control or reduce the ground vibrations caused by underground blasts in Malmberget mine, a number of blast tests were carried out during production blasts and a series of single shot waveforms were obtained. Then the single shot waveforms from the same ring or different rings were analysed and compared with each other. The results showed that the single shots are reproducible, meaning that the ground vibrations caused by underground blasts can be controlled by means of the interference of the vibration waveforms measured. Finally, a formal test using electronic detonators and employing an optimum delay time of 8 ms was done in production. The test for an 11-borehole ring shows that the maximum vertical ground vibrations are reduced to the maximum vertical vibrations of a single shot. Particularly, the total vibration history for the 11-borehole-ring blast is shortened to about 200 ms over a velocity of 2 mm/s. However, the total vibration history of a normal production blast of 11-borehole ring is always 1400 ms over a velocity of 2 mm/s, namely the total vibration time of a production blast can be reduced to one seventh of that of the common production blasts by using the vibration control method. This indicates that the vibration control method introduced in the paper is feasible for underground mining blasts.     

局部复杂场地Rayleigh波传播特性分析的SBFEM模型研究

基于土-结构动力相互作用（SSI）的原理,将求解包含局部复杂地形的散射场问题,分解为规则开挖场地的动刚度、包含复杂构造散射体的动刚度和自由场波动输入3个问题的求解,并依据子结构控制方程,提出了一种高精度的比例边界有限（SBFEM）计算模型。通过计算半圆形河谷和半圆形沉积河谷两个算例,验证了SBFEM计算模型的正确性。较为系统地讨论了矩形峡谷、垂直断层和孤凸山体等常见复杂地形对Rayleigh波场的散射作用。结果表明：峡谷深度、软弱断层破碎带和孤凸山体对Rayleigh波都有一定阻挡作用;峡谷宽度、断层宽度和硬性断层填充物等因素对Rayleigh波散射作用影响不明显。SBFEM分析模型可应用于隔震沟、隔震帷幕设计,对大坝、桥梁等工程的选址提供有益的建议。     

A perturbation stochastic finite-element method for groundwater flow models based on an undetermined-coefficients approach

A new perturbation technique and finite-element method, which incorporates an undetermined-coefficients approach, is proposed to conduct stochastic simulation for problems of groundwater flow. Formulas of the mean value and variance of groundwater head are derived to exclude the process of computing the first and second-order derivatives of groundwater head with respect to stochastic variables (coefficient of transmissibility, storage coefficient, etc.) in the calculation process of common finite element methods. For ordinary stochastic groundwater problems, the statistical properties of groundwater head can be easily obtained by using the proposed method, which is especially efficient for the stochastic problems that have fewer input stochastic variables. A stochastic numerical simulation of a two-dimensional confined-groundwater flow problem has been conducted to validate effectiveness and determine the limitations of the proposed method. The results illustrate that the accuracy and efficiency of the method proposed are satisfactory, and that the computing time is shorter when there is a small number of input stochastic variables.     

Numerical analysis of soil vibrations due to trains moving at critical speed

High-speed train induced vibrations of track structure and underlying soils differ from that induced by low-speed train. Determining the critical speed of train operation remains difficult due to the complex properties of the track, embankment and ground. A dynamic analysis model comprising track, embankment and layered ground was presented based on the two-and-half-dimensional (2.5D) finite elements combining with thin-layer elements to predict vibrations generated by train moving loads. The track structure is modeled as an Euler–Bernoulli beam resting on embankment. The train is treated as a series of moving axle loads; the embankment and ground are modeled by the 2.5D finite elements. The dynamic responses of the track structure and the ground under constant and vibrating moving loads at various speeds are presented. The results show that the critical speed of a train moving on an embankment is higher than the Rayleigh wave velocity of the underlying soil, attributed to the presence of the track structure and the embankment. It is found that the dynamic response of ground induced by moving constant loads is mostly dominated by train speed. While for the moving load with vibration frequency, the ground response is mostly affected by the vibration frequency instead of train speed. Mach effect appears when the train speed exceeds the critical speed of the track–embankment–ground system.     

A coupling of mixed and discontinuous Galerkin finite-element methods for poroelasticity

In this paper, we formulate a finite-element procedure for approximating the coupled fluid and mechanics in Biot’s consolidation model of poroelasticity. We approximate the flow variables by a mixed finite-element space and the displacement by a family of discontinuous Galerkin methods. Theoretical convergence error estimates are derived and, in particular, are shown to be independent of the constrained specific storage coefficient, c _o . This suggests that our proposed algorithm is a potentially effective way to combat locking, or the nonphysical pressure oscillations, which sometimes arise in numerical algorithms for poroelasticity.     

Application of a three-dimensional finite-element method to strain field analyses

I have programmed a three-dimensional finite-element model to spatially integrate distributed strains. The mathematics is based on Cobbold and Percevault (1983). The method finds the pre-strain configuration of a region by unstraining rectangular prisms into parallelepipeds, then rotating and translating them iteratively to minimize the interelement deviations. A numerical singular-value decomposition calculates the necessary rotations and the final cycle of further strains to make a best fit of the elements. The deviation of elements from holes formed by their nearest neighbors indicates the degree of compatibility of strain measurements.The program reproduces the rotations required in examples with analytic solutions. Even though only a single horizontal layer of elements is used, the fitting procedure correctly calculates rotations in all three dimensions from the constraints of strain compatibility.Three-dimensional strains measured in an Archean greenstone belt of northeastern Minnesota were integrated using a layer of nearly equant finite elements. Rotations calculated from the pre-tectonic configuration accord with field observations of fabrics indicating variable amounts of shear. Rotations about horizontal axes are minimal, precluding large vertical shears. An estimate of 40% true horizontal north-south shortening across the belt can be made from the undeformed configuration.     

A finite-element treatment of sea ice dynamics for different ice rheologies

In this paper the effects of four different rheologies on the evolution of a large-scale sea ice pack are determined and compared. Two rheologies are of viscous-plastic form, and two are viscous fluid relations. The initial pack domain is rectangular, and the motion is driven by wind stress and resisted by ocean drag. Two adjacent edges are rigid shore boundaries, and the other two are free boundaries at open water which move during the pack motion, so that the pack domain changes in time. Two different forms of boundary conditions at the rigid shore edges are considered, which also influence the evolution. The governing equations are solved numerically using a finite-element method, and, unlike previous numerical treatments, no artificial viscosity is incorporated to stabilise the algorithm near interfaces between converging and diverging flow. Instability arises when any tensile stress is abruptly cut-off when diverging flow is initiated, and an alternative view is offered. © 1998 John Wiley & Sons, Ltd.