渗流对岩体高边坡位移的影响

根据渗流场和位移场耦合机理 ,结合某大型船闸工程 ,采用有限元法进行计算分析和对比 ,结果表明船闸在开挖过程中 ,渗流作用力对开挖边坡的稳定性影响很大。并指出对高边坡进行稳定分析时 ,正确考虑渗流作用力的影响十分重要。     

FREE BOUNDARY PROBLEM OF THE 2D SEEPAGE FLOW

ＦＲＥＥＢＯＵＮＤＡＲＹＰＲＯＢＬＥＭＯＦＴＨＥ２ＤＳＥＥＰＡＧＥＦＬＯＷ￥ＳｈｅＹｉｎｇｈｅ（佘颖禾）ＳｕｎＹｉｎｇ（孙鹰）ＧｕｏＸｉａｏｍｉｎｇ（郭小明）（ＤｅｐａｒｔｍｅｎｔｏｆＭａｔｈｅｍａｔｉｃｓａｎｄＭｅｃｈａｎｉｃｓ，Ｓｏｕｔｈｅａｓｔ...     

Free surface seepage analysis based on the element-free method

Element-free method (EFM) for seepage analysis with a free surface presented in the paper is based on the moving least square method which needs only the information at nodes. It avoids troublesome modifications of the mesh as in the finite element method. Being irrelative to the nodes, the mesh for quadrature is fixed throughout the iterations in determining the free surface. And the nodes can be easily added, moved or deleted in the iterations. Steady seepage and transient seepage in a uniform earth dam were analyzed in the paper. The examples show that the proposed method gives satisfactory results.     

地下水地表水联合模拟的解析单元法理论及应用

本文介绍了解析单元法的基本理论及适用条件 ,并运用该方法 (GFL OW1软件 )计算了某水库蓄水过程中库首结晶岩区风化裂隙水渗流场变化 ,取得良好效果.     

改进的有自由面非稳定渗流分析复合单元渗透矩阵调整法

应用连续的罚函数,提出了一种改进的自由面边界条件渗流分析复合单元渗透矩阵调整法,优化了此类算法的稳定性,提高了收敛速度和精度,并将此改进算法编制成相应的有限元分析程序,应用于上海地铁4号线董家渡隧道修复基坑降水工程的优化设计,解决了基坑降水过程中复杂三维渗流场的高效精细模拟问题,同时预测了基坑中心水位降至地面以下40 m,位于承压含水层顶面以下,基坑内外自由面落差很大时基坑周边渗流场以及地面沉降的分布特征.     

边坡稳定分析的虚功率法

基于有限元计算所得应力场的改进极限平衡法, 对渗流与有效应力耦合作用强烈的边坡或地基的稳定性分析具有优势. 本文提出了边坡稳定分析的虚功率法, 即基于极限分析的上限定理, 利用机动许可的组合刚体滑动机构和有限元应力场, 用滑动机构的速度间断面上的抗滑力功率与滑动力功率的比值计算安全系数. 通过分步优化方法, 获得边坡给定滑动机制的稳定安全系数. 对2个典型折线滑动机构的边坡案例进行了分析, 比较了采用静力平衡应力场和静力许可应力场对安全系数的影响. 指出基于土体线弹性本构模型所得的有效应力场计算的稳定安全系数, 也是边坡稳定安全性的一个不错的度量. 算例中本文计算所得的边坡稳定安全系数, 与文献中推荐的答案很接近, 其滑动机制与有限元强度折减法分析所得的滑动机制基本一致, 安全系数也接近, 表明本文提出的方法是合理的边坡稳定分析新方法, 为边坡和地基的稳定性分析提供了新的选择.      

非规则区域中拉普拉斯方程的有限分析5点格式

建立了非规则区域的有限分析5点格式,增加了有限分析法对不规则边界的适应性。应用所提出的方法对水利工程中常见的有压和无压流动进行了计算,与实验和前人的计算结果相比较,本文的方法都能得到较为满意的结果。本文的计算格式也可以应用到其他非规则区域的计算中。     

龙井水库大坝的渗流和稳定分析

本文以龙井水库大坝为例,运用有限单元法对粘土心墙坝的渗流进行分析计算,同时运用瑞典圆弧滑动法和简化Bishop法对粘土心墙坝的坝体稳定进行分析计算,在此基础上对水库大坝进行了渗流安全评价和稳定性安全评价。     

考虑非饱和土基质吸力作用的土石坝渗流分析

传统的渗流分析主要考虑饱和区而忽略非饱和区内的渗流,本文首先对影响非饱和土渗流特性的重要物理量基质吸力进行了分析,阐述了其形成机理并推出其理论计算公式,然后在考虑基质吸力的作用下,基于饱和．非饱和渗流计算原理,采用有限元法考虑了渗流场非饱和区的影响,并以各向同性均质坝和心墙土石坝为算例,进行了计算分析。算例表明,由于基质吸力产生的虹吸作用,使得浸润线上部的非饱和区内也存在着连续的水流,否定了传统分析中浸润线是最上部流线的假设,通过分析这种水流的特点,定性的得出其对土石坝渗流稳定性的影响,对土石坝渗流分析具有一定的指导意义。     

地下水位上升下黄土斜坡稳定性分析

黄土高原一些地区,由于塬上引水灌溉使得地下水位不断抬升,造成黄土滑坡频繁发生。地下水位变化严重影响着黄土斜坡的稳定性。基于饱和-非饱和渗流理论和延伸的摩尔-库伦破坏准则,结合室内饱和和非饱和试验结果,针对泾阳南塬一典型黄土斜坡,考虑地下水位上升情况下,对其进行了瞬态饱和-非饱和渗流分析;然后将计算得到的瞬态孔隙水压力分布用于斜坡的极限平衡分析。结果表明:地下水位上升对暂态渗流场和斜坡稳定性有明显影响;考虑非饱和渗流和吸力强度的边坡稳定分析方法更加符合实际情况。     

渗流-应力耦合随机性分析方法与应用

基于摄动随机有限元法计算参数随机性对渗流-应力耦合问题的影响, 以渗透系数和弹性模量为基本随机量, 推导了渗流-应力耦合摄动随机有限元迭代格式, 在此基础上对现有计算渗流场和应力场的单场随机计算程序进行改造. 使用改造程序对某大坝渗流-应力耦合问题进行分析, 并与商用软件计算结果进行对比.结果表明, 两种方法计算结果基本一致, 揭示了工程实际中的流固耦合规律, 改造的程序还可以输出商用软件未涉及的随机特征.     

Mathematical Modeling of Slurry Infiltration and Particle Dispersion in Saturated Sand

This paper proposes a new computational method for the analysis of slurry infiltration in saturated sand considering the relationship among soil deformation, slurry seepage and particle dispersion. The nonlinear governing equations for slurry infiltration are derived, and the corresponding variational principles based on time increment are established. The finite element method is employed to solve the problem. The computational results are validated with the reported test data, which shows that this method is much better than the traditional Herzig method in predicting the particle deposition. The proposed method is demonstrated through an example of slurry infiltration in slurry trench.     

Modeling Free-Surface Seepage Flow in Complicated Fractured Rock Mass Using a Coupled RPIM-FEM Method

The prediction of the free-surface seepage flow behavior in fractured rock mass is of significance in geotechnical engineering. There are two major issues in solving the seepage flow in complicated fractured rock mass based on the fractured porous medium (FPM) flow model, in which groundwater is assumed to flow simultaneously in both rock matrix and embedded fractures: One is the mesh generation of rock mass in the presence of the fracture network, especially when there exist a large number of stochastic fractures; the other is that a robust iteration algorithm is required since the free surface is unknown at the beginning of solution. Aiming at these two issues, this paper proposes a novel numerical method by coupling radial point interpolation method (RPIM) and finite element method (FEM), in which RPIM is utilized to model the rock matrix and FEM is utilized to model the fractures. On the basis of the variational inequality (VI) theory for free-surface seepage analysis, the computation formulations of the numerical method are derived and the corresponding computation program is developed. Three examples are solved with the present method. It is found that the VI theory can be extended to solve the free-surface seepage problem based on the FPM flow model. A crucial advantage of the present method is that the mesh generation can be greatly simplified. The present method has been verified to be a robust, efficient and reliable method for modeling the groundwater flow in complicated fractured rock mass.     

节点梯度光滑有限元配点法

配点法构造简单、计算高效, 但需要用到数值离散形函数的高阶梯度,而传统有限元形函数的梯度在单元边界处通常仅具有C$^{0}$连续性,因此无法直接用于配点法分析. 本文通过引入有限元形函数的光滑梯度,提出了节点梯度光滑有限元配点法. 首先基于广义梯度光滑方法,定义了有限元形函数在节点处的一阶光滑梯度值,然后以有限元形函数为核函数构造了有限元形函数的一阶光滑梯度,进而对一阶光滑梯度直接求导并用一阶光滑梯度替换有限元形函数的标准梯度,即完成了有限元形函数二阶光滑梯度的构造.文中以线性有限元形函数为基础的理论分析表明,其光滑梯度不仅满足传统线性有限元形函数梯度对应的一阶一致性条件,而且在均布网格假定下满足更高一阶的二阶一致性条件.因此与传统线性有限元法相比,基于线性形函数的节点梯度光滑有限元法的$L_{2}$和$H_{1}$误差均具有二次精度,即其$H_{1}$误差收敛阶次比传统有限元法高一阶, 呈现超收敛特性.文中通过典型算例验证了节点梯度光滑有限元配点法的精度和收敛性,特别是其$H_{1}$或能量误差的精度和收敛率都明显高于传统有限元法.      

基于单元的静力区间有限元法

在许多工程问题中 ,结构参数和荷载具有某种程度的误差或不确定性。若不将它们定量化或模型化加以考虑 ,就不能作出合理的分析和设计。考虑到有限元法在科学界和工程界的广泛应用 ,本文以连续梁结构为例 ,建立了基于单元的静力区间有限元法。为了说明本方法的有效性 ,本文给出了一个数值例子 ,并把所得结果与文献 [1 2 ]进行了比较。     

Finite Element Analysis of Two- and Three-dimensional Flows Around Box-type Bridge Sections

Multilayer seepage model is proposed instead of three dimensional model. Optimum theory based on multilayer finite element formulation is applied to planning the efficient flow rate and pumping well layout. The Sakawa-Shindo method is used for the optimum control calculation. As a numerical example, calculations are carried out to determine an optimum pumping flow for use where a cut-off wall and pumping wells are combined.     

Flow field modelling near a well with a conductive fracture

In the technology of oil recovery the oil production rate can be increased by generation of a vertical sand-filld conductive fracture on the wall of the well. Oil diffuses through the conductive fracture to the well. In this paper the seepage flow and isothermal deformation fields in both the formation and fracture and the oil production rate at the well are studied by modelling the formation as an infinite poroelastic medium saturated with a one-phase compressible fluid. The fracture is treated as a one-dimensional poroelastic medium. Darcy flows are considered in both the formation and fracture. The plane strain condition is imposed. Our solution is obtained numerically by a finite element method based on a variational principle. The accuracy of the analysis is studied by comparison of the numerical solutions of some problems with their analytical solutions. Since we are dealing with the transient flow problem of an infinite region, an extrapolation technique is employed to find the finite element solution. The production rate of a well with the conductive fracture is compared with that of a well without the conductive fracture.     

随机有限元方法在断裂分析中的应用

在幂律非线性随机有限元基础上,以单边裂纹板为例给出计算含量钢继裂参数,J（J积分）,δ（裂纹张开位移）,Δ（由裂纹引起的裂纹板上下底面相对位移）,θ（由裂纹引起的裂纹板上下底在相对转角）及其对基本随机变量变化率的方法和分析算例。     

The analysis of unsteady incompressible flows by a three-step finite element method

This paper describes a three-step finite element method and its applications to unsteady incompressible fluid flows. Stability analysis of the one-dimensional pure convection equation shows that this method has third-order accuracy and an extended numerical stability domain in comparison with the Lax--Wendroff finite element method. The method is cost-effective for incompressible flows because it permits less frequent updates of the pressure field with good accuracy. In contrast with the Taylor-Galerkin method, the present method does not contain any new higher-order derivatives, which makes it suitable for solving non-linear multidimensional problems and flows with complicated boundary conditions. The three-step finite element method has been used to simulate unsteady incompressible flows. The numerical results obtained are in good agreement with those in the literature.     

三维压裂缝网不稳定压力半解析求解方法

受地应力及压裂工艺影响, 大斜度井水力压裂缝网展布复杂, 缝网中存在不同倾斜方向、不同展布形态及不同贯穿程度的压裂缝. 本文通过将裂缝面离散为若干矩形微元实现裂缝形态有效表征, 将渗流过程划分为基质向裂缝流动及裂缝向井筒流动两阶段, 采用有限差分方法构建离散裂缝面内不稳定渗流数值解, 结合封闭边界面源函数及叠加原理构建基质内不稳定渗流解析解, 耦合裂缝内流动数值解与基质内流动解析解, 求解了三维压裂缝网不稳定压力. 基于积分中值定理提出了点源、特殊线源代替面源求解基质内渗流的求解方法, 分析了该方法的可行性及适用条件, 在保证模型精度的同时提升了计算效率. 研究表明, 在基质内采用点源函数面积分求解面源的方法可准确求解三维压裂缝网井底压力动态但计算效率极低, 基于积分中值定理的点源、特殊线源近似面源求解方法可大大提升计算效率, 且在裂缝微元划分较为精细(微元无因次边长小于0.15)时可取得较高精度, 基于该模型分析了裂缝导流能力、裂缝倾角、裂缝高度及裂缝段间距对压裂大斜度井典型试井曲线的影响.