Numerical manifold method for dynamic nonlinear analysis of saturated porous media

It is well known that the Babuska–Brezzi stability criterion or the Zienkiewicz–Taylor patch test precludes the use of the finite elements with the same low order of interpolation for displacement and pore pressure in the nearly incompressible and undrained cases, unless some stabilization techniques are introduced for dynamic analysis of saturated porous medium where coupling occurs between the displacement of solid skeleton and pore pressure. The numerical manifold method (NMM), where the interpolation of displacement and pressure can be determined independently in an element for the solution of u–p formulation, is derived based on triangular mesh for the requirement of high accurate calculations from practical applications in the dynamic analysis of saturated porous materials. The matrices of equilibrium equations for the second‐order displacement and the first‐order pressure manifold method are given in detail for program coding. By close comparison with widely used finite element method, the NMM presents good stability for the coupling problems, particularly in the nearly incompressible and undrained cases. Numerical examples are given to illustrate the validity and stability of the manifold element developed. Copyright © 2006 John Wiley & Sons, Ltd.     

Fast iterative solution of large undrained soil‐structure interaction problems

In view of rapid developments in iterative solvers, it is timely to re‐examine the merits of using mixed formulation for incompressible problems. This paper presents extensive numerical studies to compare the accuracy of undrained solutions resulting from the standard displacement formulation with a penalty term and the two‐field mixed formulation. The standard displacement and two‐field mixed formulations are solved using both direct and iterative approaches to assess if it is cost‐effective to achieve more accurate solutions. Numerical studies of a simple footing problem show that the mixed formulation is able to solve the incompressible problem ‘exactly’, does not create pressure and stress instabilities, and obviate the need for an ad hoc penalty number. In addition, for large‐scale problems where it is not possible to perform direct solutions entirely within available random access memory, it turns out that the larger system of equations from mixed formulation also can be solved much more efficiently than the smaller system of equations arising from standard formulation by using the symmetric quasi‐minimal residual (SQMR) method with the generalized Jacobi (GJ) preconditioner. Iterative solution by SQMR with GJ preconditioning also is more elegant, faster, and more accurate than the popular Uzawa method. Copyright © 2003 John Wiley & Sons, Ltd.     

基于GTP的地下工程与围岩一体化真三维空间构模

针对地下工程开挖体的基本特征及其真三维建模要求，在广义三棱柱(GTP)模型的基础上进行扩展，提出采用E—GTP模型来构建地下工程开挖体的真三维模型。通过与其围岩地质体的G—GTP模型的耦合，实现了基于GTP的工程开挖体与围岩地质体的一体化建模。该模型将地下三维空间实体抽象为点、线、面、体四类对象，通过结点、TIN边、侧边、TIN面、侧面和GTP体元共6个基本几何元素进行统一表达。该文重点讨论了E—GTP的建模原理与方法，并介绍了基于面向对象思想的一体化空间数据结构。     

岩石变形破坏的熵突变过程与破坏判据

在岩石的变形破坏过程中,当进入不稳定的破裂发展阶段之后,系统不断调整结构抵抗外力的扰动,裂纹向局域集中的有序方向发展,应变能不断耗散,并以应变能的耗散为媒介,使系统与外扰动所追加的负熵流产生能量流通,也使系统熵值和系统的维数逐次降低,这一阶段岩石系统远离平衡态,岩石的破坏是系统熵的突变过程。基于这一认识,并在验证应变能分布与结构块度分布模式的一致性的基础上,推导出包含了结构因素和能量分布的熵表达式;对熵表达式进行平衡分析获得局部突变的分岔集,得到了岩石局部破坏的熵折迭突变破坏准则;同时,探讨了熵表达式所表征的结构有序度的尖点突变性,解出岩石系统的分岔集,这个分岔集就是岩石系统熵突变的整体破坏准则。     

环境损害鉴定评估的土壤基线确定方法

近年来,国内环境污染事故频繁发生,由此引发的环境损害问题日益严重。环境损害鉴定评估是中国推行的一项应对环境污染损害的重要环保举措,而基线则是确定损害的关键。基线确定作为损害评估与修复的重要组成部分,是科学评估的关键技术环节和重要前提,也是中国开展环境损害鉴定评估亟待解决的问题。总结国际上常用的4种基线确定方法：即历史数据法、参考点位法、环境标准法和模型推算法的优缺点及应用情况,探讨不同基线确定方法的具体工作步骤,并结合中国土壤环境研究工作积累与进展,提出中国土壤基线确定基本原则和推荐“4步法”工作程序,对中国开展土壤环境损害鉴定评估工作具有重要的理论意义和科学指导作用。     

三维脆性破裂的拉应力判据

用线弹性断裂力学对连续介质中三维裂纹(KⅢ≠0)破裂的拉应力断裂准则提出了补充性假说和相应的计算方法（第一主微分面定点法）。对于给定应力强度因子Ki（i=Ⅰ,Ⅱ,Ⅲ）的裂纹问题,从理论上给出了初始破裂面完整形式的解析表示或数值计算结果。推导结果是,三维拉张破裂的初始破裂面是以破裂点为顶点的广角锥面,跨在原始裂纹面的前缘,它的外缘为螺旋线,锥面的每一条母线都与过该线的第一主微分面重合。大量的这样的初始破裂面叠错密接,互不相交。推算的结果与已有的三锥破裂实验结果基本符合。把补充后的拉应力判据和最大拉应力理论相比较,发现在应力分量只保留奇异项的情况下,这两种判据是等价的;但如果对应力分量作零阶项修正,则两种判据只在三维(KⅢ≠0)问题中等价,在二维(KⅢ=0)问题中不完全等价。     

有限元强度折减法在边坡稳定性分析中的有效性及结果检验方法

有限元强度折减法的有效性及结果评价决定该方法是否能在工程上得到认可及推广的关键。本文基于有理论解的地基承载力问题和澳大利亚计算机应用协会（ACADS）边坡稳定性典型考题,通过计算值与理论解的对比以及塑性贯通区结果,对有限元强度折减法用于边坡稳定分析的有效性、失稳判据以及结果评价等问题进行了系统研究,提出了以塑性带宽度与长度之比检验计算结果的方法。结果发现,在足够且合理的网格密度下,有限元强度折减法分析边坡稳定性是有效的,不同类型的临界状态判据差异不大,而塑性区贯通判据最为客观;临界状态时塑性带的宽度与长度之比与安全系数的计算精度有很高的相关性,其值越小,精度越高,当塑性区相对宽度b/L小于0.05时,安全系数相对误差一般小于5%;对于强度折减法计算结果的精度评价,只要所得的等效塑性应变分布能确定滑动机制和大致的滑动面位置,其安全系数计算结果与更细密的网格的结果差异一般也在5%以内,精度就是足够的。     

Modelling peak accelerations from earthquakes

This paper deals with the prediction of peak horizontal accelerations with emphasis on seismic risk and insurance concerns. Non‐linear mixed effects models are used to analyse well‐known earthquake data and the consequences of mis‐specifying assumptions on the error term are quantified. A robust fit of the usual model, using recently developed robust weighted maximum likelihood estimators, is presented. Outlying data are automatically identified and subsequently investigated. A more appropriate model accounting for the extreme value nature of the responses, is also developed and implemented. The implication on acceleration predictions is demonstrated. Copyright © 2006 John Wiley & Sons, Ltd.     

Statistics of extremes and estimation of extreme rainfall: II. Empirical investigation of long rainfall records / Statistiques de valeurs extrêmes et estimation de précipitations extrêmes: II. Recherche empirique sur de longues séries de précipitations

Abstract

Abstract In the first part of this study, theoretical analyses showed that the Gumbel distribution is quite unlikely to apply to hydrological extremes and that the extreme value distribution of type II (EV2) is a more consistent choice. Based on these theoretical analyses, an extensive empirical investigation is performed using a collection of 169 of the longest available rainfall records worldwide, each having 100–154 years of data. This verifies the theoretical results. In addition, it shows that the shape parameter of the EV2 distribution is constant for all examined geographical zones (Europe and North America), with value κ = 0.15. This simplifies the fitting and the general mathematical handling of the distribution, which become as simple as those of the Gumbel distribution.