Parametric variational principle for elastic–plastic consolidation analysis of saturated porous media

Finite element procedures for numerical solution of various engineering problems are often based on variational formulations. In this paper, a parametric variational principle applicable to elastic-plastic coupled field problems in consolidation analysis of saturated porous media is presented. This principle can be used to solve problems where materials are inconsistent with Drucker's postulate of stability, such as in non-associated plasticity flow or softening problems. The finite element formulation was given, and it can be solved by either the conventional method or a parametric quadratic programming method.     

Efficient solution for matrix-fracture flow with multiple interacting continua

An efficient numerical procedure for implementing the multiple interacting continua (MINC) method for fractured porous media in a general-purpose multiphase simulator is presented. This procedure is substantially faster, requires less memory, is amenable to any n-component, multiphase non-isothermal package, and is readily adaptable for parallel processing computers. The present procedure results in a reduction of the computing time by a factor of the order of NMINC³ as compared to the band algorithm, where NMINC is the number of nested continua into which each matrix block is further discretized. The memory requirement approaches a reduction factor of the order of NMINC² for larger problems compared to the band algorithm. The code for the algorithm was structured so as to set up the time consuming, but independent, computations for each matrix block in a subroutine that was parallelized and tested using a Sequent machine accessed under a UNIX environment. For NMINC=10, total computing time was reduced by 33 per cent for the use of two versus one processor, with the savings increasing for increasing NMINC. The proposed procedure can be implemented with the same ease and efficiency in conjunction with any iterative or direct method, and the grid-blocks can be ordered in any non-standard manner such as in D-4, D-2, and others. Copyright © 1999 John Wiley & Sons, Ltd.     

Some aspects of transformations of compositional data and the identification of outliers

The statistical analysis of compositional data is based on determining an appropriate transformation from the simplex to real space. Possible transfonnations and outliers strongly interact: parameters of transformations may be influenced particularly by outliers, and the result of goodness-of-fit tests will reflect their presence. Thus, the identification of outliers in compositional datasets and the selection of an appropriate transformation of the same data, are problems that cannot be separated. A robust method for outlier detection together with the likelihood of transformed data is presented as a first approach to solve those problems when the additive-logratio and multivariate Box-Cox transformations are used. Three examples illustrate the proposed methodology.     

应力释放法在隧洞开挖模拟中若干问题的研究

根据快速拉格朗日法的基本原理,讨论了在其中实现应力释放法的理论根据。通过不同侧压系数下脆性岩体中圆形隧洞开挖卸荷过程的应力释放法模拟和真三维模拟,分别讨论了应力路径问题、模拟空间效应时最终计算结果的准确性及其工程应用问题。在未包含断层、软弱带等特殊地质条件的情况下,分析得到以下结论：（1）应力释放法模拟中,围岩经历的应力路径与真三维模拟不同,故只能用前者来近似模拟开挖问题;（2）不同的应力路径将导致不同的最终结果,在一定的近似程度要求及计算工作条件下应力释放法模拟的最终结果可近似真三维的模拟结果,且对于圆形隧洞问题,当侧压系数从1.0开始增大或减小时,这种近似误差将减小,并最终趋于稳定;（3）在工程应用中,由应力释放法可得到收敛约束法中的GRC曲线,从而使得它在工程应用中发挥重要的作用。     

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.     

Implications of variationally derived 3D failure mechanism

This paper revisits the variational limit equilibrium (LE) analysis of three‐dimensional (3D) slope stability in the context of limit analysis (LA). It proves the kinematic admissibility of the 3D mechanism in LA, although it was derived from LE variational extremization. It also includes algorithms in the realm of LA that are associated with the variational mechanism. A comparison between the variational results and reported LA upper‐bound or LE closed‐form results is conducted. It demonstrates that the variationally derived mechanism consistently yields upper‐bound solutions for 3D symmetrical slopes that are as accurate as those produced by postulated mechanisms in LA. However, the results are more critical than those derived from spherical failure mechanism in LE. The generalized log spiral 3D mechanism rigorously legitimizes the variational slope stability analysis in both frameworks of mechanics LE and LA. Stability charts were produced where the 3D factor of safety can be assessed for a constrained length of failure, while including factors like pore water pressure and seismic loading. The results presented within this study demonstrate the capabilities of the variational 3D solution and can be used to evaluate approximate methods, numerical or closed‐form, developed in 3D slope stability analyses. Copyright © 2016 John Wiley & Sons, Ltd.     

排水砂槽渗流试验与Signorini型变分不等式方法验证

排水是岩土体及工程构筑物渗流控制的主要措施之一,其实质是通过在渗流域内形成潜在溢出边界或低水位边界而实现渗流控制的。在排水渗控条件下,渗流场往往具有强烈的边界非线性特征,Signorini型变分不等式方法从理论上为稳定和非稳定排水渗流问题提供了有效的分析方法,但其实际效果还需要得到试验的验证。通过开展含5个排水廊道的排水砂槽模型试验,研究了复杂排水条件下砂土渗流的基本规律,并通过试验数据与数值计算成果的对比分析,论证了Signorini型变分不等式方法的有效性和正确性。试验结果表明,在稳定渗流条件下,排水砂槽上游侧3个排水廊道对渗流控制起主导作用,而下游侧2个廊道则失去排水功能,数值计算与试验成果吻合较好;在非稳定渗流条件下,受测压管精度、砂样均匀性和毛细效应的影响,数值计算与试验成果存在一定偏差,但也较好地揭示了复杂排水条件下砂槽中的非稳定渗流特征。排水砂槽试验结果验证了Signorini型变分不等式方法的有效性和正确性,为复杂排水条件下岩土体及工程构筑物的渗控结构优化设计提供了有效的分析手段。     

Fracturing and Failure Behavior of Carrara Marble in Quasistatic and Dynamic Brazilian Disc Tests

The tensile strength and fracturing behavior of Carrara marble subjected to the dynamic Brazilian disc test using the split Hopkinson pressure bar technique are determined and compared with those obtained by the conventional quasistatic Brazilian disc test. Detailed observation of the cracking processes is aided by high-speed video footage captured at a frame rate of 100,000 frames per second. The dynamic increase factor is computed, revealing a strong strain rate dependence of the Carrara marble when subjected to strain rates above 1 s^?1. Similar to the quasistatic loading tests, conspicuous white zones/patches commonly appear prior to the initiation of visible cracks in the dynamic loading tests. Identification of the white patch initiation and evolution is aided by image comparison software. Comparing the cracking and failure processes under quasistatic and dynamic loading, some distinct differences in the white patch geometry and initiation load are observed. In addition, the extent of the compressive failure zones around the contact points between the loading platens and specimens is found to increase with the strain rate.     

Applicability of the ACE algorithm for multiple regression in hydrogeology

This paper introduces the alternating conditional expectation (ACE) algorithm of Breiman and Friedman (J Am Stat Assoc 80:580–619, 1985) for estimating the transformations of a response and a set of predictor variables in multiple regression problems in hydrogeology. The proposed nonparametric approach can be applied easily for estimating the optimal transformations of different hydrogeological data to obtain maximum correlation between observed variables. The approach does not require a priori assumptions of a functional form, and the optimal transformations are derived solely based on the data set. The advantages and applicability of this new approach to solve different multiple regression problems in hydrogeology or in Earth Sciences are illustrated by means of theoretical investigations and case studies. It is demonstrated that the ACE method has certain advantages in some fitting problems of hydrogeology over the traditional multiple regression. Based on our knowledge, this is the first application of the ACE algorithm to analyze and interpret groundwater data.     

Signorini型变分不等式方法在实际工程渗流问题中的应用

对Signorini型变分不等式方法定义的罚Heaviside函数进行了改进,建立了自适应罚Heaviside函数,从而使Signorini型变分不等式方法的数值稳定性进一步得到改善,网格依赖性进一步得到克服。通过将Signorini型变分不等式方法应用于深圳市公明水库坝区渗流分析,论证了Signorini型变分不等式方法在复杂强非线性三维渗流问题中的适用性。     

A variational principle for granular materials

A major problem in the mathematical modelling of the deformation of granular materials has been the lack of an easily usable variational principle. This is because the frictional dissipation of energy in these materials does not allow the use of the classical extremum principles. In this paper, a variational principle is constructed which is valid even when frictional dissipation occurs. Its derivation uses results from the mathematical theory of envelopes. Both the stresses and the strains can be varied, and for the case of non-frictional plasticity it reduces to the maximum work principle of Hill. An example is presented to show how this new principle can be used to obtain approximate solutions to boundary-value problems with granular materials. The only requirements in advance are a displacement field that obeys the kinematic boundary conditions, and a stress field that obeys equilibrium and the static boundary conditions. The principle is therefore quite straightforward to apply.     

Reconstruction of ice flow directions south of the Baltic Sea during the Saalian and Weichselian glaciations

Till stratigraphical investigations in Berlin have been evaluated using the gravel counting method (4–12.5 mm). The results are compared with studies of several authors from the coastal area north of Berlin (Rügen and Stoltera Cliff near Warnemünde); the gravel counting results from Stoltera Cliff (Cepek 1973) are re-evaluated by means of cluster analysis, and a new stratigraphical interpretation of the sequence in the cliff is given. These results, together with a discussion of correlation problems of Weichselian and especially Saalian tills south of the Baltic Sea, lead to the following hypothesis: it is proposed that the ice margin of each glaciation has been nourished by several ice flows coming from different directions, for the most part turning from north-northeast at onset to east-northeast in later phases. Consequently, differences of composition are found in tills of the same age.     

非恒定水流计算的最优控制问题及其变分求解

为综合利用各类可用的信息源(如水流运动规律,观测资料和统计信息),在反问题的框架下构建了非恒定水流计算的变分模型.针对模型预测的可能误差来源,给出了初始条件、边界条件、物理参数三类独立参量及综合控制问题的定义.在此基础上,阐述了变分法求解这类偏微分方程最优化控制问题的基本原理及模型求解步骤.同时,为便于应用参考,选取初始条件、边界条件和物理参数作为控制向量,以实际常用的水流运动微分方程为基础,导出了一、二维非恒定水流计算的通用伴随方程.并以珠江黄浦至大虎段二维潮流计算为例,展示了变分模型的应用.     

Seepage flow problems by variational inequalities: Theory and approximation

The theory of variational inequalities enables us to formulate and solve free boundary problems in fixed domains, while most other methods assume the position of the unknown domain in solving the problem. Here the problem of seepage flow through a rectangular dam with a free boundary is formulated as a vertical inequality following the ideas of Baiocchi. In order to demonstrate the essential ideas of extending the domain of the solution of problems with free boundaries, the problem of the deflection, of a string on a rigid support is first examined. Next, variational inequalities are derived which are associated with several cases of seepage problems. An approximation theory, including a priori error estimates, is developed using finite element methods, and an associated numerical scheme is given. It is shown that for linear and quadratic finite element methods, the rates of convergence are 0(h) and 0(h^1.25-δ), 0 < δ < 0.25, respectively, if the permeability is constant.     

A new incompatible mode element with selective mass scaling for saturated soil dynamics

It is a well-known fact that addressing hydromechanical problems in saturated soils with the finite element method and equal-order interpolation formulations in displacements and pore pressures produces unstable results. Classically, stabilization has been achieved by increasing the interpolation degree of displacement with respect to pore pressure, hence fulfilling the Babuska–Brezzi condition. However, the use of quadratic elements involves high computational costs. From that point of view, the use of stabilized low-order elements is a more desirable option. Much research has been carried out in different directions in the stabilization of low-order formulations for saturated soils in quasistatic conditions, among others with the technique based on strain field enhancement through internal degrees of freedom. This article presents an alternative displacement–pore pressure formulation for saturated soil dynamics based on the enhancement of the displacement field through incompatible modes.     

Poro-viscoelasticity modelling based on upscaling quasistatic fluid-saturated solids

In this paper, quasistatic models are developed for the slow flow of compressible fluids through porous solids, where the solid exhibits fading memory viscoelasticity. Problems of this type are important in practical geomechanics contexts, for example, in the context of fluid flow through unconsolidated reservoir sands and of wellbore deformation behaviour in gas and oil shale reservoirs, all of which have been studied extensively. For slow viscous fluid flow in the poro-viscoelastic media we are able to neglect the dynamic effects related to inertia forces, as well as the dissipation associated with the viscous flows. This is in contrast to the vast body of work in the poro-elastic context, where much faster flow of the viscous fluids may give rise to memory effects associated with microflows in pores of the solid media. Such problems have been treated extensively in both the dynamic and quasistatic cases. We are taking a specific type of the porous medium subject to slow deformation processes possibly inducing moderate pressure gradients and flow rates characterised by negligible inertia effects. As the result of homogenisation of such a two-phase medium, we observe the fading memory behaviour in the Biot modulus which controls the pressure increase due to skeleton macroscopic deformation and pore fluid content. Although our derivation leads to a result which is consistent with the formal phenomenological approach proposed by Biot (J Appl Phys 23:1482–1498, 1962), we offer the reader more insight into the structure of the poro-viscoelastic constitutive relations obtained; in particular, we can show that the Biot compressibility evolves in time according to the creep function while the skeleton stiffness is driven by the relaxation function.     

The Mechanisms of Soil Regulating Nitrogen Dynamics

In recent decades, the amount of reactive nitrogen (N) has rapidly increased. While the reactive N, mainly chemical N fertilizers, meet food and economic development demands, it has also caused many environmental problems. Now, there are the triple challenges of food security, environmental degradation and climate change for the world due to the rapid increase of reactive N. Most of reactive N has been input to soil firstly, which would export to hydrosphere, atmosphere, and biosphere after transformed as different N forms through various N transformation processes. Thus, soil N transformations play very important role in regulating the fate of soil N. In this article, we review the methods determining the rates of soil N transformations, and clarify the role of soil gross N transformations to regulating soil N dynamics and its mechanisms. Our results suggest that the coupling of soil N transformation with climate and plant species-specific N preferences play important role in optimize N use efficiencies in agricultural production. However, scientists usually just qualitatively discuss the feedbacks and its mechanisms between plants and soil N transformations, due to the limitation of research methods. The quantitative investigation on the effects of these feedbacks on soil gross N transformations is of important significances to understand the feedback and its mechanisms between plants and soil N transformations, to optimize N fertilization, and to make N pollution control countermeasures and so on.     

成都市市区土壤热释汞地球化学分布特征及污染评价

首次将热释汞研究用于环境污染检测领域,对成都市市区,流经市区的主要河流沿岸以及市区内公园土壤中热释汞的地球化学特征及空间分布特征进行了分析研究,对热释汞的污染程度与其它汞的研究方法做了对比研究。结果表明:热释汞研究方法与其它汞研究趋势相符,即一环路之内的热释汞含量明显偏高;其它地方的热释汞含量为:南河>府南河>沙河>府河;建筑区>公园>河流沿岸。     

岩体裂隙网络非稳定渗流分析与数值模拟

针对裂隙岩体的非稳定渗流问题,通过将Darcy定理扩展到包含干区的整个裂隙网络区域,并令潜在溢出边界条件为Signorini型互补边界条件,将湿区上的非稳定渗流问题转化为全域上的一个新的初边值问题。为降低试探函数选取的难度,建立与定义在整个裂隙网络区域上的偏微分方程（PDE）提法等价的抛物型变分不等式（PVI）提法,并给出裂隙网络非稳定渗流分析的有限元数值分析格式和迭代算法,与砂槽模型试验数据的对比分析,验证其有效性。最后,将文中发展的计算方法应用到含复杂裂隙网络的边坡非稳定渗流分析,计算结果很好地反映出边坡内部自由面随库水降落的变化规律,并能准确地描述裂隙网络内部渗流运动特征及流量分布的不均匀性。