离散单元法同拉格朗日元法及其在岩土力学中的应用

离散单元法是一种适合于节理岩体的数值分析方法，拉格朗日元法则特点适用于解决大变形的问题。本文叙述了离散单元法和拉格朗日元法的基本原理以及有关参数的选择问题。文中还举出两种方法在岩土力学中的应用范围。     

弹塑性土质边坡的ALE方法有限元分析

有限元法被广泛用于解决几何和材料非线性的问题,但标准的有限元方法难以有效解决某些材料的大变形问题和计算中的网格扭曲问题。任意拉格朗日-欧拉法（ALE法）吸取了拉格朗日和欧拉法的优点,并克服了两者的缺点,可用于解决仅用拉格朗日或欧拉有限元法所难以解决的问题。基于ALE有限元方法和弹塑性大变形基本原理,研究了岩土工程中土质边坡在自重作用下的稳定问题;计算结果不仅能直观地显示失稳时的大变形状态,并能确定较符合实际的临界滑移面形状;同时分析了含软弱夹层复杂土质边坡的稳定性。结果表明,ALE方法能有效分析土质边坡的稳定性问题,适用于岩土工程的弹塑性分析。     

开口管桩高频振动贯入过程的ALE有限元分析

任意拉格朗日-欧拉(ALE)方法吸取了拉格朗日和欧拉法的优点,避免了常规有限元中拉格朗日方法的网格畸变问题,适用于开口管桩高频振动贯入过程的计算分析。采用ALE有限元方法,建立开口管桩高频振动贯入过程的数值模型,对沉桩过程中挤土效应、桩侧阻力和土塞效应的变化规律进行了详细研究。研究结果表明:挤土应力主要沿径向传播,且深层土体受到的挤土应力比浅层土体大;水平挤土位移随管桩贯入深度的增加而增大,而最大水平挤土位移与管桩贯入深度存在累积效应;挤土效应的影响范围约为10倍管径,因此在施工过程中要给以足够重视;桩外侧摩阻力随贯入深度增加呈近似线性增长,桩内侧摩阻力随贯入深度增加而呈非线性增长,增长速率随贯入深度增加而逐渐增大;管内土塞处于不完全闭塞状态,土塞程度由完全非闭塞向部分闭塞过渡。此外,研究了土体模量、桩土界面摩擦系数、振动频率和桩径对土体位移的影响。     

An operator‐split ALE model for large deformation analysis of geomaterials

Analysis of large deformation of geomaterials subjected to time‐varying load poses a very difficult problem for the geotechnical profession. Conventional finite element schemes using the updated Lagrangian formulation may suffer from serious numerical difficulties when the deformation of geomaterials is significantly large such that the discretized elements are severely distorted. In this paper, an operator‐split arbitrary Lagrangian–Eulerian (ALE) finite element model is proposed for large deformation analysis of a soil mass subjected to either static or dynamic loading, where the soil is modelled as a saturated porous material with solid–fluid coupling and strong material non‐linearity. Each time step of the operator‐split ALE algorithm consists of a Lagrangian step and an Eulerian step. In the Lagrangian step, the equilibrium equation and continuity equation of the saturated soil are solved by the updated Lagrangian method. In the Eulerian step, mesh smoothing is performed for the deformed body and the state variables obtained in the updated Lagrangian step are then transferred to the new mesh system. The accuracy and efficiency of the proposed ALE method are verified by comparison of its results with the results produced by an analytical solution for one‐dimensional finite elastic consolidation of a soil column and with the results from the small strain finite element analysis and the updated Lagrangian analysis. Its performance is further illustrated by simulation of a complex problem involving the transient response of an embankment subjected to earthquake loading. Copyright © 2007 John Wiley & Sons, Ltd.     

海冰动力学数值方法研究进展

在海冰动力学数值模拟和预测研究中,人们将海冰视为连续介质分别建立了欧拉坐标下的有限差分（FD）方法、拉格朗日坐标下的光滑质点流体动力学（SPH）方法、欧拉和拉格朗日坐标相结合的质点网格法（PIC）,近年来又发展了基于非连续介质的颗粒流（GF）方法。对以上几种海冰动力学数值方法的特点和适用性进行了讨论,结果表明：FD、PIC和SPH方法可适用于中长期海冰动力学数值模拟,但SPH方法的计算效率需进一步提高;GF方法在不同尺度下的海冰动力学数值模拟中的计算精度均有很强的适用性,但目前较适用于小尺度下海冰动力学基本特性的数值试验研究,计算时效还不能满足实际海冰数值模拟和预测的要求。为进一步提高海冰动力学模拟的精度和适用性,在不同时空尺度下分别发展与其相适应的数值方法是必要的。     

Large deformation FEMLIP drained analysis of a vertical cut

Understanding and modelling the whole instability mechanisms of a slope are fundamental issues from a scientific and technical viewpoint. To date, small strain Lagrangian approaches have mostly been used in solid mechanics for modelling the failure stage, whereas Eulerian approaches are common in fluid mechanics for propagation analysis. A combination of both approaches allows the stability, failure and propagation stages of a slope to be analysed in a unique mathematical framework. To this end, this paper adopts a finite element method with Lagrangian integration points (FEMLIP), which is currently implemented in the ELLIPSIS code and has been used in geophysics and civil engineering applications. The method combines the robustness of an Eulerian mesh with the flexibility of a set of Lagrangian particles, which allows the history of the material to be taken into account. FEMLIP is first validated with reference to benchmarks with analytical solutions, and is then tested in a large deformation drained analysis of a vertical cut in coarse-grained soils. The results are compared with those provided by the standard engineering methods (1) the limit equilibrium method (LEM) and (2) standard stress–strain elasto-plastic FEM analysis. The comparison shows that FEMLIP is a reliable method for the analysis of both the stability and the instability of a vertical cut, and can be confidently used to analyse more complex problems related to natural slopes.     

天山高山区与郊区降水中颗粒物特征的比较

以天山乌鲁木齐河流域为例,运用参数比较法、相关分析法,对降水中粉尘颗粒物特征在高山区和郊区随时间变化特征及其差异进行研究.结果表明,降水中颗粒物的浓度、粒径分布及化学要素组成在两个取样点都具有明显的季节变化.颗粒浓度表现为冬-春季节升高而夏-秋季节降低,与降水量成反向变化,反映了降水受中亚沙尘活动的影响明显.颗粒在冬-...     

u‐p semi‐Lagrangian reproducing kernel formulation for landslide modeling

This paper presents a u‐p (displacement‐pressure) semi‐Lagrangian reproducing kernel (RK) formulation to effectively analyze landslide processes. The semi‐Lagrangian RK approximation is constructed based on Lagrangian discretization points with fixed kernel supports in the current configuration. As a result, it tracks state variables at discretization points while allowing extreme deformation and material separation that is beyond the capability of Lagrangian formulations. The u‐p formulation following Biot theory is incorporated into the formulation to describe poromechanics of saturated geomaterials. In addition, a stabilized nodal integration method to ensure stability of the domain integration and kernel contact algorithms to model contact between bodies are introduced in the u‐p semi‐Lagrangian RK formulation. The proposed method is verified with several numerical examples and validated with an experimental result and the field data of an actual landslide.     

A finite element formulation in Lagrangian co-ordinates for heat and fluid flow in compacting sedimentary basins

This article presents a numerical model of heat and fluid flow in compacting sedimentary basins formulated in Lagrangian co-ordinates. The Lagrangian co-ordinates are the sediment particle positions of the completely compacted basin. A finite element formulation of excess water pressure and temperature in these Lagrangian co-ordinates is presented, in addition to an equivalent formulation in the real co-ordinates. The later formulation is also Lagrangian of nature, since the elements of the grid in the real co-ordinates always frame the same sediment particles. In other words, it is the Lagrangian grid mapped to the real space. This is done in an iterative loop which solves for excess water pressure, and then updates the real co-ordinates of the sediment particles. By comparing the two finite element formulations it is concluded that the one in real space is the simplest, most efficient and most precise. The model is validated by comparison with two dimensionless one-dimensional solutions, one analytical for the linear case, and one numerical for the non-linear case. Both these one-dimensional solutions are obtained on the unit interval, where the moving top boundary caused by continuous sedimentation is incorporated.     

Methods for evaluating in-stream attenuation of trace organic compounds

Wastewater treatment plants are often the most substantial contributor of trace organic compounds including pharmaceuticals, steroidal hormones, and surfactants to surface waters. Studying stream reaches below wastewater treatment plants provide valuable information on the environmental persistence of these compounds. Three methods for conducting field investigations to evaluate in-stream attenuation of trace organic compounds are presented: (1) using intrinsic tracers in wastewater, (2) environmental sampling coupled with dye studies to assess travel times between sample locations, and (3) Lagrangian sampling. Advantages and limitations of each method are discussed, along with key findings from several investigations.     

钻井船插桩对邻近桩影响的耦合欧拉-拉格朗日有限元方法研究

依据模拟钻井船在黏土层中插桩对邻近桩影响的离心模型试验结果,研究了通过耦合欧拉-拉格朗日（CEL）有限元计算并结合非线性地基梁有限元计算,分析钻井船插桩对邻近桩影响问题的可行性。CEL有限元方法将产生大变形的土体设为欧拉体,采用欧拉有限元方法计算该区域的变形响应,计算过程中,欧拉体的空间网格形状、大小位置保持不变,物质可在网格之间运动;其他土体设为拉格朗日体,采用拉格朗日有限元方法计算变形响应,计算过程中,物质的运动和网格的变形保持一致。运用罚函数方法实现欧拉体与拉格朗日体的耦合。通过CEL有限元计算,可以确定钻井船插桩导致的邻近桩桩身水平位移。进一步通过非线性地基梁有限元模型计算确定桩身弯矩。计算结果表明,利用CEL有限元方法并结合非线性地基梁有限元方法计算出的桩身位移和弯矩沿桩长的变化与离心模型试验结果基本一致。说明采用CEL有限元方法并结合非线性地基梁有限元方法分析黏土层中插桩对邻近桩的影响问题是可行的。CEL有限元模型中欧拉土体范围的设置对计算结果有明显影响。研究表明,若插桩深度小于0.75倍桩靴直径,可将欧拉土体范围设置成1.00～1.25倍桩靴直径;若插桩深度大于0.75倍桩靴直径,将欧拉土体范围取为插桩深度以下0.5倍桩靴直径是恰当的。     

对强度折减法若干问题的讨论

强度折减法是数值模拟处理边坡稳定问题的常用方法,由于影响该方法计算精度的因素很多,所以该方法仍未在工程界得到确认和推广。本文采用FLAC（显式拉格朗日有限差分法）进行计算,通过对算例结果进行比较,阐明了在边坡稳定分析中边界范围和网格的疏密对强度折减法结果的影响,特别地,在边界范围上摆脱了数值模拟方法的建模原则的束缚,即边界范围取足够大的原则,并用计算结果极好地证明了结论的可靠性。     

基于扩展Lagrange乘子的Clough接触面模型及应用

双曲线接触面本构模型能比较真实地模拟堆石材料与混凝土面板间的接触关系,扩展Lagrange乘子法能比较精确地计算接触面间接触状态。在吸取Clough双曲线接触面本构关系应用于无厚度的Goodman单元和有厚度的Desai薄层单元的成功经验的基础上,将Clough双曲线接触面模型引入扩展Lagrange乘子法进行摩擦接触问题的求解。介绍了基于扩展Lagrange乘子法的序列二次规划法（SQP）提法,详细推导了在扩展Lagrange算法的非线性接触计算中引入Clough双曲线接触面本构关系的数值列式和实施步骤。数值算例和工程实例的计算结果证明该方法是成功的,能够比较真实地模拟堆石-混凝土墙（混凝土面板）之间的接触状态。     

On the Implementation of augmented Lagrangian method in the two‐dimensional discontinuous deformation Analysis

The discontinuous deformation analysis (DDA) is a discontinuum‐based method, which employs a penalty method to represent the contact between blocks. The penalty method is easy to be implemented in the program, but the contact constraint is only approximately satisfied. Penetrations between contacting blocks are unavoidable even if the penalty value is very large. To improve the contact precision in the DDA, an augmented Lagrangian method is introduced, which can make use of advantages of both the Lagrangian multiplier method and the penalty method. This paper provides a detailed implementation of the augmented Lagrangian method in the DDA program and compares it with the standard DDA on the computational efficiency and contact precision. Copyright © 2013 John Wiley & Sons, Ltd.     

Revisiting the constitutive equations of unsaturated porous solids using a Lagrangian saturation concept

This paper aims at revisiting the constitutive equations of unsaturated porous solids at the light of a Lagrangian saturation concept. By referring the currently wetted porous volume to the reference configuration, the Lagrangian saturation is the state variable associated with the interfacial energy changes only, irrespective of the elastic energy required for deforming the solid matrix. The Lagrangian saturation concept provides the basis of a generic approach to the theory of poroelastoplasticity in unsaturated conditions. We successively examine the case where the saturating fluids occupy disconnected networks and the case where the networks are connected so that the saturating fluids can invade the porous solid or recede from it. The analysis provides the restricted situations where the averaged pore pressure may play the role of an effective pore pressure. Copyright © 2007 John Wiley & Sons, Ltd.     

Computer Simulation of Shaped Charge Detonation Using Meshless Particle Method

Shaped charges are widely applied in the defense industry and civil engineering for penetrating hardened targets. Simulations of shaped charges are generally based on traditional grid-based numerical methods. Different from the existing literature, the SPH method is applied in this paper to simulate the detonation process of shaped charge explosive. The combination of the meshless, Lagrangian and particle nature inherent in the SPH method is very attractive in dealing with large deformations and large inhomogeneities in extremely transient situations such as detonation process. The SPH method and some related numerical aspects are briefly discussed first, followed by applications in simulating shaped charge detonations. The effects of different detonation cavity angles and different charge head lengths are investigated. The results demonstrate that major shaped charge detonation phenomena are captured with revealing observations.     

Solution of quasi‐static large‐strain problems by the material point method

A procedure for solving quasi‐static large‐strain problems by the material point method is presented. Owing to the Lagrangian–Eulerian features of the method, problems associated with excessive mesh distortions that develop in the Lagrangian formulations of the finite element method are avoided. Three‐dimensional problems are solved utilizing 15‐noded prismatic and 10‐noded tetrahedral elements with quadratic interpolation functions as well as an implicit integration scheme. An algorithm for exploiting the numerical integration procedure on the computational mesh is proposed. Several numerical examples are shown. Copyright © 2010 John Wiley & Sons, Ltd.     

软泥岩井眼弹塑性变形的拉格朗日元法计算

首次将大变形原理引入井眼及其围岩弹塑性变形计算,应用拉格朗日元法对塑性泥页岩地层的井眼缩径问题进行分析求解。拉格朗日元法能够计算材料非线性和几何非线性问题,采用常用的摩尔-库仑强度准则对所选择的计算模型进行拉格朗日元分析计算,求解出井眼的收缩变形、井眼围岩位移场分布以及井眼围岩塑性区的分布规律。      

Permeability Estimation with the Augmented Lagrangian Method for a Nonlinear Diffusion Equation

We consider numerical identification of the piecewise constant permeability function in a nonlinear parabolic equation, with the augmented Lagrangian method. By studying this problem, we aim at also gaining some insight into the potential ability of the augmented Lagrangian method to handle permeability estimation within the full two-phase porous-media flow setting. The identification is formulated as a constrained minimization problem. The parameter estimation problem is reduced to a coupled nonlinear algebraic system, which can be solved efficiently with the conjugate gradient method. The methodology is developed and numerical experiments with the proposed method are presented.