自然单元法在岩土工程中应用两例

自然单元法(NEM)是较近出现的一种无网格方法,其形函数兼有无网格的特点和传统有限元的优点,是一种理想的适合岩土工程问题计算的新型数值方法。介绍了自然单元法的基本原理和特性,并讨论了其在岩土工程中的具体应用。将Goodman单元引入自然单元法以实现对不连续面的模拟,研究表明,在NEM中加入节理单元的总体原则和具体的实施细节与FEM中完全相同;而在一般的无网格方法中,则稍微复杂一点。为了实现对岩土工程中常见的无限域或半无限域问题的模拟,引入了无界单元;由于自然单元法的特性,自然单元法和无界元可实现无缝“耦合”。具体的数值算例验证了上述思路。     

一种适用于岩土力学无界域的有限元与边界元耦合法的具体实现

针对有限元与边界元耦合法在岩土力学无异域中应用的具体实现问题进行了研究，提出了在微机上实现的具体措施和需建立的程序模块，将有限元与边界元耦合法计算结果、有限元计算结果与理论解析解进行了比较。     

二维与三维问题的无界边界单元

本文通过对二维与三维问题的无界边界元的分析,指出二维问题中原有边界元上插值函数的缺点和不合理性,提出一种新型的无界边界元插值形式,对无界单元上的发散积分作了一些讨论。     

储层流固耦合的数学模型和非线性有限元方程

根据饱和多孔介质固体骨架的平衡方程和多孔介质中流体的连续性方程,建立了储层流固耦合数学模型。模型中引入了Jaumann应力速率公式描述多孔介质固体骨架的大变形效应,并考虑了地应力、初始孔隙压力、初始流体密度和初始孔隙度对耦合模型的影响。基于与微分方程等价的加权余量公式,在空间域采用有限元离散,对时间域进行隐式差分格式离散,导出了以单元节点位移和单元节点孔隙压力为未知量的储层流固耦合的非线性有限元增量方程。该模型在石油工程中有广泛的应用,为储层流固耦合的数值模拟奠定了理论基础。     

岩体初始地应力场分析方法研究

初始地应力场是影响岩土工程稳定性的重要因素之一,如何合理地模拟初始地应力场一直是岩体力学中的重要研究课题。以国内某大型水利水电工程构筑区域实测空间地应力资料为基础,以边界位移为控制对象,采用有限元（无界元）方法对工程区大范围内的岩体初始地应力场进行了分析和研究。尝试在实际边界上满足无穷远处位移为0的模型边界上引入了无界单元,实测点上的应力拟合结果有较明显的改善,这表明所采用的方法是切实可行和有效的。     

状态方程法在渗流-应力耦合场求解中的应用

提出了一种计算土体渗流-应力耦合场的状态方程法。按平面应变问题,将描述渗流-应力耦合的平面固结方程进行空间离散,并用状态方程表示了有限元控制方程。利用牛顿-柯特斯公式,导出了当前时间步节点位移向量与前一时间步位移向量之间关系的递推公式。算例表明：状态方程法解决土体渗流-应力耦合问题与传统差分法相比的优势在于用较少的机时即可得到较为精确的解。     

三向应力作用下节理岩体渗流-应力耦合特性

节理岩体渗流-应力耦合特性研究是岩石力学领域的重点和难点。水利水电工程与地下工程中天然节理岩体往往处于三向不等压应力状态,针对三向应力状态下节理岩体渗流-应力耦合特性研究较少。其中,单节理岩体渗流-应力耦合特性研究是基础。首先分析与探究了单节理岩体侧向应力作用效果及渗流作用机制,在单节理岩体渗透性-应力耦合分析模型基础上推导了单节理岩体渗流-应力耦合的理论公式。通过室内真三轴渗流-应力耦合试验,基于全局优化算法的非线性拟合及块体离散元数值仿真,验证了所提出理论公式的合理性。基于电路原理,给出了模拟电路与渗流问题的相似物理量,通过引入等效渗流阻方法,探究了典型的含正六边形主干节理网络的渗流-应力耦合特性。该研究结果对实际工程岩体的渗流分析有一定的参考价值。     

单桩承载性能的三维有限元无限元耦合分析

提出了用于单桩-承台-土相互作用分析的三维有限元无限元耦合分析程序, 通过将程序的计算与山东济南某现场实测结果作比较, 验证了计算程序的精确性, 在此基础上用该程序分析了单桩的承载性能。     

裂隙岩体流固耦合双重介质模型的有限元计算

基于孔隙-裂隙岩体的双重孔隙介质流固耦合计算的微分方程,利用伽辽金有限元法提出的相应有限元公式,并基于岩体分类指标（RQD,RMR）提出了与岩体应力状态相关的渗透系数计算公式。编制了相应的有限元程序并给出了应用算例,将计算结果与相关文献作了比较,得出相关结论。     

结构-地基动力相互作用的时域模型

结构-地基动力相互作用是结构地震响应分析及安全评估的一个非常重要课题。基于比例边界有限元法,提出了一种新颖的结构-地基动力相互作用的时域模型,即采用比例边界有限元子域模拟近场有限域部分,采用高阶透射边界模拟远场无限域部分。通过采用连分式展开和引入辅助变量,有限域的动力方程采用高阶的静力刚度矩阵和质量矩阵表示。高阶透射边界精确满足无限远处的辐射边界条件,具有全局精确、时间局部和收敛速度快等优点。它是基于改进的连分式法求解无限域动力刚度矩阵而建立的,在时域里表示为一阶常微分方程组。通过联立有限域和无限域的运动方程,建立了结构-地基相互作用的标准动力学方程,采用Newmark法可直接求解。3个算例结果表明,该算法在时域里比黏弹性边界更精确、有效。     

A 2.5-D coupled FE–BE model for the dynamic interaction between saturated soil and longitudinally invariant structures

A two-and-a-half-dimensional (2.5-D) coupled finite element–boundary element (FE–BE) model is presented to simulate the three-dimensional dynamic interaction between saturated soils and structures with longitudinally invariant geometries. A regularized 2.5-D boundary integral equation for saturated porous media is derived that avoids the evaluation of singular traction integrals. The 2.5-D coupled FE–BE model is established by using the continuity conditions on the soil–structure interface. The developed model is verified through comparison with an existing semi-analytical method. Two case studies of a tunnel embedded in a poroelastic half-space and the efficiency of a vibration isolating screen are presented.     

Computing of the Anchor by the Method of Three-Dimension Point-Radiate Infinite Elements

On the basis of the one-dimension infinite element theory, the coordinate translation and shape function of 3D point-radiate 8-node and 4-node infinite elements are derived. They are coupled with 20-node and 8-node finite elements to compute the compression distortion of the prestressed an- chorage segment. The results indicate that when the prestressed force acts on the anchorage head and segment, the stresses and the displacements in the rock around the anchorage head and segment con- centrate on the zone center with the anchor axis, and they decrease with exponential forms. Therefore, the stresses and the displacement spindles are formed. The calculating results of the infinite element are close to the theoretical results. This indicates the method is right. This article introduces a new way to study the mechanism of prestressed anchors. The obtained results have an important role in the re- search of the anchor mechanism and engineering application.     

Finite element analysis of land subsidence above depleted reservoirs with pore pressure gradient and total stress formulations

The solution of the poroelastic equations for predicting land subsidence above productive gas/oil fields may be addressed by the principle of virtual works using either the effective intergranular stress, with the pore pressure gradient regarded as a distributed body force, or the total stress incorporating the pore pressure. In the finite element (FE) method both approaches prove equivalent at the global assembled level. However, at the element level apparently the equivalence does not hold, and the strength source related to the pore pressure seems to generate different local forces on the element nodes. The two formulations are briefly reviewed and discussed for triangular and tetrahedral finite elements. They are shown to yield different results at the global level as well in a three‐dimensional axisymmetric porous medium if the FE integration is performed using the average element‐wise radius. A modification to both formulations is suggested which allows to correctly solve the problem of a finite reservoir with an infinite pressure gradient, i.e. with a pore pressure discontinuity on its boundary. Copyright © 2001 John Wiley & Sons, Ltd.     

Non-linear analysis of geomechanical problems using coupled finite and infinite elements

In modeling of many geomechanics problems such as underground openings, soil-foundation structure interaction problems, and in wave propagation problems through semi-infinite soil medium the soil is represented as a region of either infinite or semi-infinite extent. Numerical modeling of such problems using conventional finite elements involves a truncation of the far field in which the infinite boundary is terminated at a finite distance. In these problems, appropriate boundary conditions are introduced to approximate the solution of the infinite or semi-infinite boundaries as closely as possible. However, the task of positioning the finite boundary in conventional finite element discretization and the definition of the boundary and its conditions is very delicate and depends on the modeller's skill and intuition. Moreover, such a choice is influenced by the size of the domain to be discretized. Consequently, the dimensions of the global matrices and the time required for solution of the problem will increase considerably and also selection of the arbitrary location of truncated boundary may lead to erroneous result. In order to over come these problems, mapped infinite elements have been developed by earlier researchers (Simoni and Schrefier, 1987). In the present work the applicability of infinite element technique is examined for different geomechanics problems. A computer program INFEMEP is developed based on the conventional finite element and mapped infinite element technique. It is then validated using selected problems such as strip footing and circular footing. CPU time taken to obtain solutions using finite element approach and infinite element approach was estimated and presented to show the capability of coupled modeling in improving the computational efficiency. Mesh configurations of different sizes were used to explore the enhancement of both computational economy and solution accuracy achieved by incorporation of infinite elements to solve elastic and elasto-plastic problems in semi-infinite/finite domain as applied to geotechnical engineering. © Rapid Science Ltd. 1998     

A 3D composite finite element used to model a vertical drain and its surrounding remoulded soil

This work addresses an enrichment technique for the three-dimensional (3D) finite element (FE) analysis of a vertical drain foundation because (1) 1D and 2D simulations are insufficient to integrally describe the consolidation behaviour and (2) drains are small both in spacing and size, resulting in enormous computational costs for a traditional 3D FE analysis. Based on the idea of the semi-analytical finite element method (FEM), which combines general FEM with the high accuracy of a closed-form solution, a new spatial element that contains a drain well and its neighbouring smear zone is presented. This new combined element is depicted by eight global independent nodes and two local dependent nodes, and a classical analytical theory is introduced to set up the relationship between the two kinds of nodes. Because permeability diversity between the drain and the smear zone is considered, both the effects of smearing and well resistance are taken into account with the composite element method (CEM). A detailed derivation of the CEM is performed using the weighted residual method. The accuracy of the proposed method is validated with a totally penetrating, single-drain ground analysis for seven calculation conditions. Additionally, the proposed CEM saves 1/4–1/2 mesh elements and helps to avoid slender elements for the FEM analysis of the drained foundation.     

Numerical modelling of regional faults in land subsidence prediction above gas/oil reservoirs

The stress variation induced by gas/oil production may activate pre‐existing regional faults. This may enhance the expected land subsidence due to the generation of mechanically weak points close to the producing field. A class of elasto‐plastic interface elements (IE), specifically designed to address the mechanical behaviour of faults over a regional scale, is integrated into a finite element (FE) geomechanical model and used to investigate the role exerted by active faults in anthropogenic land subsidence. The importance of regional faults depends on a variety of factors including depth of the depleted reservoir, fault number, orientation and size, geomechanical properties of porous medium, pore pressure drawdown induced by fluid production, etc. With the aid of some representative examples, a useful indication is provided as to where and how fault activation may influence both magnitude and extent of the land subsidence bowl above producing gas/oil reservoirs, pointing to a generally limited impact on the ground surface. The simulation of a real faulted gas reservoir in a complex 3‐D setting shows that the proposed IE can be simply and efficiently incorporated into a FE geomechanical model, thus improving the quality of the stress and displacement prediction. Copyright © 2007 John Wiley & Sons, Ltd.     

ABAQUS动力无限元人工边界研究

针对动力场天然无限地基的数值模拟与地震波输入问题进行了一些有意义的研究,评述了现有动力计算常用无限元的优缺点,详细阐述了ABAQUS无限元理论体系框架,并加以改进,提出一种考虑外域地震动影响的ABAQUS动力无限元人工边界。采用等效边界力的叠加原理,对入射波和散射波分开处理,视入射波和散射波在边界上互不影响,将输入地震动转化为作用于有限元无限元交界面上的等效应力的方法来解决外源波的入射问题。算例验证结果表明：内源振动和固定边界会出现失真和扰动现象,同时该计算结果与黏弹性边界的计算结果对比可知,该方法对外行散射波的过滤作用优于黏弹性边界。因此,改进的ABAQUS动力无限元人工边界理论方法有效且具有一定的稳定性。     

Three-dimensional finite element analysis for soil slopes stabilisation using piles

This paper presents the analytical methods of slope-stabilising piles using the three-dimensional (3-D) finite element (FE) analysis with the strength reduction method (SRM). This 3-D FE model is employed to overcome the limitations observed in two-dimensional (2-D) FE analysis. The solutions obtained from 3-D FE analyses are verified to be less conservative in this paper. The 3-D analysis is considered to be of particular importance to pile-slope problems. The soil that flows between piles cannot be taken account properly in the 2-D FE analysis. The method adopted in this paper can avoid the assumption of soil movement and the pressure distribution along the piles subjected to soil movement. The numerical analysis employs the Mohr–Coulomb failure criterion with the strength reduction technique for soil and an elastic member for piles. The spacing effect of the pile is considered in the 3-D model, the S/D (S: centre to centre, D: diameter of pile) ratio, equal to 4.0, is found to be equivalent to the single pile stabilisation. The middle portion of the slope is identified as the optimal location to place the piles. The proper length of the pile, which can be used to stabilise the slope, is also examined using 3-D FE analyses. It is concluded that L/H greater or equal 0.70 is recommended (L: pile length, H: slope height). The numerical analyses are conducted based on a coupled analysis, which simultaneously considers both the slope stability and the pile response. The failure mechanisms of the pile-slope system subjected to the pile locations, pile head conditions and pile length are each discussed. The contact pressure, shear force and moment along the piles are presented to illustrate the pile stabilising mechanism herein.     

Embedded beam element with interaction surface for lateral loading of piles

This paper presents a numerical formulation of a three dimensional embedded beam element for the modeling of piles, which incorporates an explicit interaction surface between soil and pile. The formulation is herein implemented for lateral loading of piles but is able to represent soil–pile interaction phenomena in a general manner for different types of loading conditions or ground movements. The model assumes perfect adherence between beam and soil along the interaction surface. The paper presents a comparison of the results obtained by means of the present formulation and by means of a previously formulated embedded pile element without interaction surface, as well as reference semi‐analytical solutions and a fully 3D finite element (FE) model. It is seen that the proposed embedded element provides a better convergence behavior than a previously formulated embedded element and is able to reproduce key features of a full 3D FE model. Copyright © 2015 John Wiley & Sons, Ltd.     

Cyclic macro‐element for soil–structure interaction: material and geometrical non‐linearities

This paper presents a non‐linear soil–structure interaction (SSI) macro‐element for shallow foundation on cohesive soil. The element describes the behaviour in the near field of the foundation under cyclic loading, reproducing the material non‐linearities of the soil under the foundation (yielding) as well as the geometrical non‐linearities (uplift) at the soil–structure interface. The overall behaviour in the soil and at the interface is reduced to its action on the foundation. The macro‐element consists of a non‐linear joint element, expressed in generalised variables, i.e. in forces applied to the foundation and in the corresponding displacements. Failure is described by the interaction diagram of the ultimate bearing capacity of the foundation under combined loads. Mechanisms of yielding and uplift are modelled through a global, coupled plasticity–uplift model. The cyclic model is dedicated to modelling the dynamic response of structures subjected to seismic action. Thus, it is especially suited to combined loading developed during this kind of motion. Comparisons of cyclic results obtained from the macro‐element and from a FE modelization are shown in order to demonstrate the relevance of the proposed model and its predictive ability. Copyright © 2001 John Wiley & Sons, Ltd.