A coupling of mixed and continuous Galerkin finite element methods for poroelasticity II: the discrete-in-time case

In this paper, we formulate a finite element procedure for approximating the coupled fluid and mechanics in Biot’s consolidation model of poroelasticity. Here, we approximate the pressure by a mixed finite element method and the displacements by a Galerkin method. Theoretical convergence error estimates are derived in a discrete-in-time setting. Of particular interest is the case when the lowest-order Raviart–Thomas approximating space or cell-centered finite differences are used in the mixed formulation and continuous piecewise linear approximations are used for displacements. This approach appears to be the one most frequently applied to existing reservoir engineering simulators.     

A coupling of mixed and continuous Galerkin finite element methods for poroelasticity I: the continuous in time case

In this paper, we formulate a finite element procedure for approximating the coupled fluid and mechanics in Biot’s consolidation model of poroelasticity. Here, we approximate the pressure by a mixed finite element method and the displacements by a Galerkin method. Theoretical convergence error estimates are derived in a continuous in-time setting for a strictly positive constrained specific storage coefficient. Of particular interest is the case when the lowest-order Raviart–Thomas approximating space or cell-centered finite differences are used in the mixed formulation, and continuous piecewise linear approximations are used for displacements. This approach appears to be the one most frequently applied to existing reservoir engineering simulators.     

增量位移反分析在水电地下洞室工程中的应用

反分析是确定计算模型参数的有效方法.通常多采用量测所得全量位移进行反演计算.但地下工程中许多量测数据为增量位移,且实际施工过程可以通过建立分步开挖的有限元模型来模拟.据此,结合某水电站地下洞室工程中地下厂房的开挖,建立了模拟动态施工的有限元模型,利用某一开挖步施工前后量测值之差,采用增量位移优化反分析方法对洞室附近初始地应力场及围岩弹性模量进行了反演.计算所得增量位移与实测值符合较好,表明了这种方法的可行性.同时,根据分析结果对该方法进行了评价.     

Composite Element Model of the Fully Grouted Rock Bolt

Summary The three dimensional elasto-viscoplastic composite element method is formulated in this paper for rock masses reinforced by a fully-grouted bolt. If a bolt segment penetrates a finite element representing the rock mass, then a composite element is formed including five sub-elements corresponding to the rock material, the grout material, the bolt material, the rock-grout interface and the bolt-grout interface. The displacements in each sub-element are interpolated from the corresponding nodal displacements of the composite element. By the virtual work principle the governing equation for the solution of the nodal displacements can be formulated. The elasto-viscoplastic characteristics of the materials are considered in the formulation. The new model can be incorporated into the conventional finite element analysis grid, in which several composite elements have fully grouted bolts embedded. In this way the mesh generation of large scale bolted rock structures becomes convenient and feasible. The model has been implemented in a FEM program, and a comparative study between the numerical analysis and a pull out field test has been carried out, from which the validity and the robustness of the new model are justified.     

TECHNICAL NOTE. Model study of H-piles subjected to combined loading

A series of model tests on H-piles subject to lateral and vertical loading have been performed so that the experimental data could be used to calibrate a finite element programme. Experiments on model H-piles in dry silca sand were performed to determine the influence of lateral displacements on the vertical load-carrying capacity of the piles. The results from the nonlinear finite element computer program were compared to the experimental results and were found to be conservative. The experimental results showed greater pile capacities and lower bending moments than were predicted by the finite element program.     

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。     

Numerical modelling of large deformations associated with driving of open‐ended piles

This paper presents a ‘Eulerian‐like’ finite element technique to simulate the large accumulated displacements of piles subjected to multiple hammer blows. For each hammer blow, results are obtained using a standard small strain finite element model and, at the end of each hammer blow, material flow is taken into account with reference to a fixed finite element mesh. Residual stresses calculated at the Gauss integration points of the deformed finite element mesh are mapped on to the fixed finite element mesh, and these stresses are used as initial stresses for the next hammer blow. At the end of each hammer blow, stiffness and mass matrices are recalculated for the volume of material remaining inside the fixed finite element mesh. Results obtained with and without allowing material to flow through the fixed mesh are compared for several hammer blows. Build up of residual stresses, soil flow and yielded points around the pile are presented for plugged, partially‐plugged and unplugged piles. Using the new finite element technique, the driving of a pile from the soil surface is studied. The ability to analyse this and other large deformation problems is the main advantage of the new finite element technique. Copyright © 2000 John Wiley & Sons, Ltd.     

考虑桩土效应的双排桩模型及参数研究

双排桩作为一种新型的深基坑支护结构,目前尚无简单而有效的设计方法。首先,借助Winkler地基梁基本思想,在忽略桩土竖向摩擦效应及空间效应的前提下,对双排桩支护结构力学机制进行分析,建立了考虑桩土效应的双排桩平面杆系有限元模型。接着围绕双排桩平面杆系有限元模型的关键参数土压力分布及弹性抗力系数展开了研究,针对连梁拉力将使传统的坑后土体滑移面临界距离增加特征,利用滑动比例系数法获得了土压力分配规律;针对弹性抗力系数正分析取值不确定性,提出了采用位移反分析优化方法获得弹性抗力参数的取值。最后,根据杆系有限元及反分析中位移最优准则函数的求解步骤,分别编制了doublerowpile及doublerowpileparameter计算程序,并进行了相应的工程计算,工程计算结果表明,计算位移与监测位移趋势一致,计算内力符合规范要求,且能较准确获得弹性抗力系数取值。     

深基坑开挖与边坡支护受力分析软件包的研制

介绍了基坑开挖与边坡支护受力分析软件包。该软件包可计算多层土中的剪力与弯矩而不进行任何简化处理,并能采用弹塑性有限元预测分析支挡结构的位移。该软件包还可用于各类平面应变问题的应力与位移分析,如加筋土边坡挡土墙的稳定性预测等。该软件包在Ｗｉｎｄｏｗ９５环境下运行,全中文菜单,使用较为方便。     

三峡工程二期围堰心墙高双墙方案有限元分析

本文用自编的三维非线性程序对三峡工程二期围堰高双墙方案的应力与变形进行了有限元分析。计算模型采用双曲线应力应变关系。本次计算成果给出了围堰和防渗墙各部位的应力与位移，指出了可能出现破坏的薄弱部位。     

增量位移反分析方法在拉西瓦地下厂房中的应用

由于位移量测具有方便、准确和经济的特点,因而位移反分析法在地下工程领域获得了广泛的应用。以拉西瓦地下厂房的开挖过程为实际工程背景,应用从奥地利引进的大型岩土工程数值仿真分析系统FINAL为平台,建立了模拟分层开挖的有限元模型。采用主厂房第3层开挖前后洞壁围岩关键点的增量位移对厂区初始地应力场及围岩弹性模量进行了反演,最后利用反演结果对后续开挖过程中围岩的稳定性进行了预测。反分析所得增量位移与实测值符合较好,表明了这种方法的可行性。     

层状地基上弹性地基梁的有限元-边界元耦合分析

将地基视为多层各向同性弹性体,对Euler-Bernoulli梁进行有限单元离散分析,对地基-梁接触面采用边界积分法求解,根据地基-梁接触面的竖向位移协调和光滑接触条件,应用有限元与边界元耦合的方法推导出各向同性成层弹性地基上的Euler-Bernoulli梁的半数值半解析解。基于文中理论,编制了相应的程序,通过与现有文献对比,验证了文中理论的正确性,对比分析了分层地基与等效均匀地基两种模型上的弹性地基梁。研究结果表明,分层地基与等效均匀地基两种模型上弹性地基梁性状差异较大,实际弹性地基梁计算中应采用分层地基模型。     

加筋土挡土墙边坡的稳定性分析

加筋挡土墙边坡是一种新型的复合边坡加固技术,用传统的方法很难设计这种复杂的结构。以一工程实例叙述了采用弹塑性有限元法预测加筋土边坡的稳定性的方法;给出了不同设计方案下的位移;分析了土体力学参数对边坡最大水平位移的影响。结果表明,土体的弹性模量、内摩擦角与粘聚力是影响边坡位移的重要因素。这些土力学参数与边坡最大水平位移是非线性关系,且有呈现临界点的趋势。因此,适当控制填土的力学性能参数有助于达到安全节省的设计目标。      

Safety factor calculation of soil slope reinforced with piles based on Hill’s model theory

How to evaluate reasonably the stability of a soil slope reinforced with piles (SSRP) still is an urgent problem. At present, the three-dimensional (3D) finite element strength reduction method has been used for the soil slope stability analysis. However, to accurately determine the global instability of soil slopes is the key to implementing the strength reduction finite element method. In this paper, the 3D finite element strength reduction algorithm (FESRA), based on Hill’s model theory, is proposed to assess the stability of SSRP and study on the relationship between the safety coefficients of SSRP and the displacements of slope mass. The results show that: (1) the relationship between the safety coefficients of SSRP and the displacements of slope mass agrees with the Hill’s model; (2) the proposed method (3D FESRA based on Hill’s model theory) in this study may take into account simultaneously the pile response and slope stability, and makes the results of SSRP stability analysis reasonable and reliable, which could be used as a reference for the evaluation of stability of the same type of slope; and (3) further study should be done to confirm whether the proposed method in this study is suitable for other types of slopes.     

粗粒料接触面模型及其在土石坝工程中的应用

在土石坝工程中越来越重视岸坡与坝料之间的接触特性,将土体本构模型中使用较多的双曲线型硬化规律运用至接触面模型,提出了一个简洁的接触面本构模型,推导了接触面模型刚度矩阵表达式。通过对4组试验的预测结果与试验结果的对比,表明该模型可以较好地预测粗粒料的界面剪切试验。将提出的接触面模型嵌入有限元程序,应用于如美心墙坝河谷与坝料的接触分析。三维有限元计算结果表明：坝体两侧岸坡的剪切位移变化规律都是中间部分剪切滑移量较大,岸坡边缘部分相对较小,陡坡一侧最大滑移量大于较缓一侧。这些均符合粗粒料滑移的基本规律,可为岸坡?坝料接触特性研究以及土石坝工程计算提供参考。     

Simulation of arch dam – foundation interaction with a new friction interface element

A new model for three-dimensional non-linear contact problems with irreversible friction is presented here for the interaction between the rock foundation and an arch dam structure. Based on the finite element method and load incremental theory, a constraint contact element with displacements and contact stresses as node parameters is developed. In this approach, four contact conditions are considered, i.e. fixed, slip, free and mixed. This model can simulate frictional slippage, decoupling and re-bonding of two bodies initially mating at a common interface or with any initial gaps. Furthermore boundary conditions for this element are discussed and treatment measures proposed. This method is shown to be effective and to have the advantage of being easily implemented into standard finite element programs. Solutions are obtained for a centrally loaded, simply supported composite beam and for an end-loaded elastica with initial gaps in regional contact with a rigid surface. The results obtained for these examples are compared to the plane stress solutions by contact friction analysis. As an application example, Quanshui arch dam located in Ruyuan County of Guangdong Province in southern China is simulated with the new element.     

基于PSO-MLSSVR的土体参数反演方法在深基坑工程中的应用

为了确保基坑工程安全,常常会采用数值模拟的方法预测支护结构的位移,其中岩土体力学参数的选取对于结果的影响最大.本文使用了一种粒子群(PSO)算法结合多输出最小二乘支持向量回归机(MLSSVR)的基坑土体参数位移反分析法,以深圳某深基坑的支护桩顶水平位移监测数据为依据,基于正交设计生成具有代表性的土体参数组合,通过有限元...     

Strutted Excavation in Soft Soil Incorporating a Jet-Grout Base Slab: Analysis Considering the Consolidation Effect

The influence of the consolidation on a strutted excavation in soft soil is analysed using a computer code based on the finite element method. A base jet-grout slab is considered in order to improve stability against bottom heave failure and minimize wall displacements. The numerical model incorporates the Biot consolidation theory (coupled formulation of the flow and equilibrium equations) with soil constitutive relations simulated by the p–q–θ critical state model. Special emphasis is given to the analysis, during and after the construction period, of the pore pressures, shear stresses, stress levels and displacements in the ground, as well as strut compression loads, wall displacements and bending moments, earth pressures on the wall faces and compression loads and bending moments on the jet-grout slab. The safety factor against bottom heave is also evaluated from the finite element analysis considering formulations of the critical state soil mechanics, and also compared to values obtained with traditional methods that use limit equilibrium approach and bearing capacity fundamentals.     

Composite element model for the bonded anchorage head of stranded wire cable in tension

An elasto‐viscoplastic model is formulated using composite element technique for the bonded anchorage head of stranded wire cable in rock mass. This composite element contains sub‐elements corresponding to the rock material, the grout material, the stranded wire material, the rock/grout interface, and the grout/stranded wire interface, respectively. The displacement in each aforementioned sub‐element is interpolated from the corresponding nodal displacements of the composite element. In this manner, the mesh generation taking into account of tension cable anchors may be highly facilitated. By the application of the virtual work principle, the governing equation for solving the nodal displacements of the composite element is established. The proposed model has been incorporated into the conventional finite element algorithm and implemented in the program CORE3, in which the anchorage head is embedded within the composite elements. The comparative study concerning the pull‐out test has been carried out for the validation of the proposed model and algorithm. Copyright © 2015 John Wiley & Sons, Ltd.     

可液化土中地铁结构的地震响应

在饱和土耦合作用与土和结构相互作用理论基础上,以地铁车站为例,用有限元法研究地下结构在地震液化作用下的响应。所采用的软件为动力两相体非线性有限元软件Dyna-Swandyne-II,该软件可以应用先进的Pastor-Zienkiewicz III广义塑性模型模拟可液化土的动力特性,应用u-p形式的Biot方程,在有限元分析中充分考虑孔隙水与土之间的耦合,同时考虑地下结构与饱和土在动力作用下的非线性相互作用。分析了地铁车站的动力响应,包括地铁内力、加速度以及地铁位移。研究结果表明,地铁结构在地震液化作用下会产生较大的上浮,从而对结构造成比较严重的破坏;地铁结构在地震作用下的最大内力位于结构的交接处。因此,结构交接处的配筋应该格外小心。