非共轴本构模型的数值计算问题

应用角点非共轴本构模型结合有限元方法分析浅基础的受力沉降问题。当非共轴塑性模量较小时,包含非共轴模型子程序的ABAQUS的非线性计算可能不收敛。深入地分析表明,不收敛问题是由于在塑性变形刚开始时,非共轴的塑性应变增量明显大于共轴的塑性应变增量。为了克服数值不收敛问题,对原有的角点非共轴模型加以改进。在改进的模型中,非共轴塑性模量是累加塑性剪应变的函数。计算结果表明,这个改进的非共轴模型提高了非线性计算的收敛性,同时保持了原有非共轴模型的功能。     

Review and enhancement of 3D concrete models for large‐scale numerical simulations of concrete structures

The present paper focuses on selected plasticity and damage‐plasticity models for describing the 3D material behavior of concrete. In particular, a plasticity model and a damage‐plasticity model are reviewed and evaluated. Based on the results of the evaluation, enhancements are proposed, aiming at improving the correspondence between predicted and observed material behavior and aiming at implementing a robust and efficient stress update algorithm in a finite element program for performing large‐scale 3D numerical simulations of concrete structures. The capabilities of the concrete models are demonstrated by 3D numerical simulations of benchmark tests with combined bending and torsional loading and combined compression and shear loading and by a large‐scale 3D finite element analysis of a model test of a concrete arch dam. Copyright © 2011 John Wiley & Sons, Ltd.     

三维区域地面沉降数值模拟

由于地裂缝研究及地表变形监测技术（例如GPS,InSAR等）的快速发展,抽取地下水引起的地层水平位移受到关注。传统区域地面沉降模型虽然求解快速但不能模拟水平位移;比奥模型虽然能够模拟土体的三维变形,但模型求解的计算量较大,较少应用于大尺度的区域地面沉降数值模拟。为解决以上问题,推导了解耦三维地面沉降数学模型,模型推导过程显示：比奥模型假设法向总应力和不变,则可简化为解耦三维地面沉降模型;解耦三维地面沉降模型假设土体仅有垂向一维变形,则可简化为传统区域地面沉降模型。同时通过数值试验验证了解耦三维地面沉降模型可以作为比奥模型的替代模型和传统区域地面沉降模型的改进模型,用来模拟抽取地下水引起的三维区域地面沉降。     

Upscaling of elastic properties for large scale geomechanical simulations

Large scale geomechanical simulations are being increasingly used to model the compaction of stress dependent reservoirs, predict the long term integrity of under‐ground radioactive waste disposals, and analyse the viability of hot‐dry rock geothermal sites. These large scale simulations require the definition of homogenous mechanical properties for each geomechanical cell whereas the rock properties are expected to vary at a smaller scale. Therefore, this paper proposes a new methodology that makes possible to define the equivalent mechanical properties of the geomechanical cells using the fine scale information given in the geological model. This methodology is implemented on a synthetic reservoir case and two upscaling procedures providing the effective elastic properties of the Hooke's law are tested. The first upscaling procedure is an analytical method for perfectly stratified rock mass, whereas the second procedure computes lower and upper bounds of the equivalent properties with no assumption on the small scale heterogeneity distribution. Both procedures are applied to one geomechanical cell extracted from the reservoir structure. The results show that the analytical and numerical upscaling procedures provide accurate estimations of the effective parameters. Furthermore, a large scale simulation using the homogenized properties of each geomechanical cell calculated with the analytical method demonstrates that the overall behaviour of the reservoir structure is well reproduced for two different loading cases. Copyright © 2004 John Wiley & Sons, Ltd.     

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。     

A two‐invariant pseudoelastic model for reservoir compaction

Predicting the deformations of deep reservoirs due to fluid withdrawal/injection is a challenging task that could have important environmental, social, and economical impacts. Finite element models, if endowed with an appropriate constitutive law, represent a useful tool for computing the displacements, the deformations, and the stress distributions in reservoir applications. Several studies show that hypoelastic laws, based on a stress‐dependent vertical compressibility, are able to provide accurate results, confirmed by in situ and satellite measurements. On the other hand, such laws present some weaknesses related to the numerical implementation, in particular due to the nonsymmetry of the tangent operator. This paper presents a new constitutive model based on 2 invariants (the mean normal and deviatoric stresses), characterized by a variable pressure‐dependent bulk modulus K. This constitutive law allows for overcoming most shortcomings of the hypoelastic law, although preserving the same accuracy, reliability, and ease of use and calibration. This paper presents a procedure to identify the parameters of the new model, starting from the typically available data on the vertical compressibility. Numerical results show a good agreement between the 2 laws, suggesting the proposed approach as a valid alternative in reservoir applications.     

不连续面在双重介质热-水-力三维耦合分析中的有限元数值实现

在建立双重介质热-水-力耦合微分控制方程的基础上,提出了裂隙岩体热-水-力耦合的三维力学模型,对不同介质分别建立以节点位移、水压力和温度为求解量的三维有限元格式,开发了双重介质热-水-力耦合分析的的三维有限元计算程序,在有限元数值分析中不连续面应力计算采用等厚度空间8节点节理单元进行离散,而不连续面渗流和热能计算时采用平面4节点等参单元进行离散,这样保证了不同介质之间的水量、热量交换和两类模型接触处节点水头、温度和位移相等。通过高温岩体地热开发算例,揭示了在热-水-力耦合作用下不连续面处于低应力区,其张开度随运行时间的延长呈非线性增加,非稳定渗流阶段不连续面显著地控制着渗流场的整体分布,它的水头远高于拟连续岩体介质的水头,而进入稳定渗流阶段不连续面的控渗作用不明显,由于高温岩体地热开发系统中存在大规模的热量补给,不连续面对岩体温度场分布的影响并不显著。     

棒式光纤传感器在地下洞群模型试验中的应用

地质力学模型试验是在复杂条件下进行大型地下洞室围岩稳定性分析的重要研究手段,能够真实地反映地质构造和工程结构的空间关系,准确模拟施工过程对厂房稳定性的影响以及岩体的破坏特征。双江口水电站地下洞群模型试验中采用预留孔径灌胶方式进行高精度的棒式光纤光栅（FBG）位移传感器的埋设,以便对洞室周边的位移进行量测,同时应用FLAC3D进行数值模拟比较。结果表明：棒式光纤光栅传感器量测方法解决了模型试验中内部变形小、量测精度要求高的问题,与数值模拟结果相吻合;试验中传感器埋设的方法是成功的,无论是开挖阶段还是超载阶段传感器均能有效地监测模型内部变形,揭示地下洞室群模型在开挖阶段和超载阶段的变形机制和破坏特征。     

考虑循环软化的非线性动力本构模型在FLAC3D中的实现

已有震害研究表明,震后边坡会因持续变形而破坏,且伴随着土体强度逐渐降低的现象,即土的循环软化行为。因此,有必要研究考虑循环软化的非线性动力本构模型以用于复杂条件下地震边坡稳定性分析。在已有的非线性动力本构模型基础上,提出了考虑循环软化的处理方法。同时,在FLAC3D平台上实现了本构模型二次开发,并通过了理论公式与已有文献中试验数据的验证。结果表明：计算出的骨干曲线与理论公式一致,且计算出的动剪切模量比及阻尼比与试验数据吻合较好,能够克服Hardin-Drnevich模型和Davidenkov模型在较大应变处（>0.01%）过高地估算阻尼比的缺陷;考虑了循环软化后,计算出的剪切强度有明显降低,且当遇到骨干曲线剪应力可以连续地过渡到软化后的主干曲线上,模型的收敛性较好。所开发的本构模型可为大应变条件下软土场地及边坡地震灾害评估提供支持。     

Constitutive and numerical framework for modeling joints and faults in rock

A three‐dimensional constitutive model for joints is described that incorporates nonlinear elasticity based on volumetric elastic strain, and plasticity for both compaction and shear with emphasis on compaction. The formulation is general in the sense that alternative specific functional forms and evolution equations can be easily incorporated. A corresponding numerical structure based on finite elements is provided so that a joint width can vary from a fraction of an element size to a width that occupies several elements. The latter case is particularly appropriate for modeling a fault, which is considered simply to be a joint with large width. For small joint widths, the requisite equilibrium and kinematic requirements within an element are satisfied numerically. The result is that if the constitutive equation for either the joint or the rock is changed, the numerical framework remains unchanged. A unique aspect of the general formulation is the capability to handle either pre‐existing gaps or the formation of gaps. Representative stress–strain plots are given to illustrate both the features of the model and the effects of changes in values of material parameters. Copyright © 2015 John Wiley & Sons, Ltd.     

在ABAQUS中开发实现Duncan-Chang本构模型

美国HKS公司开发的软件产品ABAQUS是目前世界上最强大的非线性有限元分析工具之一。该软件包括了众多材料本构模型,但尚缺少国内外土工数值分析中广泛采用的Duncan-Chang本构模型。这一缺憾影响了ABAQUS软件在土工分析中的应用范围。本文旨在介绍ABAQUS中开发Duncan-Chang材料本构模型实现方法,给出了开发过程的概要,完成了两个典型常规三轴压缩模型问题数值测试。结果表明：在ABAQUS中增加Duncan-Chang材料本构模型后,不仅可以充分地利用该软件强大的非线性求解平台,而且还有可能完成复杂土工应力应变的有限元数值分析问题,同时,具有计算速度快、计算精度高和前后处理快捷方便的优点,极大地降低了土工分析程序开发的难度,并减少了维护工作量。     

粗粒土的离心模型试验与数值模拟

岩土工程数值计算中粗粒土常采用邓肯-张本构模型,为了验证该模型在轴向加载、卸载、侧向加载等复杂应力路径条件下的适用性,进行了粗粒土的三轴试验获取其力学特性及本构模型参数;根据相似性原理制作了堆石坝的离心模型试样,并采用与三轴试验同样级配与粒径的粗粒土进行复杂应力路径的堆石坝离心模型试验,试验中通过改变离心加速度模拟加载、卸载,利用上游蓄水模拟坝体的侧向加载;采用ABAQUS对离心模型试验进行三维数值模拟,并研究了模型箱侧壁摩擦系数与土体的初始应力对数值结果的影响。通过比较离心模型试验与数值模拟成果,表明土体的初始弹性模量对计算结果影响较大,初始应力应选择自重作用下的应力场;邓肯-张本构模型能较好地描述堆石坝的加载应力路径,而模拟卸载应力路径有一定的差异,需要改进邓肯-张本构模型中卸载模量的确定方法。     

A novel finite element double porosity model for multiphase flow through deformable fractured porous media

Based on the theory of double-porosity, a novel mathematical model for multiphase fluid flow in a deforming fractured reservoir is developed. The present formulation, consisting of both the equilibrium and continuity equations, accounts for the significant influence of coupling between fluid flow and solid deformation, usually ignored in the reservoir simulation literature. A Galerkin-based finite element method is applied to discretize the governing equations both in the space and time domain. Throughout the derived set of equations the solid displacements as well as the fluid pressure values are considered as the primary unknowns and may be used to determine other reservoir parameters such as stresses, saturations, etc. The final set of equations represents a highly non-linear system as the elements of the coefficient matrices are updated during each iteration in terms of the independent variables. The model is employed to solve a field scale example where the results are compared to those of ten other uncoupled models. The results illustrate a significantly different behaviour for the case of a reservoir where the impact of coupling is also considered. © 1997 by John Wiley & Sons, Ltd.     

An improved implicit numerical integration of a non‐associated,three‐invariant cap plasticity model with mixed isotropic–kinematic hardening for geomaterials

The Sandia GeoModel is a continuum elastoplastic constitutive model that captures many features of the mechanical response for geological materials over a wide range of porosities and strain rates. Among the specific features incorporated into the formulation are a smooth compression cap, isotropic/kinematic hardening, nonlinear pressure dependence, strength differential effect, and rate sensitivity. This study attempts to provide enhancements regarding computational tractability, domain of applicability, and robustness of the model. A new functional form is presented for the yield and plastic potential functions. This reformulation renders a more accurate, robust, and efficient model as it eliminates spurious solutions attributed to the original form. In addition, we achieve a high‐performance implementation, because the local iterative method is allowed to recast residual vectors with a uniform dimensionality. The model is also furnished with a smooth, elliptical tension cap to account for the tensile yielding. Moreover, an efficient algorithm is introduced, which decreases the computational cost by differentiating the updated shear yield surface from the cap surface based on the trial relative stress state. Finally, various numerical examples including a large‐scale boundary value problem are presented to demonstrate the fidelity of the modified model and to analyze its numerical performance. Copyright © 2015 John Wiley & Sons, Ltd.     

泄洪洞整体三维紊流数值模拟

利用实用、高效的泄洪洞整体三维紊流数值模型,对滩坑水电站泄洪洞进行了数值模拟,该模型采用引入VOF方法的k-ε紊流模型,结合通用性强、易扩展的非结构混合网格。为克服网格扭曲给计算精度带来的影响,用一种改进精度的格心格式计算通量,使之具有非结构网格剖分的灵活性,程序的通用性和可扩展性,又有较高的计算精度。数值模拟结果和模型试验数据的对比分析表明,该模型是实用可靠的。     

Generalized trapezoidal numerical integration of an advanced soil model

This paper investigates the numerical performance of the generalized trapezoidal integration rule by using an advanced soil model. The generalized trapezoidal integration rule can include many other integration algorithms by adjusting a single parameter α ranging from 1 to 0. The soil model used is the recently developed middle surface concept (MSC) sand model which simulates different soil response characteristics by using different pseudo‐yield functions. The generalized trapezoidal rule and MSC sand model are used to simulate the responses of sand samples with different relative densities under various initial and loading conditions. Instead of a single step, multiple loading steps bring the sample to the vicinity of failure. These comprehensive investigations examine and compare the influences of various values of α on the numerical solution of integrated constitutive equations, the convergence of Newton's iterative scheme, and the integration accuracy. Copyright © 2007 John Wiley & Sons, Ltd.     

A model of capillary cohesion for numerical simulations of 3D polydisperse granular media

We present a 3D discrete‐element approach for numerical investigation of wet granular media. This approach relies on the basic laws of contact and Coulomb friction enriched by a capillary force law between particles. We show that the latter can be expressed as a simple explicit function of the gap and volume of the liquid bridge connecting a pair of spherical particles. The length scales involved in this expression are analyzed by comparing with direct integration of the Laplace–Young equation. We illustrate and validate this approach by application to direct shear and simple compression loadings. The shear and compression strengths obtained from simulations reproduce well the experimental measurements under similar material and boundary conditions. Our findings clearly show that the number density of liquid bonds in the bulk is a decisive parameter for the overall cohesion of wet granular materials. A homogeneous distribution of the liquid within the bridge debonding distance, even at low volume contents, leads to the highest cohesion. The latter is independent of the liquid content as far as the liquid remains in the pendular state and the number density of liquid bonds remains constant. Copyright © 2007 John Wiley & Sons, Ltd.     

岩性圈闭盖层封闭动力学模型及其应用研究

岩性圈闭的泥页岩盖层阻止油气突破的过程是一个阻力克服动力的过程,本文在此基础上建立了岩性圈闭盖层封闭动力学模型及相应的数学模型。该模型认为岩性油气藏中的油气突破泥岩盖层的过程也是一个力学平衡现象,动力包括储集层地层压力、浮力,阻力主要包括盖层地层压力、毛管压力。通过对单井古孔隙度及古埋深的恢复,可以对比成藏期目的层油气突破泥岩盖层的动力与阻力之间的大小关系,定量研究泥岩盖层封闭性演化过程。应用该模型发现,白家海凸起彩43井侏罗系三工河组及西山窑组在侏罗纪末期缺乏有效泥岩盖层,白垩纪末期三工河组中下部存在有效盖层,而西山窑组盖层的封闭能力一般。     

大型复杂地质体三维数值模型构建方法比较研究

真实地质体三维数值模型构建是进行岩体工程数值分析面临的难题,开展大型复杂地质体三维数值模型构建方法比较研究具有重要意义。以3DMine数字化模型为基础,提出了3DMine-FLAC3D耦合建模方法和3DMine-Surfer-Rhino- ANSYS-FLAC3D多软件耦合建模方法,详细阐述了各建模方法具体步骤,深入分析了各建模方法优缺点及适用性,通过对比各建模方法的优势与短板,取长补短,改进了3DMine-FLAC3D耦合建模方法存在的缺陷,解决了复杂地质体三维数值模型构建难题。以广西铜坑矿锌多金属矿体开采为背景,利用大型复杂地质体三维数值建模方法,构建了锌多金属矿三维数值模型,分析了矿体上行开采地表沉陷规律。研究成果对准确构建大型复杂地质体三维数值模型具有重要指导作用。     

GIS地表塌陷计算的有限棱柱法及三维数据模型

具有强大信息管理和可视化功能的GIS已在地下硐室开挖、矿山采掘、边坡等许多工程领域中得到了广泛应用。笔者给出了一种用于地下开挖变形描述和应力分析的方法——有限棱柱法，并就该方法与GIS集成中的数据模型和数据组织方法进行了探讨，建立了基于GIS的虚拟地质体地下开挖变形描述与评价计算的三维可视化系统，并对多语言集成模式和数据可视化方法进行了探讨。同时还给出了该方法的工程应用实例，对该方法的可靠性和有效性进行了验证。