UH模型在有限元分析中的应用

由姚仰平等提出的超固结土统一硬化模型(UH模型)能够描述超固结土的硬化、软化、剪缩和剪胀等应力应变特性以及应力路径对它的影响。通过改进,直线型的Hvorslev线由抛物线型的Hvorslev线代替,UH模型的参数与剑桥模型(Cam-clay模型)的参数相同。应用该模型,对三轴试验进行有限元模拟,分析了与应用Cam-clay模型所得应力应变关系曲线的异同点;针对刚性承压板试验,进行了地基承载力的三维有限元分析,比较了与应用Cam-clay模型和摩尔库仑模型(Mohr-Coulomb模型)等所得p-s曲线的不同,分析了地基中不同点处的应力-应变关系曲线,并与Boussinesq弹性理论计算的应力做了比较;进行了地基固结沉降数值分析,比较了孔压、沉降的变化规律,体现了UH模型的优越性。     

预应力锚索损伤软化精细有限元模型

预应力锚索作为岩土工程的一种主要加固技术已得到日益广泛的应用,但现有的计算方法难以反映岩体、砂浆、钢绞线相互之间的滑移变形等实际情况,计算结果难以体现实际的加固效果。通过研究接触面的特性引入损伤软化概念,建立了包含钢绞线、砂浆、接触面的损伤软化精细有限元模型,并与现场试验进行了对比分析。该模型优点是精细地描述了钢绞线、砂浆和接触面等结构的力学行为,可以反映接触面力学材料损伤软化的过程,更加精确地反映了锚固段的力学变化过程。试验结果对比显示,两者随着荷载不断加大,锚固段接触面上的剪应力峰值由端口往里转移。当端口处于弹性阶段,峰值在端口,呈指数衰减模式;当端口处出现损伤软化,峰值往里转移。计算分析反映的锚固段应力变化规律与试验基本一致。     

Numerical approximation of water–air two-phase flow by the mixed finite element method

A new model for two-phase flow of water and air in soil is presented. This leads to a system of two mass balance equations and two equations representing conservation of momentum of fluid and gas, respectively. This paper is concerned with the verification of this model for the special case of a rigid soil skeleton by computational experiments. Its numerical treatment is based on the Raviart–Thomas mixed finite element method combined with an implicit Euler time discretization. The feasibility of the method is illustrated for some test examples of one- and two-dimensional two-phase flow problems.     

A finite element porothermoelastic model for dual-porosity media

An existing dual-porosity finite element model has been extended to include thermo-hydro-mechanical coupling in both media. The model relies on overlapping distinct continua for the fluid and solid domains. In addition, conductive and convective heat transfers are incorporated using a single representative thermodynamics continuum. The model is applied to the problem of an inclined borehole drilled in a fractured formation subjected to a three-dimensional state of stress and, a temperature gradient between the drilling fluid and the formation. A sensitivity analysis has been carried out to study the impact of thermal loading, effect of heat transport by pore fluid flow and, the effect of parameters of the secondary medium used to represent the fractures. Copyright © 2004 John Wiley & Sons, Ltd.     

层状岩质边坡开挖过程的有限元模拟

采取自编弹塑性有限元程序,在考虑岩体节理和施工爆破影响的条件下,对常－张高速公路的k135层状岩质边坡的开挖过程进行了模拟,分析了开挖过程中岩体的变形和应力状态及屈服状态,并用降低材料强度储备的有限元强度折减法,对各开挖阶段边坡的整体稳定性进行了评价。通过分析表明,k135边坡在其施工过程中是稳定的。     

An adaptive finite element model for wellbore breakout simulation

A finite element formulation is proposed and implemented for analysing the stability of excavated wells using the DiMaggio-Sandler constitutive elastoplastic model with a typical carbonate reservoir configuration. The quality of the finite element approximation is ensured by applying smooth curved elements adapted to the wellbore geometry, and h − p adaptive finite element meshes in the plastic zone. General purpose procedures are defined to transfer the elastoplastic deformation history to newly created integration points. A breakout damage criterion is proposed based on the second invariant of the deviatoric plastic deformation tensor. This damage criterion is used to apply a mesh movement algorithm to represent material collapse. The automatic successive application of the breakout damage criterion results in elliptical realistically looking geometries obtained in experiments reported in the literature.     

Three-dimensional finite element modelling for consolidation due to groundwater withdrawal in a desaturating anisotropic aquifer system

A poroelastic numerical model is presented to evaluate three-dimensional consolidation due to groundwater withdrawal from desaturating anisotropic porous media. This numerical model is developed based on the fully coupled governing equations for groundwater flow in deforming variably saturated porous media and the Galerkin finite element method. Two different cases of unsaturated aquifers are simulated for the purpose of comparison: a cross-anisotropic soil aquifer, and a corresponding isotropic soil aquifer composed of a geometrically averaged equivalent material. The numerical simulation results show that the anisotropy has a significant effect on the shapes of three-dimensional hydraulic head distribution and displacement vector fields. Such an effect of anisotropy is caused by the uneven partitioning of the hydraulic pumping stress between the vertical and horizontal directions in both groundwater flow field and solid skeleton deformation field. Copyright © 1999 John Wiley & Sons, Ltd.     

A transient finite element analysis of linear viscoelastic material model

Since the attenulation of propagating waves through soil/rock is related to the localized material properties as well as the strain developed, the commonly used Rayleigh-type damping model and its variations are not suitable for dynamic finite element analysis of such materials. A linear viscoelastic material model based on the concept of the relaxation spectrum is manipualted in place of the damping model in this paper. The method proposed by Day and Minster¹¹ to transform the convolutional form of the stress–strain relationship to a set of differential operators using the Pade approximant method is generalized to non-scalar waves and implemented for transient finite element analyses. A time-marching scheme is also proposed to incorporate the resultant differential operators into the governing equation of motion. The accuracy related to the Pade approximant method and the time-marching scheme is investigated by critically analysing some scalar wave propagation problems. The proposed technique is further verified using two one-dimensional stress wave propagation problems and a two-dimensional transient propagating wave through an unbounded linear viscoelastic medium. Some encouraging results have been obtained using the proposed technique and guidelines for using this technique are also presented. Comparisons of analytical solutions obtained by Fourier synthesis and numerical results have been provided.     

顺层路堑边坡锚杆支护稳定性的有限元模拟分析

基于理想弹塑性本构模型和Drucker-Prager准则,运用ANSYS软件和有限元数值模拟技术,建立了顺层岩体边坡的有限元分析模型。结合沪蓉国道主干线宜昌至恩施公路白氏坪-榔坪段顺层路堑高边坡工程实例,对顺层岩体路堑边坡布设锚杆支护前后的应力、变形和稳定性进行了模拟分析。分析比较表明,锚杆支护结构可以减小边坡临界状态下的最大位移、增大最危险接触面的摩擦力和提高边坡的稳定性系数,从而能有效地提高边坡的稳定性以防止顺层滑坡的发生。     

Recharge characteristics of a phreatic aquifer as determined by storage accumulation

The cumulative storage accumulation curve (CSAC) is a tool for saturated-volume fluctuation (SVF) analysis of transient recharge to shallow phreatic aquifers discharging only to springs. The method assumes that little underflow or phreatic evapotranspiration occurs. The CSAC is a modified water-table hydrograph that distinguishes storage increase caused by recharge from loss due to springflow-induced recession. Required for the analysis are water-table fluctuations at a single representative location within the catchment of a single spring and either direct measurements or robust interpolations of springflows at different aquifer stages. The method employs empirical manipulation of head observations, varying spring catchment area to minimize CSAC water-level changes in late portions of long recessions. Results include volumetric estimates of recharge integrated over individual events and instantaneous rates of recharge to the water table, at the temporal resolution of the water-level sampling interval. The analysis may also yield physically realistic information on spring catchment and recharge focusing. In a test case in West Virginia, USA, recharge estimates by this technique were consistent with integrated springflow time series but greater than estimates based on potential evapotranspiration. Results give insight into dynamic recharge behavior over time as well as an indication of recharge catchment size. Electronic Publication     

地下含水层储能两阶段热量运移数值模型研究

为了简单而准确地预测地下含水层储能情况,考虑了地下含水层储能过程时间跨度大、储能保温分阶段的实际特点,分析了地下含水层流动和换热模型物理参数的对比特点,以热平衡和热扩散原理为基础,建立分成两个连续阶段的地下含水层储能数值计算模型.模型求解中,采用控制容积法,以全隐格式进行热扩散方程的离散化,然后应用Jacobi方法迭代求解,模拟结果和实际观测数据吻合很好.该模型还分析了含水层储能循环采灌过程中抽出储能水的温度变化的一般特点.     

A dynamic programming model for optimal planning of aquifer storage and recovery facility operations

Aquifer storage recovery (ASR) is an innovative technology with the potential to augment dwindling water resources in regions experiencing rapid growth and development. Planning and design of ASR systems requires quantifying how much water should be stored and appropriate times for storage and withdrawals within a planning period. A monthly scale planning model has been developed in this study to derive optimal (least cost) long-term policies for operating ASR systems and is solved using a recursive deterministic dynamic programming approach. The outputs of the model include annual costs of operation, the amount of water to be imported each month as well as the schedule for storage and extraction. A case study modeled after a proposed ASR system for Mustang Island and Padre Island service areas of the city of Corpus Christi is used to illustrate the utility of the developed model. The results indicate that for the assumed baseline demands, the ASR system is to be kept operational for a period of 4 months starting from May through August. Model sensitivity analysis indicated that increased seasonal shortages can be met using ASR with little additional costs. For the assumed cost structure, a 16% shortage increased the costs by 1.6%. However, the operation time of ASR increased from 4 to 8 months. The developed dynamic programming model is a useful tool to assess the feasibility of evaluating the use of ASR systems during regional-scale water resources planning endeavors.     

压实黏土的脆性断裂模型及有限元算法

利用弥散裂缝理论,提出了压实黏土拉伸状态下的脆性断裂模型.当压实黏土达到其极限抗拉强度后,通过建立单元的各向异性刚度矩阵,将土体裂缝弥散于实体单元,构造了平面应变条件下考虑压实黏土脆性开裂的有限元计算模式.通过对某压实黏土单轴拉伸试验成果的模拟计算,验证了构建的脆性断裂模型和有限元算法对土体拉伸破坏特性和裂缝发展过程的适用性.本文还进行了模拟软弱面水压“楔劈效应”的简单数值试验,表明压实黏土脆性开裂模型和算法可较好地模拟裂缝扩展行为.     

基于扩展有限元法对土体滑坡破坏过程的模拟

边坡失稳一般经历滑裂面萌生、扩展和贯通的过程。近年发展起来的扩展有限元法（XFEM）可以合理地模拟这一过程,但在实际应用中仍未克服需要预先设定滑裂面的起始位置,以及滑裂面前端扩展方向的判断精度较低等缺陷。首先介绍滑裂面萌生和扩展的判断和程序实现机制。然后提出了确定滑裂面起始位置的方法,重点描述了其中的自动判断裂缝萌生位置的方法,即根据单元内的应力状态求得拉应力水平和剪应力水平,根据其相对关系并结合应力历史进行判断。接着介绍了联合运用扇形控制域和圆形控制域确定滑裂面前端扩展方向的新方法。该方法可提高XFEM对滑坡破坏过程的模拟精度。最后通过两个边坡失稳算例的计算分析验证所提方法的可靠性。     

岩质滑坡稳定性有限元分析

目前国内外大多数规范中推荐或者强制性规定滑坡稳定性分析采用极限平衡法。由于极限平衡法本身的局限性,存在诸多不合理之处,如何对其进行改进使之更加合理已成为岩土工程中的重要课题之一。针对岩质滑坡存在明显的软弱滑动带的特点,提出了有限元计算过程中不同滑动带的处理方法,结合工程中常用的不平衡推力传递法,给出了滑坡稳定性的有限元分析方法,将其应用于芡草沱滑坡,并与基于刚体极限平衡原理的不平衡推力传递法的计算结果进行了比较,表明其计算方法可靠,可直接应用于实际工程。     

Collision and stress trajectories in Taiwan: a finite element model

Field analyses of Plio-Quaternary compressional deformations in Taiwan have enabled us to reconstruct the paleostress trajectories resulting from the collision of the Luzon arc (Philippine Sea plate) with the Chinese continental margin (Eurasian plate). The direction of the maximum compressional stress σ₁ shows a fan-shaped pattern that we interpret as resulting from the collision of a rigid body (the Luzon arc) indenting a more deformable material (the thick sediments of the Chinese continental margin). Simple analytical models qualitatively explain the fan-shaped pattern, but the influence of various parameters such as boundary conditions and rheology cannot be quantitatively accounted for by this approach. Consequently, we have used a finite element technique to compute the stresses and strains induced by the push of a rigid body against a two-dimensional, viscous material. The boundary conditions are the velocities based on plate kinematics. A motion in the N300°E direction best explains the stress trajectories observed in central Taiwan. Viscosity contrasts as well as small changes in the shape of the northern edge of the indenter have little influence on the computed stress pattern. The most important parameter is the direction of convergence. Our model quantitatively explains the general pattern of the stress trajectories observed in the collision zone of Taiwan, between the Philippine Sea plate and Eurasia.     

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。     

Simulation of land subsidence using finite element method: Rafsanjan plain case study

Land subsidence caused by the excessive use of groundwater resources has caused serious damage to Rafsanjan area. In this study, using finite element method, a 2D plain strain simulation of land subsidence has been conducted. A linear elastic constitutive law has been used for the simulation of the soil material skeleton. Actual water level during the analysis period has been modeled via specifying nodal water pressure at piezometer wells situation. The solution procedure consists of two parts. First, an initial static analysis is carried out in order to find initial steady-state solution for the pore pressure and stress distribution. Then, the above solution is used as initial condition for dynamic computation of consolidation equations during pumpage period. Tectonic effect has been considered as a rigid body motion. Numerical results showed that if the rate of pumpage remains constant in the future, settlement due to water withdrawal near Rafsanjan city will reach up to 110 cm by the year 2022.     

Impacts of subsurface heat storage on aquifer hydrogeochemistry

The use of shallow aquifers for subsurface heat storage in terms of energy management and building climatisation can lead to a temperature rise in the aquifer to 70 °C and above. The influence of temperature changes on individual mineral and sorption equilibria, reaction kinetics and microbial activity is largely known. However, the impact of heating to temperatures as high as 70 °C on the aquifer overall system has not been quantified yet. Temperature-related changes in sediment ion exchange behaviour, dimension and rates of mineral dissolution and precipitation as well as microbially enhanced redox processes were studied in column experiments using aquifer sediment and tap water at 10, 25, 40, and 70 °C. At 70 °C, a change in sediment sorption behaviour for cations and organic acids was postulated based on temporal changes in pH, magnesium, and potassium concentration in the experimental solution. No clear changes of pH, TIC and major cations were found at 10–40 °C. Redox zoning shifted from oxic conditions towards nitrate and iron(III) reducing conditions at 25 and 40 °C and sulphate reducing conditions at 70 °C. This was attributed to (a) a temperature-related increase in microbial reduction activity, and (b) three times higher release of organic carbon from the sediment at 70 °C compared to the lower temperatures. The findings of this study predict that a temperature increase in the subsurface up to 25 °C and above can impair the usability of ground water as drinking and process water, by reducing metal oxides and thus possibly releasing heavy metals from the sediment. Generally, at 70 °C, where clear cation and organic carbon desorption processes were observed and sulphate reducing conditions could be achieved, a site-specific assessment of temperature effects is required, especially for long-term operations of subsurface heat storage facilities.     

Large-scale aquifer sensitivity model

A 480-square-mile region within Will County, in northeastern Illinois, was used as a test region for the development of a methodology to map the sensitivity of aquifers to contamination. An aquifer sensitivity model was developed using a geographic information system (GIS) to overlay and combine several data layers. The components used for our model are: (1) depth to sand and gravel or bedrock, (2) thickness of the uppermost sand and gravel aquifer, (3) glacial drift thickness, and (4) bedrock geology. The model is an improvement over many previous aquifer sensitivity models because it combines specific information on depth to the uppermost aquifer with information on the thickness of the uppermost sand and gravel aquifer. This county-wide model results in an aquifer sensitivity map that can be a useful tool for making land-use planning decisions regarding aquifer protection and management of groundwater resources.