无压渗流问题分析的多节点有限元方法

采用基于平均值插值的多节点有限元方法分析有自由面渗流问题。在自由面附近采用多节点单元逼近自由面,利用平均值插值建立多节点单元的形函数,在远离自由面的区域采用四边形/三角形单元剖分。给定一个初始自由面位置,通过对渗流控制方程的多节点有限元求解,根据自由面上节点水头值判断自由面节点的调整方向和大小,最终迭代求出自由面的位置。土坝渗流问题的数值分析表明了所提方法的有效性和足够的计算精度。     

Flow through porous media: A procedure for locating the free surface

A finite element procedure is developed to accurately locate the free surface of unconfined seepage flow through porous media. The free surface is taken as the boundary between wet and dry soils, with flow in the saturated region characterized by Darcy's law. The method involves equations and meshing which are fully consistent with a general formulation for geotechnical engineering problems involving simultaneous solution of pore fluid pressures and soil skeleton displacements. Accuracy and versatility of the proposed procedure are demonstrated by solving various unconfined seepage flow problems through earth structures. Free surfaces and flownets are presented for the calculated flow fields.     

模拟裂隙多孔介质中变饱和渗流的广义等效连续体方法

描述了一种计算裂隙多孔介质中变饱和渗流的广义等效连续体方法。这种方法忽略裂隙的毛细作用,设定一个与某孔隙饱和度相对应的综合饱和度极限值,并假定：（1）如果裂隙多孔介质的综合饱和度小于该极限值,水只在孔隙中存在并流动,而裂隙中则没有水的流动;（2）如果综合饱和度等于或大于该极限值,水将进入裂隙,并在裂隙内运动。分析比较了等效连续体模型的不同计算方法,并给出了一个模拟裂隙岩体中变饱和渗流与传热耦合问题的应用算例。结果表明,所述方法具有一般性,可以有效地模拟裂隙多孔介质中变饱和渗流的基本特征。     

Seepage flow problems by variational inequalities: Theory and approximation

The theory of variational inequalities enables us to formulate and solve free boundary problems in fixed domains, while most other methods assume the position of the unknown domain in solving the problem. Here the problem of seepage flow through a rectangular dam with a free boundary is formulated as a vertical inequality following the ideas of Baiocchi. In order to demonstrate the essential ideas of extending the domain of the solution of problems with free boundaries, the problem of the deflection, of a string on a rigid support is first examined. Next, variational inequalities are derived which are associated with several cases of seepage problems. An approximation theory, including a priori error estimates, is developed using finite element methods, and an associated numerical scheme is given. It is shown that for linear and quadratic finite element methods, the rates of convergence are 0(h) and 0(h^1.25-δ), 0 < δ < 0.25, respectively, if the permeability is constant.     

岩体裂隙网络非稳定渗流分析与数值模拟

针对裂隙岩体的非稳定渗流问题,通过将Darcy定理扩展到包含干区的整个裂隙网络区域,并令潜在溢出边界条件为Signorini型互补边界条件,将湿区上的非稳定渗流问题转化为全域上的一个新的初边值问题。为降低试探函数选取的难度,建立与定义在整个裂隙网络区域上的偏微分方程（PDE）提法等价的抛物型变分不等式（PVI）提法,并给出裂隙网络非稳定渗流分析的有限元数值分析格式和迭代算法,与砂槽模型试验数据的对比分析,验证其有效性。最后,将文中发展的计算方法应用到含复杂裂隙网络的边坡非稳定渗流分析,计算结果很好地反映出边坡内部自由面随库水降落的变化规律,并能准确地描述裂隙网络内部渗流运动特征及流量分布的不均匀性。     

Multiphase SPH modeling of free surface flow in porous media with variable porosity

This paper presents a numerical model for simulating free surface flow in porous media with spatially varying porosity. The governing equations are based on the mixture theory. The resistance forces between solid and fluid is assumed to be nonlinear. A multiphase SPH approach is presented to solve the governing equations. In the multiphase SPH, water is modeled as a weakly compressible fluid, and solid phase is discretized by fixed solid particles carrying information of porosity. The model is validated by several numerical examples including seepage through specimen, fast flow through rockfill dam and wave interaction with porous structure. Good agreements between numerical results and experimental data are obtained in terms of flow rate and evolution of free surface. Parameter study shows that (1) the nonlinear resistance law provides more accurate results; (2) particle size and porosity have significant influence on the porous flow.     

A 2D mixed fracture–pore seepage model and hydromechanical coupling for fractured porous media

A novel two-dimensional mixed fracture–pore seepage model for fluid flow in fractured porous media is presented based on the computational framework of finite-discrete element method (FDEM). The model consists of a porous seepage model in triangular elements bonded by unbroken joint elements, as well as a fracture seepage model in broken joint elements. The principle for determining the fluid exchange coefficient of the unbroken joint element is provided to ensure numerical accuracy and efficiency. The mixed fracture–pore seepage model provides a simple but effective tool for solving fluid flow in fractured porous media. In this paper, examples of 1D and 2D seepage flow in porous media and porous media with a single fracture or multiple fractures are studied. The simulation results of the model match well with theoretical solutions or results obtained by commercial software, which verifies the correctness of the mixed fracture–pore seepage model. Furthermore, combining FDEM mechanical calculation and the mixed fracture–pore seepage model, a coupled hydromechanical model is built to simulate fluid-driven dynamic propagation of cracks in the porous media, as well as its influence on pore seepage and fracture seepage.

     

多空隙组合地质单元渗流理论分析与试验

岩体通常是以孔隙岩石为基质并包含各种成因的裂隙和溶隙的复杂多空隙组合地质材料。为研究孔隙-裂隙-溶隙多空隙组合介质的渗流特性,在简要介绍多孔介质渗流Darcy定律、平板窄缝流Poiseuille定律和圆形管道流Darcy-Weibach理论的基础上,分析了几种孔隙-裂隙-溶隙组合情况的多空隙介质渗流特性,推导出相应组合的等效渗透系数KE,给出了描述多空隙组合介质KE的一般表达式,讨论了影响各种空隙组合KE的主要因素。以普通砖模拟岩石基质,通过砖身钻孔填充及砖间缝隙填充,试验模拟了岩溶岩体和裂隙岩体中溶孔和裂隙填充后的渗透情况。试验结果与所推求理论公式计算出的KE在同一量级且误差很小,很好地验证了所推导的多空隙组合介质渗透系数表达式的有效性。     

B‐bar based algorithm applied to meshfree numerical schemes to solve unconfined seepage problems through porous media

The object of this work is to establish a meshfree framework for solving coupled, steady and transient problems for unconfined seepage through porous media. The Biot's equations are formulated in displacements (or u − w) assuming an elastic solid skeleton. The free surface location and its evolution in time are obtained by interpolation of pore water pressures throughout the domain. Shape functions based on the principle of local maximum entropy are chosen for the meshfree approximation schemes. In order to avoid the locking involved in the fluid phase of the porous media, a B‐bar based algorithm is devised to compute the average volumetric strain in a patch composed of various integration points. The efficiency of such an implementation for one phase problems is shown through the Benchmark problem, Cook's membrane loaded by a distributive shear load. The proposed methodology is firstly applied to various classical examples in unconfined steady seepage problems through earth dams, then to the dynamic consolidation of a soil column. The results obtained for both problems are quite satisfactory and demonstrate the feasibility of the proposed method in solving coupled problems in porous media. Copyright © 2015 John Wiley & Sons, Ltd.     

破碎砂岩渗透特性与孔隙率关系的试验研究

利用一种专利装置与MTS815.02型岩石力学试验系统,进行了破碎砂岩的稳态渗透试验,得到了不同孔隙率下破碎砂岩的渗透率和非Darcy流 因子。通过线性回归得到了渗透率、非Darcy流 因子与孔隙率之间的关系。认为破碎岩石的渗透特性主要是由孔隙率决定的,孔隙率不仅与当前的应力有关,更取决于加载历史。研究表明,水在破碎砂岩中的渗流一般不服从Darcy定律,而服从Forchheimer关系,特别是在小孔隙率下,非Darcy性更为突出;渗透率、非Darcy流 因子与孔隙率之间的关系可用幂函数拟合。     

堆石坝非达西渗流场分析

坝体的渗流计算常采用近似的线性渗流计算方法,然而对于堆石结构而言,在高水力梯度的作用下,由于流体惯性力与紊流的影响,水力梯度与渗流流速之间偏离了线性的达西定律,堆石体中不同孔隙介质的交界面错综复杂更增加了渗流场形态的复杂性。此时,使用非达西渗流的计算方法,可以提高渗流计算的精度,更加客观地描述渗流场中的渗流行为。基于伽辽金加权余量法推演了Forchheimer方程的非线性有限单元法公式,应用该方法对堆石坝渗流场问题进行了数值模拟计算,并给出了工程实例。研究表明,用该方法可以很好地研究渗流场中的非达西渗流现象。对比达西渗流计算与非达西渗流计算结果之间的差异,得出了非达西渗流计算的意义。对堆石坝结构而言,非达西渗流计算的结构显示渗流场的局部区域可能出现高水力坡降区域扩散的现象。此外,水力坡降峰值对比达西渗流计算结果有所增大,这说明真实渗流场的水力坡降峰值有可能超出材料的临界水力坡降允许值,从而引起坝体的渗透破坏。     

毛细管渗流模型在黄土渗透性中的应用探讨

黄土作为一种典型的多孔介质,多孔性是其重要特性之一。多孔性不仅影响着黄土的物理力学及化学特征,也严重影响着黄土的水理性质,特别是黄土的渗透特性。然而,作为多孔介质渗流理论的经典模型——毛细管模型,已经广泛应用于油气田开采、煤成气开采以及岩土工程等领域,但将多孔介质渗流理论模型引入表征黄土的多孔构造,这方面的资料尚欠缺。因此,本文以黄土的渗透性作为研究示例,在总结分析目前相对较为成功的多孔介质毛细管渗流模型的基础上,选取适于定量表征黄土渗透性的渗流模型,结合计算结果和渗透试验结果的对比,探讨将多孔介质毛细管渗流模型引入描述黄土渗透性这一方法的适用性。并提出孔隙的“香肠”构造（或称为“莲藕”构造）,为黄土的渗透性研究提供可借鉴的理论依据。     

饱和多孔介质材料的应变局部化萌生条件

在单相介质和非渗流饱和多孔介质应变局部化萌生条件的基础上,应用饱和多孔介质控制方程和Liapunov稳定理论,导出了渗流条件下的固相应力-应变描述和有效应力-应变描述的多孔介质固相部分的应变局部化的萌生条件。不同应力描述下的萌生条件的形式有一定变化。应用简单算例,讨论了Terzaghi有效应力描述的应变局部化萌生条件中两种固、液相对运动特例下的饱和多孔介质应变局部化破坏的形式。     

基于格子博尔兹曼方法表征体元尺度土体细观渗流场的数值模拟

为了研究土体的细观渗流特性,假设土体是完全饱和且在渗流过程中水分的流动始终处于层流状态。考虑宏观统计参数（孔隙率、渗透率及有效黏滞系数等）的影响,基于表征体元（REV）尺度的格子博尔兹曼（Boltzmann）方法,建立了压力作用下土体细观渗流的数值模型。采用D2Q9模型考虑水分流动的离散速度分布,宏观边界条件为左右侧面为不透水边界 ,上下边界设置不同的密度来控制压力边界,在微观边界条件上采用非平衡态外推格式。编制相应的计算程序,将计算区域内的多孔介质材料设置成流体（孔隙率 1.0,渗透率 ）,验证了经典的Poiseuille流。此外,结合算例分别讨论了土体在压力作用下孔隙率、渗透率及渗透压力等影响因素与渗流速度的相互关系,研究表明该数值方法与Darcy定律得到的计算结果较为吻合。因此,基于REV尺度的格子Boltzmann方法可以有效地模拟土体的渗流机制,为进一步研究土体渗流特性提供了一种新的研究手段。     

高水力梯度条件下颗粒堆积型多孔介质渗流规律试验研究

煤矿开采面临的水文地质条件越来越复杂,尤其是遭遇承压含水层的水压力越来越大,突水灾害发生时必然会带来高水力梯度引起的破碎岩体突水通道内高速非线性渗流问题。据此,研制高水力梯度（最大600）条件下堆积型多孔介质中高速非线性渗流试验装置,采用堆积型钢球模拟破碎岩体,对粒径为1、2、3、4、5、6 mm共6种光滑钢球分别开展了一维均质圆柱渗流试验。试验结果表明：对于由1～6 mm钢球堆积而成的孔隙率为0.44～0.45的多孔介质,当水力梯度大于145时,通过分析水力梯度-平均流速（J-v）曲线和水力梯度-雷诺数（J-Re）关系曲线,将流动状态划分为3个模式：线性层流、非线性层流、紊流,并获得了从线性层流过渡到非线性层流的临界流速为0.23～0.78 cm/s、临界水力梯度为3～8;从层流到紊流转捩的临界流速为1.6～4.8 cm/s、临界水力梯度为90～145。从小粒径多孔介质到大粒径多孔介质的渗流过程中,临界流速越来越大,而临界水力梯度逐渐减小。 渗透率与粒径的平方、非达西流影响系数与粒径的倒数均呈线性正相关,非达西流影响系数随着渗透率的增加呈指数减小。该研究对多孔介质非线性渗流的理论研究以及实际工程中高承压含水层突涌水问题有重要借鉴意义。     

Numerical solutions for flow in porous media

A numerical approach is proposed to model the flow in porous media using homogenization theory. The proposed concept involves the analyses of micro‐true flow at pore‐level and macro‐seepage flow at macro‐level. Macro‐seepage and microscopic characteristic flow equations are first derived from the Navier–Stokes equation at low Reynolds number through a two‐scale homogenization method. This homogenization method adopts an asymptotic expansion of velocity and pressure through the micro‐structures of porous media. A slightly compressible condition is introduced to express the characteristic flow through only characteristic velocity. This characteristic flow is then numerically solved using a penalty FEM scheme. Reduced integration technique is introduced for the volumetric term to avoid mesh locking. Finally, the numerical model is examined using two sets of permeability test data on clay and one set of permeability test data on sand. The numerical predictions agree well with the experimental data if constraint water film is considered for clay and two‐dimensional cross‐connection effect is included for sand. Copyright © 2003 John Wiley & Sons, Ltd.     

孔隙结构和水动力对饱和多孔介质中颗粒迁移和沉积特性的耦合影响

为了研究孔隙结构和水动力对悬浮颗粒在饱和多孔介质中沉积和迁移特性的影响,对天然硅粉（悬浮颗粒）和荧光素钠（示踪剂）在饱和多孔介质中的渗流迁移特性进行土柱试验,分别得到了5种不同渗流速度（0.033、0.066、0.132、0.199、0.265 cm/s）、两种不同多孔介质（石英砂和玻璃球）的悬浮颗粒和示踪剂全组合下的20条穿透曲线。根据试验结果,研究孔隙结构、渗流速度对饱和多孔介质中颗粒迁移和沉积过程中水动力作用机制、弥散效应、加速效应的影响。研究表明,悬浮颗粒的穿透曲线可以用一阶沉积动力学对流弥散方程的解析解来描述。随着渗流速度的增大,水动力学作用对颗粒出流浓度的影响越来越大,而孔隙结构的影响则相对减弱。同时,存在一个临界渗流速度值。当渗流速度超出该值时,悬浮颗粒迁移要快于示踪剂,而且临界渗流速度对于玻璃球和石英砂两种多孔介质是不同的;其次,在两种介质中,随渗流速度增大,弥散度增加,回收率和回收悬浮颗粒粒径增大,沉积系数先增大后减小。此外,在孔隙比相近的情况下,悬浮颗粒在玻璃球介质中的回收率要大于其在石英砂中的。可见,孔隙结构和渗流速度是影响饱和多孔介质中颗粒输运的重要因素,渗流速度越大,孔隙结构的作用越明显。     

A new parabolic variational inequality formulation of Signorini's condition for non‐steady seepage problems with complex seepage control systems

By extending Darcy's law to the dry domain above the free surface and specifying the boundary condition on the potential seepage surfaces as Signorini's type, a partial differential equation (PDE) defined in the entire domain of interest is formulated for non‐steady seepage flow problems with free surfaces. A new parabolic variational inequality (PVI) formulation equivalent to the PDE formulation is then proposed, in which the flux part of the complementary condition of Signorini's type in the PDE formulation is transformed into natural boundary condition. Consequently, the singularity at the seepage points is eliminated and the difficulty in selecting the trial functions is significantly reduced. By introducing an adaptive penalized Heaviside function in the finite element analysis, the numerical stability of the discrete PVI formulation is well guaranteed. The proposed approach is validated by the existing laboratory tests with sudden rise and dropdown of water heads, and then applied to capture the non‐steady seepage flow behaviors in a homogeneous rectangular dam with five drainage tunnels during a linear dropdown of upstream water head. The non‐steady seepage flow in the surrounding rocks of the underground powerhouse in the Shuibuya Hydropower Project is further modeled, in which a complex seepage control system is involved. Comparisons with the in situ monitoring data show that the calculation results well illustrate the non‐steady seepage flow process during impounding and the operation of the reservoir as well as the seepage control effects of the drainage hole arrays and drainage tunnels. Copyright © 2010 John Wiley & Sons, Ltd.     

A mapping technique for steady-state unconfined seepage analysis

An approach is presented for the analysis of the unconfined steady-state seepage through homogeneous trapezoidal dams based on a bijective mapping between the flow domain, having an unknown shape, and a fixed triangular domain. It is shown that the geometrically non-linear unconfined analysis is equivalent to the problem of determining the unknown distribution of permeability, within a triangular domain with known shape, that satisfies the set of transformed boundary conditions. The flow problem in the triangular domain is solved through a finite-element technique analogous to that adopted for confined analyses and, on the basis of this solution, the shape of the free surface in the physical space is evaluated. The proposed approach is applied to the determination of the influence of the water levels in the upper and lower reservoirs on the elevation of the free surface seepage point.     

非平衡-非线性吸附情况下填埋场污染物运移分析

采用Langmuir等温吸附线方程描述非线性吸附性能, 基于改进的混合元方法，通过数值计算与分析，探讨了非平衡吸附条件下污染物运移过程及其机理。计算结果表明: 当考虑非平衡、非线性吸附性能时, 污染物穿透曲线即浓度的时程变化曲线尖锐而狭窄、峰值点前移, “拖长尾”现象不明显, 由此说明，土颗粒对污染物的非平衡、非线性吸附使得污染物的穿透能力增强, 滞留能力下降。进一步的变动参数比较分析表明：Langmuir等温线方程中的参数B、压实粘土衬里的渗透性及地下水渗流速度对污染物运移过程具有显著的影响。