A local artificial boundary for transient seepage problems with unsteady boundary conditions in unbounded domains

Numerical analysis of transient seepage in unbounded domains with unsteady boundary conditions requires a more sophisticated artificial boundary approach to deal with the infinite character of the domain. To that end, a local artificial boundary is established by simplifying a global artificial boundary. The global artificial boundary conditions (ABCs) at the truncated boundary are derived from analytical solutions for one‐dimensional axisymmetric diffusion problems. By applying Laplace transforms and introducing some specially defined auxiliary variables, the global ABCs are simplified to local ABCs to significantly enhance the computational efficiency. The proposed local ABCs are implemented in a finite element computer program so that the solutions to various seepage problems can be calculated. The proposed approach is first verified by the computation of a one‐dimensional radial flow problem and then tentatively applied to more general two‐dimensional cylindrical problems and planar problems. The solutions obtained using the local ABCs are compared with those obtained using a large element mesh and using a previously proposed local boundary. This comparison demonstrates the satisfactory performance and obvious superiority of the newly established boundary to the other local boundary. Copyright © 2017 John Wiley & Sons, Ltd.     

An axi-symmetric infinite element for transient radial flow problems

The formulation of an axi-symmetric infinite element for transient analysis of flow problems in unbounded domain is presented. The theoretical basis as well as the implementation of the element is discussed, and the element decay function is derived using the analytical solution of a one-dimensional axially symmetric configuration. The form of decay within the element is described as a function of both time and space, and thus the hydraulic head distribution in the far field is simulated rigorously. The accuracy and the efficiency of the proposed element are demonstrated through several numerical examples in infinite media. In general, it is shown that using the present infinite element transient flow problems in unbounded domains can be simulated effectively. Copyright © 1999 John Wiley & Sons, Ltd.     

A high‐frequency open boundary for transient seepage analyses of semi‐infinite layers by extending the scaled boundary finite element method

A high‐frequency open boundary has been developed for the transient seepage analyses of semi‐infinite layers with a constant depth. The scaled boundary finite element equation of pore water pressure is formulated first in the frequency domain. With the eigenvalue problem, the equation can be decoupled into modal equations whose modal dynamic permeability equation can be determined. The continued fraction technique is adopted to formulate the continued fraction solution in the frequency domain. All constants in the solution are determined recursively at the high‐frequency limit. By introducing auxiliary variables and the continued fraction solution to the relationship between the prescribed seepage flow and the pore water pressure in the frequency domain, the open boundary condition is obtained. After transformed to the time domain, the open boundary condition is expressed as a system of fractional differential equations. No convolution integral is required. The accuracy of the analysis results increases with the increasing orders of continued fraction. Copyright © 2015 John Wiley & Sons, Ltd.     

用空气单元法求解渗流场的逸出边界问题

依据空气单元模拟排水孔的思路,在渗流场任意可能逸出边界外布置一层渗透性较强的单元,与其他实体单元一起进行渗流计算,可以实现该边界的自动求解。与现行方法相比,不仅省去了逸出边界迭代计算的麻烦,而且避免了由于逸出点定位不准确而可能引起的渗流计算不合理或收敛困难等缺陷。算例分析表明,空气单元法的计算精度与空气单元的相对渗透系数R有关,与厚度L无关。当选取了合适的R值后,可以较好地逼近现行方法。对于因引入空气单元而造成的强弱透水介质界面处数值拟真性差的现象,还提出了加入接触面薄层单元的改进方法。方法改进后,计算精度可进一步提高。最后,以小湾水电站22#坝段渗流场计算为例,说明该法的实用性和可行性。     

工程中渗流问题的边界元算法与分析

针对河堤、水坝、高速公路档水墙等存在多孔单元介质中的定常渗流问题,将渗流Laplace方程,通过数学变换转化为边界积分方程,进而离散为线性代数方程组。采用边界元编写FORTRAN程序。计算结果表明:该法与有限元法相比,占用CPU时间短,不需要网格化分,使繁杂问题简单化,同时很好地切近实际。      

改进的有自由面渗流问题的Bathe算法

建议了一个新的有自由面渗流问题的变分不等式提法,该提法通过将潜在出渗面上的边界条件提为Signorini型条件,从而从理论上消除了出渗点的奇性,解决了出渗点的定位问题。同时在离散求解时,通过引进依赖于网格参数的连续型Heaviside函数,克服了Bathe算法中所固有的网格依赖性,提高了这类方法的数值稳定性。     

颗粒离散单元法动力人工边界设置方法

采用颗粒离散单元法进行动力计算时,人工截断边界上需设置吸收边界条件,以防止波的反射。鉴于颗粒离散单元数值计算模型的人工边界上颗粒单元半径大小不一、边界面凸凹不平,在连续介质的黏性、黏弹性、自由场边界条件方程基础之上,推导出适用于离散介质的等效方程。在离散介质的黏性边界条件等效方程中引入微调系数,提出比值迭代法以快速确定其最优值,以实现对波的最佳吸收。采用二维颗粒离散单元计算软件PFC2D,分别建立黏性、黏弹性、自由场边界条件相关数值分析模型,探讨颗粒分布模式对黏性边界上颗粒单元半径、速度分布及比值迭代过程的影响;采用外源波动算例及经典Lamb问题算例验证黏弹性边界设置方法的正确性;通过隧洞算例检验提出的自由场边界条件设置方法的正确性。     

弹性波数值模拟的混合边界与频散抑制

针对刚性边界条件、衰减边界条件与透射边界条件对弹性波场的影响及计算中产生的数值频散现象,将衰减边界与透射边界双重作用于人工边界,引入了混合边界条件,并在计算中采用了微量阻尼的方法,结果表明,混合边界条件能更好地吸收人工边界的反射;数值频散的阻尼算法能大大减弱由网格剖分、计算误差造成的频散现象。该方法可有效提高波场模拟精度。     

三维非恒定渗流自由面边界积分项的高精度数值积分

在三维非恒定渗流有限元计算中,不可避免地需计算自由面上的边界积分项。建议一种高精度数值积分的方法求取自由面边界积分项。其基本思路是,基于8节点空间等参单元,根据压力为零的边界条件确定自由面满足的曲面方程,将自由面边界积分转化为ξη平面上的二重积分;然后再计算自由面与三维等参单元的交点,将交点投影到局部坐标平面ξη上,并根据点与线的相对关系,确定投影点所围成的局部坐标积分区域;再将总积分区域划分成若干个三角形子区域,并利用变步长Simpson方法计算各三角形子区域上的二重积分,从而实现了高精度的自由面边界积分。该方法避免了单元中自由面为平面的假设,可提高计算精度,特别对于单元内自由面变化剧烈情况,更为显著。将该方法应用于砂槽模型和土坝的渗流分析中,计算结果与实际情况较为接近。     

杂交边界点法求解带自由面的渗流问题

将杂交边界点法与迭代法相结合,求解有自由面的渗流问题。杂交边界点法基于杂交位移变分原理和移动最小二乘近似,利用基本解插值域内的场函数,而边界上的变量则用移动最小二乘近似,是一种纯边界类型的无网格方法。利用该方法只需在边界上布点而不需要划分任何网格的特性,先假定自由面的初始位置,再进行迭代求解。数值算例表明,该方法精度较高、计算量较小,适合于求解各种具有自由面的渗流问题。     

有自由面渗流分析的三维数值流形方法

提出了求解有自由面渗流问题的三维数值流形方法,通过构造任意形状流形单元的水头函数,推导了流形单元的渗透矩阵和无压渗流分析的总体控制方程,并给出了自由面的迭代求解策略和渗透体积力的计算方法。典型算例的数值分析表明,该方法采用数学网格覆盖整个材料区域,在自由面的迭代求解过程中数学网格保持不变,只考虑自由面以下渗流区的介质,只对自由面以下的流形单元形成总体渗透矩阵,具有精度高、收敛速度快、编程简单等优点,而且能够通过单纯形积分精确计算被自由面穿越单元的渗透作用力,因此,特别适用于有自由面渗流问题的模拟。     

渗流场中岩石流变特性的数值模拟

渗流对岩石的流变特性有显著的影响,但限于试验条件,相关的试验成果较少。而数值计算技术已成为进行岩石力学研究的重要方法,因此,采用数值模拟方法对渗流场中岩石的流变特性进行了研究。对已有的岩石室内流变试验进行模拟来验证数值方法的有效性,在压缩流变试验的数值模拟中对试件分别施加单向、三向渗流场来模拟不同渗流条件对岩石流变特性的影响。模拟结果表明,在渗流方向上渗流产生的动水压力会导致试件的流变变形增大。此外,不同渗流场对流变的影响也有所差异,三向渗流场中试件受到的轴向渗透力小于单向渗流场,而侧向渗透力则大于单向渗流情况,这也导致三向渗流场中试件的轴向应变小于单向渗流场,而侧向应变大于单向渗流场。     

复杂地形尾矿坝的三维渗流分析

对于复杂地形的尾矿坝,由于二维模型不能充分反映复杂多变的渗流域,也不能考虑到三个方向渗流因素同时作用的影响,从而无法体现真正的渗流场。通过建立三维渗流数学模型,并考虑复杂断面概化和地形的简化,对实际工程进行了数值计算,其结果与试验结果吻合较好。结果表明,对复杂地形的尾矿坝渗流分析时必须采用三维模型,三维数值计算中对复杂地形进行适当的简化和概化对结果的影响较小,可以满足精度要求,因此大大减小了计算的复杂程度和难度。     

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.     

非稳定渗流条件下非饱和土质边坡稳定性的矢量和分析法研究

研究可以同时考虑渗流、变形与稳定的非饱和土质边坡稳定性分析方法具有重要的理论意义及工程实用价值。基于Fredlund双应力变量理论进行非饱和非稳定渗流-应力耦合分析,同时与传统非耦合渗流方法确定的孔压场进行对比发现,两种方法确定的浸润线变化过程相近,堤底处孔压的最大相对误差为8.8%,验证了耦合分析结果的可靠性。将基质吸力对强度的贡献纳入黏聚力中得到坡体强度参数的空间分布规律,又基于滑面强度参数时空分布规律借助Matlab平台开发了非稳定渗流条件下非饱和土质边坡稳定性的矢量和法分析程序。以库水位下降条件下堤坡的稳定性分析为例,将不同方法的计算结果进行对比,发现文中方法搜索得到的滑面位置相对于传统方法要深缓,但总体位置相差不大,不同方法对应的安全系数相差不足0.096,验证了所提方法的合理性。     

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。     

Semi‐analytical elastostatic analysis of unbounded two‐dimensional domains

Unbounded plane stress and plane strain domains subjected to static loading undergo infinite displacements, even when the zero displacement boundary condition at infinity is enforced. However, the stress and strain fields are well behaved, and are of practical interest. This causes significant difficulty when analysis is attempted using displacement‐based numerical methods, such as the finite‐element method. To circumvent this difficulty problems of this nature are often changed subtly before analysis to limit the displacements to finite values. Such a process is unsatisfactory, as it distorts the solution in some way, and may lead to a stiffness matrix that is nearly singular. In this paper, the semi‐analytical scaled boundary finite‐element method is extended to permit the analysis of such problems without requiring any modification of the problem itself. This is possible because the governing differential equations are solved analytically in the radial direction. The displacement solutions so obtained include an infinite component, but relative motion between any two points in the unbounded domain can be computed accurately. No small arbitrary constants are introduced, no arbitrary truncation of the domain is performed, and no ill‐conditioned matrices are inverted. Copyright © 2002 John Wiley & Sons, Ltd.     

隧道围岩内地下水渗流边界效应影响研究

根据水位条件、施工工艺和防排水设计原则将隧道渗流计算围岩透水边界条件大致划分为4种类型,并分析了不同透水边界条件适应的施工工况。基于复变函数理论和保角映射方法,推导得出4种透水边界条件下隧道围岩内任一点孔隙水压力和隧道涌水量解析计算公式,通过与数值解的对比,印证了解析解的准确性。在此基础上,根据不同透水边界条件下隧道涌水量和围岩关键点孔隙水压力随埋深直径比（ ）的变化规律,分析了透水边界条件的变化对浅埋隧道和深埋隧道的影响,并探讨了浅埋水下隧道渗流计算中透水边界条件的选取。相关结论与认识对于隧道渗流计算和排水设计具有一定的指导作用和参考价值。     

油藏多相渗流的面向对象有限元程序设计

近年来,面向对象的编程技术越来越受到人们的重视,并用来解决和模拟各种物理问题和工程问题,特别是在有限元方法编程和模拟中得到了广泛地应用。介绍了面向对象的程序设计方法和它与有限元程序相结合的原理和优点。在此基础上提出了面向对象有限元方法在油藏多相渗流中的应用实例,并按照面向对象的程序设计方法,基于Windows XP平台采用Visual C++.NET语言,建立了有关描述多相渗流的有限元模型的类,给出了类的描述和它的实现方法。建立的相关类及其实现方法主要包括处理矩阵计算的类、节点类、单元类、材料类、形函数类等。据此编制了油藏多相渗流的有限元分析的数值计算程序,并给出了一个数值实例。     

非饱和-非稳定渗流条件下的边坡临界滑动场

受季节性降雨或水库运行的影响,岸坡外水位及坡内孔隙水压力场的变化较大,不利于岸坡的稳定性。在水位变化过程中,利用非饱和-非稳定渗流有限元计算得到孔隙水压力场,基于非饱和土的渗流和抗剪强度理论,对水位变化过程中的边坡临界滑动场法进行改进,提出可考虑水位变化与岸坡非饱和-非稳定渗流过程的边坡临界滑动场数值模拟方法。将改进后的水位变化过程中的边坡临界滑动场法分别应用于黏土、粉土岸坡在水位升降过程中的稳定性分析,研究了水位升降速率及基质吸力对岸坡稳定性的影响,并揭示了边坡在水位变化过程中的稳定性变化历程。研究表明,该方法计算结果合理、可靠,更适用于涉水边坡的稳定性计算,且岸坡稳定性变化历程受水位升降速率、基质吸力等多种因素共同影响,只有在考虑非稳定渗流的基础上同时考虑基质吸力的作用才能正确得出水位变化过程中岸坡稳定性变化规律和实质。