正则化方法在比值类位场边缘识别方法中的研究

位场边缘识别方法有很多种,其中归一化标准差法(NSTD)、倾斜角法(Ta)和Theta Map(cosθ)等方法属于比值类方法。比值类方法在计算过程中会出现分母接近于0或者等于0这种情况,致使计算结果不稳定,并产生错误的边缘识别结果。为此,对比值类边缘识别方法计算公式中的分母加一个大于零的正则化因子,不但解决了比值类方法的数值计算稳定性问题,而且提高了部分比值类边缘识别方法识别结果的精度。通过理论模型和实际资料检验了新方法的稳定性、精度以及有效性。正则化因子的引入同样可以改善以比值类方法为基础构建的二阶导数类边缘识别方法的识别效果,如倾斜角总水平导数(Ta-THDR)的识别效果。正则化这一思想不但可以解决比值类位场边缘识别方法的数值计算问题,而且可以解决比值类方法的数值计算问题。     

A space-time discontinuous Galerkin method applied to single-phase flow in porous media

A space-time discontinuous Galerkin finite element method is proposed and applied to a convection-dominant single-phase flow problem in porous media. The numerical scheme is based on a coupled space-time finite element discretization allowing for discontinuous approximations in space and in time. The continuities on the element interfaces are weakly enforced by the flux treatments, so that no extra penalty factor has to be determined. The resulting space-time formulation possesses the advantage of capturing the steep concentration front with sharp gradients efficiently. The stability and reliability of the proposed approach is demonstrated by numerical experiments. The author is grateful to the DFG (German Science Foundation—Deutsche Forschungsgemeinschaft) for the financial support under the grant number Di 430/4-2.     

Application of the numerical manifold method for stress wave propagation across rock masses

In this paper, the numerical manifold method (NMM) is extended to study wave propagation across rock masses. First, improvements to the system equations, contact treatment, and boundary conditions of the NMM are performed, where new system equations are derived based on the Newmark assumption of the space–time relationship, the edge‐to‐edge contact treatment is further developed for the NMM to handle stress wave propagation across discontinuities, and the viscous non‐reflection boundary condition is derived based on the energy minimisation principle. After the modification, numerical comparisons between the original and improved NMM are presented. The results show that the original system equations result in artificial numerical damping, which can be overcome by the Newmark system equations. Meanwhile, the original contact scheme suffers some calculation problems when modelling stress wave propagation across a discontinuity, which can be solved by the proposed edge‐to‐edge contact scheme. Subsequently, the influence of the mesh size and time step on the improved NMM for stress wave propagation is studied. Finally, 2D wave propagation is modelled, and the model's results are in good agreement with the analytical solution. Copyright © 2013 John Wiley & Sons, Ltd.     

电阻率层析成像及演中若干问题的讨论

以双异性点电流源电流场二维地电断面为例，着重讨论了电阻率展析成像反演中有限单元法数值模拟边界条件的选择、网格剖分以及模拟精度等问题，同时也讨论了成像反演中最优化及演方法及拟合参数的评价等。文中提出的新的网格剖分方法和选择的边界条件可有效地提高计算速度和数值模拟的精度。     

非连续变形分析方法中的阻尼问题研究

定量研究了非连续变形分析(DDA)方法中的黏性阻尼与数值阻尼。首先,基于Newmark直接积分法,推导了块体系统的运动方程。其次,通过动力学中的黏性阻尼理论建立了DDA中动力系数、时间步长与黏性阻尼比的关系式,探讨了DDA中的常加速度积分方案的数值阻尼分区及阻尼比计算方法,进而得到两种阻尼共同作用时的阻尼比表达式,并分析了频域内阻尼比的分布情况。最后,以谐振激励下的块体振动为例,通过对比不同阻尼作用下块体位移的DDA计算值与理论解,验证了本文提出的阻尼比计算公式的正确性。研究表明：黏性阻尼对低频的衰减作用明显,数值阻尼则可以很快地消除高频干扰,而二者共同作用下可降低阻尼的频率相关性。该研究成果为DDA的振动、波动等动力计算的阻尼取值提供了理论依据。     

Shallow-water simulations by a well-balanced WAF finite volume method: a case study to the great flood in 2011, Thailand

A well-balanced finite volume method for solving two-dimensional shallow water equations with weighted average flux (WAF) is developed in this work to simulate flooding. Friction source terms are estimated with a semi-implicit scheme resulting in an efficient numerical method for simulating shallow water flows over irregular domains, for both wet and dry beds. A wet/dry cell tracking technique is also presented for reducing computational time. The accuracy of these methods are investigated by application to well-studied cases. For practical purposes, the developed scheme is applied to simulate the flooding of the Chao Phraya river from Chai Nat to Sing Buri provinces in Thailand during October 13–17, 2011. The numerical simulations yield results that agree with the existing data obtained from the satellite images.     

双相介质中纵波方程的高阶有限差分解法

从双相介质中的纵波方程出发,导出了求解双相各向同性介质中纵波方程的高阶差分格式,给出了吸收边界条件和稳定性条件,在此基础上实现了双相各向同性介质中纵波方程的高阶有限差分法正演模拟,数值模拟结果表明,这种算法能在少量增加计算量的前提下大大提高精度,算法可同时应用于叠前和叠后的数值模拟。     

A three‐point time discretization technique for parabolic partial differential equations

The Crank–Nicolson scheme has second‐order accuracy, but often leads to oscillations affecting numerical stability. On the other hand, the implicit scheme is free from oscillation, but it has only first‐order accuracy. In this work, a three‐point discretization scheme with variable time step is presented for the time marching of parabolic partial differential equations. The method proposed has second‐order accuracy, is unconditionally stable and dampens spurious oscillations of the numerical results. The application and effectiveness of the new method are demonstrated through several numerical examples. It is shown that, unlike the Crank–Nicolson method, the approach proposed produces no oscillatory response irrespective of the time step adopted. Copyright © 2010 John Wiley & Sons, Ltd.     

边坡大变形损伤破坏的高效无网格模拟

首先讨论了Lagrangian和Eulerian无网格近似的联系和区别,然后基于稳定节点积分和增量本构理论,建立了分析边坡静动力破坏的高效大变形无网格法,并给出了详细的计算流程。该方法采用弹塑性损伤耦合本构关系来模拟岩土类材料的破坏演化过程,其中屈服函数采用Drucker-Prager准则,损伤准则为基于应变的各项同性损伤函数。由于无网格近似和稳定节点积分具有非局部近似的特性,在保证空间离散稳定性和提高计算效率的同时,也可准确有效地模拟应变集中所形成的剪切带的发生与扩展,通过数值算例验证了方法的有效性。     

基于Eshelby张量和Mori-Tanaka等效方法的砂卵石土等效弹性模量研究

砂卵石土是物理力学性质既不同于砂土也不同于完整岩体的离散体,将其简化为砂土为基体,卵石为椭球形夹杂的两相复合材料。在小变形条件下,考虑卵石的含量和分布,采用Eshelby张量和Mori-Tanaka等效方法,运用替换迭代方式,从理论上推导出等效柔度张量一般性计算方程;重点研究卵石为球形时（椭球的一种特殊情况）砂卵石土等效弹性模量,通过编写程序求得其数值解,并与相关数值试验和理论进行对比。结果表明,此理论计算方法精度较以前的理论计算方法精度有大幅提高,当卵石体积分数小于50%时,理论计算结果与数值试验结果吻合较好,其结果可用于判断砂卵石土宏观力学特性,有利于地下工程应用;当体积分数大于50%时,理论计算结果和数值试验结果有一定误差。     

考虑冻融影响的岩土类材料导热系数计算新方法

从多孔随机混合介质理念出发,提出了考虑相变及未冻水影响的冻融条件下岩土类材料的导热系数计算的新方法,并根据已有的试验数据,利用多孔随机混合介质模型求出了同等条件下的导热系数,研究结果表明：模型的计算结果和试验结果基本一致,其平均偏差为2.3%,最大偏差为5.4%。另外,通过与现有的3种导热系数的取值方法的比较发现：目前广泛使用的指数加权平均法在0℃以上时计算结果较准确,但并不适合计算低温（0℃以下）岩土类材料的导热系数。加权调和平均法和加权算术平均法计算结果误差都很大,且不能反映相变对导热系数的影响。研究成果为低温相变条件下岩土介质温度场的正确求解提供了理论前提。     

A time‐discontinuous Galerkin method for the dynamical analysis of porous media

We present a time‐discontinuous Galerkin method (DGT) for the dynamic analysis of fully saturated porous media. The numerical method consists of a finite element discretization in space and time. The discrete basis functions are continuous in space and discontinuous in time. The continuity across the time interval is weakly enforced by a flux function. Two applications and several numerical investigations confirm the quality of the proposed space–time finite element scheme. Copyright © 2006 John Wiley & Sons, Ltd.     

An adaptive time integration scheme for blast loading on a saturated soil mass

This paper presents a time integration scheme capable of simulating blast loading of relatively high frequency on porous media, using coarse meshes. The scheme is based on the partition of unity finite element method. The discontinuity is imposed on the velocity field, while the displacement field is kept continuous. The velocity discontinuity is postulated to occur in the time domain. The developed time integration scheme is unconditionally stable and has controllable numerical dissipation in the high frequency range. An important feature of the time scheme is that it allows for controlling the numerical damping in a consistent way. The time scheme has been implemented in combination with Biot’s theory of wave propagation in saturated porous media. Numerical examples have demonstrated that the proposed time scheme is, in addition to being accurate and stable, highly effective for coarse meshes. This makes the developed scheme suitable for large scale finite element analysis.     

Semi-analytical solutions of a contaminant transport equation with nonlinear sorption in 1D

A new method to determine semi-analytical solutions of one-dimensional contaminant transport problem with nonlinear sorption is described. This method is based on operator splitting approach where the convective transport is solved exactly and the diffusive transport by finite volume method. The exact solutions for all sorption isotherms of Freundlich and Langmuir type are presented for the case of piecewise constant initial profile and zero diffusion. Very precise numerical results for transport with small diffusion can be obtained even for larger time steps (e.g., when the Courant-Friedrichs-Lewy (CFL) condition failed).     

基于Poulos弹性理论的被动桩改进算法

传统的Poulos弹性理论仅适合于均质土中土体侧向位移时桩的性状分析,无法考虑土的层状特性。通过引入层状地基中作用一水平集中力的广义Mindlin解和地面作用有竖向荷载时的应力和位移通解,对Poulos方法进行了改进,使之扩展到多层土中,还用于研究堆载条件下的被动桩变形和受力响应。算例分析表明,改进弹性理论要比Poulos方法更为严密、合理,提高了计算精度,应用范围也更广。     

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。     

基于Julia加速的射频大地电磁法正演模拟与位移电流作用研究

射频大地电磁法(Radio-magnetotelluric, RMT)是浅地表电磁勘探的重要手段之一。由于勘探频段为10～300 kHz,其电磁场传播受地下介质介电常数的影响较大。传统准静态条件下的电磁响应严重制约RMT正演模拟精度,并进一步影响反演成像分辨率。针对这一问题,提出了一种基于Julia并行加速的全电流RMT电磁响应数值模拟方法,利用Julia的分布式计算将各频点的计算发送到不同进程进行求解,从而达到加速计算的目的,同时在计算中考虑位移电流的影响,提升正演的模拟精度。通过计算几种典型高阻/高介电模型的RMT响应,分析并总结了位移电流对射频段电磁场视电阻率及相位响应的影响规律。数值模拟结果表明：当浅部存在高阻覆盖层时,基于准静态假设条件计算的RMT视电阻率和相位响应偏高,且频率越高、覆盖层电阻率越大,响应偏差越大;对于煤炭采空区模型,RMT法能有效反映异常体位置,但忽略位移电流会在采空区及其附近引起较大计算误差;起伏地形的算例表明地形会覆盖地下异常体的RMT数值响应,尤其是地形拐角处;2种不同规模的并行算例对比证明了并行算法的高效性,且随着求解问题规模增大,并行算法效率也随之...     

Dynamics of pile driving by the finite element method

It is proposed that the dynamics of pile driving based on the one-dimensional theory of wave propagation be analyzed by the finite element method. This approach enables one to continuously interpolate the displacement, velocity and acceleration profiles throughout the pile length. In contrast to the finite difference technique presented by E. A. L. Smith [1] and the finite element procedure presented by I. M. Smith [2] in which initial conditions are defined on the basis of a prescribed hammer velocity, the method presented herein defines initial conditions on the basis of a prescribed impact force versus time curve at the pile/hammer point of contact. Applications of the proposed technique to typical pile driving problems on an elastoplastic soil and using an implicit time-integration scheme are discussed using a numerical example.     

地下结构抗震设计的改进等效反应加速度法

对地下结构横向抗震分析中的等效反应加速度法进行综合分析。结合算例,以动力时程法为基准,全面评价了等效反应加速度法的适用性;进而深入分析其误差来源,并做针对性改进优化,通过引入动力响应调整系数β,提出了一种改进等效反应加速度法;结合算例分析,评价了改进等效反应加速度法对不同工况的适用性。结果表明：等效反应加速度法计算所得结构内力及变形均偏小;且计算精度随地层剪切波速的增大整体呈上升趋势,但几乎不受结构埋深的影响;同时,明确了等效反应加速度法的误差源自于其忽略了地下结构对其周围土体动力响应的干扰作用,改进优化后提出了改进等效反应加速度法;相比现有等效反应加速度法,改进等效反应加速度法具有更广泛的适用性及更优的计算精度,可为地下结构抗震设计和分析提供新的计算方法。     

岩石应变软化本构模型建立及NR-AL法求解研究

针对岩土工程材料应变软化问题及有限元对其数值计算时切线刚度矩阵负定造成求解困难的问题进行研究。建立了基于Drucker-Prager（D-P）强度准则的岩石弹塑性应变软化本构模型,本构积分算法采用一种完全隐式返回映射算法,它具有无条件稳定和精确的特点,详细论述了如何进行本构模型的程序化求解;考虑弧长法在判断切线刚度矩阵正定性导致效率低的缺点,在弹塑性增量有限元方程的迭代计算中尝试采用Newton-Raphson法和arc-length法（NR-AL法）联合迭代求解的思路,即在结构未达到极限荷载前采用NR迭代法,而当结构接近极限荷载时转换为AL法控制迭代,从而使结构越过峰值点进入软化区直至破坏,NR-AL法汲取了2者迭代求解中具有的优势;利用C++语言对所建应变软化模型的本构求解和弹塑性增量有限元方程迭代求解过程给予程序实现,应用所编程序进行数值计算,分析了D-P理想弹塑性模型、应变软化模型、应变硬化模型计算的应力-应变曲线的区别,同时将应变软化模型计算结果与试验数据进行了对比。研究结果表明：所建应变软化本构模型可以较好地模拟岩石材料的峰后软化特性,能够揭示峰后应变软化特性和破坏机制,同时NR-AL法能够求解由于应变软化造成的负刚度问题,也克服了单独使用弧长法时判断切线刚度矩阵正定性效率低的缺点。