考虑时效的高填石路堤工后沉降有限元及反馈分析研究

把填石体作为粘弹性介质,提出采用三参数本构模型来描述填石体的蠕变特性,在此基础上引入遗传算法与有限元分析,建立了填石体三参数本构模型参数确定的优化反演方法,结合某高填石路堤得实测工后沉降数据进行参数反演,并利用反演参数对类似断面进行工后沉降分析,结果表明,本文建立的填石路堤工后沉降计算方法能准确的预测工后沉降,参数便于求取,为寻求合理的路面铺筑时间和制定施工控制条件提供依据。     

地下水流数值模型的分解与叠加

叠加原理在水文地质计算中的应用相当普遍,但一般局限于地下水流模型的解析解,本文扼要介绍了线性定解问题的叠加原理,在此基础上提出了线性离散模型的叠加原理,进而讨论了线性离散模型的叠加原理在地下水流数值模型中的应用一一地下水流数值模型的分解与叠加.模型分解与叠加既可用于解析分析也可用于数值计算;同时不仅可以简化复杂模型的求解问题,更有助于理解地下水变化过程.     

基于多重响应面法的基坑位移反分析

基坑变形的反分析涉及数值模型与优化方法的耦合,常具有计算量大、使用不方便的特点。为此,提出1种可用于基坑变形反分析的多重响应面法,该方法在基坑地下连续墙不同深度处分别采用二次多项式表示地下连续墙水平位移与土层弹性模量之间的隐式关系,在此基础上利用位移观测对基坑土层弹性模量进行反分析。该方法可以解开数值模型和优化算法的耦合,从而具有较高的计算效率。工程应用实例表明,多重响应面法对基坑土层弹性模量进行反分析具有使用方便、计算效率高、计算结果准确的优点,非常适合求解基坑工程的位移反演问题。     

奇异值分解法解病态方程组的研究及在重力密度反演中的应用

本文介绍了奇异值分解法的基本原理,剖析了此种方法克服病态的实质,并将SVD方法用于根据重力异常观测值反演地下地质体密度分布的数值计算中,在计算中考虑到数据误差,计算舍入误差,以及计算机机器精度①对数值计算的综合影响,取得了较好的反演效果。     

粘弹性岩体力学模型识别与参数反演解析方法研究

本文基于圆形和非圆形隧道围岩粘弹性位移反演分析解析方法的最新进展，根据隧道围岩力学参数解析解的反演规律，提出了五个粘弹性力学模型识别与参数定理，并通过算例和工程实例对所给出的定理作了必要的验证。     

软土地基三维粘弹性反演分析与变形预测研究

针对无锡地区软土工程施工具有明显流变性的特点,运用粘弹性理论和反演分析方法,结合无锡市图书馆工程对其地基变形和粘弹性模型进行了研究,通过实测数据与计算值的对比来修正模型和计算参数;在此基础上对该工程的长期地基沉降进行了预测,取得了与实际较为吻合的结果,为本地区软土工程地基的长期变形预测提供了有效的方法和思路。     

软土地基沉降的二维非线性粘弹性反演与预测

基于Merchant粘弹性模型和简化双曲线模型，建立软土地基沉降的二维非线性粘弹性Biot固结有限元计算公式；根据最小二乘法建立目标函数，采用Simplex直接优化算法反演确定参数；为反演能获得在物理意义上合理且数学上唯一的参数，提出从简单模型到复杂模型的分步反演分析方法。实例分析表明，该方法是可行的。     

电阻率法监测地下地质变化的数值模拟

通过有限元数值模拟方法,研究了电阻率法监测地下地质变化的可行性,提出了基于多期次观测的地下电阻率监测方法,应用二维电阻率正、反演程序对模型进行了数值模拟。结果表明,电阻率相对变化率可以较好地指示电阻率变化的区域和位置。高精度、大数据量的地电阻率观测,以及基于2D或3D的电阻率正、反演计算使得应用电阻率法监测地下地质变化成为可能。     

CSAMT一维全频视电阻率反演

本文采用全频率视电阻率反演,使用2~(-3)~2~(13)Hz频率,并且不做近区和过渡区校正,直接用卡尼亚视电阻率作为反演参数。正演采用虚界面法计算有限长导线在水平层状介质的电磁场分量,反演采用有限内存拟牛顿法。数值模拟采用三层模型和实测数据进行反演,得到了符合地下电性变化的反演模型结果,证实了CSAMT一维全频视电阻率反演具有可实施性。     

用剩余信息量最小准则实现直流电测深数据的二维自动反演

自Pelton等发表第一篇直接电测深数据的二维反演文章以来，电测深数据的二维反演解释已广泛应用于资源勘探和环境监测，并取得一定效果。然而，由于该方法中加入了人为确定的平滑约束，其反演解释结果具有很大不确定性，使其在实际生产中普及应用受到限制。因此，如何在现有方法的基础上进一步改进完善成为该方法普及应用的关键。为了使反演解释结果既忠于实测数据，又合理地反映地下介质的变化，作者在本文中讨论了基于最大熵谱原理的剩余信息量最小准则实现电测深数据的二维自动反演。作者在文中还介绍了正演计算和偏导数求取中，提高精度和计算效率的技巧。用三个数值模式算例对本文的自动反演方法进行了验证。数值模拟结果表明，基于剩余信息量电小准则的二维自动反演给出的解释结果基本不受人为因素影响，能反映地下介质电阻率的详细变化。     

基于常Q模型的分数阶粘弹介质数值模拟方法

基于常Q模型的解耦分数阶拉普拉斯算子粘滞波动方程,可以分开模拟振幅衰减和相位错动。但该方程拉普拉斯算子的阶数是随空间变化的,因此数值求解存在一定困难。这里基于截断的泰勒展开,经过一系列近似,推导出拉普拉斯算子的阶数与空间无关的解耦分数阶粘滞弹性波动方程。采用中心差分计算时间导数,使用交错网格伪谱法计算空间导数。数值算例表明,新的方程在处理非均匀介质时具有精度高,计算简便的优点。     

Rational approximation for estimation of quality <Emphasis Type="Italic">Q</Emphasis> factor and phase velocity in linear,viscoelastic, isotropic media

The article presents a numerical inversion method for estimation of quality Q factor and phase velocity in linear, viscoelastic, isotropic media using reconstruction of relaxation spectrum from measured or computed complex velocity or modulus of the medium. Mathematically, the problem is formulated as an inverse problem for reconstruction of relaxation spectrum in the analytic Stieltjes representation of the complex modulus using rational approximation. A rational (Padé) approximation to the relaxation spec trum is derived from a constrained least squares minimization problem with regularization. The recovered stress-strain relaxation spectrum is applied to numerical calculation of frequency-dependent Q factor and frequency-dependent phase velocity for known analytical models of a standard linear viscoelastic solid (Zener) model as well as a nearly constant-Q model which has a continuous spectrum. Numerical results for these analytic models show good agreement between theoretical and predicted values and demonstrate the validity of the algorithm. The proposed method can be used for evaluating relaxation mechanisms in seismic wavefield simulation of viscoelastic media. The constructed lower order Padé approximation can be used for determination of the internal memory variables in time-domain finite difference numerical simulation of viscoelastic wave propagation.     

基于MPI的面波有限差分正演模拟

近年来,瑞利波波形反演技术因其避开了常规频散曲线计算,直接进行波场计算和反演不再受水平层状介质理论假设的限制,得到广大学者的高度重视。但瑞利波波形反演过程中需要不断进行波场正演和逆推计算。另外,由于浅地表速度较小,模拟计算时需要较小的网格间距才能避免数值频散,这无疑大大增加了正演模拟的计算量。对于这一问题,通常采用并行化设计来提高正演模拟的计算效率。本文基于消息传递接口（MPI）并行有限差分算法,以区域分解思路将模型区间分解成若干子区域,各区域互相通信,共同完成对模型的正演计算。并详细给出了区域分解、坐标转换、区域通信、波场合并等并行方案中的具体实现方法和实现步骤。通过对弹性模型、Kelvin黏弹性模型和标准线弹性固体（SLS）黏弹性模型不同并行方案的计算结果进行分析,验证了本文并行方案的可行性和有效性。并行计算结果表明,与单处理器计算时间相比,增加处理器数目可以明显减少计算时间,但随着处理器数目的增加,不同处理器之间的通信时间也增大;因此,并行时需要选择合适的处理器数目。对于黏弹性介质模型,SLS黏弹性模型的并行计算效率优于Kelvin黏弹性模型。     

地震波混合阶褶积算法模拟

基于正反傅立叶变换,提出了地震波模拟的混合阶褶积算法。该方法原理简单、易于实现,结合了有限差分与伪谱法的优点,具有较高的精度和计算效率,适用于地震波场的正演计算,同时还给出了二维地震波场的理论计算实例。计算结果表明,此算法模拟结果正确、精度高、速度快、能适应较为复杂地质模型,并且易于推广到各向异性介质中去。     

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.     

Seismic wave propagation in laterally inhomogeneous poroelastic media via BIEM

This work addresses in‐plane pressure P and vertically polarized shear SV seismic wave propagation in a finite, laterally inhomogeneous, multilayered poroelastic geological region resting on the homogeneous elastic half‐space. The particular approach followed here is based on a combination of the (i) viscoelastic approximation (isomorphism) to Biot's equations of dynamic poroelasticity and on the (ii) boundary integral equation method (BIEM) using frequency‐dependent fundamental solutions of the governing wave equations. The problem is formulated under plane strain conditions and time‐harmonic motions are assumed. Validation of the viscoelastic isomorphism and verification of the BIEM is done by solution of benchmark examples. These simulation studies reveal that the proposed methodology is able to depict a sensitivity of the seismic signals recovered to the following parameters: (i) poroelastic properties of fluid saturated layers; (ii) lateral geological inhomogeneity; (iii) surface topography and (iv) frequency content and direction of the incident wave. It is concluded that the combination of viscoelastic isomorphism with BIEM software provides an effective numerical tool for evaluating site‐effect phenomena in multilayered, fluid saturated geological regions with complex geometry. The numerical results obtained demonstrate that dynamic poroelasticity interacting with other physical peculiarities of the Earth's surface layers, such as lateral heterogeneity, material properties along the wave path, local geological profile and type of elastic wave, gives rise to complex seismic signals on the free surface at the site of interest. Copyright © 2010 John Wiley & Sons, Ltd.     

超声波在粘弹性混凝土介质中传播机理研究

混凝土是一种含有骨料、水泥浆、钢筋、波纹管包裹的预应力孔道及空洞、孔隙的多相非均匀复合材料,作为一种粘弹性介质,超声在混凝土中传播机理比较复杂,常规的弹性声波方程不能确切地模拟超声传播方式。这里从粘弹性介质材料性质出发,推导了基于Kelvin粘弹性介质模型的高阶有限差分方程,通过建立几种粘弹性混凝土介质数值模型,模拟了超声波在混凝土中的传播过程,分析了含空洞、裂隙等不同缺陷的混凝土介质中超声波的波形特性,讨论了缺陷部位波形的变化规律,探讨了空洞、裂隙等不同缺陷对超声传播机理的影响以及能量分布的差异,为准确判断识别混凝土内部不同结构的缺陷提供科学借鉴。     

Nearly perfectly matched layer boundary conditions for operator upscaling of the acoustic wave equation

Acoustic imaging and sensor modeling are processes that require repeated solution of the acoustic wave equation. Solution of the wave equation can be computationally expensive and memory intensive for large simulation domains. One scheme for speeding up solution of the wave equation is the operator-based upscaling method. The algorithm proceeds in two steps. First, the wave equation is solved for fine grid unknowns internal to coarse blocks assuming the coarse blocks do not need to communicate with neighboring blocks in parallel. Second, these fine grid solutions are used to form a new problem which is solved on the coarse grid. Accurate and efficient wave propagation schemes also must avoid artificial reflections off of the computational domain edges. One popular method for preventing artificial reflections is the nearly perfectly matched layer (NPML) method. In this paper, we discuss applying NPML to operator upscaling for the wave equation. We show that although we only apply NPML to the first step of this two step algorithm (directly affecting the fine grid unknowns only), we still see a significant reduction of reflections back into the domain. We describe three numerical experiments (one homogeneous medium experiment and two heterogeneous media examples) in which we validate that the solution of the wave equation exponentially decays in the NPML regions. Numerical experiments of acoustic wave propagation in two dimensions with a reasonable absorbing layer thickness resulted in a maximum pressure reflection of 3–8%. While the coarse grid acceleration is not explicitly damped in our algorithm, the tight coupling between the two steps of the algorithm results in only 0.1–1% of acceleration reflecting back into the computational domain.     

Kelvin—Voigt黏弹性介质地震波场数值模拟与衰减特征

利用高阶交错网格有限差分模拟Kelvin-Voigt黏弹性介质中传播的地震波,同时将完全匹配层吸收边界条件引入到其边界处理中。数值模拟结果表明,完全匹配层吸收边界效果好,高阶有限差分能模拟得到的黏弹性介质波场精度较高。对模拟的黏弹性波场进行分析,表明介质的粘滞性使地震反射波的能量变弱,高频衰减明显,并比低频衰减得快,主频向低频方向移动,有效频带变窄,即降低了地震波的分辨率;并且反射转换波比反射纵波要衰减得快;而且还随着传播距离的增加,其峰值频率也逐渐降低。通过数值模拟分析具有不同的粘滞系数介质对地震波的吸收和衰减,结果表明随着粘滞系数的增大,地下介质对地震波的吸收衰减更明显。