自适应时间步长法在土体冻结水热耦合模型中的应用

由于相变的存在,土体冻结过程中的温度传导与水分迁移是一个复杂的物理过程。为了更好地描述冻结过程中水分与温度的变化规律,通过对不饱和土体水分传导方程的研究,考虑冻结过程中的相变,建立了一维冻土水热耦合模型。给出了相应的差分与有限元程序,并对室内冻结实验进行了模拟。提出误差因子的概念,通过对程序计算中时间步长与计算用时、误差关系的分析,论证了进行时间步长优化的必要性。在两种不同数值方法的对比中,体现了有限元计算的稳定性。提出了调整后的自适应时间步长计算方法。计算结果表明,优化时间步的自适应步长法,在不影响模型计算准确度的前提下,可以大幅减少计算用时,提高计算效率。     

核电核岛嵌岩桩地基动力响应及液化分析

运用三维有限元差分软件FLAC3D对混凝土桩加固的地基建立模型,对天然地基以及桩基地震液化前后地基模型的加速度、位移以及桩基的液化情况等进行数值模拟和系统对比分析,得到4种工况地基的加速度变化情况以及地基液化特点。计算结果表明加速度在非液化层传播呈放大趋势,而液化层对地震波的传播有明显削弱作用。在相同地震动作用下,天然地基的超孔压比值超过0.75的单元略多于桩基,桩对消除地基液化作用有限。研究成果可以作为类似的工程实例的参考。     

基于复阻尼模型的时域数值计算方法

复阻尼模型的时域运动方程通解中包含有发散项,导致传统的逐步积分法计算结果不能稳定收敛。为克服该缺点,引入地震加速度在时间步长内是线性变化的假定,利用复化对偶原则,提出了复阻尼模型的时域数值计算方法,可在时间步长内剔除发散项,保证了时域计算结果的稳定收敛。在此基础上,结合模态叠加法,进一步提出了多自由度体系的时域数值方法。算例分析表明:复阻尼模型的时域数值计算结果与谐波作用下时域解析算法、地震动作用下频域法的计算结果近似相等,证明了方法的正确性;对于钢筋混凝土框架结构,复阻尼模型的时域计算结果与黏性阻尼模型近似相等。     

基于液化流动模型的尾矿坝地震响应分析

针对传统等效线性法对尾矿坝地震响应分析结果与实际情况存在一定的出入的问题,通过振动台模型试验和数值计算结果比对验证数值计算方法的可行性,运用考虑液化后尾矿砂流动特性的孔压上升模型,基于完全非线性动力分析方法,对尾矿坝地震响应进行分析计算,通过对坝顶位移和加速度的监测结果进行分析,得出坝顶的加速度放大系数以及坝顶位移最大值;并由坝体水平方向位移云图、竖直方向位移云图及位移矢量图,判断可能发生局部滑坡的位置;对坝体内液化情况进行判定,得到尾矿坝的地震响应规律,为尾矿坝抗震设计提供一定的理论参考.     

基于瞬时电流脉冲的三维时间域航空电磁全波形正演模拟

传统时间域航空电磁全波形正演模拟主要采用间接法(褶积算法)和直接法(时域有限差分方法等),然而褶积算法需要获得精确的电流二阶导数,这给发射电流数据采集工作带来极大挑战;时域有限差分方法受到网格和时间步长的严格限制,缺乏灵活性.为解决这些问题,本文采用时域有限元方法,通过直接改变每个时间道上的瞬时电流强度模拟任意发射波形的电磁响应.由于无需计算电流二阶导数,大大提高了正演结果的精度.利用基于非结构四面体网格的矢量有限元方法和后推欧拉技术对时间域电场扩散方程进行空间和时间离散,实现三维航空电磁时间域全波形的直接正演模拟.由此不仅可以模拟复杂的地电结构,而且基于后推欧拉法的无条件稳定性,可以更加灵活地选取时间步长,提高计算效率.通过与1D数值模拟结果进行对比验证了该方法的准确性.本文对三维柱状体模型上HELITEM MULTIPULSE和VTEM系统实际发射波形电磁响应进行模拟,并与褶积算法的结果进行比较,验证了本文算法模拟实际发射波形电磁响应的优越性.对复杂三维地质体模型上不同发射波形电磁响应进行模拟,验证了时间域有限元算法可有效处理复杂地下地质结构.     

液化土层上建筑物不均匀震陷的数值研究

饱和砂土地基在地震作用下液化引起的建筑物的不均匀沉降是地震破坏的典型特征之一,会导致建筑物倾斜和失效。建立模拟液化引起不均匀震陷的数值方法对结构抗震设计和工程减灾尤为重要。基于对不均匀震陷机制的认识,对可液化地基上某建筑物模型在输入地震波作用下的震陷情况进行了数值模拟试验,分析了不均匀震陷发展过程中地震动输入、基底动应力、孔隙水压力、地基压缩模量和结构沉降之间的关系,并提出一套数值计算液化引起地基不均匀震陷的方法。结果显示:(1)使用的孔压模型能够模拟孔压在不规则荷载作用下的上升,且能够反应固结比对孔压的影响,以及记录结构地基土体真实的孔压发展过程;(2)计算方法使用的压缩模量模型能够反应由孔压变化引起的时程变化;(3)计算方法能够跟踪记录土层变形随孔压上升的时程变化。     

可液化地基土三维地震响应分析

编制完全耦合的三维排水有效应力动力反应分析程序，对可液化地基进行三维地震响应分析，探讨了不同土性参数、不同土层构成和不同附加压重等因素对可液化地基抗液化性能的影响。结果表明：在地震荷载作用下，天然饱和砂土地基中的超孔隙水压力随深度的增大而增大；在不同深度处，超孔压峰值到达的时刻比地震加速度峰值到达的时刻要晚；随输入地震加速度的减弱，深层处的超孔压开始消散或基本保持不变，浅层处的超孔压保持不变或略有上升，这一现象与土性参数、输入地震荷载的情况等因素有关；土性参数对土体本身的抗液化性能有重要影响，初始孔隙比越小，相对密度越大，土体的抗液化能力越强；附加压重有利于地基抗液化能力的提高；随着附加压重的增大，超孔压比减小；附加压重对地基中超孔隙水压力的增长有明显的抑制作用。     

三维时间域航空电磁有理Krylov正演研究

常规的三维时间域航空电磁模拟通常采用隐式步长方法进行时间离散,需要几次矩阵分解和上百次右端源项回带,计算效率较低.为了提高正演计算效率,本文提出使用有理Krylov方法求解时间域电场扩散方程.首先使用非结构四面体网格进行空间离散,采用Nédélec矢量基函数近似四面体单元内的电场;然后基于有限元离散给出矩阵指数和矢量乘积表示的电场显式解;最后采用有理Arnoldi算法构造Krylov子空间内的正交基函数并进一步求解矩阵指数与矢量的乘积,直接得到任意时刻的电场解向量,避免步长离散过程.此外,本文还提出一种指数加权偏移参数优化方法,使得有理Arnoldi近似在瞬变衰减晚期具备更高的精度,从而降低Krylov子空间阶数并提高计算效率.通过和层状模型解析解的对比验证了有理Krylov方法的精度.针对三维异常体模型使用全局网格和局部网格剖分并和其他数值方法比较,进一步说明了有理Krylov方法的有效性.     

起伏海底地形时间域海洋电磁三维自适应正演模拟

本文基于自适应非结构有限元算法实现海洋电磁起伏海底地形三维正演模拟.通过采用隐式后推欧拉时间离散技术,保证在较大的时间步长条件下获得正确结果.为获得多时间道海洋电磁正演模拟的有效网格,我们采用基于法向电流连续的后验误差估计的自适应方法和网格融合技术;同时为了控制网格数量和保证正演模拟稳定性,我们还在网格融合过程中应用了随机网格挑选技术.对于方程组求解我们使用MUMPUS直接求解器.当时间步长不变时,只需对系数矩阵进行一次分解,大大提高计算速度.将本文计算结果与半空间模型解析解进行对比,验证了本文算法精度.针对海洋电磁半拖曳式和双船拖曳式工作方式,我们通过典型模型的模拟计算,研究海底地形影响及海底高阻层识别特征.     

砂土液化大变形本构模型及在ABAQUS软件上的实现

基于Yang和E lgam al等人提出的砂土液化大变形本构模型,对该模型的建立过程进行了详细的推导,基于新的嵌套屈服面硬化规则,对原有模型的硬化规则的不连续性做了改进,把该本构模型扩展应用到三维液化大变形的数值分析中,实现了基于ABAQUS大型商用软件计算平台上砂土液化大变形的计算子程序的开发,基于该计算平台和开发的本构模型,对动三轴试验体系中砂土试样的液化过程进行了数值试验分析,给出了试验过程中试样的竖向动位移、整体竖向应力应变关系滞回曲线和动孔压时程曲线的数值计算结果。文中初步验证了该模型在ABAQUS上开发的子程序的可靠性和数值计算模型的可行性,模型的可靠性及其子程序的稳定性还需通过试验结果和数值计算结果的对比分析与进一步验证。     

Mixed finite element methods and higher order temporal approximations for variably saturated groundwater flow

Richards’ equation (RE) is commonly used to model flow in variably saturated porous media. However, its solution continues to be difficult for many conditions of practical interest. Among the various time discretizations applied to RE, the method of lines (MOL) has been used successfully to introduce robust, accurate, and efficient temporal approximations. At the same time, a mixed-hybrid finite element method combined with an adaptive, higher order time discretization has shown benefits over traditional, lower order temporal approximations for modeling single-phase groundwater flow in heterogeneous porous media. Here, we extend earlier work for single-phase flow and consider two mixed finite element methods that have been used previously to solve RE using lower order time discretizations with either fixed time steps or empirically based adaption. We formulate the two spatial discretizations within a MOL context for the pressure head form of RE as well as a fully mass-conservative version. We conduct several numerical experiments for both spatial discretizations with each formulation, and we compare the higher order, adaptive time discretization to a first-order approximation with formal error control and adaptive time step selection. Based on the numerical results, we evaluate the performance of the methods for robustness and efficiency.     

Adaptive element free Galerkin method applied to analysis of earthquake induced liquefaction

An automatically adaptive element free method is presented to analyze the seismic response of liquefiable soils.The method is based on the element free Galerkin method (EFGM) and the fission procedure that is part of h-refinement,indicated by error estimation. In the proposed method, a posteriori error estimate procedure that depends on the energy normof stress and the T-Belytschko (TB) stress recovery scheme is incorporated. The effective cyclic elasto-plastic constitutivemodel is used to describe the nonlinear behavior of the saturated soil. The governing equations are established by u-pformulation. The proposed method can effectively avoid the volumetric locking due to large deformation that usually occursin numerical computations using the finite element method (FEM). The efficiency of the proposed method is demonstratedby evaluating the seismic response of an embankment and comparing it to results obtained through FEM. It is shown that theproposed method provides an accurate seismic analysis of saturated soil that includes the effects of liquefaction     

H-adaptivity applied to liquefiable soil in nonlinear analysis of soil–pile interaction

This paper is concerned with application of the h-adaptive finite element method to dynamic analysis of a pile in liquefiable soil considering large deformation. In finite element analysis of pile behavior in liquefiable soil during an earthquake, especially considering large deformation of liquefied ground, error due to discretization in the zone near the pile becomes very large. Our purpose was to refine the approximation of the finite element method. The updated Lagrangian formulation and a cyclic elasto-plastic model based on the kinematic hardening rule were adopted to deal with the nonlinearity of the soil. The mixed finite element and finite difference methods together with the u-p formulation and Biot's two-phase mixture theory were used. To improve the accuracy and increase the efficiency of finite element analysis, an h-adaptive scheme that included a posteriori error estimation and h-version mesh refinement was applied to the analysis. The calculated results of effective stress were smoothed locally by the extrapolation method and smoothed stress was used to calculate the L₂ norm of the effective stress error in the last step of the calculation of each time increment. The mesh was refined by a fission procedure based on the indication of the error estimate As a numerical example, a soil–pile interaction system loaded cyclically was analyzed by our method.     

求解弹性波方程的辛RKN格式

将弹性波方程变换至Hamilton体系,构造适用于弹性波模拟的高效显式二阶辛Runge-Kutta-Nystrm(RKN)格式,运用根数理论得到此格式的阶条件方程组.通过给定系数的限定条件,得到方程的对称解.为了使时间离散误差达到极小,提出数值频率与真实频率比较,通过Taylor展开,得到关于辛系数的限定方程,求解方程组得到最小频散辛RKN格式.对比分析时间演进方程的稳定性,得到使库朗数达到极大值的限定方程,求解方程组得到最稳定辛RKN格式.发现此两种格式为同一格式.新得到的辛RKN格式不依赖于空间离散方法,为了对比的需要,选取有限差分法进行空间离散.在频散、稳定性分析中,与常见辛格式对比,从理论上分析了本文提出的格式在数值频散压制、稳定性提升等方面的优势,数值实验进一步证实了理论分析的正确性.     

Numerical analysis of liquefaction of porous seabed around pipeline fixed in space under seismic loading

Liquefaction of seabed under seismic loading is one of the main points that govern the overall stability of submarine pipeline. However, most previous investigations concerned only with free seabed and searched for seismic accumulative excess pore pressure by solving Terzaghi's consolidation equation containing pore pressure source term. It is not able to introduce two-dimensional structures such as submarine pipelines in one-dimensional problem, and it is also not able to obtain the distribution of seismic accumulative excess pore pressure in seabed around submarine pipelines by such a way. In this study, a FEM numerical analysis method for determining the liquefaction of sandy seabed around a buried pipeline under seismic loading is presented. The empirical mode of dynamic increase of pore pressure under undrained shearing induced by seismic loading is incorporated with two-dimensional dynamic consolidation equation and a numerical procedure based on FEM is developed to assess the accumulative excess pore pressure. By numerical computations, the accumulative process of pore pressure and liquefaction potential of seabed soil during seismic loading is evaluated. From a series of numerical computations based on the presented model with various parameters, the effects of soil characteristic parameters and pipeline geometry on seismic accumulative excess pore pressure around submarine pipeline and along the depth of seabed are explored in detail.     

最优化辛格式广义离散奇异核褶积微分算子地震波场模拟

将波动方程变换至Hamilton体系,构造了一种新的保结构算法,即最优化辛格式广义褶积微分算子(OSGCD). 在时间离散上,首先引入了Lie算子设计二级二阶辛格式,基于最小误差原理得到了优化的辛格式. 在空间离散上,引入广义离散奇异核褶积微分算子计算空间微分,提出了一种有效方法优化GCD并得到了稳定的算子系数. 针对本文发展的新方法,给出了OSGCD稳定性条件. 在数值实验中,将OSGCD与多种方法比较,从精度和计算效率两方面分析了OSGCD的计算优势,计算结果也表明OSGCD长时程以及非均匀介质中地震波模拟亦具有较强能力.     

Asymptotic formulae for correcting finite element predicted natural frequencies of gravity and embankment dams

Extraction of natural frequencies of a gravity dam or an embankment dam plays an important role in the seismic design of the dam because the seismic response of a dam is dependent largely on the dynamic characteristics of the dam. Owing to the lack of exact solutions and the geometry of a dam, numerical methods such as finite element methods have been often used to extract the natural frequencies of the dam. Since the finite element method is an approximate one, the resulting finite element solution to the natural frequency of a dam cannot be safely used unless its accuracy is evaluated within the acceptable range for the seismic design of the dam. To solve this problem, some asymptotic formulae for correcting the finite element predicted natural frequencies of a gravity dam and an embankment dam have been developed in this paper. Since the present asymptotic formulae are derived from the fact that the finite element solution tends to the exact one if the finite element size used approaches zero, they provide a corrected solution of higher accuracy for the natural frequency of a dam so that the accuracy of a finite element solution can be evaluated against this corrected solution. After the correctness and usefulness of the present formulae are assessed, two practical examples have been given to show how the asymptotic formulae can be used to correct and evaluate the discretization error for the finite element predicted natural frequencies of gravity dams and embankment dams.     

Coordinate mapping of analytical contaminant transport solutions to non-uniform flow fields

Existing analytical solutions to 2D and 3D contaminant transport problems are limited by the mathematically convenient assumption of uniform flow. An approximate method is developed herein for coordinate mapping of 2D (vertically-averaged) transport solutions to non-uniform steady-state irrotational and divergence-free flow fields in single-layer aquifers. The method enables existing analytical transport solutions to be applied to aquifer systems with wells, non-uniform saturated thickness, surface water features, and (to a limited degree) heterogeneous hydraulic conductivity and recharge. This mass-conservative coordinate mapping approach is inexact in its approximation of the dispersion process but is still sufficiently accurate for many simple flow systems. The degree of model error is directly proportional to the variation of velocity magnitude within the domain. These mapped analytical solutions are compared to numerical simulation results and the coordinate mapping errors are investigated. The methods described herein may be used in the traditional capacity of analytical transport models, i.e., screening and preliminary site assessment, without sacrificing accuracy by assuming locally uniform flow conditions or applying an ad-hoc coordinate transformation. The solutions benefit from the traditional advantages of analytical methods, particularly the removal of artifacts due to spatial and temporal discretization: no time-stepping or numerical discretization is required.     

An automated cross‐validation method to assess seismic time‐to‐depth conversion accuracy: a case study on the Cooper and Eromanga basins,Australia

Selecting a seismic time‐to‐depth conversion method can be a subjective choice that is made by geophysicists, and is particularly difficult if the accuracy of these methods is unknown. This study presents an automated statistical approach for assessing seismic time‐to‐depth conversion accuracy by integrating the cross‐validation method with four commonly used seismic time‐to‐depth conversion methods. To showcase this automated approach, we use a regional dataset from the Cooper and Eromanga basins, Australia, consisting of 13 three‐dimensional (3D) seismic surveys, 73 two‐way‐time surface grids and 729 wells. Approximately 10,000 error values (predicted depth vs. measured well depth) and associated variables were calculated. The average velocity method was the most accurate overall (7.6 m mean error); however, the most accurate method and the expected error changed by several metres depending on the combination and value of the most significant variables. Cluster analysis tested the significance of the associated variables to find that the seismic survey location (potentially related to local geology (i.e. sedimentology, structural geology, cementation, pore pressure, etc.), processing workflow, or seismic vintage), formation (potentially associated with reduced signal‐to‐noise with increasing depth or the changes in lithology), distance to the nearest well control, and the spatial location of the predicted well relative to the existing well data envelope had the largest impact on accuracy. Importantly, the effect of these significant variables on accuracy were found to be more important than choosing between the four methods, highlighting the importance of better understanding seismic time‐to‐depth conversions, which can be achieved by applying this automated cross‐validation method.     

Dispersion-relationship-preserving seismic modelling using the cross-rhombus stencil with the finite-difference coefficients solved by an over-determined linear system

Finite-difference modeling with a cross-rhombus stencil with high-order accuracy in both spatial and temporal derivatives is a potential method for efficient seismic simulation. The finite-difference coefficients determined by Taylor-series expansion usually preserve the dispersion property in a limited wavenumber range and fixed angles of propagation. To construct the dispersion-relationship-preserving scheme for satisfying high-wavenumber components and multiple angles, we expand the dispersion relation of the cross-rhombus stencil to an over-determined system and apply a regularization method to obtain the stable least-squares solution of the finite-difference coefficients. The new dispersion-relationship-preserving based scheme not only satisfies several designated wavenumbers but also has high-order accuracy in temporal discretization. The numerical analysis demonstrates that the new scheme possesses a better dispersion characteristic and more relaxed stability conditions compared with the Taylor-series expansion based methods. Seismic wave simulations for the homogeneous model and the Sigsbee model demonstrate that the new scheme yields small dispersion error and improves the accuracy of the forward modelling.