地震波场正演模拟中的有限单元方法

本文介绍了地震波场正演模拟中的有限单元方法。首先从粘弹性波动理论出发,推导了满足粘弹性介质的有限元方程,其次用不含阻尼矩阵的有限元方程模拟了地震记录。地表实例是自由界面的瑞雷面波。VSP记录有水平层、倾斜层;有零井源距和非零井源距;有线状和对称震源。 在程序中采用了超压缩存贮和分块计算措施,对降低有限元法要求计算机内存和运算速度的苛刻条件上做了有益的尝试。     

层状粘弹性介质中SH波的反射、透射问题

处理粘弹性介质有两种方法,一种是在运动方程中加入介质的粘滞性因素,另一种是从本构方程入手,建立介质的粘弹性模型。后一种方法在研究介质物理性质上具有直接性,是目前使用较为普遍的处理方法。从本构方程的角度,以波尔兹曼(Bo ltzm ann)叠加原理为基础,建立积分型本构方程,进而建立粘弹性介质波动方程,得到二维粘弹性平面波解,并研究了层状粘弹性介质分界面处平面波的反射、透射问题,计算反射、透射系数CR、CT,同时进行了一定的理论分析。     

基于VSP的透射PS波成像

利用弹性波动方程进行了非零偏移距VSP波场的数值模拟,通过偏振投影和中值滤波技术相结合进行波场分离,对分离后的反射P波和透射PS波利用动校正(NMO)和VSPCDP叠加技术进行成像。成像结果表明:透射PS波成像与反射P波成像具有同样良好的效果,而且透射PS波成像是反射波成像很好的补充。利用透射PS波成像不需要增加数据采集的成本,所以透射波成像技术将会在石油工业中被广泛采用。     

移动荷载下瞬态振动的三维移动坐标有限元分析

针对移动荷载引起地基振动问题的特点,在随荷载移动坐标系下建立有限元方程进行分析,能够与常规有限元方法较好地符合。建立了可用于移动坐标有限元法的黏弹性边界,从而有效地模拟波在边界的透射。以Euler-Bernoulli梁模拟轨道和路基的作用,以三维实体单元模拟黏弹性分层地基,得到的数值模拟结果能够与瑞典Ledsgård地区高速铁路实测数据较好地吻合,表明移动坐标有限元法可以有效地分析此类问题。     

高速公路路基性态反分析及沉降预报

本文用三元件粘弹性流变模型模拟路基土体的流变特性, 根据施工期实测资料, 采用粘弹性有限元和非线性二乘法阻尼优化方法, 反演路基土体的地质力学参数, 然后计算路面铺筑后的工后沉降, 编制了土体粘弹性有限元正反分析程序, 并对沪宁高速公路某路段进行了反分析计算, 得到了满意的结果。     

地震波斜入射情形下水平成层半空间自由场的时域计算

在应用有限元模拟地震工程中的波动散射问题时，为了计算边界节点的运动和实现波动能量的输入，必须首先确定边界节点的内行波场即背景水平成层半空间的自由场。利用显式有限差分法的内节点位移计算公式和基于水平成层介质波动传播特点建立的相邻节点间自由场运动的关系式，给出了计算水平成层半空间自由场的时城方程(以入射侧边界节点为例)。本方法是显式有限元意义上的数值精确解，可应用于近场波动数值模拟中内行波场与散射波场的时城同步模拟。     

贮量集中有限元方法在渗流计算中的优点

普通有限元方法和有限差分方法是渗流计算中常用的数值方法,而贮量集中有限元方法则很少被实际应用。为了使渗流计算者全面了解贮量集中有限元方法,并能够较多地应用这种方法,本文将渗流计算中的贮量集中有限元方法、普通有限元方法和有限差分方法进行了对比,具体比较和分析了有限元方程组的系数矩阵特征、计算工作量,通过具体的算例分析了它们的计算精度,由此指出贮量集中有限元方法的计算精度与有限差分法基本相同,而远好于普通有限元法,它的计算工作量小于其他二种方法。     

贮量集中有限元方法在渗流计算中的优点

普通有限元方法和有限差分方法是渗流计算中常用的数值方法,而贮量集中有限元方法则很少被实际应用。为了使渗流计算者全面了解贮量集中有限元方法,并能够较多地应用这种方法,本文将渗流计算中的贮量集中有限元方法、普通有限元方法和有限差分方法进行了对比,具体比较和分析了有限元方程组的系数矩阵特征、计算工作量,通过具体的算例分析了它们的计算精度,由此指出:贮量集中有限元方法的计算精度与有限差分法基本相同,而远好于普通有限元法,它的计算工作量小于其他二种方法      

低应变下变阻抗薄壁管桩动力响应频域解析解

管桩低应变完整性检测时,桩顶一点受到瞬态集中荷载的作用,其动力响应问题是一个三维波动问题。基于三维波动理论,建立了任意段变阻抗薄壁管桩动力响应的计算模型和波动方程,结合初边值条件,采用Laplace变换法求得了该波动方程的频域解析解,采用Fourier逆变换求得了时域响应。将计算结果与三维有限元结果进行了对比分析,解析解的计算结果和三维有限元结果较为接近,两者在入射波峰、缺陷反射峰和桩底反射峰处都较为吻合,两种方法位移响应曲线基本相同。给出了桩顶不同点的动力响应,并探讨了高频干扰问题。对变截面桩和变模量桩的动力响应特性进行了分析。     

地表水平正反敲击激振下孔法剪切波速测试理论依据讨论

地表水平正反敲击激振下孔法常用于现场剪切波速测试。本文基于动力有限元方法建立了地表水平正反敲击激振下孔法剪切波速测试三维分析模型,采用时域集中质量动力有限元显式逐步积分方法求解了地表水平敲击下线弹性半空间波动响应,分析了不同深度点波形特征及地表水平正反敲击激振下孔法剪切波(S波)波速测试理论依据的合理性。结果表明:地表水平正反敲击下孔法S波波速测试的理论依据,即地表水平正反敲击下压缩波(P波)初动不反向而S波初动反向的理论依据不成立。此外,依据地表水平正反激振下线弹性半空间波动解析解,进一步佐证数值模拟结果的可靠性。     

Numerical analysis of rafts on visco-elastic media using eigenvector expansions

Problems of a raft on a visco-elastic continuum may be converted to equivalent elastic problems by means of a Laplace transformation. In this paper a numerical solution of the equivalent problem is obtained by finite element or other techniques. This solution is converted into the form of an eigenvector expansion and then transformed into a numerical solution to the original problem by inverting the Laplace transform. This form of solution has the advantage of applying to any visco-elastic model, and of requiring little additional computation as a result of changing the visco-elastic model, the relative raft-soil stiffness or the load pattern. The application of the method is illustrated by results for circular rafts, strip footings of finite length and rectangular rafts, and particular attention is paid to a realistic soil creep function which is asymptotic to a linear function of log time.     

Semi-Analytic Modelling of Subsidence

This paper presents a forward model for subsidence prediction caused by extraction of hydrocarbons. The model uses combinations of analytic solutions to the visco-elastic equations, which approximate the boundary conditions. There are only a few unknown parameters to be estimated, and, consequently, calculations are very fast. The semi-analytic model is applicable to a uniform and layer-cake stratigraphy, with visco-elastic parameters changing per layer, and an arbitrary depletion pattern. By its capabilities to handle a multi-layered visco-elastic subsurface, the semi-analytic model fills the gap between the analytic single-layered elastic models available to date and the more elaborate numerical, e.g. finite element, models.     

新疆玛纳斯河冲洪积扇地区地下水资源管理模型

为了建立新疆玛纳斯河冲洪积扇地区的地下水资源管理模型,首先恰当地建立了适合于该区水文地质条件的地下水流动有限元数值模拟模型系统,并对地下水模拟系统进行了一系列线性化处理,以适应管理方法的要求.然后采用“响应矩阵法”将数值模型和线性规划方法结合,建立了平稳流与非平稳流两类管理模型,对该区整个含水层各分布点的各种水力状态进行全面管理.最后得到一系列满足该区发展目标的决策方案.     

Coupled theory of mixtures for clayey soils

In this work, elasto-plastic coupled equations are formulated in order to describe the time-dependent deformation of saturated cohesive soils (two-phase state). Formulation of these equations is based on the principle of virtual work and the theory of mixtures for inelastic porous media. The theory of mixtures for a linear elastic porous skeleton was first developed by Biot (Theory of elasticity and consolidation for a porous anisotropic solid, Journal of Applied Physics, 1955, 26, 188–185). An extension of Biot's theory into a nonlinear inelastic media was performed by Prevost (Mechanics of continuous porous media, International Journal of Engineering Science, 1980, 18, 787–800). The saturated soil is considered as a mixture of two deformable media, the solid grains and the water. Each medium is regarded as a continuum and follows its own motion. The flow of pore-water through the voids is assumed to follow Darcy's law. The coupled equations are developed for large deformations with finite strains in an updated Lagrangian reference frame. The coupled behavior of the two-phase materials (soil-water state) is implemented in a finite element program. A modified Cam-clay model is adopted and implemented in the finite element program in order to describe the plastic behavior of clayey soils. Penetration of a piezocone penetrometer in soil is numerically simulated and implemented into a finite element program. The piezocone penetrometer is assumed to be infinitely stiff. The continuous penetration of the cone is simulated by applying an incremental vertical movement of the cone tip boundary. Results of the finite element numerical simulation are compared with experimental measurements conducted at Louisiana State University using the calibration chamber. The numerical simulation is carried out for two cases. In the first case, the interface friction between the soil and the piezocone penetrometer is neglected. In the second case, interface friction is assumed between the soil and the piezocone. The results of the numerical simulations are compared with experimental laboratory measurements.     

Stochastic finite element methods for the seismic response of soils

Some of the available stochastic finite element methods are adapted and evaluated for the analyses of response of soils with uncertain properties subjected to earthquake induced random ground motion. In this study, the dynamic response of a soil mass, with finite element discretization, is formulated in the frequency domain. The spectral density function of the response variables are obtained from which the evaluation of the root-mean-squared and the most probable extreme values of the response are made. The material non-linearities are incorporated by using strain compatible moduli and damping of soils using an equivalent linear model for stress–strain behaviour of soils and an iterative solution of the response. The spatial variability of the shear modulus is described through a random field model and the earthquake included motion is treated as a stochastic process. The available formulations of direct Monte-Carlo simulation, first-order perturbation method, a spectral decomposition method with Neumann expansion and a spectral decomposition method with Polynomial Chaos are used to develop stochastic finite element analyses of the seismic response of soils. The numerical results from these approaches are compared with respect to their accuracy and computational efficiency. © 1998 John Wiley & Sons Ltd.     

复杂地形下高密度激电法2.5维有限单元法数值模拟

目前三维有限元模拟计算量大,计算效率低,对计算机要求较高,2.5维模拟是三维问题的简化,较好地克服了上述问题。在高密度激电法模拟中,模拟的点数一般较大,要求程序计算效率高,因此对高密度激电法2.5维模拟研究是必要的。首先给出了2.5维稳定电流场的边值问题及对应的变分问题;为了能更好模拟复杂地形对极化率异常的影响,采用三角形网格,有利于模拟复杂地形又有利于将其应用于反演计算。推导了基于连续电性介质的2.5维稳定电流场的有限元法,利用等效电阻率法,编制了2.5维高密度激电法有限元模拟程序,计算了水平地形及起伏地形下的极化率异常模型,并验证了方法的可行性,分析得出了山谷地形比山脊地形对极化率观测的影响大的结果。     

Permeability determination of porous media using large‐scale finite elements and iterative solver

The problem of finite element simulation of incompressible fluid flow in porous medium is considered. The porous medium is characterized by the X‐ray microtomography technique in three dimensions. The finite calculus‐based stabilization technique is reviewed to implement the equal order finite element interpolation functions for both velocity and pressure. A noble preconditioner, the nodal block diagonal preconditioner, is considered whose performance is thoroughly investigated. Combining this preconditioner with a standard iterative solver during the computational homogenization procedure, it is possible to carry out the large‐scale fluid flow simulation for estimating permeability of the porous medium with reasonable accuracy and reliability. Copyright © 2013 John Wiley & Sons, Ltd.     

考虑大变形的静力压桩数值模拟

静力压桩过程是一种稳态贯入过程。该过程使得桩周附近区域的土体产生较大挤压作用,并出现了较大变形,因而基于传统小变形的有限元分析与真实的贯入过程有着较大的误差。基于更新的拉格朗日列式法,分析压桩时产生的大变形,引入桩-土界面间的接触作用,桩周土体采用Mohr-Coulomb模型,并运用有限元方法进行数值分析,较好地实现了静力压桩过程的数值模拟。     

大陆深俯冲的最大深度——来自数值模拟实验的结果

采用粘弹性材料8块体有限元模型并设定温度场后进行的大陆深俯冲二维数值模拟表明,在组合载荷(负浮力、洋中脊推力从上到下10～30MPa 和地幔对流拖曳力100MPa)作用下,陆壳俯冲实际垂向位移可达117km,最终俯冲深度达到147km,而洋壳实际垂向位移约162km,最终俯冲深度达到231km;在洋壳、陆壳俯冲到一定深度以前,它们的俯冲速度基本保持不变,表现为洋壳、陆壳底端的位移-时间曲线近似为直线;当俯冲时间超过9Ma,洋壳、陆壳分别达到167km、96km 深度后,俯冲速度会越来越慢。     

数值模拟在沉积盆地褶皱冲断构造变形研究中的应用与发展

数值模拟是一种利用电子计算机,通过数值计算和图像显示的方法,研究工程问题、物理问题乃至自然界各类问题的方法。随着高性能计算的不断发展,数值模拟方法在沉积盆地构造变形研究中的应用不断扩大,学术界和工业界将数值模拟方法广泛应用于盆地构造变形特征与变形机制的定量研究,取得了丰硕的成果。本文在系统分析前人数值模拟成果的基础上,阐述了有限元、有限差分、边界元和离散元四种常用数值模拟实验方法的特征和应用。同时,本文对近年来数值模拟方法在沉积盆地褶皱冲断构造变形中的研究进展进行了分类总结,重点介绍这一方法在构造特征与变形机制研究中取得的成果,为数值模拟方法在盆地构造变形领域应用的不断扩大和深入提供参考。最后,本文对数值模拟技术在目前应用中面临的问题和未来的发展方向提出了一些看法和建议。