自适应时间步长法及三维堤坝地震液化数值模拟

三维大模型数值计算因巨大的单元和结点数目而非常耗时,在地震响应分析中受计算时间步长的限值则更加耗时。在饱和砂土动力液化计算平台上开发时域离散误差评估方法和时间步长自适应调整的计算程序,并成功应用于三维堤坝地震液化响应分析。时域离散误差包括土骨架的位移误差和单元孔压误差,通过定义孔压误差影响系数计算出混合误差,根据混合误差和设定的误差允许值进行计算步长的自适应调整。在三维堤坝地震液化数值模拟中,采用自适应时间步长法有效避免小步长精确但耗时、大步长省时而不精确的缺点。在大模型和超大模型计算中,最优调整每一步的计算时间步长,完美实现既节省时间又不失精度的时域离散策略。     

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.     

面向目标自适应海洋可控源电磁三维矢量有限元正演

本文实现了一种面向目标自适应海洋可控源电磁三维矢量有限元方法.为满足三维复杂电性结构模拟的需求,网格剖分采用非结构化六面体.在组装刚度矩阵之后,形成的大型复数线性方程组分解为等价的实数形式,利用带预条件的广义最小残差法进行求解.在获得微分方程的解之后,为提高解的准确性,通过面向目标的自适应误差估计来指示网格细化,重点加密能使观测点数值模拟精度提高的网格.对于大规模三维数据,为了使模型空间的并行计算达到均衡负载的效果,我们使用METIS函数库来进行网格计算任务量的划分.最后,通过对比一维解析解与三维自适应矢量有限元计算结果,验证了程序的正确性;通过自适应过程中误差指示子的分布,验证了面向目标自适应的有效性;通过对三维复杂模型进行均衡负载下的并行计算,测试了程序的可扩展性.     

分割推算及分区积分

一、引言 CT研究中涉及分区或分片逼近和积分计算问题,本文以散射汁算[1]和波动有限元积分计算为背景,探讨节省计算量的途径。给出分割子区域上误差估计,讨论变化步长时各子域对整体积分值的贡献或影响,期望实现外推与误差自适应选择。     

UH模型有限元程序中初始超固结比的确定方法

不排水抗剪强度与初始超固结比OCR的关系可以由三轴压缩状态下的不排水抗剪强度公式表示。首先根据该公式由强度试验数据计算土体各点OCR与其深度的关系式;然后将该关系式引入到UH模型有限元程序中;最后应用UH模型的有限元程序分别对考虑OCR随深度变化和OCR为1的不排水地基进行了数值分析,并对两种情况下的载荷-沉降曲线、随时间变化的地基表面沉降、随时间变化的结点剪应变、体应变和孔压曲线作了比较。分析可知:采用OCR随深度变化的UH模型的有限元程序能够合理考虑地基土体实际的超固结比,在非均质不排水地基的有限元分析中是有必要的。     

均匀土-箱基-结构相互作用体系的计算分析

采用通用有限元程序ANSYS，针对捱动台试验中的均匀土-箱基-结构试验进行了三维有限元分析，计算中土体的本构模型采用等效线性模型，利用面-面接触单元考虑土体与基础交界面的状态非线性。计算表明，基础底面和土体发生滑移，基础侧面和土体之间发生了滑移和脱离，上部结构柱顶加速度反应主要由基础转动引起的摆动分量组成，通过与试验结果的对照研究，二者得出的规律基本一致，验证了采用的计算模型与分析方法的合理性，为进一步计算研究和实际工程应用奠定了基础。     

寒区桩基础的多场耦合分析模型及其应用

引入桩土相互作用的界面单元将冻土地基与混凝土桩联系起来, 考虑应力场、温度场、水份场三场耦合条件, 建立了冻土区桩土共同作用的粘弹塑性非线性有限元分析计算模式. 结合工程实例用本文方法对单桩冻胀过程中的应力场及位移场进行了计算, 着重揭示和研究了冻结过程中桩土间切向冻胀应力场、冻结应力场及位移场的随时间变化过程, 进而研究了单桩承载力冻结过程中的发生与发展的变化过程.     

考虑冻土的陆面过程模型及其在青藏高原GAME/Tibet试验中的应用

陆面过程的研究对于更好地认识气候和天气系统的演变规律、陆地-大气水热交换过程、人类活动对气候和环境的影响等具有重要意义. 建立了综合考虑土壤冻融、土壤水汽通量、植被覆盖和陆面-大气近地层水热交换的一维冻土-植被-大气连续体模型, 模拟了固液相变、汽态水迁移、土壤水、汽、热耦合迁移等过程, 反映了液态水从未冻区向冻结区迁移、冻结及其引起的潜热迁移的冻土物理本质, 也反映了汽态水分从高温区向低温区迁移所引起的温度及水分场的变化, 并对模型进行了检验. 水分运动方程采用混合Richards方程, 可适应各种边界条件. 土壤水热传输模型求解引入了修正的Picard迭代法, 不仅使计算迭代收敛更快, 而且能更好地保证数值计算过程中的水量平衡. 结合GAME/Tibet实验1998年5月份、7月份的观测数据, 应用该模型对青藏高原安多观测点的水热交换过程进行了模拟分析. 模拟结果表明: 土壤的冻融过程对地温变化会产生负反馈作用; 若净辐射相同, 土壤表层含水量较高的情况下考虑冻结时其地热通量在冰融化时明显增加, 显热通量减少, 而潜热通量变化不大, 但是冻结时各通量的变化不明显; 而土壤发生融化时, 尽管地热通量增加, 但是地表温度仍然减小; 土壤发生冻结时, 尽管土壤负温要比不考虑冻结时高, 但整体上热通量变化不大.     

考虑土-结构相互作用的高层建筑抗震分析

本文采用通用有限元程序ANSYS,针对上海地区一例土-箱基-高层建筑结构进行了三维有限元分析,计算中土体的本构模型采用等效线性模型,利用粘一弹性人工边界作为土体的侧向边界,并研究了土体边界位置、土性、基础埋深、基础形式以及上部结构刚度等参数对动力相互作用体系动力特性及地震反应的影响。     

基于土与高层建筑群相互作用振动台试验的土体动力非线性模拟

在动力荷载作用下,土与建筑群的动力相互作用中,土体表现出明显的动力非线性。同时振动台实测值与计算值对比分析中,土体的模拟至关重要。本文基于土与高层建筑群动力相互作用的振动台试验实测数据,应用Davidenkov地基模型实现土体动力非线性模拟。首先由土体的实测材料值拟合出Davidenkov地基模型内的相应参数值,然后用ANSYS编制计算程序,建立土与高层建筑群动力相互作用振动台试验的有限元模型,最后将计算值与试验值进行对比分析,验证Davidenkov地基模型用于此振动台试验的准确性。     

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.     

轨道交通荷载下桩板结构主动隔振效果研究

为了研究在轨道交通荷载作用下桩板结构主动隔振措施的隔振效果,通过无限元边界与有限元边界相结合的有限元分析方法在路基中建立桩板结构模型,并在沙土地基中设置混凝土桩板结构进行模型试验,通过模型试验对有限元数值模拟结果加以验证,将桩长、埋深及置换率3个因素考虑在内,研究其对隔振效果的影响。结果表明:模型试验验证有限元计算方法的可靠性;随桩长增加振幅降低比减小,隔振效果明显,随着振源距离增加其振幅降低比减小明显;埋深为桩板结构主动隔振措施中的主要影响因素,随着埋深增加振幅降低比明显减小,隔振效果越明显;有限元计算过程中置换率对隔振效果的影响不明显,但是在模型试验中置换率对隔振效果影响较显著。     

均质地基中桩-桩位移相互作用系数的有限元分析

在实际工程分析中用有限元法模拟无限域需要考虑很大一部分桩周土体来保证计算的精度,从而导致计算量的增大,同时对计算机的要求也很高。特别是对于大规模的群桩问题,有限元的计算工作量使一般的计算机无法满足其要求,这就限制了其在实际工程中的应用。本文基于叠加原理用有限元法计算桩-桩位移相互作用系数,不仅能减少群桩的计算量,又能提高计算精度。     

有限元模拟中边界条件对计算结果的影响

本文从总电位法和异常电位法两个方面,分别就直流电法有限元中所采用的三类边界条件对计算结果的影响进行了分析,为采用合适的边界条件及选取最佳边界距离来提高正演精度提供了基础.结果表明,混合边界条件精度最高,可大大缩小求解区域而不影响计算精度,其次是Dirichlet边界条件精度较高,但测点越靠边界误差会越大,必须取足够大的边界区域,齐次边界条件的误差比较大,但如果采用非二极装置,通过电位差计算得到的视电阻率,由于无穷远边界对电位差的影响基本消除,视电阻率计算误差与混合边界条件下的接近,在反演中,为了节省计算时间,经常使用齐次边界条件进行有限元正演.     

Calculating actual crop evapotranspiration under soil water stress conditions with appropriate numerical methods and time step

Calculation of actual crop evapotranspiration under soil water stress conditions is crucial for hydrological modeling and irrigation water management. Results of actual evapotranspiration depend on the estimation of water stress coefficient from soil water storage in the root zone, which varies with numerical methods and time step used. During soil water depletion periods without irrigation or precipitation, the actual crop evapotranspiration can be calculated by an analytical method and various numerical methods. We compared the results from several commonly used numerical methods, including the explicit, implicit and modified Euler methods, the midpoint method, and the Heun's third‐order method, with results of the analytical method as the bench mark. Results indicate that relative errors of actual crop evapotranspiration calculated with numerical methods in one time step are independent of the initial soil water storage in the range of soil water stress. Absolute values of relative error decrease with the order of numerical methods. They also decrease with the number of time step, which can ensure the numerical stability of successive simulation of soil water balance. Considering the calculation complexity and calculation errors caused by numerical approximation for different time step and maximum crop evapotranspiration, the explicit Euler method is recommended for the time step of 1 day (d) or 2 d for maximum crop evapotranspiration less than 5 mm/d, the midpoint method or the modified Euler method for the time step of up to one week or 10 d for maximum crop evapotranspiration less than 5 mm/d, and the Heun's third‐order method for the time step of up to 15 d. Copyright © 2011 John Wiley & Sons, Ltd.     

The effect of seasonally frozen soil on stochastic response of elevated water tank under random excitation

Significant seismic events have occurred around the world during winter months in regions where cold temperatures cause ground freezing. Current seismic design practice does not address the effects of cold temperatures in the seasonally frozen areas. Since many elevated water tank structures in cold regions are located in seismic active zones, determining the effect of seasonally frozen soil on the stochastic response of elevated water tank structures subjected to random seismic excitation is an important structural consideration. A three dimensional finite element model, which considers viscous boundaries, was built up to obtain the stochastic seismic behavior of an elevated water tank–fluid–soil interaction system for frozen soil condition. For this model, the power spectral density function represents random ground motion applied to each support point of the three dimensional finite element model of the elevated water tank–fluid–soil interaction system. Numerical results show that the soil temperature affects the seismic response of the elevated water tank; whereas the variation in the thickness of the frozen soil causes insignificant changes on the response. In addition, the effect of the variation in water tank’s fullness on the stochastic response of the coupled system is investigated in the study. As a result, the seasonal frost changes the foundation soil stiffness and may impact seismic behavior of the water tank.     

Finite element analysis of water flow in variably saturated soil

A two-dimensional Galerkin finite element model for water flow in variably saturated soil is presented. A fourth-order Runge-Kutta time integration method is employed which allows use of time steps at least 2 times greater than for a traditional finite difference approximation of time derivatives. For short total simulation times computer execution costs for the Runge-Kutta method are greater than for the finite difference approximation due to the start up cost of the Runge-Kutta method, but for longer simulation times the Runge-Kutta method requires considerably less computational effort even when automatic time-step adjustment is used with the finite difference procedure. A comparison of the method of influence coefficients and 2 × 2 Gaussian integration to compute element matrices indicates that the influence coefficient method reduces total execution time to 60% of that required for numerical quadrature. Computed pressure heads using the influence coefficient method and numerical integration are found to be in close agreement with each other even under conditions of highly non-linear soil properties in a heterogeneous domain. Fluxes computed by the two methods are also generally in close agreement except under extremely non-linear conditions when some deviations were observed at short simulation times.     

A finite element model for simulating surface run‐off and unsaturated seepage flow in the shallow subsurface

This work introduces water–air two‐phase flow into integrated surface–subsurface flow by simulating rainfall infiltration and run‐off production on a soil slope with the finite element method. The numerical model is formulated by partial differential equations for hydrostatic shallow flow and water–air two‐phase flow in the shallow subsurface. Finite element computing formats and solution strategies are presented to obtain a numerical solution for the coupled model. An unsaturated seepage flow process is first simulated by water–air two‐phase flow under the atmospheric pressure boundary condition to obtain the rainfall infiltration rate. Then, the rainfall infiltration rate is used as an input parameter to solve the surface run‐off equations and determine the value of the surface run‐off depth. In the next iteration, the pressure boundary condition of unsaturated seepage flow is adjusted by the surface run‐off depth. The coupling process is achieved by updating the rainfall infiltration rate and surface run‐off depth sequentially until the convergence criteria are reached in a time step. A well‐conducted surface run‐off experiment and traditional surface–subsurface model are used to validate the new model. Comparisons with the traditional surface–subsurface model show that the initiation time of surface run‐off calculated by the proposed model is earlier and that the water depth is larger, thus providing values that are closer to the experimental results.     

土坡抗震稳定性分析的有限元-滑动面法

提出了一种土坡抗震稳定性分析的新方法，即将有限元法和传统的滑动面法相结合。首先根据有限元法通过求解动力方程，计算出某一时刻土坡内的有效应力，然后根据有效应力计算该时刻的最危险滑动面及对应的安全系数。该方法不仅能够考虑土的应力应变性质，而且能够在任意时刻确定最危险滑动面的位置及安全系数。给出了该方法的详细算法。