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注浆抬升地层的机制、解析解及数值模拟分析 总被引：5，自引：3，他引：2
注浆抬升地表是地下工程施工控制地层和邻近建筑物沉降的常用工法。目前,注浆设计主要依靠现场监测和工程经验。数值方法模拟注浆效果通常是通过提高注浆区域的土性参数来实现的,但该方法忽略了注浆抬升对地层的补偿作用。通过研究注浆引起的土体体积膨胀的机制,将注浆体积、土体体积应变增量、位移大小三者联系在一起。采用了一种模拟注浆抬升地层的数值方法。在该数值方法中,给出了土体体积应变的计算方法,提出了施加“虚拟”膨胀压力来增加单元体积,并通过判断单元体积应变增量是否达到土体体积应变增量来控制模拟注浆的过程。其方法的优点在于：施加在单元上的膨胀压力可以是一个虚拟的压力,而无需是实际注浆压力。通过解析解与数值解对比分析,验证了这种数值方法的正确性和可行性。 相似文献
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土工极限平衡问题的非线性有限元数值分析 总被引：6，自引：1，他引：6
考虑非关联流动法则,采用几类低阶单元对条形基础下地基的极限承载力进行了二维有限元数值分析.计算表明,基于四节点四边形等参单元的有限元分析结果能够较好地吻合Prandtl理论解,且能保证数值计算的稳定性.同时,基于Mohr-Coulomb破坏准则和强度折减方法,对于边坡稳定性进行了有限元计算,建议采用无量纲位移Eδmax/γH2随强度折减系数变化的关系曲线上位移陡然增大时所对应的强度折减系数作为边坡的稳定安全系数,克服了当前强度折减有限元数值计算中关于收敛标准确定的人为不确定性,即使采用四节点四边形单元也能够保证数值解的良好收敛性. 相似文献
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复杂条件下3D电磁场有限元计算方法 总被引：8，自引：0，他引：8
从电磁场的Maxwell方程出发, 根据电磁场的边值问题及变分公式建立了有限元方程组.采用可以模拟较为复杂的空间地质构造和地形起伏的四面体单元离散计算区域; 单元中的插值函数选择了精度较高的十点双二次多项式; 并采用连续的双二次多项式插值函数来模拟计算区域内单元中电导率σ的空间变化.推导出了地下变电导率σ条件下计算三维电磁场的有限元单元方程的解析表达式; 采用伽辽金方法推导出了散度效正有限元方程组.根据所推导的公式, 编制了三维有限元的计算程序.数值计算结果表明, 上述公式推导正确, 为三维电磁场的数值计算提供了一条有效的新途径. 相似文献
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提出了求解有自由面渗流问题的三维数值流形方法,通过构造任意形状流形单元的水头函数,推导了流形单元的渗透矩阵和无压渗流分析的总体控制方程,并给出了自由面的迭代求解策略和渗透体积力的计算方法。典型算例的数值分析表明,该方法采用数学网格覆盖整个材料区域,在自由面的迭代求解过程中数学网格保持不变,只考虑自由面以下渗流区的介质,只对自由面以下的流形单元形成总体渗透矩阵,具有精度高、收敛速度快、编程简单等优点,而且能够通过单纯形积分精确计算被自由面穿越单元的渗透作用力,因此,特别适用于有自由面渗流问题的模拟。 相似文献
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天然水体具有形状复杂的计算区域和水下地形。本文采用无结构的网格以适合这一情况,并能方便地根据工程应用的要求局部地和适应性地加密网格。相应地,对二维水流计算问题采用了有限体积法的数学表示。跨单元边界的法向数值通量通过用Osher格式求解黎曼问题得到。文中给出了适合于二维浅水方程组的有关单元界面和各种物理边界的法向数值通量公式。分析了这一格式所具有的优点,包括:普适性、守恒性、逆风性、单调保持性、高效性、对间断的高分辨率、边界处理和内部格式相容,以及不引入数值边界条件等。最后,通过长江口南支水流计算的实例,阐明其良好性能。 相似文献
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目前, 国内普遍使用的“简单加和”或“概率加权加和”方法计算的区带或三(四)级圈闭资源量很大程度上与实际地质情况并不吻合.在PetroV开发过程中, 设计并实现了一种可充分考虑不同地质条件约束的油气资源量计算方法——以不确定性体积法的随机蒙氏模拟为基础, 对最新地质上识别出的、不可切分的含油气聚集单元, 进行符合不同地质模型约束的取样、组合; 在明确了哪些单元才应该同时出现的基础上, 将其他不同地质条件约束有机融合到模拟过程中, 客观描述各个计算单元体积模型的不确定性.从实例计算结果分析可以看出, “概率组合加和”可获取更加符合当前地质模型的不确定性油气资源量计算结果, 显著提升勘探部署项目优选排队的合理性. 相似文献
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To simulate debris flow run-out, the governing equations for free-surface shallow flow are corrected by setting the basal flow resistance coefficients with the quadratic rheological friction model. A well-balanced numerical scheme is developed for its run-out simulation over irregular topography. A linear reconstruction is adopted for improving the spatial accuracy of the numerical scheme. Considering the complex friction terms of governing equations of debris flow, they are estimated with a full implicit scheme for ensuring stability of the numerical scheme. The validity check of run-out simulation is implemented based on general knowledge of fluid, and a well-studied case occurred in the Xiezi Gully in Yingxiu Town, Sichuan Province of China. For practical purpose, the present numerical scheme is used for run-out prediction of debris flow in Xiaojia Gully of Panzhihua City, Sichuan Province of China. Our work aims to present a well-balanced numerical scheme for debris flow run-out simulation prediction, which can be applied quite conveniently to solve other kinds of debris flow models and helpful to promote the development in debris flow numerical calculation. 相似文献
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This paper is concerned with numerical methods for the modeling of flow and transport of contaminant in porous media. The
numerical methods feature the mixed finite element method over triangles as a solver to the Darcy flow equation and a conservative
finite volume scheme for the concentration equation. The convective term is approximated with a Godunov scheme over the dual
finite volume mesh, whereas the diffusion–dispersion term is discretized by piecewise linear conforming triangular finite
elements. It is shown that the scheme satisfies a discrete maximum principle. Numerical examples demonstrate the effectiveness
of the methodology for a coupled system that includes an elliptic equation and a diffusion–convection–reaction equation arising
when modeling flow and transport in heterogeneous porous media. The proposed scheme is robust, conservative, efficient, and
stable, as confirmed by numerical simulations.
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基于Boussinesq方程耦合泥沙运动和地形演变模型,建立海啸作用下泥沙运动数学模型。地形演变模型采用WENO差分格式,并将WENO差分格式与Lax-Wendroff格式和FTBS格式进行对比分析。运用Synolakis、Kobayashi和Young的实验数据分别对水动力模块和地形演变模块进行验证,数值模拟结果与实验数据吻合良好,模型能够很好地模拟海啸波的传播、破碎、上爬、回落过程以及岸滩的冲淤变化过程,该数学模型能够运用到海啸作用下的岸滩演变研究和预测中。 相似文献
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A systematic analysis shows how results from the finite difference code SEAWAT are sensitive to choice of grid dimension, time step, and numerical scheme for unstable flow problems. Guidelines to assist in selecting appropriate combinations of these factors are suggested. While the SEAWAT code has been tested for a wide range of problems, the sensitivity of results to spatial and temporal discretization levels and numerical schemes has not been studied in detail for unstable flow problems. Here, the Elder-Voss-Souza benchmark problem has been used to systematically explore the sensitivity of SEAWAT output to spatio-temporal resolution and numerical solver choice. A grid size of 0.38 and 0.60% of the total domain length and depth respectively is found to be fine enough to deliver results with acceptable accuracy for most of the numerical schemes when Courant number (Cr) is 0.1. All numerical solvers produced similar results for extremely fine meshes; however, some schemes converged faster than others. For instance, the 3rd-order total variation-diminishing method (TVD3) scheme converged at a much coarser mesh than the standard finite difference methods (SFDM) upstream weighting (UW) scheme. The sensitivity of the results to Cr number depends on the numerical scheme as expected. 相似文献
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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. 相似文献
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利用算子分裂迎风均衡格式解对流为主溶质运移问题 总被引：2，自引：0，他引：2
水污染模拟问题是水流问题与溶质运移问题的耦合问题.各种常见的数值解法在以对流为主溶质运移问题的求解中都会遇到困难,如用有限单元法或有限差分法时,会产生数值弥散与过量这两类误差.引入算子分裂迎风均衡格式法求解对流为主的水污染模拟问题,较好地克服了数值弥散和数值解出现振荡问题,该格式具有良好的稳定性、单调性及守恒性特点. 相似文献
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地下水开采等人类工程活动会引起地下水位变化，从而导致地面沉降问题。地面沉降具有土层变形长期发展的特点，土体的蠕变性是导致这一现象的重要原因之一。为此，针对基于Biot理论的地面沉降耦合模型，利用半解析数值原理和黏弹性流变理论，推导了可压缩土层黏弹性耦合变形的求解格式，该计算方法无需数值积分，且具有很好的解耦并行性。在此基础上，编制了FORTRAN计算程序，通过与已有解答的对比验证，说明了方法及程序的合理性，计算结果可以正确反映土体黏滞性所导致的变形滞后效应。通过数值算例，进一步探讨了渗透性、孔隙流体可压缩性和土体黏滞性等因素对土层长期变形的影响规律。 相似文献
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A numerical scheme is developed in order to simulate fluid flow in three dimensional (3‐D) microstructures. The governing equations for steady incompressible flow are solved using the semi‐implicit method for pressure‐linked equations (SIMPLE) finite difference scheme within a non‐staggered grid system that represents the 3‐D microstructure. This system allows solving the governing equations using only one computational cell. The numerical scheme is verified through simulating fluid flow in idealized 3‐D microstructures with known closed form solutions for permeability. The numerical factors affecting the solution in terms of convergence and accuracy are also discussed. These factors include the resolution of the analysed microstructure and the truncation criterion. Fluid flow in 2‐D X‐ray computed tomography (CT) images of real porous media microstructure is also simulated using this numerical model. These real microstructures include field cores of asphalt mixes, laboratory linear kneading compactor (LKC) specimens, and laboratory Superpave gyratory compactor (SGC) specimens. The numerical results for the permeability of the real microstructures are compared with the results from closed form solutions. Copyright © 2004 John Wiley & Sons, Ltd. 相似文献