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在我国西北干旱半干旱地区,处于高吸力范围内的非饱和土广泛存在于各种岩土工程中。非饱和土土水特性的研究是非饱和土渗流、强度与变形研究的基础。为研究高吸力下不同初始孔隙比非饱和土的土水特性,以一种粉土试样作为研究对象,采用饱和盐溶液蒸汽平衡法控制土试样的吸力,利用阿基米德原理量测不规则土试样的体积,通过修正的Van-Gen... 相似文献
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In this paper, we study the properties of approximate solutions to a doubly nonlinear and degenerate diffusion equation, known
in the literature as the diffusive wave approximation of the shallow water equations (DSW), using a numerical approach based
on the Galerkin finite element method. This equation arises in shallow water flow models when special assumptions are used
to simplify the shallow water equations and contains as particular cases the porous medium equation and the p-Laplacian. Diverse
numerical schemes have been implemented to approximately solve the DSW equation and have been successfully applied as suitable
models to simulate overland flow and water flow in vegetated areas such as wetlands; yet, no formal mathematical analysis
has been carried out in order to study the properties of approximate solutions. In this study, we propose a numerical approach
as a means to understand some properties of solutions to the DSW equation and, thus, to provide conditions for which the use
of the DSW equation may be inappropriate from both the physical and the mathematical points of view, within the context of
shallow water modeling. For analysis purposes, we propose a numerical method based on the Galerkin method and we obtain a
priori error estimates between the approximate solutions and weak solutions to the DSW equation under physically consistent
assumptions. We also present some numerical experiments that provide relevant information about the accuracy of the proposed
numerical method to solve the DSW equation and the applicability of the DSW equation as a model to simulate observed quantities
in an experimental setting. 相似文献
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We shall consider diffusion or single-phase flow in a multiscale porous medium which represents an infinite set of self-similar double-porosity media. At each scale, the medium consists of a highly permeable network of connected channels and low-permeable blocks. The characteristic scale of heterogeneity is ε at the highest level of hierarchy, wherein ε is a small parameter. The ratio between the channel and block permeability at each scale is ε 2. The process analyzed is described using a diffusion equation with an oscillating multiscale diffusion parameter. The macroscale behavior is of interest. The transition to the macroscale is performed by means of the two-scale homogenization procedure. One step of averaging at each level of hierarchy leads to the appearance of the memory terms in the averaged equation. The successive averaging steps lead to progressive memory accumulation, so at each step of averaging, the macroscale model changes its type, and even the result of the second step is unknown a priori. The objective was to determine the macroscopic limit model for the infinite number of scales. By the method of induction, we obtained the macroscale model for an arbitrary number of scales and its limit for the infinite hierarchy. The limit model represents the system of two equations with memory terms. The kernel of the memory operator is the solution of a nonlinear integro-differential equation. Its solution is obtained through Laplace transform. 相似文献
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Exploitation of gas hydrate requires an improved understanding of the behavior of gassy soil. In this study, a numerical simulation technique is proposed that uses the discrete element method (DEM) to evaluate the undrained mechanical behavior of gassy sand, which consists of three phases—sand particles, water, and gas. The governing equation of gassy sand under undrained condition is derived and incorporated into the DEM simulation, in which gas solution and exsolution are considered. Undrained isotropic unloading and undrained triaxial compression tests on gassy sand samples with dissolved methane and carbon dioxide are simulated. Reasonable consistency is found when the simulation results are compared with experimental observation and theoretical calculation. The simulation highlights the significant influence of the gas solubility on the undrained behavior of gassy sand. The micro-responses of the observed phenomenon are also investigated.
相似文献6.
Most practical reservoir simulation studies are performed using the so-called black oil model, in which the phase behavior
is represented using solubilities and formation volume factors. We extend the multiscale finite-volume (MSFV) method to deal
with nonlinear immiscible three-phase compressible flow in the presence of gravity and capillary forces (i.e., black oil model).
Consistent with the MSFV framework, flow and transport are treated separately and differently using a sequential implicit
algorithm. A multiscale operator splitting strategy is used to solve the overall mass balance (i.e., the pressure equation).
The black-oil pressure equation, which is nonlinear and parabolic, is decomposed into three parts. The first is a homo geneous
elliptic equation, for which the original MSFV method is used to compute the dual basis functions and the coarse-scale transmissibilities.
The second equation accounts for gravity and capillary effects; the third equation accounts for mass accumulation and sources/
sinks (wells). With the basis functions of the elliptic part, the coarse-scale operator can be assembled. The gravity/capillary
pressure part is made up of an elliptic part and a correction term, which is computed using solutions of gravity-driven local
problems. A particular solution represents accumulation and wells. The reconstructed fine-scale pressure is used to compute
the fine-scale phase fluxes, which are then used to solve the nonlinear saturation equations. For this purpose, a Schwarz
iterative scheme is used on the primal coarse grid. The framework is demonstrated using challenging black-oil examples of
nonlinear compressible multiphase flow in strongly heterogeneous formations. 相似文献
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M. K. Islam J. P. Carter M. S. A. Siddiquee M. S. Islam 《Geotechnical and Geological Engineering》2013,31(5):1587-1601
A method to derive a general equation for compression of structured soils is presented. It is shown that the general equation leads to the equation of compression for structured soils as proposed by Liu and Carter (Geotechnique 49(4):43–57, 1999). Using the compression characteristics of the structured and remolded soil, an equation is developed to determine a unique value for the structure degradation exponent term of the Liu-Carter equation. This equation is used to obtain the value of the structure degradation exponent of the Liu-Carter equation from the compression behavior of undisturbed and remolded Mexico City clay. The value of the exponent is used in the Liu-Carter equation to predict the compression behaviour of the clay. Excellent agreement is observed between predictions and experimental data. 相似文献
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水力压裂三维裂缝形态及延伸的预测是评价水力压裂效果的主要因素,采用了损伤力学与断裂力学相结合的方法,描述了裂缝表面岩体的力学行为,建立了裂缝面上的损伤判据与损伤演化方程。根据岩石力学与渗流力学,采用有限元方法建立了低渗透储层岩体的流固-损伤耦合方程,并采用Newton-Raphson与线性搜索相结合的方法进行求解,获得了低渗透油层水力压裂三维裂缝的动态扩展过程及最终形态,揭示其力学本质。通过算例验证了理论及计算方法的正确性。在此基础上,分析了影响裂缝扩展的主要因素,其结果可为水力压裂设计提供较为可靠和准确的预测手段,以提高油层水力压裂措施的成功率 相似文献
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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. 相似文献
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Y. Ichikawa K. Kawamura M. Nakano K. Kitayama T. Seiki N. Theramast 《Engineering Geology》2001,60(1-4):127-138
Bentonite clay is a micro-inhomogeneous material, which consists of clay minerals (mainly montmorillonite), macro-grains (mainly quartz), water, air and others. Properties of the saturated bentonite clay are essentially characterized by the montmorillonite and water (i.e. montmorillonite hydrate). We analyze the molecular behavior of sodium montmorillonite hydrate Na1/3Al2[Si11/3Al1/3]O10(OH)2·nH2O by applying a molecular dynamics (MD) simulation method. And by using the MD results we calculate the swelling property of the montmorillonite hydrate, and compare with an experimental result. Next, by using the same MD procedure we treat a montmorillonite mineral with a large number of external water molecules to check the properties of the water. Here we treat pure- and salt-water. Then we calculate the diffusivity and viscosity of water molecules and Na+ and Cl− ions.
For extending the microscopic characteristics of constituent materials to a macroscopic seepage behavior of the micro-inhomogeneous material we apply a homogenization analysis (HA). That is, starting with the Navier–Stokes equation with distributed viscosity that is calculated by the former MD procedure we determine macroscopic permeability characteristics of bentonite for both cases of pure- and salt-water. Then, by using the permeability property we calculate long-term consolidation behavior of buffering clay, which is planed to be used for high-level radioactive waste (HLRW) management. Here the deformation is treated under the well-defined Cam clay model. 相似文献
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The production of carbon in the ocean, the so-called primary production, depends on various physicobiological parameters:
the biomass and nutrient amounts in oceans, the salinity and temperature of the water and the light available in the water
column. We focus on the visible spectrum of the solar radiation defined as the Photosynthetically Active Radiation (PAR).
We developed a model (Chamiet al. 1997) to simulate the behavior of the solar beam in the atmosphere and the ocean. We first describe the theoretical basis
of the code and the method we used to solve the radiative transfer equation (RTE): the successive orders of scattering (SO).
The second part deals with a sensitivity study of the PAR just above and below the sea surface for various atmospheric conditions.
In a cloudy sky, we computed a ratio between vector fluxes just above the sea surface and spherical fluxes just beneath the
sea surface. When the optical thickness of the cloud increases this ratio remains constant and around 1.29. This parameter
is convenient to convert vector flux at the sea surface as retrieved from satellite to PAR. Subsequently, we show how solar
radiation as vector flux rather than P A R leads to an underestimate of the primary production up to 40% for extreme cases. 相似文献
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饱和软土的自重固结涉及许多复杂的非线性问题,而现有分析方法一般基于线性假设,将固结控制方程简化,在沉降变形较大的情况下并不合理。基于Gibson大变形固结方程,推导在单面排水和双面排水条件下的边界条件,综合考虑饱和软土的自重特性与非线性压缩、渗透关系,采用稳定性较好的Crank-Nicolson型差分格式离散并求解非线性控制方程,并从孔隙比、沉降、孔隙水流速3个方面将数值解与CS2固结数值模型进行对比验证。结合工程实例,研究土层不同初始厚度和初始孔隙比对自重固结的影响。结果表明：初始厚度与初始孔隙比较大土层最终沉降也较大。与传统方法相比,该方法所得出的数值解精度较高,实现了高度非线性固结方程的快速求解,其成果更能广泛运用于实际工程的分析之中。 相似文献
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用解析方法研究了管桩在轴向力和水平向力（倾斜力）联合作用下的受力及变形性状。在高层建筑、桥梁工程、海洋工程、新型海堤护岸等工程中桩基自由长度上作用土压力、风荷载、波浪荷载等荷载型式,基桩经常在竖向、水平向荷载同时作用下工作。国内外学者通过大量试验和理论研究得出了计算竖向、水平向荷载下基桩内力和挠度的半经验公式以及张氏法公式。为了分析竖向、水平向荷载同时作用下自由荷载的作用,在现行m法假设的基础上,从弹性桩的挠曲微分方程出发,导出了任意自由荷载作用下桩任意截面的水平变位、倾角、弯矩、剪力和地基反力计算表达式。桩的挠曲微分方程是分段函数,包括地上部分和地下部分桩,相应的内力和变位求解也分为两段。最后通过一个算例分析了桩顶竖向荷载、桩顶水平力和自由荷载对桩身的受力性状各参数的影响。计算结果表明, 桩顶水平力对桩身最大弯矩和桩顶水平变位的影响最大,而桩周内外摩阻力及桩身自重对桩身受力性状影响较小。 相似文献
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Iuliu Sorin Pop 《Computational Geosciences》2002,6(2):141-160
We present a numerical analysis of a time discretization method applied to Richards' equation. Written in its saturation-based form, this nonlinear parabolic equation models water flow into unsaturated porous media. Depending on the soil parameters, the diffusion coefficient may vanish or explode, leading to degeneracy in the original parabolic equation. The numerical approach is based on an implicit Euler time discretization scheme and includes a regularization step, combined with the Kirchhoff transform. Convergence is shown by obtaining error estimates in terms of the time step and of the regularization parameter. 相似文献
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In this paper, a coupling approach is presented to study the static responses of vertically loaded pile group embedded in multilayered transversely isotropic soils. The individual pile in pile group is modeled by the finite element method, while the analytical layer-element method is applied to represent the soil's behavior. Then, the interaction equation of piles and soils is obtained by considering the force equilibrium and displacement compatibility conditions and solved by a FORTRAN program. The results computed by the proposed approach compare favorably with those from some existing solutions and field test. Some typical parametric analysis cases are investigated to study the effect of soil anisotropy, pile stiffness ratio, and pile spacing on the behavior of vertically loaded pile group. 相似文献
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The purpose of this paper is to investigate the estimation of dynamic elastic behavior of the ground using the Kalman filter finite element method. In the present paper, as the state equation, the balance of stress equation, the strain–displacement equation and the stress–strain equation are used. For temporal discretization, the Newmark ¼ method is employed, and for the spatial discretization the Galerkin method is applied. The Kalman filter finite element method is a combination of the Kalman filter and the finite element method. The present method is adaptable to estimations not only in time but also in space, as we have confirmed by its application to the Futatsuishi quarry site. The input data are the measured velocity, acceleration, etc., which may include mechanical noise. It has been shown in numerical studies that the estimated velocity, acceleration, etc., at any other spatial and temporal point can be obtained by removing the noise included in the observation. Copyright © 2008 John Wiley & Sons, Ltd. 相似文献
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在描述非饱和土力学本构行为的Gens-Alonso模型[1]的基础上,结合化学浓度对前固结压力的软化公式[2],并考虑了化学浓度对黏聚力的软化作用,建立了描述非饱和土化学-水力-力学耦合行为的本构模型。对包括化学-水力-力学本构关系、流体流动和污染物传输的控制方程的平衡方程组进行有限元离散,并采用此非饱和土化学-水力-力学耦合行为的数值模型对非饱和土中隧道周围化学-水力-力学耦合过程进行了模拟,对纯粹的力学响应、弹性化学力学响应、弹塑性化学力学响应 3 种情况进行了分析,数值结果显示了化学浓度作用下隧道周围的体积变化量和应力状态比单纯的力学响应有较大的提高,隧道表面的收缩量也有明显的增大。数值模拟的结果显示了该方法对模拟非饱和土复杂的耦合行为的可行性。 相似文献
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非均质介质中溶质迁移往往出现非费克现象,传统的对流弥散方程(ADE)则难以较好地描述这种现象.采用连续时间的随机游走理论(CTRW)研究1250cm长一维非均质土柱中溶质运移问题,探讨CTRW模型中参数及非费克迁移的变化特征.研究结果表明,β值的大小与介质的非均质特征有关,非均质性越强,β值越小,但β值具有相对的稳定性,然而ADE的弥散系数则具有随尺度增大而增大的现象.对于介质非均质性较强和非费克现象较明显的溶质穿透曲线,尤其是在拖尾部分,与ADE相比,CTRW具有较高的模拟精度. 相似文献