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1.
Capping contaminated sediments in waterways is an alternate remediation technique to dredging and is typically much cheaper than dredging. When cap material is placed on top of contaminated sediment, it has both a short-term and long-term hydraulic impact on the underlying sediment. A numerical model of consolidation, based on a nonlinear finite strain theory for a consolidating fine-grained sediment bed was developed. The nonlinear equation of consolidation was solved in a material (or reduced) coordinate using an explicit finite difference numerical scheme. An one-dimensional advection–diffusion equation with sorption and decay was solved on a convective coordinate using a finite volume total variation diminishing (TVD) scheme for the contaminant concentration within the consolidating sediment. The contaminant transport model was coupled with the consolidation model. The time and space varying porosities, permeabilities, and advective velocities computed by the consolidation model were linked to the transport model at the same time level. A number of benchmark tests that are relevant to the consolidation of a fine-grained sediment were designed and tested. The relative contribution of consolidation-induced transient advective velocities on the migration of a contaminant during consolidation was also investigated. The coupled model performance was validated by simulating the transport of hazardous chemicals under consolidation in a confined aquatic disposal (CAD) site in the Lower Duwamish Waterway, Seattle. 相似文献
2.
In the available mathematical formulations to determine the rate of radial consolidation of stone column-improved ground, the soil properties especially permeability and compressibility are assumed to be constant during consolidation process. However, permeability changes with void ratio (void ratio also changes with consolidation) and compressibility of soil varies along the consolidation curve (compressibility is a function of effective stress and void ratio). Thus, these properties are not constant during consolidation period. In the present paper, mathematical formulation is developed to determine the rate of consolidation of stone column-improved ground due to radial flow considering change in permeability and compressibility of soft soil during consolidation period. Equal strain approach has been considered in the analysis. The parabolic variation in permeability and compressibility within smear zone are incorporated in the formulation. It is observed that the variation of degree of consolidation due to change in stress concentration ratio and diameter ratio reduces when variable soil properties are considered. The difference between the degree of consolidation obtained considering variable and constant soil properties is almost constant due to variation of smear zone parameters. The time required to achieve 90% degree of consolidation increases or decreases (depending on the properties of soil) by around 50%–100% or up to 25%, respectively, when change in soil properties during consolidation is considered. 相似文献
3.
任意荷载下成层粘弹性地基的一维固结 总被引:5,自引:0,他引:5
针对成层粘弹性地基模型,运用Laplace变换及矩阵传递法求解了任意荷载下成层粘弹性地基一维变形问题,得到了频域内的通解,通过Laplace逆变换,即可计算成层粘弹性地基在任意荷载下的一维变形.Terzaghi一维固结理论解是本文的一个特例.结合三层地基的算例,可以看到粘弹性地基的固结相对于弹性地基有个滞后过程,但随时间最终趋于一致;循环荷载下粘弹性多层地基固结时,其有效应力和变形都呈振荡增长,且不与荷载同步,而要相对滞后.此外,通过一工程实例,对该方法的可靠性进行论证,以证明该法确能指导工程实践. 相似文献
4.
An integral method technique is used in solving the governing partial differential equation which models the process of self-weight consolidation of very soft soil. The solution is in the form of a series of convenient closed-form equations. 相似文献
5.
6.
污染物在非饱和带内运移的流固耦合数学模型及其渐近解 总被引:3,自引:0,他引:3
污染物在非饱和带中运移过程是多组分多相渗流问题.在考虑气相的存在对水相影响的前提下,基于流固耦合力学理论,建立了污染物在非饱和带内运移的流固耦合数学模型.对该强非线性数学模型采用摄动法及积分变换法进行拟解析求解,得出了解析表达式.对非饱和带内的孔隙压力分布、孔隙水流速以及污染物的浓度在耦合与非耦合气相条件下的分布规律进行解析计算.对该渐近解与Faust模型的计算结果进行了对比分析,结果表明:该模型解与Faust解基本吻合,且气相作用以及介质的变形对溶质的输运过程产生较大的影响,从而验证了解析表达式的正确性和实用性.这为定量化预报预测污染物在非饱和带中迁移转化和实验室确定压力-饱和度-渗透率三者之间的关系提供了可靠的理论依据. 相似文献
7.
Steven M. Gorelick 《Mathematical Programming》1990,48(1-3):19-39
Once subsurface water supplies become contaminated, designing cost-effective and reliable remediation schemes becomes a difficult task. The combination of finite element simulation of groundwater contaminant transport with nonlinear optimization is one approach to determine the best well selection and optimal fluid withdrawal and injection rates to contain and remove the contaminated water. Both deterministic and stochastic programming problems have been formulated and solved. These tend to be large scale problems, owing to the simulation component which serves as a portion of the constraint set. The overall problem of combined groundwater process simulation and nonlinear optimization is discussed along with example problems. Because the contaminant transport simulation models give highly uncertain results, quantifying their uncertainty and incorporating reliability into the remediation design results in a class of large stochastic nonlinear problems. The reliability problem is beginning to be addressed, and some strategies and formulations involving chance constraints and Monte Carlo methods are presented. 相似文献
8.
Rubn Ansola Javier Canales Jos A. Trrago 《Finite Elements in Analysis and Design》2006,42(14-15):1220-1230
This work presents a modified version of the evolutionary structural optimization procedure for topology optimization of continuum structures subjected to self-weight forces. Here we present an extension of this procedure to deal with maximum stiffness topology optimization of structures when different combinations of body forces and fixed loads are applied. Body forces depend on the density distribution over the design domain. Therefore, the value and direction of the loading are coupled to the shape of the structure and they change as the material layout of the structure is modified in the course of the optimization process. It will be shown that the traditional calculation of the sensitivity number used in the ESO procedure does not lead to the optimum solution. Therefore, it is necessary to correct the computation of the element sensitivity numbers in order to achieve the optimum design. This paper proposes an original correction factor to compute the sensitivities and enhance the convergence of the algorithm. The procedure has been implemented into a general optimization software and tested in several numerical applications and benchmark examples to illustrate and validate the approach, and satisfactorily applied to the solution of 2D, 3D and shell structures, considering self-weight load conditions. Solutions obtained with this method compare favourably with the results derived using the SIMP interpolation scheme. 相似文献
9.
This paper presents an analytical layer-element solution to non-axisymmetric consolidation of multilayered poroelastic materials with anisotropic permeability and compressible constituents. By applying Fourier expansions, Hankel transforms and Laplace transforms to the state variables involved in the governing equations of poroelasticity with respect to the circumferential, radial and time coordinates, respectively, the analytical layer-element (i.e. a symmetric stiffness matrix) is derived, which describes the relationship between the transformed generalized stresses and displacements at the surface (z = 0) and those at an arbitrary depth z, considering the corresponding boundary and continuity conditions at the layer interfaces, the global stiffness matrix of a multilayered system is assembled in the transformed domain. The actual solutions in the physical domain are acquired by applying numerical quadrature schemes for the inversion of the Laplace–Hankel transform. Finally, numerical calculation is presented to investigate the influence of layering and poroelastic material parameters on consolidation process. 相似文献
10.
V. V. Sidoryakina A. I. Sukhinov 《Computational Mathematics and Mathematical Physics》2017,57(6):978-994
A two-dimensional linearized model of coastal sediment transport due to the action of waves is studied. Up till now, one-dimensional sediment transport models have been used. The model under study makes allowance for complicated bottom relief, the porosity of the bottom sediment, the size and density of sediment particles, gravity, wave-generated shear stress, and other factors. For the corresponding initial–boundary value problem the uniqueness of a solution is proved, and an a priori estimate for the solution norm is obtained depending on integral estimates of the right-hand side, boundary conditions, and the norm of the initial condition. A conservative difference scheme with weights is constructed that approximates the continuous initial–boundary value problem. Sufficient conditions for the stability of the scheme, which impose constraints on its time step, are given. Numerical experiments for test problems of bottom sediment transport and bottom relief transformation are performed. The numerical results agree with actual physical experiments. 相似文献
11.
Research interest in the mechanical behaviour of soils is growing as a result of an increasing number of geomechanical problems involving consolidation effects. The main aim of this paper is to validate and to solve a model for consolidation of an elastic saturated soil with incompressible fluid and variable permeability. Firstly, we prove the existence and uniqueness of the solution of the variational problem corresponding to an initial and boundary value problem (IBVP): a special case of the Biot’s ‘consolidation of clay’ model (where the applied forces depend on time). Secondly, we prove the convergence of the method using a technique based on the proof of solution’s existence. Finally, we then solved this constitutive model by the finite element method (FEM) employing repeated fixed point techniques in order to obtain the results for displacement and pore water pressure. The pore fluid is considered incompressible. The results of the numerical experiments are compared with analytical solutions and, in cases where such solutions do not exist, with experimental data. Therefore, the model can be used for quantitative predictions of consolidation behaviour of soils with permeability dependent on the settlement. 相似文献
12.
该文研究了广义边界条件下含移动污染源的泥沙反应扩散模型 及其解析解,分析了解析解计算过程中的若干问题. 该文的结果可作为文[2]和[3]的推广. 相似文献
13.
Eulerian–Langrangian localized adjoint methods (ELLAM) were developed to solve convection–diffusion–reaction equations governing contaminant transport in groundwater flowing through a porous medium, subject to various combinations of boundary conditions. In this article, we prove optimal-order error estimates and some superconvergence results for the ELLAM schemes. In contrast to many existing estimates for a variety of numerical methods, which often contain the temporal derivatives of the exact solution, our error estimates contain the total derivatives of the exact solution but do not involve any temporal derivatives of the exact solution. © 1995 John Wiley & Sons, Inc. 相似文献
14.
In this study, we analyze an inventory system facing stochastic external demands and an autonomous supply (independent return flow) in the presence of fixed disposal costs and positive lead times under a continuous review replenishment–disposal policy. We derive the analytical expressions of the operating characteristics of the system; and, construct the objective function to minimize the total expected costs of ordering, holding, purchasing and disposal per unit time subject to a fill rate constraint. An extensive numerical analysis is conducted to study the sensitivity of the policy parameters and the benefit of employing a policy which allows for disposal of excess stock in this setting. We model the net demand process as the superposition of normally distributed external demand and inflows, which is expressed as a Brownian motion process. Our findings indicate that the disposal option results in considerable savings even (i) in the presence of non-zero fixed disposal costs, (ii) large actual demand rates with high return ratios (resulting in small net demands) and (iii) for moderate return ratios with high demand variability. 相似文献
15.
On the pollution effect of quasi‐compressibility methods in magneto‐hydrodynamics and reactive flows
Andreas Prohl 《Mathematical Methods in the Applied Sciences》1999,22(17):1555-1584
The study of the asymptotics of quasi‐compressibility methods is an essential tool to construct and improve numerical schemes in hydrodynamics, like e.g., stabilized finite element methods or time‐splitting projection methods. The goal of this work is to illustrate different asymptotical solution behaviour for equations in magneto‐hydrodynamics and those that describe reactive flows for standard quasi‐compressibility methods that influences the design of numerical algorithms. Copyright © 1999 John Wiley & Sons, Ltd. 相似文献
16.
Christophe Berthon Stéphane Cordier Olivier Delestre Minh Hoang Le 《Comptes Rendus Mathematique》2012,350(3-4):183-186
In this Note, an exact smooth solution for the equations modeling the bedload transport of sediment in shallow water is presented. This solution is valid for a large family of sedimentation laws which are widely used in erosion modeling such as the Grass model or those of Meyer-Peter and Müller. One of the main interests of this solution is the derivation of numerical benchmarks to valid the approximation methods. 相似文献
17.
A detailed comparative numerical study of a continuous source discharging in a tidal flow has been performed. The advective term in the one-dimensional transport equation consists of a constant freshwater velocity and an isotropic oscillating component. Various finite element solutions are investigated. Compared to the analytical solution of the dynamic steady state concentration, the numerical results for typical estuarine conditions clearly indicate the superiority of the collocation method with Hermite basis functions. An extended Fourier series analysis that accounts for the source condition is developed to explain the numerical behaviour of the different schemes. 相似文献
18.
通过建立横观各向同性圆柱土样轴对称Biot固结问题的Green·函数,得到了用Green函数表示的径向位移分布表达式和相应的空隙水压力的精确解析解.该方法不仅避免了将问题的解分解为弹性静力学解和渗流拟动态解的叠加的过程和复杂的积分变换,而且问题的级数解形式简洁,收敛速度较快,便于数值计算和圆柱土样的全场渗流固结规律的分析.最后以此结果具体分析了Mandel-Cryer效应在圆柱土样不同位置的强弱程度和土的泊松比对Mandel-Cryer效应的影响,表明本文方法的正确性. 相似文献
19.
The combined finite volume–finite element scheme for a double nonlinear parabolic convection-dominated diffusion equation which models the variably saturated flow and contaminant transport problems in porous media is extended. Whereas the convection is approximated by a finite volume method (Multi-Point Flux Approximation), the diffusion is approximated by a finite element method. The scheme is fully implicit and involves a relaxation-regularized algorithm. Due to monotonicity and conservation properties of the approximated scheme and in view of the compactness theorem we show the convergence of the numerical scheme to the weak solution. Our scheme is applied for computing two dimensional examples with different degrees of complexity. The numerical results demonstrate that the proposed scheme gives good performance in convergence and accuracy. 相似文献
20.
The work deals with numerical modelling of 2D/3D laminar incompressible viscous flows for Newtonian and non–Newtonian fluids. The unsteady system of Navier–Stokes equations with steady boundary conditions in the form of an artificial compressibility method is solved by multistage Runge–Kutta finite volume method. Steady state solution is achieved for t→∞. Convergence is followed by steady residual behaviour. For unsteady solution high compressibility coefficient β2 is considered. (© 2008 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim) 相似文献