一种高性能迭代预处理方法及其在岩土工程中的应用

岩土工程建设的发展极大地促进了三维数值模拟的应用。大规模三维有限元计算需要求解一系列大型线性方程组,这些线性方程组的求解直接影响着整个有限元计算的效率。复杂岩土工程问题通常涉及多相和多体耦合相互作用,各相之间或不同固体材料之间性质差别显著,可能导致Krylov子空间迭代法收敛缓慢,甚至求解失败。为了提高Krylov子空间迭代法的求解效率和可靠性,提出一种新的高效预处理技术,通过算例验证了所提出的分区块迭代预处理方法的有效性。     

Flow through porous media: A procedure for locating the free surface

A finite element procedure is developed to accurately locate the free surface of unconfined seepage flow through porous media. The free surface is taken as the boundary between wet and dry soils, with flow in the saturated region characterized by Darcy's law. The method involves equations and meshing which are fully consistent with a general formulation for geotechnical engineering problems involving simultaneous solution of pore fluid pressures and soil skeleton displacements. Accuracy and versatility of the proposed procedure are demonstrated by solving various unconfined seepage flow problems through earth structures. Free surfaces and flownets are presented for the calculated flow fields.     

基于哈密顿体系辛几何算法求解空间地基问题

地基应力和位移场的求解是岩土工程中的基本问题之一,以往的求解方法是在一类变量范围内求解,属于拉格朗日体系。利用弹性力学的哈密顿理论,通过适当的变量代换,由力学的控制方程引入对偶变量,直接将方程导入到哈密顿体系,应用分离变量法求解。在哈密顿体系下,利用辛几何的性质,在完备的解空间内将方程的解用本征向量函数展开,讨论零本征值和非零本征值对应的不同本征解及其物理意义。数值算例表明,所得结果同以往结果一致。该方法不同于传统方法,为地基的研究提供了一条新途径和思路。     

基于高性能并行计算的隧道开挖数值模拟

随着岩土工程规模的不断扩大、复杂性的增加以及计算参数的多样化和计算精度的提高, 人们对于计算机计算能力的要求越来越高, 然而单处理器无法满足这类大规模计算.从数据输入、区域分解、线性方程组的迭代求解、后处理等方面详细阐述高性能计算平台上并行有限元求解大规模岩土工程的关键问题.提出了利用MPI2的新特性进行海量数据的分段并行读入, 采用ParMetis软件并行地进行区域分解, 实现了前处理过程的完全并行化; 采用基于Jacobi预处理技术的预处理共轭梯度法(PCG)进行线性方程组的并行迭代求解; 采用Paraview软件实现了后处理的并行可视化.在深腾7000系统上对某隧道工程的三维开挖过程进行了数值模拟, 对其并行性能进行了分析和评价, 验证了采用的区域分解算法和系统方程组的求解方法的可行性, 并且具有较高的加速比和并行效率.      

Arbitrary Lagrangian–Eulerian method for dynamic analysis of geotechnical problems

In this paper an arbitrary Lagrangian–Eulerian (ALE) method to solve dynamic problems involving large deformation is presented. This ALE method is based upon the operator-split technique in which the material displacements and mesh displacements are uncoupled. A brief history of the ALE method is first presented and then special issues such as time-stepping, mesh refinement, energy absorbing boundaries, dynamic equilibrium checks and remapping of state variables are explained. The ALE method and the updated-lagrangian (UL) method are then used to analyse some geotechnical problems to examine the significance of inertia effects, large deformation and contact mechanics. The results show the efficiency of the ALE method for solving dynamic geotechnical problems involving large deformation.     

非饱和土中的流-固耦合研究

概述了非饱和土变形．渗流相互作用的多相流一固耦合理论的研究进展。重点讨论了在理论研究和实际应用方面所存在的几个主要问题，其中包括理论控制方程组描述、土．水特征曲线、固体骨架的弹塑性本构模型以及各种数值算法等研究。另外，就该理论在降雨入渗滑坡、土体的蒸发固结效应等问题的应用进行了简单的讨论，并指出了目前应用的热点和新的研究领域。研究结果表明，进一步发展非饱和土流．固耦合理论对解决非饱和士力学和环境地质灾害的工程问题有着重要的意义。     

Evaluating the performance of an explicit dynamic relaxation technique in analyzing non-linear geotechnical engineering problems

Explicit dynamic relaxation is an efficient tool that has been used to solve problems involving highly non-linear differential equations. The key feature of this method is the ability to use explicit dynamic algorithms in solving static problems. Few attempts have been made to date to apply this technique in conventional geotechnical engineering. In this study, an algorithm that incorporates the application of a stiffness dependent time step scheme is proposed. The algorithm has been successfully used to solve 2D and 3D non-linear geotechnical engineering problems. To calibrate the developed algorithm, numerical simulations have been conducted for a strip and square footings supported by Mohr–Coulomb material. Performance of four different types of brick elements used in collapse load calculation is examined in terms of convergence speed and accuracy. In addition, the role of employing adaptive time steps in reducing the number of iterations needed for convergence is also evaluated.     

A numerical study on the impact of thermal alterations in porous media during hot fluid injection process employing a modified Boussinesq model

The Oberbeck-Boussinesq (OB) approximation is widely employed as a simplifying assumption for density-dependent flow problems. It reduces the governing differential equations to simpler forms, which can be handled analytically or numerically. In this study, a modified OB model is formulated to account for the variation of rock permeability and porosity with temperature during the hot fluid injection process in an oil-saturated porous medium under the assumption of local thermal equilibrium (LTE). The mathematical model is solved numerically using a fully implicit control volume finite difference discretization with the successive over relaxation (SOR) method to handle the non-linearity. Subsequently, the numerical model is validated with the analytical solution of the simplified problem successfully. Through detailed sensitivity analyses, the simulation results reveal the hot fluid injection rate as the most important operational parameter to be optimized for a successful thermal flood. The numerical runs show that that for single-phase core-flood simulation, the effect of temperature on the rock absolute permeability and porosity can be neglected without introducing any significant errors in the estimated recovery and temperature profile.     

基于热-流-固耦合模型的石油钻井施工过程数值分析

岩土介质多场耦合问题需考虑诸多因素,温度、渗流及应力之间的耦合关系复杂,试验条件不易控制,且难以实现,因此,辅以数值模拟手段具有重要的意义。基于混合物理论,推导出岩土介质温度、渗流和应力耦合的数学模型及其控制方程,提出该数学模型的求解方法,以MATLAB语言为平台,将Abaqus程序作为一个模块嵌入迭代算法程序中,编制了多场耦合分析程序,并给出了2个典型算例验证该方法的有效性和实用性。然后,将建立的多场耦合模型和计算程序应用于石油钻井施工过程的模拟,重点分析井壁围岩内温度场、渗流场和应力场的变化规律,以及钻井液温度的变化对井壁稳定性的影响。研究成果对我国地下石油、核废料储存等工程设计和施工具有一定的指导意义。     

Numerical simulation of NAPL flow in the subsurface

A three-dimensional, three-phase numerical model is presented for simulating the movement of immiscible fluids, including nonaqueous-phase liquids (NAPLs), through porous media. The model is designed to simulate soil flume experiments and for practical application to a wide variety of contamination scenarios involving light or dense NAPLs in heterogeneous subsurface systems. The model is derived for the three-phase flow of water, NAPL, and air in porous media. The basic governing equations are based upon the mass conservation of the constitutents within the phases. The descretization chosen to transform the governing equations into the approximating equations, although logically regular, is very general. The approximating equations are a set of simultaneous coupled nonlinear equations which are solved by the Newton-Raphson method. The linear system solutions needed for the Newton-Raphson method are obtained using a matrix of preconditioner/accelerator iterative methods. Because of the special way the governing equations are implemented, the model is capable of simulating many of the phenomena considered necessary for the sucessful simulation of field problems including entry pressure phenomena, entrapment, and preferential flow paths. The model is verified by comparing it with several exact analytic test solutions and three soil flume experiments involving the introduction and movement of light nonaqueous-phase liquid (LNAPL) or dense nonaqueous-phase liquid (DNAPL) in heterogeneous sand containing a watertable. This revised version was published online in August 2006 with corrections to the Cover Date.     

方腔回流区水流运动特性三维数值分析

建立了一个三维水动力学模型,对方腔回流区水流运动特性进行了模拟分析。数学模型以三维浅水环流方程为基础,在垂向空间引入σ坐标变换,采用高分辨率半隐有限元离散格式。计算结果与解析解及水槽试验数据吻合良好。应用该模型对方腔回流区的水流运动特性进行了计算分析,进一步揭示了方腔回流运动的非定常非对称不封闭特性、流动结构表现为竖轴环流与立面环流相叠加、流速沿垂线分布相对均匀等流动规律。     

Numerical Laplace-Fourier transform inversion technique for layered-soil consolidation problems: I. Fundamental solutions and validation

A numericl method for solving consolidation problems of layered soils is developed. Starting from the governing differential equations for the coupled poro-elastic medium, the governing partial differential equations are reduced to ordinary differential equations by means of the appropriate displacement functions and Laplace-Fourier transformation. Once the fundamental solution in the transformed domain has been found, the solution in the physical domain is obtained by numerically inverting the transformations. A series of soil consolidation problems have been solved and validated against existing solutions in order to compare the feasibility and the accuracy of the present technique.     

Thermo-Hydro-Mechanical-Chemical Simulation of Methane Hydrate Dissociation in Porous Media

The vast amount of methane deposits in permafrost and oceanic sediments has significant energy and environmental implications. There are increasing interests in the development of numerical simulation techniques to predict the reservoir responses due to natural gas recovery from methane hydrate dissociation. There has been extensive amount of work on modeling the chemo- thermo- hydro-responses associated with hydrate dissociation. The mechanical responses of hydrate bearing ground, however, have largely been overlooked and are just starting to receive more and more attention. From energy recovery perspective, a comprehensive model that includes the mechanical responses of hydrate disassociation is crucial for predicting the mechanical stability of gas hydrate reservoir and potential geohazards. This paper proposes a thermo-hydro-mechanical-chemical model for simulating the dissociation of methane hydrate. The governing equations for the conservation of energy (thermal), mass (hydraulic) and momentum (mechanical) were derived from the local balance equations. The proposed governing equation system for methane hydrate as a four-phase four-component composite was simplified based on reasonable assumptions to facilitate numerical implementations. The dissociation reaction was considered using chemical kinetics. Auxiliary relationships such as the soil water characteristic curve, constitutive correlations, stress formulation based on the mixture theory were employed to mathematically close the formulation. The mathematical model was implemented using the finite element method. The simulation results were evaluated and compared with those obtained by conventional simulators based on thermo-hydro-chemical models. The mechanical module of this new model was applied to predict the geotechnical responses induced by gas recovery in a typical oceanic reservoir.     

Application of a Coupled Eulerian–Lagrangian approach on geomechanical problems involving large deformations

Geotechnical boundary value problems involving large deformations are often difficult to solve using the classical finite element method. Large mesh distortions and contact problems can occur due to the large deformations such that a convergent solution cannot be achieved. Since Abaqus, Version 6.8, a new Coupled Eulerian–Lagrangian (CEL) approach has been developed to overcome the difficulties with regard to finite element method and large deformation analyses. This new method is investigated regarding its capabilities. First, a benchmark test, a strip footing problem is investigated and compared to analytical solutions and results of comparable finite element analyses. This benchmark test shows that CEL is well suited to deal with problems which cannot be fully solved using FEM. In further applications the CEL approach is applied to more complex geotechnical boundary value problems. First, the installation of a pile into subsoil is simulated. The pile is jacked into the ground and the results received from these analyses are compared to results of classical finite element simulations. A second case study is the simulation of a ship running aground at an embankment. The results of the CEL simulation are compared to in situ measurement data. Finally, the capabilities of the new CEL approach are evaluated regarding its robustness and efficiency.     

Finite-element method in modeling geologic transport processes

Deterministic mathematical modeling of complex geologic transport processes may require the use of odd boundary shapes, time dependency, and two or three dimensions. Under these circumstances the governing transport equations must be solved by numerical methods. For a number of transport phenomena a general form of the convective-dispersion equation can be employed. The solution of this equation for complicated problems can be solved readily by the finite-element method. Using quadrilateral isoparametric elements or triangular elements and a computational algorithm based on Galerkin's procedure, solutions to unsteady heat flux from a dike and seawater intrusion in an aquifer have been obtained. These examples illustrate that the finite-element numerical procedure is well suited for solving boundary-value problems resulting from modeling of complex physical phenomena.     

Ordering-based nonlinear solver for fully-implicit simulation of three-phase flow

The Fully Implicit method (FIM) is often the method of choice for the temporal discretization of the partial differential equations governing multiphase flow in porous media. The FIM involves solving large coupled systems of nonlinear algebraic equations. Newton-based methods, which are employed to solve the nonlinear systems, can suffer from convergence problems—this is especially true for large time steps in the presence of highly nonlinear flow physics. To overcome such convergence problems, the time step is usually reduced, and the Newton steps are restarted from the solution of the previous (converged) time step. Recently, potential ordering and the reduced-Newton method were used to solve immiscible three-phase flow in the presence of buoyancy and capillary effects (e.g., Kwok and Tchelepi, J. Comput. Phys. 227(1), 706–727 2007). Here, we improve the robustness of the potential-based ordering method in the presence of gravity. Furthermore, we also extend this nonlinear approach to interphase mass transfer. Our algorithm deals effectively with mass transfer between the liquid and gas phases, including phase disappearance (e.g., gas going back in solution) and reappearance (e.g., gas coming out of solution and forming a separate phase), as a function of pressure and composition. Detailed comparisons of the robustness and efficiency of the potential-based solver with state-of-the-art nonlinear/linear solvers are presented for immiscible two-phase (Dead-Oil), Black-Oil, and compositional problems using heterogeneous models. The results show that for large time steps, our nonlinear ordering-based solver reduces the number of nonlinear iterations significantly, which leads to gains in the overall computational cost.     

A sequential sparse polynomial chaos expansion using Bayesian regression for geotechnical reliability estimations

Polynomial chaos expansions (PCEs) have been widely employed to estimate failure probabilities in geotechnical engineering. However, PCEs suffer from two deficiencies: (a) PCE coefficients are solved by the least-square minimization method which easily causes overfitting issues; (b) building a high order PCE is often computationally expensive. In order to overcome the aforementioned drawbacks, the Bayesian regression technique is employed to evaluate PCE coefficients, which not only provides a sparse solution but also avoids overfitting. With the aid of the predictive means and variances given by Bayesian analysis, a learning function is proposed to sequentially select the most informative samples that are critical to build a PCE. This sequential learning scheme can highly enhance the computational efficiency of PCEs. Besides, importance sampling (IS) is incorporated into the sequential learning (SL)-PCEs to deal with geotechnical problems with small failure probabilities. The proposed method of SL-PCE-IS is applied to three illustrative examples, which shows that the improved PCE method is more effective and efficient than the common PCEs method, leading to accurate estimations of small failure probabilities using fewer training samples.     

Ordering-based nonlinear solver for fully-implicit simulation of three-phase flow

The Fully Implicit Method (FIM) is often the method of choice for the temporal discretization of the partial differential equations governing multiphase flow in porous media. The FIM involves solving large coupled systems of nonlinear algebraic equations. Newton-based methods, which are employed to solve the nonlinear systems, can suffer from convergence problems—this is especially true for large time steps in the presence of highly nonlinear flow physics. To overcome such convergence problems, the time step is usually reduced, and the Newton steps are restarted from the solution of the previous (converged) time step. Recently, potential ordering and the reduced-Newton method were used to solve immiscible three-phase flow in the presence of buoyancy and capillary effects (e.g., Kwok and Tchelepi, J. Comput. Phys. 227(1), 706–727 9). Here, we improve the robustness of the potential-based ordering method in the presence of gravity. Furthermore, we also extend this nonlinear approach to interphase mass transfer. Our algorithm deals effectively with mass transfer between the liquid and gas phases, including phase disappearance (e.g., gas going back in solution) and reappearance (e.g., gas coming out of solution and forming a separate phase), as a function of pressure and composition. Detailed comparisons of the robustness and efficiency of the potential-based solver with state-of-the-art nonlinear/linear solvers are presented for immiscible two-phase (Dead-Oil), Black-Oil, and compositional problems using heterogeneous models. The results show that for large time steps, our nonlinear ordering-based solver reduces the number of nonlinear iterations significantly, which leads to gains in the overall computational cost.     

Heat-exchanger piles for the de-icing of bridges

Of the various types of road structures, bridges are the most exposed to icing; the problem of icing is widely addressed through salting, which reduces the lifespan of the bridge. One promising solution to avoid the use of salt is the seasonal storage of solar heat energy captured directly through the asphalt layer; however, this solution can only be achieved cost effectively if a necessary geostructure is used as a heat exchanger. In this study, such an approach is studied for a bridge crossing a canal, and the geotechnical and energy-related challenges of such a solution are discussed. Bridge piers and abutments are located on piles, which are used as heat exchangers. Depending on local conditions, seasonal storage and natural thermal reload are two possible solutions for the operation of such a system. In particular, the presence of underground water flow is thought to be a significant factor in such a design and is considered here. This study aims to determine the geotechnical and energy design parameters through thermo-hydro-mechanical simulations. A three-dimensional finite-element model analysis is necessary given the distance between bridge piles. Various underground water flow scenarios are studied. The capture of energy and de-icing requirements is based on the few existing structures that use other means of energy exchange with the ground. The results indicate that the use of heat-exchanger piles for de-icing bridges can only be considered at specific sites; however, the efficiency of the solution at those sites is high. Possible foundation and structure stability problems are also considered, such as vertical displacements due to the dual use of the foundation piles.     

Dynamic response to fluid extraction from a poroelastic half‐space

In this study, the dynamic response of a poroelastic half‐space to a point fluid sink is investigated using Biot's dynamic theory of poroelasticity. Based on Biot's theory, the governing field equations are re‐formulated in frequency domain with solid displacement and pore pressure. In a cylindrical coordinate system, a method of displacement potentials for axisymmetric displacement field is proposed to decouple the Biot's field equations to three scalar Helmholtz equations, and then the general solution to axisymmetric problems are obtained. The full‐space fundamental singular solution for a point sink is also derived using potential methods. The mirror‐image method is finally applied to construct the fundamental solution for a point sink buried in a poroelastic half‐space. Furthermore, a numerical study is conducted for a rock, that is, Berea sandstone, as a representative example. Copyright © 2013 John Wiley & Sons, Ltd.