三维N-S方程混合有限分析多重网格方法

提出了一种求解三维定常不可压N-S方程的混合有限分析多重网格方法(HFA-FMG).以三维方腔流动作为算例,计算表明提出的数值格式能极大地节省计算工作量且稳定有效.三维方腔流动的模拟成果较好地表现方腔内复杂的流动特征并和其他成果吻合.     

不同方法求解疏排水引起的地面沉降对比研究

地下水开发利用和疏排水过程引起的地面沉降是一个渗流场与应力场耦合的过程。基于算例模型,分别采用目前常用的基于渗流-沉降分步计算的土力学经验公式、渗流-沉降部分耦合的GMS软件中SUB模型以及目前少用的基于渗流-沉降全耦合的COMSOL Multiphysics模型对疏排水引起的地面沉降量进行了计算。对比不同方法计算结果表明,COMSOL Multiphysics计算疏排水引起的地面沉降可行且计算结果较经验公式法、GMS中SUB模型的结果更为合理、更符合实际沉降特征。在此基础上,采用COMSOL Multiphysics和GMS中SUB模型对比研究了不同渗透系数对地面沉降计算的影响,结果进一步验证了COMSOL Multiphysics求解疏排水引起地面沉降的可靠性。     

Mortar Upscaling for Multiphase Flow in Porous Media

In mortar space upscaling methods, a reservoir is decomposed into a series of subdomains (blocks) in which independently constructed numerical grids and possibly different physical models and discretization techniques can be employed in each block. Physically meaningful matching conditions are imposed on block interfaces in a numerically stable and accurate way using mortar finite element spaces. Coarse mortar grids and fine subdomain grids provide two-scale approximations. In the resulting effective solution flow is computed in subdomains on the fine scale while fluxes are matched on the coarse scale. In addition the flexibility to vary adaptively the number of interface degrees of freedom leads to more accurate multiscale approximations. This methodology has been implemented in the Center for Subsurface Modeling's multiphysics multiblock simulator IPARS (Integrated Parallel Accurate reservoir Simulator). Computational experiments demonstrate that this approach is scalable in parallel and it can be applied to non-matching grids across the interface, multinumerics and multiphysics models, and mortar adaptivity. Moreover unlike most upscaling approaches the underlying systems can be treated fully implicitly.     

淤泥质酸性土水泥土强度试验研究

水泥搅拌桩加固有机质含量较高和呈酸性的土层时,我国规范建议采用现场试验的方法。通过深层搅拌法加固太湖应天河工程富含有机质的淤泥质酸性土地基的多组现场水泥土强度试验,分析了淤泥质酸性土中影响水泥土强度的各种因素。试验和工程实践表明,使用高标号水泥(525#)并掺入适量的外加剂可大幅提高酸性淤泥水泥土的强度, 复合地基承载力可达120 kPa以上,水泥搅拌桩可以加固淤泥质酸性土地基。     

Comparison of numerical methods for simulating strongly nonlinear and heterogeneous reactive transport problems—the MoMaS benchmark case

Although multicomponent reactive transport modeling is gaining wider application in various geoscience fields, it continues to present significant mathematical and computational challenges. There is a need to solve and compare the solutions to complex benchmark problems, using a variety of codes, because such intercomparisons can reveal promising numerical solution approaches and increase confidence in the application of reactive transport codes. In this contribution, the results and performance of five current reactive transport codes are compared for the 1D and 2D subproblems of the so-called easy test case of the MoMaS benchmark (Carrayrou et al., Comput Geosci, 2009, this issue). This benchmark presents a simple fictitious reactive transport problem that highlights the main numerical difficulties encountered in real reactive transport problems. As a group, the codes include iterative and noniterative operator splitting and global implicit solution approaches. The 1D easy advective and 1D easy diffusive scenarios were solved using all codes, and, in general, there was a good agreement, with solution discrepancies limited to regions with rapid concentration changes. Computational demands were typically consistent with what was expected for the various solution approaches. The differences between solutions given by the three codes solving the 2D problem are more important. The very high computing effort required by the 2D problem illustrates the importance of parallel computations. The most important outcome of the benchmark exercise is that all codes are able to generate comparable results for problems of significant complexity and computational difficulty.     

Modeling of self‐desiccation in a cemented backfill structure

After placement of cemented tailings backfill (CTB), which is a mixture of tailings (man‐made soil), water, and binder, into underground mined‐out voids (stopes), the hydration reaction of the binder converts the capillary water into chemically bound water, which results in the reduction of the water content in the pores of the CTB, thereby causing a reduction in the pore‐water pressure in the CTB (self‐desiccation). Self‐desiccation has a significant impact on the pore‐water pressure and effective stress development in CTB and paramount and practical importance for the stability assessment and design of CTB structures and barricades. However, self‐desiccation in CTB structures is complex because it is a function of the multiphysics or coupled (i.e., thermal, hydraulic, mechanical, and chemical) processes that occur in CTB. To understand the self‐desiccation behavior of CTB, an integrated multiphysics model of self‐desiccation is developed in this study, which fully considers the coupled thermal, hydraulic, mechanical, and chemical processes and the consolidation process in CTB. All model coefficients are determined in measurable parameters. Moreover, the predictive ability of the model is verified with extensive case studies. A series of engineering issues are examined with the validated model to investigate the self‐desiccation process in CTB structures with respect to the changes in the mixture recipe, backfilling, and the surrounding rock and curing conditions. The obtained results provide in‐depth insight into the self‐desiccation behavior of CTB structures. The developed multiphysics model is therefore a potential tool for assessing and predicting self‐desiccation in CTB structures.     

Sensitivity analysis applied to finite element method model for coupled multiphase system

Today multiphysics problems applied to various fields of engineering have become increasingly important. Among these, in the areas of civil, environmental and nuclear engineering, the problems related to the behaviour of porous media under extreme conditions in terms of temperature and/or pressure are particularly relevant. The mathematical models used to solve these problems have an increasing complexity leading to increase of computing times. This problem can be solved by using more effective numerical algorithms, or by trying to reduce the complexity of these models. This can be achieved by using a sensitivity analysis to determine the influence of model parameters on the solution. In this paper, the sensitivity analysis of a mathematical/numerical model for the analysis of concrete as multiphase porous medium exposed to high temperatures is presented. This may lead to a reduction of the number of the model parameters, indicating what parameters should be determined in an accurate way and what can be neglected or found directly from the literature. Moreover, the identification parameters influence may allow to proceeding to a simplification of the mathematical model (i.e. model reduction). The technique adopted in this paper to performing the sensitivity analysis is based on the automatic differentiation (AD), which allowed to develop an efficient tool for the computation of the sensitivity coefficients. The results of the application of AD technique have been compared with the results of the more standard finite difference method, showing the superiority of the AD in terms of numerical accuracy and execution times. From the results of the sensitivity analysis, it follows that a drastic simplification of the model for thermo‐chemo‐hygro‐mechanical behaviour of concrete at high temperature, is not possible. Therefore, it is necessary to use different model reduction techniques in order to obtain a simplified version of the model that can be used at industrial level. Copyright © 2012 John Wiley & Sons, Ltd.     

A global method for coupling transport with chemistry in heterogeneous porous media

Modeling reactive transport in porous media, using a local chemical equilibrium assumption, leads to a system of advection–diffusion PDEs coupled with algebraic equations. When solving this coupled system, the algebraic equations have to be solved at each grid point for each chemical species and at each time step. This leads to a coupled non-linear system. In this paper, a global solution approach that enables to keep the software codes for transport and chemistry distinct is proposed. The method applies the Newton–Krylov framework to the formulation for reactive transport used in operator splitting. The method is formulated in terms of total mobile and total fixed concentrations and uses the chemical solver as a black box, as it only requires that one be able to solve chemical equilibrium problems (and compute derivatives) without having to know the solution method. An additional advantage of the Newton–Krylov method is that the Jacobian is only needed as an operator in a Jacobian matrix times vector product. The proposed method is tested on the MoMaS reactive transport benchmark.     

A FORM-based approach for probabilistic analysis in geotechnics: Application to a reinforced concrete drainage culvert

As numerical models are increasingly used as a design tool in geotechnical engineering, it is highly desirable if geotechnical reliability analysis can be conducted based on numeral models. Currently, the practical use of geotechnical reliability analysis-based numerical models is still quite limited. In this study, an easy to access method is derived to conduct geotechnical reliability analysis based on numerical models. To facilitate its application, a procedure is outlined to implement the suggested method such that geotechnical reliability analysis can be automated using existing geotechnical numerical packages. The procedure is illustrated in detail with an example, and the source codes provided can be easily adapted to analyze other similar problems. The method described in this paper is used to study the reliability of a deteriorating reinforced concrete drainage culvert in Shanghai, China. The suggested method provides a convenient means for reliability analysis of complex geotechnical problems.     

Consolidation in spatially random unsaturated soils based on coupled flow‐deformation simulation

This paper integrates random field simulation of soil spatial variability with numerical modeling of coupled flow and deformation to investigate consolidation in spatially random unsaturated soil. The spatial variability of soil properties is simulated using the covariance matrix decomposition method. The random soil properties are imported into an interactive multiphysics software COMSOL to solve the governing partial differential equations. The effects of the spatial variability of Young's modulus and saturated permeability together with unsaturated hydraulic parameters on the dissipation of excess pore water pressure and settlement are investigated using an example of consolidation in a saturated‐unsaturated soil column because of loading. It is found that the surface settlement and the pore water pressure profile during the process of consolidation are significantly affected by the spatially varying Young's modulus. The mean value of the settlement of the spatially random soil is more than 100% greater than that of the deterministic case, and the surface settlement is subject to large uncertainty, which implies that consolidation settlement is difficult to predict accurately based on the conventional deterministic approach. The uncertainty of the settlement increases with the scale of fluctuation because of the averaging effect of spatial variability. The effects of spatial variability of saturated permeability k_sat and air entry parameters are much less significant than that of elastic modulus. The spatial variability of air entry value parameters affects the uncertainties of settlement and excess pore pressure mostly in the unsaturated zone. Copyright © 2016 John Wiley & Sons, Ltd.     

Slope reliability analysis accounting for spatial variation

A practical and transparent procedure is described for implementing a generalized limit equilibrium method via cell-object-oriented constrained optimization in the spreadsheet platform. The formulation allows switching among the Spencer, Bishop simplified and wedge methods on the same template by specifying different side-force inclination and different constraints of optimization. Search for the critical circular or non-circular slip surface is possible. The deterministic procedure is extended probabilistically by implementing the first-order reliability method via constrained optimization of the equivalent dispersion ellipsoid in the original space of the random variables. This procedure is illustrated for an embankment on soft ground, and for a clay slope in southern Norway, both involving spatially correlated soil properties. The effects of autocorrelation distance on the results of reliability analysis are studied. Shear strength anisotropy is modelled via user-created simple function codes in the programming environment of the spreadsheet. The meaning of probability of failure is discussed.     

Numerical solution of nonlinear equations in chemical speciation calculations

Speciation calculations involve the computation of the concentration of each individual chemical species in a multicomponent–multiphase chemical system. The numerical problem is to solve a system of coupled linear and nonlinear equations subject to the constraint that all unknowns are positive. The performance and accuracy of a series of nonlinear equation solvers are evaluated: A quasi-Newton method with the global step determined by different line search and trust region algorithms, the conjugate gradient method with the global step determined by line search, and the solvers in the codes TENSOLVE, CONMIN and LBFGS.     

地基处理技术规范中关于沉降计算公式的使用条件分析

刚性桩复合地基沉降计算应按现行国家标准,可采用分层总和法进行沉降计算。该沉降计算方法是目前绝大多数工程采用的方法。但该法在理论上还需要进一步完善,结合工程实例,详细分析地基处理规范中沉降计算公式的适用条件,对以后工程实践过程中有针对性地收集工程数据,指导规范修改有一定积极意义。     

Modelling heat and fluid flow in sedimentary basins by the finite element method

In this article we solve the equations for a 2D model of compaction of sedimentary basins saturated with water by the finite-element method. This compaction model considers the rock described by the porosity as a function of effective stress, and both the anisotropic permeability and the anisotropic heat conductivity as functions of porosity. The water density is approximated linearly in the water pressure and temperature, and the water viscosity is a function of temperature. The main variables in the model are the water excess pressure and the temperature, and we account for an implicit solution scheme where we solve for both main variables simultaneously. The non-linearities in the model are either dealt with by the Newton method or by fixed-point iterations. We compare the coupled solution of temperature and pressure with the same decoupled equations. Then we study the contribution to the temperature by convection, the effect of the non-constant water density, and some anisotropic case examples.     

求解地下水非稳定流问题的局部坐标有限分析法

给出了一种求解地下水非稳定流方程的局部坐标有限分析法，证明了格式的稳定性。用该格式计算了两个典型问题，表明该方法有较高的计算精度，并能运用几何形状较复杂的渗流问题的计算。     

Coupled discrete element and finite volume solution of two classical soil mechanics problems

One dimensional solutions for the classic critical upward seepage gradient/quick condition and the time rate of consolidation problems are obtained using coupled routines for the finite volume method (FVM) and discrete element method (DEM), and the results compared with the analytical solutions. The two phase flow in a system composed of fluid and solid is simulated with the fluid phase modeled by solving the averaged Navier–Stokes equation using the FVM and the solid phase is modeled using the DEM. A framework is described for the coupling of two open source computer codes: YADE-OpenDEM for the discrete element method and OpenFOAM for the computational fluid dynamics. The particle–fluid interaction is quantified using a semi-empirical relationship proposed by Ergun [12]. The two classical verification problems are used to explore issues encountered when using coupled flow DEM codes, namely, the appropriate time step size for both the fluid and mechanical solution processes, the choice of the viscous damping coefficient, and the number of solid particles per finite fluid volume.     

Multiphysics modelling of backfill grouting in sandy soils during TBM tunnelling

Acta Geotechnica - During the tunnel boring machine-based tunnelling, the grout loss caused by the grout penetration and filtration in sandy soils is a complicated multiphysics process. In this...     

对滑坡防治工程相关规范中渗流问题的研究

渗流对滑坡稳定性至关重要,在松散堆积层滑坡稳定性评价中如何正确反映渗透力的作用是岩土工程界近年来讨论的热点。目前涉及滑坡防治工程的有关国家规范已经考虑渗流的影响,但在渗透力的重复计算上存在突出的问题,一些重要的概念和原理亟待从源头上进行澄清。文中以流体力学的基本理论为依据,从渗透力概念定义的微观源头上,证明了渗透力是一种等效力。在非压缩流体条件下,无论稳定流还是非稳定渗流,渗透力与浮力的共同作用效果与周边孔隙水压力是完全等效的。针对滑坡渗流模型,从宏观上再次证明了上述等效性原理,且表明在流网比较简单的条件下,采用渗透力计算比较简便,论证了更为严格的条件下条分法的下滑力中应考虑渗透力和浮力的影响。在此基础上,对现有规范的稳定性评价和滑坡推力计算方法进行了修正,定性和定量地评价了现行规范评价方法的偏差对滑坡设计推力和工程造价影响的程度。实际算例表明,现行规范的设计推力偏大5 %以内,主体工程造价偏大幅度基本与此相当,并略低。     

悬臂支护桩变形计算方法探讨

指出了悬臂支护桩变形计算方法现行有关规范[ 1 , 2]的欠妥之处, 提出了幂级数精确解法和在现行规范基础上的简化计算方法。 经与工程实测结果对比, 现行规范计算方法计算值比实测值小约 20%, 而作者提出的两种计算方法较为合理。     

尾矿连续沉积过程中超孔隙水压力演化的温度-渗流-力学-化学耦合模型

尾矿胶结充填技术可避免矿渣的地表堆存、改善采场围岩稳定性、提高矿石回采率,因此在国内外的矿山开采中得到了广泛应用。充填系统的稳定性取决于尾矿连续充填过程中多场耦合作用造成的孔隙水压力演化。本研究基于经典Biot孔隙弹性理论建立尾矿的温度-渗流-力学-化学耦合模型框架,进而提出连续沉积过程中尾矿热-化学固结的一维超压模型,并推导化学反应造成水压变化的临界温度闭合公式。通过分析不同沉积速率、不同初始和边界温度条件下的充填过程,揭示了多场耦合作用对尾矿超孔隙水压力的影响机理。