Parallel Krylov methods and the application to 3-d simulations of a triphasic porous media model in soil mechanics

We introduce a general parallel model for solving coupled nonlinear and time-dependent problems in soil mechanics, where we employ general purpose linear solvers with specially adjusted preconditioners. In particular, we present a parallel realization of the GMRES method applied to a triphasic porous media model in soil mechanics, where we compute the deformation of unsaturated soil together with the pore-fluid flow of water and air in the soil. Therefore, we propose a pointwise preconditioner coupling all unknowns at the nodal points. In two large-scale numerical experiments we finally present an extended evaluation of our parallel model for demanding configurations of the triphasic model.     

非饱和地基中Love波的传播特性

基于非饱和多孔介质的波动方程,考虑了土中水,气体与土骨架之间的粘性耦合作用,建立了弹性半空间上非饱和土层中Love波的弥散方程。首先分析了饱和度与频率对非饱和孔隙介质中剪切波速的影响。然后运用数值方法得到了不同饱和度下土层中多种Love模态波的弥散特性和位移分布情况,并用图表的形式给出。数值计算结果表明,上覆非饱和土层中Love波的传播速度和衰减系数不仅具有频散性,而且与土层的饱和度有关。在不同饱和度时的高模态(n≥2)的Love波的截止频率值不同。此外,讨论了饱和度对Love波水平位移幅值的影响。     

Strain localization in a solid‐water‐air system with random heterogeneity via stabilized mixed finite elements

Unsaturated soils are solid‐water‐air systems that include a solid skeleton, pore water, and pore air. Heterogeneities in porosity or degree of saturation are salient features of unsaturated soils. These heterogeneities may trigger localized deformation (eg, shear banding) in such materials as demonstrated by numerical simulations via a pseudo three‐phase model. In this article, we formulate a true three‐phase mathematical framework implemented via stabilized low‐order mixed finite elements. With this mathematical framework, we study the evolution of pore air pressure and its role in the inception of strain localization triggered by initial heterogeneity either in porosity or suction. The numerical simulations show that pore air pressure is nonzero and nonuniform in the process of progressive failure in unsaturated soils. The heterogeneity of pore air pressure may also play a significant role in the onset of localized deformation of unsaturated soils. Therefore, a three‐phase model considering the pore air phase is physically more appropriate for modeling strain localization in unsaturated soils.     

A fully coupled finite element analysis of water‐table fluctuation and land deformation in partially saturated soils due to surface loading

A fully coupled numerical model is presented for the water‐table fluctuation and land deformation in partially saturated soils due to surface loading. This numerical model is developed based on the poroelastic governing equations for groundwater flow in deforming variably saturated porous media and the Galerkin finite element method. The numerical model is verified and validated against a one‐dimensional consolidation problem concerning surface loading on a soil column which has six different initial water‐table elevations. The numerical model is then applied to a two‐dimensional consolidation problem of surface loading on a partially saturated soil at a construction site. Results from the numerical simulations of both problems show that the water table fluctuates in the partially saturated soils, and the unsaturated zone above the water table has significant effects on the consolidation behaviour of the partially saturated soils under surface loading. Such effects are caused by the permanent absorption of a portion of the mechanical loading stress and the weak hydromechanical coupling between the solid skeleton deformation field and the groundwater flow field in the unsaturated zone due to its partial saturation. Copyright © 2000 John Wiley & Sons, Ltd.     

多相非饱和多重孔隙介质的有效应力定律

多孔介质的有效应力定律广泛应用于流固耦合变形分析问题。该文考虑孔隙的重数、孔隙流体的相数、各向异性、非饱和、基质吸力等条件,提出了广义多相非饱和多重孔隙介质的有效应力定律。在固体相及各流体相线弹性变形的假设下,首先通过应力状态分解、边界条件叠加方法,得到了不考虑基质吸力的多相等效饱和各向异性多重孔隙介质的有效应力。考虑到非饱和多孔介质中两相界面张力引起的基质吸力,在线弹性变形基础上,叠加了基质吸力引起的变形部分,推导得到非饱和多孔介质的有效应力定律的一般形式。将所得公式根据实际需要进行简化处理,可以得到目前常用的有效应力定律的表达形式,充分说明了该文所得结论的合理性。     

An effective stress based numerical model for hydro-mechanical analysis in unsaturated porous media

 A fully coupled flow-deformation model is presented for the behaviour of unsaturated porous media. The governing equations are derived based on the equations of equilibrium, effective stress concept, Darcy's law, Henry's law, and the conservation of fluid mass. Macroscopic coupling between the flow and deformation fields is established through the effective stress parameters. The microscopic link between the volumetric deformations of the two pore system (i.e. the pore-air and the pore-water) is established using Betti's reciprocal theorem. Both links are essential for a proper modelling of flow and deformation in unsaturated porous media. The discretised form of the governing equations is obtained using the finite element technique. As application of the model, experimental results from several laboratory tests reported in the literature are modelled numerically. Good agreement is obtained between the numerical and the experimental results in all cases.     

An efficient finite element procedure for analyzing three‐phase porous media based on the relaxed Picard method

Effective simulation of the solid‐liquid‐gas coupling effect in unsaturated porous media is of great significance in many diverse areas. Because of the strongly nonlinear characteristics of the fully coupled formulations for the three‐phase porous media, an effective numerical solution scheme, such as the finite element method with an efficient iterative algorithm, has to be employed. In this paper, an efficient finite element procedure based on the adaptive relaxed Picard method is developed for analyzing the coupled solid‐liquid‐gas interactions in porous media. The coupled model and the finite element analysis procedure are implemented into a computer code PorousH2M, and the proposed procedure is validated through comparing the numerical simulations with the experimental benchmarks. It is shown that the adaptive relaxed Picard method has salient advantage over the traditional one with respect to both the efficiency and the robustness, especially for the case of relatively large time step sizes. Compared with the Newton‐Raphson scheme, the Picard method successfully avoids the unphysical ‘spurious unloading’ phenomenon under the plastic deformation condition, although the latter shows a better convergence rate. The proposed procedure provides an important reference for analyzing the fully coupled problems related to the multi‐phase, multi‐field coupling in porous media. Copyright © 2014 John Wiley & Sons, Ltd.     

A hierarchical sequential ALE poromechanics model for tire‐soil‐water interaction on fluid‐infiltrated roads

This paper introduces a hierarchical sequential arbitrary Lagrangian‐Eulerian (ALE) model for predicting the tire‐soil‐water interaction at finite deformations. Using the ALE framework, the interaction between a rolling pneumatic tire and the fluid‐infiltrated soil underneath will be captured numerically. The road is assumed to be a fully saturated two‐phase porous medium. The constitutive response of the tire and the solid skeleton of the porous medium is idealized as hyperelastic. Meanwhile, the interaction between tire, soil, and water will be simulated via a hierarchical operator‐split algorithm. A salient feature of the proposed framework is the steady state rolling framework. While the finite element mesh of the soil is fixed to a reference frame and moves with the tire, the solid and fluid constituents of the soil are flowing through the mesh in the ALE model according to the rolling speed of the tire. This treatment leads to an elegant and computationally efficient formulation to investigate the tire‐soil‐water interaction both close to the contact and in the far field. The presented ALE model for tire‐soil‐water interaction provides the essential basis for future applications, for example, to a path‐dependent frictional‐cohesive response of the consolidating soil and unsaturated soil, respectively. Copyright © 2017 John Wiley & Sons, Ltd.     

Fully coupled hydromechanical multiscale model with microdynamic effects

In this paper, a multiscale finite element framework is developed based on the first‐order homogenization method for fully coupled saturated porous media using an extension of the Hill‐Mandel theory in the presence of microdynamic effects. The multiscale method is employed for the consolidation problem of a 2‐dimensional saturated soil medium generated from the periodic arrangement of circular particles embedded in a square matrix, which is compared with the direct numerical simulation method. The effects of various issues, including the boundary conditions, size effects, particle arrangements, and the integral domain constraints for the microscale boundary value problem, are numerically investigated to illustrate the performance of a representative volume element in the proposed computational homogenization method of fully coupled saturated porous media. This study is aimed to clarify the effect of scale separation and size dependence, and to introduce characteristics of a proper representative volume element in multiscale modeling of saturated porous media.     

隧道水平冻结施工过程的数值模拟

地层冻结是一个水、热、力三场耦合的复杂问题,为了直观了解冻结壁形成过程中,土体温度场分布极其随时间的变化规律,得到合适的地层冻结工艺参数和指标,并掌握冻结壁的力学特性,了解开挖隧道对土层稳定性的影响,保证工程的安全,针对某隧道工程,采用准耦合数值分析方法,对其水平冻结施工过程进行了数值模拟,研究表明:地层冻结加固有效地控制了地层和地表的变形,提高了隧道土体的稳定性。计算结果可供类似工程参考,并提供了一种概念清晰、计算简便、实用的水平冻结施工过程的数值模拟方法。     

复杂地层中自升式平台插桩的数值模拟

以胜利9号平台在老174号井位插桩过程为例,基于RITSS大变形数值计算方法,建立了自升式平台桩靴贯入多层地基的有限元模型,研究该平台插桩过程中的土体变形以及地基承载力随深度的变化规律。与SNAME（美国造船与轮机工程师学会）规范推荐的桩靴插桩过程地基承载力公式的计算结果进行对比,规范结果与数值结果的规律较为一致,数值上相差10%,验证了RITSS方法研究桩靴在软硬相间地基上插桩的有效性。结果表明:RITSS数模方法可以有效地模拟自升式平台插桩过程中各个土层的变形、土体流动,并得到合理的地基承载力结果;对于砂土层下卧软土层地基,可以得到承载力峰值。     

Centrifuge modeling of air sparging - a study of air flow through saturated porous media

The success of air sparging as a remedial technology for treatment of contaminated aquifers is well documented. However, there is no consensus, to date, on the mechanisms that control the flow of injected air through the saturated ground. Currently, only qualitative results from laboratory experiments are available to predict the zone of influence of a sparging well. Given that the patterns of air flow through the soil will ultimately determine the efficiency of an air sparging treatment, it is important to quantify how sparged air travels through a saturated porous medium. The main objective of this research is to develop a model that describes air transport through saturated porous media. This paper presents results from an ongoing study that employs centrifuge modeling to reproduce in situ air sparging conditions. Centrifuge testing is an experimental technique that allows reduced-scale duplication, in the laboratory, of the stresses and pressure distributions encountered in the field. In situ conditions are critical in the development of actual air flow patterns. Experiments are being conducted in a transparent porous medium consisting of crushed borosilicate glass submerged in fluids of matching indices of refraction. Air is observed as it flows through the porous medium at varying gravitational accelerations. Recorded images of experiments allow the determination of flow patterns, breakthrough velocities, and plume shapes as a function of g-level and injection pressure. Results show that air flow patterns vary from fingering, at low g-levels, to pulsing at higher accelerations. Grain and pore size distribution of the porous medium do not exclusively control air flow characteristics. Injector geometry has a definite effect on breakthrough velocities and air plume shapes. Experiments have been conducted to compare the velocity of air flow through the saturated porous medium to that of air in pure liquids. Results show that the velocity of air through the medium is lower than that in the pure fluid, as expected. At high g-levels however, plume breakthrough velocities are proportional to the velocity of the air in the pure fluid.     

基于扰动变量的非饱和原状土本构模型

该文根据复合材料均匀化理论的思想建立了考虑水的滞后性与应力-应变特性相祸合的非饱和原状土本构模型。复合材料均匀化理论的主要思想是将变形的岩土材料视为由相对完整状态土（RISP）和完全调整状态土（FASP）混合而成的复合材料，RISP和FASP的力学性能分别与原状土和重塑土的力学性能相同。另外，在土体的变形过程中，RIS...     

Steady-state flow of compressible rigid–viscoplastic media

Computational methods for modeling steady-state flow of compressible rigid viscoplastic fluids are proposed. The constitutive equation used captures the combined effects of high-strain rate and high-pressure on the behavior of porous materials.A mixed finite-element and finite-volume strategy is developed. Specifically, the variational inequality for the velocity field is discretized using the finite element method and a finite volume method is adopted for the hyperbolic mass conservation equation. To solve the velocity problem a decomposition–coordination formulation coupled with the augmented lagrangian method is used. This approach is accurate in detecting the viscoplastic regions and permit us to handle the locking medium condition.The proposed numerical method is then applied to model the penetration of a rigid projectile into cementitious targets. The numerical model accurately describes the density changes around the projectile, the stress field, as well as the shape and location of the deformation zone (viscoplastic region) in the target.     

Study on in-situ test on mechanical properties of the particle improved roadbed in permafrost

The adoption of particle improved roadbed (PIR) is one of the proactive measures to protect permafrost from warming and thawing in cold regions. The field plate loading test was performed to study the mechanical parameters of fillings after a freeze–thaw cycle, including bearing capacity, modulus of deformation, etc. In addition, the deformation features of the roadbed fillings were analyzed and discussed. The results indicated that the allowable bearing capacity of the roadbed fillings was 418.78 kPa, and the deformation modulus and shear modulus decreased with the increase of the loads. It is reasonable to consider the roadbed fillings as a three-dimensional elastic continuous medium to establish a model to study deformation of permafrost. The calculated deformation agreed well with the measured. Therefore, the model can provide reference for the deformation predication of other roadbed fillings in permafrost.     

饱和两相介质近场波动问题的一种时域全显式数值计算方法

基于 u -p形式的饱和两相介质弹性波动方程,开展了饱和两相介质近场波动问题时域显式数值计算方法的研究。通过对波动方程中的质量矩阵和孔隙流体压缩矩阵进行对角化处理,消除了方程中的动力耦联,实现了波动方程的解耦。分别应用中心差分法和Newmark常平均加速度法求解固相位移和速度,基于向后差分法求解孔隙流体压力,推导得到了饱和两相介质动力响应的时域显式逐步积分的计算列式,建立了饱和两相介质近场波动问题的一种新的时域全显式数值计算方法。进行了该文方法中矩阵对角化合理性的验证。将该方法的数值解与相应的解析解进行对比,二者符合良好,验证了该方法的正确性。将该文建立的时域数值计算方法与透射人工边界方法相结合,应用于饱和两相介质的近场波动问题,进行了饱和土场地地震响应的计算研究,计算结果符合弹性波动理论的基本规律,表明该方法对于饱和两相介质近场波动问题时域计算求解的适用性。基于该方法中时域递推计算格式的传递矩阵,进行了该方法稳定性特性的研究。该文建立的数值计算方法具有时域全显式算法的基本特征。方法中对动力响应的全部分量均采用递推和迭代的模式进行求解,避免了求解耦联的动力方程组。该方法具有较高的计算效率,是进行饱和两相介质近场波动问题时域计算求解的一种有效的算法。     

一种基于应变插值大变形梁单元的刚-柔耦合动力学分析

柔性多体系统动力学中的“动力刚化”现象起因于变形间的耦合。一次近似模型成功地解决了小变形情况下的刚柔耦合建模问题,但在大变形情况下则需要考虑更多的耦合效应。本文选取表征梁弯曲应变的曲率和轴向应变作为单元参数进行离散;在大变形大转动基础上得到了单元两端节点运动学参数的递推关系,构造出了能够自动计及“动力刚化项”且适用于大变形刚柔耦合动力学分析的平面梁单元。最后采用本文所提应变插值单元求解了包含大变形和刚柔耦合动力学柔性梁的数值算例,验证了文中算法的正确性和有效性。     

基于格子Boltzmann方法非饱和土体水热耦合模型研究

考虑热源作用下非饱和土体水热耦合作用机制,基于格子Boltzmann方法,采用双分布函数分别描述温度场及水分场的演化过程,建立了相应的水热耦合模型。同时,编制了计算程序,并结合半无限空间的水热耦合算例,验证了该计算模型的正确性。最后考虑水热耦合作用模式、热源温度以及土体孔隙率等因素的影响,讨论了非饱和土体温度场及水分场的演化规律。研究结果表明:传统的单向耦合模式无法表征水分迁移对土体导热特性的影响,从而导致温度场的演化规律有所偏差,而所提出的双向耦合模式更具合理性。在恒温热源作用下,不同热源温度对土体温度场及水分场的演化均会产生较大影响,且在非饱和土体温度升高速率较快的位置,体积含水率也相应的变化较快。在相同热源作用下,当初始体积含水率一定时,孔隙率较小的土体,温度升高速度较快,但总体差别不大,从而使得体积含水率分布也较为接近。     

Some results of mathematical simulation of the process of peat ignition

A formulation and numerical solution of the problem about peat layer ignition as a result of the action of a creeping fire bed are proposed based on a mathematical model of a porous reactive medium. Ignition of the initial reagent is shown to be determined by processes of drying, peat pyrolysis, oxidation of carbon oxide, and moisture content. The results of the numerical solution are compared with experimental data, and an estimate of the mass content of combustion products contaminating the atmosphere is presented.     

A coupling extended multiscale finite element method for dynamic analysis of heterogeneous saturated porous media

A coupling extended multiscale finite element method (CEMsFEM) is developed for the dynamic analysis of heterogeneous saturated porous media. The coupling numerical base functions are constructed by a unified method with an equivalent stiffness matrix. To improve the computational accuracy, an additional coupling term that could reflect the interaction of the deformations among different directions is introduced into the numerical base functions. In addition, a kind of multi‐node coarse element is adopted to describe the complex high‐order deformation on the boundary of the coarse element for the two‐dimensional dynamic problem. The coarse element tests show that the coupling numerical base functions could not only take account of the interaction of the solid skeleton and the pore fluid but also consider the effect of the inertial force in the dynamic problems. On the other hand, based on the static balance condition of the coarse element, an improved downscaling technique is proposed to directly obtain the satisfying microscopic solutions in the CEMsFEM. Both one‐dimensional and two‐dimensional numerical examples of the heterogeneous saturated porous media are carried out, and the results verify the validity and the efficiency of the CEMsFEM by comparing with the conventional finite element method. Copyright © 2015 John Wiley & Sons, Ltd.