Parallel finite element modeling of earthquake ground response and liquefaction

Parallel computing is a promising approach to alleviate the computational demand in conducting large-scale finite element analyses. This paper presents a numerical modeling approach for earthquake ground response and liquefaction using the parallel nonlinear finite element program, ParCYCLIC, designed for distributed-memory message-passing parallel computer systems. In ParCYCL1C, finite elements are employed within an incremental plasticity, coupled solid-fluid formulation. A constitutive model calibrated by physical tests represents the salient characteristics of sand liquefaction and associated accumulation of shear deformations. Key elements of the computational strategy employed in ParCYCL1C include the development of a parallel sparse direct solver, the deployment of an automatic domain decomposer, and the use of the Multilevel Nested Dissection algorithm for ordering of the finite element nodes. Simulation results of centrifuge test models using ParCYCLIC are presented. Performance results from grid models and geotechnical simulations show that ParCYCLIC is efficiently scalable to a large number of processors.     

A SANISAND model with anisotropic elasticity

Numerous experimental studies indicate that as a result of shear stress, the elastic behavior of granular media becomes both non-linear and anisotropic. This paper presents a simple constitutive model for sands with respect to anisotropic elasticity. To this aim, using the concept of second order fabric tensor, a simplified elasticity theory is presented which is capable of considering the effect of induced anisotropy on the elastic response. SANISAND is the name used for a family of simple anisotropic sand models developed in the framework of critical state soil mechanics and bounding surface plasticity. An existing SANISAND model is modified in order to include the proposed anisotropic elasticity. The modified model simulations are compared with those obtained from the other members of this family. It is shown that considering anisotropic elasticity can take part in explanation of drastic loss of mean principal stress when sand is subjected to reverse loading in dilative branch of behavior and as a result, improve the liquefaction simulations.     

Layered convection with an interface at a depth of 1000 km: stability and generation of slab-like downwellings

We investigate the stability of hypothetical layered convection in the mantle and the mechanisms how the downwelling structures originating in the lower layer are generated. The stability is studied by means of numerical simulations of the double-diffusive convection in a 2D spherical model with radially dependent viscosity. We demonstrate that the stability of the layering strongly depends not only on the density contrast between the layers but also on the heating mode and the viscosity profile. In the case of the classical Boussinesq model with an internally heated lower layer, the density contrast of about 4% between the compositionally different materials is needed for the layered flow to be maintained. The inclusion of the adiabatic heating/cooling in the model reduces the temperature contrast between the two layers and, thus, enhances the stability of the layering. In this case, a density contrast of 2-3% is sufficient to preserve the layered convection on a time scale of billions of years. The generation of the downwelling structures in the lower layer occurs via mechanical or thermal coupling scenarios. If the viscosity dependent on depth and average temperature at each depth is considered, the low viscosity zone develops at a boundary between the two convecting layers which suppresses mechanical coupling. Then the downwelling structures originating in the lower layer develop beneath upper layer subductions, thus resembling continuous slab-like structures observed by seismic tomography.     

On the transport of moisture in polythermal glaciers

Abstract

We reconsider the problem of formulation of a model for polythermal glaciers, focussing attention in particular on the temperate zone where ice and water can coexist at the melting temperature. The energy equation for the ice-water mixture in this zone introduces a moisture flux, and a constitutive law for this flux is required. By analogy with the flow through a porous medium, we use Darcy's law (i.e. the second momentum equation of a two-phase flow model with “porous” geometry), and then require a mechanical constitutive relation relating the water pressure p _w to the average ice pressure p _i . Experience in two phase flows suggests that p _w =p _i may be problematical, and experience in soil mechanics suggests it is inaccurate. A constitutive relation is therefore presented based on work of Nye (1976), and its effect on the well-posedness of the model is examined. Considerations of the sort presented here have clear relevance in the formulation of similar problems in other geophysical situations, notably mantle convection.     

A displacement finite element modelling for convection-diffusion problems

The development of a displacement finite element formulation and its application to convective transport problems is presented. The formulation is based on the introduction of a generalized quantity defined as transport displacement. The governing equation is expressed in terms of this quantity and by using generalized coordinates a variational form of the governing equation is obtained. This equation may be solved by any numerical method, though it is of particular interest for application of the finite element method. Two finite element models are derived for the solution of convection-diffusion boundary value problems. The performance of the two element models is discussed and numerical results are given for different cases of convection and diffusion with two types of boundary conditions. The numerical results obtained show not only the efficiency of the numerical models in handling pure convection, pure diffusion and mixed convection-diffusion problems, but also good stability and accuracy. The applications of the developed numerical models are not limited to diffusion-convection problems but can also be applied to other types of problems such as mass transfer, hydrodynamics and wave propagation.     

A heuristic framework for next-generation models of geostrophic convective turbulence

Many geophysical and astrophysical phenomena are driven by turbulent fluid dynamics, containing behaviors separated by tens of orders of magnitude in scale. While direct simulations have made large strides toward understanding geophysical systems, such models still inhabit modest ranges of the governing parameters that are difficult to extrapolate to planetary settings. The canonical problem of rotating Rayleigh-Bénard convection provides an alternate approach - isolating the fundamental physics in a reduced setting. Theoretical studies and asymptotically-reduced simulations in rotating convection have unveiled a variety of flow behaviors likely relevant to natural systems, but still inaccessible to direct simulation. In lieu of this, several new large-scale rotating convection devices have been designed to characterize such behaviors. It is essential to predict how this potential influx of new data will mesh with existing results. Surprisingly, a coherent framework of predictions for extreme rotating convection has not yet been elucidated. In this study, we combine asymptotic predictions, laboratory and numerical results, and experimental constraints to build a heuristic framework for cross-comparison between a broad range of rotating convection studies. We categorize the diverse field of existing predictions in the context of asymptotic flow regimes. We then consider the physical constraints that determine the points of intersection between flow behavior predictions and experimental accessibility. Applying this framework to several upcoming devices demonstrates that laboratory studies may soon be able to characterize geophysically-relevant flow regimes. These new data may transform our understanding of geophysical and astrophysical turbulence, and the conceptual framework developed herein should provide the theoretical infrastructure needed for meaningful discussion of these results.     

Coupled Process Models of Fluid Flow and Heat Transfer in Hydrothermal Systems in Three Dimensions

Geothermal fields and hydrothermal mineral deposits are manifestations of the interaction between heat transfer and fluid flow in the Earth’s crust. Understanding the factors that drive fluid flow is essential for managing geothermal energy production and for understanding the genesis of hydrothermal mineral systems. We provide an overview of fluid flow drivers with a focus on flow driven by heat and hydraulic head. We show how numerical simulations can be used to compare the effect of different flow drivers on hydrothermal mineralisation. We explore the concepts of laminar flow in porous media (Darcy’s law) and the non-dimensional Rayleigh number (Ra) for free thermal convection in the context of fluid flow in hydrothermal systems in three dimensions. We compare models of free thermal convection to hydraulic head driven flow in relation to hydrothermal copper mineralisation at Mount Isa, Australia. Free thermal convection occurs if the permeability of the fault system results in Ra above the critical threshold, whereas a vertical head gradient results in an upward flow field.     

Variable-density flow and transport in porous media: approaches and challenges

We review the state of the art in modeling of variable-density flow and transport in porous media, including conceptual models for convection systems, governing balance equations, phenomenological laws, constitutive relations for fluid density and viscosity, and numerical methods for solving the resulting nonlinear multifield problems. The discussion of numerical methods addresses strategies for solving the coupled spatio-temporal convection process, consistent velocity approximation, and error-based mesh adaptation techniques. As numerical models for those nonlinear systems must be carefully verified in appropriate tests, we discuss weaknesses and inconsistencies of current model-verification methods as well as benchmark solutions. We give examples of field-related applications to illustrate specific challenges of further research, where heterogeneities and large scales are important.     

地磁扰动期间等离子体层顶结构的模拟研究

本文选取2001年6月8-10日的一个亚暴事件,模拟了在这期间等离子体层的结构演化过程.选取Weimer(2001模式)电场和Tsyganenko(1996模式)磁场作为背景电磁场,基于E×B的漂移运动计算磁赤道面内的带电粒子分布,模拟磁扰期间的等离子体层变化.模拟了等离子体层顶的结构和形状,结果有羽状、肩状和通道状结构,与同一时间点的EUV/IMAGE探测结果一致.     

Observing Convective Aggregation

Convective self-aggregation, the spontaneous organization of initially scattered convection into isolated convective clusters despite spatially homogeneous boundary conditions and forcing, was first recognized and studied in idealized numerical simulations. While there is a rich history of observational work on convective clustering and organization, there have been only a few studies that have analyzed observations to look specifically for processes related to self-aggregation in models. Here we review observational work in both of these categories and motivate the need for more of this work. We acknowledge that self-aggregation may appear to be far-removed from observed convective organization in terms of time scales, initial conditions, initiation processes, and mean state extremes, but we argue that these differences vary greatly across the diverse range of model simulations in the literature and that these comparisons are already offering important insights into real tropical phenomena. Some preliminary new findings are presented, including results showing that a self-aggregation simulation with square geometry has too broad distribution of humidity and is too dry in the driest regions when compared with radiosonde records from Nauru, while an elongated channel simulation has realistic representations of atmospheric humidity and its variability. We discuss recent work increasing our understanding of how organized convection and climate change may interact, and how model discrepancies related to this question are prompting interest in observational comparisons. We also propose possible future directions for observational work related to convective aggregation, including novel satellite approaches and a ground-based observational network.     

Complex-parameter kelvin model for elastic foundations

A new rigorous approach in modelling mechanical behaviour is developed. The dynamic response of a rigid disc resting on an elastic half-space is approximated by a macroscopic force-displacement relationship, where not only the coefficients but also the order of time derivatives are complex valued. It is shown that comlex-parameter constitutive models are not simply an elegant alternative in modelling mechanical behaviour, but are the outcome of rigorous non-linear regression analysis on complex-valued functions, like the dynamic stiffness of dissipative systems. Complex-parameter constitutive models are very attractive since a minimum number of parameters is required to obtain a satisfactory fit of the ‘exact’ response. A two-parameter generalized Kelvin model reproduces closely the ‘exact’ dynamic stiffness of the disc for all three vertical, horizontal and rocking modes studied herein. Frequency- and time-domain algorithms to solve complex-order differential equations are developed, validated and used to calculate the foundation–response under earthquake excitation. It is the excellent agreement of results and the economy in number of parameters that make complex-parameter models so attractive in constitutive modelling.     

Impact of fracture network geometry on free convective flow patterns

The effect of fracture network geometry on free convection in fractured rock is studied using numerical simulations. We examine the structural properties of fracture networks that control the onset and strength of free convection and the patterns of density-dependent flow. Applicability of the equivalent porous medium approach (EPM) is also tested, and recommendations are given, for which situations the EPM approach is valid. To date, the structural properties of fracture networks that determine free convective flow are examined only in few, predominantly simplified regular fracture networks. We consider fracture networks containing continuous, discontinuous, orthogonal and/or inclined discrete fractures embedded in a low-permeability rock matrix. The results indicate that bulk permeability is not adequate to infer the occurrence and magnitude of free convection in fractured rock. Fracture networks can inhibit or promote convection depending on the fracture network geometry. Continuous fracture circuits are the crucial geometrical feature of fracture networks, because large continuous fracture circuits with a large vertical extent promote convection. The likelihood of continuous fracture circuits and thus of free convection increases with increasing fracture density and fracture length, but individual fracture locations may result in great deviances in strength of convection between statistically equivalent fracture networks such that prediction remains subject to large uncertainty.     

Dynamic response of an elastic-viscoplastic system in modal co-ordinates

A dynamic analysis of elastic–viscoplastic systems, incorporating the modal co-ordinate transformation technique, is presented. The formulation results in uncoupled incremental equations of motion with respect to the modal co-ordinates. The elastic–viscoplastic model adopted allows the analysis not to involve yielding regions and loading/unloading processes. An implicit Runge–Kutta scheme together with the Newton–Raphson method are used to solve the non-linear constitutive equations. Stability and accuracy of the numerical solution are improved by utilizing a local time step sub-incrementing procedure. Applications of the analyses to multi-storey shear buildings show that good results can be obtained for the maximum displacement response by including only a few lower modes in the computation, but the prediction of the ductility factor response tends to underestimate the peak values when too few modes are used. In addition, stable and valid results can be obtained even with a sizable time step increment.     

含不同弹性模量包体复合模型中的应力及其变化

用光弹性法分别研究了一组含软包体,等模量包体,及硬包体的复合模型中的应力及其变化,结果表明,在硬包体中的应力更高,硬包体的存在的乃是复合模型中形成和积累高应力区的结构构成条件,从而为坚固体孕震模式的力学机制研究提供了基本的实验依据。     

Numerical modelling of bifurcation and localisation in cohesive-frictional materials

Methods are reviewed for analysing highly localised failure and bifurcation modes in discretised mechanical systems as typically arise in numerical simulations of failure in soils, rocks, metals and concrete. By the example of a plane-strain biaxial test it is shown that strain softening and lack of normality in elasto-plastic constitutive equations and the ensuing loss of ellipticity of the governing field equations cause a pathological mesh dependence of numerical solutions for such problems, thus rendering the results effectively meaningless. The need for introduction of higher-order continuum models is emphasised to remedy this shortcoming of the conventional approach. For one such a continuum model, namely the unconstrained Cosserat continuum, it is demonstrated that meaningful and convergent solutions (in the sense that a finite width of the localisation zone is computed upon mesh refinement) can be obtained.     

Testing Hypotheses for the Mount Isa Copper Mineralisation with Numerical Simulations

We have applied reactive transport simulations to evaluate conceptual models of hydrothermal fluid flow related to the Mesoproterozoic Mount Isa copper mineralisation. Numerical experiments have been performed specifically to investigate whether fluid flow was driven by mechanical deformation, higher than hydrostatic fluid pressure gradients, or thermal buoyancy, and what the mechanism of ore deposition was. One distinct feature of the Mount Isa mineralising system is a region of massive silica-rich alteration that surrounds the copper ore bodies within the Urquhart shale, indicating upward flow of a cooling fluid. Hydromechanical modelling revealed that contraction and horizontal shear can produce a dilation pattern that favours upward fluid flow, whereas strike slip movement causes dilation of pre-existing vertical structures. Reactive transport models show that hydraulic head driven flow is more likely to produce a more realistic silica alteration pattern than free thermal convection, but neither process generates a flow pattern capable of precipitating copper at the appropriate location. Instead we propose that gravity driven flow of a dense oxidised basin brine led to chalcopyrite mineralisation by fluid-rock reaction.     

Variable-density groundwater flow and solute transport in porous media containing nonuniform discrete fractures

Variations in fluid density can greatly affect fluid flow and solute transport in the subsurface. Heterogeneities such as fractures play a major role for the migration of variable-density fluids. Earlier modeling studies of density effects in fractured media were restricted to orthogonal fracture networks, consisting of only vertical and horizontal fractures. The present study addresses the phenomenon of 3D variable-density flow and transport in fractured porous media, where fractures of an arbitrary incline can occur. A general formulation of the body force vector is derived, which accounts for variable-density flow and transport in fractures of any orientation. Simulation results are presented that show the verification of the new model formulation, for the porous matrix and for inclined fractures. Simulations of variable-density flow and solute transport are then conducted for a single fracture, embedded in a porous matrix. The simulations show that density-driven flow in the fracture causes convective flow within the porous matrix and that the high-permeability fracture acts as a barrier for convection. Other simulations were run to investigate the influence of fracture incline on plume migration. Finally, tabular data of the tracer breakthrough curve in the inclined fracture is given to facilitate the verification of other codes.     

Solar dynamo theory: a new look at the origin of small-scale magnetic fields

Fausto Cattaneo and David W Hughes delve beneath the surface of the Sun with numerical models of turbulent convection.
Although magnetic dynamo action is traditionally associated with rotation, fast dynamo theory shows that chaotic flows, even without rotation, can act as efficient small-scale dynamos. Indeed, numerical simulations suggest that granular and supergranular convection may generate locally a substantial part of the field in the quiet photosphere.     

Non-isothermal soil water transport and evaporation

A detailed model was formulated to describe the non-isothermal transport of water in the unsaturated soil zone. The model consists of the coupled equations of mass conservation for the liquid phase, gas phase and water vapor and the energy conservation equation. The water transport mechanisms considered are convection in the liquid phase, and convection, diffusion and dispersion of vapor in the gas phase. The boundary conditions at the soil–atmosphere interface include dynamical mass flux and energy flux that accounts for radiation transport. Comparison of numerical simulations results with published experimental data demonstrated that the present model is able to describe water and energy transport dynamics, including situations of low and moderate soil moisture contents. Analysis of field studies on soil drying suggests that that dispersion flux of the water vapor near the soil surface, which is seldom considered in soil drying models, can make a significant contribution to the total water flux.     

MR阻尼器对桅杆结构风振响应的智能半主动控制

本文基于修正的拉格朗日坐标描述法，推导了空间四节点纤绳单元的大位移刚度矩阵的具体表达式。在将桅杆结构离散为空间四节点纤绳单元和梁单元的计算模型的基础上，建立了桅杆结构非线性风振响应分析的有限元方法。根据瞬时最优主动控制的原则，提出了MR阻尼器对桅杆结构风振反应智能半主动控制基于阻尼器位移的“开关—耗能”半主动控制策略。算例结果表明MR阻尼器能有效地减小桅杆结构的风振反应。