Numerical Analysis of Space–Time Finite Element Formulations for Miscible Displacements

A finite element formulation is proposed to approximate a nonlinear system of partial differential equations, composed by an elliptic subsystem for the pressure–velocity and a transport equation (convection–diffusion) for the concentration, which models the incompressible miscible displacement of one fluid by another in a rigid porous media. The pressure is approximated by the classical Galerkin method and the velocity is calculated by a post-processing technique. Then, the concentration is obtained by a Galerkin/least-squares space–time (GLS/ST) finite element method. A numerical analysis is developed for the concentration approximation. Then, stability, convergence and numerical results are presented confirming the a priori error estimates.     

Numerical Analysis of Space–Time Finite Element Formulations for Miscible Displacements

A finite element formulation is proposed to approximate a nonlinear system of partial differential equations, composed by an elliptic subsystem for the pressure–velocity and a transport equation (convection–diffusion) for the concentration, which models the incompressible miscible displacement of one fluid by another in a rigid porous media. The pressure is approximated by the classical Galerkin method and the velocity is calculated by a post-processing technique. Then, the concentration is obtained by a Galerkin/least-squares space–time (GLS/ST) finite element method. A numerical analysis is developed for the concentration approximation. Then, stability, convergence and numerical results are presented confirming the a priori error estimates.     

Nucleation and growth of kink bands

The geometric and strain properties of an ideal kink band in a perfectly plastic material with one slip surface are determined and two plausible modes by which a kink band can grow while maintaining these properties are presented. The first mode involves change in the orientation of the boundary surface of the kink band as it broadens. In the second mode the initial orientation of this boundary surface is maintained during broadening.A theoretical model is proposed for kink band formation in three stages: first, in an elastically strained material with a suitably oriented planar anisotropy; a small nucleus is either present or develops, and grows in thickness by one or the other or by both of the growth modes; second, as some critical thickness is reached, this nucleus propagates longitudinally until the excessive elastic distortion surrounding its ends is sufficiently relieved, or until the boundary of the body is reached; and third, the band widens by lateral migration of its boundaries, most probably by mode 2 growth.It is proposed that the direction of longitudinal propagation—and hence the orientation of the kink band with respect to principal normal stress—is decided by the value of a, the kink angle, in the nucleus at the time the critical thickness for propagation is reached. A further proposal is that this value of a is in turn decided by a principle of maximum plastic work: the instantaneous increment in strain or in volume within a nucleus is always the one for which the instantaneous increment in plastic work is a maximum at constant deviatoric stress.Calculations based on this theory for the two growth modes working either separately or together as competing processes yield three models of kink band nucleation in reasonable agreement with published experimental data. The most appealing of these models physically is one in which early mode 1 growth is replaced by mode 2 growth as the increments in mechanical work for the two modes become equal.     

Generating large stochastic simulations—The matrix polynomial approximation method

An algorithm for producing a nonconditional simulation by multiplying the square root of the covariance matrix by a random vector is described. First, the square root of a matrix (or a function of a matrix in general) is defined. The square root of the matrix can be approximated by a minimax matrix polynomial. The block Toeplitz structure of the covariance matrix is used to minimize storage. Finally, multiplication of the block Toeplitz matrix by the random vector can be evaluated as a convolution using the fast Fourier transform. This results in an algorithm which is not only efficient in terms of storage and computation but also easy to implement.     

Temporal characteristics of the Indian southwest monsoon

In this study, we elucidate the temporal characteristics of the onset and withdrawal of the Indian southwest monsoon, making use of the model integration and daily analyses of the National Centre for Medium Range Weather Forecasting, India. The onset of the Indian southwest monsoon over the Bay of Bengal is discernable by a gradual increase in the adiabatic generation of kinetic energy, while over the Arabian Sea it is first noticeable by a steep and abrupt increase of generation. The horizontal transport of heat indicates a convergence regime over the Bay of Bengal prior to onset, while over the Arabian Sea a convergence regime is indicated by a change from the divergence to the convergence regime. The withdrawal of the southwest monsoon is characterized by the horizontal transport of heat and moisture that evince a transition from the convergence to divergence regime; similarly, diabatic heating noticed during the active period changes to cooling. The withdrawal over the Arabian Sea is characterized by the divergence regime of the horizontal transport of moisture. This change precedes even the circulation changes over northwest India, which may be regarded as a precursor. The withdrawal is further supported by a monotonic decrease in the net tropospheric moisture over the Arabian Sea, followed by a similar change at land locations.     

Probabilistic domain decomposition for the solution of the two-dimensional magnetotelluric problem

Probabilistic domain decomposition is proposed as a novel method for solving the two-dimensional Maxwell’s equations as used in the magnetotelluric method. The domain is split into non-overlapping sub-domains and the solution on the sub-domain boundaries is obtained by evaluating the stochastic form of the exact solution of Maxwell’s equations by a Monte-Carlo approach. These sub-domains can be naturally chosen by splitting the sub-surface domain into regions of constant (or at least continuous) conductivity. The solution over each sub-domain is obtained by solving Maxwell’s equations in the strong form. The sub-domain solver used for this purpose is a meshless method resting on radial basis function-based finite differences. The method is demonstrated by solving a number of classical magnetotelluric problems, including the quarter-space problem, the block-in-half-space problem and the triangle-in-half-space problem.     

Dynamic response of a thick plate on viscoelastic foundation to moving loads

A finite element algorithm is presented to evaluate the dynamic response of pavements including aircraft-guideway-foundation interaction. The pavement-foundation system is modeled by a series of thick plate elements supported by discrete springs and dashpots at the nodal points representing the viscoelastic foundation. The moving aircraft loads are represented by masses each supported by a spring and dashpot suspension system and having a specified horizontal velocity and acceleration. The accuracy of the algorithm is verified by comparing the finite element solution with available analytical results. A parametric study is conducted to determine the effects of various parameters on the dynamic response of pavements to moving loads.     

Origin and evolution processes of hybrid event beds in the Lower Cretaceous of the Lingshan Island,Eastern China

On the basis of detailed sedimentological investigation, three types of hybrid event beds (HEBs) together with debrites and turbidites were distinguished in the Lower Cretaceous sedimentary sequence on the Lingshan Island in the Yellow Sea, China. HEB 1, with a total thickness of 63–80 cm and internal bipartite structures, is characterised by a basal massive sandstone sharply overlain by a muddy sandstone interval. It is interpreted to have been formed by particle rearrangement at the base of cohesive debris flows. HEB 2, with a total thickness of 10–71 cm and an internal tripartite structure, is characterised by a normal grading sandstone base, followed by muddy siltstone middle unit and capped with siltstones; the top unit of HEB 2 may in places be partly or completely eroded. The boundary between the lowest unit and the middle unit is gradual, whereas that between the middle unit and the top unit is sharp. HEB 2 may be developed by up-dip muddy substrate erosion. HEB 3, with a total thickness up to 10 cm and an internal bipartite structure, is characterised by a basal massive sandstone sharply overlain by a muddy siltstone interval. The upper unit was probably deposited by cohesive debris flow with some plant fragments and rare mud clasts. HEB 3 may be formed by the deceleration of low-density turbidity currents. The distribution of HEBs together with debrites and turbidites implies a continuous evolution process of sediment gravity flows: debris flow → hybrid flow caused by particle rearrangement → high-density turbidity current → hybrid flow caused by muddy substrate erosion → low-density turbidity current → hybrid flow caused by deceleration.     

Arcuate hinge cleavage associated with welded contacts: an example

Arcuate hinge cleavage (a.h.c.) shows a near bedding-parallel, concentric, arcuate development within the inner arcs of hinge zones. It is favoured by alternating layers of marked viscosity contrasts with little layer-parallel shortening prior to parallel folding. A field example of a.h.c. from a greywacke/pelite sequence of the Variscan of Central Europe is presented. The a.h.c. is developed as a slaty cleavage in the inner-arc hinge zones of pelite beds close to and welded to the outer arc of greywacke layers. Microscopically it is defined by the alignment of platy minerals and oblate quartz grains. The a.h.c. (S_a) is cut by a divergently fanning crenulation cleavage (S_b) which, in turn, is cut by slip surfaces parallel to bedding. The slip surfaces are cut by a fracture cleavage which is the macroscopically observed axial surface cleavage (S_c). This sequence of deformational increments implies the onset of bedding slip after the formation of a.h.c. (S_a) and (S_b). We therefore suspect inhibited bedding slip by welded contacts to favour the development of a.h.c.     

Petrology of rapakivi granites in Salmi massif

Crystallization of rapakivi is accompanied by a progressive decrease in the alkali content of the high-temperature granitic magma and by the concurrent increase in its iron content, during the crystallization of potassium feldspar which is followed by the crystallization of biotite. The pressure is not high enough to permit a simultaneous crystallization of potassium feldspar, as e. g. of albite. The potassium feldspar-biotite sequence is upset by Mg, in the ovoid varieties of rapakivi in which the potassium feldspar crystallization is arrested, short of its completion, by the crystallization of Mg biotite. – IGR Staff.     

考虑应力路径影响下砂土的三维本构模型

应力路径是影响土的应力-应变关系的一个重要因素。通过对一组砂土（日本Toyoura砂）三轴试验结果的详细分析,揭示了应力路径对剪应变及体积应变的影响规律,进而建立了能反映应力路径影响的应力-应变增量本构模型,提出的统一硬化参数反映了其剪胀特性,引入的变换应力能反映三维应力-应变特性。     

湿陷性黄土结构性变形特性分析

基于结构性黄土应力应变特性认识和大量试验结果的分析,揭示了黄土结构性参数与应变、含水率、固结压力之间的关系,并给出了结构性参数的数学表达式。将该式引入结构性黄土应力应变特性分析,提出了考虑结构性参数的应力-应变关系。分析计算所得的应力-应变关系与试验结果有较好的一致性,说明了原状黄土结构性参数描述的合理性和基于结构性参数应力-应变关系的合理性。     

Financially Efficient Ore Selections Incorporating Grade Uncertainty

Traditional mining selection methods focus on local estimates or loss functions that do not take into account the potential diversification benefits of financial risk that is unique to each location. A constrained efficient set model with a downside risk function is formulated as a solution. Estimates of this nonlinear mixed-integer combinatorial optimization problem are provided by a simulated annealing heuristic. A utility framework that is congruent with the proposed efficiency model is then used to choose the optimal set of local mining selections for a decision-maker with specific risk-averse characteristics. The methodology is demonstrated in a grade control environment. The results show that downside financial risk can be reduced by around 33% while the expected payoff is only reduced by 1% when compared to ore selections generated by traditional cut-off grade techniques.     

Scattering of elastic wave by a partially sealed cylindrical shell embedded in poroelastic medium

Scattering of an elastic wave by a cylindrical shell embedded in poroelastic medium is investigated theoretically with the assumption that the shell material is also a porous elastic medium. The porous medium is modellized via Biot's theory and the scattering by cylindrical shell is expressed by the definition of scattering matrix. The normal mode expansion technique is employed for analysing the scattering field, and the asymptotic solutions of displacements, stresses and pore pressure are derived. Two limiting cases‐scattering by a poroelastic cylinder in Biot medium and a elastic cylindrical shell in elastic medium are obtained from the general solutions. The dispersion curves of displacement amplitude at the interface of shell and medium is compared with the case of elastic shell. The scattering amplitude associated with the fast, slow and transverse waves are identified by numerical simulation. Furthermore, the influence of the poroelastic property of shell material on scattering amplitude is analysed. Copyright © 2005 John Wiley & Sons, Ltd.     

Spatial foundation structures over no tension soil

The problem of the stress distribution induced in the soil by a single circular foundation structure is approached in a three‐dimensional analysis. Since the soil is typically made by not‐cohesive materials, its behaviour is modelled by means of the not resisting tension (NRT) hypothesis, thus assuming that its very low resistance to tensile stresses can be completely neglected and that it keeps linearly elastic under pure compression. After developing the problem from a theoretical point of view on the basis of an energetic approach, a numerical application—which is able to reproduce the stress distribution induced by a circular foundation on the soil—is performed. Copyright © 2005 John Wiley & Sons, Ltd.     

Tectono-metamorphic history of the ophiolitic Lento unit (northern Corsica): evidences for the complexity of accretion-exhumation processes in a fossil subduction system

The Alpine Corsica (Corsica Island, France) is characterized by a stack of continent- and ocean-derived tectonic units, known as Schistes Lustrés complex. This complex is affected by deformation and metamorphic imprint achieved during Late Cretaceous – Early Tertiary subduction- related processes connected with the closure of the Ligure-Piemontese oceanic basin and subsequent continental collision. In the Schistes Lustrés complex, the Lento oceanic unit is characterized by four deformation phases, from D1 to D4 phase. The D1 phase, characterized by blueschist metamorphism, is regarded as related to coherent underplating in a subduction zone at a depth of about 25-30 km. The subsequent deformation phases can be referred to exhumation history, as suggested by the continuous decrease of metamorphic conditions. The transition from accretion to exhumation is represented by the D2 phase, achieved during the development of a duplex structure of accreted units. The D3 phase is in turn achieved by a further horizontal shortening, whereas the D4 phase is developed during an extensional event representing the final exhumation of the Lento unit.

On the whole, the data collected for the Lento unit suggest an history that include an accretion by coherent underplating followed by exhumation, more complex than previous described.     

具空间约束效应边坡的稳定性研究

当边坡的变形不仅受底部边界约束而且还受侧限作用时,其稳定性计算按平面问题简化常存在较大的误差。本文通过李家峡电站导流洞进口边坡的实例分析,旨在对此粗具空间约束效应边坡的生分析问题进行一个初步的探讨。     

造山的高原——青藏高原巨型造山拼贴体和造山类型

有机质丰度是传统评价烃源岩方法的重要指标,笔者认为有机粘土复合体是烃源岩有机质的主要赋存形式。有机质生烃反应是一种有机粘土化学反应,有机质脱羧基反应是有机粘土的氧化-还原反应,有机质的热解反应是一个加氢裂解过程,含有剩余C0是烃源岩的基本特征,它说明在烃源岩生烃反应中C0始终是有剩余的,不会因为C0的不足而影响烃源岩的生烃能力。笔者认为制约烃源岩生烃能力大小的不是烃源岩C0的丰度,而是氢的来源和丰度,烃源岩粘土通过吸附水分子为生烃反应提供H+能力(Br nsted酸性)的大小和时间是决定生烃潜力大小的关键。烃源岩粘土的不同催化特性是影响油气组成的重要因素,蒙皂石对甾烷的异构化有明显促进作用。     

Numerical analysis of rafts on visco-elastic media using eigenvector expansions

Problems of a raft on a visco-elastic continuum may be converted to equivalent elastic problems by means of a Laplace transformation. In this paper a numerical solution of the equivalent problem is obtained by finite element or other techniques. This solution is converted into the form of an eigenvector expansion and then transformed into a numerical solution to the original problem by inverting the Laplace transform. This form of solution has the advantage of applying to any visco-elastic model, and of requiring little additional computation as a result of changing the visco-elastic model, the relative raft-soil stiffness or the load pattern. The application of the method is illustrated by results for circular rafts, strip footings of finite length and rectangular rafts, and particular attention is paid to a realistic soil creep function which is asymptotic to a linear function of log time.