Boundary element analysis of transversely isotropic bi-material halfspaces with inclined planes of isotropy and interfaces

In this paper, a single-region boundary element method (BEM) is presented for the analysis of transversely isotropic bi-material halfspaces with arbitrarily inclined planes of isotropy and material interfaces. The proposed BEM uses the fundamental solution of a transversely isotropic bi-material fullspace and five boundary element techniques. Infinite boundary elements are introduced to consider the far-fields of a transversely isotropic bi-material halfspace. The effective integration methods are proposed for dealing with various integrals in the discretized boundary integral equation. The stresses at internal points are obtained using the coordinate transformation of kernel functions, and the stresses on the boundary surface are calculated using an improved traction recovered method. Numerical verifications of displacements and stresses for a benchmark problem are conducted, and excellent agreement with previously published results is obtained. Numerical examples are presented to illustrate the influence of non-horizontal or horizontal planes of isotropy in bi-material halfspaces on the displacements and stresses induced by the tractions on the horizontal boundary surface. Results reveal that the elastic fields vary clearly with the dip angle of the isotropic plane and the stresses across the bi-material interface are closely related to the ratios of the elastic parameters of the bi-material.     

Grain growth and inclusion formation in partially molten carbonate rocks

To learn more about the kinetics and mechanisms of coarsening and melt inclusion formation, we investigated the effects of melt content, viscosity, and topology on the microstructural evolution of partially molten and melt-free calcite aggregates. Synthetic marbles with eutectic melts were produced by annealing mixtures of calcite and either calcium hydroxide or lithium carbonate for up to 80 h at a confining pressure of 300 MPa and temperatures of 973-1,023 K. The melts produced in the two systems are expected to differ significantly in viscosity. Generally, coarsening rates decrease with increasing melt fraction, probably because the diffusion length across melt pockets increases. Analysis of grain shapes in the samples with about 40% melt indicated that coarsening was accommodated by agglomeration in the samples of the calcium/lithium carbonate system. In the calcium carbonate/hydroxide system, classical Ostwald ripening occurred. For melt contents about 10% and below, melt-filled pores are either dropped from or dragged along with migrating grain boundaries, depending on the pore size and the grain boundary curvature. These data can be used to constrain the conditions where fluid or melt inclusions form under natural conditions. Combining our results and previous studies illustrates a systematic relation between the grain boundary mobility in calcite aggregates and the diffusion kinetics associated with second phases residing on the grain boundaries. In particular, boundaries with no porosity are most mobile, those boundaries dragging melt-filled pores are slower, those with gas-filled pores are slower yet, and those containing solid phases are slowest or may even be motionless.     

A general viscous‐spring transmitting boundary for dynamic analysis of saturated poroelastic media

A time‐domain viscous‐spring transmitting boundary is presented for transient dynamic analysis of saturated poroelastic media with linear elastic and isotropic properties. The u–U formulation of Biot equation in cylindrical coordinate is adopted in the derivation. By this general viscous‐spring boundary, the effective stress and pore fluid pressure on the truncated boundary of the computational area are replaced by a set of continuously distributed spring and dashpot elements, of which the parameters are defined assuming an infinite permeability and considering the two dilatational waves. Numerical examples demonstrate good absorption of both the two cylindrical dilatational waves by the proposed ‘drained’ boundary. For general two‐dimensional wave propagation problems, acceptable accuracy can still be achieved by setting the proposed boundary relatively far away from the scatter. Numerical comparison shows that the results obtained by using this boundary are more accurate for all permeability values than those by the traditional viscous‐spring or viscous boundaries established for u–U formulation. Copyright © 2015 John Wiley & Sons, Ltd.     

Numerical Simulations of Free Convection about a Vertical Flat Plate Embedded in a Porous Medium

We consider the free convection about a vertical flat plate embedded in a porous medium within the framework of a boundary layer approximation. In some cases, similarity solutions arise in the modelization of such phenomena, allowing a reduction of the dimension of the problem. We suggest two complementary and rather simple numerical methods to compute such solutions. When possible, the numerical analysis for the two discretizations is performed and convergence results are given. Numerical experiments with a physical model are presented to confirm the efficiency of both approaches.     

Experimental exsolution textures in the system bornite-chalcopyrite: Genetic implications concerning natural ores

Textural interpretation of ore-mineral assemblages, such as bornite-chalcopyrite (bn-cpy) intergrowths, should be based on definite experimentation. Appropriate exsolution and coarsening experiments were performed using sealed, evacuated, silicaglass tubes; synthetic bn-cpy solid solutions were annealed between 100° and 350°C for times of 20 min to 10 weeks. Early-formed textures develop through nucleation and growth and depend on the initial degree of supersaturation and the metal diffusivities. Final textures, due to additional growth and coarsening, are very sensitive to temperature and may serve as geothermometers. Mutual boundary textures which form above 250°C can originate by: (1) simultaneous precipitation; (2) exsolution during slow cooling from above the solvus; and (3) metamorphism to temperatures above about 250°C. Widmanstätten textures are not compatible with slow cooling, but indicate: (1) low-temperature replacement of bn; or (2) exsolution of cpy lamellae from anomalous bn heated to around 200°–250°C during mild metamorphism.     

混合润湿孔隙介质中油自吸实验研究

混合润湿孔隙介质普遍存在, 使得多相流体渗流过程十分复杂, 但对其研究和认识至今仍很肤浅, 是油气运移成藏、剩余油气分布等方面研究中必须解决的关键难题。本文通过对饱和水的混合润湿模型进行油自吸实验, 观察不同混合润湿程度条件下油自吸运移过程, 分析认识混合润湿孔隙介质中多相渗流的机理。实验结果表明, 在混合润湿孔隙介质中油是否能够自发地运移与介质中亲油颗粒的比例关系密切, 但并非简单的单调变化关系。研究认为, 亲油颗粒与亲水颗粒随机分布, 导致多种与喉道配位颗粒的亲油-亲水关系, 当亲油颗粒比例占优才表现为亲油喉道。机理上, 混合润湿孔隙介质中油自吸运移的发生与否及程度取决于亲油喉道在空间上的连通程度, 后者与孔隙介质中亲油颗粒比例相当。仅有当孔隙介质中亲油颗粒足够多, 且组成的亲油喉道能够相互接触形成连续亲油通道时, 油才能够通过自吸运移进入多孔介质。     

沙质河道冲刷不平衡输沙机理及规律研究

通过动床水槽试验,观测沙波运动,揭示了湍流扫荡河床使表层床沙产生频发的群体起动冲刷现象。据此,提出了床沙交换及冲刷粗化分二个层次的物理模式;分析了冲刷时表层床沙粗化的必然性,确定了悬移质扩散过程中适于非均匀沙河床的新的近底边界条件。依据所建立的不平衡输沙立面二维数学模型,计算了大量不同情况下的含沙量扩散恢复过程,据此总结出了冲刷时含沙量恢复饱和系数α的预报公式及变化规律。     

Growth of multilayered polycrystalline reaction rims in the MgO–SiO<Subscript>2</Subscript> system,part II: modelling

Part I of this contribution (Gardés et al. in Contrib Mineral Petrol, 2010) reported time- and temperature-dependent experimental growth of polycrystalline forsterite-enstatite double layers between single crystals of periclase and quartz, and enstatite single layers between forsterite and quartz. Both double and single layers displayed growth rates decreasing with time and pronounced grain coarsening. Here, a model is presented for the growth of the layers that couples grain boundary diffusion and grain coarsening to interpret the drop of the growth rates. It results that the growth of the layers is such that (Δx)² ∝ t ^1−1/n , where Δx is the layer thickness and n the grain coarsening exponent, as experimentally observed. It is shown that component transport occurs mainly by grain boundary diffusion and that the contribution of volume diffusion is negligible. Assuming a value of 1 nm for the effective grain boundary width, the following Arrhenius laws for MgO grain boundary diffusion are derived: log D _gb,0^Fo (m²/s) = −2.71 ± 1.03 and E _gb^Fo = 329 ± 30 kJ/mol in forsterite and log D _gb,0^En (m²/s) = 0.13 ± 1.31 and E _gb^En = 417 ± 38 kJ/mol in enstatite. The different activation energies are responsible for the changes in the enstatite/forsterite thickness ratio with varying temperature. We show that significant biases are introduced if grain boundary diffusion-controlled rim growth is modelled assuming constant bulk diffusivities so that differences in activation energies of more than 100 kJ/mol may arise. It is thus important to consider grain coarsening when modelling layered reaction zones because they are usually polycrystalline and controlled by grain boundary transport.     

Thick-skinned Contractional Salt Structures in the Kuqa Depression, the Northern Tarim Basin: Constraints from Physical Experiments

Thick-skinned contractional salt structures are widely developed in the western Kuqa depression, northern Tarim basin. To understand the mechanisms that govern the development of these structures, physical experiments are conducted and the results show that they are largely governed by the activities of basement faults and the forming of paleo-uplifts and basement slopes. The model materials in this study are dry sand, vaseline and plasticene （or hard foam）, simulating the suprasalt, salt, and subsalt layers respectively. The experiments show that, due to the activities of basement faults and the forming of the paleo-uplifts, salt bodies usually accumulate and thicken significantly on the middle top of the paleo-uplifts which are constrained by the pre-exiting boundary faults. The development of large-scale thrust faults and salt nappes is favored by the basement slops with larger dips. The experiments also conclude that differential structural deformation could occur between the subsalt and suprasalt layers because of the presence of salt layers. Their geometries and the locations of structural highs are different, despite of the great similarities in the uplifted areas. The pierced salt diapir is not observed in the experiments, which indicates that the contractional shortening does not effectively accelerate the development of the salt diapir.     

Grain coarsening in polymineralic contact metamorphic carbonate rocks: The role of different physical interactions during coarsening

The microstructural evolution of polymineralic contact metamorphic calcite marbles (Adamello contact aureole) with variable volume fractions of second-phase minerals were quantitatively analyzed in terms of changes in grain size and nearest neighbor relations, as well as the volume fractions, dispersion and occurrences of the second phases as a function of changing metamorphic conditions. In all samples, the calcite grain size is controlled by pinning of grain boundaries by second phases, which can be expressed by the Zener parameter (Z), i.e., the ratio between size and volume fraction of the second phases. With increasing peak metamorphic temperature, both the sizes of matrix grains and second phases increase in dependence on the second-phase volume fraction. Two distinct coarsening trends are revealed: trend I with coupled grain coarsening limited by the growth of the second phases is either characterized by large-sized or a large number of closely spaced-second phase particles, and results finally in a dramatic increase in the calcite grain size with Z. Trend II is manifest by matrix controlled grain growth, which is retarded by the presence of single second-phase particles that are located on calcite grain boundaries. It is supported by grain boundary pinning induced by triple junctions, and the calcite grain size increases moderately with Z. The two different grain coarsening trends manifest the transition between relatively pure polymineralic aggregates (trend II) and microstructures with considerable second-phase volume fractions of up to 0.5. The variations might be of general validity for any polymineralic rock, which undergoes grain coarsening during metamorphism. The new findings are important for a better understanding of the initiation of strain localization based on the activation of grain size dependent deformation mechanisms.     

Experiments with Higdon's absorbing boundary conditions for a number of wave equations

Simulation of wave propagation for seismic purposes is usually restricted to a small portion of the earth. Artificial boundary conditions are required where the subsurface model is truncated. Absorbing boundaries should ensure that waves hitting the artificial boundaries are not reflected. The vast amount of literature on the subject suggests that “good” conditions have not been found, and only “reasonable” solutions exist. A cursory overview of existing and a few new ideas is presented that may guide the construction of suitable boundary conditions. Because the intended application of the boundary conditions was a high-order finite-difference code that runs on a parallel computer, we have restricted our attention to local boundary conditions. A fundamental problem in the design of accurate local boundary conditions is pointed out: accuracy is required to keep the amount of reflected energy small, but at the same time allows for growing low-frequency modes. We have settled for Higdon’s boundary conditions. Higdon proposes to include some damping to suppress the growing low-frequency modes. We show that third-order conditions provide acceptable results for the simple scalar wave equation and the acoustic equation. In the elastic case, an additional low-frequency growing mode may occur. This mode can be suppressed by using a dissipative boundary scheme and by increasing the amount of damping. The increase in damping results in an increase in the amount of reflected energy, which is larger than in the scalar case. Numerical experiments exhibit a reasonable performance, although some improvement would be useful, particularly in the anisotropic elastic case. This revised version was published online in July 2006 with corrections to the Cover Date.     

Segregating gas from melt: an experimental study of the Ostwald ripening of vapor bubbles in magmas

Diffusive coarsening (Ostwald ripening) of H₂O and H₂O-CO₂ bubbles in rhyolite and basaltic andesite melts was studied with elevated temperature–pressure experiments to investigate the rates and time spans over which vapor bubbles may enlarge and attain sufficient buoyancy to segregate in magmatic systems. Bubble growth and segregation are also considered in terms of classical steady-state and transient (non-steady-state) ripening theory. Experimental results are consistent with diffusive coarsening as the dominant mechanism of bubble growth. Ripening is faster in experiments saturated with pure H₂O than in those with a CO₂-rich mixed vapor probably due to faster diffusion of H₂O than CO₂ through the melt. None of the experimental series followed the time^1/3 increase in mean bubble radius and time⁻¹ decrease in bubble number density predicted by classical steady-state ripening theory. Instead, products are interpreted as resulting from transient regime ripening. Application of transient regime theory suggests that bubbly magmas may require from days to 100 years to reach steady-state ripening conditions. Experimental results, as well as theory for steady-state ripening of bubbles that are immobile or undergoing buoyant ascent, indicate that diffusive coarsening efficiently eliminates micron-sized bubbles and would produce mm-sized bubbles in 10²–10⁴ years in crustal magma bodies. Once bubbles attain mm-sizes, their calculated ascent rates are sufficient that they could transit multiple kilometers over hundreds to thousands of years through mafic and silicic melt, respectively. These results show that diffusive coarsening can facilitate transfer of volatiles through, and from, magmatic systems by creating bubbles sufficiently large for rapid ascent.     

基于单、双重渗透介质降雨边界处理的改进

在降雨入渗模拟中,现有研究无法准确实现复杂降雨条件下降雨边界在流量与压力两类边界之间的双向动态转换。基于饱和?非饱和渗流理论,将降雨补给流量与实际入渗流量的差值作为两类边界动态转换的判别条件,改进了单重渗透介质降雨边界动态转换控制方程,并进一步提出了双重渗透介质降雨边界处理方法及控制方程,在此基础上进行了数值试验及工程实例验证。结果表明：改进的降雨边界动态转换控制方程克服了传统降雨边界只能实现流量到压力边界单向转换的局限性,可准确实现流量边界与压力边界的双向动态实时转换;案例边坡的降雨入渗模拟结果说明了改进后降雨边界的正确性和工程适用性。     

复杂水力路径下非饱和流动的数值分析

多孔介质中的流动问题,与孔隙介质的特性,含水量状态以及含水量的变化历史密切相关。基于毛细循环滞回理论模型,考虑含水量变化历史对土水特征关系的影响,在开发的U-DYSAC2有限元程序中进行了相应的数值实施。在试验给定的初边值条件下进行了非饱和渗流模拟分析,并将模拟结果与实测数据比较,表明在压力边界条件反复变化下,考虑滞回效应能获得更接近实测的结果,证实该模型在模拟各种循环变化条件下非饱和土渗流初边值问题的适用性与必要性。对入渗重分布反复变化条件下非饱和土柱流动的数值模拟表明,考虑滞回与不考虑滞回条件下,含水量、孔隙水压力和湿峰的迁移的预测在入渗后的重分布过程差异较大。考虑滞回效应时,土柱上部的脱湿速率、下部的吸湿速率比不考虑滞回时要低。从而证实了非饱和多孔介质中的土水状态依赖于含水量变化,而且强烈依赖于土体的水力路径变化。因此,循环边界条件变化下,毛细滞回效应在非饱和渗流模拟中的影响显著,必须加以考虑。     

Experimental study on the effects of temperature cycling on coarsening of plagioclase and olivine in an alkali basalt

We conducted experiments on an alkali basalt at 1-atmosphere in order to investigate the effects of temperature cycling on crystal coarsening. Experiments at 1,150 °C near the Ni–NiO buffer indicate that coarsening of plagioclase and olivine crystals is greatly accentuated by temperature cycling. For a given experiment duration, crystal number density decreases with temperature cycle amplitude and average crystal size increases with increasing amplitude. We observed little correlation between cycle period and crystal number density or average crystal size. We suggest that dissolution and size-proportional crystal growth during repeated heating and cooling decrease crystal number density and increase average crystal size. These experiments indicate that the texture of silicate minerals can be modified by temperature cycling and that phenocrysts may develop quicker in silicate magmas when the magma temperature is cycled.     

Distribution of brine in grain boundaries during static recrystallization in wet, synthetic halite: insight from broad ion beam sectioning and SEM observation at cryogenic temperature

We report observations from room temperature static recrystallization experiments (annealing times from minutes to year) of cold-pressed, synthetic, coarse-grained, wet sodium chloride, prepared by broad ion beam polishing and SEM observations at cryogenic temperature to observe directly the brine in grain boundaries. At all stages of annealing, the majority of the brine in the samples is connected in 2D sections along grain boundaries. Another part of the brine is in isolated brine inclusion arrays along grain boundaries and in brine inclusions left behind by migrating brine-filled grain boundaries. Most of these boundaries are mobile because the aggregate is coarsening. We interpret that the boundaries without observable brine films (<15 nm) and brine inclusion arrays are healed and immobile. Evolution of grain boundary structure involves three major processes. First, dissolution on one side of the grain boundary and precipitation on the other side, resulting in grain boundary migration. Second, the development of facets formed by low-index crystallographic planes of the grains bounding the grain boundary brine. When both sides of a grain boundary are able to develop low-index facets in a thick brine film, the resulting impingement boundary is interpreted to be immobile and may prevent the new grain from migrating into a deformed neighbor. When one side of a faceted boundary consists of low-index crystallographic planes and the other side passively follows this faceted shape along irrational surfaces, the boundary is mobile. Third, the healing of grain boundary brine films, producing solid–solid grain boundaries without resolvable brine films.     

Taking into account general boundary conditions in upscaling absolute permeability

Upscaling methods that need to solve local problems subject to boundary conditions are addressed in this article. We define a new upscaling method based on optimization problems, which can take into account general boundary conditions applied to local problems. The determination of upscaled permeability leads to minimizing the difference of dissipated energies (or averaged velocity) at fine and large scale. Using optimal control techniques, we obtain an effective computing algorithm that allows us to recover, with classical boundary conditions, the well-known results. The uniqueness issue is tackled for the optimization problems introduced in our approach. We show that the method is stable with respect to G-convergence, a property that establishes a link with homogenization theory, and finally, 2D numerical experiments are presented.     

三门峡地区黄土L9的重磁化现象及原因探析

对黄河三门峡地区曹村黄土剖面L₁至L₁₃(年代持续约1.1Ma)的高分辨率古地磁研究发现:布容/松山界线位于第8层古土壤(S₈)的顶部,贾拉米洛正极性亚时的顶、底界分别位于S₁₀和L₁₃的顶部,上述古地磁极性转换界线与洛川标准剖面一致。“上粉砂层”(L₉)的绝大多数样品特征剩磁方向与现代地磁场方向一致,而其中的弱发育古土壤层(L₉SS₁)则呈预期的反极性特征。综合L₉的厚度、岩性和岩石磁学特征,认为这一巨厚的正极性带可能反映了完全由岩性所控制的重磁化特征。对于L₉重磁化的原因,似乎很难用后生的化学剩磁和粘滞剩磁来解释。文章尝试性地提出,可能在L₉沉积后的间冰期(对应S₈)和布容正极性时内气候较湿润的时期,由于雨水的向下渗透而诱导了其中强磁性矿物(磁铁矿)在沉积后随地磁场方向的变化而进行了重新排列。     

非饱和土土-水特征曲线的温度效应

基于热力学的理论,利用van Genuchten的土-水特征曲线表达式,建立了一种能考虑温度影响的土-水特征曲线方程,并给出了推导过程。该表达式综合考虑了温度对表面张力和浸润系数的影响。相对于根据试验数据拟合的表达式,该表达式具有更加坚实的理论基础,更具适用性和一般性。选用MX-80斑脱土和黄土土样的试验结果,将该方程预测结果和试验结果进行了比较;可以看到,所提出的方程能较好地反映非饱和土土-水特征曲线随温度而变化的情况。     

Seasonal effects on geophysical–geotechnical relationships and their implications for electrical resistivity tomography monitoring of slopes

Current assessments of slope stability rely on point sensors, the results of which are often difficult to interpret, have relatively high costs and do not provide large-area coverage. A new system is under development, based on integrated geophysical–geotechnical sensors to monitor groundwater conditions via electrical resistivity tomography. So that this system can provide end users with reliable information, it is essential that the relationships between resistivity, shear strength, suction and water content are fully resolved, particularly where soils undergo significant cycles of drying and wetting, with associated soil fabric changes. This paper presents a study to establish these relationships for a remoulded clay taken from a test site in Northumberland, UK. A rigorous testing programme has been undertaken, integrating the results of multi-scalar laboratory and field experiments, comparing two-point and four-point resistivity testing methods. Shear strength and water content were investigated using standard methods, whilst a soil water retention curve was derived using a WP4 dewpoint potentiometer. To simulate seasonal effects, drying and wetting cycles were imposed on prepared soil specimens. Results indicated an inverse power relationship between resistivity and water content with limited hysteresis between drying and wetting cycles. Soil resistivity at lower water contents was, however, observed to increase with ongoing seasonal cycling. Linear hysteretic relationships were established between undrained shear strength and water content, principally affected by two mechanisms: soil fabric deterioration and soil suction loss between drying and wetting events. These trends were supported by images obtained from scanning electron microscopy.