Numerical modeling of the motion of rigid ellipsoidal objects in slow viscous flows: A new approach

A simple algorithm for modeling the rotation of rigid ellipsoidal objects in viscous flows based on Jeffery's (1922, Proceedings of the Royal Society of London A102, 161–179) theory is presented and is implemented in a fully graphic mathematics application Mathcad^® (http://www.mathsoft.com). The orientation of ellipsoidal objects is specified in terms of polar coordinate angles that can be easily converted to the trend and plunge angles of the three principal axes rather than the Euler angles. With the Mathcad worksheets presented in the supplementary data associated with this paper, modeling the rotation paths of individual rigid objects, the development of inclusion trail geometry within syn-kinematic porphyroblasts, and the development of preferred orientation and shape fabrics for a population of rigid objects becomes as easy a task as using a spreadsheet. The shape and preferred orientation fabrics for a population of rigid objects can be presented in both a three-dimensional form and a two-dimensional form, allowing easy comparison between field data and model predictions. The modeler can customize the type and format of the output to best fit the purpose of the investigation and to facilitate the comparison of model predictions with geological observations. Application examples are presented for various types of modeling involving rigid objects.     

A new theoretical method for analyzing confined dry granular flows

A granular body may deform in a continuous fashion such that the solid particles remain in close contact. Previous research works have always used the frictional Coulomb-like continuum treatment for analyzing granular bodies. However, this approach is only applicable for quasi-static conditions and cannot capture the complicated granular contact behavior of solid particles inside a failing granular body. This paper applies a revised Savage–Hutter equation to model granular flows moving down a confined, sloping channel. The Coulomb contact friction law is modified to consider the effect of the shear rate inside a granular body. This new method also considers the confinement effect of a sloping channel on granular flow mobility. The derived depth-averaged equations of motion bear a resemblance to nonlinear shallow-water wave equations. Results computed using the derived equations are compared with measurements from flume model tests, and consistency is found between the two.     

Modeling of unsaturated granular flows by a two-layer approach

Flows of partially saturated grain-fluid mixtures over complex curved topography are commonly observed in nature. However, comprehensive understanding of the physics behind them is to date out of reach. To investigate their dynamic process, a two-layer approach is proposed, in which the fluid-saturated granular layer is overlaid by the pure granular material. More specifically, the lower layer is described by a two-phase mixture theory of density preserving solid and fluid constituents. For the upper layer, the single-phase granular mass is treated as a frictional Coulomb-like continuum, and the dilation effect and the influence of the interstitial air are ignored. The capillarity effects and grains-size segregation are not considered in both the layers. The lower and upper layers interact at an interface which is a material surface for the fluid phase, but across which the mass exchange for the granular phase may take place. The granular mass exchange across the layer interface is parameterized by an entrainment type postulate. In addition, the classical jump conditions are employed to connect both layers at the interface dynamically. Furthermore, we perform the depth-averaged technique for the saturated grain-fluid mixture lower layer and the pure granular upper layer, respectively, to simplify the governing equations established. It is demonstrated that the resulting model equations can be reduced to most of the existing single-layer pure granular flow models and saturated two-phase single-layer debris flow models. Numerical solutions demonstrate that the present two-layer model can describe flows of partially saturated grain-fluid mixtures and the transition process of a saturated grain-fluid mixture into an under-saturated state.     

A thermomicromechanical approach to multiscale continuum modeling of dense granular materials

A new method is proposed for the development of a class of elastoplastic thermomicromechanical constitutive laws for granular materials. The method engenders physical transparency in the constitutive formulation of multiscale phenomena from the particle to bulk. We demonstrate this approach for dense, cohesionless granular media under quasi-static loading conditions. The resulting constitutive law—expressed solely in terms of particle scale properties—is the first of its kind. Micromechanical relations for the internal variables, tied to nonaffine deformation, and their evolution laws, are derived from a structural mechanical analysis of a particular mesoscopic event: confined, elastoplastic buckling of a force chain. It is shown that the constitutive law can reproduce the defining behavior of strain-softening under dilatation in both the mesoscopic and macroscopic scales, and reliably predict the formation and evolution of shear bands. The thickness and angle of the shear band, the distribution of particle rotation and the evolution of the normal contact force anisotropy inside the band, are consistent with those observed in discrete element simulations and physical experiments.     

A neural network approach to geostatistical simulation

Neural networks offer a non-algorithmic approach to geostatistical simulation with the possibility of automatic recognition of correlation structure. The paper gives a brief overview of neural networks and describes a feedforward, back-propagation network for geostatistical simulation. The operation of the network is illustrated with two simple one-dimensional examples which can be followed through with hand calculations to give an insight into the operation of the network. The convergence of the network is described in terms of the variogram calculated from the values at each of the output nodes at each iteration.     

A new approach to quantification of metamorphism using ultra-small and small angle neutron scattering

In this paper we report the results of a study using small angle and ultra-small angle neutron scattering techniques (SANS and USANS) to examine the evolution of carbonates during contact metamorphism. Data were obtained from samples collected along two transects in the metamorphosed Hueco limestone at the Marble Canyon, Texas, contact aureole. These samples were collected from the igneous contact out to ∼1700 m. Scattering curves obtained from these samples show mass fractal behavior at low scattering vectors, and surface fractal behavior at high scattering vectors. Significant changes are observed in the surface and mass fractal dimensions as well as the correlation lengths (pore and grain sizes), surface area to volume ratio and surface Gibbs Free energy as a function of distance, including regions of the aureole outside the range of classic metamorphic petrology. A change from mass-fractal to non-fractal behavior is observed at larger scales near the outer boundary of the aureole that implies significant reorganization of pore distributions early in the metamorphic history. Surface fractal results suggest significant smoothing of grain boundaries, coupled with changes in pore sizes. A section of the scattering curve with a slope less than −4 appears at low-Q in metamorphosed samples, which is not present in unmetamorphosed samples. A strong spike in the surface area to volume ratio is observed in rocks near the mapped metamorphic limit, which is associated with reaction of small amounts of organic material to graphite. It may also represent an increase in pore volume or permeability, suggesting that a high permeability zone forms at the boundary of the aureole and moves outwards as metamorphism progresses. Neutron scattering data also correlate well with transmission electron microscopic (TEM) observations, which show formation of micro- and nanopores and microfractures during metamorphism. The scattering data are, however, quantifiable for a bulk rock in a manner that is difficult to achieve using high-resolution imaging (e.g. TEM). Thus, neutron scattering techniques provide a new approach to the analysis and study of metamorphism.     

DEM simulation of collapse behaviours of unsaturated granular materials under general stress states

In this study, a numerical simulation of true triaxial tests was conducted using the three-dimensional distinct element method (DEM) in order to examine how unsaturated granular materials collapse under general stress states. The collapse process was simulated by reducing the intergranular adhesive forces corresponding to the effect of the capillary suction during the isotropic compression and the shearing processes under general stress states. Based on the relationship between the void ratio and the mean principal stress after collapsing, it was found that the initially soaked compression line obtained with an inundation test may be used to predict the collapse of granular materials under a general stress state. From the analysis for the fabric tensor in the particle aggregate after collapsing, the skeleton structures became identical to those in which no intergranular adhesive force was applied. Furthermore, even though the collapse process was simulated under a plane strain condition, the shear band inside the sample did not occur clearly, and the slippage between particles was instead induced randomly during collapsing.     

A 4th order fabric tensor approach applied to granular media

In this paper, we propose a micromechanical approach of the behavior of granular media, which takes into account the anisotropy by means of a fourth order fabric tensor. The proposed approach is implemented in an homogenization scheme based on Voigt and Reuss localization assumption. The fabric tensor-based approach is then combined with a new kinematic localization rule and yields a general homogenization scheme for anisotropic granular media.     

Numerical simulation of liquefaction behaviour of granular materials using Discrete Element Method

In this paper, numerical simulation of 3-dimensional assemblies of 1000 polydisperse sphere particles using Discrete Element Method (DEM) is used to study the liquefaction behaviour of granular materials. Numerical simulations of cyclic triaxial shear tests under undrained conditions are performed at different confining pressures under constant strain amplitude. Results obtained in these numerical simulations indicate that with increase in confining pressure there is an increase in liquefaction resistance.     

一种采用固结快剪强度指标的应力路径分析法

本文介绍了一种应用固结快剪强度指标的应力路径法。与传统的基于三轴强度指标应力路径法相比,它能直接求出安全系数K,可以更方便地作为控制软土地基上堆载速率的依据。在一个工程中,对两种应力路径法的应用情况进行了比较,结果表明,新方法能够反映地基的稳定性状态。由于其应用方便,更易于在工程界推广使用。     

The effect of inertia,viscous damping,temperature and normal stress on chaotic behaviour of the rate and state friction model

A fundamental understanding of frictional sliding at rock surfaces is of practical importance for nucleation and propagation of earthquakes and rock slope stability. We investigate numerically the effect of different physical parameters such as inertia, viscous damping, temperature and normal stress on the chaotic behaviour of the two state variables rate and state friction (2sRSF) model. In general, a slight variation in any of inertia, viscous damping, temperature and effective normal stress reduces the chaotic behaviour of the sliding system. However, the present study has shown the appearance of chaos for the specific values of normal stress before it disappears again as the normal stress varies further. It is also observed that magnitude of system stiffness at which chaotic motion occurs, is less than the corresponding value of critical stiffness determined by using the linear stability analysis. These results explain the practical observation why chaotic nucleation of an earthquake is a rare phenomenon as reported in literature.     

淹没丁坝群二维水流数值模拟新方法

为模拟淹没丁坝群平面二维水流运动,提出了淹没丁坝群二维水流数值模拟新方法并建立了数学模型。新方法的主要实施方案:① 将丁坝视为无厚度坝,用网格线概化丁坝;② 采用新的网格节点布置形式,即水深、流速节点布置于网格界面上,水位节点布置于网格中心,有别于一般交错网格节点布置。模型采用基于结构网格下的有限体积法对方程组进行离散,同时将淹没丁坝坝顶水深代入离散方程中进行求解。采用已有的水槽试验资料,进行了初步验证,模拟了长江下游东流水道已建丁坝群工程实施后河道的流场和水位场,结果表明计算和实测符合较好。     

3D DEM simulation of principal stress rotation in different planes of cross-anisotropic granular materials

Three-dimensional Discrete Element Method simulations have been performed to study the deformation of cross-anisotropic granular materials under principal stress rotation (PSR), for rotation planes oriented at different angles θ with respect to the bedding plane. The simulations have been conducted with a novel technique for applying specified stresses at three-dimensional boundaries. The results are qualitatively in agreement with experimental results from literature. Cumulative volume contraction is always observed under continuous PSR and increases with increasing θ. The dilatancy rate decreases with increasing number of PSR cycles, tending to zero. The noncoaxiality angle between the strain increment and the stress in the PSR plane increases with increasing number of cycles, reaching the same asymptotic value for samples of various densities and for various θ. Periodic oscillations of the dilatancy rate and noncoaxiality angle within each PSR cycle are observed with an increasing oscillation magnitude with increasing θ, due to the larger fabric anisotropy within the PSR plane. When θ = 30 or 60°, significant noncoaxial strain accumulation occurs in the plane perpendicular to the PSR plane due to the oblique angle between the PSR plane and the bedding plane, echoing the major principal fabric direction's being neither parallel nor perpendicular to the PSR plane. The macroscopic behavior of the samples is related to the microscopic parameters including coordination number and fabric anisotropy. With increasing number of cycles, the difference between normalized stress/strain/fabric increment tensors tends to become constant, with only a small lag between each pair, irrespective of θ.     

Micro-mechanism and efficiency of baffle structure in deceleration of granular flows

Acta Geotechnica - Baffle system is a promising disaster mitigation measure, while the mechanism of debris-baffle interaction at grain scale has not been fully understood, and especially the effect...     

A new approach to detecting vegetation and land-use change using high-resolution lipid biomarker records in stalagmites

A hundred-year stalagmite lipid biomarker record from Mechara, southeastern Ethiopia, is presented. The record has been recovered at a 10-yr temporal resolution, marking the first time this has been achieved in stalagmite biomarker work and providing the first opportunity to investigate the relationship between stalagmite lipid records and hydrological transport lags, a vital issue in interpreting palaeoenvironmental signals. Preserved plant-derived n-alkanes and n-alkanols show clear changes in composition over time, relating to known land-use changes in the area, particularly the expansion of agriculture in the early twentieth century. The level of environmental detail provided by this technique, combined with the long-term chronological framework offered by stalagmites, holds significant promise for the investigation of early human environments and their associated climatic and anthropogenic controls.     

边坡落石运动轨迹计算新方法

考虑落石形状对落石运动轨迹的影响,将落石近似成椭圆形。根据落石运动的5种常见形式,即自由落体运动、斜抛运动、碰撞、滑动和滚动,分别得到了各种运动形式的运动速度计算公式。在碰撞阶段考虑了地面的弹塑性变形,得到了与碰撞前速度、落石形状和地面材料有关的恢复系数计算公式,并根据接触力学的有关理论得到了碰撞冲击力的计算公式,给出了落石连续滚动的判别条件。将理论公式应用于重庆万州首立山落石运动轨迹预测,验证了理论公式的可行性和有效性。