A novel coupled FDM-DEM modelling method for flexible membrane boundary in laboratory tests

Difficulties are involved in discrete element method (DEM) modelling of the flexible boundary, that is, the membranes covering the soil sample, which can be commonly found in contemporary laboratory soil tests. In this paper, a novel method is proposed wherein the finite difference method (FDM) and DEM are coupled to simulate the rubber membrane and soil body, respectively. Numerical plane strain and triaxial tests, served by the flexible membrane, are implemented and analysed later. The effect of the membrane modulus on the measurement accuracy is considered, with analytical formulae derived to judge the significance of this effect. Based on an analysis of stress-strain responses and the grain rotation field, the mechanical performances produced by the flexible and rigid lateral boundaries are compared for the plane strain test. The results show that (1) the effect of the membrane on the test result becomes more significant at larger strain level because the membrane applies additional lateral confining pressure to the soil body; (2) the tested models reproduce typical stress and volumetric paths for specimens with shear bands; (3) for the plane strain test, the rigid lateral boundary derives a much higher peak strength and larger bulk dilatation, but a similar residual strength, compared with the flexible boundary. The latter produces a more uniform (or ‘diffuse') rotation field and more mobilised local kinematics than does the former. All simulations show that the proposed FDM-DEM coupling method is able to simulate laboratory tests with a flexible boundary membrane.     

Effects of the geometry of two‐dimensional fractures on their hydraulic aperture and on the validity of the local cubic law

Flow through rough fractures is investigated numerically in order to assess the validity of the local cubic law for different fracture geometries. Two‐dimensional channels with sinusoidal walls having different geometrical properties defined by the aperture, the amplitude, and the wavelength of the walls' corrugations, the corrugations asymmetry, and the phase shift between the two walls are considered to represent different fracture geometries. First, it is analytically shown that the hydraulic aperture clearly deviates from the mean aperture when the walls' roughness, the phase shift, and/or the asymmetry between the fracture walls are relatively high. The continuity and the Navier–Stokes equations are then solved by means of the finite element method and the numerical solutions compared to the theoretical predictions of the local cubic law. Reynolds numbers ranging from 0.066 to 66.66 are investigated so as to focus more particularly on the effect of flow inertial effects on the validity of the local cubic law. For low Reynolds number, typically less than 15, the local cubic law properly describes the fracture flow, especially when the fracture walls have small corrugation amplitudes. For Reynolds numbers higher than 15, the local cubic law is valid under the conditions that the fracture presents a low aspect ratio, small corrugation amplitudes, and a moderate phase lag between its walls.     

Time–space fractional governing equations of transient groundwater flow in confined aquifers: Numerical investigation

In order to model non‐Fickian transport behaviour in groundwater aquifers, various forms of the time–space fractional advection–dispersion equation have been developed and used by several researchers in the last decade. The solute transport in groundwater aquifers in fractional time–space takes place by means of an underlying groundwater flow field. However, the governing equations for such groundwater flow in fractional time–space are yet to be developed in a comprehensive framework. In this study, a finite difference numerical scheme based on Caputo fractional derivative is proposed to investigate the properties of a newly developed time–space fractional governing equations of transient groundwater flow in confined aquifers in terms of the time–space fractional mass conservation equation and the time–space fractional water flux equation. Here, we apply these time–space fractional governing equations numerically to transient groundwater flow in a confined aquifer for different boundary conditions to explore their behaviour in modelling groundwater flow in fractional time–space. The numerical results demonstrate that the proposed time–space fractional governing equation for groundwater flow in confined aquifers may provide a new perspective on modelling groundwater flow and on interpreting the dynamics of groundwater level fluctuations. Additionally, the numerical results may imply that the newly derived fractional groundwater governing equation may help explain the observed heavy‐tailed solute transport behaviour in groundwater flow by incorporating nonlocal or long‐range dependence of the underlying groundwater flow field.     

The Upper Devonian Kellwasser event recorded in a regressive sequence from inner shelf to lagoonal pond,Catalan Coastal Ranges,Spain

This study, conducted in the Catalan Coastal Ranges, north‐east Spain, describes the Upper Devonian Kellwasser event in a shallowing‐upward sequence of black shales, siltstones and quartz arenites. This sequence was deposited in a progradational and regressive coastal system where the sedimentary environment evolved from the inner shelf to a lagoonal pond located landward of the shoreline. Three anomalous succeeding steps have been identified by geochemical analysis. The first one, detected on the inner shelf, was characterized by oxygen depletion and high organic productivity. The second, detected in the nearshore, was caused by hydrothermal activity occurring under normal oxic conditions. The third and most intense step was identified in the muds of the lagoonal pond and has been linked to strong anoxic conditions, elevated clastic input derived from changes in the weathering regime at the source area and moderate hydrothermal activity. The Kellwasser event is thus defined in the study area as stepwise and multi‐causal. This is the first time that the Kellwasser event has been identified in a sedimentary environment behind the shoreline. It is also the first time that it has been reported in the Catalan Coastal Ranges.     

On a global expansion of the disturbing function in the planar elliptic restricted three-body problem

Starting with a simple Taylor-based expansion of the inverse of the distance between two bodies, we are able to obtain a series expansion of the disturbing function of the three-body problem (planar elliptic case) which is valid for all points of the phase space outside the immediate vicinity of the collision points. In particular, the expansion is valid for very high values of the eccentricity of the perturbed body. Furthermore, in the case of an interior mean-motion resonant configuration, the above-mentioned expression is easily averaged with respect to the synodic period, yielding once again a global expansion of (R) valid for very high eccentricities.Comparisons between these results and the numerically computed exact function are presented for various resonances and values of the eccentricity. Maximum errors are determined in each case and their origin is established. Lastly, we discuss the applicability of the present expansion to practical problems.     

On the stability of particular solutions of the singly averaged Hill problem

We consider the particular solutions of the evolutionary system of equations in elements that correspond to planar and spatial circular orbits of the singly averaged Hill problem. We analyze the stability of planar and spatial circular orbits to inclination and eccentricity, respectively. We construct the instability regions of both particular solutions in the plane of parameters of the problem.     

济宁市嘉祥县石灰岩矿山地质环境评价与治理

在对嘉祥县石灰岩矿进行地质灾害危险性评估、矿山环境地质问题评价的基础上,建立了一套评价体系,其中地质灾害危险性评估分为2个评价指标,矿山环境地质问题评价分为2种要素3个指标,同时将矿山恢复治理难易程度也作为一个评价因子。评价过程中对各指标危害性大、中、小程度均单独赋值,然后将各指标的分值进行叠加,确定出矿山环境地质问题的等级,将概划出的13个评价单元分为极差、差、一般3个区。提出了强化矿山管理、植树造林、科学避让、修建拦水坝等保护与治理措施及建议。