Analytical investigation of the exact groundwater divide between rivers beyond the Dupuit–Forchheimer approximation

The groundwater divide is a key feature of river basins and significantly influenced by subsurface hydrological processes. For an unconfined aquifer between two parallel rivers or ditches, it has long been defined as the top of the water table based on the Dupuit–Forchheimer approximation. However, the exact groundwater divide is subject to the interface between two local flow systems transporting groundwater to rivers from the infiltration recharge. This study contributes a new analytical model for two-dimensional groundwater flow between rivers of different water levels. The flownet is delineated in the model to identify groundwater flow systems and the exact groundwater divide. Formulas with two dimensionless parameters are derived to determine the distributed hydraulic head, the top of the water table and the groundwater divide. The locations of the groundwater divide and the top of the water table are not the same. The distance between them in horizontal can reach up to 8.9% of the distance between rivers. Numerical verifications indicate that simplifications in the analytical model do not significantly cause misestimates in the location of the groundwater divide. In contrast, the Dupuit–Forchheimer approximation yields an incorrect water table shape. The new analytical model is applied to investigate groundwater divides in the Loess Plateau, China, with a Monte Carlo simulation process taking into account the uncertainties in the parameters.     

A multiscale work-analysis approach for geotechnical structures

This paper presents a second-order work analysis in application to geotechnical problems by using a novel effective multiscale approach. To abandon complicated equations involved in conventional phenomenological models, this multiscale approach employs a micromechanically-based formulation, in which only four parameters are involved. The multiscale approach makes it possible a coupling of the finite element method (FEM) and the micromechanically-based model. The FEM is used to solve the boundary value problem (BVP) while the micromechanically-based model is utilized at the Gauss point of the FEM. Then, the multiscale approach is used to simulate a three-dimensional triaxial test and a plain-strain footing. On the basis of the simulations, material instabilities are analyzed at both mesoscale and global scale. The second-order work criterion is then used to analyze the numerical results. It opens a road to interpret and understand the micromechanisms hiding behind the occurrence of failure in geotechnical issues.     

Canonical theory of perturbations using eccentric anomaly as independent variable

It is shown in this paper how to build a canonical transformation of variables, so that the eccentric anomaly becomes the new independent variable. In the case of eccentric elliptical orbits it changes the equations of motion so, that they can be integrated analytically to any order of approximation comparatively easy.     

Simulations of multimode bolometric interferometers

We describe a procedure for the numerical modelling of astronomical interferometers, with particular relevance to far-infrared and submillimetre wavelengths. The scheme is based on identifying a set of modes that carry power from the sky to the detector. The procedure is extremely general, and can be used to model scalar or vector fields, in any state of coherence and polarization, the only limitation being that the propagation of a coherent field through the system be described by an integral transform, a constraint that is in practise always met.
We present simulations of ideal, multimode two-dimensional interferometers, and show that the modal theory reproduces the correct behaviour of both Michelson and Fizeau interferometers. We calculate simulated visibility data for a multimode bolometric Michelson interferometer, with a synthesized source, and produce a dirty map, recovering the original source with the usual artefacts associated with interferometers.     

Plane of elastic non-resisting tension material under foundation structures

In the frame of 2D-static problems one approaches the problem of elastic-NRT (not-resisting tension) semi-plane loaded on its limit line. This problem is intended to model the stress situation induced in the soil by a foundation structure. The solution, in terms of activated stress field, is searched for in the class of stress fields satisfying equilibrium and admissibility conditions, by applying an energy approach. Copyright © 2004 John Wiley & Sons, Ltd.     

Transient‐state groundwater flow in various geometries with wells at arbitrary positions: analytical methods

We have developed a method for analytically solving the porous medium flow equation in many different geometries for horizontal (two‐dimensional), homogeneous and isotropic aquifers containing impermeable boundaries and any number of pumping or injection wells located at arbitrary positions within the system. Solutions and results are presented for rectangular and circular aquifers but the method presented here is easily extendible to many geometries. Results are also presented for systems where constant head boundary conditions can be emulated internal to the aquifer boundary. Recommendations for extensions of the present work are briefly discussed. Copyright © 2003 John Wiley & Sons, Ltd.