Dynamic sliding of tetrahedral wedge: The role of interface friction

The role of interface friction is studied by slow direct shear tests and rapid shaking table experiments in the context of dynamic slope stability analysis in three dimensions. We propose an analytical solution for dynamic, single and double face sliding and use it to validate 3D‐DDA. Single face results are compared with Newmark's solution and double face results are compared with shaking table experiments performed on a concrete tetrahedral wedge model, the interface friction of which is determined by constant velocity and velocity stepping, direct shear tests. A very good agreement between Newmark's method on one hand and our 3D analytical solution and 3D‐DDA on the other is observed for single plane sliding with 3D‐DDA exhibiting high sensitivity to the choice of numerical penalty value. The results of constant and variable velocity direct shear tests reveal that the tested concrete interface exhibits velocity weakening. This is confirmed by shaking table experiments where friction degradation upon multiple cycles of shaking culminated in wedge run out. The measured shaking table results are fitted with our 3D analytical solution to obtain a remarkable linear logarithmic relationship between friction coefficient and sliding velocity that remains valid for five orders of magnitude of sliding velocity. We conclude that the velocity‐dependent friction across rock discontinuities should be integrated into dynamic rock slope analysis to obtain realistic results when strong ground motions are considered. Copyright © 2011 John Wiley & Sons, Ltd.     

A class of analytic solutions of the magnetic force-free field equations

Abstract

Formation of electric current sheets in the corona is thought to play an important role in solar flares, prominences and coronal heating. It is therefore of great interest to identify magnetic field geometries whose evolution leads to variations in B over small length-scales. This paper considers a uniform field B ₀[zcirc], line-tied to rigid plates z = ±l, which are then subject to in-plane displacements modeling the effect of photospheric motion. The force-free field equations are formulated in terms of field-line displacements, and when the imposed plate motion is a linear function of position, these reduce to a 4 × 4 system of nonlinear, second-order ordinary differential equations. Simple analytic solutions are derived for the cases of plate rotation and shear, which both tend to form singularities in certain parameter limits. In the case of plate shear there are two solution branches—a simple example of non-uniqueness.     

Convection in a rotating magnetic system and taylor's constraint part II,numerical results

Abstract

Results are presented of a numerical study of marginal convection of electrically conducting fluid, permeated by a strong azimuthal magnetic field, contained in a circular cylinder rotating rapidly about its vertical axis of symmetry. To this basic state is added a geostrophic flow U_G (s), constant on geostrophic cylinders radius s. Its magnitude is fixed by requiring that the Lorentz forces induced by the convecting mode satisfy Taylor's condition. The nonlinear mathematical problem describing the system was developed in an earlier paper (Skinner and Soward, 1988) and the predictions made there are confirmed here. In particular, for small values of the Roberts number q which measures the ratio of the thermal to magnetic diffusivities, two distinct regions can be recognised within the fluid with the outer region moving rapidly compared to the inner. Otherwise, conditions for the onset of instability via the Taylor state (U_G 0) do not differ significantly from those appropriate to the static (U_G = 0) basic state. The possible disruption of the Taylor states by shear flow instabilities is discussed briefly.     

The formation and evolution of an isolated submarine valley in the North Channel,Irish Sea: an investigation of Beaufort's Dyke

Beaufort's Dyke is a submarine depression located in the North Channel of the Irish Sea. With a maximum depth of 312 m, the dyke is one of the deepest areas within the European continental shelf. Integration and interpretation of 450 km of sparker seismic data and full‐coverage bathymetric data derived from multi‐beam echo sounder surveys allow for the investigation of the formation processes of Beaufort's Dyke and the evolution of geomorphological features within it. The dyke, formed by composite subglacial processes dominated by subglacial meltwater discharge, is interpreted as a tunnel valley. The regional isolation of Beaufort's Dyke may be explained by the bounding of the North Channel by the bedrock masses of Ireland and Scotland, coupled with the exploitation of structural weakness along a fault plane and presence of halite in the eroded substrate enhancing the erosive potential of the overlying glacier. Beaufort's Dyke has probably been maintained as an open feature by strong rectilinear tidal currents. The morphology of lunate sediment waves and a large parabolic bedform towards the south of the dyke contradict the observed dominant S–N mean hydrodynamic flow recorded within the North Channel, suggesting an alternative hydrodynamic regime either within the dyke or during bedform creation. Copyright © 2011 John Wiley & Sons, Ltd.     

Bayesian dynamic modelling for nonstationary hydroclimatic time series forecasting along with uncertainty quantification

Forecasting of hydrologic time series, with the quantification of uncertainty, is an important tool for adaptive water resources management. Nonstationarity, caused by climate forcing and other factors, such as change in physical properties of catchment (urbanization, vegetation change, etc.), makes the forecasting task too difficult to model by traditional Box–Jenkins approaches. In this paper, the potential of the Bayesian dynamic modelling approach is investigated through an application to forecast a nonstationary hydroclimatic time series using relevant climate index information. The target is the time series of the volume of Devil's Lake, located in North Dakota, USA, for which it was proved difficult to forecast and quantify the associated uncertainty by traditional methods. Two different Bayesian dynamic modelling approaches are discussed, namely, a constant model and a dynamic regression model (DRM). The constant model uses the information of past observed values of the same time series, whereas the DRM utilizes the information from a causal time series as an exogenous input. Noting that the North Atlantic Oscillation (NAO) index appears to co‐vary with the time series of Devil's Lake annual volume, its use as an exogenous predictor is explored in the case study. The results of both the Bayesian dynamic models are compared with those from the traditional Box–Jenkins time series modelling approach. Although, in this particular case study, it is observed that the DRM performs marginally better than traditional models, the major strength of Bayesian dynamic models lies in the quantification of prediction uncertainty, which is of great value in hydrology, particularly under the recent climate change scenario. Copyright © 2008 John Wiley & Sons, Ltd.     

Modification and testing of a one‐dimensional energy and mass balance model for supraglacial snowpacks

A one‐dimensional energy and mass balance snow model (SNTHERM) has been modified for use with supraglacial snowpacks and applied to a point on Haut Glacier d'Arolla, Switzerland. It has been adapted to incorporate the underlying glacier ice and a site‐specific, empirically derived albedo routine. Model performance was tested against continuous measurements of snow depth and meltwater outflow from the base of the snowpack, and intermittent measurements of surface albedo and snowpack density profiles collected during the 1993 and 2000 melt seasons. Snow and ice ablation was simulated accurately. The timing of the daily pattern of meltwater outflow was well reproduced, although magnitudes were generally underestimated, possibly indicating preferential flow into the snowpack lysimeter. The model was used to assess the quantity of meltwater stored temporally within the unsaturated snowpack and meltwater percolation rates, which were found to be in agreement with dye tracer experiments undertaken on this glacier. As with other energy balance studies on alpine valley glaciers, the energy available for melt was dominated by net radiation (64%), with a sizable contribution from sensible heat flux (36%) and with a negligible latent heat flux overall, although there was more complex temporal variation on diurnal timescales. A basic sensitivity analysis indicated that melt rates were most sensitive to radiation, air temperature and snowpack density, indicating the need to accurately extrapolate/interpolate these variables when developing a spatially distributed framework for this model. Copyright © 2008 John Wiley & Sons, Ltd.     

Estimating finite difference block equivalent hydraulic conductivity for numerically solving the Richards' equation

A method is proposed for calculating the equivalent hydraulic conductivity (EHC) within a finite difference block (FDB). Application of the constant‐flux assumption of Darcy's Law, the EHC equals to the integration of effective hydraulic conductivity (K_w) as a function of pressure head (h_w) divided by the head difference at the ends of the FDB. Error analysis show that the constant‐flux (CF) EHC estimates are better than those computed by the commonly used arithmetic‐mean (AM), geometric‐mean (GM), and harmonic‐mean (HM) techniques. CF EHC results are even more superior at larger interblock head difference situations. Simulations of water infiltration experiments show that simulations using the CF EHC or AM or GM weighting technique have only slight difference while applying the Neumann type boundary condition at the ground surface. In case of the Dirichlet type boundary condition, however, the CF EHC is superior to the other two in correctly estimating the depth of infiltration while enlarging the grid size. Therefore, it is recommended to adopt the CF EHC with a larger grid size to the more stable and more efficient results. Copyright © 2007 John Wiley & Sons, Ltd.     

Green's function for three-dimensional elastic wave equation with a moving point source on the free surface with applications

High-speed train seismology has come into being recently. This new kind of seismology uses a high-speed train as a repeatable moving seismic source. Therefore, Green's function for a moving source is needed to make theoretical studies of the high-speed train seismology. Green's function for three-dimensional elastic wave equation with a moving point source on the free surface is derived. It involves a line integral of the Green's function for a fixed point source with different positions and corresponding time delays. We give a rigorous mathematical proof of this Green's function. According to the principle of linear superposition, we have also obtained the Green's function for a group of moving sources which can be regarded as a model of a traveling high-speed train. Based on a temporal convolution, an analytical formula for other moving sources is also given. In terms of a moving Gaussian source, we deal with the issue of numerical calculations of the analytical formula. Applications to modelling of a traveling high-speed train are presented. We have considered both the land case and the bridge case for a traveling high-speed train. The theoretical seismograms show different waveform features for these two cases.     

On the causes of pressure oscillations in low‐permeable and low‐compressible porous media

Nonphysical pressure oscillations are observed in finite element calculations of Biot's poroelastic equations in low‐permeable media. These pressure oscillations may be understood as a failure of compatibility between the finite element spaces, rather than elastic locking. We present evidence to support this view by comparing and contrasting the pressure oscillations in low‐permeable porous media with those in low‐compressible porous media. As a consequence, it is possible to use established families of stable mixed elements as candidates for choosing finite element spaces for Biot's equations. Copyright © 2011 John Wiley & Sons, Ltd.     

The Campo Felice late Pleistocene Glaciation (Apennines,central Italy)

Study of the glacial deposits and lacustrine sediments of Campo Felice (Apennines, central Italy) has enabled the glacial phases of the last 40 ka to be dated more precisely, and has demonstrated that the maximum glacial advance did not occur in correspondence with the last global glacial maximum and with the coldest and most arid phase suggested by the pollen, but in a period dated between about 33 and 27 ka, characterized by a less extreme climate. Furthermore, a glacial expansion took place also in the period prior to 35 ka. Correlation with the Alpine glacial variations has shown that the Apennine last glacial maximum occurred before that of the southern slope of the Alps. Copyright © 2012 John Wiley & Sons, Ltd.