On the enhanced confining pressure aproach to the mechanics of reinforced soil

Summary A review is presented of conceptual approaches that are currently in use for interpreting the operation of reinforced soil. The concepts of enhanced confining pressure and of reduced normal tensile strains are found to be closely related to current experimental and theoretical investigations as well as to the design methodologies available at present for reinforced soil applications. Focusing on the enhanced confining pressure concept, analytical expressions are developed that allow the estimation of the value of equivalent confining stress increase when the properties of soil and reinforcement and the state of stresses acting on a cylindrical reinforced soil element are known. The derived expressions can also be utilized for estimating the soil-reinforcement friction angle from the results of triaxial tests on cylindrical samples reinforced with horizontal layers of reinforcement.     

La constante solar

Zusammenfassung Aus der Temperatur der Sonnenoberfläche und der Entfernung Sonne-Erde ergiebt sich die Solarkonstante 2.4 in Uebereinstimmung mit dem rohen Wert, der die Instrument-Temperatur berücksichtigt. Da an den meisten Observatorien die mittägliche Sonnenhöhe nicht ausreicht für eine genaue Bestimmung der Solarkonstante, wird 2.4 als rohe vorläufige Solarkonstante vorgeschlagen, bis im Laufe der nächsten 2 Jahre eine genauere Bestimmung vorliegt. Vermutlich ist auch die Strahlungskonstante von dem Temperaturfehler beeinflusst.     

Non-linear channel–shoal dynamics in long tidal embayments

The dynamics of finite-amplitude bed forms in a tidal channel is studied with the use of an idealized morphodynamic model. The latter is based on depth-averaged equations for the tidal flow over a sandy bottom. The model considers phenomena on spatial scales of the order of the tidal excursion length. Transport of sediment mainly takes place as suspended load. The reference state of this model is characterized by a spatially uniform M₂ tidal current over a fixed horizontal bed. The temporal evolution of deviations from this reference state is governed by amplitude equations: these are a set of non-linear equations that describe the temporal evolution of bed forms. These equations are used to obtain new morphodynamic equilibria which may be either static or time-periodic. Several of these bottom profiles show strong similarity with the tidal bars that are observed in natural estuaries. The dependence of the equilibrium solutions on the value of bottom friction and channel width is investigated systematically. For narrow channels (width small compared to the tidal excursion length) stable static equilibria exist if bottom friction is slightly larger than r_cr. For channel widths more comparable to the tidal excursion length, multiple stable steady states may exist for bottom friction parameter values below r_cr. Regardless of channel width, stable time-periodic equilibria seem to emerge as the bottom friction is increased.Responsible Editor: Jens Kappenberg     

The atmospheric tide as a continuous spectrum: Lunar semidiurnal tide in surface pressure

Summary The standard equations for the theory of atmospheric tides are solved here by an integral representation on the continuous spectrum of free oscillations. The model profile of back-ground temperature is that of the U.S. Standard Atmosphere in the lower and middle atmosphere, and in the lower thermosphere, above which an isothermal top extends to arbitrarily great heights. The top is warm enough to bring both the Lamb and the Pekeris modes into the continuous spectrum.Computations are made for semidiurnal lunar tidal pressure at sea level at the equator, and the contributions are partitioned according to vertical as well as horizontal structure. Almost all the response is taken up by the Lamb and Pekeris modes of the slowest westward-propagating gravity wave. At sea level, the Lamb-mode response is direct and is relatively insensitive to details of the temperature profile. The Pekeris mode at sea level has an indirect response-in competition with the Lamb mode-and, as has been known since the time of its discovery, it is quite sensitive to the temperature profile, in particular to stratopause temperature. In the standard atmosphere the Lamb mode contributes about +0.078 mb to tidal surface pressure at the equator and the Pekeris mode about –0.048 mb.The aim of this investigation is to illustrate some consequences of representing the tide in terms of the structures of free oscillations. To simplify that task as much as possible, all modifying influences were omitted, such as background wind and ocean or earth tide. Perhaps the main defect of this paper's implementation of the free-oscillation spectrum is that, in contrast to the conventional expansion in the structures of forced oscillations, it does not include dissipation, either implicity or explicity, and thus does not satisfy causality. Dissipation could be added implicity by means of an impedance condition, for example, which would cause up-going energy flux to exceed downgoing flux at the base of the isothermal top layer. To achieve complete causality, however, the dissipation must be modeled explicity. Nevertheless, since the Lamb and Pekeris modes are strongly trapped in the lower and middle atmosphere, where dissipation is rather weak (except possibly in the surface boundary layer), more realistic modeling is not likely to change the broad features of the present results.Symbols a earth's mean radius; expansion coefficient in (5.3) - b recursion variable in (7.4); proximity to resonance in (9.2) - c sound speed in (2.2); specific heatc _p in (2.2) - f Coriolis parameter 2sin in (2.2) - g standard surface gravity - h equivalent depth - i ; discretization index in (7.3) - j index for horizontal structure - k index for horizontal structure; upward unit vectork in (2.2) - m wave number in longitude - n spherical-harmonic degree; number of grid layers in a model layer - p tidal pressure perturbation; background pressurep ₀ - q heating function (energy per mass per time) - r tidal state vector in (2.1) - s tidal entropy perturbation; background entropys ₀ - t time - u tidal horizontal velocityu - w tidal vertical component of velocity - x excitation vector defined in (2.3); vertical coordinate lnp _*/p ₀ [except in (3.8), where it is lnp /p ₀] - y vertical-structure function in (7.1) - z geopotential height - A constant defined in (6.2) - C spherical-harmonic expansion coefficient in (3.6) - D vertical cross section defined in (5.6) and (5.9) - E eigenstate vector - F vertical-structure function for eigenstate pressure in (3.2) [re-defined with WKB scaling in (7.2)] - G vertical-structure function for eigenstate vertical velocity in (3.2) [re-defined with WKB scaling in (7.2)] - H pressure-scale height - I mode intensity defined in (8.1) - K quadratic form defined in (4.4) - L quadratic form defined in (4.4); horizontal-structure magnification factor defined in (5.11) - M vertical-structure magnification factor defined in (4.6) - P eigenstate pressure in (3.2); tidal pressure in (6.2) - R tidal state vector in (5.1) - S eigenstate entropy in (3.2); spherical surface area, in differential dS - T background molecular-scale (NOAA, 1976) absolute temperatureT ₀ - U eigenstate horizontal velocityU in (3.2); coefficient in (7.3) - V horizontal-structure functionV for eigenstate horizontal velocity in (3.2); recursion variable in (7.3) - W eigenstate vertical velocity in (3.2) - X excitation vector in (5.1) - Y surface spherical harmonic in (3.7) - Z Hough function defined in (3.6) - +dH/dz - (1––)/2 - Kronecker delta; Dirac delta; correction operator in (7.6) - equilibrium tide elevation - (square-root of Hough-function eigenvalue) - ratio of specific gas constant to specific heat for air=2/7 - longitude - - - background density ₀ - eigenstate frequency in (3.1) - proxy for heating functionq =c _P/t - latitude - tide frequency - operator for the limitz - horizontal-structure function for eigenstate pressure in (3.2) - Hough function defined in (6.2) - earth's rotation speed - horizontal gradient operator - ()₀ background variable - ()_* surface value of background variable - () value at base of isothermal top layer - Õ state vector with zerow-component - , energy product defined in (2.4) - | | energy norm - ()^* complex conjugate With 10 Figures     

A Note on the Flux-Variance Similarity Relationships for Heat and Water Vapour in the Unstable Atmospheric Surface Layer

Atmospheric surface layer (ASL) experiments over the past 10 years demonstrate that the flux-variance similarity functions for water vapour are consistently larger in magnitude than their temperature counterpart. In addition, latent heat flux calculations using the flux-variance method do not compare as favorably to eddy- correlation measurements when compared to their sensible heat counterpart. These two findings, in concert with measured heat to water vapour transport efficiencies in excess of unity, are commonly used as evidence of dissimilarity between heat and water vapour transport in the unstable atmospheric surface layer. In this note, it is demonstrated that even if near equality in flux-profile similarity functions for heat and water vapour is satisfied, the flux-variance similarity functions for water vapour are larger in magnitude than temperature for a planar, homogeneous, unstably-stratified turbulent boundary-layer flow.     

Comment and reply regarding Changyou Zhang (1995) A general formula and its inverse formula for gravimetric transformation by use of convolution and deconvolution techniques.

The incorrectness in the derivations of error formula (52) in Zhang's paper is pointed out and the correction is given. Table 3 [list of error formulae of Eqs (5)–(8)] in Zhang's paper is also corrected. Received: 25 February 1998 / Accepted: 30 June 1998     

An analytical solution for rainfall infiltration into an unsaturated infinite slope and its application to slope stability analysis

Surficial slope failures in residual soils are common in tropical and subtropical regions as a result of rainfall infiltration. This study develops an analytical solution for simulating rainfall infiltration into an infinite unsaturated soil slope. The analytical solution is based on the general partial differential equation for water flow through unsaturated soils. It can accept soil–water characteristic curve and unsaturated permeability function of the exponential form into account. Numerical simulations are conducted to verify the assumptions of the analytical solution and demonstrate that the proposed analytical solution is acceptable for the coarse soils with low air entry values. The pore‐water pressure (pwp) distributions obtained from the analytical solution can be incorporated into a limit equilibrium method to do infinite slope stability analysis for a rain‐induced shallow slip. The analysis method takes into account the influence of the water content change on unit weight and hence on factor of safety. A series of analytical parametric analyses have been performed using the developed model. The analyses indicate that when the residual soil slope, consisting of a completely decomposed granite layer underlain by a less permeable layer, is subjected to a continuous heavy rainfall, the loss of negative pwp and the reduction in factor of safety were found to be most significant for the shallow soil layer and during the first 12 h. The antecedent and subsequent rainfall intensity, depth of a less permeable layer and slope angle all have a significant influence on the pwp response and hence the slope stability. Copyright © 2012 John Wiley & Sons, Ltd.     

Modelling dispersion in complex open channel flows: Fuzzy calibration (2)

Part 1 of this study assessed the effectiveness of dispersion models based around random particle tracking (RPT) applied an overbank flow in the Flood Channel Facility at HR Wallingford. Several of the RPT models that were used predicted the mixing behaviour of the tracer in the complex channel flow to within an acceptable accuracy. If there is no uniqueness in the model structure which can be used to represent the true system to within the limitations of the available observations, then this implies an inherent degree of ambiguity in our knowledge of the physically based model structure. This suggests that we should be less forthright in the optimisation of each individual model structure, and perhaps investigate more of the parameter combinations for each model which yield feasible simulations of the system. An alternative fuzzy calibration technique is introduced which avoids the optimisation process and takes account of uncertainties in the model structure, parameter sets and observed data in prediction.     

Solar–terrestrial effects possibly stronger in biblical times

Paleomagnetic studies have shown that, moving backwards in time, the geomagnetic dipole moment increased to a peak nearly 50% greater than at present ca. 2500 years ago. Attempts to model how changes in dipole moment affect solar–terrestrial relations have hitherto invoked a scaling relation for the size of the magnetosphere based on finding where the magnetic pressure of the dipole field balances the ram pressure of the solar wind. This approach predicts that, following a solar storm, the strength of the terrestrial response represented by the electrical potential across the auroral zones in the ionosphere should vary as the 1/3 power of dipole moment. Such a weak dependence suggests that a 50% increase in dipole moment would minimally effect (14%) terrestrial manifestations of solar storms. Recent work, however, based on a feedback mechanism involving electrical currents coupling the magnetosphere and ionosphere has identified a stronger 4/3, power scaling relation applicable to storm conditions. Here we use a global MHD simulation to calculate for a 50% increased dipole moment the correspondingly increased auroral-zone potential and its extension to low latitudes.