Optimum design of nailed soil slopes

In this paper, a generalized method of computer based optimum design of soil-nailed slopes is reported. A limit equilibrium formulation satisfying overall and internal equilibrium and considering the effect of tensile resistance of the reinforcement has been used in computing the stability of nailed slopes. The quantity of steel requirement for raising the factor of safety to a desired value is estimated. The location, size (length and diameter) and orientation of the nails and the location and shape of the critical shear surface have been treated as variables. The solutions have been isolated by formulating the problem as one of non-linear programming. The applicability of the developed method has been verified by comparing the predicted failure surfaces with those observed in model tests as well as in the field and also reported theoretical results.     

The general solution of the HENON–HEILES problem

The general solution of the Henon–Heiles system is approximated inside a domain of the (x, C) of initial conditions (C is the energy constant). The method applied is that described by Poincaré as ‘the only “crack” permitting penetration into the non-integrable problems’ and involves calculation of a dense set of families of periodic solutions that covers the solution space of the problem. In the case of the Henon–Heiles potential we calculated the families of periodic solutions that re-enter after 1–108 oscillations. The density of the set of such families is defined by a pre-assigned parameter ε (Poincaré parameter), which ascertains that at least one periodic solution is computed and available within a distance ε from any point of the domain (x, C) for which the approximate general solution computed. The approximate general solution presented here corresponds to ε = 0.07. The same solution is further improved by “zooming” into four square sub-domain of (x, C), i.e. by computing sufficient number of families that reduce the density parameter to ε = 0.003. Further zooming to reduce the density parameter, say to ε = 10⁻⁶, or even smaller, although easily performable in both areas occupied by stable as well as unstable solutions, was found unnecessary. The stability of all members of each and all families computed was calculated and presented in this paper for both the large solution domain and for the sub-domains. The correspondence between areas of the approximate general solution occupied by stable periodic solutions and Poincaré sections with well-aligned section points and also correspondence between areas occupied by unstable solutions and Poincaré sections with randomly scattered section points is shown by calculating such sections. All calculations were performed using the Runge-Kutta (R-K) 8th order direct integration method and the large output received, consisting of many thousands of families is saved as “Atlas of the General Solution of the Henon–Heiles Problem,” including their stability and is available at request. It is concluded that approximation of the general solution of this system is straightforward and that the chaotic character of its Poincaré sections imposes no limitations or difficulties.     

Numerical Exploration of Chermnykh’s Problem

We study the equilibrium points and the zero-velocity curves of Chermnykh’s problem when the angular velocity ω varies continuously and the value of the mass parameter is fixed. The planar symmetric simple-periodic orbits are determined numerically and they are presented for three values of the parameter ω. The stability of the periodic orbits of all the families is computed. Particularly, we explore the network of the families when the angular velocity has the critical value ω = 2√2 at which the triangular equilibria disappear by coalescing with the collinear equilibrium point L₁. The analytic determination of the initial conditions of the family which emanate from the Lagrangian libration point L₁ in this case, is given. Non-periodic orbits, as points on a surface of section, providing an outlook of the stability regions, chaotic and escape motions as well as multiple-periodic orbits, are also computed. Non-linear stability zones of the triangular Lagrangian points are computed numerically for the Earth–Moon and Sun–Jupiter mass distribution when the angular velocity varies.     

‘Surface Drag in the Arctic Marginal Sea-ice Zone: A Comparison of Different Parameterisation Concepts’

Two parameterisation schemes for the turbulent surface fluxes and drag coefficients over the Arctic marginal sea-ice zone (MIZ) are (further) developed, and their results are compared with each other. Although the schemes are based on different principles (flux averaging and parameter averaging), the resulting drag coefficients differ only slightly in the case of neutral and stable stratification. For unstable stratification and sea-ice conditions being typical for the north-eastern Fram Strait, the drag coefficients resulting from the parameter-averaging concept are 5–10% larger than those of the flux-averaging concept. At a sea-ice concentration of 45%, the parameter-averaging method overestimates the heat fluxes by a factor of 1.2. An inclusion in the schemes of form drag caused by floe edges and ridges has a much larger effect on the drag coefficient, and on the momentum fluxes, than the choice between the parameter-averaging or flux-averaging methods. Based on sensitivity studies with the flux-averaging scheme, a simple formula for the effective drag coefficient above the Arctic MIZ is derived. It reduces the computational costs of the more complex parameterisations and could also be used in larger scale models. With this simple formula, the effective drag coefficient can be calculated as a function of the sea-ice concentration and skin drag coefficients for water and ice floes. The results obtained with this parameterisation differ only slightly from those using the more complex schemes. Finally, it is shown that in the MIZ, drag coefficients for sea-ice models may differ significantly from the effective drag coefficients used in atmospheric models.     

Variance Method to Determine Turbulent Fluxes of Momentum And Sensible Heat in The Stable Atmospheric Surface Layer

Evidence is presented that in the stable atmospheric surface layer turbulent fluxes of heat and momentum can be determined from the standard deviations of longitudinal wind velocity and temperature, σ _u and σ _T respectively, measured at a single level. An attractive aspect of this method is that it yields fluxes from measurements that can be obtained with two-dimensional sonic anemometers. These instruments are increasingly being used at official weather stations, where they replace the standard cup anemometer–wind vane system. With methods such as the one described in this note, a widespread, good quality, flux network can be established, which would greatly benefit the modelling community. It is shown that a ‘variance’ dimensionless height (ζ _σ) defined from σ _u and σ _T is highly related to the ‘conventional’ dimensionless stability parameter ζ=z/L, where z is height and L is the Obukhov length. Empirical functions for ζ _σ are proposed that allow direct calculation of heat and momentum fluxes from σ _u and σ _T. The method performs fairly well also during a night of intermittent turbulence.     

Second Tesseral Harmonic Torque Due to the DynamicS of the Oceanic Surface Layer as Detected by TOPEX/POSEIDON Altimetry 1993-2000

Estimates of the second tesseral torque due to the variations in the radial space position of the mean ocean surface as monitored by TOPEX/POSEIDON altimeter system are derived. The magnitude of the studied torque may be compared to the tidal torque and to the tesseral torque caused by deformations due to the Earths rotation. However, such torque estimates strongly depend on the thickness of the ocean surface layer adopted in the spherical model of which the dynamics is believed to be responsible for the derived torque. The dependence on the thickness is discussed.     

Surface area, porosity and water adsorption properties of fine volcanic ash particles

Our understanding on how ash particles in volcanic plumes react with coexisting gases and aerosols is still rudimentary, despite the importance of these reactions in influencing the chemistry and dynamics of a plume. In this study, six samples of fine ash (<100 m) from different volcanoes were measured for their specific surface area, a_s, porosity and water adsorption properties with the aim to provide insights into the capacity of silicate ash particles to react with gases, including water vapour. To do so, we performed high-resolution nitrogen and water vapour adsorption/desorption experiments at 77 K and 303 K, respectively. The nitrogen data indicated a_s values in the range 1.1–2.1 m²/g, except in one case where a a_s of 10 m²/g was measured. This high value is attributed to incorporation of hydrothermal phases, such as clay minerals, in the ash surface composition. The data also revealed that the ash samples are essentially non-porous, or have a porosity dominated by macropores with widths >500 Å. All the specimens had similar pore size distributions, with a small peak centered around 50 Å. These findings suggest that fine ash particles have relatively undifferentiated surface textures, irrespective of the chemical composition and eruption type. Adsorption isotherms for water vapour revealed that the capacity of the ash samples for water adsorption is systematically larger than predicted from the nitrogen adsorption a_s values. Enhanced reactivity of the ash surface towards water may result from (i) hydration of bulk ash constituents; (ii) hydration of surface compounds; and/or (iii) hydroxylation of the surface of the ash. The later mechanism may lead to irreversible retention of water. Based on these experiments, we predict that volcanic ash is covered by a complete monolayer of water under ambient atmospheric conditions. In addition, capillary condensation within ash pores should allow for deposition of condensed water on to ash particles before water reaches saturation in the plume. The total mass of water vapour retained by 1 g of fine ash at 0.95 relative water vapour pressure is calculated to be ~10^–2 g. Some volcanic implications of this study are discussed.Editorial responsibility: J. Gilbert     

Chlorinated hydrocarbons in the seawater and surface sediments of Blanca Bay,Argentina

In order to characterize our study area and to provide reference values to be used in the future to measure the changes produced by an increase in contamination, the concentrations of chlorinated hydrocarbons have been investigated in fifty-one samples of seawater, taken at four different depths: air-sea interface, surface, one metre and bottom waters, and in twenty-three samples of surface sediments from Blanca Bay, Argentina. Of eleven organochlorine compounds we were looking for (α BHC, lindane, heptachlor, δ BHC. aldrin, heptachlor epoxide, dieldrin, o-p′DDD, p-p′DDD, o-p′DDT and p-p′DDT), seven could be detected in seawater and three in surface sediments with the following mean concentrations: α-BHC=48·2 ng l^?1; lindane=54·2 ng l^?1; heptachlor=45·0 ng l^?1; δ BHC=12·5 ng l^?1; aldrin=61·8 ng l^?1 and ΣDDT=67·0 ng l^?1; and δ BHC=3·2 ng g^?1; lindane=4·2 ng g^?1 and heptachlor=1·0 ng g^?1 for seawater, regarding the surface waters, and sediment samples, respectively.Concentration factors among the different water layers were also studied to see if there was any correlation between chlorinated hydrocarbon contents and the water depths from which the samples were taken. As a mean value, the air-sea interface water contains 18 times more of these compounds than that of the water near the bottom. A comparison of the values corresponding to seawater and surface sediments from our study area with those levels measured in samples from other geographic locations is also presented.With the purpose to detect a relationship between chlorinated hydrocarbon concentrations and the contents of particulate matter (PM) on the one hand, and particulate organic material (POM) on the other hand, four groups of samples containing different amounts of PM and POM, respectively were formed. From a comparison of the results obtained, lindane, heptachlor and δ BHC showed a tendency to lower concentrations in those samples containing little PM whereas α BHC and aldrin remained without important changes. No significant correlation was found between organochlorine levels and contents of POM.     

TREND SURFACE ANALYSIS OF GLACIALLY BURIED PLEISTOCENE ORGANIC DEPOSITS IN CENTRAL MICHIGAN*

Trend surfaces were determined and compared for the bedrock surface, two characteristics of the present topography, and 42 water well log reports of glacially buried carbonaceous horizons within drift from an area in central Michigan. Data almost certainly indicate that the glacially buried Pleistocene organic deposits represent two or more pre-Woodfordian paleosurfaces. Trend surface analysis of buried organic horizons may be useful for recognizing paleosurfaces and separating drift sheets in other areas with limited subsurface data.