Fast iterative solution of large undrained soil‐structure interaction problems

In view of rapid developments in iterative solvers, it is timely to re‐examine the merits of using mixed formulation for incompressible problems. This paper presents extensive numerical studies to compare the accuracy of undrained solutions resulting from the standard displacement formulation with a penalty term and the two‐field mixed formulation. The standard displacement and two‐field mixed formulations are solved using both direct and iterative approaches to assess if it is cost‐effective to achieve more accurate solutions. Numerical studies of a simple footing problem show that the mixed formulation is able to solve the incompressible problem ‘exactly’, does not create pressure and stress instabilities, and obviate the need for an ad hoc penalty number. In addition, for large‐scale problems where it is not possible to perform direct solutions entirely within available random access memory, it turns out that the larger system of equations from mixed formulation also can be solved much more efficiently than the smaller system of equations arising from standard formulation by using the symmetric quasi‐minimal residual (SQMR) method with the generalized Jacobi (GJ) preconditioner. Iterative solution by SQMR with GJ preconditioning also is more elegant, faster, and more accurate than the popular Uzawa method. Copyright © 2003 John Wiley & Sons, Ltd.     

Oxygen compounds in Titan's stratosphere as observed by Cassini CIRS

We have investigated the abundances of Titan's stratospheric oxygen compounds using 0.5 cm⁻¹ resolution spectra from the Composite Infrared Spectrometer on the Cassini orbiter. The CO abundance was derived for several observations of far-infrared nadir spectra, taken at a range of latitudes (75° S-35° N) and emission angles (0°-60°), using rotational lines that have not been analysed before the arrival of Cassini at Saturn. The derived volume mixing ratios for the different observations are mutually consistent regardless of latitude. The weighted mean CO volume mixing ratio is 47±8 ppm if CO is assumed to be uniform with latitude. H₂O could not be detected and an upper limit of 0.9 ppb was determined. CO₂ abundances derived from mid-infrared nadir spectra show no significant latitudinal variations, with typical values of 16±2 ppb. Mid-infrared limb spectra at 55° S were used to constrain the vertical profile of CO₂ for the first time. A vertical CO₂ profile that is constant above the condensation level at a volume mixing ratio of 15 ppb reproduces the limb spectra very well below 200 km. This is consistent with the long chemical lifetime of CO₂ in Titan's stratosphere. Above 200 km the CO₂ volume mixing ratio is not well constrained and an increase with altitude cannot be ruled out there.     

Stochastic Modelling of the Impact of Flood Protection Measures Along the River Waal in the Netherlands

River flooding is a problem of international interest. In the past few years many countries suffered from severe floods. A large part of the Netherlands is below sea level and river levels. The Dutch flood defences along the river Rhine are designed for water levels with a probability of exceedance of 1/1250 per year. These water levels are computed with a hydrodynamic model using a deterministic bed level and a deterministic design discharge. Traditionally, the safety against flooding in the Netherlands is obtained by building and reinforcing dikes. Recently, a new policy was proposed to cope with increasing design discharges in the Rhine and Meuse rivers. This policy is known as the Room for the River (RfR) policy, in which a reduction of flood levels is achieved by measures creating space for the river, such as dike replacement, side channels and floodplain lowering. As compared with dike reinforcement, these measures may have a stronger impact on flow and sediment transport fields, probably leading to stronger morphological effects. As a result of the latter the flood conveyance capacity may decrease over time. An a priori judgement of safety against flooding on the basis of an increased conveyance capacity of the river can be quite misleading. Therefore, the determination of design water levels using a fixed-bed hydrodynamic model may not be justified and the use of a mobile-bed approach may be more appropriate. This problem is addressed in this paper, using a case study of the river Waal (one of the Rhine branches in the Netherlands). The morphological response of the river Waal to a flood protection measure (floodplain lowering in combination with summer levee removal) is analysed. The effect of this measure is subject to various sources of uncertainty. Monte Carlo simulations are applied to calculate the impact of uncertainties in the river discharge on the bed levels. The impact of the “uncertain” morphological response on design flood level predictions is analysed for three phenomena, viz. the impact of the spatial morphological variation over years, the impact of the seasonal morphological variation and the impact of the morphological variability around bifurcation points. The impact of seasonal morphological variations turns out to be negligible, but the other two phenomena appear to have each an appreciable impact (order of magnitude 0.05–0.1 m) on the computed design water levels. We have to note however, that other sources of uncertainty (e.g. uncertainty in hydraulic roughness predictor), which may be of influence, are not taken into consideration. In fact, the present investigation is limited to the sensitivity of the design water levels to uncertainties in the predicted bed level.     

Pilot‐scale field validation of the long electrode electrical resistivity tomography method

A validation experiment, carried out in a scaled field setting, was attempted for the long electrode electrical resistivity tomography method in order to demonstrate the performance of the technique in imaging a simple buried target. The experiment was an approximately 1/17 scale mock‐up of a region encompassing a buried nuclear waste tank on the Hanford site. The target of focus was constructed by manually forming a simulated plume within the vadose zone using a tank waste simulant. The long electrode results were compared to results from conventional point electrodes on the surface and buried within the survey domain. Using a pole‐pole array, both point and long electrode imaging techniques identified the lateral extents of the pre‐formed plume with reasonable fidelity but the long electrode method was handicapped in reconstructing vertical boundaries. The pole‐dipole and dipole‐dipole arrays were also tested with the long electrode method and were shown to have the least favourable target properties, including the position of the reconstructed plume relative to the known plume and the intensity of false positive targets. The poor performance of the pole‐dipole and dipole‐dipole arrays was attributed to an inexhaustive and non‐optimal coverage of data at key electrodes, as well as an increased noise for electrode combinations with high geometric factors. However, when comparing the model resolution matrix among the different acquisition strategies, the pole‐dipole and dipole‐dipole arrays using long electrodes were shown to have significantly higher average and maximum values within the matrix than any pole‐pole array. The model resolution describes how well the inversion model resolves the subsurface. Given the model resolution performance of the pole‐dipole and dipole‐dipole arrays, it may be worth investing in tools to understand the optimum subset of randomly distributed electrode pairs to produce maximum performance from the inversion model.     

Spatial behaviour of Rayleigh waves in layered half‐spaces under active surface sources

In the free state, Rayleigh waves are assumed to travel in the form of planar wavefronts. Under such an assumption, the propagation behaviour of the modes of Rayleigh waves in layered half‐spaces is only frequency dependent. The frequency behaviour, which is often termed as dispersion, is determined by the shear wave velocity profile of layered soils within the depth related to wavelength (or frequency). According to this characteristic, the shear wave velocity profile can be back‐analysed from the dispersion. The technique is widely used in the surface wave testing. However, the wavefronts of Rayleigh waves activated by the surface sources are non‐planar. The geometric discrepancy could result in Rayleigh waves manifesting distance‐dependent behaviour, which is referred to as spatial behaviour in this paper. Conventional analysis ignoring this spatial behaviour could introduce unexpected errors. In order to take the effects of sources on the propagation behaviour into account, a new mathematical model is established for Rayleigh waves in layered elastic media under vertical disc‐like surface sources using the thin‐layer method. The spatial behaviour of the activated modes and the apparent phase velocity, which is the propagation velocity of Rayleigh waves superposed by the multiple modes, are then analysed. Aspects of the spatial behaviour investigated in this paper include the equilibrium path, the particle orbit, and the geometric attenuation of the activated Rayleigh waves. The results presented in this paper can provide some guidelines for developing new inverse mathematical models and algorithms.     

Hybrid machine learning model with random field and limited CPT data to quantify horizontal scale of fluctuation of soil spatial variability

Acta Geotechnica - The scale of fluctuation (SOF) is the critical parameter to describe the soil spatial variability, which significantly influences the embedded geostructures. Due to the limited...     

Laboratory sulfurisation of the marine microalga Nannochloropsis salina

To understand more fully the mode of preservation of organic matter in marine sediments, laboratory sulfurisation of intact cells of the cultured microalga Nannochloropsis salina was performed using inorganic polysulfides in seawater at 50°C. Solvent extractable and non-extractable materials were analysed by GC–MS and Py–GC–MS, respectively, to study the incorporation of sulfur into the microalgal organic matter. No GC-amenable sulfur-containing compounds were found in the extracts apart from some minor thiophenes with a phytanyl carbon skeleton. The residue after extraction and hydrolysis contained abundant macromolecular sulfur-containing moieties as revealed by the presence of dominant C₂₈–C₃₂ thiols, thiophenes, thianes and thiolanes in the flash pyrolysates. These products are thought to be formed from moieties derived from sulfurisation of C₂₈–C₃₂ diols and alkenols, characteristic lipids of N. salina. C₁–C₂ alkylated thiophenes were also found in the pyrolysates and probably result from moieties formed upon sulfurisation of carbohydrates. The highly resistant biomacromolecule (algaenan) synthesised by N. salina remains unaffected by sulfurisation. The non-hydrolysable residue isolated from the sulfurised N. salina thus comprises algaenan and (poly)sulfide-bound long alkyl chains. The sulfurisation experiments show that both selective preservation of algaenans and lipid and carbohydrate “vulcanisation” can be involved in the preservation of algal organic matter in marine environments.