Principal axes of m-DOF structures PartⅠ:Static loading

This paper is the first in a two-part series that discusses the principal axes of M-DOF structures subjected to static and dynamic loads. The primary purpose of this series is to understand the magnitude of the dynamic response of structures to enable better design of structures and control modification devices/systems. Under idealized design conditions, the structural responses are obtained by using single direction input ground motions in the direction of the intended control devices/systems,and by assuming that the responses of the structure is decoupleable in three mutually perpendicular directions. This standard practice has been applied to both new and retrofitted structures using various seismic protective systems. Very limited information is available on the effects of neglecting the impact of directional couplings (cross effects - of which torsion is a component) of the dynamic response of structures. In order to quantify such effects, it is necessary to examine the principal axes of structures under both static and dynamic loading.This first paper deals with quantitative definitions of principal axes and "cross effects" of three-dimensional structures under static load by using linear algebra. It shows theoretically that, for three-dimensional structures, such principal axes rarely exist. Under static loading conditions, the cross effect is typically small and negligible from the viewpoint of engineering applications. However, it provides the theoretical base for subsequent quantification of the response couplings under dynamic loads, which is reported in part Ⅱ of this series.     

Experimental validation of the wavefield transform of electromagnetic fields

The wavefield transform is a mathematical technique for transforming low-frequency electromagnetic (EM) signals to a non-diffusive wave domain. The ray approximation is valid in the transform space and this makes traveltime tomography for 3D mapping of the electrical conductivity distribution in the subsurface possible. The transform, however, imposes stringent frequency bandwidth and signal-to-noise ratio requirements on the data. Here we discuss a laboratory scale experiment designed to collect transform quality EM data, and to demonstrate the practical feasibility of transforming these data to the wavefield domain.
We have used the scalable nature of EM fields to design a time-domain experiment using graphite blocks to simulate realistic field conditions while leaving the time scale undisturbed. The spatial dimensions have been scaled down by a factor of a thousand by scaling conductivity up by a factor of a million. The graphite blocks have two holes drilled into them to carry out cross-well and borehole-to-surface experiments. Steel sheets have been inserted between the blocks to simulate a conductive layer.
Our experiments show that accurate EM data can be recorded on a laboratory scale model even when the scaling of some features, such as drill-hole diameters, is not maintained. More importantly, the time-domain EM data recorded in cross-well and surface-to-borehole modes can be usefully and accurately transformed to the wavefield domain. The observed wavefield propagation delay is proportional to the direct distance between the transmitter and receiver in a homogeneous medium. In a layered medium, data accuracy is reduced and, hence, our results are not so conclusive. On the basis of the experimental results we conclude that the wavefield transform could constitute a valid approach to the interpretation of accurate, undistorted time-domain data if further improvement in the transform can be realized.     

On the spatial relationship between landslides and causative factors on Lantau Island, Hong Kong

This paper presents a statistical approach to study the spatial relationship between landslides and their causative factors at the regional level. The approach is based on digital databases, and incorporates such methods as statistics, spatial pattern analysis, and interactive mapping. Firstly, the authors propose an object-oriented conceptual model for describing a landslide event, and a combined database of landslides and environmental factors is constructed by integrating the various databases within such a conceptual framework. The statistical histogram, spatial overlay, and dynamic mapping methods are linked together to interactively evaluate the spatial pattern of the relationship between landslides and their causative factors. A case study of an extreme event in 1993 on Lantau Island indicates that rainfall intensity and the migration of the center of the rainstorm greatly influence the occurrence of landslides on Lantau Island. A regional difference in the relationship between landslides and topography is identified. Most of the landslides in the middle and western parts of the island occurred on slopes with slope angles of 25–35°, while in the eastern part, the corresponding range is 30–35°. Overlaying landslide data with land cover reveals that a large number of landslides occurred in the bareland and shrub-covered area, and in the transition zones between different vegetation types. The proposed approach can be used not only to analyze the general characteristics of such a relationship, but also to depict its spatial distribution and variation, thereby providing a sound basis for regional landslide prediction.     

Landslide susceptibility analysis using GIS and artificial neural network

The purpose of this study is to develop landslide susceptibility analysis techniques using an arti?cial neural network and to apply the newly developed techniques to the study area of Yongin in Korea. Landslide locations were identi?ed in the study area from interpretation of aerial photographs, ?eld survey data, and a spatial database of the topography, soil type and timber cover. The landslide‐related factors (slope, curvature, soil texture, soil drainage, soil effective thickness, timber age, and timber diameter) were extracted from the spatial database. Using those factors, landslide susceptibility was analysed by arti?cial neural network methods. The landslide susceptibility index was calculated by the back‐propagation method, which is a type of arti?cial neural network method, and the susceptibility map was made with a geographic information system (GIS) program. The results of the landslide susceptibility analysis were veri?ed using landslide location data. The validation results showed satisfactory agreement between the susceptibility map and the existing data on landslide location. A GIS was used to ef?ciently analyse the vast amount of data, and an arti?cial neural network to be an effective tool to maintain precision and accuracy. The results can be used to reduce hazards associated with landslides and to plan land use and construction. Copyright © 2003 John Wiley & Sons, Ltd.     

Vanadium in peridotites as a proxy for paleo-fO2 during partial melting : prospects, limitations, and implications

The compatibility of vanadium (V) during mantle melting is a function of oxygen fugacity (fO₂): at high fO₂’s, V becomes more incompatible. The prospects and limitations of using the V content of peridotites as a proxy for paleo-fO₂ at the time of melt extraction were investigated here by assessing the uncertainties in V measurements and the sensitivity of V as a function of degree of melt extracted and fO₂. V-MgO and V-Al₂O₃ systematics were found to be sensitive to fO₂ variations, but consideration of the uncertainties in measurements and model parameters indicates that V is sensitive only to relative fO₂ differences greater than ∼2 log units. Post-Archean oceanic mantle peridotites, as represented by abyssal peridotites and obducted massif peridotites, have V-MgO and -Al₂O₃ systematics that can be modeled by 1.5 GPa melting between FMQ − 3 and FMQ − 1. This is consistent with fO₂’s of the mantle source for mid-ocean ridge basalts (MORBs) as determined by the Fe³⁺ activity of peridotitic minerals and basaltic glasses. Some arc-related peridotites have slightly lower V for a given degree of melting than oceanic mantle peridotites, and can be modeled by 1.5 GPa melting at fO₂’s as high as FMQ. However, the majority of arc-related peridotites have V-MgO systematics overlapping that of oceanic mantle peridotites, suggesting that although some arc mantle may melt under slightly oxidizing conditions, most arc mantle does not. The fact that thermobarometrically determined fO₂’s in arc peridotites and lavas can be significantly higher than that inferred from V systematics, suggests that V retains a record of the fO₂ during partial melting, whereas the activity of Fe³⁺ in arc peridotitic minerals and lavas reflect subsequent metasomatic overprints and magmatic differentiation/emplacement processes, respectively.Peridotites associated with middle to late Archean cratonic mantle are characterized by highly variable V-MgO systematics. Tanzanian cratonic peridotites have V systematics indistinguishable from post-Archean oceanic mantle and can be modeled by 3 GPa partial melting at ∼FMQ − 3. In contrast, many South African and Siberian cratonic peridotites have much lower V contents for a given degree of melting, suggesting at first glance that partial melting occurred at high fO₂’s. More likely, however, their unusually low V contents for a given degree of melting may be artifacts of excess orthopyroxene, a feature that pervades many South African and Siberian peridotites but not the Tanzanian peridotites. This is indicated by the fact that the V contents of South African and Siberian peridotites are correlated with increases in SiO₂ content, generating data arrays that cannot be modeled by partial melting but can instead be generated by the addition of orthopyroxene through processes unrelated to primary melt depletion. Correction for orthopyroxene addition suggests that the South African and Siberian peridotites have V-MgO systematics similar to those of Tanzanian peridotites. Thus, if the Tanzanian peridotites represent the original partial melting residues, and if the South African and Siberian peridotites have been modified by orthopyroxene addition, then there is no indication that Archean cratonic mantle formed under fO₂’s significantly greater than that of modern oceanic mantle. Instead, the fO₂’s inferred from the V systematics in these three cratonic peridotite suites are within range of modern oceanic mantle. This also suggests that the transition from a highly reducing mantle in equilibrium with a metallic core to the present oxidized state must have occurred by late Archean times.     

Computational study of tetrahedral Al–Si and octahedral Al–Mg ordering in phengite

 As part of a wider study of the nature and origins of cation order–disorder in micas, a variety of computational techniques have been used to investigate the nature of tetrahedral and octahedral ordering in phengite, K₂ ^[6](Al₃Mg)^[4](Si₇Al)O₂₀(OH)₄. Values of the atomic exchange interaction parameters J _n used to model the energies of order–disorder were calculated. Both tetrahedral Al–Si and octahedral Al–Mg ordering were studied and hence three types of interaction parameter were necessary: for T–T, O–O and T–O interactions (where T denotes tetrahedral sites and O denotes octahedral sites). Values for the T–T and O–O interactions were taken from results on other systems, whilst we calculated new values for the T–O interactions. We have demonstrated that modelling the octahedral and tetrahedral sheets alone and independently produces different results from modelling a whole T–O–T layer, hence justifying the inclusion of the T–O interactions. Simulations of a whole T–O–T layer of phengite indicated the presence of short-range order, but no long-range order was observed. Received: 8 August 2002 / Accepted: 14 February 2003 Acknowledgements The authors are grateful to EPSRC (EJP) and the Royal Society (CIS) for financial support. Monte Carlo simulations were performed on the Mineral Physics Group's Beowulf cluster and the University of Cambridge's High Performance Computing Facility.