Elastic solutions for stresses in a transversely isotropic half‐space subjected to three‐dimensional buried parabolic rectangular loads

In many areas of engineering practice, applied loads are not uniformly distributed but often concentrated towards the centre of a foundation. Thus, loads are more realistically depicted as distributed as linearly varying or as parabola of revolution. Solutions for stresses in a transversely isotropic half‐space caused by concave and convex parabolic loads that act on a rectangle have not been derived. This work proposes analytical solutions for stresses in a transversely isotropic half‐space, induced by three‐dimensional, buried, linearly varying/uniform/parabolic rectangular loads. Load types include an upwardly and a downwardly linearly varying load, a uniform load, a concave and a convex parabolic load, all distributed over a rectangular area. These solutions are obtained by integrating the point load solutions in a Cartesian co‐ordinate system for a transversely isotropic half‐space. The buried depth, the dimensions of the loaded area, the type and degree of material anisotropy and the loading type for transversely isotropic half‐spaces influence the proposed solutions. An illustrative example is presented to elucidate the effect of the dimensions of the loaded area, the type and degree of rock anisotropy, and the type of loading on the vertical stress in the isotropic/transversely isotropic rocks subjected to a linearly varying/uniform/parabolic rectangular load. Copyright © 2002 John Wiley & Sons, Ltd.     

三维抛物方程Douglas交替方向隐格式的稳定性和收敛性

作者研究三维变系数抛物方程 Douglas交替方向隐格式的稳定性和收敛性。采用 H1能量估计方法 ,证明格式按离散 H1范数是绝对稳定的 ,并且收敛阶为 O(Δ t2 + h2 )     

Parabolic Wave Propagation Modelling in Orthogonal Coordinate Systems

This paper presents a numerical model study of the propagation of water waves using the parabolic approximation of the mild-slope equation in the orthogonal coordinate system. Two types of coordinate systems are studied: (a) a general form of orthogonal coordinate system and (b) the conformal system, a special form of orthogonal coordinate system. Two typical examples, namely, expanded breakwaters and a circular channel, are studied to validate the model. First, the examples are studied by use of the general orthogonal coordinates. Then the same examples are computed by use of the confonnal system. The computational results show that the confonnal coordinate system generally gives better predictions than the general orthogonal system. A numerical technique for generating the conformal grid is combined with the numerical model to improve the practicability of the model. The comparison between the result from the numerical grid system and that from the analytical grid system shows that reliable computational results can be obtained by use of the numerical confonnal grid system.     

国外海岸沙丘形成与演化的研究

自20世纪80年代以来，国外对海岸沙丘的研究已从主要对其地貌形态的研究转向海岸海丘与海岸变迁尤其是全球变化关系的研究上，海岸沙丘形成与演化的研究倍受关注，进行了大量研究并取得了一定的研究成果。这里介绍了国外在海岸沙丘形成与演化研究方面的主要进展及其成果，并以此探讨了国内今后开展海岸沙丘形成与演化研究的主要方向与问题。     

On solving Kepler's equation for nearly parabolic orbits

We deal here with the efficient starting points for Kepler's equation in the special case of nearly parabolic orbits. Our approach provides with very simple formulas that allow calculating these points on a scientific vest-pocket calculator. Moreover, srtarting with these points in the Newton's method we can calculate a root of Kepler's equation with an accuracy greater than 0.001 in 0–2 iterations. This accuracy holds for the true anomaly || 135° and |e – 1| 0.01. We explain the reason for this effect also.Dedicated to the memory of Professor G.N. Duboshin (1903–1986).     

The gawler ranges,South Australia: an unusual volcanic massif

The volcanic residuals of the Gawler Ranges together form an extensive massif that in its gross morphology differs markedly from most exposures of silicic volcanic rocks. The upland developed in two stages, the first involving differential fracture‐controlled subsurface weathering, the second the stripping of the regolith. As a result, an irregular weathering front was exposed, with domical projections prominent. These bornhardts are etch forms, and they are of considerable antiquity.

The differential weathering of the rock mass reflects the exploitation of various fracture systems by shallow groundwaters. Orthogonal fracture systems at various scales, sheet fractures and columnar joints control the morphology of the bornhardts in gross and in detail.

The exploitation of the structural base, which was established in the Middle Protero‐zoic, probably took place throughout the Late Proterozoic and the Palaeozoic, though only minor remnants of the Proterozoic land surface remain. The major landscape features developed during the Mesozoic. The weathering which initiated the bornhardts occurred in the Jurassic or earlier Mesozoic, and the landforms were exposed in Late Cretaceous to Early Tertiary times.

Though structural forms dominate the present landscape, some major and some minor landforms are best explained in terms of climatic changes of the later Cainozoic. The palaeodrainage system, established under humid conditions by the Early Tertiary, was alluviated during the Cainozoic arid phases, and salinas were formed. The sand dunes of the region also reflect this aridity.     

A consideration of the dune:antidune transition in fine gravel

Hydraulic data defining the dune:antidune transition in fine gravel are compared with potential flow theory, and information is drawn from published experiments and field‐based studies. Attention is given to both transitional bedforms and the development of downstream‐migrating antidunes. In the latter case, most data pertain to sand beds and not to gravel. Empirical data provide some weak support for the theoretical notion that the transition occurs at progressively lower Froude numbers at greater relative depths. Although a critical Froude number of 0·84 may reasonably be applied for the beginning of the dune to antidune transformation, lag effects (and a possible depth limitation) ensure that transitional bedforms may persist across a broad range of Froude numbers from 0·5 to 1·8. This latter observation has great relevance for palaeohydraulic estimates derived from outcrop data. Whereas the application of theoretical bedform existence fields, based upon potential flow theory, to fine gravel was previously purely speculative, the addition of experimental and field data to these plots provides a degree of confidence in applying stability theory to practical geological problems. For the first time, laboratory data pertaining to downstream‐migrating gravel antidunes are compared with theory. These bedforms have been reported from certain experimental near‐critical flows above sand or gravel beds, but have been observed infrequently in natural streams. However, there are no detailed studies from natural rivers and only a few contentious identifications from outcrops. Nevertheless, the limited hydraulic data conform to theoretical expectations.     

Dynamic processes of a simple linear dune—a study in the Taklimakan Sand Sea, China

Samples of dune sands, surveys of the morphology and field measurements of wind velocity and direction of a simple linear dune in Taklimakan Sand Sea show that the airflow and sand flux vary with the change of wind direction on the dune surface. Decrease of the airflow stress on the lee flank does not result in much decrease of the sand flux because of the low threshold shear velocities and the airflow conditions. There are no significant relations between the sand flux on the lee flank and the angle of incidence of the airflow. The low threshold shear velocities and the maintenance of the sand flux at the lee flank are the main mechanisms keeping the linear shape of the dunes. Measurements of the sand flux shows that it reaches a maximum on the crest of the dune. The grain size of the transported sands has some differences compared to that of the dune surface. The sands transported are finer than that on the dune surface, but better sorted under the influence of the medium to low wind activity. The field experiment results exhibit that it is possible for the dunes to be shaped as linear dunes during the processes of accumulation and elongation.     

Simulation and measurement of surface shear stress over isolated and closely spaced transverse dunes in a wind tunnel

Topographic interactions generate multidirectional and unsteady air?ow that limits the application of velocity pro?le approaches for estimating sediment transport over dunes. Results are presented from a series of wind tunnel simulations using Irwin‐type surface‐mounted pressure sensors to measure shear stress variability directly at the surface over both isolated and closely spaced sharp‐crested model dunes. Findings complement existing theories on secondary air?ow effects on stoss transport dynamics and provide new information on the in?uence of lee‐side air?ow patterns on dune morphodynamics. For all speeds investigated, turbulent unsteadiness at the dune toe indicates a greater, more variable surface shear, despite a signi?cant drop in time‐averaged measurements of streamwise shear stress at this location. This effect is believed suf?cient to inhibit sediment deposition at the toe and may be responsible for documented intermittency in sand transport in the toe region. On the stoss slope, streamline compression and ?ow acceleration cause an increase in ?ow steadiness and shear stress to a maximum at the crest that is double that at the toe of the isolated dune and 60–70 per cent greater than at ?ow reattachment on the lower stoss of closely spaced dunes. Streamwise ?ow accelerations, rather than turbulence, have greater in?uence on stress generation on the stoss and this effect increases with stoss slope distance and with incident wind speed. Reversed ?ow within the separation cell generates signi?cant surface shear (30–40 per cent of maximum values) for both spacings. This supports ?eld studies that suggest reversed ?ow is competent enough to return sediment to the dune directly or in a de?ected direction. High variability in shear at reattachment indicates impact of a turbulent shear layer that, despite low values of time‐averaged streamwise stress in this region, would inhibit sediment accumulation. Downwind of reattachment, shear stress and ?ow steadiness increase within 6 h (h = dune height) of reattachment and approach upwind values by 25 h. A distance of at least 30 h is suggested for full boundary layer recovery, which is comparable to ?uvial estimates. The Irwin sensor used in this study provides a reliable means to measure skin friction force responsible for sand transport and its robust, simple, and cost‐effective design shows promise for validating these ?ndings in natural dune settings. Copyright © 2003 John Wiley & Sons, Ltd.     

The response of subaqueous dunes to floods in sand and gravel bed reaches of the Dutch Rhine

Abstract The branches of the River Rhine in the Netherlands, characterized by a sand–gravel bed in the upstream part and a sand bed in the downstream part of the river system, show migrating dunes, especially during floods. In the last 20 years, these dunes have been studied extensively. High-resolution echo-sounding measurements of these dunes, made with single and multibeam equipment, were analysed for three different sections of the Rhine river system during several floods. This analysis was done to quantify the growth, decay and migration rates of the dunes during floods. In addition, the migrating dunes were used to calculate bedload transport rates with dune tracking. The results of dune growth and decay and migration rate are shown to be very different for the various sections during the various floods, and these differences are related to differences in grain size of the bed and to differences in the distribution of discharge over the main channel and the floodplain. The relations are used to show that the growth and migration rate of dunes, and the calculated bedload transport rates during the rising stage of a flood wave can be predicted from the mobility of the bed material with simple power relations.