A numerical rock fragmentation model was elaborated, producing a 3D puzzle of convex polyhedra, geometrically described in a database. In the first scenario, a constant proportion of blocks are fragmented at each step of the process and leads to fractal distribution. In the second scenario, division affects one random block at each stage of the process, and produces a Weibull volume distribution law. Imposing a minimal distance between the fractures, the third scenario reveals a power law. The inhibition of new fractures in the neighbourhood of existing discontinuities could be responsible for fractal properties in rock mass fragmentation. To cite this article: L. Empereur-Mot, T. Villemin, C. R. Geoscience 334 (2002) 127–133.相似文献
We investigated the existence of a fractal law (power law) distribution of size pyroclastic fragments erupted during the fallout phase of the 79 A.D. Plinian eruption at Mt. Vesuvius. In particular, we performed a particle size distribution analysis on 18 white and grey pumice samples collected in six sites distributed in the SW sector of Mt. Vesuvius. Our measurements show that the fragmentation of samples in the investigated range (from 32 mm to 850 μm) follows a power law, guaranteeing the scale invariance of the process. The relationship frequency-size distribution of the fragments is verified independently from the nature (i.e., pumices and lithics) and stratigraphic height of the considered samples in the pyroclastic deposit. Therefore, the fractal fragmentation theory can be indicated for evaluating the relationship between the intensity of fragmentation (fractal dimension D) and eruption energy. In this way the apparent chaotic distribution of the particles in the fallout deposits hides a self-organized complexity revealed by the retrieved power law distribution. We further remark that a key aspect of our analysis is the founded evidence that the fractal dimension of the lithics is systematically greater than that of the pumices. 相似文献
Argillaceous rocks cover about one thirds of the earth's surface. The major engineering problems encountered with weak- to medium-strength argillaceous rocks could be slaking, erosion, slope stability, settlement, and reduction in strength. One of the key properties for classifying and determining the behavior of such rocks is the slake durability. The concept of slake durability index (SDI) has been the subject of numerous researches in which a number of factors affecting the numerical value of SDI were investigated. In this regard, this paper approaches the matter by evaluating the effects of overall shape and surface roughness of the testing material on the outcome of slake durability indices.
For the purpose, different types of rocks (marl, clayey limestone, tuff, sandstone, weathered granite) were broken into chunks and were intentionally shaped as angular, subangular, and rounded and tested for slake durability. Before testing the aggregate pieces of each rock type, their surface roughness was determined by using the fractal dimension. Despite the variation of final values of SDI test results (values of Id), the rounded aggregate groups plot relatively in a narrow range, but a greater scatter was obtained for the angular and subangular aggregate groups. The best results can be obtained when using the well rounded samples having the lowest fractal values. An attempt was made to analytically link the surface roughness with the Id parameter and an empirical relationship was proposed. A chart for various fractal values of surface roughness to use as a guide for slake durability tests is also proposed. The method proposed herein becomes efficient when well rounded aggregates are not available. In such condition, the approximate fractal value for the surface roughness profile of the testing aggregates could be obtained from the proposed chart and be plugged into the empirical relation to obtain the corrected Id value. The results presented herein represent the particular rock types used in this study and care should be taken when applying these methods to different type of rocks. 相似文献
Both the Hausdorff dimension and the K-entropy supply a measure of the irregularity of the landspace surface. The relationship between the two measures is investigated over a variety of terrains in Britain and a method of calculating the entropy is checked against an independent estimate of the dimension with reasonable agreement. The calculation of the K-entropy requires that the landscape surface be represented by an homogenous ergodic random field. This condition is satisfied by the tendency of soil-covered terrains to progressively approximate to a form well represented by a Gaussian field. Gaussian random fields can either be very smooth, possessing derivatives of all orders at every point or they are highly irregular and non-differentiable everywhere. Within the regular conceptualization the Rice-Kac theory is used to predict the numbers of crossing points and the extent of excursion sets. These predictions are tested against an example terrain from the High Weald of East Sussex with very good agreement, apart from predictions of local maxima. A worked example of the calculation of the K-entropy is given as an appendix. The potential role of information theory in geomorphology extends beyond the use made of entropy in this investigation. In particular ergodic theory has important practical and theoretical implications. 相似文献
