Luis E. Vallejo

Fractal analysis of the roughness and size distribution of granular materials

The roughness, i.e. general shape and surface irregularity, of particulate soil is an important characteristic that affects the mass behavior of the soil. Characterization of roughness has typically been limited to visual comparison of particles to standard charts, although other more quantitative methods such as Fourier analysis have also been used. Particle size distribution is another important mass-behavioral characteristic of granular soils, and similar to roughness, is defined within limited boundaries. Fractal geometry can be applied to irregular or fragmented patterns such as roughness and grain size distribution to provide quantifying and unique numerical values. This paper presents an evaluation of the applicability of fractal dimensioning techniques to the quantification of both physical particle roughness and grain size distribution of granular soil. The divider and the area-perimeter fractal dimensioning techniques are used to quantify roughness of planar profiles of individual sand grains. The characterization of the size distribution of granular material using fractal geometry is evaluated through Korcaks fragmentation theory. As shown herein, both the divider and the area-perimeter fractal dimensioning techniques are useful in characterizing soil particle roughness, and the results confirm the importance of differentiating between textural and structural aspects of roughness. Fractal geometry can also be used to quantify the size distribution of granular soils with relatively well-graded size distributions.

Porosity influence on the shear strength of granular material–clay mixtures

Materials forming part of rock fill dams, glacial tills, mudflows, debris flows, solifluction sheets, residual and colluvial soil deposits have a distinct structure, consisting of a mixture of large particles (gravel or hard clay fragments) and a soft matrix of clay. In order to analyze the stability of slopes made of granular material–clay mixtures, a measure of their shear strength is needed. Laboratory tests on these types of mixtures have indicated that their shear strength will depend upon the relative concentrations of the large particles and the clay. If the percentage by weight of the granular material in the granular material–clay mixture was >75%, the shear strength of the mixture was basically that of the granular material alone. When the concentration by weight of the granular material in the mixtures was <40%, the shear strength of the mixtures was basically that of the clay that surrounded the granular material. For the case in which the percentage of the granular materials in the solids mixture was between 40 and 75%, the shear strength of the mixtures was partially controlled by the granular phase. To date, no explanation has been put forward to account for why these limits of granular material in the mixtures exist at which it either controls, partially controls or has no control at all on the shear strength of the mixtures. This study presents an explanation for the existence of these limits. This explanation is based upon the resulting porosity of the mixtures.

Fractal analysis of the fabric changes in a consolidating clay

Electron microscopy and mercury intrusion porosimetry studies on the fabric of clays undergoing consolidation tests have indicated that the clays have pores of different sizes and shapes. After pressure is applied to the clay samples, the larger pores change in size and shape, with the smaller pores being relatively unaffected. The size of the pores and their distribution have been determined from mercury porosimeter tests. The shape of the pores and the changes they experience during the consolidation process have received only a qualitative evaluation from the photomicrographs obtained with the scanning electron microscope. In this study, a quantitative evaluation of the shape of the pores in a clay subjected to consolidation stresses is presented. This evaluation is done using fractal theory. Fractal theory employs the concept of fractal dimension to evaluate the shape (roughness) of closed profiles such as pores. The larger the fractal dimension, the rougher is the shape of a closed profile. The fractal dimension of a pore in a clay sample undergoing consolidation changed progressively from 1.4623 (very rough pore) to 0.9856 (very smooth pore). Thus, during consolidation, the pore, besides changing in size, also experienced a change in its degree of roughness. In addition, a theoretical analysis of the influence of the shape of the pores on the rate of water flow from a saturated clay undergoing consolidation is presented.

Bluff response to wave action

Abstract The unconsolidated materials forming the bluffs along the coasts of the Great Lakes are subject to active wave erosion which results in losses in millions of dollars annually due to property damage and reduction in property values. An understanding of the mechanics of bluff recession and the long-term trends in the evolution of coastal bluffs is required for an evaluation of engineering and management solutions for the problems created by retreating coastal bluffs. Bluff retreat is usually analyzed and measured from airphotos. However, since airphotos are taken at discrete points in time they are not capable of providing a full account of bluff retreat mechanisms. Field investigations, coupled with analytical methods, can enable investigators to identify patterns of bluff retreat. These patterns, subsequently incorporated into slope evolution models, shed light on data obtained over long periods from airphotos. The present paper explains recession rates and bluff profile changes as measured from airphotos with the help of bluff evolution models already established for the bluffs forming the Great Lakes shorelines.

Fractal Assessment of the Surface Texture of Pavements

Fractal analysis was employed to evaluate the texture of profile tracers obtained from three different pavement surfaces. Fractal analysis uses the concept of the fractal dimension, D, as a way to evaluate the texture of simple and complex profiles. In this study it was determined that the fractal dimension, D, of the profiles of the pavement surfaces increased as the roughness of the texture profiles increased. For example, the smoothest of the three profiles had a fractal dimension, D, equal to 1.047; the roughest of the surface profiles had a fractal dimension, D, equal to 1.578. In addition, a good correlation was found to exist between the skid resistance of the pavement surfaces analyzed and their respective fractal dimension values. Thus, it is suggested that the fractal dimension can be used as a measure not only of the degree of roughness of the texture of the pavement surfaces but to relate surface texture to skid resistance (friction) on pavements as well.

Fault movement and its impact on ground deformations and engineering structures

In many regions around the world, engineering structures such as earth dams, buildings, pipelines, landfills, bridges, roads and railroads are often built in areas very close to strike-slip fault segments. For the safe design of these structures, earthquake and geotechnical engineers need a reliable estimate of the ground deformations that fault movements will induce at the sites of the proposed structures. The estimation of the vertical ground deformations associated with the movement of strike-slip fault segments is the focus of this proposed study. These vertical ground deformations are the result of stresses concentrated by the ends of active fault segments. In this study, the stresses and the resulting tri-dimensional vertical ground deformations that develop around moving fault segments were obtained using linear elastic fracture mechanics theory. The theoretical analysis was used to estimate the amount of vertical deformation experienced by the ground surrounding a strike-slip fault segment in China that mobilized during the 1970 Tonghai earthquake. The calculated vertical deformations and the ones measured in the field compared well.

Fractal dimension of profiles and surfaces using fuzzy morphological coverings

In this paper, we propose a new method, based on fuzzy morphology coverings, to estimate the fractal dimension of profiles and surfaces. This method is geometrically intuitive and simple to implement. Algorithmically, the method fits a covering to the frames or blocks of the profile or surface using fuzzy morphology. Varying the dimension of the frame or block, estimates of the length or area covered are then used to find the fractal dimension. Validation of the proposed method is performed by comparing its results with known fractal dimensions of mathematical profiles. The method is used to obtain the fractal dimension of rock profiles and surfaces.

Collapse of Granular Columns With Fractal Particle Size Distribution: Implications for Understanding the Role of Small Particles in Granular Flows

According to field measurements, the basic character of the particle size distributions obtained from the landslide accumulations is fractal. The collapse of the granular columns with fractal particle size distribution (FPSD) is performed numerically and experimentally to form dry granular flows and the mechanism of how FPSD affects the particle movements is then investigated. Numerical and experimental analyses show that particle flow mobility increases as the fractal dimension increases. Several linear relationships exist between the fractal dimension and flow mobility parameters. By analyzing the kinetics of granular flows, it is found that a large number of small-sized particles will form a boundary layer where the particle shearing and velocities are remarkably increased and will thus have a lubricant effect on the flow mobility. Moreover, the number of particle collisions increases, and small-sized particles are more likely to obtain higher spreading velocities via the greater contribution of particle interactions.

Shear Strength of Sand-Gravel Mixtures: Laboratory and Theoretical Analysis

Many natural slopes and rock fill structures are made of a mixture of dispersed rock fragments (gravel) and sand-size particles. To analyze the stability of such structures, the shear strength of the sand-gravel mixtures is needed. For this purpose, direct shear tests were carried out on mixtures of Ottawa sand (d50 = 0.59 mm) and fine gravel (d50 = 5 mm). The shear strength of the sand and the sand-gravel mixtures was measured under two normal stresses. These normal stresses were equal to 52 kPa and 103 kPa. During the tests, the initial void ratio of the matrix was maintained relatively constant at a value equal to 0.8. The concentration by weight of the gravel in the mixtures tested varied between 0 and 30%. These concentrations by weight correspond to a concentration by volume equal to 0 and 19.3%. The results of the direct shear strength tests indicated that the angle of internal friction improved with an increase in the concentration of the gravel in the mixtures. The angle of internal friction was equal to 40.4 o for the sand alone. The friction angle increased to 46.9 o for the sand sample with a concentration of gravel by weight equal to 20% (12.1% by volume). It was determined that the shear strength of the sand-gravel mixtures can be determined from the shear strength of the sand matrix alone and the concentration by volume of the gravel in the mixtures if one uses the equation: Sc = Sm (1+2.5 C). In this equation, Sc is the shear strength of the sand-gravel mixture, Sm is the shear strength of the sand matrix alone, and C is the concentration by volume of the gravel in the mixture. However, the validity of the equation has not yet been determined to be general and has only been shown to apply to the type and size of materials, stress conditions and type of equipment used in the reported testing program.

Evaluation of test methods designed to obtain the undrained shear strength of muds

Abstract One parameter needed for the stability analysis of seafloor mud‐covered slopes is the undrained shear strength, cu, of the mud. A literature review dealing with mudslides shows that six methods exist to measure the cu of muds either in the laboratory or in the field. These methods are: 1) the vane shear test, 2) the cylinder‐strength meter test, 3) the sphere‐strength meter test, 4) the cone penetrometer test, 5) the pullout test using a cylinder, and 6) the use of the vertical profile of a mudslide in the direction of movement. The present study reports a laboratory investigation of the undrained shear strength of artificially prepared muds using the six methods in order to evaluate their accuracy. It was found that for mud samples with low clay content (less than 45% by weight), the cylinder‐strength meter test, the mudslide profile test, the cone penetrometer test, and the pullout test gave similar results for cu and therefore compare well. However, the sphere and vane shear tests gave values ...