Sebastian Lobo-Guerrero

A Network of Fractal Force Chains and Their Effect in Granular Materials under Compression

Granular materials forming part of civil engineering structures such as rockfill dams and the granular base in pavement systems are subjected to large compressive stresses resulting from gravity and traffic loads respectively. As a result of these compressive stresses, the granular materials break into pieces of different sizes. The size distribution of the broken granular material has been found to be fractal in nature. However, there is no explanation to date about the mechanisms that cause the granular materials to develop a fractal size distribution. In the present study, a compression test designed to crush granular materials is presented. The tests used 5 mm glass beads and a plexiglass cylinder having an internal diameter equal to 5 cm. As a result of compression in the cylinder, the glass beads broke into pieces that had a fractal size distribution. The compression test was numerically simulated using the Discrete Element Method (DEM). The DEM simulation indicated that the particles developed a network of force chains in order to resist the compressive stress. These force chains did not have a uniform intensity but was found to vary widely through out the sample. Also, the distribution of the force chains in the sample did not involve all the grains but only a selective number of them. Thus, the force chains did not cover the whole sample. Using the box method, it was determined that the distribution of the force chains in the sample was fractal in nature. Also, the intensity of the force chains in the sample was found to be fractal in nature. Thus, the fractal nature of the intensity of the force chains and their distribution were found to be the main reason why granular material develop fractal fragments as a result of compression.

Fibre-reinforcement of granular materials: DEM visualisation and analysis

Mechanical properties of granular materials can be significantly improved by the inclusion of small amounts of short synthetic fibres. This phenomenon has been experimentally studied before by many researchers who have found that the shear strength of a granular material can be significantly improved. This study presents a visualisation of the phenomenon using discrete element method (DEM) simulations of direct shear tests conducted on mixtures of an idealised granular material and randomly oriented fibres. Snapshots showing the deformation of the samples, the velocity vectors of the particles and the force chains produced inside the samples are presented at different stages of the tests. Changes in shear strength and porosity are also illustrated. It was found that the reinforcement produced depends mostly on the rigidity of the fibres.

The shear strength of granular materials containing dispersed oversized particles: DEM analysis

Abstract <p>Granular soils containing dispersed rock particles form part of many soil deposits. To obtain the shear strength of these mixtures, large representative samples need to be tested in either large triaxial or direct shear apparatuses. The use of this type of equipment makes the tests very time consuming and expensive. This study is designed to verify a theory of filler reinforcement presented by Guth (1945) that asserts that a mechanical property of a composite made of a mixture of a solid material reinforced by dispersed large particles (<i>p</i>^*) can be obtained from the related mechanical property, <i>p</i>, of the matrix, and the concentration by volume of the added dispersed oversized particles, <i>C_f</i>, if the following relationship is used: <i>p</i>^* = <i>p</i>(1 + 2.5 <i>C_f</i>). In this study, <i>p</i>^* represents the shear strength of a soil-rock mixture, <i>p</i> represents the shear strength of the soil matrix, and <i>C_f</i> as defined above. With the use of this relationship it is very easy to determine the shear strength of the mixture since one only needs to know the easily determinable quantities <i>p</i> and <i>C_f</i> in order to obtain <i>p</i>^*.</p><p>The validity of the relationship advanced by Guth (1945) was assessed using actual direct shear tests on sand with dispersed gravel, and direct shear test simulations that use the Discrete Element Method (DEM). The results of the actual direct shear tests were predicted very well by Guths approach. The DEM simulations also validated it.</p>

Fractal Fragmentation of Granular Materials under Compression

Granular materials forming part of rockfill dams or the base of pavements are subjected to large compressive stresses. As a result of these stresses, the granular materials break into pieces of different sizes. The size distribution of the broken granular material has been found to be fractal in nature. However, there are few explanations to date about the mechanisms that cause a granular material to develop a fractal size distribution. In this study, a simulated compression test designed to crush granular materials is presented. The compression test was numerically simulated using the Discrete Element Method (DEM). The DEM simulation indicated that the particles developed a network of force chains in order to resist the compressive stress. These force chains did not have a uniform intensity but was found to vary widely through out the sample. The intensity of the force chains was found to be fractal in nature. Also, the force chains in the sample did not involve all the grains. Thus, the force chains did...

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.

DEM analysis of the effect of granular crushing on the bearing capacity of footings

Abstract Granular materials underneath footings are subjected to static and dynamic loads. As a result of these loads particle crushing may occur depending on the strength of the soil particles. Since particle crushing reduces the shear strength of a granular material and produces settlements, the performance of an engineering structure supported on a crushable soil can be compromised due to granular crushing. This paper presents the results of two DEM (Discrete Element Method) simulations intended to compare the effect of crushing on the bearing capacity of a simulated dense granular material. Also, a comparison with the theoretical bearing capacity is presented. Even though the two simulations considered the same idealized material, crushing was allowed only in one simulation. Particle crushing was possible by replacing the particle fulfilling a predefined failure criterion with a group of smaller particles. It was found that the ultimate bearing capacity of the material was strongly reduced as a consequence of only a moderate amount of crushing. This paper also presents the visualization of the failure mechanisms involved in the two analyzed cases.