Analysis of wave propagation in granular soils using discrete element method

Doctoral Thesis

Soil and Foundation Mechanics

Abstract

In this research, the discrete element method is used to analyze wave propagation and investigate factors affecting wave speed in granular soils. The method of separate elements is important due to the possibility of preparing completely similar samples and checking the effect of changes of a certain parameter on the behavior of the samples. Also, this method provides an understanding of the changes that have occurred at the micro scale of granular materials, which cannot be obtained with other laboratory and numerical methods. For the purpose of modeling, samples are created from a collection of discs with a certain granularity for two-dimensional studies. PFC 2D software has been used to perform simulations and related analyses.

Studies in the field of pressure wave transmission in sandy soils have been conducted by various researchers. They investigated the effect of different factors on the speed of wave propagation. Factors such as sample width, damping ratio, particle shape, particle arrangement, vibration frequency, particle surface diameter and hardness, pressure or depth are the parameters that most studies and simulations of different researchers have focused on. Despite the significant research conducted on wave propagation and the parameters affecting it, there are still various factors that may affect wave propagation in grain soils, which have not been investigated. For this reason, in this research, the effect of particle friction coefficient, particle set porosity, particle density, particle size non-uniformity coefficient and particle set granulation on wave propagation speed has been investigated. The variables used to investigate the above factors are the changes in the porosity of the soil sample during the application of the wave, the speed of the particles, the display of the chain of contact forces, as well as the average contact number of each soil sample and the unbalanced forces. The results of this study indicate that there is a direct relationship between the number of contacts of the collection of particles and the speed of wave propagation. Also, material properties such as particle density are among the most important parameters affecting wave speed. Keywords: separate element, wave speed, porosity, friction, soil granularity Chapter 1 Introduction Granular materials are composed of individual particles that show complex macroscopic behavior against external loads. Soils are materials composed of particles of different sizes and their behavior is determined by the forces between these particles. However, this characteristic of them is usually not considered in modeling. The forces between soil particles include the forces caused by boundary conditions, interparticle forces (contact forces), and the relative balance between these forces reveals different aspects of soil behavior. The phenomenon of wave propagation plays an essential role in various dynamic issues such as the interaction of soil and structure tremors, liquefaction and foundation vibration. Understanding the local effects of construction on strong ground motions and evaluating the response and deformation of the ground against strong motions is of great importance for critical structures and facilities. The study of wave propagation in granular materials also has important industrial applications. Granular materials are used to absorb shock waves during the transportation of heavy equipment and to isolate sensitive equipment from ground vibrations. They are also used in the manufacture of ceramic components that require dynamic densification of ceramic powders. In all these applications, it is necessary to study the speed of the wave and the nature of its propagation in granular materials.

Researches in the field of compression wave transmission in granular soils have been carried out by various researchers. They investigated the effect of different factors on the speed of wave propagation. Factors such as sample width, damping ratio, particle shape, particle arrangement, vibration frequency, particle surface diameter and hardness, pressure or depth are the parameters that most studies and simulations of different researchers have focused on.  Despite the considerable research done on wave propagation, there are still parameters that may affect wave propagation in grain soils, and the extent of their influence on the wave propagation process has not been investigated.  

The main goal of this research is to use a numerical technique (DEM) to simplify and scale the complex phenomenon of wave propagation in soil.. Since there are still effective factors in wave propagation that have either not been investigated or have not been given comprehensive and detailed attention, this motivation was created to investigate some of these factors and their effectiveness by continuing research in this field. So that we can model the phenomenon of wave propagation in a real soil and calculate the speed of wave propagation with sufficient accuracy without the need to perform costly and time-consuming geophysical tests on site or in the laboratory. Based on the investigations and suggestions made by various researchers in their studies, in this study, the effect of parameters such as: grain size non-uniformity coefficient (PDI), soil granularity, friction coefficient, porosity, density on wave speed has been investigated. The two-dimensional discrete element method has been used for analysis. It should be noted that the modeling was done using PFC2D software.

The content of this thesis is presented in 6 chapters. The first chapter is the introduction and introduces the study and its features. The second chapter deals with the review of the discrete element method formulation and the introduction of the micromechanics of granular environments. In the third chapter, the research carried out by the discrete element method on shear and compression wave propagation in granular materials is examined and the areas that need further research are introduced. In the fourth chapter, the stages and methods of modeling have been examined. In addition, in this chapter, the validity of the modeling has also been examined. In the fifth chapter, the parameters affecting the speed of wave propagation have been examined. The causes and extent of the influence of these parameters on the wave propagation speed and its results are presented graphically at the end of each section. Finally, the most important results of this research have been presented and summarized in the sixth chapter. Second chapter

Discrete element method

The discrete element method is one of the numerical methods that has been developed specifically to model the behavior of discontinuous systems such as granular environments. The basis of the method is based on a study conducted by Cundall in 1971 to investigate the stability of stone blocks. After that, several researchers such as Cundall & Stark (1979a) and Ghaboussi & Barbosa (1990) developed a method to model the behavior of granular materials and different geometric shapes.

In this method, each particle of the set of particles is modeled physically separately, taking into account the geometric conditions of its surface and a description of its physical state (location, direction, volume forces, etc.). The movement of particles is determined according to the forces applied to them and using Newton's second law. The physical and mechanical conditions of particles are determined by using the micromechanical relationships of particles in order to model them mathematically. Micromechanics deals with theories and definitions that are used to describe the mechanical behavior of granular materials based on their microstructural variables. Granular materials are a collection of separate particles with specific shapes and sizes. The set of particles show mechanical resistance in the presence of all-round pressure. Individual soil particles are in static equilibrium under the forces applied to them by contact with neighboring particles (Figure 1-2).

Resistance of materials depends on the average number of contacts for each particle and the amount of contact forces. The average number of contacts of particles (Average Coordination Number, C.N) is defined as the average number of contacts per particle. In a set consisting of particles, the average number of contacts ( ) is defined as follows:

which is twice the number of interparticle contacts in the set. The results of a large number of conducted studies indicate that the average number of particle contacts is important in terms of the stability of the sample, so that the sets with a higher average number of contacts have more stability and, as a result, more resistance to the applied load. Another parameter for describing the microstructure of particles is Average Contact Density, which is defined as follows:

which in the above expression is the volume of the collection of particles.

Discrete element method is a numerical method that, as its name implies, is used to solve problems where there is no continuity between its components. As mentioned earlier, this method was originally used by Cundall (1971) to model progressive failure in rocky slopes.