The Distinct Element Method (DEM) and Discontinuous Deformation Analysis (DDA) are the two most commonly used discrete element methods in rock mechanics. Discrete element approaches are computationally expensive as they involve the interaction of multiple discrete bodies with continuously changing contacts. Therefore, it is very important to ensure that the method selected for the analysis is computationally efficient. In this research, a general assessment of DDA and DEM is performed from a computational efficiency perspective, and relevant enhancements to DDA are developed. The computational speed of DDA is observed to be considerably slower than DEM. In order to identify reasons affecting the computational efficiency of DDA, fundamental aspects of DDA and DEM are compared which suggests that they mainly differ in the contact mechanics, and the time integration scheme used. An in-depth evaluation of these aspects revealed that the openclose iterative procedure used in DDA which exhibits highly nonlinear behavior is one of the main reasons causing DDA to slow down. In order to improve the computational efficiency of DDA, an alternative approach based on a more realistic rock joint behavior is developed in this research. In this approach, contacts are assumed to be deformable, i.e., interpenetrations of the blocks in contact are permitted. This eliminated the computationally expensive open-close iterative procedure adopted in DDA-Shi and enhanced its speed up to four times. In order to consider deformability of the blocks in DDA, several approaches are reported. The hybrid DDA-FEM approach is one of them, although this approach captures the block deformability quite effectively, it becomes computationally expensive for large-scale problems. An alternative simplified uncoupled DDA-FEM approach is developed in this research. The main idea of this approach is to model rigid body movement and the block internal deformation separately. Efficiency and simplicity of this approach lie in keeping the DDA and the FEM algorithms separate and solving FEM equations individually for each block. Based on a number of numerical examples presented in this dissertation, it is concluded that from a computational efficiency standpoint, the implicit solution scheme may not be appropriate for discrete element modelling. Although for quasi-static problems where inertia effects are insignificant, implicit schemes have been successfully used for linear analyses, they do not prove to be advantageous for contact-type problems even in quasi-static mode due to the highly nonlinear behavior of contacts.

Master of Science / Department of Civil Engineering / Dunja Peric / The main objective of this study was to experimentally investigate the Mohr-Coulomb strength parameters of masonry sand mixed with varying amounts of water and lignin. Lignin is a plant-derived biomass, which is a co-product of bio-fuel production. It exhibits binding qualities when mixed with water thus making it an ideal candidate for sustainable non-traditional sand stabilization. An experimental program was devised and carried out to quantify the compaction and early age stress-strain and dilatancy responses of sand-lignin mixes. The program included sieve analysis, Atterberg limit tests, standard Proctor tests, and direct shear tests. The experimental results were used to find the cohesion and the angle of internal friction of the tested material, therefore determining the influence of the amount of lignin and water on the strength of the samples. An extensive data analysis was subsequently completed to gain deeper understanding of the underlying strength gain mechanism. It was found that the normalized cohesion benefit due to lignin is controlled by two variables; water to lignin ratio and void ratio. The lignin and water create a paste, which provides particle bonding at the contacts of sand particles, thus increasing the stress-bearing cross sectional area. Increase in the portion of cross-sectional area occupied by water and lignin normalized by gravimetric lignin content, increases the normalized cohesion up to a point, while the cohesion per gravimetric lignin content decreases with the increasing area ratio. This in turn indicates that cohesion increases only up to 6% of lignin, beyond which it starts to decrease due to the presence of too much fine material within the pores. The presence of lignin in the pores consistently decreases the angle of internal friction. However, for all configurations with lignin tested herein, cohesion was larger than for dry sand, thus indicating strength benefits at low confining pressures or at normal stresses below the so-called limiting normal stress.

The surface roughness of unfilled rock discontinuities has a major influence on the hydro-mechanical behaviour of discontinuous rock masses. Although it is widely recognized that surface roughness is comprised of large-scale (waviness) and small-scale (unevenness) components, most investigations of surface roughness have been restricted to small fracture surfaces (<1m2). Hence, the large-scale components of roughness are often neglected. Furthermore, these investigations typically define roughness using two-dimensional profiles rather than three-dimensional surfaces, which can lead to biased estimates of roughness. These limitations have led to some contradictory findings regarding roughness scale effects. This thesis aims to resolve some of these issues. The main findings indicate that discontinuity roughness increases as a function of the sampling window size contrary to what is commonly assumed. More importantly, it is shown that the estimated roughness significantly decreases as the resolution of surface measurements decrease, which could lead to the under estimations of roughness and, consequently, discontinuity shear strength.

Cemented Paste Backfill (CPB) is a relatively new backfilling technology for which a better understanding of binder hydration is required. This research uses electromagnetic (EM) wave-based techniques to non-destructively study a CPB consisting of tailings, sand, process water and binder (90% blast-furnace slag; 10% Portland cement). EM experiments were performed using a broadband network analyzer (20 MHz to 1.3 GHz) in the lab and capacitance probes (70 MHz) in the lab and field. Results showed that the EM properties are sensitive to curing time, operating frequency and specimen composition including binder content. The volumetric water content interpreted from dielectric permittivity varied little with curing. Temporal variations in electrical conductivity reflected the different stages of hydration. Laboratory results aided interpretation of field data and showed that a reduction in binder content from 4.5% to 2.2% delays setting of CPB from 0.5 days to over 2 days, which has important implications for mine design.

Cemented Paste Backfill (CPB) is a relatively new backfilling technology for which a better understanding of binder hydration is required. This research uses electromagnetic (EM) wave-based techniques to non-destructively study a CPB consisting of tailings, sand, process water and binder (90% blast-furnace slag; 10% Portland cement). EM experiments were performed using a broadband network analyzer (20 MHz to 1.3 GHz) in the lab and capacitance probes (70 MHz) in the lab and field. Results showed that the EM properties are sensitive to curing time, operating frequency and specimen composition including binder content. The volumetric water content interpreted from dielectric permittivity varied little with curing. Temporal variations in electrical conductivity reflected the different stages of hydration. Laboratory results aided interpretation of field data and showed that a reduction in binder content from 4.5% to 2.2% delays setting of CPB from 0.5 days to over 2 days, which has important implications for mine design.

Blasting is a complex phenomenon and many parameters affect the outcome of a blast. The process of rock fragmentation by blasting is not well understood yet. Therefore, as a first step, blast-induced dynamic fractures must be studied under highly controlled conditions. The whole cycle of conducting a series of laboratory-scale blast, analyzing the results, and using them to test the validity of an advanced numerical code is reported in this thesis. Initially, the respective contributions by both shock energy and gas energy fractions in an explosive in the blasting process are explained. Then, microstructural, physical and mechanical properties of Laurentian and Barre granites as the selected rock types are investigated. Explosively driven fractures in a blast are controlled by rock and explosive properties, coupling media and coupling ratio. Sample geometries, types of explosives and coupling media used in the experiments are explored in the next step. In order to isolate the effect iii of shock energy from the gas energy in explosively driven fractures, copper liners were installed in the blast holes to prevent gas penetration into the shock induced cracks. The aim of the experiments was to study exclusively the nature of shock-driven fractures, and to contain the dynamic fractures within the samples and avoid sample fragmentation. At the same time and in order to investigate the stress field as a function of distance from the borehole, pressure gauges were installed in the samples. The measured pressures were used in a numerical-experimental procedure to estimate the attenuation properties of the rocks. Blasted samples were cut and impregnated with a mix of epoxy and fluorescent dye. Next, dynamic fracture patterns were highlighted using a strong ultraviolet source. After taking photographs, fracture patterns were manually mapped and crack densities were calculated at different depths and distances from the boreholes. The parameters that affect the development of dynamic fracture patterns are also discussed and relation between crack densities and pressures applied by explosives are investigated. Finally, the dynamic fracture patterns and measured pressures will be used for calibrating the selected equation of state, strength and failure models implemented in AUTODYN. Governing equations, the procedure for obtaining the model constants, applicability of the selected model for predicting the blast experiments and its limitations are discussed in detail.

The surface roughness of unfilled rock discontinuities has a major influence on the hydro-mechanical behaviour of discontinuous rock masses. Although it is widely recognized that surface roughness is comprised of large-scale (waviness) and small-scale (unevenness) components, most investigations of surface roughness have been restricted to small fracture surfaces (<1m2). Hence, the large-scale components of roughness are often neglected. Furthermore, these investigations typically define roughness using two-dimensional profiles rather than three-dimensional surfaces, which can lead to biased estimates of roughness. These limitations have led to some contradictory findings regarding roughness scale effects. This thesis aims to resolve some of these issues. The main findings indicate that discontinuity roughness increases as a function of the sampling window size contrary to what is commonly assumed. More importantly, it is shown that the estimated roughness significantly decreases as the resolution of surface measurements decrease, which could lead to the under estimations of roughness and, consequently, discontinuity shear strength.

Blasting is a complex phenomenon and many parameters affect the outcome of a blast. The process of rock fragmentation by blasting is not well understood yet. Therefore, as a first step, blast-induced dynamic fractures must be studied under highly controlled conditions. The whole cycle of conducting a series of laboratory-scale blast, analyzing the results, and using them to test the validity of an advanced numerical code is reported in this thesis. Initially, the respective contributions by both shock energy and gas energy fractions in an explosive in the blasting process are explained. Then, microstructural, physical and mechanical properties of Laurentian and Barre granites as the selected rock types are investigated. Explosively driven fractures in a blast are controlled by rock and explosive properties, coupling media and coupling ratio. Sample geometries, types of explosives and coupling media used in the experiments are explored in the next step. In order to isolate the effect iii of shock energy from the gas energy in explosively driven fractures, copper liners were installed in the blast holes to prevent gas penetration into the shock induced cracks. The aim of the experiments was to study exclusively the nature of shock-driven fractures, and to contain the dynamic fractures within the samples and avoid sample fragmentation. At the same time and in order to investigate the stress field as a function of distance from the borehole, pressure gauges were installed in the samples. The measured pressures were used in a numerical-experimental procedure to estimate the attenuation properties of the rocks. Blasted samples were cut and impregnated with a mix of epoxy and fluorescent dye. Next, dynamic fracture patterns were highlighted using a strong ultraviolet source. After taking photographs, fracture patterns were manually mapped and crack densities were calculated at different depths and distances from the boreholes. The parameters that affect the development of dynamic fracture patterns are also discussed and relation between crack densities and pressures applied by explosives are investigated. Finally, the dynamic fracture patterns and measured pressures will be used for calibrating the selected equation of state, strength and failure models implemented in AUTODYN. Governing equations, the procedure for obtaining the model constants, applicability of the selected model for predicting the blast experiments and its limitations are discussed in detail.

The objective of the research presented in this thesis is to validate the parallel-bonded modeling method in the context of coupled thermo-mechanical simulations. The simulation results were compared with analytical and experimental data, in the attempt to assess the usability of this particular modeling method. Previous studies of numerical approaches that related to the thermal fracturing of hard rock had used continuum-based models with constitutive relations. The simulations in the thesis were conducted using Particle Flow Code (PFC) which was chosen for the research because of its several benefits. The code has unique features such as spontaneous damage development without imposed conditions, and emergent properties such as material heterogeneity, and dynamic behavior giving possibility to monitor synthetic seismic events. The basic code has been available since 1995 and research using the code has produced hundreds of publications. The thermal option for the code is a recent addition and lacked verification, validation and applications. The thesis is the answer for that. In the course of the research work new particle clustering and grouping routines were developed and tested. Three modeling studies were conducted varying from laboratory to field scales. The 2D modeling study of the heated cylinder experiment yielded similar results both in fracture-behavioral and acoustic emission (AE) magnitude ranges when compared with the laboratory data. The 3D cubic numerical specimens, created with breakable particle clusters, were heated, and the induced damage was observed by P wave velocity measurements. The results showed trends comparable to the laboratory data: P wave velocity decreases with rising temperatures of up to 250°C and cluster-boundary cracking occurs, comparable to grain-boundary cracking in the heated rock samples. The large 2D tunnel models captured the phenomena observed in-situ displaying the difference in the damage to the roof and floor regions, respectively. This damage was due to the filling material confinement of about 100 kPa on the tunnel floor. In general, the results of the thermo-mechanical simulations were in accordance with the experimental data. The modeled temperature evolutions during the heating and cooling periods were also in accordance with the experimental and analytical data.

The objective of the research presented in this thesis is to validate the parallel-bonded modeling method in the context of coupled thermo-mechanical simulations. The simulation results were compared with analytical and experimental data, in the attempt to assess the usability of this particular modeling method. Previous studies of numerical approaches that related to the thermal fracturing of hard rock had used continuum-based models with constitutive relations. The simulations in the thesis were conducted using Particle Flow Code (PFC) which was chosen for the research because of its several benefits. The code has unique features such as spontaneous damage development without imposed conditions, and emergent properties such as material heterogeneity, and dynamic behavior giving possibility to monitor synthetic seismic events. The basic code has been available since 1995 and research using the code has produced hundreds of publications. The thermal option for the code is a recent addition and lacked verification, validation and applications. The thesis is the answer for that. In the course of the research work new particle clustering and grouping routines were developed and tested. Three modeling studies were conducted varying from laboratory to field scales. The 2D modeling study of the heated cylinder experiment yielded similar results both in fracture-behavioral and acoustic emission (AE) magnitude ranges when compared with the laboratory data. The 3D cubic numerical specimens, created with breakable particle clusters, were heated, and the induced damage was observed by P wave velocity measurements. The results showed trends comparable to the laboratory data: P wave velocity decreases with rising temperatures of up to 250°C and cluster-boundary cracking occurs, comparable to grain-boundary cracking in the heated rock samples. The large 2D tunnel models captured the phenomena observed in-situ displaying the difference in the damage to the roof and floor regions, respectively. This damage was due to the filling material confinement of about 100 kPa on the tunnel floor. In general, the results of the thermo-mechanical simulations were in accordance with the experimental data. The modeled temperature evolutions during the heating and cooling periods were also in accordance with the experimental and analytical data.