The majority of faults display a layer of crushed wear material ("fault gouge") between the fault blocks, which influences the strength and stability of faults. This thesis describes the results of a numerical model used to investigate the process of comminution in a sheared granular material. The model, based on the Discrete Element Method, simulates a layer of 2-D circular grains subjected to normal stress and sheared at constant velocity. An existing code was modified to allow grains to break when subjected to stress conditions that generate sufficient internal tensile stresses. A suite of five numerical runs was performed using the same initial system of grains with sizes randomly chosen from a pre-defined Gaussian distribution. A range of confining pressures was explored from 4.5 MPa to 27.0 MPa (in case of quartz grains with average diameter of 1 mm). The average effective friction coefficients of the five simulations were relatively unaffected by comminution and displayed a constant value of about 0.26. The amount of breakage was directly related to both the applied confining pressure and logarithm of the displacement along the fault. The particle size distribution evolved during the runs, but it was apparently determined only by the cumulative number of grain breakage events: two runs with the same number of breakage events had identical particle size distributions, even if they deformed to different extents under different stress conditions. These results suggest that the knowledge of both the local displacement and stress state on a fault can be used to infer the local particle size distribution of the gouge.

京都大学 / 0048 / 新制・課程博士 / 博士(工学) / 甲第17864号 / 工博第3773号 / 新制||工||1577(附属図書館) / 30684 / 京都大学大学院工学研究科社会基盤工学専攻 / (主査)教授 後藤 仁志, 教授 戸田 圭一, 准教授 原田 英治 / 学位規則第4条第1項該当 / Doctor of Philosophy (Engineering) / Kyoto University / DFAM

京都大学 / 0048 / 新制・課程博士 / 博士(工学) / 甲第18934号 / 工博第3976号 / 新制||工||1613(附属図書館) / 31885 / 京都大学大学院工学研究科社会基盤工学専攻 / (主査)教授 後藤 仁志, 教授 戸田 圭一, 准教授 原田 英治 / 学位規則第4条第1項該当 / Doctor of Philosophy (Engineering) / Kyoto University / DGAM

This study investigates the February 17th, 2006 massive rockslide that occurred in the island of Leyte, Philippines following heavy rainfall and four minor earthquakes. The rockslide is considered one of the largest and most catastrophic slides in the last few decades as it completely inundated the village of Guinsaugon, taking the lives of approximately 1,400 of the 1,800 residents of the village. The distinct element simulation of the rockslide is performed using 3DEC (Three-Dimensional Distinct Element Code) in order to investigate the underlying triggering mechanism of the slide as well as the behavior of the debris flow. The 3DEC models were established based on field observations from the U.S. Reconnaissance team and material and joint properties based on in-situ and laboratory test results. The possible triggering mechanisms considered in the distinct element analyses were the rainfall-induced hydraulic pressurization of the fault forming part of the main scarp, as well as the seismic acceleration due to the minor earthquakes that occurred the morning of the slide. The results of the analyses and simulations indicate that the rainfall-induced hydraulic pressurization of the fault was potentially the main trigger for the initiation of the slide. The minor earthquakes, which occurred before and around the time of the slide initiation, appeared to have very little effect on the triggering mechanism and the debris flow are comparable to witness accounts and field observations. The results presented in this study are expected to provide better understanding of rockslides such as the one that occurred in the Philippines on February 17, 2006. With further improvements in computational capabilities in the future, distinct element simulations can have the potential to reliably predict the initiation and behavior of slides, and help mitigate their impact. / Master of Science

<p>The equivalent continuum approach uses equivalent propertiesof rock mass as the input data for a continuum analysis. Thisis a common modeling method used in the field of rock mechanicsand hydrogeology. However, there are still unresolvedquestions; how can the equivalent properties be determined andis the equivalent continuum approach suitable for modeling thediscontinuous fractured rock mass.</p><p>The purpose of this paper is to establish a methodology todetermine the equivalent hydraulic and mechanical properties offractured rock masses by explicit representations of stochasticfracture systems, to investigate the scale-dependency of theproperties, and to investigate the conditions for theapplication of the equivalent continuum approach for thefractured rock masses. Geological data used for this study arefrom the site characterization of Sellafield, Cumbria, UK. Aprogram for the generation of stochastic Discrete FractureNetwork (DFN) is developed for the realization of fractureinformation and ten parent DFN models are constructed based onthe location, trace length, orientation and density offractures. Square models with the sizes varying from 0.25 m× 0.25 m to 10 m × 10 m are cut from the center ofthe each parent network to be used for the scale dependencyinvestigation. A series of the models in a parent network arerotated in 30 degrees interval to be used for investigation oftensor characteristic. The twodimensional distinct elementprogram, UDEC, was used to calculate the equivalentpermeability and compliance tensors based on generalizedDarcy’s law and general theory of anisotropic elasticity.Two criteria for the applicability of equivalent continuumapproach were established from the investigation: i) theexistence of properly defined REV (Representative ElementaryVolume) and ii) existence of the tensor in describing theconstitutive equation of fractured rock The equivalentcontinuum assumption cannot be accepted if any one of the abovetwo criteria is not met. Coefficient of variation and meanprediction error is suggested for the measures toquantitatively evaluate the errors involved in scale dependencyand tensor characteristic evaluation.</p><p>Equivalent permeability and mechanical properties (includingelastic modulus and Poisson’s ratios) determined onrealistic fracture network show that the presence of fracturehas a significant effect on the equivalent properties. Theresults of permeability, elastic moduli and Poisson's ratioshow that they narrow down with the increase of scale andmaintain constant range after a certain scales with someacceptable variation. Furthermore, Investigations of thepermeability tensor and compliance tensor in the rotated modelshow that their tensor characteristics are satisfied at acertain scale; this would indicate that the uses of theequivalent continuum approach is justified for the siteconsidered in this study.</p><p>The unique feature of the thesis is that it gives asystematic treatment of the homogenization and upscaling issuesfor the hydraulic and mechanical properties of fractured rockswith a unified approach. These developments established a firmfoundation for future application to large-scale performanceassessment of underground nuclear waste repository byequivalent continuum analysis.</p><p><b>Keywords :</b>Equivalent continuum approach, Equivalentproperty, Representative Elementary Volume (REV), DistinctElement Method, Discrete Fracture Network (DFN)</p>

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.

Se ha llevado a cabo:A) Un estudio de las propiedades básicas del suelo no saturado (tipo limo) a escala microestructural, incluyendo esqueleto sólido, fase liquida y fase gaseosa. B) Elaboración de un modelo conceptual discontinuo de comportamiento. La geometría interna esta construida por partículas, agua retenida en forma de meniscos alrededor de los contactos y aire ocupando los restantes poros. La interfase liquido gas esta gobernada por la succión y la tensión superficial. Los meniscos tienen un efecto rigidizador del esqueleto.Se observa la posible redistribución de la humedad y del aire, quedando acoplados en definitiva los aspectos mecánicos y de flujo.C) En base a lo anterior, implementación de un modelo numérico discontinuo de ensayo de comportamiento basado en ordenador. Se ha adaptado y modificado el D.E.M. de P.A. Cundall (diferencias finitas explicitas en el tiempo), indicado en el caso que se trata, con no-linealidades geométricas. Se han desarrollado importantes algoritmos de control geométrico. D) Verificación parcial del modelo y aplicación a casos típicos en suelo no saturado, especialmente el colapso.En conjunto es una herramienta útil para su estudio y permite apreciar algunos interesantes mecanismos de actuación de la succión a escala microscópica.

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.

The objective of this master’s thesis is to evaluate the use of Bonded Block Modelling (BBM) in 3DEC software combined with hybrid rock bolts, for three different cases. These cases included the laboratory rock bolt case, the shearing case and the blocky rock mass case. 3DEC is a Distinct Element Method (DEM) numerical software which can be used to simulate both continuum and discontinuum media in 3D. The Bonded Block Model in 3DEC can be used to simulate a rock mass as bonded polyhedral elements. The BBM is a relatively new numerical modelling technique. Earlier studies have focused mainly on laboratory test cases and less on field scale studies. The laboratory rock bolt test was introduced by Hoek and the main idea was to describe the way that rock bolts work. Four different rock bolt spacing designs were simulated and one unsupported model, in order to validate Hoek’s results. The diameter of the blocks was 15 cm while the zones were modelled with length of 5 cm. The tunnel on the shearing case was excavated at the depth of 1500 m. For the stress field, the in-situ stresses of Kiirunavaara mine were considered. The tunnel on the blocky case was excavated at the depth of 30 m and a gravitational stress field was assumed. The shearing model as well as the blocky model, were simulated on a quasi-3D model. The zone length for both cases was 0.1 m. In both cases, a discontinuum non-BBM was modelled first and then, a discontinuum BBM with different rock UCS values was simulated. The discontinuum BBM on the shearing case was simulated for rock UCS of 200, 100, and 50 MPa, while on the blocky case, it was simulated for rock UCS of 50 MPa. The Mohr – Coulomb constitutive model was selected for all three modelling cases. The conclusions of this work were the following: –       The laboratory rock bolt model validated the results of Hoek. Hoek suggested that rock bolt spacing less than three times the average rock piece diameter would be sufficient to produce positive results. The stabilization of the rock pieces as well as the forming of the compression zone were achieved when this equation was satisfied. The geometry of the stabilized material as well as the compression zone, were also correct. –       The discontinuum BBM on the shearing case with intact rock UCS of 200 MPa, produced similar results as the discontinuum non-BBM. This indicates that BBM can be applied for these cases and produce reliable results. The displacement of the fault was expected to be higher than the resulting values. The discontinuum BBM with reduced rock strength (100 MPa and 50 MPa) resulted in rock mass fragmentation. However, the fragmented rock pieces did not detach from the rock mass as the displacement values were not high enough.   –       The discontinuum BBM on the blocky case with intact rock UCS of 50 MPa, produced similar results as the discontinuum non-BBM. There were two discontinuities that affected the smooth transition of the displacement/stress results on the different blocks. The fragmentation of the rock mass due to the existence of the discontinuities did not produce any further rock mass movements.   –       The interaction between rock mass and rock bolts was evident in any modelling case. For the laboratory rock bolt model, the hybrid bolts design was vital for producing correct results. For the shearing model, the hybrid bolts were subjected to shearing movements due to fault movements. In the blocky model, the bolts in the roof of the tunnel were subjected to axial displacements, due to the existence of blocks. The recommendations for further work were the following: –       The hybrid bolts in the laboratory rock bolt test were pretensioned only in the beginning of the computation phase. In reality, the tensioned bolts act at every moment and not only in the beginning. However, it would be interesting to see if the results are similar with continuously tensioned hybrid bolts. It is anticipated that the constantly tensioned hybrid bolts should be able to keep the compressive zones with high values throughout the whole cycling process. Thus, it is suggested for future modellers that this case could be modelled with continuously tensioned hybrid bolts. –       The installation of rock bolts in the shear case as well as in the blocky case, was at the exact same time as the tunnel was excavated.  This is not realistic fact because it is impossible to install the rock bolts exactly the same time as the tunnel excavated. Thus, it is suggested that those two cases could be modelled in the future with more focus on the stress relaxation factor.

The equivalent continuum approach uses equivalent propertiesof rock mass as the input data for a continuum analysis. Thisis a common modeling method used in the field of rock mechanicsand hydrogeology. However, there are still unresolvedquestions; how can the equivalent properties be determined andis the equivalent continuum approach suitable for modeling thediscontinuous fractured rock mass. The purpose of this paper is to establish a methodology todetermine the equivalent hydraulic and mechanical properties offractured rock masses by explicit representations of stochasticfracture systems, to investigate the scale-dependency of theproperties, and to investigate the conditions for theapplication of the equivalent continuum approach for thefractured rock masses. Geological data used for this study arefrom the site characterization of Sellafield, Cumbria, UK. Aprogram for the generation of stochastic Discrete FractureNetwork (DFN) is developed for the realization of fractureinformation and ten parent DFN models are constructed based onthe location, trace length, orientation and density offractures. Square models with the sizes varying from 0.25 m× 0.25 m to 10 m × 10 m are cut from the center ofthe each parent network to be used for the scale dependencyinvestigation. A series of the models in a parent network arerotated in 30 degrees interval to be used for investigation oftensor characteristic. The twodimensional distinct elementprogram, UDEC, was used to calculate the equivalentpermeability and compliance tensors based on generalizedDarcy’s law and general theory of anisotropic elasticity.Two criteria for the applicability of equivalent continuumapproach were established from the investigation: i) theexistence of properly defined REV (Representative ElementaryVolume) and ii) existence of the tensor in describing theconstitutive equation of fractured rock The equivalentcontinuum assumption cannot be accepted if any one of the abovetwo criteria is not met. Coefficient of variation and meanprediction error is suggested for the measures toquantitatively evaluate the errors involved in scale dependencyand tensor characteristic evaluation. Equivalent permeability and mechanical properties (includingelastic modulus and Poisson’s ratios) determined onrealistic fracture network show that the presence of fracturehas a significant effect on the equivalent properties. Theresults of permeability, elastic moduli and Poisson's ratioshow that they narrow down with the increase of scale andmaintain constant range after a certain scales with someacceptable variation. Furthermore, Investigations of thepermeability tensor and compliance tensor in the rotated modelshow that their tensor characteristics are satisfied at acertain scale; this would indicate that the uses of theequivalent continuum approach is justified for the siteconsidered in this study. The unique feature of the thesis is that it gives asystematic treatment of the homogenization and upscaling issuesfor the hydraulic and mechanical properties of fractured rockswith a unified approach. These developments established a firmfoundation for future application to large-scale performanceassessment of underground nuclear waste repository byequivalent continuum analysis. <b>Keywords :</b>Equivalent continuum approach, Equivalentproperty, Representative Elementary Volume (REV), DistinctElement Method, Discrete Fracture Network (DFN) / NR 20140805