In this research, a novel, unique systematic procedure was implemented to investigate the influence of the fracture networks and confining stresses on the jointed coal mass strength (JCMS). Both a laboratory experimental scheme and a numerical modeling scheme were carried out at the 3-D level. The laboratory experiments were performed to achieve the following three goals. Firstly, the geomechanical properties for the intact coal and coal discontinuities were estimated through the laboratory geomechanical property tests. Secondly, naturally existing fracture networks in the cubic coal blocks were first detected by the industrial Computed Tomography (CT) scanning technique and then quantified by the fracture tensor based methodology. Thirdly, polyaxial tests were conducted on the same cubic coal blocks to obtain the JCMS values under different confining stresses. With respect to the numerical modeling, PFC^3D and 3DEC software packages were used to simulate the polyaxial compression tests for intact and jointed cubic coal blocks, respectively. From more than twenty intact rock strength criteria, nine criteria were selected for this research. The intact coal strength data bank obtained from PFC^3D modeling was used to evaluate the applicability of nine different intact rock strength criteria. A modified grid search (MGS) procedure is proposed and used to find the best fitting parameter values and calculate the coefficient of determination (R²) values for each criterion. These criteria are compared in detail using the following features: R² values, σ₁ - σ₂ plots for different σ₃, shapes on the deviatoric planes, linearity or nonlinearity on the meridian planes. The regression analysis and the MGS procedure were found to be equivalent in finding the best fitting parameter values for a certain intact rock strength criterion. Through the comparisons, the modified Wiebols-Cook and modified Lade criteria were found to provide the highest R² values and fit the intact coal strength data best on the σ₁ - σ₂ coordinate plane and meridian planes. Based on the appearances on the deviatoric plane, the nine intact rock strength criteria are categorized into three types: the single shear stress criteria, the octahedral shear stress criteria and the criteria incorporating the maximum principal shear stress and partial intermediate principal shear stress. The relative positions of the different criteria on two specific meridian planes are also discussed. The geometric model of the jointed coal block was first set up by incorporating the fracture network constructed from the CT scanning into the intact coal block using a modified fictitious joint procedure. The numerical parameter values of intact coal and coal discontinuities were then calibrated and validated through a trial and error procedure using the laboratory test results of some selected samples. Next the JCMS data bank was consummated by performing a four-phase numerical investigation on several jointed coal blocks having selected fracture networks and five additional artificial fracture networks under different confining stress combinations. Finally, a new empirical coal mass strength criterion was developed to estimate the JCMS values at the 3-D level. The developed new model is capable of capturing the scale effect and anisotropic strength behaviors. It can also be applied to rock masses having approximately orthogonal fracture systems or for masses where fracture system can be reduced to an equivalent orthogonal fracture system.The following new contributions were made in this dissertation to advance the existing state-of-art on the dissertation topic: (a) A new, unique methodology as shown in Fig. 1.1 incorporating the following aspects was used to develop a new 3-D coal mass strength criterion: a complete set of geomechanical property tests, fracture network detection and quantification, polyaxial compression tests, numerical decomposition techniques; (b) A new procedure was developed to construct the fracture network in the coal cubes starting from CT scans to perform numerical modeling using 3DEC. In this procedure, a modified fictitious joint framework was also proposed to extend the applicability of the original fictitious joint framework, which allows incorporating a large quantity of non-persistent joints with acceptable numerical calculation effort; (c) A new 3-D coal mass strength criterion was developed to incorporate the fracture network and 3-D confining stress system to capture the anisotropy and scale effect of coal mass strength. The proposed criterion not only includes the influence of the intermediate principal stress, which is ignored by some existing strength criteria, but also includes the intensity and orientation and size probability distributions of the fracture system explicitly by a fracture tensor based methodology, which is far more advanced than most of the current criteria that are based on rock mass classification systems having only scalar indices; (d) A modified grid search procedure was proposed and used to evaluate the applicability of nine different intact rock strength criteria. The best intact rock strength criteria applicable for the intact coal data obtained through PFC^3D modeling were found by performing the most detailed intact rock strength criteria evaluation incorporating σ₁ - σ₂ - σ₃ plots and behaviors on the deviatoric and meridian planes, which improves the understanding of the available intact rock strength criteria.

Two new three-dimensional rock mass strength criteria are developed in this dissertation by extending an existing rock mass strength criterion. These criteria incorporate the effects of the intermediate principal stress, minimum principal stress and the anisotropy resulting from these stresses acting on the fracture system. In addition, these criteria have the capability of capturing the anisotropic and scale dependent behavior of the jointed rock mass strength by incorporating the effect of fracture geometry through the fracture tensor components. Another significant feature of the new rock mass strength criterion which has the exponential functions (equation 6.7) is having only four empirical coefficients compared to the existing strength criterion which has five empirical coefficients; if the joint sets have the same isotropic mechanical behavior, the number of the empirical coefficients reduces to two in this new strength criterion (equation 6.10). The new criteria were proposed after analyzing 452 numerical modeling results of the triaxial, polyaxial and biaxial compression tests conducted on the jointed rock blocks having one or two joint sets by the PFC3D software version 5. In this research to have several samples with the same properties a synthetic rock material that is made out of a mixture of gypsum, sand and water was used. In total, 20 joint systems were chosen and joint sets have different dip angles varying from 15 to 60 at an interval of 15 with dip directions of 30 and 75 for the two joint sets. Each joint set also has 3 persistent joints with the joint spacing of 42 mm in a cubic sample of size 160 mm and the joints have the same isotropic mechanical behavior. The confining stress combination values were chosen based on the uniaxial compressive strength (UCS) value of the modeled intact synthetic rock. The minimum principal stress values were chosen as 0, 20, 40 and 60 percent of the UCS. For each minimum principal stress value, the intermediate principal stress value varies starting at the minimum principal stress value and increasing at an interval of 20 percent of the UCS until it is lower than the strength of the sample under the biaxial loading condition with the same minimum principal stress value. The new rock mass failure criteria were developed from the PFC3D modeling data. However, since the joint sets having the dip angle of 60 intersect the top and bottom boundaries of the sample simultaneously, the joint systems with at least one of the joint sets having the dip angle of 60 were removed from the database. Thus, 284 data points from 12 joint systems were used to find the best values of the empirical coefficients for the new rock mass strength criteria. λ, p and q were found to be 0.675, 3.16 and 0.6, respectively, through a conducted grid analysis with a high R2 (coefficient of determination) value of 0.94 for the new criterion given by equation 6.9 and a and b were found to be 0.404 and 0.972, respectively, through a conducted grid analysis with a high R2 value of 0.92 for the new criterion given by equation 6.10. The research results clearly illustrate how increase of the minimum and intermediate principal stresses and decrease of the joint dip angle, increase the jointed rock block strength. This dissertation also illustrates how different confining stress combinations and joint set dip angles result in different jointed rock mass failure modes such as sliding on the joints, failure through the intact rock and a combination of the intact rock and joint failures. To express the new rock mass strength failure criteria, it was necessary to determine the intact rock strengths under the same confining stress combinations mentioned earlier. Therefore, the intact rock was also modeled for all three compression tests and the intact rock strengths were found for 33 different confining stress combinations. Suitability of six major intact rock failure criteria: Mohr-Coulomb, Hoek-Brown, Modified Lade, Modified Wiebols and Cook, Mogi and Drucker-Prager in representing the intact rock strength was examined through fitting them using the aforementioned 33 PFC3D data points. Among these criteria, Modified Lade, Modified Mogi with power function and Modified Wiebols and Cook were found to be the best failure criteria producing lower Root Mean Square Error (RMSE) values of 0.272, 0.301 and 0.307, respectively. Thus, these three failure criteria are recommended for the prediction of the intact rock strength under the polyaxial stress condition. In PFC unlike the other methods, macro mechanical parameters are not directly used in the model and micro mechanical parameter values applicable between the particles should be calibrated using the macro mechanical properties. Accurate calibration is a difficult or challenging task. This dissertation emphasized the importance of studying the effects of all micro parameter values on the macro mechanical properties before one goes through calibration of the micro parameters in PFC modeling. Important effects of two micro parameters, which have received very little attention, the particle size distribution and the cov of the normal and shear strengths, on the macro properties are clearly illustrated before conducting the said calibration. The intact rock macro mechanical parameter values for the Young’s modulus, uniaxial compression strength (UCS), internal friction angle, cohesion and Poisson's ratio were found by performing 3 uniaxial tests, 3 triaxial tests and 5 Brazilian tests on a synthetic material made out of a mixture of gypsum, sand and water and the joint macro mechanical parameter values were found by conducting 4 uniaxial compression tests and 4 direct shear tests on jointed synthetic rocks with a horizontal joint. Then the micro mechanical properties of the Linear Parallel Bond Model (LPMB) and Modified Smooth Joint Contact Model (MSJCM) were calibrated to represent the intact rock and joints respectively, through the specific procedures explained in this research. The similar results obtained between the 2 polyaxial experiments tests of the intact rock and 11 polyaxial experimental tests of the jointed rock blocks having one joint set and the numerical modeling verified the calibrated micro mechanical properties and further modification of these properties was not necessary. This dissertation also proposes a modification to the Smooth Joint Contact Model (SJCM) to overcome the shortcoming of the SJCM to capture the non-linear behavior of the joint closure varying with the joint normal stress. Modified Smooth Joint Contact Model (MSJCM) uses a linear relation between the joint normal stiffness and the normal contact stress to model the non-linear relation between the joint normal deformation and the joint normal stress observed in the compression joint normal stiffness test. A good agreement obtained between the results from the experimental tests and the numerical modeling of the compression joint normal test shows the accuracy of this new model. Moreover, another shortcoming associated with the SJCM application known as the interlocking problem was solved through this research by proposing a new joint contact implementation algorithm called joint sides checking (JSC) approach. The interlocking problem occurs due to a shortcoming of the updating procedure in the PFC software related to the contact conditions of the particles that lie around the intended joint plane during high shear displacements. This problem increases the joint strength and dilation angle and creates unwanted fractures around the intended joint plane.