<p> The Killarney Igneous Complex, composed of an intrusive granite and a hypabyssal or extrusive porphyry was implaced near and at the surface in the general locality of Killarney, Ontario. The crystallization age of the intrusive portion of the complex is approximately 1740 million years. These rocks have experienced deformation by forces which in some instances produced complicated shearing motions. Mesoscopic samples show a foliation and a lineation supporting a history of deformation. The foliation is clearly the more visible fabric and is interpreted as a plane of flattening.</p> <p> Kinematic indicators, specifically asymmetric pressure shadow wings, are present within the rocks; however the patterns are too complicated to interpret by a simple sense of shear. The geometry of these kinematic indicators does suggest an active plane of foliation.</p> / Thesis / Bachelor of Science (BSc)

Most rock masses encountered in civil and mining engineering projects contain pre-existing discontinuities. These discontinuities weaken the rock masses to an extent, which depends very much on the size of engineering structure relation to discontinuity spacing. The strength and deformability of rock mass is controlled not only by the intact portion of rock, but by the characteristic of the joints that break up the mass, particularly their pattern and their orientation with respect to the in-situ stresses. In considering the effect of joints, the discrete approach emerged as an efficient tool and advocated since 1970s (Cundall, 1971). However, the numerical approach with modelling the joints explicitly has the limitation of computational complexity for modelling large-scale problems with extremely large number of joints. As an alternative to this limitation, the equivalent continuum approach models the jointed rock masses as a continuum with the equivalent properties that represent implicitly the effects of the joints. Several numerical methods have been developed by various researchers to model jointed rock masses as equivalent continuum, using various techniques. However, the existing equivalent continuum models are complicated and need more input data from experimental or field testing in order to carry out the analysis. Present approach attempts to use statistical relations, which are simple and obtained after analyzing a large data from the literature on laboratory test results of jointed rock masses. Systematic investigations were done including laboratory experiments to develop the methodologies to determine the equivalent material properties of rock mass and their stress-strain behaviour, using a hyperbolic approach (Duncan and Chang, 1970). Present study covers the development of equivalent continuum model for rock mass right from developing statistical correlations to find out equivalent material properties based on experimental results, to the implementation of the model in FLAC3D for 3-dimensional applications and subsequently verification leading to real field application involving jointed rocks. Experimental work carried out to study the strength and deformation characteristics of jointed rock by using standard laboratory tests on cylindrical specimens of plaster of Paris by introducing artificial joints. The objective was to derive the compressive strength and elastic modulus of rock mass as a function of intact rock strength/modulus and joint factor. The obtained experimental results and developed relations were compared with the previous experimental data on jointed rocks. Further, a failure criterion as proposed by Ramamurthy (1993) has been validated from these experimental results of intact and jointed rock specimens. Empirical relationships similar to Ramamurthy’s relations are established for the prediction of rock mass strength and were compared with proposed equation by Ramamurthy (1993) and are found comparable. However, the equations by Ramamurthy were based on different variety of rocks and therefore recommended for further use and were used in numerical models. For efficient application to the field problems the equivalent continuum model is implemented in the program Fast Lagrangian analysis of continua (FLAC3D). The model was rigorously validated by simulating jointed rock specimens. Element tests were conducted for both uniaxial and triaxial cases and then compared with the respective experimental results. The numerical test program includes laboratory tested cylindrical rock specimens of different rock types, from plaster of Paris representing soft rock to granite representing very hard rock. The results of the equivalent continuum modelling were also compared with explicit modelling results where joints were incorporated in the model as interfaces. To represent highly discontinuous system, the laboratory investigation on block jointed specimens of gypsum plaster (Brown and Trollope, 1970) was modelled numerically using equivalent continuum approach. To extend the applicability of the model to field applications, investigation were done by undertaking numerical modelling of two case studies underground caverns, one Nathpa Jhakri hydroelectric power cavern in Himachal Pradesh, India, and the other one Shiobara hydroelectric power cavern in Japan. This study verifies the efficiency of the present approach in estimating ground movement and stress distribution around the excavations in jointed rock masses. The modelling results were also compared with six other computation models as presented by Horii et al. (1999) for the Shiobara power house cavern. An attempt has also been made to numerically model the support system for the cavern and investigate the efficiency of reinforcements using FLAC3D. The model was also used for analyzing large scale slope in jointed rocks using the equivalent continuum model by undertaking numerical modelling of Anji bridge abutment slopes, in Jammu and Kashmir, India. Slope stability analysis is done using equivalent continuum approach for both, the original profiles as well as with the pier loads on cut profiles. Attempt was also made to exhibit the shear strength dependency of the strain though the hyperbolic stress- strain model. The shear strain developed in the slope increases with reducing the shear strength. The relationship between the shear strength reduction ratio ‘R’ and axial strain ‘ε’, for different values of failure ratio ‘Rf’ was studied and it was observed that, the value of ‘ε’ increases, as the value of ‘R’ increases especially it increases rapidly when the value ‘R’ approaches certain critical value, which varies with the value of ‘Rf’. This critical value of R is known as the critical shear strength reduction factor Rc and is highly sensitive to the confining stress. As the value of Rf increases, representing a transition from linear elastic nature to nonlinear nature, the value of critical shear strength reduction ratio also decreases. Relationship between the critical shear strength reduction ratio and the safety factor were examined to elucidate their physical meaning. It was observed that at critical value of the shear strength reduction ratio, a well defined failure shear zone developed from the toe to the crest of the slope. Intelligent models using ANNs were also developed to predict the elastic modulus of jointed rocks as an alternative to empirical equations and without predefining a mathematical model to correlate the properties.

Infrastructure is developing at an extremely fast pace which includes construction of metros, underground storage places, railway bridges, caverns and tunnels. Very often these structures are found in or on the rock masses. Rock masses are seldom found in nature without joints or discontinuities. Jointed rocks are characterized by the presence of inherent discontinuities of varied sizes with different orientations and intensities, which can have significant effect on their mechanical response. Constructions involving jointed rocks often become challenging jobs for Civil Engineers as the instability of slopes or excavations in these jointed rocks poses serious concerns, sometimes leading to the failure of structures built on them. Experimental investigations on jointed rock masses are not always feasible and pose formidable problems to the engineers. Apart from the technical difficulties of extracting undisturbed rock samples, it is very expensive and time consuming to conduct the experiments on jointed rock masses of huge dimensions. The most popular methods of evaluating the rock mass behaviour are the Numerical methods. In this thesis, numerical modelling of jointed rock masses is carried out using computer program FLAC (Fast Lagrangian Analysis of Continua). The objective of the present study is to study the effect of various joint parameters on the response of jointed rock masses in static as well as seismic shaking conditions. This is achieved through systematic series of numerical simulations of jointed rocks in triaxial compression, in underground openings and in large rock slopes. This thesis is an attempt to study the individual effect of different joint parameters on the rock mass behaviour and to integrate these results to provide useful insight into the behaviour of jointed rock mass under various joint conditions. In practice, it is almost impossible to explore all of the joint systems or to investigate all their mechanical characteristics and implementing them explicitly in the model. In these cases, the use of the equivalent continuum model to simulate the behaviour of jointed rock masses could be valuable. Hence this approach is mainly used in this thesis. Some numerical simulations with explicitly modelled joints are also presented for comparison with the continuum modelling. The applicability of Artificial Neural Networks for the prediction of stress-strain response of jointed rocks is also explored. Static, pseudo-static and dynamic analyses of a large rock slope in Himalayas is carried out and parametric seismic analysis of rock slope is carried out with varying input shaking, material damping and shear strength parameters. Results from the numerical studies showed that joint inclination is the most influencing parameter for the jointed rock mass behaviour. Rock masses exhibit lowest strength at critical angle of joint inclination and the deformations around excavations will be highest when the joints are inclined at an angle close to the critical angle. However at very high confining pressures, the influence of joint inclination gets subdued. Under seismic base shaking conditions, the deformations of rock masses largely depend on the acceleration response with time, frequency content and duration rather than the peak amplitude or the magnitude of earthquake. All these aspects are discussed in the light of results from numerical studies presented in this thesis.