Jointed rock masses are formed of intact rock and joints. There-fore, proper characterization of rock mass behavior has to consid-er the combined behavior of the intact rock blocks and that of the joints. This thesis presents the theoretical background of the Synthetic Rock Mass (SRM) modeling technique along with example applica-tions. The SRM technique is a new approach for simulating the mechanical behavior of jointed rock masses. The technique uses the Bonded Particle Model (BPM) for rock to represent intact ma-terial and the Smooth-Joint Contact Model (SJM) to represent the in situ joint network. In this manner, the macroscopic behaviour of an SRM sample depends on both the creation of new fractures through intact material, and slip/opening of pre-existing joints. SRM samples containing thousands of non-persistent joints can be submitted to standard laboratory tests (UCS, triaxial loading, and direct tension tests) or tested under a non-trivial stress path repre-sentative of the stresses induced during the engineering activity under study. Output from the SRM methodology includes pre-peak properties (modulus, damage threshold, peak strength) and post-peak proper-ties (brittleness, dilation angle, residual strength, fragmentation). Of particular interest is the ability to obtain predictions of rock mass scale effects, anisotropy and brittleness; properties that can-not be obtained using empirical methods of property estimation. Additionally, the nature of yielding and fracturing can be studied as the rock mass fails. This information can improve our understand-ing of rock mass failure mechanisms. / QC20100720

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.

When the point under consideration is not near to the source of vibration, the strains developed in the rock mass due to the passage of waves are usually of small magnitude, and within the elastic range. However, the rock mass may be subjected to a wide range of strain levels depending on the source of vibration and the wave frequency, even within the elastic limit. The present study is based on the two general conditions existing at field, long wave length propagation of waves and intermediate wavelength propagation of waves. When the wavelength of propagating wave is much longer than the joint spacing, it is referred to as long wavelength condition and is associated with propagation of low frequency waves across closely spaced joints. When wavelength of propagating wave is nearly equal to joint spacing, it is known as intermediate wavelength condition and is associated with propagation of high frequency waves. Long wave length propagation of waves has been studied by conducting laboratory experiments using Resonant Column Apparatus on developed plaster gypsum samples. The influence of joint types, joint spacing and joint orientation on wave propagation has been analyzed at three confining stresses under various strain levels. The wave velocities and damping ratios at various strain levels have been obtained and presented. Shear wave velocities are more dependent on confining stress than compression wave velocities across frictional joints whereas, compression wave velocities are more dependent on confining stress than shear wave velocities across filled joints. Wave velocities are at minimum and wave damping is at maximum across horizontal joints whereas wave velocities are at maximum and wave damping is at minimum across vertical joints. Shear wave velocity and shear wave damping are more dependent on joint orientations than compression wave velocity and compression wave damping. As Resonant Column Apparatus has some limitations in testing stiff samples, a validated numerical model has been developed using Discrete Element Method (DEM) that can provide resonant frequencies under torsional and flexural vibrations. It has been found from numerical simulations, that reduction of normal and shear stiffness of joint with increasing strain levels leads to wave velocity reduction in jointed rock mass. Intermediate wave length propagation of waves has been studied by conducting tests using Bender/ extender elements and the numerical simulations developed using 3DEC (Three Dimensional Distinct Element Code).Parametric study on energy transmission, wave velocities and wave amplitudes of shear and compression waves, has been carried out using the validated numerical model. The propagation of waves across multiple parallel joints was simulated and the phenomenon of multiple reflections of waves between joints could be observed. The transformations of obliquely incident waves on the joint have been successfully modeled by separating the transmitted transformed P and S waves. The frequency dependent behavior of jointed rocks has been studied by developing a numerical model and by applying a wide range of wave frequencies. It has been found that low frequency shear waves may involve slips of rock blocks depending on the strength of rock joint, leading to less transmission of energy; while low frequency compression waves are well transmitted across the joints. High frequency shear and compression waves experience multiple reflections and absorptions at joints.

[pt] O objetivo deste trabalho foi o de verificar a influência da modificação no campo de tensões ao redor de uma escavação em um maciço rochoso fraturado, observando a ocorrência do fechamento de fraturas e a redução da condutividade hidráulica na região ao redor da escavação. São apresentadas inicialmente as características básicas que devem ser consideradas ao analisar problemas em maciços rochosos fraturados e apontados os possíveis efeitos de uma escavação neste tipo de material. Uma breve revisão bibliográfica mostra alguns tipos de técnicas de análises numéricas disponíveis para simulação de problemas em meios descontínuos, com ênfase no método dos elementos discretos e, em especial, no método dos elementos distintos (DEM), empregado no software UDEC da Itasca Consulting Group Inc., utilizado neste trabalho. As simulações utilizam um acoplamento hidromecânico, onde o maciço é representado por um conjunto de blocos e as descontinuidades são tratadas como contornos dos blocos, sendo o fluxo permitido apenas no interior das fraturas. Foi utilizado um modelo hipotético com escavação circular para validação da modelagem a partir de soluções analíticas presentes na literatura. Além disso, foi realizado um estudo de caso real, de dois túneis localizados em uma importante via na cidade do Rio de Janeiro. A análise paramétrica do problema mostra a influência da modificação de algumas variáveis importantes neste tipo de fenômeno. Por fim, foram analisados os resultados de todos os casos, com suas considerações finais e sugestões para trabalhos futuros. / [en] This work aims to verify the influence of the stress field changing around an excavation in a jointed rock mass, noticing the fracture closure and the hydraulic conductivity decrease in the region surrounding the excavation. At first, the basic characteristics that should be considered in jointed rock masses analyses are presented, pointing out the potential effects caused by excavations in such materials. A brief literature review presents some types of numerical analysis techniques available for discontinuous medium modeling, focusing on the discrete elements methods and, specifically, in the distinct element method (DEM), applied in the UDEC software by Itasca Consulting Group Inc., which was utilized in this work. The simulations make use of a hydromechanical coupling, being the rock mass represented by an assembly of blocks. The water flow takes place among the discontinuities, which are treated as blocks’ boundaries. A hypothetical model was used for modeling validation by comparison with analytical solutions from the literature. Besides that, it was accomplished a real case study of two tunnels located at an important road in Rio de Janeiro city. The parametric analyses of the problem show the influence of changing some important variables in this type of phenomenon. At last, all the results have been discussed, with final considerations and future works suggestions.

The distinct element method (DEM) is a useful tool in rock engineering to model jointed rock masses. To simulate a jointed rock mass realistically, the main challenge is to be able to capture its complex geometry which consists of blocks with various shapes and sizes, and to model the interactions between these blocks. The main contribution of this thesis is the development of novel algorithms in the DEM to model jointed rock masses, namely rock slicing procedures for block generation, and algorithms for contact detection between polygonal blocks in 2-D or polyhedral blocks in 3-D. These algorithms make use of convex optimisation techniques, for which there exist efficient solution procedures. They do not rely on conventional vertex-edge-face hierarchical data structures and tedious housekeeping algorithms. The algorithms have been verified against analytical and numerical solutions, as well as validated against experimental results published in the literature. Among those, the results of DEM simulations were compared against the experimental model tests and numerical simulations of jointed beams carried out by Talesnick et al. (2007) and Tsesarsky & Talesnick (2007) respectively. Emphasis was placed on modelling the stiffness of the block interfaces accurately, and this was accomplished by reinterpreting the laboratory data published by the investigators. The capabilities of the numerical tools are also examined and demonstrated in areas for which the DEM has found practical application. A substantial fraction of this thesis is devoted to illustrating how these tools can assist the engineer in designing support systems; for example, designing the length and spacing of rock bolts and the lining thickness for a tunnel. Algorithms to model rock bolt and lining support were implemented for this purpose. Interesting comparisons with elastic solutions for supported openings were obtained. Further, it is shown that the relative benefit of introducing more rock bolts or thicker lining can be evaluated using the numerical tools with the aid of an interaction diagram. In the final part of this thesis, the case history of the 1963 Vaiont rock slide in Italy is studied. The 2-D analyses led to useful insights concerning the influence of the reservoir water level, the rock mass strength and deformability, and the slide surface shear stiffness. 3-D analyses were undertaken to investigate the influence of the eastern boundary of the slope, and interesting insights were obtained concerning the slope kinematics. Overall, the case study shows that the tools are capable of modelling problems with specific physical and geometrical detail in both 2-D and 3-D.

The behavior of jointed rock mass is very complex and is influenced by many factors such as location of joints, joint frequency, joint orientation and joint strength. A thorough review of literature on different aspects of jointed rock mass indicate that the discontinuities or planes of weakness present in rock mass significantly influence its behavior. Numerous experimental tests were conducted to study the behavior of natural as well as artificial joints in rocks. Laboratory tests are time consuming and give results applicable to specific joint fabric and confining pressure. Numerical methods are the best alternative to laboratory tests to study the behavior of jointed rock mass. With the advent of computers numerical methods of analysis have become very popular, as they are highly flexible and can represent all complex geometries and material behavior. The accuracy of a numerical model depends upon the how well constitutive relations for the jointed rock mass are defined in the analysis. Empirical relationships for describing the mechanical behavior of discontinuities obtained from scaling the laboratory data is crucial unresolved problem, which will affect the quality of results obtained. One more important aspect in the numerical model is strength criteria used for jointed rock mass. The applicability of existing strength criteria to a particular jointed rock has to be carefully examined before they are used. Equivalent continuum approach simplifies the modeling of jointed rock mass as the joints are not modeled separately. Instead in equivalent continuum approach the jointed rock mass is represented by an equivalent continuum whose properties are defined by a combination of intact rock properties and joint properties. The accuracy of this kind of modeling depends upon the relationships used to define the jointed rock mass properties as a function of intact rock properties and joint properties. In the present study, an effort has been made (i) to establish empirical relations to define the properties of jointed rock mass as a function of intact rock properties and joint factor (ii) to develop a numerical model based on equivalent continuum approach using the empirical relations derived above, for easy and efficient modeling of jointed rock mass (iii) comparison of existing strength criteria for jointed rock masses using the equivalent continuum model developed above (iv) Modeling of joints explicitly and comparing these results with the equivalent continuum model results. Empirical relationships expressing the uniaxial compressive strength and elastic modulus of jointed rock as a function of corresponding intact rock properties and joint factor have been derived based on the statistical analysis of large amount of experimental data of uniaxial and triaxial tests collected from the literature. The effect of joints in the jointed rock is taken in to account by the joint factor. A comparative study of the empirical relationships arrived by the above analysis has been made to choose the best relation for the numerical analysis. Empirical relationships thus arrived for jointed rock mass are used in the equivalent continuum approach to represent the jointed rock properties as a combination of intact rock properties and joint factor. Equivalent continuum model developed is thoroughly tested, validated and applied for single, multiple and block jointed rocks. The equivalent continuum model developed has been applied for analysis of the power cavern for Shiobara power station. Different strength criteria available for jointed rock namely Mohr-Coulomb, Hoek and Drown, Yudhbir et al. and Rarnamurthy are incorporated in the equivalent continuum model to evaluate their applicability for jointed rock masses. Ramarnurthy's strength criterion gives the best values of failure stress for almost all the test cases and hence used in the equivalent continuum model. Alternatively, the joints in jointed rock mass are represented explicitly using interface element in the nonlinear finite element analysis. The explicit finite element model has been tested and validated using the experimental stress strain curves and failure stress values. Comparison of results obtained using equivalent continuum analysis and explicit modeling of joints has been given in the form of stress strain curves and failure stress plots for jointed rock masses along with the experimental results. Some of the major conclusions from the present study are as follows. Statistical relationships arrived to express the properties of the jointed rock as a function of intact rock and joint factor give a fair estimate of jointed rock in the absence of experimental data. Equivalent continuum model developed using statistical relations arrived above simplifies the numerical modeling of jointed rock to a large extent and also gives a fair estimate of jointed rock behavior with minimum input data. From the equivalent continuum analysis of Shiobara power cavern, it can be concluded that this approach is very advantageous for modeling highly discontinuous systems provided the joint factor is estimated properly so that it represents the real fabric of the joints present in the system. Comparison of different strength criteria shows that Ramamurthy's strength criterion is the best for jointed rocks. When the rock mass has one or two major joints it is advantageous to model it explicitly so that the behavior of the joint can be studied in detail. Explicit representation of the joints in the finite element analysis gives a lair estimate of the zones most susceptible to failure in a jointed rock. From comparison of experimental values, equivalent continuum model results and the explicit joint model results, it can be concluded that results obtained using equivalent continuum model are nearest to the experimental results in almost all the cases.

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.