Abstract The problem of fluid flow in a fractured reservoir has been a topic of interest to researchers since considerable amount of time. A coupled solid-fluid numerical procedure has always been a requirement in the petroleum and geotechnical industry. Porous media is modelled using Biot's theory using Darcy law for fluid flow. Naturally discontinuous porous rock mass constitutes two phases: fluid flow through pore spaces in rock matrix and fluid flow through fractures, joints, faults, etc. Because rock and discontinuities exhibit differential fluid storage capacity and fluid conductivity, modelling such dual porosity system poses mathematical as well as numerical challenges. Most of the existing coupled formulations of fluid rock interaction flow behavior are pressure based and this results in unsymmetrical stiffness matrices for absorbing viscous boundary condition in dynamic analysis. Hence, a displacement based extended finite element formulation is developed and presented in this paper for dual porous media having multiple intersecting discontinuities like joints, faults for symmetrical representation and for future application of infinite boundary conditions. This paper will mainly highlight on the formulation derivation based on rock displacement (u), joint displacement (a) and displacement of water in pore spaces (w) with its numerical implementation. A numerical example is illustrated in the later section for the efficacy of the procedure. 1. Introduction Rock mass in general is a composite of discrete fracture networks, faults planes, shear zones, fluid in the rock pores, fluid in the discontinuities and rock skeleton with different material properties. Understanding such complex phenomenon under different time varying stress loading conditions is vital for designing a stable underground structure. Classical one-dimensional consolidation theory of porous media was first proposed by Terzaghi in 1943 considering effective stress concept. Following the work done by Terzaghi, Biot (1941, 1955, 1956, 1957) thereby proposed a three-dimensional consolidation theory for porous media under static and dynamic loading conditions; which accounted for Darcy fluid flow in the rock matrix. A complete review on the historical development of the theory of porous media can be found in de Boer, 1996. Presence of fluid in the rock mass obviously causes difference in stress regime as compared to the conventional estimation (Theory of Elasticity) considering dry rock. Essentially nature of fluid flow in fractures is different than that in rock matrix showcasing two different permeability. Hence, such media is often referred to as Dual Porosity media (Barenblatt et al., 1960). Many researchers (Warren and Root, 1963; Aifantis, 1977; 1979; Ghafouri and Lewis, 1996; Bai et al., 1994; 1999) came up with analytical solutions for dual porosity media considering rock matrix and fracture network separately. Interaction between the two phases is achieved via a transfer function which is essentially fluid influx and out flux from the fracture to rock and vice versa. Complete closed form solution for such complex phenomenon is almost an impossible task considering huge variability in rock physics. Advent of numerical procedures have helped to solve approximately any kind of complicated physical problems. A brief review on the FEM procedures in porous media can be found in Khoei, 2015.

Abstract Rocks in deep underground are subjected to different stresses inherent to natural orogeny, therefore, rock behaviour becomes complicated in response to extraction activities of deep earth resources. Rock behaviour and failure in deep underground is not well understood, leading to flaw engineering designs. In this sense, the complete stress-strain characteristics of intact rock, i.e. the pre-peak and post-peak stress-strain regimes are relevant in the understanding of the total process of rock deformation under in-situ stress. In this study post-peak characteristics of different rocks types, having unconfined compressive strengths of 7 to 123 MPa were investigated in a series of quasi-static monotonic uniaxial and triaxial compression tests. Post-peak stress-strain measurement was achieved by implementing lateral-strain rate feedback method in a closed-loop system to apply axial load to the rocks. In uniaxial and triaxial compressive testing, measurement of complete stress-strain behaviour showed i) either class II behaviour or a combination of class I-II behaviour and ii) a noticeable shifting from class II behaviour toward class I behaviour as the ratio between confining pressure to the unconfined compressive strength increases significantly. The results of the experimental study then were used to develop an index to describe the pre-peak and post-peak behaviour of the rocks, encompassing both confined and unconfined conditions. Reasonable correlation was observed between the new index and confining pressure. 1. Introduction Prediction of rock failure is very important for civil engineering and mining development projects. With this, engineers can investigate the effect of rock behaviour on drilling and excavation performance and rock burst occurrence in deep mining. Some researchers have attempted to develop brittleness indices to describe rock failure behaviour based on rock compressive and tensile strength (Hucka & Das 1974, Coates 1966, Altindag 2003, Yarali & Soyer 2011). In addition, several brittleness indices based on the energy of the rock under loading have been proposed (Baron et al. 1962). However, these indices are only considered pre-peak rock behaviour. Munoz et al. (2016a) found that brittleness indices that are developed based on rock strength and pre-peak rock behaviour are unable to predict rock drilling performance. As a result, they developed new brittleness indices to describe rock failure behaviour in uniaxial compressive loading based on pre-peak and post-peak properties (Munoz et al. 2016b). This approach, however, ignores the residual strength of rocks, which might be significant under confined loading conditions. In addition, brittle to ductile transition of rock post failure behaviour is overlooked in the previous work as only uniaxial loading condition were investigated. Therefore, it is required to develop relevant methods able to describe rock pre-peak and post-peak stress-strain behaviour during uniaxial and triaxial loading condition.

Abstract The transition zone, i.e. where the pressurized water enters the steel lined section of the waterway, is a key component of the entire tunnel system in any underground hydropower project utilizing unlined pressure tunnels. Not only is it important for conveying the pressurized water into the turbine, its positioning also defines the location, length and layout of several other tunnels. The key for deciding on positioning of the transition zone is to identify a place with sufficient in-situ rock mass stress to withstand the internal water pressure generated from the hydraulic head of the pressure tunnel. To prepare complete tender documents, preliminary positioning of the transition zone must be defined before sufficient stress data for final positioning are available. In Norway, such early assessments have often been made on empirical basis with little or no testing. Even though this approach normally is necessary in the preliminary phase of a project development, the final decision on transition zone positioning, must be based on in-situ testing. Recognizing that stress testing is required for safe design of the transition zone, flexibility in both layout and construction schedule should be incorporated in the project. To ensure this flexibility, the tender documents must include a specific plan that describes what ground investigations should be done, where they should be done, what the acceptable criteria for such tests are, and how the results should be adopted in the design. In this paper, a proposal on the outline of such a plan will be presented based on Norwegian experience and practice in investigation, design and construction of the transition zone area for selected projects. The work presented is part of the hydropower research being performed at HydroCen, based at NTNU in Trondheim, Norway. 1. Introduction As water conduits for energy production, rock tunnels constitute an integral part of underground hydropower projects. In Norway, the use of unlined pressure tunnels has become the norm for any underground hydropower project, and the concept has achieved worldwide recognition (Rancourt, 2010). The main motivation for adopting the unlined concept is the potential for very large cost reductions when replacing a steel or concrete lined tunnel with an unlined tunnel. There are, however, several reports of unlined pressure tunnels not performing as expected due to hydraulic failure of the tunnel caused by the internal water pressure, as documented by Broch (1982), Merritt (1999) and Palmstrom and Broch (2017) amongst others. To reduce the risk associated with hydraulic failure of unlined pressure tunnels, knowledge about rock stresses in the area of interest is required. Obtaining such information in due time for preparation of tender documents can be difficult due to the inherent limitations of the stress measuring methods, combined with the often difficult physical access to the investigation point. Therefore, project owners and engineers often have to make their tender stage tunnel design without direct stress measurements, and postpone rock stress measurements to the construction phase. This implies that changes to the tender design must be allowed for, in case insufficient stress levels are identified during construction stage stress measurements (Halvorsen and Roti, 2013). A specific plan describing the testing- and design methodology for the siting of the transition zone is a useful common basis for both Contractor and Client when deciding the final design. The outline of such a plan is presented herein, based on Norwegian experience and practice in investigation, design and construction of the transition zone area in hard rock conditions. The plan is specially emphasizing the rock stress measurements, though it is recognized that knowledge about the overall rock mass conditions is essential in any underground design. A key requirement for using unlined pressure tunnels is that, at any point along the pressurized waterway, the rock stress surrounding the tunnel must be larger than the internal water pressure. If not, the water pressure can lift, or jack, the rock mass so that hydraulic failure and associated large leakages occur. Excessive leakages from the pressure tunnel can cause catastrophic events such as flooding of nearby underground structures and even landslides as reported by Brekke and Ripley (1987), Benson (1989) and Palmstrom and Broch (2017). To avoid such incidents it is absolutely required to ensure that any section of unlined pressure tunnel has sufficiently high rock stresses to accommodate the internal water pressure.

Abstract The objective of this paper is to investigate the three-dimensional strength characteristics of a porous sandstone, which is referred to as Zigong sandstone, under true triaxial stress states ( σ 1 ≥ σ 2 ≥ σ 3 ) by means of a Mogi-type true triaxial testing apparatus. Three series of tests ( σ 3 = 0, 20, and 60 MPa) are conducted. Within each series, σ 2 is varied from σ 2 = σ 3 to σ 2 =σ 1 from test to test. For each test, σ 1 is raised monotonically to failure while σ 2 and σ 3 are kept constant and the post-peak behavior is also captured. Deformability and strength are investigated in term of the effect of σ 2 . It is found that, for a constant σ 3 , the onset of dilatancy generally increases with the increase of σ 2 . Regarding peak strength, the variation of σ 1 at failure versus σ 2 exhibits a typical ascending-then-descending trend. A versatile deviatoric function is used to replace the one of Hoek-Brown strength criterion, which is referred to as the modified Hoek-Brown strength criterion and is further adopted to depict the strength characteristics in the three-dimensional principal stress space. Results show that the effect of σ 2 on rock strength is actually a combined effect of mean stress and Lode angle. 1. Introduction Sandstone is one of the main formations in the earth's crust. Many human activities, such as hydrocarbon production, CO 2 sequestration, and waste disposal, are intimately related to the failure of host sandstones. Understanding and charactering the mechanical responses of sandstone under different stress conditions is essential to the design and construction of many underground projects. In the past several decades, efforts have been taken to investigate the failure mechanisms of porous sandstones based on laboratory tests. Extensive conventional triaxial tests have been conducted on cylindrical specimens of different sandstones (Wong T et al., 2012), revealing that mechanical responses of sandstones, such as failure modes, strength, deformability, and porosity evolution, are heavily dependent on the first two stress invariants related to the mean stress and the differential principal stress (Wong T et al., 1997; Grueschow E et al., 2005; Baud P et al., 2006), respectively. The effect of the third stress invariant, however, is rarely known except for the limited comparison between conventional triaxial compression (CTC: σ 1 > σ 2 = σ 3 ) and conventional triaxial extension (CTE: σ 1 = σ 2 >σ 3 ) (Murrell S, 1963; Mogi K, 1967). Moreover, in situ stress measurements at depths indicate a state of stress in the earth's crust that is totally non-uniform ( σ 1 ≠ σ 2 ≠ σ 3 ) (Haimson BC, 1978; Brace WF et al., 1980; Vernik L et al., 1992). It is important to consider general states of stress to fully understand failure characteristics of sandstone.

Abstract TBM excavation is very common these days and its market is expected to grow at 4–6% every year. In TBM excavation, estimation of cutting performance is of great importance in design stage as well as during construction. The performance is highly dependent on the geological conditions, i.e. characteristics of rock and discontinuities, and operational conditions, i.e. selection of cutter, cutting forces, cutter spacing, etc. For performance estimation, prediction models can be used in which index properties of rock and rock cutting database are correlated. Establishing the database surely takes much time and effort. And the models are subject to be modified when new sets of database are added. Other way of performance estimation is conducting a full scale linear cutting machine test. In the test, both rock and operational conditions can be easily controlled. However, linear cutting machine test is not often carried out because it requires large block of specimen, large stiff frame and precise control system. Therefore, numerical simulation can have benefits over experimental method and it recently provided decent outputs. In this presentation, recent researches on performance assessment of rock cutting including punch penetration test, full size linear cutting machine test, and numerical simulation are introduced.

Abstract En-echelon fractures have been often identified in faults in rocks at different length scales. To enhance our understanding of the role of en-echelon cracks in the formation of a shear rupture, blocky Carrara Marble specimens, containing multiple artificial en-echelon flaws (about 13 mm long), are uniaxially tested in this study. Based on the experimental observation, the fracturing process can be divided into four stages. These stages indicate that instead of tensile wing cracks commonly observed as linking cracks in moulded gypsum specimens, Carrara Marble only produces white patches along similar trajectories to bound an elliptical rock bridge, while the linking coalescence cracks directly connect a flaw tip to the neighboring flaw tip to divide the elliptical rock bridge into two parts. A large relative sliding across the shear rupture is observable only after the initiation of the cracks along the path of either quasi-coplanar or oblique white patches at the two outer flaw tips. A short discussion over the influence of flaw configuration, loading condition and material property will be provided towards the end of the paper, suggesting that different combinations of these factors can possibly lead to the same coalescence pattern.

Abstract To minimize the social cost and interference with existing facilities, tunnels for cable and electricity have been mostly constructed using trenchless technology in recent years. In this study, a new small-scale excavation method using a multi-hammer tunnelling machine was suggested. To evaluate the optimum operating conditions of the machine, linear percussion testing system to experiment with various conditions was established. Linear percussion tests were conducted considering the air pressure and RPM (i.e., two dominant-field operating conditions). The optimum operating condition of a multi-hammer tunnelling machine for three rock classes was obtained from the test results. Based on the penetration rate data measured from a field test, a prediction chart of the penetration rate was proposed for various rock classes.

Abstract The evolution of gas permeability in coal a wellbore is not only induced by the damage of coal matrix but also by the dilation deformation of fractures. This study focuses on two fundamental issues: evolutions of the coal matrix damage and the dilation deformation of fractures, and their impacts on the evolution of gas permeability. As the volumetric strain increases with the number of fractures, the equation of coal damage can be considered as a function of the volumetric strain. Then a stress-depended permeability model with the damage incorporated is proposed for the coal matrix. The permeability evolution model for the fractures under the influence of shearing dilation is obtained based on the Hurst coefficient which presents the roughness of fracture surface. These two permeability models for the coal matrix and the fractures, respectively, are incorporated into a fully coupled model of gas flow field and coal deformation field. A 2D case of the wellbore cross-section is presented to show the permeability evolution. The result shows that the gas permeability increases drastically in the wellbore due to the influence of the effective stress and the damage factor. The result also indicates that the shear displacement plays a dominant role on the evolution of fracture permeability around the wellbore.

Abstract Computer modeling can be used to explore insights into the effect of rockbolt intersecting joints in rock masses and to estimate the effectiveness of the rock reinforcement system. In this paper, the fully grouted rockbolts are modeled within the frame work of the two-dimensional discontinuous deformation analysis (2D-DDA). In DDA, the rock block is modeled by elastic, perfect plastic behavior, while the rockbolt material is modeled in the elastic, followed by the linear strain-hardening behavior. In addition, the shear force generated by slippage along the interface is assumed to have a linear relationship with respect to the relative slipping distance between the rockbolt and the rock. After the unit shear force reaches to the critical value, the frictional debounding will occur following the assumed interface mechanical behavior. Three pullout tests are simulated to predict fully grouted rockbolt behaviors in different kinds of rock masses. The results show that in hard rock, the mechanical interlock between the rockbolt and the rock dominants the fully grouted rockbolt behavior However, when the rockbolt intersects joints in soft rock, the interface debounding is constrained to a small area. In that case, the interface behavior would be much less effective. It can be seen that the reinforcement efficiency of fully grouted rockbolt is affected by the surrounding rock mass.

Abstract Carbon Dioxide (CO 2 ) sequestration in deep coal seams is a potential mitigation option for global warming. In deep coal seams, the temperature is higher (>40°C) which makes the kinetic energy of the gas molecules to be increased. Accordingly, it increases the rate of diffusion and results in reduction of adsorption capacity that affects the coal gas permeability. Among several previous works conducted regarding the temperature effect for coal gas permeability, the attention paid for brown coal is very less which enhance the necessity of a detailed study. Therefore, the main objective of this study is to investigate the effect of temperature on the permeability of Victorian Brown Coal. A series of tri-axial experiments was conducted on brown coal specimens that were collected from Latrobe Valley basin, Victoria. Permeability tests were carried out under 10 MPa confinement for two different temperatures (25 and 40°C). Both CO 2 and N 2 were injected to the sample in various injecting pressures to obtain a proper comparison between the reactive and non-reactive gas permeability. According to the experimental results, CO 2 permeability of coal decreases for higher injecting pressures (at 8 MPa) at lower temperatures (less than 40 °C), due to the process of swelling occurs inside the coal sample during the CO 2 injection. However, the influence of temperature on N 2 permeability was negligible compared to the CO 2 permeability. Basically it may because; N2 is a nonreactive gas which does not make any adsorption or swelling effect in coal matrix like CO 2 .

ABSTRACT In this paper, several new developments regarding the failure, fracture and fragmentation of rocks will be discussed. The first topic discussed is the development of true-triaxial failure criteria that involve all three principal stresses. The next topic is a new approach to modelling the propagation of cracks and fractures using accurate local calculations of the stress intensity factor. Lastly, a method for fracture-driven rock fragmentation with a velocity-dependent propagation law is discussed.

ABSTRACT Controlled blasting for loosening coal seam is one of the most important measures to enhance the gas drainage and thus to prevent coal and gas outburst. The formation and development of blasting-induced damage zone, as well as the gas flow in damaged coal seam, can be considered as a coupled process among gas flow, solid deformation and damage. In this work, a coupled multiphysical model for the interaction of blasting damage of coal seam and gas flow is proposed, based on which, the effect of loosening blasting on draining gas in coalbed is numerically simulated and the associated mechanisms for enhanced gas drainage induced by blasting damage is clarified. In this model the loosening of coal seam induced by blasting is considered as damage process that is dominated by the combined contribution of blasting stress wave and blasting-induced gas pressure. Then, by considering the effect of coal seam damage on the gas permeability, the gas drainage enhanced by blasting damage is quantified based on the numerical simulations. It is demonstrated that, the blasting damage around the borehole can not only alleviate the stress concentration at the perimeter of borehole, but also enhance the gas drainage due to the increase of the gas permeability in the damaged coal seam.

ABSTRACT Failure in rocks is attributed to crack initiation and coalescence processes upon loading. Crack behavior study, which has been extensively conducted in various rock types containing artificially created flaws under a quasi-static loading condition over the past decades, is extended to dynamic loading conditions by using the Split Hopkinson Pressure Bar (SHPB) technique. The loading tests are conducted on specimens containing a single pre-existing open flaw (60mm × 30mm × 20mm) in Carrara marble. Similar to those loaded quasi-statically, white patches are observed to develop in the specimens loaded dynamically at the early stage of the loading prior to the development of observable cracks. The respective failure modes are however significantly different. For quasi-static compression, normally two macro-cracks linking the two opposite corners of the specimen and the flaw tips cause the failure of the marble specimens, producing two main fragments. In contrast, under high strain rate, four fragments associated with "X" shape deformation bands are produced irrespective of the inclination angle of the flaws. The failure is attributed to the more or less simultaneous propagation of the horsetail and anti-wing cracks. In this paper, the detailed cracking processes will be compared and discussed.

ABSTRACT Anisotropy is one of the mechanical properties to be considered as a factor in the design of underground structures. The object of this paper is to determine five independent elastic constants of a transversely isotropic rock experimentally. Tests are successfully accomplished and data are acceptable over all, for total 35 specimens of 7 different angles from a large block of rhyolite from Haenam area. Saint-Venant approximation is used in data analysis of the every individual angle. Near-true values of E 1 , E 2 , V 1 and V 2 can be directly measured from the two special specimens and G 2 can be obtained from the five specimens of inclined angles. Two values of tangential modulus on the anisotropic plane, averaged G 2 and G 2-sv , are almost same each other within 6 % of difference. And test data of the apparent Young's modulus can be referred as a monotonous increasing. From these results, it is proved that SV approximation may be very applicable for rhyolite. It is proposed that displacement by sliding on account of the excess tangential stress on a transversely isotropic plane may be assumed in this paper to explain a wide difference in the longitudinal strain. Sliding model can be one of the future studies to answer why Saint-Venant approximation may not become well applicable in the analysis of transversely isotropic rocks.

ABSTRACT This paper presents numerical simulation for predicting fracture and failure growth of geomaterial using smoothed particle hydrodynamics (SPH). The first example deals with slope stability analysis of a chromite mine having friable chromite as ore body. The ultimate pit may reach upto 144 m below the surface having an ultimate pit angle 30° for 19 benches. It is required to forecast the stability of the ultimate pit slope for the given materials and pit geometry. The paper analyzes the stability of this slope considering Drucker-Prager rock mass medium in SPH procedure. The second example comprises of fracture growth of a circular rock specimen under diametrically opposite concentrated angle loads. In order to determine the plastic regime of the specimen for a given tensile strength, Rankine maximum tensile failure criterion has been implemented in the SPH framework.

ABSTRACT Biological stabilisation of dump slope is one of the widely used techniques for controlling erosion and stabilisation of dump slope to maintain the local climate conditions least affected. Vegetation physically and mechanically reinforces the dump material, resists erosion and reduces pore water pressure. It also provides some information about the slope movement. Dump materials are heterogeneous, anisotropic and behave neither like soil nor like rock. The modeling of such materials is difficult and continuum material and boundary conditions do not provide appropriate and accurate results. The present paper evaluates the effect of vegetation on dump slope stability for a given dump geometry through discrete modeling approach. The dump slope angle and height was kept constant at 37° and 60m respectively and its stability analyzed without and with vegetation cover. It was found that vegetation increases the stability of the slope as approximately 85.5% reduction in maximum displacement was observed. Hence, the bioremedial measures are better than the physical measures to protect the erosion and contamination more effectively and acceptable without deteriorating the surrounding ecological balance.

Abstract: This paper extends the numerical manifold method (NMM) for complete rock slope failure analysis. A fracturing algorithm based on the Mohr-Coulomb criterion with a tensile cutoff is implemented into the NMM code. The developed program is first calibrated through two typical crack problems and then applied to analyze the potential footwall slope instability. Parametric studies are carried out. Numerical results indicate that the developed program can simulate the sliding along pre-existing discontinuities, fracturing through intact rock, as well as kinematics of failed slope, and can reproduce the major failure mechanisms observed in footwall slope collapses. The NMM is promising for such problems and deserves to be further developed to be practically used in rock slope stability analysis and open pit slope design. 1. INTRODUCTION Open pit mining is a very cost-effective mining method. In open pit mining, pit slopes are formed. With the mining depths steadily increased to 500 meters or even higher, design of open pit slope angles is becoming more and more important. Small change in the overall pit slope angle has significant influence on the overall economy. An ideal design method must be able to predict where and under what conditions a failure surface may develop; predict the kinematics of the failed slope. Current design methods can be distinguished into four groups: empirical design method; physical model tests; limit equilibrium methods; numerical methods. Among them, numerical methods have become popular in recent years. Currently existing numerical methods can be generally grouped into two categories: continuum methods (e.g. FDM, FEM, BEM, etc.) and discontinuum methods (e.g. the distinct element method with the commercial codes as UDEC, 3DEC, etc. and the discontinuous deformation analysis (DDA) [1]). Existing continuum codes are able to simulate the location and shape of the failure surface developing in a slope. However, an actual failure surface discontinuity is not formed. Pre-existing fractures are usually not incorporated. Discontinuum codes model the discontinuities presented in rock mass explicitly and have been successfully used to simulate structurally controlled failures. They are, however, difficult to simulate failures through intact rock. Actual slope failure involves both sliding along pre-existing discontinuities as well as fracturing through intact rock. A general method which can simulate the actual slope failure becomes essential. In this paper, the recently developed numerical manifold method (NMM) [2] is explored to account for complete rock slope failure process. Footwall slope is considered. Footwall slopes are often excavated parallel to dip and extensive along both strike and down-dip. When mining continues down-dip, the length of the exposed footwall slope increases and the potential instability of the slope may arise. Footwall slope instability is a relatively common occurrence in open pit mines situated in area of steeply dipping strata particularly where mountainous topography exists. The importance of footwall instability has long been recognized. Failures only occur along the pre-defined discontinuities. In this paper, non-persistent joints are allowed, both sliding along pre-existing discontinuities and fracturing through intact rock will be captured.

ABSTRACT: The numerical manifold method (NMM) is a combination of the finite element method (FEM) and discontinuous deformation analysis (DDA) method. It provides a robust numerical solution to a solid medium with dense discontinuities. This paper extends the numerical manifold method to the three dimensional domain from the fundamental concepts. It explains the three essential entities, i.e, the mathematical cover, the physical cover and the manifold element in the 3-D version under the framework of the finite cover system. Furthermore, it tests the robustness and accuracy of the proposed algorithm through a tetrahedral wedge sliding simulation in a rock slope. 1. INTRODUCTION Recently, high frequent and prevalent geologic hazards cause catastrophic damage and human death. The increased consciousness regarding safety and economy has led the engineers to seek more rational solutions to the geotechnical problems related to civil and underground engineering. It is more and more urgent to have a proper analysis tool for strengthening the understanding to hazard mechanism and designing efficiency to reduce disaster damage. Following the characteristics of geotechnical applications, the 2-D framework of NMM was proposed in 1991 [1], which is one of most suitable numerical methods in rock engineering. NMM could be considered as the combination of FEM and DDA. Although the 2-D NMM has already been widely proven by various applications, the real problems in engineering practices are always in the three dimensional domain. It has been a long time challenge to extend the 2-D NMM to 3-D due to the complexity in geometry description and the absence of a reliable 3-D contact algorithm. In this paper, we firstly introduce basic concepts for 3-D NMM. It later utilizes simple tetrahedral wedge sliding in the rock slope to test the accuracy of the proposed algorithm 2. FUNDEMENTALS OF 3-D NUMERICAL MANIFOLD METHOD The numerical manifold method is proposed by Shi [1] as a combination of the mathematical domain and physical domain. The Target Physical Objects (TPOs) in physical domain includes the boundaries of the material volume, joints, and the interfaces of different material zones. The TPOs represents material conditions which cannot be chosen artificially. The mathematical mesh defines the fine or rough approximation of unknown functions. This mesh is chosen by the user according to the problem geometry, solution accuracy requirement, and the physical property zoning. The mathematical mesh is used to build mathematical covers that represent small regions of the whole field and can be of any shape and size. They can overlap each other and do not need to coincide with the physical cover as long as they are large enough to cover the physical blocks. The 3-D NMM is also based on the three important concepts, i.e, the mathematical cover (MC), the physical cover (PC) and the manifold element (ME). MCs are user-defined overlapping patches. One significant advantage is that arbitrary geometric shapes (e.g. polyhedron in 3-D) can be the basic MC of the mathematical domain. Each different shaped MC has its own mathematical description inside.

ABSTRACT: In this study, the solid rock is represented by an assembly of particles joined together by breakable bonds using PFC3D. The contact bonding model supported in PFC3D can transmit a force which acts only at the contact points and it consists of shear and normal strength components. No slip is possible when the contact bond remains intact, but it offers no resistance to rolling. While determining the micro parameters of the model, the effect of stiffness of the particles on Young's modulus and Poisson's ratio are studied. The effect of confining pressure is studied by considering the values corresponding to typical overburden pressures. Along with the stress strain plots at various confining pressures, the extracted micromechanical data are also presented to analyze the strain softening behaviour with special emphasis on the breakage of the bonds. The variation in the strength and mechanical behaviour of the rock masses with respect to the bond strength is thoroughly studied by conducting axisymmetric triaxial tests. The effect of varying bond strengths on the uniaxial compressive strength is also studied at various confining pressures. It can be clearly seen that as the bond strength increases, the compressive strength also increases. Further as the confining pressure increases, there is an increase in compressive strength for the same contact bond strength. Similarly the variation of the values of cohesion and angle of internal friction are also studied for various values of bond strengths. The parametric studies indicate that as the bond strength increases, there is a linear increase in the value of cohesion at various confining pressures, but the angle of internal friction remains almost the same with minor fluctuations. INTRODUCTION Majority of the earth"s crust is covered by sedimentary rocks which are formed by the sedimentation of materials. In due course of time, they will be deposited in layers forming rocks and their strength will depend on various factors including the matrix which bind these particles together. Usually the damage of rock masses occur when the entire bond breaks and the material changes from solid to granular material. Sandstone is a type of sedimentary rock which is comprised of rock fragments or minerals held together by natural cementing materials. Depending upon the strength of the cementation, the behaviour of the rocks also changes. Numerical simulations adopting discrete element method generally represents rock mass as an assembly of particles joined together by breakable bonds. The Bonded Particle Model (BPM) suggested by Potyondy & Cundall [1] states that particles can be bonded together at contacts forming a cemented granular material and the macro-scale mechanical behaviour of this cemented material can be related to the rock mass behaviour. But the suitable selection of the particle-contact parameters for the modeling is very challenging. Unless suitable particle-contact parameters are used, the macro-scale response of the modeled block will not be reliable. Experimental studies have showed that the behavior of intact rock in compression is complex, resulting in a nonlinear failure envelope with high frictional resistance [2].

ABSTRACT: This paper discusses the results of a numerical study which examines the influence of the choice of joint constitutive model on the stability of jointed masses. The modeling methods and procedures presented here demonstrate a new approach to the simulation of a rock mass and the stability analysis of excavations. With this new approach, study of the stability of excavations can be carried out in such a way that the development and movement of the rock mass and failure process can be visualized. With the understanding of where the failure will start, how it develops and what the final failure can be studied and appropriate measures can be taken. In order to further study the damage mechanism of jointed and fractured rock mass, Burgers Model of joint rock model has been built by discrete element program (Particle Flow Code) to carry out numerical simulation. It adopts particle contact constitutive relationship, changes the properties of particle unit in calculation model and proposes macroscopic properties of samples in different parameters of particle unit to simulate damage process of granite sample with hole. The comparison of stress-strain curves obtained by the two-dimensional code of the Particle Flow Code (PFC) and by the test results has been made to further verify Burgers Model feasibility in the field of rock damage, and has certain application value to perfect rock constitutive relationship. At the same time, Particle contact constitutive relationship has been adopted to build the model of joint rock sample to carry out numerical simulation. It can describe non-linear behavior and localization with accuracy that cannot be matched by typical finite element programs. The consistency of stress-strain curves obtained by PFC2D and by the test results shows that PFC2D is a practical tool to produce AE events of jointed rock mass, and the Burgers Model is feasible in the field of rock failure, which provides an analysis of the microcracking activity inside the rock volume to predict jointed rock fracture patterns. The modeling of rock opening stability and failure reveals that the failure scale and failure mode of a tunnel of heavily joint rock are dominated by the joint quantity and quality in addition to the intact rock properties. The examples demonstrate the representational capability of the PFC code, this assessment will have very general application in jointed rock mass. 1 Introduction With the development of national economic and defense construction, people gradually recognize that the uses of underground space play an important role in the improvement of ground environment, such as subway, tunnels and underground caverns. Take the collapse of Hangzhou Metro in China (Zhou, et al 2009), for example, the safety of the excavation disturbed or damaged zone (EDZ) around underground rock attracts more attentions. The study of damage formation in jointed or bulk rock under stress has been a subject of widespread interest, the results of which have led to a number of comprehensive texts (Chang, et al, 2004;Eberhardt, 1998,1999; Stephen, et al 1998; Golshani, et al 2007).