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Keywords: finite element method

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Proceedings Papers

Paper presented at the ISRM International Symposium - EUROCK 2016, August 29–31, 2016

Paper Number: ISRM-EUROCK-2016-101

... displacement increases if the dynamic fric- tion angle is considered during slip. Therefore, the computed sliding displacement is closed to the mea- sured displacement if the dynamic friction angle is considered. 3.2 Simulation by

**finite****element****method**The shaking table test result is simulated by a**finite**...
Abstract

ABSTRACT: With increase of design seismic intensity, analytical methods and modeling for evaluating deformation and failure of rock slopes during earthquakes appropriately are needed. In this study, shaking table model tests of rock slopes with a sliding plane inclined at angle of 15 degrees were conducted and the dynamic response of sliding block was observed using laser displacement sensors and accelerometers. To simulate the block interaction such as sliding or separation, the numerical simulations are conducted by the dynamic limit equilibrium method and the finite element model, the applicability of analytical methods is verified. 1 INTRODUCTION Dynamic response analysis is conducted to evaluate the stability of slopes under seismic conditions at important structures such as main traffic routes, nuclear power plants etc. Stability analyses are commonly carried out through numerical analysis assuming that rock mass is elastic and homogeneous on the basis of the results from PS logging and/or the seismic coefficient method. However, the behavior of rock masses is greatly influenced by the geometrical distribution of discontinuities within the rock mass. It's necessary to figure out dynamic behavior and fracture morphology of discontinuous rock slope. With increase of design seismic intensity, analytical methods and modeling for evaluating deformation and collapse of rock slope under earthquake appropriately are expected. In this study, shaking table tests on rock slopes with a sliding plane inclined at an angle of 15 degrees were conducted and the dynamic response of sliding block was measured using laser displacement sensors and accelerometers. To simulate the block interaction such as sliding or separation, the numerical simulations are conducted by the dynamic limit equilibrium method and the finite element model, the applicability of analytical methods is verified. 2 MODEL EXPERIMENTS ON SEISMIC STABILITY OF DISCONTINUOUS ROCK SLOPE 2.1 Outline of experiment In order to understand the dynamic response and stability of rock slopes, several shaking table tests on rock slopes with a potentially unstable block on a dipping plane shown in Figure 1 were carried out. The assumed rock slope with a height of 50 m and having a potential plane at an angle of 5 degrees is scaled down to a model with a scale of 1/500. The model material is sandy Ryukyu limestone and locally is knows as Awa-ishi. The input-wave, the acceleration of upper block acceleration and relative displacement of the potentially unstable blocks were measured using accelerometers and laser displacement transducers as shown in Figure 1. Table 1 gives the specifications of the shaking table and monitoring devices.

Proceedings Papers

Paper presented at the ISRM International Symposium - EUROCK 2016, August 29–31, 2016

Paper Number: ISRM-EUROCK-2016-109

... failure mechanisms is essential to ensure stability. In this paper, stability analyses of a 75-year-old masonry-lined Turkish State Railway Tunnel and the stratified rock slope above the tunnel following the road cut excavation are presented.

**Finite****Element****Method**is used to evaluate the stability of this...
Abstract

ABSTRACT: In mountainous areas natural slopes are adapted for construction of roads and other infrastructure, and slope instability is the major problem arising from artificial slopes. Investigating the endangered areas and potential slope failure mechanisms is essential to ensure stability. In this paper, stability analyses of a 75-year-old masonry-lined Turkish State Railway Tunnel and the stratified rock slope above the tunnel following the road cut excavation are presented. Finite Element Method is used to evaluate the stability of this structurally coupled system. The tunnel is located next to Zonguldak-Amasra-Kurucasile highway which is under construction at present. 1 INTRODUCTION On the transition section of Zonguldak-Amasra-Kurucasile highway route between Km 26 + 590 and Km 26 + 700, a road cut will be excavated by bench blasting to obtain a road cut slope consisting of different number of benches at various cross sections. Slope excavation will be made on a rock mass that is above No 50 Turkish State Railway Tunnel. This shallow railway tunnel has been in service for more than 75 years, and it is stable. Figure 1 shows tunnel portal, nearest residential area and natural terrain around the tunnel. Figure 2 shows masonry lining and inner view of the railway tunnel. When the road-cut slope is excavated, some of the rockmass will be removed and a stress relief is likely to occur in the rock mass surrounding the tunnel. In a typical section accepted as critical, some of the benches are planned to be as close as around 66 m horizontally to the tunnel sidewall. Overburden amount is expected to be around 55 m above the upper boundary of the railway tunnel at that critical section. Another critical factor is the distance of tunnel and planned slope cut section to the nearest apartment building at Denizkent Condominium Site. The distance between the apartments and intersection point of a line drawn from the tunnel roof to the surface is around 88 m horizontally (Fig. 3).

Proceedings Papers

Paper presented at the ISRM International Symposium - EUROCK 2016, August 29–31, 2016

Paper Number: ISRM-EUROCK-2016-083

... utilization. In the presented model, the first level of the mining tunnel is designed by

**finite****element****method**in the horizon of 2300 m and the last level in the horizon of 2240 m. Hence, the instability radius on surface facilities will be great. According to analysis done by**finite****element****method**, the...
Abstract

ABSTRACT: Excavation for underground spaces (especially copper mines), requires accurate identification of the ground condition. One of the problems that can arise due to the extraction of underground resources is land subsidence that can affect mining activities both technically and economically. Thus, controlling this phenomena plays a key role in mineral extraction process. The first step is to calculate and forecast maximum subsidence in different areas, also to estimate subsidence angle. Chahargonbad copper mine is among the fewest mines in Iran which intended to extract by sub-level caving method. This method is designed by caving several excavating tunnels for mining in different levels. Excavating the hanging wall of the mineral is extremely important because a systematic extraction method can guarantee the safety of excavating faces during the project's construction and utilization. In the presented model, the first level of the mining tunnel is designed by finite element method in the horizon of 2300 m and the last level in the horizon of 2240 m. Hence, the instability radius on surface facilities will be great. According to analysis done by finite element method, the failure angle of the hanging wall is estimated by 45°. Accordingly, all the facilities be constructed on the hanging wall of the Chahargonbad mine and located in subsidence zone, are in serious danger. 1 INTRODUCTION Sublevel caving method is a large scale mining which is based on the use of ore blasting gravity flow and destroyed waste ore (Janelid & Kvapil 1966). Sublevel caving method in many cases can be used as a method for the second phase of extraction especially when the value of the ore is quite high. The caved waste from the overlying rock mass fills the void created by ore extraction. The original application of the SLC mining method was in soft ground at the Minnesota and Michigan iron ore mines in the early 1900s (Hustrulid 2000). The method functions on the principle that ore is fragmented by blasting, while the overlying host rock fractures and caves under the action of mine-induced stresses and gravity (Bull & Page 2000). The method was later adapted to stronger ore bodies (requiring blasting) enclosed by weaker overlying and wall rock masses. In the past 40 years SLC geometries have increased significantly, resulting in increases of scale and extent of industrial application, and decreases in production costs (Brady & Brown 2013). Form, size, and the path of progressive failure and caving depend on many factors. The most important factors among them are consist of: The mineral slope angle β 0 , the width of the mineral ore W, lower cartridge H 1 depth which is used later in mining, H 2 height of the caved waste rock zone where the arch forces resist against breakage, the cutting resistance of rock mass which influences advancing failure and is determined by the efficient cohesion and the waste rock mass density γ.

Proceedings Papers

Paper presented at the ISRM Regional Symposium - EUROCK 2015, October 7–10, 2015

Paper Number: ISRM-EUROCK-2015-124

... material

**finite****element****method**flow in porous media fracture density effective transport property permeability CCM model aspect ratio matrix percolation threshold mechanics ABSTRACT: In the paper, two modeling strategies for the computation of the effective permeability of heterogeneous...
Abstract

Abstract In the paper, two modeling strategies for the computation of the effective permeability of heterogeneous, fractured rocks utilizing homogenization over a representative elementary volume (REV) are proposed and compared. One method is based on a new continuum micromechanics model. Here, the REV represents distributed fractures idealized as penny shaped inclusions in a porous matrix. The effective properties computed by this model are anisotropic and depend on the intrinsic properties of the porous matrix and the topology and density of the fractures. We propose a novel Cascade Continuum Micromechanics model (CCM), which is able to predict a fracture percolation threshold for a particular fracture density as a function of the topology of the fractures. The second modeling strategy is based on an Extended/Generalized Finite Element model (XFEM-GFEM) recently developed for numerical simulations of hydraulic fracturing in deep geothermal reservoirs. The predictions for the effective permeability from both models are compared for a REV containing distributed fractures with different aspect ratios and crack densities. 1 Introduction The effective transport property of heterogeneous rocks with diffusively distributed fractures at various scales (from microcracks in the sub-mm to macroscopic fractures in the m range) is strongly influenced by their distribution, orientation and their interactions with the porous matrix material. Reliable estimates for effective transport properties of fractured rocks are relevant in various projects in subsurface engineering, such as the construction of tunneling or caverns, the exploitation of oil and gas and geothermal energy reservoirs or the installation of underground storage systems (see, e.g. Tiab & Donaldson (2012), Economides & Nolte (2000) and references therein). In this paper, we propose two methods to determine the effective permeability of heterogeneous rocks. The first strategy is based on continuum micromechanics. Based on a representative elementary volume element (REV), representing distributed fractures idealized as penny shaped inclusions in a porous matrix, the effective anisotropic permeability is predicted. To investigate the percolation probability of the fracture network, we use a novel Cascade Continuum Micromechanics model (CCM) (Timothy & Meschke 2013). The model predicts a fracture percolation threshold for a particular fracture density as a function of the topology of the fractures. This provides initial estimates for the connectivity characteristics of the fracture system and allows to characterize the interrelations between diffusivity, permeability and the anisotropic stiffness. The second strategy uses computational homogenization based on a discrete representation of distributed cracks using a novel Extended/Generalized Finite Element model (Meschke & Leonhart 2015) recently proposed for numerical simulations of hydraulic fracturing in deep geothermal reservoirs. Both modeling strategies are investigated and compared by means of different configurations of fractured rocks.

Proceedings Papers

Paper presented at the ISRM Regional Symposium - EUROCK 2015, October 7–10, 2015

Paper Number: ISRM-EUROCK-2015-193

... Computation excavation deformation vector

**finite****element****method**rock bolt cement grout Aydan element ABSTRACT: Rock bolts as construction elements are often used in underground civil engineering projects. We used Aydan finite elements for numerical description of rock bolt reinforcement and...
Abstract

Abstract Rock bolts as construction elements are often used in underground civil engineering projects. We used Aydan finite elements for numerical description of rock bolt reinforcement and isoparametric bilinear finite elements for description of rock massif. We derived corresponding stiffness matrices and right hand sides and developed a finite element code for the calculation of rock deformations and stresses. The code was tested on several numerical examples. We computed in detail deformations and stresses in a round tunnel, first without any rock bolts and then with rock bolts placed in the tunnel arch. We compared deformations and stresses obtained by our calculations to approximate analytical solution. 1 Introduction Rock bolts as reinforcing construction elements are often used in underground civil engineering projects. Today it is common to use numerical modelling for designing and verification of various types of constructions and rock bolts are no exception. Several special rock bolt elements were created for this purpose. The most widely used elements was presented in the work of Ömer Aydan (1988). The so-called Aydan element is represented by four nodes in its simplest 2D form. Two nodes create a rod sub-element, which is a simple model of a steel bar. Remaining nodes represent the connection of this bar with surrounding rock massif by cement grout. This paper deals with composition of the stiffness matrix of Aydan element and its application to a simple two-dimensional numerical model of a circular excavation reinforced by rock bolts that are fastened by cement grout along their full length.

Proceedings Papers

Paper presented at the ISRM Regional Symposium - EUROCK 2014, May 27–29, 2014

Paper Number: ISRM-EUROCK-2014-170

... & Gas Rock mechanics elastic displacement

**finite****element****method**construction displacement tunnel construction total displacement tunnel deformation calculation vault excavation Zhoujiazui tunnel finite element model mechanics Rock Engineering and Rock Mechanics: Structures in and on...
Abstract

Abstract By summing up the field monitoring during tunnel construction of some highways in Henan Province of China, the monitoring data combine with finite element model are employed to analyze the predisplacement of the surrounding rock during the tunneling. The formula for calculating the pre-displacement of the surrounding rock is obtained from the elastic mechanics and integral creep model. Numerical results indicate that the pre-displacement appear at 1~1.5D away from the tunnel face in the beginning, and turn to a stable state at 2~3D away from the tunnel face; the pre-displacement of the surrounding rock accounting for 30% of the total displacement. Thereby, sufficient attention must be paid to the pre-displacement of the surrounding rock in design and construction of the tunnel. 1. General Instructions Along with the development of national economy and the pace of highway construction, the quantities of the highway tunnels are increasing. The stability and deformation of tunnel become prominent issues in engineering construction. Field monitoring is an important part of NATM principles, however, the monitoring data of the surrounding rock of the tunnel are gotten after the tunnel face cross. [1] In fact, the deformation is generate long away before tunnel face, and these pre-deformation have an important impact on the stability of the tunnel construction. Non-linear numerical methods have become a key tool in modeling geotechnical or transportation engineering for the analysis of stresses and deformations in the structures such as tunnel, highway, slopes and foundations. Based on observations, pre-displacement and total displacement behavior models can be constructed. The models can be either analytical or numerical. The numerical model leads to correct answers within the framework of axioms underlying the mathematics. Vlachopoulos and Diederichs use a series of numerical analyses to develop a newseries of functions defining robust longitudinal displacement profiles, as a function of maximum normalized plastic radius. A reasonable numerical model and 3D finite element model for the tunnel should be used to calculate the pre-displacement and total displacement of the tunnel, which results in non-linear behavior. In this paper, a new approach to modeling pre-displacement in tunnel is reported.

Proceedings Papers

Paper presented at the ISRM Regional Symposium - EUROCK 2014, May 27–29, 2014

Paper Number: ISRM-EUROCK-2014-234

... preferential flow channels within the geological formation. The numerical approach proposed in this paper is a fully coupled hydro-mechanical model in saturated conditions involving single-phase flow both in fractures and the porous matrix. The extended

**finite****element****method**(XFEM) is employed to model...
Abstract

Abstract In the present work, we address the issue of groundwater flow in fractured porous media submitted to local or regional stress-state variations. Due to the increasing pore pressure fluid, the size and aperture distribution of the fractures are modified resulting in the formation of preferential flow channels within the geological formation. The numerical approach proposed in this paper is a fully coupled hydro-mechanical model in saturated conditions involving single-phase flow both in fractures and the porous matrix. The extended finite element method (XFEM) is employed to model fracture dynamic and fluid flow assuming fracture cutting through the elements. 1. General Introduction Faults or fractures play a key role as preferential pathways for migration of pollutants or circulation of mineralizing fluids in geological subsurface reservoirs. In case of local stress variations, fracture orientation and permeability may change and new ones may occur. Due to the relevance of these channels for the assessment of flow and solute transport in geological formations, modeling their behavior with time is highly suitable for environmental, geotechnical, petroleum and mining applications. Here a new numerical modeling approach, hereafter referred to as the XFEM-HM (Extended Finite Element Method for Hydro Mechanical processes) method, is proposed to model the complex processes involved and provide an accurate dynamic description of the geological reservoir that evolves with time. The formulation of the XFEM-HM model is based on the governing balance equations of coupled hydromechanical processes for fully saturated porous media. A zero-thickness finite element is used to model the fracture (Cornec et al., 2003; Carrier et al., 2012). The XFEM-HM model takes into account (Adachi et al., 2008): preferential fluid flow inside and through the fracture depending on its aperture; fluid exchanges between rock formation and fracture; fracture dynamics (initiation, opening or closure); porous medium deformation due to the fluid pressure inside the fracture. The eXtended Finite Element Method (XFEM) (Belytschko et al., 1999; Moës et al., 1999) is used for spatial discretization of the above problem close to the fracture within the porous medium. The XFEM method, based on the partition of unity (Melenk et al., 1996) overcomes the mesh dependences of the fracture representation by enriching the classical finite element approximation of the displacement and pore pressure fields with additional degrees of freedom (dof). Especially, the geometry does not need to be updated with each time step and the edge-elements do not have to match the fracture walls. Discontinuity of those fields is directly taken into account in the constitutive equations.

Proceedings Papers

Paper presented at the ISRM Regional Symposium - EUROCK 2014, May 27–29, 2014

Paper Number: ISRM-EUROCK-2014-019

... difficulties, it's better to use straight notch core specimen under impact. Explanation of dynamic crack propagation by numeric analyses is limited. Among numeric methods, extended

**finite****element****method**is an effective way to study dynamic fracturing. This study used the X-FEM software (ABAQUS) to create a 3D...
Abstract

Abstract Dynamic fracture plays a vital role in geotechnical problems. Limited attempts have been made to measure dynamic parameters of straight notch cubic sample under impact. This is due to some difficulties in preparation of samples and high accuracy needed for its testing. To solve these difficulties, it's better to use straight notch core specimen under impact. Explanation of dynamic crack propagation by numeric analyses is limited. Among numeric methods, extended finite element method is an effective way to study dynamic fracturing. This study used the X-FEM software (ABAQUS) to create a 3D model of dynamic crack propagation of two samples; straight notch cubic and straight notch core specimen under impact load; then results obtained from ABAQUS are compared. Present study showed that Dynamic toughness for core specimen is lower than cubic specimen, Dynamic stress intensity factor for core specimen increases linearly but for cubic specimen is oscillating before fracture initiation. 1. Introduction Fracture mechanic has been suggested as possible tool for solving a variety of rock engineering problems, such as rock cutting, hydro fracturing, explosive fracturing and, rock stability and, based on the extension of Griffith theory and Irvin's modification (Chen, Pan & Amadei 1998). Concept of stress intensity factor K (SIF) has been introduced by Irvin (Mohammadi 2008). Fracturing may take place under static or dynamic condition. Earlier measurements of rock fracture toughness followed the ASTM-E399 standard method. Because most rock are brittle, fatigue pre-cracking required in ASTM standard has been found to be very difficult to produce (Chen, Pan & Amadei 1998). To solve rock fracture problems, The International Society for Rock Mechanics (ISRM) recommended three suggested methods by core based specimens; for determining static fracture parameters (Iqbal & Mohanty 2007). Dynamic fracture plays a vital role in geotechnical applications frequently encountered in various engineering problems; including blasting, protective design, rock burst, projectile penetration and seismic events (Zho, Xia & Li et al. 2012, Chen, Xia & Dai et al. 2009, Dai, Xia & Zeng et al. 2011). These processes are governed by rock dynamic fracture parameters, such as fracture initiation toughness, fracture energy and fracture velocity.

Proceedings Papers

Paper presented at the ISRM International Symposium - EUROCK 2013, October 23–26, 2013

Paper Number: ISRM-EUROCK-2013-102

... slope is the very often solved problem in the geotechnical practice. For the solution of such problem there can be used many computational methods based on limit equilibrium methods (LEQM) or numerical methods (for example

**finite****element****method**(FEM)), which more or less reflect the various factors...
Abstract

Abstract The paper specifies the fundamentals of stochastic simulation Latin Hypercube Sampling Method (LHS) and presents examples of application of this method for the solution of the stress-strain and stability state of the slope. The stochastic simulation methods enable to involve into the calculation the stochastic character of the input parameters. In the first example the stochastic character of shear strength characteristics of soils is considered. The second example takes into account the stochastic character of the basic parameters of dynamic load (frequency and amplitude of the dynamic load) for the solution of dynamic response (stability factor and displacements) of the slope subjected to surface blasting seismic effect. On the basis of the stochastic analysis we can determine the probability of the model response. Introduction The stress-strain and stability analysis of the slope is the very often solved problem in the geotechnical practice. For the solution of such problem there can be used many computational methods based on limit equilibrium methods (LEQM) or numerical methods (for example finite element method (FEM)), which more or less reflect the various factors determining the behavior of slope. Predicative power of the modeling results is always fundamentally determined by the reliability of the input data. To increase the predicative power of model results (model response) can be used stochastic simulation methods, which are based on the assumption, that the input values of the model are considered as stochastic variables governed by certain laws of probability. Based on the accepted type of the probability distribution of the input parameters of the model and the type of simulation methods the specific values of input parameters are generated. To determine the appropriate random model responses the series of repeated parametric calculations with the generated input values are carried out. Based on the statistical evaluation of the model responses (stochastic variables) the determination of probability range of response results can be obtained.

Proceedings Papers

Paper presented at the ISRM International Symposium - EUROCK 2010, June 15–18, 2010

Paper Number: ISRM-EUROCK-2010-133

... ABSTRACT: The case of controlled bench failure on the open-pit is considered. An approach to rock slope stability analysis using

**finite****element****method**and modeling on equivalent materials is offered. Critical deformation parameters for rock mass and the form of sliding surface are determined...
Abstract

ABSTRACT: The case of controlled bench failure on the open-pit is considered. An approach to rock slope stability analysis using finite element method and modeling on equivalent materials is offered. Critical deformation parameters for rock mass and the form of sliding surface are determined. The sliding surface for a rock slope is interpreted as a geometrical locus in which the combination of normal and shearing stresses satisfy the phenomenological failure criterion. 1 INTRODUCTION The field of slope stability encompasses the analysis of static and dynamic stability of earth slopes, rockfill dams, excavated slopes in soil and soft rock. Under the gravity action the rock slide occurs and plane of sliding forms. The probability of this happening can be calculated in advance using method of slices, Bishop's method, Lorimer's method, Solov'yev method and others. But despite of a variety of methods the problem of sliding surface localization remains not solved for any given situation. Many landslides have only been analyzed after the fact. At an estimation of pit walls, benches and dams stability the big attention is paid to determination of their boundary parameters which cause sliding. For example, in the case of controlled failure technology application on open-pit benches the slope is undermined on the certain distance ( a1 ) from a toe. This parameter is called failure spacing. To provoke the sliding process a cutoff slit in the bench roof on the certain distance ( a2 ) from a crest is fulfilled (Golub, V.V. & Polischuk, S.Z. 2000). Boundary parameters a1 and a2 depend on rock properties and structure, groundwater mode, geometry of the investigated part of rock mass. 2 OBJECT OF THE RESEARCH The Marganetskyi ore-dressing and processing plant, the worldwide leading enterprise on manganese mining located at the Dnepropetrovsk region (Ukraine), has been chosen as an object of research.

Proceedings Papers

Paper presented at the ISRM International Symposium - EUROCK 2005, May 18–20, 2005

Paper Number: ISRM-EUROCK-2005-006

... has a wide rage of values. The difference in mechanical properties sets a limit of accuracy of analysis. The

**finite****element****method**was applied for forecasting the stress state of rock mass near the mined out spaces during development of mining works. FINITE ELEMENT MODEL The results of...
Abstract

ABSTRACT Numerical simulation is performed for the changes of stress field at consecutive extraction of a diamond ore deposit, The features of stress distribution around openings are examined. Failure zones of rock mass are determined With using of Coulomb-Mohr criterion. The results of calculations were compared with the experimental data of observations in situ. Geomechanical recommendations are proposed for placing of technological workings. INTRODUCTIO Open-pit mining method is used for excavation of ore at Siberian diamond deposits. The maximum depths of open-pits are reached. Last years the deep mining IS applied, The features of stress distribution around openings are examined at experimental industrial block of the "International" kimberlite pipe, which is mined at the depth onOO-800 m. Cut-and-fill mining 111 slices about3.5–5 m in height and about 5 m in width is applied in various variants of room and pillar mining with a combine. As a result some cylindrical mined out spaces with a diameter 60 m and a height 10- 70 m were filled with the solidifying fillings. Under these conditions a number of geomechanical problems arises. The main of them is the possible rock fall into workings. The experience of application of geomechanical investigations in practice is discussed. Numerical simulation is performed for the changes of stresses in ore mass and in country rock at consecutive extraction of the diamond deposit. Character of failure in rock mass is researched. Strength of rock has a wide rage of values. The difference in mechanical properties sets a limit of accuracy of analysis. The finite element method was applied for forecasting the stress state of rock mass near the mined out spaces during development of mining works. FINITE ELEMENT MODEL The results of experimental investigations showed the Initial principal horizontal stresses are approximately equal to 0.7–0.8 of vertical pressure been due to a weight of overlying rock thickness at this depth (Baryshnikov et al. 2003). Therefore the numerical solutions of axisymmetrical problems were used. The initial stress state of rock mass is following (Equation in full paper) where z is a distance from the surface of the earth, γ is specific gravity of rock (27 KN/m 3 ), λ - ratio of initial horizontal stress to vertical one at the depth H (800 m).The problems were solved in terms additional displacements (Boltengagen 1999) under the following boundary conditions on the external boundary (the surface of the cylinder with a diameter 4 km and a height 2 km): the upper horizontal boundary is free from stresses, additional displacements are equal to zero on the lower horizontal boundary, additional horizontal displacements and tangential stresses are equal to zero on the vertical boundary. Elastic modulus of rock was taken equal to 10 GPa, Poisson's ratio of rock γ is equal to 0.25. The height of mined-out spaces (cylinders with the diameters 60 m) are quoted on the corresponding illustrations of problems. Elastic modulus of artificial fillings is one-tenth or one-hundredth of elastic modulus of rock.

Proceedings Papers

Paper presented at the ISRM International Symposium - EUROCK 2005, May 18–20, 2005

Paper Number: ISRM-EUROCK-2005-061

... the system V" is analogous to the transport in the porous media environment. . There is an important point of the choice ofnumer- real method. We consider the

**finite****element****method**, which is suited for complex unstructured meshes. Mixed methods are known to approximate accurately the velocity field...
Abstract

ABSTRACT Modelling of flow in fractured environment is very important problem for applied hydrogeology (for example for simulations of the neighbourhood of the radioactive waste repositories). We present the transport model composed of two parts. First, the fracture fluid flow model is based on the description by the Darcy's law and the mass balance equation with Dirichlet boundary conditions. The second part of the transport model Includes the convection term using the velocity computed in the fluid flow model, diffusion-dispersion term With dual porosity (representing micro fractures), and chemical term describing sorption, radioactive decay, and chemical interactions. INTRODUCTION The weakest link in the nuclear energy production is the safe storage of highly radioactive spent fuel. One of the proposed repositories of dangerous nuclear waste are underground granitoid massifs. However, these massifs are always disrupted by a system of geological faults, fractures, therefore the majority of the fracture flow occurs. In general, there are three main possibilities of modelling the fracture flow. In large-scale without need to now detail flow and transport behaviour in any site subarea, it is possible to use equivalent porous medium models. More complex are the double porosity models, with two distinct interacting subsystems: fractures and porous blocks. As a third and most accurate possibility, we can approximate the original 3-D fractures y planar elliptic or polygonal disks whose frequency, Size, assigned aperture, and orientation are statistically derived from field measurements (Fig. 2, 3), and then consider the 2-D Darcy flow through such a network. However, due to high computer requirements, it is possible to solve just local problems by using these stochastic discrete fracture network models. We refer for instance to Bear & Bachmati (1991) or Wanfang, Z., Wheater & Johnston (1997) for more details. (Figure in full paper) In this text, a stochastic discrete fracture network model is presented. We generate the fracture network based on statistical data obtained from geological measurements. The original 3-D fractures are approximated by planar circle disks (Fig. 1), and each disk is subsequently discretized onto a triangular mesh respecting the intersections with its neighbours. In order to simplify the geometrical situation in fracture planes, the computed intersections can be slightly moved and stretched. One then obtains a better mesh, however for the price of vanishing of real 3-D correspondence; the connectivity information is preserved. Finally, an aperture distribution function assigns an imaginary aperture to each triangle element. (Figure in full paper) Our contemporary simulation system makes it possible to solve real-world problems of contaminant transport in fractured-rock environment. But there is relatively strong limitation of the spatial dimensions of the computational domain. The problem is solvable only on the domains of volume in order of hundreds of cubic meters, which means only a close neighbourhood of the source of the contaminant. This limitation is caused by used model of fluid flow in the fractured-rock environment, which calculates the flow field on all fractures in the domain, even on the very small ones.

Proceedings Papers

Paper presented at the ISRM International Symposium - EUROCK 2005, May 18–20, 2005

Paper Number: ISRM-EUROCK-2005-117

... show that the method is effective and accurate in 3D problems. INSTRUCTION Thus far

**finite****element****method**has reached a high degree of effectiveness in structure failure analysis. However some problems appeared in its application, among which the following are the most remarkable Ones. (1) Pre...
Abstract

ABSTRACT The study and application of Element-free Galerkin Method (EFGM) to three-dimensional problems is presented. Based on moving least squares method (MLSM), EFGM formulates the discrete model by using only a set of nodes, so the pre-processing of the method is simplified and the approximating function is Continuous with higher-order differentials over the entire domain. The relevant theories of EFGM are introduced and the derivation of discrete equations using variational principle is presented. The visibility criterion is used to deal with the effect of discontinuities on the influence domain of a gauss point. Contribution to the system of equilibrium equations of the reciprocity between two surfaces of discontinuities is considered. To investigate the accuracy of the proposed method, a cantilever beam and Laxiwa arch dam-foundation system are analyzed In detail. The results show that the method is effective and accurate in 3D problems. INSTRUCTION Thus far finite element method has reached a high degree of effectiveness in structure failure analysis. However some problems appeared in its application, among which the following are the most remarkable Ones. (1) Pre-processing of finite element methods is always a far more time-consuming and hard task, especially in three-dimensional problems, even with powerful mesh generators. (2) Finite element method always seem to exhibit volumetric locking when the Poisson ratio is close to 0.5. (3) Despite the continuity of results of displacement, they always appear discontinuous and a post-processing smoothing work of those variables is necessary. (4) Mesh refinement of finite element method in problems of crack growth and large deformation is accompanied by a heavy computational burden. As these problems are associated with the fundamental characters of finite element methods, meshless methods have been developed to deal with them. Meshless methods formulate the discrete model by using only a set of nodes, with a suitable weight function on compact support and a proper integral approach, and the equilibrium equations can be congregated to solve the problem. On eliminating parts of the mesh structure used in finite element methods, meshless methods can simplify the pre-processing of the numerical simulation and it becomes possible to solve large classe of problems which are very awkward with mesh-based methods. Nayroles, et al (1992) were evidently the first to promote mesh less method in 1992. Moving least-square approximations were used in a Galerkin method called the diffuse element method (DEM). Later, lots of mesh less methods have been developed, such as the element-free Galerkin method (EFGM), meshless local Petrov-Galerkin method (MLPGM), wavelet- Galerkin method (WGM), reproducing kernel particle method (RKPM), partition of unity method (PUM), natural element method (NEM), manifold method (MM) and so on. Among all this methods, the EFGM, which is refined and modified from the diffuse element method by Belytschko et al (1994), is probably the most influential one. The EFGM constructs the trial and test functions for variational principle (weak form) using moving leasts-quare interpolants and solves the partial differential equation using the Galerkin method.

Proceedings Papers

Paper presented at the ISRM International Symposium - EUROCK 2002, November 25–27, 2002

Paper Number: ISRM-EUROCK-2002-070

...STABILITY ANALYSIS FOR THE OXIDIZED ORE STOPE OF SONGSHUJIAO TIN MINE WITH

**FINITE****ELEMENT****METHOD**YD, XIANBIN Kunming University of Science and Technology, Kunming, P.R.CHINA, xianbin@ist.utl.pt DINIS DA GAMA, CARLOS I.S.T., Lisboa, PORTUGAL, dgama@ist.utl.pt ABSTRACT Stability analyses were...
Abstract

Stability analyses were conducted with the finite element method to study the stability of the oxidized ore stope of Songshujiao Tin Mine, China. The most important feature of the deposit is that the oxidized ore is weaker than the country rocks because it behaves like a soil. Results of the numerical simulation have shown that ore excavation does not influence the stability of the country rocks. The main threat to the working safety during ore extraction from the stopes is the risk of falling blocks created by discontinuities. When joints are well developed In the roof, long bolts are thus needed to reinforce the roof. 1. INTRODUCTION Songshujiao Tin Mine is located in the mountainous region of the Yunnan province, southwest of China. In this mine, the depth of the present excavating stopes with respect to the surface is around 700 meters, yet the main development openings of the Mine are drifts and some of the horizontal openings communicate directly to the surface. Although these are richer than the sulphide deposits that were excavated in the past, the dimensions of the oxidized ore bodies are usually much smaller. The deposits were formed by Weathering action in the cavities and both roof and floor of the stopes are formed by marble and/or dolomitic limestone. The oxidized ore is weathered as a soil and its strength is extremely low, although there are some compact blocks of iron nodules existing in the ore. In fact, the compressive strength of the ore is below 1MPa and it is approximately the same as that of the cover soil near the surface. Country rocks have moderate strength and are not very stable. Due to weathering action, the direct roof is less stable than the remaining part of the roof. However, no evident boundary exists between the direct roof and the immediate roof, which makes excavation conditions very difficult. The mining system adopted in the oxidized ore is by sublevel stoping methods with previous bolt supports in the roof. In effect, the first step of excavation is to cut a slot with an height of about 2 meters at the top of the ore, to remove the unstable direct roof. Then the roof is reinforced with metal bolts of 1.8m long and after that excavation of the ore is possible. Inside the ore body, stope size is 40m wide and about 8m high, which is the natural height of the ore body. The stopes are divided into rooms along the strike of the deposit and the rooms are perpendicular to the strike. The width of a room, or the size along the strike is 10m, and so the stope is divided into 4 rooms. The length of the rooms (or the stope size along the dip) is about 50 to 60m. When the length of an ore body along the dip is greater than 60m, it is divided into sections at the inclination direction and different sections would be excavated separately.

Proceedings Papers

Paper presented at the ISRM International Symposium - EUROCK 96, September 2–5, 1996

Paper Number: ISRM-EUROCK-1996-161

... possible dilatancy inside the rock mass, which could affect its tightness. Upstream Oil & Gas surface subsidence procedure France subsidence single cavity cavity Artificial Intelligence numerical method application evolution

**finite****element****method**Fluid Dynamics boundary Tersanne...
Abstract

ABSTRACT: The behavior of Tersanne natural gas underground storage field in bedded rock salt formations is described in an analytical way and compared to available in situ measures. Evolution of surface subsidence and cavity volume loss is of main concern. Although the problem is three dimensional in nature, an axisymmetric model for a single cavity is used together with a superposition method previously validated. There is a reasonable agreement between in situ data and numerical values. RESUME: Le comportement du champ de cavites de Tersanne pour stockage de gaz naturel en sel gemme est decrit d'une façon analytique et compare à des mesures in situ disponibles. L'evolution de la subsidence en surface et la diminution de volume des cavites sont suivis en particulier. Bien que Ie problème soit tridimensionnel on utilise un modèle axisymetrique pour une cavite isolee en conjonction avec une methode de superposition valide avant. On trouve une raisonnable accord entre les valeurs in situ et ceux obtenues numeriquement. ZUSAMMENFASSUNG: Das Deformations und Spannungsverhalten Naturgasspeicher in salzigem Untergrund wird analytisch beschrieben und mit vorhandenen Messwesten veglichen. Dabei werden insbesandere die Absenkunz der Oberflache und der Volumen Schwund der Kavernen vesfolgt. Das dreidimensionale Problem wird fuer eine Kaverne axisymetrisch berechnet, zusammen mit der bekannten Superpositionsmethode. Die berechneten werte stimmer mit den Messergebnissen gut ueberein. 1 INTRODUCTION The search for a good characterisation of long term behavior of leached rock salt cavities is justified by the need to minimise eventual damages resulting from the subsidence on the surface. In two locations in France, Tersanne and Etrez, a subsidence control has been performed during more than ten years. Simulation by numerical methods allows to perform some predictions on future evolution, and also to test specific numerical procedures. The issue is to obtain a good accuracy in the far field region, e.g. the surface subsidence. For the moment, only Tersanne case has actual in situ measures available. The subsidence data have been already subjected to numerical analyses (Nguyen-Minh et al, 1993), where a two step finite element procedure was used, by taking advantage of the two-layered medium and the elastic response of the cover-layer. Herein, such procedure in not needed as the far field region can be efficiently discretized with boundary elements and special infinite elements (Bettess, 1992). A special procedure is used to speed up numerical calculations (Menezes & Nguyen-Minh, 1993). TERSANNE FIELD DATA At Tersanne, located in France, subsidence has been measured continuously for more than ten years (Durup, 1990, 1991). The observation zone (Figure 1) covers an area of 15 Km 2 , where cavities are leached 1500 m depth, in a thick 650 m bedded salt layer, and are located 150 m beneath the clay cover. Beyond 2000 m depth there is a rigid sandstone base. There are fourteen cavities spaced 600 m in a hexagonal arrangement, each one with an equivalent volume of 268 000 m 3 . At Etrez there is the same number of cavities with the same equivalent number. We will admit that all the cavities are leached at the same time and that they have the regular distribution as seen in Figure 2. A quasi axisymmetric subsidence pattern can be observed on the surface at Tersanne (Figure 3). The volume loss at the surface to the total caverns volume loss shows out a 60% ratio (Figure 4). As rock salt is believed to behave as an incompressible material, one can suspect a possible dilatancy inside the rock mass, which could affect its tightness.

Proceedings Papers

Paper presented at the ISRM International Symposium - EUROCK 96, September 2–5, 1996

Paper Number: ISRM-EUROCK-1996-080

... benches (Fig.2). Fig. 3 shows three-cross sections of the failed slope. strength back analysis coal seam

**finite****element****method**Engineering stability analysis Displacement response configuration lignite seam Thickness charbon safety factor metals & mining axial stress seam...
Abstract

ABSTRACT: A very complex failure took place at an open-pit coal mine in the eastern Turkey. The floor of the open-pit heaved up as a result of the buckling failure of the coal seam and a combined form of shear and sliding failure of slope benches occurred. The investigations showed that a weak clay band within the coal seam was the main cause of the failure. The friction angle of this band was less than 3° and dipped into the pit. with an angle of 5–7°. The failure took place while the coal seam was uncovered. In this paper, the causes of the failure are investigated through some back analyses of failure modes on the basis of geotechnical investigations, limiting equilibrium techniques and finite element analyses and the outcomes of these studies are presented and discussed. RESUME: Une rupture tress complex est. serene dans une mine de carbon à ceil overt à lest de la Turquie. Le planchcr de la mine s'est souleve à la suite du flambage d'une veine de carbon. Les terrasses en pente se sont effondrees sous une forme combinee de cisaillement et de glissement. Les recherches ont indique que la cause principale de la rupture fut la presence d'une couche d'argile situee dans la veine du carbon. Cette couche ayant un angle de frottement inferieur à 3° etait inclinee de 5° à 7° vers la pente. La rupture s'est produit lors de I'excavation de cette couche. ZUSAMMENFASSUNG: In einer offenen Grube einer Kohlenminein der Osttuerkei fand ein komplizierter Bruch statt. Der Boden der offenen Grube hob sich auf Grund eines knicken eines kohlestreifens welcher mit einer Scherung und einer Abrutschung einer treppenartigen Böschung kombiniert war. Untersuchungen haben gezeigt, dass ein weiches Tonlage die Hauptursache des Bruches war. Der Reinbungswinkel dieser Lage betrug weniger als 3° und hatte einen Einfallswinkel von 5°-7°. Der Bruch ereignete sich wahreud der Ausgrabung del' Kohlendecke. 1 INTRODUCTlON A very complex failure took place at the Kişlaköy open-pit mine of Afşin-Elbistan Lignite Mining Complex in the Eastern Turkey in 1984. The pit-floor heaved up as a result of the buckling failure of the lignite seam and a combined form of shear and sliding failure of mining benches occurred. The investigations showed that weak clay layers existed in the lignite seam of about. 20 m thick and one of these clay layers played an important role in the failure. The friction angle of this layer was about 3° and dipped into the pit with an angle of 6° (Ulusay et al. 1986). The main failure occurred on July 1, 1984 at the North-West slope of the kişlaköy open-pit. (Polat and Yueksel 1984). The failure involved a region, which was 650 m long and 250 wide (Fig. 1). The length of the region was later extended to 1000 m with subsequent failures. The final horizontal movement of the failed slope was more than 50 metres. The lignite seam of the pit-floor was heaved up and it had a set of buckles whose strikes were almost perpendicular to direction of movement and parallel to the axis of benches (Fig.2). Fig. 3 shows three-cross sections of the failed slope.

Proceedings Papers

Paper presented at the ISRM International Symposium - EUROCK 96, September 2–5, 1996

Paper Number: ISRM-EUROCK-1996-105

... shown. In the following we will briefly review the state of practical applications of numerical simulation in tunnelling. Next we will examine the use of two of the main methods of simulation, namely, the

**Finite****Element****Method**(F.E.M.) and the Boundary Element Method (B.E.M.). 2 CURRENT STATE OF...
Abstract

ABSTRACT: The paper is concerned with the numerical simulation of tunnel advance using the Finite Element and Boundary Element methods. On practical examples the advantages and disadvantages of each method and their applicability to certain classes of tunnelling problems will be shown. RESUME: Le rapport contend la simulation numerique du progression du tunnel a I'aide de la methode des elements finis et de la methode des elements limites. Au moyen des examples pratiques on mont les avantages ales desavantages chacune methode aussie bien que I'utilite pratique en fonctions differents. ZUSAMMENFASSUNG: Der Bericht befasst sich mit der numerischen Simulation des Tunnelvortriebs mit Hilfe der Methode der Finiten Elemente und der Methode der Randelemente. An Hand von praktischen Beispielen werden die Vor- und Nachteile jeder Methode sowie die Anwendbarkeit auf unterschiedliche Aufgabenstellungen im Tunnelbau gezeigt. 1 INTRODUCTION Despite significant advances made in numerical simulation methods the accuracy of the results, as far as deformations and stresses are concerned, is not comparable to that achieved for example, in structural engineering. This is mainly due to the fact that the material the tunnel is built in, namely rock or soil, is extremely heterogeneous and has a large variation in its mechanical properties. Futhermore the rock mass is transected by Joints and faults and, in some cases, discontinuous behaviour may play an important role. In contrast to problems in structural engineering where loadings are specified, in tunnelling we usually have very little knowledge of the stress field in the rock/soil prior to excavation. Last but not least, tunnelling involves a complex sequence of excavation and construction with new materials (shotcrete, rock bolts) being introduced at various stages. For these reasons numerical simulation plays a different role in tunnelling and, in many cases, we do not require specific values of stresses or displacements but may be interested instead if zones in the rock mass are potentially unstable, or in major trends (i.e. areas of high stress vs. low stress) rather than in exact numerical values. Furthermore, because of the difficulty in determining virgin stresses and geological features ahead of the tunnel face numerical simulation methods themselves, in conjunction with field measurements, may be used to obtain the information, as will be shown. In the following we will briefly review the state of practical applications of numerical simulation in tunnelling. Next we will examine the use of two of the main methods of simulation, namely, the Finite Element Method (F.E.M.) and the Boundary Element Method (B.E.M.). 2 CURRENT STATE OF PRACTICAL APPLICATION OF NUMERICAL SIMULATION IN TUNNELLING Most numerical simulations carried out to date have been 2-D analysis using the F.E.M. At present, 3-D models cannot be considered as a standard tool for practical tunnel design because of the expenditure with respect to manpower and computer resources involved. To a large extent their practical application is restricted to investigate specific details, as for example, stresses in the shotcrete lining of tunnel intersections. However tunnelling is definitely a 3-D problem and restricting oneself to two dimensions may lead to significant deviations when compared to actual field behaviour. Plane strain models, for example, are only able to predict displacements and stresses some distance from the tunnel face and cannot account for stress redistribution and displacement ahead and in the vicinity of the face. This, however is very important for tunnels constructed with the New Austrian Tunnelling Method (NATM) which uses complex excavation sequences and support measures like shotcrete and rock bolts. Furthermore, if major inhomogeneities and faults are present then simplified 2-D analyses may lead to results which are in significant error.

Proceedings Papers

Paper presented at the ISRM International Symposium - EUROCK 93, June 21–24, 1993

Paper Number: ISRM-EUROCK-1993-017

.... Thirdly, by use of these parameters in future, reliability analysis of

**finite****element****method**can predict the stability in probability values. Lastly, a practical coal mine roadway example shows that the proposed method is a good one. RÉSUMÉ: En ingenierie des roches, la prevision des carasteristiques...
Abstract

ABSTRACT: It is very important to predict the stability around openings in rock engineering. However, the input parameters and the results of present prediction methods mostly depend on the experiences of engineers. In this paper, considering these difficulties, a new prediction method is presented. First, a Grey system differential equation which can describe the deformation process of surrounding rock is set up, and a deformation forecasting model can be obtained. And then based on the forecasting displacements and probability back analysis, rock property parameters are back-analyzed. Thirdly, by use of these parameters in future, reliability analysis of finite element method can predict the stability in probability values. Lastly, a practical coal mine roadway example shows that the proposed method is a good one. RÉSUMÉ: En ingenierie des roches, la prevision des carasteristiques de stabilite des roches englobantes releve dúne importance capitale. Jusqu'à present, ces carasteristiques s'obtiennent essentiellement à partir de parametres de donnees empiriques et les resultats obtenus varient selon que l'imgenieur soit plus ou moins experimente. Nous proposons donc dans notre artiele une nouvelle methode plus sûr. D'abord nous representons Ie processus des deformations de la roche encaissante par un systeme gris d'equations differentielles, de là nous pouvons obtenir un modele des deformations previsibles. Emsuite, sur cette base mous feroms une analyse inver, se des probabilitites et des deplacements prevus et une analyse inverse des parametres carasteristiques de la roche. Puis nous utiliserons ces parametres à vemir pour prevoir, par la methode d'analyse du degrè de certitude des elements finis et compte tenu des valeurs de probabilite, les proprietes de stabilite. Enfin, nous allons donner un exemple dapplication de notre nouvelle methode dans le cas particulier des galeries d'un minerai de houille. ZUSAMMENFASSUNG: Es ist im felsenwesen sehr wichtig, die stabilitat des umgebenden felsea zu prophezeisen. Aber zur zeit sind die eingangsparameter und resultate der propherzeiungsmethode abhangig von den inginierserfahrungen. In dieser arbeit sind solche schwierigkeiten ueberlegt und wird eine neue propherzeiungsmethode gestellt. Zuerst, die differentialen gleichungen eines grausystem, das den deformierungsvongang des umgebnden felses beschreiben, werden gegrundet, daraug entsteht ein propherzeiungsmodell fur diesen deformierungsvongang, und dann werden die felseigenschaften durch die vorhengesagte verschiebung und die probabilitat ruckanalyse ruckanalysient. Drittens, mit solchen parametern in zukunft kann die zuverlassigkeitganalyse der finite elementsmethode durch den wahnscheinlichkeitwert die stabilitat propherzeien. Letzteng, ein beispiel eines kohelentunnels bestãitigt, dap die vorliegende methode sehn gut ist. 1 INTRODUCTION It is very necessary to estimate the present and future stability condition of surrounding rock in rock engineering. Thus, the prediction theory of stability around openings comes into the field of rock mechanics. Up to now, many prediction methods have been proposed which can be categorized as follows: Experience analogy methods, such as J. Scki & M. Okada (1988), A. Guenot & M. Panet(1985), M. Matsuo & K. Kawmura(1980) have contributed to this field, moreover many in-situ engineers have proposed the regression methods and analogy predictions; Mechanics model methods, these methods are mostly used to investigate the evolution of the time-dependent deformation with the help of the rheology theory, such as M. Panet (1979), Wang Zhiyin (1988) et al; Numerical analysis methods, such as finite element method and boundary element methods, which are used to analyse present or future deformation evolution behavior, as I.G. Vardoulakis (1988), Huang Hongwei (1990) et al; Process model methods, which consider deformation evolution as a stochastic process or dynamic process to model it using these corresponding mathematics theories as D. B. Ashey (1980), Chen Zhiyin (1988), Liu Huaiheng (1900) et al; Combined prediction methods, which include expert system, fuzzy combined prediction, such as Huang Hongwei (1990) et al.