File Name: dynamic relaxation applied to continuum and discontinuum numerical models in geomechanics .zip

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Published: 06.06.2021

*An imperative task for successful underground mining is to ensure the stability of underground structures. This is more so for deep excavations which may be under significantly high stresses.*

- Flowchart of DEM Modeling Stability Analysis of Large Underground Powerhouse Caverns
- discrete element modelling (DEM)
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*What problems can be solved? The flowchart is provided and applied to analyze the stability of UPC in this paper.*

Tunnelling processes lead to stress changes surrounding an underground opening resulting in the disturbance and potential damage of the surrounding ground. Especially, when it comes to hard rocks at great depths, the rockmass is more likely to respond in a brittle manner during the excavation. Continuum numerical modelling and discontinuum techniques have been employed in order to capture the complex nature of fracture initiation and propagation at low-confinement conditions surrounding an underground opening.

## Flowchart of DEM Modeling Stability Analysis of Large Underground Powerhouse Caverns

What problems can be solved? The flowchart is provided and applied to analyze the stability of UPC in this paper. With the guide of the flowchart, the damage index Di is used as a failure type gravity-controlled or stress-induced judgment indicator.

Through the calculation of three typical engineering, the problems of random blocks stability, dynamic calculation, and support system evaluation are studied, respectively, with the help of the DEM code 3DEC. The method and results of this paper can give reference to engineering projects of its category.

Vast underground caverns are used for a variety of purpose in civil engineering. Stability of underground openings under different conditions is an essential issue in construction [ 1 ].

Numerical simulation has become an important method to solve the rock mechanics problem of this kind of engineering, while how to choose a suitable numerical method is a crucial stage. In the continuous mechanics method for the analysis of the stability of underground caverns, three-dimensional stability analyses and displacement predictions of large UPC were carried out by using FLAC 3D [ 3 ].

For simulating the hydraulic-mechanical interaction in the process of cracking, a coupling method which based on the elastoplastic finite element method FEM is proposed [ 4 ]. A hybrid intelligent method is proposed for a large cavern excavated in alternate hard and soft rock strata, and the method is an integration of an evolutionary neural network and FEM analysis using a genetic algorithm [ 5 ].

Detailed performance-monitoring studies have been carried out for determining the deformations and stress distribution around underground powerhouse caverns in the nonhomogeneous rock mass, using the three-dimensional finite element method [ 6 ]. The stability of a large cavern group at great depth is discussed by large-scale three-dimensional geomechanical model tests and numerical simulations of FLAC 3D [ 7 ]. In underground excavated in jointed rock masses at relatively shallow depth, the most common types of failure are those involving wedges falling from the roof or sliding out of the sidewalls of the openings [ 8 ].

If the stability of rock mass has a close relationship with the discontinuity, the discontinuous method is indispensable, and the continuum method will not get a reasonable answer. Considering modeling in engineering practice, the interest has been placed on the adoption of discontinuum models which give a far more realistic and representative picture of rock mass behavior than equivalent continuum models [ 9 ].

The distinct element method DEM [ 10 ] and discontinuous deformation analysis DDA [ 11 ] are better suited than the finite element, boundary element, and finite difference methods to perform discontinuum analysis of underground excavations in jointed rock masses [ 12 ]. It is thought that DDA is a special type of discrete element method [ 13 ].

Stability analysis with 3DEC was, thus, conducted to examine each of the potential issues stress-inducing brittle failure, large deformation, and block instability with various scenarios corresponding to each of the layout proposals [ 16 ]. Triaxial creep tests and back analysis of the time-dependent behavior of Siah Bisheh cavern by 3DEC [ 17 ]. The displacement-based back analysis using univariate optimization algorithm was applied, and numerical modeling results of 3DEC were in good agreement with measured displacements [ 18 ].

An expanded distinct element method EDEM was developed for simulating the crack generation and propagation due to the shear and tension failures in the matrix rock blocks [ 19 ]. There is no doubt that the application of the DEM has been widely recognized by the industry, especially in underground rock engineering.

However, for different complex engineering problems, systematic and multifaceted research of how to use 3DEC should be proposed. In this paper, we firstly present a practical flowchart of rock mechanics modeling for the steps in the UPC evaluation process.

It is intended that these flowcharts should cover the principles and different aspects of the problems. Based on the flowchart, this paper is to conduct stability analysis of the caverns with DEM numerical modeling and study the mechanical behavior of the rock mass at three typical projects Jurong, Dagangshan, and Qiongzhong; Figure 1 , The three projects are all underground powerhouse cavern projects in large-scale hydropower projects. Jurong and Qiongzhong are pumped storage power plants, while Dagangshan is a conventional hydropower project.

The response of a rock mass is often dominated by discontinuities that cut through the rock because they are usually much weaker and more deformable than the intact rock. Cundall [ 10 ] described such a numerical model and applied it to the toppling failure of a rock slope.

Subsequently, the method became known as the distinct element method or the discrete element method DEM. It has been extended to deformable rock blocks and applied to such diverse systems as granular material, masonry structures, and hydraulic fracturing [ 21 , 22 ]. Although rock discontinuities had previously been introduced as specialized elements into the finite element method [ 23 ], the DEM is different because it characterizes a joint as a nonlinear boundary condition, rather than an element, and it allows arbitrary displacement and rotation of rock blocks and unlimited freedom for any purpose to interact with any other object.

Any viable DEM code requires an underlying process that continuously identifies pairs of neighboring blocks and the specific entities corners, edges, and faces that may interact between each pair. These tasks must execute in linear time for the code to be efficient for simulating systems with thousands of blocks and complex block shapes. One such scheme is described by Cundall [ 24 ], but there are other algorithms that also avoid the polynomial-time searches implied by a brute-force approach.

The DEM is a powerful technique to perform stress analyses in blocky rock masses formed by discontinuities [ 12 ]. But, how is it used in plant design? When to use and what should be paid attention to when applying? There have been many earlier presentations on this subject: for example, the flowcharts developed by Hoek and Brown [ 25 ] and Hudson and Feng [ 26 ].

We provide an applicable flowchart in Figure 2 ; the work starts with a collection of geological data, and then, there is the division between types of instability—leading to the two rows in the flowchart considering instability due to adverse structural geology and excessively high rock stress. It, then, leads to decisions on the excavation processes, support evaluation, and operating maintenance of the site. It is noted that the flow chart is mainly aimed at how to choose suitable numerical simulation methods to solve different failure types of UPC projects.

Notes on the DEM evaluation strategy. It provides the overall process as indicated in Figure 2. In the excavation of jointed rock masses at relatively shallow depth, the most common types of failure are those involving wedges falling from the roof or sliding out of the sidewalls of the openings. These wedges are formed by intersecting structural features, such as bedding planes and joints, which separate the rock mass into discrete but interlocked pieces.

When the excavation of the opening creates a free face, the restraint from the surrounding rock is removed.

One or more of these wedges can fall or slide from the surface if the bounding planes are continuous or rock bridges along the discontinuities are broken [ 8 ]. Martin et al. At low in situ stress magnitudes, the failure process is controlled by the continuity and distribution of the natural fractures in the rock mass.

However, as in situ stress magnitudes increase, the failure process is dominated by new stress-induced fractures growing parallel to the excavation boundary.

This fracturing is generally referred to as brittle failure. It is indicated that the initiation of brittle failure occurs when the damage index D i expressed as the ratio of the maximum tangential boundary stress to the laboratory unconfined compressive strength exceeds 0.

Fractures or faults are often modeled deterministically. Actual existing faults that have been mapped are represented explicitly in the model by specifying a location, dip, and dip direction. It is possible to consider hundreds of individual faults in this manner, but the procedure is quite labor intensive.

The other alternative is a stochastic representation of faults. With this approach, which is called the discrete fracture network DFN , specific faults are not modeled explicitly. Instead, a set of statistical parameters are defined, and a joint set is generated based on the statistical input.

In this way, the joints do not represent specific mapped joints, and the joint set is nonunique. Different realizations will satisfy the statistical criteria [ 33 ]. The underground powerhouse complex is located in the Northeast of Lun Mountain peak mountain slopes, which is magnificent. The diorite porphyrite veins invasion also can be found. The maximum in situ stress of the Jurong plant is about 7.

It can be considered that the damage index D i of the plant is generally between 0. Accordingly, the numerical results show that stress-induced instability is not a common phenomenon, which only occurs at the position of small scale with the ratio of more than 0. From Figure 2 , the conclusion can be deduced that the failure type is that the block will slide along the discontinuities. In other words, after excavation, the failure of the rock mass is controlled by discontinuity mostly. One or more of these wedges will fall or slide from the surface.

The DEM is an appropriate choice to simulate the behavior of the engineering rock mass. DFN modeling is increasingly being used to help provide solutions for many geotechnical and mining engineering problems. The DFN approach can be defined as the analysis and modeling process that explicitly incorporates the geometry and properties of discrete fractures as a central component controlling rock mass behavior.

With the DFN module of 3DEC, the fracture population embedded into a rock mass is viewed as a set of discrete, planar, and finite-size fractures. By default, the discrete fractures are disk-shaped. The DFN modeling approach is stochastic: the geometrical features of a DFN model are only constrained through independent statistical distributions of its geometrical properties.

The geometrical characteristics supported by the DFN module are the fracture size diameter , orientation, and position distributions.

The fracture size distribution is determined from a probability function that describes the distribution of disk diameters. In each case, the dip and dip direction are drawn from the specified distribution. Numerous realizations of different DFN have been generated statistically. The statistical parameters associated with a DFN typically characterize the fracture size distribution, orientation distribution, and density of each fracture set [ 35 ].

The DFN used in this study consists of 3 fracture sets, each with a given statistical distribution Table 1. Through the function of the DFN, we get the jointed rock model, as shown in Figures 3 a and 3 b.

Properties assigned to blocks are generally derived from laboratory testing programs Table 2. Joint properties are conventionally derived from laboratory testing e. The joint cohesion and friction angle correspond to the parameters in the Coulomb slip constitutive model Table 3.

To speed up the solution, a rigid blocks method is used for calculation. Based on the calculation result, we can divide the blocks into several types according to the displacement. It is a practical method to judge the stability through full displacement, although it is not perfect.

The results are shown in Figure 4 , unstable blocks are mainly distributed in the main powerhouse, and the main powerhouse arch near the downstream side is the most dangerous position. It is necessary to fix a certain number of long anchor cables at the crown part of the main powerhouse cavern beside the systematic support. Also, there are a small number of unstable blocks in the upstream and downstream sidewalls of the main powerhouse, and the downstream blocks are more than the upstream.

Simulation results indicate that the potential problem of stability will give priority to failure of structurally control. Also, the failure blocks have little relationship with the stress field after excavation. Figure 4 discovered, clearly, that instability blocks and latent instability blocks are not in accordance with the stress field distribution but have a close correspondence with the spatial location of the joints attitude, and the stress is not the primary control factor. Numerical analysis provides a useful tool to enhance understanding of the rock mass behavior after excavation.

According to the absolute displacement, the surrounding rock mass of the Jurong complex and unstable blocks are mainly distributed around the main powerhouse, and the main powerhouse arch near the downstream side is the most dangerous position. It is necessary to fix a certain number of long anchor cables at the crown part of the main powerhouse cavern.

The force-displacement law is used to find contact forces from known and fixed displacements.

## discrete element modelling (DEM)

A generalized weighted residual method is used to formulate the discrete element method DEM for rigid or deformable bodies. It is shown that this approach provides a unified methodology for deriving many of the different discrete element techniques in current use today. This procedure is used to develop a number of different element formulations for use in problems in which the distinct bodies exhibit complex deformation behaviour such as beam or plate flexure, membrane action, and additional reinforcement of a jointed discontinuum. A number of examples are also presented which illustrate the usefulness of different discrete element types in engineering analyses of discontinuum problems. Report bugs here. Please share your general feedback.

Abstract The goal of this review paper is to provide a summary of selected discrete element and hybrid finite—discrete element modeling techniques that have emerged in the field of rock mechanics as simulation tools for fracturing processes in rocks and rock masses. The fundamental principles of each computer code are illustrated with particular emphasis on the approach specifically adopted to simulate fracture nucleation and propagation and to account for the presence of rock mass discontinuities. This description is accompanied by a brief review of application studies focusing on laboratory-scale models of rock failure processes and on the simulation of damage development around underground excavations. The goal of this review paper is to provide a summary of selected discrete element and hybrid finite— discrete element modeling techniques that have emerged in the field of rock mechanics as simulation tools for fracturing processes in rocks and rock masses. Production and hosting by. A large body of experimental research shows that the failure process in brittle rocks under compression is characterized by complicated micromechanical processes, including the nucleation, growth and coalescence of microcracks, which lead to strain localization in the form of macroscopic fracturing Lockner et al.

Koliji, A. The Hongrin north dam is a double curvature concrete arch dam located in western Swiss Prealps, which attains m high. The right bank abutment of the dam mainly consists of intensively jointed Neocomian limestone and exhibits zones of potential instability. At the time of construction — , this slope was reinforced with rock anchors. Subsequent hydrogeological study and groundwater monitoring revealed the presence of water pressure due to a slight seepage flow through the rock joints in the dam foundation.

In book: Innovative Numerical Modelling in Geomechanics (pp). Authors: Download full-text PDF Continuum and discontinuum representations –. FLAC When dynamic relaxation algorithms are used to.

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The paper presents a description of the methods used to model rock as DEM simulation of an underground structure subjected to dynamic loading Morris et al. bring to the geomechanics community recent advances in numerical modeling sion regarding continuum versus discontinuum methods is in-.