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Mechanical degradation of emplacement drifts at Yucca Mountain-A modeling case study. Part II: Lithophysal rock
Abstract
This paper outlines rock mechanics investigations associated with mechanical degradation of planned emplacement drifts at Yucca Mountain, which is the designated site for the proposed US high-level nuclear waste repository. The welded tuff emplacement horizon consists of two groups of rock with distinct engineering properties: nonlithophysal and lithophysal units, based on the relative proportion of lithophysal cavities. The term ‘lithophysal’ refers to hollow, bubble like cavities in volcanic rock that are surrounded by a porous rim formed by fine-grained alkali feldspar, quartz, and other minerals. Lithophysae are typically a few centimeters to a few decimeters in diameter. Part I of the paper concentrated on the degradation behavior of the generally hard, strong, and fractured nonlithophysal rock. Part II concentrates on the host rock in the lithophysal units. Lithophysal rock is characterized by lithophysal cavities interconnected by fracturing. Fracture sets are not as clearly defined as in the nonlithophysal rock. The rock mass porosity in the lithophysal units has been shown to be the primary physical factor that governs elastic and strength properties. The degradation behavior of the tunnels in the lithophysal rock is controlled by the spalling of the surrounding rock mass. A discontinuum material model has been developed to represent the drift scale rock mass properties in which slip and separation of contacting rock blocks can be estimated. Two-dimensional discontinuum analyses were developed with the consideration of in situ, thermal, and seismic loads. Time-dependent degradation was also considered. In this study, field and laboratory data and numerical analyses are well integrated to provide a solution for the unique problem of modeling drift degradation.
... The purpose was to understand the impact of macroporosity on Young's modulus on rocks and to use the correlation from these models, if successful, to augment rock test data or even as a substitute. Modeling aspects of PFC and UDEC simulations were provided in Rigby (2004) and Damjanac et al. (2007). A summary of the approaches and details of the modeling is provided in Table 3, located at the end of the paper. ...
... His FLAC 2D models incorporated a simple linear elastic material compared to the more advanced discrete element models which were based on sophisticated constitutive models derived from actual tuff test results. Figure 7 presents the modeling results, excluding the results from Avar (2002) due to the significant Young's modulus difference with Rigby (2004) and Damjanac et al. (2007). The UDEC 2D simulations yielded the highest modulus values and the highest coefficient of determination. ...
... Modulus from numerical models with best-fit regression curves. Curves are the same color as data points.The PFC 2D simulations(Damjanac et al., 2007) that used stenciled lithophysae shapes show wider scatter and yielded the lowest modulus values. The variability in the modulus values is thought to be from the complex macropore shape, size, and distribution. ...
It is well known that rock porosity reduces rock Young’s modulus of intact rock specimens. However, it is not well understood how different types and amount of macroporosity in forms of non-connected or isolated cavities (e.g., vesicular basalt, lithophysal tuff) or interconnected vugs (e.g., vuggy limestone) affect rock elastic properties. Such macroporosity leads to challenges in deriving engineering properties of rock. This paper compiles an existing database for porosity and Young’s modulus of macroporous rocks. The database includes Young’s modulus determined from unconfined compression testing on intact rock specimens and analogue specimens used to prepare rock-like test samples and numerical simulations of compression testing on similar materials. The database is used to develop the relationship between porosity and Young’s modulus. In addition to the porosity, the macropore shapes, sizes, locations, and proximity of a macropore to its neighboring macropore play a role in how porosity affects intact rock Young’s modulus.
1. INTRODUCTION
Macroporosity, which is the porosity due to visible large voids or cavities, impacts mechanical properties, such as strength and Young’s modulus (E). Examples of such rocks are primarily volcanic (e.g., vesicular basalt, lithophysal tuff, lithophysal rhyolite, pumice, and scoria) and sometimes sedimentary (e.g., vuggy limestone and coquina). Engineering characterization of such rock is challenging due to macroporosity variation within the rock mass, distribution (void-to-void proximity, void alignment), and shape of the macropores (Jespersen et al., 2010; Davis et al., 2017). Preparing test specimens of standard sizes from rock cores or outcrop blocks can be difficult due to macroporosity. Obtaining a representative specimen is also challenging as the size of the macropores becomes too large to prevent large macropores from being sampled. For example, the lithophysal tuffs of Yucca Mountain, Nevada, had macropores ranging in size from approximately 1 to 50 cm, with a maximum size up to 1 m (CRWMS M&O 2000). When laboratory compression tests are carried out on these limited number of specimens, the distribution of data is typically scattered.
... Although the research results are very rich about the strength, deformation and failure mechanism of rock or rock-like materials containing crack-like flaws, there are relatively few studies on hole-like flaws. In fact, on a macroscopic scale, rock materials such as tuff [16], weakly cemented coarse sandstone [17] and some other natural rock masses [18] always contain many macroscopic cavities, as shown in Figs. 1a-1c. ...
... And three basic coalescence modes can be observed in their results: tensile mode, shear mode, and mixed mode by tensile and shear. In addition, the effect of hole density (or macroporosity) on strength and deformation of void-rich rock specimens have been studied based on tuff [16,[30][31][32][33][34][35], sandstone [36][37][38] and pre-holed plaster specimens [32,33]. Their results showed that the uniaxial compression strength (UCS) and elastic modulus tend to decrease with the increasing macroporosity (or hole density). ...
... Although the above experiments can reveal some macroscopic mechanical behavior of rock materials containing void-like flaws, the mesoscopic Figure 1: Hole-like flaws in real rock or coal materials. (a) Tuff specimens [16]. (b) Poor cemented coarse sandstone [17]. ...
Hole-like defects are very common in natural rock or coal mass, and
play an important role in the failure and mechanical behaviors of rock or coal
mass. In this research, multi-holed coal specimens are constructed numerically
and calibrated based on UDEC-GBM models. Then, the strength, deformation
and failure behavior of the porous specimens are analyzed, with consideration
of hole density (P) and confining pressure (σ3). The simulation results are highly
consistent with those available experiment results, and show that the compressive
strength decreases exponentially with the increasing hole density. The strength
loss is mainly caused by the reduction of cohesion when P < Pcr (critical hole density)
and the reduction of frictional angle when P > Pcr. Also, the increasing hole
density linearly reduces the tangent and secant modulus and causes greater nonlinear
deformation of multi-holed specimens. Finally, the failure patterns, coalescence
mechanism and damage behavior of the multi-holed specimens are revealed
based on the analysis of mesoscopic displacement fields and stress distribution
around holes. This research promotes a better understanding of the effects of hole
density and confining pressure on the failure and mechanical behavior of porous
geomaterials.
... Studies using field-scale BBMs have been conducted in the past decade, although they are much less common than laboratory-scale studies. Such studies have largely consisted of sensitivity analyses, where the relative influences of loading conditions (Damjanac et al., 2007;Garza-Cruz et al., 2014;, support Kang et al., 2015;Bai et al., 2016), or material properties (Garza-Cruz and Pierce, 2014) were tested. While these prior studies have all provided qualitatively "realistic" results, there has been a relative lack of detailed model calibration and validation at the field-scale. ...
... Additionally, there has been limited investigation of what components of field-scale models (i.e. block stiffness heterogeneity, contact strength heterogeneity, block inelasticity) are most critical in replicating different behaviours; most prior field-scale studies have employed a homogeneous and elastic block representation (Damjanac et al., 2007;Preston et al., 2013;Bai et al., 2016). ...
... Whereas laboratory-scale BBMs have direct physical analogs for block stiffness heterogeneity (mineral stiffness heterogeneity), block contact strength heterogeneity (different mineral-to-mineral contact types), and block inelasticity (intragranular fracturing), the size of blocks in field-scale models means that such analogs are no longer useful. In particular, field-scale models have historically used block sizes ranging from 10 cm to 50 cm, primarily due to the computational demand of finer-scale block structures (Damjanac et al., 2007;Preston et al., 2013;Bai et al., 2016;. ...
Stress-induced damage of sparsely fractured rockmasses around excavations has
historically been modeled using continuum methods, but these approaches are highly
phenomenological in nature and, as a consequence of their formulation, cannot be used to
predict the influence of rock reinforcement on ground behaviour. Relatively new
discontinuum tools such as bonded block models (BBMs) have the potential to overcome
these limitations. This paper documents recent advances in bonded block modeling at both
the laboratory and field scales, with an emphasis on research by the authors. Additionally,
the following critical questions about BBMs are answered: (1) What physical phenomena
can BBMs reproduce, and how does this depend on the choices made during model
development? (2) Can BBMs reproduce field-scale behaviour (not just in terms of strength,
but also deformation and dilation characteristics)? (3) Can BBMs quantitatively reproduce
the influence that rockbolt reinforcement has on ground behaviour?
... 3. Разработать компьютерную программу для расчетов длительного деформирования массивов горных пород. 4. Разработать программу для графического отображения и анализа результатов расчетов. ...
... Максимальное значение коэффициента поврежденности и скорость снижения прочностных свойств приняты по результатам численного моделирования с использованием модели с коррозией под напряжением Д. Потионди [2]. [2,4,22] Кемени на основе теории допредельного роста трещин предложил способ расчета зависимости сцепления и прочности на разрыв от времени и напряжений [3]. ...
... Первая функция ранее использована Б. Дамьянацем и Ч. Фэйрхёрстом, консалтинговой группой Итаска в работах [4,22]. Похожая на четвертую функцию кривая приводится в исследованиях Д. Потионди [2]. ...
Существующие способы определения предельных, или критических, параметров деформаций массивов горных пород зачастую не позволяют выполнять прогнозирование на основе маркшейдерских наблюдений разрушений на ранних стадиях деформационного процесса. Более раннее и точное прогнозирование разрушений позволит снизить стоимость и улучшить безопасность проведения противодеформационных мероприятий, поэтому разработка новых способов определения предельных параметров деформаций представляет большой практический и научный интерес.
С развитием вычислительной техники стало возможным широкое применение численных методов механики дискретной среды для решения прикладных задач геомеханики. Сегодня продолжается развитие методов механики дискретной среды, предлагаются новые методы и совершенствуются существующие. Например, разработка метода конечно-дискретных элементов приходится на начало 2000-х годов, а его активное развитие продолжается по сегодняшний день. Метод конечно-дискретных элементов обладает определенными преимуществами по сравнению с различными численными методами механики дискретных сред.
Для моделирования длительного деформирования массива горных пород должно учитываться изменение свойств пород во времени. Разработка моделей со снижением прочности горных пород со временем для методов дискретных и отдельных элементов в середине 2000-х годов показала применимость численных методов механики дискретной среды для моделирования процессов длительного деформирования массивов горных пород.
Перечисленное выше определяет актуальность разработки способа расчета предельных кинетических параметров длительных деформационных процессов с использованием метода конечно-дискретных элементов.
... In the first group, the model is represented as an assembly of disk-shaped particles in the manner of PFC. In the second group, the model is represented as an assembly of polygon-shaped particles as proposed by Damjanac et al. [16] and Lan et al. [17]. ...
... In terms of explicit representation of the microstructure of rock in a direct manner, it appears more desirable to make use of polygonal grains instead of circular grains. Damjanac et al. [16] showed the applicability of the Universal Distinct Element Code (UDEC) model consisting of polygonal blocks to the modeling of rock materials. They simulated the mechanical behavior of lithophysal rock in Yucca Mountain and applied the approach to the estimation of thermally induced and time-dependent rockfall of the emplacement drift walls. ...
The microstructure of rock was numerically reproduced by a polygonal grain-based model, and its mechanical behavior was examined by performing the uniaxial compression test and Brazilian tests via the Universal Distinct Element Code. The numerical results of the model demonstrated good agreement with the experimental results obtained with rock specimens in terms of the stress–strain behavior, strength characteristics, and brittle fracture phenomenon. An encouraging result is that the grain-based model-Universal Distinct Element Code model can reproduce a low ratio of tensile to compressive strength of 1/20 to 1/10 without the need for an additional process. This finding is ascribed to the fact that the geometrical features of polygons can effectively capture the effects of angularity, finite rotation, and interlocking of grains that exist in reality. A numerical methodology to monitor the evolution of micro-cracks was developed, which enabled us to examine the progressive process of the failure and distinguish the contribution of tensile cracking to the process from that of shear cracking. From the observations of the micro-cracking process in reference to the stress–strain relation, crack initiation stress, and crack damage stress, it can be concluded that the failure process of the model closely resembles the microscopic observations of rock. We also carried out a parametric study to examine the relationships between the microscopic properties and the macroscopic behavior of the model. Depending on the micro-properties, the model exhibited a variety of responses to the external load in terms of the strength and deformation characteristics, the evolution of micro-cracks, and the post-peak behavior. Copyright
... Christianson et al. [7] demonstrated application of the approach in reproducing laboratory test data. Damjanac et al. [8] examined the mechanical degradation of a rock mass around emplacement drifts. Lorig et al. [9] employed the method to simulate the effect of brittle fracture in causing catastrophic collapse of a slow moving landslide. ...
... However, UDEC-GBM element generation typically does not take into consideration the underlying spatial structure of the grains, nor their shape, despite thin-section analysis suggesting that grain distributions display spatially heterogeneous behaviour [58][59][60][61][62]. The incorporation of such heterogeneities has been shown to cause increased asymmetry in the strain distribution, resulting in alteration of the macro-scale output behaviour [8,18,21,[63][64][65][66]. This strain accumulation results in a fundamental change in the output uncertainty due to spatial data aggregation issues [67][68][69][70]. ...
... However it is impossible to carry out plenty of laboratory experiments because of the difficulty to core the lithophysal rock and prepare specimens. So many compression tests have been simulated using numerical modeling to estimate the potential strength and deformability of the lithophysal rock mass as a function of lithophysal porosity [4,14,18,19]. ...
... Also it is ineluctable to prepare samples having any voids intersecting the edge [4], as shown in Fig. 1. All of these aspects play vital roles on mechanical behaviors of the Brazilian disc [16,19]. The ideal macropore used in the models still provides some insight into how hole sizes, numbers and distributions influence the tensile fracture initiation, propagation and coalescence and also the tensile strength. ...
Macroporosity, pores or holes are common in rock mass, and play important roles on mechanical behaviors of rock mass. The aim of the numerical study presented in this paper is to investigate the fracture mechanism of rock disc containing hole(s) and its influence on tensile strength using the discrete element method (DEM). With special reference to experimental tests, the methodology of using triangle blocks in the Universal Distinct Element Code (UDEC) to simulate tensile fracture process in Brazilian disc tests has been validated herein. First, the properties used in the UDEC Trigon model were determined depending on numerical calibrations to the published experimental results. Secondly, the fracture process of the rock disc containing a central or eccentric hole was simulated numerically, and the numerical results were compared with the experimental tests available. Special attention was given to the effect of the hole size and location on the tensile fracture pattern and tensile strength of the specimen. A series of numerical simulations were implemented to suggest a critical scope in which the hole plays an important role on tensile fracture onset and propagation and then determining the tensile strength. Thirdly, the influence of multiple holes on the initiation and propagation of tensile cracks inside a specimen were simulated. Fracture mechanism of disc containing two holes and its influence on tensile strength were highlighted. The effect of the hole numbers (void porosity), hole sizes and their distribution on tensile fracture patterns and strength were also investigated.
... Lorig & Cundall (1987) performed an early application to the fracture analysis of a concrete beam simulated by an assembly of bonded Voronoi-shaped blocks. Damjanac et al. (2007) studied the micro-mechanical behavior of lithophysal tuff specimens with both particle (PFC) and block (UDEC) models (Fig. 21). Lan et al. (2010) represented the microstructure of brittle rock by means of a deformable polygonal grain-like assembly, in order to study effect of heterogeneity of grain deformability properties on the behavior under uniaxial compression. ...
... Figure 21. UDEC model of uniaxial compression test on lithophysal tuff specimen (Damjanac et al. 2007). ...
... Numerical investigations for the hydro-mechanical (H-M) coupling model are also conducted if the degradation modelling of concrete material or rock material is available. Exponential softening laws of the materials have been proposed by researchers (Tating et al. 2013;Gu et al. 2020;Damjanac et al. 2007). By incorporating these empirical strength degradation laws, the ground reaction curves (GRCs) and support reaction curves (SRCs) are simulated, considering the factor of safety associated with the tunnel linings. ...
Understanding the time-dependent performance changes in tunnel supports through the monitoring data is crucial to predict the long-term stability of deep hydraulic tunnels. This paper provides an analytical solution for assessing the long-term stability of the diversion tunnels from the perspective of support permeability degradation. An evaluation factor Rgl, which denotes the ratio of the hydraulic conductivities of the grouted rock and the concrete lining, is proposed to analyse the degradation characteristics of tunnel support performance over time. The time-dependent changes in Rgl and its controlling factors are discussed using the monitoring data of the Jinping II diversion tunnel. The results show that there are ascending or descending trends of Rgl over time, linking to the evolutions of hydraulic conductivity in the grouted rock and the lining. The reliabilities of the analytical model for explaining the changes in tunnel support permeability are examined using numerical methods. The comparisons between the numerical solutions and monitoring results show good agreements in the hypothetical cases characterising the potential degradation of support of the diversion tunnel.
... Numerical simulation can predict the crack extension process of specimens under loading conditions and verify the accuracy of experimental results. The mechanical numeri-cal calculation methods of rock mass with defects are mainly divided into three kinds: finite element method (FEM) [20,21], boundary element method (BEM) [22,23], and discrete element method (DEM) [9,24,25]. Previous studies have shown that parallel bonding modeled by the particle flow code (PFC2D) under uniaxial compression conditions is consistent with laboratory testing phenomena [14] in simulating rock cracking results [26][27][28]. Although PFC2D can only be performed on a 2D planar scale, it can be used to simulate many problems in rock engineering: crack propagation and coalescence of brittle rock materials [29][30][31]. ...
Joined fractures are an important factor affecting natural rock masses’ mechanical and deformation properties. In this paper, indoor uniaxial compression experiments reproduce prefabricated cracks’ generation, extension, and coalescence in rock-like specimens. For the fractured specimens, a single crack with an inclination of α = 45° was placed on the left and right sides, and a third crack with an angle of β = 30°, 45°, 60°, and 90° to the single crack on the right side was placed in groups III–VI, respectively. All cracks extended in the thickness direction. Vertical pressure was applied at a constant loading rate of v = 0.1 mm/min until the stress dropped dramatically. In addition, numerical calculations were performed on the rock specimens using PFC2D, a sub-module of the Discrete Element Method (DEM). The experimental results agree with the numerical simulations in that the strength of the specimens containing a conjugate crack is significantly reduced, and the mechanical and deformation properties of the specimens are related to the internal angle of the conjugate crack, with the lowest peak strength and lowest percentage energy dissipation at β = 45°.
... Subsequently, it was recognized that the development of new fractures could be addressed by defining potential crack paths, initially bonded, which could then fail under the applied loading. This type of simulation of cracking and fracture was used, for example, to study underground waste storage projects [23,24] and to investigate fundamental issues of crack propagation [25]. The suitability of randomly generated Voronoi polygons/polyhedra to represent the internal structure of rock materials has been recognized in various studies [26]. ...
Discrete element models are being increasingly applied to model rock failure processes. Bonded-particle models, based on circular or spherical particle systems, have been successfully used for two decades. More recently, bonded-block models, using polygonal or polyhedral elements, have proven to be a powerful alternative. This paper describes the basis of the application of these models in the numerical simulation of failure in rock materials. The critical governing parameters are identified, and their influence is discussed. The model calibration procedure based on the analysis of laboratory tests is discussed. An application example of an underground excavation problem is presented using a simple bonded-block model employing rigid blocks and a bilinear softening contact model. The results show the capability of this approach to reproduce observed failure modes involving block fractures.
... Thuật ngữ mô hình nền tảng hạt (GBM) phản ánh việc sử dụng các cấu trúc hạt đa giác (Voronoi hoặc Trigon) để mô phỏng vật liệu có cấu trúc dạng hạt trong các chương trình mô phỏng số 10,21,22 . Ví dụ áp dụng GBM trong UDEC (gọi là UDEC-GBM) xuất hiện lần đầu trong Lorig và Cundall 9 để khắc phục nhược điểm của UDEC không thể mô phỏng tường minh phá hủy khối nguyên. ...
Sự ổn định khối đá xung quanh lò chợ hoặc công trình ngầm trong mỏ than hầm lò là điều kiện tiên quyết để hoạt động sản xuất than diễn ra bình thường và đảm bảo an toàn. Tuy nhiên, các lò chợ thực tế vẫn thường xảy ra các sự cố mất ổn định tại gương khai thác hoặc trên nóc gây tai nạn lao động nghiêm trọng, thậm chí chết người. Các nghiên cứu về sự mất ổn định này cho tới nay chưa làm rõ thỏa đáng sự hình thành và phát triển phá hủy khối đá trong biểu hiện, nguyên nhân phần lớn là bởi đặc trưng bất đẳng hướng, không liên tục, không đồng nhất và không đàn hồi của khối đá mỏ. Nhằm phục vụ nghiên cứu biểu hiện ổn định khối đá nêu trên, nội dung bài báo trình bày một nghiên cứu hoàn thiện kỹ thuật mô phỏng số khối đá xung quanh lò chợ bằng mô hình nền tảng hạt. Kỹ thuật mô phỏng sử dụng phương pháp phần tử rời rạc và cấu trúc hạt Voronoi. Một quy trình hiệu chỉnh tính chất vật liệu trong kỹ thuật mô phỏng được đề xuất và kiểm chứng tính đúng đắn thông qua áp dụng cho đất đá thực địa mỏ than Hà Lầm, tỉnh Quảng Ninh. Nội dung bài báo cũng trình bày một kỹ thuật lựa chọn kích thước khối hạt đa giác và giám sát mô phỏng hiệu quả. Quy trình đề xuất cùng với bộ mã lập trình mô phỏng tương ứng sẽ phục vụ đắc lực công tác nghiên cứu ổn định khối đá xung quanh công trình ngầm, từ đó đề xuất các giải pháp kỹ thuật đảm bảo an toàn và sản xuất theo kế hoạch.
(http://stdjsee.scienceandtechnology.com.vn/index.php/stdjsee/article/view/711)
... The micro-mechanical parameters of the Voronoi block model are adjusted in order to match the stiffness and strength of the intact rock. As example calibration exercises, stress-strain curves obtained from numerical experiments for different states of confinement (unconfined, 1 MPa confinement, and 3 MPa confinement) and loading (tension and compression) for the Yucca Mountain tuff (lower bound of stiffness and strength) (Damjanac et al. 2007) are shown in Fig. 3. The mode of failure is also illustrated for each case in plots of displacement vectors and the developed fracturing (in red) in the failure state. ...
Evaluation of the stability of placement rooms and excavation damage in the surrounding geological formations of a deep geological repository (DGR) for high-level nuclear waste are essential components when assessing the overall repository performance. Assessment of the geomechanical performance of placement rooms for the duration of the regulatory period (typically 1 million years) usually involves simulations using numerical models capable of simulating coupled thermo-hydro-mechanical (THM) processes induced by different natural and repository-induced perturbations over different time and length scales. The numerical constitutive model used to represent the host medium should be capable of capturing highly nonlinear responses to stress changes, including development of damage and fracturing. In this paper, a novel approach for simulating the evolution of damage and fracturing around the repository rooms considering coupled THM processes is presented, including validation examples for the approach. The important and novel feature of this modeling approach is the use of the bonded-block model based on the distinct element method (DEM) to represent deformation, damage, and fracturing of the surrounding rock that could potentially result in rock fragmentation and collapse of the rock surrounding the placement rooms. As part of the study, the predictions of damage around placement rooms obtained using the new approach are compared with the conventional continuum mechanics model. Subsequently, the capability of the bonded-block model to simulate damage caused by in-situ and thermally induced stresses is validated by comparison with monitoring data and observations from field-scale experiments.
... GBM reflects the use of polygonal structures (e.g, grain mesh, Voronoi, and Trigon tessellations) to model grain -shaped material mostly in DEM based numerical programs (Damjanac et al., 2007;Potyondy, 2010;Lan et al., 2010;Gao and Stead, 2014). GBM was first used in UDEC by Lorig and Cundall (1987) to overcome the intrinsic limitation of UDEC that this program cannot explicitly model intact block failure. ...
Longwall-associated geotechnical problems have been extensively studied by using numerical modelling methods. However, proper representation of its geological structures remains a challenging task. This paper presents a systematic understanding of numerical modelling techniques for studying longwall coal mining with geological structures. The modelling techniques derived from conventional and advanced continuum and discontinuum methods were reviewed in detail with emphasiz on their mechanic's formulation and applications. This study suggests that the successful selection of a proper modelling technique should be based on the physical principle of longwall problem, texture and shape of materials, and mechanics formulation of the numerical program used for modelling. The paper's conclusions assist numerical modellers in quickly and properly selecting modelling technique for investigating a site-specific longwall problem.
... Os blocos Voronoi precisam ser pequenos suficientemente para que não sejam formadas regiões preferenciais de ruptura (Damjanac et al., 2007). Com isso em mente e levando-se em conta o custo computacional da simulação, definiu-se um mosaico Voronoi com comprimento médio de juntas igual a 7,5 cm. ...
In this work, a new numerical approach based on the Finite Element Method and an implicit continuum formulation, called Continuum Voronoi Block Model-CVBM, is proposed to represent the fracturing process in hard rocks and also the rupture of underground works with high field stresses. In this model, developed with the RS2 program, the rock mass was simulated by a set of blocks, formed by a Voronoi mosaic, joined at their interfaces by joint elements. Different case studies were represented on a laboratory (Lac du Bonnet pink granite and Creighton granite) and field scale (Mine-By tunnel and Creighton pillar). The model proved to be robust on the laboratory scale and described the rock's relevant macro-properties in conventional tests: crack initiation stress, crack damage stress, simple and triaxial compression strength, tensile strength, Young's modulus and Poisson's ratio. The calibrated laboratory model served as the basis for a sensitivity study that analyzed how micro-properties influence macroscopic responses, thus generating a calibration methodology for Brazilian and UCS tests. On a field scale, the model represented the mass deterioration process explicitly, captured the rupture geometry, and the excavations' convergence displacements. The real case studies supported the use of CVBM for parametric studies that sought to assess the influence of discontinuity families on deep underground works' behaviour. It was found that the presence of discontinuities tends to promote stress relief due to shear. Consequently, discontinuities in the mass with high in situ stresses tend to favour excavation stability. Such results show the CVBM's potential for modelling the behaviour of underground works with high field stress.
... However, with increasing deviatoric stress, and as yield starts to occur and micro-cracks accumulate and coalesce, shearing becomes dominant (Diederichs 2007), making Voronoi GBMs advantageous for simulating brittle fracturing. Many studies have shown the ability of these GBM methods to capture the progressive fracturing and failure behaviour of different rock types due to mechanical loading over a range of stresses within the brittle field (Christianson et al. 2006;Gao and Stead 2014;Damjanac et al. 2007;Stavrou and Murphy 2018;Farahmand 2017). ...
Thermo-mechanical loading can occur in numerous engineering geological environments, from both natural and anthropogenic sources. Different minerals and micro-defects in rock cause heterogeneity at a grain scale, affecting the mechanical and thermal properties of the material. Changes in strength and stiffness can occur from exposure to elevated temperatures, with the accumulation of localised stresses resulting in thermally induced micro-cracking within the rock. In this study we investigated thermal micro-cracking at a grain scale through both laboratory experiments and their numerical simulations. We performed laboratory triaxial experiments on specimens of fine-grained sandstone at a confining pressure of 5 MPa and room temperature (20 ∘ C ), as well as heating to 50 ∘ C , 75 ∘ C and 100 ∘ C prior to mechanical loading. The laboratory experiments were then replicated using discrete element method simulations. The geometry and granular structure of the sandstone was replicated using a Voronoi tessellation scheme to produce a grain based model. Strength and stiffness properties of the Voronoi contacts were calibrated to the laboratory specimens. Grain scale thermal properties were applied to the grain based models according to mineral percentages obtained from quantitative X-ray diffraction analysis on laboratory specimens. Thermo-mechanically coupled modelling was then undertaken to reproduce the thermal loading rates used in the laboratory, before applying a mechanical load in the models until failure. Laboratory results show a reduction of up to 15% peak strength with increasing thermal loading between room temperature and 100 ∘ C , and micro-structural analysis shows the development of thermally induced micro-cracking in laboratory specimens. The mechanical numerical simulations calibrate well with the laboratory results, and introducing coupled thermal loading to the simulations shows the development of localised stresses within the models, leading to the formation of thermally induced micro-cracks and strength reduction upon mechanical loading.
... Os polígonos Voronoi precisam ser pequenos o suficiente para que não sejam formadas regiões preferenciais de ruptura [2]. Com isso em mente e levando-se em conta o custo computacional da simulação, definiu-se um mosaico Voronoi com comprimento médio de juntas igual a 7,5 cm. ...
This work presents a new numerical approach, called Continuum Voronoi Block Model. This tool aims to represent the rupture process in underground works, and it simulates the rock mass by a set of blocks, formed by a Voronoi mosaic, joined at their interfaces by Godman's elements. For validate the tool, the Mine-By tunnel was numerically simulated. The model captured the excavation's v-notch and also explicitly simulated the spalling process. These results show the Continuum Voronoi Block Model's potential to predict the behaviour of excavations with high field stress.
... Rock parameters are the same as those listed in Table 1 and No. 2 rock blasting emulsion explosive is used. As verified in the previous publication [31][32][33], the material model * MAT_HIG H_EXPLOSIVE_BURN embedded in LS-DYNA can be used, and the JWL equation of state is selected and used to describe the state of stress variation under dynamic and static combined loads. e detailed parameters are listed in Table 2. ...
With the progress of deep mining in mine exploitation, the effect of the in situ stress field plays a more and more significant and crucial role in rock blasting. To uncover the impact of in situ stress field on empty-hole effect during parallel-hole cutting, the distribution and the trend of changes in dynamic stress around empty hole during blasting under different in situ stress conditions are simulated based on the basic model for parallel-hole cutting using 3D finite element analysis software ANSYS/LS-DYNA and implicit-explicit analysis method. Subsequently, the law of variation in the empty-hole effect under different in situ stress conditions is determined, and the effects of horizontal and vertical stress fields are analyzed in detail. The simulation results show that the overall increase in in situ stress can facilitate compressive failure and inhibit tensile failure in the rock mass around an empty hole during blasting. When empty holes are arranged horizontally, the effect of the vertical stress field is consistent with that of the in situ stress field, while the effect of the horizontal stress field is opposite to that of the in situ stress field. With the increased stress, the inhibitive effect of the vertical stress field on tensile stress around an empty hole is remarkably stronger than that of the horizontal stress field. Finally, the numerically simulated results are verified by the theoretical calculation. This study can provide new insight and a simple but accurate numerical simulation method to investigate how the in situ stress field affects the empty-hole effect, especially in deep mining.
... Field-scale models have historically used block sizes ranging from 6.5 cm to 50 cm. 20,22,24,26,59 Generally, BBM responses are dependent on the block size chosen, but for sufficiently small block sizes (such as that used in this study), changes in block size on the order of ~20% or less tend to not have much effect on the model response. 60 For all three pillar geometries, the width of the pillar was set to 8 m and the height was varied to achieve the target W/H ratio. ...
In this study, Bonded Block Models (BBMs) are used to investigate the pillar damage mechanisms and rock-support interaction in massive-to-sparsely-fractured rockmasses. Hypothetical granite pillar models of width-to-height (W/H) ratio of 1, 2 and 3 are developed, and the input parameters are constrained by matching the stress-strain response of the BBMs to the stress-strain curves from FLAC3D models that were
previously calibrated to an empirical pillar strength database. Two different block representations are also considered – elastic and inelastic. It was found that inelastic blocks are necessary to capture the behavioral transition from strain-softening to pseudo-ductile with increase in pillar W/H. Post-calibration, different rockbolt combinations are tested in the BBM and their influence on the pillar strength and lateral deformations are analyzed. It was found that as the support density is increased, the peak pillar strengths
also increase but the effect is dependent on the W/H. Deformation of the outer stress-fractured region and bulking systematically decreased with increasing support density, but the exact trend evolved as the pillars were loaded to various points on their stress-strain curves. Lastly, a BBM pillar was developed with explicit intra-block fracturing capability (i.e., individual blocks could break) and the support analysis was repeated.
The goal was to understand if the continuum representation of damage within the inelastic blocks led to some underestimation of the rock-support interaction mechanism. It was ultimately concluded that the continuum inelastic representation of smaller-scale damage within individual blocks allows for a more appropriate representation of the rock-support interaction than the explicit intra-block representation.
... Polyhedral shaped DEM particles directly address this shortcoming allowing for densely packed rock bodies using trigons [23], tetrahedrons [21] and Voronoi tessellations [17,22,24], albeit at a higher computational cost, thus limiting the number of particles to be considered. To circumvent the computational cost, a hybrid spheropolyhedron approach represents polyhedrons as spherical particles at the vertices have been proposed [19]. ...
The Discrete Element Method (DEM) is increasingly used to study the failure behavior of rock. Despite DEM's intrinsic capability to capture the mechanical behavior of discontinua, there remains several open questions that include the numerical modelling of the meso-fracture evolution and behavior of brittle rock bodies. A Cohesive Fracture Model (CFM) designed explicitly for polyhedral shaped DEM particles is proposed for the simulation of the fracture and behavior of brittle rock bodies. A rock body is discretized into a series of rigid polyhedral blocks which are bonded along the boundary faces along the normal and shear directions. A cohesive criterion dictates the normal and shear break strengths of the bonds for the CFM. The computational efficiency of the CFM for poly-hedral shaped DEM simulations is enhanced by parallelization over multiple graphical processing units (GPUs) in the Blaze-DEM framework. A series of numerical and laboratory tests are conducted. For marble, these include three-point bending and uniaxial tests to investigate the relationship between the meso-mechanical parameters and macro-mechanical behavior. Following a sensitivity analysis of the meso-mechanical parameters, an inversion procedure is established to estimate the numerical meso-mechanical parameters of the CFM model. Two different failure modes for different rocks are proposed.
... However, Lorig and Cundall (1989) showed that Voronoi tessellation could allow the micro-structure of rock to be represented, with the development of micro-cracks occurring when the stress level at Voronoi block contacts exceeds a predefined threshold. Many studies have since shown the ability of these grain based modelling (GBM) methods to capture the progressive fracturing and failure behaviour of different rock types due to mechanical loading over a range of stresses within the brittle field (Christianson et al., 2006;Gao and Stead, 2014;Damjanac et al., 2007;Stavrou and Murphy, 2018;Farahmand, 2017). DEM GBMs have also proven to be a useful tool to scale the mechanical behaviour of intact rock at the laboratory scale to the behaviour of rock blocks at an engineering scale (Stavrou and Murphy, 2018;Stavrou et al., 2019). ...
Thermo-mechanical loading can occur in numerous engineering geological environments, from both natural and anthropogenic sources. Different minerals and micro-defects in rock cause heterogeneity at a grain scale, affecting the mechanical and thermal properties of the material. Changes in strength and stiffness can occur from exposure to elevated temperatures, with the accumulation of localised stresses resulting in thermally induced micro-cracking within the rock. In this study we investigated thermal micro-cracking at a grain scale through both laboratory experiments and their numerical simulations. We performed laboratory triaxial experiments on specimens of fine grain sandstone at a confining pressure of 5MPa and room temperature (20°C), as well as heating to 50°C, 75°C and 100°C prior to mechanical loading. The laboratory experiments were then replicated using discrete element method simulations. The geometry and granular structure of the sandstone was replicated using a Voronoi tessellation scheme to produce a grain based model. Strength and stiffness properties of the Voronoi contacts were calibrated to the laboratory specimens. Grain scale thermal properties were applied to the grain based models according to mineral percentages obtained from quantitative X-ray diffraction analysis on laboratory specimens. Thermo-mechanically coupled modelling was then undertaken to reproduce the thermal loading rates used in the laboratory, before applying a mechanical load in the models until failure. Laboratory results show a reduction of up to 15% peak strength with increasing thermal loading between room temperature and 100°C, and microstructural analysis shows the development of thermally induced micro-cracking in laboratory specimens. The mechanical numerical simulations calibrate well with the laboratory results, and introducing coupled thermal loading to the simulations shows the development of localised stresses within the models, leading to the formation of thermally induced micro-cracks and strength reduction upon mechanical loading. Subsequently the potential for up-scaling the results for inclusion in future engineering design is discussed.
... To simulate the extensile crack opening forces at the micro-scale in DEM models, the rigid or deformable particles are approximated by simple geometries. The three commonly used geometries are disks (spheres in 3D), (Potyondy & Cundall 2004;Scholtès & Donzé 2013), Voronoi grains (Damjanac et al. 2007), and triangles (tetrahedra in 3D), (Gao & Stead 2014). The geometry of the particles plays a key role in the generation of the crack extension and shearing forces acting on the sliding fractures. ...
... Although some other numerical studies did not include the scale effect in terms of specimen size, the influence of size was considered indirectly by simulating pre-existing defects of different intensities within single laboratory or rock block scale samples. Damjanac et al. (2007) tested in UDEC and PFC large-size GBMs of the Lithophysal Tuff to supplement existing laboratory data and to investigate the variability of mechanical properties as a function of lithophysal porosity. Material heterogeneity was represented explicitly within the models in the form of lithophysal cavities and a strength-deformability decreasing effect was captured with increased porosity due to an increasing tendency for axial splitting. ...
Micro-discrete fracture networks (μDFNs) have been integrated into grain-based models (GBMs) within the numerical software UDEC to assess rock block strength through a series of unconfined compressive strength (UCS) tests of progressively larger in size numerical specimens. GBMs were generated by utilizing a Voronoi tessellation scheme to capture the crack evolution processes within the intact rock material, and μDFNs were separately created and embedded into the GBMs to simulate the effect of pre-existing defects. Various μDFNs realisations were generated stochastically within the software FracMan to assess the combined impact of defect intensity, persistence, strength and specimen size. The resulting synthetic rock block (SRB) models were used to assess the “flawed” material strength at block scale through a rigorous sensitivity numerical analysis. The acquired results predict a progressive strength reduction with decreasing intact rock quality and certain trends are captured when rock block strength is expressed as a function of a newly proposed “Defect Intensity × Persistence” (DIP) factor. This allow us to standardise the data along specific strength reduction envelopes and to propose generic relationships that cover a wide range of defect geometrical combinations, defect strengths and sample sizes. Accordingly, an attempt is undertaken to refine two existing empirical approaches that consider the effect of scale and micro-defects explicitly for predicting the UCS of rock blocks.
... A discrete element (DEM) rock mass model ( Figure 2) was developed using the Universal Distinct Element Code (UDEC) version 6 (Itasca 2015). The basic approach has previously been used by Damjanac et al. (2007) for simulating earthquake damage to idealised emplacement drifts for an underground nuclear repository. The rock mass model has the capability to: (1) fail and deform in a ductile manner when under high confining stress, (2) fail and deform in a brittle manner when under low confining stress, (3) fracture and allow discrete rock blocks to detach from the intact rock mass under both static and dynamic loading conditions, and (4) transmit elastic waves with minimal distortion. ...
Rockbursts are a serious hazard to workers in deep and high stress mines. Researchers with the National Institute for Occupational Safety and Health, Spokane Mining Research Division in Spokane, Washington, United States of America are using fully dynamic numerical modelling software to investigate rock fracture, ejection, and ground support demand in underground mine openings resulting from strong ground motion induced by a remote seismic source. In this study, a discrete element model of a typical metal mine drift supported by grouted rockbolts was subjected to seismic loading from a remote source. A parameter study was performed with respect to the ground motion by varying the peak particle velocity and frequency content of the input waveform. For each modelled seismic event, the resulting energy demand on the ground support is calculated. Other parameters-peak particle acceleration, duration, and radiated seismic energy-are considered implicitly. The results of this work provide insight into seismic loading of excavations and ground support and may partially explain why, in some cases, peak particle velocity does not correlate well with observed damage. Better understanding of the effects of seismic loading on excavations may lead to developments that improve the safety of workers in underground mines. 1 Introduction Rockbursting is a major challenge in mining ground control. Although not all rockbursts cause damage, and fortunately even fewer result in injury or fatality to underground workers, the economic and human consequences of a rockburst can be severe. There has been a considerable volume of rockburst research in recent decades. This work has focused primarily on dynamic mechanical and blast testing of ground support components and empirical observation of rockbursts and mining seismicity. Although this important work provides real world data, there have been few geomechanics based studies. While mechanical tests are useful for determining relative energy capacities of ground support components, the loads applied in these tests are significantly different than those of real rockbursts. Further, the complex interactions between seismic waves, excavations, and ground support cannot be studied with these tests. Underground blast tests are conceptually more relatable to rockbursts, but the induced loads still differ significantly. Blast tests are also difficult to repeat and costly to perform. Empirical studies lend themselves to regression analyses of large databases that can yield great insight but are based solely on experience rather than the fundamental underlying mechanics. Until recently, fully dynamic discrete element modelling codes were not readily accessible and computing times required to run models with hundreds or thousands of discrete elements would have been unreasonable (even by research standards). This is no longer the case, and to advance understanding of rockbursting and dynamic ground support, fully-dynamic numerical modelling should play a larger role in research.
... Especially most of stability analysis for Silo in SFR 1 is outdated without due consideration of new monitoring data, and no predictive modelling has been made for the mechanical stability of SFR 3. Numerical modelling for predictive analyses can provide valuable insight into the long-term behaviour of underground cavern. Systematic case studies are available in Canada and USA (Kemeny, 2005;Damjanac et al., 2007;Itasca, 2011). Because the rock chambers in SFR 3 are planned to be directed toward North-East direction which is almost perpendicular to the direction of major horizontal stress, its effect needs to be evaluated as well. ...
This report has been developed as part of the initial review phase of the extension of
the SFR facility. It focuses on the properties of the bentonite components of the
SFR facility and their contribution to the performance and safety of the repository.
The objective has been to identify the usage of bentonite in different parts of the
repository, and to preliminarily comment on the scientific soundness and overall
quality of SKB’s reporting. Moreover the aim has been to review the evolution of
geochemical and geomechanical properties of bentonite, as well as their impact on
the long-term safety of the repository. Finally, potential bentonite-related issues that
need to be addressed by SKB are proposed, as well as bentonite-related issues that
are of importance and need to be focused on during the main review phase. Based on
the reviews conducted during this initial review task, it appears that SKB has
undertaken and documented a highly competent and systematic safety assessment
for the SFR. SKB’s documentation safety assessment is generally well structured
and well written, and it seems to cover the necessary areas. The documentation also
appears to be generally transparent and traceable to underlying references, although
this aspect has not been tested extensively during this review task. Assessing the
scientific soundness of the many and various studies that underlie the safety
assessment will need to be a part of the main review. SKB’s technical solutions for
the disposal of the wastes are mature in the sense that SFR already exists and has
been operating safely for a number of years. There is still a need though for SKB to
demonstrate that the engineered barriers can be installed as designed under realistic
conditions underground. SKB’s assessment methodology has been developing for
over a decade and has been applied in several safety assessments for different waste
types (e.g. spent fuel, low and intermediate level radioactive wastes). The
assessment methodology is regarded as appropriate, but SSM may wish to request
further information to supplement the safety assessment.
... С е т е в о е п е р и о д и ч е с к о е н а у ч н о е и з д а н и е Используемые в модели зависимости аналогичны зависимостям, представленным в работах [6,7]. В общем виде схема выполнения вычислений с акцентом на схеме снижения прочности со временем показана на рис. 3. ...
С использованием ПК PROROCK выполнены расчеты деформаций группы уступов с различными горнотехническими и структурно-геологическими условиями. Возможность явного моделирования трещинообразования и разрушения, реализованная в данном программном комплексе, позволяет проследить образование тела обрушения, закономерности его формирования в зависимости от направления падения систем
трещин.
Модели групп уступов отличаются углами заоткоски и углами наклона систем трещин. Рассмотрено три варианта углов откосов и углов наклона систем трещин, расчеты выполнены
для девяти моделей. Прочностные свойства пород в моделях заданы как функция времени и напряженного состояния, то есть учитывается длительная прочность горных пород.
Анализ результатов расчетов показал наличие зависимости направления смещений как от угла падения трещин, так и от угла наклона участка борта карьера. Сделан вывод, что по направлениям смещений можно оценить степень опасности наблюдаемых деформаций. По результатам моделирования возможен прогноз контуров
и объема потенциального тела обрушения с учетом структурно-геологических условий, определяются предельные величины смещений, после достижения которых начинается стадия прогрессирующего разрушения борта.
... Any tessellation style serves as only a structure generator in UDEC rather than aims to alter the element geometry as is the purpose of PFC-GBM. Most GBMs have been so far implemented using UDEC (Christianson et al., 2006;Damjanac et al., 2007;Nicksiar and Martin, 2014;Mayer and Stead, 2017). The 3DEC-GBM (with only unbreakable grains) has been realized (Lan et al., 2013;Ghazvinian et al., 2014), while the PFC-GBM stagnates at the 2D level (Peng et al., 2017). ...
... On the other hand, large-scale in situ tests of porous rock masses are economically costly and generally impractical in reality at present [1][2][3][4][5]. Lithophysal tuff and poorly cemented coarse sandstone are two representative rocks mass containing macroporosity, as shown in Fig. 1 [6][7][8]. As in laboratory research it is difficult to control the specific location and size of the pores of the natural rocks, the rock containing multiple holes is normally sampled artificially (Fig. 2) [9,10]. ...
Discrete element method (DEM) has been extensively used for studying the properties of rock mass through numerical simulation, which includes bonded particle (or grain) model method (BPM) and discrete fracture network method. In this paper, utilization of BPM for modeling uniaxial compressive strength (UCS) of lithophysal rock is explored and associated stages are discussed and calibrated including generation of particles, sample scale, loading method, macro- and micro-parameters of BPM. In order to investigate the impacts of pore size and distribution of lithophysal tuff on UCS, various combinations of different pore sizes in one sample and different pore locations with the same pore size are simulated using BPM-DEM. The simulation results show that UCS significantly decreases due to the existence of pores with the same condition of porosity, and when the pore radii increase, the minimum value of UCS slightly declines. Moreover, combinations of different pore sizes in one sample show that greater proportion of small pore radii increases UCS of the sample, while the differences of UCS values decrease. Meanwhile, associated fracture has been observed to develop along the pore and generally tends to develop along the large pores at the edge of the sample in the process of uniaxial compression simulation, with relatively small associated UCS values.
... Naturally, discrete modeling techniques provide the most accurate description of discontinuous materials (Riahi and Curran 2009). Numerical experiments using discontinuum techniques provide significant insight and understanding into rock mechanics processes that are difficult to test in the laboratory (Fairhurst et al. 2006;Damjanac et al. 2007;Gao and Stead 2014). Within this paper, a discontinuum model of a rock mass that is modeled at a size comparable to or above the representative elemental volume (REV) is considered to be the most accurate representation of the strength and deformation response of the sample. ...
Anisotropic rock masses, the behavior of which is dominated by closely spaced planes of weakness, present particular difficulties in rock engineering analyses. The orientation of discontinuities relative to an excavation face has a significant influence on the behavioral response. At the present time, discontinuum modeling techniques provide the most rigorous analyses of the deformation and failure processes of anisotropic rock masses. However, due to their computational efficiency continuum analyses are routinely used to represent laminated materials through the implementation of a Ubiquitous-Joint model. The problem with Ubiquitous-Joint models is that they do not consider the effects of joint spacing, length and stiffness. As such, without an understanding of the limitations of the modeling approach and detailed calibration of the material response, simulation results can be misleading. This paper provides a framework to select and validate ubiquitous-joint constitutive properties.
... The simplified convergenceconfinement approach considers the degradation of the rock mass and concrete separately. Damjanac et al. (2007) outlined the degradation behavior of the tunnels in a discontinuum material model that was developed to represent the drift-scale rock mass properties in which slip and separation of contacting rock blocks is estimated. Two-dimensional analyses, based on the distinct element method, were developed with the consideration of in-situ thermal and seismic loads as well as time-dependent degradation. ...
The underground transit system of the Paris metro was built in the early 20th century. Many tunnels and galleries of this underground system were constructed with old masonry whose properties have changed with time and increasing use, and its strength may have deteriorated under the impact of several weathering factors. Therefore, research has been initiated to diagnose structural deterioration of the tunnels and galleries used by the Paris metro system. This paper outlines the current state of the metro galleries in which cracks have developed in the tunnel lining caused by degradation of the abutment materials. The initial state of the stresses applied to the structure immediately after the construction is also analyzed through a double comparison (analytical–numerical and numerical 2D–3D). Then the damage of the galleries is modeled by taking into account the effect of the tunnel linings’ reduced strength. By means of an equivalent homogeneous model and a strain-softening approach, deformations associated with crack appearance can be located. The numerical results show that the state of different components of the underground structure during the lifetime of the galleries can be assessed.
... UDEC has been utilized to mimic progressive fall of roadway and longwall mining (Alejano et al., 2008;Vakili and Hebblewhite, 2010), but the limitation of this model is that it only allows fracture development along pre-defined discontinuities. To overcome this limitation, the UDEC-Voronoi approach was adopted (Chen et al., 2015;Damjanac et al., 2007;. This approach has been modified to solve discrepancies between simulations and field observations or laboratory tests . ...
Progressive failure of roadway roofs is a common failure mechanism in underground coal mines, especially when water-rich roofs are in close proximity to the roadway. In this case study at a Chinese coal mine, the UDEC-Voronoi method was used to investigate the process of progressive roof failure in a wide coal roadway from water-rich roofs. In the numerical scheme, the studied domain was partitioned into polygonal blocks bonded through contacts with pre-defined dimensions. The parameters of polygons and contacts in the Voronoi program were calibrated to rock mass properties obtained through laboratory tests. Based upon laboratory tests and previous research findings, a time-dependent strength degradation process from water absorption was assumed and implemented in the numerical modeling. Next, the progressive failure of a roadway from water-rich roofs was analyzed in detail. The numerical results agreed well with field measurements and observations. This method was demonstrated to reproduce the real phenomenon of roof failure in all of its complexity. The numerical results revealed that the progressive failure mechanism was characterized by an initial fracturing of the roof due to strength degradation, which was followed by significant dilation as fractures grew. The large span of the roadway further contributed to the roof failure process. The results also clearly showed that shear cracks were predominant in the roof and played a major role in the behavior of the roadway roof. Additionally, support and excavation schemes that affect roof stability were observed.
... Attempts to overcome the limitations of bonded particle models have included use of multi-faceted bonded blocks in place of circular/spherical particles. In 2D, numerical experiments using UDEC showed promising results (Damjanac et al. 2007;Gao 2013;Lan et al. 2010;Nicksiar and Martin 2014). In 3D, models based on bonded tetrahedral blocks were used with some success by Gao (2013) to model compression experiments on coal specimens and by Garza-Cruz et al. (2014) to create SRM-type models to replicate rock spalling in underground drifts. ...
Synthetic rock mass (SRM) modelling, based on bonded particle models (BPM), has been successfully used to model jointed and veined rock. BPM models, however, have significant limitations in simulating some key elements of the behaviour of intact rock. In particular, BPMs have difficulties in reproducing the compressive to tensile strength ratio and determining the angle of internal friction characteristic of typical hard rock specimens. Use of bonded block models (BBM), where angular blocks are used in place of spherical particles in BPM, demonstrated improvements in modelling the behaviour of intact rock. However, SRM-style models using BBM have been only used on a limited basis to model foliated and veined rock. In previous applications the BBM based models lacked use of discrete fracture networks which are key in SRM simulations. This paper reports on an original application of bonded block SRM for modelling of intact veined rock and presents the developed methodology for SRM modelling of intact veined rock based on BBM. It has been demonstrated that that BBM models of intact rock are an improvement over modelling of intact rock using BPM. Finally, this paper presents the results of BBM SRM numerical simulations of compressive experiments on intact veined rock under a series of confining pressures.
... Compared to other discrete element modelling approaches, e.g. the particle-based synthetic rock mass approach (Mas Ivars et al. 2011) and the grain-based Voronoi tessellation method (Damjanaca et al. 2007;Ghazvinian et al. 2014), the FEMDEM model is able to capture the realistic fracturing behaviour of brittle rocks governed by fundamental fracture mechanics principles associated with strength and fracture energy parameters. A detailed review about the FEMDEM method and various other discrete modelling techniques can be found in the paper by Lisjak and Grasselli (2014). ...
An empirical joint constitutive model (JCM) that captures the rough wall interaction behaviour of individual fractures associated with roughness characteristics observed in laboratory experiments is combined with the solid mechanical model of the finite-discrete element method (FEMDEM). The combined JCM-FEMDEM formulation gives realistic fracture behaviour with respect to shear strength, normal closure, and shear dilatancy and includes the recognition of fracture length influence as seen in experiments. The validity of the numerical model is demonstrated by a comparison with the experimentally established empirical solutions. A 2D plane strain geomechanical simulation is conducted using an outcrop-based naturally fractured rock model with far-field stresses loaded in two consecutive phases, i.e. take-up of isotropic stresses and imposition of two deviatoric stress conditions. The modelled behaviour of natural fractures in response to various stress conditions illustrates a range of realistic behaviour including closure, opening, shearing, dilatancy, and new crack propagation. With the increase in stress ratio, significant deformation enhancement occurs in the vicinity of fracture tips, intersections, and bends, where large apertures can be generated. The JCM-FEMDEM model is also compared with conventional approaches that neglect the scale dependency of joint properties or the roughness-induced additional frictional resistance. The results of this paper have important implications for understanding the geomechanical behaviour of fractured rocks in various engineering activities.
... As a result, the overall stiffness of the rockmass is a function of the stiffness of the joints and the stiffness of the intact rock beams forming between these joints. The value of the normal stiffness assigned to the joints is required to be scaled based on the spacing between joints (S j ) and Young's modulus of the intact beams (E i ) in a way that equivalent overall stiffness of this combined system represents the Young's modulus of the rockmass (E rm ) ( Damjanac et al., 2007;Perras, 2014). The Young's modulus of the rockmass can be estimated using the empirical Hoek-Diederichs equation (Eq. ...
Although it is recognized that the peak strength of the rock is a unique function of confining stress minus pore pressure (σ3 – P), examples of laboratory or numerical studies that focused on investigating the effects of pore pressure on weakening or strengthening the crack damage (CD) stress has received less attention. The objective of this study is to examine, and gain a better insight into the capability of the Grain-based Discrete Element Method (GDEM) approach in mimicking the effect of pore pressure in weakening the peak strength, crack damage threshold (CD) threshold of material. A cohesive crack-based UDEC-Voronoi code is generated considering the real mineral heterogeneity of a crystalline rock. The hydraulic and mechanical properties of the micro-constituents of the model is calibrated. The compressibility and Biot coefficient of the material is determined by applying hydrostatic stress on a square sample. The simulation results demonstrate that like the peak strength, crack damage threshold also follows the “Terzaghi's effective stress law”. The modeling approach is able to evaluate the Biot coefficient of the crystalline rock based on its derived drained and solid matrix bulk moduli.
... However, UDEC-GBM element generation typically does not take into consideration the underlying spatial structure of the grains, nor their shape, despite thin-section analysis suggesting that grain distributions display spatially heterogeneous behaviour (Oren and Bakke 2003;Okabe and Blunt 2005;Okabe and Blunt 2007;Politis et al. 2008;Méndez-Venegas and Díaz-Viera 2014). The incorporation of such heterogeneities has been shown to cause increased asymmetry in the strain distribution, resulting in alteration of the macro-scale output behaviour (Cho et al. 2007;Damjanac et al. 2007;Lorig 2009;Jefferies et al. 2008;Lan et al. 2010;Srivastava 2012;Nicksiar and Martin 2014). This strain accumulation results in a fundamental change in the output uncertainty due to spatial data aggregation issues (Gehlke and Biehl 1934;Isaaks and Srivastava 1989;Deutsch 2002;Haining 2003). ...
Uncertainty analysis remains at the forefront of geotechnical design, due to the predictive nature of the applied discipline. Designs must be analysed within a reliability-based framework, such that inherent risks are demonstrated to decision makers. This research explores this paradigm in three important areas of geotechnical design; namely, continuum, Discrete Fracture Network (DFN) and discontinuum modelling. Continuum modelling examined the negative effects of ignoring spatial heterogeneity on model prediction. This was conducted through the stochastic modelling of spatial heterogeneities found within a large open pit mine slope. DFN analysis introduced a novel approach to fracture generation to solve issues associated with the incorporation of traditional DFNs into geomechanical simulation models. Finally, discontinuum modelling explored the inherent mesh dependencies that exist in UDEC grain boundary models (UDEC-GBM). Conclusions suggest that a transition is required from deterministic to uncertainty based design practices within the geotechnical discipline.
... Brittle fracture failure of the intact rock block is modeled by Voronoi block approximation Fairhurst 2010, Damjanac et al. 2007). Voronoi tessellation is a micromechanical model in which brittle rock is represented as an assembly of relatively small polygonal blocks (Damjanac et al. 2007). The Voronoi model is formed by ubiquitous, randomly distributed, and oriented joints with relatively short edges. ...
A computational methodology is presented to model an erosion damage mechanism by simulating both the high velocity water jet and geomechanical behavior of the rock mass. The erosive capacity of water is addressed by computational fluid dynamics simulation of the flow and turbulence to generate transient water pressure. The resistive capacity of the rock is addressed by dynamic discontinuum modeling of the jointed rock subjected to hydrodynamic forces obtained from the flow analysis. The discontinuum approach presented in this paper models the rock block ejection and brittle fracture of blocks explicitly without assuming any specific failure mode. The numerical approach allows multiple full-scale flow and geomechanical analyses providing advantages over existing empirical-based approaches, reducing dependence on hydraulic model studies, and aiding in mitigation design (e.g., rock bolts and rock anchors). The Kariba Dam plunge pool erosion is used as an example to demonstrate the capability of the methodology.
This chapter introduces the mathematical formulations, numerical models and solution schemes used throughout the book. The discrete and distinct element methods are introduced and defined. The calculation cycle, including equations of motion for grid points and constitutive models for zones and contact, are explained. The differential and discrete forms of the equations of motion are presented. The contact detection is an important part of the discrete element codes. The algorithm used for three-dimensional polygonal blocks is briefly described. The bonded particle model is a novel approach for simulation of deformation and damage of massive, brittle rocks used in a number of examples presented in the book. Some of challenges of calibration of the bonded particle model, including the calibration scaling laws, are discussed. The lattice, a simplified version of the bonded particle model, offers greater computational speed in implementation of the discrete element method without sacrifice of important mechanics. The fluid mechanics concepts important and used in coupled hydro-mechanical processes in fractured and granular media are presented at the end of the chapter.
As underground mining operations move deeper and the stresses encountered become more adverse, mine pillars are experiencing increased stress-induced damage and rock mass bulking. This has led to significant challenges in designing effective support systems, leading to costly mine development, production delays and support maintenance and rehabilitation requirements. Efforts to assess rock mass bulking have relied almost exclusively on the use of continuum modelling techniques, employing plasticity theory to predict the depth of brittle failure and associated post-yield deformations. However, rock mass bulking in high stress environments is largely driven by brittle fracturing resulting in geometric dilation, which involves shearing and buckling of spalled rock pieces as they deform into the excavation. Continuum techniques are inherently limited in their ability to model this behavior. This paper presents the results of research investigating the application of discontinuum-based numerical modelling techniques for assessing rock mass spalling and bulking in highly stressed pillars. The 3-D distinct-element program 3DEC is used to develop a bonded block modelling approach, referred to here as 3DEC-BBM. The method developed allows for the explicit modelling of brittle fracturing, spalling and geometric bulking, and the corresponding support responses, in reaction to the simulation of different mine stress paths and operation scenarios. Several different support strategies are investigated to test their effectiveness as a means to improve displacement-based support design in highly stressed pillars. These are based on the simulation of an extraction-level drawpoint pillar for a block cave mining operation that is exposed to the abutment stresses from an undercut passing over it. Based on the results, three key findings are presented and discussed: (1) Adding a small support pressure has a significant impact on the performance of the pillar. However, the benefits gained by further increasing this pressure diminish and have a less dramatic impact on spalling damage and bulking with increasing effort. (2) It is crucial to install appropriate support before the undercut passes over the extraction level pillars. The depth of damage and amount of bulking can increase significantly during pillar unloading following passing of the undercut. Extra confinement applied to the failed pillar skin allows it to carry more load and thus provide more confinement to the pillar core, helping to limit further damage and bulking. (3) The addition of support pressure through shotcrete and rock bolting performs similarly to “perfectly” installed steel sets. Thus, a heavier support system will not necessarily result in better pillar performance.
Rib spalling is a major hazard in the mining industry and in absence of coal rib support guidelines, accidents have continued to occur in recent years. Developing effective support guidelines requires a complete understanding of pillar damage mechanisms as well as the rock-support interaction mechanism. Bonded Block Models (BBMs) represent a convenient tool for this purpose, as they can reproduce the rock fracturing process reasonably well, but it is not known whether this modeling technique can quantitatively replicate the impact of reinforcement (bolts) on otherwise unsupported ground. To bridge this gap in research, we employed the BBM approach to simulate the behavior of a supported coal pillar rib located in a longwall mine in Australia. This case study presents a unique opportunity in that two otherwise identical chain pillars with different support densities adjacent to one another were instrumented. After calibrating a model against displacement and stress measurements made over the course of mining in one pillar, the support in the calibrated BBM was modified to match that of the adjacent chain pillar. This model could predict the rib displacement to within 6 mm of what was measured insitu. Given the ability of the BBM to match field-measured displacements and stresses and also field observations for varying support densities, it seems that such a model has the potential to aid in the development of a support design tool. Lastly, the effect of block shape was investigated by replacing the elongated blocks with isotropic polygonal blocks. This model could not reproduce the ground-support interaction very well, likely due to the inaccurate geometric representation of an anisotropic rock like coal.
The mechanical characteristics of sedimentary rocks, such as carbonates, are highly sensitive to the influence of water. In carbonate-rich regions, rock failures induced by water corrosion have been widely reported, such as the collapse of cliffs and rockslides. In this study, a 2D model was built to investigate the time-dependent strength degradation of carbonate rocks under the influence of water. First, degradation laws for two types of bonds were derived based on the different behaviors of depositional and diagenetic cements in water. Then, via developing customized code using the Fish language, the degradation laws were coupled with UDEC to build the numerical procedure. Finally, the ability of the proposed model to reproduce the macroscopic short- and long-term behaviors of carbonate rocks under the influence of water was validated by comparing the numerical results with the lab observations and measurements. The results show that the presented procedure is capable of simulating the strength properties of carbonate rocks submerged in water for different time periods (uncoupled tests), as well as the lifetime (time-to-failure) of rocks in a chemo-mechanically coupled condition.
This paper describes the results of a back analysis of pillar failures at Troy Mine, Montana, and the use of this experience to make forward predictions on pillar stability in the nearby Montanore deposit which lies in a similar geomechanical setting. At Troy Mine, a progression of pillar failures in areas within the Middle Quartzite of the Revett formation led to the observed surface subsidence. The Troy Mine experience was used to understand the level of stresses and failure mechanism leading to the collapse of some pillars in the North Orebody to estimate pillar strength in quartzite beds within Troy’s mountainous terrain. The model elucidated that the dipping orebody geometry in relation to topography led to shear stresses in pillars at Troy Mine. Shear stresses resulted in significant loss of confinement in pillar cores (many theoretically in tension), even at width-to-height ratios that would be deemed stable under zero shear stress (flat seam under flat topography). A calibrated model was achieved, which allowed us to evaluate the impact that different pillar geometric characteristics (such as width, length, height, and shape) have on pillar performance under shear conditions for different depths and extraction ratios. Design charts were then generated to provide guidance on pillar geometry based on expected demand. Mine-wide models were developed to predict the level of vertical stress and horizontal shear stress for pillars in the different ore-bearing beds at Montanore. A sensitivity study was performed for various conditions, including extraction ratio, spatial location under the mountainous terrain, and local orebody geometry with the aim of performing a mine-wide evaluation of the factor of safety against shear. The results of the analyses performed in the present work show that the use of design methods that do not take the effect of shear stresses into account may result in under-designed pillars, while a false impression of rock mass strength could be derived from back analysis.
Grain and contact are the two key components in 3DEC-GBMs (grain-based models) because they control the micro-mechanical behavior and consequently the macro-mechanical behavior of rock. Three types of grains – rigid, elastic, and breakable grains – are considered in this study to explore the influence of grain properties on the mechanical behavior of rock. Equivalent 2D plane strain problems are solved using 3DEC to reduce computation time. A non-uniform distribution of grain size is used to generate numerical models using Neper, a software package for polycrystal generation and meshing. A comprehensive parametric study of properties of contact and grain of the three types of grains is conducted and calibration procedures are suggested for numerical modeling. The modeling results indicate that both the contact and the grain properties affect the macroscopic mechanical behavior of synthetic rock specimens. All the three types of grains produce reasonable results for pre-peak deformation (E and υ) and macroscopic strength (UCS, σt, C and ϕ) parameters. Each grain type has advantages and disadvantages in numerical modeling. Rigid grains cannot produce volumetric strain properly and a near-zero residual friction angle of contact is needed to capture post-peak deformation behavior due to the grain interlocking effect. Elastic grains also need a very low residual friction angle of contact and brittle rock deformation behavior cannot be captured. The complex calibration procedure and long computation time are the main issues of breakable grains, although it simulates well the volumetric strain, does not require a very low contact residual friction angle, and captures brittle rock behaviors better than other two types of grains. The findings from this study are useful for rock failure process simulation using the 3DEC-GBM modeling approach.
This work describes investigation of the long-term strength of marble rocks in a stability assessment of deeply buried Jinping headrace tunnels. First, a series of long-term axial compression tests were conducted, with which the fitted long-term strength curve for marble rocks was determined. Then, Potyondy’s parallel-bonded stress corrosion (PSC) model was used to perform a numerical static fatigue test. The PSC parameters of the marble rocks were back-analyzed based upon the long-term loading tests. Finally, a small-scale Particle Flow Code (PFC)-based model was constructed for a headrace tunnel, and the long-term stability of the modeled tunnel was assessed.
This paper presents a detailed study of the mechanisms contributing to fracture development around river valleys associated with mining operations. Due to the geology and geomorphology of the Southern Coalfield of New South Wales, Australia, non-conventional subsidence effects usually occur. The influences associated with valley closure and upsidence are principally tensile and shear fracturing/cracking of the river and underlying strata, which act as underground flow paths for surface water. This paper explicitly simulates the mining-induced fracture development around the valley structure, utilising a distinct element method modelling technique with Voronoi tessellation. The fracture propagations within intact rock as well as along existing discontinuities are simulated in this study. It is demonstrated that the presence of natural geological discontinuities and the mining-induced stress field play an important role in determining the extent and pattern of fracture propagation. Analysis of the mining-induced explicit fracturing system in the vicinity of valley provides an improved understanding of the near-surface hydrological cycle and enables effective remediation of the mining-induced adverse impacts on river valleys.
В статье описаны наиболее распространенные способы определения предельных параметров деформаций бортов карьеров. Также приведен пример расчета предельных деформаций участка борта карьера методом конечно-дискретных элементов.
This study presents a methodology to reproduce the mechanical behavior of isotropic or transversely isotropic rock using the polygonal grain-based distinct element model. A numerical technique to monitor the evolution of micro-cracks during the simulation was developed in the present study, which enabled us to examine the contribution of tensile cracking and shear cracking to the progressive process of the failure. The numerical results demonstrated good agreement with general observations from rock specimens in terms of the behavior and the evolution of micro-cracks, suggesting the capability of the model to represent the mechanical behavior of rock. We also carried out a parametric study as a fundamental work to examine the relationships between the microscopic properties of the constituents and the macroscopic behavior of the model. Depending on the micro-properties, the model exhibited a variety of responses to the external load in terms of the strength and deformation characteristics. In addition, a numerical technique to reproduce the transversely isotropic rock was suggested and applied to Asan gneiss from Korea. The behavior of the numerical model was in good agreement with the results obtained in the laboratory-scale experiments of the rock.
Samples of Barre granite were creep tested at room temperature at confining pressures up to 2 kbar. The time to fracture increased with decreasing stress difference at every pressure. The time to fracture increased with increasing pressure, even when the stress difference was normalized to account for the increase of strength with pressure. Two theories of static fatigue are shown to explain the data adequately. Both suggest that the activation enthalpy for the stress corrosion process controls the creep rate and increases with pressure. Purely mechanical effects of pressure are not, however, discounted.
A large data base from more than 100 experiments on drillhole core samples of Yucca Mountain silicic tuff has been assembled. These data have been analyzed and empirical expressions were found which relate elastic properties and strength with porosity plus clay content. These relationships are presented here, in addition to an application of simple elastic composite theory to explain the observed variation of bulk modulus with functional porosity. 4 figs.
The time-dependent growth of an axial crack in single-crystal quartz tested in uniaxial compression with a constant load was studied as a function of temperature, T stress σ and partial pressure of water P. The time-dependent growth can be approximated by an equation of the form C − C0 = Atn, where C is crack length. Typically, as any one of the three variables was increased, the rate of crack growth increased. The data were analyzed by comparing the relative times required for two cracks, with the same initial length, to extend an arbitrarily selected increment of 0.20 mm as one of the parameters was varied. The experimental results indicate that the changes in the rate of crack growth due to a variation in any of three variables could be treated independently over the range studied and expressed by where t1 and t2 are the times required for a crack to extend 0.20 mm. The relation between environment-sensitive time-dependent crack growth and creep in brittle rocks is discussed. The increase in the rate of creep strain in rocks due to an increase in temperature or stress is consistent with the explanation of creep in terms of crack growth. The static fatigue of glasses, brittle rocks, and quartz is shown to obey a dependence on stress, temperature, and moisture similar to the time-dependent crack growth in quartz.
Over two hundred fifty mechanical experiments have been run on samples of tuff from Yucca Mountain, Nevada Test Site. Cores from the Topopah Spring, Calico Hills, Bullfrog and Tram tuff units were deformed to collect data for an initial evaluation of mechanical (elastic and strength) properties of the potential horizons for emplacement of commercial nuclear wastes. The experimental conditions ranged in sample saturation from room dry to fully saturated, confining pressure from 0.1 to 20 MPa, pore pressure from 0.1 to 5 MPa, temperature from 23 to 200{sup 0}C, and strain rate from 10{sup -7} to 10{sup -2} s{sup -1}. These test data have been analyzed for variations in elastic and strength properties with changes in test conditions, and to study the effects of bulk-rock characteristics on mechanical properties. In addition to the site-specific data on Yucca Mountain tuff, mechanical test results on silicic tuff from Rainier Mesa, Nevada Test Site, are also discussed. These data both overlap and augment the Yucca Mountain tuff data, allowing more definitive conclusions to be reached, as well as providing data at some test conditions not covered by the site-specific tests.
Sample of Barre granite were subjected to a uniaxial stress equal to 87% of their fracture strength for various lengths of time. Crack growth and development as a function of time under load was studied with the scanning electron microscope. New stress-induced cracks appear to be continuously generated. Average crack lengths increased with time as much or more than they did upon loading, but average crack widths remained relatively unchanged, suggesting that cracks close down to an equilibrium value after the sample has been unloaded. Crack interaction with other cavities seemed to increase in time as the numbers of individual cracks increased, until near the onset of tertiary creep crack coalescence may have become more important than the slow growth of individual cracks. The tensile character of stress-induced cracks and other observatios by Tapponnier and Brace [7] were confirmed. There may be a difference in the mode of crack development between tests at constant stress and tests at constant strain rate. Differences in inelastic strain and acoustic emission generated in the two test types also suggest this.
A numerical model for rock that extends the formulation of the bonded-particle model (BPM) to include time-dependent behavior by adding a damage-rate law to the parallel-bond formulation is described. The BPM represents rock by a dense packing of non-uniform-sized circular or spherical particles that are bonded together at their contact points and whose mechanical behavior is simulated by the distinct-element method using the two- and three-dimensional discontinuum programs PFC2D and PFC3D (Particle Flow Code in 2/3 Dimensions). The extended model is called the parallel-bonded stress corrosion (PSC) model, because it mimics the stress-dependent corrosion reaction that occurs in silicate rocks in the presence of water. Force transmission through rock, and through a BPM, produces many sites of microtension, and it is postulated that stress-corrosion reactions may be occurring at these sites. The stress–corrosion process is implemented by removing bonding material at a specified rate at each parallel bond that is loaded above its micro–activation stress, and the form of the damage-rate law arises from considerations of chemical reaction-rate theory. Global force redistribution occurs throughout the process, and parallel bonds are removed from the system either by breakage (when their strength is exceeded) or by complete bond dissolution. The PSC model parameters can be chosen to match both the static–fatigue curve (time-to-failure versus applied load) and the damage mechanisms and deformation behavior (a creep curve showing primary, secondary and tertiary creep) of Lac du Bonnet granite.
A numerical model for rock is proposed in which the rock is represented by a dense packing of non-uniform-sized circular or spherical particles that are bonded together at their contact points and whose mechanical behavior is simulated by the distinct-element method using the two- and three-dimensional discontinuum programs PFC2D and PFC3D. The microproperties consist of stiffness and strength parameters for the particles and the bonds. Damage is represented explicitly as broken bonds, which form and coalesce into macroscopic fractures when load is applied. The model reproduces many features of rock behavior, including elasticity, fracturing, acoustic emission, damage accumulation producing material anisotropy, hysteresis, dilation, post-peak softening and strength increase with confinement. These behaviors are emergent properties of the model that arise from a relatively simple set of microproperties. A material-genesis procedure and microproperties to represent Lac du Bonnet granite are presented. The behavior of this model is described for two- and three-dimensional biaxial, triaxial and Brazilian tests and for two-dimensional tunnel simulations in which breakout notches form in the region of maximum compressive stress. The sensitivity of the results to microproperties, including particle size, is investigated. Particle size is not a free parameter that only controls resolution; instead, it affects the fracture toughness and thereby influences damage processes (such as notch formation) in which damage localizes at macrofracture tips experiencing extensile loading.
Sixteen creep experiments were performed on welded tuff specimens from the vicinity of Yucca Mountain, NV. The tests were performed under two conditions. One suite of measurements was performed on nominally dry specimens at a confining pressure of 10 MPa, a temperature of 225°C, and differential stresses between 40 and 130 MPa. The second suite of experiments was conducted on water saturated specimens at a confining pressure of 5.0 MPa, a pore pressure of 1.0 MPa, and a temperature of 150°C over a range of differential stresses from 115 to 150 MPa. Six of the specimens tested at 150°C failed in shear. The remaining experiments were terminated after 106 seconds prior to failure. All of the specimens tested showed primary and secondary stages of creep. The secondary creep strain increased as the differential stress was increased. The specimens that failed exhibited a tertiary creep stage. The specimens brought to failure were analyzed in terms of static fatigue. Based on limited data, the time to failure, 〈t〉, is given by an expression of the form 〈t〉=1041 e-0.646 σ where σ is the differential stress applied to the specimen.
This paper outlines rock mechanics investigations associated with mechanical degradation of planned emplacement drifts at Yucca Mountain, which is the designated site for the proposed US high-level nuclear waste repository. The factors leading to drift degradation include stresses from the overburden, stresses induced by the heat released from the emplaced waste, stresses due to seismically related ground motions, and time-dependent strength degradation. The welded tuff emplacement horizon consists of two groups of rock with distinct engineering properties: nonlithophysal units and lithophysal units, based on the relative proportion of lithophysal cavities. The term ‘lithophysal’ refers to hollow, bubble like cavities in volcanic rock that are surrounded by a porous rim formed by fine-grained alkali feldspar, quartz, and other minerals. Lithophysae are typically a few centimeters to a few decimeters in diameter. Part I of the paper concentrates on the generally hard, strong, and fractured nonlithophysal rock. The degradation behavior of the tunnels in the nonlithophysal rock is controlled by the occurrence of keyblocks. A statistically equivalent fracture model was generated based on extensive underground fracture mapping data from the Exploratory Studies Facility at Yucca Mountain. Three-dimensional distinct block analyses, generated with the fracture patterns randomly selected from the fracture model, were developed with the consideration of in situ, thermal, and seismic loads. In this study, field data, laboratory data, and numerical analyses are well integrated to provide a solution for the unique problem of modeling drift degradation.
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