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Paper presented at the ISRM International Symposium - 10th Asian Rock Mechanics Symposium, October 29–November 3, 2018
Paper presented at the ISRM International Symposium - 10th Asian Rock Mechanics Symposium, October 29–November 3, 2018
Paper presented at the ISRM International Symposium - 10th Asian Rock Mechanics Symposium, October 29–November 3, 2018
Paper presented at the ISRM International Symposium - 10th Asian Rock Mechanics Symposium, October 29–November 3, 2018
Paper presented at the ISRM International Symposium - 10th Asian Rock Mechanics Symposium, October 29–November 3, 2018
Paper presented at the ISRM Regional Symposium - 7th Asian Rock Mechanics Symposium, October 15–19, 2012
Paper presented at the ISRM Regional Symposium - 7th Asian Rock Mechanics Symposium, October 15–19, 2012
Paper presented at the ISRM Regional Symposium - 7th Asian Rock Mechanics Symposium, October 15–19, 2012
Paper presented at the ISRM International Symposium - 6th Asian Rock Mechanics Symposium, October 23–27, 2010

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Proceedings Papers

Paper presented at the ISRM International Symposium - 10th Asian Rock Mechanics Symposium, October 29–November 3, 2018

Paper Number: ISRM-ARMS10-2018-007

... wetting deterioration. To examine the failure patterns, the failure

**planes**of all specimens occurred on the foliation**planes**, indicating reasonable failure patterns. 1. Introduction Foliation is a geological structure formed by shearing forces or differential pressure during regional metamorphism...
Abstract

Abstract The tensile strength of rock is an important property of rock engineering. However, the measurement of tensile strength of rock is often overlooked due to difficulties of specimen preparation and accuracy of testing result. This study adopted the pull-off test to measure the foliation tensile strength of metamorphic rock, including slate, green schist and black schist. Compared with contemporary tensile tests, this method is relatively simple and effective, with easy specimen preparation. Besides, this approach can be conducted not only in the laboratory but also in the field, which is quite useful for evaluating the rock slope stability. This study suggested the procedures of sample preparation and testing as well. The test results indicate that the black schist exhibited the greatest tensile strength, and the slate had the lowest strength. Besides, the slate exhibited significant wetting deterioration. To examine the failure patterns, the failure planes of all specimens occurred on the foliation planes, indicating reasonable failure patterns. 1. Introduction Foliation is a geological structure formed by shearing forces or differential pressure during regional metamorphism history. Compared to other discontinuities, the foliation is repetitive layering with sheet-like planar structures, and common exists in metamorphic rocks, such as slate, phyllite and schist. In geology, the foliation is a significant feature to distinguish the level of metamorphism in rocks. In engineering, the presence of foliation causes rocks to exhibit high anisotropy and heterogeneity, which greatly influence the analysis of mechanical properties. Foliated metamorphic rocks are easily split along the direction of foliation under external loading; consequently, the properties of foliation heavily influence rock engineering with respect to stability. For instance, in metamorphic rock slopes with strong foliation, interlayer splitting along foliation occurs frequently, inducing toppling failure to form bending folds in the upper slope and subsequent rock falls. (Weng et al., 2015; Lo and Weng, 2016). In addition, because of the wetting process, the strength of foliation commonly decreases significantly. Therefore, how to evaluate the tensile strength of foliation under different environmental conditions is an important issue of rock mechanics and associated engineering.

Proceedings Papers

Paper presented at the ISRM International Symposium - 10th Asian Rock Mechanics Symposium, October 29–November 3, 2018

Paper Number: ISRM-ARMS10-2018-139

... description method for the rock face was proposed. This method is based on the circular structural profile line observed in the borehole and digital borehole camera technology application in three-dimensional topographical feature of the rock structure

**plane**. This paper is based on the borehole wall**plane**...
Abstract

Abstract In the process of engineering investigation of rock mass, it is of great significance to obtain precise rock structural surface properties for rational design of the project and prevention of geological disasters during construction. A new three-dimensional topological feature description method for the rock face was proposed. This method is based on the circular structural profile line observed in the borehole and digital borehole camera technology application in three-dimensional topographical feature of the rock structure plane. This paper is based on the borehole wall plane development graph as the basic data, the basic information such as the occurrence of rock structural planes on the borehole wall is analyzed, and the structural surface section lines extracted from the borehole plane development diagram of the digital image processing technology are used. According to the three-dimensional information feature of the profile line on the structural wall of the hole wall, the profile feature parameters of the profile lines in each direction are calculated, and the structural surface is formed by referring to the correspondence between the profile feature parameters and the structural surface roughness coefficient ( JRC ). Then the roughness coefficient rose diagram is made to describe the three-dimensional roughness of the rock structure surface. 1. Introduction In recent years, China has gradually attached importance to the use of underground space in cities and the exploration and development of deep resources. Many major projects have gradually been put on the agenda, and engineering safety issues have also increased. The use of test technology by engineering designers to obtain precise and accurate engineering properties of deep rock masses is of great significance to the rational design of the project and the prevention of geological disasters during construction. The study of rock structural planes is the basic work of analyzing the engineering properties of rock masses. Numerous studies and experiments have shown that the mechanical properties of the rock face are not only related to the characteristics of the wall rock and the combined state of the face, but also affected by the surface morphology of the face. For a hard structural surface with a small degree of filling, the surface morphology of the structural surface is the main influencing factor controlling the mechanical properties of the structural surface (Gao et al.,2010). However, obtaining information on deep rock structural planes by drilling and coring has many limitations. First, during the core drilling process, due to the rotational displacement of the core, the exact information of the rock structural plane is destroyed. Secondly, the disturbances such as high-speed rotation of the drill bit and the circulation of the drilling fluid in the coring tube generate a structural plane on the core affect the determination of structural surface closure (openness) and structural surface filling. It can be seen that using core data as a source of rock structural plane information is not accurate enough. Therefore, it is necessary to propose an in-situ measurement technique to directly measure the structural plane of the hole wall of the drilled hole and obtain the surface morphology information of structural plane on the hole wall.

Proceedings Papers

Paper presented at the ISRM International Symposium - 10th Asian Rock Mechanics Symposium, October 29–November 3, 2018

Paper Number: ISRM-ARMS10-2018-066

... development blast

**plane**identification cluster**plane**Blast Induced Seismic Response at the Goldcorp Eleonore Mine: Identification, Delineation and Characterization J. Tuleaua*, K. Woodwardb, M. Grenona and P.L. Lajoiec a Laval University, Quebec City, Quebec, Canada b Australian Centre for Geomechanics...
Abstract

Abstract Seismicity in the mining environment is controlled by factors including stope and development blasting, the presence of geological features, and stress conditions. The Goldcorp Eleonore mine is located in the James Bay region, Quebec, Canada. It's 800-metre depth makes Eleonore a relatively shallow mine when compared to other seismically active Canadian mines. Despite the mine's depth, seismicity is a geotechnical hazard that may be arguably attributed to a particular stress regime and complex geology. An improved understanding of the seismic responses following blasting can decrease seismic risk and is beneficial to mine planning and productivity. Seismic responses to blasting were spatially delineated using a density-based clustering approach. The spatial characteristics of clusters were assessed using Principal Component Analysis (PCA). The best-fit planar representation of seismic event clusters was identified. The orientation of the best-fit planar representations was then compared to the mine's local jointing to investigate the causative seismic source mechanism for these events. The results of this study show that seismicity is linked to local jointing, and in particular to the different structural domains. 1. Introduction Blasting is a significant factor in triggering seismic events at mine sites (Vallejos and McKinnon, 2008). Seismicity is defined as a stress wave resulting from inelastic deformation or failure in the rock mass (Hudyma and Mikula, 2002). Seismicity in the mining environment is controlled by factors including stress, geological structures or rock mass weakness, and mining activities. This induced seismicity—directly connected to mining operations—is associated with formations of fractures at stope faces and with movement on major discontinuities (Gibowiicz and Kijko, 1994). Fig. 1 illustrates the different source mechanisms of induced seismicity in an underground mine environment (Hudyma et al., 2003). Many authors have observed that well-located seismic events exhibit strong spatial clustering (Leslie and Vezina, 2001; Dogde and Sprenke, 1992; Kijko et al., 1993). Hudyma and Mikula (2002) hypothesized that clusters of seismic events represent a separate seismic source mechanism. Limited quantitative means of assessing a seismic source mechanism have been presented in the scientific literature especially in the case of clusters of seismic events. A better understanding of induced seismicity source mechanisms in underground mining can help to optimize mining operations, reduce delays and production losses. Understanding the main source mechanism in mines is essential to a better prediction of the rock mass response to mining.

Proceedings Papers

Paper Number: ISRM-ARMS10-2018-116

... Abstract The loading rate has a significant effect on the mechanical properties of shale and its influence degree is related to the angle of weak

**plane**. Tri-axial compression tests were performed on shale samples from Longmaxi reservoir formation with GCTS RTR1500 mechanical testing system...
Abstract

Abstract The loading rate has a significant effect on the mechanical properties of shale and its influence degree is related to the angle of weak plane. Tri-axial compression tests were performed on shale samples from Longmaxi reservoir formation with GCTS RTR1500 mechanical testing system. The failure modes and mechanical parameter sensitivity characteristics of shale under different loading rates were investigated. The relationship between compressive strength and loading rate was generally linear under different conditions of weak plane angles (β), meanwhile, elastic modulus manifested obviously nonlinear. With the increase of loading rate, the compressive strength and elastic modulus measured by the experiment were higher. The mechanical sensitivity of rock will be different due to the different weak angle. When the loading rate was increased from 0.05mm/min to 0.2mm/min, specimens with the angle β of 30° had the largest growth amplitude, reaching to 17.16%, while the largest amplification in elastic modulus belonged to the β =70° group. Moreover, elastic modulus was most sensitive to the loading rate at 0.12mm/min. Since then, this trend was beginning to stabilize. Specially, shear failure was in charge under the rate of 12mm/min, while tensing fractures started to increase as loading rates going up. 1. Introduction The mechanical characteristics of shale are not only one of the significant topics in the field of shale rock mechanics but the theoretical basis for stimulating shale oil and gas reservoir successfully. The influence of loading rate change induced by engineering construction on the mechanical properties of rock has always been the focus of academic research. Many scholars at home and abroad have conducted many studies on the mechanical characteristics and failure modes of rocks. Chen et al. (2009) conducted acoustic emission experiments on coarse sandstone and found that for plastic rock, the increase of the loading rate would cause the stress value corresponding to the Kaiser point to increase. Wu et al. (1982) and Zhu et al. (1984) demonstrated respectively that the fracture strength of granite increases significantly with the increase of loading rate and the ratio of compressive strength and tensile strength also increases slightly with the increase of loading rate. M. S. Paterson and T. F. Wong (2005) made a very detailed summary of the studies on rock brittle failure and considered that rock failure has various forms such as single shear failure, double shear failure and split fracture. By means of experiments, Huang D and Huang R.Q et al. (2012) pointed that with the increase of the loading strain rate, the fracture initiation and critical expansion stress are closer to the peak stress and the fracture mode of the rock sample transitions from extensional shear type to extensional chapping or even cleavage ejection. Artemov V G and Lykhin P A (1968) theoretically established the relationship between external static loading and dynamic rock failure. Huang et al. (2012) and Yin et al. (2010) analyzed the effect of loading rate on rock failure modes from the aspects of damage morphology, fractures space shape and location. Saurav Rakhaiyar and Narendra K S (2017) found that rock compressive strength decreased logarithmically with the increase of loading rate when the limestone was subjected to cyclic loading experiments. From the energy point of view, Guo (2013), based on the experimental results of acoustic emission experiments tri-axial experiments, concluded that the faster the loading rate, the higher the acoustic emission energy rate and the rock destruction time, While there are no discrepancy in the rock acoustic emission energy rate. In terms of energy distribution, from related experimental results, Zhang and Kou (2000) obtained that the increase of the loading rate would reduce the energy utilization rate. Zhang and Zhao (2013) pointed out that the fracture toughness and dimensionality of granite were depended on the loading rate and experimentally observed the influence of the micro-damage mechanism of the loading rate granite. Zdeněk P. Baɢant (1993) further pointed out that although the toughness and nominal strength of cracks decreased with the decrease of the loading rate, the length of fractures and the failure surface brittleness were not affected by them. Zhang and Kou et al. (1999) found static joint toughness as a constant, while dynamic joint toughness was positively correlated with loading rate. Xu and Chen et al. (2017) found that the peak strength and elastic modulus of rock samples increased with the increase of the loading rate, moreover, the logarithm of the loading rate showed a cubic polynomial fitting relationship. The peak strain decreased with the increase of loading rate and performed a linear fitting relationship with the logarithm of the loading rate. Considering the influence of temperature, Xu and Liu (2017) concluded the marble stamping test and it was verified that in condition of the high temperature, the peak stress and peak strain of marble showed a significant loading rate enhancement effect, which is similar to increased linearly with the increase of loading rate. Cai and Zhao (2001) considered the loading rate basing on the static BB model and proposed the normal behavior pattern of nonlinear dynamic joints.

Proceedings Papers

Paper Number: ISRM-ARMS10-2018-122

...) criterion by appealing to the assumption that the friction angle and cohesion of a

**plane**can be evaluated as a function of relative orientation of the**plane**referred to the weakness**plane**. The implication of the employed spatial distribution function is that the M-C parameter value of a**plane**is the...
Abstract

Abstract The strengths of many sedimentary and metamorphic rocks varies considerably with the loading direction and the manifested feature in the variation of strength is often transversely isotropic. Therefore, when planning excavations in rock formations exhibiting periodic planar microstructures such as bedding and foliation, it is important to accurately define the condition at failure in the framework of transverse isotropy. In view of this, this work focuses on the formulation of a transversely isotropic rock failure condition, which is an extension of the isotropic Mohr-Coulomb (M-C) criterion by appealing to the assumption that the friction angle and cohesion of a plane can be evaluated as a function of relative orientation of the plane referred to the weakness plane. The implication of the employed spatial distribution function is that the M-C parameter value of a plane is the smallest when a plane is parallel to the weakness plane, while it is the largest when the plane is perpendicular to the weakness plane. The formulation takes into consideration of the general 3-D stress state, so that the proposed criterion can capture the salient failure characteristics of transversely isotropic rock in true triaxial stress condition. In order to validate the performance of the proposed failure condition, a series of conventional and true triaxial compression tests on inclined rock samples is simulated. Based on these numerical experiments, the influence of the relative orientation of weakness planes to loading direction on the failure behavior of transversely isotropic rocks is discussed. 1. Introduction Many transversely isotropic rocks exhibiting periodic weak planar structures, such as bedding and foliation, show a strong directional dependence in their failure strength. In general, the strength is the highest when the load is applied in the direction parallel or perpendicular to the weak plane, while it is the lowest when the loading direction is 30° ∼ 45° to the weak plane. According to the experimental research (Ramamurthy, 1993; Saroglou and Tsiambaos, 2008), the ratio of the maximum to the minimum strength of the transversely isotropic rock is about 1.0∼2.0 for shale, 2.0∼6.0 for slate and phyllite, and 2.0∼4.0 for gneiss. As such, it is important to incorporate the strength and failure characteristics of transversely isotropic rocks in the stability analysis of rock excavations, including tunnels and slopes. Therefore, considering that the failure criteria of materials define not only the onset of failure but also the orientation of associated fracture plane, the establishment of accurate failure condition for transversely isotropic rocks in 3-D stress state is important for understanding and reproducing the failure phenomena observed in many sedimentary and metamorphic rocks. Since the 1960s, a number of transversely isotropic failure criteria have been proposed along with the accumulation of laboratory data on transversely isotropic rock samples. An extensive review of several well-known criteria is given by Duveau et al. (1998). Among the existing criteria the single plane of weakness (SPW) theory proposed by Jaeger (1960) is the simplest and assumes the respective sets of M-C strength parameters for failure along the weakness and failure across the weakness plane. Jaeger also proposed a criterion where cohesion is a continuous function of sample inclination. McLamore and Gray (1967) extended the Jaeger's theory by postulating that the friction angle also varies with the orientation of the weaknesss plane. Similar formulations of transversely isotropic failure conditions in the context of the nonlinear Hoek-Brown (H-B) criterion can be found in Hoek (1983) and Saroglou and Tsiambaos (2008). However, these kinds of criteria are fully empirical in their derivation nature and suffer from a lack of physical and mathematical background. Examples of mathematically more rigorous formulations include Pariseau (1972), Cazacu and Cristescu (1999), Pietruszcak and Mroz (2001) and Lee and Pietruszczak (2008), which employ the general 3-D stress state, although these approaches, in general, require more material parameters to be identified from an extensive experimental program. The main advantage of 3-D formulation lies in the fact that the resulting criteria enable the assessment of the response of the failure strength to the orientation of the weakness plane in true triaxial stress condition, which is more realistic than the laboratory triaxial compression condition.

Proceedings Papers

Paper Number: ISRM-ARMS10-2018-227

... strength criterion is proposed for anisotropic rocks and jointed rock mass. The proposed criterion is an extension of Jaeger two-dimensional (2D) anisotropic criterion into three-dimension (3D) using Mogi-Coulomb strength criterion. It is concluded from the study that the most critical anisotropic

**plane**is...
Abstract

Abstract Strength and deformation behaviour of the isotropic rock under triaxial stress state has been studied extensively, but the studies on the behaviour of the anisotropic rock under true triaxial stress state are scant. The experimental study conducted on the anisotropic rocks are not conclusive due to limited experimental data. In reality, construction of any underground opening results in the application of true triaxial stress state on surrounding geomaterial even the isotropic rocks behave anisotropically due to the presence of the geological structures. In this study, a theoretical strength criterion is proposed for anisotropic rocks and jointed rock mass. The proposed criterion is an extension of Jaeger two-dimensional (2D) anisotropic criterion into three-dimension (3D) using Mogi-Coulomb strength criterion. It is concluded from the study that the most critical anisotropic plane is at angle β = (45+ ϕ /2)° and ω = 90°. For all the other orientations, the strength is observed to be more than this critical orientation. It is also observed that intermediate principal stress enhances the strength and its influence on foliation or joint is negligible when its orientation is perpendicular to the foliation or joint plane. 1. Introduction The strength behaviour of anisotropic rocks has been extensively studied under the triaxial stress state (Jaeger, 1960; Hoek, 1964; Donath, 1964; Chenevert and Gatlin, 1965; Rao 1984; Ramamurthy et al., 1988, 1993; Singh, 1988; Singh et al., 1989; Behrestaghi et al., 1996; Nasseri et al., 2003; Saroglou and Tsiambaos, 2008; Saeidi et al., 2014 among others). These studies on the anisotropic behaviour of rocks consider the plane of anisotropy perpendicular to the intermediate principal stress ( σ 2 ) and hence neglecting its influence on the strength behaviour. However, it is experimentally confirmed that the strength of rock and rock mass is also a function of intermediate principal stress (Mogi, 1971; Kwa'sniewski and Mogi, 1990; Haimson and Chang, 2000; Chang and Haimson, 2000; Tiwari and Rao, 2006; Tiwari and Rao, 2007; Oku et al., 2007; Lee and Haimson, 2011; Singh and Singh, 2012; Sriapai et al., 2013; Ma and Haimson, 2016; Rukhaiyar and Samadhiya, 2017; Li et al. 2018 among others). Hence, various 3D criteria are proposed for isotropic rocks some of them are theoretical criteria such as: time-dependent 3D strength criterion (Aubertin et al., 2000), an explicit yield criterion coupled with anisotropic damage in Cauchy stress space for materials initially obeying J 2 plasticity (Yang et al. 2005), 3D criterion based on fracture mechanics (Zuo et al., 2008), non-linear failure criterion considering the penny shaped micro cracks (Zhou et al., 2014), which was later extended to dynamic loads (Zhou et al., 2015) and for creep (Zhou et al., 2017), Drucker-Prager (Drucker and Prager, 1952), modified Wiebols-Cook criterion (Zhou, 1994), modified Lade criterion (Ewy, 1999) using simple triaxial compression test parameters among others. However, the majority of the criteria mentioned above are complex involving a larger number of non-conventional material parameters. Other simple empirical or semi-empirical for isotropic rocks are Mogi criterion (Mogi, 1971), 3D Hoek-Brown (1988) (Pan and Hudson, 1988), Mohr-Coulomb extension in 3D by (Yu et al., 2002), Mogi-Coulomb criterion (Al-Ajmi and Zimmerman, 2005), 3D Hoek-Brown (2007) (Zhang and Zhu, 2007), Ramamurthy criterion (2007) (Ramamurthy, 2007), Modified Hoek-Brown analogues to Yu et al. (2002) by Zhou et al. (2010), Singh and Singh (2011) gave non-linear Mohr-Coulomb criterion. Singh (2018) concluded that Mogi-Coulomb criterion is relatively modest criterion among others and predict the strength fairly good in 3D stress condition.

Proceedings Papers

Paper Number: ISRM-ARMS10-2018-127

... comprise strong banded iron formations discretely interbedded with very weak shales. Slope failure mechanisms typically involve sliding along bedding (anisotropy)

**planes**combined with joints or faults acting as release**planes**or forming step-path failure mechanisms. Slope stability modelling techniques...
Abstract

Abstract Bedded coal and iron ore deposits in Australia are usually hosted in complexly jointed, faulted or folded, highly anisotropic rock masses. In coal, these often comprise moderately strong siltstones and sandstones with weak coal seams, siltstones and shales. For iron ore, these comprise strong banded iron formations discretely interbedded with very weak shales. Slope failure mechanisms typically involve sliding along bedding (anisotropy) planes combined with joints or faults acting as release planes or forming step-path failure mechanisms. Slope stability modelling techniques have evolved over the years and increased in complexity with continuous improvements in computing capability and available software. Less than 20 years ago, basic kinematic analysis was the primary means of designing large rock slopes. In the 2000s, the use of two-dimensional limit equilibrium analysis and numerical modelling rapidly increased with faster computing. As we approach the 2020s, three-dimensional limit equilibrium and finite element analysis software are readily available and offer a range of options to model the behavior of complex, anisotropic rock masses. The results obtained by these different modelling approaches, for example, isotropic vs. anisotropic, or 2D vs. 3D can vary significantly depending on the geological conditions. This paper presents case studies from both open pit iron ore and coal mines that compare the factor of safety (FoS) obtained from 2D and 3D limit equilibrium modelling approaches. The case studies clearly show the limitations of 2D modelling when the rock mass being excavated is highly anisotropic in nature and when large-scale geological structures are present whose geometry cannot be adequately represented in plane strain. Results further indicate that modelling solely in 2D can lead to either the over-estimation or under-estimation of FoS, by failing to locate the section of slope with the lowest FoS or failing to adequately model the anisotropic conditions under which failure is likely to occur. The tools are now readily available to facilitate 3D modelling techniques alongside existing 2D techniques to complete a comprehensive review of slope stability. This will allow both the optimization of slope designs to be completed, and increase design reliability by identifying the sections of slope more susceptible to failure in true 3D space. 1. Introduction In 2014–15, income from sales and services from coal and iron ore mines in Australia was approximately $115 Billion (AUD), which accounted for approximately 80% of total mining and quarrying sector (ABS, 2016). The Pilbara Region of Western Australia hosts the majority of economically extractable iron ore deposits in Australia. Hundreds of open cut mines are operated by major mining companies near the townships of Newman, Paraburdoo and Tom Price with single operations often having access to several individual pits in similar ground conditions. Due to the broad regional expanse of the operations, particularly in the iron ore sector, a very high extraction rate is achieved despite vertical development rates remaining relatively low (typically one to three benches or 10m to 30m per year in a single iron ore pit). Final pit depths or total rock slope heights range from less than 100m to 350m. The Hunter Valley Region of New South Wales and the Bowen Basin Region in Queensland host the main coal deposits used for energy and steel manufacturing. Mining typically begins with an initial excavation, called a box cut, and then progresses down dip in a series of strips, with the coal closest to the surface extracted first. Pit geometry is dictated by equipment capabilities, the location of economic coal seams, and geotechnical constraints to achieve an acceptable design. Individual bench heights typically do not exceed 60m and overall excavated slope heights rarely exceed 150m.

Proceedings Papers

Paper Number: ISRM-ARMS10-2018-263

... Abstract In anisotropic rocks such as shale, the value of the maximum principal stress required to cause shear failure depends not only on the other two principal stresses, but also on the angle β between the maximum principal stress and the normal to the bedding

**plane**. According to Jaeger's...
Abstract

Abstract In anisotropic rocks such as shale, the value of the maximum principal stress required to cause shear failure depends not only on the other two principal stresses, but also on the angle β between the maximum principal stress and the normal to the bedding plane. According to Jaeger's plane of weakness model, for β near 0° or 90°, failure will occur at a stress determined by the failure criterion for the "intact rock", and the failure plane will cut across the bedding planes. At intermediate angles, failure will occur along a bedding plane, at a stress determined by the strength parameters of the bedding plane. Data were analyzed from a set of triaxial ( σ 2 = σ 3 ) compression tests conducted on a suite of shale samples, at different confining stresses, and a range of angles β and it was found that the data could be fit reasonably well with the four-parameter plane of weakness model. Based on these results, a model has been developed for the stability of boreholes drilled in shales. The fully anisotropic Lekhnitskii-Amadei solution is used to compute the stresses around the borehole wall. The Mogi-Coulomb failure criterion is used for the strength of the "intact rock", and the plane of weakness model is used for the strength of the bedding planes. The model can be used to predict the minimum mud weight required to avoid shear failure, for arbitrary borehole orientations and anisotropy ratios. The results show the importance of using a fully anisotropic elastic model for the stresses, and using a true-triaxial failure criterion, in borehole stability analysis. 1. Introduction A fundamental problem in rock mechanics is to predict, based on the stress state, whether or not a rock will "fail". There are several modes of failure, one of the most important being shear failure, in which the initially intact rock breaks along a plane whose orientation is controlled by the orientations and magnitudes of the principal stresses. For isotropic rocks, the simplest and oldest failure criterion is the Coulomb failure criterion (Jaeger et al., 2007), which states that failure will occur if and when where σ 1 ≥ σ 2 ≥ σ 3 are the three principal stresses, S o is the cohesion, C o is the uniaxial compressive strength, β = 45°+( ϕ /2) is the angle between the normal vector to the failure plane and the maximum principal stress, ϕ = tan −1 μ is the angle of internal friction, and μ is the coefficient of internal friction. Many other shear failure criteria have also been proposed (Jaeger et al., 2007; Labuz et al., 2018).

Proceedings Papers

Paper presented at the ISRM International Symposium - 8th Asian Rock Mechanics Symposium, October 14–16, 2014

Paper Number: ISRM-ARMS8-2014-049

... determine the coefficient of friction for the rock. Fairhurst asian rock mechanics symposium arms8 Detournay Sapporo Upstream Oil & Gas reservoir geomechanics scratch test strength specimen compressive strength Wawersik

**plane**october 2014 compression Reservoir Characterization...
Abstract

Abstract Uniaxial Compressive Strength (UCS) is the most widely used index of rock strength. Strength under confined conditions most often is characterized by a straight line Mohr-Coulomb failure envelope. Although required as input to engineering design, reliable values of one or both of these parameters often are not available to the design engineer because of the exacting requirements, and the cost of preparing specimens and conducting a sufficient number of tests, under uniaxial and confined pressure conditions. The Scratch Test was developed at the University of Minnesota in the late 1990s, when a remarkably strong correlation was discovered between the specific energy required to cut a shallow groove into the surface of a rock and the UCS ( http://www.cefor.umn.edu/facilities/rsd/ ). The test now has matured into a reliable and relatively inexpensive practical procedure to provide the necessary engineering design information. The procedure has the added advantage that, except for a shallow groove cut along the edge of the core, the test is ‘non-destructive’, leaving the core available for other studies. This paper discusses the theoretical basis for the equivalence between the specific energy of cutting, ε, and the UCS (q) , and indicates that the 1:1 relationship between these values has a sound mechanistic basis. The Mohr- Coulomb strength envelope also can be obtained by substitution of a blunt cutting tool in the Rock Strength Device (RSD) — or Scratcher — to determine the coefficient of friction for the rock.

Proceedings Papers

Paper presented at the ISRM International Symposium - 8th Asian Rock Mechanics Symposium, October 14–16, 2014

Paper Number: ISRM-ARMS8-2014-056

... as respective scalar functions of orientation vector. These two distribution functions employ the 2nd order symmetric traceless tensor which describes the directional bias of the strength parameter from the orientation average. Critical

**Plane**Approach is applied to find the 3-D stress conditions at...
Abstract

Abstract Although the commonly used rock failure criteria such as the Mohr-Coulomb and the Hoek-Brown neglect the influence of the intermediate principal stress (2σ) on the strength of rock, experimental evidence appearing in many publications on the polyaxial strengths of rock strongly suggests that the 2σ effect exists for many rocks. Along with the accumulation of the polyaxial test data, a number of rock failure functions taking into consideration of the 2σ effect have been proposed. Most of the suggested polyaxial strength criteria, however, focus on the phenomenological description of rock strength observed in the true triaxial tests, so that they fail to provide the theoretical explanation for the cause of the strengthening effect of 2σ. In this study, a series of numerical polyaxial tests on the transversely isotropic rock samples are conducted to verify that the presence of microstructures and their alignment to a prevalent orientation could be one of the plausible causes of the 2σ effect. In order to incorporate the strength anisotropy into a failure condition, the Mohr-Coulomb criterion is extended to the anisotropic version by defining the internal friction angle and the cohesion as respective scalar functions of orientation vector. These two distribution functions employ the 2nd order symmetric traceless tensor which describes the directional bias of the strength parameter from the orientation average. Critical Plane Approach is applied to find the 3-D stress conditions at failure and the orientation of the corresponding failure plane. The simulation results hint that both the inclusion of the weak planes in the rock samples and their alignment to the preferred direction with respect to the loading direction are closely related to the 2σ dependency of rock strength.

Proceedings Papers

Paper presented at the ISRM Regional Symposium - 7th Asian Rock Mechanics Symposium, October 15–19, 2012

Paper Number: ISRM-ARMS7-2012-042

.... The dynamic fracture toughness K ic was determined by using loading pressure-time curves measured on the transmitted bar and the failure time of the specimen calculated by non-contact laser gap gauge system. fracture toughness rift

**plane**shpb system SR sample hydraulic fracturing rapid...
Abstract

ABSTRACT An experimental approach for determining dynamic fracture toughness of rock materials at high strain rate is presented. Split Hopkinson pressure bar (SHPB) system was used to load the SR (Short Rod) sample of Po-cheon granites and Ham-yeol granites which have anisotropy physical properties under static loading and the smaple were prepared to consider main three direction of pre-exist micro-cracks (Rift, Hardway, Grain). In order to make sure dynamic stress uniformity and constant strain rate of the specimen before the failure, a pulse shaping technique is employed to the SHPB system. The dynamic fracture toughness K ic was determined by using loading pressure-time curves measured on the transmitted bar and the failure time of the specimen calculated by non-contact laser gap gauge system.

Proceedings Papers

Paper presented at the ISRM Regional Symposium - 7th Asian Rock Mechanics Symposium, October 15–19, 2012

Paper Number: ISRM-ARMS7-2012-024

... little discernible effect over for the limited range of friction surfaces investigated. reservoir geomechanics strength variation

**plane**Upstream Oil & Gas composite specimen in-fill material specimen reduction hydraulic fracturing test specimen fracture**plane**discontinuity loading...
Abstract

ABSTRACT A study was undertaken to investigate changes in the strength and failure pattern of otherwise standard rock core specimens containing regularly spaced discontinuities. The objective was to assess changes in the nature of rock failure resulting from these discontinuities. Test core specimens were prepared from sandstone having dimensions of 44 and 110 mm for diameter and height respectively. The core specimens were cut at right angles to the longitudinal axis of the core producing composite specimens having 2, 3, 4 or 5 regularly-spaced surfaces. As well as testing specimens having dry, clean fracture surfaces, the test program also considered different infill materials and hence friction values using dry and oiled-impregnated paper. The study found the strength of specimens decreased with the number of discontinuities. While the UCS strength of the intact rock specimen was 35.8 MPa, the strength of composite specimens having five segments was reduced by 50% to 17.9 MPa. This is despite the reduction in the slenderness ratio of each segment in the composite specimen that would usually result in an increase in strength. Less sensitive were changes in infill material having little discernible effect over for the limited range of friction surfaces investigated.

Proceedings Papers

Paper presented at the ISRM Regional Symposium - 7th Asian Rock Mechanics Symposium, October 15–19, 2012

Paper Number: ISRM-ARMS7-2012-020

... specimens and G 2 can be obtained from the five specimens of inclined angles. Two values of tangential modulus on the anisotropic

**plane**, averaged G 2 and G 2-sv , are almost same each other within 6 % of difference. And test data of the apparent Young's modulus can be referred as a monotonous increasing...
Abstract

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

Proceedings Papers

Paper Number: ISRM-ARMS7-2012-055

..., ) = (±12.2°, ±5.6°, ±0.3). Furthermore Shear stress ratio? t f / t f f is decreased especially in the case a f < 0. classification variation test result strength property Upstream Oil & Gas accuracy shear

**plane**rock mass Reservoir Characterization slip**plane****plane**MPa concrete...
Abstract

ABSTRACT The variations of strength properties of rock shear tests are significantly large because of the discontinuous nature of rock masses and the accuracy of loading control. For the purpose of clarifying the latter reason, in this study, the rotation angles of the concrete block of failure about horizontal axis a f and about the vertical axis ß f , the horizontal displacement perpendicular to the shear direction lf are investigated. As a result, the average values ( a f, av , ß f, av , ( l f / h f ) av )= (0.5°, 4.9°, 0.2). The standard deviations (s a, s ß, , s l, ) = (±12.2°, ±5.6°, ±0.3). Furthermore Shear stress ratio? t f / t f f is decreased especially in the case a f < 0.

Proceedings Papers

Paper Number: ISRM-ARMS7-2012-090

... through visual C++ and computer graphics. This model assumed that rock mass consists of blocks and each block is formed by particles arranged in a specific way, thus formulating a combination of block model and particle model. This software adopted vector analysis, which can simulate all excavation

**planes**...
Abstract

ABSTRACT Analytical solution and simplified design procedure was presented for evaluating the response of existing joint rock slope subjected to excavation. In jointed rock slope engineering, the stability of rock is controlled in a sense by the number of blocks, i.e. the size, orientation and locations of the discontinuities, especially the key blocks for a given excavation geometry. Key block failures occur where blocks of rock are separated from the rest of the rock mass by discontinuities. In this research, according to block theory, the new block stability analysis model was developed through visual C++ and computer graphics. This model assumed that rock mass consists of blocks and each block is formed by particles arranged in a specific way, thus formulating a combination of block model and particle model. This software adopted vector analysis, which can simulate all excavation planes especially in the tunnel and other underground structures. It can also create three-dimensional structural model and analyze mobility of key blocks in the simulation planes by means of geometry and kinematics theory. The distribution of all key blocks and the quantitative data were analyzed by means of the newly developed program. It can be concluded that the new code was a tool for modeling blocky rock masses. Moreover, this model was verified by an example of rock masses under uniaxial loading. It was shown that numerical results agree well with the theoretical ones and laboratory tests not only for deformation process but also for the failure process.

Proceedings Papers

Paper Number: ISRM-ARMS7-2012-127

.... displacement geomechanical parameter stability ubiquitous-joint model Tunnel Stability cohesion safety factor rock mass support design

**plane**internal friction angle Anisotropy Effect bedding**plane**Reservoir Characterization weakness**plane**characteristic anisotropy angle different anisotropy...
Abstract

ABSTRACT One of the adverse condition in the tunneling is the strength anisotropy that effect the displacement and stability of the tunnel perimeter. Main purpose of this study, is stability analysis and Sardasht conveyance tunnel support system design with consider anisotropy condition, that tunnel cross through slate rocks. The numerical simulation program FLAC3D with ubiquitous-joint model was used to simulate and analysis the anisotropy effect on the stability and support system design. In this study different anisotropy plan dip (with attention to the site condition) of 0 to 90 degree and dip direction 35 degree to the tunnel axis have been considered. Safety factor for different degree was determined. With attention to stability, axial force and moment, three type of reinforcement system for all degree of anisotropy with ubiquitous and also Mohr Columbus models have been designed.

Proceedings Papers

Paper presented at the ISRM International Symposium - 6th Asian Rock Mechanics Symposium, October 23–27, 2010

Paper Number: ISRM-ARMS6-2010-156

..., the location of sliding

**planes**, and the strength parameters, such as cohesion and the internal friction angle, from the measured displacements, even only from the surface displacements. The back analysis procedure was successfully developed by introducing both an "anisotropic parameter" and...
Abstract

Abstract: The stability of slopes can be assessed by a factor of safety, which is usually determined by a limit equilibrium method. In order to evaluate the factor of safety, we need such strength parameters as cohesion and the internal friction angle. In the monitoring of slope stability, displacements are commonly measured. Therefore, the strength parameters should be evaluated from the measured displacements. Sakurai and Nakayama (1999) developed a back analysis procedure for determining the strength parameters from the measured displacements. The back analysis procedure was successfully developed by introducing both an "anisotropic parameter" and "critical shear strain". Recently, on the basis of this back analysis procedure, a computer code called the "Universal Back Analysis Program for Slope Stability" (UBAPSS) has been completed. In this paper, UBAPSS is briefly described, and a case study is shown to demonstrate its applicability for assessing the slope stability at an open pit coal mine. The surface displacements were measured in the mine by GPS and the data were collected until failure occurred. The strength parameters were determined using the data obtained just one day before the failure occurred. The results of the back analysis indicate that the factor of safety becomes approximately 1.0. This means that the computer code UBAPSS is well applicable to the assessment of the stability of slopes. 1. INTRODUCTION The stability of slopes can be assessed by a factor of safety, which is usually determined by a limit equilibrium method. In order to evaluate the factor of safety, we need such strength parameters as cohesion and the internal friction angle. However, determining the strength parameters is not an easy task, because soil and rock have numerous geological and geotechnical uncertainties. However, the question of how to evaluate the strength parameters from the measured displacements is raised. To answer this question, Sakurai (1992) developed a back analysis procedure which can determine the mechanism of the slope deformation, whether it is sliding or toppling, the location of sliding planes, and the strength parameters, such as cohesion and the internal friction angle, from the measured displacements, even only from the surface displacements. The back analysis procedure was successfully developed by introducing both an "anisotropic parameter" and "critical shear strain". Recently, on the basis of this back analysis procedure, a computer code called the "Universal Back Analysis Program for Slope Stability (UBAPSS) has been completed. In this paper, UBAPSS is briefly described, and a case study is shown to demonstrate the applicability of the proposed back analysis procedure for assessing the slope stability at an open pit coal mine, where the surface displacements were measured by GPS and the data were collected until failure occurred. The strength parameters were determined using the data obtained just one day before the failure occurred. The results of the back analysis indicate that the factor of safety becomes approximately 1.0. This proves that the computer code UBAPSS is well applicable to the assessment of the stability of slopes.

Proceedings Papers

Paper presented at the ISRM International Symposium - 6th Asian Rock Mechanics Symposium, October 23–27, 2010

Paper Number: ISRM-ARMS6-2010-060

... geometric shapes (e.g. polyhedron in 3-D) can be the basic MC of the mathematical domain. Each different shaped MC has its own mathematical description inside. NMM tetrahedral wedge discontinuity manifold element friction angle Artificial Intelligence Singapore

**plane**analytical solution...
Abstract

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

Proceedings Papers

Paper presented at the ISRM International Symposium - 6th Asian Rock Mechanics Symposium, October 23–27, 2010

Paper Number: ISRM-ARMS6-2010-172

...-history, with the yield acceleration used as reference datum. 2.2 Single Face Sliding in 3D The two dimensional formulation shown in Equation 4 has been expanded by Bakun Mazor [3]to three dimensions for a single block on an inclined

**plane**, in order to validate 3D-DDA under three components of...
Abstract

Abstract: The application of the numerical Discontinuous Deformation Analysis method (DDA) in rock engineering is discussed here. Following a review of recent 2D and 3D DDA validations, application of the method in analysis of natural rock slopes and underground openings are presented. Two interesting problems are explored in the applied section of this paper: the deformation of discontinuous overhanging rock slopes, and the stability of karstic caverns underneath active open pit mines. The numerical DDA method is shown here to be a powerful tool for modeling dynamic rock mass deformation when the interaction between multiple discrete elements dictates the expected global deformation. 1. introduction Recent developments in the validation and application of Discontinuous Deformation Analysis (DDA), originally developed by Shi and Goodman [1] are presented. We begin with a brief review of recently published 2D - DDA validations for cases of dynamic loading [2] along with new 3D - DDA validations for single and double face sliding [3]. Following these validations we present dynamic DDA applications in natural rock slopes and underground openings. 2. Dynamic DDA Validations 2.1 Single Face Sliding in 2D A displacement based sliding block model was first proposed by Newmark [4] and Goodman and Seed [5], is now largely referred to as "Newmark" type analysis. Determination of the amount of displacement during an earthquake involves two steps [5]: Determination of horizontal acceleration required to initiate down slope motion, also known as "yield acceleration" (ay), which can be found by pseudo-static analysis, and Evaluation of the displacement developed during time intervals when yield acceleration is exceeded, by double-integration of the acceleration time-history, with the yield acceleration used as reference datum. 2.2 Single Face Sliding in 3D The two dimensional formulation shown in Equation 4 has been expanded by Bakun Mazor [3]to three dimensions for a single block on an inclined plane, in order to validate 3D-DDA under three components of input motion. The analytical solution is based on the original static limit equilibrium formulation presented by Goodman and Shi [6]. A typical three dimensional model of a block on an incline is illustrated in Fig. 2(a). The dip and dip direction angles are, α = 20 ° and β = 90°, respectively. A Cartesian coordinate system (x,y,z) is defined where X is horizontal and points to east, Y is horizontal and points to north, and Z is vertical and points upward. In an unpublished report, Shi [7] refers only to the case of a block subjected to gravitational load, where the block velocity and the driving force have always the same sign. The same is true for the original equations published in the block theory text by Goodman and Shi [6]. For the complete set of equations of the three dimensional solution see [3]. The relative error of the new analytical solution and 3D-DDA method with respect to the existing Newmark's solution is shown in the lower panel of Figure 3(A) and are both found to be less the 3% in the final position.

Proceedings Papers

Paper Number: ISRM-ARMS6-2010-044

... treatment has been tackled mainly by the

**plane**of weakness theory. In this study, an extended**plane**of weakness theory is applied to a well documented jointed rock physical model. For the failure mechanisms observed in the experiment, the non linear strength envelope provided by this extended**plane**of...
Abstract

Synopsis: The appropriate assessment of the strength of a jointed rock mass is a fundamental requirement for the successful design of structures built in or on rock. Due to the complexity of the rock mass, a large number of empirical methods are developed, for its estimation. Its analytical treatment has been tackled mainly by the plane of weakness theory. In this study, an extended plane of weakness theory is applied to a well documented jointed rock physical model. For the failure mechanisms observed in the experiment, the non linear strength envelope provided by this extended plane of weakness theory fits well to the experimental data. 1 INTRODUCTION Rock mass strength estimation belongs to the problems that are too complex to be tackled easily with analytical methods. Complexity is mainly due to fracturing, anisotropy inhomogeneity, and the variety of pertinent modes of failure. Therefore, empirical correlations, that do not need theoretical treatment, are usually employed. They come from the systematic observation of the factors that affect the strength. Analytical methods for the estimation of jointed rock strength have been developed, for the case of sparsely jointed rock masses. The most widely known analytical method for such a purpose is the plane of weakness theory, presented by Jaeger [1]. This method has been extended in order to take into account the roughness of joint surfaces. This extended method is presented and then, both the original and extended theories of weakness plane are applied to a jointed rock physical model. 2 THE EXTENDED THEORY OF WEAKNESS PLANE The original theory of weakness plane (Jaeger, [1]) allows for the analytical evaluation of the anisotropic or equivalent isotropic strength of jointed rock. This theory uses the Mohr - Coulomb failure criterion for the joints. However, this linear criterion is unable to describe adequately the shearing behaviour of rock joints, which are rarely smooth, and their strength is a non linear function of the existing normal stress. Experiments ondiscontinuities have shown that for low normal stresses, the surface roughness causes expansion with shear movement, while for higher normal stresses there is failure of asperities and suppression of any expansion. 3 EXPERIMENTAL EVIDENCE ON DISCONTINUOUSSPECIMENS Various researchers, such as for example, Goldstein et al. [5], Hayashi [6], Lama [7], Brown [8], Einstein and Hirschfield [9], experimented on artificial specimens made by blocks, usually of plaster, arranged in such a way to form a jointed structure. By this procedure, the jointed structure of the specimen is considered to represent the rock mass. For low values of confining stress, shear failures of joints or in intact material, were observed. For higher lateral stresses, the failure was due to the formation of many almost parallel shear planes, mainly within the intact material. The strength of the specimens depended on joint dip, except from the case of high lateral pressures, where the strength of the specimen was nearly equal to that of the intact material. The behaviour of specimens was brittle for low lateral pressures and ductile for higher.