Neil Chandler, Atomic Energy of Canada Limited, Pinawa ... David Potyondy, Itasca Consulting Group Inc., Minneapolis, Minnesota ... de la roche cristalline.
COMPUTING BRITTLE ROCK FRACTURE AND EXCAVATION STABILITY USING THE PARTICLE FLOW CODE Neil Chandler, Atomic Energy of Canada Limited, Pinawa Rodney Read, RSRead Consulting Inc., Okotoks, Alberta David Potyondy, Itasca Consulting Group Inc., Minneapolis, Minnesota R. Paul Young, University of Liverpool, UK James Hazzard, University of Liverpool, UK ABSTRACT The development of conceptual and numerical models for cracking in brittle crystalline rock is described in this paper. The Particle Flow Code (PFC) was used as the platform to implement this conceptual model. PFC can be used to simulate the development of internal micro-tensions thus providing a mechanism for axial splitting during unconfined tests on rock samples. A strength degradation model, applied within PFC, was consistent with the theory of stress corrosion of crystalline rock. The PFC stress-corrosion model was calibrated to the time-to-failure data from laboratory static fatigue tests on Lac du Bonnet granite. The numerical modelling was integrated with laboratory testing, in situ investigations of excavation stability conducted at the Canada’s Underground Research Laboratory, and field acoustic emission/microseismic measurements. RÉSUMÉ On décrit dans le présent document l’élaboration de modèles conceptuels et numériques pour la fissuration dans la roche cristalline fragile. Le code d’écoulement des particules (PFC) a été utilisé comme plate-forme pour mettre en œuvre ce modèle conceptuel. On peut utiliser le PFC pour simuler la création des micro-tensions internes offrant ainsi un mécanisme pour la fissuration axiale au cours des essais non confinés d’échantillons de roche. Un modèle de dégradation de la résistance, mis en œuvre à l’intérieur du PFC, était conforme à la théorie de corrosion sous contrainte de la roche cristalline. On a étalonné le modèle de corrosion sous contrainte du PFC selon les données du moment de rupture provenant des essais de fatigue statique en laboratoire sur le granite de Lac du Bonnet. On a intégré la modélisation numérique avec les essais en laboratoire, les études in situ de la stabilité de l’excavation menée au Laboratoire de Recherches Souterrain du Canada et les mesures d’émission acoustique et microsismique.
1. INTRODUCTION The failure of rock in compression is not as simple to analyse as might initially be perceived. Unconfined tests on brittle rock in the laboratory fail by splitting along the axis of the sample, whereas confined samples develop more traditional shear planes as generally observed in ductile materials. However, a closer investigation of the shear planes in rock reveals a coalescence of smaller axially aligned micro-cracks. The initiation and propagation of the axially aligned cracks implies that internal microscopic tensions are developing within the rock sample in response to the macroscopic compression. Representation of this phenomenon within a continuum model (i.e. finite element or finite difference) is not straightforward. The † Particle Flow Code (PFC) is a distinct element code that simulates a material as a collection of discs (or particles) bonded together where the particles are in contact. Micro-tensions develop where the particles are pushed apart resulting in an axial alignment of bond breakages analogous to axial splitting in rock.
under constant load conditions well below the unconfined strength of the material. Back-analysis of rock failure around excavations in the well-characterized rock mass of the Underground Research Laboratory (URL) near Lac du Bonnet Manitoba led to the conclusion that the in situ strength of granite is about half the strength defined from standard laboratory tests. The challenge, therefore, is to develop a model for rock response that can be applied to both laboratory and field simulations. The development of a conceptual and numerical model for rock failure was an important component of the Thermal-Mechanical Stability Study, a program aimed at developing tools for use in the engineering design of repository excavations (Chandler et al. 2000). 2.
THE UNDERGROUND RESEARCH LABORATORY AND THE MINE-BY EXPERIMENT
The challenge of modelling rock failure is further complicated by the fact that rock will ultimately fracture
In Canada, there has been over twenty years of research and development into the technologies ‡ required for isolation of the spent fuel from CANDU nuclear reactors in a deep geologic repository. In response to the needs of the research programs, Atomic Energy of Canada Limited (AECL) constructed the URL
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The Particle Flow Code is commercially available from Itasca Consulting Group Inc. Minneapolis Minnesota
CANDU (Canadian Deuterium Uranium) is a registered trademark with AECL.
to provide a representative geological environment in which to conduct large-scale multidisciplinary experiments. The URL is located within the Lac du Bonnet batholith in southeastern Manitoba, on the Western extreme of the Canadian Shield. The batholith is considered representative of many granitic intrusions in Precambrian rock. The batholith has a surface area of 75 by 25 km, extends to a depth of about 10 km, and is relatively uniform in texture and composition. The URL shaft has been excavated to a depth of 443 m and there are working levels at depths of 240 and 420 m on which experiments and demonstrations have been conducted (Figure 1). Below 300 m the rock mass at the URL is relatively unfractured and measured horizontal in situ stresses are greater than 60 MPa, which is much higher than horizontal stresses measured in Canadian Shield mines at similar depths, where fracturing is generally more pervasive. The high horizontal stresses, and predominantly intact rock, make the URL an ideal location for the study of stress-induced fracture initiation and propagation in crystalline rock.
Although the overall stability of tunnels is the important concern for most underground engineering applications, microscopic damage that might increase the hydraulic connectivity and permeability of the near-field rock mass is also a concern within Ontario Power Generation’s Deep Geologic Repository Technology Program. In recent years, the rock mechanics program at the URL has focused on understanding the micro-mechanical processes leading to the creation of fractures or microcracks near the surface of excavations. Increasing the understanding of both the process leading to rock failure and the potential consequences of a zone of damaged rock has resulted in improved conceptual models for rock mass response. These models may ultimately be incorporated within numerical design tools to predict the long-term rock mass performance under loading conditions expected over the lifetime of the repository. The resulting knowledge gained with respect to initiation and propagation of cracks in the rock can be applied to develop credible models for overall stability of any tunnels excavated in highly stressed rock.
In the AECL’s concept for deep geological waste isolation, the rock mass around the repository will be subjected to mechanical loads (excavation-induced stress redistribution, confining pressures from swelling backfill materials, and glacial loads) and thermal loads. Given the long time period over which these loads will be applied, numerical and analytical models must be relied upon to design stable openings and to predict the long-term rock mass behaviour under a variety of loading conditions. These models should ultimately simulate both coupled and uncoupled thermal, mechanical and hydraulic responses of the rock mass.
Since 1990, in situ full-scale excavation experiments have been conducted at the URL to increase our understanding of the mechanics of rock failure around underground openings. These experiments include the Mine-by Experiment (Read and Martin 1996), the Heated Failure Test (Read et al 1997a), the Excavation Stability Study (Read et al. 1997b) and the Tunnel Sealing Experiment (Chandler et al. 2002).
130 Level
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300 Level Heated Failure Tests
420 Level The Mine-by Experiment
The Excavation Stability Study
Figure 1. The Underground Research Laboratory (left) and the Mine-by Experiment (right).
The Mine-by Experiment involved excavation of a 46-mlong circular test tunnel using a non-explosive rock breaking technique (Figure 1). The central axis of the excavation was nearly parallel to the direction of the intermediate principal stress in the rock mass creating a very high stress differential acting in the plane of the tunnel cross-section. High horizontal in situ stress magnitudes (60 MPa), coupled with a high in situ stress ratio (≈6:1), resulted in the rock’s in situ strength being exceeded in the roof and floor of the tunnel and the subsequent formation of v-shaped breakout notches. A three-dimensional numerical analysis of the experiment revealed that the macroscopic failure associated with this notch formation initiated at a location on the excavation surface where the maximum compressive stress was approximately half the unconfined compressive strength. The use of continuum-based numerical models to predict the onset and evolution of fracturing around the Mine-by Experiment tunnel was problematic. It was concluded by Read and Martin (1996) that simulation of progressive failure requires the ability to represent the transition from a continuum to a discontinuum, and that none of the continuum-based codes used to model the Mine-by Experiment could reproduce this failure process adequately. Such codes predict no failure surrounding the Mine-by Experiment tunnel when the laboratorymeasured rock strength is used. Arbitrarily reducing the rock strength by 50% resulted in failed rock zones that were too large and did not reflect the geometry of the vshaped notch. These deficiencies of continuum-based models rendered their use in forward prediction of measured results questionable, and therefore, the emphasis of the modelling effort since the Mine-by
Experiment has been directed at understanding the fundamentals of rock mass failure. 3. IN SITU INVESTIGATIONS The Mine-by Experiment was only the first in a series of rock response investigations conducted at the URL. The Heated Failure Tests investigated the effects of thermal loading, as would be expected in the rock mass immediately surrounding a geologic repository for used reactor fuel, on progressive rock failure and excavationinduced damage (Read et al. 1997a). Large diameter (600 mm) boreholes were drilled into the floor of the Mine-by Experiment tunnel. These boreholes were subjected to various thermal and internal confinement loading sequences. Acoustic emission monitoring and acoustic velocity measurements represented an important component of this work. The results from the Heated Failure Test indicated that a damaged zone developed near the perimeter of excavations that was affected by both the magnitude of radial and tangential stress and the sequence in which the thermal and excavation-related stress redistribution loads were applied (Read et al. 1997b). To investigate various factors affecting tunnel design, a series of nine different shaped openings were constructed subparallel to the Mine-by Experiment tunnel (i.e. subparallel with the intermediate principal stress). These tunnels were designed based on a twodimensional elastic analysis of the tangential stress on the tunnel boundary (Read et al. 1998). This experiment is referred to as the Excavation Stability Study (Read et al. 1997b).
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Upper Level (Room 418) 125 MPa
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Main Level (Room 417) 120 MPa
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Mine-by Experiment tunnel (Figure 1) 140 MPa
Lower Level (Room 421)
Figure 2. Two Examples of Excavations from the Excavation Stability Study (left) and the Nine Tunnel Geometries Investigated.
The two ovaloid tunnel photographs in Figure 2 have the same cross-sectional dimensions, however the major axis of the tunnel in the upper photograph was aligned parallel with the maximum in situ stress (approximately 11º from horizontal). Orienting the tunnel cross-section more favourably with the in situ stress field was the apparent difference between the creation of a large vshaped notch in one tunnel and only minor spalling (1020 mm thick slabs) on the surface of the second tunnel. A cylindrical tunnel excavated using drill-and-blast techniques produced essentially the same v-shaped notches observed for the mechanically-excavated Mineby Experiment tunnel pictured in Figure 1. The findings from the Excavation Stability Study illustrated that it is possible to construct large stable underground openings with only limited excavation damage in adverse stress conditions such as those that exist at the 420 m depth of the URL. Read (1994) analysed the response of 399 individual displacement measurements taken during excavation of the Mine-by Experiment tunnel, using tunnel convergence arrays and 11 multi-point extensometers strings installed in the surrounding rock. Read concluded that, with the exception of regions of failed rock near the surface of the tunnel, the granite at the URL can be modelled as a linear elastic solid. Investigating the responses from the nine different tunnel shapes of the Excavation Stability Study (Read et al. 1998), it was evident that a three-dimensional linear elastic modelling approach was useful in predicting whether or not failure (i.e. notching) would occur. However, where rock failure was observed, the linear elastic modelling was insufficient to determine the extent of fracturing and/or notching. The simple linear elastic approach also could not address issues related to the sequence of loading during heating and application of confinement (representative of backfilling) for the Heated Failure Test. Read et al. (1998) also concluded that two dimensional modelling alone cannot account for three-dimensional stress effects occurring ahead of the advancing tunnel face. An example of linear elastic modelling output for a tunnel where failure did not occur is provided in Figure 3.
4.
ACOUSTIC EMISSION MEASUREMENTS
The definition of acoustic emission/microseismicity (AE/MS) varies across scientific and engineering literature but is defined here as it applies to the URL. The AE term is used for that frequency spectrum of induced seismicity, which is recorded by ultrasonic transducers in the range of 50 to 5000 kHz, while the MS term is used for induced micro seismicity recorded by accelerometers in the range of 0.1 to 50 kHz. A typical MS event is analogous to a hammer blow, while and AE event has the energy of a pencil lead break. The objective of AE/MS monitoring is to remotely record brittle deformation by digitally collecting the waveforms emitted when rock cracks or fractures slip.
Figure 3. Elastic Modelling of the Rock Surrounding an Excavation Where a V-Shaped Notch Did Not Form. The model represents the tunnel in the upper photograph in Figure 2.
AE/MS monitoring has been an important component of the URL testing program, and has been used in a wide variety of in situ and laboratory projects (Young and Collins 1997). The studies at the URL have shown that AE and MS techniques are extremely valuable for validating numerical models by comparing the calculated extent of excavation induced damage with the limit of damage mapped by the acoustic monitoring system. Source locations of MS events during excavation of the Mine-by Experiment tunnel (Figure 4) indicated that rock damage occurred not only in the roof and floor of the tunnel, where the notches eventually formed, but also in the rock just ahead of the tunnel face (Read and Martin 1996). The absence of events within the rock mass a metre or so away from the excavation surface is consistent with observations that damage is localized near the excavation. The observation that damage occurs ahead of the tunnel face, potentially weakening the rock in the region where no excavation yet exists, underlies the importance of considering threedimensional stress paths in the analysis of rock failure (Read et al. 1998).
5.
PARTICLE FLOW CODE MODELLING
The Particle Flow Code (PFC) (Itasca, 1999) is a conceptual departure from finite element, finite difference or boundary element codes traditionally used to model the behaviour of rock or other geotechnical materials. In a PFC two-dimensional model, a synthetic material is created from an assembly of bonded circular particles. By defining load-displacement and strength characteristics at the contacts between the particles, a simulated material is created that displays many of the characteristics of rock.
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Figure 4. Location of Microseismic Events Recorded During Excavation of the Mine-by Experiment Tunnel.
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The physical laws of motion govern the velocity and acceleration of each disc within the synthetic material. Artificial tests are performed on the assembly of bonded particles to calibrate the properties of the contacts in order that the entire assembly replicates laboratory defined strength and stress-strain characteristics of the material being modelled. An example of a twodimensional PFC model subjected to biaxial loading is illustrated in Figure 5. The Lac du Bonnet granite at the URL has very definite time-dependent properties. Schmidtke and Lajtai (1985) conducted static fatigue tests on Lac du Bonnet granite by applying a constant axial load greater than about 60% of the unconfined strength and measured times-tofailure of between a minute and several days (Figure 6). The model of rock used in the PFC analysis for Lac du Bonnet granite assumes that the strength of the rock degrades with time, and the tensile loads at the contacts between particles control the rate of strength reduction (Potyondy and Cundall 2001).
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Figure 5. A Biaxially Loaded Synthetic PFC Material. Upper left: contact forces are illustrated by the thickness of the black lines. Upper right: Locations of bond breakages: Lower: A plot of axial stress versus axial strain through to sample failure.
Stress Level/Peak Strength
A synthetic PFC material is assembled from a collection of randomly sized and positioned discs. Contacts are formed where the discs touch and each contact is assigned shear and normal strengths and stiffnesses. The discs have mass, but are rigid, therefore, all deformation occurs at the contacts
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Time to Failure (days) Figure 6. Static Fatigue Test Data on Lac du Bonnet Granite (from Schmidtke and Lajtai 1985).
The strength degradation model is consistent with the mechanism of stress-corrosion in crystalline rock, and is referred to as the PFC stress-corrosion, or s-c, model. The time-dependent PFC s-c model was calibrated
through back-analysis of Schmidtke and Lajtai’s laboratory data (Figure 6) as well as the data from Lau et al. (2000). The s-c model is controlled by three microparameters, which are obtained by matching the numerically generated time-to-failure data with laboratory results. The bonds at the contacts of the s-c model (referred to as parallel bonds) are assigned a radius (i.e., they can be represented as discs of glue between two spherical particles). When the tensile stress in the bond exceeds a micro-activation stress, the bond radius decreases. This produces both a stiffness reduction and a stress increase in the remaining bond material, which fails when the stress exceeds the bond strength (Potyondy and Cundall 2001). The velocity (v) at which the bond radius decreases in size is given by:
simulations respectively. The assembly of particles was set within an infinite elastic boundary. The stresses applied to the model were the maximum and minimum principal stresses measured at the 420 m depth of the URL: 60 MPa, and 11 MPa respectively, with the maximum stress inclined at 11º from horizontal. The PFC crack distributions from the three tunnel simulations are provided in Figure 8; these can be compared with photographs of the failed zone around each tunnel (Figures 1 and 2).
v 1 exp 2 c
Log of Time-to-Failure (secs)
where σ is the tensile stress in the bond, σc is the bond strength and β1 and β2 are model parameters determined through calibration. The time to failure as a function of stress applied to a sample (the stress is normalized relative to strength) for the PFC s-c model is compared with data for Lac du Bonnet granite Figure 7.
Axial Stress / Unconfined Strength
Figure 7. Time-to-Failure Versus Normalized Axial Load for Unconfined Samples of Lac du Bonnet Granite Compared with the PFC s-c model.
The PFC s-c two-dimensional model, calibrated to laboratory test data, was applied to simulate full-scale excavations at the URL (Potyondy and Cundall 1999). One of the simulations was the circular Mine-by test tunnel (Figure 1). Two other simulations represent tunnels excavated at the same depth and nearly the same alignment as the Mine-by Experiment tunnel (i.e. aligned subparallel to the intermediate principal stress) but having an ovaloid cross-section (these two excavations are illustrated by photographs in Figure 2). The simulations required 52,381 and 62,767 particles for construction of the circular and ovaloid tunnel
Figure 8. Microcrack Modelling Using the PFC s-c Model for Three Tunnels Excavated in the Same Alignment at the URL. The top simulation is the Mine-by Experiment tunnel (shown in Figure 1); the lower two simulations represent the two tunnels shown in Figure 2.
In a qualitative visual comparison the model provides a good simulation of tunnel response. PFC displacement vectors in Figure 9 illustrate the process of notch formation in one of the tunnels. The figure depicts large dilation and inward displacement in the failing region while displacements in the intact rock are small and elastic. This mimics the rock response observed in the Mine-by Experiment (Read and Martin 1996). Also, the notch formation process and notch formation time predicted by the PFC s-c model are reasonable. Notches form by a progressive failure process that starts at the excavation boundary and proceeds inward forming slab-like pieces of material. Potyondy and Cundall (2001) produced a refined PFC s-c model of the Mine-by Experiment that produced a small notch after 2 days of simulated time, and this notch grows to resemble that seen in the field after 2 months of simulated time.
occurring close together in space and time are clustered together to form larger AE events. This is probably a realistic assumption since studies into AE events suggest that each event is made up of smaller scale ruptures. Young et al. (2001) provide a description of particle damping and event clustering as applied to PFC modelling. The PFC s-c model with low damping and event clustering was applied to a numerical simulation of the Mine-by Experiment. The location and relative magnitudes of clustered acoustic emissions produced by PFC are compared with measured AE in Figure 10. The simulated PFC event magnitudes, and the temporal and spatial event distributions for the Mine-by Experiment model were qualitatively realistic. The PFC numerical modelling developments provided by Hazzard (1998) represent important new directions in simulating the phenomena associated with in situ rock failure.
Figure 9. Displacement Field During Notch Formation in the PFC s-c Model.
6. PFC AND ACOUSTIC EMISSIONS The underlying formulation of PFC involves dynamic displacement of the PFC particles. PFC, therefore, is capable of producing synthetic acoustic emissions (Hazzard 1998, Young et al. 2001). Damping of the motion of PFC particles is intrinsic within the numerical code and allows stable equilibrium solutions to be achieved in the simulations. Hazzard (1998) decreased the dynamic damping of the PFC particle motion to allow waves to propagate through the synthetic material after each bond breakage. This phenomenon is analogous to dynamic waves responding to cracking within the rock. If each bond breakage in PFC is considered to be an individual acoustic emission event, then the magnitudes of the events will be unrealistically low compared with event magnitudes measured in the field, such as for the Mine-by Experiment. Therefore, PFC bond breakages
Figure 10. AE Events from PFC Simulations (below) and Measured (above) for the Mine-by Experiment, Scaled for Moment Magnitude.
7.
SUMMARY
The development of conceptual and numerical models for cracking in brittle crystalline rock has been described in this paper. The Particle Flow Code (PFC) was used as the platform to implement this conceptual model. PFC can simulate the development of micro-tensions within the rock and, therefore, provides a mechanism for axial splitting of unconfined rock samples tested in the laboratory. A strength degradation model, implemented within PFC, was consistent with the theory of stress corrosion of crystalline rock. The PFC stress-corrosion (s-c) model was calibrated to the time-to-failure data from laboratory static fatigue tests on Lac du Bonnet granite.
The numerical modelling was integrated with laboratory testing, in situ investigations of excavation stability conducted at the URL, and field acoustic emission/microseismic measurements. The integrated modelling and experimental study had its beginnings with the Mine-by Experiment at the URL in 1990 and developed into its own program referred to as the Thermal-Mechanical Stability Study, which was concluded in 2001. PFC has many attributes that make it a useful tool in analysing rock failure and cracking around excavated openings including the ability to replicate many of the attributes of measured acoustic emissions. The results from this program of study will have application to other rock types and other geological environments.
ACKNOWLEDGEMENTS The Excavation Stability Study and the numerical modelling program described in this paper was funded by Ontario Power Generation for application in their Deep Geologic Repository Technology Program. The Mine-by Experiment was funded jointly by AECL and OPG (formerly Ontario Hydro) under the auspices of the CANDU Owners Group.
REFERENCES Chandler, N., Read, R., Cundall, P., Potyondy, D., Detournay, E., Young, R. P., and Lau, J. S. O. 2000. An integrated approach to excavation design - A project within Canada's Used Fuel Disposal Program. In: Pacific Rocks Proc. 4th North American Rock Mech. Symp. Seattle. pp. 12711278. Rotterdam: Balkema. Chandler, N. , Cournut, A. Dixon, D., Fairhurst, C., Hansen, F., Gray, M., Hara, K., Ishijima, Y., Kozak, E., Martino, J., Masumoto, K., McCrank, G., Sugita, Y. Thompson, P. Tillerson, J. and Vignal, B. 2002. The five year report of the Tunnel Sealing Experiment: an international project of AECL, JNC, ANDRA and WIPP. Atomic Energy of Canada * Limited Report AECL-12727 . Hazzard, J. F. 1998. Numerical Modelling of Acoustic Emissions and Dynamic Rock Behaviour, Ph.D. thesis. Keele University, Staffordshire, UK. 2D Itasca 1999. PFC Particle Flow Code in 2 Dimensions. rd Itasca Consulting Group Inc., 708 South 3 St. Suite 310, Minneapolis, Minnesota, 55415, USA. Lau, J. S. O., Gorski, B., Conlon, B., and Anderson, B. 2000. Long-term loading tests on saturated granite and granodiorite. Ontario Power Generation Nuclear Waste Management Division Report 06819-REP** 01200-10016 R00 .
*
Available through the Scientific Document Distribution Office (SDDO) AECL Chalk River Laboratories, ON. ** Available from Ontario Power Generation, Nuclear Waste Management Division, 700 University Avenue, Toronto, ON.
Potyondy, D. O. and Cundall, P. A. 1999. Modeling of notch formation mechanisms in the URL Mine-by Experiment tunnel: Phase IV - enhancements to the PFC model of rock. Ontario Power Generation Nuclear Waste Management Division Report 06819* REP-01200-10002-R00 . Potyondy, D. O. and Cundall, P. A. 2001. The PFC model for rock: predicting rock mass damage at the Underground Research Laboratory. Ontario Power Generation Nuclear Waste Management Division Report 06819-REP-01200-10061 R00**. Read, R. S. 1994. Interpreting excavation-induced displacements around a tunnel in highly stressed granite. PH.D. Thesis. University of Manitoba. Read, R. S. and Chandler, N. A. 1999. Excavation damage and stability studies at the URL – rock mechanics considerations for nuclear fuel waste disposal in Canada. In: Proc.37th U. S. Rock Mechanics Symposium. Vail, Colorado, pp.861-868. Balkema: Rotterdam. Read, R. S., Chandler, N. A., and Dzik, E. J. 1998. In situ strength criteria for tunnel design in highlystressed rock masses. Int. J. Rock Mech. Min. Sci. 35 ,261-278. Read, R. S. and Martin, C. D. 1996. Technical summary of AECL’s Mine-by Experiment, Phase 1: Excavation response. Atomic Energy of Canada Limited Report AECL-11311*. Read, R. S., Martino, J. B., Dzik, E. J., Oliver, S., Falls, S., and Young, R. P. 1997a. Analysis and interpretation of AECL’s Heated Failure Tests. Ontario Power Generation Nuclear Waste Management Division Report 06819-REP-012000070-R00**. Read, R. S., Martino, J. B., Dzik, E. J., Chandler, N. A. 1997b. Excavation Stability Study – Analysis and Interpretaion of results. Ontario Power Generation Nuclear Waste Management Division Report 06819REP-01200-0028-R00**. Schmidtke, R. H. and Lajtai, E. 1985. The long-term strength of Lac du Bonnet granite. Int. J. Rock Mech. Min. Sci. & Geomech. Abstr 22 (6), pp: 461-465. Young, R. P. and Collins, D. S. 1997. Acoustic emission/microseismic research at the Underground Research Laboratory, Canada (1987-1997). Ontario Power Generation Nuclear Waste Management Division Report 06819-REP-01200-0045 R00**. Young, R. P. and Collins, D. S. 1999. Monitoring an experimental tunnel seal in granite using AE and ultrasonic velocity. In: Proc.37th U.S.Rock Mechanics Symposium, Vail, Colorado, pp. 869-876. Balkema: Rotterdam. Young, R. P., Collins, D. S., Hazzard, J., Pettitt, W. S., and Baker, C. 2001. Use of acoustic emission and velocity methods for validation of micromechanical models at the URL. Ontario Power Generation Nuclear Waste Management Division Report 06819REP-01200-10060 R00**.
