Erik Eberhardt

Professor

Relevant Degree Programs

 

Graduate Student Supervision

Doctoral Student Supervision (Jan 2008 - May 2019)
Impact of faults and fault damage zones on large open pit slopes (2017)

The demand for metals combined with diminishing near surface resources has prompted the increasing development of complex and unprecedented open pit designs to recover deeper resources. These designs include pushback extensions, intentional over-steepening of toes, or the transition to underground retreat or mass mining methods. While past designs rarely involved pit depths exceeding 500 m, steeper and deeper designs approaching or exceeding 1000 m are now considered. Experiences with large open pits demonstrate that complex failure mechanisms occur with higher propensity within these slopes. New technologies used to monitor slope displacement, such as radar interferometry, along with increased real-time data processing have given engineers more data and faster tools to investigate the fundamental rock mechanics that occur within large slopes. Radar allows for the collection of large amounts of real-time data with millimeter precision. Emphasis is given in this thesis to the use of radar monitoring in resolving displacements in proximity to fault damage zones. Research was conducted to develop and execute a first of its kind 3-D radar experiment involving the simultaneous deployment of two radar systems. This experiment demonstrates that valuable knowledge, in the form of a 3-D displacement map, was used to resolve the influence of large fault zones in promoting complex slope deformation kinematics and failure mechanisms.In parallel, numerical modelling continues to develop as a key tool in understanding deep-seated rock slope deformation mechanisms. Research was conducted to investigate the characterization and representation of key fault properties within sensitivity analyses used to provide guidance on the impact of simplification of these complex structures. Representative geometries and input parameters based on case studies were used to show the influence of fault location, orientation and complexity, on stress heterogeneity created by the interaction between faults and deepening large open pits, as well as the transition to underground massmining. These interactions can create zones of plastic shear strain or extensional strain damage not typically accounted for in most stability analyses. The inclusion of stress heterogeneity and subsequent rock mass damage is shown to modify the observed mechanisms of slope movement and allow previously unviable kinematics to develop.

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Experimental investigation of the effect of broken ore properties on secondary fragmentation during block caving (2016)

Block cave mining is experiencing a global growth in importance as new large, lower grade and deeper ore bodies favouring underground mass mining methods are developed. With block caving, the rock mass fragmentation process is decisive in the design and success of the operation. The last stage of this fragmentation process known as secondary fragmentation, plays a major role in the design and success of a caving operation. Despite this, it is the least understood fragmentation stage due in part to the complex mechanisms and the numerous variables involved in this phenomenon. The broken ore density (BOD) and the inter-block friction angle (ϕ') are comprehensively investigated here. A conceptual framework describing the BOD distribution and a procedure to evaluate this parameter under both an isolated movement zone and interactive flow are proposed, and an approach to evaluate ϕ' under different broken ore properties and draw column conditions is developed to be applied to early stage feasibility studies and design. A comprehensive laboratory testing program was carried out using concrete cuboids, controlling their size, shape and compressive strength. These are used as a proxy for broken ore fragments. These results were used to develop empirical design charts for assessing secondary fragmentation and hang-ups potential. Several factors influencing the secondary fragmentation for feasibility and advanced engineering assessments have been investigated including: air gap thickness, BOD, segregation of large blocks due to draw column surface topology, broken ore strength heterogeneity, block strength damage and crushing under high confining stresses, water within draw columns, and cushioning by fines. This new knowledge will contribute to more accurate secondary fragmentation predictions at the drawpoints. Finally, a new empirical approach to predict secondary fragmentation and drawpoint block size distribution (BSD) directed at early-stage conceptual and feasibility engineering design studies is developed. This methodology, built with relevant data from related fields and supplemented by generated data, was tested against field data from the El Teniente mine, Chile, confirming satisfactory predictions for stronger rocks and mixtures of strong and weak broken ore materials. The results were not as reliable for predicting drawpoint BSD for weak rocks.

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Rock fall engineering : development and calibration of an improved model for analysis of rock fall hazards on highways and railways (2015)

My research on rock falls over the last five years is an extension of my 45 year professionalcareer that has included a wide variety of rock fall projects. This experience has provided mewith an excellent understanding of rock fall behavior; the objective of my research has been toapply this to developing improvements in rock fall modeling methods and design of rock fallcontainment structures. My research to meet these objectives has involved the following: Case studies – details of rock fall behavior at six locations with varied topography and geologyare presented, and the results have been used to verify the application of impact mechanicstheory to rock falls, and to calibrate modeling programs. Rock fall trajectories and velocities – the application of Newtonian mechanics to rock falltrajectories and velocities is described, and results compared with actual translational andangular velocities, and trajectory heights. Impact mechanics – the application of theoretical impact mechanics to rock fall impacts isdiscussed in terms of [normal impulse – relative velocity] diagrams for rough, rotating bodies,and equations relating impact and restitution velocities and angles. Coefficient of restitution – it is shown that the normal coefficient of restitution defined by the normal final and impact velocities is related primarily to impact angle rather than slope materialproperties. Furthermore, for shallow impact angles less than about 20 degrees, the normalcoefficient of restitution can be greater than 1.0. Energy changes – energy is lost during impact and gained during trajectories. Equations forenergy changes are developed, as well as diagrams showing values of changing potential, kineticand angular energies during rock falls. Rock fall modeling – results of rock fall modeling using the RocScience program RocFall 4.0 forfive case studies are presented; the applicable input parameters are listed. Design of protection structures –impact mechanics and scale model tests of protection netsshow that these structures can be designed to redirect rather than stop rock falls, and to absorbenergy uniformly during impact. These properties mean that only a portion of the impactenergy is absorbed by the net and that forces induced in the net are minimized.

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Numerical simulation of hydraulic fracture, stress shadow effects and induced seismicity in jointed rock (2013)

Hydraulic fracturing provides a means to optimize shale gas completions by enhancing the permeability of what is otherwise very tight rock. However, the coupled nature of the processes involved (e.g., thermo-hydro-mechanical-chemical), interlinked with geological variability and uncertainty, makes it extremely difficult to fully predict the spatial and temporal evolution of the hydrofrac and surrounding invaded zone. Numerical design tools have been developed to contend with this complexity, but these have largely focused on the mechanics of brittle fracture propagation at the expense of making simplifying assumptions of the host geology within which the hydraulic fracture is propagating, namely treating it as a linear elastic continuum. In contrast, the reservoir rock conditions are much more complex. Present are natural discontinuities, including bedding planes, joints, shears and faults superimposed by the in-situ stress field. The natural discontinuities under the applied in-situ stress have the potential to either enhance or diminish the effectiveness of the hydraulic fracturing treatment and subsequent hydrocarbon production. Improved understanding of the interactions between the hydraulic fracture and natural fractures under the stress field would allow designers and operators to achieve more effective hydraulic fracturing stimulation treatments in unconventional reservoirs. To better account for the presence of natural discontinuities in shale gas reservoirs, this thesis investigates the use of the 2-D commercial distinct-element code UDECTM (Itasca Consulting Group, 1999) to simulate the response of a jointed rock mass subjected to static loading and hydraulic injection. The numerical models are developed to illustrate some important concepts of hydraulic fracturing such as the effect of natural fractures in fracture connectivity, effects of stress shadowing in multiple horizontal well completion, and the effect of fluid injection in induced seismicity, so they can be used to qualitatively evaluate the effects of the in-situ environment on the design and the consequences of the design on the in-situ environment.

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Characterization and analysis of discontinuous subsidence associated with block cave mining using advanced numerical modelling and insar deformation monitoring (2011)

While block caving presents an economic means to develop lower grade ore deposits, it often leads to significant ground deformations threatening the safety of overlying mine infrastructure. For guidance on relationships between caving depth and surface subsidence, a comprehensive cave mining database was developed and the database clearly shows caving-induced surface deformations tend to be discontinuous and asymmetric due to large movements around the cave being controlled by geologic structures, rock mass heterogeneity and topographic effects. Also shown is that as undercut depth increases, the magnitude and extent of the caved zone on surface decreases. Numerical modelling conducted in a benchmark study testing several different numerical methods (finite-element, distinct-element, FEM-DEM with brittle fracture and 3-D finite-difference) indicates this is only the case for macro deformations and the lateral extent of smaller strain deformations increases as a function of undercut depth, which indicates caution should be taken against relying on existing empirical design charts for estimates of caving-induced subsidence where small strain subsidence is of concern, as the empirical data does not properly extrapolate beyond the macro deformations. In addition,sophisticated 3-D numerical modelling was investigated as a means of predicting the extent and magnitudes of caving-induced surface subsidence. Results from a back analysis of the cave-pit interactions at the Palabora mine were used to constrain the rock mass properties and far-field in-situ stresses derived from field characterization data. The “best fit” set of input properties obtained was then used for forward modelling. Further calibration was performed using high-resolution InSAR monitoring data. The close fit achieved between the predictive 3-D numerical model and InSAR monitoring data demonstrates the significant value of InSAR calibrated 3-D numerical models.Collectively, the results of this research help to further the characterization, assessment and understanding of block-caving subsidence, by addressing existing limitations in the use of empirical and numerical subsidence analysis methods. The limitations and uncertainty arising from mine site data are described, specifically the representation of mine geology, rock mass properties, in-situ stresses and cave propagation, together with means to constrain these inputs and calibrate sophisticated 3-D numerical models through back analysis and integration with InSAR data.

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Improved characterization and analysis of bi-planar dip slope failures to limit model and parameter uncertainty in the determination of setback distances (2009)

A dip slope is a natural or man-made rock slope with a persistent discontinuity behind the slope face that is coincident with, or similar to the slope inclination. Most dip slope failures occur in weak, orthogonally jointed sedimentary rock with toe breakout involving sliding along joints, plastic failure of intact blocks, and/or intense deformation of the slope that facilitates kinematic release. Dip slope failures have been reported to extend more than 20 percent of the slope’s height behind the crest, making this rock slope failure mechanism relevant in the context of engineering projects. Nonetheless, dip slope failure mechanisms and evaluation methods are not well understood because of the complexity of the toe breakout. This thesis provides an overview of dip slope failure mechanisms where bi-planar failures may occur. It provides specific guidance for evaluating a dip slope’s stability state predicated on an extensive literature review, numerical modeling, and parametric evaluations. The thesis provides methods for effectively planning and executing geotechnical investigations with the goal of establishing a dip slope’s stability state. Finally the thesis uses a comprehensive case study where very detailed geotechnical information is available as data for dip slope design. In summary, the results of this study and research suggest that: 1) typical failure mechanisms for dip slopes can be characterized and anticipated based on documented case histories and therefore site investigations should be customized towards evaluating the potential for those failure mechanisms, 2) typical geotechnical investigation and analysis methods (supplemented with numerical modeling where appropriate) may be used to evaluate a dip slope's stability state, 3) the influence of the rock mass shear strength at the toe and the failure mechanisms assumed for toe breakout is paramount while establishing a dip slope’s stability state where slopes are steeper than about 45 degrees, 4) the stability state of shallow dip slopes is dominated by the shear strength of the slope-coincident sliding surface, 5) statistical evaluations of other geotechnical parameters that dictate a dip slope’s stability suggest that at a scoping level, geotechnical investigation methods can be cost effectively planned to provide value to the geotechnical project, and 6) risk sharing dictates the current methods of dip slope evaluation and these methods can be improved based on the research contained herein.

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Master's Student Supervision (2010 - 2018)
Experimental and numerical investigation of hydraulic stimulation as a risk mitigation technique for fault slip rockburst hazards in deep underground mining (2018)

Fault slip and associated rockbursting present a significant risk to the safety of personnel and infrastructure in deep underground mines. Sudden displacement can occur on pre-existing fault planes when mining alters the stress regime present at depth, with the resulting energy release causing potentially extensive damage to mine workings. Recently, hydraulic stimulation, defined here as the injection of fluid in proximity to a fault, has been explored as a method of reducing fault slip risk. This has the potential to release the built-up stress and strain energy driving slip events before mining is advanced and workers are exposed; however, field trials to date have yielded varying degrees of success. In response, a two-part investigation has been conducted to examine the effectiveness of hydraulic stimulation in preventing fault slip for a range of geometric characteristics. In the first investigation, a laboratory testing procedure was developed in which pressurized water was injected through cylindrical granite specimens containing different offset saw cuts subject to triaxial loading. A state-of-the-art servo-controlled system was used to measure displacements, stress drops and moment magnitudes. Results indicate that heterogeneous fault surfaces produce slip events with greater moment magnitudes than smooth surfaces, and tend to respond less effectively to injection. Three-dimensional (3D) post-test specimen imaging demonstrates that variations in moment magnitude and stress release are linked to the breakdown of asperities and accompanying cohesive strength loss that occurs during shearing. This explains why stimulation is less effective on highly irregular fault surfaces, such as those containing asperities or rock bridges, since fluid pressure acts to reduce frictional strength only. In the second investigation, a numerical model of a hypothetical mining sequence was created to determine the effect of hydraulic stimulation on the frequency and severity of mining-induced slip. Though injection was effective at mitigating slip in planar fault models, increasing fault strength was observed to correlate with larger, more damaging slip events. Additionally, when fault heterogeneity was explicitly incorporated, stimulation treatments were less effective as slip and fluid propagation were impeded by intact rock segments, illustrating the importance of understanding fault geometry before the successful implementation of field-scale treatments.

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Influence of a weak layer on depth of rock failure in underground limestone mines in high horizontal stress environments (2016)

High horizontal stress environments have plagued the aggregate industry in shallow room and pillar mining operations, particularly in the northeastern United States. With population density increasing around Southern Ontario and environmental regulations becoming more stringent, it appears that Ontario’s aggregate industry could be looking underground in the near future as the source of material to meet the ever-increasing demand. Given that the near surface horizontal stress conditions in Southern Ontario are uniquely high (σH/σV = 4-6 to depths of 200m; Lo, 1978), it can be expected that slabbing and buckling failures observed in similar mining operations with lower stress regimes in the U.S. will be exacerbated in Southern Ontario. In an effort to be proactive with this expected geotechnical design issue, a distinct element analysis using UDEC was carried out to understand the mechanisms driving failure in stratified rock environments under high horizontal stress conditions as well as to observe the impact of the high horizontal stress on the maximum depth of failure in the roof where the roof is composed of limestone interbedded with a weak shale layer. Accordingly, 116 models representing a variation of rock mass conditions subjected to stress ratios (σH/σV) ranging from 1 to 4 were simulated. A Voronoi tessellation was used to represent the intact rock mass directly above the excavation so that the failure profile through intact rock could be explicitly modelled. Key conclusions from the modelling were as follows:1) A shale layer within a defined distance from the roof of the excavation could increase the depth of failure to three times what would normally be estimated for stratified rock masses of limestone only.2) Failure driven by the influence of a weak shale interbed occurs through diagonal fracturing, supporting an experimental conclusion published by Stimpson and Ahmed (1992), as opposed to slabbing or buckling. Slabbing and buckling are the common failure mechanisms in stratified rock masses without weak interbeds.Therefore, it is critical to understand the interbedded nature of the rock mass comprising the roof over a mine opening so that a proper ground support design can be developed.

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Runout exceedance prediction for open pit slope failures (2015)

Consequences from recent large open pit slope failures have increased industry and regulatory interest in establishing exclusion zones beneath an impending slope failure. Damaged infrastructure, equipment, and fatalities have resulted despite geotechnical staff effectively identifying the hazard and predicting the timing of the failure. Creating exclusion zones is a common response to reduce risk, however uncertainty remains as to how far they should extend. Advances in natural landslide research have created useful tools for landslide risk management. These tools have clear applications to pit slopes but most have not been tested or validated. This thesis validates empirical runout tools to a dataset of 105 pit slope failures and provides design charts to explicitly account for runout and runout exceedance in emergency response procedures. Results from the analysis presented demonstrate that Fahrböschung angle vs. volume, Fahrböschung angle vs. slope angle, and inundation area vs. volume relationships follow the general trend of established natural landslide models with similar scatter. However differences in liquefiable substrate, topographic confinement, and a clear dependence on material properties and slope angle necessitate a tool calibrated to open pits. Open pit specific linear regressions are provided and a new mobility index is proposed to accommodate the geometric and material constraints affecting mobility. A design tool is provided to map the inundation area back from the estimated deposit toe. These tools are best applied in a probabilistic framework to scale runout to the mine’s tolerable risk level. Runout exceedance probability charts and simple equations are provided to estimate exclusion zones and integrate runout into the mine’s risk management plan.

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Assessing fracture network connectivity of prefeasibility-level high temperature geothermal projects using discrete fracture network modelling (2014)

The Meager Creek geothermal anomaly has been identified as one of Canada’s most promising high temperature geothermal sites. Results from exploratory drilling and the presence of natural hot springs indicate that a convective hydrothermal system exists within the crystalline basement rocks at the site. These positive results prompted several companies to engage in production drilling campaigns as early as 1981. To date, all attempts to establish sustainable levels of geothermal fluid production have been unsuccessful. Low permeability and poor hydraulic connectivity of the basement granodiorites are often cited as the key geological factors limiting the development of the Meager Creek site. These conclusions are inferred from qualitative assessments of core samples and the low production yields of completed test wells, and are not based on a detailed analysis of the geometric properties of the underlying fracture network. Through the interpretation and analysis of geomechanical and hydrogeological data collected during historical field investigations at the site, stochastic discrete fracture network (DFN) models were constructed. An iterative process of simulation and analysis of individual DFN models led to a rigorous assessment of the existing connectivity of the natural fracture network. The connectivity of the existing fracture network at the Meager Creek site appears to be favourable in the area surrounding the Meager Creek Fault, which was not intersected by any of the test wells drilled. It was found that the use of DFN models was useful in estimating fracture network connectivity and can serve as a tool for optimizing the location and orientation of production wells. A high degree of uncertainty is associated with fracture network connectivity estimates due to the absence of downhole linear fracture intensity measurements and a rigorous surface mapping methodology. Fracture network connectivity estimates can be greatly improved by adjusting the design of prefeasibility-level field investigations. The additional cost and time required to incorporate these adjustments into standard prefeasibility-level geothermal field investigations is minimal.

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Development of an early warning time-of-failure analysis methodology for open pit mine slopes utilizing the spatial distribution of ground-based radar monitoring data (2013)

Slope surface deformation monitoring in open pit mines is an essential component of day-to-day operations, playing a key role in assisting mine operators in maintaining safety and production schedules. The introduction of ground-based radar within the past decade to complement conventional geodetic monitoring programs provides near real-time deformation measurements over a broad coverage area; this allows geotechnical engineers to observe the distribution of pit wall movements and their progression over time. However, when a slope deformation alarm and/or accelerating deformation trend is observed in the radar measurements, common practice is to arbitrarily select a single or small cluster of pixels for analysis rather than following a systematic procedure that utilizes the full coverage. In addition, the absence of a methodical means of efficiently carrying out “Time-of-Failure” (TOF) analyses in real time can limit the effectiveness of the early warning, pressuring the geotechnical engineer to provide action response recommendations based on a partial and/or subjective assessment.This thesis presents a new systematic multi-pixel selection technique termed the “percent deformation method” where a benchmark pixel is methodically chosen within the deforming slope and multiple surrounding pixels are selected based on a percentage of the benchmark deformation. The percent deformation method was applied to eight slope failures captured by GroundProbe Slope Stability Radar (SSR) and detailed back-analyses conducted for each case using both the inverse-velocity and the SLO TOF analysis methods. The percent deformation multi-pixel selection technique was then incorporated into a newly proposed real-time TOF analysis procedure designed for use with ground-based radar measurements.The utilization of the percent deformation method in the proposed real-time TOF analysis methodology gives more reliable results than current practice by providing recommendations for pixel selections, data filtering, where and how to undertake TOF analyses, and presenting TOF results in real time. It is hoped that the addition of a more rigorous, methodical treatment of radar monitoring data when faced with a critical slope instability will reduce uncertainty and increase confidence in any trigger action response decisions, helping to ensure a safer work environment.

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An analytical geomechanical upscaling approach for modeling jointed rock mass behaviour using ubiquitous joints (2011)

Over the past few years, the increase in scale of open pit mines and a need to more accuratelypredict the subsidence induced by block cave mining have highlighted the need to develop newanalytical techniques to replace empirical rock mass rating systems in order to better evaluatefractured rock mass properties and simulate its behaviour.This thesis focuses on the development of an analytical geomechanical upscaling approach formodeling jointed rock mass behaviour in continuum simulations based on the information thatcan be derived from Discrete Fracture Network (DFN) modelling and laboratory test results. Forthis research, many approaches have been evaluated using different constitutive models andtechniques to derive the rock mass properties.The Ubiquitous Joint Rock Mass (UJRM) constitutive model has proven to be an ideal tool tocapture both the softening effect and directionality imposed by the discontinuities on the rockmass. A good agreement has been observed between the outcomes from simulations using theupscaling approach in FLAC and similar 2D models run in ELFEN. The potential for theupscaling approach to accurately reproduce fractured rock mass behaviour was further confirmedby testing its ability to reproduce the scale effect and applying it to four different slope models.This research indicates that the developed geomechanical approach developed can reproduce thebehavior of fractured rock masses in continuum simulations while necessitating minimumpreparation time, being less computationally intensive than its discontinuum counterparts andstaying as close as possible to the data acquired in the field and from laboratory testing.

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Distinct-element modelling of intermittent deformation behaviour and fatigue in two large rock slides (2010)

This thesis reports the assessment of two large, slow moving landslides. The Campo Vallemaggia slide is located in the southern Swiss Alps, and has a recorded history of movements dating back hundreds of years. The other slide, Little Chief, is located in British Columbia, and is affected by toe submergence due to the presence of a dam. These slides have well developed sliding surfaces along which the majority of the movement takes place. A process of modelling the effects of time, involving different water tables to represent the wet and dry seasons of the year, was undertaken using UDEC (Universal Distinct Element Code, Itasca, 2009). The models were run with first the high, then low water tables, alternating repeatedly to represent model years. They were analyzed for signs of fatigue, internal deformations and long term movement trends. The Little Chief Slide was also analyzed using this method to verify the positions and existence of the sliding surface.Mohr-Coulomb plasticity was applied to both slides, and found to be sufficient for representing the Campo Vallemaggia slide, and developing fatigue indications. A sharp drop in the number of yielded elements in the model was seen at approximately 1300 years. This coincided with a slowing of the model movement and a change in the rate of opening of a fault. This was concluded to be similar to the fatigue effect commonly seen in metal.However the Little Chief slide did not develop as desired under this constitutive model, therefore the strain softening plasticity criterion was applied to this slide for models that investigated internal deformation of the sliding mass, and those focussing on development of the sliding surface.Initial strain softening models using the properties expected for the site did not give satisfactory results, likely due to geologic and geometric complications not captured in a two dimensional model using a homogeneous rockmass. Instead, lowerbound properties were applied to the slide, resulting in the development of a sliding surface similar to that interpreted at the site. As well, significant internal deformation was found using these properties, including some suggestive of a fatigue effect.

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