Erik Eberhardt

Numerical analysis of initiation and progressive failure in natural rock slopes—the 1991 Randa rockslide

The 1991 Randa rockslide in the Swiss Alps involved several complex mechanisms relating to geological, mechanical and hydrological processes for which no clear trigger can be asserted. This paper investigates the concept of progressive failure and the numerical modelling of rock mass strength degradation in natural rock slopes using the Randa rockslide as a working example. Results from continuum (i.e. finite-element) modelling are presented to illustrate a hypothesis, suggesting that initiation of a progressive rock mass degradation process, ultimately leading to failure, began following deglaciation of the valley below. Discontinuum (distinct-element) modelling is then applied to investigate the underlying mechanisms contributing to the episodic nature of the rockslide. Finally, the use of a hybrid method that combines both continuum and discontinuum techniques to model fracture propagation are discussed in the context of modelling progressive slide surface development linking initiation and degradation to eventual catastrophic failure.

Quantifying progressive pre-peak brittle fracture damage in rock during uniaxial compression

This paper presents the findings of an extensive laboratory investigation into the identification and quantification of stressinduced brittle fracture damage in rock. By integrating the use of strain gauge measurements and acoustic emission monitoring, a rigorous methodology has been developed to aid in the identification and characterization of brittle fracture processes induced through uniaxial compressive loading. Results derived from monocyclic loading tests demonstrate that damage and the subsequent deformation characteristics of the damaged rock can be easily quantified by normalizing the stresses and strains observed in progression from one stage of crack development to another. Results of this analysis show that the crack initiation, sci, and crack damage, scd, thresholds for pink Lac du Bonnet granite occur at 0.39sUCS and 0.75sUCS, respectively. Acoustic emissions from these tests were found to provide a direct measure of the rapid release of energy associated with damage-related mechanisms. Simplified models describing the loss of cohesion and the subsequent development of microfractures leading up to unstable crack propagation were derived using normalized acoustic emission rates. Damage-controlled cyclic loading tests were subsequently used to examine the eAects of accumulating fracture damage and its influence on altering the deformation characteristics of the rock. These tests revealed that two distinct failure processes involving the progressive development of the microfracture network, may occur depending on whether the applied cyclic loads exceed or are restrained by the crack damage stress threshold. # 1999 Elsevier Science Ltd. All rights reserved.

Numerical modelling of three-dimension stress rotation ahead of an advancing tunnel face

As underground excavations and construction works progress into deeper and more complex geological environments, understanding the three-dimensional redistribution of excavation-induced stresses becomes essential given the adverse consequences such stresses will have on the host rock strength and the subsequent excavation stability. This paper presents the results from a detailed three-dimensional finite-element study, which explores near-field stress paths during the progressive advancement of a tunnel face. These results demonstrate that as the tunnel face approaches and passes through a unit volume of rock, the spatial and temporal evolution of the three-dimensional stress field encompasses a series of deviatoric stress increases and/or decreases as well as several rotations of the principal stress axes. Particular emphasis is placed on the rotation of the principal stress axes as being a controlling factor in the direction of fracture propagation. If this orientation changes in time, i.e. during the progressive advancement of the tunnel face, the type of damage induced in the rock mass and the resulting failure mechanisms may also vary depending on the type and degree of stress rotation. The significance of these effects is discussed in terms of microfracture initiation and propagation, brittle fracture damage and rock strength degradation. Further analysis is also presented for varying tunnelling conditions including the effects of tunnel alignment with respect to the initial in situ stress field, excavation sequencing and elastoplastic material yielding. Implications with respect to the new Gotthard base tunnel, currently under construction in Switzerland, are presented using examples from the nearby Furka tunnel. r 2001 Elsevier Science Ltd. All rights reserved.

The Hoek–Brown Failure Criterion

List of Symbols r1 Major principal stress r3 Minor principal stress Co Uniaxial compressive strength mi Hoek–Brown material constant (intact rock) mb Hoek–Brown material constant (rock mass) s Hoek–Brown material constant a Hoek–Brown material constant GSI Geological Strength Index D Disturbance factor To Uniaxial tensile strength r3max Upper limit of confining stress r Coefficient of determination

Changes in acoustic event properties with progressive fracture damage

Laboratory results from uniaxial compression tests performed on pink Lac du Bonnet granite samples indicate that a number of stages in the progressive failure process of rock can be identified through the combined analysis of strain gauge and acoustic emission (AE) data. Testing focused on identifying the crack initiation (σ ci ) and crack damage (σ cd ) stress thresholds, two key components in the brittle fracture process. Results from this testing also showed that the properties of the acoustic events are markedly different throughout loading most notably before and after crack initiation. This proved valuable in substantiating observations made using strain gauge data. This paper explores the use of acoustic emissions and the interpretation of the acoustic event properties in identifying the different stages of crack development.

Developments in the analysis of footwall slopes in surface coal mining

Abstract Surface mining of coal, particularly in areas of mountainous topography, often involves the formation of extensive footwall slopes parallel to the strata dip. Due to structural deformation steep dips on the limbs of folds may be encountered in association with thrust faults, jointing and residual shear strength conditions. Such an environment necessitates a rigorous assessment of footwall stability in order to ensure safe and economic exploitation of the coal. This paper provides a detailed review of the factors influencing footwall slope instability in surface coal mining and the major instability mechanisms which have been recognized within the published literature. The analysis of footwalls in the design stage and the back analysis of footwall slope failures has in general been undertaken using predominantly two-dimensional limit equilibrium techniques often incorporating a simplistic elastic column analysis. The application of numerical modelling techniques to surface coal mine footwalls has received little attention. In this paper the authors attempt to illustrate the potential for investigating footwall failure mechanisms and stability using principally the distinct element method.

Numerical Investigation of Seismically Induced Rock Mass Fatigue as a Mechanism Contributing to the Progressive Failure of Deep-Seated Landslides

The importance of earthquakes in triggering catastrophic failure of deep-seated landslides has long been recognized and is well documented in the literature. However, seismic waves do not only act as a trigger mechanism. They also contribute to the progressive failure of large rock slopes as a fatigue process that is highly efficient in deforming and damaging rock slopes. Given the typically long recurrence time and unpredictability of earthquakes, field-based investigations of co-seismic rock slope deformations are difficult. We present here a conceptual numerical study that demonstrates how repeated earthquake activity over time can destabilize a relatively strong rock slope by creating and propagating new fractures until the rock mass is sufficiently weakened to initiate catastrophic failure. Our results further show that the damage and displacement induced by a certain earthquake strongly depends on pre-existing damage. In fact, the damage history of the slope influences the earthquake-induced displacement as much as earthquake ground motion characteristics such as the peak ground acceleration. Because seismically induced fatigue is: (1) characterized by low repeat frequency, (2) represents a large amplitude damage event, and (3) weakens the entire rock mass, it differs from other fatigue processes. Hydro-mechanical cycles, for instance, occur at higher repeat frequencies (i.e., annual cycles), lower amplitude, and only affect limited parts of the rock mass. Thus, we also compare seismically induced fatigue to seasonal hydro-mechanical fatigue. While earthquakes can progressively weaken even a strong, competent rock mass, hydro-mechanical fatigue requires a higher degree of pre-existing damage to be effective. We conclude that displacement rates induced by hydro-mechanical cycling are indicative of the degree of pre-existing damage in the rock mass. Another indicator of pre-existing damage is the seismic amplification pattern of a slope; frequency-dependent amplification factors are highly sensitive to changes in the fracture network within the slope. Our study demonstrates the importance of including fatigue-related damage history—in particular, seismically induced fatigue—into landslide stability and hazard assessments.

Applications of Finite/Discrete Element Modeling to Rock Engineering Problems

AbstractIn this paper, the authors review recent applications of an integrated numerical modeling approach based on the analysis of the mechanical behavior of discrete systems. The numerical analysis includes both a more realistic representation of fracture networks and the simulation of rock mass behavior as a combination of failure through intact rock and displacement/rotation along predefined discontinuities. Selected examples are presented with respect to a variety of engineering problems, including shear testing, failure of hard-rock pillars, slope stability, and block/panel cave mining. The results clearly illustrate the importance of including natural jointing to better capture rock mass behavior in response to loading and unloading. Particular emphasis is given to modeling cave development and surface subsidence, and the proposed numerical method is shown to capture fully the complex rock mass response to caving associated with multi lift extraction. Whereas the use of relatively complex numerical...

The effect of neighbouring cracks on elliptical crack initiation and propagation in uniaxial and triaxial stress fields

Abstract The study of brittle fracture and its relationship to strength is a fundamental part of rock mechanics and a number of other engineering disciplines. The initiation, propagation and coalescence of these fractures results in the degradation of material strength and eventually leads to failure. Results show that the interaction of stresses between neighbouring tips of elliptical cracks aligned parallel to the direction of loading can have a significant influence on one another in terms of crack initiationand propagation. Depending on the distance separating each crack and the loading conditions imposed on the medium surrounding them, the addition of neighbouring cracks can act to either suppress or promote crack growth.

Discrete Fracture Network approach to characterise rock mass fragmentation and implications for geomechanical upscaling

Abstract Natural fragmentation is a function of the fracture length and connectivity of naturally occurring rock discontinuities. This study reviews the use of a Discrete Fracture Network (DFN) method as an effective tool to assist with fragmentation assessment, primarily by providing a better description of the natural fragmentation distribution. This approach has at its core the development of a full-scale DFN model description of fracture orientation, size and intensity built up from all available geotechnical data. The model fully accounts for a spatially variable description of the fracture intensity distribution. The results suggest that DFN models could effectively be used to define equivalent rock mass parameters to improve the predictability achieved by current geomechanical simulations and empirical rock mass classification schemes. As shown in this study, a mine-scale DFN model could be converted to equivalent directional rock mass properties using a rapid analytical approach, allowing the creation of a rock mass model that incorporates the influence of a local variable structure with continuous spatial variability. When coupled with more detailed numerical synthetic rock mass simulations for calibration and validation, a balanced and representative approach could be established that puts more equal emphasis on data collection, local- and large-scale characterisation, conceptualisation and geomechanical simulation.