Mark S. Diederichs

Stability of large excavations in laminated hard rock masses: the voussoir analogue revisited

Abstract The voussoir beam analogue has provided a useful stability assessment tool for more than 55 years and has seen numerous improvements and revisions over the years. In this paper, a simplified and robust iterative algorithm is presented for this model. This approach includes an improved assumption for internal compression arch geometry, simplified displacement determination, support pressure and surcharge analysis and a corrected stabilizing moment in the two dimensional case. A discrete element simulation is used to verify these enhancements and to confirm traditional assumptions inherent in the model. In the case of beam snap-through failure, dominant in hard rock excavations of moderately large span, design criteria are traditionally based on a stability limit which represents an upper bound for stable span estimates. A deflection threshold has been identified and verified through field evidence, which corresponds to the onset of non-linear deformation behaviour and therefore, of initial instability. This threshold is proposed as a more reasonable stability limit for this failure mode in rockmasses and particularly for data limited cases. Design charts, based on this linearity limit for unsupported stability of jointed rock beams, are presented here summarizing critical span–thickness–modulus relationships.

Evaluating roadside rockmasses for rockfall hazards using LiDAR data: optimizing data collection and processing protocols

Highways and railroads situated within rugged terrain are often subjected to the hazard of rockfalls. The task of assessing roadside rockmasses for potential hazards typically involves an on-site visual investigation of the rockmass by an engineer or geologist. At that time, numerous parameters associated with discontinuity orientations and spacing, block size (volume) and shape distributions, slope geometry, and ditch profile are either measured or estimated. Measurements are typically tallied according to a formal hazard rating system, and a hazard level is determined for the site. This methodology often involves direct exposure of the evaluating engineer to the hazard and can also create a potentially non-unique record of the assessed slope based on the skill, knowledge and background of the evaluating engineer. Light Detection and Ranging (LiDAR)–based technologies have the capability to produce spatially accurate, high-resolution digital models of physical objects, known as point clouds. Mobile terrestrial LiDAR equipment can collect, at traffic speed, roadside data along highways and rail lines, scanning continual distances of hundreds of kilometres per day. Through the use of mobile terrestrial LiDAR, in conjunction with airborne and static systems for problem areas, rockfall hazard analysis workflows can be modified and optimized to produce minimally biased, repeatable results. Traditional rockfall hazard analysis inputs include two distinct, but related sets of variables related to geological or geometric control. Geologically controlled inputs to hazard rating systems include kinematic stability (joint identification/orientation) and rock block shape and size distributions. Geometrically controlled inputs include outcrop shape and size, road, ditch and outcrop profile, road curvature and vehicle line of sight. Inputs from both categories can be extracted or calculated from LiDAR data, although there are some limitations and special sampling and processing considerations related to structural character of the rockmass, as detailed in this paper.

Appropriate Uses and Practical Limitations of 2D Numerical Analysis of Tunnels and Tunnel Support Response

In spite of the gradual development of three-dimensional analysis packages utilizing finite element models or finite difference algorithms for stress–strain calculations, two-dimensional (2D) analysis is still used as the primary engineering tool for practical analysis of tunnel behavior and tunnel support performance for design—particularly at the preliminary stage of a project. The applicability of 2D finite element analysis or analytical convergence confinement solutions to staged support installation depend on the application of an assumed or validated longitudinal displacement profile. Convergence in commonly applied 2D staged models is controlled by boundary displacement or internal pressure relaxation. While there have been developments to improve this methodology, this often assumes independence between the ground reaction curve and the support resistance, independence between the longitudinal displacement profile to support application, and the assumption that non-isotropic stresses and non-circular geometries can be handled in the same way as circular tunnels in isotropic conditions. This paper examines the validity of these assumptions and the error inherent in these extensions to 2D tunnel analysis. Anisotropic stresses and lagged (staged) excavation present a particular problem. Practical solutions are proposed for support longitudinal displacement LDPs in simplified conditions.

Effects of Grain Scale Heterogeneity on Rock Strength and the Chipping Process

AbstractHeterogeneity is an important factor controlling fracture initiation, accumulation, and propagation within polycrystalline rock. Internal spatial variability in terms of mineralogy, grain size, and anisotropy affect the yielding process. To investigate these factors, a texture-generating algorithm integrated within a numerical model was developed to create realistic rock analogs and provide user control over geological characteristics including mineral type, grain size, and anisotropic crystal shape. A mineral-specific constitutive model was created and calibrated using published values and real laboratory strength values. Brazilian tensile strength and unconfined compressive strength (UCS) model tests were developed using the finite-difference modeling software FLAC to perform parametric analysis of a series of geological characteristics. The results show that the methodology is capable of realistically reproducing damage propagation and failure behavior similar to that observed during laboratory...

Dilation and Post-peak Behaviour Inputs for Practical Engineering Analysis

Numerical models used by engineers to simulate rockmass behaviour are often limited by poor or incomplete representations of post-yield behaviour. Although conventional plasticity theory is often capable of predicting stress distributions around excavations, it is more difficult to fully capture the complex displacement patterns that are observed in situ. This is largely because conventional material models fail to capture the confinement and damage accumulation dependencies of post-yield dilatancy. Even with these mechanistic limitations in mind, simple constitutive models can be used for practical applications, although no reliable methodology for parameter selection exists. This study aims to remedy this deficiency. In this work, existing models for dilatancy based on laboratory testing data are considered and their limitations are discussed. The most accurate of these models add complexity to the analyses and also require additional input parameters beyond those which are typically obtained from laboratory testing. While the concept of a constant dilation angle during yield is not physically valid, it may be, in some cases, a sufficient model for ground response prediction. It is of interest, for practical engineering analyses, to understand the conditions where this additional complexity is required and where simplified models may be adequate. For the case of circular excavations in a uniform stress field, plastic zone displacements for mobilized and constant dilation angle models are compared and parametric sensitivities are discussed. Many material parameter combinations representative of relatively ductile rockmasses are tested, and it is shown that for most of these cases, the results obtained using a mobilized dilation angle can be well approximated through the use of an appropriate best-fit constant dilation angle. Through a statistical analysis of the data, a practical methodology for the selection of a constant dilation angle for use in simpler continuum numerical models is proposed. Further analysis under more general conditions performed using finite-difference models shows that the methodology can be applied to non-circular excavation geometries (errors are only significant near corners), general strain softening behaviour, and non-hydrostatic stress conditions where the stress anisotropy is moderate. An example of the methodology is presented in the context of extensometer data from a deep mine shaft, and the success of the methodology in providing a reasonable dilation angle estimate is demonstrated.

A New Model for the Dilation of Brittle Rocks Based on Laboratory Compression Test Data with Separate Treatment of Dilatancy Mobilization and Decay

In this study, a new model is presented for the dilation angle of rocks which deform through brittle mechanisms in laboratory compression tests. This model, which is defined by a smaller number of independent parameters than similar models, is shown to fit laboratory test data for a wide variety of rocks (sedimentary rocks, diabase, marble, granites, and quartzite). A detailed investigation of each model parameter is performed, and potential links to geological and geotechnical properties are made. A mechanistic interpretation of the observed dilation angle data is also presented, in the context of the new model. Model parameters for the rock types studied are presented, and recommendations for parameter determination/estimation are made. The key strength of the model is shown to be its flexibility to accommodate a data-poor or data-rich analysis, as well as a simplified or comprehensive implementation. Practical guidance for model modifications is provided.

An Investigation on the Fabric Type Dependency of the Crack Damage Thresholds in Brittle Rocks

AbstractFabric-guided micro-fracturing phenomenon in brittle rocks and its effect on crack damage thresholds remains subject to continuing research. The available fabric in rocks can act as a motivator for nucleation and/or extension and interaction of micro-fractures in a preferred orientation, or as a suppressor for growth of micro-cracks in a given direction by different mechanisms such as compliance (stiffness contrast) or preferred orientation of minerals and their boundaries. While anisotropy of brittle rocks in terms of their mechanical strengths can play a significant role in the stability of underground openings, the understanding of the dependency of crack initiation (CI) and crack propagation (CD) thresholds on the available fabric in rocks can improve predictions of the extension and density of micro-fracturing in different directions in the walls of underground openings. To better understand the fabric-guided micro-fracturing phenomenon, and also to study the effect of fabric types available in brittle rocks on their anisotropic behaviour, four types of brittle rocks with different types of fabric are investigated in terms of crack damage anisotropy in this paper. The rocks that are chosen for this study are limestone from the Cobourg Formation, Queenston shale, Olkiluoto mica gneiss and Lac du Bonnet granite. For each rock type, CI and CD thresholds are identified from the unconfined compressive strength testing data. The mechanical behaviour of the four rock types are investigated at each damage stress level and the contributing factors to the isotropic or anisotropic behaviour of the rocks at different crack damage thresholds are discussed.

Sensitivity Testing of the Newly Developed Elliptical Fitting Method for the Measurement of Convergence in Tunnels and Shafts

Light Detection and Ranging (LiDAR) has become more widely used in the geotechnical community as its number of applications increases. It has been shown to be useful in tunneling for applications such as rockmass characterization and discontinuity measurement. LiDAR data can also be used to measure deformation in tunnels, but before a comprehensive methodology can be developed, the accuracy issues associated with scanning must be fully understood. Once the accuracy issues associated with LiDAR are well understood, any analysis technique that uses LiDAR data must be tested to ensure that the determined accuracy issues have minimal impact on the results of the analysis. To prove the usefulness of the newly developed elliptical fitting method for the measurement of convergence in tunnels and shafts proposed by Delaloye et al. (Eurock 2012), a comprehensive analysis of accuracy issues associated with LiDAR scanning was conducted and then a sensitivity test of the convergence measurement technique was completed. The results of the analysis show that using the statistical techniques built into the elliptical fit analysis and LiDAR profile analysis, levels of real change (convergence), within the nominal level of random and systematic noise included in the data, can be measured with confidence. Furthermore, the new analysis is robust enough to handle large amounts of occlusion or missing perimeter coverage within data sets.

Geomechanical interpretation of the Downie Slide considering field data and three-dimensional numerical modelling

Downie Slide has been interpreted as a massive, composite rockslide, and a number of landslide zones have been defined based on the interpretation of morphological features and a detailed assessment of spatially discriminated slope behaviour. Key factors controlling the mechanics of massive slow-moving landslides can be interpreted through the observation and detailed study of the slope behaviour and physical characteristics. Once identified, key components influencing slope deformation can be tested using three-dimensional numerical models. Two series of numerical simulations have been developed to test how explicitly defined internal shear zones, and the interaction between landslide morphological regions, influence global landslide behaviour. Results from these numerical simulations, when compared to field monitoring data, indicate that internal shear zones have little influence on Downie Slide deformation, while the interaction between morphological zones plays a larger role in slope kinematics.

Integration of Lidar-Based Structural Input and Discrete Fracture Network Generation for Underground Applications

In this study the authors present an approach of establishing and validating discrete fracture networks (DFNs) for underground projects using LiDAR (Light Detection and Ranging) as the source data. With the use of LiDAR in geotechnical and geological engineering becoming increasingly popular, it is necessary to establish the interactive application of this technology with other tools. Such a tool is the generation of DFNs and their integration into the geomechanical design, with a specific focus on underground projects such as tunnels, caverns, repositories etc. This paper attempts to show an approach in which LiDAR data from the Brockville Tunnel, located in Ontario, Canada, is used as the source for the determination of input parameters of DFN modelling based on manual and automatic mapping techniques. Having determined a representative set of input parameters, a deterministic DFN model is created in order to calibrate other modelling parameters associated with the generation process, leading to the creation of multiple DFN models. By employing the representative elementary volume (REV) concept, these models are used in order to examine the effect of the different joint sets on the estimated REV, and to introduce an approach of determining the required number of DFN realizations and the size of the DFN models.