Gabriel Walton

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.

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.

Laboratory Determination of Rock Fracture Shear Stiffness Using Seismic Wave Propagation and Digital Image Correlation

Seismic wave propagation and digital image correlation were used during direct shear experiments on Indiana limestone specimens to investigate the stiffness of rock discontinuities (fractures) approaching shear failure. An instrumented direct shear apparatus was used to apply shear stress to the discontinuity. Compressional and shear wave pulses were transmitted through and reflected from the discontinuity, whereas digital images of the specimen surface were acquired during the test. To measure the dynamic shear stiffness of the rock discontinuities, the displacement discontinuity theory was used and the stiffness was calculated based on the ratio of transmitted to reflected wave amplitudes. The static shear stiffness was calculated based on the ratio of an increment in the applied shear stress to the corresponding increment of relative shear displacement (slip) along the discontinuity. The dynamic shear stiffness measured by seismic wave propagation showed roughly five to ten times greater magnitude than the static values measured by digital image correlation technique. This observation is found to be in agreement with available studies indicating that the frequency-dependent fracture stiffness arises from probabilistic and spatial distributions of stiffness and that dynamic moduli are typically greater than the static values.

Scale Effects Observed in Compression Testing of Stanstead Granite Including Post-peak Strength and Dilatancy

Scale effects refer to changes in mechanical behaviour associated with the volume of material being loaded or deformed. Scale effects in rocks and rockmasses are particularly complex, as an increased volume of interest changes not only the measured behaviour of intact rock, but also results in an increased sampling of natural fractures, which can often significantly influence rockmass mechanical behaviour. To isolate one component of these effects, laboratory tests performed using different size specimens can be used (scale effects in the absence of jointing). Previous studies on scale effects based on laboratory testing have tended to focus on changes in stiffness and peak strength, particularly under unconfined conditions. In this study, data are examined from specimens tested in uniaxial and triaxial compression considering not only stiffness and peak strength, but also strength evolution and post-peak dilatancy evolution. The crack initiation and crack damage stresses are found to be scale independent, whereas the post-yield rate of cohesion loss appears to change as a function of specimen size. Trends in the dilation angle are shown to be relatively scale independent, which is consistent with prior studies that found laboratory-based dilation angle models could be used to accurately replicate data collected from sparsely fractured in situ rockmasses.

Crack Damage Parameters and Dilatancy of Artificially Jointed Granite Samples Under Triaxial Compression

A database of post-peak triaxial test results was created for artificially jointed planes introduced in cylindrical compression samples of a Blanco Mera granite. Aside from examining the artificial jointing effect on major rock and rock mass parameters such as stiffness, peak strength and residual strength, other strength parameters related to brittle cracking and post-yield dilatancy were analyzed. Crack initiation and crack damage values for both the intact and artificially jointed samples were determined, and these damage envelopes were found to be notably impacted by the presence of jointing. The data suggest that with increased density of jointing, the samples transition from a combined matrix damage and joint slip yielding mechanism to yield dominated by joint slip. Additionally, post-yield dilation data were analyzed in the context of a mobilized dilation angle model, and the peak dilation angle was found to decrease significantly when there were joints in the samples. These dilatancy results are consistent with hypotheses in the literature on rock mass dilatancy.

Experimental study on the confinement-dependent characteristics of a Utah coal considering the anisotropy by cleats

Characterizing a coal from an engineering perspective for design of mining excavations is critical in order to prevent fatalities, as underground coal mines are often developed in highly stressed ground conditions. Coal pillar bursts involve the sudden expulsion of coal and rock into the mine opening. These events occur when relatively high stresses in a coal pillar, left for support in underground workings, exceed the pillars load capacity causing the pillar to rupture without warning. This process may be influenced by cleating, which is a type of joint system that can be found in coal rock masses. As such, it is important to consider the anisotropy of coal mechanical behavior. Additionally, if coal is expected to fail in a brittle manner, then behavior changes, such as the transition from extensional to shear failure, have to be considered and reflected in the adopted failure criteria. It must be anticipated that a different failure mechanism occurs as the confinement level increases and conditions for tensile failure are prevented or strongly diminished. The anisotropy and confinement dependency of coal behavior previously mentioned merit extensive investigation. In this study, a total of 84 samples obtained from a Utah coal mine were investigated by conducting both unconfined and triaxial compressive tests. The results showed that the confining pressure dictated not only the peak compressive strength but also the brittleness as a function of the major to the minor principal stress ratio. Additionally, an s-shaped brittle failure criterion was fitted to the results, showing the development of confinement-dependent strength. Moreover, these mechanical characteristics were found to be strongly anisotropic, which was associated with the orientation of the cleats relative to the loading direction.

An approach for automated lithological classification of point clouds

Terrestrial light detection and ranging (LiDAR) data can be acquired from either static or mobile platforms. The latter presents some challenges in terms of resolution and accuracy, but the opportunity to cover a larger region and repeat surveys often prevails in practice. This paper presents a machine learning algorithm (MLA) for automated lithological classification of individual points within LiDAR point clouds based on intensity and geometry information. Two example data sets were collected by static and mobile platforms in an oil sands pit mine and the MLA was trained to distinguish sandstone and mudstone laminations. The type of approach presented here has the potential to be developed and applied for geological mapping applications such as reservoir characterization or underground excavation face mapping.