Stephen D. McKinnon

Fracture initiation, growth and effect on stress field: a numerical investigation

A numerical investigation was made of the relationships between fracture initiation, growth, stress field and boundary conditions. Two-dimensional plane strain continuum models were used in which fractures appeared as zones of strain localization developed through application of a strain softening Mohr–Coulomb constitutive model. R and R′ fractures developed first, followed by Y fractures at larger strains. The models showed that equal development of conjugate R and R′ fractures is easily changed to favor one or the other set by minor variations in model initial conditions. Strength loss in fractures caused stress field rotations in regions bounded by fractures, altering the orientation of subsequent fractures. The amount and sense of stress field rotation is dependent on the strength loss during displacement on the fractures, the orientation of fractures, and on the boundary conditions. Y oriented fractures could be explained on the basis of a Mohr–Coulomb failure criterion provided that stress field rotation is accounted for. Monitoring of fracture slip activity showed that, under conditions of constant boundary velocity, slip was discontinuous in time, alternating on fractures throughout the model.

Analysis of stress measurements using a numerical model methodology

A method is described that enables the boundary conditions of numerical models to be calibrated to individual or groups of stress measurements. The method was developed to interpret stress measurements made in mines where it is not possible to locate the measurement points far enough away from excavations to obtain a direct measurement of the pre-mining stress field. It can also be used to analyze measurements that are influenced by surface topography. The stress field at any point is assumed to be comprised of gravitational and tectonic components. The tectonic component is assumed to act entirely in the horizontal plane in the far-field and at the model boundary. Unit normal and shear tractions are applied to the model boundaries and the response is computed at the location of the measurement points in the model. An optimization procedure is used to compute the proportions of each unit response tensor that is required, in addition to the gravitational stress, to reproduce the measured stress at the measurement point in the model. Scaling of the measured stress tensor can be included in the optimization to account for incorrect rock modulus scaling of the measured strains. The method is demonstrated using a synthetic set of stresses from a numerical model in which the measurements are influenced by a nearby excavation and topography.

Stress field analysis at the El Teniente Mine: evidence for N-S compression in the modern Andes

Abstract There is a large database of triaxial stress measurements at the El Teniente Mine, Central Chile, but the complex geology, severe topography, and proximity of all measurements to extensive mining excavations made interpretation of the stress field difficult. The measurements were analyzed using three-dimensional numerical stress analysis and decomposition of the stress field into gravitational and tectonic components. By removing gravitational stresses plus local effects from the tectonic component of the stress field a calculation of the far-field tectonic stress tensor is made. It is shown that variations in the tectonic component of stress are related to shear zones cutting through the mine. The far-field major principal component of the tectonic stress field was found to be oriented approximately N–S. This is consistent with the most recent direction of local shortening based on kinematic analysis of faults, but is perpendicular to the direction of regional crustal shortening. There appears to be a limiting envelope to the magnitude of the stress field implying that the shear zones are in a state of limiting equilibrium with regional tectonic driving forces.

Rock Mass Characteristics and Tomographic Data

Good quality geomechanics data are as hard to come by in mining engineering as it is to find a geomechanics report that does not recommend more data collection. There is wide acceptance of the fact that data are integral to our understanding of the rock mass. An even higher value is placed on data that can be obtained and used in advance of drifting. Unfortunately, our current methods of data acquisition limit quality and usefulness. The most commonly available data before drifting consist of drill core mapping. Boreholes are often few and far between due to their costs, with their spacing often too wide for accurate interpolation of geomechanical characteristics. Additionally, core mapping involves significant resources, and it is not necessarily clear what information is useful. After drifting, mapping of limited faces is possible, but building a 3-D model of these data can be difficult due to poor spatial coverage. Additional data acquisition techniques are needed. Those who work in rock mechanics dream about methods that are non-invasive, inexpensive, robust, and reliable. Approaches that can provide information about the geomechanical characteristics of the rock mass as soon as possible enable timely, risk-mitigating design. It is with this in mind that correlations between velocity tomography and geomechanical characteristics are explored. Tomographic velocity models are based on seismic wave travel times within a seismic monitoring sensor array. These techniques have been used extensively and successfully in the Earth Sciences to map characteristics of the Earth at great depths, for example, the identification of the Mohorovicic Discontinuity (Moho); see Rawlinson et al. (2010) for a description of the history of tomographic techniques. To a lesser extent, these techniques have been applied in the mining environment, which is at a much smaller scale, where correlations between velocities and i) geomechanical characteristics of the rock mass (Cai et al. 2014; Hemmati Nourani et al. 2017; Watanabe and Sassa 1996), and ii) stress anomalies (Cao et al. 2015; Friedel et al. 1995, 1997; He et al. 2011; Hosseini et al. 2013; Krauß et al. 2014; Luxbacher et al. 2008; Ma et al. 2016; Young and Maxwell 1992) are evaluated. Much of this work was conducted in soft rock environments (coal mines). A general consensus about the usefulness of tomography in hard rock environments is not yet exhibited in the literature. The intention of this technical note is to present the evaluation of possible correlations between the velocity models created by Lund et al. (2017) and the geomechanical model created by Vatcher et al. (2016) for the Luossavaara-Kiirunavaara AB (LKAB) Kiirunavaara Mine, Sweden. If such correlations exist, tomography is a relatively inexpensive exploration method that may provide insight into the characteristics of the rock mass. A brief background on the two input data sources is given, followed by the grid-based statistical analysis required to understand the data and their potential correlation. Results are discussed with focus on the potential and limitations of tomographic data for rock mass characterization at the Kiirunavaara Mine. Concluding remarks are offered, which expand the results to a broader range of geological settings. J. Vatcher: Formerly Luleå University of Technology, Luleå, Sweden.