Knowledge of stresses is important for many aspects of mine design, but conventional methods of measuring stresses produce estimates at only a limited number of points in space and time. Furthermore, stresses are known to be affected by geological structures, particularly faults, but mapping of how the stress field is affected by such structures is not currently possible. Therefore, there is a compelling reason to consider the use of techniques that can map such local stress field variations. The method of seismic stress inversion is utilised to address this limitation and its application is illustrated using seismic data collected from Nickel Rim South Mine (NRS) located in Sudbury, Ontario, Canada. NRS is a modern mine using blasthole open stoping with backfill as a means of bulk mining. The ellipsoidally shaped orebody is located between 1,160 and 1,710 m below ground surface, strikes east-west and is steeply dipping. Although the NRS host rock and orebody are relatively massive with high strength, the mine is structurally complicated. Many faults appear to influence the stress field, in addition to being the sources of seismic events. The seismic monitoring array in NRS has good coverage over the active volume of the mine and consists of uniaxial and triaxial geophones and accelerometers. This combination of sensors results in a large catalogue of events with good focal sphere coverage that permits source mechanism analyses to be performed. Extensive filtering has been applied to the seismic data to improve the quality, and for the stress inversion process the first motion stress inversion (MOTSI) software is used. MOTSI only uses the first motion polarities and estimates the stress tensor components with more complete uncertainties compared to other nonlinear methods. To facilitate development and refinement of the seismic stress inversion process, numerous clusters of seismic events over a period of seven months during the early stages of mining were initially analysed so as to minimise perturbations caused by the interaction between mining and geological structures. More than 500 manually processed events throughout the mine are utilised for the stress inversions. Results show that the clusters in the earlier stages of mining and further away from excavation boundaries demonstrate reasonable agreement with pre-mining stress estimates based on overcoring and breakouts.
The majority of seismic hazard assessment tools are solely based on statistical analyses of several seismic source parameters such as event rate and time, and seismic moment. These analyses are often applied to the entire mining area which can impact the accuracy and reliability of the hazard assessment tool in each zone. Experience has shown that mining geomechanical risk is complex and its mitigation needs a broad understanding of other geotechnical factors such as rock mass properties, geological structures, mining method, stress regime, etc. Since all the contributing parameters and their impact are not entirely understood, it is critical to apply a range of geotechnical/geomechanical analyses in correlation to each other and quantify the changes in the rock mass behaviour. The goal of this paper is to develop a seismic hazard assessment tool calibrated for each geotechnical domain within the mine. To develop the tool, we incorporated mine geotechnical and geological data, seismic source parameters, and tomography analyses from a hard rock underground mine in North America. There exist several sub-vertical faults and one horizontal structure in the mine which create clear contrasts in rock mass behaviour across the structure. The results show good correlation among the different datasets, and a calibrated seismic hazard tool has been developed that provides ongoing updates to the mine operation.
The seismic stress inversion method has been developed and used in the field of crustal seismology, but due to the technical challenges and lack of a mining-specific application methodology, it has rarely been used for the analysis of mining-induced seismicity. The technique is based on assumptions that the stress is uniform in the volume of study (less satisfied in mining environments and near geological structures), and slip on any fault plane occurs in the direction of maximum resolved shear stress. Currently, there is a variety of seismic stress inversion algorithms available which use multiple seismic events to constrain the fault plane solutions for determining the four parameters of the stress tensor (orientations of principal stresses and their relative magnitude). First motion stress inversion (MOTSI) is a widely used code that uses first motion data in the inversion. For a group of events, MOTSI runs a test on two factors; dS and dM. The parameter dS specifies rejection of the homogeneous stress hypothesis when it exceeds 2.32 (95% confidence level) and the parameter dM defines the similarity between the stress-constrained and unconstrained focal mechanisms (dM = 1, represents no change). Events with large deviations from acceptable levels of dS and dM should not be used in the stress inversion process. These events are expressed as outliers because there is not enough information to infer their relation to the other events. The goal of this paper is to use statistical techniques to explore the characteristics of these outlier events. Outliers are of particular interest in this case because by indicating non-compliance with the homogeneous stress hypothesis, they may be good indicators of zones where there is strong influence of geological structures on the stress field. The seismic events for this study are recorded over a period of ten months during the early stages of mining (to satisfy the uniform stress assumption) and from a specific area (to have a better coverage of focal sphere) of the Nickel Rim South Mine in Sudbury, Canada. More than 500 seismic events were manually processed and after removing noise and applying different filters, we were able to determine the orientation of the principal stresses through seismic stress inversion from the middle level of the mine. The aggregate of the inversions inferred a north-south, northeastsouthwest orientation of the maximum principal stress and near vertical minimum principal stress. In each inversion processed, several events were tagged as outliers according to the mentioned criteria. Several statistical analyses including mean, standard deviation, variance, t-test, box plot, Kurskal-Walles test, and principal component analysis (PCA) were conducted over 10 seismic source parameters (i.e. source radius, seismic moment, etc.) to determine the relation between outliers and used data.
The paper demonstrates the use of the response surface method (RSM) to carry out probabilistic assessment of the seismic bearing capacity of shallow footings seated near naturally occurring heterogeneous slopes. To this end, a pseudo-static loading is applied to a randomly uniform slope, which is homogeneous in each case but random between realizations. The method substantially reduces the number of Monte Carlo simulations required to carry out cumbersome probabilistic slope stability analyses. A finite element limit analysis model based on the lower bound theorem is developed, which is then used to generate a large synthetic database of numerical results for the seismic bearing capacity of shallow foundations resting on inherently variable natural slopes. To this end, a permutation of the key parameters is formed and lower bound FELA-based limit loads are sought through optimization in MATLAB. A closed-form solution is formulated using RSM-based polynomials. The RSM equations, which are acquired from least squares regression analyses, are used to carry out probabilistic Monte Carlo simulations and the results are presented in forms of cumulative distribution functions. Results from the probabilistic analyses are introduced into some reliability-based design approach to render design loads for different reliability levels.
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