Davide Elmo

A key characteristic of cave mining is the formation of a significant surface subsidence crater, which may impact nearby infrastructures, as well as have important environmental impacts. The most used empirical method in cave mining for estimating subsidence damage limits is the Laubscher method (2000). The original dataset at the core of the Laubscher chart does not reflect the conditions of the modern caves (i.e., deeper orebodies, stronger rock masses, and higher production rates). In addition, there is a need to review the definition of cave material factor. This research explains the limitations related to the method and evaluates new cases from recent cave mining operations for checking the validity of the empirical subsidence chart. In addition, the predicted cave angles could be used to calculate the volume of broken rock; however different factors could affect the proportion between the tons extracted and the growth of the crater, which are evaluated in this research using a case study. Among the limitations of this method are the MRMR, which has a lack of detailed guidelines to calculate its values; the unconfined area, related to the lower end of the “factor” and MRMR scale of the chart, which shows predicted cave angles too conservatives; the irregular topography with a greater difference in elevation, which is seen to result in lower cave angles over the peaks than the cave angles predicted using the method; the mining sequence and the structures, which are not considered in the method. The evaluation of new cases from recent cave mining operations showed that Laubscher’s method performs well in the prediction of cave angles; due to the average distance between the measured data values and the predicted data values is 4°. Moreover, the database shows a similar tendency that Laubscher’s chart because for a depth greater than 600 m the measured cave angles tend towards the same range of values (80°±4°) regardless of their geotechnical quality. Among the factors that affect the relationship between tons extracted by caving mine and estimated growth of the surface crater are the percentage of extraction, the topography, geotechnical quality, and mining sequence.

View record

In hard rock open pit mining environments the stability conditions of the bench are controlled bythe structural discontinuities. Kinematic analyses of rigid blocks provide a prediction of theexpected breakback following mining activities. In general, the observed breakback is steeperthan that predicted using conventional kinematic analysis methods, which are known to haveconservative assumptions such as ubiquity and full continuity of structures. However, this cannotbe relied upon in all cases (i.e., exploration projects or mining projects not yet into construction)and design optimization or steepening does not occur until backed by empirical evidence.Utilizing a discrete fracture network (DFN) method involving polyhedral kinematics an attemptis made to see if the steeper observed designs can be predicted using structure that is stochasticand discontinuous. DFNs have limitations due to data uncertainty, in particular to the continuityof structures. Sensitivity assessments of the continuity of structures within a DFN are alsoinvestigated. Results of the DFN based kinematic analyses indicate steeper expected breakbackangles compared to conventional kinematic analyses, however, the DFN results are inconsistentwith the observed breakback conditions. Ultimately the DFN models failed to generate sufficientblocks to represent the actual breakback conditions. Future work is required particularly withregard to determining the validity of a DFN. Simple statistical assessments of DFNs onlyconfirm that the DFN adheres to the input parameters such as orientation, continuity, andspacing. An additional check needs to be performed to assess if the spatial locations of thegenerated structures matches those of the observed structures. Additionally the potential ofprogressive failure of key blocks at the bench scale requires further analysis to determine itscontribution to breakback of benches in a mining environment.

View record

An understanding of the fragmentation of rock blocks is an important parameter in the planning and development of a block cave mine. Traditional methods for block fragmentation analysis use empirical relationships and rule-based approaches that heavily rely on the block geometry, rather than block-to-block interactions. This thesis presents a study of fragmentation processes using a hybrid finite-element/discrete-element method (FEM/DEM). The approach is capable to account for the numerical instability generally associated with the simulation of high-velocity surface interactions and subsequent fracturing. The analysis has focused on the simulation of free-falling blocks onto a fixed surface. The initial and final block breakage has been compared against parameters including the roughness and curvature of the impacted surface, and the rock block orientation in space during free fall. The fractal relationship between resulting fragments was also explored to observe if a size invariable relationship exists and could be used for block breakage prediction. The results show that the curvature of the impacted surface reduces the fragmentation of the rock block regardless of whether the surface is concave or convex. In addition, the angle at which the rock block contacts the impacted surface is critical with more eccentric angles resulting in less final fragmentation. Little to no correlation with the numeric JRC characterisation of surface roughness is seen. The fractal relationships show promising results for size invariability of fragmentation with some variability noticed possibly due to the mechanism of fracturing. These results could provide an increased understanding of the complexities of secondary fragmentation estimates and the range of fragmentation that could be expected in block caving.

View record

Volumetric fracture intensity (P₃₂) is a parameter that plays a major role in the mechanical and hydraulic behaviour of rock masses. Although it is not possible to measure P₃₂ directly using current technologies, P₃₂ can be estimated from borehole and surface data using either simulation or analytical solutions.In this thesis we use Discrete Fracture Network (DFN) models to addresses the problem of estimating P₃₂ using information from boreholes (1D data), and we also investigate the problem of quantify the uncertainty range of the calculated P₃₂. Based on the comparison between actual P₃₂ and the intensity sampled using synthetic boreholes, we propose a new methodology to estimate P₃₂ variability from linear intensity. This methodology can be useful to quantify and understand the expected variability of P₃₂ values of a project when linear intensity is the only information available.It is common practice, when calculating P₃₂ based on Terzaghi Weight (1965), to use drill run lengths, and limit the minimum angle between the borehole and the intersected fractures. The analysis presented in this thesis indicated that limiting the minimum angle of intersection would result in an underestimation of the calculated P₃₂. Additionally, the size of the interval has a great impact on the variability of the calculated P₃₂. To account for that we propose a methodology to calculate P₃₂ using variable lengths, depending on the angle between the fractures and the borehole. This methodology allows to capture the spatial variation in intensity and at the same time it avoids the artificial increasing or decreasing of the intensity sampled along borehole intervals. This can be useful when the interval intensity is used as input for interpolating P₃₂ values in block models.Finally, the research has addressed another fundamental issue, that is the impact of boundary effects in DFN models. The results confirmed that DFN models do present boundary effects with respect to the modelled fracture intensity and that these boundary effects are dependent on the size of the generation box in relation to the volume of interest and the size of the fractures.

View record

Transitioning from previous or current surface (open pit) mining to underground mass mining (caving) allows operators to extend mine life and to maintain economical production of low-grade ore bodies. The application of advanced numerical models is essential to adequately analyze and design different geotechnical aspects of open pit-to-cave transitions. This thesis offers a critical assessment of numerical methods centered around the hypothesis that a model cannot perfectly imitate reality. Therefore, the numerical modelling of large-scale mining projects requires the real problem to be idealized and simplified. It is in this simplification process that limitations arise. The objective of this research is to investigate the role of numerical analysis applied to pit-to-cave transition, and to develop models to understand the geomechanical interaction between open pit and cave mining based on different geological and mine design variables. This thesis uses primarily conceptual models, with special consideration of the planned caving operation at the Red Chris Operations in northern British Columbia. Results from hybrid continuum-discontinuum models highlight the effects of uncertainty and variability of geological materials and structural geology. Modifying discontinuous features results in significant changes to overall caving behaviour and interaction with the open pit. Overall, both conceptual models and the Red Chris case study have emphasized the need for a whole suite of models to understand outcomes. With proper use, numerical analysis can provide insight for the identification of critical scenarios which may impact future design and operations. The results demonstrate that forward modelling should be performed in the context of a risk-based approach, with numerical models as investigative tools to assess risk and evaluate the impact of different unknowns, thus classifying modelling outputs in terms of expected consequences.

View record

Strength scale effect refers to the decreasing of rock strength when specimen size increases. The drop of strength is specific of the rock type and is related to the presence of natural defects. Scale effect has been widely studied in laboratory test and numerical simulations and there is consensus on the importance of upscaled rock strength for excavation design. However, due to lack of data at scale of rock block, is not uncommon that non-upscaled laboratory properties are applied directly for geotechnical assessment. Besides, literature is scarce on practical applications of scaled rock block strength. In this thesis, numerical upscaling of rock strength is performed and used to back analyze a major instability. The study case corresponds to a highly defected and fractured leached rock that participated in a major slope failure of an open pit mine. First, geological and geotechnical characterization of the defected rock is presented. Then, rock strength is numerically upscaled using synthetic rock numerical samples. Finally, the upscaled rock strength is applied to estimate rock mass strength as input for a bidimensional slope failure back analysis. Synthetic rock experiments were performed in ELFEN FDEM code, on bidimensional samples with diameters between 5 centimeters to 1 meter. A discrete defect network was built in Fracman software based on core logging data. Uniaxial, biaxial and indirect tensile test were performed. The FDEM code was able to simulate realistically cracking patterns and stress-strain curves. The scale effect of the unconfined strength was verified while friction angle showed to be size invariant. The back analysis of slope failure demonstrated that the confined strength was overestimated, likely due to the lack of constraint that the third dimension impose.The bidimensional back analysis of the slope instability was performed in ELFEN FDEM code and RS2 continuum code. A discrete fracture network of faults was included in ELFEN analysis. Assessments applying upscaled and non-upscaled properties were compared. There was small difference between the two cases due to the larger influence of the joints regarding the upscaled rock strength. However, the case based on upscaled properties reproduced the failure more accurately in both, FDEM and continuum code.

View record

The thesis investigates the influence of data characterization process on kinematic slope stability analysis using a Discrete Fracture Network (DFN) approach. The first aspect of the data characterization process considered in this thesis is the influence of separate statistical procedure to define fracture set (aggregate vs disaggregate approach). The DFN models generated using aggregate and disaggregate approaches are compared in terms of simulated fracture properties and the kinematic slope stability analysis. The results showed the aggregate approach either overestimates or underestimates the important fracture properties such as fracture intensity and length. Accordingly, the number and volume of blocks formed on the slope would not be truly representative of field condition. The second aspect of data characterization process is the influence of conditioning (incorporation of mapped fractures) to DFN models. The unconditioned and conditioned DFN model are compared in terms of kinematic slope stability analysis, with emphasis on the locations of potential block formations. The results showed that the conditioned DFN model would allow for a better consideration of spatial locations of potentially unstable blocks. Lastly, the thesis presents the application of DFN approach to study the variability of Geological Strength Index (GSI). The Particle Size Distribution (PSD) plots obtained from DFN models are combined with the quantification method of GSI to estimate the GSI rating. Additionally, the implication of two-dimensional (2D) versus three-dimensional (3D) data to characterize rock mass blockiness is examined. The results showed that the range of GSI rating for a rock mass could be as large as ±10. This suggests the limitation on using a unique value of GSI rating, when the GSI rating is variable due to the inherent uncertainty of the rock mass in reality. The comparison between 2D and 3D blockiness showed that the blockiness observed on a 2D plane does not necessarily correspond to the true 3D blockiness of the rock mass. In these contexts, DFN models offer the opportunity to characterize this variability and provide better estimates of rock mass blockiness.

View record

Prediction of cave fragmentation has been one of the biggest concerns for caving operation, since the inadequate assessment can potentially result in loss of project value and safety. The spatial variability of the natural fracture network holds significant implications with respect to block cave mine fragmentation. In this thesis, an in situ fragmentation model is generated, based on Discrete Fracture Network (DFN) models. The volumetric fracture intensity value (P₃₂), derived from the DFN model, is used as an indicator of the rock mass’ structural character, and it provides a direct link to rock mass fragmentation. Major structures were included in the model in a deterministic manner, and the spatial variability of the fracture intensity was analyzed to derive a geostatistical model of rock mass fragmentation. The fragmentation ‘block model’ was then superimposed onto a PCBC draw schedule model, in an attempt to link fragmentation and height of draw.Poor data can potentially compromise DFN analysis, and may result in flawed validation and understanding. At the same time, it is important to define clear and objective methodologies, when analyzing field data, and when deriving input for DFN models. Piecewise Linear Interpolation and recreation of the conceptual DFN model are both used to study the influence of fracture intensity interval length and role of human uncertainty, on the final DFN-derived 3D spatial model. The results show that interval lengths are related to a resolution that can be effectively used in large-scale 3D continuum models, to represent the Representative Elementary Volume (REV) for the rock mass. A digital image processing technique is applied in order to assess caved ore fragmentation. Validation of this method has been gained from the study of lab experiments. Furthermore, a conversion factor for relating 1D image-based measurement to 3D objects is calculated, since the DFN-based in situ fragmentation model yields volumetric size distribution, whereas image processing techniques yield equivalent spherical diameters. Finally, by using the above-mentioned input data analyses, this thesis investigates the possible links between natural fragmentation, secondary fragmentation, height of draw, and observed over-sized material and hang-up.

View record

RQD measurements are performed on the assumption that the drilling cores of the rock mass would be representative of in situ geological conditions. This thesis focuses on the use of Discrete Fracture Network (DFN) modelling to study the influence of core length on RQD measurements for synthetic “homogeneous” rock masses. An homogeneous rock mass is considered to have a measurable global volumetric intensity and representing a single geotechnical domain, without the occurrence of shear zones, fault zones and closely spaced weakness planes. For a given fracture intensity, the results show that the variability of RQD measurements decreases with increasing core length size, which is consistent with the concept of Representative Elementary Volume (REV). Furthermore, an attempt is made to demonstrate the link between DFN based fracture intensity indicators (i.e. Linear Intensity, P₁₀ and Volumetric Joint Count, P30) and RQD measurements. The analysis is repeated using field data collected at two different room-and-pillar mines, and the results further demonstrate the existence of a Representative Elementary Length (REL) for RQD measurements, analogue to the concept of REV. In this research, the REL of geometrical property P₂₁, which is the length of fracture traces per unit area of sampling plane, is compared to that of RQD. Using an implicit block search algorithm, the blockiness character of the synthetic rock masses is also studied with given fracture intensities used to measure RQD values.

View record

Block cave mining is a widely employed mining method around the world due to its low operating cost. One of the key factors that affects block caving mine’s productivity is fragmentation; accordingly, significant efforts have been made and are currently being made to study fragmentation processes, including the use of numerical modelling and remote sensing techniques. It is desirable to develop fragmentation models that could be used to provide reliable estimates of the range and distribution of the sizes of the rock blocks expected to be induced by caving. In the context of block and panel cave mining, fragmentation processes are characterised as: i) In-situ (natural) Fragmentation: in-situ blocks that are naturally present within the rock mass before any mining activity takes place. They are defined by the pre-existing discontinuities. ii) Primary Fragmentation: blocks that separates from the cave back as the undercut is mined and caving is initiated.iii) Secondary Fragmentation: fragmentation that occurs as the blocks move down through the ore column to the drawpoints. The main goal of this thesis is to attempt to establish a relationship between in-situ fragmentation and secondary fragmentation. This is achieved by:i) Measuring secondary fragmentation observed at the drawpoints. Digital image processing is employed in this process, using WipFrag (WipWare, 2014) and PortaMetrics (MotionMetrics, 2015). ii) Using Discrete Fracture Networks (DFN) to generate in-situ fragmentation curves based on data mapped from boreholes and drifts. The code FracMan (Golder, 2014) is used to generate the DFN model and the fragmentation curves. Additionally, the height of draw data from code PCBC (Systems, 2015) is used to establish a relationship between modelled in-situ fragmentation and measured secondary fragmentation.iii) This research is considered to benefit the assessment of block caving fragmentation specifically the estimate of oversizes (hang-ups) at draw columns. Also as a part of the on-going project Cave-to-Mill (Nadolski, et al., 2015) conducted at UBC Mining, this research will feed into the further analysis of Cave - to - Mill study.

View record

Numerous studies presented in this thesis have reported failure of the rock mass surrounding an anchor, as a result of applied external tensile loads (i.e. pullout loads) transferred to rock mass from the anchor and the overlying structure. Resistance to this failure mechanism is provided in design by assuming that the dead weight of a uniformly shaped inverted “cone”, with an assumed initiation point and breakout angle, provides resistance to the design loads. In some cases, a minor contribution of rock mass tensile or shear strength is considered by designers across the area of the assumed pullout cone. Strength estimates for this additional resistance are based primarily on sparse historic testing data, rock mass rating type relationships developed for other applications, and engineering judgement. However, rock mass rating systems assume that the rock mass is homogenous and isotropic, and at the scale of the anchor this assumption may not be valid since individual fractures may influence anchor stability.As an alternative to the current foundation anchor design method, this research presents a new approach to the rock cone pullout problem using Discrete Fracture Networks (DFN) combined with numerical simulations. The simulations presented in the research investigate the influence of fractures in a synthetic rock mass on ultimate anchor strength, with the purpose of developing a method for incorporation of scale effects of jointing in anchor design.By using numerical simulations that allow the load transfer mechanism from the anchor to the rock mass to vary with stiffness, it is contended that the failure mechanism of the rock mass under the applied loading can be considered more appropriately in anchor designs. It is also contended that some aleatory variability associated with fractures can be quantified using a DFN-based approach. Fractures are observed to have an influence on both the load distribution in the anchor as well as the ultimate resistance of the rock mass to pullout. The mapping considerations required to produce a DFN model for anchor pullout are described in this thesis and recommendations for incorporating DFN based models in anchor design are provided herein.

View record

This thesis presents the application of the finite-discrete element method for simulation of the impact of external blast loads on tunnels in rock. An extensive database of field tests of underground explosions above tunnels is used for calibrating and validating the proposed numerical method. The numerical results are shown to be in good agreement with published data for large-scale physical experiments. 1D and 2D model results are compared to analytical spalling equations and to the field test findings. It was found that only the 2D models are suitable for support design. The influence of rock strength on tunnel durability to withstand blast loads is investigated. It was found that higher rock strength will increase the tunnel resistance to the load on one hand, but decrease attenuation on the other hand. Thus, under certain conditions, results for weak and strong rock masses are similar. Finally, a discussion on tunnel support design to withstand blasting is presented. A distinction between heavy spalling and light rockfall is made based on an estimation of the ratio of peak stress of the arriving wave to the rock tensile strength. Accordingly, different design approaches are suggested: for heavy spalling a low impedance isolating layer between the tunnel liner and surrounding rock is recommended. For light rockfall, a simplified static FEM analysis procedure is presented.

View record