Davide Elmo

Associate Professor

Relevant Degree Programs


Graduate Student Supervision

Doctoral Student Supervision (Jan 2008 - May 2021)
Derivation of an equivalent boundary method for ground-support interaction problems (2020)

This thesis presents a novel approach termed ‘Equivalent Boundary’ (EB) for the analysis of ground-support interaction problems. The basic idea of the proposed method is to simplify these problems by representing the ground as analogous structural entities. Similar to the convergence-confinement method, increased efficiency is attained by focusing on the ground-support boundary, rather than simulating a great portion of the surrounding ground, as is required in finite-element models.Within this thesis, a number of different ground-support problems are addressed: room and pillar mines, vertical circular shafts, and tunnels. Different structural analogues are chosen for each problem according to the nature of each problem: the pillar is represented by a spring, the shaft by a ring, and the tunnel by a series of beam elements. Expressions for the stiffness of the structural analogues are derived. Subsequently, the unsupported ground displacements are used as an input; based on these, the displacements, internal forces, and factor of safety of the supported ground can readily be computed. All results have been validated against numerical models.For the tunnel problem, a methodology for the analysis of circular tunnels in elastic ground is derived. The underlying assumption of the traditional convergence-confinement approach is that the tunnel is subjected to a hydrostatic stress field, a simplification which poses considerable practical limitations. Within the proposed method, the case of a tunnel subjected to a non-uniform stress field can be addressed. Subsequently, the methodology is further modified to address two more complex conditions: 1) a circular tunnel in plastic ground, and 2) a non-circular horseshoe shaped tunnel in elastic ground. Due to the efficient computational process, the method developed in this thesis is well-suited for probabilistic analyses that require a large number of iterations. A methodology for the cost estimation of tunnel support based on the construction method is presented. A practical example is used to demonstrate the advantages of the EB method developed in this thesis. Additionally, this methodology constitutes a useful stand-alone concept, which can be implemented using other available tunnel analysis methods.

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Cave-to-Mill: mine and mill integration for block cave mines (2019)

Population growth and economic development are expected to increase future global copper demand. The depletion of significant near-surface deposits and advances in detecting deeply buried ore has led to the mining industry progressively exploring further below the surface to discover new copper deposits. Accordingly, block and panel cave mining methods are being increasingly proposed as they allow massive, deeply situated ore-bodies to be mined economically. To improve the productivity of a mining method that will be used to excavate a growing proportion of global copper supply, an integrated mine and mill approach for planning and operating block cave mines, termed Cave-to-Mill, was developed. Key distinguishing features of cave mining, in comparison to other mining methods, are the uncertainty in the size of rock being fed to the mill and the lack of selectivity. As part of the Cave-to-Mill framework, fragmentation and sensor-based sorting studies were carried out at the New Afton block cave mine to investigate opportunities to improve overall productivity.Cave fragmentation is a key cave-to-mill parameter as it has implications on the productivity of both mining and milling processes. Fragmentation measurements of drawpoint muck, comminution tests and calibrated mill models were used to assess the impact of variations in feed size and hardness on New Afton mill performance. Analysis of historical mine and mill data showed that mill feed size and subsequently mill throughput are sensitive to the areas being mucked within the cave. A sensor-based ore sorting study, incorporating bulk and particle sorting systems, showed that rock from the New Afton copper-gold porphyry deposit is amenable to prompt gamma neutron activation analysis, and to X-Ray fluorescence sensors. A conceptual flowsheet, where both technologies are used as separate unit operations, was evaluated. It was found that the sorting concept demonstrated an improvement in the net smelter return of excavated material. Results from the study were used to develop a method to design and evaluate a block cave for the case where sensor-based sorting systems are included in the flowsheet.

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Failure characterization in rock engineering using a unified DFN-FDEM analysis approach (2019)

The full abstract for this thesis is available in the body of the thesis, and will be available when the embargo expires.

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Experimental investigation of the effect of broken ore properties on secondary fragmentation during block caving (2016)

Block cave mining is experiencing a global growth in importance as new large, lower grade and deeper ore bodies favouring underground mass mining methods are developed. With block caving, the rock mass fragmentation process is decisive in the design and success of the operation. The last stage of this fragmentation process known as secondary fragmentation, plays a major role in the design and success of a caving operation. Despite this, it is the least understood fragmentation stage due in part to the complex mechanisms and the numerous variables involved in this phenomenon. The broken ore density (BOD) and the inter-block friction angle (ϕ') are comprehensively investigated here. A conceptual framework describing the BOD distribution and a procedure to evaluate this parameter under both an isolated movement zone and interactive flow are proposed, and an approach to evaluate ϕ' under different broken ore properties and draw column conditions is developed to be applied to early stage feasibility studies and design. A comprehensive laboratory testing program was carried out using concrete cuboids, controlling their size, shape and compressive strength. These are used as a proxy for broken ore fragments. These results were used to develop empirical design charts for assessing secondary fragmentation and hang-ups potential. Several factors influencing the secondary fragmentation for feasibility and advanced engineering assessments have been investigated including: air gap thickness, BOD, segregation of large blocks due to draw column surface topology, broken ore strength heterogeneity, block strength damage and crushing under high confining stresses, water within draw columns, and cushioning by fines. This new knowledge will contribute to more accurate secondary fragmentation predictions at the drawpoints. Finally, a new empirical approach to predict secondary fragmentation and drawpoint block size distribution (BSD) directed at early-stage conceptual and feasibility engineering design studies is developed. This methodology, built with relevant data from related fields and supplemented by generated data, was tested against field data from the El Teniente mine, Chile, confirming satisfactory predictions for stronger rocks and mixtures of strong and weak broken ore materials. The results were not as reliable for predicting drawpoint BSD for weak rocks.

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Master's Student Supervision (2010 - 2020)
Numerical investigation on strength upscaling and its application to a back analysis of an open pit slope failure (2020)

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.

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Influence of data characterization process on the kinematic stability analysis of engineered rock slopes using discrete fracture network models and its implications for rock mass classification system (2018)

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.

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Linking the fracture intensity of an in situ rock mass to block cave mine fragmentation (2017)

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.

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Study of scale effects of rock quality designation (RQD) measurements using a discrete fracture network approach (2017)

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.

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Characterisation of Block Cave Mining Secondary Fragmentation (2016)

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.

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Numerical Modelling of Rock Anchor Pullout and the Influence of Discrete Fracture Networks on the Capacity of Foundation Tiedown Anchors (2016)

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.

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Numerical analysis of the effects of external blasts on tunnels (2015)

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.

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