Discontinuum Modelling Research Articles

Practical Use of the Ubiquitous-Joint Constitutive Model for the Simulation of Anisotropic Rock Masses

Anisotropic rock masses, the behavior of which is dominated by closely spaced planes of weakness, present particular difficulties in rock engineering analyses. The orientation of discontinuities relative to an excavation face has a significant influence on the behavioral response. At the present time, discontinuum modeling techniques provide the most rigorous analyses of the deformation and failure processes of anisotropic rock masses. However, due to their computational efficiency continuum analyses are routinely used to represent laminated materials through the implementation of a Ubiquitous-Joint model. The problem with Ubiquitous-Joint models is that they do not consider the effects of joint spacing, length and stiffness. As such, without an understanding of the limitations of the modeling approach and detailed calibration of the material response, simulation results can be misleading. This paper provides a framework to select and validate ubiquitous-joint constitutive properties.

Simulating the Single- and Multi-Stage Hydraulic Fracturing: Some Insights Gleaned from Discontinuum and Continuum Modelling

Discontinuum and continuum modelling approaches were used to simulate the single- and multi-stage hydraulic fracturing. Two-dimensional discontinuum modelling of single-stage fracturing revealed a marked modification of the stress field in the vicinity of the fracture (stress shadow effect) during fracture propagation which was identified as the reason for the significant asymmetry of fracture propagation about the wellbore observed for multi-stage fracturing. Allowing the fracturing fluid to flow back after each fracturing stage appeared to minimize this stress shadow effect on fracture propagation geometry. Three-dimensional discontinuum modelling results showed similar behaviors as two-dimensional modelling. Inclined orientation of wellbores with respect to principal stresses and enabling fluid backflow after each fracturing stage were found to be effective to minimize the stress shadow effect on fracture propagation geometry after three-dimensional discontinuum modelling. Our three-dimensional continuum modelling of hydraulic fracture propagation so far revealed some promising results demonstrating its capability to simulate hydraulic fracturing applications. Finally, the specific and contrasting features of both approaches are discussed here giving some useful insights into both approaches to assist users with choosing the appropriate method for a particular simulation project.

A New Continuum Based Model for the Simulation of a Seismically Induced Large-scale Rockslide

A powerful earthquake can actuate large number of landslides due to the impact from seismic vibrations. Understanding the mechanism of such seismically induced landslide failures and the resulting landmass runout is crucial for the design of suitable preventive measures. In nature rock slopes occur in a complex physical form, therefore, numerical models are prepared to rationally reflect upon their characteristics. In present study, a numerical analysis has been performed to simulate the post-failure behaviour of a rock slope which is subjected to multi-direction seismic forces for which a continuum model has been adopted. Dynamic Finite Element method available in ABAQUS was used as the computational solver. Since rockslide is a large deformation problem, traditional Lagrangian finite element formulation is incapable of correctly simulating such phenomenon. To address this problem, the Coupled Eulerian Lagrangian (CEL) method has been used in present study. Lagrangian description is given to the stable base block, while Eulerian description is given to the fluid like sliding mass. The seismic motion is applied as a transient boundary condition on the base block. Results showed that seismicity has a major influence on failure of the rock slope. Furthermore, post-failure behaviour of the rock slope reproduced by the CEL based continuum model is fairly in agreement when compared with the results procured from conventional discontinuum modelling approach.

Novel surgical machining via an impact cutting method based on fracture analysis with a discontinuum bone model

Cutting (including sawing and drilling) is a common procedure in orthopedics. Although it is widely used, cutting is associated with surgical problems, such as bone breakthrough and necrosis. In this study, the phenomenon of large fractures was analyzed with a discontinuum model of a bone by initially predicting crack propagation. A cutting method utilizing impacts by vibration was then proposed, and experiments were performed. The results indicated that the principal cutting force decreased by more than 80% in each cutting direction. The findings suggest that the method can realize low load, high efficiency, and high accuracy of bone machining.

Evaluating orthotropic continuum analysis of stress wave propagation through a jointed rock mass

Continuum modeling and discontinuum modeling are two approaches that are used to study the problem of stress wave propagation in jointed rock masses. In this study, a numerical analysis of blast wave propagation through a rock mass of three orthogonal joint sets was conducted by replacing the discontinuous media with orthotropic continua. The features of the simulated blast waveforms were fitted to those of the real seismograms (recorded at a distance of 300 m from a production blast at the Gol-e-Gohar iron ore mine) by iterative adjustment of the variable parameters. In order to account for the effect of rock joint dilation using the orthotropic elastic constitutive model, a search range was considered for the nonzero off-diagonal terms of the compliance matrix of the equivalent media, within which these three parameters were back-calculated independently. A simulated annealing search algorithm was used in conjunction with the numerical modeling to supervise the parameter adjustment. Finally, the response of the equivalent continuous model to dynamic loading was compared with the in situ records and the response observed in previously performed discrete modeling. The results demonstrated that the values of the peak particle velocities and the predominant frequencies in the model and those from site monitoring were in good accord. However, eliminating joints led to wider response Fourier spectra than seen for the real records and the jointed model results, and the numerical model required increased additional damping to compensate for this simplification.

Discontinuum Modelling Approach for Stress Analysis at a Seismic Source: Case Study

Rockbursts in underground mines can cause devastating damage to mine workings; hence, it is important to be able to assess the potential for their occurrence. The present study focuses on a large seismic event that took place at an underground base metal mine in Canada. The event took place in a dyke near the 100/900 orebodies on 3880 Level (1180 m below surface) of the Copper Cliff Mine in Sudbury, Canada. A 3D continuum stress analysis of the orebodies, i.e., 100 and 900, using an orebody-wide model encompassing the major geological structures and in situ stress heterogeneity in the mine shows low potential for rockburst at the seismic source location—a result which contradicts the fact that a large seismic event actually took place. A postulation is thus made that there had been highly stressed regions caused by geological disturbances at the source location before mining activities took place. In order to verify the postulation, a further study is undertaken with the discrete element modelling technique, whereby a cube-shaped model containing a fracture network is subjected to a stress state similar to that at the source location. A model parametrical study is conducted with respect to the distribution of the fracture (joint) network and its mechanical properties. The results reveal that when joints are densely distributed at the source location, the stress state becomes significantly burst prone. It is observed that the length, density, stiffness, and orientation of joints have a large influence on the stress state along the joints, while the friction angle, cohesion, and tensile strength do not influence the stress state. A cube-shaped model is constructed with joint sets actually mapped at the mine and a stress analysis is performed. The results demonstrate the generation of highly stressed regions due to the interaction of the joints with the applied in situ stress fields, thus leading to burst-prone conditions. The present study numerically confirms that a preexisting fracture network found within a stiff rockmass could lead to burst-prone stress state at relatively moderate mining depths.

A Numerical Investigation of Segmental Lining Joints Interactions in Tunnels-Qomrud Water Conveyance Tunnel

A comprehensive analysis of segmental lining joints can assist to guarantee a safe construction during tunnelling and serviceably stages. This paper has thoroughly investigated the interaction mechanism of precast concrete lining joints in tunnels. The Universal Distinct Element Code (UDEC), a two-dimensional numerical program based on the distinct element method (DEM) for discontinuum modelling, was implemented to simulated a typical segmental lining model consisting of six segment rings. In the analyses, the typical segmental lining design parameters of Qomrud water conveyance tunnel, aimed to transfer 100 million cu. m. water from the origins of Dez River to central Iranian desert, were employed to fulfil the purpose of the research. In the conducted analyses, the worst-case scenario of the loading faced during the boring of Qomrud tunnel was considered. This was highly associated with the existence of the crushed zone dipping at 75 degree at the location of the key segment. The worst scenario based on the condition that concerns the crushed zone intersect segmental lining at the location of key segment has been taken into consideration. In this study, the load acting on the joints of the segments includes the gravity load from the tunnel overburden and the crushed zone stratum force that intersects tunnel with 75 slopes at the location of the key segment, the gravity force of the segments and the earth pressure. The numerical investigation has been used for the different coefficients of stress concentration of 0.5, 1, 1.5, 2 and also different geological conditions of the saturated crushed zone under critical scenario.

Uncertainty analysis of groundwater inflow into underground excavations by stochastic discontinuum method: Case study of Siah Bisheh pumped storage project, Iran

This paper presents a framework for the near-field stochastic discontinuum modeling and uncertainty analysis of groundwater inflow into underground excavations by direct utilization of discrete fracture network (DFN) concept. The sources of uncertainty in the groundwater inflow into underground excavations in fractured rocks were classified into two different groups including the geometrical and hydraulic properties of fractures. The main input data for stochastic discontinuum modeling of groundwater inflow were captured from site investigations in Siah Bisheh pumped storage project in Iran. Detailed measurements of groundwater inflow into powerhouse and transformer caverns provided the possibility to determine the hydraulic aperture through back calibration. The validity of calibrated hydraulic aperture was explored by simulation results of the groundwater inflow into transformer cavern, and shows high accuracy when compared with data obtained from field measurements. The statistical results of these groundwater flow simulations with constant calibrated hydraulic aperture reflected the uncertainty associated with geometrical properties of fractures. Finally, the role of hydraulic properties of fractures on the uncertainty of groundwater inflow was investigated by the variation of standard deviation of hydraulic aperture through the sensitivity analysis. The results of this study demonstrated that the geometrical properties of fractures did much greater uncertainty in the groundwater inflow into underground excavations than hydraulic properties. Moreover, it was found that both the mean and standard deviation of simulated groundwater inflow into underground excavations decrease non-linearly by increasing the standard deviation of hydraulic aperture even though it is generally anticipated that the uncertainty of hydrogeological systems increases by increasing the variance of hydraulic parameters.

A coupled thermo-mechanical discontinuum model for simulating rock cracking induced by temperature stresses

Temperature change often induces thermal stresses in brittle materials, such as rock, causing cracking and hazardous accidents under certain circumstances. Within the framework of the discontinuous deformation analysis (DDA) method, this paper presents a coupled thermo-mechanical discontinuum model for simulating the rock cracking process induced by temperature stresses. Firstly, based on the energy conservation principle, heat transfer process in the block system is analyzed to determine changes in the temperature field; secondly, thermal stresses are calculated and coupled with the original stress field by applying the theory of thermoelasticity; thirdly, the interface between any two adjacent blocks is checked with two failure criteria to determine whether cracking occurs; fourthly, the proposed model is incorporated into a DDA-based program for failure analysis; finally, several numerical experiments are performed for verification, the simulated results agree well with the existing analytical and test results, indicating that the proposed approach is effective for thermal cracking simulation.

A two‐dimensional coupled hydromechanical discontinuum model for simulating rock hydraulic fracturing

SummaryWithin the framework of our discontinuous deformation analysis for rock failure algorithm, this paper presents a two‐dimensional coupled hydromechanical discontinuum model for simulating the rock hydraulic fracturing process. In the proposed approach, based on the generated joint network, the calculation of fluid mechanics is performed first to obtain the seepage pressure near the tips of existing cracks, and then the fluid pressure is treated as linearly distributed loads on corresponding block boundaries. The contribution of the hydraulic pressure to the initiation/propagation of the cracks is considered by adding the components of these blocks into the force matrix of the global equilibrium equation. Finally, failure criteria are applied at the crack tips to determine the occurrence of cracking events. Several verification examples are simulated, and the results show that this newly proposed numerical model can simulate the hydraulic fracturing process correctly and effectively. Although the numerical and experimental verifications focus on one unique preexisting crack, because of the capability of discontinuous deformation analysis in simulating block‐like structures, the proposed approach is capable of modeling rock hydraulic fracturing processes. Copyright © 2014 John Wiley & Sons, Ltd.

Interaction between block caving and rock slope deformation kinematics as a function of cave position and orientation of discontinuities

Several operations are considering the transition from surface mining to underground block caving to access deeper resources. Depending on the geometry of the orebody, the undercut may be positioned beneath the foot of a large open pit slope, or behind its crest. The latter scenario also arises where a natural rock slope is present. Results are reported here from a numerical modelling study investigating the mechanics of deep-seated slope displacements in response to caving. Different failure models are investigated as a function of the orientation of the jointing pattern relative to the location and progressive development of the block cave. A 2-D discontinuum modelling approach is utilised based on the distinct-element method. The results show that the cave location and the resultant strain field, plays a significant role in the rock mass interactions that develop and the subsequent kinematic response of the slope with respect to translational, rotational and toppling behaviour.

Simulation and Application of Rock Fracture Mechanics Model

This paper study a discontinuum model on the rock mass, which represented by an assembly of jointed elements and a fracture is initiated when the stress in the joint between two elements exceeds a critical value. The rock fracture mechanics model in this paper show that the continuum damage mechanics is based on the fact that the brittle rock has pre-existing defects, and the material failure is a process of growth and nucleation of these defects.

Discontinuum Modelling in Rock Engineering

The evolution of numerical modelling in rock mechanics has made possible a more realistic representation of the behaviour of rock masses, and a more reliable prediction of the response of rock engineering structures. Discontinuum modelling techniques, namely the discrete element method, based on the explicit representation of the rock mass discontinuous structure, have progressively acquired a broader role. In this lecture, the essential concepts and main features of these numerical techniques are discussed, with reference to their historical development. The use of these idealizations is exemplified by two areas in which they proved very effective. On one hand, the analysis of practical rock engineering problems, intended, for example, for safety assessment or monitoring interpretation. This type of application is illustrated herein by dam foundation analyses based on deformable block models. A second level of discontinuum modelling involves research aimed at the understanding of the fundamental behaviour of rock and rock masses. An example of this approach is the analysis of fracture phenomena with particle models, primarily of laboratory specimens, but being extended to larger scales. Critical issues identified in the effective application of these modelling tools are examined, as well as some foreseeable evolution trends.

The role of geologic structure and stress in triggering remote seismicity in Creighton Mine, Sudbury, Canada

A study was undertaken at the Creighton Mine, near Sudbury, Canada, to investigate the relationships between geologic structure, stress, and seismicity. Creighton Mine hosts numerous families of shear zones and experiences frequent microseismic and often macroseismic events. Underground structural mapping as well as microstructural and kinematic analysis are used to characterize faults. Fault geometries are then compared to those derived from seismic event focal mechanisms. Focal mechanism information is next used for stress inversion to obtain estimates of in-situ principal stresses for three spatial clusters of events on the 7400-foot (2256m) level. Fault characteristics are then integrated into a numerical discontinuum model of the 7400-foot level of the mine to examine the distribution of stresses in the study volume. The synthesis of these elements is used to determine the sources of seismicity within the deepest levels of the mine. The major shear zones within the mine have not been found to contribute to seismicity via fault-slip but do influence the flow of stress around the main excavation. An anomalous cluster of microseismic events is postulated to be a result of induced stresses from mine development on deeper levels.

Numerical analysis of alternative mining sequences to minimise potential for fault slip rockbursting

Mining in the production area Block 19 in the LKAB Kiirunavaara Mine has resulted in extensive seismic activity and several serious rockfalls. This paper describes a modelling study aimed at quantifying the seismic potential for future mining of Block 19, considering several different mining sequences. A three-dimensional discontinuum model was used, in which geological structures were included explicitly to simulate the development of fault slip seismic events. Four different mining sequences were simulated: three of which involved leaving the whole, or part of, Block 19 as an unmined pillar. Mining was simulated from the current active mining level and for a production period of >20 years ahead in time. The results were evaluated in terms of stress influences on critical infrastructure in the footwall of Block 19 and, more importantly, the possible extent of fault slip seismic events due to mining (by calculating seismic moments). The results showed that leaving a pillar in Block 19 may be less desirable as higher seismic moments will develop in the final mining stages. However, continued mining without a pillar will also likely result in an increased seismic activity in Block 19, which needs to be addressed appropriately. Block 19 should be mined before the neighbouring production areas, but additional and more detailed numerical modelling may be needed to fine-tune the extraction sequence for each level mined.

Integration of three-dimensional laser scanning with discontinuum modelling for stability analysis of tunnels in blocky rockmasses

This paper demonstrates and evaluates 3-dimensional laser scanning (Lidar), in conjunction with block modelling, as a tool for underground rockmass characterization and stability analysis. As a drill-and-blast tunnel advances, Lidar scanning allows for the documentation of the rockmass by collecting creating millions of rock surface point locations in space creating geometric scenes. Databases of structural geology data (joints) can be created by interpreting the “virtual” rockmass. These databases, which include the location of each measurement, can be much more extensive than what is obtained by hand-mapping in traditional geotechnical data collection. The advantages and challenges of Lidar data for underground rockmass evaluation are discussed. The joint database can be subsequently be used in discontinuum modelling in order to evaluate structurally-controlled failure in blocky rockmasses, although not without a number of critical caveats addressed here. These joint system models, either statistically generated or discretely represented, can be far more representative block models than previously possible due to joint position information and a wealth of joint measurements, although a number of pitfalls can occur. The authors present a workflow from data collection and analysis to design outputs for integrating Lidar-derived point-cloud data into rockmass stability modelling.

Application of equivalent continuum and discontinuum stress analyses in three-dimensions to investigate stability of a rock tunnel in a dam site in China

Deformation and stability around a tunnel in a limestone rock mass is investigated using both (a) an equivalent continuum/discontinuum model and (b) a fully discontinuum model through three-dimensional stress analyses. In model (a), the Representative Elementary Volume (REV) mechanical properties estimated in a previous paper are used to represent the combined behavior of intact rock and 4 of the five fracture sets that had significantly smaller sizes compared to the fifth fracture set (bedding planes). To this system the bedding plane fractures were added according to its statistical geometric properties. In model (b), all five fracture sets were generated according to the obtained fracture geometry statistical models. Using model (a), effect of several factors, such as REV property values, bedding plane modeling method, the average horizontal stress to the vertical stress and tunnel depth, on the geotechnical behavior around the tunnel was studied in detail. A comparison is made between the stress analyses results obtained through the aforementioned two models.

Displacement-based numerical back analysis for estimation of rock mass parameters in Siah Bisheh powerhouse cavern using continuum and discontinuum approach

Back analysis as a modern observational method is a helpful technique for evaluation of soil and rock mass parameters and prediction of their mechanical behavior. Most back analysis techniques in geotechnical engineering problems are based on the methods that utilize the monitored data of stresses, strain and displacements. This technique is one of the prominent processes in design and evaluation of the stability of caverns that reveals the shortcoming of supports design and in fact is essential for evaluation of design parameters. Siah Bisheh pumped storage project with complex geometry, changeable geological formations and diverse geotechnical properties of rocks, is under construction on the Chalus River at the north of Iran. The underground complex consists of three main caverns placed near each other. In this study displacement based direct back analysis using continuum and discontinuum numerical modeling were applied and geomechanical properties of rocks, stress ratio and joints parameters were identified and then calculated parameters were compared with the initial design parameters. Both continuum and discontinuum modeling results were in a good agreement with measured displacements which confirm the numerical modelings correctness and back analysis results.

Estimation of width of fracture process zone in spruce wood by radial tensile test

Fracture behavior of spruce wood under radial tension was analyzed using nonlinear fracture mechanics as wood is classified as a quasi-brittle material. Stress–strain relationship with a strain-softening branch was obtained by digital image analysis and stress redistribution process, and the energy release rate of serial end-matched specimens was measured by performing a single-edge-notched tension test. The width of the fracture process zone (FPZ) was estimated by comparing two kinds of fracture energies. One was the dispersion energy per unit area to model strain localizations using a discontinuum model of damage theory, by integrating the stress–strain function with the strain-softening branch. The other was the energy release rate to determine crack growth. From this analysis, we determined that the width of the FPZ ranged from 0.3 mm to 0.5 mm in the radial direction. However, for a few specimens, the approximate stress–strain function could not be fitted into the stress–strain relationship obtained by the image analysis; it was observed that the fracture planes of these specimens tended to be more or less inclined.

Earthquake Stability Analysis of Rock Slopes: a Case Study

Stability analysis of Surabhi landslide in the Dehradun and Tehri districts of Uttaranchal located in Mussoorie, India, has been simulated numerically using the distinct element method focusing on the weak zones (fracture). This is an active landslide on the main road toward the town centre, which was triggered after rainfall in July–August 1998. Understanding the behaviour of this landslide will be helpful for planning and implementing mitigation measures. The first stage of the study includes the total area of the landslide. The area identified as the zone of detachment is considered the most vulnerable part of the landslide. Ingress of water and increased pore pressures result in reduced mobilized effective frictional resistance, causing the top layer of the zone of detachment to start moving. The corresponding total volume of rock mass that is potentially unstable is estimated to 11.58 million m3. The second stage of this study includes a 2D model focussing only on the zone of detachment. The result of the analyses including both static and dynamic loading indicates that most of the total displacement observed in the slide model is due to the zone of detachment. The discontinuum modelling in the present study gives reasonable agreement with actual observations and has improved understanding of the stability of the slide slope.