Conference PaperPDF Available

Block caving modelling using the Y-Geo hybrid finite-discrete element code

Authors:
  • Geomechanica Inc.
  • Geomechanica Inc.
  • Geomechanica Inc.
Block caving modelling using the Y-Geo hybrid finite-discrete element code
Andrea Lisjak
Department of Civil Engineering, University of Toronto, Canada
Bryan S. A. Tatone
Department of Civil Engineering, University of Toronto, Canada
Omid K. Mahabadi
Department of Civil Engineering, University of Toronto, Canada
Giovanni Grasselli
Department of Civil Engineering, University of Toronto, Canada
Abstract
The objective of this paper is to show the capabilities of a new combined finite-discrete element method
(FEM/DEM) code, known as Y-Geo, to numerically model block cave mining. Unique feature of the
FEM/DEM method is its ability to explicitly simulate fracture initiation and propagation within the rock
mass without having to define the failure surface a priori. The block caving modelling methodology is
first illustrated with particular emphasis on the excavation and production simulation and the
incorporation of a Discrete Fracture Network (DFN) into the model. Successively, the effectiveness of the
approach is demonstrated by a conceptual example of block caving operation with an undercut depth of
100m. The effect induced by a joint network with different orientation is qualitatively analyzed.
1 Introduction
The block caving method has been used for many years to mine lower grade ore bodies economically.
Estimates of the magnitude and extent of surface subsidence are needed to better understand the risk to
surface infrastructures. The use of numerical modelling has recently started to provide an opportunity to
investigate the factors governing caving mechanisms and to develop improved methodologies for the
prediction of associated surface subsidence (Vyazmensky et al., 2007). The objective of this paper is to
demonstrate the capabilities of a new combined finite-discrete element method (FEM/DEM) code, known
as Y-Geo (Mahabadi, Lisjak, Munjiza, & Grasselli, 2012), to simulate the propagation of a block caving
operation to surface. Due to the ability of FEM/DEM of explicitly simulating fracture propagation, within
one model, the progressive excavation of an undercut can be realized and the subsequent initiation and
propagation of the caving front (primary fragmentation) and many mechanisms of secondary
fragmentation of the fallen blocks can be simulated as ore is drawn.
2 Basic principles of the combined finite-discrete element method (FEM/DEM)
Widely used continuum-based numerical models (i.e., finite element and finite differences) are limited in
their ability to realistically address rock engineering problems involving failure along existing joint sets
together with fracturing of intact rock material. In order to overcome these limitations, Munjiza, Owen,
and Bicanic (1995) proposed a new hybrid finite-discrete element (FEM/DEM) method. Within the
framework of FEM/DEM, discrete element method (DEM) principles are used to model interaction
between different solids, whose deformation is analyzed by finite element analysis (FEM). Since an
explicit time-marching scheme is used to integrate Newton’s equations of motion, fully dynamic
simulations can be performed. A unique characteristic of such a numerical tool is the ability to model the
transition from continuum to discontinuum by explicitly simulating fracture and fragmentation processes
(Munjiza, 2004). The key processes in this hybrid approach include: contact detection and interaction
between discrete bodies; elastic deformation of discrete bodies; and fracture of discrete bodies. The
contact detection and interaction and fracture are discussed further in the following sub-sections.
Deformability, however, follows an approach similar to that in any standard explicit finite element
analysis and is not discussed any further here.
2.1 Contact detection and interaction
A FEM/DEM simulation can comprise a very large number of potentially interacting distinct elements. To
correctly capture this behaviour, contacting couples (i.e., pairs of contacting discrete elements) must first
be detected. Subsequently, the interaction forces resulting from such contacts can be defined. Contact
interaction forces are calculated between all pairs of elements that overlap in space. Two types of force are
applied to the elements of each contacting pair: repulsive forces and frictional forces. The repulsive forces
between the elements of each contacting pair are calculated using a penalty function method (Munjiza &
Andrews, 2000). Contacting couples tend to penetrate into each other, generating distributed contact
forces, which depend on the shape and size of the overlap between the two bodies. Body impenetrability
condition is reached as a limit condition for penalty values that tend to infinity. The frictional forces are
calculated using a Coulomb-type friction law and used to simulate the shear strength of intact material and
the frictional behaviour of rock joints (Mahabadi & Grasselli, 2010).
2.2 Fracture model
For pre-existing discontinuities, the shear strength is modelled by a Coulomb-type friction law while the
transition from continua to discontinua is accomplished by driving fractures across the interface between
adjacent triangular finite elements. A combined single and smeared crack model (Munjiza, Andrews, &
White, 1999), also known as the discrete crack model, is implemented in Y-Geo. Rock behaves elastically
until the strength limit, defined by a Mohr-Coulomb criterion with tension cut-off, is reached. Upon
overcoming the elastic limit, a new fracture is driven across the interface between adjacent triangular
finite elements. Material separation mechanisms and crack process zone are modelled by means of
cohesive elements as a gradual strength reduction governed by a softening law. Material strength
mobilization is represented by normal and shear bonding stresses,
σ
and
τ
, which are generated by the
separation of the crack edges. As depicted in Figure 1, these stresses are assumed to be a function of crack
opening, o, and sliding distance s. Fracture behaviour is ultimately controlled by the following input
parameters: tensile strength ft, internal cohesion c and internal friction angle
φ
, and mode I and II fracture
energy release rates G1 and G2. Although re-meshing is not performed ahead of the crack tip, the direction
of fracture propagation can be correctly captured as long as a sufficiently small element size is adopted.
Figure 1. Fracture model constitutive laws: A) mode I and B) mode II.
3 Block caving modelling methodology with FEM/DEM
3.1 Boundary conditions and in situ stress initialization
Due to the dynamic nature of the FEM/DEM code, special attention must be given to properly simulate
the initial state of rest for the caving system (i.e., prior to undercutting). In Y-Geo, a state of rest is
achieved through dynamic relaxation techniques whereby a viscous damping is introduced to dissipate
energy from the system. To avoid unwanted inertial effects and correctly simulate the prior-to-excavation
stress state, the caving model requires two separate runs. In the first run, the vertical and horizontal in situ
stress conditions are applied to the model domain. To prevent the development of damage in response to
this dynamic loading, all the elements are considered infinitely elastic and therefore are not allowed to
fracture. By continuing this run until the stress waves have attenuated, the revised nodal coordinates
corresponding to the system at rest (i.e., static equilibrium) are obtained. These revised nodal coordinates
are then used as the current nodal coordinates (i.e., deformed mesh) of the second run in which the actual
material strengths are assigned. By changing the lateral far-field boundaries to be fixed horizontally with
rollers and changing the basal boundary to be fixed in the vertical direction with rollers, the first order in
situ stress conditions are maintained while allowing the caving simulation to initiate.
3.2 Simulation of undercut excavation and production
With the correct in situ stress conditions achieved, the undercut is excavated. In Y-Geo, material
excavation is performed by removing the selected triangular elements from the modelling domain. A
staged undercut excavation can be simulated by specifying in the input file different removal times for
different excavation slots. An example of staged undercut excavation is illustrated in Figure 2.
Figure 2. Example of staged undercut excavation and associated fracturing mechanisms.
After creating the undercut and initiating caving, a uniform draw of caved material is simulated using a
dedicated routine of Y-Geo. Falling rock blocks are first let consolidated in the undercut under the effect
of gravity. Then, the material fallen inside the undercut perimeter is dynamically removed from the
simulation. By repeating this removal procedure multiple times, a uniform production is obtained together
with the propagation of the caving front.
3.3 Discrete Fracture Network (DFN)
Information about the rock mass fabric can be explicitly accounted for in the FEM/DEM model by
incorporating discrete fracture networks (DFNs) generated with third party software. By decreasing the
element size below the nominal block size of the rock mass, actual rock mass discontinuities can be
simulated and intact rock properties can be assigned to the model materials. By doing so, the equivalent
continuum rock mass parameters (e.g., rock mass modulus) can be abandoned and the rock mass
properties are captured as an emergent property of the model. Also, the kinematical constraint induced by
preferably oriented discontinuities can be explicitly simulated. After defining the topology of the DFN, the
fracture network is imported in the meshing software where the domain is triangulated. In Y-Geo a purely
frictional strength is assigned to the element edges that coincide with the pre-existing discontinuities.
Also, a different stiffness, represented by the penalty value, can be specified along the discontinuities.
4 Conceptual example
In order to demonstrate the capabilities of Y-Geo in modelling block caving, a bi-dimensional conceptual
model was built. The Y-GUI software (Mahabadi, Grasselli, & Munjiza, 2010) was used to assign
boundary conditions and properties to the model.
4.1 Model topology
An initiation depth of 100m was assumed together with an undercut length of 100m comprising five 20m
x 7m slots sequentially excavated from right to left. As depicted in Figure 3, four rock mass fabrics were
modelled using the Discrete Fracture Network approach: (a) homogeneous model with no pre-existing
discontinuities, (b) homogenous model with a horizontal joint set, (c) homogenous model with a joint set
inclined at 45o, and (d) homogenous model with a vertical joint set. Normal distributions were assumed for
the geometrical parameters of the DFNs. The following values were used: crack length = 10±1m, bridge
length = 6±1m, spacing = 6±1m. Joint orientation was set equal to 0o, 45o and 90o for model b), c) and d)
model, respectively.
Figure 3. Discrete Fracture Networks used in the FEM/DEM analysis.
The finite element mesh for the cross-section under analysis was created using the Delaunay
triangulation scheme of Cubit. A nominal average element size of 1.5m was used in the region interested
by the propagating cave. The mesh was then gradually graded towards the model boundaries where an
average element size of 10m was used. Each model comprised about 70,000 triangular elements.
4.2 Parameters
The following strength and deformation parameters were assumed for the intact rock material: tensile
strength ft = 0.1MPa, cohesion c = 12MPa, friction angle
φ
= 35o, mode I fracture energy G1 = 1J/m2, mode
II fracture energy G2 = 5J/m2, Young's modulus = 1GPa, Poisson's ratio ν = 0.35. A friction angle of 25o
was assigned to the pre-existing discontinuities. The model was critically damped.
The in situ stress field was characterized by a horizontal stress
σ
h equal to the vertical stress
σ
v (i.e.,
K=1). Both components of the far field stress tensor were assumed to increase linearly with the depth z:
σ
h =
σ
v =27,000z.
4.3 Results
Figure 4 and 5 show the total displacement field of the models under investigation for a total extracted
volume of 1,300m2 and 2,300m2, respectively. As can be noticed from the figures, the presence of pre-
existing discontinuities strongly affects both the strength of the rock mass and its failure kinematics.
As expected, rock joints reduce the overall rock mass strength and therefore increase its caveability. If no
DFN is applied to the model (model a), the cave front is not able to propagate to the surface due to a
stabilizing arch effect.
The joint orientation seems to play a key role in controlling the extent of the surface subsidence profile.
The presence of vertically oriented joints (model d) tends to induce steeper angles of break which result in
steeper angles of subsidence and narrower subsidence areas. The shallowest angle of subsidence,
corresponding to the widest surface subsidence area, is obtained for a joint network having an orientation
of 45o (model c).
Figure 4. Total displacement fields for a total extracted volume of 1,300m2.
Figure 5. Total displacement fields for a total extracted volume of 2,300m2.
5 Summary and conclusions
A new modelling tool for block caving mining, known as Y-Geo (Mahabadi et al., 2012) and based on the
combined finite-discrete element method (FEM/DEM) (Munjiza, 2004), was illustrated. Unlike
continuum-based numerical methods, FEM/DEM simulates rock mass damage and failure process by
explicitly modelling fracture propagation. Therefore, mechanisms of both primary and secondary
fragmentation can be captured as emergent phenomena of the simulation. Also, the approach allows
accounting for information relative to the rock mass fabric by directly incorporating a discrete fracture
network (DFN) into the modelling domain. Application of the approach was demonstrated by means of a
conceptual example of 100m deep caving operation. Numerical results showed the strong influence of the
rock mass fabric on both caveability and failure kinematics.
References
Cubit (Version 11) [Computer Software]. Albuquerque, NM: Sandia National Laboratories.
Mahabadi, O.K., & Grasselli, G. (2010). Implementation of a rock joint shear strength criterion inside a
combined the finite-discrete element method (FEM/DEM) code. 5th International Conference on
Discrete Element Methods. London, UK.
Mahabadi, O. K.; Grasselli, G. & Munjiza, A. (2010). Y-GUI: A graphical user interface and pre-processor
for the combined finite-discrete element code, Y2D, incorporating material inhomogeneity. Computer
and Geosciences, 36, 241-252.
Mahabadi, O. K., Lisjak, A., Grasselli, G., & Munjiza, A. (2012). Y-Geo: a new combined finite-discrete
element numerical code for geomechanical applications. Accepted for publication in the
International Journal of Geomechanics.
Munjiza, A. (2004). The combined finite-discrete element method. Hoboken, NJ: John Wiley & Sons Ltd.
Munjiza, A., Andrews, K. R. F., & White, J. K. (1999). Combined single and smeared crack model in
combined finite-discrete element analysis. International Journal for Numerical Methods in
Engineering, 44, 41-57.
Munjiza, A., Owen, D. R. J., & Bicanic, N. (1995).A combined finite-discrete element method in transient
dynamics of fracturing solids. Engineering Computations, 12, 145-174.
Vyazmensky, A., Elmo, D., Stead, D., & Rance, J. R. (2007). Combined finite-discrete element modelling
of surface subsidence associated with block caving mining. In E. Eberhardt, D. Stead & T. Morrison
(Eds.), 1st Canada-US Rock Mechanics Symposium, 467-475.
... Failure conditions can take place in the boundary parts of openings at high depths of excavation and wall drilling. In some cases, the failure has a zonal character (Figure 1), where tensile macrocrack zones alternate with relatively monolithic rock mass (Adams & Jager 1980;Shemjakin et al. 1986;Qian et al. 2009;Lisjak et al. 2012;Cumming-Potvin et al. 2016). Many attempts have been made to describe the zonal character of rock mass failure near openings based on classical mechanics (Metlov et al. 2002;Odintsev 1996;Reva & Tropp 1995;Shemjakin et al. 1987). ...
... Some attempts to describe zonal failure near openings have been done with the finite element method/discrete element method (FEM/DEM) (Lisjak et al. 2012) where the block caving method of excavation has been applied. But FEM/DEM is founded on the classical theory of the continuous media where the compatibility conditions have been met and cannot be applied to the highly stressed rock mass with the zone failure description purposes (Reva & Tropp 1995;Mirenkov 2014). ...
... Although the natural fractures in coal seams have been fully studied [145,146], their effects on fracture development have not been well considered under longwall mining conditions. The hybrid continuum/discontinuum models, which share similar ability as DEM to represent fracture development, have been successfully employed to simulate the mass block caving process and surface subsidence [37,147]. Therefore, the hybrid method can also be applied to investigate longwall mining-induced fracture behaviors. ...
... Joints and cleats were considered in the model based on the SRM approach. The hybrid models containing DFN were also successfully used to simulate block caving [37,147]. ...
Article
Full-text available
It is believed that underground longwall mining usually produces fractures in the surrounding rocks. On the one hand, mining-induced fractures not only degrade the strength of the rock mass but also serve as main channels for fluids (e.g., water and methane). Fractures facilitate the failure of the rock mass and fluid inrush into working spaces. Therefore, mining-induced fractures are significant for the safety evaluation of underground structures and finding feasible solutions. On the other hand, the fractures are also beneficial for methane collection and coal fragmentation, which are essential for the successful operation of longwall top coal caving mining. Therefore, determining the characteristics of induced fractures is significant for underground longwall mining. From a global perspective, longwall mining-induced fractures in the overburden have been well studied, which improves the understanding of the mining pressure and ground control. However, induced fractures near the longwall face, which have more significant effects on mining activities, have not been summarized. The goal of this review paper is to provide a general summary of the current achievements in characterizing mining-induced fractures in near-face regions. The characteristics of mining-induced fractures in the coal wall, chain pillar, immediate roofs and top coal, and floors are reviewed and summarized. Remarks are made on the current progress of, fundamental problems with, and developments in methodologies for characterizing mining-induced fractures using methods such as field observations, small-scale laboratory tests, physical modeling, and numerical modeling. Based on a comprehensive analysis, the advantages and disadvantages of each method are discussed, and the ideal conditions for applying each of these methods are also recommended.
... The presence of a discontinuous damage profile ahead of the cave can be seen in a number of studies utilising a range of approaches. It can be seen in studies using physical modelling (Cumming-Potvin et al. 2016a, b;Nishida et al. 1986;McNearny & Abel 1993), numerical modelling (Vyazmensky et al. 2007;Lisjak et al. 2012;Li et al. 2014) and site observations (Panek 1981;Sharrock et al. 2002;Carlson & Golden 2008;Cumming-Potvin 2018). Additionally, there are a number of studies in which a discontinuous damage profile was found around deep mine tunnels and tabular stopes (Adams & Jager 1980;Shemyakin et al. 1986a, b;Jia et al. 2012). ...
... Consistent spacing of parallel fractures adjacent to the cave was also found by Panek (1981) through site observations and brick-based physical models of caving (McNearny & Abel 1993). While the spacing was not specifically addressed, the figures given in a number of other studies also indicate a consistent spacing of fractures in physical models (Nishida et al. 1986) and numerical models of caving (Lisjak et al. 2012;Vyazmensky et al. 2007;Li et al. 2014). While the spacing was at times difficult to determine, Cumming-Potvin (2018) found that the spacing of bands of microseismic events was consistent. ...
Conference Paper
The Duplancic conceptual model is the industry accepted model of caving and is the framework within which most results from numerical modelling and cave monitoring are interpreted. The Duplancic conceptual model implies that the damage ahead of the cave back decreases continuously with increasing distance from the cave surface. Evidence from a variety of sources indicates that this may not always be the case and that a discontinuous damage profile may be present. Cumming-Potvin et al. (2016b) describes a physical modelling program which was undertaken to investigate the fracturing and propagation of the cave. The results of these centrifuge tests showed that caving could occur via a series of fractures oriented parallel to the cave surface and that the cave back progressed vertically via ‘jumps’ to the next successive parallel fracture. In Cumming-Potvin et al. (2016a), this caving mechanism was termed ‘fracture banding’. Multiple examples of a similar mechanism of failure were observed in literature. In addition, the patterns in microseismic event location indicate that fracture banding could be occurring in currently operating caving mines. This paper examines evidence from a number of sources in the field of caving mechanics and presents an extended conceptual model of caving. The new model is able to account for the mechanism of fracture banding, along with the continuous style of failure from the Duplancic conceptual model. There are still many unknowns about the fracture banding mechanism and propagation of caves. These include the specific conditions under which the caving mechanism changes and whether the mechanisms lie on a continuum, or if there is a sharp, sudden change. Two conceptual models are presented: one which includes only that which is known about the mechanisms of cave propagation and one which speculates upon the factors involved and the underlying origins of the fractures.
... There are several other studies, focusing on areas other than cave mechanics, that contain illustrations showing discontinuous damage ahead of the cave back, often in the form of a series of fractures parallel to the cave back (Vyazmensky i., 2007;Lisjak et al., 2012;Li et al., 2014). All of these examples use combined continuum-discontinuum (finite-discrete element method) codes. ...
Article
Full-text available
The Duplancic model of caving is widely accepted in industry and is the framework within which most monitoring and numerical modelling results in caving mines are interpreted. As a result, the damage profile ahead of the cave back is often interpreted as continuously decreasing damage with increasing distance ahead of the cave back. Physical modelling of the caving process performed in a centrifuge did not support this expected behaviour, but instead suggested a discontinuous damage profile ahead of the cave caused by fracture banding. Some support is found in the literature to suggest that the behaviour observed in the models may also be present in the field. This notion is further supported by banding behaviour observed from microseismic monitoring at two block cave mines. Combining the information from the physical models, field observations referred to in the literature, and the microseismic analyses, it is concluded that the Duplancic model needs to be extended to include the phenomenon of fracture banding. It is also reasonable to expect that fracture banding may play a more important role in the caving process than has previously been recognized
Conference Paper
Full-text available
The Duplancic conceptual model is the industry accepted model of caving and is the framework within which most results from numerical modelling and cave monitoring are interpreted. The Duplancic conceptual model implies that the damage ahead of the cave back decreases continuously with increasing distance from the cave surface. Evidence from a variety of sources indicates that this may not always be the case and that a discontinuous damage profile may be present. Cumming-Potvin et al. (2016b) describes a physical modelling program which was undertaken to investigate the fracturing and propagation of the cave. The results of these centrifuge tests showed that caving could occur via a series of fractures oriented parallel to the cave surface and that the cave back progressed vertically via ‘jumps’ to the next successive parallel fracture. In Cumming-Potvin et al. (2016a), this caving mechanism was termed ‘fracture banding’. Multiple examples of a similar mechanism of failure were observed in literature. In addition, the patterns in microseismic event location indicate that fracture banding could be occurring in currently operating caving mines. This paper examines evidence from a number of sources in the field of caving mechanics and presents an extended conceptual model of caving. The new model is able to account for the mechanism of fracture banding, along with the continuous style of failure from the Duplancic conceptual model. There are still many unknowns about the fracture banding mechanism and propagation of caves. These include the specific conditions under which the caving mechanism changes and whether the mechanisms lie on a continuum, or if there is a sharp, sudden change. Two conceptual models are presented: one which includes only that which is known about the mechanisms of cave propagation and one which speculates upon the factors involved and the underlying origins of the fractures.
Conference Paper
Full-text available
Caving geomechanics is still not well-understood, mainly because it is not possible to enter the cave and measure all the rock mass parameters involved in the caving process. Caving geomechanics is a typical example of rock mechanics being a data-limited problem. However, even if the problem cannot be completely physically described, it is critical to make stepwise advances towards its understanding. Numerical models have an advantage over empirical methods when it comes to understanding the physics of a rock mechanics problem such as caving geomechanics. In using numerical modelling, various hypotheses can be tested and compared to the actual behaviour of the rock mass response to caving. Predicting rock mass caveability remains a challenge. Available empirical tools aiming to predict caveability are known to be unreliable, while numerical modelling has the challenge of identifying and accounting for potential factors to be included in such models to make the outputs reliable. The complexity of these models and their sizes result in excessive run times. This paper presents the next step in numerical modelling in an attempt to understand caving mechanics as a basis for a better caveability prediction guide in the process of mine design in caving mines. The study is based on identifying the critical factors and their role in caving performance. These issues are investigated using a discrete element code where pre-existing discontinuities are explicitly incorporated.
Conference Paper
Full-text available
Discontinua modeling techniques, such as Discrete Element Method (DEM), Discontinuum Deformation Analysis (DDA), Combined Finite-Discrete Element Method (FDEM) and Numerical Manifold Method (NMM) have become important analysis tools within the Computational Mechanics field. These methods can now be grouped as methods of Computational Mechanics of Discontinua. The Combined Finite-Discrete Element Method bridges the gap between Finite and Discrete Element Methods. As such, it has become a tool of choice for problems involving fracturing, fragmenting and complex shapes. The key advantage of FDEM is the introduction of finite displacements, finite rotations, and finite strain based deformability combined with suitable material laws; these are then merged with discrete element-based transient dynamics, contact detection, and contact interaction solutions and objective discrete crack initiation and crack propagation solutions that have a great deal of fidelity in reproducing complex fracture patterns and eventual fragmentation. After nearly 25 years of development, the method has been successfully applied in rock mechanics, biomedical engineering, structure engineering and mechanical engineering. This paper summarizes the most recent development efforts in FDEM. 1 HOSS Engineers have encountered discontinua in their practice for a long time. A classic example is the existence of discontinuities in rock masses. Shi was one of the pioneers in attempting to address the simulation of these features via the Discontinuous Deformation Analysis (DDA), Shi [1] Shi & Goodman [2]. DDA was at first developed for static problems and later on extended to dynamic problems. In parallel, Cundall [3] developed the Distinct Element Method (DEM) for dynamic problems, which was extended by many other researchers (Cundall [4]
Article
Full-text available
This manuscript discusses the implementation of the Giovanni Gras-selli shear strength criterion for rock joints inside a combined finite-discrete element method code. The relevance of the criterion, its for-mulation, and application by a simple case study are presented.
Article
Full-text available
The purpose of this paper is to present Y-Geo, a new numerical code for geomechanical applications based on the combined finite-discrete element method (FDEM). FDEM is an innovative numerical technique that combines the advantages of continuum-based modeling approaches and discrete element methods to overcome the inability of these methods to capture progressive damage and failure processes in rock. In particular, FDEM offers the ability to explicitly model the transition from continuum to discontinuous behavior by fracture and fragmentation processes. Several algorithmic developments have been implemented in Y-Geo to specifically address a broad range of rock mechanics problems. These features include (1) a quasi-static friction law, (2) the Mohr-Coulomb failure criterion, (3) a rock joint shear strength criterion, (4) a dissipative impact model, (5) an in situ stress initialization routine, (6) a material mapping function (for an exact representation of heterogeneous models), and (7) a tool to incorporate material heterogeneity and transverse isotropy. Application of Y-Geo is illustrated with two case studies that span the capabilities of the code, ranging from laboratory tests to complex engineering-scale problems.
Article
This paper discusses the issues involved in the development of combined finite/discrete element methods; both from a fundamental theoretical viewpoint and some related algorithmic considerations essential for the efficient numerical solution of large scale industrial problems. The finite element representation of the solid region is combined with progressive fracturing, which leads to the formation of discrete elements, which may be composed of one or more deformable finite elements. The applicability of the approach is demonstrated by the solution of a range of examples relevant to various industrial sections.
Article
Large-scale discrete element simulations, combined finite-discrete element simulations as well as a whole range of related problems, involve a large number of separate bodies that interact with each other and in general deform and fracture. In this context there is a need for a robust fracture algorithm applicable to simultaneous multiple fracturing of large numbers of bodies.In this work a fracture model for both initiation and propagation of mode I loaded cracks in concrete in the context of the combined finite-discrete element method is reported. The algorithm is based on accurate approximation of experimental stress–strain curves for concrete in tension. Copyright © 1999 John Wiley & Sons, Ltd.
Article
Numerical modelling of a discontinuous medium has gained much popularity in recent decades. The combined finite-discrete element method (FEM/DEM) is a state-of-the-art numerical modelling technique pioneered in the mid-1990s. Y2D is a robust two-dimensional FEM/DEM research code developed by Munjiza in 2004. The major limitations of this code are (1) the lack of a graphical user interface (GUI) meaning that all pre-processing has to be made directly on an ASCII input file and (2) the inability of dealing with heterogeneous media. This contribution presents the first GUI and pre-processor, known as Y-GUI, developed for Y2D and the implementation of a new algorithm that allows for the use of heterogeneous materials. In the text all major FEM/DEM concepts are described, together with the main features available in the Y-GUI. The use of Y-GUI is presented in detail and some of its functionalities, including the heterogeneity module to be used to randomly assign materials to a mesh, are introduced. At the end of the manuscript, four case studies, including Brazilian tests of a homogeneous and a layered rock sample and a rock avalanche, are presented.