Numerical modelling in Geomechanics

152
National Seminar on Underground Coal Mining
“ THE FUTURE OF OVERGROUND LIES BELOWGROUND”
* Chief General Manager, CP&P, Singareni Collieries Co. Ltd,
* * Associate Professor, Department of Mining Engineering, IIT, Kharagpur,
*** Dy. Manager, Corporate Project and Planning, Singareni Collieries Co. Ltd,
**** Under Manager, Project and Planning, Singareni Collieries Co. Ltd,
NUMERICAL MODELLING
- AN EFFECTIVE TOOL FOR STRATA CONTROL IN COAL MINES
*B. Ramesh Kumar, **Debasis Deb,
***VNS Prasad.M, and ****U.Siva Sankar
ABSTRACT
Proper understanding of complex behavior of rock mass has always been difficult for reliable design and
safe operation of mining structures. Numerical modelling has emerged as a popular tool solving the static
as well as the dynamic processes assisting in proper design and operation of the structures. This paper
introduces the basics of different numerical modelling approaches, various applications of numerical
modelling techniques for strata management in mines and various numerical modelling codes that are
being used elsewhere in the world in the field of mining. A practical example of shield strata interaction in
longwall panel using ANSYS finite element code is also illustrated.
INTRODUCTION
Understanding the behaviour of rock in general and the jointed rock mass, in particular, has always been
difficult for mining engineers involved in reliable planning & design and safe operation of mining projects
under complex and difficult conditions. Although there exist a number of analytical techniques that can be
used in engineering design, the simplicity of these models and the complexity of the real world often force
the engineer to search for alternative methods of analysis. Numerical modelling techniques require far
more computational power than analytical techniques, but they are well suited in addressing complex
geometries and material behaviour.
A model is a simplification of reality rather than an imitation of reality. It is an intellectual tool that has to be
designed or chosen for a specific task1. Most of the numerical modelling undertaken in the process of mine
planning and design involves using linear elastic, static, and boundary element programs.
The speed, memory efficiency and ease of use of these codes render them well suited to quick design
analysis. It is sometimes necessary, however, to incorporate non-linearties, such as brittle failure or joint
slip, and also to solve problems involving dynamic stresses, plastic displacements, thermal properties and
heat transfer, time dependent behaviour, etc., into particular analysis.

153
Numerical models can represent complex geometries with a high degree of accuracy. The approach adopted
in all numerical methods is to “divide the problem into small physical and mathematical components and
then sum the influence of the components to approximate the behaviour of the whole system”. The series of
complete mathematical equations formed in this process are then solved approximately. By definition, the
computational solutions are always approximations of the exact solution.
A numerical model code is simply capable of: (1) solving the equations of equilibrium, (2) satisfying the
strain compatibility equations, and (3) following certain constitutive equations - when prescribed boundary
conditions are set forth.
The main sources of the input data for the numerical model are, site investigations, and laboratory and field
tests. Numerical methods will give approximate solution, but not the exact solution of the problem. The
numerical modelling technique seems to be a valid tool for mine design, if it is properly used.
NUMERICAL MODELLING APPROACHES
Various numerical modelling techniques have been developed and are currently being used by engineers
and scientists world over. The methods are categorized as Continuum, Discontinuum and Hybrid Continuum/
Discontinuum.
The continuum assumption implies that at all points in a problem region; the materials cannot be torn open
or broken into pieces. All material points originally in the neighbourhood of a certain point in the problem
region remain in the same neighbourhood throughout the deformation or transport process.
1. Continuum methods
Finite Difference Method (FDM),
Finite Element Method (FEM),
Boundary Element Method (BEM).
2. Discontinuum methods
Discrete Element Method (DEM),
Discrete Fracture Network (DFN) methods.
3. Hybrid Continuum / Discontinuum methods
Hybrid FEM/BEM,
Hybrid DEM/BEM,
Hybrid FEM/DEM, and
Other hybrid models.

154
BOUNDARY ELEMENT METHOD (BEM)
This method derives its name from the fact that the user ‘discretizes’, or divides into elements, only
boundaries of the problem geometry (i.e., excavation surfaces, the free surface for shallow problems, joint
surfaces and material interfaces), thus reducing the problem dimensions by one and greatly simplifying the
input requirements. In this method the conditions on a surface could be related to the state at all points
throughout the remaining medium, even to infinity. The information required in the solution domain is separately
calculated from the information on the boundary, which is obtained by solution of boundary integral equation.
Boundary element methods (BEM) are simpler and faster, but usually not powerful enough to accommodate
complex geometry and excessive variations in rock mass properties.
Finite Element Method (FEM) and Finite Difference Method (FDM)
In practice finite element method is usually indistinguishable from the finite difference method. In these
methods, relate the conditions at few points with in the medium (nodal points) to the state within a finite
closed region formed by these points (element). The physical problem is being modeled numerically by
discretizing (i.e. dividing into zones or elements) the problem region.
The FDM is a direct approximation of the governing partial differential equations (PDEs) by replacing partial
derivatives with differences at regular or irregular grids imposed over problem domains, transferring the
original PDEs into a system of algebraic equations in terms of unknowns at grid points. The solution of the
system equation is obtained after imposing necessary initial and boundary conditions. This method is the
oldest member in the family of numerical methods, one that is widely applied.
In FEM, trial functions, usually polynomial, are used to approximate the behaviour of PDEs at the element
level and generate the local algebraic equations representing the behaviour of the elements. The local
elemental equations are then assembled, according to the topologic relations between the nodes and elements,
into a global system of algebraic equations whose solution then produces the required information in the
solution region, after imposing the properly defined initial and boundary conditions.
Finite Differential techniques (FDM) are far more powerful and versatile. Complicated problems involving
complex geo-mining and stress environments, as often found in actual mining complexes, can be studied
and solved in much more elaborate and realistic fashions in these methods. “FDM results into conditionally
stable solution. That is, the convergence of the solution at different stages of iteration to a true solution
depends on the size of elements and size of the load steps. It has also got the advantage of time-stepping
which allows a better understanding of the trend and mode of a failure”.
FEM is perhaps the most versatile of all methods and capable of yielding the most realistic results even in
complex geo-mining conditions. Complexity in problem formulation and requirements of long computer time
and large memory space seem to be its major shortcomings. As his requires more memory, it may not able
to accommodate layer problems.

155
Discrete Element Method (DEM)
The DEM for modeling a Discontinuum is relatively different compared with BEM, FEM and FDM, and focuses
mainly on applications in the fields of fractured or particulate geological media. The essence of DEM is to
represent the fractured medium as assemblages of blocks formed by connected fractures in the problem
region, and solve the equations of motion of these blocks through continuous detection and treatment of
contacts between the blocks. The blocks can be rigid or be deformable with FDM or FEM discretizations.
Hybrid approaches
To make use of the merits of the above methods, a few hybrid simulation procedures coupling more than
one method have also been evolved. The main types of hybrid models are the hybrid BEM/FEM, DEM/BEM
models. The hybrid models of DEM/FEM are also developed. The BEM is most commonly used for simulating
far-field rocks as an equivalent elastic continuum, and FEM and DEM for the non-linear or fractured near-
field where explicit representation of fractures or no-linear mechanical behaviour, such as plasticity, is needed.
Various numerical approaches to model an excavation and the representation of fractured rockmass are as
shown in figures1 and 2 respectively.
Fig.1 (a) and (b) Numerical approaches to model an excavation in a rock mass2
Fig.2 Representation of a fractured rock mass showed in (a), by FDM or FEM shown in
(b), BEM shown in (c), and DEM shown in (d) 2

156
Applications
The various applications of numerical modelling programs in the field of mining are as follows;
1. Design of Openings, and Pillars.
2. Design of Supports for Bord and Pillar and Longwall workings.
3. Design of pit slopes and dumps and estimating their stability in case of opencast mines.
4. Prediction of Main and periodic weightings in Bord & Pillar and Longwall workings.
5. Analysis of shield support interaction in case of Longwalls.
6. Analysis of long term stability of permanent mine excavations.
7. Prediction of surface subsidence over mine excavations., and
8. Simulating effects of blasting on stability of mine workings in Underground as well as in opencast
mines.
Being totally computer based, numerical modelling techniques have a special touch of glamour and
sophistication compared to other approaches in rock mechanics and ground control studies. The results of
the modern software packages are presented in attractive and convincing fashions.
In short, to-day’s numerical modelling software programs have such interesting and charming features with
make believe style of presentations of their results, that very commonly their users and sometimes the
experts as well, get carried away by the impression that these methods are far superior to all other conventional
approaches. It is strongly believed by many that these techniques are capable to provide answers to all the
questions regarding ground control in little time; their results and subsequent predictions cannot go wrong
and no other studies, whether observational, empirical or analytical, are required to support or supplement
them.
Model Calibration
Any numerical modelling exercise on rock excavations, without proper calibration and validation is incomplete
and should not be fully relieved upon. Of course, un calibrated models may be used to have a preliminary
idea for the likely situation that may be encountered in and around a rock excavation, or for arbitrary case
studies, provided the input parameters are realistic.
It is a wrong concept that precise numerical simulation of a real mining problem needs much less time than
other alternatives. Initial task of calibration and validation of a model is perhaps a long and more complicated
process than other methods. But, this technique reveals much more information and once validated, more
reliable and accurate predictions are possible from a model. The information required for calibrating a numerical
model is shown in Figure.3.

157
Fig.3. information required to calibrate a model3
The various numerical modeling softwares available and are being used in the field of mining are as given in
the below Table 1. The complexity rating from easiest to most difficult to use is: simple, mediocre, advanced,
complex, specialist.
Code Source Type Use Complexity
BESOL Mining Stress Systems 2D/3D BEM Common Simple
EXAMINE Roc Science Inc 2D/3D BEM Rare Mediocre
MAP 3D Mine Modelling Ltd 3D BEM Moderate Mediocre
LaMODEL -- 3D BEM Moderate Simple
MUSLIM/NL USBM 3D BEM Moderate Mediocre
FLAC Itasca Consultancy Ltd 2D/3D FDM Common Advanced/Complex
COSFLOW CSIRO 3D FEM Rare Advanced
Phase2 Roc Science Inc 2D FEM Moderate Simple
ANSYS ANSYS, Inc 2D/3D FEM Moderate Advanced
ABAQUS Dassault Systems Simulia Corp FEM Moderate Advanced
PFC Itasca Consultancy Ltd 2D/3D DEM Rare Complex
3DEC Itasca Consultancy Ltd 3D DEM Rare Complex
UDEC Itasca Consultancy Ltd 2D DEM Moderate Advanced
BEFE -- 2D/3D FE &BEM Rare Complex
ELFEN Rockfield Software Ltd 2D/3D FE &DEM Rare Complex
Table 1: Comparison of various Numerical modeling Softwares

158
Application of finite element method in Longwall mining
Finite-element method has found wide application in ground control study of longwall mining. This widespread
use is related to their ability to model the irregular structure, non-linear, non-homogeneous, and anisotropic
nature of rock strata.
Generally, rock strata, such as sandstone, limestone, shale, clays, and other intermixed sediments that
occur with coal seams, do not behave elastically in actual engineering problems. They may go into plastic
state (or change in material property due to load) after the load on them exceeds a certain limit, which is
called elastic-to-plastic state (Cook et. al., 2001). Thus, in the case of analyzing inelastic and nonlinear
behavior of strata related coal mining, the nonlinear material model should be employed.
Peng, 1980 applied three-dimensional finite element analysis to determine the major controlling factors in
the design of an advancing longwall panel and its support systems. In the same manner, Peng et. al., 1980
again employed a three-dimensional finite element model to analyze a retreating longwall panel. Szwedzicki,
1981 simulated a longwall entry model using the result of stress distribution around underground openings
that had a fracture zone. The fracture zone was modeled by either changing the elastic constants of rock
mass or using Goodman’s joint element. This study emphasized that fracturing of rock around working face
caused a distressing of the rock mass around the underground opening. Qian et. al., 1983 carried out a
study using finite element modeling based on data from field observations of rock pressures in two faces
under different conditions and movement of the overlaying strata and stress distribution. He studied the
effects of support resistance on face convergence. Wu, 1985 analyzed the horizontal supporting force of
powered support on longwall faces for ground control. Park and Ash, 1985 and Park and Gall, 1989 analyzed
a progressive-failure of longwall coal and used in finite element analysis by applying different failure criterion
such as Mohr-Coulomb criterion, Hoek-Brown criterion, and Griffith’s criterion. Park and Saab, 1990 attempted
to simulate the interaction between face supports and overburden strata under various mining conditions
using three-dimensional finite-element models. They also simulated the fault effects on the face by simply
employing weak material elements for faults in the numerical model. Lee, 1993 simulated the interaction
between shields and surrounding strata, and main roof behavior and its effect on shields. Detailed simulations
of the interactions were performed by developing a small scale longwall model equipped with exact dimension
of shield structures and applying the non-linear elastic behavior of shield legs.
Finite Element Analysis of Longwall Panel - A case study from Panel No.1. of Adriyala Longwall
Project
However, in India, it was planned to deploy a 2 leg shied having a capacity of 1150 tonnes in Adriyala
Longwall project, SCCL This high capacity value is incorporated into the study keeping in view of the future
prospects of longwall mining in deeper seams which is of paramount importance for future coal mining in
India in general and to SCCL in particular.

159
E (Gpa) Poisons ratio Cohesion (Pa) Friction angle Dilation angle
2.2 0.35 6.00E+06 30 15
2.3 0.35 6.00E+06 30 15
4 0.35 6.00E+06 30 15
2 0.28 7.00E+06 30 15
3.7 0.28 7.00E+06 30 15
2.3 0.28 7.00E+06 30 15
4.9 0.28 7.00E+06 30 15
3.2 0.28 6.00E+06 30 15
3.2 0.28 9.00E+06 30 15
2.6 0.28 5.50E+06 30 15
7.5 0.28 6.50E+06 30 15
2.7 0.15 8.00E+06 30 15
2 0.27 4.00E+06 30 15
2 0.27 4.50E+06 30 15
0.8 0.35 5.00E+06 30 15
2.7 0.28 7.50E+06 30 15
2.7 0.19 7.50E+06 30 15
4.9 0.19 7.50E+06 30 15
2.8 0.27 5.50E+06 30 15
5.4 0.29 5.50E+06 30 15
2.3 0.29 5.50E+06 30 15
2.3 0.29 7.00E+06 30 15
6.9 0.29 7.00E+06 30 15
2.8 0.12 1.40E+06 30 15
4.3 0.02 1.50E+06 30 15
Table 2. Various parameters used for finite element modeling (Ref BHNO.R 1203)
Parameters considered for giving input data to LW Panel No.1 modeling are listed in the table below.
Apart from the above density of the different layers is the additional input to the modeling. Assumed friction
angle of the rock layers as 30 degrees and dilation angle as half of the frictional values in our modeling,
Shield capacity of 2x 1152 T of double telescopic type and various layers were prepared and material
properties were assigned as above for the simulation of original LW panel condition and finally the boundaries
were fixed by giving boundary conditions.

160
Fig 4. Inserted shield into the model
A general purpose software called ANSYS 10.0 (USA based) was used to run the model and to know
the interaction between shield and surrounding strata and also load coming on to the actual shield legs. All
finite element models are analyzed with non-linear material behavior using Drucker-Prager yield criterion.
Rock layers, coal seam and powered support structure except hydraulic legs and lemniscate links are
modeled with 6-noded quadratic triangular elements by this software. Two noded bar elements are used for
shield legs and lemniscate links. The finite element model of longwall panel represents the vertical cross-
section along the middle of the longwall panel and hence plane strain constitutive material behavior is
assumed(4)&(5).
Behaviour of Shield legs
Hydraulic legs are assumed to behave as elastic-perfectly plastic material based on their load-
deformation characteristics as shown in figure 5. In case of yielding, total strain increment of hydraulic leg
is divided into elastic and plastic strain. The elastic strain increment contributes to stress (or load) increment
of the leg. The plastic strain increment changes the shape and size of the yield surface. Hence, in finite
element analysis, the load on the hydraulic leg does not exceed the yield load. However, the total strain of
yielded leg varies with the capacity of powered supports and other geo mining conditions. As a result, for
statistical and neural network analysis, it is necessary to incorporate the total load based on the total strain
of the hydraulic leg assuming its behavior as a linear spring with unlimited capacity (dotted line in figure 5 )4.

161
Figure 5. Load convergence characteristics of hydraulic leg (Ref after Deb.et.al
) Figure 5. shows
three different phases of loading (oa, ab, and bc) on the shield leg for different capacity of chock-shield
supports. In the initial phase (oa), the shield does not respond to the roof convergence because the deflection
of the roof, is caused during the advancement and prior to setting up with the roof. In this case, an average
18 mm of initial convergence is taken based on the field observations at various longwall faces. In the
second phase (ab), operating phase, an equivalent elastic modulus of shield leg is applied to simulate roof
loading and finally last phase (bc) simulate the yielding of chock-shield support. Calculated 52 Mpa as yield
stress and assumed shield is in full contact with the immediate roof and floor.
Analysis and results
From the analysis one can understand different kinds of stresses coming on to the shield from all directions
and the plastic & elastic zones surrounding the shied area. The peak stresses observed on the legs after
cutting the face is about 48 Mpa, which is slightly less than the yield value of the shield.
Result of axial stress on the shield leg for a linear model and resulted linear strain values observed are as
follows
SAXL=-0.24879E+08 (MPa) EPELAXL=-0.004013(M)
Fig 6. Interaction of shield support with surrounding strata
convergence of the leg, m

162
Conclusions
1. Numerical modelling is a very promising and effective tool in understanding the rock mass response
subjected to complex loading conditions. Efficient use of this tool for reliable design and fixing of strata
management problems requires a thorough knowledge of the modelling theory, scope and limitations.
2. Using numerical models, shield, rock strata, coal seam and goaf interactions can be modeled effectively
for different in-situ loading conditions.
3. Proper analysis of model response is very important which requires the basic understanding of the
mechanisms involved in the physical process being modeled and the requirement for its numerical
simulation.
4. Result of axial stress on the shield leg for a linear model and resulted linear strain values observed
from this model respectively are SAXL=-0.24879E+08 (MPa) EPELAXL=-0.004013(M)
5. Results from numerical simulation should be compared with field measurements for back calculations
and improved input data.
6. More experiences are needed in comparative study between numerical simulations and other analytical
methods for precise numerical simulation.
One point worth remembering about the mathematical mystery, in which strata control is so often
shrouded, is that the rock was there first. The science was derived from what people saw the rock do.
The mathematics is really only a handy form of short hand to generalize descriptions of the behaviour
of the rock. Nobody should allow math’s to get in the way of strata control. If there is a dispute, the rock
is always right. - Dr. J Nielen Van Der Merwe
Acknowledgments
The authors are thankful to the management of SCCL and Director General Of Mines Safety for their
co-operation and encouragement for this work. The views expressed in this paper are opinion of the
authors and not necessarily of the organization they serve.
References
1. A. M. Starfield and P. A. Cundall (1988), “Towards a Methodology for Rock Mechanics Modelling” Int. J, Rock
Mech. Min. Sci. & Geomech. Abstr. Vol. 25, No. 3, pp. 99--106, 1988
2. Jing, L.(2003), “A review of techniques, advances and outstanding issues in numerical modelling for rock mechanics
and rock engineering” International Journal of Rock Mechanics and Mining Sciences, Volume 40, Issue 3, April
2003, Pages 283-353
3. A.Studney and C.Scior (2009), “Advanced numerical solutions for strata control in mining” Proc. of Int. workshop
on numerical modelling for underground mine excavation design’ pg 101-109, IC9512.
4. Verma A. K., Deb D. 2007. Analysis of chock shield pressure using finite element method and face stability index.
Mining Technology (Trans. IMMA), 116(2), 67-78.
5. Lee SM ‘Analysis of interaction between longwall face supports and overburden strata’ Doctoral thesis, 1993,
University ofAlabama, 49-52.

Numerical modelling in Geomechanics

More Related Content

What's hot (20)

Viewers also liked (20)

Similar to Numerical modelling in Geomechanics (20)

More from Ulimella Siva Sankar (10)

Recently uploaded (20)

Numerical modelling in Geomechanics