International Journal of Civil Engineering and Technology (IJCIET)
Volume 10, Issue 04, April 2019, pp. 975-984, Article ID: IJCIET_10_04_103
Available online at http://www.iaeme.com/ijciet/issues.asp?JType=IJCIET&VType=10&IType=04
ISSN Print: 0976-6308 and ISSN Online: 0976-6316
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CALIBRATION OF A UNIAXIAL
COMPRESSION TEST FOR ROCK USING THE
DISCRETE ELEMENT METHOD IN LS-DYNA
Muhammad I. Shahrin
Department of Geotechnics and Transportation, School of Civil Engineering, Faculty of
Engineering, Universiti Teknologi Malaysia, Johor, Malaysia
Rini A. Abdullah
Department of Geotechnics and Transportation, School of Civil Engineering, Faculty of
Engineering, Universiti Teknologi Malaysia, Johor, Malaysia
Seokwon Jeon
Department of Energy Systems Engineering, Seoul National University, Seoul, Korea
Radzuan Sa’ari
Department of Hydraulics and Hydrology, School of Civil Engineering, Faculty of
Engineering, Universiti Teknologi Malaysia, Johor, Malaysia.
ABSTRACT
The discrete element method (DEM) was combined with the finite element method
(FEM) approach to investigate the numerical response of granite material under
uniaxial compression loading. A calibration analysis was performed in this study using
the commercial software LS-DYNA. The aim of this work was to calibrate the microparameters in a numerical simulation using a bonded particle model of granite rock.
In this DEM-FEM simulation, the rock specimen was modelled in DEM, while the steel
plates were simulated using FEM. The numerical analysis was then compared to
experimental data from a standard uniaxial compression test. The results show that the
DEM-FEM simulation can reproduce the trends in the experimentally observed stressstrain curve for granite rock under uniaxial compressive loading. Comparisons were
carried out of the values for UCS and Young’s modulus from experimental data and
numerical analysis, and these showed that the UCT DEM/BPM model fits within the
range of values for UCS and Young’s modulus from laboratory test results, i.e. 52.63–
87.96 MPa and 10.13–20.76 GPa.
Keywords: Calibration, Discrete element method, Granite rock, LS-DYNA, Uniaxial
compression test.
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Cite this Article: Muhammad I. Shahrin, Rini A. Abdullah, Seokwon Jeon and
Radzuan Sa’ari, Calibration of a Uniaxial Compression Test for Rock Using the
Discrete Element Method in Ls-Dyna. International Journal of Civil Engineering and
Technology, 10(04), 2019, pp. 975-984
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1. INTRODUCTION
Recent rapid developments in numerical analysis with the aid of computer technology have
provided alternatives to expensive and large-scale experimental testing.[1] have shown that
rock behaves like a cemented granular material with complex-shaped grains, in which both the
grains and the cement can deform and break. In principle, this model describes all aspects of
its mechanical behaviour.
The bonded particle model (BPM) defined by these authors consists of a dense packing of
non-uniform-sized circular or spherical particles that are bonded together at their contact points
with parallel bonds [1]. Its mechanical behaviour can be simulated by the discrete element
method (DEM) using commercial programs such as PFC2D, PFC3D and LS-DYNA. BPM can
provide both a scientific tool to investigate micro-mechanisms and an engineering tool to
predict macroscopic behaviour. DEM was introduced for the analysis of mechanics problems,
and was later applied to soils by [2]. According to [1], rigid particles only interact at a soft
contact with finite values of the normal and shear stiffness. Fig. 1 shows the contact bond
between particles, with the force and moment acting at each contact. Newton’s laws of motion
provide the fundamental relations between the motion of the particles and the resultant forces
and moments causing this motion. Several assumptions are inherent in the BPM:
I.
The particles are circular or spherical rigid bodies with a finite mass;
II.
The particles move independently of one another, and can undergo both translation
and rotation;
III.
The particles interact only at contacts, and since the particles are circular or
spherical, a contact involves only two particles;
IV.
The particles are allowed to overlap one another, and all overlaps are small in
relation to the particle size, such that contacts occur over a small region (i.e., at a
point);
V. Bonds of finite stiffness can exist at contacts, and these bonds carry load and can
break. The particles at a bonded contact need not overlap;
VI.
Generalised force–displacement laws at each contact relate the relative particle
motion to the force and moment at the contact.
The contacts in this bond model carry limited tension, but if this tension exceeds the normal
bond strength, the contact bonds will break. In addition, the shear deformation is controlled by
the shear spring constant. The shear strength of the contact is limited to the shear bond strength.
The behaviour of the shear bond is similar to that of the tensile bond, and shear failure takes
place when the shear force is greater than the shear bond strength. The shear resistance of the
contact is governed by Coulomb’s law with a friction coefficient.
[3] Reviewed advances in the field of rock mechanics and gave a brief summary of the
recent advances in numerical modelling in this area, including distinct/discrete element
methods, discontinuous deformation analysis methods and BPM. There have been many
previous studies of numerical modelling related to uniaxial compression testing (UCT) in the
laboratory [4]–[7].
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Calibration of a Uniaxial Compression Test for Rock Using the Discrete Element Method in LsDyna
Figure 1 Illustration of contact bond between particles [8]
Fig. 2 shows the bonded particles in BPM, where all of the particles are linked to their
neighbours through bonds. These bonds represent the complete mechanical behaviour of solid
mechanics, and are independent of the DEM. Every bond is subjected to tension, bending,
shearing and twisting [9].
Figure 2 Illustration of bonded particles [9]
[10] Explained the typical results for the UCT of rock as shown in Fig. 3. The mechanical
behaviour of intact rock can be tested under UCT, such as its peak strength or uniaxial
compressive strength, and its Young’s modulus. The initial portion of the curve has a concave,
upwards shape due to the effects of micro-crack closure and void filling. Following this, a
linear portion of the curve reflects elastic behaviour, and is followed by damage initiation and
crack propagation. There is then a sudden loss of load bearing capacity and residual strength.
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Figure 3 Typical stress-strain curve of a rock compression test [10]
2. EXPERIMENTAL METHODS
2.1. Laboratory works
Several rock samples were taken from a rock pile at Gemencheh Granite Sdn Bhd (GGSB)
quarry in Gemencheh, Negeri Sembilan, Malaysia, and were transported to the laboratory to
study the engineering properties of the samples. The macroscopic properties of the rock
specimens, such as their unconfined compressive strength (UCS), Young’s modulus, Poisson’s
ratio, tensile strength and shear strength were obtained using UCT, triaxial testing, Brazilian
testing and direct shear testing, respectively. These laboratory tests were carried out according
to the suggested method of the ISRM [11], [12] to obtain the properties of granite. The
properties of the intact rock obtained from these laboratory tests are shown in Table 1.
The collected granite samples were then cored and saw-cut into a diameters of ≈ 42 to 50
mm and heights of 96 to 100 mm for use in laboratory tests. Fig. 4 (a) shows a cored granite
specimen that is ready for testing, and Fig. 4 (b) shows the failed rock specimen after the
uniaxial compression strength test. It was observed that the failure mode was similar for all
specimens, which failed via axial splitting.
Table 1: Intact rock properties selection for analysis in LS-DYNA
Test type
Density test
UCT test
Brazilian test
Shear test
Parameter
Density (g/cm3)
UCS (MPa)
E (GPa)
Poisson ratio
Tensile strength (MPa)
Shear strength (MPa)
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Value
2.75
87.96 (AVG: 67.29)
20.76
0.25
9.57
9.52
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Calibration of a Uniaxial Compression Test for Rock Using the Discrete Element Method in LsDyna
42mm
96 mm
(a)
(b)
Figure 4 Granite specimen (a) before and (b) after experimental uniaxial compression test
2.2. Numerical methods
In this study, rock samples were constructed using the BPM in LS-DYNA. The DEM was
combined with the finite element model (FEM) approach to numerically investigate the
response of granite material under uniaxial compression loading. Our aim was to calibrate the
micro-parameters in a numerical model of granite rock using BPM. In this DEM-FEM
simulation, the rock specimen was modelled in DEM while the steel plates were simulated
using FEM.
One of the most important steps in DEM is the generation of particles. In LS-PREPOST, a
disc/sphere generation method is built into the software that can generate the discrete element
particles. The particle radius can be determined according to the flow of the input calibration,
as shown in Fig. 5. In this method, the calibration procedures should meet the requirements of
the elastic modulus and UCS tolerance of an intact rock specimen from laboratory testing; if it
does not, the cement volume and micro-parameters need to be modified. Finally, the failure
envelope of the model must be compared with the experimental failure envelope.
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START
Initial guess based on
UCT experimental data
and PBM formulation
Satisfy UCT elastic
modulus tolerance?
NO
Modify cement
volume
YES
Modify microstrength parameters
Satisfy UCS
tolerance?
NO
YES
Still meet UCT
elastic modulus
tolerance?
NO
YES
Compare model failure
envelope with experimental
failure envelope
END
Figure 5 Flow of input calibration
In DEM of geomaterials, certain microproperties must be specified that cannot be measured
in laboratory testing. In order to calibrate the numerical model, several initial values for the
microproperties must be found in order to create a model similar to the actual rock. These initial
values were taken from those suggested by [6]. Trial and error methods were used to calibrate
the numerical model. Four models were successfully calibrated, and the input parameters for
these calibrated models are shown in Table 2 below. Two sizes of particle were successfully
calibrated in this study: 1.75 to 2 mm and 2 to 2.5 mm.
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Calibration of a Uniaxial Compression Test for Rock Using the Discrete Element Method in LsDyna
Table 2: Input parameters of the calibrated model
Properties
Trial 1
Particle radius/mm
Trial 2
Trial 3
2.0 - 2.5
Trial 4
1.75 - 2
Parallel-bond normal stiffness (PBN) / GPa
10.11
20.76
20.76
20.76
Parallel-bond shear stiffness (PBS)
0.25
0.25
0.25
0.25
Parallel-bond maximum normal stress
(PBN_S)
30
30
30
35
Parallel-bond maximum shear stress (PBS_S)
20
20
20
25
Bond radius multiplier (SFA)
1.32
1.3
1.31
1.3
Numerical damping (ALPHA)
0.5
0.5
0.5
0.5
Maximum gap between two bonded spheres
(MAXGAP)
-1.32
-1.3
-1.31
-1.3
Normal damping coefficient (NDAMP)
0.7
0.7
0.7
0.7
Tangential damping coefficient (TDAMP)
0.01
0.01
0.01
0.01
Friction coefficient (Fric)
0.99
0.99
0.99
0.99
Rolling friction coefficient (FricR)
0.98
0.98
0.98
0.98
Normal spring constant (NormK)
0.1
0.1
0.1
0.1
Shear spring constant (ShearK)
0.4
0.4
0.4
0.4
Fig. 6 shows the DEM/BPM numerical model before and after UCT. In the numerical
model, there are two steel plates at the top and bottom of the rock specimen. The top plate is
configured to move vertically and is fixed in all other directions, while the bottom steel plate
is fixed in all directions. The material of the plates is typical steel, with mass density 7 g/cm 3,
Young’s modulus 200 GPa and Poisson’s ratio 0.3. The parameters for the rock specimen, such
as its density, Young’s modulus and Poisson’s ratio, were assigned as shown in Table 1. The
friction coefficient between the steel plates and rock specimen is 0.39 for both top and bottom
plates, and the damping coefficient is 0.5.
It can be seen that the failure mode observed for the granite specimen in Fig. 4 (b) and Fig.
6 (b) is axial splitting. These results are similar to those of [13].
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(a)
(b)
Figure 6 Simulation of (a) before and (b) after uniaxial compression test using DEM/BPM
3. COMPARISON OF NUMERICAL AND EXPERIMENTAL RESULTS
In this study, several comparisons have been made for calibration purposes. Firstly, the UCT
DEM/BPM model should fall within the ranges for the UCT elastic modulus and Young's
modulus given by laboratory testing. Table 3 shows that the Young's modulus for Trials 1 to 3
is within this range, but Trial 4 does not fall within this range of values. This might be due to
the smaller particle radius than in the other trials, meaning that a particle size of 1.75–2 mm
would not be suitable for this study. Another comparison that is required is the uniaxial
compression strength, which should also fall within the range of values from laboratory testing.
It can be seen from Table 3 that all of the trials show a successful fit for the accepted range of
values from the experimental results, i.e. 52.63 to 87.96 MPa. This indicates that the bonds
between particles can effectively represent those in the granite rock specimen.
Other comparisons required are the failure mode observed for the granite specimen, i.e.
axial splitting, and the axial strain trend. Fig. 7 shows a graphical comparison of the axial stress
versus axial strain for the UCT DEM/BPM model and the laboratory tests. The shapes of the
graphs for Trials 2 and 3 are similar to those of Samples 1 and 3 of the laboratory test results.
It can be concluded that Trials 2 and 3 meet the requirements in all of the comparisons that
have been made; however, Trial 3 shows higher values for UCS and Young's modulus, and this
was therefore chosen as the best calibrated UCT DEM/BPM model in this study.
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Calibration of a Uniaxial Compression Test for Rock Using the Discrete Element Method in LsDyna
Table 3: Comparison of UCS and E value between UCT DEM/BPM model and laboratory test
Laboratory test
Trial 1
Trial 2
Trial 3
Trial 4
Uniaxial compression
strength, UCS (MPa)
52.63 - 87.96
79.92
55.41
55.66
56.23
Young's modulus, E (GPa)
10.13 - 20.76
11.55
10.13
10.55
5.02
Axial stress (MPa) versus axial strain (%)
90
80
Axial stress (MPa)
70
Sample 1
Sample 2
Sample 3
Trial 1
Trial 2
Trial 3
Trial 4
60
50
40
30
20
10
0
0.00
0.50
1.00
Axial strain (%)
Figure 7 Comparison UCT DEM/BPM model with experimental data of granite specimen
5. CONCLUSION
This paper presents a calibration procedure for the micro-parameters in a BPM of intact rock
using DEM. Comparisons of the UCS and Young’s modulus values were made between the
calibrated numerical models and the experimental results, and these show that the UCT
DEM/BPM model fits within the range of values for UCS and Young’s modulus from
laboratory test results. Trial 3 was chosen as the best calibrated UCT DEM/BPM model in this
study, i.e. the one that was closest to the laboratory test results. It can be concluded that DEMFEM simulation can reproduce the trends in an experimentally observed stress-strain curve for
granite rock under uniaxial compressive loading.
ACKNOWLEDGMENTS
This study is supported by Universiti Teknologi Malaysia and Ministry of Higher Education
Malaysia under Research University Grant – Tier 1 (PY/2017/01396).
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REFERENCES
[1]
[2]
[3]
[4]
[5]
[6]
[7]
[8]
[9]
[10]
[11]
[12]
[13]
D. O. Potyondy and P. A. Cundall, A bonded-particle model for rock, International Journal
of Rock Mechanics and Mining Sciences, 41(8), 2004, 1329–1364.
P. A. Cundall and O. D. L. Strack, A discrete numerical model for granular assemblies,
Géotechnique, 29, (1), 1979, 47–65.
A. Bobet, A. Fakhimi, S. Johnson, J. Morris, F. Tonon, and M. R. Yeung, Numerical
Models in Discontinuous Media: Review of Advances for Rock Mechanics Applications,
Journal of Geotechnical and Geoenvironmental Engineering, 135(11), 2009, 1547–1561.
J. Rojek, E. Oñate, C. Labra, and H. Kargl, Discrete element simulation of rock cutting,
International Journal of Rock Mechanics and Mining Sciences, 48(6), 2011, 996–1010.
A. Manes and P. Milano, An investigation in constitutive models for damage simulation of
rock, Proc. 45° Convegno Nazionale: Associazione Italiana Per L’analisi Delle
Sollecitazioni (AIAS), 2016.
A. Amiri, Investigation of Discrete Element and Bonded Particle Methods for Modelling
Rock Mechanics Subjected to Standard Tests and Drilling, M.Sc Thesis, Politecnico di
Milano, Milan, Italy, 2017.
L. Xuefeng, W. Shibo, G. Shirong, R. Malekian, and L. Zhixiong, Investigation on the
influence mechanism of rock brittleness on rock fragmentation and cutting performance by
discrete element method, Measurement: Journal of the International Measurement
Confederation, 113, 2018, 120–130.
E. A. Flores-Johnson, S. Wang, F. Maggi, A. El Zein, Y. Gan, G. D. Nguyen, and L. Shen,
Discrete element simulation of dynamic behaviour of partially saturated sand, International
Journal of Mechanics and Materials in Design, 12(4), 2016, 495–507.
N. Karajan, Z. Han, H. Teng, and J. Wang, Interaction Possibilities of Bonded and Loose
Particles in LS-DYNA, International 9th European LS-DYNA Conference, 2013, 1, 1–27.
J. A. Hudson and J. P. Harrison, Engineering Rock Mechanics : An Introduction to the
Principles. (Elsevier Science, 2000).
R. Ulusay and J. A. Hudson, ISRM Blue Book: The Complete ISRM Suggested Methods
for Rock Characterization, Testing and Monitoring:1974-2006. 2007.
R. Ulusay, ISRM The Orange Book: The ISRM Suggested Methods for Rock
Characterization, Testing and Monitoring: 2007-2014. 2015.
A. Basu, D. A. Mishra, and K. Roychowdhury, Rock failure modes under uniaxial
compression, Brazilian, and point load tests, Bulletin of Engineering Geology and the
Environment, 72(3–4), 2013, 457–475.
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