Arab J Geosci (2013) 6:3703–3708

DOI 10.1007/s12517-012-0632-4

ORIGINAL PAPER

Two-dimensional dynamic finite element simulation

of rock blasting
M Sazid & T N Singh

Received: 10 May 2012 / Accepted: 12 July 2012 / Published online: 27 July 2012
# Saudi Society for Geosciences 2012

Abstract In the present study, the two-dimensional blast and to control its effect, various precautionary measures
model has been simulated using finite element software have been taken by users, but it is still not clear about the
Abaqus/CAE. The John–Wilkins–Lee equation of state has internal changes in the phenomena. The large-scale experi-
been used to calculate the pressure caused by the release of mentation in the field may not be feasible due to various
the chemical energy of the explosive. Detonation point from uncontrolled parameters as well as time consumed to under-
center of hole has been defined for the traveling path of stand the mechanism. The fast computational tools which
explosive energy. Elastoplastic dynamic failure constitutive can be able to simulate the real-time phenomena attract
with kinematic hardening model was adopted for rock mass many researchers to resolve the complicated and complex
responses under high explosive pressure to understand the phenomena like blasting (Yang et al. 1996; Liu and Katsa-
mechanism of blast phenomena. In this model, it is assumed banis 1998; Taylor et al. 1986; Paine and Please 1994). This
that failure of rock occurs under tensile failure when yield will certainly improve the understanding of mechanism
plastic stress exceeded to its static tensile strength. The which is not available by any other means.
hydrostatic pressure was used as a failure measure to model Blasting creates number of problems in the surrounding
dynamic spall or a pressure cut off. Variation of detonation area if not properly designed and executed. Numerical sim-
velocity has been measured in terms of simulation blast ulation can provide basic understanding to increase the
output energies index results. effective and efficient use of explosive energy for better
fragmentation and to control the damage to surroundings.
Keywords Finite element method . Abaqus . Rock blasting If fragmentation is better, then replacement by many other
side effect of the blast abuse like ground vibration, fly rock,
back breaks, etc. can be minimize simultaneously (Monjezi
et al. 2011; Monjezi et al. 2012).
Introduction
Numerical simulations can be of great help for better
understanding of the utilization of explosive energy as well
Application of blasting to breakage of rock mass and over-
as more reliable for control of blast. The present study
burden is increasing day by day due to the faster rate of
involved only simple understanding of blasting wave on
tunneling, mining, and other civil construction work world-
the model, explosive effects on some blast energy index
wide. Explosives are the key source of concentrated chem-
(Sanchidrian et al. 2007), and confirmation with previous
ical energy for either breaking the rock or displacing the
reported work by Xin-pu and Li-li (2009).
rock mass for various uses. Performance and efficiency of
explosive energy can be assessed by various modes like
vibration measurement, fragmentation, rock movement,
etc. (Sanchidrian et al. 2007). The performance of explosive Dynamic tensile failure criteria

M. Sazid (*) : T. N. Singh Generally, Abaqus/explicit offers two dynamic failure mod-
Department of Earth Sciences,
els which are suitable only for high-strain-rate dynamic
Indian Institute of Technology-Mumbai,
Mumbai 400076, India problems—shear failure and tensile failure. Shear model is
e-mail: sazidmohd@gmail.com determined for plastic yielding, whereas tensile failure for
3704 Arab J Geosci (2013) 6:3703–3708

tensile loading. Both models can be used simultaneously.

These models are based on limiting load carrying capacity
of element once stresses reached the predefined limit. Shear
failure model either used for the Mises or the Johnson–Cook
plasticity models, whereas tensile failure was used for either
the Mises or the Johnson–Cook plasticity models or the
equation of state (EOS) material model (Abaqus/CAE
2011). Tensile failure criteria were used for rock mass fail-
ure model in this study. When tensile failure criterion is met
at an element integration point, the material point fails. Spall
or breakdown of a material can be used as element removal
by death of element or an alternative failure option as shown
in Fig. 1, rather than element removal. Zero (0) point shows
that model has not used tensile failure criteria, whereas
material moved from Zero (0) to Point C when hydrostatic Fig. 2 Full sketch of the model
pressure cut off was used as spall of material.
Dynamic loading during blasting

Model description The EOS is a thermodynamic or constitutive equation which

provides a mathematical relationship between two or more
Design and dimension of model description has been illus- state functions associated with the matter, such as its tem-
trated in Fig. 2. The rock structure and material properties perature, pressure, volume, or internal energy. A number of
will generally have greater effects on performance of blast- EOS have been reported (Braithwaite et al. 1996) but the
ing. For the purpose of this modeling, it has been assumed EOS by John–Wilkins–Lee (JWL) equation is the most
that rock mass is isotropic and homogenous; however, this is popular in geotechnical problems due to its simple form,
generally not in realistic case. Joints and bedding plane of experimental basis, and ease of calculations as hydrodynam-
rock mass affect the transmission and reflection of blast ic calculation (He et al. 2002; Itoh et al. 2002). JWL equa-
wave through the rock (Ash 1963; Duvall and Atchison tion describes the explosive material behavior under high
1957; Persson et al. 1970; Frantzos 1989; Fourney 1993; rate intense pressure environment. The JWL equation is
Bhandari 1997; Nie and Olsson 2000; Olsson et al. 2001) given below in Eq. 1 in terms of internal energy Em0 per
but create some complication in numerical model. To avoid unit mass.
some convolution and for simple understanding of breakage    
wρ ð R1 ρ0 Þ wρ
eðR2 ρ Þ
ρ ρ0
mechanism, only one fourth part of square rock mass with P¼A 1 e þB 1
R1 ρ0 R 2 ρ0
3 m of the sides was used, and a borehole with 0.05 m radius
are adopted in the simulation as shown in Fig. 3. Medium wρ2
þ Em0 ð1Þ
strength of rock was assigned to model with density 0 ρ0
2,500 kg/m3, Young's modulus E050 GPa, Poisson's ratio
ν00.3, and plastic yield stress pt 0215 MPa. Details of Where, A, B, R1, R2, and ωρ are constants, P is the
elastoplastic model have been described in detail by Yang pressure (depended variable), ρ0 is the user-defined density
et al. (1996). of explosive, and ρ is the density of the detonation product.
The JWL equation of states parameters as follows: A0
520.6 GPa, B05.3 GPa, R1 04.1, R2 01.2, ωρ00.35, density
ρ0 01,900 kg/m3, and the detonation velocity varied from
2,500 to 6,000 m/s. The explosive material detonated from
the center of the blast hole as shown in Fig. 3. During the
detonation of explosive, a high pressure is generated which
can be simulated from JWL equation applied to rock mass.

Simulation conditions

In practice, rock blasting is generally executed near face

Fig. 1 Tensile failure criteria for blasting boundaries to either split or displace the rock mass. It is a
Arab J Geosci (2013) 6:3703–3708 3705

Fig. 3 Two dimension Abaqus 3m

blast model with meshing

3m
Detonation point

general concurrence that when an explosive charge in a blast contained in the material in the form of elastic deformation
hole is detonated, it generates high amounts of shock wave energy. It is the product of stress and strain, a more natural
and gas pressures. Stress wave is responsible for generation criterion for rock damage and fragmentation.
of radial cracks around the blast hole then highly confine Generally, blasting triggering time is a phenomenon with
gas pressure penetrates into cracks and extend them and a very short duration; however, initial strain energy was
dislodge the rock mass where least resistance flock for transferred to the rock mass in this period at very rapid rate
release of gas pressure. The model study in this paper is (0.1×10−3 s) as indicated in Fig. 5. It is a general fact that
concerned with blast damage caused by stress wave only. higher detonation velocity explosive formed the high strain
Traveling of stress wave around a blast hole as compression energy in surrounding rock mass. The highest value of
wave and reflected as tensile wave when any anomalies or initial strain energy is −51.99 and −12.89 kJ for highest
free face found. If the reflected tensile wave is sufficiently and lower detonation velocity of explosive used,
strong than dynamic tensile strength of the media, there is respectively.
possibility of spall. Movement of wave motion through rock The store initial strain energy further converted into
mass and the resulting breaking of rock mass is an extremely kinetic energy due to high momentum of rock mass as
complex process which can only be modeled numerically exhibited in Fig. 6. Rapid increase of kinetic energy from
with the help of under simplifying assumptions. Progression zero to peak point and rapidly come down within 0.1×10−3
of shock wave has been shown in Fig. 4, but pressure cut off s, also, which show the decay of pressure within a couple of
during reflecting wave and model does not support the millisecond. Generally, the rise time for the explosive ener-
removal of element. gy is around 0.1×10−3 s (Jung et al. 2001). The observed
Kinetic energy is 31.73 kJ for 6,000 m/s detonation velocity
whereas for lower detonation velocity (2,500 m/s) is found
Dynamic blasting energy to be 7.45 kJ. Peak value of kinetic energy reduces with the
decrease of detonation velocity of explosive as illustrated in
Changes in overall explosive energy index during rock Fig. 6. The results were compared with Xin-pu and Li-li
blasting are shown in Figs. 5, 6 and 7. Figure 5 demonstrates (2009), studied, and found close to it.
the distribution of initial strain energy which is captured and The viscous dissipation of explosive energy is also illus-
liberated within surrounding rock mass. The strain energy trated in Fig. 7, which indicated that changes of explosive
associated with a stress wave is the internal energy energy in blasting within 0.1×10−3 s. Similar observations
3706 Arab J Geosci (2013) 6:3703–3708

(a) t = 0.20×10-3 Second (b) t = 0.40×10 -3 Second

(c) t = 0.60×10-3 Second (d) t = 0.40×10 -3 Second

Fig. 4 Progression of stresses as wave and reflected within 0.80×10−3 s. a t00.20×10−3 s; b t00.40×10−3 s; c t00.60×10−3 s; d t00.80×10−3 s

were reported by Xin-pu and Li-li (2009). Peak viscous

0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2 dissipation energy varies with different velocity of detona-
0
-5 Second, 10-3 tion as shown in Fig. 8. Increasing of peak viscous dissipa-
-10 tion energy follow mostly exactly linear nature as noticed in
-15
-20 Fig. 8. Viscous dissipation energy can be measured from
Strain Energy, KJ

-25 2500 VD
detonation velocity or vice versa as equation indicated
-30 3000 VD
-35 Fig. 8.
-40 4000 VD
-45 5000 VD
-50 6000 VD
-55
-60 Conclusions
-65
-70
-75 The study provides results of two-dimensional dynamic
Fig. 5 Distribution of initial strain energy with time and different type blast model and some blast energy index curves. Changes
of explosive detonation velocity in peak blast energy index with velocity of detonation are
Arab J Geosci (2013) 6:3703–3708 3707

32

Peak Viscous Dissipation Energy, KJ

31
30
28
y = 0.0056x - 1.2445
26
26 R² = 0.9387
2500 VD
24 3000 VD 21
22
Kinetic Energy, KJ

4000 VD
20 16
5000 VD
18
16 6000 VD
11
14
12 6
10 1500 2500 3500 4500 5500 6500
8 Velocity of Detonation, m/sec
6
Fig. 8 Distribution of peak viscous dissipation energy with variation
4 of velocity of detonation
2
0
0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2 crease with identical mode and produced additional
Second, 10-3
energies for rock displacement.

Fig. 6 Distribution of kinetic energy with time and different type of Acknowledgments The first author expresses his sincere thanks to
explosive detonation velocity the Council of Scientific & Industrial Research for their financial
support through Central Institute of Mining & Fuel Research, Dhanbad
(India) during the research study.
found. Blast energy on surrounding rock mass within
0.1×10−3 s is reported which may be useful to under-
stand the mechanism of fractures in rock mass. This
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