sustainability
Article
Assessment of the Blasting Efficiency of a Long and
Large-Diameter Uncharged Hole Boring Method in Tunnel
Blasting Using 3D Numerical Analysis
Min-Seong Kim 1 , Chang-Yong Kim 1 , Myung-Kyu Song 2 and Sean Seungwon Lee 2, *
1
2
*
Citation: Kim, M.-S.; Kim, C.-Y.;
Song, M.-K.; Lee, S.S. Assessment of
the Blasting Efficiency of a Long and
Large-Diameter Uncharged Hole
Boring Method in Tunnel Blasting
Using 3D Numerical Analysis.
Sustainability 2022, 14, 13347.
https://doi.org/10.3390/
su142013347
Department of Geotechnical Engineering Research, Korea Institute of Civil Engineering and Building
Technology, 283 Goyang-daero, Goyang-si 10223, Korea
Department of Earth Resources and Environmental Engineering, Hanyang University, 222 Wangsimni-ro,
Seoul 04763, Korea
Correspondence: seanlee@hanyang.ac.kr
Abstract: Cut blasting is one of the most essential processes to reduce blast-induced vibration in
tunnel blasting. The long and large-diameter uncharged hole boring (LLB) method is an example
of one of the cut blasting methods, which utilizes large-diameter uncharged holes drilled in the
tunnel face. In this study, blasting simulations were performed to analyze its blasting mechanism,
and the LLB method and the traditional burn-cut method were simulated to compare their blasting
efficiency. A 3D numerical analysis using LS-DYNA code, a highly non-linear transient dynamic
finite element analysis using explicit time integration, was used to simulate the blasting process, and
a Johnson–Holmquist constitutive material model, which is optimal for simulating brittle materials
under dynamic conditions, was used to simulate the rock behavior under blasting. The modified
LLB method showed a 3.75-fold increase in the advance per round compared to the burn-cut method,
due to the increased formation of long and large-diameter uncharged holes compared to blast holes.
This modified LLB method used 30% less explosives, so its failure range was approximately 1.25 times
less than that of the burn-cut method, but its advance was approximately 4 times larger than the
burn-cut method, which was similar to the original LLB method. This confirmed that the modified
LLB method is significantly more efficient in terms of increased blasting efficiency (particularly the
advance per round) as well as reduced blast-induced vibration, compared to the traditional cut
blasting method.
Academic Editors: Jian Zhou,
Mahdi Hasanipanah and Danial
Keywords: tunnel excavation; cut blasting method; LLB method; uncharged hole; numerical simulation
Jahed Armaghani
Received: 14 September 2022
Accepted: 10 October 2022
Published: 17 October 2022
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4.0/).
1. Introduction
A drill and blast method is the most common rock excavation method in mining and
civil engineering. However, this method causes environmental pollution and hazards
such as noise, vibration, and flying rocks generated by the blasting, and blast-induced
vibration can damage nearby structures in urban areas, when it exceeds specific values [1,2].
In tunnel construction, the advance rate is one of the key factors because it is directly
related to the overall construction period and influences the economic feasibility of a project.
Therefore, the ultimate goal of blast excavation in the new Austrian tunneling method
(NATM) is to maximize the advance per round, while meeting the allowable criteria for
blast-induced vibration. It is well known that blast-induced vibration is the most significant
factor that affects the surrounding structures [3]. In the rock fragmentation caused by
blasting, it has been found that only 20–30% of the energy is used in the breakage of the
surrounding rocks, while the residual energies are dissipated in the forms of vibration, noise,
and flying rocks [4,5]; thus, the current blasting techniques have inevitable limitations [6].
When the vibration exceeds a critical value, internal cracks in the rock mass can be induced,
potentially harming nearby structures [7]. Given the recent rise in environmental concerns,
Sustainability 2022, 14, 13347. https://doi.org/10.3390/su142013347
https://www.mdpi.com/journal/sustainability
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complaints about blast-induced vibration and noise continue to increase, and regulations
are becoming commensurately stricter [8].
Several parameters affect blast-induced vibration [9], and the free face is one of the
most efficient factors in maximizing the blasting efficiency, as well as reducing vibration.
Unlike open-pit mines, tunnel structures generally have only one free face, so the cut
blasting method is necessary to create artificial additional free faces to improve the blasting
efficiency. V-cuts and burn-cuts, which are the traditional cut blasting methods, are widely
used in tunnel blasting. Using the traditional cut method, more explosives are needed to
increase the advance, but there are limits to increasing the amount of explosives, while
keeping to the allowable limit of vibration.
A long and large-diameter uncharged hole boring (LLB) method is an advanced
cut blasting method that involves boring large-diameter uncharged holes. This method
has been reported to have significantly less blast-induced vibration than traditional cut
methods [10]. The high-performance LLB machine generally drills 50 m with a 382-mm
hammer bit at a time, considering the overall working process and drilling time. Thus, this
method has the great advantage of creating large-diameter uncharged holes (free faces) that
are deeper than regular blast holes, thus significantly increasing the advance per round
compared to the traditional cut method [11].
However, the cut methods in tunnel blasting that utilize large-diameter uncharged
holes (over 350 mm) have not yet been fully analyzed in terms of failure mechanisms and
blasting efficiency. In addition, in some tunnel construction sites where the LLB method
was used, the advance per round was similar to, or even less than, the traditional cut
methods. In the actual tunnel construction site, if explosive material detonates inside
the rock mass, there is a limit to investigating the failure mechanism of the LLB method
because an instantaneous explosion reaction occurs. To investigate the failure mechanism
of blasting more accurately, experimental studies should be conducted, but several risks
and limitations are involved because they are very expensive and time-consuming [12].
Instead, numerical approaches have been widely used to overcome the many limitations of
experimental research [13–15].
In this study, a series of numerical analyses were carried out to investigate the failure
mechanism of tunnel blasting with the LLB method. The LS-DYNA software, which is
a finite element software that can handle dynamic and non-linear problems, was used to
simulate the tunnel blasting. The traditional burn-cut method and the LLB method, as
employed to create uncharged holes for reducing blast-induced vibration, were modeled,
to compare their blasting mechanisms and efficiency, especially the advance per round.
Additional analysis was performed to compare the blasting efficiency when a reduced
amount of explosives was used with the LLB method.
2. Long and Large-Diameter Uncharged Hole Boring Method
2.1. Introduction to the LLB Method
The LLB method is an advanced cut blasting method to minimize the vibration generated by blasting in a NATM tunnel. This method creates long and large-diameter (382-mm)
uncharged holes at a cut area using a high-performance boring machine, as shown in
Figure 1. The LLB hole serves to release the confining stresses of the rock mass before
blasting. When an explosive detonates in the blast hole, the adjacent uncharged hole can
not only provide a larger space for moving breaking rocks, but can also change the stress
distribution in the rocks around the uncharged hole, which is called the “uncharged hole
effect” [16].
One of the outstanding characteristics of this method is that it typically drills 50 m at
a time, and can efficiently drill up to 65 m without any problems. Thus, additional free
faces are formed beyond the depth of the blast hole, which theoretically has the advantage
of increasing the advance per round. In addition, one to three holes are generally drilled
in the LLB method, depending on what is applicable in the site conditions. Unlike the
conventional cut blasting methods, such as V-cut and burn-cut, this method is applicable
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for both weak and hard rock masses. The field application of the LLB machine and a tunnel
face with completed drilling are shown in Figure 2 [10].
(a)
(b)
Figure 1. Comparison of general blasting and controlled blasting using the LLB method. (a) General
blasting; (b) controlled blasting using the LLB method.
One of the outstanding characteristics of this method is that it typically drills 50 m at
a time, and can efficiently drill up to 65 m without any problems. Thus, additional free
faces are formed beyond the depth of the blast hole, which theoretically has the advantage
of increasing the advance per round. In addition, one to three holes are generally drilled
in the LLB method, depending on what is applicable in(b)
the site conditions. Unlike the
(a)
conventional cut blasting methods, such as V-cut and burn-cut, this method is applicable
Figure
1. Comparison
of general
and
blasting using
LLBmachine
method. (a) General
for both
weak and hard
rock blasting
masses.
Thecontrolled
field application
of thethe
LLB
a tunFigure
1. Comparison
of general
blasting and
controlled
blasting using
the
LLB method. and
(a) General
blasting; (b) controlled blasting using the LLB method.
nel
face
with
completed
drilling
are
shown
in
Figure
2
[10].
blasting; (b) controlled blasting using the LLB method.
One of the outstanding characteristics of this method is that it typically drills 50 m at
a time, and can efficiently drill up to 65 m without any problems. Thus, additional free
faces are formed beyond the depth of the blast hole, which theoretically has the advantage
of increasing the advance per round. In addition, one to three holes are generally drilled
in the LLB method, depending on what is applicable in the site conditions. Unlike the
conventional cut blasting methods, such as V-cut and burn-cut, this method is applicable
for both weak and hard rock masses. The field application of the LLB machine and a tunnel face with completed drilling are shown in Figure 2 [10].
(a)
(b)
Figure 2.
2. Images
Figure
Images of
of field
field application
application of
of the
the LLB
LLB machine
machine and
and aa tunnel
tunnel face
face with
with completed
completed drilling.
drilling.
(a) Field application of the LLB machine; (b) tunnel face with completed drilling.
(a) Field application of the LLB machine; (b) tunnel face with completed drilling.
Tensile Fracturing
Fracturing by
by Long
Long and
and Large-Diameter
Large-Diameter Uncharged
UnchargedHoles
Holes
2.2. A Mechanism of Tensile
When an explosive detonates in a blast hole, gaseous detonation products fill the
high-pressure
detonation
gas gas
is imblast hole
hole with
with high
highpressure
pressureand
andtemperature.
temperature.This
This
high-pressure
detonation
is
mediately applied
to to
thethe
surface
ofofa ablast
immediately
applied
surface
blasthole
holeand
andgenerates
generatesradial
radialcompressive
compressive stress,
stress,
which
generally greater than the strength
strength of
of the
the rock
rock [17,18].
[17,18].
(a) is generally
(b) The compressive stress
wave
a tensile
stress
wave
when
it reaches
a free
face,face,
and
wave generated
generatedby
byblasting
blastingturns
turnsinto
into
a tensile
stress
wave
when
it reaches
a free
Figure 2. Images of field application of the LLB machine and a tunnel face with completed drilling.
the
tensiletensile
wave returns
throughthrough
the rockthe
mass
[19–21].
behavior
is generally
andreflected
the reflected
wave returns
rock
mass This
[19–21].
This behavior
is
(a) Field application of the LLB machine; (b) tunnel face with completed drilling.
called
the called
Hopkinson
effect, andeffect,
the principle
this theory
is illustrated
in Figure 3in[22].
generally
the Hopkinson
and the of
principle
of this
theory is illustrated
Figis well known that the dynamic tensile strength of rock is much lower than the
ure A
3It[22].
2.2.
Mechanism of Tensile Fracturing by Long and Large-Diameter Uncharged Holes
dynamic compressive strength [23,24]. If the tension stress waves exceed the dynamic
When
an explosive
detonates
in abeblast
hole, gaseous
detonation
products
fillleads
the
tensile
strength
of the rock,
cracks will
generated
gradually,
and this tensile
stress
blast
hole
with
high
pressure
and
temperature.
This
high-pressure
detonation
gas
is
imto greater damage to the rock mass in the vicinity of the free face [16]. Therefore, when
mediately
applied
to the surface
of a blast
and generates
radialreaches
compressive
stress,
a propagated
compressive
stress wave
fromhole
the detonated
explosive
an uncharged
which
generally
strength
therock
rockis [17,18].
Thecrushed
compressive
stress
hole, itisturns
into agreater
tensile than
stressthe
wave;
thus,ofthe
effectively
around
the
wave
generated
by
blasting
turns
into
a
tensile
stress
wave
when
it
reaches
a
free
face,
uncharged hole. A tunnel structure generally has only one free face, which is the tunnel
and the reflected tensile wave returns through the rock mass [19–21]. This behavior is
generally called the Hopkinson effect, and the principle of this theory is illustrated in Figure 3 [22].
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face. To effectively blast in tunneling, adding free faces is the most vital factor for initiating
or maximizing the Hopkinson effect.
Figure 3. Principle of
the Hopkinson
effect.
Figure
3. Principle of
the Hopkinson effect.
3. Numerical Analysis
It is well known that the dynamic tensile strength of rock is much lower than the
3.1. Analysis Model
dynamic compressive strength [23,24]. If the tension stress waves exceed the dynamic tenThis study used the LS-DYNA software, which is widely used for blasting simulations,
sile strength of the rock,
cracks will be generated gradually, and this tensile stress leads to
to simulate dynamic and non-linear problems. The arbitrary Lagrangian–Eulerian (ALE)
greater damage to the rock mass in the vicinity of the free face [16]. Therefore, when a
formulation was employed to investigate blast-induced pressure and its interaction with
propagated compressive
stress wave
fromThe
theALE
detonated
explosive
reaches
an uncharged
various materials
[25–27].
formulation
contains
both Lagrangian
and Eulerian
hole, it turns intoformulations
a tensile stress
wave;
thus,
the
rock
is
effectively
crushed
around
the to move
to utilize the advantages of each approach [28]; it allows
the mesh
uncharged hole. A
tunnel structure
generally
only
face,inwhich
is the
independently
from the
materialhas
flow,
andone
eachfree
element
the mesh
cantunnel
contain mixtures
ofblast
different
materials [29].
face. To effectively
in tunneling,
adding free faces is the most vital factor for initiating
The burn-cut
method and the LLB method were modeled to investigate their effects
or maximizing the Hopkinson
effect.
on the blasting efficiency, including the advance per round in tunnel blasting. Both analysis
models included the rock, explosives, and stemming in the charge hole, as well as
3. Numerical Analysis
uncharged holes. The rock was modeled using the Lagrangian method, with a geometry
3.1. Analysis Modelof 1500 mm × 1500 mm × 1500 mm to focus on the cut area, as shown in Figure 4. The
diameter
of the blastsoftware,
holes waswhich
50 mmisand
they used
contained
300 mm simulaof explosives and
This study used
the LS-DYNA
widely
for blasting
700
mm
of
stemming,
which
were
modeled
with
the
ALE
method.
The
diameters of the
tions, to simulate dynamic and non-linear problems. The arbitrary Lagrangian–Eulerian
uncharged
holes
for
the
burn-cut
and
the
LLB
method
were
102
mm
and
382 mm, respec(ALE) formulation was employed to investigate blast-induced pressure and its interaction
tively. The spacing between the blast hole and the uncharged hole for the burn-cut was
with various materials [25–27]. The ALE formulation contains both Lagrangian and Eu200–300 mm and 400 mm for the LLB method. The geometries were modeled based on
lerian formulations
to utilize
advantages
of each
[28];sites
it allows
theKorea.
meshIntoboth cases,
actual
designthe
cases
from subway
tunnelapproach
construction
in South
move independently
from thewere
material
andat each
element
in the
can conditions
contain were set
the explosives
set to flow,
detonate
the same
time, and
the mesh
boundary
mixtures of different
materials
[29].
as non-reflecting boundaries for all sides, except the tunnel face.
The burn-cut method and the LLB method were modeled to investigate their effects
3.2. JH-2 Constitutive
for Rock per
Material
on the blasting efficiency,
including Model
the advance
round in tunnel blasting. Both analA
Johnson–Holmquist
(JH-1)
constitutive
modelhole,
was initially
for
ysis models included the rock, explosives, and stemming inmaterial
the charge
as well proposed
as
studying
the
behavior
of
metals
such
as
copper
and
nickel
under
large
strain,
high
strain
uncharged holes. The rock was modeled using the Lagrangian method, with a geometry
rate, and high-pressure conditions. Based on the JH-1 model, an improved material model,
of 1500 mm × 1500 mm × 1500 mm to focus on the cut area, as shown in Figure 4. The
named as the JH-2 constitutive model, was suggested to describe the mechanical behavior
diameter of the blast
holes was 50 mm and they contained 300 mm of explosives and 700
under dynamic conditions, considering the softening property of brittle materials. The JH-2
mm of stemming,model
which
with the ALE
method.
diameters
of (blasting)
the un- of rocks.
is were
widelymodeled
used in LS-DYNA
to simulate
the The
dynamic
behavior
charged holes forThis
the improved
burn-cut model
and the
LLB method
were 102
andof382
mm, as
respecrepresented
the strength
andmm
damage
material
functions of the
tively. The spacing between the blast hole and the uncharged hole for the burn-cut was
200–300 mm and 400 mm for the LLB method. The geometries were modeled based on
actual design cases from subway tunnel construction sites in South Korea. In both cases,
the explosives were set to detonate at the same time, and the boundary conditions were
Sustainability 2022, 14, 13347
14, x FOR PEER REVIEW
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representative variables and the damage evolution within the material was considered.
In addition, this model considers the pressure, strain-rate dependent strength, damage,
and fracture of materials [30–32]. Granite is one of the most brittle materials and a widely
5 of 15 were
distributed underground rock material in South Korea. Therefore, granite properties
used here to simulate the tunnel blasting, as shown in Table 1 [33]. A general overview of
the model is illustrated in Figure 5.
(a)
(b)
Figure 4. Geometry Figure
of numerical
simulations
for simulations
the burn-cut
the LLBand
methods.
(a) Burn-cut
4. Geometry
of numerical
for and
the burn-cut
the LLB methods.
(a) Burn-cut
method; (b) LLB method.
method; (b) LLB method.
Table 1. Input parameter for JH-2 model in LS-DYNA.
3.2. JH-2 Constitutive
Model for Rock Material
Parameter
Value
Parameter
Value
A
Johnson–Holmquist (JH-1)
constitutive material model
was initially proposed for
3
studying
the
behavior
of
metals
such
as
copper
and
nickel
under
large
strain,
high
strain
Density (kg/m )
2560
Maximum normalized fractured strength
0.160
Shear and
modulus
(GPa)
11.606 Based on the JH-1
Hugoniot
elastic limit
4.500
rate,
high-pressure
conditions.
model,
an(GPa)
improved material
Intact normalized strength parameter A
1.248
Pressure component at the Hugoniot elastic limit (GPa)
2.930
model, named as the JH-2 constitutive
model, was suggested
to describe the mechanical
Fractured normalized strength parameter B
0.680
Fraction of elastic energy loss
1.000
behavior
underCdynamic conditions,
the softening
of brittle
materiStrength parameter
0.005 considering
Parameter
for a plasticproperty
strain to fracture
D1
0.008
Fractured
strength
parameter
M is widely used
0.830in LS-DYNAParameter
for a plastic
to fracture
D2
0.435
als. The
JH-2
model
to simulate
the strain
dynamic
behavior
(blastIntact strength parameter N
0.676
First pressure coefficient K1 (GPa)
10.720
ing) of rocks. This improved model represented the strength and damage of material as
Reference strain rate
1.000
Second pressure coefficient K2 (GPa)
−386
functions
of the (GPa)
representative variables
and the damage
evolution
within the material
Maximum
tensile strength
0.015
Elastic constant
K3 (GPa)
12,800
was considered. In addition, this model considers the pressure, strain-rate dependent
strength, damage, and fracture of materials [30–32]. Granite is one of the most brittle materials and a widely distributed underground rock material in South Korea. Therefore,
granite properties were used here to simulate the tunnel blasting, as shown in Table 1 [33].
A general overview of the model is illustrated in Figure 5.
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Figure
Figure 5.
5. Strength
Strength model
model for
for the
the JH-2
JH-2 constitutive
constitutive model.
model.
TableThe
1. Input
for JH-2the
model
in LS-DYNA.
JH-2parameter
model includes
following
three types of strength: intact state, damaged
state, and fractured state, as shown in Figure 5. The three states have their own strength
Parameter
Value
Parameter
Value
equations, which present the relationship between the normalized equivalent stress and
Density (kg/m3)the normalized pressure,
2560
Maximum
normalized
fractured
strength
0.160
expressed as
Shear modulus (GPa)
11.606
Hugoniot elastic limit (GPa)
4.500
Intact normalized strength parameter A 1.248 Pressure
component
2.930 (1)
σ∗ =
σi∗ − D (σi∗at−the
σ∗f )Hugoniot
= σ/σHELelastic limit (GPa)
Fractured normalized strength parameter B 0.680
Fraction of elastic energy loss
1.000
∗
∗ is the normalized fracture stress, D is
where
intact
equivalent
Strength parameter
C σi is the normalized
0.005
Parameter
for a stress,
plasticσstrain
to fracture 𝐷1
0.008
f
the damage
coefficient
D ≤ 1), σ isfor
thea actual
stress calculated
by0.435
the von
Fractured strength parameter
M
0.830 (0 ≤ Parameter
plasticequivalent
strain to fracture
𝐷2
Mises
stress
formula,
and
σ
is
the
equivalent
stress
at
the
Hugoniot
elastic
limit
(HEL).
HEL
Intact strength parameter N
0.676
First pressure coefficient K1 (GPa)
10.720
The
HEL
stands
for
the
net
compressive
stress
at
which
a
one-dimensional
shock
wave
Reference strain rate
1.000
Second pressure coefficient K2 (GPa)
−386
with uniaxial strain exceeds the elastic limit of the material. The brittle material begins
Maximum tensile strength (GPa)
0.015
Elastic constant K3 (GPa)
12,800
to soften when the damage begins to accumulate, and this process can be expressed by
Equation (1). Although the softening does not continue when the material is completely
The JH-2 model includes the following three types of strength: intact state, damaged
damaged (D = 1), it allows for gradual softening of the brittle material under increasing
state, and fractured state, as shown in Figure 5. The three states have their own strength
plastic strain. The normalized intact strength and fracture strength are given by
equations, which present the relationship between the normalized equivalent stress and
.∗
the normalized pressure, expressed
as
σi∗ = A( P∗ + T ∗ ) N 1 + C × ln ε
(2)
(1)
𝜎 ∗ = 𝜎𝑖∗ − 𝐷(𝜎𝑖∗ − 𝜎𝑓∗ ) = 𝜎/𝜎𝐻𝐸𝐿
∗ .∗
where 𝜎𝑖∗ is the normalized intact
𝑓 εis the normalized fracture stress,
σ∗f =equivalent
B( P∗ ) M 1stress,
+ C × 𝜎ln
(3)
𝐷 is the damage coefficient (0 ≤ 𝐷 ≤ 1), 𝜎 is the actual equivalent stress calculated by
where
B, C, M,
andformula,
N are all and
constants.
The
P∗ =
P/PHEL , elastic
where
the
vonA,Mises
stress
𝜎𝐻𝐸𝐿 is
thenormalized
equivalentpressure
stress atis the
Hugoniot
∗
P
is
the
actual
pressure
and
P
is
the
pressure
at
the
HEL.
The
normalized
maximum
tensile
limit (HEL). The HEL stands for the net compressive stress at which a one-dimensional
hydrostatic
is T ∗ =
T/Pexceeds
is thelimit
maximum
hydrostatic
pressure.
HEL , where
shock
wavepressure
with
uniaxial
strain
the Telastic
of thetensile
material.
The brittle
mate.∗
. .
.
.
−1 is the reference strain rate.
The
strain
is
ε
=
ε/
ε
,
where
ε
is
the
actual
strain;
ε
=
1
s
0
0
rial begins to soften when
the damage begins to accumulate,
and this process can be exTheby
damage
is mainly
accumulated
due to thedoes
generation
of fractures,
damage
pressed
Equation
(1). Although
the softening
not continue
whenand
the the
material
is
graph
is
shown
in
Figure
6a.
The
damage
in
the
JH-2
model
can
be
expressed
as
follows:
completely damaged (𝐷 = 1), it allows for gradual softening of the brittle material under
increasing plastic strain. The normalized
intact strength and fracture strength are given
p
D = ∑ ∆ε p /ε f = ∑ ∆ε p /[ D1 ( P∗ + T ∗ ) D2 ]
(4)
by
∗
∗
𝑁
(2)
+ 𝑇 ∗ )of
(1
+ C × ln 𝜀̇∗ )ε p is the plastic strain to the
where ∆ε p is the plastic strain𝜎during
a cycle
integration,
𝑖 = 𝐴(𝑃
f
∗
∗ )𝑀
∗
𝐵(𝑃 D (1
+D
C ×are
ln 𝜀̇the
) damage factors for ε p . The
(3)
fracture under constant pressure𝜎𝑓P,=and
and
1
2
f
∗
where
𝐴,of𝐵,state
𝐶, (EOS)
𝑀, and
are
all constitutive
constants. The
normalized
= 𝑃/𝑃𝐻𝐸𝐿
equation
for𝑁the
JH-2
model,
as shownpressure
in Figureis6b,𝑃presents
the,
∗
where
𝑃
is
the
actual
pressure
and
𝑃
is
the
pressure
at
the
HEL.
The
normalized
maxirelationship between hydrostatic pressure and volumetric strain, which consists of a pure
mum
hydrostatic
is 𝑇 ∗ =
𝑇/𝑃
𝑇 is thebefore
maximum
tensile and
hyelastictensile
stage and
a plastic pressure
damage stage.
The
hydrostatic
the fracture
𝐻𝐸𝐿 , wherepressure
∗
−1
drostatic
pressure.starts
The to
strain
is 𝜀̇ = 𝜀̇can
/𝜀̇0 be
, where
𝜀̇ is the
actual strain; 𝜀̇0 = 1s is the
after the damage
accumulate
expressed
as follows:
reference strain rate.
P = K1 µ + K2 µ 2 + K3 µ 3 · · · ( D = 0 )
(5)
the relationship between hydrostatic pressure and volumetric strain, which consists of a
pure elastic stage and a plastic damage stage. The hydrostatic pressure before the fracture
and after the damage starts to accumulate can be expressed as follows:
7(5)
of 15
𝑃 = 𝐾1 𝜇 + 𝐾2 𝜇2 + 𝐾3 𝜇3 ⋯ (𝐷 = 0)
(6)
𝑃 = 𝐾1 𝜇 + 𝐾2 𝜇2 + 𝐾3 𝜇3 + ∆𝑃 ⋯ (0 < 𝐷 < 1)
3
+ K2bulk
µ2 + Kmodulus),
0 < D𝜇<=1)𝜌/𝜌0 − 1 for the(6)
where 𝐾1 , 𝐾2 , and 𝐾3 are constants P(𝐾=1 Kis
3 µ + ∆P · · · (and
1 µ the
current density 𝜌 and
𝜌0 . When
fracture
occurs
wherethe
K1 , initial
K2 , and density
K3 are constants
(K1 is the
the bulk
modulus),
and in
µ =the
ρ/ρmaterial,
0 − 1 for the
density ρ and
the initial
ρ0 . When the
fracture occurs
the material,
which
which is caused bycurrent
the bulking
energy,
thedensity
incremental
pressure
∆𝑃 isinadded.
In this
is
caused
by
the
bulking
energy,
the
incremental
pressure
∆P
is
added.
In
this
analysis
analysis model, erosion was set to occur when the tensile stress exceeds the maximum
model, erosion was set to occur when the tensile stress exceeds the maximum tensile
tensile strength of the
rockofmass,
using
to simulate
the
failure.
strength
the rock
mass,blasting
using blasting
to simulate
therock
rock failure.
Sustainability 2022, 14, 13347
(a)
(b)
Figure 6. Damage and
EOS6. models
forEOS
themodels
JH-2for
constitutive
model.
(a) (a)
Damage
model;
Figure
Damage and
the JH-2 constitutive
model.
Damage model;
(b)(b)
EOSEOS
model.
model.
3.3. Explosive and Stemming Material Models
To model the pressure generated by the expansion of the detonation product, a Jones-
3.3. Explosive and Stemming
Material
Models of state (EOS) was used [34]. The JWL EOS is widely used
Wilkins–Lee
(JWL) equation
in explosives
modelingby
forthe
describing
the relationship
of pressure–volume–energy
To model the pressure
generated
expansion
of the detonation
product, a Jones-for
detonation products. In this study, JWL EOS was used to simulate the blasting process, and
Wilkins–Lee (JWL) this
equation
of state (EOS) was used [34]. The JWL EOS is widely used in
equation can be expressed as follows:
explosives modeling for describing the relationship of pressure–volume–energy for deto
− R1 V
− R2 V
ω used
ω the
ω
nation products. In this study, JWL
to+simulate
blasting
P =EOS
A 1 was
−
B 1−
+ E0 process, and(7)
R
V
R
V
V
2
this equation can be expressed as follows: 1
where P is pressure, E and V are the detonation energy per unit volume and the relative
−𝑅1 𝑉
−𝑅2 𝑉
𝜔 coefficients,
𝜔respectively. A high explosive
volume, and A, B, R𝜔
1 , R2 , and ω are the EOS
(7)
𝑃
=
𝐴
(1
−
)
+
𝐵
(1
−
)
+
𝐸
burn (HEB) material
𝑅1card
𝑉 was used to simulate
𝑅2 𝑉the detonation
𝑉 0of the explosives. The input
values for JWL EOS and HEB for an emulsion material are provided in Table 2 [35].
where 𝑃 is pressure, 𝐸 and 𝑉 are the detonation energy per unit volume and the relaTable 2. Input parameter for JWL EOS in LS-DYNA.
tive volume, and 𝐴, 𝐵, 𝑅1 , 𝑅2 , and 𝜔 are the EOS coefficients, respectively. A high exA
B was used to simulate the detonation of Ethe
V0
plosive Parameter
burn (HEB) material
card
explosives.
0
R1
R2
ω
JWL
(GPa)
(GPa)
(GPa/m3 /m3 ) (m3 /m3 )
The inputValue
values for 276
JWL EOS and
HEB for
an emulsion
material
are provided
in Table
2
8.44
5.215
2.112
0.501
3.868
1.0
[35].
RO
D
Pcj
Parameter
3)
to prevent the release
filling the
(GPa)
(kg/mused
(m/s) of detonation gases by
HEB Stemming is a material
Value
1180
5122
9.530
remaining areas in the blast hole, and it helps the pressure generated by the explosives to
where RO, D, and Pcj are the density, detonation velocity, and Chapman–Jouguet pressure, respectively.
crush the rock efficiently. Here,
the stemming material was modeled using the
Stemming is a material used to prevent the release of detonation gases by filling the
remaining areas in the blast hole, and it helps the pressure generated by the explosives to
crush the rock efficiently. Here, the stemming material was modeled using the FHWA_SOIL
material model developed by the U.S. Federal Highway Administration (FHWA) [36]. This
Sustainability 2022, 14, 13347
8 of 15
model is an isotropic material with damage, and it is effective at modeling the behavior of
soil under the consideration of strain-softening, kinematic hardening, strain rate effects,
element deletion, excess pore water effects, and stability with no soil confinement; the input
parameters are listed in Table 3 [37–39].
Table 3. Input parameter for FHWA_SOIL model in LS-DYNA.
Parameter
Value
Parameter
Value
Density (kg/m3 )
2350
Eccentricity parameter
0.700
Specific gravity
2.650
Moisture content
6.200
Density of water (kg/m3 )
1000
Skeleton bulk modulus (MPa)
0.153
Viscoplasticity parameter Vn
1.100
Minimum internal friction angle (radians)
0.063
0.001
Viscoplasticity parameter γr
0.0
Volumetric strain at initial damage threshold
Maximum number of plasticity iterations
10.00
Void formation energy
10.00
Bulk modulus (MPa)
15.30
Strain hardening, percent of ϕmax where non-linear effects start
10.00
0.0
Shear modulus (MPa)
19.50
Pore water effects on bulk modulus PWD1
Peak shear strength angle (radians)
0.420
Pore water effects on effective pressure PWD2
0.0
Cohesion (MPa)
0.011
Strain hardening, amount of non-linear effects
10.00
The uncharged holes were modeled using the NULL material card, and the void was
modeled using the LINEAR_POLYNOMIAL EOS material card, which is given by
P = C0 + C1 µ + C2 µ2 + C3 µ3 + C4 + C5 µ + C6 µ2 E
(8)
where C0 , C1 , C2 , C3 , C4 , C5 , and C6 are constants, and µ = ρ/ρ0 − 1, which is the ratio
of the current density to the initial density. The detailed parameters for air are given in
Table 4.
Table 4. Material model and EOS parameter for air.
ρ (kg/m3 )
C0
C1
C2
C3
C4
C5
C6
E0 (MPa)
1.29
0.0
0.0
0.0
0.0
0.4
0.4
0.0
0.25
3.4. Results of Numerical Analyses
Figure 7 displays the results of numerical analyses for the burn-cut and LLB methods
over time, and shows side views of the analysis models in the wireframe element mode for
observing the state of fracturing around the blast holes inside the rock mass. The number
of elements of the burn-cut and LLB methods was 6,800,190 and 6,816,395, respectively.
When the explosives detonate after 0 s, the high-temperature and high-pressure gases
are generated by the four blast holes; thus, compressive fractures are generated near the
blast holes, and the explosion energy is propagated in the form of a compressive stress wave
to the rock mass [40,41]. The propagated compressive stress wave reaches the uncharged
holes before it reaches the tunnel face because of the shorter burden. The compressive
stress wave first reaches the surface of the uncharged holes, and then is reflected as a tensile
wave that begins to crush the rock around the uncharged holes at 0.2 ms in both cases. At
0.2 ms, in the burn-cut method, the spacing between the explosives and the uncharged
hole is shorter than that of the LLB method; thus, the crushed zone around the uncharged
hole was wider than in the LLB method. Then, the crushed area near the uncharged holes
gradually increases. At the same time, the continuously propagated stress wave finally
reaches the tunnel face and the rock is crushed, due to the reflected tensile stress at 0.8 and
1.0 ms, respectively. The crushed zones continuously increase due to the high pressure and
the reflected tensile stress generated by the uncharged holes and the tunnel face.
Sustainability 2022, 14, 13347
and the uncharged hole is shorter than that of the LLB method; thus, the crushed zone
around the uncharged hole was wider than in the LLB method. Then, the crushed area
near the uncharged holes gradually increases. At the same time, the continuously propagated stress wave finally reaches the tunnel face and the rock is crushed, due to the reflected tensile stress at 0.8 and 1.0 ms, respectively. The crushed zones continuously
in9 of 15
crease due to the high pressure and the reflected tensile stress generated by the uncharged
holes and the tunnel face.
0s
0.2 ms
0.8 ms
1.0 ms
0.4 ms
0.6 ms
1.2 ms
1.4 ms
0.4 ms
0.6 ms
1.2 ms
1.4 ms
(a)
0s
0.2 ms
0.8 ms
1.0 ms
(b)
Figure 7.
7. Results
method; (b)
Figure
Results of
of the
the numerical
numerical analyses
analyses of
of the
the burn-cut
burn-cut and
and LLB
LLBmethods.
methods.(a)
(a)Burn-cut
Burn-cut
method;
LLB method.
(b) LLB method.
4. Discussion
4.1. Effect of Increasing the Advance Rate in the Burn-Cut and LLB Methods
Figure 8 summarizes the numerical analysis results at the last step (at 1.4 ms) to
investigate the influence of the advance rate in the burn-cut and LLB methods. In the
case of the Burn-cut method, the rock was crushed up to 0.09 m from the end line of the
explosives, whereas the rock was crushed up to 0.37 m in the LLB method, which was more
than four times the advance rate. It is believed that the large-diameter uncharged hole that
was longer than the ordinary blast holes contributed significantly to the generation of more
extensive tensile failure. In particular, in the burn-cut method, the blast-induced stress was
of the Burn-cut method, the rock was crushed up to 0.09 m from the end line of the explosives, whereas the rock was crushed up to 0.37 m in the LLB method, which was more
than four times the advance rate. It is believed that the large-diameter uncharged hole that
was14,longer
than the ordinary blast holes contributed significantly to the generation
of15
Sustainability 2022,
13347
10 of
more extensive tensile failure. In particular, in the burn-cut method, the blast-induced
stress was used more to crush rocks between the blast holes and the tunnel face than to
used more
rocks
between
the blast holes
and the
tunnel
face
than to was
increase
the
increase the advance.
On to
thecrush
other
hand,
blast-induced
stress
in the
LLB
method
used
advance. On the other hand, blast-induced stress in the LLB method was used more to
more to increase the advance. Therefore, the long and large-diameter uncharged hole is
increase the advance. Therefore, the long and large-diameter uncharged hole is believed to
believed to contribute
greatly
the
advance.
contribute
greatlyto
toincreasing
increasing the
advance.
(a)
(b)
Figure 8. Comparison
advanceofbetween
thebetween
burn-cut
LLBand
methods.
(a) Burn-cut
method;
Figureof8.the
Comparison
the advance
the and
burn-cut
LLB methods.
(a) Burn-cut
method;
(b) LLB method. (b) LLB method.
When explosives detonate near the cut area in the first stage, the long and large-
When explosives
detonate near the cut area in the first stage, the long and large-didiameter uncharged hole provides a larger space for crushed rock to move into, thus
ameter uncharged
hole provides
a larger
space
crushed rock
to move
into,
thus reducreducing
the confining
pressures
of for
the surrounding
rocks.
Efficient
moving
of these
ing the confining
pressures
of theansurrounding
moving of
thesethe
crushed
crushed
rocks creates
additional free rocks.
face andEfficient
reduces interference
between
crushed
in the second
stage.and
Considering
the entire blasting
process
the sequential
rocks creates anrocks
additional
free face
reducesthat
interference
between
theuses
crushed
rocks
blasting technique, which has a detonating delay time in the actual blasting, this method is
in the second stage. Considering that the entire blasting process uses the sequential blastsignificantly beneficial in that the long and large-diameter uncharged hole provides a larger
ing technique, which
a detonating
delay
time
in the actual
blasting,
thislarge-diameter
method is
space tohas
move
the crushed rocks
into.
In addition,
the formed
long and
significantly beneficial
that
theblasting
long and
large-diameter
hole provides
a
unchargedinhole
before
provides
an opportunity uncharged
to reduce the amount
of explosives;
thus,
the
advance
rate
can
be
increased
and
the
blast-induced
vibration
can
be
reduced.
larger space to move the crushed rocks into. In addition, the formed long and large-diameter uncharged 4.2.
holeEffect
before
blasting provides an opportunity to reduce the amount of exof Increasing the Advance in the Burn-Cut and LLB Methods
plosives; thus, the advance
rate can be increased and the blast-induced vibration can be
Additional analysis of the LLB method was carried out to investigate the blasting
reduced.
efficiency with the large-diameter uncharged hole with the same depth as the blast holes
(a shorter depth than in the original LLB method). Figure 9 summarizes the results of
the numerical
analysisinfor
theBurn-Cut
original LLB
and the modified LLB with a shorter
4.2. Effect of Increasing
the Advance
the
andmethod
LLB Methods
uncharged hole. The number of elements of the modified LLB method was 6,719,248. The
Additionalresults
analysis
the
method
was carried
out towith
investigate
blasting
showof
that
theLLB
advance
in the modified
LLB method
its shorter the
uncharged
hole
efficiency with the
uncharged
hole3.36
with
theless
same
as the blast
holes
was large-diameter
0.11 m, which was
approximately
times
thandepth
in the original
LLB method.
the advance
the modified
LLB
method9 was
approximately
timesoflonger
(a shorter depthHowever,
than in the
originalinLLB
method).
Figure
summarizes
the 1.22
results
the
than
in
the
burn-cut
method,
as
shown
in
Figure
8a.
This
suggests
that
the
advance
numerical analysis for the original LLB method and the modified LLB with a shorter unincreased due to the long and large-diameter uncharged hole that caused a more extensive
charged hole. The
number of elements of the modified LLB method was 6,719,248. The
range of tensile failure compared to the burn-cut method. Given that the wider and longer
results show that
the advance
in the modified
LLB
its shorter
uncharged
uncharged
hole significantly
contributed
to method
increasingwith
the blasting
efficiency
as well as
the advance,
the LLB
method has pronounced
advantages
compared
the traditional
hole was 0.11 m,
which was
approximately
3.36 times
less than
in the to
original
LLB
burn-cut
method. However,
the method.
advance in the modified LLB method was approximately 1.22
times longer than in the burn-cut method, as shown in Figure 8a. This suggests that the
Sustainability 2022, 14, 13347
advance increased due to the long and large-diameter uncharged hole that caused a more
extensiveincreased
range of tensile
failure
to the burn-cut
method.
Given
that theawider
advance
due to the
longcompared
and large-diameter
uncharged
hole
that caused
more
and
longer
uncharged
hole
significantly
contributed
to
increasing
the
blasting
efficiency
extensive range of tensile failure compared to the burn-cut method. Given that the
wider
as well
as the
advance, hole
the LLB
method has
pronounced
advantages
compared
to the traand
longer
uncharged
significantly
contributed
to increasing
the
blasting efficiency
11 of 15
ditional
burn-cut
method.
as well as the advance, the LLB method has pronounced advantages compared to the traditional burn-cut method.
(a)
(b)
(a)of blasting efficiency depending on the length
(b) of the large-diameter unFigure 9. Comparison
charged hole. (a) Original LLB method; (b) modified LLB method with reduced uncharged hole
Figure
blasting efficiency
efficiencydepending
depending
length
of large-diameter
the large-diameter
unFigure9.9.Comparison
Comparison of
of blasting
onon
thethe
length
of the
uncharged
length.
charged
hole.
(a)
Original
LLB
method;
(b)
modified
LLB
method
with
reduced
uncharged
hole
hole. (a) Original LLB method; (b) modified LLB method with reduced uncharged hole length.
length.
4.3.
4.3.Effect
EffectofofReducing
Reducingthe
theAmount
AmountofofExplosives
Explosives
Additional
numerical
analysis
was
4.3. Effect
of
Reducing
the
Amount
of
Explosives
Additional numerical analysis wasperformed
performedtotoestimate
estimatethe
theeffect
effectofofreducing
reducingthe
the
amount
of
explosives
when
applying
the
LLB
method.
The
total
length
of
the
Additional
numerical
analysis
wasthe
performed
to estimate
thelength
effect of reducing
the
amount
of explosives
when
applying
LLB method.
The total
theexplosives
explosives
was
byby
30%,
from
300
to 210
mm,
and method.
the results
aretotal
illustrated
in the
Figure
10. The10.
wasreduced
reduced
30%,
from
300
to 210
and
the results
arelength
illustrated
in
Figure
amount
of explosives
when
applying
themm,
LLB
The
of
explosives
number
of
elements
of
the
modified
LLB
method
was
6,801,550.
The
crushed
zone
around
Thereduced
numberby
of30%,
elements
of the
modified
LLBthe
method
6,801,550. in
The
crushed
zone
was
from 300
to 210
mm, and
resultswas
are illustrated
Figure
10. The
the
blastofthe
hole
washole
about
times
smaller
thanwas
with
the
original
LLB design,
but the
around
blast
was2.25
about
2.25
times
smaller
than
with
the
LLB
design,
but
number
elements
of the
modified
LLB
method
6,801,550.
Theoriginal
crushed
zone
around
advance
was
similar,
0.37
mm
compared
to
0.36
mm
with
the
original
LLB
design.
Altthe
advance
was
similar,
0.37
mm
compared
to
0.36
mm
with
the
original
LLB
design.
the blast hole
about 2.25 times smaller than with the original LLB design, but the
hough
the
overall
failure
range
decreased
as
of explosives
was
decreased,
the
Although
thesimilar,
overall
failure
decreased
asamount
the amount
explosives
was
decreased,
advance
was
0.37
mmrange
compared
to the
0.36
mm
with
theoforiginal
LLB
design.
Alttensile
failure
caused
by
the
long
and
large-diameter
uncharged
hole
had
a
significant
the tensile
failurefailure
causedrange
by the
long andas
large-diameter
a significant
hough
the overall
decreased
the amount ofuncharged
explosiveshole
washad
decreased,
the
influence.
Therefore,
blasting,
the
LLB
with
a areduced
influence.
Therefore,
sequential
blasting,
themodified
modified
LLBmethod
method
with
reduced
tensile
failure
caused in
byinsequential
the
long and
large-diameter
uncharged
hole had
a significant
amount
explosives
ininthe
can
totohave
similar
blasting
asas
amountofofTherefore,
explosivesin
thecut
cutarea
area
canbebeexpected
expected
have
similar
blasting
efficiency
influence.
sequential
blasting,
the modified
LLB
method
withefficiency
a reduced
the
LLB
theoriginal
original
LLBmethod.
method.
amount
of explosives
in the cut area can be expected to have similar blasting efficiency as
the original LLB method.
(a)
(b)
(a) of failure zones depending on the amount (b)
Figure 10. Comparison
of explosives in the LLB methods.
(a) Total explosives length of 300 mm (original LLB method); (b) total explosives length of 210 mm
(modified LLB method).
Figure 11 shows the numerical analysis results of blasting with the burn-cut method
and the modified LLB method with a reduced amount of explosives. As mentioned above,
although the total influence range near the explosives was decreased due to the reduction
in the amount of explosives in the modified LLB method, its advance was four times longer
(a) Total explosives length of 300 mm (original LLB method); (b) total explosives length of 210 mm
(modified LLB method).
Figure 11 shows the numerical analysis results of blasting with the burn-cut method
and the modified LLB method with a reduced amount of explosives. As mentioned above,
12 of 15
although the total influence range near the explosives was decreased due to the reduction
in the amount of explosives in the modified LLB method, its advance was four times
longer than that of the burn-cut method, as shown in Figure 11. Even in terms of blasting
design,
it isof
estimated
that it
is desirable
to reduce
the amount
compared
to
than that
the burn-cut
method,
as shown
in Figure
11. Evenofinexplosives
terms of blasting
design,
the
existing
design,
due
to
the
large-diameter
uncharged
hole
formed
before
blasting.
it is estimated that it is desirable to reduce the amount of explosives compared to the
Thus,
the design,
modified
method
showed pronounced
advantages
in reducing
existing
dueLLB
to the
large-diameter
uncharged hole
formed before
blasting.blast-inThus, the
duced
vibration
by reducing
the pronounced
amount of explosives
in in
thereducing
cut area,blast-induced
as well as increasing
modified
LLB method
showed
advantages
vibration
the
byadvance.
reducing the amount of explosives in the cut area, as well as increasing the advance.
Sustainability 2022, 14, 13347
(a)
(b)
Figure
11.11.
Comparison
ofofrange
modified LLB
LLBmethods.
methods.(a)
(a)Burn-cut
BurnFigure
Comparison
rangeofoffailure
failureininthe
theburn-cut
burn-cut and
and the
the modified
cutmethod;
method;(b)
(b)design
designofofreduced
reduced
explosives
in
the
modified
LLB
method.
explosives in the modified LLB method.
4.4.
Comparison
Each
Analysis
Model
using
Eroding
Elements
4.4.
Comparison
of of
Each
Analysis
Model
using
Eroding
Elements
Figure
presents
the
total
deleted
eroding
volume
detonation
the
original
LLB
Figure
1212
presents
the
total
deleted
eroding
volume
byby
detonation
inin
the
original
LLB
method,
the
burn-cut
method,
and
the
modified
LLB
method
with
reduced
explosives.
method, the burn-cut method, and the modified LLB method with reduced explosives.
Thetotal
totalnumber
number
erodingelements
elements
can
used
compare
the
extent
thefailure
failure
The
ofoferoding
can
bebe
used
totocompare
the
extent
ofof
the
zones
according
to
each
method,
and
the
number
of
deleted
elements
for
each
method
was
zones according to each method, and the number of deleted elements for each method
101,953,
86,622,
andand
81,753,
respectively.
TheThe
original
LLBLLB
method
showed
the widest
range
was
101,953,
86,622,
81,753,
respectively.
original
method
showed
the widest
of theofcrushing
zone, which
about
1.18
times1.18
larger
thanlarger
in the burn-cut
method.
In the
range
the crushing
zone, was
which
was
about
times
than in the
burn-cut
modified
method with
reduced
theexplosives,
total number
deleted
eroding
method.
In LLB
the modified
LLB 30%
method
with explosives,
30% reduced
theof
total
number
of
elements
decreased
by
about
1.25
times
compared
to
the
original
LLB,
and
was
about
deleted eroding elements decreased by about 1.25 times compared to the original LLB,
1.06was
times
lower
thelower
burn-cut
The modified
LLB modified
method showed
similar
and
about
1.06than
times
thanmethod.
the burn-cut
method. The
LLB method
failure
patterns
compared
to
the
original
LLB
method,
but
the
number
of
deleted
eroding
showed similar failure patterns compared to the original LLB method, but the number of
elements around the blast holes decreased as the amount of explosives decreased. The
Sustainability 2022, 14, x FOR PEERdeleted
REVIEW eroding elements around the blast holes decreased as the amount of explosives
13 of 15
main effect
of main
the burn-cut
was the
reduction
thereduction
failure zone
between
blast
decreased.
The
effect ofmethod
the burn-cut
method
wasinthe
in the
failurethe
zone
holes
and
the
tunnel
face,
rather
than
contributing
to
increasing
the
advance.
between the blast holes and the tunnel face, rather than contributing to increasing the ad-
vance.
(a)
(b)
(c)
Figure
forfor
each
analysis
model.
(a) Original
LLBLLB
method;
(b)
Figure 12.
12. Comparison
Comparisonofofdeleted
deletedelements
elements
each
analysis
model.
(a) Original
method;
burn-cut method; (c) modified LLB method with reduced explosives.
(b) burn-cut method; (c) modified LLB method with reduced explosives.
In summary, the reduction in explosives in the modified LLB method reduced the
overall size of the failure zones, but had a substantial advantage in that it contributed
significantly to increasing the advance rate. Therefore, the LLB method clearly had better
crushing efficiency than the traditional burn-cut method and, even when the amount of
explosives in the cut area was reduced, this method had similar blasting efficiency compared to the traditional burn-cut method. Therefore, the modified LLB method can be
Sustainability 2022, 14, 13347
13 of 15
In summary, the reduction in explosives in the modified LLB method reduced the
overall size of the failure zones, but had a substantial advantage in that it contributed
significantly to increasing the advance rate. Therefore, the LLB method clearly had better
crushing efficiency than the traditional burn-cut method and, even when the amount
of explosives in the cut area was reduced, this method had similar blasting efficiency
compared to the traditional burn-cut method. Therefore, the modified LLB method can be
considered an excellent alternative blasting method in that it not only reduces blast-induced
vibration by reducing the amount of explosives needed in the cut area, but also increases the
advance rate. However, since this is the result of the analysis using computer simulation,
numerous field tests should be carried out for validation of the results.
5. Conclusions
In this study, numerical analysis using LS-DYNA software was performed to investigate the blast mechanism and efficiency by applying an advanced LLB cut blasting method
that can effectively reduce blast-induced vibration. The Johnson–Holmquist (JH-2) constitutive model, which was developed for brittle materials subjected to dynamic conditions,
was used to model the tunnel rock material, and the explosives and stemming materials
were modeled using relevant emulsion and soil properties, respectively. The original LLB
method was compared to the traditional burn-cut method as well as the modified LLB
method, which shortened the depth of its large-diameter uncharged hole to match that of
the blast holes and reduced the amount of explosives by 30%.
The numerical analysis confirmed that the new LLB method not only contributed to
increasing the rock failure range in the cut area by forming an approximately 3.75 times
larger uncharged hole than in the conventional burn-cut method, but also increased the advance rate by about 3.36 times by generating more tensile failure in the excavation direction.
The modified LLB method used 30% less explosives and produced about 1.25 times fewer
deleted eroding elements than the original LLB method (and 1.06 times fewer than the
burn-cut method). In the traditional burn-cut method, which uses relatively small-diameter
uncharged holes, explosives are used in crushing rocks more finely instead of contributing
to increasing the advance rate. In contrast, the modified LLB method, with its long and
large-diameter uncharged hole, generated more tensile failure in the excavation direction,
so its advance rate increased four-fold compared to the burn-cut method. The long and
large-diameter uncharged hole, which was already formed before blasting, reduces the
initial confining stress of rock mass and can efficiently utilize the free face effect, thereby
reducing the amount of explosives. Therefore, the modified LLB method, with its reduced
amount of explosives, is significantly beneficial as an alternative method for reducing
blast-induced vibration and increasing blasting efficiency, particularly in terms of advance
per round, compared to the traditional burn-cut method. If a multi-LLB method that uses
several long and large-diameter uncharged holes instead of one hole is considered, the
blasting efficiency would increase significantly. Therefore, based on the numerical analysis,
this method can be considered as an economical and eco-friendly blasting method for
reducing the overall construction period and addressing environmental concerns.
Author Contributions: Conceptualization, S.S.L.; Data curation, M.-S.K.; Formal analysis, M.-S.K.;
Funding acquisition, S.S.L.; Investigation, S.S.L.; Methodology, S.S.L.; Project administration, S.S.L.;
Resources, M.-K.S.; Software, M.-S.K.; Supervision, S.S.L.; Validation, C.-Y.K.; Visualization, M.-S.K.;
Roles/Writing—original draft, M.-S.K.; Writing—review and editing, S.S.L. All authors have read
and agreed to the published version of the manuscript.
Funding: This work was supported by a Korea Agency for Infrastructure Technology Advancement
(KAIA) grant funded by the Ministry of Land, Infrastructure, and Transport (grant 22UUTI-C157786-03).
Institutional Review Board Statement: Not applicable.
Informed Consent Statement: Not applicable.
Sustainability 2022, 14, 13347
14 of 15
Data Availability Statement: Some or all data that support the findings of this study are available
from the corresponding author upon reasonable request.
Conflicts of Interest: The authors declare that they have no known competing financial interest or
personal relationship that could have appeared to influenced the work reported in this paper.
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