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Blast-resistant analysis for a tunnel passing beneath
Taipei Shongsan airport–a parametric study
M. W. GUI1,w and M. C. CHIEN2
1National Taipei University of Technology, No 1, Sec 3, Chung-Hsiao E Road, Taipei 106,Taiwan2Dept of Rapid Transit Systems, Taipei, Taiwan
(Received 10 February 2004; revised 18 October 2004; accepted 28 October 2004)
Abstract. This paper covers the blast-resistant analysis for a tunnel passing beneath TaipeiShongsan airport. It briefly discusses the overall analysis process to obtain the maximumlining thrust caused by a bomb explosion for use in the structural lining design. Because there
have not been any established common standards or practices governing the design of such astructure, a series of parametric studies have been carried out in order to evaluate the sig-nificance and sensitivity of several parameters on the lining thrust. The parameters evaluated
are: intensity of blast loading, size of crater, dynamic undrained shear strength, dynamicYoung’s modulus, and soil-damping ratio. It was concluded that a designer should adoptdynamic soil parameters, obtained from good ground investigation and soil testing, asfavorable dynamic soil properties can result in a more economical analysis. For parameters
(e.g. bomb type) that are beyond the control of the designer, an additional protective layerover the tunnel structure may be considered in order to minimize the impact of the explosion,instead of designing a more costly rigid structure.
Key words. blast-resistant, bomb explosion, conventional weapon, lining, numerical analysis,tunnel.
1. Introduction
Analysis of blast-resistant of structures has been an active topic of concern as a result
of a series of terrorist events worldwide. Events such as the truck bomb explosion in
the World Trade Center in New York City in February 1993, the bombing of the
Alfred P. Murrah Federal Building in Oklahoma City in April 1995, the bomb
explosions at the financial centers of London and Buenos Aires in July 1994 and
more recently at hotels in Jakarta and Turkey have caused considerable concern as
how to protect the integrity of structures and their occupants from the threat of
bombings and other direct physical attacks.
Blast-resistant analysis is also important in the design of structures to minimize the
impact of missile attack. For instance, because of its strategic location, Taiwan has
been subjected to varying degrees of missile threat from its neighboring countries.
wCorresponding author: Assoc. Prof., Civil Eng. Dept, National Taipei University of Technology, No
1, Sec 3, Chung-Hsiao E Road, Taipei 106, Taiwan. e-mail: mwgui@yahoo.com
Geotechnical and Geological Engineering (2006) 24: 227–248 � Springer 2006DOI 10.1007/s10706-004-5723-x
One of its strategies in response to the military modernization and missile buildup of
its neighboring countries is to design its civil and military targets to minimize the
impact of missile attacks (Swaine and Runyon, 2002). This is considered a relatively
cost-effective and efficient means of defending against possible attacks and should
allow Taiwan to preserve its military forces and its ability to resist follow-on attacks
(Swaine and Runyon, 2002).
There have not been many established standards or practices governing the design
of civilian blast-resistant structures. This is mostly due to the security classification
of military technology, such as the design methodologies and construction tech-
niques developed for the protection of military facilities, which has denied the
civilian sector the information needed in applying such technology (National Re-
search Council, 1995). Besides, experimental studies related to any particular com-
bination of structure, soil and loading are scarce as full-scale experiments are
expensive and model tests seem to be unrealistic, especially in replicating the self-
weight of overburden soil.
Numerical simulation is relatively affordable and is becoming more and more
indispensable in engineering analysis and design. The use of it is essential in the
understanding of the complex response seen in some experiments prior to the
development of any design guidelines. For example, the response of a partially
embedded structure subjected to combined air-blast and ground shock had been
performed (Isenberg et al., 1973). However, the study did not take into account the
failure behavior of the soil around the blast crater, as it used an idealized elastic soil
model. A more sophisticated structural response analysis of a buried reinforced
concrete arch has been performed by Stevens and Krauthammer (1991 a, b). Fur-
thermore, the concrete was simulated using a nonlocal continuum damage/plasticity
model, the steel using an elastic/strain hardening plasticity model, and the soil using
a straight Drucker-Prager yield surface model. However, the result was only eval-
uated from the viewpoint of concrete and steel reinforcement, no assessment being
made on the effects of soil properties on such structure.
Clearly, it is necessary to understand the effects and sensitivity of soil character-
istics on the buried structure during blasting. A parametric study for a tunnel passing
beneath Taipei Shongsan airport is presented here. During a war, the airport runway
would be an obvious military target while an underground tunnel passing beneath it
might serve as a bunker. Therefore such a tunnel must be designed to minimize the
impact of missile attack. Stresses and displacements induced by blast loading at a
distance are required for structural design. They must be derived from numerical
analysis because of the complex soil/tunnel interaction that cannot be accounted for
through simple analytical expressions.
The main objective of this paper is to stimulate interest from researchers and
practising engineers so that the behavior of underground tunnels under non-nuclear
explosions can be understood further. With that purpose, numerical simulation was
carried out to examine the significance and sensitivity of the dynamic soil stiffness,
undrained shear strength, soil damping ratio, intensity of blast loading, and crater
M. W. GUI AND M. C. CHIEN228
size on the tunnel. Parametric studies were carried out as it is impossible to evaluate
their significance without repeated parametric calculations and to determine the
sensitivity of the tunnel response to these parameters.
2. Ground Conditions at Shongsan Airport Tunnel
The Taipei Rapid Transit (TRT) system consists of four main lines: (1) Danshui to
Xindian; (2) Muzha Zoo to Zhongsan Junior High School; (3) Kunyang to Xinbu;
and (4) Nanshijiao to Beitou. Due to the increase in passenger volume, extensions of
the Kunyang to Xinbu Line from Xinbu station to Tucheng, and the Muzha Zoo to
Zhongsan Junior High School Line from Zhongsan Junior High School to Neihu
have been planned. The extensions involve a total of 68 tunnel drives, with a total
length of 48 km (Hwang et al., 1996). Contract CB431 of the Zhongsan Junior High
School to Neihu extension line required a tunnel to pass beneath Taipei Shongsan
airport (Figure 1). The depth of the 6 m diameter tunnel varies between 21.0 and
25.3 m beneath the Shongsan airport. The center of the studied section of the tunnel
is approximately 24.3 m deep with a 21 m thick overburden.
Taipei city is located in a basin called the Taipei basin, which is surrounded by
Datun Volcano on the north, Linkou Terrace on the west, and foothills on the east
and the south. The basin was formed by a series of sedimentation events several
hundred years ago. The formation of the Taipei basin consist of 1–6 m thick top soil
or fill material, followed by a 40–60 m thick alluvial deposit (the Shongsan forma-
tion), which lies above the Jingmei formation. The Shongsan formation comprises
six alternating silty sand and silty clay layers with varying thicknesses, while the
Jingmei formation is mainly composed of dense sands and gravels with diameter of
up to 30 cm (Chow and Ou, 1999). The sub-formations of the Shongsan formation
Figure 1. Cross sectional view of the soil stratification at Shongsan airport tunnel.
BLAST-RESISTANT ANALYSIS FOR A TUNNEL 229
and their average SPT ‘N’ values are given in Table 1. For a detailed description of
the characteristics of the Taipei basin, readers are referred to Woo and Moh (1990).
In total, seven boreholes have been drilled at various location at the Shongsan
airport. The ground water table was found to vary between 1.7 and 3.5 m below the
ground level. The average properties of the subsoils obtained from conventional soil
laboratory testing are given in Table 2.
3. Weapon Characteristics
A large body of theoretical and empirical knowledge regarding explosions and their
effects has been developed from a series of research and tests sponsored by U.S.
government agencies. As a result, a number of manuals on protective structures such
as those by U.S. Dept of Army (1986, 1990) and were issued in order to address the
threats of both nuclear and conventional weapons. These manuals provide infor-
mation for the estimation of weapon explosion loadings, the attenuation of pressure
effects in the air and ground, the proportioning of structural elements, etc.
Due to the frequency of their development and modification, there is an enormous
variety of weapon systems available. In this study, the high-explosive-general-pur-
pose bomb (GP 2000), which is used for general destruction by blast and fragmen-
tation was assumed. The bomb penetrates into the earth and causes considerable
Table 1. Description of typical Taipei basin soil formations
Layers Sub-layers Description
Thickness
(m)
SPT
‘‘N’’-value
Top soil – 1–6 –
VI Yellowish brown or gray silty clay (CL-ML) 0–6 4
V Gray silty fine sand (SM) 0–20 4
Shongsan IV Gray silty clay (CL-ML) 5–30 5
formation III Gray medium dense sand interstratified
with silt or silty clay seams (SM)
0–15 13
II Gray silty clay (CL, ML) 2–15 14
I Medium dense to dense silty sand (SM)
or sand gravel
0–5 20
Jingmei formation – 0–140 –
Table 2. Average soils parameters obtained from Shongsan airport site
Depth (m) Soil type SPT ‘N’ value
Unit Weight
(kN/m3)
Cohesion
(kPa)
Angle of
friction (�)
Young’s
modulus
(MPa)
0–2.5 Fill 2 17.0 0 33 15
2.5–30 Low plasticity silty/sandy clay 5 18.3 30 31 28
30–48 Low plasticity sandy clay 13 20.1 50 32 32
48–50 SM silty sand 40 21.1 0 35 47
M. W. GUI AND M. C. CHIEN230
damage to nearby buried structures by a confined explosion. The general charac-
teristics of GP 2000 bomb are (U.S. Dept of Army, 1986): total weight = 2090 lbs
(950 kg); charge-weight = 1100 lb (500 kg); body diameter =23 inch (585 mm);
slenderness ratio = 3.0; and striking velocity = 1100 ft/s (335 m/sec).
3.1. BOMB PENETRATION DEPTH
Research has shown that stresses from a buried burst are usually greater in mag-
nitude and much longer in duration than the corresponding burst in the air (U.S.
Dept of Army, 1986). It is therefore necessary to first derive the penetration and
explosion depth of a bomb prior to the determination of the blast loading. The
penetration of the GP 2000 bomb into the earth varies with the type of soil
encountered and it normally follows a J-shaped path, such that the final penetration
depth is less than the penetration path length. It is difficult to accurately calculate the
bomb penetration depth but an estimate may be made using the semi-empirical
formulae (U.S. Dept of Army, 1986):
Db ¼ 3:2W 0:333T ð1Þ
where Db is the bomb penetration depth (ft), and WT the projectile weight
(=2090 lb). The factor 3.2 takes into consideration the type of soil and also the
corresponding energy loss during penetration in the soil. Db of about 12.5 m was
thus derived.
Protective layers of concrete or rock rubble are often provided over a buried
structure with the purpose of limiting bomb penetration, hence reducing the blast
effects on the structure. For the Shongsan airport, in addition to the 0.5 m thick
subgrade, there was a 1.0 m thick concrete runway. Therefore, the resistance pro-
vided by both the subgrade and concrete runway can be accounted for. U.S. Dept of
Army (1986) suggested that at least half of the penetration energy would be dissi-
pated as a result of such penetration. As such, the final penetration depth estimated
here was conservatively assumed to be about 70% of the bomb penetration depth,
which gave a depth of about 8.8 m (Figure 2).
3.2. BLAST LOADING
The blast effect of an explosion is in the form of a shock wave composed of a high-
pressure shock front that expands outward from the center of the detonation, with
pressure intensity decaying with distance (Balsara, 2002). As the wave front impinges
on the tunnel, a portion of the tunnel will be engulfed by the shock pressures. The
magnitude and distribution of the blast load acting on the tunnel then depends on
the tunnel geometry and flexibility, blast pressure-time history, and the dynamic soil
characteristics (Balsara, 2002).
The blast loading may be characterized as a pulse with an exponential-shape time
history that attenuates rapidly in amplitude and broadens as it propagates outward
BLAST-RESISTANT ANALYSIS FOR A TUNNEL 231
from the detonation center, Figure 3. Thus it was also necessary to establish the
variation and decay of the incident pressure with time because the effects on the
tunnel structure depend not only on the peak pressure Po but also on the pressure-
time history of the blast loading. In general, for sandy clay, Po (psi) may be estimated
from the following expression (U.S. Dept of Army, 1986):
Po ¼ 160 � cg
� �� C
144
� �� R
W1=3
� ��nð2Þ
where, c is the unit weight of the soil (=18.3 kN/m3 =116 lb/ft3); C the average
seismic velocity (=1630 m/s =5350 ft/s); R is the distance from the explosion
0
5
10
15
20
25
0 0.005 0.01 0.015 0.02 0.025 0.03
Time (sec)
lB
astp
ress
uer
M(P
a) Po
Figure 3. Blasting pressure-time history curve applied to the crater inner boundary.
8.9 m
12.1 m
Tunnel
Crater
6.0 mwith 0.3 m thick lining
Figure 2. Location of the tunnel studied section in relation to the detonation center.
M. W. GUI AND M. C. CHIEN232
(=12.2 m =40 ft); W the charge weight (=500 kg =1100 lb); n is the attenuation
coefficient which is controlled by the irreversible crushing of the void volume within
a soil matrix by the passage of a stress wave; for sandy clay n ¼ 2:5 (U.S. Dept of
Army, 1986).
The rise time tr taken to reach Po may be estimated from
tr ¼ 0:1ta ¼ 0:1R
Cð3Þ
where ta is the elapsed arrival time from the instant of detonation to the time at
which the shock arrives at a given point of the tunnel. Equation (2) thus gives a Po
value of about 725 psi or 5.0 MPa at the tunnel crown with an elapsed arrival time taof 7.48 msec and rise time tr of 0.748 msec.
From Po, the shock wave decays monotonically to nearly zero over a time period
of about one to three times the value of ta in the fashion of the following equation:
Pt ¼ Poe� t
ta ð4Þ
where Pt is the blast pressure at any given time t. Note that the arrival time ta is
inversely proportional to the seismic velocity, thus an explosion in high-velocity
Figure 4. (a) Finite difference mesh used in the analysis; (b) close-up mesh for and around the lining; and
(c) two layers of transverse reinforcement used in the lining (longitudinal reinforcement not shown).
BLAST-RESISTANT ANALYSIS FOR A TUNNEL 233
media such as saturated clay will produce very short, high-frequency pulses with high
accelerations and low displacements. In contrast, detonations in dry, loose materials
will produce ground motions of much longer duration and lower frequency.
3.3. CRATERING
A crater is normally defined as a hole in the ground formed by an explosion. The true
crater is normally masked by the dirt or debris that falls back into the crater. If the
explosion occurs deep enough to be completely contained below the surface, the true
crater will consist of a cavity called a camouflet (U.S. Dept of Army, 1986).
Factors such as the type and amount of explosive, bomb penetration depth, and
the type of material in which the crater forms, control the final dimension of the
crater. In general, a crater that forms in sandy soil is smaller than those in clay (U.S.
Dept of Army, 1986). There is no formulation to estimate the crater diameter but an
estimate may be made from Figure 5.7 in U.S. Dept of Army (1986). Therefore, one
of the parametric studies carried out below examines the sensitivity of the lining
moment to crater size. The initial estimate of the crater diameter for the type of soil
and charge weight assumed for Shongsan airport is about 4.0 m.
4. Numerical Modelling
Numerical analysis has been found to be suited for analyzing wave propagation in
continuous nonlinear media with large deformations because the complicated
boundary conditions and soil models involved could be reasonably accounted for via
simple equations (Stevens and Krauthammer, 1991a). The finite difference program
used in this study was FLAC2D (Fast Lagrangian Analysis of Continua) that is well
suited for modelling nonlinear systems (Itasca Consulting Group, 1999). The pro-
gram adapts the dynamic equations of motion so as to ensure a stable numerical
scheme when the physical system being modeled is unstable (Itasca Consulting
Group, 1999).
As mentioned earlier, ground shock propagation in earth media is a function of the
dynamic soil properties, type of explosive materials and geometry of the explosion.
Here, the significance and sensitivity of dynamic soil properties (undrained shear
strength, soil stiffness, damping ratio), soil/tunnel interface resistance, intensity of
blast loading, and crater size are studied. The major simplification made in this
analysis was that the propagation of the three-dimensional blast wave was repre-
sented by a two-dimensional (2D) blast wave. The 2D result seemed conservative as
it treated the source of the explosion as a cylindrical geometry instead of a spherical
one. As a result, the whole tunnel, instead of only a particular section, is subjected to
the 5 MPa blast loading. Further work in 3D modelling is required to examine the
effects of two-way bending and axial loading of the lining.
M. W. GUI AND M. C. CHIEN234
4.1. CONSTITUTIVE MODELS AND MATERIAL PARAMETERS
4.1.1. Soil
As the soil surrounding the crater would inevitably fail under such intense loading,
the Mohr-Coulomb elasto-plastic model with a non-associated flow rule was chosen
to represent the behavior of the soil which will undergo large deformation. Its failure
envelope corresponds to a Mohr Coulomb criterion (shear yield function) with
tension cutoff (tension yield function).
In FLAC, the parameters associated with the Mohr-Coulomb model for an un-
drained analysis are: unit weight c, undrained shear strength Cu, Young’s modulus E,
and Poisson’s ratio. These parameters have been obtained from a series of laboratory
triaxial tests and are tabulated in Table 3. For the damping ratio, an average value of
3.5% has been adopted (Barkan, 2002). Groundwater is modeled simply by
assigning a water table at 2.5 m below the ground level.
4.1.2 Tunnel lining and steel reinforcement
According to Stevens and Krauthammer (1991a), the nonlinear response of concrete
may be created through the combination of micro-crack growth and frictional slip.
Micro-cracks that induced strength and stiffness degradation could be modeled using
the theory of continuum damage mechanics; and the plastic flow and pre-peak
nonlinearity of concrete created by frictional slip could be modeled by the theory of
plasticity. However, this was not being considered here, as micro-crack behavior of
reinforced concrete was beyond the scope of this paper. For simplicity, the general
behavior of the concrete was modeled in FLAC using the strain hardening/softening
model with a non-associated flow rule. Its associated properties are tabulated in
Table 3. Note that the dynamic strengths of the concrete have been taken to be 1.2
times the static strengths (U.S. Dept of Army, 1986).
To account for the possible slip between the soil and the liner after a limiting stress
condition had been reached, interface elements that were characterized by Coulomb
sliding were inserted between the liner and the soil (Itasca Consulting Group, 1999).
The interface element adopted here has the properties of friction, interface resistance,
tensile strength, and normal Kn and shear Ks stiffnesses. Kn and Ks may be derived
from Timoshenko and Goodier (2002):
Kn ¼4Gro1� m
and Ks ¼32ð1� mÞGr3o
7� 8mð5Þ
where ro is the tunnel radius; G the shear stiffness of the soil; and m the Poisson’s
ratio. The corresponding interface parameters are shown in Table 3. As soil is poor
in sustaining tension, only 1 kPa of tensile strength is used here.
For reinforced concrete lining without shear reinforcement, the transverse shear is
resisted by the plain concrete, the dowel effects of the reinforcement, and the
aggregate interlock across any large cracks (Stevens and Krauthammer, 1991a). It
BLAST-RESISTANT ANALYSIS FOR A TUNNEL 235
may then be assumed that the contribution of the reinforcement to the shear resis-
tance is small and the steel response may be taken as uniaxial. Thus, the one-
dimensional structural cable element in FLAC that was capable in sustaining uni-
axial tension was used to model the steel reinforcement of the tunnel lining. The
disadvantage of using cable element is that the lining bending moment profile cannot
be calculated automatically, but it can be used to simulate the tensile and com-
pressive yield strength of the reinforcement (Itasca Consulting Group, 1999).
Rate effects were not included because experimental data from strain rate tests on
steel showed that strain rates up to 10% per second had no apparent effect on the
Table 3. Materials properties adopted in FLAC
Materials Properties Unit Static Dynamic
Fill Unit weight kN/m3 17.0 17.0
Undrained shear strength Kpa 0 45
Friction angle � 33 33
Young’s modulus Mpa 15 15
Poisson ratio – 0.28 0.49
CL-Soil Unit weight kN/m3 18.3 18.3
Undrained shear strength KPa 0 45
Friction angle � 31 0
Young’s modulus Mpa 28 253
Poisson ratio – 0.32 0.49
Damping ratio % 0 3.5
Concrete Unit weight kN/m3 24 24
Cohesion Mpa 10.4 12.5
Friction angle � 37 37
Young’s modulus Mpa 30500 30500
Poisson ratio – 0.20 0.20
Uniaxial compressive strength Mpa 42 50.4
Tensile strength Mpa 0.36 0.43
Yield strain % 0.35 0.35
Cable element(Grade 60 Steel) Unit weight kN/m3 78 78
Young’s modulus Mpa 210000 210000
Poisson ratio – 0.20 0.20
Tensile strength Mpa 420 462
Yield strain % 0.20 0.20
Soil-tunnel interface Friction � 32 32
Interface resistance, f Kpa 22.5 33.75
Normal stiffness, Kn Mpa 187 2000
Shear stiffness, Ks Mpa 1402 12160
Tensile strength KPa 1 1
M. W. GUI AND M. C. CHIEN236
material properties of steels with yield strengths of 340 N/mm2 or more (Soroushian
and Choi, 1987). The general properties of this cable element are shown in Table 3.
4.2. MODELLING SEQUENCE
Figure 4(a) shows the rectangular finite difference mesh created for the analysis;
Figure 4(b) shows the close-up of the mesh near the tunnel and Figure 4(c) shows the
layers of reinforcement in the lining. During the static run to achieve the in-situ stress
state, both the left and right boundaries were fixed in the horizontal direction while
the bottom boundary was restrained from both horizontal and vertical movements.
Quiet boundaries were then added in the subsequent dynamic runs in order to
simulate the far field condition that absorbed shock waves and prevented the waves
from reflecting back in to the model.
After achieving the initial stress state of the ground, the mesh elements at the
tunnels locations were switched to null model to model tunnels excavation, and the
properties of the elements at the tunnel circumference were changed to concrete
properties to model the lining installation process. Structural cable elements and
structural interface elements were used to represent the steel reinforcement in the
lining and the interface between the soil and the concrete lining, respectively. At this
initial stage, the maximum lining thrust was found to be 230 kN. The crater was then
created by nulling the mesh elements and internal pressure applied in the fashion of
Figure 3 to simulate the blast loading. The applied internal pressure has been set to
about 20 MPa so that the peak pressure of 5 MPa, as calculated using Equation (2),
could be obtained at the tunnel crown.
4.3. MODELLING RESULTS
Immediately after the burst at the crater, the surrounding soil redistributes the blast
loading pressure in response to relative displacement of the tunnel, and thrust in the
lining. Consider a flexural segmental lining member of width bð¼ 1:0mÞ and height
hð¼ 0:3mÞ. The relationship between its bending moment and maximum stress ry at
its outer fibers may be related using (Itasca Consulting Group, 1999):
M ¼ rybh2
6ð6Þ
Here, ry is taken to be the maximum lining thrust divided by the lining’s cross
sectional area ðbhÞ.As the critical location of the explosion was directly above the left tunnel, the
maximum displacement was always observed at the crown of this tunnel; in addition,
a symmetrical deformation shape was also observed around both the crater and
tunnel locations (Figure 5). Ground heaving was more obvious than the tunnel
deformation because the overburden above the crater was insufficient to hold the
explosion. In the following, the numerical results obtained were presented in the
BLAST-RESISTANT ANALYSIS FOR A TUNNEL 237
form of effective major principal stress of the soil at tunnel crown, maximum lining
thrust (inclusive of initial and dynamic stages) and its corresponding bending mo-
ment. A typical dynamic time function for soil major principal stress above the
crown, crown displacement, and maximum lining thrust is shown in Figure 6. No
discernable oscillation was observed on these data during the explosion. In partic-
ular, the displacement profile was similar to the displacement profile caused by air
blast loading on ground obtained by Das (1985).
5. Results and Discussion
For better understanding of the problem, the sensitivity of several parameters on the
response of tunnel structure under blast loading have been performed in order to
alert a designer to the input parameters to take into account, and to help optimize
similar design in the future. In particular, the effects of dynamic soil properties
(undrained shear strength, soil stiffness, and soil damping ratio), and weapon
characteristics (blasting pressure, and crater size) have been studied.
5.1. DYNAMIC UNDRAINED SHEAR STRENGTH
There are many methods that can be used to estimate the soil static undrained shear
strengthCuðstaticÞ; for example, using the undrained unconsolidated triaxial test, in-situ
vane shear test, or using various empirical correlations. On the other hand, the value of
dynamic undrained shear strength CuðdynÞ is not normally measured directly, and the
empirical correlation proposed by Das (1993) (with b ¼ 1:5) is normally employed:
CuðdynÞ ¼ bCuðstaticÞ ð7Þ
In view of this, it was necessary to examine the importance and sensitivity of the
lining thrust on CuðdynÞ. This was easily done simply by varying the values of CuðdynÞ in
the numerical analysis. Figure 7(a) shows that the major principal stress of the soil at
tunnel crown increased slightly from 4.61 to 4.93 MPa for 1:5 < b < 15 and then
Figure 5. (a) Displacement field observed around the crater; and (b) magnified displacement field ob-
served around the left tunnel after blasting.
M. W. GUI AND M. C. CHIEN238
remains nearly constant between 4.93 and 5.13 MPa for 15 < b < 150. This was
because the stresses in the soil mainly depended on the applied loading rather than its
own strength property. As a result, the lining thrust and its corresponding bending
moment also attain a similar profile with b (Figure 7(b) and (c)). The lining thrust
increased from 1518 to 1578 kN for 1:5 < b < 15 and then fluctuated between 1578
and 1618 kN for 15 < b < 150; the bending moment remained nearly constant be-
tween 76 and 81 kNm.
5.2. DYNAMIC SOIL STIFFNESS
The downhole velocity-logging test carried out on site revealed that the average
dynamic Young’s modulus, E, was about 253 MPa. However, only two tests were
carried out and it was reported that noise and vibration from within the airport
-2
0
2
4
6
8
0.5 0.52 0.54 0.56 0.58 0.6
Time History (sec)
apicnirProja
MssertSl
)aPM(
-30-25-20-15-10-50
0.5 0.52 0.54 0.56 0.58 0.6
Time History (sec)
orC
siD
nw
pme cal
tne)
mm(
0
500
1000
1500
2000
0.5 0.52 0.54 0.56 0.58 0.6
Time History (sec)
niL
xaM
itsurh
Tgn
)Nk(
(a)
(b)
(c)
Figure 6. Time history function for: (a) major principal stress of soil at tunnel crown; (b) crown dis-
placement; and (c) maximum lining thrust.
BLAST-RESISTANT ANALYSIS FOR A TUNNEL 239
might corrupt the measured values. Thus, this sensitivity analysis was performed to
evaluate its importance and sensitivity on the lining thrust analysis. Figure 8(a)
shows the relation between E and effective major principal stress of the soil at the
tunnel crown location. The major principal stress initially increased with the increase
of E until E � 1520 MPa; this is followed by a nearly stable profile between 1520 and
8100 MPa before it gradually decreased again.
Figure 8(b) shows the relation between E and maximum lining thrust. The thrust
decreased by 17% from 1518 to 1263 kN when E was increased 100% from 253 to
506 MPa. The rate of decrease of the lining thrust reduces when E > 1012 MPa. The
0
2
4
6
8
0 50 100 150Factor β
irProja
Mn
ssertSlapic)aP
M(
0
500
1000
1500
2000
0 50 100 150Factor β
)Nk(tsurh
Tgnini
Lxa
M
0
20
40
60
80
100
0 50 100 150Factor β
oM
gnid neB
)m
Nk(tnem
(a)
(b)
(c)
Figure 7. Sensitivity of (a) major principal stress of soil at tunnel crown; (b) maximum lining thrust; and
(c) lining bending moment to dynamic undrained shear strength CuðdynÞ, where CuðdynÞ ¼ bCuðstaticÞ andthat CuðstaticÞ ¼ 30 kPa.
M. W. GUI AND M. C. CHIEN240
reduction showed that a stiffer soil medium would be more capable in restraining
ground movement and thus lining deformation than a softer soil, therefore the thrust
induced in the lining decreased as E was increased. As the value of bending moment
was directly derived from the value of lining thrust, Figure 8(c) therefore shows a
similar profile as Figure 8(b).
5.3. SOIL DAMPING RATIO
The characteristics of a vibration that undergo a gradual decrease of amplitude with
time are referred to as damping. There are two types of damping: (1) the loss of the
amplitude of waves due to spreading out is defined as geometrical damping; and (2)
0
2
4
6
8
0 5000 10000 15000 20000
Dynamic Young's modulus(MPa)
ssertSlapicnirProja
Mse
)aPM(
0
500
1000
1500
2000
0 5000 10000 15000 20000
Dynamic Young's modulus (MPa)
xaM
gniniL
surhT
)Nk(t
0
20
40
60
80
100
0 5000 10000 15000 20000
Dynamic Young's modulus (MPa)
)m
Nk(tnemo
Mgnidne
B(a)
(b)
(c)
Figure 8. Sensitivity of (a) major principal stress of soil at tunnel crown; (b) maximum lining thrust; and
(c) lining bending moment to dynamic soil stiffness.
BLAST-RESISTANT ANALYSIS FOR A TUNNEL 241
the loss due to absorption in real earth material is called material damping (Das,
1993). The values of the material damping could vary between 1% and 10% (Hardin,
1965; Stevens, 1996). Thus, it was necessary to examine the sensitivity of this effect
on the lining thrust.
Figure 9(a) shows the effective major principal stress of the soil observed at the
tunnel crown. It decreased linearly from 5.18 to 4.11 MPa with the increase of soil
damping ratio from 0.2% to 10%. The relation between the lining thrust and soil
damping ratio is shown in Figure 9(b). The thrust decreased linearly by a total of
13.2% when the damping ratio was increased from 0.2% to 10%. The result was
reasonable as a higher damping value corresponds to more energy absorption in the
soil and therefore exerted less thrust in the lining. Figure 9(c) shows that the bending
moment was also linearly related to the soil-damping ratio.
0
2
4
6
8
0.1% 1.0% 10.0%
Damping (%)
)aPM(
ssertSlapicnirProja
M
0
500
1000
1500
2000
0.1% 10.0%
Damping (%)
niL
xaM
k(tsurhT
gni)
N
0
20
40
60
80
100
0.1% 1.0%
1.0%
10.0%
Damping (%)
mgnidne
Bo
mNk(tne
m)
(a)
(b)
(c)
Figure 9. Sensitivity of (a) major principal stress of soil at tunnel crown; (b) maximum lining thrust; and
(c) lining bending moment to damping ratio.
M. W. GUI AND M. C. CHIEN242
5.4. INTENSITY OF BLAST LOADING
The intensity of blast loading depends mainly on the characteristic of the bomb such
as the charge weight, and the properties of the soil such as the acoustic impedance
and attenuation characteristics. Uncertainty exists in the determination of the values
of the acoustic impedance and attenuation coefficient. To examine its significance
and sensitivity, several values of blasting intensity have been used in the analysis.
Figure 10(a) shows that the relation between the intensity of blast loading with
effective major principal stress of the soil at the tunnel crown is a linear one. A 100%
0
2
4
6
8
10
12
0 10 20 30 40 50
Intensity of blast-loading (MPa)
P rojaM
rssertS lapicni
)aPM(
0
1000
2000
3000
0 10 20 30 40 50
Intensity of blast-loading (MPa)
iniL xa
M)
Nk( tsurhT gn
0
50
100
150
0 10 20 30 40 50
Intensity of blast-loading (MPa)
nidneB
g)
mNk( tne
mom
(a)
(b)
(c)
Figure 10. Sensitivity of (a) major principal stress of soil at tunnel crown; (b) maximum lining thrust; and
(c) lining bending moment to intensity of blast loading.
BLAST-RESISTANT ANALYSIS FOR A TUNNEL 243
increase in the intensity of blast loading leads to almost 100% of an increase in the
major principal stress.
Figure 10(b) shows the relation between the intensity of blast loading and maxi-
mum lining thrust. It is obvious that the thrust increased with the increase of the
intensity of blast loading in the fashion of a power law (this is to force the trend line
passing through the graph origin). If the intensity of the blast loading at the crater
was increased 100% from 20 to 40 MPa, the corresponding lining thrust increased
by nearly 53% from 1518 to 2329 kN. For completeness, Figure 10(c) shows its
corresponding bending moment.
This parameter has a significant effect on the lining thrust. However, this is a
parameter that is highly uncertain and is beyond the control/knowledge of the de-
signer. It is uneconomical to design such a structure to withstand an extremely high
blast loading. Therefore, other measures such as providing a protective layer should
be considered in order to reduce the bomb penetration and hence the impact of
bomb blasting on the lining structure. Having said that, the maximum charge weight
found in the list of high-explosive bombs in U.S. Dept of Army (1996) was only
857 kg (1890 lb), which is equivalent to a 30 MPa pressure applied in this case at the
crater.
5.5. CRATER SIZE
Most conventional bombs were designed in such a way that once they hit the surface
of the ground, they would first penetrate into the ground for a certain depth before
they finally exploded. The true crater would consist of a cavity in which the earth
material remains in place but has been severely disturbed by the force of explosion.
The rupture zone is, in turn, surrounded by a larger region of lesser disturbance. The
main variables that govern the crater dimension are the amount and type of
explosive, depth of burst, and the type of material in which the cratering occurs (U.S.
Dept of Army, 1986). Therefore, there was uncertainty in the determination of the
crater size.
Figure 11(a) shows that the soil effective major principal stress at the crown in-
creased with the increase of crater size. Figure 11(b) shows that the relation between
crater radius and maximum lining thrust is a nonlinear one. A 100% increase in the
crater radius from 2 to 4 m caused the thrust to increase by 43% from 1518 to
2177 kN. This was mainly due to the reduction in the clear distance between the
source of the explosion and the tunnel crown (Figure 2). For a 2 m radius crater, the
clear distance was 10.2 m but for a 4 m crater, this distance reduced accordingly to
8.2 m. Thus, there should be more forces exerted on the lining in the latter case. Its
corresponding bending moment is shown, for completeness, in Figure 11(c).
For structural lining design, provisions in the ACI 318-99 (ACI, 1999) code may be
adopted. The lining is considered as a ‘‘wall’’ for calculation of its capacity. The
capacity for a 0.3 m thick lining with 16 numbers of D22 high yield bars, in the form of
force-moment interaction diagram, is presented in Figure 12. The values of the lining
M. W. GUI AND M. C. CHIEN244
thrust andmoment obtained from the above analyses are also shown in this figure so as
to evaluate the performance of the lining, which is safe for all the above cases.
6. Practical Considerations
The parameters used in a blast-resistant analysis of an underground tunnel may be
divided into two major groups: soil parameters and weapon characteristics. The soil
parameters are determinable or controllable by the designer whereas the weapon
characteristics are most likely undeterminable or uncontrollable by the designer.
0
2
4
6
8
10
0.0 1.0 2.0 3.0 4.0 5.0Crater radius (m)
lapicnirP rojaM
ssertSP
M(a)
0
1000
2000
3000
0.0 1.0 2.0 3.0 4.0 5.0
Crater radius (m)
xaM
gniniL
surhT
)Nk( t
0
50
100
150
0.0 1.0 2.0 3.0 4.0 5.0
Crater radius (m)
nidneB
gmo
m e
)m
Nk( tn(a)
(b)
(c)
Figure 11. Sensitivity of (a) major principal stress of soil at tunnel crown; (b) maximum lining thrust; and
(c) lining bending moment to crater radius.
BLAST-RESISTANT ANALYSIS FOR A TUNNEL 245
For the controllable parameters, it is obvious that the dynamic soil properties
should be obtained and used instead of the static soil properties. The use of static
soil properties would result in a conservative and costly structure. As the values of
soil properties used can under- or over-estimate the lining thrust, these parameters
must be obtained through good quality ground investigation and dynamic labo-
ratory testing performed on undisturbed soil specimens. In particular, the dynamic
Young’s stiffness is the most sensitive soil parameter to the lining thrust derivation.
Therefore, ground improvement may be considered in order to enhance the stiff-
ness of the soil.
For the uncontrollable parameters, it is unwise to assume a very high intensity of
blast-loading for the lining thrust analysis because this would result in a tunnel
structure that can not fulfill its economic purpose. Instead of designing a rigid
tunnel, the designer may consider laying a protective layer, such as an concrete apron
at the ground surface directly over the tunnel. This would help to minimize the
penetration of the bomb thus reduce its impact on the tunnel structure.
7. Conclusion
Analysis of blast-resistant of structures has been an active topic of concern as a result
of a series of terrorist events worldwide. However, due to the classification of mili-
tary technology there have not been many established standards or practices gov-
erning the design of civilian blast-resistant structures. Because full-scale experiments
are expensive and model tests are unrealistic, numerical simulation becomes essential
in the understanding of the complex response of underground structure subjected to
a buried blast.
A blast-resistant analysis for an underground tunnel passing beneath Taipei
Shongsan airport has been performed. A series of parametric studies has been
-500
-250
0
250
500
-2500 0 2500 5000 7500 10000
0.8 x Force (kN)
.0)
mNk( tne
moM x 8
Crater size Blast Intensity E_dyn Damping Ratio Cu_dyn
Figure 12. Force–moment interaction diagram for a 0.3 m thick lining with 16 numbers of D22 bars.
M. W. GUI AND M. C. CHIEN246
carried out in order to study the significance and sensitivity of certain soil parameters
and weapon characteristics on the lining response. Dynamic Young’s modulus of soil
was found to be more sensitive than soil damping ratio and undrained shear strength
in controlling the magnitude of the lining thrust. The effects of weapon character-
istics (intensity of blast loading and crater size) were found to be even more sensitive
than the soil parameters in the lining thrust analysis but they are most likely beyond
the control of the designer. It is therefore suggested that a protective layer, which can
absorb most of the bomb penetration energy, be considered instead of designing a
very rigid and costly structure to resist extremely high blast loading.
Acknowledgements
This work was partial supported (D922608) by the Dept. of Technology and
Vocational Education, Ministry of Education, ROC. The writers would like to thank
Dr Steve Huang of NTUT, and Dr Robert Wang of Integrate International Engrng.
Inc. for their technical support in the above study. The second writer acknowledged
the suggestions given by China Engrng. Consultants Inc. and Sinotech Engrng.
Consultants Ltd. in performing the numerical work.
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