blast-resistant analysis for a tunnel passing beneath taipei shongsan airport–a parametric study

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: [email protected]

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


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


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.


(=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).


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.


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


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




Damping ratio % 0 3.5

Concrete Unit weight kN/m3 24 24

Cohesion Mpa 10.4 12.5




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



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


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


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.


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.


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.


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)


(c) lining bending moment to dynamic soil stiffness.


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)


(c) lining bending moment to damping ratio.


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


iniL xa

M)

Nk( tsurhT gn

0

50

100

150

0 10 20 30 40 50


nidneB

g)

mNk( tne

mom

(a)

(b)

(c)


(c) lining bending moment to intensity of blast loading.


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


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)


(c) lining bending moment to crater radius.


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.


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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blast-resistant analysis for a tunnel passing beneath taipei shongsan airport–a parametric study

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