Physical Modeling of Seismic Responses of underground Structures.pdf

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The 12th

International Conference of International Association for Computer Methods and Advances in Geomechanics (IACMAG)1-6 October, 2008Goa, India

Physical Modeling of Seismic Responses of underground Structures

O. Kusakabe, J .Takemura, A.Takahashi, J . Izawa and S.ShibayamaDept. of Civil and Environmental Engineering, Tokyo Institute of Technology, Tokyo, Japan

Keywords: seismic d isplacement method, centri fuge modeling, active type shear box, shake table

ABSTRACT: In the framework of performance based design codes, numerical analysis and physical modellingare equally recommended to adopt for the verification of performance of designed structures. To establish thecommunication between numerical and physical modelling communities are of vital importance for verificationof performance of geo-structures. This paper introduces the recent development of experimental seismic

displacement method in a centrifuge and some applications to underground structures.

1 Introduction

It is widely accepted from past experiences that underground structures are generally stable, when the groundis stable because of confining effects from the surrounding ground. Underground structures are considered tofollow the movement of the surrounding ground, since the effect of inertia force is relatively small, and also theoscillation of the underground structures rapidly ceases due to radial damping. Underground structures are,therefore, considered to have higher seismic stability (Kawashima, 2000).Past experiences suggest, however, the following cases where possible damage might occur as are illustratedin Figure 1.(1) Changes in ground conditions: Amplitude of seismic horizontal displacement is larger for thicker and softerlayer. Consequently, when long buried structures run through the ground where thickness of soft layer suddenly

changes, or run through the different ground conditions, such as running through fill (or reclamation) andoriginal ground, strain concentration in the longitudinal direction occurs at the location near the change inthickness of soft layer, or at the interface between the different ground conditions (Iai, 2004). Most commondamage observed in the past is the failure of joints of small diameter buried pipes installed in these groundconditions. (2) Changes in structure: The seismic response of underground structure varies with the type of structure and stiffness of structure. Thus connection parts of different structures, such as the connectionbetween vertical shaft and tunnel, and branches of tunnel, are subjected to strain concentration (Kitamura et al.1996). (3) Liquefiable layer: Loose saturated sandy soil may liquefy during earthquake. When liquefactionoccurs, uplift pressure increases at the base of the underground structure and shear resistance decreasesalong and above the underground structure, resulting in uplifting the underground structure. When (a) theliquefied layer is overlying a sloping layer or (b) a gently sloping ground liquefies or (c) a liquefied ground isretained by a quay wall that is vulnerable to an earthquake, lateral spreading occurs (Takahashi et al., 2005).

The underground structure is then subjected to horizontal displacement. Common observed damage during thepast earthquakes are uplift of manholes of buried pipes and damage of joints due to vertical and horizontal

displacement (Koseki et al. 2002). (4) Shallow depth: Underground structures at the shallow depth in the softlayer are subjected to shear deformation during seismic events. During 1995 Hyogoken-Nanbu Earthquake,Daikai station, one of subway stations in Kobe, experienced the collapse of centre pillars of RC box-typestructure. It is considered that the structure was subjected to larger shear deformation during the earthquake,causing the overstress at the connection between upper and lower slabs and some centre pillars, leading to re-distribution of stress in the structure and to progressive failure of other pillars (Iida et al., 1996). The damage toportal section and to linings near the portal in the mountain tunnel was also observed due to the ground sheardeformation (Asakura et al., 1996). Typically the cracks appear at the shoulder of the portal. (5) Close proximityof fault zones or crossing fault zones (Yashiro et al., 2007): Damage of tunnels occurs when an earthquakefault crosses a tunnel. In the 1978 Izu-Oshima-Kinaki Earthquake, the Inatori Tunnel showed severe damage,such as a collapse of the tunnel lining and longitudinal displacement of the track. According to the surveyresults, the relative displacement of the fault was 700mm and 200mm in horizontal and vertical respectively.Performance-based design framework has been introduced in geotechnical design. Although calculationmethods are, in principle, to use for routine design practice, physical modelling and numerical analysis are

equally recommended to adopt for the verification of performance of designed structures. In particular, physicalmodelling is highly recommended to adopt for cases where the level of uncertainties is high (J GS 4001-2004,2006). In the physical modelling, new and unexpected phenomena are often discovered, whereas numerical

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simulation provides the results totally governed by the model used. To bridge between the numerical andphysical modelling and to establish the communication between numerical and physical modelling communitiesare of vital importance for verification of performance of geo-structures.

This paper describes briefly the principle of seismic displacement method used in the structural analysis forunderground structures and then introduces the recent development of experimental seismic displacementmethod in a centrifuge, followed by the verification of the experimental seismic displacement method by

comparing the structural responses between the observations in dynamic centrifuge tests and thecorresponding static centrifuge tests. Some applications of the experimental seismic displacement method tounderground structured are also presented.

2 Evaluation of seismic performance of underground structure in the transverse direction

Evaluation of seismic performance of underground structure in the transverse direction is becomingincreasingly important, since in recent years many tunnels with a large cross-sectional areas or a complexcross-sectional profile have been constructed at relatively shallow depth in urban area and they need to bedesigned with consideration of large earthquakes. Seismic displacement method has been developed fordynamic soil-structure interaction problems (Kawashima, 2000).Deformation of an underground structure may be represented as shown in Figure 2. Defining interface forcesacting on the structure from the ground as {-FI}, the equation of motion of the ground and the structure can be

written as

0 0

0

S S SS SI S

I I IS II I I

M u K K u

M u K K u F

%%

%%(1)

where, I : nodes of the interface between the structure and the groundS : nodes at the rest of the ground and the structure{ul} : displacements at the interface between the structure and the ground (nodes I){us} : displacements at the rest of the ground and the structure (nodes S)[MI] : mass matrices of I nodes[MS] : mass matrices of S nodes[KSS], [KSI], [KIS], [KII]: partial stiffness matrices for SS, SI, IS and II nodes, respectively.

If one assumes that the displacements at the interface are obtained by the free field displacements and thedisplacements induced by the interface forces {Fl}, {uI}can be written as

1 2 I I I u u u (2)

where, {uI1}and {uI2}indicates the displacement due to earthquake motion and the interface force {Fl}respectively. Since the interface forces {Fl}are given as

Portal

Slope failure

Rock fall FaultFractured zone

Large shear deformation

Crack

Possible damage due to liquefaction Possible damage in a mountain tunnel

UpliftLateral spreading

Liquefiable layer

Figure 1 Illustrations of possible damage of underground structures during earthquakes

Strain concentration

Stiff layer

Soft layer

Possible damage due to change in ground condition Possible failure due to change in structure type

BranchCurved zone

Connection

Vertical shaft

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2 I I F k u (3)

in which [k] = ground impedance that characterizes soil-structure interaction. By substituting Eq. (2) into Eq. (3),

one obtains 1 I I I

F k u k u (4)

Substituting Eq. (4), Eq. (1) becomes,

1

00

0

S S SS SI S

I I I IS II I

M u K K u

k u M u K k K u

%%

%%(5)

Rewriting Eq. (5), one obtains

1

0 0

0

SS SI S S S

I IS II I I I

K K u M u

k uK k K u M u

%%

%%(6)

This is the basic equation used in the Seismic Displacement Method. The first and second terms in the right-hand side represent the forces induced by the ground displacement (shear force at the interface, dynamic earthpressure and inertia force). They act to the underground structure elastically supported by the soil springs. Thisequation indicates that the dynamic soil-structure problems can be replaced by the equivalent static problemsby means of the ground impedance that characterizes soil-structure interaction.

3 Experimental seismic disp lacement method

3.1 Development of active type shear box

3.1.1 Preliminary considerationsAn active type shear box in a geotechnical centrifuge has been initially developed for investigating thebehaviour of a pile subjected to a large soil movement (Takahashi et al., 2001). The shear box was designedfocusing on deformation of a pile due to lateral movement of soil during earthquake under pseudo-staticconditions, neglecting inertial effects of soil and pile. As a preliminary consideration, 2D FEM analyses werecarried out to examine the effect of the geometry of the shear box on the deformation and stress conditions of the soil in it, varying the aspect ratios ( W/H: W: width of the shear box, H: height of the shear box). In theanalyses, the soil was modelled as elastic perfectly plastic employing the extended von Mises yield criterionwith non-associated flow rule. From the analyses, we concluded that the aspect ratio of 2 - 3 is the best to usefor the tests with dense sand, although it was expected that the narrower box is better for the test with loosesand. Another issue was the flexural rigidity of plate springs to transmit the forces applied by actuators. FEManalysis was also conducted to examine possible maximum displacements of the laminae within the elasticlimit of the plate spring. Considering the fact that the tests will be done under 50G to 100G and 20 mm indisplacement is large enough in terms of displacement of pile, higher rigidity of the plate spring seems to be abetter condition. Based on the above preliminary considerations, we decided to have the specifications for theshear box as is shown in Table1.

3.1.2 System description The active type shear box was designed to fit the 0.9m by 0.9m swing platform of the Mark 3 centrifuge at Tokyo Institute of Technology(Takemura et al. 1999) to be operational under 100 G. Schematic diagram andphotograph are shown in Figure 3 and Photo 1 respectively. The shear box can be disassembled into two parts:

(a) Soil-structure system and interfaceforces action on the boundary

(b) Scattered response (c) Response due to interface forces

Figure 2 Idealization of an underground structure by two dimensional Finite Element Models

FI uI2 k {FI} {uI1}

Underground structure

Excavated ground Excavated ground

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the laminar box and actuators. The laminar box was made of duralumin with inner size of 450 mm in width, 200mm in breadth and 325 mm in height. The box consists of thirteen-stacked 24mm thick alumite coatedduralumin laminae. The outer size of the lamina is W512xB262xH24mm and the inner sizes areW452xB202xH24mm. The laminae are supported by roller bearings, which are mounted in grooves on eachlamina. To prevent the movement perpendicular to the loading direction, four external columns with rollers areplaced just outside of the box. A rectangular shape rubber sheet is placed in the box to inhibit soil particles fromgetting into the gaps between the laminae. This aluminium shear sheet roughened by glued Toyoura sand lie

just inside both end walls and are fixed to the base of the box. These sheets are for developing shear stresseson the vertical and horizontal contact surfaces with the soil. The three actuators are connected with the threelaminae directly and horizontal forces are transmitted to the other laminae through four linked sets of thin platespring. Each thin plate spring consists of three-layers of 0.6 mm-thick spring steel sheets. The actuators have astroke of +/- 20mm and force capacity of 25.8 kN and 18.0 kN at 20.5MPa oil pressure when moving outwardand inward, respectively.A series of preliminary tests was carried out to examine the characteristics of the shear box and to observe thedeformation of the soil in the shear box. Toyoura sand with relative density of 80% was used for the modelground. The test results reveal that the displacements of the laminae to which the actuators were directlyconnected showed quite good agreement with the target displacements, though the non-direct-connectedlaminae did not attain the target displacements, resulting in many kinks in the horizontal displacementdistributions. However, the distributions of the horizontal ground displacement observed at the centre of themodel were similar to the input motions. The ground displacement at the centre of the model became almost70-80% of the input value and they were smoother than those of the laminae.

3.2 Verification of experimental displacement method

A comparative study between dynamic shake table test and active type shear box test was carried out toexperimental verify the seismic displacement method.

3.2.1 Model and test descriptions Two types of 2-D centrifuge test: dynamic shake table test (termed as D-test hereafter) and pseudo-static activetype shear box test (termed as S-test), were conducted for the same prototype configuration of 3.25m wide and5.0m high rectangular tunnel with a cover of 5.875m embedded in dry dense sand under the same centrifugalacceleration of 50 G. Each model setup is shown in Figures 4 and 5, respectively.

The centrifuge shake table test (D-test) was conducted in the centrifuge at Kajima Research Institute (Kajima Technical Research Institute). The model ground was prepared in a 15-stacked 20mm-thick aluminium laminarshear box with 500mm in height, 450mm in width and 200mm in breadth. Four dynamic events were input witha peak horizontal acceleration of 5G, 10G, 15G and 20G, respectively. 20 sinusoidal waves with a frequency of

100Hz by a hydraulic dynamic actuator were applied to the model ground for each dynamic event. Theacceleration time histories are given in Figure 6.

The pseudo-static shear box test (S-test) was carried out in the Mark 3 centrifuge at the Tokyo Institute of

Table 1 Specifications of the active type shear boxMaximum operation centrifugal acceleration 100-g

Number 3 for laminar box, for pile head

Stroke +/- 20 mm for laminar box, +/- 40 mm for pile headForce capacity at 20.5 MPa oil pressure 25.8 kN for outward, 18.0 kN for inwardActuator

Peak velocity 133 mm/sec

Number of stacks 13

Inner size W450×B200× H325mmLaminar box

Flexural rigidity of plate spring: EI 0.14 N.m2, 0.56 N.m

2

Applying lateral load on pile head with an actuator

Imposing soil deformationwith three actuators

Pile

Soil

Platesprings

Laminar box Figure 3 Schematic diagram of the active type shear box Photo 1 A view of the active type shear box

Laminar box Actuators

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Technology, using the active type shear box apparatus explained in 3.1. It may be considered that tests in theactive type shear box are an experimental version of the seismic displacement method. A sinusoidal wave witha frequency of 0.01Hz and half a cycle was applied to the shear box as is shown in Figure 7, where “base”indicates the bottom of the shear box. Input distribution of the horizontal displacement at the jack locations waslinearly decreasing with depth and the horizontal displacement at the top laminar ring was about 6mm,imposing a nominal shear strain of 2.0% to the model ground. Figure 8 shows the measured distribution of horizontal displacement measured by displacement transducers attached to each laminar ring, showing that thehorizontal displacements at the laminar rings neighbouring those connected to the jack move slightly less thanthose originally intended as described before.A two dimensional rectangular model tunnel used in the two tests had the outer dimensions of 100mm wide,65mm high with a circular arc of 23.75mm radius at the four corners, and was made of aluminium with 2mm

thickness. Surface conditions of the model tunnel were considered to be smooth. Figures 9 (a) and (b) show theschematic illustrations of the rectangular model tunnel, together with the locations of a set of strain gauges inD-test and S-test, respectively. Strain gauges were attached on both outer and inner sides of the model in pairs.It should be noted that the number of strain gauges differs for the two tests; 18 sets for D-test and 5 sets for S-test, but the locations of the 5 sets, gauge No.10, 12, 14, 16 and 18, are identical to each other for directcomparison.Model ground conditions and the test procedures were identical to both tests. Dry Toyoura sand (Gs=2.64,D50=0.19mm, Uc=1.56, emax=0.978, emin=0.605) was used for preparing the model ground of 300 mm thick by

air pluviation method to achieve a relative density of 80% (d=15.4kN/m3, =42deg.). The tunnel model was

installed in position during the placement of the sand. 13 accelerometers were laid in the ground as well as inthe model tunnel in the D-test, as is shown in Figure 4. Potentiometers were attached to each laminar ring tomeasure the lateral ground movement. Horizontal and vertical relative displacements between upper and lowerslabs were measured at the mid-height and at the centre of the tunnel respectively by two gap sensors installedin the model tunnel for both test as is illustrated in Figure 10.

3.2.2 Results and discussion The purpose of this comparative study was to compare the tunnel lining stresses in the tunnel, and the tunnel

Figure 4 Model setup for D-test Figure 5 Model setup for S-test

250mm

1 1 7 . 5 m m

1 1 7 . 5 m m

6 5 m m

3 0 0 m m

Potentiometer

Toyoura sand Dr=80%

Gap sensor

Potentiometersfor ring displacement

50m

250mm

1 1 7 . 5 m m

1 1 7 . 5 m m

6 5 m m

VerticalAccelerometer

Horizontal Accelerometer

3 0 0 m m

Potentiometer

Toyoura sandDr=80%

Potentiometersfor ring displacement

Gap sensor

-8-6-4-200

2.5

5

7.5

10

12.5

15

17.5

20

22.5

25

27.530

32.5ground surface 13R jack

9R jack

5R jack

Horizontal displacement (mm)

H e i g h t ( c m )

Figure 8 Distributions of lateralmovement in S-test

0 20 40 60

-5

0

5

Ring13 312.5mmRing9 212.5mmRing5 112.5mm

from the base of the box

Time (sec.)

R i n g

i s p a c e m e n t m m

Figure 7 Time histories of ringdisplacement in S-test

0 0.1 0.2 0.3 0.4 0.5

-20

-10

0

10

20

Time (sec.)

4thshake

-20

-10

0

10

203rd shake

-20

-10

0

10

20

A c c e l e r a t i o n ( G )

2nd shake

-20

-10

0

10

201stshake

Figure 6 Examples of input waves

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deformation of the two types of test to verify that the results obtained from the S-test are practically equivalentto those obtained from the D-test. Shear strain rate of S-test was about 0.02%/sec on an average, which wasmuch slower than that of D-test.Figure 11 shows the bending moment distributions in D-test and S-test for four different dynamic events with

respect to the values at the same horizontal relative displacement between upper and lower slabs ( TH) of thetunnel. Note that only five sets of strain gauge data are available for S-test as described before. Similarly Figure12 compares the axial force distributions between D-test and S-test at the same value of the horizontal relativedisplacement. Positive axial force indicates the compressive axial force. Positive bending moment is defined asthe case for the inner surface of the tunnel suffers tension force. Considering Figures 11 and 12 together, it can

be said that both bending moment and axial force distributions are practically identical to each other, when thetunnel is subjected to the same magnitude of the horizontal relative displacement.

a) for D-test b) for S-test

Figure 9 Schematic illustrations of rectangular model tunnel and strain gauge arrangements

100mm

6 5 m m

R =

23.75mm

In1 In1 In1 In2

Out17 Out18 Out1 Out2

In1 In1 In9 In8

Out11 Out10 Out9 Out8

Out16

Out15

Out14

Out13

Out12 Out7

Out4

Out5

Out6

Out3

In1

In1

In1

In4

In5

In6

In1 In3

In1 In7

: strain gauge

100mm

6 5 m m

R =

23.75mm

In1

Out18

In1

Out10

Out16

Out14

Out12 Out7

Out5

Out3

In1 In5

In1 In3

In1 In7

Gap sensor

TH Relative displacement

between upper and

lower slabs

Target forGap sensor

Gap sensors

Figure 10 Arrangement of gap sensors

a) Vertical direction b) Horizontal direction

Figure 13 Relationships between TH

and R at D-test and S-test

-2 -1 0 1 2-2

-1

0

1

2

dynamic 20Gdynamic 15Gdynamic 10Gdynamic 5Gstatic

Relative displacement of shear rings: R (mm)

H o r i z o n t a l r e l a t i v e d i s p l a c e m e n t

b e t w e e n u p p e r a n d l o w e r s l a b s : T H ( m m )

S-test

Figure 11 Bending moment distributions in D-test and S-test

+100 kN・m/m

+50

-50

-100

10G, TH =0.30mm

dynamicstatic

+100 kN・m/m

+50

-50

-100

20G, TH =0.50mm

dynamicstatic

Figure 12 Axial force distributions in D-test and S-test

+2000 kN/m

+1000

-1000

-2000

10G, TH =0.30mm

dynamic

static

+2000 kN/m

+1000

-1000

-2000

20G, TH =0.50mm

dynamic

static

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The horizontal relative displacement between upper and lower slabs, TH, must be related to the ground

movement. The values of horizontal relative displacement, TH, for the four dynamic events in D-test as well as

S-test are plotted against the values of relative horizontal displacement of the ground around the tunnel, R in

Figure 13. Here, the value of R was determined from the relative horizontal displacement between two laminarrings, which were located near upper and lower slabs of the tunnel. The broken line in the figure is a skeleton

curve of TH- R relations for the four dynamic events in D-test. It agrees well with the TH- R curves obtainedfrom S-test. This provides strong experimental evidence, confirming that the relationship between the horizontaldisplacement of the ground and the horizontal relative displacement of the tunnel shows almost one to onerelation and D-test and S-test give a practically identical relationship. Thus, if the same magnitude of horizontalrelative displacement is imposed to the tunnel, the same stresses would generate in the tunnel lining, both in D-

test and S-test. And, if the same horizontal displacement is applied to the ground, almost the same horizontalrelative displacement between upper and lower slabs would take place regardless of the static and dynamicloading.It can be concluded, therefore, that S-test can be a practical substitute for D-test for the study of dynamicbehaviour of underground structures such as tunnel. The similar conclusion was derived from a series of comparative study of a rectangular tunnel with some countermeasures, which will be described later (Izawa, etal., 2006).

4 Applications to shallower tunnels

4.1 Influence of tunnel shapes and tunnel-soil-tunnel interaction

In order to utilize limited urban underground spaces, construction of new type tunnels with various cross-

sections is increasing. In such areas, road tunnels are very closely located each other, especially near thehighway junction. To assess the seismic performance of road tunnels near the highway junction, tunnel-soil-

Center Column 2 0 0

2 5

1

4 9

1 0 0

4 9

1

2 5

4.5*3.5

4.5*7.0A A'

1 0 0

1 0 0

5 5

A A'

B B' 2 0 0

Friction Cut Face

Cross Section B-B'

Top

Bottom

:Strain gauge

Cross Section A-A'

Top

Bottom

External Diameter = 60

Internal Diameter = 56Thickness = 2

1

1

Friction Cut Face

R = 2 3

. 7 5

6 5

100

4.5

Cross Section A-A'Bottom

Top

(a) Circular Tunnel (b) Rectangular Tunnel

a

b

Thickness = 2.5

:Strain gauge: Horizontal Relative Displacement between

top slab (a) and bottom slab(b) using

non-contact displacement sensor

Dimensions are in millimeters

Figure 15 Outlines of tunnel models and measurements

Figure 14 Test cases

Single Circular Tunnel Single Rectangular Tunnel Triple-faced Tunnel

CASE1 CASE2 CASE3 No.

Rectangular TunnelH:65mm(3.25m)W:100mm(5m)

3 0 0 m m

( 1 5 m )

R13

R9

R5 T e s t M o d e l

Actuator-sideCounter-sideＣＬ

R2 3 0 0 m m

( 1 5 m )

Circular Tunnel

D:60mm(3m)

R13

R9

R5

Actuator-sideCounter-side

R2

1 4 0 m m

( 7 m )

3 0 0 m m

( 1 5 m )

R13

R9

R5

Actuator-sideCounter-side

R2

( 5 . 4 m )

1 0 7 . 5 m m

( 5 . 4 m )

1 0 7 . 5 m m

( 3 . 8 m )

7 5 m m

****

**

**

ＣＬＣＬ

Rectangular tunnel

H: 65mm (3.25m)

W: 100mm (5m)

Circular Tunnel

D: 60mm(3m)

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tunnel interaction has to be properly considered. If the shape of a slip road tunnel is different from that of amain road tunnel, the problem being solved becomes more complicated.

To examine such a tunnel-soil-tunnel interaction for two different shape tunnels, three model tests wereperformed with the active type shear box (Yamada et al., 2002). Two different types of model tunnel wereprepared: circular tunnel and rectangular tunnel with central columns. The former models the main road tunnel,while the latter models the slip road tunnel. Model setup and the locations of instrumentation are shown inFigures 14 and 15. The model situation can be considered as shallow tunnel and C/D ratios were 1.79 forcircular tunnel, and 1.65 for rectangular tunnel. The model ground was prepared by air pluviation method toachieve a relative density of 90%. The model tunnels were made of aluminium. All the tests were conductedunder 50 G. 8 steps with three cycles of triangular-shaped horizontal displacement were applied to the laminarbox, and nominal shear strain applied ranged from 0.015 up to 2.0%.

To examine the effects of tunnel-soil-tunnel interaction on the tunnel members’ response, the bending momentdistributions of the tunnels in Case 3, in which two types of tunnels are aligned, were compared with those inCases 1 and 2 having circular or rectangular tunnels, respectively. Figure 16 plots the bending moment

distributions of the tunnels when the largest shear deformation was imposed to the model ground (nominalshear strain of 2.0%). For the circular tunnel, there is not much difference between Cases 1 and 3, even thoughthe C/D ratio for Case 1 is smaller than that for Case 3. On the other hand, for the rectangular tunnel, themaximum bending moment around the corner for Case 2 is larger than that for Case 3. The C/D ratio for Case2 is different from Case 3 and is larger than that for Case 3. To compare the rectangular tunnels response indetail, the bending moment distributions at the three relative horizontal displacement levels are plotted in Figure17. As the relative horizontal displacement between the top and bottom slabs in Step 2 for Case 2 was thesame as that in Step 3 for Case 3, these are plotted in the same symbols (open symbols for Case 2 while filledsymbols for Case 3). As seen in the figure, at the same relative horizontal displacement level, the bendingmoment at the lower right corner for Case 3, that is adjacent to the circular tunnel, seems to become slightlygreater than that in the single tunnel (Case 2). These results suggest that the effects of tunnel-soil-tunnelinteraction on the tunnel members’ response were not so remarkable in the present study.

4.2 Effectiveness of countermeasures

4.2.1 Verification of effectiveness of countermeasuresSeismic performance of the flat cross section tunnel was examined in the centrifuge, with and withoutcountermeasures (Yamada et al., 2004). Model tunnel was made with mortal (unconfined compressivestrength=21MPa). In the case with countermeasures, rubber membrane (thickness=1.0mm, elasticmodulus=1.5GPa) was glued around the outer surface of the tunnel as a seismic isolation layer. Furthermore,the tunnel area surrounded by round-shaped cement treated soil (unconfined compressive strength=1.0MPa)was arranged surrounding tunnel as a ground improvement. Schematic illustrations of both model tunnels areindicated in Figure 18. The model ground was the same as the model used in section 3.2. In this test series,only the dynamic tests were conducted. Sinusoidal waves were applied to the model ground in the centrifugalacceleration of 50G.Figure 19 shows time history of input ground acceleration, the lining strains and relative displacement of the

tunnel. Sudden changes in time strain history after step 5 are seen only in the data of the tunnel withoutcountermeasures, suggesting that the model tunnel underwent structural damage. Photo 2 shows a view of themodel tunnel without countermeasure observed after the test. Longitudinal crack are evident at the four corners

Figure 16 Comparison between single tunnel and triple facedtunnel (Bending moment)

Figure 17 Comparison between single tunneland triple faced tunnel (Bending moment) forapproximately the same displacement

CASE1(Single) Step8CASE3(Triple) Step8

CASE3(Triple) Step3CASE3(Triple) Step4CASE3(Triple) Step5

-16

16

16

-16

1 6

- 1 6

0

0

0

(kNm/m)

Case2 (S ingle)Step2Step3Step4

Case3 (Triple)Step2Step3Step4


-100

100

100

-100

1 0 0

- 1 0 0

0

0

0

-200

-200

200

(kNm/m)(kNm/m)


Case2 (Single)Step2Step3Step4

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and the crown and invert. In contrast, no damage was observed in the tunnel with countermeasures by rubbermembrane and improved ground, as is seen in Photo 2. It clearly demonstrates that the countermeasures areeffective even for brittle structures like mortal made tunnel without reinforcement.

Figure 18 Illustrations of mortal tunnel models with and without countermeasures

= 1 3 5 m

Rubber membrane

Soil cement

100mm

①

②

③

④

⑤

⑥

6 5 m

Strain gauge

Gap sensor

Mortal tunnelwith 8.5mm

thickness

(a) without countermeasures (b) with countermeasures

-400

-200

0

200

400

S t r a i n ( )

at outside of upper slab of the tunnel(No. 2 point in Figure)

-200

-100

0

100

200

S t r a i n ( )

at outside of upper corner of the tunnel(No. 1 point in Figure)

-0.2

-0.1

0

0.1

0.2

L a t e r a l r e l a t i v e

d i s p l a c e m e n t ( m m )

0 1 2-20

-10

0

10

20

A c c e l e r a t i o n ( G ) Step1 Step2 Step3 Step4 Step5 Step6

Time (sec.)

-400

-200

0

200

400

S t r a i n ( )

at outside of upper slab of the tunnel(No. 2 point in Figure)

-200

-100

0

100

200

S t r a i n ( )

at outside of upper corner of the tunnel(No. 1 point in Figure)

-0.2

-0.1

0

0.1

0.2

L a t e r a l r e l a t i v e

d i s p l a c e m e n t ( m m )

0 1 2-20

-10

0

10

20

A c c e l e r a

t i o n ( G ) Step1 Step2 Step3 Step4 Step5 Step6

Time (sec.)

(a) without countermeasures (b) with countermeasuresFigure 19 Test results for mortal tunnel model

Bold line: Location of crack

Photo 2 Mortal tunnel without countermeasuresafter shake table test

Soil cement

Photo 3 Mortal tunnel with countermeasuresafter shake table test

Rubber membrane

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4.2.2 Investigation of effectiveness of countermeasures

1) Model and test descriptionsEffectiveness of countermeasures was confirmed in the previous section. In this section, the mechanism of countermeasures and applicability of seismic displacement method are examined. Aluminium tunnel modelwith 2.0mm thickness, which was the same model used in 3.2, was used in order to measure the sectionalforces of the tunnel in detail. Three types of the following seismic countermeasures were adopted. (1) Rubbermembrane was glued around the outer surface of the tunnel as a seismic isolation layer (hereafter, called asRM) (2) Round-shaped soil cement ground (unconfined compressive strength=1.0MPa) was arrangedsurrounding tunnel as ground improvement (hereafter called SC), and (3) Combination of these (called RM+SC).

The test without any countermeasures is termed as NC. Model ground condition and test procedures adopted inthe tests are the same as D-test and S-test described in 3.2. Three seismic countermeasures are illustrated inFigure 20.

2) Results and discussions

i) Effectiveness of countermeasuresIt is interesting to compare the vertical relative displacement between upper and lower slabs for various

Figure 20 Countermeasures applied for the aluminium tunnel

(a) Rubber membrane (RM) (b) Round shaped soil cement ground (SC) (c) Combination (RM+SC)

1 3 5

m m

Soil cement

1 3 5

m m

Rubber membrane

Soil cement

Rubber membranewith 1.0mm thickness

Alminium tunnel modelwith 2.0mm thickness

NC SCRM RM+SC

Figure 22 Distributions of sectional forces at 50G

1 2 3 4 5 6 7 8 9 10 111213 1415 16 1718-100

0

100

B e n

d i n g m o m e n

t ( k N m /

m )

NC SCRM RM+SC

Strain gage number

1 2 3 4 5 6 7 8 9 10 111213 1415 16 1718-1000

0

1000

A x

i a l f o r c e

( k N / m )

Strain gage number

Figure 21 Vertical relative displacements between upper and lower slabs

0 10 20 30 40 50

-0.3

-0.2

-0.1

0

Centrifugal acceleration (G)

V e r t i c a l r e l a t i v e d i s p l a c e

m e n t ( m m ) NC SC

RM RM+SC

SC

RM + SC

RM

NC

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countermeasures conditions during spinning up the centrifuge, as are shown in Figures 21. Up to the centrifugalacceleration of 50G, the vertical relative displacement in NC case linearly increases and RM case shows almostthe same displacement as that of NC case except smaller displacement at smaller g-level. This observationsuggests that the seismic isolation layer is not beneficial to reduce vertical relative displacement. In contrast,the ground improvement substantially reduces the vertical displacement to one-third, compared to NC case,which is largely due to stiffer soil cement ground and smaller C/D ratio. The displacement of RM+SC is inbetween NC and SC cases. Figure 22 shows the sectional forces at 50 G after spinning up the centrifuge. Fromthe data of bending moment, it is noted that all the cases show the maximum negative bending moments at theside walls(strain gauge Nos. 4-6 and 13-15) and the maximum positive bending moments at the upper(Nos. 1,2, 17 and 18) and lower(Nos. 8-11) slabs and that SC case shows the smaller bending moment values followed

by RM+SC. The data of NC and RM are almost identical to each other. Axial force diagram however shows thatRM+SC case gives the smallest values while SC case exhibits the largest axial force at the lower right corner(strain gauge No. 7) and the largest tensile forces at the upper-left corner(No. 16).Figure 23 plots the amplitude of relative vertical and horizontal displacements over one wave between two slabsduring dynamic loading against input base acceleration. It is noticed that the displacements approximatelyincrease linearly with the acceleration for both directions. The effect of countermeasures is seen in SC case forthe horizontal direction and in SC and RM+SC for the vertical direction respectively, although the magnitude of relative vertical displacement is one order smaller compared to that of the horizontal displacement.

The seismic isolation layer is effective in reducing the dynamic sectional forces due to the isolation of thetransmission of the shear stress induced by seismic ground strain to the tunnel. Obviously the effectivenessdepends on the value of ratio Gm/Gg (Gm: shear modulus of isolation layer, Gg: shear modulus of the ground)and the thickness of layer. Since the value of Gg depends on the strain level of ground, the ratio of Gm/Gg mayvary from 0.01 to 0.05 in this study. Figure 24 shows the amplitude of sectional forces for input accelerationlevels of 10G and 20G. The bending moment increases as the input acceleration increases. The differences are

limited among the 4 cases. From the observation that the effect of RM is very limited although the sectionalforces are less than those of NC case, the value of Gm/Gg may have exceeded the threshold of 0.01 due to

0

0.02

0.04

0.06

0.08

0.1

NCRMSCRM+SC

5G 10G 15G 20G A m p l i t u d e o f v e t r i c a l d i s p l a c e m e n t ( m m )

Input acceleration (G)

0

0.5

1

NCRMSCRM+SC

A m p l i t u d e o f h o r i z o n t a l d i s p l a c e m e n

t ( m m )

5G 10G 15G 20G

Input acceleration (G)

Figure 23 Amplitude of relative displacement between upper and lower slabs during dynamic loading

Figure 24 Amplitude of sectional forces during dynamic loading

(b) Axial force

0

1000

2000

10G

1 2 3 4 5 6 7 8 9 10111213141516171819

1000

2000

0

20G

Strain gage number

A m p

l i t u d e o

f a x

i a l f o r c e

( k N / m )

NC SCRM RM+SC

(a) Bending moment

0

100

200 10G

1 2 3 4 5 6 7 8 9 10111213141516171819

100

200

0

20G

Strain gage number

A m p l i t u d e o f b e n d i n g m o m e n t ( k N m / m )

NC SCRM RM+SC

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plastic zone formed in the ground at the larger input acceleration. An apparent difference is seen in the axialforce distribution. That is, the axial forces in SC case at the side walls remarkably larger than those of the othercases. Furthermore, RM+SC case can ease such concentration of axial force at the corners.Based on the above observations, it may be said that RM has a certain advantage as countermeasures toreduce the sectional forces. In the case of SC, the vertical relative displacement of the tunnel could be reducedduring spinning up the centrifuge. However, the axial forces occurred in the lining due to shear deformation

cannot be reduced. Combination of RM+SC may provide the better countermeasures. SC contributes thereduction of vertical displacement, while RM contributes to reduce the sectional forces under dynamic situation.

ii) Verification of the experimental seismic displacement methodFigure 25 shows the distributions of bending moments and axial forces in D-test and S-test at the same

horizontal relative displacement, TH. As a whole, almost the same trend and values can be observed in D-testand S-test. This means that the same sectional forces are induced in the tunnel with countermeasuresregardless of dynamic or static loading, when the tunnel is subjected to the same magnitude of the horizontal

relative displacement. Figure 26 shows the relationships between TH and R. Similarly to the result of NC case

shown in 3.2, the relation in D-test shows good agreement with the TH- R curves obtained from S-test. That isto say, if the same horizontal displacement is applied to the ground, almost the same horizontal relativedisplacement between upper and lower slabs would take place regardless of the static and dynamic loading. Itcan be concluded, therefore, that the effectiveness of countermeasures for the tunnel can be evaluated usingthe experimental seismic displacement method.

+100 kN・m/m

+50

-50

-100 dynamicstatic

SC: TH =0.28mm

0

+100 kN・m/m

+50

-50

-100 dynamicstatic

0

RM: TH =0.28mm

+100 kN・m/m

+50

-50

-100 dynamicstatic

RM+SC: TH =0.27mm

0

(a) Bending moment

(b) Axial forceFigure 25 Bending moment and axial force distributions in D-test and S-test of tunnels with countermeasures

+2000 kN/m

+1000

-1000

-2000 dynamicstatic

RM: TH =0.25mm

0

+2000 kN/m

+1000

-1000

-2000 dynamicstatic

0

SC: TH =0.28mm

+2000 kN/m

+1000

-1000

-2000 dynamicstatic

RM+SC: TH =0.27mm

0

-2 -1 0 1 2-2

-1

0

1

2

dynamic 20Gdynamic 15Gdynamic 10Gdynamic 5Gstatic H

o r i z o n t a

l r e l a t i v e d i s p l a c e m e n

b e t w e e n u p p e

r a n d l o w e r s l a b s : T H ( m m )

Relative displacement of shear rings: R (mm)

-2 -1 0 1 2-2

-1

0

1

2

dynamic 20Gdynamic 15Gdynamic 10Gdynamic 5Gstatic H

o r z o n t a

r e a

t v e

s p a c e m e n

b e

t w e e n u p p e

r a n

d l o w e r s

l a b s : T H

( m m

)

Relative displacement of shear ring : R (mm)

-2 -1 0 1 2-2

-1

0

1

2

dynamic 20Gdynamic 15Gdynamic 10Gdynamic 5Gstatic

Relative displacement of shear ring : R(mm)

H o r i z o n t a

l r e

l a t i v e

d i s p

l a c e m e n

b e

t w e e n u p p e

r a n

d l o w e r s

l a b s : T H

( m m

)

Figure 26 Relationships between TH and R in D-test and S-test of the tunnels with countermeasures

RM case SC Case RM +SC case

S-tes S-test S-test

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5 Applications to deeper tunnels

As the second stage of the present study, the pseudo-static shear test using the active type shear box was usedfor the study of earth pressure on tunnel lining before and after earthquake.

5.1 Modification of active type shear box

In the model test of urban tunnel, tunnel cover-diameter or width ratio is very important parameter, as the depthcontrols the stress condition of tunnel surrounding, including formation of arching above the tunnel. Using theoriginal active type shear box, tests of shallower tunnels were conducted as described above. However, due tothe limitation of the box depth of original active type shear box, a small diameter model tunnel (e.g., 60mm)was used to have tunnel C/D ratio of about two. Although the depth of urban tunnel is relatively shallow, itnormally has the depth a several times the tunnel width. In order to simulate the various tunnel depths using a

model tunnel of reasonable size (e.g., D=100mm) with various instrumentations, the active type shear box wasmodified especially in the depth.Photo 4 shows a view of the modified active type shear box. Major modifications of the new box are the heightof the box and number of actuators. Number of laminae was increased from 13 to 21 and the height of the boxfrom 325mm to 524mm. The increase in the height is equivalent to C/D ratio of two for the model tunnel with100mm width. Removing the small actuator for the pile head loading, one hydraulic actuator for displacinglaminae was added to produce the continuous displacement of the laminae.

5.2 Model and Test description

Assuming horseshoe-shaped mountain tunnel, a semi-circular aluminium model tunnel was used, in which onlytunnel lining was modelled. It has a diameter of 100mm, a height of 75mm and a thickness of 2mm withsmooth surface, which approximately corresponds to a 5m diameter tunnel with a RC lining of 300mmthickness in the prototype scale. The ends of the lining were rigidly fixed to a 5mm thick aluminium plate. 22

strain gauges were attached on both outer and inner sides of the model in pairs to obtain bending moments of the tunnel lining. 5 earth pressure cells of 6.2mm diameter and 0.75mm thick were embedded to measure the

actuators

laminae

Plate springs

LVDTs

actuators

laminae

Plate springs

LVDTs

actuators

laminae

Plate springs

LVDTs

Photo 4 A view of the modified active typeshear box for tests on deeper tunnels

Potentiometer

Actuator1

Actuator2

Actuator3

Actuator4

D=100100 h = 7 5 m m

Potentiometer

Actuator1

Actuator2

Actuator3

Actuator4

Dry silica sand No.6

Displacement

transducers

C =

3 D : 3

0 0 m m

3 7 5 m m

Positive shearstrain :γ

Rough base

D=100mm

Rubber sleeve

Shear plate

with roughsurface

t=2mm

Potentiometer

Actuator1

Actuator2

Actuator3

Actuator4

D=100100 h = 7 5 m m

100 h = 7 5 m m

Potentiometer

Actuator1

Actuator2

Actuator3

Actuator4

Dry silica sand No.6

Displacement

transducers

C =

3 D : 3

0 0 m m

3 7 5 m m

Positive shearstrain :γ

Rough base

D=100mm

Rubber sleeve

Shear plate

with roughsurface

t=2mm

Figure 28 Test setup

0 100 200-4

-2

0

2

4

Time(sec)

S h e a r s t r a i n ( % )

M4 (first)

0 100 200

M1

0 100 200

M2

0 100 200

M4 (second)

Figure 29 Input shear strain history

4 5 °

4 5 °

2 0°

epc3

epc4

epc5

epc2

epc1

:Strain gauge :Earth pressure cell

Figure 27 Positions of strain gaugesand earth pressure cells

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distribution of the earth pressure acting on the lining on the outer surface of the tunnel at the tunnel crown,spring lines and the mid-parts between the crown and spring lines. Figure 27 illustrates the positions of thestrain gauges and the earth pressure cells.Dry silica sand No.6 (Gs=2.64, D50=0.51mm, Uc=1.74, emax=0.922, emin=0.565) was used for the model groundin the test. The model ground was constructed by the same method described in, section 3.2 to achieve a

relative density of 80% (d=15.8kN/m3

, =41deg.). The height of the model ground was selected to be 375mm,creating the cover of 300mm, which corresponds to a C/D ratio of 3. The vertical and horizontal displacementswere measured at the ground surface by a potentiometer and a laser displacement transducer respectively. Themodel setup is illustrated in Figure 29.

The input shear strain history is shown in Figure 28. The two cycles sinusoidal shear strains with 0.01 Hz, of which amplitudes were 4%, 1%, 2% and 4% respectively (termed as M4(first), M1, M2 and M4(second),respectively), were imposed to the model ground continuously.

5.3 Results and Discussion

Figure 30 shows variations of earth pressure measured at the tunnel crown and the mid-part between crown

and left spring line in the loading steps of M4 (first) and M4 (second) with shear strain, =4%. Variations of bending moments near the two parts are also shown in Figure 31. The positive bending moment means that theinner surface of the tunnel suffers tension force. In the cycles of M4 (first), the model was first sheared, whilethe cycles of M4 (second) were applied after several shear strain cycles were applied to the model including M4(first) (Figure 29). Earth pressures in the first cycle show a gradual increase during shearing. Cyclic variation of earth pressure and bending moment at the crown is smaller than those at the mid-part. It is interesting to notethat at the left mid-part the earth pressure varies randomly (Figure 30 (b)), while the bending moment varies inthe same phase with the input sinusoidal shear strain (Figure 31 (b)).Figures 32 and 33 show earth pressures and bending moments measured before and after cyclic shearing inM4(first) and M4(second) respectively. The terms ‘before’ and ‘after’ in the figures correspond to the testelapsed time of 0 second and 200 seconds respectively in Figure 28. Figure 34 (a) and (b) show earth

pressures and bending moments measured when the positive maximum strain first applied in the M4 (first) andM4 (second) which corresponding to elapsed time of 25 seconds in Figure 28.

(a) at crown

0 100 200-400

-200

0

200

400

-4

-2

0

2

4

Time(sec)

E a r t p r e s s u r e

P a

M4(first) M4(second) shear strain

S h e a r s

t r a i n ( % )

(a) at crown

0 100 200

-400

-200

0

200

400

-4

-2

0

2

4

Time(sec)

B e n

i n g m o m e n

t N m


S h e a r s

t r a i n ( % )

Figure 30 Measured earth pressureat crown and left mid-part

0 100 200-400

-200

0

200

400

-4

-2

0

2

4

Time(sec)

E a r t p r e s s u r e

P a


S h e a r s

t r a i n ( % )

(b) at left mid-part

Figure 31 Measured bending momentat crown and left mid-part

0 100 200

-400

-200

0

200

400

-4

-2

0

2

4

B e n

i n g m o m e n

t N m


S h e a r s

t r a i n ( % )

Time(sec)

(b) at left mid-part

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From Figure 32, two observations can be made. The first one is that the initial earth pressures before the firstshearing (M4(first)) are much smaller, probably due to the formation of arch action during the period of increasing centrifugal acceleration up to 50G.

The second one is that the earth pressures increase after the first shearing history, suggesting that deteriorationof the arch action takes place. In Figure 32 (b), the earth pressures before and after M4(second) loading cyclesare almost the same, because the ground has already been subjected to 4%, 1% and 2% shear strain cyclesand arch action diminished by shearing. After applied several shear histories, the soil-tunnel interaction showedelastic behaviour with no change of earth pressures and bending moments before and after shearing as shownin Figures 32(b) and 33(b). It is interesting to note that bending moment distributions show no appreciablechange before and after shearing even if a 4% shear strain cycle is imposed.From the moment distribution at the maximum shear strain shown in Figure 34, it can be confirmed that thebending moment due to shear deformation of the ground becomes maximum at about 45

ofrom the tunnel

crown, which were also found by Yamada et al. (2002) from the circular shield tunnel model in sand.

6 Concluding remarks

This paper introduced the physical modelling technique for an experimental seismic displacement method and

confirmed the usefulness of the method by comparing the structural responses between the observations indynamic centrifuge tests and the corresponding static centrifuge tests. A few applications were presented toseismic stability problems of tunnels constructed both shallow and deeper depths. Further studies on the

Figure 32 Earth pressure measured before and after shearing

(a) M4(first)

Before shearingAfter shearing

Earth ressure(kPa)

(b) M4(second)Earth ressure(kPa)


Figure 33 Bending moment measured before and after shearing

(a) M4(first)


Bending moment (Nm/m)

(b) M4(second)



Figure 34 Earth pressure and bending moment at maximum shear strain, =4%

(a) Earth pressure

M4 (first)M4 (second)

Earth ressure(kPa)

(b) Bending moment

M4 (first)M4 (second)


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development of possible countermeasures against earthquakes for underground structures are expected usingin this facility.

7 Acknowledgements

This research was partially supported by Grant-in-Aid for Scientific Research (A), 2005-2007, No.17206050, ”Seismic stability of the large cross-section urban tunnel with located in relatively shallow depth”.

The authors gratefully acknowledge the funding for this research from the 21st

Century Centre of Excellence(COE) program entitled “Evolution of Urban Earthquake Engineering”. The authors would like to thank Mr.

Takemine Yamada, Dr. Hideki Nagatani and Dr. Naoto Ohbo, Kajima Technical Institute, for their cooperation.

8 References

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Iida H., Hiroto, T., Yoshida N., & Iwafuji M. 1996. SPECIAL ISSUE on Geotechnical Aspects of the J anuary 17 1995 Hyogoken-Nambu Earthquake, Soils and Foundations, No. 1, pp. 283- 300.

Izawa J ., Kusakabe O., Nagatani H., Yamanda T. and Ohbo N. 2006. Centrifuge modelling on seismic behaviour of rectangulartunnels, Proceedings of Physical Modelling in Geotechnics, Proc. of 6th International Conf. on Physical Modelling inGeotechnics, pp. 1163-1169.

J apanese Geotechnical Society. 2006. Principles for Foundation Designs Grounded on a Performance-based Design Concept.

Kajima Technical Research Institute, GEOTECHNICAL CENTRIFUGE, http://www.kajima.co.jp/tech/katri/leaf/pdf/2002-37.pdf

Kawashima K. 2000. Seismic design of underground structures in soft ground: A review, Proceedings of Geotechnical Aspects of Underground Structures in Soft Ground, pp. 3-20.

Kitamura M. and Miyajima M. 1996. Damage to water supply pipelines, SPECIAL ISSUE on Geotechnical Aspects of the J anuary 171995 Hyogoken-Nambu Earthquake, Soils and Foundations, No. 1, pp. 325- 333.

Koseki J ., Matsuo O., Sasaki T., Saito K., and Yamashita M., 2002. Damage to sewer pipes during the 1993 Kushiro-Oki and the1994 Hokkaido-Toho-Oki earthquakes, Soils and Foundations, Vol.40, No.1, pp.99-111.

Shibayama S., Izawa J ., Takahashi A., Takemura J . and Kusakabe O. 2008. Centrifuge modelling of seismic displacement methodof tunnel in dry sand, (submitted to International J ournal of Physical Modelling in Geotechnics for review).

Takahashi A., Takemura A., Suzuki A., and Kusakabe O. 2001. Development and performance of an active type shear box in acentrifuge, International J ournal of Physical Modelling in Geotechnics, Vol.1, No.2, 1-17.

Takahashi A. and Takemura J . 2005. Liquefaction-induced large displacement of pile-supported wharf, Soil Dynamics andEarthquake Engineering, Vol.25, No.11, 811-825.

Takemura J ., Izawa J ., Shibayama S. and Kusakabe O. 2006. Active type shear box and its application on a stability of shallowtunnel in a centrifuge, Proceedings of 3rd International Conference on Urban Earthquake Engineering, pp. 639-646.

Takemura J ., Kondo M., Esaki T., Kouda M. and Kusakabe O. 1999. Centrifuge model tests on double propped wall excavation insoft clay, Soils and Foundations, Vol. 39, No. 3, pp. 75-87.

Yamada T., Nagatani H., Igarashi H. and Takahashi A. 2002. Centrifuge model tests on circular and rectangular tunnels subjectedto large earthquake-induced deformation, Proceedings of Geotechnical Aspects of Underground Structures in Soft Ground, pp.673-678.

Yamada T., Nagatani H., Ohbo N., Izawa J ., Shigesada H. and Kusakabe O. 2004. Seismic performance of flat cross-sectionaltunnel with countermeasures, Proceedings of 13th World Conference on Earthquake Engineering, paper No. 706.

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