dynamic behaviors of vertical shafts in e-defense experiment

1

DYNAMIC BEHAVIORS OF VERTICAL SHAFTS IN E-DEFENSE EXPERIMENT

Yohsuke KAWAMATA1, Manabu NAKAYAMA2, Ikuo TOWHATA3,

Susumu YASUDA4, Koichi MAEKAWA5, Kentaro TABATA6 and Koichi KAJIWARA7

ABSTRACT

Using one of the world largest shake table, E-Defense, a series of shake table tests on soil-underground structure was performed in 2012. In verification process of data obtained from the tests, it was found there is significant inconsistency between shaft top displacements directly measured with laser displacement transducers and calculated from strain gage array placed along the shaft. Comparing the various test results, a hypothesis, the bottom of the shaft was lifted up during shaking, is developed. Based on this assumed idea, the test results are reviewed, and simple pushover analyses are performed. As a result, it can be proved that the developed hypothesis is reasonable.

INTRODUCTION

In urban areas of mega cities, effective usage of underground space has been promoted in various ways because of their limited land available above the ground surface. Upgrade of city functions by extending underground structure network is one of its typical examples. In addition, some countries have future big projects, such as express railway construction, and building tunnels and terminals beneath existing urban areas is one of the most possible options.

In case when underground structures and/or structures with in-ground portions are close enough to others, those structures are usually connected each other with in-ground joints for convenience. However, the structures connected each other are often owned by different organizations, designed with different codes and demands, and built in different period, and therefore, design and behavior prediction of the complicated coupled-structures are significantly difficult in some cases, especially around in-ground joints. In practice, seismic performance of the joint is usually estimated by performing sophisticated numerical analyses, but there are not enough amounts of suffer examples which can be used for assessment of the numerical solutions.

In light of this, a series of larger-scale soil-underground structure experiments was performed using the world largest shaking table, nicknamed E-Defense (Ohtani et al. 2003), at Hyogo Earthquake Engineering Research Center, National Research Institute for Earth Science and Disaster Prevention (NIED), Japan at the end of February of 2012 in order to obtain benchmark data. In this series of shake

1 Research Fellow, National Research Institute for Earth Science and Disaster Prevention (NIED), Miki, Japan, [email protected] 2 Associate Professor, Kobe Gakuin University, Kobe, Japan, [email protected] 3 Professor, University of Tokyo, Tokyo, Japan, [email protected] 4 Professor, Tokyo Denki University, Hiki, Japan, [email protected] 5 Professor, University of Tokyo, Tokyo, Japan, [email protected] 6 Senior Researcher, NIED, Miki, Japan, [email protected] 7 Director, NIED, Miki, Japan, [email protected]

2

table tests, the test specimen was excited with various step sine motions and an actual earthquake records observed in 1995 Kobe Earthquake. During and after the experiments, a large number of useful data including sensor records, movies and inspection results could be obtained.

This paper focuses on dynamic behaviors of the vertical shafts including profiles of curvature, rotation, and displacement obtained in the series of E-Defense shake table experiments. Firstly, descriptions of the tests, such as test setup and a list of input motions are briefly provided. In addition, comparing some inspection results and sensor records on the vertical shafts, the test results are assessed, and then, discussions about verification results of the test results are summarized by developing hypothesis and performing simple pushover analyses at the last part of this paper. Details on dynamic behaviors of the container used, section deformation of tunnels and failure at the in-ground joints are available elsewhere (Kawamata et al. 2012 and Kawamata et al. 2013) as well as papers to be published in close future.

SPECIFICATIONS OF TEST

(1) Test Setup Test setup is illustrated in Figure 1. The test specimen was built in a large-scale laminar container with inside diameter of 8 m and height of 6.5 m. The container is composed of 40 shear rings and 2-dimensional linear sliders between the rings. The specimen had 2 soil strata, inclined bedrock and wet sand surface layer, and 5 structure models including 2 vertical shafts, a cut-and-cover tunnel interconnecting the shafts and 2 shield tunnels crossing a boundary between the bedrock and the surface layer. The vertical shafts minutely described in this paper were built by welding 4 plates of 12 mm thick aluminum. Their sections were 800 mm square in outside dimensions.

Figure 2 presents fixed condition at the bottom of the shafts. A 1 m by 1 m aluminum plate was welded to the shaft bottom. Placing steel plates arranged in a double cross with 3 pieces of bolts, the aluminum plate was suppressed against any movement, lateral displacement and rotation. It was assumed that this fixing method gave sufficient fixity because additional fixity would be provided by embedment of the shaft bottoms in approximately 1 m thick cement-mixed sand. Further details of the shaft construction are described in another paper (Kawamata et al. 2012).

800

800

AACL

A-A Section

CL

Shield TunnelO.D. = 400

Inclined Bedrock (Cement-mixed Sand)

Surface Layer

Cut-and-Cover Tunnel300 (H) x 600 (W)

Shield Tunnel

Vertical Shaft(800 x 800)

400

4700

X(+)

Y(+)

Z(+)

Y(+)

Vertical ShaftMaterial: AluminumThickness: 12 mm

48004000

FlexibleJoint

Flexible Joint

Cut-and-CoverTunnel

6000

8000

Section of Vertical Shaft Placement of Vertical Shafts

Laminar Container

Figure 1. Test Setup

Y. Kawamata, M. Nakayama, I. Towhata, S. Yasuda, K. Maekawa, K. Tabata and K. Kajiwara

Vertical Shaft

Steel Bar fixed on Container

Fixed withBolts

Steel Plates arranged in a double cross

Another Boltbehind Shaft

Figure 2. Fixed Condition at the Shaft Bottoms

(2) Input Motions Input motions used are listed in Table 1. 2 types of the input motions were applied to the test specimen for this series of the shake table tests. Step sine motions with frequency components within 1 through 20 Hz were used as a basic input motion. Also, 50% and 80% of JR Takatori motion (Nakamura et al. 1996) were applied to the specimen. Takatori motion is one of the most typical inputs for geotechnical shake table tests because this motion provides large ground displacement.

Figure 3 compares target and observed table motions at input of JR Takatori motion. From this figure, it is apparent both the motions show great agreement. In the below sessions and chapters, dynamic behaviors of the vertical shafts in JR Takatori motion are described in detail because the shafts showed obvious responses.

Table 1. Summary of Input Motions

Date Motion Acc. Level1) Direction2) Date Motion Acc.

Level1) Direction2)

2/23, 2012 Step Sine 1 – 20 Hz

0.1 m/s2 0 Deg.

2/24, 2012Step Sine 1 - 20 Hz

0.3 m/s2 90 Deg.

0.1 m/s2 90 Deg. 0.5 m/s2 0 Deg.

0.3 m/s2 0 Deg. 0.5 m/s2 90 Deg.

0.3 m/s2 90 Deg. JR Takatori 50 % See Note3)

0.3 m/s2 30 Deg.

2/28, 2012Step Sine 1 - 20 Hz

0.3 m/s2 90 Deg.

0.3 m/s2 45 Deg. 0.3 m/s2 0 Deg.

0.3 m/s2 135 Deg. JR Takatori 80 % See Note3)

1) “Acc. level” shows the maximum acceleration for Step Sine motion, and amplification from the actual records for JR Takatori motion.

2) “Direction” means angle from x-axis; i.e. 0 degree is x-axis and 90 degree is y-axis. 3) EW and NS components of JR Takatori were input in x- and y-axes, respectively.

-4

-2

0

2

4

0 10 20 30 40

Acc

eler

atio

n (m

/s2 )

Time (sec)

NS-comp. input in Y-axis

TargetObserved

-4

-2

0

2

4

0 10 20 30 40

Acc

eler

atio

n (m

/s2 )

Time (sec)

EW-comp. input in X-axis

TargetObserved

Figure 3. Input Motions (50% of JR Takatori motion)

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(3) Sensor Locations A large number of strain gages were placed in axial direction along the shafts as shown in Figure 4 in order to measure bending of the shafts. In addition, displacement transducers were placed at the top of the shafts to capture top rotations as well as top displacements. For protection of gages and their cables, it was ideal to place the strain gages inside of the shafts, but using chemical for cleaning the shaft surface around gage locations in closed inside space of the shafts was unsafe because the strain gages needed to be glued after construction of the shafts by welding alminum plates. Therefore, the gages were placed inside and outside of the shafts at shallow and large depths, respectively.

400 400

400

400

Type 3

400 400

400

400

Type 1

Type 4

400200 200

200400200

Type 2

400200 200

200400200

Strain Gages in Axial Direction

Displacement Transducers

100

600

100

100 100600

Section Type

122

G.L.

0-350-750

3 -1250

3 -1750

3 -2350

3 -2900

3 -3500

3 -4100

4 -46003 -49004 -52003 -5600

Displacement Transducers

+900 X(+)

Y(+)

X(+)

Y(+)

Z(+)

Y(+)

Figure 4. Sensor Locations along the Shafts

NOTICEABLE INSPECTION RESULTS

At dismantlement of the specimen, in-ground inspection was performed to see conditions of the ground and the structure models after shaking. Figure 5(a) shows significant crack generated on the surface of the inclined bedrock around the vertical shaft on the rigid joint side. The crack ran in direction of residual displacement of the shaft. This crack implies non-negligible shaft displacement at the boundary of the cement-mixed sand and the surface layer in this direction. Figure 5(b) presents approximately 20 mm wide gap around the shaft on the rigid joint side. This gap also indicates shaft displacement at the boundary. The gap was also observed around the shaft on the flexible joint side. From the above observations, the shaft should have 10 mm order horizontal displacement at the boundary. This fact can be used for verification of displacement profiles along the shafts.

DYNAMIC BEHAVIORS OF SHAFTS

(1) Horizontal Displacement of Shaft Tops Figure 6 gives comparison of displacement time histories at the shaft tops. From this figure, the displacements at the shafts on the flexible and the rigid joint sides show minor difference. It indicates type of the in-ground joints does not affect to the displacements of the shafts above the ground surface. Red marks in this figure give peak displacements in their time histories. Profiles of curvature, rotation and displacement at the times with these marks are described in the below discussions.


Vertical Shaft(Rigid Joint Side)

Direction of Residual Ground Displacement

Approx. 20mm wide Gap

Vertical Shaft(Rigid Joint Side)

Direction of Residual Ground Displacement

Cement-mixedSand

(a) Crack on the inclined Bedrock (b) Significant Gap

Figure 5. Inspection Results around Shaft on Rigid Joint Side

-40

-20

0

20

40

60

2 4 6 8 10 12 14

Dis

plac

emen

t (m

m)

Time (sec)

-80

-60

-40

-20

0

20

40

2 4 6 8 10 12 14

Dis

plac

emen

t (m

m)

Time (sec)

Shaft on Rigid Side (G.L. +0.9)Shaft on Flex. Side (G.L. +0.9)

in X-axis

in Y-axis

Figure 6. Displacement Time Histories at the Shaft Tops

(2) Profiles of Curvature, Rotation and Displacement Figure 7 shows time histories of curvatures around the in-ground joints (G.L. -350 and -750) and the boundary between the cement-mixed sand and the surface strata (G.L. -4600 and -5200). In the curvatures around both the X- and the Y-axes, the 2 vertical shafts reasonably agree at G.L. -4600 and -5200. On the other hand, significant difference appears in the curvatures around the in-ground joints, especially around the X-axis. In this curvature, the shaft on the flexible joint side shows significantly smaller values than one on the rigid joint side. It implies that the different types of the in-ground joints affected to the shaft behavior around the joints. This kind of interaction occurs only when multiple structures with in-ground joints and their surrounding soil exist, and therefore, it is defined soil-structure-structure interaction herein to distinguish from soil-structure interaction which appears between soil and single underground structure. More details of the soil-structure-structure interaction are available elsewhere (Towhata et al. 2014) and will be published in close future.

Profiles of curvature, rotation and displacement along the shafts on the rigid and the flexible joint sides are shown in Figure 8 and Figure 9, respectively. The rotation and the displacement at the top of the shafts are also plotted in these figures. Based on the figures, the follows are obtained; 1) the peak curvatures appear around the boundary between the cement-mixed sand and the surface layers, 2) the top rotations and the top displacements directly measured with the displacement transducers were significantly larger than ones calculated from the strain gage arrays, and 3) the displacement at the boundary of the soil strata was insignificant, and therefore, this fact is not consistent with the above observations; i.e. 10 mm order displacement at the boundary. In summary, the rotation and the displacement of the shaft include not only ones due to shaft bending of the shaft, but also ones generated from other behaviors.

6

-2.0E-04

-1.0E-04

0.0E+00

1.0E-04

2 4 6 8 10 12 14Time (sec)

G.L. -350

on Flex. Side on Rigid Side

-1.0E-04

0.0E+00

1.0E-04

2.0E-04

3.0E-04

2 4 6 8 10 12 14Time (sec)

G.L. -750


-1.0E-03

-5.0E-04

0.0E+00

5.0E-04

1.0E-03

2 4 6 8 10 12 14Time (sec)

G.L. -4600


-1.0E-03

-5.0E-04

0.0E+00

5.0E-04

1.0E-03

2 4 6 8 10 12 14Time (sec)

G.L. -5200

on Flex. Sideon Rigid Side

-3.0E-05

0.0E+00

3.0E-05

6.0E-05

9.0E-05

2 4 6 8 10 12 14

Cur

. (ra

d/m

)

Time (sec)

G.L. -350


-4.0E-05

-2.0E-05

0.0E+00

2.0E-05

4.0E-05

2 4 6 8 10 12 14

Cur

. (ra

d/m

)

Time (sec)

G.L. -750


-6.0E-04

-3.0E-04

0.0E+00

3.0E-04

6.0E-04

2 4 6 8 10 12 14

Cur

. (ra

d/m

)

Time (sec)

G.L. -4600


-1.2E-03

-8.0E-04

-4.0E-04

0.0E+00

4.0E-04

2 4 6 8 10 12 14

Cur

. (ra

d/m

)

Time (sec)

G.L. -5200


(a) Around Y-axis (b) Around X-axis

Figure 7. Time Histories of Curvature along Shafts

-6

-5

-4

-3

-2

-1

0

1-80 -60 -40 -20 0

Displacement (mm)

-6

-5

-4

-3

-2

-1

0

1-0.015 -0.01 -0.005 0

Rotation (radians)

3.130sec.3.490sec.5.770sec.7.165sec.

-6

-5

-4

-3

-2

-1

0

1-0.001 -0.0005 0 0.0005

Dep

th (G

.L.,

m)

Curvature (rad/m)

3.130sec.3.490sec.5.770sec.7.165sec.

From Displ. Transducers

From Strain Gauge Array

(a) Curvature and Rotation around Y-axis and Displacement in X-axis

-6

-5

-4

-3

-2

-1

0

10 10 20 30 40 50

Displacement (mm)

-6

-5

-4

-3

-2

-1

0

1-0.005 0 0.005 0.01

Rotation (radians)

3.235sec.3.615sec.5.530sec.7.265sec.

-6

-5

-4

-3

-2

-1

0

1-0.0005 0 0.0005 0.001

Dep

th (G

.L.,

m)

Curvature (rad/m)

3.235sec.3.615sec.5.530sec.7.265sec.



(b) Curvature and Rotation around X-axis and Displacement in Y-axis

Figure 8. Profiles of Curvature, Rotation and Displacement along the Shaft on Rigid Joint Side


-6

-5

-4

-3

-2

-1

0

1-80 -60 -40 -20 0

Displacement (mm)

-6

-5

-4

-3

-2

-1

0

1-0.01 -0.005 0

Rotation (radians)

3.130sec.3.490sec.5.770sec.7.165sec.

-6

-5

-4

-3

-2

-1

0

1-0.002 -0.001 0 0.001

Dep

th (G

.L.,

m)

Curvature (rad/m)

3.130sec.3.490sec.5.770sec.7.165sec.



(a) Curvature and Rotation around Y-axis and Displacement in X-axis

-6

-5

-4

-3

-2

-1

0

10 10 20 30 40 50

Displacement (mm)

-6

-5

-4

-3

-2

-1

0

10 0.004 0.008

Rotation (radians)

3.235sec.3.615sec.5.530sec.7.265sec.

-6

-5

-4

-3

-2

-1

0

1-0.0005 0 0.0005 0.001

Dep

th (G

.L.,

m)

Curvature (rad/m)

3.235sec.3.615sec.5.530sec.7.265sec.



(b) Curvature and Rotation around X-axis and Displacement in Y-axis

Figure 9. Profiles of Curvature, Rotation and Displacement along the Shaft on Flexible Joint Side

(3) Comparison of Shaft, Ground and Container Responses Figure 10 presents comparison of displacement time histories at the shaft top, the ground surface and the container wall. From the comparison, it is obvious that all the time histories are almost identical except the negative displacement at the shaft top in the X-axis seems little larger than the others.

Acceleration time histories in the X- and the Y-axes at several depths are shown in Figure 11. Some high frequency components appeared at the container wall around the ground surface, but all the rest shows identical time histories.

In conclusion of the above comparisons, it can be reasonably assumed that the displacements of the container is close enough to ones of the shaft at any depth. Therefore, the displacements of the container wall were used as the displacements of the shafts in the below discussion.

-60

-40

-200

20

4060

80

2 4 6 8 10 12 14

Dis

plac

emen

t (m

m)

Time (sec)

-80

-60-40

-20

020

40

60

2 4 6 8 10 12 14

Dis

plac

emen

t (m

m)

Time (sec)

Shaft on Rigid Side (G.L. +0.9)Ground Surface (G.L. 0)Container Wall (G.L. 0)

in X-axis in Y-axis

Figure 10. Comparison of Displacement Time Histories

8

-8

-4

0

4

8

2 4 6 8 10 12 14

G.L. 0 m

GroundContainer WallVertical Shaft

-6

-3

0

3

6

2 4 6 8 10 12 14Time (sec)

G. L. -1.0 m

-4

-2

0

2

4

2 4 6 8 10 12 14Time (sec)

G.L. -2.0 m

-4

-2

0

2

4

2 4 6 8 10 12 14

G.L. -3.8 m

-8

-4

0

4

8

2 4 6 8 10 12 14

Acc

. (m

/s2 )

G.L. 0 m

-6

-3

0

3

6

2 4 6 8 10 12 14

Acc

. (m

/s2 )

Time (sec)

G. L. -1.0 m

-4

-2

0

2

4

2 4 6 8 10 12 14

Acc

. (m

/s2 )

Time (sec)

G.L. -2.0 m

-4

-2

0

2

4

2 4 6 8 10 12 14

Acc

. (m

/s2 )

G.L. -3.8 m

Time (sec) Time (sec)

Figure 11. Comparison of Acceleration Time Histories

(4) Possible Modification on Profiles of Curvature, Rotation and Displacement Performing careful analyses on the inspection results and the test records, it is hypothesized the shafts rotated as rigid bodies due to uplift of the bottom plates of the shafts. Based on the test data, this hypothesis is verified and possible modification is proposed in this session.

Figure 12 and Figure 13 show modified profiles of the rotation and the displacement along the shafts. The rotations at the shaft bottoms are calculated by adjusting the top displacements equivalent to ones directly measured with the displacement transducers. Marks in these figures are rotations and displacements measured at the shaft top and the container wall. It is quite obvious that application of the bottom rotation significantly improves the profiles of the displacement and the rotation at the top. Also, these profiles give 10 mm order displacement around the boundary of the 2 different soil strata, and it is consistent with the inspection results mentioned above.

Figure 14 shows ratio of displacement due to the shaft rotation to the total displacement in virgin displacements of the shaft top. In the X-axis, the ratio seems relatively small in the positive direction. Because length of embedment in the cement-mixed layer is larger on the positive side than on the negative side, the fixity at the bottom against the shaft rotation is stronger in the positive direction, and therefore, the ratio in Figure 14 becomes less. On the other hand, in the Y-axis, the ratio of the shaft on the rigid side is larger in the positive direction, but smaller in the negative direction than one on the flexible side. It means the shafts rotate more easily in the direction without the cut-and-cover tunnel. This is also one of the soil-structure-structure interactions defined above, and more analyses are necessary to capture the detailed responses.


-6

-5

-4

-3

-2

-1

0

1-80 -60 -40 -20 0

Dep

th (m

)

Displacement (mm)

-6

-5

-4

-3

-2

-1

0

1-0.015 -0.01 -0.005 0

Dep

th (G

.L.,

m)

Rotation (radians)

From Displacement Transducers:At Shaft Top (G.L. +0.9m) and Container Wall


3.130sec.3.490sec.5.770sec.7.165sec.

3.130sec.3.490sec.5.770sec.7.165sec.

a1) Rotation around Y-axis a2) Displacement in X-axis

-6

-5

-4

-3

-2

-1

0

10 10 20 30 40 50 60

Dep

th (m

)Displacement (mm)

-6

-5

-4

-3

-2

-1

0

1-0.005 0 0.005 0.01

Dep

th (G

.L.,

m)

Rotation (radians)



3.235sec.3.615sec.5.530sec.7.265sec.

3.235sec.3.615sec.5.530sec.7.265sec.

b1) Rotation around X-axis b2) Displacement in Y-axis

Figure 12. Improved Rotation and Displacement Profiles along the Rigid Joint Side Shaft with Bottom Rotation

-6

-5

-4

-3

-2

-1

0

1-80 -60 -40 -20 0

Dep

th (m

)

Displacement (mm)

-6

-5

-4

-3

-2

-1

0

1-0.01 -0.005 0

Dep

th (G

.L.,

m)

Rotation (radians)



3.130sec.3.490sec.5.770sec.7.165sec.

3.130sec.3.490sec.5.770sec.7.165sec.

a1) Rotation around Y-axis a2) Displacement in X-axis

-6

-5

-4

-3

-2

-1

0

10 20 40 60

Dep

th (m

)

Displacement (mm)

-6

-5

-4

-3

-2

-1

0

10 0.005 0.01

Dep

th (G

.L.,

m)

Rotation (radians)



3.235sec.3.615sec.5.530sec.7.265sec.

3.235sec.3.615sec.5.530sec.7.265sec.

b1) Rotation around X-axis b2) Displacement in Y-axis Figure 13. Improved Rotation and Displacement Profiles along the Flex. Joint Side Shaft with Bottom Rotation

10

00.10.20.30.40.50.60.70.80.9

1

-40 -20 0 20 40 60Total Displacement (mm)


in Y-axis

00.10.20.30.40.50.60.70.80.9

1

-80 -60 -40 -20 0 20 40

Dis

pl. f

rom

Rot

atio

n / T

otal

Dis

pl.

Total Displacement (mm)


in X-axis

Figure 14. Ratio of Displacement due to Shaft Rotation to Total Shaft Displacement

For further verification of the hypothesis, pushover analysis with OpenSees (Open System for

Earthquake Engineering Simulation) is performed using a numerical model with linear beam and springs as shown in Figure 15(a). Comparing the test and the numerical results with and without rotational spring at the shaft bottom, validity of its application is assessed. As horizontal soil-shaft interaction, API sand p-y springs (American Petroleum Institute 1987) are used herein. Figure 15(b) illustrates assumed concept of the rotational spring at the shaft bottom. In this concept, fixity at the bottom works relatively well in small rotation, but the fixity becomes less once the shafts start lifting up. Because there may be minor gap between the double cross steel plates and the bottom plates of the shaft (refer to Figure 2), and therefore, probably the rotational spring shows very small stiffness until the bottom plate touches the steel plates and properties of the rotational spring is still improvable. In this study, parametric analyses are performed to find appropriate properties of the rotational spring which give reasonable agreements in the rotation and the displacement profiles along the shafts between the test and the numerical results.

Cement-mixed Sand

Surface Layer

Rotational Spring @ Bottom of Shaft due to Shaft Lift-up

Vertical Shaft Linear Beam

Soil-Structurep-y springs

Input: Displacement at shaft top

Mom

ent

Rotation

Once shaft starts lifting up, the shaft rotates more smoothly.

(a) Beam-spring model (b) Moment-rotation Spring at Shaft Bottom

Figure 15. Numerical Model of the Shaft for p-y Analysis

Comparisons of the rotational profiles along the shaft on the rigid joint side are shown in Figure

16. In this figure, circle marks show rotations calculated from strain gage array with the shaft bottom rotation given as the lines in Figure 12. From this figure, the installation of the rotational spring at the bottom is helpful to explain the bottom rotation. Figure 17 presents comparison of the displacement profiles at the corresponding times to the rotation profiles plotted in Figure 16. The circle marks in this figure are the container displacements directly measured with the laser transducers. From this comparison, it is apparent the rotational spring at the bottom can significantly improve the numerical results.


-6

-5

-4

-3

-2

-1

0

1-0.01 -0.005 0

Rotation (radians)

3.490sec.-6

-5

-4

-3

-2

-1

0

1-0.005 0

Dep

th (G

.L.,

m)

Rotation (radians)

3.130sec.

Experimentw/ Rot. Sprw/o Rot. Spr

-6

-5

-4

-3

-2

-1

0

1-0.02 -0.01 0

Rotation (radians)

7.165sec.

-0.015 -0.01 -0.005 0Rotation (radians)

5.770sec.

Figure 16. Comparison of Rotation Profiles in X-axis (on Rigid Side)

-6

-5

-4

-3

-2

-1

0

1-80 -60 -40 -20 0

Displacement (mm)

7.165sec.

-60 -40 -20 0Displacement (mm)

5.770sec.-6

-5

-4

-3

-2

-1

0

1-50 -40 -30 -20 -10 0

Displacement (mm)

3.490sec.-6

-5

-4

-3

-2

-1

0

1-20 -10 0

Dep

th (G

.L.,

m)

Displacement (mm)

3.130sec.

Experimentw/ Rot. Sprw/o Rot. Spr

Figure 17. Comparison of Displacement Profiles in X-axis (on Rigid Side)

Figure 18 compares ratios of displacement due to the shaft rotation to the total diplacement at

the shaft top from the experiment and the pushover analysis. There is still significant difference between the experiment and the numerical results in small positive displacement range, but these results show reasonably similar trend. This comparison indicates that the assumed concept of the rotational spring in Figure 15(b) is reasonable, but it is important to make more efforts for quantification of its properties.

0.4

0.5

0.6

0.7

0.8

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-80 -60 -40 -20 0 20 40

Dis

pl. f

rom

Rot

atio

n / T

otal

Dis

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Total Displacement (mm)

ExperimentPushover Analysis

Figure 18. Comparison of Displacement Ratio in X-axis along the Shaft on Rigid Joint Side

12

CONCLUSIONS

Using test records obtained in E-Defense shake table test on soil-underground structure, data analysis of dynamic responses of the underground vertical shafts was performed in order to capture their behaviors. Based on the data analysis, conclusions are summarized as follows; 1. Bending strains along the vertical shafts were quite small, and the rotations and the displacements

at the shaft top calculated from the bending strains do not agree with ones directly measured using displacement transducers at the shaft top.

2. To explain this disagreement, a hypothesis, the shafts rotated as rigid body due to uplift of the bottom plate of the shaft, is developed. Reviewing the test data and performing simple pushover analysis, the hypothesis can reasonably explain the experiment results. Further analyses are required for more details.

ACKNOWLEDGMENT

To successfully promote this experimental project, many advice and comments have been provided by Dr. Hosoi (TUGs Corporation), Dr. Goto (University of Tokyo) and the other Japanese engineers concerned. In addition, participants of NEES/E-Defense joint meetings from NEES gave lots of cooperations for this research project. All their supports are greatly acknowledged.

REFERENCES

Ohtani, K., Ogawa, N., Katayama, T. and Shibata, H. (2003) “Construction of E-Defense (3-D full-scale earthquake testing facility)”, 2nd International Symposium on New Technologies for Urban Safety of Mega Cities in Asia, pp. 69-76.

Kawamata, Y., Nakayama, M., Towhata, I., Yasuda, S. and Tabata, K. (2012) “Large-scale Experiment using E-Defense on Dynamic Behaviors of Underground Structures during Strong Ground Motions in Urban Areas”, 15th World Conference of Earthquake Engineering, Lisbon.

Kawamata, Y., Nakayama, M., Towhata, I., Yasuda, S., Maekawa, K. and Tabata, K. (2013) “Considerations on Seismic Behaviors of In-ground Structural Joint Observed in E-Defense Large-scale Experiment”, 6th Civil Engineering Conference in Asia Region (CECAR6), Jakarta.

Nakamura, Y., Uehan, F. and Inoue, H. (1996) “Waveform and its Analysis of the 1995 Hyogo-Ken-Nanbu Earthquake (II)”, JR Earthquake Information No. 23d.

American Petroleum Institute (API) (1987) “Recommended Practice for Planning, Designing, and Constructing Fixed Offshore Platforms”, API Recommended Practice 2A (RP-2A), 17th edition

Open System for Earthquake Engineering Simulation, http://opensees.berkeley.edu/index.php Towhata, I., Kawamata, Y., Nakayama, M. and Yasuda, S. (2014) “E-Defense Shaking Test on Large Model of Underground

Shaft and Tunnels”, Keynote Lecture, IS-Seoul (in print)

dynamic behaviors of vertical shafts in e-defense experiment

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