a seismic design of the underground box-type rc …

A SEISMIC DESIGN OF THE UNDERGROUND BOX-TYPE RC

STRUCTURE CONSIDERING THE THREE-DIMENSIONALITY

Hideki NAGAI1, Tadashi KAWAI

2, Motoki KAZAMA

3

ABSTRACT

A seismic evaluation method is proposed for determination of planar shear deformation of a shear wall,

considering the three-dimensionality, which is an underground box-type structure such as screen chamber and

pump chamber of intake facilities in large-scale energy power plants. In underground box-type structures, as

results of large-scale ground motion side walls that are perpendicular to the direction of ground motion is pushed

by the ground, hence earth pressure acting on the side wall centre is reduced by the deformation occurred due to

the decrease in the rigidity. On the other hand, earth pressure acting on the side wall end and the shear force

acting on the shear wall surface is increased, resulting in in-plane shear deformation of the shear wall, which can

lead to cases where critical breakage of the entire structural system occurs. In this case, a method for calculating

the limit value of deformation angle “limit deformation angle” is proposed by applying the index of structural

member’s deformation angle to the damage index of the shear wall of an underground box-type structure, and

the validity of this method is verified by utilising it in a seismic evaluation.

Keywords: Underground RC structure, Numerical analysis, Damage index, Centrifuge experiment, three

dimensionalities

1. INTRODUCTION

This paper proposes the new seismic design procedure considering the three-dimensionality of the

underground box-type RC structure subjected to seismic motion, based on the results of centrifuge

model vibration test and 3D nonlinear dynamic analysis. As a performance-based earthquake

engineering, it is to purpose of performing seismic evaluation of an underground box-type structure,

such as screen chamber and pump chamber of intake facilities in large-scale energy power plants with

each side wall surrounded by soil.

This box type structure is connected to multiple culvert and a structural joint is given between the two,

and there is an opening on the first floor as shown in Figure 1. Two-dimensional analysis by two-

dimensional sliced cross section has been carried out until now, but seismic design method

considering three-dimensionality is proposed in this paper.

(a) Image of overall structure (b) Name of structure members

Figure 1. An underground box-type structure

1 Deputy general manager, Obayashi corporation, Tokyo, Japan, [email protected]

2 Associate professor, Tohoku University, Sendai, Japan, [email protected]

3 Professor, Tohoku University, Sendai, Japan, [email protected]

Multiple culvert

Structural joint

Pump chamber

Direction of the input wave

Base slab

Shear wall

Front -back wall

Opening

2

2. CENTRIFUGE EXPERIMENT

2.1 Outline of experiment

A centrifuge model vibration test is performed to confirm 3D seismic behavior of underground box

type structure and the load acting on each member of the structure, as shown in Figure 2. The box type

structure, which is 1/50 scale model with an opening on lower part of one of its side wall surface, was

made of aluminum and the wall thickness is 12 mm. The outer dimensions of the model are 250 mm

×350 mm in planar shape and 350 mm in height (actual size scale, planar shape 12.5 m×17.5 m, height

17.5 m). Here, the material physical properties of the aluminum material are elastic modulus

E=7.00×107

kN/m2, Poisson's ratio νA=0.30, yield stress σsy=1.00×10

5 kN/m

2. It is put in the central

part of the shear soil tank in the centrifuge apparatus.

Upper layer of ground is a sand and lower layer is a cement improved soil. The sand layer is made of

Gifu's No.7 silica sand (Gs=2.645, γmax=1.529 g/cm3, γmin=1.184 g/cm

3) and aimed at a relative density

of 70% (γd=1.406 g/cm3) by compacted, which is C=50.1 kN/m

2, φ=36.0°, according to the

consolidated non-drainage (CU) triaxial compression test (JGS 0523) of the soil.

The cement improved soil was formed in the lower layer of the shear soil tank, and the thickness was

150 mm with the same height as the load cell. The uniaxial strength qu of the cement improved soil is

1.51 MN/mm2, and the modulus of elasticity is 3.24×106 kN/m2.

Input waves are the sign waves of 100 Gal, 200 Gal, and 400 Gal, inputted from undersurface of the

shear soil tank. Accelerometers, displacement gauges, earth pressure gauges, shear stress meters and

load cells were used as the measurement of the experiment.

(b) Material of closing the opening

(a) Shear soil tank and box type structure model (c) Picture of box type structure and gauges

Figure 2. Centrifuge model vibration test

2.2 Experiment results

2.2.1 Classification of applied load

As the results of experiment, increase of the applied load and its convergence situation due to gradual

increase of the input waves has been revealed by classifying the load acting on each structural

member, as shown in Figure 3.

Front-back earth pressure force and circumferential shear force, which are main loads except inertia

force, show the little increase rate from 200 Gal to 400 Gal against increasing tendency until 100 Gal.

Here, the front-back earth pressure is taken as the sum of earth pressure on the two side walls

perpendicular to the input wave direction.

250

160

L150(t=9mm)

Rubber(t=15mm)

Boltφ5mm

4-PL6mm 160

Rubber(t=15mm)

150

316

L150(t=9mm)

4-PL6mm

Boltφ5mm

3

The circumferential shear force tends to converge first comparing with front-back earth pressure force

and inertial force. The inertial force increases approximately linearly as the input acceleration

amplitude increases. The ratio of the inertial force to the total horizontal force is approximately 20% or

less, and its ratio is small like general underground culvert structure. In the ratio to the total horizontal

force, the front-back earth pressure was the largest, and the circumferential shear force was the second.

Figure 3. Relationship between acting force and ground response displacement of each case

2.2.1 The distribution of front earth pressure

The distribution of earth pressure acting on the front wall at the time, when the largest load in the

historical data is calculated, is shown in Figure 4. The earth pressure of the opening side and the

central part, due to deformation of the structure against the deformation of the ground, has little

change even if the input acceleration is increased. Especially, the earth pressure of the central part is

50% or less compared with earth pressure at the end of the front wall.

On the other hand, earth pressure at the end of the front wall increases due to the rigidity of the

structure and the response displacement of the surrounding soil. Earth pressure at the end of the front

wall approaches to static passive earth pressure (σp=Kp·σv, where Kp=tan2(π/4+φ/2), σv: effective

weight of the ground kN/m2) in 400 Gal. This is because the deformation of the shear wall is small and

the relative displacement between the ground and the structure increases.

Figure 4. Distribution of earth pressure acting on the front wall

2.2.3 Deformation of the entire structure

Planar maximum deformation of the front wall and the shear wall is summarized as shown in Figure

5(a). The relationship between the out-of-plane deformation angle of the front-back wall and the in-

plane deformation angle of the shear wall, and the relationship between the out-of-plane deformation

angle of the front-back wall and the torsional deformation angle of the shear wall are shown in Figure

Dir. of input waveS-side

W-side　Shear wall

Opening sideN-side

Deformation

0 150 300Earth pressure(kPa)

100Gal

200Gal

400Gal

Ho

rizo

nta

l lo

ad (

MN

)

-80

-40

0

40

80

-300 -200 -100 0 100 200 300

荷重

(MN

)

応答変位(mm)

400Gal200Gal100Gal

-80

-40

0

40

80

-300 -200 -100 0 100 200 300

荷重

(MN

)

応答変位(mm)

400Gal200Gal100Gal

-80

-40

0

40

80

-300 -200 -100 0 100 200 300

荷重

(MN

)

応答変位(mm)

400Gal200Gal100Gal

-80

-40

0

40

80

-300 -200 -100 0 100 200 300

荷重

(MN

)

応答変位(mm)

400Gal200Gal100Gal

Response displacement(mm)


Ho

rizo

nta

l lo

ad (

MN

)

Ho

rizo

nta

l lo

ad (

MN

)

-80

-40

0

40

80

-300 -200 -100 0 100 200 300

荷重

(MN

)

応答変位(mm)

400Gal200Gal100Gal

-80

-40

0

40

80

-300 -200 -100 0 100 200 300

荷重

(MN

)

応答変位(mm)

400Gal200Gal100Gal

-80

-40

0

40

80

-300 -200 -100 0 100 200 300

荷重

(MN

)

応答変位(mm)

400Gal200Gal100Gal

-80

-40

0

40

80

-300 -200 -100 0 100 200 300

荷重

(MN

)応答変位(mm)

400Gal200Gal100Gal



Ho

rizo

nta

l lo

ad (

MN

)

0

20

40

60

80

0 50 100 150 200 250 300

作用水平荷重（M

N)

自由地盤の応答地盤変位(mm)

前背面土圧周面せん断力

慣性力全水平力

100Gal

200Gal400Gal

Ho

rizo

nta

l lo

ad (

MN

)

Response displacement of free field (mm)

Front-back

earth pressure

Inertial force

Circumferential

shear force Total force

Dir. of the input wave

Earth pressure gauge

Front

Planar view

Total force

Front-back earth pressure force

Circumferential shear force

Load

Inertial force

4

5(b). For the out-of-plane deformation angle of the front-back wall and the in-plane deformation angle

of the shear wall, it was confirmed that the approximate straight line was y=0.38x, and in-plane

deformation of the shear wall occurred. As the results, in the case of concrete wall members, because

out-of-plane fracture (limit value of deformation angle of out-of-plane bending interlayer :1.0%) and

in-plane fracture (limit value of deformation angle of in-plane shear strain of RC wall :0.4%) is 1: 0.4,

it is assumed that the shear wall and the front-back wall are destroyed almost at the same time. For the

out-of-plane deformation angle of the front-back wall and the torsional deformation angle of the shear

wall, the approximate straight line is y=0.33x, and even if the input wave’s direction is one direction,

the torsional deformation was proved to be occurring. we found that it was necessary to always

consider deformation in both directions (out-of-plane, in-plane) in the shear wall. In seismic

performance evaluation, it is necessary to select an analysis method that can take three-dimensional

deformation into consideration.

(a) Maximum deformation of planar view (b) Rrelationship of deformation angle

Figure 5. Relationship of deformation angle between front wall and shear wall

3. 3D-NUMERICAL ANALYSIS

3.1 Experimental verification analysis

Detailed time history dynamic analysis by 3D FEM model was carried out to confirm the

reproducibility of the experiment. The finite element analysis program "FINAL-GEO" developed by

Obayashi Corporation was used. This analysis program has many verification results in the concrete

material constitution model and also has a modified GHE model as a structural model of the ground.

In addition, the computational speed has dramatically increased from the conventional speed by using

simultaneous equation solving method suitable for large-scale high-speed operation. Geometric

nonlinearity is not considered in the analysis. The calculation method of dynamic analysis applies the

Newmark-β method.

In the analysis model, the structure is a shell element, and the ground is a hexahedral solid element.

The number of elements of the structure is 1870, and the number of elements of the ground is 74500.

Also, the shell element has 5 degrees of freedom, and the hexahedral solid element has 3 degrees of

freedom. Repeated triaxial tests were carried out to determine the deformation characteristics of the

ground material for silica sand No.7 (Dr=70%), and the fitting by the H-D model which is the skeleton

curve of the modified GHE model was performed. The nonlinear relationships between stiffness

(G/G0), damping ratio (h) and strains in the upper layer of ground are modelled by the modified GHE

model. Relationship between the dynamic shear coefficient and the damping constant of the ground

used for the modified GHE model (G-γ, h-γ) is shown in Figure 6. The history law can satisfy arbitrary

G/G0-γ relation, h-γ relation and strength characteristic (upper limit value of shear stress) by

y = 0.38x

-0.2

-0.1

0

0.1

0.2

-0.2 -0.1 0 0.1 0.2

せん断壁の

面内変形

(%)

前面壁の

面外変形角(%)

400Gal

200Gal

100Gal

Deformation angle

of front wall (%)

Def

orm

atio

n a

ngle

of

shea

r w

all

(%)

Dir. of input wave

y = 0.33x

-0.2

-0.1

0

0.1

0.2

-0.2 -0.1 0 0.1 0.2

せん断壁の

面外変形角

(%)

前面壁の

面外変形角(%)

400Gal

200Gal

100Gal

Deformation angle

of front wall (%)

Def

orm

atio

n a

ngle

of

shea

r w

all

(%)

Dir. of input wave

t=12s

t=11.5s

振動前位置Before deformation

Opening-side

Shear wall-side -0.1

0.1(%)

-0.1 0.1(%)

5

improving the Masing rule.

(a) Analysis model (b) G/G0-γ relation and h-γ relation

Figure 6. Analysis model of soil and structure system

3.2 Confirmation of reproducibility

The time history analysis was carried out in good convergence. Overall deformation is shown in

Figure 7. Relationship between displacement and horizontal force is almost the same as the above

tests results as shown in Figure 8. The comparison of deformation of planar view is shown in Figure 9,

as the results, the both results are almost the same.

The load and the deformation of an underground box-type structure computed by the dynamic analysis

are confirmed to become almost the same as the above tests results. It was confirmed that in-plane

deformation and torsional deformation of the shear wall occurred.

Figure 7. Overall deformation (200Gal) Figure 8. Relationship between displacement and force

Figure 8. Relative displacement of structure(400Ga

Figure 9. Deformation of planar view

解析は３次元地盤―構造物連成問題とし、地盤は 3次元ソリッド要素でモデル化し、箱型構造物は 3次

元シェル要素でモデル化した。構造物と地盤間にはジョイント要素で連結する。図 1-1～図 1-5 に解析モデ

ルを示す。

550

500

1200 1200

500

550 Strain of soil

Dam

pin

g r

atio

Opening side

Shear wall side

-0.1

0.1(%)

-0.1 0.1(%)

N-side S-side

Experiment ( - dir.)

Analysis ( - dir.)

Experiment ( + dir.)

Analysis ( + dir.)

Before deformation

Earth pressure of

front & back

Interrail force

Circumferential

shear force

Total force

Solid line : Analysis

Dot line : Experiment

Displacement of free ground

Ho

rizo

nta

l fo

rce

(MN

)

6

4. A NEW DESIGN METHOD CONSIDERING 3-DIMENSIONALITY OF STRUCTURE

4.1 A new design method considering three dimensionalities

Dynamic analysis of 3D FEM model takes a lot of time and cost, so it is difficult to evaluate all the

designed ground and structure systems. Therefore, we propose a new design method considering three

-dimensionality. Design flow of the new design method for an underground box-type structure is shown in

Figure 10. Earthquake resistance assessment is performed by using detailed nonlinear dynamics below

seat of 3D FEM model. The method for calculating the index of "critical deformation angle" applied in

the design method is introduced in next section. The maximum response deformation angle of the

shear wall is obtained by acting the seismic wave of coupled analysis. And finally, it is a value smaller

than the critical deformation angle. It is a simple checking method to compare the critical deformation

angle and the maximum response deformation angle.

Figure 10. Design flow of an underground box-type structure

4.2 Calculation method of “limit deformation angle”

For the various assumed load distributions, the critical deformation angle of the shear wall of the box

type structure was calculated as shown in Table 1, by load control gradual increase analysis by the

three-dimensional laminated shell model. We changed the load distribution in the depth direction to

the front wall and the shear wall to parametric in the examination series of K1 ~ K6. The relationship

between the horizontal load and the shear deformation angle of the shear wall is determined in this

analysis. When the wall member reaches the horizontal yield strength (maximum value) in the in-

plane direction and undergoes in-plane shear deformation, it becomes brittle (sharply decreasing the

horizontal yield stress). The deformation angle at the time when the horizontal yield strength is

reached is calculated as the critical deformation angle. It is possible to obtain the minimum critical

deformation angle of the box type structure with respect to the shear wall, and it can be a threshold

value of the damage index used in the seismic evaluation. The method of calculating the critical

deformation angle is proposed by the following study.

Table 1 shows the results of determining the critical displacement angle of each case. The load -

Setting of structure dimension

2D section model※

・Feature of design method

Design of section

Design of shear wall

・Feature of analysis method

2D FEM model

Spring-frame model

Calculation of Limit value (Rd)

・Limit deformation angle

・Load step analysis by 3D model

Calculation of Response (Sd)

・Response of deformation angle

・Dynamic analysis by 3D model

NGRd ＞ Sd

Verification

END

OK

2D Model 3D Model

YES

YESNO

NO

※ Guideline and recommendation for

seismic performance verification of underground reinforced concrete structures in nuclear power stations.

START

Classification by parameter of structure shape

Classification by structure arrangementand soil condition

Specified

Proposal

In this paper, the explanations of classification are omitted.

7

displacement curves of each case are shown in Figure11 and Figure12. In-plane shear deformation of

the shear wall preceded by the load distribution of the lower triangle (K3-3) with the load of only the

peripheral shear stress, resulting in the smallest shear deformation angle (=0.462%). From this, we

propose a case where circumferential shear force acts on the shear wall with a lower triangular

distribution as a method for finding the minimum value of the critical deformation angle.

Table 1. Evaluation result of critical deformation angle*

No. Struct

ure Load type

Loading

place Load distribution

Limit

deformati

on angle

(%)

K1

Openi

ng

Acceleration All walls Uniform distribution 0.621

K2-1 Front and

back earth

pressure

Front

back wall

Uniform distribution 0.853

K2-2 Upper triangular distribution 0.644

K2-3 Lower triangular distribution 0.650

K3-1 Circumferen

tial shear

force

Shear

wall

Uniform distribution 0.787

K3-2 Upper triangular distribution 0.956

K3-3 Lower triangular distribution 0.462

K4-1

Front and

back earth

pressure

Circumferen

tial shear

force

All walls

Lower triangular 75% (front and back wall side)

Lower triangular 25% (shear wall side) 0.625

K4-2 Lower triangular 50% (front and back wall side)

Lower triangular 50% (shear wall side) 0.760

K5-1

Front and

back earth

pressure

Circumferen

tial shear

force

The

lower

half of all

walls

Uniform distribution 75% (front and back wall

side)

Uniform distribution 25% (shear wall side)

0.691

K5-2

Uniform distribution 50% (front and back wall

side)

Uniform distribution 50% (shear wall side)

0.565

K6

Response

displacemen

t method

All walls Ground spring + Response displacement 0.491

* Calculated by the three-dimensional laminated shell model

Figure 11. Relationship between shear deformation angle and load (K1, K2, K3)

Lower

triangular Upper

triangular Uniform

distribution Uniform

distribution

Inertial force Earth pressure distribution

Shear deformation angle

Inertial force Uniform distribution Upper triangular Lower triangular

Ho

rizo

nta

l fo

rce

(kN

)


Ho

rizo

nta

l fo

rce

(kN

)

Uniform distribution

Upper triangular

Lower triangular

8

Figure 12. Relationship between shear deformation angle and load (K4, K5)

4.3 Case study in actual structure

4.3.1 Analysis condition

3D nonlinear dynamic analysis of a box type structure only, which is a structure of real size with an

opening, simulating real structures, is performed. The target structure is a two-story box-shaped

structure, the outer shape is 23.9 m (side wall width perpendicular to the direction of the input

horizontal seismic wave) ×32.1 m (side wall width parallel to the direction of the input horizontal

seismic wave) ×29.0 m (height), as shown in Figure13. The structure has an opening on the lower first

floor of one side wall having four walls. As a coupled model, the structure and the ground were

hexahedral solid elements (number of elements: 37060, number of nodes: 59740).

The structure is a foundation structure which is directly installed on the rock (CM class), and the

ground constituent law is based on the rock under the structure as an elastic body. For the upper layer

of soil, a modified GHE model that can account for the nonlinearity of the ground is applied.

The analysis software is a large-scale, high-speed nonlinear finite element method program "FINAL-

GEO" which can greatly shorten the calculation time.

Figure 13. Target structure of a two-story box-shaped structure

Ho

rizo

nta

l fo

rce

(kN

)


Fornt:1.00, Shear:0.00




Ho

rizo

nta

l fo

rce

1st, Uniform dis. ,Fornt:1.00, Shear:0.00



Section[1] Section[2]

Shear wall

2.0m

3.0m

23.9m

32.1m

29.0m

Front - back wall

h

Dam

pin

g r

atio

(h

)

Sti

ffn

ess

(G/G

0)

Shear strain ()

G/G0

Middle Deck

Dir. of input wave

1st floor

2nd

floor

Location of opening

9

4.3.2 Analysis results

In the underground box-type structure, as the results of large-scale ground motion, front-back walls

that are perpendicular to the direction of ground motion is pushed by the ground, hence earth pressure

acting on the front wall centre is reduced by the deformation occurred due to the decrease in the

rigidity. On the other hand, acting earth pressure on the front wall end and the shear force acting on the

shear wall surface is increased, resulting in in-plane shear deformation of the shear wall, which can

lead to cases where critical breakage of the entire structural system occurs.

Input seismic waves are shown in Figure14. Input range of analysis is 30.0s to be shorten analysis

times. In original input wave, overall deformation and crack graph of the structure are shown in

Figure15. Maximum deformation angle of shear wall occurs in 8.4s of input range to analysis. Then,

the large strain of rebar and minimum principal strain of concrete occur in the lower end of front-back

wall and lower of shear wall as shown in Figure16 and Figure17. In 3times input wave, compression

softening in lower of shear wall is expended as shown in Figure18.

Figure14. Input wave motions (NS-dir., UD-dir., original)

Horizontal (X dir.) Vertical (Z dir.)

Figure16. Rebar strain distribution (t=8.4s)

Section[1] Section[2]

Figure17. Minimum principal strain distribution (t=8.4s)

Figure15. Analysis results (Deformation, Crack)

全体変形図 (変位倍率：100) ひび割れ図

5.0s

8.4s

(最大

層間変

形時)

15.0s

Overall deformation Crack graph

Max

deform

ation

angle

Section[1]

2000

1600

1200

800

400

0 (μ)

2000

1600

1200

800

400

0 (μ)

Section[2]

0

-200

-400

-600

-800

-1000 (μ)

10

Original of input wave

(Maximum amplitude of acc. 460Gal) 3 times of input wave

(Maximum amplitude of acc. 1380Gal)

Figure 18. Crack graph at maximum interlaminar deformation

4.3.3 Seismic safety judgment of structure system

The evaluation is based focusing on "shear deformation angle of shear wall”. In this case, a method for

calculating the limit value of deformation angle, which is “limit deformation angle”, is proposed by

applying the index of structural member’s deformation angle to the damage index of the shear wall of

an underground box-type structure. As the results, Figure 19 shows the result of obtaining the member

deformation angle of the time history from the response displacement of the three-dimensional

coupled analysis. Here, the horizontal axis is the shear deformation angle of the shear wall of the

whole-time history, and the vertical axis is the horizontal load applied to the lower end of the shear

wall at that time. In the case of seismic wave 6 times the limit deformation angle occurred and the

deformation angle exceeded. The deformation angle (θmax=0.695%) at the response load peak shows a

value larger than the critical deformation angle (θu=0.365%) which was analysed as the proposed

method by using the structure model of hexahedral solid elements, which is the verification of the

applicability of the critical deformation angle calculation method.

The response maximum deformation angle of the shear wall and front-back wall that was obtained by

loading original, 3 times and 6 times seismic waves of coupled analysis, as shown in Table 2 and

Table 3. In case of 3 times seismic waves, the breakage of the shear wall was occurred first and the

deformation angle of shear wall became a larger value (Sd/Rd =1.03) than “limit deformation angle”.

Figure 19. Relationship between "Out-of-plane deformation angle of member"

and "Horizontal load at lower end of wall"

Table 2. Evaluation result of shear wall

Input wave Original 3 times 6 times

Maximum deformation angle, Sd 0.132 0.377 1.281

Limit deformation angle, Rd 0.365

Examination result, Sd/Rd 0.36 1.03 3.51

Judge OK NG NG

Deformation ratio:100times

(a) Shear wall

0.0E+00

2.0E+05

4.0E+05

6.0E+05

8.0E+05

1.0E+06

0 0.5 1 1.5 2

水平荷重(M

N)

せん断変形角（％）

地震波6倍地震波3倍

地震波1倍限界変形角

θmax＝0.695

θu＝0.365

Ho

rizo

nta

l lo

ad (

kN

)

Deformation angle (%)

6 times

3 times

Original

Limit angle

0.0E+00

1.0E+05

2.0E+05

3.0E+05

4.0E+05

5.0E+05

0 0.5 1 1.5 2

水平荷重(kN)

変形角(%)

地震波6倍地震波3倍

地震波1倍限界変形角

θmax＝1.078

θu＝0.996

(b) Front-back wall

Deformation angle (%)

6 times

3 times

Original

Limit angle

Ho

rizo

nta

l lo

ad (

kN

)

Concrete element that led to compression softening

Open crack

11

Table 3. Evaluation result of front and back wall Input wave Original 3 times 6 times

Maximum deformation angle, Sd 0.220 0.559 1.554

Limit deformation angle, Rd 0.996

Examination result, Sd/Rd 0.22 0.56 1.56

Judge OK OK NG

5. CONCLUSION

(1) As the results of the centrifuge model vibration test and the detailed time history dynamic analysis

by 3D FEM model, we confirmed that it was necessary to select an analysis method that can take

three-dimensional deformation into consideration in seismic performance evaluation.

(2) In designing RC structure, in-plane shear failure of the shear wall is a brittle fracture that causes a

sharp drop in the horizontal yield strength. Therefore, to grasp the damage mode preceding such

fracture, it is necessary to evaluate by a simple method in advance. The deformation and failure

modes of the entire structure can grasp easily by evaluating the inspection of the entire structure

and the out-of-plane and in-plane destruction of each member with one index of only the

deformation angle. It is necessary to grasp the macro response of the whole structure and it is

considered that the proposed method will be useful.

(3) The proposed seismic evaluation method is a simple checking method to compare the critical

deformation angle and the maximum response deformation angle. We expect it to be carried out by

actual seismic performance evaluation in the future. The evaluation results and the proposed

method in this paper are the result of examination by a box type structure with a simplified

structure assuming horizontal stratification ground, and it is necessary to pay attention to the scope

of its application.

6. REFERENCES

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based on inelastic displacement concept.

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Japanese)

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evaluation of reinforced concrete underground structures, Japan Society of Civil Engineers, Earthquake

Engineering, Vol. 27, pp.1~pp.8 (in Japanese)

Naganuma, K., Yonezawa, K., Kurimoto, O. and Eto, H. (2004). Simulation of nonlinear dynamic response of

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Nishimura, A., Murono, Y. (1999). Proposal and Experimental Verification of Soil Nonlinear Model Using GHE

Model and Simple History Rule, The 25th Earthquake Engineering Research Presentation, pp.309-312. (in

Japanese)

a seismic design of the underground box-type rc …

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