2D STATIC MODELLING OF DIP-SLIP FAULTS
USING APPLIED ELEMENT METHOD
応用要素法(AEM)を用いた縦ずれ断層の2次元静的モデリング
From the wide spread damage caused by the recent events, it is now clear that earthquakes in different geological regions
show drastic variations in their effects such as, large surface upliftment/displacements of unconsolidated soil deposits
commonly lying over the active and potentially active faults. For this reason, we attempted to develop a new application ofApplied Element Method (AEM) to study the ground surface deformation near fault rupture zone. First, preliminary analysis iscarried out to check the applicability of the method. Results are compared with the results from analytical and experimental
methods and they showed good agreement. Non-linear modeling is carried out to study the effects of dip-slip faults on theground surface. Detailed study is carried out using two cases of dip angles in both normal and reverse dip-slip fault conditions.
本研究は地下の浅い位置で発生した地震断層の破壊が地表の地盤変状に与えるメカニズムを分析するものである．近年発生したトルコ・コジャエリ地震(Mw7.4，1999年8月17日)や 台湾・集集地震 (Mw.7.5，1999年9月21日)では，断層運動による大きな変位が地表に現れ，この影響で甚大な被害が発生した.
地表に現れる地盤変状の大きさやその位置/分布は，地震断層の破壊メカニズムと地表堆積物の物性や厚さによって大きく変化すると考えられることから，これらの関係の解明は活断層近くに建設される構造の設計をはじめとして，都市計画や国土計画において重要な意味を持つ．特に我が国のように，国土に多数の活断層が分布する地域での重要性は非常に高い．従来この種の研究には実験的な手法が用いられることが多かったが，材料の物性値や境界条件など,実験を実施する上での制約条件が厳しいことから，多様な条件下での解析は不可能であった．一方，数値解析的なアプローチ法では，物性値や境界条件を多様に変化させることは容易であるが，断層の破壊挙動は非線形性の高い大変形挙動であることから，今日一般的に用いられている連続体解析法の適用には限界がある．そこで本研究では，微小変形領域から大変形領域までの挙動を高精度に解析できる応用要素法(AEM：Applied Element Method)を用いて解析を進めている．ここでは研究の第一歩として行った逆断層運動による地表堆積層の静的破壊現象の解析例を紹介する．

FAULT
FAULTTERMINOLOGYTERMINOLOGYCOMPARISONCOMPARISONWITH
WITHEXPERIMENTAL
EXPERIMENTALRESULTSRESULTS

Fault Plane

ANDAND

Shear
Shearband
band

NUMERICALNUMERICALMODEL
MODEL

Dip angle
Surface rupture
Safetyzone

Tension Compression

150 m

Foot WallCo
mpression
Stressratio
ratio
StressTensionBedrock

Soil deposit

SafetySafetyzone
zone

Safetyzone

Hanging Wall

Average
distribution
Averagenormal
normalstressstressdistribution-15

6

Displacement (m)

655m

44m

33m

200123

L/H

COMPARISONCOMPARISONWITHWITHANALYTICALANALYTICALRESULTSRESULTS2m

11m

510-13m

22m

1Ground surface

04m

3Bedrock-5155m41m

00.3-1-1

1.00E+05
7.50E+04
5.00E+04
2.50E+04
0.00E+00-2.50E+04-5.00E+04-7.50E+04-1.00E+05-1.25E+05
0200

400
600
Length (m)

800

1000

020 m
40 m
60 m
120 m
100 m
80 m

200

200

400

400
600
Length (m)

800

1000

1.50E+05
1.25E+05
1.00E+05
7.50E+04
5.00E+04
2.50E+04
0.00E+0-2.50E+04-5.00E+04-7.50E+04-1.00E+050600

Length (m)SURFACE DISPLACEMENT
Stress (kN/m2)

0800

1000

20 m
40 m
60 m

Surface displacement (m)Displacement (m)5Stress (kN/m2)-10

Stress (MPa)1000 mAnalysisAnalysisAnalysisresults
resultsforfordipdipangle
angle==454500
Analysisresults
resultsforfordipdipangle
angle==90
9000

0.2
0.1
01m
2m

-0.1

3m
4m

-0.2

5m

-0.3

120 m
100 m
80 m
200

400
600
Length (m)

800

-750

-600

-450-300

-150

0150

300

450

600

750

600

750

Distance from fault (m)OKADA’S MODEL RESULT

1000
0.3

NORMAL STRESSES IN SOIL DEPOSIT AT REGULAR INTERVALS

5m

0.2

2.50E+04

0.00E+00

Stress (kN/m2)

Stress (kN/m2)

2.50E+04
120 m-2.50E+04

40 m-7.50E+04
20 m-1.00E+05
200

400
600
Length (m)120 m

0.00E+00-2.50E+04

100 m
60 m

80 m

-5.00E+04-1.25E+05
0

Displacement (m)4m

5.00E+045.00E+04

100 m
60 m

80 m

-5.00E+04

1000-1.25E+05
03m

01m
2m

-0.1

40 m

-7.50E+04-0.2

20 m-1.00E+05
800

0.1-0.3

200400600

800

Length (m)SHEAR STRESSES IN SOIL DEPOSIT AT REGULAR INTERVALS

1000-750-600-450-300-1500150300450Distance from fault (m)AEM RESULTMeguro Lab., IIS

2D STATIC MODELLING OF DIP-SLIP FAULTS
USING APPLIED ELEMENT METHOD
応用要素法(AEM)を用いた縦ずれ断層の2次元静的モデリング
REVERSE
REVERSE FAULT
FAULT
41m4m

33m

22m

11m

4m
33m
22m
11m
00-1-1200

400
600
Length (m)1000 0800

SURFACE DISPLACEMENT
2.50E+03

8002Stress (kN/m2)-7.50E+0360 m
20 m 40 m-1.00E+04-1.25E+04-1.50E+04
0200

400600Length (m)1000 0800

120 m

5m

-520 m 40 m 60 m

-1.00E+04
0200

200

400

600

800

400600Length (m)2m-23m-34m-45m

-5-60

1000

200

400

800

800

1000

SURFACE DISPLACEMENT
2.50E+03

80 m 100 m

120 m

80 m

100 m

120 m

20 m

40 m

60 m

200

400

0.00E+00-2.50E+03-5.00E+03 20 m

40 m

60 m

-7.50E+03-1.00E+04-2.50E+03-5.00E+03-7.50E+03-1.25E+04-1.50E+04
0

1000

600

Length (m)0.00E+00-7.50E+03

NORMAL STRESSES-4

2.50E+03

80 m 100 m-2.50E+03-5.00E+034m

SURFACE DISPLACEMENT-2.50E+03-5.00E+03

3m-31m-1

Length (m)2.50E+03
0.00E+00

2m-2-601000

SURFACE DISPLACEMENT

80m 100m 120m

0.00E+00

400600Length (m)200Stress (kN/m2)

000-1
Displacement (m)

5m

4105m

Displacement (m)55Dip
Dipangle
angle==454500

Stress (kN/m2)

6
Displacement (m)Displacement (m)DipDipangle
angle==909000

Dip
Dipangle
angle==454500

Dip
Dipangle
angle==909000

Stress (kN/m2)

NORMALNORMAL FAULTFAULT

200

400600Length (m)8001000-1.00E+040

NORMAL STRESSESNORMAL STRESSES

6008001000

Length (m)NORMAL STRESSESYYDEVELOPEDDEVELOPEDRUPTURERUPTUREZONE
ZONE

X

L1H

DEVELOPEDDEVELOPEDRUPTURERUPTUREZONE
ZONE

X

L2

PARAMETRICPARAMETRIC
STUDY
STUDY

sit
SSooilil DDeeppoo sit
Vd
L e n g th
2 .0 0

3 .0 0H a n g in g w a ll

D ip a n g le = 9 0

2 .5 0D ip a n g le = 4 5

1 .0 0Normalized surface
displacement (m)Normalized surface
displacement1 .5 0
r 2 (= L 2 /H )0 .5 00 .0 0-0 .5 0

F o o t w a llr 1 (= L 1 /H )-1 .0 0
-1 .5 0

2 .0 0r 1 (= L 1 /H )1 .5 0
1 .0 0N o rm a l fa u lt
R e v e rs e fa u lt

0 .5 00 .0 0
-0 .5 0r 2 (= L 2 /H )-1 .0 0
-1 .5 0

-2 .0 0-2 .0 00246810120

H a n g in g w a ll d is p la c e m e n t (m )3045607590

D ip a n g leEFFECT OF HANGING WALL DISPLACEMENTEFFECT OF DIP ANGLE
2 .0 0

2 .0 0r 1 (= L 1 /H )1 .5 0H a n g in g w a ll

1 .5 0r 2 (= L 2 /H )1 .0 0

1 .0 00 .5 0Normalized surface
displacement

Normalized surface
displacement

15D ip a n g le = 4 5 d e g re e s

0 .0 0D ip a n g le = 9 0 d e g re e s-0 .5 0
-1 .0 0
-1 .5 0r 2 (= L 2 /H )0 .5 00 .0 0-1 .5 0
-2 .0 0-2 .5 0-2 .5 045607590105

120T h ic k n e s s o f d e p o s it (m )EFFECT OF THICKNESS

135150r 1 (= L 1 /H )D ip a n g le = 9 0-1 .0 0-2 .0 030

D ip a n g le = 4 5-0 .5 0F o o t w a ll
510152025230

35

M o d u lu s o f e la s tic ity (k N /m )EFFECT OF STIFFNESS

Meguro Lab., IIS