ᕤᏛⓗᇶ┙䛾ഴᩳ䛜ᆅ┙㟈ື≉ᛶ䛻ཬ䜌䛩ᙳ㡪䛻㛵䛩䜛◊✲䠄1䠅ᘓ⠏◊✲ᡤᅜ❧◊✲㛤Ⓨἲேᵓ㐀◊✲䜾䝹䞊䝥䚷୺௵◊✲ဨ䚷୰ᕝ༤ே

1. 䛿䛨䜑䛻䖃㻌ᆅ㟈᫬ࡢᒁᡤⓗ䛺⿕ᐖ䜔䜖䜜䛾኱䛝䛥䜢ㄝ᫂䛩䜛⌮⏤䛾䜂䛸䛴䛸䛧䛶䚸 ┅ᆅᵓ㐀䜔ᇶ┙ഴᩳᵓ㐀䛺䛹䛾୙ᩚᙧᆅ┙䛾㻌 ᙳ㡪䛜ᣦ᦬䛥䜜䛶䛔䜛䚹 䠄e. g., Kawase[1996]; ΎỈ 䞉 ๓⏣ [2010]䠅
䖃㻌୙ᩚᙧᆅ┙䛾᳨ウ䛿ྂ䛟䜘䜚䛺䛥䜜䛶䛔䜛 䠄e. g., ⧴⧭ [1991]䠅 䛜䚸 ᆅ┙ㄪᰝ⤖ᯝ䛾䛒䜛䝃䜲䝖䛻䛚䛡䜛ᆅ㟈ほグ㘓䛸䛾㻌 ẚ㍑ 䞉 ᳨ド䛿ᚲ䛪䛧䜒༑ศ䛷䛺䛟䚸 ᳨ウ஦౛䛾⵳✚䛜㔜せ䛷䛒䜛䚹䖃㻌᪤ 䛾᳨ウ䛿 2 ḟඖゎᯒ䛜ከ䛟䚸 ධᑕἼື䛜᪉఩ゅ 䞉 ධᑕゅ䜢᭷䛩䜛ሙྜ 㻔2.5 ḟඖゎᯒ 㻕 䜔㻌3 ḟඖⓗ䛺ຠᯝ 㻔3 ḟඖゎ㻌 ᯒ 㻕 ➼䛻䛴䛔䛶䛾᳨ウ䛿ᑡ䛺䛔䚹㻌 ᮏ◊✲䛷䛿䚸 ᐇ㝿䛾ᇶ┙ഴᩳ䝃䜲䝖䜢ᑐ㇟䛻ほグ㘓䛸䛾ẚ㍑䜢⾜䛖䛸䛸䜒䛻䚸㻌 2.5 ḟඖ䛚䜘䜃 3 ḟඖゎᯒ䛻ᇶ䛵䛝ᇶ┙䛾ഴᩳ䛜ᆅ┙㟈ື≉ᛶ䛻ཬ䜌䛩ᙳ㡪䛻䛴䛔䛶᳨ウ䛧䛯䚹

2. ゎᯒᡭἲ䛸ゎᯒ䝥䝻䜾䝷䝮䛾᳨ドNormalized Amplitude8䖃㻌୙ᩚᙧᆅ┙䛻ᑐ䛧䛶௵ព䛾᪉఩ゅ 䞉 ධᑕゅ䜢᭷䛩䜛ධᑕἼື䜢⪃៖䖃㻌ゎᯒᡭἲ䛿᭷㝈せ⣲ἲ䛸ษḞ䛝ᆺ䛾ືⓗ䝃䝤䝇䝖䝷䜽䝏䝱䞊ἲ

Normalized Amplitude( ୰஭ [1985]) 䛻ᇶ䛵䛔䛶䛔䜛䚹 䛩䛺䜟䛱䚸 ゎᯒᑐ㇟䜢᭷㝈せ⣲䛻㻌 䜘䜚䝰䝕䝹໬䛧䛶䚸 ቃ⏺䛻䜲䞁䝢䞊䝎䞁䝇 [Kc*] 䜢௜ຍ䛩䜛䛸䛸䜒䛻㻌 䝗䝷䜲䝡䞁䜾䝣䜷䞊䝇 {fc*} = [Kc*]{uc}+{pc} 䜢ධຊ䛧䛶䛔䜛䚹㻌 㻔{uc} 䛿ኚ఩䚸 {pc} 䛿ษḞ䛝ຊ䛷䛒䜛䚹 㻕䖃㻌సᡂ䝥䝻䜾䝷䝮䛾᳨ド䛾䛯䜑䚸 ᅗ 1 ྑୖ䛻♧䛩Ἀ✚㇂ᆅ┙䜢ᑐ㇟䛻䚸㻌 ᪤ 䛾⤖ᯝ 㻔 ᅗ 1 ୰䛾䕿䚸 de Barros & Luco[1995]㻕 䛸䛾ẚ㍑䜢⾜䛔䚸㻌 ୧⪅䛜䜋䜌୍⮴䛧䛶䛔䜛䛣䛸䜢☜ㄆ䛧䛯䚹

Normalized Amplitude㻌䛩䜛䛣䛸䛾䛷䛝䜛ゎᯒ䝥䝻䜾䝷䝮䜢సᡂ䛧䛯䚹 (Nakai & Nakagawa[2014])

8Ux

66442Ux

Ψ=0°(Vert. Inci.)
Ψ=30°
Ψ=60°

Geometry ofvalley embedded
in a half-space20-3 -2
4Uy-1

01203 -3 -2
12Uy-1012

Ψ=0°(Vert. Inci.)
Ψ=30°
Ψ=60°

312

3

92

66

1

3

30-3 -2
8Uz

-1

01

2

30-3 -2
8Uz-1

90
3 -3 -28Uz
Ψ=0°(Vert. Inci.)
01

2

Ψ=30°
Ψ=60°

664

442220-3-2-1

01y /a20
3 -3-2-1

Uy-1

0123-101y /a23601y /a

203 -3-2                 ࠉ         ᅗ 1Ἀ✚㇂ᆅ┙࡟࠾ࡅࡿᆅ⾲㠃ᛂ⟅ゎࡢẚ㍑

3. ᇶ┙ഴᩳ䝃䜲䝖䛻䛚䛡䜛ほグ㘓䛸䛾ẚ㍑䚷㻙 ᳨ウᑐ㇟䝃䜲䝖䛾ᴫせ 㻙䖃㻌ᕤᏛⓗᇶ┙䛜ഴᩳ䛧䛶䛔䜛䝃䜲䝖 㻔 䛔䜟䛝ᕷᙺᡤ 㻕 䜢ᑐ㇟䛻ᆅ㟈ほ䖃㻌ᩜᆅෆ䛷䛿 2011 ᖺ䛾ᮾ໭ᆅ᪉ኴᖹὒἈᆅ㟈䛾వ㟈ほグ㘓䛸䛾ẚ㍑䜢⾜䛳䛯䚹䛜ᐇ᪋䛥䜜䛶䛚䜚䚸 ᩜᆅ䛾໭ഃ 㻔GL-N㻕 䛸༡ഃ 㻔GL-S㻕 䛷༟㉺㻌 ࿘ᮇ䛜䛭䜜䛮䜜 0.2s ⛬ᗘ䛸 0.8s ⛬ᗘ䛻ㄆ䜑䜙䜜䚸 ␗䛺䜛䛣䛸䛜☜ㄆ䛥䜜䛶䛔䜛䚹䖃㻌ᆅ┙ㄪᰝ⤖ᯝ䛻ᇶ䛵䛝⾲ᒙᆅ┙䝰䝕䝹䜢సᡂ䛧䚸 ᩜᆅෆ䛾ᚤືほ㮵ᔱ࣭௚ [2011] ࠉグ㘓䛸䛾ẚ㍑䜢⾜䛳䛶䛔䜛䚹ᅗ 2䚸 ୰ᕝ࣭௚ [2015]䖃㻌୰ᕝ࣭௚ [2015] 䛻䜘䜛⾲ᒙᆅ┙䝰䝕䝹䜢䜒䛸䛻ᅗ 3 䛻♧䛩 FEM ゎᯒ䝰䝕䝹䜢సᡂ䛧䛯䚹N

GL-NW

Depth [m]Azimuth angle,ȭ

E

X(NS dir.)S

GL-C

Incident angle,Ψ

Y(EW dir.)Embedded Rigid Foundation(30x60x9m)

Z
Soil Properties

Incident S-wave
GL-S

GL-C

GL-N

36m

GL-S

36m

Underlying Layer (Bedrock)

2063m

0m

9m

Vs[m/s]120

Vp[m/s]560

Density[kg/m3]
1600

150

560

1800

120

1000

1600

200

1390

1800

410

1720

1900

Damping Factor = 7.5 / Vs200m

ᅗ 2 ᕤᏛⓗᇶ┙ୖ㠃῝ᗘศᕸ㸦ୖ ࡜ N ್ศᕸ࠾ࡼࡧ     ᅗ 3 FEM ゎᯒ࡟౑⏝ࡋࡓࣔࢹࣝࡢᴫせ㻌 㻌 PS ᳨ᒙ⤖ᯝ ୗ 㸦୰ᕝ࣭௚ [2015] ࡟ຍ➹㸧           㸦Nakagawa et al.[2015]㸧

ᕤᏛⓗᇶ┙䛾ഴᩳ䛜ᆅ┙㟈ື≉ᛶ䛻ཬ䜌䛩ᙳ㡪䛻㛵䛩䜛◊✲䠄2䠅ᅜ❧◊✲㛤Ⓨἲே

3. ᇶ┙ഴᩳ䝃䜲䝖䛻䛚䛡䜛ほᘓ⠏◊✲ᡤᵓ㐀◊✲䜾䝹䞊䝥䚷୺௵◊✲ဨ䚷୰ᕝ༤ேグ㘓䛸䛾ẚ㍑䚷㻙 ゎᯒ⤖ᯝ 㻙

䖃㻌ᅗ 3 䛾 FEM 䝰䝕䝹䛻ᑐ䛧䚸 ᪉఩ゅ 45°䛾 SV Ἴ䜢ධᑕ䛧䛯䚹 ධᑕゅࡣ 3 䜿䞊䝇 㻔0°䚸 10°䚸 20°㻕 䛸䛧䛯䚹䖃㻌ᅗ 4 ᕥ䛾䝇䝘䝑䝥䝅䝵䝑䝖䜢ぢ䜛䛸䚸 ᇶ┙䛾ഴᩳ䜔ᇶ♏䛾Ꮡᅾ䛻䜘䜚Ἴືሙ䛜」㞧䛸䛺䛳䛶䛔䜛䛣䛸䛜䜟䛛䜛䚹䖃㻌వ㟈グ㘓䛾䝇䝨䜽䝖䝹ẚ䛸䛾ẚ㍑ 㻔 ᅗ 4 ྑ 㻕 䜢ぢ䜛䛸䚸 3-4Hz ௜㏆䛷 1 ḟඖゎᯒ⤖ᯝ䛻䛿⌧䜜䛺䛔䝢䞊䜽䛜ㄆ䜑䜙䜜䜛䚹䖃㻌௒ᅇ䛾ゎᯒ᮲௳ୗ䛷䛿䚸

4

Induced by inclined boundary
Amplitude ratio㻌 ධᑕゅ䛾㐪䛔䛻䜘䛳䛶㻌 ゎᯒ⤖ᯝ䛿኱䛝䛟䛿ኚ䜟㻌 䜙䛺䛔䜘䛖䛻ぢ䛘䜛䛜䚸㻌 ⾲ᒙᆅ┙䛾䝟䝷䝯䞊䝍➼

40º10º220002468
Frequency [Hz]10(a) 2.5-D Analysis (w/o Foundation)㻌 ᚲせ䛷䛒䜛䚹

20º20㻌 䛻䛴䛔䛶䛥䜙䛺䜛᳨ウ䛜

402468Frequency [Hz]1002468
Frequency [Hz]10(a) 2.5-D Analysis (w/o Foundation)
4

Induced by inclined boundary

44

Amplitude ratio

Scattered wave
0º10º20º22200002468
Frequency [Hz]10(b) 3-D Analysis (with Foundation)

02468
Frequency [Hz]1002468
Frequency [Hz]10(b) 3-D Analysis (with Foundation)

ᅗ 4 ࣜࢵ࣮࢝Ἴධᑕ᫬ࡢࢫࢼࢵࣉࢩࣙࢵࢺ㸦ᕥ ࡜ゎᯒ⤖ᯝ࡜ほ グ㘓࡜ࡢẚ㍑ ྑ㻌 㻌 㻌 䝸䝑䜹䞊Ἴ䛾୰ᚰ࿘Ἴᩘ䛿 4Hz 䛷㖄┤ୗ᪉ධᑕ᫬䛾䜿䞊䝇䜢♧䛧䛶䛔䜛䚹 㸦Nakagawa et al.[2015]㸧

4. ᇶ┙䛾ഴᩳゅᗘ䛾㐪䛔䛜ᆅ┙㟈ື≉ᛶ䛻୚䛘䜛ᙳ㡪
䖃㻌3 ✀㢮䛾ᇶ┙ഴᩳゅ 㻔45°䚸 18.4°䚸 6.3°㻕 䜢᭷䛩䜛஧ᒙᆅ┙ 㻔 ᅗ 5㻕 䜢ᑐ㇟䛻䚸 㻿 Ἴ䛾㖄┤ୗ᪉ධᑕ䛻䜘䜛ゎᯒ䜢ᐇ᪋䛧䛯䚹㻌 䛺䛚䚸 ධᑕἼ䛾᣺ື᪉ྥ䛻䜘䜛㐪䛔䛻䛴䛔䛶䜒᳨ウ䛩䜛䛯䜑᪉఩ゅ䜢 3 ࢣ࣮ࢫ 㻔0°䚸 45°䚸 90°㻕 䛸䛧䛯䚹䖃㻌ఏ㐩㛵ᩘ 㻔 ᅗ 6 ᕥ 㻕 䜢ぢ䜛䛸䚸 ᆅ┙䛾 1 ḟᅛ᭷᣺ືᩘ௜㏆䜘䜚䜒㧗᣺ືᩘ

Massless Foundation
20x20x10m

X㻌 ഃ䛻䛚䛔䛶䚸 ᇶ┙䛾ഴᩳ䛚䜘䜃ධᑕἼ䛾᣺ື᪉ྥ䛻䜘䜛ᙳ㡪䛜ㄆ䜑䜙䜜䜛䚹

Vs=200m/s

12mZ

Vs=200m/s

12mθθ
Vs=400m/s

X㻌 䛻䜘䜚ᇶ┙ഴᩳ䛾ᙳ㡪䛿┦ᑐⓗ䛻ᑠ䛥䛟䛺䜛䛣䛸䛜䜟䛛䜛䚹 ᵓ㐀≀䜈䛾ධຊ㻌 䛸䛔䛖ほⅬ䛛䜙䛩䜛䛸䚸 ᆅ┙䛸ᇶ♏䛾᮲௳䛻䜘䛳䛶䛿㧗᣺ືᩘഃ䛷ධຊᦆኻ0ºY

Vibration
Direction

Transfer function䖃㻌ᇙ㎸䜏๛ᇶ♏䛜䛒䜛ሙྜ䛾ఏ㐩㛵ᩘ 㻔 ᅗ 6 ྑ 㻕 䜢ぢ䜛䛸䚸 ධຊ䛾┦஫స⏝

Ndofs = 323,727

XYղ
VS=400m/s
VP=800m/s
ρ =1500kg/m3
h=0.01

Rigid Foundation(20x20x10m)

Z12m

X
45º
Rigid Foundation(20x20x10m)

12m

88m

12m

ձ

18.4º
88m

88m

X76m

12120m11w/o Foundation
002
462with Foundation
0024
68 102
Horizontally Layeredθ = 45°
θ = 18.4°
θ = 6.3°

76m

120m
120m

810

100224m

ղ0m

Vibration
Direction

20m
120m

Y90ºVibration
Directionwith Foundation

246810100

Horizontally Layeredθ = 45°
θ = 18.4°
θ = 6.3°

1w/o Foundation
6.3º

24m

76m

12Y

Vs=400m/s

212m

24m

45º

Rigid Foundation(20x20x10m)

Transfer functionձ
VS=200m/s
VP=800m/s
ρ =1500kg/m3h=0.01

Transfer function㻌 ຠᯝ䛜ぢ㎸䜎䜜䜛ሙྜ䜒䛒䜚䚸 ᐇ㝿䛾≧ἣ䛻༶䛧䛯᳨ウ䛜ᮃ䜎䜜䜛䚹

24m

0022468 10
Horizontally Layeredθ = 45°
θ = 18.4°
θ = 6.3°

1w/o Foundation
2468Frequency [Hz]1000with Foundation
2468Frequency [Hz]10& Nakai[2014]㸧     ᅗ 6 ఏ㐩㛵ᩘࡢẚ㍑ᅗ 5 FEM ゎᯒࣔࢹࣝ ᕥ࠿ࡽഴᩳゅ 45°ࠊ18.4°ࠊ6.3° 㸦Nakagawa
ㅰ㎡䛔䜟䛝ᕷᙺᡤ䜘䜚ᆅ┙ㄪᰝ㈨ᩱ䜢䚸 ⚟ᓥ┴䜘䜚ᆅ㟈ほグ㘓䜢䛤ᥦ౪䛔䛯䛰䛝䜎䛧䛯䚹 వ㟈ほ䞉 ᚤືほ䛔䜟䛝ᕷᙺᡤ䚸 ᘓ⠏◊✲ᡤ䛾௚䚸 䛯䛟䛥䜣䛾᪉䚻䛻䛤༠ຊ䜢䛔䛯䛰䛝䜎䛧䛯䚹 グ䛧䛶ㅰព䜢⾲䛧䜎䛩䚹䛾ᐇ᪋䛻䛒䛯䜚䚸