➨10ᅇ ᵓ㐀≀ࡢ⾪ᧁၥ㢟㛵ࡍࡿࢩ࣏ࣥࢪ࣒࢘ㄽᩥ㞟( 2010ᖺ12᭶) ᅵᮌᏛ
ಶูせ⣲ἲࢆ⏝࠸ࡓỈᖹሁ✚ᒙ࠾ࡅࡿⴠ▼ࡼࡿ⾪ᧁຊࡢఏ㐩ᣲືゎᯒ
Propagation analysis of impact force of rockfall into granular mat using DEM
ส⏣ᆂ୍*㸪๓⏣୍**㸪⩚ᰘᐶᩥ***㸪∵Ώ⿱****㸪ᕝ℩Ⰻྖ*****
Keiichi Karita, Kenichi Maeda, Hirofumi Hashiba, Yuji Ushiwatari, Ryoji Kawase
*ᵓ◊࢚ࣥࢪࢽࣜࣥࢢ㸪㜵⅏タ㒊㸦ࠛ065-8510ᮐᖠᕷᮾ༊18᮲ᮾ17┠1-1㸧
**ᕤ༤㸪ྡྂᒇᕤᴗᏛ㸪㒔ᕷ♫ᕤᏛ⛉㸦ࠛ466-8555ྡྂᒇᕷ༊ᚚჾᡤ⏫㸧
***ྡྂᒇᕤᴗᏛᏛ㝔㸪༤ኈ๓ᮇㄢ⛬㸪♫ᕤᏛᑓᨷ㸦ࠛ466-8555ྡྂᒇᕷ༊ᚚჾᡤ⏫㸧
****ᵓ◊࢚ࣥࢪࢽࣜࣥࢢ㸪㜵⅏タ㒊㸦ࠛ065-8510ᮐᖠᕷᮾ༊18᮲ᮾ17┠1-1㸧
*****ᕤ༤㸪ᵓ◊࢚ࣥࢪࢽࣜࣥࢢ㸪ྲྀ⥾ᙺ㸦ࠛ065-8510ᮐᖠᕷᮾ༊18᮲ᮾ17┠1-1㸧
Key Words:(granular mat, rock impact, propagated impact, Discrete Element Method , stress wave, particle ability)
࣮࣮࢟࣡ࢻ㸸ሁ✚ᒙ㸪ⴠ▼⾪ᧁຊ㸪ఏ㐩⾪ᧁຊ㸪ಶูせ⣲ἲ㸦DEM㸧㸪ᛂຊఏ㐩㸪⢏Ꮚ≉ᛶ
㸬ࡣࡌࡵ
ᡃࡀᅜ࠾࠸࡚㸪ẖᖺከࡃࡢⴠ▼ᨾࡀⓎ⏕ࡋ࡚࠾ࡾ㸪
ࡲࡓⓎ⏕௳ᩘࡣቑຍഴྥ࠶ࡿ㸬㏆ᖺ࡛ࡣ㸪ⴠ▼⅏ᐖࢆ
㜵ࡄᑐ⟇ᕤࡣ⤒ᖺຎᑐᛂ࡛ࡁࡎ㸪Ᏻవ⿱ᗘࡀపୗ
ࡋ࡚࠸ࡿ㸬
᭱㏆࡛ࡣࡑࡢᑐᛂࡋ࡚㸪ⴠ▼ࡀ㜵ㆤᕤ⾪✺ࡍࡿ๓
ⴠ▼࢚ࢿࣝࢠ࣮ࢆศᩓ࣭పῶࡉࡏࡿᕤἲ࡛࠶ࡿⴠ▼㜵 ㆤࢿࢵࢺࡸሁ✚ᒙὀ┠ࡀ㞟ࡲࡗ࡚࠸ࡿ㸬ࡲࡓ㸪ࣟࢵࢡ ࢩ࢙ࢵࢻୖ㠃タ⨨ࡉࢀࡿᩜ◁࡞ࡢ⦆⾪ᮦࡶࡇࢀ
ヱᙜࡍࡿ㸬ሁ✚ᒙࡣⴠ▼ࡢࡁ࡞࢚ࢿࣝࢠ࣮ࡲ࡛ᑐᛂ
࡛ࡁࡿ≉ᚩࡀ࠶ࡾ㸪ᮏ◊✲࡛ࡣࡇࡢሁ✚ᒙ╔┠ࡍࡿ㸬 ሁ✚ᒙࡢຠᯝࡣ㸪ⴠ▼㏿ᗘࢆᢚ࠼ࡿࡇࡼࡿⴠ▼࢚
ࢿࣝࢠ࣮ࡢపῶࡸ⾪ᧁຊࡢపῶ࡞ࡀᣲࡆࡽࢀ㸪ẚ㍑ⓗ
పࢥࢫࢺ࡛࠶ࡾ࡞ࡀࡽᏳవ⿱ᗘࢆຠᯝⓗྥୖࡉࡏ
ࡽࢀࡿྍ⬟ᛶࡀ࠶ࡿ㸬ࡑࡇ࡛ᮏ◊✲࡛ࡣ㸪ሁ✚ᒙࡢⴠ▼
࢚ࢿࣝࢠ࣮పῶᛶ⬟╔┠ࡋ㸪ⴠ▼ࡼࡿ⢏≧ᛶࡢሁ✚
ᒙෆࡢ⾪ᧁຊఏ㐩ᣲືࡘ࠸࡚ಶูせ⣲ἲ㸦Discrete Element Method: DEM㸧1)ࢆ⏝࠸࡚ㄪࡓ㸬ⴠ▼ࡼࡿⴠ యࡢཷࡅࡿ⾪ᧁຊ㸦ⴠ▼⾪ᧁຊ㸧ᗏ㠃ఏ㐩ࡍࡿ⾪ᧁ ຊ㸦ఏ㐩⾪ᧁຊ㸧ࡘ࠸࡚㸪ゎᯒ⤖ᯝ1/2ࢫࢣ࣮ࣝࡢ ᶍᆺᐇ㦂⤖ᯝࢆẚ㍑ࡋ㸪DEM ゎᯒࡀᐃ㔞ⓗ⾪ᧁຊࢆ
⾲⌧ྍ⬟࡛࠶ࡿࡇࢆ♧ࡋࡓୖ࡛㸪⢏Ꮚ◳ᗘ㸪⢏ᚄ㸪⢏
Ꮚᙧ≧࠸ࡗࡓ⢏Ꮚ≉ᛶ㸪ሁ✚ᐦᗘࡸᒙཌ࠸ࡗࡓሁ✚
≉ᛶࡀࣆ࣮ࢡ⾪ᧁຊཬࡰࡍᙳ㡪ࡘ࠸࡚ㄪࡓ㸬ࡉࡽ
㸪ᒙཌࡸᐦᗘࡀ␗࡞ࡿሁ✚ᒙఏ㐩ࡍࡿ⾪ᧁຊࡢ้
Ṕሁ✚ᒙෆࡢᛂຊ࣭ࡦࡎࡳศᕸࡸ࢚ࢿࣝࢠ࣮ᾘᩓࡢ 㛵ಀࡘ࠸࡚ㄪࡓ㸬ⴠయ≉ᛶࡘ࠸࡚ࡣ㸪㖄┤ⴠୗࡢ ሙྜࡢሗ࿌ࡍࡿ㸬
⾪ᧁຊ㛵ࡍࡿᶍᆺᐇ㦂 '(0 ゎᯒ⤖ᯝࡢẚ㍑
ᶍᆺᐇ㦂࠾ࡼࡧ '(0 ゎᯒࡢᴫせ
ᅗ㸫1♧ࡍࡼ࠺㸪ᐇ㦂ࡣࢡ࣮࡛ࣞࣥᣢࡕୖࡆࡓ㗽
ࢆ1/2ࢫࢣ࣮ࣝࡢࣟࢵࢡࢩ࢙ࢵࢻୖ㠃タ⨨ࡉࢀࡓሁ✚
ᒙ㖄┤⮬⏤ⴠୗࡉࡏࡿࡶࡢ࡛࠶ࡿ㸬ᐇ㦂࡛ࡣ㗽タ⨨
ࡉࢀࡓຍ㏿ᗘィࡢ್㗽㉁㔞ࡢ✚࡛ồࡵࡽࢀࡿࠕⴠ▼⾪
ᧁຊࠖᗏ㠃యఏ㐩ࡋࡓຊࡢྜィ࡛࠶ࡿࠕఏ㐩⾪ᧁ ຊࠖࡀᚓࡽࢀࡿ㸬ࡇࡇ࡛ࡣ㸪㖄┤᪉ྥࡢຊࡘ࠸࡚ࡢࡳ
᳨ウࡍࡿ㸬ఏ㐩⾪ᧁຊࡣ㸪⦆⾪ᮦᗏ㠃ࡢ๛ᇶ♏」ᩘᇙ
ࡵ㎸ࡵ㎸ࡲࢀࡓⲴ㔜ィ(࣮ࣟࢻࢭࣝ)ࡢ್ࢻ࣮ࢼࢶ≧ࡢ ᗏ㠃ศ⥺ෆࡢ㠃✚ࡢ✚ࡼࡾồࡵࡽࢀ࡚࠸ࡿ㸬ࡲࡓ
๓ሁ✚ᒙ࡛ᐇࡉࢀࡓᆅ┙ㄪᰝ⤖ᯝࢆ⾲♧ࡍ㸬㗽㔜 ࡉࡸⴠୗ㧗ࡉ➼ࡢᐇ㦂᮲௳ࡣࡇࡇ࡛ࡣ⾲㸫1ࡢ3ࢣ࣮ࢫ ࡢ⤖ᯝࡢࡳࢆཧ↷ࡋࡓ㸬
1/2䝇䜿䞊䝹䛾䝻䝑䜽䝅䜵䝑䝗 ⴠୗ㧗䛥
㗽
ሁ✚ᒙ䠄ᩜ◁䠅
ᅗ㸫1 ⾪ᧁᶍᆺᐇ㦂ࡢᵝᏊ
㪈㪐㪌
(37)
'(0 ゎᯒࡢᴫせ
ᮏㄽᩥ࡛ࡣ㸪せ⣲㛫ࡢ᥋ゐࣔࢹࣝᆶ┤࣭᥋⥺᪉ྥࡢ
ࣂࢿࡸࢲࢵࢩ࣏ࣗࢵࢺ㸪᥋⥺᪉ྥࡢࢫࣛࢲ࣮࠸ࡗࡓ
㏻ᖖࡢࣔࢹࣝࢆࡗࡓ2ḟඖDEMゎᯒࢆ⾜ࡗࡓ㸬⏝࠸
ࡓゎᯒࣃ࣓࣮ࣛࢱࡣ㸪⢏Ꮚ㞟ྜయࡢ≉ᛶ⢏Ꮚ≉ᛶࡢ
㛵ಀ2)-8)ࢆ⪃៖ࡋ࡚Ỵᐃ࡛ࡁࡿࡼ࠺࣐ࢽࣗࣝࡋ9)㸪
⾲㸫1♧ࡍᆅ┙ㄪᰝ⤖ᯝ࡞ࢆᇶỴᐃࡋࡓ㸬ᇶᮏⓗ
࡞ゎᯒࣔࢹࣝࣃ࣓࣮ࣛࢱࢆᅗ㸫2(a)♧ࡍ㸬ᗏ㠃ഃ
㠃ࡢቃ⏺ࡢ⢏Ꮚ⨨ࡣᅛᐃࡋࡓ㸬ࡇࡇ࡛㸪᥋ゐ㠃ᆶ┤
᪉ྥ᥋⥺᪉ྥࡢࡑࢀࡒࢀࡢࡤࡡᐃᩘ kn ksࡢẚࡣ kn/ks=4ࡋ㸪ῶ⾶ᐃᩘࡣ⮫⏺ῶ⾶h=1.0ࡓ㸬ࡲࡓ㸪ᮏㄽ
ᩥ࡛ࡣ㸪ᙧ⢏Ꮚࡢࡳࡢ⤖ᯝࢆ♧ࡍ㸬
⾲㸫1 ᶍᆺᐇ㦂㛵ࡍࡿᆅ┙ㄪᰝ⤖ᯝᐇ㦂᮲௳
ᆅ┙ㄪᰝ⤖ᯝ ᐇ㦂᮲௳
N್ - 1.0 㗽᮲௳
୍⯡
ᅵ⢏Ꮚࡢᐦᗘ g/cm3 2.68 ⴠୗ㧗ࡉ
⮬↛ྵỈẚ % 13.2 CASE01 m 10.0 ᆒ➼ಀᩘ - 2.1 CASE02 m 20.0 ศ㢮 ᆅ┙ᮦᩱࡢศ㢮 - ศ⣭ࡉࢀࡓ◁ CASE03 m 30.0
ศ㢮グྕ - (SP) ᙧ≧ - ⌫ᙧ
⥾ᅛࡵ ᭱⇱ᐦᗘ g/cm3 1.48 㗽㔜㔞 t 2.0
᭱㐺ྵỈẚ % 19.9 ┤ᚄ m 1.0
᭱ᑠᐦᗘ࣭
᭱ᐦᗘ
᭱㛫㝽ẚ - 1.14 ሁ✚ᒙ᮲௳
᭱ᑠ㛫㝽ẚ - 0.70 ᖜ×㛗ࡉ m 4.0×4.0
◁⨨ἲ
ࡼࡿᐦ ᗘヨ㦂
ྵỈẚ % 12.4 ᒙཌ m 0.9
‵₶ᐦᗘ g/cm3 1.53
⇱ᐦᗘ g/cm3 1.36
Df
x y o
T
W fall mass
granular mat (grain shape, Dmax, Dmin, 䃠s,
䃥䃛, kn, ks, h) (Df, 䃠fs, 䃥f䃛, kfn, kfs)
H Mf
(a)
(b) ᅗ㸫2 DEMゎᯒࣔࢹࣝ㸸(a)ゎᯒࣃ࣓࣮ࣛࢱ; (b)࣓ࢵࢩ
ࣗࢆ⏝࠸ࡓᛂຊ࣭ࡦࡎࡳቑศ࣭㛫㝽ẚࡢ⟬ᐃ
ࡉࡽ,ᆅ┙ࢆ㐺ᙜ࡞㡿ᇦ㸦࣓ࢵࢩࣗ㡿ᇦ㸹㸧࡛ศࡋ㸪
⢏Ꮚస⏝ࡍࡿ᥋Ⅼຊࢆ࣓ࢵࢩࣗෆࡢ⢏Ꮚࡀ༨ࡵࡿ㠃
✚࡛ᖹᆒࡍࡿࡇ࡛ᛂຊࢆ⟬ฟࡋࡓ㸦ᅗ㸫2(b)㸧㸬ᮏㄽ
ᩥ࡛ࡣ㸪0.1m×0.1mࡢ࣓ࢵࢩࣗࡋࡓ㸬ఏ㐩⾪ᧁຊࡣ㸪
ୖグ࣓ࢵࢩࣗᛂຊࡢ⟬ฟᚋ㸪ᗏ㠃࠾ࡅࡿఏ㐩㖄┤ᛂຊ ᡂศࡢ⪃࠼ࡿࡇࡀ࡛ࡁࡿ㸬2ḟඖDEM࡛ᚓࡽࢀ
ࡿᗏ㠃ࡢఏ㐩㖄┤ᛂຊࡣ㸪ዟ⾜ࡁ᪉ྥ༙↓㝈ࡢሁ✚ᒙ
ⴠ▼Ⲵ㔜ࡀ⥺㍕Ⲵ࡛ຍ࠼ࡽࢀࡓ㝿ࡢ㖄┤ᛂຊ⪃࠼
ࡿࡇࡀ࡛ࡁࡿ㸬ࡑࡢࡓࡵ㸪ᐇ㦂㸦3ḟඖ㸧࡛⾜ࢃࢀࡓ ఏ㐩⾪ᧁຊᐃ㔞ⓗ࡞ẚ㍑ࡀ࡛ࡁ࡞࠸㸬ࡑࡇ࡛,ࡲࡎ㸪ࣈ
ࢩࢿࢫࢡゎࡢⅬ㍕Ⲵ⥺㍕Ⲵࡢᗏ㠃ࡢ⨨࡛ᚓࡽࢀ
ࡿ㖄┤ᛂຊゎࢆẚ㍑ࡋ㸪DEM ゎᯒ࡛ᚓࡽࢀࡓᗏ㠃ࡢఏ 㐩㖄┤ᛂຊࢆⅬ㍕Ⲵస⏝ᚓࡽࢀࡿ࡛࠶ࢁ࠺ᛂຊ
ಟṇࡍࡿ㸬ḟ㸪ఏ㐩㖄┤ᛂຊࡣ㖄┤㍈y㍈୰ᚰྠᚰ
≧୍ᵝศᕸࡍࡿࡳ࡞ࡋ㸪y ㍈୰ᚰᅇ㌿ࡉࡏࡓ
࣓ࢵࢩࣗᑐᛂࡍࡿᗏ㠃㠃✚స⏝ࡉࡏࡓࡁࡢఏ㐩 ຊࡢࢆồࡵ㸪ࡇࢀࢆ⿵ṇࡋࡓఏ㐩⾪ᧁຊࡋࡓ㸬ᮏ❶
࡛ࡣ㸪ᐇ㦂⤖ᯝࡢẚ㍑ࡢࡓࡵ⿵ṇࡋࡓఏ㐩⾪ᧁຊࢆ
⏝࠸ࡿ㸬ḟ❶௨㝆ࡣ㸪ィ⟬ࡢ⡆␎ࡢࡓࡵ㸪ᗏ㠃⢏Ꮚࡀ ᗏ㠃ቃ⏺ఏ㐩ࡍࡿຊࡢࢆఏ㐩⾪ᧁຊ㸦2ḟඖィ⟬ࡢ
ࡲࡲࡢ್㸧ࡋ࡚࠸ࡿ㸬
0 100 200 300 400 500
0 1000 2000
3000 ࠉⴠ▼⾪ᧁຊ
ࠉఏ⾪ᧁຊ
㛫(ms)
⾪ᧁຊ (kN) ᐇ㦂⤖ᯝࠉCASE 01 Hf=10m
0 100 200 300 400 500
0 1000 2000
3000 ࠉⴠ▼⾪ᧁຊ
ࠉఏ⾪ᧁຊ
⾪ᧁຊ (kN)
㛫 (ms) ゎᯒ⤖ᯝࠉCASE 01 Hf=10m
0 100 200 300 400 500
0 1000 2000
3000 ࠉⴠ▼⾪ᧁຊ
ࠉఏ⾪ᧁຊ
⾪ᧁຊ (kN)
㛫(ms) ᐇ㦂⤖ᯝࠉCASE 02 Hf=20m
0 100 200 300 400 500
0 1000 2000
3000 ࠉⴠ▼⾪ᧁຊ
ࠉఏ⾪ᧁຊ
⾪ᧁຊ (kN)
㛫 (ms) ゎᯒ⤖ᯝࠉCASE 02 Hf=20m
0 100 200 300 400 500
0 1000 2000
3000 ࠉⴠ▼⾪ᧁຊ
ࠉఏ⾪ᧁຊ
⾪ᧁຊ (kN)
㛫(ms) ᐇ㦂⤖ᯝࠉCASE 03 Hf=30m
0 100 200 300 400 500
0 1000 2000
3000 ࠉⴠ▼⾪ᧁຊ
ࠉఏ⾪ᧁຊ ゎᯒ⤖ᯝࠉCASE 03 Hf=30m
⾪ᧁຊ (kN)
㛫 (ms)
ᅗ㸫3 ⾪ᧁຊ㛵ࡍࡿᐇ㦂⤖ᯝゎᯒ⤖ᯝࡢẚ㍑
ᐇ㦂⤖ᯝゎᯒ⤖ᯝࡢẚ㍑
ᅗ㸫3(ᕥ)ࡣCASE01ࡽCASE03ࡢᐇ㦂ࡼࡾᚓࡽࢀ
ࡓ⾪ᧁἼᙧ࡛࠶ࡾ㸪ᅗ㸫3 (ྑ)ࡣ2ḟඖDEMゎᯒ⤖ᯝࡢ ⴠ▼⾪ᧁຊ⿵ṇࡋࡓఏ㐩⾪ᧁຊ࡛࠶ࡿ㸬ሁ✚ᒙࡢゎᯒ
ࣃ࣓࣮ࣛࢱࡣ㸪᭱⢏ᚄ Dmax=0.0250m, ᭱ᑠ⢏ᚄ Dmin=0.0125m㸪ᅵ⢏Ꮚࡢᐦᗘs㸻2.68㸪kn=2×107㸦N/m㸧
=4ks㸪⢏Ꮚ㛫ᦶ᧿ಀᩘtanȭȣ=0.466࡛࠶ࡿ㸬⾪ᧁຊἼᙧ ࡢᙧ≧㸪ࣆ࣮ࢡ್㸪⾪ᧁຊ⥅⥆㛫ࢆẚ㍑ࡍࡿ࠾࠾ࡼ
ࡑᐃ㔞ⓗ࡞୍⮴ࡀぢࡽࢀ㸪DEM ゎᯒࡼࡗ࡚ᚓࡽࢀࡓ
⾪ᧁຊࡀ࠶ࡿ⛬ᗘጇᙜ࡞ࡶࡢ࡛࠶ࡿ࠸࠼ࡿ㸬
࠸ࡎࢀࡢCASE࠾࠸࡚ࡶ㸪ⴠ▼⾪ᧁຊࡼࡾࡶሁ✚ᒙ ᗏ㠃ࡲ࡛ఏ㐩ࡋࡓఏ㐩⾪ᧁຊࡢ᪉ࡀࡁࡃ࡞ࡗ࡚࠸ࡿ
ࡶ㸦ᐇ㦂1.6㹼1.8ಸ㸪ゎᯒ1.4㹼1.7ಸ㸧㸪ⴠ▼⾪ᧁ
㪈㪐㪍
ຊ࡛ࡣ2ᅇࣆ࣮ࢡ್ࡀ⏕ࡌ࡚࠸ࡿ㸬ࡲࡓ㸪ⴠୗ㧗ࡉࡀ㧗 ࡃ࡞ࡾ࢚ࢿࣝࢠ࣮ࡀከࡃ࡞ࡿ⾪ᧁຊࡣࡁࡃ࡞ࡾ⾪
ᧁຊࡢ⥅⥆㛫ࡣ▷ࡃ࡞ࡗ࡚࠸ࡿࡇࡀศࡿ㸬ḟ❶࡛
ࡣ㸪⾪ᧁຊ≉ᛶཬࡰࡍ⢏Ꮚ≉ᛶ㸪ሁ✚≉ᛶࡢᙳ㡪ࡘ
࠸᳨࡚ウࡍࡿ㸬
⾪ᧁຊཬࡰࡍ⢏Ꮚ≉ᛶࡸሁ✚≉ᛶࡢᙳ㡪 ࡤࡡಀᩘࡢᙳ㡪
ᮏ❶࡛ࡣ≉᩿ࡾࡀ࡞࠸ሙྜࡣ㸪ሁ✚ᒙࡣW=4.0m㸪 T=0.9m࡛⦆ワࡵ㸦e = 0.245㸧㸪ⴠయ≉ᛶD f=1.0m㸪ⴠୗ
᮲௳ࡋ࡚H=10mࡋ࡚࠸ࡿ㸬
⢏Ꮚ㛫ࡢ⾪ᧁຊࢆㄪ⠇ࡍࡿࡤࡡಀᩘࡣ㸪⾪ᧁࡢఏ㐩
࠾࠸࡚ࡁࢃࡵ࡚㔜せ࡞ᙺࢆᢸࡗ࡚࠸ࡿ⪃࠼㸪ࡤࡡಀ
ᩘknࢆ2.0107㹼1.01010㸦N/m㸧ࡢᗈ⠊࡞್ࡢ6ࢣ࣮
ࢫ⏝ពࡋࡓ㸬ࡲࡓ㸪ሁ✚ᒙࢆ≉ᛶࡣᵓᡂࡍࡿ⢏Ꮚࡢࢧ
ࢬࡶ౫Ꮡࡍࡿࡢ࡛㸪᭱⢏ᚄDmax=0.0250m, ᭱ᑠ⢏ᚄ Dmin=0.0125mDmax=0.0500m, Dmin=0.0250mࡢ2ࢣ࣮ࢫ
ࢆタᐃࡋࡓ㸬⢏Ꮚࡣࡑࢀࡒࢀ㸪᭱⢏ᚄ᭱ᑠ⢏ᚄࡢ㛫
୍࡛ᵝ࡞Ⓨ⏕☜⋡࡛Ⓨ⏕ࡉࡏࡓ㸬
10 100 1000 10000
100 1000 10000
ࣂࢿᐃᩘ, kn (MN/m)
⾪ᧁຊ (kN)
ⴠ▼⾪ᧁຊ ఏ㐩⾪ᧁຊ
Dmax=0.0250m, Dmin=0.0125m
(a)
10 100 1000 10000
100 1000 10000
ࣂࢿᐃᩘ, kn (MN/m)
⾪ᧁຊ (kN)
ⴠ▼⾪ᧁຊ ఏ㐩⾪ᧁຊ
Dmax=0.0500m, Dmin=0.0250m
(b) ᅗ㸫4 ᭱⾪ᧁຊཬࡰࡍࡤࡡಀᩘࡢᙳ㡪 ᅗ㸫4ࡣ᭱⾪ᧁຊཬࡰࡍࡤࡡಀᩘࡢᙳ㡪ࢆ♧ࡋ࡚
࠸ࡿ㸬ࡤࡡᐃᩘࡀ㧗ࡃሁ✚ᒙࡢ๛ᛶࡀ㧗࠸ⴠ▼࣭ఏ 㐩⾪ᧁຊࡶࡁࡃ࡞ࡿࡇࡀศࡿ㸬⢏Ꮚࢧࢬ
㛵ࢃࡽࡎྠᵝࡢഴྥࢆ♧ࡋ࡚࠸ࡿࡀ㸪⢏ᚄࡀࡁ࠸᪉ࡀ
⾪ᧁຊࡣࡁ࠸㸬ࡲࡓ㸪2ḟඖゎᯒ࡛ࡣ㸪ఏ㐩⾪ᧁຊ
ⴠ▼⾪ᧁຊࡣࡰྠ➼࡛࠶ࡾ㸪㧗࠸ࣂࢿᐃᩘ࡛ࡣⱝᖸ
ࡁ࠸㸪ࡉࡽ㸪ࡤࡡಀᩘknࡀ5×108㸦N/m㸧⛬ᗘࡼࡾࡶ
ࡁࡃ࡞ࡿ㸪⾪ᧁຊࡢ್ࡀࡰ᮰ࡋ࡚࠸ࡿࡇࡀศ
ࡿ㸬⾪ᧁຊᙳ㡪ࢆ࠼ࡿ⪃࠼ࡽࢀࡿሁ✚ᒙࡢኚ ᙧ࣭◚ቯ≉ᛶࡣ㸪⢏Ꮚࡢᙎᛶ⢏Ꮚࡢ┦ᑐ㐠ື࠾ࡼࡧࡑ
ࡢᢠࡼࡗ࡚Ỵᐃࡉࢀࡿ㸬ୖグࡢ⤖ᯝࡣ㸪࠶ࡿ⛬ᗘࡢ
⢏Ꮚࡢ◳ࡉࡀ࠶ࢀࡤ⢏Ꮚࡢ┦ᑐ㐠ື≉ᛶࡸࡑࡢᢠࡢ ᙳ㡪ࡀయ࡞ࡿࡇࢆពࡋ࡚࠸ࡿ㸬ゝ࠸࠼ࡿ㸪
ࣃ࣓࣮ࣛࢱ⟬ᐃࡤࡡᐃᩘknࡀ5×108㸦N/m㸧௨ୖࡢ
್࡞ࡗࡓሙྜ࡛ࡶ㸪᭱⾪ᧁຊ╔┠ࡍࡿࡢ࡛࠶ࢀࡤ㸪 knࢆ5×108㸦N/m㸧⛬ᗘࡋ࡚㸪ィ⟬㈇Ⲵࢆࡉࡅࡿࡇࡶ
ྍ⬟࠸࠼ࡿ㸬⾪ᧁ㛫ࡘ࠸࡚ࡣู㏵᳨ウࢆせࡍࡿ㸬 ⢏Ꮚࢧࢬࡢᙳ㡪
ᅗ㸫5ࡣ㸪ⴠయࡢ┤ᚄD fࡢሁ✚ᒙࡢᖹᆒᚄD50ᑐࡍ
ࡿẚࢆ┦ᑐⴠ▼ᚄD f/D50ࡋ㸪⾪ᧁຊཬࡰࡍᙳ㡪ࡘ
࠸࡚♧ࡋ࡚࠸ࡿ㸬ࡲࡓ㸪ࡤࡡಀᩘknࢆኚ࠼࡚ഴྥࡢ㐪࠸
ࡘ࠸࡚ࡶㄪ࡚࠸ࡿ㸬ࡑࢀࡒࢀࡢࡤࡡಀᩘ࠾࠸࡚㸪 ⴠ▼࣭ఏ㐩⾪ᧁຊࡣሁ✚ᒙࡢ⢏Ꮚࢧࢬࡀᑠࡉࡃ࡞ࡿ
㸦┦ᑐⴠ▼ᚄD f/D50ࡀࡁࡃ࡞ࡿ㸧ᚑࡗ࡚పୗࡋ࡚࠸
ࡿࡇࡀศࡿ㸬ࡉࡽ⢏Ꮚࢆ࠶ࡿ⛬ᗘᑠࡉࡃࡍࡿ㸪
୍ᐃ್㏆࡙ࡃࡇࡀศࡿ㸬ࡇࢀࡣ㸪⢏Ꮚࢧࢬࢆప
ୗࡉࡏࡿྠ୍య✚୰ࡢ⢏Ꮚᩘࡀቑຍࡋ㸪ሁ✚ᒙయ
ࡋ࡚ࡢ๛ᛶࡀపୗࡍࡿࡓࡵ⾪ᧁຊࡣపୗࡍࡿࡓࡵ⪃
࠼ࡽࢀࡿ㸬ࡲࡓ㸪ሁ✚ᒙࡢ⢏Ꮚࢧࢬࡀࡁ࠸ሙྜࡣ㸪 ⴠయࡼࡾሁ✚ᒙෆࡢᒁᡤⓗ࡞ኚᙧ࣭◚ቯ࣮ࣔࢻࡀᣊ᮰ ࡉࢀ㸪༑ศ࡞⦆⾪ຠᯝࡀᮇᚅࡉࢀࡎ⾪ᧁຊࡀ㧗ࡃ࡞ࡿ
⪃࠼ࡽࢀࡿ㸬
ᅗࡼࡾ⾪ᧁຊ୍ᐃ್᮰ࡋጞࡵࡿ⢏Ꮚࢧࢬࡀ㸪ࡤ ࡡಀᩘࡀప࠸ሙྜ࡛ࡣD f/D50=10㸪㧗࠸ሙྜ࡛D f/D50=20
⛬ᗘ࠶ࡿ㸬⢏ᚄࡣ⾪ᧁຊࡶᙳ㡪ࢆ࠼ࡿࡀ㸪୍ᐃ௨ୗ
ࡢࢧࢬࡢ⢏Ꮚࢆ⏝࠸ࢀࡤࡑࡢᙳ㡪ࡣᑡ࡞࠸㸬ሁ✚ᒙࡢ
⢏ᚄࡣⴠయᚄࡢ 1/10 ࡼࡾࡶᑠࡉ࠸್ࡀᮃࡲࡋ࠸ゝ࠼
ࡿ㸬࡛ࡁࡿࡔࡅᑠࡉ࠸⢏ᚄ࡛ゎᯒࢆࡍࡿࡇࡀᮃࡲࡋ࠸
ࡢࡔࡀ㸪⢏Ꮚᩘࡀቑຍࡋ㸪ゎᯒຠ⋡ࡀⴭࡋࡃୗࡀࡗ࡚ࡋ
ࡲ࠺ࡢ࡛㸪⢏ᚄ⢏ᚄ௨እࡢࣃ࣓࣮ࣛࢱࡢ┦㛵ಀࢆ
ᢕᥱࡋ㸪ㄪ⠇ࡍࡿᚲせࡀ࠶ࡿ㸬
10 100
100 1000 10000
┦ᑐⴠ▼ᚄ, D f / D50
⾪ᧁຊ (kN)
ⴠ▼⾪ᧁຊ ఏ㐩⾪ᧁຊ
kn=50 (MN/m)
10 100
100 1000 10000
┦ᑐⴠ▼ᚄ, D f / D50
⾪ᧁຊ (kN)
ⴠ▼⾪ᧁຊ ఏ㐩⾪ᧁຊ
kn=100 (MN/m)
10 100
100 1000 10000
┦ᑐⴠ▼ᚄ, D f / D50
⾪ᧁຊ (kN)
ⴠ▼⾪ᧁຊ ఏ㐩⾪ᧁຊ
kn=500 (MN/m)
10 100
100 1000 10000
┦ᑐⴠ▼ᚄ, D f / D50
⾪ᧁຊ (kN)
ⴠ▼⾪ᧁຊ ఏ㐩⾪ᧁຊ
kn=1000 (MN/m)
ᅗ㸫5 ᭱⾪ᧁຊཬࡰࡍ┦ᑐⴠ▼ᚄࡢᙳ㡪 ሁ✚ᒙࡢᒙཌ㸪ᒙᖜࡢᙳ㡪
ሁ✚ᒙࡢᒙࡉࡣ㸪ࣟࢵࢡࢩ࢙ࢵࢻ࡞ୗ㒊ᵓ㐀≀࠾
࠸࡚タィୖ㔜せ࡞᳨ウ㡯┠࡛࠶ࡿ㸬ⴠ▼ᑐ⟇౽ぴ࡛ࡣ㸪
㪈㪐㪎
ᒙཌTᑐࡍࡿⴠయᚄD fࡢẚ(T/D f)ࡀᑠࡉ࠸⛬㸪⾪ᧁຊ ࡀୖ᪼ࡍࡿ⛬ᗘࢆቑࡋಀᩘ࡛⪃៖ࡋ࡚࠸ࡿ㸬ࡓࡔࡋ㸪 ࡇࢀࡣⴠ▼⾪ᧁຊᑐࡍࡿࡶࡢ࡛ఏ㐩⾪ᧁຊ㛵ࡋ࡚
ࡣ᫂グࡉࢀ࡚࠸࡞࠸㸬
ࡇࢀࡽࢆ㚷ࡳ㸪T/D f =0.25㹼2.0㸪W/D=2.0㹼12ࡢሁ✚
ᒙࡢᗄఱ≉ᛶࡀ㸪᭱⾪ᧁຊࡘ࠸࡚ᩚ⌮ࡋࡓ⤖ᯝࢆᅗ 㸫6♧ࡍ㸬ᅗࡽ㸪W/DࡼࡿᕪࡣT/D >0.5࡛ࡣ
ࢇ࡞࠸ࡀ㸪T/D f <0.5࡛ࡣࡤࡽࡘ࠸࡚࠸ࡿࡼ࠺࡛࠶ࡿ㸬
୍᪉㸪ⴠ▼⾪ᧁຊࡣT/Dࡀᑠࡉ࠸⛬㸪⾪ᧁຊࡣࡁࡃ࡞
ࡿࡇࡀ☜ㄆࡉࢀࡓ㸬୍᪉㸪ఏ㐩⾪ᧁຊࡣT/D f >0.5࡛ࡣ ఏ㐩⾪ᧁຊࡣࢇኚࡋ࡚࠸࡞࠸ࡀ㸪T/D f <0.5ࡼࡾ
ࡶⷧࡃ࡞ࡿᛴ⃭࡞ୖ᪼ࡀࡳࡽࢀࡿ㸬ࡇࡢഴྥࡣࡤࡡಀ
ᩘࡀኚࢃࡗ࡚ࡶኚࢃࡽ࡞࠸ࡀ㸪ࡤࡡಀᩘࡀࡁࡃ㸪ሁ✚
ᒙࡢຊᏛᣲືࡀ⢏Ꮚ㓄ิ࠾ࡼࡧࡑࡢኚ㉳ᅉࡍࡿ
ྜࡀ㧗ࡃ࡞ࡿ㸪㞳ᩓయࡋ࡚ࡢ≉ᚩࡀᨭ㓄ⓗ࡞ࡿ
ゝ࠼ࡿ㸬ࡑࡇ࡛㸪ሁ✚ᒙෆࡢຊࡢศᩓ≉ᛶ╔┠ࡋ㸪 ఏ㐩⾪ᧁຊ᭱ࡢᗏ㠃࠾ࡅࡿఏ㐩ᛂຊศᕸ≧ἣࢆ
ㄪࡓ㸦ᅗ㸫7㸧㸬ࡑࡢ⤖ᯝ㸪ศᕸᙧ≧ࡣT/D f 㸻0.5࡛ࡣ
㍕Ⲵ┤ୗࢆ୰ᚰᴟࡵ࡚ᒁᡤࡍࡿഴྥࡀ᫂ࡽ࡞
ࡗࡓ㸦ศᩓᖜ1.5mࡍࡿศᩓᖜศᩓゅᗘࡣ27ᗘ⛬ᗘ
࡛࠶ࡿ㸧㸬῝ࡃ࡞ࡿศᩓᖜࡣⴠయᚄ㸦1m㸧ࡢ4ಸࡶ
㐩ࡋ࡚࠸ࡿ㸦ศᩓゅᗘࡣ45ᗘ㸧㸬ࡲࡓT/D f 㸼1࡛ࡣศᕸ ᙧࡣ࠶ࡲࡾࡁࡃኚࡋ࡞࠸㸬
௨ୖࡼࡾ㸪ఏ㐩⾪ᧁຊࡢࣆ࣮ࢡ್ࡣᒙཌࡼࡾࢇ
ኚࡋ࡞࠸ࡀ㸪T/D f 㸺1࡛ࡣᛂຊศᕸᙧࡀ୰ᚰᒁᡤ
ࡋጞࡵࡿ㸬ࡼࡗ࡚㸪T/D f 㸺1࡛ࡣ⌧⾜ࡢ౽ぴࡀ♧ࡍᅵ ᅽศᕸᖜࡼࡾࡶ⊃࠸ศᕸ࡞ࡿࡇ୪ࡧᒁᡤࡋ
ࡁ࡞ᛂຊ࡞ࡿࡇࡢ୧⪅㓄៖ࡀᚲせ࡞ࡿࡇࡀ
᫂ࡽ࡞ࡗࡓ㸬
0.1 1
100 1000 10000
┦ᑐᒙཌ, T / D f
⾪ᧁຊ (kN)
[ W/D f ] 2, 4, 8, 12 ⴠ▼⾪ᧁຊ
ఏ㐩⾪ᧁຊ
kn=50 (MN/m)
(a)
0.1 1
100 1000 10000
┦ᑐᒙཌ, T / D f
⾪ᧁຊ (kN)
[ W/D f ] 2, 4, 8, 12 ⴠ▼⾪ᧁຊ
ఏ㐩⾪ᧁຊ
kn=500(MN/m)
(b) ᅗ㸫6 ᭱⾪ᧁຊཬࡰࡍᒙཌẚᒙᖜẚࡢᙳ㡪
-2.00 -1.0 0 1.0 2.0
5 10 15 20
x (m)
ఏ㐩ᛂຊ (MPa)
loose granular mat T/D f=0.5 T/D f=0.9 T/D f=1.5
ᅗ㸫7 ᗏ㠃ఏ㐩ᛂຊศᕸཬࡰࡍሁ✚ᒙࡢᒙཌࡢᙳ㡪 ῶ⾶ಀᩘࡢᙳ㡪
ᅗ㸫8♧ࡍ㏻ࡾ㸪ῶ⾶ಀᩘࡢቑຍࡼࡗ࡚⾪ᧁຊࡢ ⱝᖸࡢపୗഴྥࡀࡳࡽࢀࡿࡀᙳ㡪ࡣࢇ࡞࠸ࡇ
ࡀࢃࡿ㸬ࢲࢵࢩ࣏ࣗࢵࢻࡣ⢏Ꮚ༢యྠኈࡀ⾪✺ࡍࡿሙ
ྜࡣ㊴ࡡ㏉ࡾಀᩘࡣ┤᥋ⓗᙳ㡪ࡍࡿࡀ㸪ሁ✚ᒙ
ࡘ࠸࡚ࡣ⢏Ꮚ㞟ྜయ࡛࠶ࡿ㞳ᩓయࡋ࡚ࡢ≉ᛶࡀ㔜せ
⪃࠼ࡽࢀࡿ㸬ࡋࡓࡀࡗ࡚㸪h=1.0 ࡋィ⟬ୖࡢᏳᐃࢆ
ඃඛࡍࡿࡇࡀྍ⬟࡛࠶ࡿ㸬
0.1 1
100 1000 10000
ῶ⾶ᐃᩘ, h
⾪ᧁຊ (kN)
kn=50 (MN/m) ⴠ▼⾪ᧁຊ
ఏ㐩⾪ᧁຊ
ᅗ㸫8 ᭱⾪ᧁຊཬࡰࡍῶ⾶ಀᩘࡢᙳ㡪
⢏Ꮚᦶ᧿ゅࡢᙳ㡪
ᅗ㸫9 ࡣ⢏Ꮚᦶ᧿ゅȭ䃛ࢆኚࡉࡏࡓሙྜࡢ⤖ᯝࡢ୍
࡛࠶ࡿ㸬⢏Ꮚ㛫ᦶ᧿ゅࡀࡁࡃ࡞ࡿⱝᖸ㸪⾪ᧁຊࡀ
ࡁࡃ࡞ࡗ࡚࠸ࡿࡼ࠺࡛࠶ࡿࡀࡢࣃ࣓࣮ࣛࢱࡢᙳ㡪
ࡽẚࡿ࡞ࡾᑠࡉ࠸㸬ḟࡢࡼ࠺࡞⌮⏤ࡀ⪃࠼ࡽࢀ
ࡿ㸬⢏Ꮚ㛫ᦶ᧿ゅࡢቑຍక࠸⢏Ꮚ㞟ྜయࡢ๛ᛶࡸᙉᗘ ࡣࡁࡃ࡞ࡿࡶࡢࡢ㸪ᙧ⢏Ꮚࡢሙྜࡣ㸪ȭ䃛>30r࡛
ࡣࡰ୍ᐃ್᮰ࡋ࡚ࡋࡲ࠺4)㸬ࡋࡓࡀࡗ࡚㸪ሁ✚ᒙ
⮬యࡢຊᏛ≉ᛶࡶ⢏Ꮚ㛫ᦶ᧿ಀᩘࡢᙳ㡪ࡣᑠࡉ࠸ࡓࡵ㸪
≉ȭ䃛ࡢࡁ࡞⠊ᅖ࡛ࡣ⢏Ꮚ㛫ᦶ᧿ࡢᙳ㡪ࡣᑠࡉࡃ࡞
ࡿ⪃࠼ࡽࢀࡿ㸬ࡲࡓ㸪ⴠయࡢ㈏ධࡼࡗ࡚ሁ✚ᒙࡣᨭ ᣢຊࡢᒁᡤ◚ቯࡸ⯡◚ቯⓗ࡞ᵝᏊ 10), 11)ࢆぢࡏࡿࡶࡢ ࡢ㸪╔┠ࡋࡓ⾪ᧁຊࡢ್᭱ࡀⓎࡉࢀࡿⅬ࡛ࡣⴠయ
┤ୗࡢ⾪ᧁఏᣲືࡀయ࡛࠶ࡾ㸪ᒙࡋ࡚ࡢ◚ቯࡲ
࡛⮳ࡗ࡚࠾ࡽࡎ⢏Ꮚ㛫ᦶ᧿ಀᩘࡢᙳ㡪ࡣᑠࡉ࠸⪃࠼
ࡽࢀࡿ㸬
㪈㪐㪏
0 30 60 90 100
1000 10000
⢏Ꮚ㛫ᦶ᧿ゅ (deg.)
⾪ᧁຊ (kN)
kn=50 (MN/m) ⴠ▼⾪ᧁຊ
ఏ㐩⾪ᧁຊ
ᅗ㸫9 ᭱⾪ᧁຊཬࡰࡍ⢏Ꮚᦶ᧿ゅࡢᙳ㡪 ሁ✚ᒙࡢᐦᗘࡢᙳ㡪
ᅗ㸫10 ࡣ⾪ᧁຊἼᙧཬࡰࡍሁ✚ᒙࡢᐦᗘࡢᙳ㡪ࢆ
♧ࡋ࡚࠸ࡿ㸬ᐦワࡵ㸦㛫㝽ẚ e=0.214㸧⦆ワࡵ㸦㛫㝽 ẚ e=0.245㸧ࡢ⤖ᯝࢆẚ㍑ࡍࡿ㸪⦆ワࡵࡢ᪉ࡀ⾪ᧁຊ ࡢ⥅⥆㛫ࡶ㛗ࡃ㸪᭱⾪ᧁຊࡢ್ࡣᑠࡉࡃ࡞ࡾ㸪ఏ㐩
⾪ᧁຊࡢ᪉ࡀపୗࡢ⛬ᗘࡣ㢧ⴭ࡛࠶ࡿ㸬㏻ᖖࡢ⦆⾪ᮦ
ྠᵝ๛ᛶࡀప࠸⦆࠸ሁ✚ᒙࡢ᪉ࡀ㸪⦆⾪ຠᯝࡀ㧗࠸
⌮ゎ࡛ࡁࡿ㸬ࡲࡓ㸪ᅗࡣⴠయࡀᣢࡘ⥲࢚ࢿࣝࢠ࣮㸦
⨨࢚ࢿࣝࢠ࣮୪㐍㐠ື࢚ࢿࣝࢠ࣮ࡢ㸧ࢆึᮇ⥲࢚ࢿ
ࣝࢠ࣮࡛ṇつࡋࡓ࢚ࢿࣝࢠ࣮ẚࡢ้Ṕࡶ♧ࡋ࡚࠸
ࡿ㸬ᐦワࡵࡢሙྜ㸪᭱ⴠయ⾪ᧁຊࡣ࢚ࢿࣝࢠ࣮ࡣ
ึᮇࡢ 70%㸪᭱ఏ㐩⾪ᧁຊࡢ࢚ࢿࣝࢠ࣮ࡣึᮇࡢ 30%ࡲ࡛పୗࡋ࡚࠸ࡿࡢᑐࡋ࡚㸪⦆ワࡵࡢሙྜࡣࡑ
ࢀࡒࢀ80%60%⛬ᗘ࡞ࡗ࡚࠸ࡿ㸬᭱⾪ᧁຊࡢ࢚
ࢿࣝࢠ࣮⦆⾪ᗘࡣᐦワࡵࡢሙྜࡢ᪉ࡀ㧗ࡃ࡞ࡗ࡚࠸ࡿ㸬
0 20 40 60 80 100
0 1000 2000
0 0.2 0.4 0.6 0.8 1.0
dense granular mat
⾪ᧁຊ (kN)
㛫 (ms)
ࠉⴠయ⥲࢚ࢿࣝࢠ࣮
ࠉⴠ▼⾪ᧁຊ ࠉఏ⾪ᧁຊ
ⴠయࡢ⥲࢚ࢿࣝࢠ࣮ẚ
(a)ᐦワࡵ
0 20 40 60 80 100
0 1000 2000
0 0.2 0.4 0.6 0.8 1.0
loose granular mat
⾪ᧁຊ (kN)
㛫 (ms)
ࠉⴠయ⥲࢚ࢿࣝࢠ࣮
ࠉⴠ▼⾪ᧁຊ ࠉఏ⾪ᧁຊ
ⴠయࡢ⥲࢚ࢿࣝࢠ࣮ẚ
(b)⦆ワࡵ
ᅗ㸫10 ᭱⾪ᧁຊཬࡰࡍሁ✚ᒙࡢᐦᗘࡢᙳ㡪 ࡘࡂ㸪ᅗ㸫2(b)ࡢࡼ࠺ⴠయ┤ୗࡢ࣓ࢵࢩࣗෆࡢᛂ ຊἼᙧࡢ῝ࡉ᪉ྥࡢఏ㐩ࡢᵝᏊࢆᅗ㸫11♧ࡍ㸬ᅗ୰
ࡣ㸪ẚ㍑ࡋࡸࡍ࠸ࡼ࠺㸪ⴠ▼⾪ᧁຊఏ㐩⾪ᧁຊࢆ
῝ࡉ0m0.9mࡢ⟠ᡤ◚⥺࡛♧ࡋ࡚࠸ࡿ㸬ὸ࠸᪉ࡽ
㡰ᛂຊἼࡀఏ㐩ࡋ࡚࠸ࡿᵝᏊࡀࢃࡿ㸬
0 10 20 30 40 50
0
1.0
time (ms) ᗏ㠃ࡢఏ㐩⾪ᧁຊ
depth (m)
dense granular mat ⴠ▼⾪ᧁຊ from elem. 9 to elem. 1
0 10 20 30 40 50
0
1.0
time (ms) ᗏ㠃ࡢఏ㐩⾪ᧁຊ
depth (m)
loose granular mat ⴠ▼⾪ᧁຊ from elem. 9 to elem. 1
ᅗ㸫11 ⴠయ┤ୗࡢᛂຊἼࡢఏ㐩ᣲືཬࡰࡍሁ✚ᒙ ࡢᐦᗘࡢᙳ㡪
-2.0 -1.0 0 1.0 2.0
0 10 20 30
x (m)
ఏ㐩ᛂຊ (MPa)
granular mat dense loose pre peak
-2.0 -1.0 0 1.0 2.0
0 10 20 30
x (m)
ఏ㐩ᛂຊ (MPa)
granular mat dense loose at peak
-2.0 -1.0 0 1.0 2.0
0 10 20 30
x (m)
ఏ㐩ᛂຊ (MPa)
granular mat dense loose post peak
ᅗ㸫12 ᗏ㠃ࡢఏ㐩ᛂຊศᕸཬࡰࡍሁ✚ᒙࡢᐦᗘࡢ ᙳ㡪㸸 ఏ㐩⾪ᧁຊࡢࣆ࣮ࢡ๓㸪ࣆ࣮ࢡ㸪ࣆ࣮ࢡᚋ
ⴠయ┤ୗ࡛ࡢఏ㐩ᛂຊࡢ้ṔἼᙧࡣࡁ࡞ᒣࢆ᭷
ࡋ࡚࠾ࡾ㸪῝ࡉ᪉ྥࡑࡢࣆ࣮ࢡ್ࡣῶᑡࡋ࡞ࡀࡽఏ㐩 ࡋ࡚࠸ࡿ㸬ᐦ࡞᪉ࡀᒣ୍ࡘࡢᙧ≧㸦ࡓࡔࡋ㸪ࣆ࣮ࢡ㏆
㪈㪐㪐
࡛ࡣพฝࡀ᭷ࡿ㸧࡞ࡗ࡚࠾ࡾ㸪⦆ࡃ࡞ࡿྠ⛬ᗘࡢࣆ
࣮ࢡ್ࢆᣢࡘᒣࡀࡘ㐃࡞ࡗࡓᙧ≧࡞ࡿࡇࡀศ
ࡿ㸬ᚋ⥆ࡢࣆ࣮ࢡࡢᏑᅾࡀⴠ▼࣭ఏ㐩⾪ᧁຊἼᙧࢆᨭ㓄 ࡋ࡚࠸ࡿ⪃࠼ࡿࡇࡀ࡛ࡁࡿ㸬ࡘ┠ࡢᒣࡣቃ⏺ࡽ
ࡢᑕἼ࡛࠶ࡿྍ⬟ᛶࡶ࠶ࡿ㸬ⴠ▼࣭ఏ㐩⾪ᧁຊἼᙧࢆ
⌮ゎࡍࡿࡣ῝ࡉ᪉ྥఏࡍࡿᛂຊἼቃ⏺ࡽࡢ
ᑕἼࡶ⪃៖ࡋ᳨࡚ウࡍࡿᚲせࡀ࠶ࡿ㸬
ࡉࡽ㸪ᗏ㠃ቃ⏺࡛ࡢఏ㐩㖄┤ᛂຊࡢỈᖹ᪉ྥࡢศ ᕸ≉ᛶཬࡰࡍሁ✚ᒙࡢᐦᗘࡢᙳ㡪ࢆᅗ㸫12♧ࡍ㸬ᅗ ࡣᗏ㠃ࡢఏ㐩⾪ᧁຊࡢࣆ࣮ࢡ๓㸪ࣆ࣮ࢡ㸪ࣆ࣮ࢡᚋࡢ ศᕸ࡛࠶ࡿ㸬ᒙཌࡢᙳ㡪ẚࡿ⛬ᗘࡣᑠࡉ࠸ࡀ㸪⦆
ワࡵࡢ᪉ࡀⴠయ┤ୗᛂຊࡣ㞟୰ࡋ࡚࠸ࡿᵝᏊࡀศ
ࡿ㸬ࡋࡓࡀࡗ࡚㸪ᐦᗘࡢ㐪࠸ࡼࡿሁ✚ᒙෆࡢᒁᡤⓗ࡞
ኚᙧ࣭◚ቯࢆヲ⣽ほᐹࡍࡿᚲせࡀ࠶ࡿ㸬
㸲 ࡲࡵ
ᮏ◊✲࡛ࡣ㸪ⴠ▼ࡼࡿ⢏≧ᛶࡢሁ✚ᒙෆࡢ⾪ᧁຊఏ 㐩ᣲືࡘ࠸࡚㸪2ḟඖಶูせ⣲ἲ㸦DEM㸧ࢆ⏝࠸࡚ㄪ
ࡓ㸬ⴠ▼⾪ᧁຊఏ㐩⾪ᧁຊࡘ࠸࡚㸪⿵ṇࡋࡓゎᯒ
⤖ᯝ1/2ࢫࢣ࣮ࣝᶍᆺᐇ㦂⤖ᯝࢆẚ㍑ࡋ㸪DEMゎᯒࡀ ᐃᛶⓗ࣭ᐃ㔞ⓗ⾪ᧁຊ≉ᛶࢆᴫࡡ⾲⌧ྍ⬟࡛࠶ࡿࡇ
ࢆ♧ࡋࡓ㸬ࡼࡾヲ⣽࡞᳨ウࡢࡓࡵ㸪ᚋ3ḟඖゎᯒࡶ
⾜࠺ࡇࡍࡿ㸬
ࡲࡓ㸪⢏Ꮚ◳ᗘ㸪⢏ᚄ㸪⢏Ꮚᙧ≧࡞ࡢ⢏Ꮚ≉ᛶ㸪ሁ
✚ᐦᗘࡸᒙཌ࡞ࡢሁ✚≉ᛶࡀࣆ࣮ࢡ⾪ᧁຊཬࡰࡍ ᙳ㡪ࡘ࠸࡚ㄪࡓ㸬ࡑࡢ⤖ᯝ㸪௨ୗࡢࡇࡀศࡗࡓ㸬 1㸧ࡤࡡᐃᩘࡢቑຍక࠸ࣆ࣮ࢡ⾪ᧁຊࡣቑຍࡍࡿࡀ㸪 ሁ✚ᒙࡢ㞳ᩓᛶࡢᙳ㡪ࡀᙉࡃ 5108ࡼࡾࡶࡁࡃ࡞ࡿ
࠶ࡓࡾࡽ⾪ᧁຊࡢୖ᪼ࡀぢࡽࢀ࡞ࡃ࡞ࡿ㸬ሁ✚ᒙࡢሙ
ྜ㸪⾪ᧁຊࡢࡁࡉ㛵ࡋ࡚ࡣ㸪ィ⟬ࢆ㈇Ⲵࢆ㑊ࡅࡿࡓ
ࡵ 5108ࢆ㉸࠼ࡿࡼ࠺࡞ࡤࡡಀᩘࡶ⏝࠸ࡿᚲせࡀ࡞
࠸ࡇࢆពࡋ࡚࠸ࡿ㸬
2㸧ⴠ▼࣭ఏ㐩⾪ᧁຊࡣ⢏Ꮚࢧࢬࡀᑠࡉࡃ࡞ࡿᚑࡗ
࡚పୗࡍࡿ㸬ሁ✚ᒙࡢ⢏ᚄࡀⴠయᚄࡢ1/10⛬ᗘ௨ୗ࡛࠶
ࢀࡤ㸪ࡰ୍ᐃ್᮰ࡍࡿࡇࡀศࡗࡓ㸬
3㸧⾪ᧁຊᒙᖜࡢᙳ㡪ࡣࢇ࡞࠸ࡇࡀศࡗࡓ㸬 ᒙཌ㛵ࡋ࡚ࡣ㸪ⴠ▼⾪ᧁຊࡣT/Dࡀᑠࡉ࠸⛬ࡼࡾࡁ
࡞⾪ᧁຊ࡞ࡾ㸪ఏ㐩⾪ᧁຊࡣT/Dࡀᑠࡉࡃ࡞ࡗ࡚ࡶఏ 㐩⾪ᧁຊࡢࣆ࣮ࢡ್ࡣࢇኚࡋ࡞࠸㸬ఏ㐩⾪ᧁຊ
้࡛᭱ࡢᗏ㠃࠾ࡅࡿᛂຊศᕸ≧ἣࡣ㸪 T/D㸺1࡛ ࡣ⌧⾜ࡢ౽ぴࡀ♧ࡍᅵᅽศᕸᙧ≧ࡼࡾࡶᖜࡀ⊃ࡃᑤࡗ ࡓᙧ≧࡞ࡿ㸬ⴠ▼┤ୗࡢ⠊ᅖᒁᡤࡋࡁ࡞ᛂຊࡀ
Ⓨ⏕ࡍࡿ㸬
4㸧ሁ✚ᒙ⮬యࡢຊᏛ≉ᛶࡀ⢏ᏊࡢᗄఱᏛⓗ㓄⨨࡛࠶ࡿ
ᐦᗘࡸ␗᪉ᛶ㸪⢏Ꮚᅇ㌿ᨭ㓄ࡉࢀࡿࡓࡵ㸪⾪ᧁ≉
ᛶࡶ㸪⢏Ꮚ㛫ᦶ᧿ಀᩘࡸῶ⾶ᐃᩘࡢᙳ㡪ࡣ࡞࠸㸬ࡋࡓࡀ ࡗ࡚㸪ᚋࡣ㸪ࡼࡾ◁ࡽࡋ࠸ᣲືࢆ♧ࡍ㠀ᙧ⢏Ꮚࡼ
ࡿゎᯒ⤖ᯝࡢ᳨ウࢆ㐍ࡵࡿ㸬
5㸧ሁ✚ᒙࡀ⦆࠸⛬㸪ⴠ▼࣭ఏ㐩⾪ᧁຊࡣపୗࡋ㸪ఏ㐩
⾪ᧁຊࡢ᪉ࡀపୗྜࡣ㧗࠸㸬ᗏ㠃ᛂຊศᕸࡶ⦆࠸ሙྜ
ࡢ᪉ࡀⴠୗ┤ୗ㞟୰ࡋ࡚࠾ࡾ㸪ᐦ࡞᪉ࡀᗈ⠊ศᕸࡋ
࡚࠸ࡿ㸬ⴠయ┤ୗ࡛ࡢఏ㐩ᛂຊࡢ้ṔἼᙧࡣࡁ࡞ᒣ
ࢆ᭷ࡋ࡚࠾ࡾ㸪῝ࡃ࡞ࡿࡑࡢࣆ࣮ࢡ್ࡣపୗࡍࡿ㸬ᐦ
࡞᪉ࡀ㸪ᒣ୍ࡘࡢᙧ≧㸦ࡓࡔࡋ㸪ࣆ࣮ࢡ㏆࡛ࡣࡁ࡞
พฝ㸧㸪⦆ࡃ࡞ࡿྠ⛬ᗘࣆ࣮ࢡ್ࢆᣢࡘᒣࡀࡘ㐃࡞
ࡗࡓᙧ≧࡞ࡿࡇࡀศࡗࡓ㸬ᚋ⪅ࡢᚋ⥆ࡢࣆ࣮ࢡࡢ Ꮡᅾࡀⴠ▼࣭ఏ㐩⾪ᧁຊἼᙧࢆᨭ㓄ࡋ࡚࠸ࡿ㸬
ㅰ㎡
ࡇࡢ◊✲⏝࠸ࡓ⨨ࡢ୍㒊ࡣ᪥ᮏᏛ⾡⯆⛉Ꮫ
◊✲㈝⿵ຓ㔠ᇶ┙◊✲% ࡼࡿࡶࡢ࡛࠶ࡾ㸪
῝ㅰࡢពࢆ⾲ࡋࡲࡍ㸬
ཧ⪃ᩥ⊩
1) Cundall, P. A. and O. D. L. Strack.㸸A Discrete Models for Granular Assemblies㸪Geotechnique, Vol.29, No.1, pp.47-65, 1979.
2) ୕➟ṇே㸸ᅵࡢᙉᗘᏳᐃィ⟬ἲ, ᇶ♏ࡢࡓࡵࡢᅵ
㉁ᕤᏛ, 37ᖺᗘㅮ:⩦ࢸ࢟ࢫࢺ, 1963
3) 㔝ඖᙪ㸸◚ቯࡢࢩ࣑࣮ࣗࣞࢩࣙࣥ, ᳃ฟ∧, 2004 4) Maeda, K. and Hirabayashi, H.㸸Influence of grain
properties on macro mechanical behaviors of granular media by DEM, Journal of Applied Mechanics, JSCE, pp.623-630, 2006.
5) Maeda, K. et al..: Stress-chain based micromechanics of sand with grain shape effect, Granular Matter, Vol. 12, pp.499-505, 2010.
6) Maeda,K. and Yuasa,T.㸸Performance estimation of countermeasures for falling rock using DEM, IS-KYOTO, pp.193-199, 2009.
7) Yuasa,T., Maeda,K. and Waku,A.㸸A risk evaluation method of countermeasure for slope failure and rockfall with account of initial investment, Geotechnical risk and safety, IS-GIFU, pp.221-228, 2009.
8) ๓⏣୍ࡽ㸸ㅮᗙࠕ⢏Ꮚ≉ᛶࡢホ౯ᕤᏛⓗព⩏ 7㸬
⢏Ꮚ㞟ྜయࡋ࡚ࡢホ౯ຊᏛᣲືࠖ㸪ᅵᇶ♏㸪ᆅ
┙ᕤᏛ㸪Vol.55㸪No.9㸪pp.31-39㸪2007.
9) ῦ▱ⱥ: , ྡྂᒇᕤᴗᏛᏛ㝔, ಟኈㄽᩥ, 2010
10) ส⏣ᆂ୍: DEM ࡼࡿሁ✚ᒙࡢⴠ▼ࡼࡿ⾪ᧁຊ
ゎᯒ, ᅵᮌᏛ➨ 65 ᅇᖺḟᏛ⾡ㅮ₇ᴫせ㞟, Ϫ -397, pp.793-794, 2010.
11) ส⏣ᆂ୍: ⴠ▼ࡢᩳࡵධᑕࡼࡾཷࡅࡿ⾪ᧁຊࡢ
DEM ゎᯒ, ᅵᮌᏛ➨65ᅇᖺḟᏛ⾡ㅮ₇ᴫせ㞟, Ϫ-398, pp.795-796, 2010.
㪉㪇㪇
