4ᅵ▼ὶ࡟ྵࡲࢀࡿᚤ⣽ᅵ◁ࡢᣲື࡟㛵ࡍࡿᐇ㦂ⓗ᳨ウ⟃Ἴ኱Ꮫ⏕࿨⎔ቃ⣔ ‫ۑ‬ᇼ⏣ ⣖ᩥ㛗㔝┴ 㔠Ꮚ Ᏹᘯ༓ⴥ┴ ᒾ⏣ ▱அ
1. ◊✲ࡢ⫼ᬒ࡜┠ⓗ▼♟ᆺᅵ▼ὶෆ㒊ࡢᛂຊᵓ㐀࡟ࡘ࠸࡚ࡢ◊✲ࡣ㸪༢⣧໬ࡢࡓࡵ࡟ᆒ୍⢏ᚄࢆ௬ᐃࡍࡿࡇ࡜࡛㸪◁♟⢏Ꮚ㛫ࡢ⾪✺࣭᥋ゐ㸪࠾ࡼࡧ㛫㝽ὶయ࡟࠾ࡅࡿᛂຊࡢࣔࢹࣝ໬࡟ᡂຌࡋ࡚ࡁࡓ㸬୍᪉㸪ᚤ⣽࡞ᅵ◁࡟ࡼࡗ࡚ᵓᡂࡉࢀࡿἾὶ࡟ࡘ࠸࡚ࡢ◊✲ࡣ㸪⢏Ꮚ㛫ࡢ┦஫స⏝࡟❧ࡕධࡽࡎ㸪ࣅ࣒ࣥ࢞ὶయࡸ஘ὶࣔࢹࣝ࡟ࡼࡗ࡚Ἶὶࢆグ㏙ࡍࡿࡇ࡜ࡀከ࠸㸬ࡋ࠿ࡋ࡞ࡀࡽ㸪⌧ᆅ࡛ほ ࡉࢀࡿᅵ▼ὶࡢ⢏ᗘศᕸࡣᖜᗈࡃ㸪▼♟ᆺᅵ▼ὶ࡜ࡳ࡞ࡏࡿࡼ࠺࡞ᅵ▼ὶ࡜࠸࠼࡝ࡶ㸪ࡑࡢෆ㒊࡟኱㔞ࡢᚤ⣽ᅵ◁ࢆྵࡴ㸬㏆ᖺࡢ◊✲࡛ࡣ㸪≉࡟኱つᶍ࡞ᅵ▼ὶࡢὶୗࢩ࣑࣮ࣗࣞࢩࣙࣥࢆᐇ᪋ࡍࡿ㝿࡟ࡣ㸪ᅵ▼ὶࢆᵓᡂࡍࡿᚤ⣽ᅵ◁ࡢ୍㒊ࢆᾮ┦࡜ࡳ࡞ࡍࡇ࡜࡛⌧㇟ࡢ෌⌧ᛶࡀྥୖࡍࡿࡇ࡜ࡀሗ࿌ࡉࢀ࡚࠸ࡿ 1)㸬▼♟ᆺᅵ▼ὶ୰ࡢᚤ⣽ᅵ◁ࡣ஘ὶᵓ㐀࡟ྲྀࡾ㎸ࡲࢀࡿࡇ࡜࡛ᾮ┦࡜ࡋ࡚᣺ࡿ⯙࠺࡜⪃࠼ࡽࢀࡿࡀ㸪஘ὶᵓ㐀࡟ྲྀࡾ㎸ࡲࢀࡿ࠿࡝࠺࠿ࡣ◁♟ࡢ⢏ᚄࡑࡢࡶࡢ࡛ࡣ࡞ࡃ㸪┦ᑐỈ῝㸦ὶື῝㸭⢏ᚄ㸧࡟ࡼࡗ࡚ᩚ⌮ࡉࢀࡿ࡜ࡢᣦ᦬ 2)ࡶ࠶ࡾ㸪ᅵ▼ὶෆࡢᚤ⣽ᅵ◁ࡢᣲື࡟ࡘ࠸࡚ࡣᮍࡔ༑ศ࡟᫂ࡽ࠿࡟࡞ࡗ࡚࠸࡞࠸㸬ᮏ◊✲࡛ࡣ㸪ΰྜ⢏ᚄࡢᅵ▼ὶ࡟࠾ࡅࡿᚤ⣽ᅵ◁ࡢᣲື࡜㸪ࡑࢀࡀᅵ▼ὶࡢὶືᛶ࡟ཬࡰࡍᙳ㡪ࢆ᫂ࡽ࠿࡟ࡍࡿࡇ࡜ࢆ┠ⓗ࡜ࡋ࡚Ỉ㊰ᐇ㦂ࢆᐇ᪋ࡋࡓ㸬2. ᐇ㦂ᴫせᐇ㦂ࡣ㸦㈈䠅ᘓタᢏ⾡◊✲ᡤ࡟࠾࠸࡚⾜ࡗࡓ㸬඲㛗 10m㸪ᖜ 10cm ࡢྍኚ໙㓄Ỉ㊰ࢆ⏝࠸㸪ୖὶഃ 4.5m ࡢ㊰ᗋࢆ 10cm ୗࡆ࡚ᅵ◁ࢆሁ✚ࡉࡏ㸪ୖὶ➃ࡼࡾ⤥Ỉࡍࡿࡇ࡜࡟ࡼࡗ࡚ᅵ▼ὶࢆⓎ⏕ࡉࡏࡓ㸬඲࡚ࡢᐇ㦂࡛Ỉ㊰໙㓄ࡣ 15 ᗘ㸪ୖὶ➃࠿ࡽࡢ౪⤥ὶ㔞ࡣ 2 㺶㺍㺢㺷/sec ࡜ࡋࡓ㸬Ỉ㊰ᗋ࡟ࡣ⢒ᗘ࡜ࡋ࡚ᖹᆒ⢏ᚄ⣙ 2.9mm ࡢ◁⢏Ꮚࢆ㈞ࡾ
௜ࡅࡓ㸬ᐇ㦂࡛ࡣ㸪Ỉ㊰ୗὶ➃࡛ᅵ▼ὶࢆ᥇ྲྀࡋ࡚ᅵ◁⃰ᗘࢆ ᐃࡍࡿ࡜࡜ࡶ࡟㸪᥇ྲྀ᫬㛫ࢆグ㘓ࡋ࡚ᅵ▼ὶࡢὶ㔞ࢆồࡵࡓ㸬ࡲࡓ㸪Ỉ㊰ୗὶ➃ࡼࡾ 1m ࡢ఩⨨࡛㉸㡢Ἴࢭࣥࢧ࣮䠄E4PA, OMRON䠅ࢆ⏝࠸࡚Ỉ῝ࢆ ᐃࡋ㸪ᅵ▼ὶὶ㔞ࡢࢹ࣮ࢱ࡜ྜࢃࡏ࡚ᖹᆒὶ㏿ࢆ⟬ฟࡋࡓ㸬㻌 㻌 㻌 Table 1 ᐇ㦂ᮦᩱᐇ㦂ᮦᩱ࡟ࡣ㸪⠠࠸ศࡅ࡛࡞ࡿ࡭ࡃᆒ୍ࡢ⢏ᚄ࡟ࡋࡓ 5 ✀㢮ࡢᅵ
Monogranular
Two diameter mixed◁ࢆ⏝࠸ࡓ㸦Table 1㸧㸬5 ✀㢮ࡢᆒ୍⢏ᚄ࡛ࡢᐇ㦂࡜㸪2 ✀㢮ࡢΰྜ⢏ᚄ࡛ࡢᐇ㦂ࢆᐇ᪋ࡋࡓ㸬ΰྜ⢏ᚄࡢᐇ㦂࡛ࡣ㸪2.9mm ࡢ◁♟⢏Ꮚࢆ኱⢏ᚄ⢏Ꮚ࡜ࡋ࡚ᅛᐃࡋ㸪ᑠ⢏ᚄ⢏Ꮚ࡜ࡋ࡚ 0.11㹼1.3mm ࡢ◁♟ࢆ⏝࠸ࡓ㸬ࡲࡓ㸪ึᮇΰྜẚࡣ 1:1 ࡜ 1:4 ࡢ 2 ㏻ࡾ࡜ࡋ㸪஦๓࡟ᐇ㦂ᮦᩱࢆ༑ศ࡟ΰྜࡋ࡚Ỉ㊰ୖ㒊࡟ሁ◁ࡉࡏࡓ㸬ᐇ㦂࡛᥇ྲྀࡋࡓᅵ▼ὶࢧࣥࣉࣝࢆ஝⇱ᚋ࡟⠠࠸ศࡅ㸪ࡑࢀࡒࢀࡢ⢏ᚄࡢᅵ◁⃰ᗘࡶồ
ࡵࡓ㸬
3. ゎᯒ
ᐇ㦂⤖ᯝࡢゎᯒࡣḟࡢ 2 ࡘࡢ᢬ᢠಀᩘࢆ⏝࠸࡚⾜ࡗࡓ㸬     f ex

size

large

2.9mm

ratio

1.3mm

1.3mm
0.84mmsmall

0.84mm
2.9mm

0.23mm0.11mm0.23mm

1:1&
1:40.11mm

2 gh sin T ······································································ (1)
um

2

2

     f cal

25§h·K (c, U )¨ ¸ ·························································· (2)
2U m
©d ¹

ࡇࡇ࡛㸪g ࡣ㔜ຊຍ㏿ᗘ㸪h ࡣὶື῝㸪um ࡣᖹᆒὶ㏿㸪Um ࡣᅵ▼ὶࡢᐦᗘ㸪c ࡣᅵ◁⃰ᗘ㸪Uࡣᅵ▼ὶࡢ㛫㝽ὶయࡢᐦᗘ㸪K(c, U)ࡣᅵ▼ὶࡢᵓᡂ๎࠿ࡽᑟฟࡉࢀࡿ c ࡜Uࡢ㛵ᩘࢆ⾲ࡋ㸪d ࡣ⢏ᚄ࡛࠶ࡿ㸬ᘧ(1)ࡢ᢬ᢠಀᩘ fex ࡣᐇ㦂್࡛࠶ࡾ㸪ᘧ(2)ࡢ fcal ࡣᅵ▼ὶ࡟࠾ࡅࡿ᢬ᢠಀᩘࡢ⌮ㄽ್ࢆ⾲ࡍ 2)㸬
ᮏ◊✲࡛ࡣ㸪ΰྜ⢏ᚄᐇ㦂ࡢ fcal ࡣḟࡢࡼ࠺࡞ 2 ࡘࡢࣔࢹࣝ㸦Fig.
1㸧࡛ィ⟬ࢆ⾜࠸㸪࡝ࡕࡽࡢࣔࢹࣝࡀࡼࡾ fex ࡜㏆࠸࠿ࢆẚ㍑ࡋࡓ㸬ࣔࢹࣝϨ㸸ᑠᚄ⢏Ꮚࡀ඲࡚ᅛయ⢏Ꮚ࡜ࡋ࡚᣺ࡿ⯙࠺࡜௬ᐃࡋ㸪ィ
Fig. 1 䝰䝕䝹 I 䛸 II 䛾ᴫᛕᅗ⟬࡟ࡣ኱ᑠ஧⢏ᚄࡢᖹᆒ⢏ᚄࢆ⏝࠸ࡓ㸬ࣔࢹࣝϩ㸸ᑠᚄ⢏Ꮚࡀ඲࡚Ỉ࡜୍య໬ࡍࡿ࡜ࡋ࡚㛫㝽ὶయࡢᐦᗘࢆቑຍࡉࡏ㸪ィ⟬࡟ࡣ⢏ᚄ 2.9mm ࢆ⏝࠸ࡓ㸬㪄㩷㪙㪄㪈㪈㪍㩷㪄4. Ỉ㊰ᐇ㦂ࡢ⤖ᯝ࡜⪃ᐹྛᐇ㦂࡟࠾ࡅࡿᅵ◁⃰ᗘࢆẚ㍑ࡍࡿ࡜㸪ᆒ୍⢏ᚄࡢᐇ㦂࡛ࡣ㸪඲࡚ࡢࢣ࣮ࢫ࡟࠾࠸࡚ྠ⛬ᗘࡢ⃰ᗘࡀ ᐃࡉࢀࡓ㸬ΰྜ⢏ᚄࡢᐇ㦂࡟࠾࠸࡚ࡶ㸪0.84mm㸪1.3mm ࡢᐇ㦂ࡣᆒ୍⢏ᚄࡢᐇ㦂࡜ྠ⛬ᗘࡔࡗࡓ㸬0.11mm㸪0.23mm ࡢΰྜ⢏ᚄࡢᐇ㦂࡛ࡣ㸪ΰྜẚ࡟ࡼࡽࡎ⃰ᗘࡀ㧗࠿ࡗࡓ㸬⢏ᚄูࡢ⃰ᗘ࡟╔┠ࡍࡿ࡜㸪0.11mm㸪0.23mm ࡢᐇ㦂࡛ࡣ㸪ΰྜẚ 1:4 ࡢᐇ㦂࡛኱⢏ᚄ⢏Ꮚ㸦⢏ᚄ 2.9mm㸧ࡢ⃰ᗘࡀᆒ୍⢏ᚄࡢ⃰ᗘ࡜࡯ࡰ୍⮴ࡋ࡚࠾ࡾ㸪ࡇࢀࡽࡢࢣ࣮
ࢫ࡛ࡣᑠ⢏ᚄࡢ◁♟⢏Ꮚࡀ኱⢏ᚄ⢏Ꮚࡢ㛫㝽࡟ྲྀࡾ㎸ࡲࢀࡓ࡜ࡶ⪃࠼ࡽࢀࡿ㸬࡞࠾㸪඲࡚ࡢΰྜ⢏ᚄᐇ㦂࡟࠾ࡅࡿΰྜẚࡣ㸪ሁ✚᫬ࡢΰྜẚ㸦1:1㸪1:4㸧࡜㏆࠸್ࢆྲྀࡗࡓ㸬㻌㻌㻌㻌 㻌 Fig. 2 ὶື῝䛾ẚ㍑㻌 (a) ᆒ୍⢏ᚄ䠈(b) ΰྜẚ 1:4䠈(c) ΰྜẚ 1:1

ὶື῝ࡢ⤖ᯝࢆ Fig. 2 ࡟♧ࡍ㸬0.11mm㸪0.23mm ࡢΰྜẚ 1:4 ࡢࢣ࣮ࢫ࡛ࡢࡳ㸪௚ࡢΰྜ⢏ᚄࡢᐇ㦂ࡼࡾࡶὶື
῝ࡀ኱ࡁࡃ㸦㸸Fig. 2b ࡢ୸࡛ᅖࡲࢀࡓ㒊ศ㸧㸪2.9mm ࡢᆒ୍⢏ᚄࡢᐇ㦂࡜ྠ⛬ᗘࡢ್ࢆྲྀࡗࡓ㸬ᆒ୍⢏ᚄࡢᅵ▼ὶ࡟࠾࠸࡚ࡣ㸪⢏ᚄ࡜ᅵ◁⃰ᗘ௨እࡢ᮲௳ࡀྠࡌ࡛࠶ࢀࡤ㸪ᅵ▼ὶࢆᵓᡂࡍࡿ◁♟⢏Ꮚࡢ⢏ᚄࡀ኱ࡁࡃ㸪ᅵ◁⃰ᗘࡀ㧗࠸࡯࡝ὶࢀ࡟࠿࠿ࡿ᢬ᢠࡀ኱ࡁ࠸ࡇ࡜ࡀᵓᡂ๎ࡼࡾᑟ࠿ࢀࡿ㸬Fig. 2b ࡛㧗࠸⃰ᗘࡀ᳨ฟࡉࢀࡓࡢࡣ㸪ᆒ୍⢏ᚄࡢᅵ▼ὶࡼࡾ⃰ᗘࡀ㧗ࡃ㸪኱⢏ᚄࡢ㛫㝽࡟ᑠ⢏ᚄࡀྲྀࡾ㎸ࡲࢀ࡚࠸ࡿ࡜ࡳ࡞ࡏࡿࢣ࣮ࢫ࡛࠶ࡗࡓ㸬ᅵ◁⃰ᗘ࡜ὶື῝ࡢ⤖ᯝࢆྜࢃࡏ࡚⪃ᐹࡍࢀࡤ㸪ࡇࢀࡽࡢࢣ࣮ࢫ࡟࠾࠸࡚ࡣᑠ⢏ᚄᅵ▼ὶࡀὶࢀࡢᛂຊ࡟࠶ࡲࡾᐤ୚ࡋ࡚
࠸࡞࠸ྍ⬟ᛶࡀᣦ᦬࡛ࡁࡿ㸬
5. ᢬ᢠಀᩘࡢẚ㍑
ୖグࡢᐇ㦂⤖ᯝࢆࡼࡾヲ⣽࡟᳨ウࡍࡿࡓࡵ࡟㸪᢬ᢠಀᩘࡢẚ㍑ࢆ⾜ࡗࡓ㸬Fig. 3 ࡣ fex ࡜ fcal
ࡣࢆẚ㍑ࡋࡓ⤖ᯝ࡛࠶ࡿ㸬fcal
ࡣ๓㏙ࡢࡼ࠺࡟ 2 ࡘࡢࣔࢹ࡛ࣝồࡵ࡚࠾ࡾ㸪▮༳࡛୧⪅ࡢ್ࡢ㐪࠸ࢆ♧ࡋࡓ㸬⤖ᯝࡣΰྜẚ 1:1
࡜ 1:4 ࢆศࡅ࡚♧ࡋ࡚࠸ࡿ㸬
Fig. 3 ࠿ࡽ㸪ᐇ㦂್࡜⌮ㄽ್ࡢ᢬ᢠಀᩘࡀྠ⛬ᗘࡢ್ࢆྲྀࡿ
ࡢࡣ㸪ᐇ㦂᮲௳࡟ࡼࡗ࡚ࣔࢹࣝ
I ࢆ⏝࠸ࡓሙྜ࡜ࣔࢹࣝ II ࢆ⏝㻌 㻌 㻌 㻌 㻌 㻌 㻌 㻌 㻌 㻌 㻌 㻌 㻌 㻌 㻌 㻌 㻌 㻌 Fig. 3 ᢬ᢠಀᩘ䛾ẚ㍑
࠸ࡓሙྜ࡜࡟ศ࠿ࢀࡓ㸬ࡲࡓ㸪࡝ࡕࡽࡶ୍⮴ࡋ࡞࠸ᐇ㦂᮲௳ࡶ࠶ࡗࡓ㸬ࣔࢹࣝ I ࡜ II ࡢ࠺ࡕ㸪࡝ࡕࡽࡀᐇ⌧㇟ࢆ཯ᫎࡋ࡚࠸ࡿ࠿ࢆ☜ㄆࡍࡿࡓࡵ࡟㸪௨ୗࡢࡼ࠺࡞ᣦᶆDࢆᑟධࡋࡓ㸬     f ex

Df cal:I  1  D f cal:II ·························································· (3)fcal:I ࡜ fcal:II ࡣࡑࢀࡒࢀࣔࢹࣝ I ࡜ II ࠿ࡽồࡵࡽࢀࡓ᢬ᢠಀᩘࡢ⌮ㄽ್࡛࠶ࡿ㸬ᘧ(3)ࡢࡼ࠺࡟᢬ᢠಀᩘࡢᐇ㦂್࡜⌮ㄽ್ࡀ➼ࡋࡃ࡞ࡿ㸦᮲௳࡟ࡼࡗ࡚ࡣ᭱ࡶ㏆࠸್ࢆྲྀࡿ㸧Dࢆồࡵࡓ࡜ࡇࢁ㸪ᑠ⢏ᚄ⢏Ꮚࡢ⢏ᚄࡢቑ኱࡟క࠸Dࡣ኱ࡁࡃ࡞ࡗࡓࡀ㸪ྠ୍⢏ᚄ࡛ࡶΰྜẚ࡟ࡼࡗ࡚Dࡢ್ࡣ␗࡞ࡗࡓ㸬 0.23mm ࡢ◁♟⢏Ꮚ࡟࠾࠸࡚㸪ᅛ┦࡜ぢ࡞ࡏࡿሙྜ࡜㸪୍㒊ࡀᾮ┦࡜ࡳ࡞ࡏࡿ㑄⛣ᇦࡀᏑᅾࡍࡿ࡜ࡢ⤖ᯝࡀᚓࡽࢀࡓࡇ࡜࡟╔┠ࡍࡿ࡜㸪ᅵ▼ὶ୰࡛ᾮ┦࡜ࡳ࡞ࡏࡿࠕᚤ⣽⢏Ꮚࠖࡢ⢏ᚄࡣ㸪ᗄఱᏛⓗ࡞᮲௳࡛ࡣ࡞ࡃຊᏛⓗ࡞᮲௳࡟ࡼࡗ࡚Ỵᐃࡉࢀࡿ࡜⪃࠼ࡽࢀࡓ㸬ཧ⪃ᩥ⊩㸸1) すཱྀࡽ (2011) ◁㜵Ꮫ఍ㄅ, 64 (3), 11-20 2) Hotta N. & Miyamoto K. (2008) International Journal ofErosion Control Engineering, 1 (2): 54-61.

㪄㩷㪙㪄㪈㪈㪎㩷㪄