東急建設技術研究所報 No. 46

U.D.C 624. 012. 016 : 624. 042. 2

㕲㦵㒊ᮦ࡜⁐᥋ࡉࢀࡓ㗰〇ࣉ࣮ࣞࢺࡀ㕲➽ࢥࣥࢡ࣮ࣜࢺ༊㛫࡜㕲㦵༊㛫ࡢቃ⏺࡟㓄ࡉࢀࡓᇙ㎸ࡳᙧᘧࡢ」ྜᱱࡢ㒊ᮦ๛ᛶホ౯ࣔࢹ࣮ࣝࡑࡢ㸰ࠉ㠀ᙎᛶᇦ࡟࠾ࡅࡿホ౯ࣔࢹࣝࡢᛶ㉁࣮బ⸨ࠉⰋ௓ࠉᑠ⃝ࠉ₶἞ࠉ୰⏣ࠉᐶ஧せ⣙ ࠉ๓ሗࡑࡢ 1 ࡛ࡣ  㕲➽ࢥࣥࢡ࣮ࣜࢺ༊㛫࡜㕲㦵༊㛫ࡢቃ⏺࡟㓄ࡉࢀ㕲㦵㒊ᮦ࡜⁐᥋ࡉࢀࡓ㗰〇ࣉ࣮ࣞࢺࢆ᭷ࡍ
ࡿᇙ㎸ࡳᙧᘧࡢ」ྜᱱ࡟ࡘ࠸࡚  ᙎᛶᇦ࡟࠾ࡅࡿ㒊ᮦ๛ᛶࡢホ౯ࣔࢹࣝࡢᐃᘧ໬ࢆ⾜࠸  ࣔࢹࣝࡀ୚࠼ࡿホ౯್
ࡢᛶ㉁ࡢ⢭ᰝࢆヨࡳࡓࠋᮏሗࡑࡢ 2 ࡛ࡣ  ྠࡌホ౯ࣔࢹࣝࡢホ౯ᑐ㇟ࢆ㠀ᙎᛶᇦ࡟ࡲ࡛ᣑᙇࡋ࡚๓ሗྠᵝࡢࣃ࣓ࣛࢺࣜࢵࢡ࣭ࢫࢱࢹ࢕ࢆ⾜࠺ࡇ࡜࡛  ᮏ」ྜᱱࡢ㒊ᮦ๛ᛶࡢ㠀ᙎᛶᇦ࡟࠾ࡅࡿᛶ㉁࡟ࡶ᳨ウࡀຍ࠼ࡽࢀ࡚࠸ࡿࠋ
㺕㺎㺺㺎㺢㺼  ᇙ㎸ࡳᙧᘧࡢ」ྜᱱ , 㒊ᮦ๛ᛶ , 㦵᱁᭤⥺ , ࢺࣜࣜࢽ࢔ࣔࢹࣝ
3. ࡲ࡜ࡵ

┠ḟ  1. ࡣࡌࡵ࡟2. ホ౯ࣔࢹࣝࡢ㠀ᙎᛶᇦ࡟࠾ࡅࡿᐃᘧ໬࡜ࡑࡢᛶ㉁ࠉࡣࡌࡵ࡟ࠉࡑࡢ 2 ࡛ࡣ  ࡑࡢ 1 1) ࡛ᙎᛶᇦ࡟ࡘ࠸࡚ゐࢀࡽࢀࡓホ㝆అᙉᗘ , rcd ࡣ RC ༊㛫ࡢ᭷ຠࡏ࠸ , n ࡣ㕲➽࡜ࢥࣥࢡ࣮ࣜࢺࡢᮦᩱ๛ᛶẚ , pt ࡣ RC ༊㛫ࡢᘬᙇ㕲➽ẚ , rcD ࡣ౯ࣔࢹࣝ࡟㛵ࡋ  ࡑࡢ㠀ᙎᛶᇦࡢホ౯᪉ἲࡢᐃᘧ໬࠾RC ༊㛫ࡢᱱࡏ࠸࡛࠶ࡿࠋ࡞࠾㝆అⅬ࡟࠾ࡅࡿ๛ᛶపୗ⋡ D y ࢆồࡵࡿᘧ ( 3 ) ୰ࡢࢩ࢔ࢫࣃࣥ a ࡟ࡘ࠸࡚ࡣ , RC

ࡼࡧᛶ㉁ࡢ⢭ᰝࢆヨࡳࡿࠋ༊㛫ࡢ㛗ࡉ rcl ࡀࡇࡢ a ࡟┦ᙜࡍࡿࡇ࡜࡜ࡍࡿ 3)ࠋࡲࡓࡇ
ࡢ๛ᛶపୗ⋡ D y ࡟ࡘ࠸࡚ࡣࡉࡽ࡟ , ᘧ ( 3 ) ࡢ㐺⏝⠊ᅖ࡜㸬ホ౯ࣔࢹࣝࡢ㠀ᙎᛶᙧᇦ࡟࠾ࡅࡿᐃᘧ໬࡜ࡑࡢᛶ㉁ࠉ㠀ᙎᛶᇦ࡟࠾ࡅࡿ㒊ᮦ๛ᛶࡢホ౯ࡋ࡚ࠕࢩ࢔ࢫࣃࣥẚ 2.0 㹼 5.0 ࠖࡀ RC つ‽࡟࡚ᐃࡵࡽࠉホ౯ࣔࢹࣝࡢ㠀ᙎᛶᇦ࡟࠾ࡅࡿ㒊ᮦ๛ᛶࡣ , ྛᵓᡂせࢀ࡚࠸ࡿ 2) ࡀ , ᮏㄽᩥ࡛ࡣ㐣ཤࡢ᳨ウ⤖ᯝ 4) ࢆ཯ᫎࡉࡏ ,⣲ࡢࡑࢀࡒࢀ࡟㠀⥺ᙧᛶࢆ୚࠼ , ┦஫࡟㔜ࡡྜࢃࡏࡿࡇ

ࢩ࢔ࢫࣃࣥẚࡢ್ࡢ኱ᑠࢆၥࢃࡎᘧ ( 3 ) ࢆ᥇⏝ࡍࡿࠋ࡜࡛ホ౯ࡍࡿࠋࡍ࡞ࢃࡕ , ࡲࡎ RC 㐀ᱱࡢ㒊ᮦ๛ᛶࡣ ,ࠉࡲࡓ᭤ࡆࣂࢿࡣ , ᅗ 1 ( c ) ࡀ⾲⌧ࡍࡿࡼ࠺࡟ RC 㐀ᱱ

㏻ᖖࡢ RC 㐀ᱱ࡜ྠᵝ࡟ , RC つ‽2)࡟‽ࡌࡓࢺࣜࣜࢽྠᵝࡢࢺࣜࣜࢽ࢔ᆺࡢ㠀ᙎᛶᛶࢆ♧ࡍࡶࡢ࡜ࡍࡿࠋࡇ

࢔ᆺࡢపୗࢆ࿊ࡍࡿࡶࡢ࡜ࡍࡿࠋࡇࢀࡣ , ᅗ 1 ( b ) ୰ࡢ᭤ࡆࡦࡧ๭ࢀ࣮࣓ࣔࣥࢺ rcM c , 㝆అ࣮࣓ࣔࣥࢺ rcM y , 㝆ࢀࡣ , ࡑࡢ 11) ࡛ᐃ⩏ࡋࡓ㏻ࡾ , ࡇࡢኚᙧᡂศࡀ RC ༊㛫㰯ඛ࡟࠾ࡅࡿ S 㒊ᮦࡢ๛యᅇ㌿ゅ࡟ẚ౛ࡋ , ࠿ࡘࡑࡢ2)

అⅬ࡟࠾ࡅࡿ๛ᛶపୗ⋡ D y ࢆ , ࠸ࡎࢀࡶ RC つ‽ ࡀ๛యᅇ㌿ゅࡀ RC ༊㛫ࡢኚᙧ࡜ࡢ㐃⥆᮲௳ࢆ㉳Ⅼ࡟ồᐃࡵࡿḟᘧ ( 1 ) 㹼ᘧ ( 3 ) ࡟ࡼࡗ࡚ồࡵࡽࢀࡿࡇ࡜ࢆព

ࡵࡽࢀ࡚࠸ࡿࡓࡵ࡛࠶ࡿࠋࡍ࡞ࢃࡕᅗ 1 ( c ) ࡣ , ⮬⏤➃࡟స⏝ࡍࡿࡏࢇ᩿ຊ Q ࡜ S 㒊ᮦࡢ๛యᅇ㌿࡟ࡼࡿኚᙧ

࿡ࡍࡿࠋrc Mc = 0.56√

c σB × rc Ze࡟┦ᙜࡍࡿ s G r ࡀ , RC 㐀ᱱࡢ๛ᛶపୗ࡜ྠᮇࡋ࡚ᣲື

(1)ࡍࡿࡼ࠺࡟ᥥ࠿ࢀࡓࠕ࣮࣓ࣔࣥࢺ࡜㒊ᮦኚᙧゅࡢ㛵ಀࠖrc My = 0.9αy =(2)at r σy rc d

a0.043 + 1.64 n pt + 0.043
rc Drc drc D࡛࠶ࡾ , RC 㐀ᱱࡢ᭤ࡆࡦࡧ๭ࢀ࣮࣓ࣔࣥࢺ࠾ࡼࡧ㝆అ࣮࣓ࣔࣥࢺ࡟ᑐᛂࡍࡿⅬࡀ , ࡑࢀࡒࢀ rc M c ࠾ࡼࡧ rc M y

2(3)࡟ ( s ln / l ) ࢆ஌ࡌࡿࡇ࡜࡛ᚓࡽࢀ࡚࠸ࡿࠋ

ࠉࡇࡇ࡟ , c V B ࡣࢥࣥࢡ࣮ࣜࢺࡢᮦᩱᙉᗘ , rcZe ࡣ᭷➽ࡢሙྜࡢ᩿㠃ಀᩘ 2), a t ࡣᘬᙇ㕲➽ࡢ᩿㠃✚ , r V y ࡣ㕲➽ࡢ
M fa

M faRC ༊㛫➃䛻స⏝䛩䜛᭤䛢䝰䞊䝯䞁䝖ࠉ࡞࠾ S 㐀ᱱࡢ㠀ᙎᛶᇦ࡟ࡘ࠸࡚ࡣ , ᅗ 1 ( d ) ࡟♧ࡍ㏻
ࡾ , ㏻ᖖࡢ S 㐀ᱱ࡜ఱࡽኚࢃࡿࡇ࡜࡞ࡃ , 㝆అ࣮࣓ࣔࣥ
Mno RC ༊㛫㰯ඛ䛻స⏝䛩䜛RC ༊㛫➃䛻స⏝䛩䜛᭤䛢䝰䞊䝯䞁䝖sln

rc Q y ᫬My䕰rc M yD y rc S
S' = D' SMcSR㒊ᮦኚᙧゅ( a )ホ౯ࣔࢹࣝrc Rrc Sslnsln

 lll

D rc Src M cMno RC ༊㛫㰯ඛ䛻స⏝䛩䜛᭤䛢䝰䞊䝯䞁䝖㒊ᮦኚᙧゅD sS rsS r᭤䛢䝰䞊䝯䞁䝖sMyrc Q y ᫬17

rc Q y ᫬䕰䕰Dy s S r䕰sRr

㒊ᮦኚᙧゅ( b )RC 㐀ᱱ( c )᭤ࡆࣂࢿ
ᅗ㸯ࠉホ౯ࣔࢹࣝ࡜ࡑࡢᵓᡂせ⣲ࡢ㠀ᙎᛶᇦ࡟࠾ࡅࡿᣲື* ᢏ⾡◊✲ᡤࠉᵓᕤἲ࣭ᮦᩱࢢ࣮ࣝࣉࠉࠉ** ᢏ⾡◊✲ᡤࠉᇶ♏࣭ᵓ㐀ࢢ࣮ࣝࣉsMprc Q u ᫬sS es Re㒊ᮦኚᙧゅ( d )S 㐀ᱱ

東急建設技術研究所報 No. 46ࠉ➨஧໙㓄༊㛫࡟࠾ࡅࡿホ౯ࣔࢹࣝ඲యࡢ㒊ᮦ๛ᛶࠉ๓ᥖᅗ 1 ࡣ  ホ౯ࣔࢹࣝ  RC 㐀ᱱ  ᭤ࡆࣂࢿࡢ➨ࢺ࡜඲ረᛶ࣮࣓ࣔࣥࢺ࡛㒊ᮦ๛ᛶࢆኚ໬ࡉࡏࡿ㦵᱁᭤⥺࡜ࡋ࡚ࣔࢹࣝ໬࡛ࡁࡿࡇ࡜࡜ࡍࡿࠋࠉᮏ」ྜᱱ࡟ࡼࡗ࡚ᵓ⠏ࡉࢀࡿᯫᵓࡢ㸰ḟタィࢆ⾜࠺஧໙㓄༊㛫ࡢᵝ┦ࢆࡼࡾヲ⣽࡟ᥥ࠸ࡓ࣮࣓ࣔࣥࢺ㸫㒊
ᮦኚᙧゅ㛵ಀ࡛࠶ࡿࠋࡇࡢᅗ 1 ୰࡟ぢࡿ D y ࡣ  ᘧ ( 3 )ሙྜ  ᙜヱᯫᵓࢆᵓᡂࡍࡿྛ㒊ᮦࡢ᳨ウࡣ  ࡑࢀࡒࢀ࡟♧ࡋࡓ㏻ࡾ RC つ‽ 2) ࡀᐃ⩏ࡍࡿ㝆అⅬ࡟࠾ࡅࡿ๛ࡀᙎᛶᇦࢆ㉸࠼ࡓ㠀ᙎᛶᇦ࡛ᣲືࡍࡿࡇ࡜ࢆ๓ᥦ࡟ᐇ᪋ࡉࢀࡿࠋࡇࡢ㐣⛬࡟࠾࠸࡚  ᅗ 1 ࡢࡼ࠺࡟⾲⌧ࡉࢀᛶపୗ⋡࡛࠶ࡿࡀ  ࡇࢀࡣඖ᮶  ➨஧໙㓄༊㛫ෆࡢ௵ࡿᮏホ౯ࣔࢹࣝࡢᵓᡂせ⣲ࡢኚᙧࡢ࠺ࡕ  RC 㐀ᱱࡢࡑࡌࡓ๭⥺๛ᛶࠖ࡟ࡼࡗ࡚≉ᐃࡍࡿࡇ࡜ࢆពᅗࡋ࡚ᑟධࡉࢀࡓಀᩘ࡛࠶ࡿ 2)ࠋࡍ࡞ࢃࡕ  RC 㐀ᱱࡢ㦵᱁᭤⥺ࢆࠉ㠀ᙎᛶᇦ࡟࠾ࡅࡿᮏホ౯ࣔࢹࣝࡢᛶ㉁ពࡢⅬࢆ  ྠᵝ࡟ࠕ㒊ᮦᙎᛶ๛ᛶ࡟๛ᛶపୗ⋡ D ࢆ஌ࢀ࡟㛵ࡋ࡚ࡣࡼࡾៅ㔜࡞⌮ゎࡀᚲせ࡜࡞ࡿࠋࠉࡇࡢᵓᡂせ⣲ࡣ ࠕ୍㒊࠶ࡿ࠸ࡣ඲㒊࡟ S 㒊ᮦࡀᇙ౛♧ࡋࡓᅗ 1 ( b ) ࡛࠶ࢀࡤ  ᭤ࡆ㝆అⅬ࡟࠾ࡅࡿ๭⥺๛ᛶࢆ D y rc S  ➨஧໙㓄༊㛫ෆࡢ௵ពࡢⅬ࡟࠾ࡅࡿ๭㎸ࡲࢀࡓ RC ༊㛫ࠖࢆᢳ㇟໬ࡋࡓࡶࡢ࡛࠶ࡿࡓࡵ  ᙜヱ㒊ࡢタィ࡟࠶ࡗ࡚ࡣ ࠕ RC ࡟ S 㒊ᮦࡀᇙ㎸ࡲࢀ࡚⥺๛ᛶࢆ D rc S ࡜⾲⌧ࡋࡓሙྜࡢ D y ࡜ D ࡣ  ᘧ ( 4 ) ࡟࠸ࡿᙳ㡪ࠖࢆ㐺ษ࡟཯ᫎࡉࡏࡓ᳨ウࡀồࡵࡽࢀࡿ 5)ࠋ

ࡼࡗ࡚㛵㐃௜ࡅࡽࢀࡿ 2)ࠋ

᪤࡟ከࡃࡢሗ࿌ࡀⅭࡉࢀ࡚࠸ࡿࡼ࠺࡟  ࡇࡢ࠺ࡕ≉࡟RC ࡣ  S 㒊ᮦࡀᇙ㎸ࡲࢀࡿࡇ࡜ࡢᙳ㡪ࡀࡏࢇ᩿ᙉᗘ࡟

1=1+αࡲ࡛ཬࡪ࡜ࡉࢀࡇࢀࡲ࡛࡟ࡶάⓎ࡞㆟ㄽࡀ㔜ࡡࡽࢀ࡚࠾ࡾࡓ࡜࠼ࡤ 6),7)  㕲➽ࢥࣥࢡ࣮ࣜࢺ㐀ᘓ≀ࡢ㠎ᛶಖドᆺ⪏

1−1αy
rc M c1−Mf arc M c1−rc My(4)㟈タィᣦ㔪࣭ྠゎㄝᘧ 8)㸦௨ᚋ ࠕ㠌ᛶᣦ㔪ᘧࠖ࡜␎グ㸧ࠉᮏホ౯ࣔࢹࣝ࡟࠾࠸࡚ࡣ  ๓グࡢࡼ࠺࡟ࠕ RC 㐀ᱱࢆಟṇࡍࡿ࢔ࣉ࣮ࣟࢳࡀ✀ࠎᥦ᱌ࡉࢀ࡚࠸ࡿࠋࠉࠕ RC 㐀ᱱࡢኚᙧ࡟  ࡼࡾៅ㔜࡞⌮ゎࡀᚲせ࡜࡞ࡿࠖ࡜᭤ࡆࣂࢿࡀ๛ᛶపୗ⋡ D y ࢆඹ᭷ࡍࡿࠖ࡜ࡢ௬ᐃࡀタࡅࡽࢀ࡚࠸ࡿࡀ  ࡇࡢ௬ᐃࡣྠ᫬࡟ ࠕ RC 㐀ᱱ࡜ᡤ௨ࡣ  ࡇࡢࡼ࠺࡟᥼⏝ࡉࢀࡿ㠌ᛶᣦ㔪ᘧࡀ  ᅗ 2 ࡢࡼ᭤ࡆࣂࢿࡀ  ➨஧໙㓄༊㛫ෆࡢ௵ពࡢⅬࢆᐃࡵࡿ๛ᛶ࠺࡞ᴫᛕ࡛ࠕ᭤ࡆ㝆అᚋࡏࢇ᩿◚ቯࠖࢆ⾲⌧ࡋ࡚࠸ࡿⅬపୗ⋡ D ࡶඹ㏻ࡉࡏࡿࠖࡇ࡜ࢆព࿡ࡍࡿ 9)ࠋࡍ࡞ࢃࡕ ホ౯ࣔࢹࣝ඲యࡀᅗ 1 ( a ) ୰ࡢࠐ༳࡟♧ࡍࡼ࠺࡞ࠕ㦵࡟࠶ࡿࠋࡇࡢࡏࢇ᩿タィἲ࡛ࡣ  ᭤ࡆ㝆అᚋࡢረᛶኚᙧ
ࡢ㐍ᒎ࡟క࠺ࡏࢇ᩿ᙉᗘࡢపୗࡀረᛶࣄࣥࢪࡢᅇ㌿ゅࡢ᱁᭤⥺ୖࡢ➨஧໙㓄༊㛫ෆࡢ௵ពࡢⅬ࡟┦ᙜࡍࡿࠖኚ
ᙧ≧ែ࡟࠶ࡿ᫬  ࡇࢀࢆᵓᡂࡍࡿ RC 㐀ᱱ࡜᭤ࡆࣂࢿ㛵ᩘ࡜ࡉࢀ࡚࠸ࡿ 8)ࠋ
ࠉᮏ」ྜᱱࡀࠕ S 㒊ᮦ࡟ඛࢇࡌ࡚ RC ༊㛫➃࡟࡚᭤ࡆ㝆అࡍࡿࠖሙྜ  RC ࡢࡏࢇ᩿タィ࡟ࡇࡢᙳ㡪ࢆ཯ᫎࡉࡢኚᙧࡶࡑࢀࡒࢀࡢ㦵᱁᭤⥺ࡢ➨஧໙㓄༊㛫ෆࡢⅬ࡛≉ᐃࡉࢀࡿ≧ែ࡟࠶ࡾ  ࠿ࡘࡇࢀࡽ஧Ⅼࡣ  ᘧ ( 4 ) ࡟ࡏ  ᭤ࡆ㝆అᚋࡢࡏࢇ᩿ᙉᗘࡢపୗࢆṇࡋࡃ⪃៖ࡋ࡞ࡼࡗ࡚୚࠼ࡽࢀࡿྠ୍ࡢ๛ᛶపୗ⋡ D ࢆྛࠎࡢ㒊ᮦࡅࢀࡤ࡞ࡽ࡞࠸ࡇ࡜ࡣゝ࠺ࡲ࡛ࡶ࡞࠸ࠋࡑࡋ࡚ࡑࡢ㝿ࡢᅗ 1 ୰ࡢረᛶኚᙧ⬟ຊ rc Rp ࡣ ࠕ」ྜᱱ඲యࡢ㒊ᮦኚᙎᛶ๛ᛶ࡟஌ࡎࡿࡇ࡜࡛ᐃࡵࡽࢀࡿ㛵ಀ࡟࠶ࡿࠋࡋࡓࡀࡗ࡚  RC ༊㛫➃ࡢ᭤ࡆ㝆అࡀඛ⾜ࡍࡿሙྜ  S 㐀

ᙧゅ R ࡛ࠖࡣ࡞ࡃࠕ᭤ࡆ㝆అᚋࡢ RC ༊㛫ࡢ㒊ᮦኚᙧᱱࡀ⤊ጞᙎᛶᣲືࢆಖࡘࡇ࡜ࢆ⪃៖ࡍࡿ࡜  」ྜᱱ඲ゅ rc R ࠖࢆᇶㄪ࡟⟬ᐃࡍ࡭ࡁ࡜⪃࠼ࡿࡢࡀ⮬↛࡛࠶ࡿࠋࠉ୍᪉ᐇົୖࡣ  ࡓ࡜࠼ࡤᯫᵓタィ࡟࠶ࡗ࡚  㒊ᮦࡢయࡀᅗ 1 ( a ) ࡢࡼ࠺࡞➨஧໙㓄༊㛫ෆࡢ௵ពࡢኚᙧ≧ែ࡟࠶ࡿ㝿ࡢྛᵓᡂせ⣲ࡢᵓᡂ㛵ಀࡣ  ᘧ ( 5 ) ࡜ࡋ࡚┠ᶆᵓ㐀ᛶ⬟ 10) ࡀࠕ」ྜᱱ඲యࡢረᛶኚᙧ⬟ຊࠖ࡜ࡋᩘᘧ⾲グ࡛ࡁࡿࡇ࡜࡟࡞ࡿࠋ᩿◚ቯࡢ᳨ウ࡟㝿ࡋ࡚ࡢᡂ⇍ࡋࡓ㆟ㄽࡢᐇ⌧ࢆ┠ⓗ࡟ ⎧⎧
Mf arc δ⎪⎪⎪=rc R =M=αSR⎪⎪
farcrc⎪⎪αSlrcrc⎪⎪⎪⎪⎪⎪⎨⎨Mno
Mf a s ln s δr==(5)Mno= α s Sr s R r ⇔ s Rr =⎪⎪α s Srα s Sr ls ln⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎩M = S R⎪⎩s Re = Mno = Mf a s ln = s δe
nos es els Ses Ses lnᮏホ౯ࣔࢹࣝࡀ୚࠼ࡿ㠀ᙎᛶᇦࡢኚᙧ࡟ࡘ࠸࡚  ࣔࢹࣝ

ࠉᘧ ( 5 ) ࡼࡾ  ホ౯ࣔࢹࣝ඲యࡀ➨஧໙㓄༊㛫࡟࠶ࡿ඲య࡜ྛᵓᡂせ⣲ࡢ┦஫㛵ಀ࡟㛵ࡍࡿ᳨ウࢆ⾜࠺ࠋሙྜࡢྛᵓᡂせ⣲ࡢኚᙧ rc G  s G r  s G e ࡀồࡵࡽࢀࡿࡓ

Q 䛫䜣᩿ຊࡵ  ࡇࢀࢆྜ⟬ࡍࡿࡇ࡜࡛  㠀ᙎᛶᇦ࡟࠾ࡅࡿ඲యࡢ
ࡓࢃࡳ G ࡀᘧ ( 6 ) ࡜ࡋ࡚ᚓࡽࢀࡿࠋ࡚タᐃࡉࢀࡿࡇ࡜ࡶ᝿ᐃࡍ࡭ࡁ࡛࠶ࡾ  ࡇࡢሙྜ ࠕ」ྜᱱ඲యࡢ㒊ᮦኚᙧゅ R ࡜ RC ༊㛫ࡢ㒊ᮦኚᙧゅ rc R ࡜ࡢ㛵ಀࠖ࡟ᇶ࡙࠸ࡓ㆟ㄽࡀᮃࡲࢀࡿࡇ࡜࡟࡞ࡿࠋࠉ௨ୖࡼࡾࡇࡇ࡛ࡣ  ᮏ」ྜᱱࡢ㸰ḟタィ᫬  ≉࡟ࡏࢇ䛫䜣᩿ᙉᗘ䛫䜣᩿◚ቯδ =rc δ +sδr +sδe = Q᭤䛢㝆అ᫬rc R p

rc R yrc R u(6)ࠉD = 1 ࡢ᫬  ࡑࡢ 1 ࡛ᐃ⩏ࡋࡓ㒊ᮦᙎᛶࡓࢃࡳ࡜୍⮴ࡍࡿᘧ ( 6 ) ࡣ  ᮏ」ྜᱱ඲యࡢ⮬⏤➃ࡓࢃࡳࢆᙎᛶᇦረᛶኚᙧ⬟ຊ᭤䛢䜂䜃๭䜜᫬

22l rc ls lns ln+=R l+α rc S
α s Srs Serc R࡟㝈ᐃࡍࡿࡇ࡜࡞ࡃ⾲⌧ࡍࡿ୍⯡ᘧ࡟┦ᙜࡋ  ࡉࡽ࡟
ྠᘧ ( 6 ) ࡟௜ࡋࡓ㏻ࡾ  ࡇࡢ G ࢆࢩ࢔ࢫࣃࣥ l ࡛㝖ࡍ㒊ᮦኚᙧゅᅗ㸰ࠉ㠌ᛶᣦ㔪࡟࠾ࡅࡿࡏࢇ᩿◚ቯࣔࢹࣝ

18

東急建設技術研究所報 No. 46

ࡇ࡜࡛  㒊ᮦኚᙧゅ R ࡶ୍⯡ᘧ࡜ࡋ࡚ᐃ⩏࡛ࡁࡿࠋᅗ
1 ( a ) ୰ࡢ S' ࡣ  」ྜᱱ඲యࡢ㦵᱁᭤⥺࡟࠾࠸࡚  ᮦィ࡟๓ᥖᅗ 2 ࡢᴫᛕࢆ཯ᫎࡉࡏࡿ࡟ࡣ  ࡓ࡜࠼ࡤࠕ⤊ᒁ᫬ࡢ」ྜᱱ඲యࡢ㒊ᮦኚᙧゅ R ࠿ࡽ RC ༊㛫ࡢ㒊ᮦ➃᭤ࡆ࣮࣓ࣔࣥࢺ M fa ࡜඲యࡢ㒊ᮦኚᙧゅ R ࡛ᐃࡲࡿኚᙧゅ rc R ࢆᑟฟࡋࡓ࠺࠼࡛ࡑࡢረᛶኚᙧ⬟ຊ rc Rp ࡟ࡘࠐ༳ࢆᣦࡋ♧ࡍ๭⥺๛ᛶ࡟┦ᙜࡋ  ࡇࢀࢆࠕホ౯ࣔࢹࣝ඲యࡢ㒊ᮦᙎᛶ๛ᛶ S ࡟๛ᛶపୗ⋡ D ' ࢆ஌ࡌࡿࡇ࡜࠸᳨࡚ウࡍࡿࠖࡀせࡉࢀࡿ➼ࡀ᝿ᐃࡉࢀ  ࡑࡢࡓࡵ࡟࡛ồࡵࡽࢀࡿࠖ࡜ࡋࡓሙྜࡢ D ' ࡣ  ᘧ ( 7 ) ࡜࡞ࡿࠋࡢ┦஫㛵ಀࢆṇࡋࡃᢕᥱ࡛ࡁࡿ⎔ቃࡀᩚࡗ࡚࠸ࡿࡇ࡜ࡣ  ホ౯ࣔࢹࣝ඲యࡢኚᙧ࡜ᵓᡂせ⣲ࡑࢀࡒࢀࡢኚᙧ
ࡀᮃࡲࡋ࠸ࠋl rc l + rc S s S e s ln 2 + rc S s S r s ln 2(7)22 αSSls r s erc l + rc S s S e s ln + α rc S s S r s lnsSr sSeα=ࠉࡑࡇ࡛  ホ౯ࣔࢹࣝ඲యࡢࡓࢃࡳ G ࠾ࡼࡧ㒊ᮦኚᙧ
ゅ R ࡟ᑐࡍࡿྛᵓᡂせ⣲ࡢᐤ୚ศࢆࡑࢀࡒࢀࠕࡓࢃࡳ

ࠉ D = 1 ࡢ᫬࡟ D ' ࡶ 1 ࡜࡞ࡾ  ホ౯ࣔࢹࣝ඲యࡢ㒊ᮦࡢᡂศẚࠖ࠾ࡼࡧࠕ㒊ᮦኚᙧゅࡢᡂศẚࠖ࡜ᐃ⩏ࡍࡿ࡜ ᘧ ( 5 ) ࡜ᘧ ( 6 ) ࡟ᇶ࡙࠸࡚ࡑࢀࡒࢀࢆḟࡢᘧ ( 9 ) ࠾ࡼ๛ᛶࡣᙎᛶ๛ᛶ S 1) ࡟୍⮴ࡍࡿࠋࡧᘧ ( 10 ) ࡜ࡋ࡚⾲⌧࡛ࡁࡿࠋࠉࠉ඲యኚᙧ࡜ᵓᡂせ⣲ࡢኚᙧࡢ㛵ಀ
ࠉᅗ 1 ( a ) ࡟♧ࡋࡓᮏ」ྜᱱ඲యࡢᵓᡂ㛵ಀࡣ  ᘧ ( 7 )⎧rc δs S r s S e l rc l
⎪
⎪
=⎪22
⎪δ
⎪
s S r s S e l rc l + rc S s S e s ln + α rc S s S r s ln⎪⎪⎪
2
⎨ δrc S s S e s lns r=⎪ δSSll+S s S e s ln 2 + α rc S s S r s ln 2srsercrc
⎪⎪
⎪⎪⎪ δ
⎪
α rc S s S r s ln 2⎪⎩s e=22
δs S r s S e l rc l + rc S s S e s ln + α rc S s S r s ln

ࡢ D ' ࢆά⏝ࡋࡓ๭⥺๛ᛶࢆ⏝࠸ࡿࡇ࡜࡛  ᘧ ( 8 ) ࡢࡼ࠺࡟ࡑࡢᙎᛶᇦ࠿ࡽ㠀ᙎᛶᇦࡲ࡛ࡢᣲືࢆ㐃⥆ⓗ࡟⾲⌧࡛ࡁࡿࠋMf a = S  R ⇔ Mf a = α S R

(8)

(9)

⎧2
⎪sSr sSe l⎪ rc R =⎪⎪22⎪R⎪
s S r s S e l rc l + rc S s S e s ln + α rc S s S r s ln⎪⎪
⎨ Rrc S s S e l s lns r=( 10 )⎪RSSll+S s S e s ln 2 + α rc S s S r s ln 2
⎪srsercrc⎪⎪⎪⎪α rc S s S r l s ln
⎪s Re⎪=⎩22Rs S r s S e l rc l + rc S s S e s ln + α rc S s S r s lnࠉࡍ࡞ࢃࡕᘧ ( 8 ) ࡟ࡼࡗ࡚  ᮏ」ྜᱱࢆ㸯ᮏࡢ➼㉁ᮦ
࡜ゎ㔘ࡋ  ホ౯ࣔࢹࣝࢆᵓ⠏ࡍࡿࡇ࡜࡞ࡃ⡆᫆࡟  ࡑࡢᮦ➃᭤ࡆ࣮࣓ࣔࣥࢺ Mfa ࡟ᑐࡍࡿᵓᡂ㛵ಀࢆ㠀ᙎᛶᇦࡲ࡛⾲⌧ࡍࡿࡇ࡜ࡶ࡛ࡁࡿࠋ
ࠉࡋ࠿ࡋ࡞ࡀࡽᅗ 1 ( a ) ࡜ᅗ 1 ( b ) ࡢᑐẚ࠿ࡽ᫂ࡽ࠿࡞ࡼ࠺࡟  RC ༊㛫➃ࡢ㈇ᢸ᭤ࡆ࣮࣓ࣔࣥࢺ M fa ࡟ᑐࡋ ホ౯ࣔࢹࣝ඲య࡜ RC 㐀ᱱࡢࡑࢀࡒࢀࡀ୚࠼ࡿኚᙧࡣ 

ࠉᘧ ( 9 ) ࠾ࡼࡧᘧ ( 10 ) ࡣ࡜ࡶ࡟  ᮦ㍈᪉ྥࡢᗄఱᏛ

୧⪅ࡢ㒊ᮦ๛ᛶࡀ␗࡞ࡿࡓࡵ୍⮴ࡍࡿࡇ࡜ࡣ࡞࠸ࠋࡋ
ࡓࡀࡗ࡚  ᮏ」ྜᱱࡢ㸰ḟタィ࡟㝿ࡋ RC ࡢࡏࢇ᩿タⓗ᮲௳࡜ྛᵓᡂせ⣲ࡢ㒊ᮦᙎᛶ๛ᛶ  ࠾ࡼࡧ๛ᛶపୗrc l / l= 0.30

1.0/s r/s e/

1.6rc1.4
1.2

s lb / rc l = 0.80
rc l / l= 0.30

1.0/
s r/
s e/

1.6

rc

1.4
1.2

s lb / rc l = 0.92
rc l / l= 0.30

1.0/
s r/
s e/

1.6

rc

1.4
(-)

1.2

s lb / rc l = 0.69

(-)

(-)

1.4

(-)

1.6

⋡ D ࠿ࡽᵓᡂࡉࢀ࡚࠸ࡿࠋࡍ࡞ࢃࡕྛᡂศẚࡣ  ࡲࡎ

1.2

0.8

0.8

0.8

0.6

0.6

0.6

0.6

0.4

0.4

0.4

0.4

0.2

0.2

0.2

0.2

0.0
1.0

0.0
1.0

0.0
1.0

0.6

0.4
0.2
(-)

0.8

0.6

0.4
0.2
(-)

0.8

0.6

rc l / l= 0.30

0.0
1.0

0.4
0.2(-)

rc

/

s r/
s e/

1.0

0.8

0.8

s lb / rc l = 1.00

0.8

0.6

0.4
0.2
(-)

( a )s lb ࡢᙳ㡪

rc l / l= 0.20

1.0/
s r/
s e/

1.6

rc

1.4
1.2

s lb / rc l = 0.92
rc l / l= 0.30

1.0/
s r/
s e/

1.6

rc

1.4
1.2

s lb / rc l = 0.92
rc l / l= 0.40

1.0/
s r/
s e/

1.6

rc

1.4(-)

1.2

s lb / rc l = 0.92

(-)

(-)

1.4(-)

1.6

1.2

0.8

0.8

0.8

0.6

0.6

0.6

0.6

0.4

0.4

0.4

0.4

0.2

0.2

0.2

0.2

0.0
1.0

0.0
1.0

0.0
1.0

0.6

0.4
0.2
(-)

0.8

0.6

0.4
0.2
(-)

0.8

0.6

0.4
0.2
(-)

( b )rc l ࡢᙳ㡪ᅗ㸱ࠉ๛ᛶపୗ⋡ D ࡢ₞ῶ࡟క࠺ࡓࢃࡳࡢᡂศẚࡢ᥎⛣19

rc l / l= 0.50

0.0
1.0

rc

/s r/s e/

1.0

0.8

0.8s lb / rc l = 0.92

0.8

0.6

0.4
0.2
(-)

東急建設技術研究所報 No. 46

ᮦ㍈᪉ྥࡢᗄఱᏛⓗ᮲௳࡜ྛᵓᡂせ⣲ࡢ㒊ᮦᙎᛶ๛ᛶ㐀ᱱࡢࡓࢃࡳ rc G ࡢ㡰࡟ホ౯ࣔࢹࣝ඲యࡢࡓࢃࡳ G ࡟࡟ࡼࡗ࡚ࡑࡢึᮇ್  ࡘࡲࡾᙎᛶᇦ࡟࠾ࡅࡿ┦஫㛵ಀࡀ☜ᐃࡉࢀ  ࡑࡢᚋ RC ༊㛫➃࡟࠾ࡅࡿ᭤ࡆࡦࡧ๭ࢀ

ᑐࡍࡿᐤ୚ᗘࢆᑠࡉࡃࡋ࡚࠸ࡃࠖᛶ㉁࡜ ࠕホ౯ࣔࢹࡢⓎ⏕ࢆ㉳Ⅼ࡟  ࡑࡢ್ࢆ 1 ࠿ࡽᚎࠎ࡟₞ῶࡉࡏࡿ๛

ࣝ࡜ࡋ࡚ࡢኚᙧࡀ㐍⾜ࡋ࡚ᙎᛶ㝈࠿ࡽ㐲ࡊ࠿ࡿ࡟ࡘࢀ࡚ RC 㐀ᱱ࡜᭤ࡆࣂࢿࡀ඲యࡢࡓࢃࡳ࡟༨ࡵࡿ๭ྜࡀ

ᛶపୗ⋡ D ࡟ࡼࡗ࡚㠀ᙎᛶᇦ࡟࠾ࡅࡿᣲືࡀグ㏙ࡉࢀቑ኱ࡋ࡚࠸ࡃࠖᛶ㉁ࢆಖࡗ࡚࠸ࡿࠋ๓⪅ࡣࡑࡢ 1 ࡟ぢࡿᛶ㉁࡟࠶ࡿࠋ
ࠉᅗ 3 ࡟  ௨ୖࢆ㋃ࡲ࠼  ࡑࡢ 1 ࡛ࡢࣃ࣓ࣛࢺࣜࢵࢡ࣭ࡓᛶ㉁࡜ྜ⮴ࡋ࡚࠸ࡿⅬ࡛  ᚋ⪅ࡣࠕ๛ᛶపୗ⋡ D ࡢ₞ῶ࡟ᚑࡗࡓ RC 㐀ᱱ࡜᭤ࡆࣂࢿࡢ㒊ᮦ๛ᛶࡢపୗ࡟

ࢫࢱࢹ࢕࡟࠾ࡅࡿᶓ㍈࡜⦪㍈࡟┦ᙜࡍࡿ slb  rcl ࡜ rcl  lకࡗ࡚ࡇࢀࡽࡢᵓᡂせ⣲ࡢᡂศࡀୖ᪼ࡋ  S 㐀ᱱࡢࡓࡢኚື࡟క࠺ࠕᮏ」ྜᱱࡢࡓࢃࡳࡢᡂศẚࡢ๛ᛶపୗ

ࢃࡳࡀ┦ᑐⓗ࡟ᑠࡉࡃ࡞ࡿࠖ࡜ࡢㄆ㆑࡜ྜ⮴ࡍࡿⅬ࡛ጇᙜ࡞⤖ᯝ࡜ุ᩿ࡉࢀࡿࡀ  ࡑࡢᵝ┦࡟ slb  rcl  ࡍ࡞

⋡ D ࡢ₞ῶ࡟ᚑࡗࡓ᥎⛣ࠖࢆ♧ࡍࠋ࠸ࡎࢀࡢࢢࣛࣇࡶ 
ࡑࡢ 1 ࡜ྠ୍ࡢඹ㏻ᅉᏊࢆ๓ᥦ࡜ࡋࡓ࠺࠼࡛  ୖẁࡢࢃࡕ RC ༊㛫࡟ᇙࡵ㎸ࡲࢀࡿ S 㒊ᮦࡢ㛗ࡉ࡟ࡼࡿᙳ㡪ᅗ 3 ( a ) ࡟࠾࠸࡚ࡣ  rcl  l ࢆ 0.30 ࡜୍ᐃ࡟ಖࡗࡓ≧ែࡀ཯ᫎࡉࢀࡿࡇ࡜ࡀ࡞࠸ࡇ࡜ࢆ  ࡇࢀࡽࡢࢢࣛࣇࡣ♧࡛ slb  rcl ࡀ  ୗẁࡢᅗ 3 ( b ) ࡟࠾࠸࡚ࡣ  slb  rcl ࢆ 0.92
࡜୍ᐃ࡟ಖࡗࡓ≧ែ࡛ rcl  l ࡀ₞ቑࡋ࡚࠸ࡃ୰࡛ࡢࡓࢃ

ࡋ࡚࠸ࡿࠋࡳࡢᡂศẚࡢ᥎⛣ࡀᅗ♧ࡉࢀ࡚࠸ࡿࠋࡇࡢ㝿  ᶓ㍈ࡀࠕD = 1 ࡜࡞ࡗ࡚๭⥺๛ᛶ࡜ᙎᛶ๛ᛶࡀ୍⮴ࡍࡿⅬ㸦ᙎᛶ࠿ࡽࡣ  ๓グࡢࠕᙎᛶ㝈㏆ഐ࡛ࡢᡂศẚࡢ኱ᑠ㛵ಀࠖ࡜ࠕኚᙧࡢ㐍⾜࡟క࠺ RC 㐀ᱱࡢᙎᛶࡓࢃࡳ rc G ࡜᭤ࡆࣂࢿ㝈㸧ࢆ㉳Ⅼ࡟₞ῶࡋ࡚࠸ࡃࠖࡼ࠺࡟᥇ࡽࢀ࡚࠸ࡿࡓࡵ ᅗ 3 ࡟࠾࠸࡚ࡣ  ࡑࡢ 1 ࡛᫂ࡽ࠿࡟ࡉࢀࡓᙎᛶᇦࡢᛶ

ࡢᙎᛶኚᙧ sG r ࡢᐤ୚ศࡢቑ኱ഴྥࠖࡀᅗ 3 ( a ) ࡛ぢࡓࡑࠉࡘ࠸࡛  ኚືᅉᏊ rc l  l ࡢᙳ㡪࡟ࡘ࠸࡚♧ࡋࡓᅗ 3 ( b )ࢀ࡜୍⮴ࡋ࡚࠸ࡿ୍᪉࡛  ࡇࢀࡽࡢഴྥ࡟ᑐࡍࡿኚືᅉ
Ꮚ rc l  l ࡢᙳ㡪ࡀ㢧ࢃࢀ࡚࠸ࡿࡇ࡜ࡀ┳ྲྀࡉࢀࡿࠋࡍ࡞

㉁ࡀᙎᛶ㝈࡟┦ᙜࡍࡿ D = 1 ᫬ࡢᡂศẚ࡜ࡋ࡚⾲ࡉࢀ࡚ࢃࡕ  ࡑࡢ 1 ࡛ࡶぢࡓࡼ࠺࡟  ᮏホ౯ࣔࢹࣝ࡟࠾࠸࡚ࡣ rc l  l ࡀ኱ࡁࡃ࡞ࡗ࡚ rc l ࡀ㛗ࡃ࡞ࡿ㸦 sln ࡀ▷ࡃ࡞ࡿ㸧࡟࠾ࡾ  ࡑࡢẚ⋡ࡀࡑࡢᚋ  ᭤ࡆࡦࡧ๭ࢀ  ᭤ࡆ㝆అࢆ⤒࡚᥎⛣ࡋ࡚࠸ࡃᵝࡀྍど໬ࡉࢀ࡚࠸ࡿࡇ࡜࡟࡞ࡿࠋ
ࠉࡣࡌࡵ࡟ᅗ 3 ( a ) ࠿ࡽぢ࡚࠸ࡃ࡜  ࢢࣛࣇ㛫ࡢ┦㐪ࡀṤ࡝࡞ࡃ  ྛࡓࢃࡳࡢᡂศẚࡀ  ኚືᅉᏊ࡛࠶ࡿ s l bࡘࢀ࡚  RC 㐀ᱱࡢᙎᛶࡓࢃࡳ rcG ࡜᭤ࡆࣂࢿࡢᙎᛶኚᙧs G r ࡀ኱ࡁࡃ࡞ࡗ࡚ S 㐀ᱱࡢᙎᛶࡓࢃࡳ s G e ࡀᑠࡉࡃ࡞ࡿ

 rc l ࡟ᑐࡋ࡚㕌ឤ࡟᥎⛣ࡋ࡚࠸ࡿࡇ࡜ࡀ⌮ゎࡉࢀࡿࠋࡍ࡞ࢃࡕ  ྛᵓᡂせ⣲ࡢኚᙧࡣ  slb  rcl ࡜ࡣ࡯ࡰ↓㛵

ᛶ㉁࡟࠶ࡿࡓࡵ  ࡲࡎᙎᛶ㝈࡟࠾ࡅࡿᡂศẚࡢ኱ᑠ㛵ಀ࡟ࡑࡢᙳ㡪ࡀዴᐇ࡟཯ᫎࡉࢀ࡚࠸ࡿࠋຍ࠼࡚  ࡇࡢ RCಀ࡟ ࠕᙎᛶ㝈࡟㏆࠸㡿ᇦ࡟࠾࠸࡚ࡣ S 㐀ᱱࡢࡓࢃࡳ
s G e ࡀ✺ฟࡋ࡚኱ࡁࡃ  ࡘ࠸࡛᭤ࡆࣂࢿࡢኚᙧ s G r  RC㐀ᱱࡢᙎᛶࡓࢃࡳ rcG ࡜᭤ࡆࣂࢿࡢᙎᛶኚᙧ sG r ࡢᣲື࡟╔┠ࡍࡿ࡜  ๓ᥖᅗ 3 ( a ) ྠᵝ ࠕ๛ᛶపୗ⋡ D ࡢ₞ῶrcR / Rrc l / lsRr / R= 0.30

sRe / R

1.6
1.4
1.2s lb / rc l = 0.80

rcR / Rrc l / lsRr / R= 0.30

sRe / R

1.6
1.4
1.2

s lb / rc l = 0.92

rcR / Rrc l / lsRr / R= 0.30

sRe / R

1.6
(-)

1.2

s lb / rc l = 0.69

(-)

1.4

(-)

(-)

1.6

1.4
1.2

1.0

1.0

1.0

1.0

0.8

0.8

0.8

0.8

0.6

0.6

0.6

0.6

0.4

0.4

0.4

0.4

0.2

0.2

0.2

0.2

0.0
1.0

0.0
1.0

0.0
1.0

0.8

0.6

0.4
0.2
(-)

0.8

0.6

0.4
0.2
(-)

0.8

0.6

0.4
0.2
(-)

s lb / rc l = 0.92

rcR / Rrc l / lsRr / Rs lb / rc l = 1.00

rcR / Rrc l / lsRr / R= 0.30

sRe / R

0.0
1.00.80.60.40.2(-)

s lb / rc l = 0.92

rcR / Rrc l / lsRr / R( a )s lb ࡢᙳ㡪
rcR / Rrc l / lsRr / R= 0.20sRe / R

1.6
1.4
1.2

s lb / rc l = 0.92

rcR / Rrc l / lsRr / R= 0.30

sRe / R

1.6
1.4
1.2= 0.40

sRe / R

1.6(-)

1.2s lb / rc l = 0.92(-)

1.4(-)

(-)

1.6

1.4
1.2

1.0

1.0

1.0

1.0

0.8

0.8

0.8

0.8

0.6

0.6

0.6

0.6

0.4

0.4

0.4

0.4

0.2

0.2

0.2

0.2

0.0
1.0

0.0
1.0

0.0
1.0

0.8

0.6

0.4
0.2
(-)

0.8

0.6

0.4
0.2
(-)

0.8

0.6

0.4
0.2
(-)

( b )rc l ࡢᙳ㡪ᅗ㸲ࠉ๛ᛶపୗ⋡ D ࡢ₞ῶ࡟క࠺㒊ᮦኚᙧゅࡢᡂศẚࡢ᥎⛣

20

0.0
1.0

= 0.50sRe / R

0.8

0.6

0.4
0.2(-)

東急建設技術研究所報 No. 46࡟కࡗ࡚₞ቑࡍࡿࠖഴྥࢆඹ㏻ࡉࡏࡘࡘ  ࡇࢀࡽࡢ₞ቑࡀࠕ rc l  l ࡀ኱ࡁࡃ࡞ࡗ࡚ rc l ࡀ㛗ࡃ࡞ࡿ㸦 s ln ࡀ▷ࡃ࡞ࡿ㸧ᵓᡂせ⣲ࡢኚᙧ࡟㓄៖ࡋ࡞࠸ࡇ࡜ࡣࠕ S 㒊ᮦ࡜ࡋ࡚ࡢ

࡟ࡘࢀ⦆៏࡟࡞ࡾ┤⥺ᣲື࡟㏆࡙ࡃഴྥ࡟࠶ࡿࠖࡇ࡜ࢆ

ᐇົୖࡣࡇࡢⅬࡶ඘ศ࡟ㄆ㆑ࡋ࡚࠾ࡃࡇ࡜ࡀᚲせ࡜⪃ㄞࡳྲྀࡿࡇ࡜ࡀ࡛ࡁࡿࠋ
ࡘ࡙ࡃᅗ 4 ( a ) ࠾ࡼࡧᅗ 4 ( b ) ࡣ  ࡓࢃࡳࡢᡂศẚྠ࠼ࡽࢀࡿࠋᵝ  ᘧ ( 10 ) ࡟ࡼࡗ࡚ồࡵࡽࢀࡿ㒊ᮦኚᙧゅࡢᡂศẚ࡜㸬ࡲ࡜ࡵኚᙧࣞ࣋ࣝࡢ㐣ᑠホ౯ࠖ࡟ࡘ࡞ࡀࡿྍ⬟ᛶࡀ࠶ࡿࡓࡵ ๛ᛶపୗ⋡ D ࡢ₞ῶ࡜ࡢ㛵ಀ࡟ࡘ࠸࡚ᐇ᪋ࡋࡓᮦ㍈᪉ࠉ㕲㦵㒊ᮦ࡜⁐᥋ࡉࢀࡓ㗰〇ࣉ࣮ࣞࢺࡀ㕲➽ࢥࣥࢡྥࡢᗄఱᏛⓗ᮲௳࡟ᑐࡍࡿࣃ࣓ࣛࢺࣜࢵࢡ࡞᳨ウࡢ⤖࣮ࣜࢺ༊㛫࡜㕲㦵༊㛫ࡢቃ⏺࡟㓄ࡉࢀࡓᇙ㎸ࡳᙧᘧࡢᯝࢆ♧ࡍࡶࡢ࡛࠶ࡿࡀ  ࡇࡇ࠿ࡽࡶࡓࢃࡳࡢᡂศẚ࡜࡯ࡰྠᵝࡢഴྥࡀ☜ㄆࡉࢀ࡚࠸ࡿࠋࡍ࡞ࢃࡕ RC 㐀ᱱ」ྜᱱࡢ㒊ᮦ๛ᛶࢆホ౯ࡍࡿࣔࢹࣝࢆᵓ⠏ࡋ  ࣔࢹࣝࡢ㒊ᮦኚᙧゅ rcR ࡜᭤ࡆࣂࢿ࡟ࡼࡿ㒊ᮦኚᙧゅ s R r ࡣ ᙎᛶ㝈㏆ഐ࡟࡚ホ౯ࣔࢹࣝ඲యࡢ㒊ᮦኚᙧゅ R ࡼࡾࡶ▱ᜳ  ࡞ࡽࡧ࡟ࡑࡇ࠿ࡽᚓࡽࢀࡿࠕᐇ㝿ࡢタィ᫬࡟᭷ᑠࡉࡃホ౯ࡉࢀ  㠀ᙎᛶᇦ࡟࡚ࡑࢀࡒࢀࡢᐤ୚ศࢆ₞ቑࡉࡏ࡚࠸ࡃࡀ  ࡑࡢᣲືࡣ slb  rcl ࡟ᑐࡋ㕌ឤ࡛ rcl  l࡜  ௨ୗࡢࡼ࠺࡟࡞ࡿࠋ( 1 ) ᮏ」ྜᱱࡢ㒊ᮦ๛ᛶࡣ  ᪤ ࡢᇙ㎸ࡳᙧᘧࡢ࡟ᑐࡋᩄឤ࡞ᛶ㉁ࢆ᭷ࡋ࡚࠸ࡿࠋ᥮ゝࡍࢀࡤ  RC 㐀ᱱࡢ㒊ᮦኚᙧゅ rc R ࡜᭤ࡆࣂࢿ࡟ࡼࡿ㒊ᮦኚᙧゅ s R r ࡣ 」ྜᱱࡢホ౯ᡭἲ࡟‽ࡌࡓኚᙧᣲືゎᯒࡢ࢔ࣉᙎᛶᇦ࡟࠾࠸࡚ホ౯ࣔࢹࣝ඲యࡢ㒊ᮦኚᙧゅ R ࡼࡾ኱ࡁࡃ࡞ࡿࡇ࡜ࡣ࡞࠸ࡶࡢࡢ  RC ༊㛫ࡢ㛗ࡉ rc l ࡀ㛗࠸⪃៖ࡢ࠺࠼  ỗ⏝ࣉࣟࢢ࣒ࣛ࡜ࡢぶ࿴ᛶࢆ☜ಖ᮲௳ୗ࡛㠀ᙎᛶᇦ࡟࠶ࡿሙྜ࡟ࡣ  S 㐀ᱱࡢ㒊ᮦኚᙧᇦࡲ࡛ホ౯࡛ࡁࡿࠋ
( 2 ) ᮏ」ྜᱱ඲యࡢ㒊ᮦኚᙧゅ R ࡣ  ᙎᛶᇦ࡟࠶ࡗ

ࡢᛶ㉁ࡢ⢭ᰝࢆヨࡳࡓࠋᮏホ౯ࣔࢹࣝࡀ᭷ࡍࡿᛶ㉁ࡢ
⏝࡞▱ぢࡢ࿊♧ࠖࢆ┠ⓗ࡜ࡋࡓ㆟ㄽࡢ⤖ᯝࢆࡲ࡜ࡵࡿ࣮ࣟࢳ 6) ࢆ㋃くࡋࡘࡘ  ቃ⏺ࣉ࣮ࣞࢺࡢᙳ㡪ࢆࡋ࡞ࡀࡽࣔࢹࣝ໬ࡍࡿࡇ࡜࡛ᙎᛶᇦ࠿ࡽ㠀⥺ᙧ

ゅ s Re ࢆ㉸࠼ࡿᐤ୚ࢆぢࡏࡿྍ⬟ᛶࡶ࠶ࡿࠋࡲࡓࡑࢀࡒࢀࡢᐤ୚ᗘࡣ  RC ༊㛫ࡢ㛗ࡉ rc l ࡟ከ኱࡞ᙳ㡪ࢆཷࡅ࡚ࡶ㠀ᙎᛶᇦ࡟࠶ࡗ࡚ࡶ RC ༊㛫ࡸ S ༊㛫ࡢ㒊ࡿ୍᪉࡛ S 㒊ᮦࡢᇙ㎸ࡳ㛗ࡉ s lb ࡛ࡣไᚚ࡛ࡁ࡞࠸ᛶ㉁࡟࠶ࡿࡓࡵ  タィᐇົ࡟࠾࠸࡚  ≉࡟㠌ᛶᣦ㔪ᘧ 8) ࢆ

ᮦኚᙧゅࡢᙳ㡪ࡀ」㞧࡟཯ᫎࡉࢀࡓ್ࢆ࡜ࡿࠋࡑࢀᨾ  」ྜᱱ඲యࡢ㒊ᮦኚᙧゅ R ࡜ᐇ㝿࡟᥼⏝ࡍࡿሙྜ࡟ࡣ  ࡇࡢᛶ㉁ࢆ඘ศ࡟ព㆑ࡍࡿᚲせࡀRC ༊㛫࠾ࡼࡧ S ༊㛫࡟⏕ࡌ࡚࠸ࡿ㒊ᮦኚᙧゅ࡟࠶ࡿ࡜⪃࠼ࡽࢀࡿࠋ
ᅗ 4 ࡟࠾࠸࡚ࡉࡽ࡟␃ពࡍ࡭ࡁࡣ  ᙎᛶᇦ࡟㏆࠸≧ࡣ஋㞳ࡀᏑᅾࡍࡿࡓࡵ  ྛ༊㛫ࡢヲ⣽タィ࡟㝿ែࡢ S 㐀ᱱࡢ୍㒊࡟  ᡂศẚࡀ 1 ࢆ㉸࠼࡚࠸ࡿࡶࡢࡀ
ᏑᅾࡍࡿⅬ࡟࠶ࡿࠋᘧ ( 5 ) ࡟♧ࡋࡓ㏻ࡾ  S 㐀ᱱ࡛ࡣせࡀ࠶ࡿࠋࡋ࡚ࡣ  ࡇࡢᕪ␗ࢆṇࡋࡃᢕᥱࡋ཯ᫎࡉࡏࡿᚲ
࡞࠾ᮏㄽᩥ࡛ࡣ ,ࠕ S 㒊ᮦ࡟ඛࢇࡌ࡚ RC ༊㛫➃ࡀ᭤ᙎᛶࡓࢃࡳ s G e ࢆ sln ࡛㝖ࡋ࡚㒊ᮦኚᙧゅ s Re ࡀồࡵࡽࢀࡿ୍᪉࡛  ホ౯ࣔࢹࣝ඲య࡛ࡣ  ᘧ ( 6 ) ࡜ࡋ࡚ࡓࢃ

ࡆ㝆అࡍࡿࠖሙྜ࡟≉໬ࡋ࡚ㄽࢆᒎ㛤ࡋ࡚ࡁࡓࡀ , ᮏホ

ࡳ G ࢆࢩ࢔ࢫࣃࣥ l ࡛㝖ࡋ࡚㒊ᮦኚᙧゅ R ࡀồࡵࡽࢀࡆ㝆అࡀඛ⾜ࡍࡿሙྜ࡟ࡶᐜ᫆࡟ᑐᛂࡍࡿࡇ࡜ࡀ࡛ࡁࡿࠋࡓࢃࡳࢆ㒊ᮦ㛗࡛㝖ࡋ࡚↓ḟඖ໬ࡍࡿࡇࡢ㐣⛬࡟ࡿࠋࡓࡔࡋ , ᪤࡟㏙࡭ࡓࡼ࠺࡟ , ᮏホ౯ࣔࢹࣝࡣ , ᮏ」࠾࠸࡚ᇶ‽࡜࡞ࡿ㛗ࡉࡀ␗࡞ࡿࡇ࡜࡟㉳ᅉࡍࡿࡇࡢ⤖ྜᱱࡢ᭤ࡆኚᙧࡢ㏣㊧ࡢࡳ࡟≉໬ࡋ࡚࠸ࡿࡓࡵ , ᐇ㝿ࡢᯝࡣ ࠕᮏホ౯ࣔࢹࣝ࡟࠶ࡗ࡚ࡣ  ඲యࡢ㒊ᮦኚᙧゅࡼࡾࡶ S 㐀ᱱࡢ㒊ᮦኚᙧゅࡀ኱ࡁࡃ࡞ࡗ࡚࠸ࡿሙྜࡀタィ࡟㝿ࡋ࡚ࡣࡏࢇ᩿ኚᙧࡢᙳ㡪ࢆࡶ⟬ධࡋࡓ᳨ウࢆ࠶ࡿࠖࡇ࡜ࢆྠ᫬࡟♧၀ࡍࡿࠋࡍ࡞ࢃࡕ  」ྜᱱࡢᵓ㐀タィ࡟㝿ࡋ  ඲యࡢ㒊ᮦኚᙧゅ R ࡢࡳ࡟╔┠ࡋ࡚ྛࡃタィࡋ࡚ , ᮏホ౯ࣔࢹࣝᵓ⠏ࡢ㝿࡟タࡅࡓ๓ᥦ᮲௳ࢆ

౯ࣔࢹࣝࡣ , ࡑࡢᵓᡂ࠿ࡽ᫂ࡽ࠿࡞ࡼ࠺࡟ , S 㒊ᮦࡢ᭤⾜࠺ᚲせࡀ࠶ࡿࠋࡲࡓࡶࡕࢁࢇ , ቃ⏺ࣉ࣮ࣞࢺ➼ࢆṇࡋ☜ಖࡋ࡞ࡃ࡚ࡣ࡞ࡽ࡞࠸ࠋࠉཧ⪃ᩥ⊩ బ⸨Ⰻ௓ , ᑠ⃝₶἞ , ୰⏣ᐶ஧ : 㕲㦵㒊ᮦ࡜⁐᥋ࡉࢀࡓ㗰〇ࣉ࣮ࣞࢺࡀ㕲➽ࢥࣥࢡ࣮ࣜࢺ༊㛫࡜㕲㦵༊㛫ࡢቃ⏺࡟㓄ࡉࢀࡓᇙ㎸ࡳᙧᘧࡢ」ྜᱱࡢ㒊ᮦ๛ᛶホ౯ࣔࢹࣝࠉ㸫ࡑࡢ㸯ࠉ㠀ᙎᛶᇦ࡟࠾ࡅࡿホ౯ࣔࢹࣝࡢᛶ㉁㸫 , ᮾᛴᘓタᢏ⾡◊✲ᡤሗ , No. 46, pp.
. 2021. 2 ᪥ᮏᘓ⠏Ꮫ఍ : 㕲➽ࢥࣥࢡ࣮ࣜࢺᵓ㐀ィ⟬つ‽࣭ྠゎㄝ , 2010
 బ⸨Ⰻ௓, ᑠ⃝₶἞, ௚ 2 ྡ : 㕲㦵㒊ᮦ࡜⁐᥋ࡉࢀࡓ㗰〇ࣉ࣮ࣞࢺ࡛㕲➽ࢥࣥࢡ࣮ࣜࢺ༊㛫ࢆᙉ໬ࡋࡓᇙ㎸ࡳᙧᘧࡢ」ྜᵓ㐀ᱱࡢ㒊ᮦ๛ᛶࡢホ౯ᡭἲ , ࢥࣥࢡ࣮ࣜࢺᕤᏛᖺḟㄽᩥ㞟 , Vol. 35, No. 2, 2013
 బ⸨Ⰻ௓, ᑠ⃝₶἞, ୰⏣ᐶ஧ : 㕲➽ࢥࣥࢡ࣮ࣜࢺ༊㛫࡜㕲㦵༊㛫ࡢቃ⏺࡟㗰〇ࣉ࣮ࣞࢺࡀ㓄ࡉࢀࡓᇙ㎸ࡳᙧᘧࡢ」ྜᱱࡢ㒊ᮦ๛ᛶホ౯ᡭἲࡢ㐺⏝ᛶ , ࢥࣥࢡ࣮ࣜࢺᕤᏛᖺḟㄽᩥ㞟 , Vol. 38, No. 2, 201621東急建設技術研究所報 No. 465) ᪥ᮏᘓ⠏Ꮫ఍ : 㗰ࢥࣥࢡ࣮ࣜࢺᵓ㐀᥋ྜ㒊ࡢᛂຊఏ㐩࡜᢬ᢠᶵᵓ , 20116) 㕥ᮌⱥஅ , すཎᐶ : ᮦ➃㒊 RC 㐀୰ኸ㒊㕲㦵㐀࡛ᵓᡂࡉࢀࡿ」ྜᵓ㐀ᱱࡢࡏࢇ᩿⪏ຊ࡜ኚᙧᛶ⬟ , ᪥ᮏᘓ⠏Ꮫ఍ᵓ㐀⣔ㄽᩥ㞟 ,➨ 73 ᕳ , ➨ 631 ྕ , 20087) 㔠ᮏΎ⮧ , ┿℩ఙ἞ , ᒣ㔝㎶ᏹ἞ : 㕲➽ࢥࣥࢡ࣮ࣜࢺᰕ࡟᥋ྜࡉࢀࡓ㕲㦵ᱱ➃㒊ࢆ㕲➽ࢥࣥࢡ࣮ࣜࢺ࡛ᕳ࠸ࡓΰྜᵓ㐀ᱱࡢ⪏ຊホ౯ , ᪥ᮏᘓ⠏Ꮫ఍኱఍ᵓ㐀⣔ㄽᩥ㞟 , ➨ 76 ᕳ , ➨ 659 ྕ , 20118) ᪥ᮏᘓ⠏Ꮫ఍ : 㕲➽ࢥࣥࢡ࣮ࣜࢺ㐀ᘓ≀ࡢ㠌ᛶಖドᆺ⪏㟈タィᣦ㔪 , 1999.
9) బ⸨Ⰻ௓ , ᑠ⃝₶἞ , ୰⏣ᐶ஧ : 㕲㦵㒊ᮦ࡜⁐᥋ࡉࢀࡓ㗰〇ࣉ࣮ࣞࢺࢆ᭷ࡍࡿᇙ㎸ࡳᙧᘧࡢ」ྜᵓ㐀ᱱࡢ㒊ᮦ๛ᛶࡢホ౯ᡭἲ࡜ࡑࡢ㠀⥺ᙧᛶ࡟㛵ࡍࡿ୍⪃ᐹ , ᪥ᮏᘓ⠏Ꮫ఍኱఍Ꮫ⾡ㅮ₇᱾ᴫ㞟㸦㏆␥㸧, ᵓ㐀 III, 201410) ᪥ᮏᘓ⠏Ꮫ఍ : ྜᡂᵓ㐀タィつ‽ , 2014

A DESIGN MODEL FOR STRUCTURAL BEHAVIOR OF A STEEL BEAM WITH REINFORCED CONCRETE ENCASED ENDS STRENGTHENED WITH STEEL PLATE WELDED TO STEEL MEMBER- FORMULATION OF THE MODEL AND ITS CARACTERISTICS IN INELASTIC REGION R. Sato, J. Ozawa, and H. Nakata
This paper proposes a design model for structural behavior of a steel beam with reinforced concrete encased ends. The steel beamwith reinforced concrete encased ends has steel plates installed at boundaries between reinforced concrete regions and steel region,
which are not only connected to rebars with nuts but also welded to steel member to strengthen reinforced concrete regions.
Aimed at being introduced into practical use, the design model complies with the existing system of structural design in Japan.
Normally, the deformation of steel beam with reinforced concrete encased ends is devided into three constituents as a previous
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deformation of each component is formulated by solving elastic curve equations set up based on an existing mechanical model for
embedded steel column base. Moreover, the model is also possible to simulate structural behaviors in inelastic deformation by addLQJQRQOLQHDULW\WRHDFKFRPSRQHQW%HVLGHVH൵HFWVRIJHRPHWULFFRQGLWLRQDORQJPHPEHUD[LVD൵HFWHGE\VKHDUVSDQOHQJWKRI
reinforced concrete region, and embedded length of steel member were evaluated by analysis results through the design model.
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concrete region.
( 3 ) Drift angle of the steel beam with reinforced concrete encased ends has complicated relationship between that ofreinforced concrete region and of steel region. It makes disagreement between integrated drift angle and other drift
angle occurs in reinforced concrete region or steel region. Thus, it is needed to recognize this disagreement in order toUHÀHFWWKHLQÀXHQFHWRFRQVLGHUDWLRQVIRUGHWDLOVDERXWWKHVHUHJLRQVLQFDVHRISUDFWLFDOVWUXFWXUDOGHVLJQ22