土木学会第66回年次学術講演会(平成23年度)

Ⅲ‑053ከᩘ࢔࣮ࣥ࢝⿵ᙉᅵቨࡢᘬᢤࡁ◚ቯ࣮ࣔࢻ࡟ᑐࡍࡿ LRFD ࢟ࣕࣜࣈ࣮ࣞࢩࣙࣥ㜵⾨኱Ꮫᰯ ṇ ᐑ⏣႐ኖRoyal Military College of Canada R.J. Bathurstᒸ୕ࣜࣅࢵࢡ ṇ ᑠᾉᓅ἞ࡣࡌࡵ࡟ ᆅ┙ᵓ㐀≀ࡢタィἲࡣୡ⏺ⓗ࡟ಙ㢗ᛶ࣮࣋ࢫࡢ㝈⏺≧ែタィἲ࡟⛣⾜ࡋ࡚࠸ࡿ㸬ᮏᩥ࡛ࡣ㸪ከᩘ࢔࣮ࣥ࢝⿵ᙉᅵቨࡢᘬᢤࡁ◚ቯ࣮ࣔࢻࢆᑐ㇟࡟⾜ࡗࡓ LRFD ࢟ࣕࣜࣈ࣮ࣞࢩࣙࣥࡢ᳨ウ⤖ᯝࢆሗ࿌ࡍࡿ㸬タィࣔࢹࣝࡢࣂ࢖࢔ࢫゎᯒ࡟ᇶ࡙ࡃ /5)' ࢟ࣕࣜࣈ࣮ࣞࢩࣙࣥ LRFD ࣇ࢛࣮࣐ࢵࢺ࡛㸪ᘬᢤࡁ◚ቯ࣮ࣔࢻࡢ↷ᰝᘧࢆ᭩ࡅࡤ௨ୗࡢ࡜࠾ࡾ࡜࡞ࡿ㸬
MR R ! J Q Tmax

(1)R㸸⿵ᙉᮦࡢᘬᢤࡁᙉᗘ㸪Tmax㸸ᅵ୰࡟ᩜタࡋࡓ⿵ᙉᮦ࡟⏕ࡌࡿᘬᙇࡾຊ㸦⿵ᙉᮦຊ㸧㸪IR㸸᢬ᢠ࡟㛵ࡍࡿ㒊ศᏳ඲ಀᩘ㸦᢬ᢠಀᩘ㸧㸪JQ㸸Ⲵ㔜࡟㛵ࡍࡿ㒊ศᏳ඲ಀᩘ㸦Ⲵ㔜ಀᩘ㸧࡛࠶ࡿ㸬 㒊ศᏳ඲ಀᩘࡢ⟬ᐃ࡟ࡣ࠸ࡃࡘ࠿ࡢ᪉ἲࡀ࠶ࡿࡀ㸪Ⲵ㔜࣭᢬ᢠഃ࡜ࡶᐇ࡟ࡘ࠸࡚ࡣ㸪ᐇ࣮࣋ࢫࡢ㒊ศᏳ඲ಀᩘ⟬ᐃࡢ◊✲࡛ሗ࿌ࡉࢀ࡚࠸ࡿ⿵ᙉᮦຊࡢ⌧ሙィ1),2)್ࡀ‽ഛ࡛ࡁࡿ㝈⏺≧ែࡢ↷ᰝࡀྜ⌮ⓗ࡜⪃࠼ࡽࢀࡿ㸬ⴭ⪅ࡽࡣ⿵ᙉᅵቨࢆᑐ㇟࡟㸪᪤ ⤖ᯝ㸪ᘬᢤࡁヨ㦂⤖ᯝࢆࢹ࣮ࢱ࣮࣋ࢫ໬ࡋ㸪㒊ศᏳ඲ಀᩘࢆ⟬ᐃࡍࡿྲྀࡾ⤌ࡳࢆ⾜ࡗ࡚࠸ࡿ㸬ከᩘ࢔࣮ࣥ࢝⿵ᙉᅵቨ࡟㛵ࡍࡿᡂᯝࡣᩥ⊩ 3),4)ࢆཧ↷࠸ࡓࡔࡁࡓ࠸㸬ᥦ᱌ἲ࡛ࡣᐇ㝿ࡢⲴ㔜࣭᢬ᢠ್ࡢタィࣔࢹࣝணJ Q = PQ (1+ n s COVQ )್࡟ᑐࡍࡿẚࢆࣂ࢖࢔ࢫ࡜ࡋ㸪ḟᘧ࡛㒊ศᏳ඲ಀᩘࢆ⟬ᐃࡍࡿ㸬(2)(3)
IR = J Q M V exp ( E T ln V )PQ㸪 PR㸸Ⲵ㔜ഃ࣭᢬ᢠഃࡑࢀࡒࢀࡢࣂ࢖࢔ࢫࡢᖹᆒ㸪COVQ㸪COVR㸸ྠࡌࡃኚືಀᩘ㸪M㸸M=PR/PQ㸪V㸸
V=(1+COVQ2)(1+COVR2)㸪ET㸸┠ᶆಙ㢗ᛶᣦᶆ㸪nVࡣⲴ㔜ࢆ࡝ࡢ⛬ᗘᏳ඲ഃ࡟ぢࡿ࠿ࡢᐃᩘ࡛࠶ࡿ㸬 ୍㐃ࡢ᳨ウ࡛ࡣ㸪ᩘከࡃࡢᐇ኱ᐇ㦂ࡢ⤖ᯝࡢࢹ࣮ࢱ࣮࣋ࢫ໬ࡋ㸪⌧⾜ࡢタィࣔࢹࣝ㸸ᘧ(4)㸪ᘧ(5)࡜㸪ⴭ⪅ࡽࡀᥦ᱌ࡍࡿಟṇࣔࢹࣝ㸸ᘧ(6)㸪ᘧ(7)࡟ࡘ࠸࡚ࣂ࢖࢔ࢫ⤫ィ㔞ࢆィ⟬ࡋ㸪㒊ศᏳ඲ಀᩘࡢヨ⟬ࢆ⾜ࡗࡓ㸬Tmax =Tmax =K aV vSvSh(4)

R p = ª¬cN c +K a  v (N q -1) º¼ B2(5)1
K a HD tmax ) cSvSh
2(6)

R p =SL ª¬cN 'c +K a Sd  v (N 'q -1) º¼ SB B2(7)Ka㸸ቨ㠃ᦶ᧿ゅࢆ⪃៖ࡋࡓ୺ാᅵᅽಀᩘ㸪Vv㸸⿵ᙉᮦࢆᩜタࡍࡿ఩⨨࡛ࡢ㖄┤ᅵᅽ㸪Sv㸸⿵ᙉᮦࡢ㖄┤᪉ྥࡢᩜタ㛫㝸㸪Sh㸸ᙉᮦࡢỈᖹ᪉ྥࡢᩜタ㛫㝸㸪c㸸┒ᅵᮦࡢ⢓╔ຊ㸪Nc㸪Nq㸸Kotter ᘧࢆ࢔࣮ࣥ࢝ࡢᘬᢤࡁၥ㢟ࢆ᝿ᐃࡋࡓቃ⏺᮲௳ࡢࡶ࡜࡛ᩘ್ⓗ࡟ゎ࠸ࡓᨭᣢຊಀᩘ㸪%㸸ṇ᪉ᙧ࢔࣮ࣥ࢝ࣉ࣮ࣞࢺࡢ୍㎶ࡢ㛗ࡉ㸪Dtmax㸸⿵ᙉᮦຊࡢศᕸ㛵ᩘ㸪)c㸸⢓╔ຊࡢᙳ㡪࡟㛵ࡍࡿಟṇಀᩘ)c=1–Oc/(JH)㸪N’c࣭N’q㸸ಟṇࡋࡓᨭᣢຊಀᩘ㸪SL࣭Sd࣭SB㸸⿵ᙉᮦࡢ㛗ࡉ㸪ᩜタ῝ࡉ㸦ᣊ᮰ᅽ㸧㸪࢔࣮ࣥ࢝ࣉ࣮ࣞࢺࡢ኱ࡁࡉ࡟㛵ࡍࡿಟṇಀᩘ࡛࠶ࡿ㸬ゎᯒ⤖ᯝ࡜⪃ᐹ ⌧⾜ࡢタィࣔࢹࣝ㸪ⴭ⪅ࡽࡀᥦ᱌ࡋ࡚࠸ࡿಟṇࣔࢹࣝ࡟ࡼࡿண್࡜ᐇ್ࡢẚ㍑ࢆᅗ㸪 ࡟♧ࡍ㸬⾲ ࡣࡇࢀࡽࡢ⤖ᯝࡼࡾ⟬ᐃࡋࡓࣂ࢖࢔ࢫ⤫ィ㔞࡛㸪⤖ᯝࢆ඲య㸪Iᮦ㸪FIᮦࡈ࡜࡟♧ࡋࡓ㸬ࡇࢀࡼࡾ⌧⾜ࣔࢹࣝࡣ㸪Ⲵ㔜࣭᢬ᢠ࡜ࡶᏳ඲ഃ࡟ぢ✚ࡶࡿࣔࢹ࡛ࣝ࠶ࡾ㸪ಟṇࣔࢹࣝࡣ⌧⾜ࣔࢹࣝࡢ᥎ᐃ⢭ᗘࢆᨵၿࡋࡓࡶࡢ࡛࠶ࡿࡇ࡜ࡀࢃ࠿ࡿ㸬ࡇࡢ⤖ᯝࢆࡶ࡜࡟㸪᢬ᢠಀᩘࡢヨ⟬⤖ᯝࢆᅗ ࡟♧ࡍ㸬ࡇࡇ࡛㸪Ⲵ㔜ಀᩘJQ=2.0 ࢆ௬ᐃࡋࡓ㸬┠ᶆಙ㢗ᛶࡀ㧗࠸࡜ࡁ࡯࡝㸪ィ⟬ࡉࢀࡿ᢬ᢠಀᩘࡣಟṇࣔࢹࣝࡢ᪉ࡀ኱ࡁࡃ࡞ࡿ㸬ࡇࡢࡼ࠺࡟ᥦ᱌ࡍࡿゎᯒἲࡣ㸪タィࣔࢹࣝࡢ⢭ᗘ࡟ᛂࡌ࡚㒊ศᏳ඲ಀᩘࢆ⟬ᐃ࡛ࡁࡿ㸬ࡇࡢࡼ࠺࡞ゎᯒⓗ᳨ウ࡟ᪧ᮶タィἲࡀᇵࡗ࡚ࡁࡓタィࣀ࢘ࣁ࢘ࢆ⤌ࡳྜࢃࡏ㸪ྜ⌮ⓗ࡞ಀᩘࢆ⟬ᐃࡍࡿࡢࡀ௒ᚋࡢㄢ㢟࡛࠶ࡿ㸬࣮࣮࢟࣡ࢻ ⿵ᙉᅵቨ㸪LRFD㸪࢟ࣕࣜࣈ࣮ࣞࢩࣙࣥ㸪ከᩘ࢔࣮ࣥ࢝㐃⤡ඛ   ࠛ ᶓ㡲㈡ᕷ㉮Ỉ  㜵⾨኱Ꮫᰯᘓタ⎔ቃᕤᏛ⛉ 7HO  ‑105‑土木学会第66回年次学術講演会(平成23年度)

Ⅲ‑053

PQ (1+COVQ)
100
frictional soil (c = 0, I > 0)300

1PQ (1-COVQ)
Measured, Rm (kN)

10

1

1
1

PR (1+2xCOVR)

PR (1-2xCOVR)

100

0.1

100.1

11010010100(a) Ⲵ㔜ࣔࢹࣝ

300

Predicted, Rp (kN)

Predicted load, Tmax (kN)(b) ᢬ᢠࣔࢹࣝᅗ ⌧⾜ࡢタィࣔࢹࣝࡢࣂ࢖࢔ࢫゎᯒ⤖ᯝPR (1+COVR)

PQ (1+COVQ)
PQ = 1.00
PQ (1-COVQ)

100
frictional soil (c = 0, I> 0)

300

PR (1+2xCOVR)
Measured, Rm (kN)110

1PR = 1.00
PR(1-COVR)

1

1

cohesive frictional soil (c > 0, I> 0)

Measured load, Tmax (kN)

PR(1-COVR)

frictional soil (c = 0, I> 0)cohesive-frictional soil (c > 0, I> 0)1

cohesive-frictional soil (c > 0, I > 0)

Measured load, Tmax (kN)

PR (1+COVR) PR = 1.09

PQ = 0.81

1

PR (1-2xCOVR)

100

frictional soil (c = 0, I > 0)cohesive-frictional soil (c > 0, I> 0)
100.1
0.1

11010100

300

100

Predicted, Rp (kN)

Predicted load, T max (kN)(a) Ⲵ㔜ࣔࢹࣝ(b) ᢬ᢠࣔࢹࣝᅗ ಟṇࡉࢀࡓタィࣔࢹࣝࡢࣂ࢖࢔ࢫゎᯒ⤖ᯝModified model

1.0

Granularsoil (c=0)

c-I soil(c>0)

0.9

All
PQ

0.81

1.14

0.50

0.7

COVQ (%)

796562

PR

1.21

0.96

1.39

COVR (%)

353130

PQ

1.00

1.00

1.00

COVQ (%)

5053

46

PR

1.00

1.00

1.00

COVR (%)

191124

Assumed load factor JQ = 2.0

0.8

Resistance factor, I

Current model⾲ タィࣔࢹࣝࡢࣂ࢖࢔ࢫ⤫ィ㔞ࡢẚ㍑

0.6

Modified model

0.5
0.4

Current model

0.3
0.2
0.1
0.0
2.0

2.5

3.0

3.5

4.0

Reliability index, Eᅗ ⌧⾜ࣔࢹࣝ࡜ಟṇࣔࢹࣝ࡟ᑐࡍࡿ᢬ᢠಀᩘㅰ㎡㸸ᮏ◊✲ࡣ⛉Ꮫ◊✲⿵ຓ㔠 21360229, ◊✲௦⾲⪅㸸ᐑ⏣႐ኖ ࡢ◊✲ᡂᯝ࡛࠶ࡿ㸬ཧ⪃ᩥ⊩ 1) Allen TM, Nowak AS and Bathurst RJ. 2005. Calibration to Determine Load and Resistance Factors forGeotechnical and Structural Design. Transportation Research Board, Circular E-C079. 2) Bathurst RJ, Allen TM and Nowak AS.
2008. Calibration concepts for load and resistance factor design (LRFD) of reinforced soil walls, Canadian Geotechnical Journal,45-10, 1377̽1392. 3) Miyata Y, Bathurst RJ and Konami T. 2009. Measured and predicted loads in multi-anchor reinforced soilwalls in Japan, Soils and Foundations, 49-1, 1-10. 4) Miyata Y. Bathurst RJ and Konami T. 2011. Influence of Model Accuracy on
Load and Resistance Factor Calibration of Multi-anchor Walls, Proc. on 3rd Int. Symp. on Geotechnical Safety and Risk, Munich.

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