䈖䈉䈋䈇䊐䉤䊷䊤䊛╙ 㪈㪈 ภ㩷 㪆㩷㪉㪇㪇㪊㪅㪈㩷䊃䊮䊈䊦⛽ᜬ▤ℂ䈮䈍䈇䈩 LCC ⹏ଔ䉕ታ⃻䈜䉎䈢䉄䈱੍᷹⸃ᨆᛛⴚ
PREDICTION SIMULATION TECHNOLOGY FOR ANALYZING LIFE CYCLE COST IN A
TUNNEL MAINTENANCE MANAGEMENT᧻↰⽵ೣ*䊶᪉੗㆐ᦶ*Sadanori MATSUDA and Tatsuro SAKURAIIn this paper, a finite element analysis is conducted to investigate the long-term stability ofa cracked tunnel due to creep behavior of surrounding ground and the effectiveness ofcorresponding remedial works. The material parameters involved in the model are determinedthrough a series of laboratory tests. Particular attention is paid to the selection of a suitable
remedial work for the cracked tunnel. By comparing the calculated results with the fieldobservation, it is found that the approach for assessing the long-term stability of the cracked
tunnel and the effectiveness of the remedial works is quite accurate and applicable.

 Key Words㧦 mountain tunnel, maintenance-repairs, reinforcement design, life cycle cost,time dependency, finite element method㪈㪅㩷㩷ᐨ⺰㩷
1999 ᐕ䈱䊃䊮䊈䊦ⷒᎿ䉮䊮䉪䊥䊷䊃䈱೸⪭੐᡿䉕ᄾᯏ䈮䇮ᗧ๧䈚䇮䈠䈱䉮䉴䊃䉕⚻ᷣ⊛ 䈮଻䈧䈢䉄䈮䈲䇮⛽ᜬ▤ℂ⸘↹ᛛⴚ䋨LCC ⹏ଔ䋩䈏㕖Ᏹ䈮㊀ⷐ䈭ⷐ⚛䈮䈭䉎䇯ᣢ⸳ 䊃䊮䊈䊦䈱⛽ᜬ▤ ℂ䈱䈅䉍ᣇ䉇࿯ᧁ᭴ ㅧ‛䈱⠴ਭ ᕈ 䈱䈖䈱䉋䈉䈭⁁ᴫ䉕〯䉁䈋䈩䇮ᧄ⺰ᢥ䈪䈲䇮࿑䋭㪈 䈮␜䈜䉋䈉⠨䈋ᣇ䈏⋓䉖䈮⼏⺰䈘䉏䈩䈇䉎䇯ᧄ᧪䇮䊃䊮䊈䊦䈲䇮ઁ䈱᭴ㅧ䈭䊤䉟䊐䉰䉟䉪䊦䉮䉴䊃䉕ౕ૕⊛䈮⹏ଔ䈜䉎䈉䈋䈪ᔅⷐ䈮䈭䉎䊃‛䈮Ყ䈼㐳䈇⠴↪ᐕᢙ䉕᦭䈜䉎䇯50 ᐕએ਄䉅䈱⚻ᐕ䉕Ⓧ䉖䊮䊈䊦䈱⚻ᤨ⊛䈭ഠൻ․ᕈ䈍䉋䈶⵬ୃ䊶⵬ᒝᎿᴺ䈱ᯏ⢻⛽䈣䊃䊮䊈䊦䈪䉅䇮ቯᦼ⊛䈭⛽ᜬ▤ℂ䈱䉅䈫䈪቟ో䈭ⓨ㑆೑↪

ᜬ䈅䉎䈇䈲ᯏ⢻ᡷༀ䈮ኻ䈜䉎⚻ᤨ⊛䈭ലᨐ䉕ቯ㊂⊛䈮⹏ଔ䈱৻べ䉕ᜂ䈦䈩䈇䉎䊃䊮䊈䊦䈲ᄙᢙ䈅䉎䇯䈜䉎䈢䉄䇮࿾ጊ䈫䊃䊮䊈䊦ⷒᎿ䈫䈱⋧੕૞↪䉕ᤨ㑆䉴䊁䉾䊒䈪䈫䈖䉐䈏䇮䉒䈏࿖䈱䊃䊮䊈䊦䈲䇮࿾࿶䈭䈬䈱ᄖജ䈏૞↪䈚䉇䉲䊚䊠䊧䊷䉲䊢䊮น⢻䈭ᢙ୯⸃ᨆᚻᴺ 1 䋩 ,2 䋩 䉕ታ㓙䈱ᄌ⁁䊃䊮䊈䈜䈇࿾ᒻ䊶࿾⾰䊶࿾ਅ᳓᧦ઙਅ䈮⟎䈎䉏䈩䈇䉎႐ว䈏ዋ䈭䈒䊦䈮ㆡ↪䈚䇮䈠䈱᦭ലᕈ䉕ᬌ⸽䈚䈢䈱䈪䇮䈖䈖䈮⚫੺䈜䉎䇯䈭䈇䇯䈖䈱䈢䉄䇮䊃䊮䊈䊦ⷒ Ꮏ 䈮䈍䈔䉎䈵䈶ഀ 䉏䉇ᄌ ᒻ ╬ 䈱ᕈ⢻ᄌ ⁁ 䈏䈚䈳䈚䈳໧ 㗴 䈮䈭䉍䇮ኻ ╷ 䉕૛ ௾ 䈭䈒䈘䉏䉎႐ ว 䉅䈅ೋᦼ⁁ᘒ#⵬ᒝ䉎䇯䉁䈢䇮็ઃ䈔䉮䊮䉪䊥䊷䊃䈫䊨䉾䉪䊗䊦䊃䉕ਥ䈭ᡰ଻䈫䈜䉎ጊ⃻ᴫጪᎿᴺ䋨NATM䋩એ೨䈱䊃䊮䊈䊦䋨ᧁ⵾⍫᧼Ꮏᴺ䋩䈪䈲䇮䊃䊮䊈ഠൻߩㅴⴕ$⵬ୃ䊦ⷒ Ꮏ 䈱⢛ 㕙 䈮ⓨ ᵢ 䈏ᒻ ᚑ 䈘䉏䉇䈜䈒䇮ᄌ ⁁ 䉕ഥ 㐳 䈜䉎ⷐ࿃䈮䈭䈦䈩䈇䉎䈖䈫䈏䇮⚻㛎⊛䈮⍮䉌䉏䈩䈇䉎䇯䊃䊮䊈䊦ⷒ Ꮏ 䈮䈍䈔䉎䈵䈶ഀ 䉏䉇ᄌ ᒻ 䈱ㅴ ⴕ ᕈ 䈮䈲䇮࿾ᯏ⢻㓚ኂߩ⊒↢㒢⇇⁁ᘒ%ήኻ╷ጊ䈱ᤨ㑆⊛䈭ᒝᐲૐਅ䋨㘑ൻഠൻ䇮䉪䊥䊷䊒䈭䈬䈱ᤨ㑆ଐሽᑧ๮ൻലᨐᕈ䋩䈏ᓇ㗀䈚䈩䈇䉎䉅䈱䈫⠨䈋䉌䉏䉎䇯䈚䈢䈏䈦䈩䇮੹ᓟ䇮ᣢ⸳䊃䊮䊈䊦䈱㐳ᦼ䈮䉒䈢䉎቟ోᕈ䈅䉎䈇䈲ᯏ⢻䈮㑐䈜䉎ᬌ⸛䉕ⴕ䈉႐ว䈮䈲䇮ᤨ㑆䈱ⷐ⚛䉕⠨ᘦ䈚䈢⹏ଔ䈏ᔅⷐ䈮䈭䉎䇯䈜䈭䉒䈤䇮䈅䉎䊃䊮䊈䊦䈏⛽ᜬ䈜䈼䈐ᯏ⢻䈫䈠䈱ଏ↪ᦼ㑆䇮⠴↪

ᑪ⸳ᤨ⃻࿷ ήኻ╷ᤨߩ੍ᗐ⠴↪ᐕᢙᤨ㑆࿑䋭㪈㩷 䊃䊮䊈䊦䈱⚻ᤨഠൻᦛ✢䈫ኻ╷ലᨐ䈱᭎ᔨ㩷ᐕᢙ䉕᣿⏕䈮䈚䈢䈉䈋䈪䇮䈠䈱ᦼ㑆ਛ䈱䊃䊮䊈䊦䈱቟ోᕈ䇮䊃䊷䉺䊦䈫䈚䈩䈱⚻ᷣᕈ䉕⹏ଔ 䈜䉎䈖䈫䈏᳞䉄䉌䉏䈩䈇䉎䇯䈖䉏㪉㪅㩷㩷䊝䊂䊦䊃䊮䊈䊦䈱᭎ⷐ㩷䈲䇮LCC䋨䊤䉟䊐䉰䉟䉪䊦䉮䉴䊃䋩䉕⠨䈋䈭䈔䉏䈳䈭䉌䈭䈇䈖䈫䉕࿑䋭㪉 䈲䇮ᧄ⺰ᢥ䈪ኻ⽎䈮䈚䈢䊝䊂䊦䊃䊮䊈䊦䈱࿾⾰᭴ㅧ*䈍䉋䈶䊃䊮䊈䊦ᒻ⁁䉕␜䈚䈢䉅䈱䈪䈅䉎䇯䊝䊂䊦䊃䊮䊈䊦䈲䇮ᤘ␠ળⅣႺ䉣䊮䉳䊆䉝䊥䊮䉫੐ᬺㇱ 䍵䍐䍪䍙䍐䍖䍷䍭䍦䍚䍼䍰䍻䍢 ㇱ㪈㪈㪌㩷࠻ࡦࡀ࡞⛽ᜬ▤ℂߦ߅޿ߡ .%% ⹏ଔࠍታ⃻ߔࠆߚ߼ߩ੍᷹⸃ᨆᛛⴚ!

๺ 39 ᐕ䈮ㆇ↪䉕㐿ᆎ䈚䈢᳓ജ⊒㔚ᚲ䈱᳓〝䊃䊮䊈䊦䈪䇮࿯㪊㪅㩷㩷䊃䊮䊈䊦㐳ᦼᄌᒻ⸃ᨆ㩷ⵍ䉍䈲⚂ 400m䇮ోᑧ㐳 6,200m 䈱ౝ䇮䈵䈶ഀ䉏䈮䉋䉎䊃䊮䊈䋨㪈䋩㩷 ቶౝ⹜㛎⚿ᨐ෸䈶᧚ᢱ䊌䊤䊜䊷䉺䈱⸳ቯ!

䊦ⷒᎿ䈱ᄌ⁁䈏⪺䈚䈇඙㑆䈲⚂ 100m 䈪䈅䉎䇯ᄌ⁁඙㑆䈱࿾ ⾰ 䈲䇮ਛ ฎ ↢ ઍ 䈱☼ ᧼ ጤ ጀ 䈮⽾ ౉ 䈚䈢䈫⠨ 䈋䉌䉏䉎⍹ ⧷᢬ጤጀ䈪භ䉄䉌䉏䇮⍹⧷᢬ጤ䈱਄ㇱ䈲䇮╙ਃ♿䈱ṁ⚿ಝἯ!

ጤጀ䈮ਇᢛว䈮ⷒ䉒䉏䈩䈇䉎䇯⍹⧷᢬ጤ䈲ᾲ᳓ᄌ⾰䉕ฃ䈔䈩䈍䉍䇮ਇᢛว㕙๟ㄝ䈱ṁ⚿ಝἯጤጀ䇮⍹⧷᢬ጤጀ䈫䉅䈮㘑ൻ䈏ㅴ䉖䈪䈇䉎䇯䉁䈢䇮ቢᚑ䈎䉌⚂ 30 ᐕᓟ䈱ᐔᚑ 6 ᐕ䈮ታ!

ᣉ 䈚䈢䊗䊷䊥䊮䉫⺞ ᩏ 䈮䉋䉏䈳䇮䊃䊮䊈䊦๟ ㄝ 䈮䈲ห ᔃ ౞ ⁁䈮⚂ 2m 䈱▸࿐䈪࿾ጊ䈱✭䉂ၞ䈏䈅䉍䇮䊃䊮䊈䊦ⷒᎿ䈱ᄤ┵!

⢛㕙䈮䈲䇮㜞䈘 20䌾30cm 䈾䈬䈱ⓨᵢ䈏⏕⹺䈘䉏䈩䈇䉎䇯䊃䊮䊈䊦ⷒᎿ䈱䉴䊒䊥䊮䉫䊤䉟䊮䌾䉝䊷䉼⢋ઃㄭ䈮䈲䇮ቢᚑ䈚䈩㑆䉅䈭䈇ᤨᦼ䋨ᤘ๺ 40 ᐕ䋩䈎䉌᏷ 1䌾3mm ⒟ᐲ䈱❑ᢿ!

䈵䈶ഀ䉏䈏⊒↢䈚䇮䈵䈶ഀ䉏䈱⵬ୃᓟ䋨ᤘ๺ 43 ᐕ䋩䉅ㅴⴕ䈏⏕⹺䈘䉏䈩䈇䉎䇯࿑䋭㪊 䈲䇮ᐔᚑ 11 ᐕ䈮⋡ⷞὐᬌ䈚䈢㓙䈱䈵⸃ᨆ䈮↪䈇䉎࿾ጊ䈱᧚ᢱ䊌䊤䊜䊷䉺䈲䇮ㅢᏱ䇮ቯ䈵䈝䉂ㅦᐲਃゲ࿶❗⹜㛎䈍䉋䈶ਃゲ䉪䊥䊷䊒⹜㛎䈪ᓧ䈢୯䉋䉍᳿ቯ䈜䉎䈏䇮ᧄ੐଀䈪䈲䇮⹜㛎ᢙ㊂䈱೙⚂䉅䈅䉍䇮ᄙᲑ㓏ਃゲ࿶❗
⹜㛎䇮৻ゲ䉪䊥䊷䊒⹜㛎䈪ᓧ䉌䉏䈢․ᕈ୯䉋䉍᳿ቯ䈚䈢䇯࿑䋭㪋 䈲䇮᦭㒢ⷐ⚛⸃ᨆ䈪૶↪䈜䉎⸃ᨆ䊜䉾䉲䊠䈪䇮䊃䊮䊈䊦䈮䈍䈇䈩䈍䈍䉃䈰ኻ ⒓ 䈭࿾ ⾰ ᭴ ㅧ 䈪䈅䉎䈢䉄䇮࿑ 䈮␜ 䈜
50×50m 䈱▸࿐䉕⸃ᨆ㗔ၞ䈫䈜䉎䇯࿾ጊ䈱ೋᦼᔕജ႐䈮䈧䈇䈩䈲䇮⸃ ᨆ 㗔 ၞ ౝ 䈪৻ ᭽ 䈪䈅䉎䈫ᗐ ቯ 䈚䇮࿯ ⵍ 䉍㜞 䈘ಽ䋨400m䋩䈱㕒 ᳓ ࿶ ⁁ ᘒ 䋨9.6MPa䋩䈫䈜䉎䇯䉁䈢䇮࿑ 䋭㪋 ਛ 䈱G4 ጀ䈲䊃䊮䊈䊦ជ೥䈮⿠࿃䈚䈢㐳ᦼ䈮䉒䈢䉎ഠൻㅴⴕ䈱ᓇ㗀䉕⠨ᘦ䈚䈩䇮ᔕജ䊶䈵䈝䉂䈱㕖✢ᒻᕈ䈍䉋䈶ᤨ㑆ଐሽᕈ䉕ข䉍ᛒ䈉䇯䈠䉏એᄖ䈱࿾ጊ䈮䈧䈇䈩䈲䇮✢ᒻᒢᕈ૕䈫䈚䈢䇯䈖䉏䉌࿾ጊ䈱᧚ᢱ䊌䊤䊜䊷䉺䈲䇮⴫䋭㪈 䇮 㪉 䈮␜䈜䇯䈶ഀ䉏ዷ㐿࿑䈪䈅䉎䈏䇮ฝ䉝䊷䉼⢋䌾ᄤ┵䉪䊤䉡䊮ઃㄭ䈮䈍!

䈇䈩䈲䇮䈝䉏᏷ 8䌾13mm 䈱ᲑᏅ䈮䉁䈪ᄌ⁁䈏ㅴⴕ䈚䈩䈇䉎䇯!

O㩷㩷㩷㩷㩷O!

) ጀਇᢛว㕙) ጀOOṁ⚿ಝἯጤ!

) ጀO) ጀ࠻ࡦࡀ࡞㘑ൻㇱ!

O㘑ൻㇱ‫ޣ‬ጤ⋚╬⚖‫ޤ‬!

D⚖ⓨᵢ⺞ᩏ✭ߺၞ

R=1,550mm
R=4,650mm㧡‫ ޓ‬㧠‫ ޓ‬㧟‫ ޓ‬㧞‫ ޓ‬㧝m࿑䋭㪋㩷 ⸃ᨆ䊜䉾䉲䊠࿑䋨䊊䊷䊐䊝䊂䊦䋩㩷㩷

CL⚖C M⚖!
!

) ጀਇᢛว㕙m㧝‫ ޓ‬㧞‫ ޓ‬㧟‫ ޓ‬㧠‫ ޓ‬㧡⍹⧷᢬ጤ࿯ⵍࠅ400m

࿑䋭㪉㩷 ⸃ᨆ䊃䊮䊈䊦ᢿ㕙๟ㄝ䈱࿾⾰⁁ᴫ䋨ᐔᚑ 㪍 ᐕ⺞ᩏ䋩㩷⴫䋭㪈㩷 ࿾ጊ᧚ᢱቯᢙ䋨ᒢ☼႟ᕈ૕䋺㪞㪋 ጀ䋩㩷ᒢᕈଥᢙC ᤨ 㑆 ଐ ሽ ᕈ ࡄ ࡜' /2C ࡐࠕ࠰ࡦᲧǵ% ࡔ࡯࠲D /2C /H  ᱷ ⇐ ᒝ ᐲ ᤨ ߩ ᔕ႟ᕈࡐ࠹ࡦࠪ
ǻOD /2C/Oࡖ࡞ࡄ࡜ࡔ࡯࠲)̉

ᦨᄢ૕Ⓧ࿶❗
ᤨߩᔕജᲧǼജᲧ෸߮㒰⩄࡮ౣタ⩄ߩೋᦼធ✢൨㈩ᔕജጁᱧࡄ࡜ࡔ࡯࠲⴫䋭㪉㩷 ࿾ጊ᧚ᢱቯᢙ䋨✢ᒻᒢᕈ૕䋩㩷Ꮐ஥ო㨪㨼㩧㩔㩨㨺㩎࿾ጀฬᒢᕈଥᢙ' /2C ࡐࠕ࠰ࡦᲧǵ᏷ OOᏀ㩇㩖㩩㩢㩧㩂㩨㩡㨼㩧ᄤ┵㩂㩡㨽㩧ᲑᏅ޽ࠅ 㨪OO᏷ OO᏷ 㨪OOฝ஥ო㨪㨼㩧㩔㩨㨺㩎ㅊട〒㔌 O⸃ᨆᢿ㕙OO㧦߭߮ഀࠇ⵬ୃ〔࿑䋭㪊㩷 ⸃ᨆᢿ㕙ㄭற䈱䊃䊮䊈䊦ᄌ⁁⁁ᴫ䋨ᐔᚑ 㪈㪈 ᐕ⺞ᩏ䋩㩷㪈㪈㪍㩷)
)
)
⴫䋭㪊㩷 ㇱ᧚ቯᢙ䋨ㇱಽ✢ᒻᒢᕈ૕䋺㪹㫀㪄㫃㫀㫅㪼㪸㫉 ဳ䋩㩷ࠕ࡯࠴࡮஥ო㧔Ꮞෘ EO㧕ࠗࡦࡃ࡯࠻㧔Ꮞෘ EO㧕ᡰ଻Ꮏ㧔*㧕ࡠ࠶ࠢࡏ࡞࠻㧔&㧕ᒢᕈଥᢙG G G G ᢿ㕙ੑᰴ䊝䊷䊜䊮䊃ᢿ㕙Ⓧ䈵䈶ഀ䉏⊒↢䊝䊷䊜䊮䊃㧙㧙ㇱ᧚ฬฝ㩇㩖㩩㩢㩧㩂㩨㩡㨼㩧)

'0OO+EO # EO
/[ M0㨯OO 䈖䈉䈋䈇䊐䉤䊷䊤䊛╙ 㪈㪈 ภ㩷 㪆㩷㪉㪇㪇㪊㪅㪈㩷䋨㪉䋩㩷 䊃䊮䊈䊦ⷒᎿ䈱䊝䊂䊦ൻ෸䈶᧚ᢱ䊌䊤䊜䊷䉺䋨㪊䋩㩷 ㆊ෰䈱ᄌ⁁ጁᱧ䈫⸃ᨆ䉴䊁䉾䊒䊃䊮䊈䊦ⷒᎿ䈍䉋䈶⵬ᒝ䉶䊮䊃䊦䋨H ᒻ㍑䋩䈲⭯⡺䈭ㇱ᧚䈪࿑䋭㪌 䈲䇮䊝䊂䊦䊃䊮䊈䊦䈱ᑪ⸳Ꮏ੐⸥㍳䉇ဒౝⷰኤ⸥

䈅䉎䈢䉄᪞ ⷐ ⚛ 䈪䊝䊂䊦ൻ 䈚䇮䊨䉾䉪䊗䊦䊃䋨ో 㕙 ቯ ⌕ ᑼ 䋩䈲㍳䉕䉅䈫䈮⸳ቯ䈚䈢⸃ᨆ䉴䊁䉾䊒䈪䈅䉎䇯䊝䊂䊦䊃䊮䊈䊦䈪䈲䇮ゲജવ㆐䈣䈔䉕⠨ᘦ䈚䈩᫔ⷐ⚛䈪䊝䊂䊦ൻ䈜䉎䇯⴫䋭㪊 䈮ฦㆊ෰䈱ᄌ⁁ኻ╷䈫䈚䈩䇮ቢᚑ䈎䉌 32 ᐕᓟ䈮 H ᒻ㍑䈮䉋䉎䊃䊮ㇱ᧚䈱᧚ᢱ䊌䊤䊜䊷䉺䈍䉋䈶ᐞ૗䊌䊤䊜䊷䉺䉕␜䈜䇯䉁䈢䇮⴫䊈䊦ⷒᎿ⵬ᒝ䇮䈘䉌䈮䈠䈱 3 ᐕᓟ䈮䈲䇮ⵣㄟ䉄ᵈ౉Ꮏ䈮䉋䉎䊃䋭㪊 ਛ䈱 M y 䈲䈵䈶ഀ䉏⊒↢䊝䊷䊜䊮䊃䉕⴫䈚 3 䋩 䇮ㇱ᧚䈮௛䈒䊮䊈䊦ⷒᎿ䈫࿾ጊ䈫䈱ኒ⌕ᕈ䈱ᡷༀ䈍䉋䈶䊨䉾䉪䊗䊦䊃䊝䊷䊜䊮䊃䈏 M y 䉕⿥ㆊ䈚䈢႐ว䇮ㇱ᧚䈱ೋᦼ䈱ᦛ䈕೰ᕈ EI䋨L=3m䇮8 ᧄ/m䋩䈮䉋䉎࿾ጊ⵬ᒝ䉕ⴕ䈦䈩䈍䉍䇮⸃ᨆ䈪䈲䇮䈖䈲 1/1,000 䈮ૐᷫ䈘䉏䈩䇮䊃䊮䊈䊦ⷒᎿ䉮䊮䉪䊥䊷䊃䈲ഠൻ䈜䉏䉌䉕⸘ 5 䉴䊁䊷䉳䈪ౣ⃻䈚䈩䈇䉎䇯㩷䉎䈖䈫䈮䈭䉎䇯㩷㩷ជ೥೨ជ೥ᔕജ⸃᡼ ⷒᎿ⸳⟎ㅢ᳓ᓟ㧝ᐕ㩷㧔ᤘ๺ᐕ㧕ㅢ᳓ᓟ㧟ᐕ㧔ᤘ๺ᐕ㧕ㅢ᳓ᓟᐕ㧔ᤘ๺ᐕ㧕㩷⸃ᨆࡕ࠺࡞ߩ᭎ᔨ࿑㩷ⓨᵢⓨᵢ 䈵䈶ഀ䉏㩷㱟㫄㪇䈵䈶ഀ䉏⵬ୃ䈵䈶ഀ䉏ౣ⊒㩷㩷㩷㩷ࠬ࠹࡯ࠫ ࠬ࠹࡯ࠫ ᄌ⁁࡮ኻ╷ጁᱧࠬ࠹࡯ࠫ 㩷࡮ࡩ᦬㑆ߩᤨ㑆⚻ㆊߦ઻߁࿾ ࡮ᤨ㑆⚻ㆊߦ઻߁࿾ጊߩᤨ㑆 ࡮߭߮ഀࠇ⵬ୃߦࠃࠆ⁁ᘒᄌጊߩᤨ㑆ଐሽᕈ᜼േࠍ⸃ᨆߔ ଐሽᕈ᜼േࠍ⸃ᨆߔࠆ‫ޕ‬ൻߪ⠨ᘦߒߥ޿‫ޕ‬㩷ࠆ‫ޕ‬࡮ᤨ㑆⚻ㆊߦ઻߁࿾ጊߩᤨ㑆࡮ߘߩᓟ‫ⷒޔ‬Ꮏࠦࡦࠢ࡝࡯࠻ ࡮࠻ࡦࡀ࡞ⷒᎿߦ௛ߊㇱ᧚ߩ ଐሽᕈ᜼േߩߺࠍ⸃ᨆߔࠆ‫ޕ‬㩷㧔ᄤ┵㨪ࠕ࡯࠴࡮஥ო㧕ࠍㅊ ᢿ㕙ജ߇㧘߭߮ഀࠇ⊒↢ࡕ࡯ടߔࠆ‫ޕ‬ࡔࡦ࠻ߦ㆐ߒߚ႐วߦߪ㧘ᦛ㩷࡮ࠗࡦࡃ࡯࠻ߪࡩ᦬ㆃࠇߡㅊ ߍ೰ᕈࠍߦૐᷫߔࠆ‫ޕ‬ടߔࠆ‫ޕ‬࡮ᤨ㑆⚻ㆊߦ઻߁࿾ጊߩᤨ㑆ଐሽᕈ᜼േߦߟ޿ߡㅙᰴࠬ࠹࠶ࡊ⸃ᨆߔࠆ‫ޕ‬࡮⍹⧷᢬ጤߩ਄ㇱߦṁ⚿ಝἯጤ߇ၸⓍߒߡ޿ࠆ‫ޕ‬࡮ṁ⚿ಝἯጤߣ⍹⧷᢬ጤߣߩਇᢛว㕙ઃㄭߩ㘑ൻ㧘⽾౉ጤߢ޽ࠆ⍹⧷᢬ጤ⥄૕ߩᄌ⾰߇⹺߼ࠄࠇࠆ‫ޕ‬࡮࠻ࡦࡀ࡞๟ㄝ࿾ጊߪ࿕⚿ᐲ߇ૐߊ⣀ᒙߢ޽ࠆߚ߼㧘࿾ጊߩ᛼಴ߒ⃻⽎߿࠻ࡦࡀ࡞ᄤ┵⢛㕙࿾ጊߩዊ፣⪭㧔⢛㕙ⓨᵢߩᒻᚑ㧕߇↢ߓߚ߽ߩߣផኤߐࠇࠆ‫ޕ‬࡮⃻࿾ߢߪ㧘ࠕ࡯࠴Ꮐฝ⢋ㇱߦ᏷㨪OO⒟ᐲߩ❑ᢿ߭߮ഀ㩷ࠇ߇⊒↢ߔࠆ‫ޕ‬࡮⃻࿾ߢߪ㧘ࠕ࡯࠴Ꮐ⢋ㇱߦ❑ᢿ߭߮ഀࠇ߇ౣ⊒↢ߔࠆ‫ޕ‬ㅢ᳓ᓟᐕ㧔ᤘ๺ᐕ㧕ㅢ᳓ᓟᐕ㧔ᐔᚑᐕ㧕ㅢ᳓ᓟᐕ㧔ᐔᚑᐕ㧕㩷࡮࿯ⵍࠅOಽߩ㕒᳓࿶⁁ᘒߣᗐቯߒೋᦼᔕജ᧦ઙߣߒߡ⸃ ⸳ቯߔࠆ‫ޕ‬ᨆ ‫ޓ‬ೋᦼᐔဋਥᔕജǻO/2C᧦ઙ㩷㩷࡮⃻࿾ߢߪ㧘ࠕ࡯࠴Ꮐฝ⢋ㇱߦ↢ߓߚ❑ᢿ߭߮ഀࠇߦߟ޿ߡ⵬ୃࠍታᣉ‫ޕ‬࡮࠻ࡦࡀ࡞ᄤ┵⢛㕙ⓨᵢߩᓇ㗀ߢ㧘࠻ࡦࡀ࡞ⷒᎿߦਇဋ৻㩷ߥ࿾࿶߇૞↪ߒߚ߽ߩߣᗐቯߐࠇࠆ‫ޕ‬㩷㩷ㅢ᳓ᓟᐕ㧔ᐔᚑᐕ㧕㩷䈵䈶ഀ䉏ౣ⊒లႯㇱ㩷 ᫔ⷐ⚛
᪞ⷐ⚛

లႯㇱ ᫔ⷐ⚛

㩷㩷㩷㩷ࠬ࠹࡯ࠫ ࡮ᤨ㑆⚻ㆊߦ઻߁࿾ጊߩᤨ㑆ଐሽᕈ᜼േߦߟ޿ߡㅙᰴࠬ࠹࠶ࡊ⸃ᨆߔࠆ‫ޕ‬ࠬ࠹࡯ࠫ㩷 ࡮઒ฃߌᡰ଻Ꮏ⋧ᒰ㧔*㧕 ࡮⢛㕙ⓨᵢㇱߦࡕ࡞࠲࡞⋧ᒰ㩷ߩ᪞ⷐ⚛ࠍㅊടߒ⸃ᨆߔࠆ‫ࠍ⚛ⷐߩ ޕ‬ㅊടߒ⸃ᨆߔࠆ‫ޕ‬࡮߹ߚหᤨߦ㧘࿾ጊౝߦ᫔ⷐ㩷⚛ߦߡࡠ࠶ࠢࡏ࡞࠻㧔.O㧕ࠍㅊടߔࠆ‫ޕ‬㩷ࠬ࠹࡯ࠫ ࡮ᐕ㑆ߩᤨ㑆⚻ㆊߦ઻߁࿾ጊߩᤨ㑆ଐሽᕈ᜼േࠍ⸃ᨆߒ㧘ᦨ⚳⊛ߥᔕജ࡮ᄌᒻ⁁ᘒࠍᛠីߔࠆ‫ޕ‬㩷࡮⃻࿾ߢߪ㧘ࠕ࡯࠴ฝ⢋ㇱߦ❑ᢿ߭߮ഀࠇ߇ౣ⊒↢ߔࠆ‫ޕ‬㩷࡮⃻࿾ߢߪ㧘઒ฃߌᡰ଻Ꮏ࡮߭߮ഀࠇ⵬ୃࠍታᣉ‫ޕ‬
㧔*㧕ࠍ⸳⟎ߔࠆߎߣߢᦨ ࡮ⓨᵢలႯᎿࠍታᣉ‫ޕ‬㩷ೋߩ⵬ᒝኻ╷ࠍታᣉ‫ޕ‬࡮ࡠ࠶ࠢࡏ࡞࠻⵬ᒝᎿ‫ ޓ‬.O࡮ᧄᢿ㕙 ࠍታᣉ‫ޕ‬㩷࡮⸘᷹ࠍ㐿ᆎߔࠆ‫ޕ‬࡮⚂ᐕ㑆ಽߩ⸘᷹࠺࡯࠲߇⫾Ⓧߐࠇࠆ‫ޕ‬㩷࿑㪄㪌㩷 ⸃ᨆኻ⽎䈫䈚䈢䊝䊂䊦䊃䊮䊈䊦䈱ᄌ⁁䊶⵬ᒝጁᱧ䈫⸃ᨆ䉴䊁䉾䊒㩷㪈㪈㪎㩷࠻ࡦࡀ࡞⛽ᜬ▤ℂߦ߅޿ߡ .%% ⹏ଔࠍታ⃻ߔࠆߚ߼ߩ੍᷹⸃ᨆᛛⴚ

䋨㪋䋩㩷 ⸃ᨆ䈮䉋䉎⃻ᴫ䈱ౣ⃻ᕈ㩷 㩷 ࿑㧙 䈲䇮ቢᚑ䈎䉌䈱䊃䊮䊈䊦ⷒᎿ䈮⊒↢䈜䉎䊝䊷䊜䊮䊃䈱ᔕജጁᱧ࠹ࡦ࠰࡞஍Ꮕᚑಽ

S*⚻ ᤨ ᄌ ൻ 䉕␜ 䈚䈢䉅䈱䈪䈅䉎䇯ቢ ᚑ ⋥ ᓟ 䈎䉌䊃䊮䊈䊦ⷒ Ꮏ 䈱

M *f  Line⢛㕙䈮ⓨᵢ䈏ሽ࿷䈚䈢႐ว䇮䉝䊷䉼⢋ 45°䈫ᄤ┵䉪䊤䉡䊮䈮䈧䈇䈩䈲ቢᚑ䈎䉌⚂ 2 䊰᦬ᓟ䈮䇮䉴䊒䊥䊮䉫䊤䉟䊮䈮䈧䈇䈩䈲٨⚂ 6 ᐕᓟ䈮䈵䈶ഀ䉏⊒↢䊝䊷䊜䊮䊃 M y 䈮㆐䈜䉎䈖䈫䈏䉲䊚䊠K*  Line$䊧䊷䉲䊢䊮䈘䉏䉎䇯࿑㧙 䈲䇮ቢᚑ䈎䉌 2 䊰᦬ᓟ䈮䈍䈔䉎䊃䊮䊈䊦ⷒᎿ䈱䊝䊷䊜䊮䊃ಽᏓ䈪䇮䉝䊷䉼⢋ 45°䈫ᄤ┵䉪䊤䉡䊮䈮䊝٨ᢿᣇะ䈮᏷ 1mm ⒟ᐲ䈱䈵䈶ഀ䉏䈏⏕⹺䈘䉏䈢䈫⸥㍳䈘䉏䈩䈍䉍䇮䉲䊚䊠䊧䊷䉲䊢䊮䈮䉋䈦䈩ᓧ 䉌䉏䈢䈵䈶ഀ 䉏⊒ ↢ ૏ ⟎ 䈫ᤨᦼ䈲䇮ታ㓙䈱⁁ᴫ䈫䉋䈒৻⥌䈚䈩䈇䉎䇯ᔕജጁᱧ࠹ࡦ࠰࡞

V *m ╬ᣇᚑಽ䊷䊜䊮䊃䈏㓸ਛ䈚䈩䈇䉎⁁ᘒ䈏䉋䈒ಽ䈎䉎䇯⃻࿾䈱ဒౝⷰኤ⸥㍳䈮䉋䉏䈳䇮ቢᚑ䈎䉌 1 ᐕᓟ䈱ὐᬌᤨ䈮䇮Ꮐฝ䉝䊷䉼⢋䈱❑#٨㩷 㩷 㩷 㩷 㩷 ࿑㪄㪏㩷 ഠൻଥᢙ 㪩 䈱ቯ⟵ 4 䋩
ഠൻଥᢙ

RK*M *fBA(1)࿑䋭㪐 䈲䇮䉲䊚䊠䊧䊷䉲䊢䊮䈮䉋䈦䈩ᓧ䉌䉏䈢ቢᚑ䈎䉌⚂ 30㩷㩷ᐕᓟ䈱ഠൻଥᢙ R 䈱ಽᏓ䈪䈅䉎䇯ഠൻଥᢙ R 䈲✭䉂ၞ䈱▸㩷࿐䈍䉋䈶䉮䉝ⷰኤ䉕䉅䈫䈮᳿ቯ䈚䈢ጤ⋚╬⚖䈫䉋䈒⺞๺䈚䈩䈍䉍䇮࿾ጊ䈱✭䉂䈮㑐䈜䉎ജቇ⊛䈭⁁ᘒ㊂䉕⴫䈜ᜰᮡ䈫䈚䈩᦭㩷㩷㩷߭߮ഀࠇ⊒↢ࡕ࡯ࡔࡦ࠻ല䈪䈅䉎䈖䈫䈏ಽ䈎䉎䇯䈘䉌䈮䇮⸃ᨆ䈱⚿ᨐ䈲䇮࿑䋭㪈㪈 䈮␜䈜M0㨯OO⸘᷹䊂䊷䉺䈫䉅䈍䈍䉃䈰ᢛว䈜䉎⚿ᨐ䉕␜䈚䈩䈍䉍䇮࿑䋭㪈 䈮㩷␜䈜ೋᦼ⁁ᘒ䌾⃻ᴫ䉁䈪䈱䊃䊮䊈䊦ഠൻ䊒䊨䉶䉴䉕ౣ⃻䈚䈩㩷䈇䉎䉅䈱䈫⠨䈋䉌䉏䉎䇯㩷㪋㪅㩷㩷䊃䊮䊈䊦⵬ᒝലᨐ䈮㑐䈜䉎዁᧪੍᷹⹏ଔ㩷㩷䋨㪈䋩㩷 ⸃ᨆౝኈ㩷㩷৻⥸䈮䇮ᄌ⁁䊃䊮䊈䊦䈱⵬ᒝᎿᴺ䈲䇮࿾ጊ䈱ᄌᒻ䈱ㅴⴕ䈫࿑㪄㪍㩷 䊃䊮䊈䊦ⷒᎿ䈮⊒↢䈜䉎䊝䊷䊜䊮䊃⚻ᤨᄌൻ㩷䈫䉅䈮ലᨐ䉕⊒⃻䈜䉎䈢䉄䇮࿾ጊ䈱ᄌᒻ․ᕈ䈮ᄢ䈐䈒ଐሽ䈜᧪੍᷹⹏ଔ䈏࿎㔍䈭䈢䉄䇮⸳⸘ታോ䈪䈲䇮ᣢᓔ䈱㘃ૃ੐଀

⢛㕙ⓨᵢ

㩷

0QFG 5. 㩷ᕈ䈍䉋䈶䊃䊮䊈䊦ౝⓨᄌ૏䈮ਈ䈋䉎ᓇ㗀䉕ቯ㊂⊛䈮᣿䉌䈎䈮

0.3
0.8

䈜䉎䇯䉲䊚䊠䊧䊷䉲䊢䊮䈪䈲䇮ቢᚑ䈎䉌 32 ᐕᓟ䈱ᤨὐ䈪⵬ᒝ䈚

1 .2

䈢႐ว䉕⸳ቯ䈚䇮䈠䉏䈡䉏䈱䈠䈱ᓟ䈱 30 ᐕ㑆䉕዁᧪੍᷹䈚
1.9
3. 4

- 0 .6

-7 .6

3.8
3.8

㩷

䊦䉕↪ 䈇䈩੍ ᷹ 䉲䊚䊠䊧䊷䉲䊢䊮䉕ⴕ 䈇䇮࿾ ጊ 䈱ഠ ൻ 䈱ㅴ ⴕ- 2. 3

㩷䊨䉾䉪䊗䊦䊃䋨L=3m䋩䈱⸘ 3 Ꮏᴺ䉕ኻ⽎䈮䇮వ䈱䊝䊂䊦䊃䊮䊈-0.0-7 .6

㩷

0.0
1.1

㩷

0QFG %. 
0QFG #TEJ 3.1

㩷䈩੐଀䈱ᄙ䈇䇮㽲⵬ᒝ䉶䊮䊃䊦䋨H-100䋩䇮㽳ⵣㄟ䉄ᵈ౉䇮㽴

7. 6 .3
6㩷䈮ၮ䈨䈒⚻㛎⊛䈭ᚻᴺ䈏ᢙᄙ䈒೑↪䈘䉏䈩䈇䉎䇯䈠䈖䈪䇮ᧄ ⺰ ᢥ 䈪䈲䇮ᄌ ⁁ 䊃䊮䊈䊦䈱⵬ ᒝ ኻ ╷ 䈱ታ ❣ 䈫䈚42.

㩷

8-1.
4- .9

㩷

-7 .5

䉎䇯䈚䈎䈚䈭䈏䉌䇮ᓥ᧪䈎䉌࿾ጊ䈱ഠൻ䊶ᄌᒻ․ᕈ䈮㑐䈜䉎዁㩷
- 6. 8㩷ާ-0㨯OOި

࿑㪄㪎㩷 䊃䊮䊈䊦ⷒᎿ䈮⊒↢䈜䉎䍱䍎䍰䍻䍢ಽᏓ䋨ቢᚑᓟ 㪉 䊱᦬䋩㩷䈩䈇䉎䇯䋨㪉䋩㩷 ⸃ᨆ䈮䉋䉎⵬ᒝᎿᴺലᨐ
࿑㧙 䈲䇮஍࿶᜼േ䈏㗼⪺䈭䉝䊷䉼⢋ 45°⢛㕙䈱࿾ጊⷐ⚛䉕ኻ⽎䈮䇮ഠൻଥᢙ R 䈱⚻ᤨᄌൻ䉕⵬ᒝᎿᴺ೎䈮␜䈚䈢ᧄ ⎇ ⓥ 䈪䈲䇮࿾ ጊ 䈱ഠ ൻ ㅴ ⴕ ⁁ ᴫ 䉕ᱷ ⇐ ᒝ ᐲ 䈻䈱೔ ㆐䉅䈱䈪䈅䉎䇯䉁䈢䇮࿑䋭㪈㪊䌾㪈㪋 䈲䇮࿑䋭㪎 䈮␜䈜ᄤ┵䉪䊤䉡䊮ᐲว䈇䈪⹏ଔ䈜䉎䈢䉄䈮䇮ᣂ䈢䈭⁁ᘒ㊂䈫䈚䈩䇮ഠൻଥᢙ R䋨Node532䋩䈍䉋䈶䉝䊷䉼⢋ 45°䋨Node519䋩䈮䈍䈔䉎䊃䊮䊈䊦䉕࿑䋭㪏䇮ᑼ(1)䈱䉋䈉䈮ቯ⟵䈚䇮⸃ᨆ⚿ᨐ䉕⠨ኤ䈚䈢䇯ഠൻଥౝⓨᄌ૏䈱⚻ᤨᄌൻ䉕䈠䉏䈡䉏␜䈚䈢䉅䈱䈪䈅䉎䇯ᧄ੐଀䈪ᢙ R 䈲䇮࿾ጊ䈱ഠൻㅴⴕ䈱ᐲว䈇䉕⴫䈜䈱䈮ㆡ䈚䈢ᔕജጁᱧᲧ㱓*䈱⃻࿷୯䈫ᱷ⇐ᒝᐲ⁁ᘒ䈮䈍䈔䉎୯ M f *䈫䈱Ყ䈪䈅䉍䇮M f *䈲⴫䋭㪈 䈮␜䈚䈩䈅䉎䇯㪈㪈㪏㩷䈲䇮䈖䉏䉌䈱࿑䉋䉍䇮䊨䉾䉪䊗䊦䊃䈫ⵣㄟ䉄ᵈ౉䈫䉕૬↪䈚䈢ᣇᴺ䈏䇮䊃䊮䊈䊦䉕⵬ᒝ䈜䉎䈉䈋䈪ᯏ⢻⊛䈮ᦨ䉅᦭ല䈪䈅䉎䈖䈫䈏ಽ䈎䉎䇯䈖䈉䈋䈇䊐䉤䊷䊤䊛╙ 㪈㪈 ภ㩷 㪆㩷㪉㪇㪇㪊㪅㪈㩷⺞ᩏ✭ߺၞ %. ⚖઒ฃߌᡰ଻Ꮏߩゲജ VQPH

1.00.8ࠬࡊ࡝ࡦࠣ࡜ࠗࡦࠕ࡯࠴⢋qᄤ┵ࠢ࡜࠙ࡦ

ታ᷹୯



0.6(a) ઒ฃߌᡰ଻Ꮏߩゲജࡠ࠶ࠢࡏ࡞࠻ߩゲജ VQPH

ഠൻଥᢙ 4⸃ᨆ୯

0.40.2⸃ᨆ୯ታ᷹୯⺞ᩏ✭ߺၞ & ⚖࠻ࡦࡀ࡞ⷒᎿ⢛㕙߆ࠄߩ〒㔌 O(b) ࡠ࠶ࠢࡏ࡞࠻ߩゲജ㧔S.L ㈩⟎㧕㩷 㩷 ࿑㪄㪐㩷 ࿾ጊ✭䉂ၞ䋨ቢᚑᓟ 㪊㪇 ᐕ䋩㩷 㩷 㩷 㩷 㩷 㩷 ࿑㪄㪈㪇㩷 ᄌ૏䊔䉪䊃䊦䋨ቢᚑᓟ 㪊㪇 ᐕ䋩㩷 㩷 㩷 㩷 㩷 㩷 㩷 ࿑㪄㪈㪈㩷 ⃻࿾⸘᷹䊂䊷䉺䈫䈱Ყセ ࿾ጊ෻ജലᨐ߇⊒ើߐࠇ‫࡞ࡀࡦ࠻ޔ‬ᄤ┵ ߩ⓭߈਄ߍᄌᒻ᜼േߪᛥ೙ߐࠇࠆ‫ޕ‬ኻ╷ᤨᦼኻ╷ᤨᦼ࿾ጊഠൻㅴⴕ߇ዋߥ޿‫ޕ‬ኻ╷ᤨᦼ ஥ᣇ߆ࠄߩ᛼಴ߒࠍ᜔᧤ߒ‫ޔ‬ ᢿ㕙❗ዊߪᛥ೙ߐࠇࠆ‫ޕ‬࿑㪄㪈㪉㩷 ഠൻଥᢙ䈱⚻ᤨᄌൻ䋨䍏䍎䍟⢛㕙࿾ጊ䋩㩷 ࿑㪄㪈㪊㩷 ౝⓨᄌ૏䈱⚻ᤨᄌൻ䋨ᄤ┵䍖䍵䍑䍻䋩㩷 ࿑㪄㪈㪋㩷 ౝⓨᄌ૏䈱⚻ᤨᄌൻ䋨䍏䍎䍟⢋ 㪋㪌㫦䋩㩷䉁䈢䇮䉲䊚䊠䊧䊷䉲䊢䊮䈮䉋䉏䈳䇮ᄤ┵䈫஥ო⿷䈧䈔ઃㄭ䈱㽲㩷 䊝䊂䊦䊃䊮䊈䊦䉕ኻ⽎䈮䇮⃻ᴫ䉁䈪䈱ㆊ෰ 30 ᐕ㑆䉕䊨䉾䉪䊗䊦䊃䉕⋭⇛䈚䈢႐ว䋨L=3m䋬4 ᧄ/m䋩䈪䉅䇮䈠䈱⵬ᒝ䉲䊚䊠䊧䊷䉲䊢䊮䈚䈢⚿ᨐ䈲䇮䊃䊮䊈䊦ⷒᎿ䈮⊒↢䈚䈢ലᨐ䈮᦭ᗧ䈭Ꮕ䈲䈭䈒䇮࿾ጊ䈱ᄌᒻ᜼േ䈮ᔕ䈛䈩䊨䉾䉪䊗䊦䊃ታ㓙䈱䈵䈶ഀ䉏૏⟎䈍䉋䈶ᤨᦼ䇮⸘᷹䊂䊷䉺䈫䈍䈍㈩ ⟎ ⸳ ⸘ 䉕ว ℂ ൻ 䈚ᓧ 䉎䈖䈫䈏␜ ໂ 䈘䉏䉎 䇯⵬ ᒝ ඙ 㑆 䉕⚂䉃䈰ᢛว䈚䇮䊃䊮䊈䊦๟ㄝ䈱✭䉂ၞ䈱▸࿐䈭䉌䈶䈮䉮

100m 䈫䈚䈢႐ว䇮䊨䉾䉪䊗䊦䊃䈱ᧄᢙ೥ᷫ䈮䉋䉎Ꮏ੐䉮䉴䊃䈱䉝ⷰ ኤ 䉕䉅䈫䈮᳿ ቯ 䈚䈢ጤ ⋚ ╬ ⚖ 䈫䉅䉋䈒⺞ ๺ 䈚䈩䈇❗ᷫലᨐ䈲䇮⋥ធᎿ੐⾌䈪䈍䉋䈠 20 ⊖ਁ౞ᷫ䈮䈭䉎䇯䈖䈖䉎䇯䈚䈢䈏䈦䈩䇮ᧄ ⺰ ᢥ 䈪↪ 䈇䈢ᄙ Ბ 㓏 ਃ ゲ ࿶ ❗ ⹜䈪ኻ ⽎ 䈮䈚䈢⊒ 㔚 ↪ 䈱᳓ 〝 䊃䊮䊈䊦䈱႐ ว 䈮䈲䇮Ꮏ ੐ ᦼ 㑆㛎䈍䉋䈶৻ゲ 䉪䊥䊷䊒⹜㛎䈱⚿ᨐ䈲䇮࿾ጊ 䈱㐳ᦼ䈮ਛ䈱ᢿ᳓䈮䉋䉎⊒㔚஗ᱛ䈲෼⋉ᕈ䈱ૐਅ䈮ዋ䈭䈎䉌䈝ᓇ㗀䉒䈢䉎ഠൻ䊶ᄌᒻ․ᕈ䉕ౣ⃻䈜䉎䈢䉄䈱᧚ᢱ䊌䊤䊜䊷䉕෸䈿䈜䈢䉄䇮Ꮏᦼ⍴❗䈲Ꮏ੐䈱ᤨ㑆⊛䉮䉴䊃䈱ૐᷫ䈮䉅ነ䉺䈫䈚䈩ㆡᒰ䈪䈅䉎䈖䈫䈏ಽ䈎䉎䈫หᤨ䈮䇮䈖䈖䈮ㆡ↪

ਈ䈜䉎䈭䈬䇮䊃䊮䊈䊦⵬ᒝኻ╷䈱⾌↪-ଢ⋉ലᨐ䈱ᡷༀ䈮ะ䈚䈢ᢙ୯⸃ᨆᚻᴺ䈱᦭ലᕈ䉅᣿䉌䈎䈮䈭䈦䈢䇯䈔䈢ᧄᢙ୯⸃ᨆᚻᴺ䈱Ⓧᭂ⊛䈭೑↪䈏ᦼᓙ䈪䈐䉎䇯㽳㩷 ⵬ᒝᓟ䈎䉌዁᧪䈮ะ䈔䈢 30 ᐕ㑆䈱੍᷹䉲䊚䊠䊧䊷䉲䊢䊮䈮䉋䉎䈫䇮ⵣㄟ䉄ᵈ౉䈫䊨䉾䉪䊗䊦䊃䈮䉋䉎⵬ᒝ䈲䇮㪌㪅㩷㩷⚿⺰㩷䈖䉏䉁䈪䈱ᬌ⸛䈮䉋䈦䈩ᓧ䉌䉏䈢ਥ䈭⚿⺰䈲䇮䈧䈑䈱䉋䈉䈮䉁䈫䉄䉌䉏䉎䇯࿾ ጊ 䈱ഠ ൻ 䈍䉋䈶䊃䊮䊈䊦ⷒ Ꮏ 䈱ᄌ ᒻ 䉕㕖 Ᏹ 䈮䉋䈒᜔᧤䈚䈩䈇䉎䈖䈫䈎䉌䇮ᧄ੐଀ 䈪䈲䇮ᯏ⢻⊛ 䈮ᦨ䉅᦭ല䈭⵬ᒝᣇᴺ䈪䈅䉎䈖䈫䈏ಽ䈎䉎䇯㪈㪈㪐㩷࠻ࡦࡀ࡞⛽ᜬ▤ℂߦ߅޿ߡ .%% ⹏ଔࠍታ⃻ߔࠆߚ߼ߩ੍᷹⸃ᨆᛛⴚ㽴㩷 ᧄ⺰ᢥ䈪↪䈇䈢ഠൻଥᢙ R 䈲䇮࿾ጊ䈱ഠൻㅴⴕ⁁ᴫ 䈱䉂䈭䉌䈝䇮䊃䊮䊈䊦ో ૕ 䈱቟ ቯ ᕈ 䈮ᡰ ㈩ ⊛ 䈭࿾ጊ䈱㒢⇇ ⁁ᘒ 䉕᣿⏕ 䈮䈜䉎䈉䈋䈪᦭ല䈭ᜰ ᮡ䈮䈭䉎䉅䈱䈫⠨䈋䉌䉏䇮⵬ᒝ䊶⵬ୃ䈱ⷐุ䉇ኻ╷ⷙᮨ䈏䉋䉍⊛⏕䈮⹏ଔ䈪䈐䉎䉅䈱䈫ᦼᓙ䈘䉏䉎䇯䈖䉏䈮䉋䉍䇮ㆊ೾䈭ኻ ╷ 䈏ㆱ 䈔䉌䉏䉎䈭䈬䇮ୃ❲ ⾌ 䈮ኻ 䈜䉎ᛩ ⾗ ၮ Ḱ䈱᣿⏕ൻ䉇Ꮏ੐䉮䉴䊃䈱❗ᷫ䈮ነਈ䈜䉎䉅䈱䈫⠨䈋䉌䉏䉎䇯㽵㩷 ․ 䈮䇮䊃䊮䊈䊦䈱⵬ ᒝ ⷙ ᮨ 䈏ᄢ 䈐䈒䈭䉎䈫ᗐ ቯ 䈘䉏䉎੐଀䈪䈅䉏䈳䇮⾌↪-ଢ⋉ലᨐ䈱ᡷༀ䈮ะ䈔䈢ᧄᢙ୯⸃ᨆ ᚻᴺ 䈱Ⓧᭂ⊛ 䈭೑↪ 䈏ᦼ ᓙ䈪䈐䉎䇯੹ᓟ䉅䇮ታ੐଀䉕ኻ⽎䈮ᬌ⸽䉕㊀䈰䇮䊃䊮䊈䊦⛽ᜬ▤ℂ䈮䈍䈇䈩 LCC ⹏ଔ䉕ታ⃻䈜䉎䈢䉄䈱ታോ⊛೑↪䈮ะ䈔䈢ᢛ஻䉕ㅴ䉄䈩䈇䈐䈢䈇䇯ෳ⠨ᢥ₂1)

T.Adachi 䋬 F.Oka 䋬 F.Zhang 䋺 An FEM analysis of tunnel
excavation based on the constitutive model with strain
softening䋬࿯ᧁቇળ╙ 47 ࿁ᐕᰴቇⴚ⻠Ṷળ䋬1992䋬pp.716-7172)

ጟੑਃ↢䋺࿾⋚䈱ᒢ☼႟ᕈ᭴ᚑᑼ䇮᫪ർ಴3)᧻ጟ⨃䇮⋉↰ᓆਭ䇮᧻የᐣ䊆䇮ᩉඳᢥ䋺䈵䈶ഀ䉏䉕⠨ᘦ䈚䈢䊃䊮䊈

䇮2000

䊦 ⷒᎿ ⸃ ᨆ䈮 㑐 䈜 䉎⎇ ⓥ 䇮࿯ ᧁ ቇળ ⺰ ᢥ㓸 䇮 No.554/㸉 -37 䇮
1996.12䇮pp.147-1554)

㑐ᩮ⵨ᴦ䇮౓⮮⧷᣿䇮᧻↰⽵ೣ䋺䉪䊥䊷䊒᜼േ䉕␜䈜エጤ䊃䊮䊈䊦䈱 ⵬ ᒝ Ꮏ ᴺ ല ᨐ 䈮 㑐 䈜 䉎 ⹏ ଔ 䇮 㔚 ജ ࿯ ᧁ 䇮 No.299 䇮 2002.5 䇮
pp.19-24㪈㪉㪇㩷