䈖䈉䈋䈇䊐䉤䊷䊤䊛╙ 㪈㪈 ภ㩷 㪆㩷㪉㪇㪇㪊㪅㪈㩷⠧᧎ൻ䈚䈢䉮䊮䉪䊥䊷䊃䈱䊧䊷䉻ᴺ䈮䉋䉎ᒝᐲផቯᴺ䈮㑐䈜䉎⎇ⓥ
EVALUATION OF OLD CONCRETE STRENGTH THROUGH RADAR METHOD㊄ᧄᐽብ䋪䊶⮮ේ㋕ᦶ䋪䊶᧻ጊ౏ᐕ䋪䊶ᄥ↰⾗㇢䋪Yasuhiro KANEMOTO, Tetsuro FUJIWARA, Kimitoshi MATSUYAMA and Shiro OHTARadar is a measurement technology based on electromagnetic echo. Using radar, we canfind reinforced steel bars and voids in concrete structures, so radar is now in common use forinvestigations in civil engineering. Radar measurement has advantages to investigate bigstructures, such as continuously and non-destructively. This paper presents a study of theapplication of radar technology to estimate concrete strength. We pay attention to the relation
between concrete strength and the electro-characteristics of concrete, such as the velocity andenergy loss of electromagnetic waves.

Key Words : Non-destructive testing, radar measurement, concrete strength, velocity ofelectromagnetic wave㪈㪅㩷㩷䈲䈛䉄䈮㩷䉮䊮䉪䊥䊷䊃᭴ ㅧ ‛ 䈱⛽ᜬ▤ ℂ 䈪䈲䇮䉮䊮䉪䊥䊷䊃䉇㋕╭ 䈭䉁䈢䇮ᧄᚻᴺ䈪ᒝᐲ䈏ផቯ䈘䉏䈢䉮䊮䉪䊥䊷䊃⴫㕙䈎䉌䈱ᷓ䈘䈮䈧䈇䈩䇮ᬌ⸽䉕ⴕ䈉䈢䉄䈱ታ㛎䉕ⴕ䈦䈢䇯䈬䈱᭴ㅧ‛䉕᭴ᚑ䈜䉎᧚ᢱ䈱ஜోᐲ䉕ᛠី䈜䉎䈖䈫䈏㊀ⷐ䈪䈅䉎䇯䈠䈚䈩䇮䉮䊮䉪䊥䊷䊃䈱ஜోᐲ䉕␜䈜ᜰᮡ䈱 1 䈧䈮࿶❗
ᒝᐲ䈏䈅䉎䇯⃻ ࿷ 䇮᭴ ㅧ‛ 䈱䉮䊮䉪䊥䊷䊃ᒝ ᐲ 䉕⺞ ᩏ䈜䉎႐ ว䇮᭴ㅧ ‛䈎䉌䉮䊮䉪䊥䊷䊃䉮䉝䉕ណข䈚䇮৻ゲ࿶❗⹜㛎䉕ⴕ䈉ᣇᴺ䈏৻⥸⊛䈪䈅䉎  䇯䉁䈢㕖⎕უ⹜㛎ᴺ䈫䈚䈩䈲䇮䉲䊠䊚䉾䊃䊊䊮䊙䊷䈪෻⊒ᐲ䉕᷹ቯ䈚䈩࿶❗ᒝᐲ䉕ផቯ䈜䉎ᣇᴺ䉇䇮⿥㖸ᵄ䈱વ៝ㅦᐲ䈎䉌࿶❗ᒝᐲ䉕ផቯ䈜䉎ᣇᴺ䈏䈅䉎䇯䈚䈎䈚䇮䈖䉏䉌䈱ᣇᴺ䉕㐳ᄢ䈭࿯ᧁ᭴ㅧ‛䈮ㆡ↪䈚䈢႐ว䇮ᒝᐲ䈮㑐䈜䉎ᖱႎ䉕ല₸⊛䈮ᓧ䉎䈖䈫䈲࿎㔍䈪䈅䉎䇯䉁䈢䇮᳓〝䊃䊮䊈䊦䈭౮⌀䋭㪈㩷 ⠧᧎ൻ䈚䈢䉮䊮䉪䊥䊷䊃䈱䉮䉝⹜ᢱ㩷䈬䈱⚻ ᐕ ഠ ൻ 䈱⪺ 䈚䈇䉮䊮䉪䊥䊷䊃䈪䈲䇮৻ ゲ ࿶ ❗ ⹜ 㛎 䈮↪
䈇䉎䉮䉝⹜ᢱ䉕ណข䈪䈐䈭䈇䈖䈫䉅䈅䉎䋨౮⌀䋭㪈䋩䇯䈠䈖䈪䇮⠧ ᧎ ൻ 䈚䈢䉮䊮䉪䊥䊷䊃᭴ ㅧ ‛ 䈱࿶ ❗ ᒝ ᐲ 䉕ല ₸⊛䋨㕖⎕უ䇮ㅪ⛯⊛䇮⍴ᤨ㑆䋩䈮⺞ᩏ䈜䉎ᣇᴺ䈫䈚䈩䇮㔚⏛ᵄ
䊧䊷䉻ᴺ䋨એਅ䇮䊧䊷䉻ᴺ䋩䈮䉋䉎䉮䊮䉪䊥䊷䊃ᒝᐲផቯᴺ䈱㐿⊒ 䉕ᧄ ⎇ ⓥ 䈱⋡ ⊛ 䈫䈚䈢䇯䉁䈝䇮⪺ ⠪ 䉌䈲䉮䊮䉪䊥䊷䊃䈱‛ ℂ․ᕈ䈫㔚᳇․ᕈ䈱㑐ଥ䉕ၮ␆ታ㛎䈎䉌᣿䉌䈎䈮䈚䇮䉮䊮䉪䊥䊷䊃ᒝᐲ䉕ផቯ䈜䉎ᣇᴺ䈮䈧䈇䈩ឭ᩺䈚䈢䇯 䋲䋩ᧄⓂ䈪䈲䇮䈠䈱ᓟ䈮ታᣉ䈚䈢᳓〝䊃䊮䊈䊦╬䈮䈍䈔䉎䊧䊷䉻⺞ᩏ⚿ᨐ䉕䉅䈫䈮䇮ၮ␆ታ㛎䈪ឭ᩺䈚䈢䉮䊮䉪䊥䊷䊃ᒝᐲផቯᴺ䈏ᣢ⸳᭴ㅧ‛䈪ห᭽䈮ㆡ↪น⢻䈪䈅䉎䈎䉕ᬌ⸛䈚䈢䇯㪉㪅㩷㩷䊧䊷䉻ᴺ㩷䋨㪈䋩㩷 䊧䊷䉻ᴺ䈫䈲䊧䊷䉻ᴺ䈫䈲䉝䊮䊁䊅䈎䉌ᇦ⾰ਛ䈻㔚⏛ᵄ䉕ㅍା䈚䇮㔚᳇⊛․ᕈ䈏⇣䈭䉎‛⾰䈱Ⴚ⇇㕙䈪෻኿䈚䈢㔚⏛ᵄ䉕ฃା䉝䊮䊁䊅䈪᝝䉌䈋䉎ᛛⴚ䈪䈅䉎䇯䉋䈦䈩䇮㔚⏛ᵄ䉕ㅍฃା䈜䉎䈖䈫䈪䇮㔚᳇․ᕈ䈱⇣䈭䉎‛⾰䈱Ⴚ⇇㕙䉕⷗䈧䈔䉎䈖䈫䈏䈪䈐䉎䇯䈖䈱ᛛⴚ䈲᳇⽎䊧䊷䉻䉇ⓨ᷼䈱▤೙Ⴁ䈪↪䈇䉌䉏䈩䈇䉎䉅䈱䈪䈅䉍䇮ㄭᐕ䈲࿯ᧁ䊶ᑪ▽ಽ㊁䈪䉅᦭ല䈭㕖⎕უ⹜㛎ᴺ䈫䈚䈩᭴ㅧ⺞ᩏ䈮ㆡ↪䈘䉏䈩䈇䉎䇯֣֣֣֣֣֣֣֣֣֣֣֣֣֣֣֣֣֣֣֣֣֣֣֣֣֣֣㧖 ␠ળⅣႺࠛࡦࠫ࠾ࠕ࡝ࡦࠣ੐ᬺㇱ 㩡㨼㩖㩅㨼㩂㩣㩙㩒㩆㩨㩜㩧㩎 ㇱ㩷㪐㪌㩷老朽化したコンクリートのレーダ法による強度推定法に関する研究࿑䋭㪈㩷 䉝䊮䊁䊅䈎䉌ㅍฃା䈘䉏䉎㔚⏛ᵄ㩷䉝䊮䊁䊅䈎䉌ㅍା䈘䉏䈢㔚⏛ᵄ䈲⃿㕙ᵄ䈫䈚䈩ᇦ⾰ਛ䉕વ៝䈜䉎䇯ฃା䉝䊮䊁䊅䈮䈲䉁䈝䇮ᇦ⾰䈱⴫㕙ઃㄭ䉕વ៝䈚䈩౮⌀䋭㪉㩷 䊧䊷䉻⸘᷹⁁ᴫ䋨㋕╭តᩏ䋩㩷䈐䈢⋥ ធ ᵄ 䈏ฃ ା 䈘䉏䇮䈠䈱ᓟ 䈎䉌ᇦ ⾰ ਛ 䈱㔚 ᳇ ․ ᕈ 䈱⇣䈭䉎Ⴚ⇇䋨Ყ⺃㔚₸䈱⇣䈭䉎Ⴚ⇇䋩䈎䉌䈱෻኿ᵄ䈏㗅ᰴฃା䈘䉏䉎䇯࿑䋭㪈 䈮䊧䊷䉻䉝䊮䊁䊅䈎䉌ㅍฃା䈘䉏䉎㔚⏛ᵄ䈱ᮨᑼ࿑䉕␜䈜䇯㽲⸘᷹೙ᓮ䉲䉴䊁䊛㩷 㩷 䊉䊷䊃䊌䉸䉮䊮䈪⸘᷹ᤨ䈱ฦ⒳⸳ቯ䉕೙ᓮ䇮⸘᷹䊂䊷䉺䈱⸥㍳㽳䉝䊮䊁䊅䉝䊷䊛䋨䉝䊮䊁䊅ⵝ⌕ᤨ䋩㩷 㩷 㜞ᚲ䈱㆏〝䊃䊮䊈䊦ⷒᎿ䈮䉝䊮䊁䊅䉕⿛ᩏ䈘䈞䉎㓙䈮૶↪䇮⚵䉂┙䈩ᑼ㽴䊧䊷䉻䉝䊮䊁䊅䋨100MHz䋩㩷 㩷 ࿾ਅၒ⸳‛䈱តᩏ䈮૶↪
࿑䋭㪉㩷 䊧䊷䉻ᴺ䈮䉋䉎㋕╭តᩏ⚿ᨐ㩷㽵䊧䊷䉻䉝䊮䊁䊅䋨400MHz䋩㩷 㩷 ࿾ਅၒ⸳‛䈱តᩏ䊶䉮䊮䉪䊥䊷䊃䉇䉝䉴䊐䉜䊦䊃䈱ㇱ᧚ෘ䊶ᡰ଻Ꮏ䊶⢛ᓟⓨᵢតᩏ䈮૶↪
㽶䊧䊷䉻䉝䊮䊁䊅䋨600MHz䋩㩷 㩷 䉮䊮䉪䊥䊷䊃䉇䉝䉴䊐䉜䊦䊃䈱ㇱ᧚ෘ䊶ᡰ଻Ꮏ䊶⢛ᓟⓨᵢតᩏ䈮૶↪
㽷䊧䊷䉻䉝䊮䊁䊅䋨800MHz䋩㩷 㩷 䉮䊮䉪䊥䊷䊃䉇䉝䉴䊐䉜䊦䊃䈱ㇱ᧚ෘ䊶ᡰ଻Ꮏ䊶⢛ᓟⓨᵢតᩏ䈮૶↪
㽸䊧䊷䉻䉝䊮䊁䊅䋨1GHz䋩㩷 㩷 䉮䊮䉪䊥䊷䊃ਛ䈱㈩╭តᩏ䈮૶↪
㽹䊧䊷䉻䉝䊮䊁䊅䋨1.5GHz䋩㩷 㩷 䉮䊮䉪䊥䊷䊃ਛ䈱㈩╭តᩏ䈮૶↪
㽺䊗䉝䊖䊷䊦䊧䊷䉻䉝䊮䊁䊅䋨600MHz䋩㩷 㩷 䊗䊷䊥䊮䉫ሹ䉕೑↪䈚䈢䊧䊷䉻តᩏ䈮૶↪
㩷 㩷 䋨ᝌ౉㐳15m䉁䈪ኻᔕ䋩౮⌀䋭㪊㩷 ᄙ⋡⊛䊧䊷䉻⸘᷹䉲䉴䊁䊛㩷96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 䊧䊷䉻⸘᷹䈱੐଀䉏䈡䉏㔚⏛ᵄ䈱વ៝䈜䉎ㅦ䈘䇮㔚⏛ᵄ䈏ᷫ⴮䈜䉎ഀว䈱ઍᣢ⸳䉮䊮䉪䊥䊷䊃᭴ㅧ‛䈱ਛ䈮䈲䇮⸳⸘࿑㕙䈱⚗ᄬ䉇⸳⸘⴫୯䈪䈅䉎䈖䈫䈏䉒䈎䉎䇯䉋䈦䈩䇮ᣢ⸳䈱䉮䊮䉪䊥䊷䊃᭴ㅧ‛䈪࿑㕙䈫⇣䈭䉎ᣉᎿ䈏䈘䉏䈢䈢䉄䇮᭴ㅧ䈏ਇ᣿䈭䉅䈱䈏ዋ䈭䈒䈭ⶄ⚛Ყ⺃㔚₸䉁䈢䈲㔚⏛ᵄવ៝ㅦᐲ䈫㔚⏛ᵄ䈱ᷫ⴮․ᕈ䉕䈇䇯䈖䈱䉋䈉䈭᭴ㅧ‛䈏⠧᧎ൻ䈚䇮⵬ୃ䉇⵬ᒝ䈏ᔅⷐ䈫䈭䉎႐ᢙ୯ൻ䈚䈢୯䉕ᛠី䈪䈐䉏䈳䇮䉮䊮䉪䊥䊷䊃ᒝᐲ䈏ផቯ䈪䈐䉎ว䇮⃻࿷䈱᭴ㅧ䉕ᛠី䈚䈢਄䈪䇮วℂ⊛䈭⵬ୃ䊶⵬ᒝ⸳⸘䉕䈫⠨䈋䈢䇯ⴕ䈉ᔅⷐ䈏䈅䉎䇯䈖䈖䈪䈲৻⥸䈮࿯ᧁ䊶ᑪ▽ಽ㊁䈪ᄙ䈒ㆡ↪䈘䉏䈩䈇䉎䉮䊮䉪䊥䊷䊃ਛ䈱㋕╭តᩏ䈱੐଀䈮䈧䈇䈩⺑᣿䉕䈜䉎䇯㋕ ╭ 䉮䊮䉪䊥䊷䊃᭴ ㅧ ‛ 䈮䈍䈇䈩䇮㋕ ╭ 䈱㈩ ╭ ⁁ ᘒ 䈲⵬ୃ䊶⵬ᒝ䈱⸘↹䉕╷ቯ䈜䉎਄䈪㊀ⷐ䈭ᖱႎ䈫䈭䉎䇯ᬌ⸛䈱⚿ᨐ䇮⃻࿷૶↪䈚䈩䈇䉎䊧䊷䉻⸘᷹䉲䉴䊁䊛䈮䈍䈇䈩䇮౉኿ᤨ䈱㔚⏛ᵄ䈱䊌䊦䉴ᵄ䈫䉮䊮䉪䊥䊷䊃ਛ䉕વ៝䈚䈩ᷫ⴮䈚䈢䊌䊦䉴ᵄ䈱Ყ䉕䇮ᷫ⴮․ᕈ䉕␜䈜䊌䊤䊜䊷䉺䈫䈚䈩⸳ቯ䈜䉎䈖䈫䈪䇮વ៝ㅦᐲ䈫ᷫ⴮․ᕈ䊌䊤䊜䊷䉺䈎䉌䉮䊮䉪䊥䊷䊃ᒝᐲ䉕ផቯ䈜䉎䈖䈫䈫䈚䈢䇯䉮䊮䉪䊥䊷䊃䈫㋕╭䈪䈲㔚 ᳇⊛․ᕈ Ყ ⺃㔚₸ 䈏⇣ 䈭䉎䈖⴫䋭㪈㩷 ⶄ⚛Ყ⺃㔚₸䈫䉮䊮䉪䊥䊷䊃䈱㔚᳇․ᕈ㩷䈫䈎䉌䊧䊷䉻ᴺ 䉕ㆡ↪䈜䉏䈳䇮䉮䊮䉪䊥䊷䊃䉕䈲䈧䉎䈖䈫䈭䈒㋕╭䈱૏⟎䈫䈎䈹䉍ෘ䈘䉕․ቯ䈜䉎䈖䈫䈏䈪䈐䉎䇯㔚᳇․ᕈ౮⌀䋭㪉 䈲䉮䊮䉪䊥䊷䊃ᠩო䈱⺞ᩏ⁁ᴫ䈪䈅䉎䇯䈖䈱䉋䈉䈮䉮㔚⏛ᵄ䈱વ៝ㅦ䈘㔚⏛ᵄ䈱ᷫ⴮䊮䉪䊥䊷䊃⴫㕙䈮䊧䊷䉻䉝䊮䊁䊅䉕⿛ᩏ䈘䈞䉎䈣䈔䈪䇮㈩╭⁁ⶄ⚛Ყ⺃㔚₸ 㱑㵭䋨ታᢙㇱ䋩 㱑㵭㵭䋨⯯ᢙㇱ䋩ᘒ䉕ᛠី䈜䉎䈖䈫䈏䈪䈐䉎䇯࿑䋭㪉 䈲䊧䊷䉻⺞ᩏ⚿ᨐ䈱↹௝䈪䈅䉎䇯䉮䊮䉪䊥䊷䊃ਛ䈱㋕ᓇ㗀䈘䉏䉎ⷐ࿃╭䈲࿑䈮␜䈜䉋䈉䈮↹௝䈫䈚䈩⸥㍳䈘䉏䉎䇯㋕╭䈱૏⟎䈲⍫ශ䈪ᜰ䈚␜䈘䉏䈩䈇䉎䊑䊷䊜䊤䊮⁁ᮨ᭽䈱㗂ὐ䈮૏⟎䈚䈩䈇᳓ಽ䊶ⓨ㓗䊶Ⴎಽ䊶㛽᧚䉎䇯䋨㪉䋩㩷 ᣢ⸳᭴ㅧ‛䈮䈍䈔䉎ᒝᐲផቯᴺᬌ⸽⹜㛎䋨㪊䋩㩷 ᄙ⋡⊛䊧䊷䉻⸘᷹䉲䉴䊁䊛౮⌀䋭㪊 䈲 2001 ᐕ䈮ዉ౉䈚䈢ᄙ⋡⊛䊧䊷䉻⸘᷹䉲䉴䊁䊛䈪䈅䉎䇯䈖䈱⸘᷹䉲䉴䊁䊛䈲䊌䊦䉴ဳ䊧䊷䉻䈪䈅䉍䇮䈠䈱․ᓽ
䈲䇮๟ᵄᢙ 100䇮400䇮600䇮800MHz䇮1䇮෸䈶 1.5GHz 䈱䉝⠧᧎ൻ䈚䈢ᣢ⸳䉮䊮䉪䊥䊷䊃䈮䈧䈇䈩ቶౝ⹜㛎䈫ห᭽䈱ᣇᴺ䈪䉮䊮䉪䊥䊷䊃ᒝᐲ䉕ផቯ䈜䉎⹜㛎䉕ታᣉ䈚䈢䇯⹜㛎ᚻ㗅䉕એਅ䈮␜䈜䇯㽲ኻ⽎䈫䈜䉎ᣢ⸳䉮䊮䉪䊥䊷䊃᭴ㅧ‛䈲᳓〝䊃䊮䊈䊦䋨1⃻႐䋩䊮䊁䊅䉕ㆬ ᛯ 䈚䈩૶ ↪ 䈪䈐䉎䈖䈫䈪䈅䉎䇯䉋䈦䈩䇮᭴ ㅧ ‛䈱ᒻ䈫ၮ␆᭴ㅧ‛䋨1⃻႐䋩䈫䈜䉎䇯᭴ㅧ‛䈱છᗧὐ䈮䈍䈇䈩᷹⁁䊶᭴ㅧ䊶ౝㇱᰳ㒱⺞ᩏ䋨ኻ⽎䋺㆏〝䈱〝ᐥ䊶〝⋚䇮䊃䊮䊈䊦䇮ὐ䉕⸳⟎䈜䉎䇯Ṗ ⿛ 〝䇮⼔ ጯ䈭䈬䋩䉇࿾ਅ ၒ⸳ ‛ 䈱⺞ ᩏ䋨ኻ ⽎ 䋺᧮ 䈭䈬䈱ၮ㽳␆ ᭴ ㅧ ‛䇮䉧䉴▤ 䇮ਅ ᳓ ▤䇮ᑄ ᫈ ‛ 䈭䈬䋩䈻䈱䊧䊷䉻ᴺ 䈱ㆡ↪䈏น⢻䈫䈭䉎᳢↪ᕈ䈱㜞䈇⸘᷹䉲䉴䊁䊛䈫䈭䈦䈩䈇䉎䇯㑆䈱㔚⏛ᵄવ៝ᤨ㑆䉕⸘᷹䈜䉎䇯㽴䉁䈢䇮㔚⏛ᵄ䈱વ៝ㅦᐲ䉕ផቯ䈜䉎ᒰ␠⁛⥄䈱⸘᷹䉲䉴䊁䊛  䋨․⸵㗿䇮․㗿ᐔ 7-186021 ภ 䈏៞タ䈘䉏䈩䈍䉍䇮ᬺ᷹ὐ䈮䈍䈇䈩䊧䊷䉻⸘᷹䉕ⴕ䈇䇮᷹ὐ䈮䈍䈔䉎䉝䊮䊁䊅᷹ὐ䈮䈍䈇䈩䉮䊮䉪䊥䊷䊃䉮䉝䊥䊮䉫䉕ታᣉ䈚䈩䇮䉮䉝䉰䊮䊒䊦䉕ណข䈜䉎䇯㽵㔚⏛ᵄ䈱વ៝ㅦᐲ䈫ᷫ⴮․ᕈ䉕␜䈜䊌䊤䊜䊷䉺䈪䈅䉎ᷫോ䈮䈍䈔䉎೑↪䈱䈾䈎䇮䊧䊷䉻ᛛⴚ䈮㑐䈜䉎⎇ⓥ䈻䈱ㆡ↪䉅⴮⋧ኻᲧ䉕᳞䉄䉎䇯ᷫ⴮⋧ኻᲧ䈫䈲ᷫ⴮․ᕈ䉕␜䈜䈢䉄น⢻䈭⸘᷹䉲䉴䊁䊛䈫䈚䈩䈇䉎䇯䈮ᧄᚻᴺ䈪ዉ౉䈚䈢୯䈪䈅䉍䇮ၮḰᵄ䈫⋥ធᵄ䈱Ყ䈮䉋䈦ᄙ⋡⊛䊧䊷䉻⸘᷹䉲䉴䊁䊛䈲 2000 ᐕ 11 ᦬䈮ዉ౉䈚䈢䉅䈱䈪䈅䉍䇮2001 ᐕ 8 ᦬䉁䈪䈮ᯅ⣉ၮ␆᧮䈱⺞ᩏ䉇㆏〝䊃䊮䊈䈩᳞䉄䉎䈖䈫䈏䈪䈐䉎䇯㽶䊦䈱⺞ᩏ䈭䈬 6 ઙ䈱⃻႐䈮䈍䈔䉎⸘᷹ታ❣䈏䈅䉎䇯ណข䈚䈢䉮䊮䉪䊥䊷䊃䈱䉮䉝䉰䊮䊒䊦䉕↪䈇䈩䇮䉮䊮䉪䊥䊷䊃䈱࿶❗⹜㛎䉕ታᣉ䈚䈩䇮䉮䊮䉪䊥䊷䊃ᒝᐲ䉕᳞䉄䉎䇯㽷㔚⏛ᵄ䈱વ៝ㅦᐲ䈫䉮䊮䉪䊥䊷䊃ᒝᐲ䈱㑆䈮⋧㑐㑐ଥ䈏䈅㪊㪅㩷㩷䊧䊷䉻ᴺ䈮䉋䉎䉮䊮䉪䊥䊷䊃ᒝᐲផቯᣇᴺ 㪉㪀㩷 㩷䉎䈖䈫䉕⏕⹺䈜䉎䇯ട䈋䈩䇮㔚⏛ᵄ䈱ᷫ⴮⋧ኻᲧ䈫䉮䊮䉪䊥䋨㪈䋩㩷 䊧䊷䉻ᴺ䈮䉋䉎䉮䊮䉪䊥䊷䊃ᒝᐲផቯᣇᴺ䈱ේℂ䊷䊃ᒝᐲ䈱㑆䈮䇮⋧㑐㑐ଥ䈏䈅䉎䈖䈫䉕⏕⹺䈜䉎䇯ㆊ෰䈮ታᣉ䈚䈢ቶౝ⹜㛎⚿ᨐ  䈎䉌䇮䉮䊮䉪䊥䊷䊃ᒝᐲ䈫䉮䊮䉪䊥䊷䊃䈱㔚᳇․ᕈ䉕␜䈜ⶄ⚛Ყ⺃㔚₸䈱㑆䈮䇮⋧㑐㑐ଥ䈏⹺䉄䉌䉏䈢䇯⴫䋭㪈 䈲ⶄ⚛Ყ⺃㔚₸䈫䉮䊮䉪䊥䊷䊃䈱㔚᳇․ᕈ䈱㑐ଥ䉕␜䈚䈩䈇䉎䇯䈖䈱⴫䈎䉌ⶄ⚛Ყ⺃㔚₸䈱ታᢙㇱ䇮⯯ᢙㇱ䈲䈠㽸䈖䉏䉌䈱ੑ䈧䈱⋧㑐㑐ଥ䉕೑↪䈚䈩㊀࿁Ꮻಽᨆ䉕ⴕ䈇䇮વ៝ᤨ㑆䈫ᷫ⴮⋧ኻᲧ䈎䉌䉮䊮䉪䊥䊷䊃ᒝᐲ䉕ផቯ䈜䉎ផቯᑼ䉕▚಴䈜䉎䇯⋧㑐㑐ଥ䈏䈬䈤䉌䈎৻䈧䈮䈍䈇䈩䈱䉂ᚑ䉍┙䈧႐ว䈮䈲䇮࿁Ꮻಽᨆ䈮䉋䉍䉮䊮䉪䊥䊷䊃ᒝᐲ䉕ផቯ䈜䉎ផቯᑼ䉕▚಴䈜䉎䇯㪐㪎㩷⠧᧎ൻߒߚࠦࡦࠢ࡝࡯࠻ߩ࡟࡯࠳ᴺߦࠃࠆᒝᐲផቯᴺߦ㑐ߔࠆ⎇ⓥ㽹䈖䈱ផቯᑼ䈱ᬌ⸽䉕ⴕ䈉䈢䉄䇮⸘᷹䈚䈢વ៝ᤨ㑆䈫ᷫ⴮⋧಴䈚䈢ᒝᐲផቯᑼ䉕ᑼ 1 䈮␜䈜䇯࿑䋭㪌 䈲ห৻᷹ὐ䈮䈍䈇ኻᲧ䉕ផቯᑼ䈮ઍ౉䈚䈩䇮ផቯ䉮䊮䉪䊥䊷䊃ᒝᐲ䉕▚಴䈜䈩ផቯᑼ 1 䈎䉌ផቯ䈘䉏䈢䋨વ៝ㅦᐲ䈎䉌ផቯ䈘䉏䈢䋩ᒝᐲ䉎䇯ផቯ䉮䊮䉪䊥䊷䊃ᒝᐲ䈫ታ᷹䈱䉮䊮䉪䊥䊷䊃ᒝᐲ䉕Ყセ䈚䈫ታ᷹ᒝᐲ䈱Ყセ䈪䈅䉎䇯Ყセ䈱⚿ᨐ䇮ᧄᚻᴺ䈲㫧2.5MPa

䈩䇮ᧄផቯᣇᴺ䈱ᬌ⸽䉕ⴕ䈉䇯䈱⺋Ꮕ䈪䉮䊮䉪䊥䊷䊃ᒝᐲ䉕ផቯ䈪䈐䉎䈖䈫䈏ᬌ⸽䈘䉏䈢䇯䇼ታ᷹ㅦᐲ䋽ផቯᒝᐲ䇽䋨㪊䋩㩷 ⹜㛎⚿ᨐ䈫ᣢ⸳᭴ㅧ‛䈮䈍䈔䉎䊧䊷䉻ᴺ䈮䉋䉎䉮䊮䉪䊥䊷䊃࿑䋭㪊 䈮㔚⏛ᵄ䈱વ៝ㅦᐲ䈫䉮䊮䉪䊥䊷䊃ᒝᐲ䈱㑐ଥ䉕䇮࿑䋭㪋 䈮㔚⏛ᵄ䈱ᷫ⴮⋧ኻᲧ䈫䉮䊮䉪䊥䊷䊃ᒝᐲ䈱㑐ଥ䉕␜䈜䇯࿑䋭㪊 䉋䉍વ៝ㅦᐲ䈫䉮䊮䉪䊥䊷䊃ᒝᐲ䈱㑆䈮䈲䇮ቶౝ⹜㛎ห᭽䈮⋧㑐㑐ଥ䈏⹺䉄䉌䉏䈢䇯䈚䈎䈚䇮࿑䋭㪋 䉋䉍ᷫ⴮⋧ኻᲧ䈫䉮䊮䉪䊥䊷䊃ᒝᐲ 䈱㑆 䈮䈲䇮⋧ 㑐 㑐 ଥ 䉕⹺䉄䉎䈖䈫䈏䈪䈐䈭䈎࿶❗ᒝᐲ㩷 㩿㪤㫇㪸㪀ᒝᐲផቯᣇᴺ䈱ᬌ⸽}᭴ㅧ‛㪘䈦䈢䇯䂦 ᭴ㅧ‛㪙࿶❗ᒝᐲ㩷 㩿㪤㫇㪸㪀}᭴ㅧ‛㪘䂦 ᭴ㅧ‛ታ᷹ㅦᐲ㩷 㩿㪤㫇㪸㪀㪙᭴ㅧ‛A 㧦 ዉ᳓〝࠻ࡦࡀ࡞᭴ㅧ‛B 㧦 ၮ␆᭴ㅧ‛࿑䋭㪌㩷 ታ᷹ᒝᐲ䈫ផቯᒝᐲ䈱㑐ଥ㩷▚಴䈘䉏䈢䉮䊮䉪䊥䊷䊃ᒝᐲផቯᑼ
y = 62.1 䋭 6.76 㬍 10 -7 x1y 䋺 ផቯᒝᐲ䋨MPa䋩㩷 㩷 㩷 x 䋺 વ៝ㅦᐲ䋨m/s䋩વ៝ㅦᐲ䇭䌸㪈㪇㪎㩷㩿㫄㪆㫊㪀䋨㪋䋩㩷 ⠨ኤ࿑䋭㪊㩷 વ៝ㅦᐲ䈫࿶❗ᒝᐲ䈱㑐ଥ㩷ᬌ⸽䈱⚿ᨐ䈎䉌ᧄᚻᴺ䈱ᚻ㗅䈮ᓥ䈋䈳䇮䉮䊮䉪䊥䊷䊃ᒝᐲ
䉕㫧2.5MPa 䈪ផቯ䈜䉎䈖䈫䈏䈪䈐䉎䈫⠨䈋䉌䉏䉎䇯䈢䈣䈚䇮੹ᓟ 䉅䊂䊷䉺䈱⫾ Ⓧ 䉕ⴕ 䈇䇮ᧄ ᚻ ᴺ䈱ㆡ↪ኻ ⽎ 䈮䈧䈇䈩ᬌ ⸛}᭴ㅧ‛㪘࿶❗ᒝᐲ㩷 㩿㪤㫇㪸㪀䂦 ᭴ㅧ‛㪙䉕ⴕ䈉ᔅⷐ䈏䈅䉎䇯ቶౝ⹜㛎䈮䈍䈇䈩䈲ᷫ⴮․ᕈ䈫䉮䊮䉪䊥䊷䊃ᒝᐲ䈱㑆䈮⋧㑐㑐ଥ䈏⹺䉄䉌䉏䈢䈏䇮ᣢ⸳᭴ㅧ‛䈪䈲⹺䉄䉎䈖䈫䈏䈪䈐䈭䈎䈦䈢䇯䈖䉏䈲ᣢ⸳᭴ㅧ‛䈮䈍䈇䈩䉮䊮䉪䊥䊷䊃⴫㕙䈮ᓸᅱ䈭ಳಲ䈏䈅䉎䈖䈫䈎䉌䇮䊧䊷䉻⸘᷹䉕ⴕ䈉㓙䈮䉝䊮䊁䊅䈫䉮䊮䉪䊥䊷䊃⴫㕙䈱〒㔌䈏৻ቯ䈫䈭䉌䈝䇮෻኿ᵄᒻ䈱ᝄ᏷䈮ᄢ䈐䈭ᓇ㗀䉕ਈ䈋䈩䈚䉁䈉䈖䈫䈏ේ࿃䈪䈅䉎䉅䈱䈫⠨䈋䉌䉏䉎䇯㪋㪅㩷㩷䊧䊷䉻⸘᷹䈮䈍䈔䉎㔚⏛ᵄ䈱વ៝⚻〝䈱⏕⹺  㩷䋨㪈䋩㩷 ⋥ធᵄ(⴫㕙ᵄ)䈱વ៝⚻〝ᷫ⴮✚ኻᲧᚒ䇱䈲䉝䊮䊁䊅㑆䉕વ៝䈜䉎⋥ធᵄ ⴫㕙ᵄ 䊏䊷䉪䈱⚻〝䉕䉮䊮䉪䊥䊷䊃⴫㕙ઃㄭ䈫઒ቯ䈚䇮䉝䊮䊁䊅䈱ㅍฃା㑆䉕⋥࿑䋭㪋㩷 ᷫ⴮⋧ኻᲧ䈫࿶❗ᒝᐲ䈱㑐ଥ㩷ធ ᵄ 䈱વ ៝ 〒㔌 䈫䈚䈩⸃ ᨆ 䉕ㅴ 䉄䈩䈇䉎䇯䈢䈣䈚䇮෩ ኒ 䈮䈲⋥ធᵄ䈫䈚䈩ㅍฃା䈘䉏䉎㔚⏛ᵄ䈲䇮䊖䉟䊓䊮䉴䈱ේℂ䈮䉋䉍䉋䈦䈩䇮䉮䊮䉪䊥䊷䊃ᒝᐲផቯᑼ䈲䇮㔚⏛ᵄ䈱વ៝ㅦᐲ䈫䉮䊮䉪䊥䊷䊃ᒝᐲ䈮䈍䈔䉎࿁Ꮻಽᨆ䉕ⴕ䈉䈖䈫䈮䉋䉍▚಴䈚䈢䇯▚㪐㪏㩷࿑䋭㪍 䈱䉋䈉䈭⚻〝䉕䇮ᦨ䉅ᄢ䈐䈭ᝄ᏷䈪ᦨ⍴〒㔌䈫䈚䈩વ៝䈜䉎䇯䈖䈉䈋䈇䊐䉤䊷䊤䊛╙ 㪈㪈 ภ㩷 㪆㩷㪉㪇㪇㪊㪅㪈㩷䈖䈖䈪䈲䇮䊧䊷䉻ᴺ䉕ㆡ↪䈚䈢৻ㅪ䈱⸘᷹⚿ᨐ䉇⎇ⓥ⚿ᨐ䋨㪊䋩㩷 ታ㛎⚿ᨐ䈱♖ᐲ䉕ะ਄䈘䈞䉎䈢䉄䇮䊧䊷䉻䉝䊮䊁䊅䈱⋥ធᵄ䈱વ៝⚻〝䉕ᛠី䈜䉎䈖䈫䉕⋡⊛䈫䈚䈢ታ㛎䉕ⴕ䈦䈢䇯࿑䋭㪏 䈮⸘᷹⚿ᨐ䉕␜䈜䇯࿑䋭㪏 䈲 800MHz 䈱䉝䊮䊁䊅䉕ଏ⹜૕਄䈪⿛ᩏ䈘䈞䈢㓙䈮⸘᷹䈘䉏䈢㔚⏛ᵄ䈱ᵄᒻ䉕⊕㤥㓏⺞䈪␜䈚䈢࿑䈪䈅䉎䇯䉴䊁䊮䊧䉴᧼䈎䉌䈱෻኿ᵄ䈲䇮䉮䊮䉪䊥䊷䊃ෘ䈘䈏ዊ䈘䈒䈭䉎䈮ᓥ䈇⋥ធᵄ䈮ㄭ䈨䈇䈩䈐䈩䈇䉎䈖䈫䈏䉒䈎䉎䇯࿑䋭㪐 䈲 800MHz 䈱䉝䊮䊁䊅䈪⸘᷹䈚䈢㓙䈱ฦ䉮䊮䉪䊥䊷䊃ෘ䈘䈮䈍䈔䉎㔚⏛ᵄ䈱ᵄᒻ䈪䈅䉎䇯⋥ធᵄ䈫෻኿ᵄ䈱䊏䊷䉪䈏㊀䈭䈦䈢䈫䈐䈱䉮䊮䉪䊥䊷䊃ෘ䈘䈲 4.9cm 䈪䈅䈦䈢䇯ᵄ㕙ታ㛎⚿ᨐ䈎䉌䇮ฦ䉝䊮䊁䊅䈪⋥ធᵄ䈫䈚䈩ㅍฃା䈘䉏䉎㔚⋥ធᵄ(ࡇ࡯ࠢ)ߩવ៝⚻〝࿑䋭㪍㩷 ⋥ធᵄ㩿⴫㕙ᵄ㪀䈱વ៝⚻〝㩷⏛ᵄ䈏વ៝䈜䉎ᷓ䈘䉕⴫䋭㪉 䈮␜䈜䇯䈖䈱ᷓ䈘䈲ฦ䉝䊮䊁䊅䈱䉮䊮䉪䊥䊷䊃ෘ䈘᷹ቯ䈱㒢⇇୯䉕␜䈜䈖䈫䈮䉅䈭䉎䇯䋨㪉䋩㩷 ታ㛎ᣇᴺ࿑䋭㪎 䈮␜䈜䉋䈉䈭䉮䊮䉪䊥䊷䊃ଏ⹜૕䉕૞ᚑ䈚䈢䇯ଏ⹜૕䈱ᐩ㕙䈮䈲䉴䊁䊮䊧䉴᧼䈏⸳⟎䈚䈩䈅䉎䇯䉝䊮䊁䊅䉕ଏ⹜૕㩷࿑䋭㪏㩷 ⸘᷹⚿ᨐ䋨⊕㤥㓏⺞⴫␜䋩㩷౮⌀䋭㪋㩷 ታ㛎⁁ᴫ㩷࡟࡯࠳࡯ࠕࡦ࠹࠽⿛ᩏᣇะࠦࡦࠢ࡝࡯࠻㜞ߐ20cm

࿑䋭㪐㩷 ⸘᷹⚿ᨐ䋨ᵄᒻ䋩㩷ࠬ࠹ࡦ࡟ࠬ᧼ 㐳ߐ 120cm

㩷⴫䋭㪉㩷 ๟ᵄᢙ䈱㆑䈇䈮䉋䉎વ៝⚻〝䈱ᷓ䈘㩷࿑䋭㪎㩷 ታ㛎ଏ⹜૕㩷਄䈪⿛ᩏ䈘䈞䈩䇮ෘ䈘䈱⇣䈭䉎䉮䊮䉪䊥䊷䊃ਛ䉕વ៝䈜䉎⋥ធᵄ㩷䉝䊮䊁䊅વ៝⚻〝䈱ᷓ䈘㪏㪇㪇㪤㪟㫑㪋㪅㪐㪺㫄㪈㪞㪟㫑㪊㪅㪊㪺㫄㪈㪅㪌㪞㪟㫑㪉㪅㪇㪺㫄䈫䉴䊁䊮䊧䉴᧼ 䈎䉌䈱෻኿ᵄ䉕⸘᷹䈚䈢䇯⋥ធᵄ䈱વ៝⚻〝䈫෻኿ᵄ䈱વ៝⚻〝䈏㊀䈭䈦䈢૏⟎䈪䇮⋥ធᵄ䈱䊏䊷䉪䈫෻኿ ᵄ 䈱䊏䊷䉪䈏ว ᚑ 䈘䉏䇮৻ 䈧䈱䊏䊷䉪䉕ᒻ ᚑ 䈜䉎䈖䈫䈫䈭䉎䇯䈖䈱䈫䈐䈱䉮䊮䉪䊥䊷䊃ෘ䈘䈏⋥ធᵄ䋨䊏䊷䉪䋩䈱વ៝⚻〝䈱ᷓ䈘䈪䈅䉎䈖䈫䈏⠨䈋䉌䉏䉎䇯㪐㪐㩷⠧᧎ൻߒߚࠦࡦࠢ࡝࡯࠻ߩ࡟࡯࠳ᴺߦࠃࠆᒝᐲផቯᴺߦ㑐ߔࠆ⎇ⓥ㪌㪅㩷㩷䉁䈫䉄㩷䈖䈖䈪ᬌ ⸽ 䈚䈢䊧䊷䉻ᴺ 䈮䉋䉎䉮䊮䉪䊥䊷䊃ᒝ ᐲ ផ ቯ ᴺ 䈪
䈲䇮㫧2.5MPa 䈱⺋Ꮕ䈪ផቯ䈜䉎䈖䈫䈏䈪䈐䈢䇯䈢䈣䈚䇮੹࿁ኻ⽎䈫䈚䈢䉮䊮䉪䊥䊷䊃䈲૕Ⓧ᳓ಽ₸䈱Ყセ⊛ᄢ䈐䈭䉮䊮䉪䊥䊷䊃䋨⚂ 20%એ਄䋩䈪䈅䉍䇮ੇ῎䈚䈢䉮䊮䉪䊥䊷䊃䈪ᧄᚻᴺ䈏ㆡ↪น⢻䈪䈅䉎䈎䈲⏕⹺䈏ᔅⷐ䈪䈅䉎䇯䊧䊷䉻⸘ ᷹ 䈮䈍䈔䉎⋥ ធ ᵄ 䈱વ ៝ ⚻ 〝 䈱⏕ ⹺ ታ 㛎 䈎 䉌䈲䇮⋥ធᵄ䈮㑐䈜䉎⸃ᨆ䈪䈲䉮䊮䉪䊥䊷䊃⴫㕙䈎䉌ᷓ䈘ᢙ cm
䈮䈍䈔䉎䉮䊮䉪䊥䊷䊃䈱㔚᳇․ᕈ䈏෻ᤋ䈘䉏䉎䈫⠨䈋䉌䉏䉎䇯䉁䈢䇮⋥ធᵄ䈱વ៝ㅦᐲ䉕䉅䈫䈮ⴕ䈉䉮䊮䉪䊥䊷䊃ᒝᐲផቯᴺ䈮䉋䉍ផቯ䈘䉏䉎ᒝᐲ䈲䇮䈖䈱ᷓ䈘䈮䈍䈔䉎ᒝᐲ䉕ᦨ䉅෻ᤋ䈜䉎䈖䈫䈏⠨䈋䉌䉏䉎䇯㪍㪅㩷㩷⺖㗴㩷
੹ᓟ䈱⺖㗴䈫䈚䈩એਅ䈱㗄⋡䈏䈅䈕䉌䉏䉎䇯㩷 · 䊧䊷䉻ᴺ䈮䉋䉎䉮䊮䉪䊥䊷䊃ᒝᐲផቯᴺ䈱♖ᐲะ਄䈫ㆡ↪
▸࿐䈱⛉䉍ㄟ䉂㩷 · 䉮䊮䉪䊥䊷䊃ᒝᐲផቯᴺ䈱♖ᐲ䈮⷗ว䈦䈢೑↪ᣇᴺ䈱ᬌ⸛㩷 · ᣢ⸳᭴ㅧ‛䈮䈍䈔䉎䊂䊷䉺䈱ขᓧෳ⠨ᢥ₂1)

ዊᨋ৻テ䋺䉮䉝ណข䈮䉋䉎䉮䊮䉪䊥䊷䊃᭴ㅧ‛䈱ഠൻ⸻ᢿᴺ䇮᫪ർ಴2䋩㊄ᧄᐽብઁ䋺䊧䊷䉻ᴺ䈮䉋䉎䉮䊮䉪䊥䊷䊃ᒝᐲផቯᴺ䈮㑐䈜䉎⎇ⓥ䇮
╙䋲࿁᭴ㅧ‛䈱⸻ᢿ䈮㑐䈜䉎䉲䊮䊘䉳䉡䊛⺰ᢥ㓸䇮pp.87-92䇮
1999.83䋩

㊄ᧄᐽብઁ䋺䊧䊷䉻䉝䊮䊁䊅䈎䉌⋥ធᵄ䈫䈚䈩ㅍฃା䈘䉏䉎㔚⏛ᵄ䈱䉮䊮䉪䊥䊷䊃ਛ䈮䈍䈔䉎વ៝⚻〝䇮╙ 56 ࿁࿯ᧁቇળᐕᰴቇⴚ⻠Ṷળ᭎ⷐ㓸 V-411䇮pp.822-823䇮2001.10

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